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Multiple-chemical equilibria in chiral partition systems Koska, Jurgen 1998

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Multiple-Chemical Equilibria In Chiral Partition Systems by JURGEN KOSKA Dipl.-Ing., Mannheim Institute of Technology, Germany, 1991 M.A.Sc, University of British Columbia, Canada, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUESTMENTS FOR THE DEGREE OF DOCTOR OF PHILOSPHY in THE FACULTY OF GRADUATE STUDIES Department of Chemical and Bio-Resource Engineering and The Laboratory of Biotechnology We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1998 © Jiirgen Koska, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of £fo?/&i>tf The University of British Columbia u Vancouver, Canada Date 91/Z 78 DE-6 (2/88) 11 A B S T R A C T Enantiomers are molecules with nearly identical physical properties. The separation of such molecules presents one of the most difficult separation problems in chemical industries. In particular, pharmaceutical companies are challenged with the design of new enantioseparation methods and equipment to meet stricter regulations required for the approval of optically active drugs. Ligand-exchange systems utilize the unique configuration of transition-metal complexes with a chiral ligand for the separation of enantiomers. Equilibrium ternary amino-acid-enantiomer complexes are formed via copper(II) ions and a chiral selector. These ternary complexes have distinct equilibrium binding constants, which depend on the enantiomer type and optical configuration, as well as on solvation effects. The chemical equilibria in ligand-exchange separation systems are governed by a large number of complexation reactions. In this work, a comprehensive model, based on multiple-chemical-equilibria, was developed which is capable of completely describing ligand-exchange separation systems. Equilibrium formation constants were measured experimentally by potentiometric titrations in the aqueous phase and by partition experiments in the organic phase. The work shows that solvent molecules significantly affect the enantioselectivity of the ligand. By solubilizing a water insoluble analogue of the chiral selector in an n-octanol phase, the enantioselectivity increased by nearly an order of magnitude for some enantiomers. Molecular mechanics calculations support experimental findings that water molecules significantly affect ligand selectivity and the highest enantioselectivities were Ill predicted in non-aqueous environments, which agreed with experimental measurements performed in organic solvents. Due to low ligand enantioselectivities, the multiple-chemical-equilibria model was extended to multi-staged extraction systems. Experimentally, a hollow-fibre membrane two-phase extraction system was designed to test the model. The system consisted of a chiral selector that was solubilized in an organic phase flowing in counter-current direction to an aqueous stream containing the racemates. The enantiomer-concentration profiles predicted at different conditions were in good agreement with experiments. The work showed that ligand-exchange separations are difficult to operate due to the large number of complexation reactions. In particular, the enantioseparation performance is very sensitive to solution conditions. The developed models are useful in the prediction of chiral separation performances as a function of operating conditions and for system optimization. Furthermore, the models are applicable to any separation schemes that are governed by multiple-chemical equilibrium. T A B L E O F C O N T E N T S A B S T R A C T II T A B L E O F C O N T E N T S I V L I S T O F T A B L E S I X L I S T O F F I G U R E S X I I A B B R E V I A T I O N S X X V I A C K N O W L E D G M E N T S X X V I I 1 Introduction 1.1 Chiral Synthesis 1.2 Racemic Resolution Techniques 1.2.1 Crystallisation , 1.2.2Enzymatic Transformations 1.3 Chromatographic Chiral Separation Methods 1.3.1 Chiral Recognition Mechanisms 1 1.3.2Ligand-Exchange Phases 1 1.3.3 Protein Phases 1 1.3.4Polymer Phases 1.3.5Chiral Cavity Phases..... 1.3.6Charge-Transfer Phases 1.3.7Novel Developments 1.4 Continuous Chiral Separation Systems 1.4.1 Simulated Moving-Bed Chromatography 1.4.2 Two-Phase Liquid Partition Systems 1.5 CLEC-Ligand Development 1.5.1 CLEC-Ligand Evaluation 1.5.2 Theoretical Characterization of Chiral Ligands 1.6 Chemical Equilibria 1.6.1 Chemical Equilibria In Single-Phase Systems.. 1.6.2 Chemical Equilibria In Two-Phase Systems 1.7 Calculation of Multiple-Chemical Equilibria 38 1.7.1 Aqueous Systems 38 1.7.2 Two-Phase Systems 40 1.8 Chiral Extraction Systems 40 1.8.1 Liquid-Liquid Chiral Extraction 40 1.8.2Chiral Extraction with Membranes 45 1.8.3 Micellar Systems 48 1.9 Modelling of Chiral Separation Systems 49 1.9.1 Two-Phase Systems 49 1.9.2 Chromatographic Separations 53 1.10 Research Objectives 55 2 Theory and Model Development 58 2.1 Nonlinear Regression 58 2.2 Molecular Modelling 61 2.2.1 Introduction to Molecular Mechanics Modelling 61 2.2.2 The Program MOMEC 64 2.3 Modelling of Multiple-Chemical Equilibria 64 2.3.1 Determination of Equilibrium Formation Constants by Potentiometry 66 2.3.1.1 Computational Approach 67 2.3.1.2 Regression of Equilibrium Formation Constants 69 2.3.1.3 Statistical Data Analysis 72 2.3.2Modelling of Two-Phase Multiple-Chemical Equilibria 76 2.3.2.1 Single Stage Two-Phase Extraction Systems 77 2.3.2.2 Regression of Equilibrium Formation Constants in Two-Phase Systems 80 2.3.2.3 Fractional Extraction with Two Moving Phases 81 2.3.2.4 Numerical Solution Methods 84 2.4 Mass Transfer in Hollow-Fibre Membranes 88 2.5 Modelling of Ligand-Exchange Chromatography 91 2.5.1 Numerical Solution 95 3 Materials and Methods 100 3.1 Buffer Preparation 100 3.2 pH Measurements 101 3.3 Ligand Synthesis 101 3.4 Hollow-Fibre Membrane System 102 vi 3.4.1 Design of Hollow-Fibre Modules 103 3.4.2Hollow-Fibre Membrane Two-Phase Extractions 106 3.4.3Measuring Hollow-Fibre Mass-Transfer Coefficients 107 3.5 Analytical Methods 110 3.5.1 HPLC System 110 3.5.2Measuring Amino-Acid Concentrations 110 3.5.3 Measuring Copper Concentrations I l l 3.5.4Measuring Benzoic-Acid Concentrations 112 3.6 Molecular Mechanics Calculations 112 3.7 Partition Experiments 113 3.7.1 Copper Partitioning 113 3.7.2 Amino-Acid Partitioning 115 3.8 Potentiometric Titrations 116 3.8.1 Electrode Calibration 1IV 3.8.2Titration Procedure 118 3.8.3 Titration-Data Analysis 119 3.9 Chiral Column System 120 3.9.1 Chiral Column Preparation 122 4 Equilibrium Formation Constants 123 4.1 Aqueous Phase 124 4.1.1 Protonation Constants 124 4.1.2 Binary Equilibrium Formation Constants • 124 4.1.3 Ternary Equilibrium Formation Constants 129 4.2 Mixed Solvent System 135 4.2.1 Protonation Constants 135 4.2.2Binary Equilibrium Formation Constants 137 4.2.3 Ternary Equilibrium Formation Constants 139 4.3 Organic Solvents 142 4.3.1 Binary Equilibrium Formation Constants 142 4.3.2Ternary Equilibrium Formation Constants 144 4.3.3 Solvent and Ligand Effects on the Equilibrium Formation Constants 155 4.4 Enantiomer Partitioning in Two-Phase Systems 157 5 Molecular Modelling Calculations 167 5.1 Solvation Effects on Complex Stability and Enantioselectivity 168 5.1.1 Absence of Solvent 170 5.1.2 Presence of Solvent 171 5.2 Effects of Alkyl-Tail 179 5.3 Comparing Molecular Mechanics Results with Measured Equilibrium Formation Constants 182 5.3.1 Aqueous Phase 182 5.3.2Non-Aqueous Phase 184 5.4 Conclusions 186 6 Model Predictions in Two-Phase Systems 188 6.1 Single Amino-Acid Partitioning in a Two-Phase System 189 6.2 Enantiomer Partitioning in a Two-Phase System 196 6.3 Enantiomer Partitioning in a Buffered Two-Phase System 215 6.4 Conclusions 221 7 Stage Systems For Enantiomer Separations 222 7.1 Hollow-Fibre Mass Transfer 223 7.2 Enantiomer Separation in Two-Phase Systems 230 7.2.1 Chiral Extractions in a Single-Hollow Fibre Modules 232 7.2.2 Two-Module Chiral Extractions 245 7.3 Model Predictions for Multi-Stage Chiral Separations 253 7.4 Conclusions 266 8 Modelling of Ligand-Exchange Chromatography 268 8.1 Introduction 268 8.2 Computing Enantiomer-Elution Profiles on a CLEC Column 269 8.3 Ligand-Exchange Chromatography Elution Profiles 270 8.4 Modelling of Ligand-Exchange Chromatography 274 8.5 Modelling of CLEC Chromatograms Using On-Column Ternary Equilibrium Formation Constants 278 8.6 Conclusions 286 9 Final Conclusions 288 V l l l 10 Research Recommendations 291 N O M E N C L A T U R E 294 Subscripts and Superscripts 297 Greek Letters 297 Dimensionless Numbers 298 B I B L I O G R A P H Y 299 A P P E N D I C E S 316 1. Molecular Structures 316 2. Implicit Differentiation 317 3. Example Calculations for Speciation Reactions 319 Single-Phase System 319 Two-Phase System 320 4. Gibbs Phase Rule For Reacting Systems 322 Single-Phase System 322 Two-Phase System 323 5. Molecular Modelling Results 324 6. Hollow Fibre Chiral Extraction Results 330 7. Computational Source Codes 331 Equilibrium Formation Constant Regression 331 Single Phase (Chemeq) 331 Two Phase (Chemeq2) 341 Multi-Stage Multiple-Chemical-Equilibria Codes 345 Steady-State Two-Phase Equilibria (MChemeql) 345 Transient Ligand-Exchange Chromatography (Chico) 356 IX LIST O F T A B L E S Table 1.1: Sales of chiral therapeutics in 1995 (in millions of US dollars) 5 Table 3.1: Hollow-fibre membrane parameters 103 Table 3.2: Hollow-fibre membrane cartridge dimensions 106 Table 3.3: Fluid and solute properties (20 °C) 109 Table 3.4: HPLC and column properties 121 Table 4.1: Amino-acid equilibrium protonation constants in water (7= 0.1 M, 25 °C). ..125 Table 4.2: Binary amino-acid/copper equilibrium formation constants in water (7=0.1 M, 25 °C) 126 Table 4.3: Binary amino-acid/copper equilibrium formation constants in water (7=0.1 M, 25 °C) 127 Table 4.4: Ternary amino-acid/copper equilibrium formation constants, differences in the formation energies (8AG), and enantioselectivities containing L-hydroxy-proline (L-HyPro) in water (7 = 0.1 M, 25 °C) 130 Table 4.5: Ternary amino-acid/copper equilibrium formation constants, differences in the formation energies (8AG), and enantioselectivities containing L-proline (Pro) in water (7 = 0.1 M, 25 °C) 130 Table 4.6: Proton-corrected ternary amino-acid/copper equilibrium formation constants for the Pro and L-HyPro ligand in water (7= 0.1 M, 25 °C) 131 Table 4.7: Ternary amino-acid/copper equilibrium formation constants, differences in the formation energies (8AG), and enantioselectivities containing jVT-methyl-L-histidine (MHis) in water (7 = 0.1 M, 25 °C) 131 Table 4.8: Solute protonation constants in water/methanol (MeOH) mixtures (7=0.1 M, 25 °C) 136 Table 4.9: Binary amino acid/copper complex equilibrium formation constants in water/methanol (MeOH) mixtures (7 = 0.1 M, 25 °C) 138 Table 4.10: Ternary amino-acid/copper equilibrium formation constants containing L-hydroxy-proline (L-HyPro) in water/methanol (MeOH) mixtures (7=0.1 M, 25 °C) 140 Table 4.11: Difference in formation energies (SAG) and enantioselectivities for ternary complexes containing L-hydroxy-proline (L-HyPro) in water/methanol mixtures (7= 0.1 M, 25 °C) 140 Table 4.12: Measured binary and ternary equilibrium formation constants in the n-octanol phase containing A-dodecyl-L-hydroxy-proline (LiH) (7aq = 0.1 M, 25 °C)... 145 Table 4.13: Corrected ternary equilibrium formation constants from Table 4.12 (7 = 0.1 M, 25 °C) 145 Table 4.14: Amino-acid side-chain hydrophobicity (n) values (Tayar El et al., 1992), corrected ternary equilibrium formation constants, and Gibbs free energy values SAG for the A-alkyl-L-hydroxy-proline ligand in the n-octanol phase (7=0.1 M, 25 °C) 149 Table 5.1: Molecular modelling energy-minimization results of ternary complexes formed with the L-HyPro ligand in different solvation environments 170 Table 5.2: Molecular modelling energy-minimization results of the L-Pro ligand in different solvation environments 174 Table 5.3: Molecular modelling energy-minimization results of ternary L-HyPro complexes in the presence and absence of the octyl-tether in vacuum 180 Table 5.4: Comparison of calculated energy-differences of ternary complexes (STitotai) and experimentally determined Gibbs free energy values (SAG) for the L-HyPro ligand in an aqueous environment 183 Table 5.5: Comparison of calculated energy-differences of ternary complexes (87itotai) and experimentally determined Gibbs free energy values (SAG) for the L-Pro ligand in an aqueous environment 183 Table 5.6: Comparison of calculated energy-differences of ternary complexes (STitotai) in vacuum and methanol, with experimentally determined Gibbs free energy values (SAG) for the #-alkyl-L-HyPro ligand 185 Table 7.1: Lumen and shell mass-transfer coefficients for various velocities 225 Table 7.2: Calculated minimum number of equilibrium stages (NTUm\n) at optimized Y m i n and pH m j n for Leu and Phe enantioseparations in a fractional extraction system to achieve a performance factor (pf) > 99%; A-dodecyl-L-HyPro = 20 mM, [D] = 1.0 mM, [L] = 1.0 mM, to = 0.1, NTUH = lA x NTUmin (7= 0.1 M) 264 Table 8.1: Comparison of ternary equilibrium formation constants for Leu and Phe enantiomers determined from CLEC elution profiles and potentiometric titrations (7= 0.1 M, 20% MeOH, 25°C) 282 Table 8.2: Proton-corrected ternary equilibrium formation constants and measured values in the aqueous phase, in n-octanol, on the column, and in 20% MeOH (7=0.1 M, 25°C) 283 Table A . l : Strain-energy contributions for ternary Leu/Cu/L-HyPro ligand complexes in several solvent environments 324 Table A.2: Strain-energy contributions for ternary Val/Cu/L-HyPro ligand complexes in several solvent environments 324 XI Table A.3: Strain-energy contributions for ternary Phe/Cu/L-HyPro ligand complexes in different solvent environments 325 Table A.4: Strain-energy contributions for ternary Leu/Cu/L-Pro ligand complexes in several solvent environments 325 Table A. 5: Strain-energy contributions for ternary Val/Cu/L-Pro ligand complexes in several solvent environments 326 Table A.6: Strain-energy contributions for ternary Phe/Cu/L-Pro ligand complexes in several solvent environments 326 Table A.7: Strain-energy contributions for ternary Leu and Phe/Cu/A-n-octyl-L-HyPro ligand complexes in the absence of solvent molecules (i.e., vacuum) 327 Table A.8: Strain-energy contributions for ternary Leu and Phe/Cu/A-n-octyl-L-Pro ligand complexes in the absence of solvent molecules (i.e., vacuum) 327 Table A. 9: Strain-energy contributions for ternary Leu/Cu/L-Pro ligand complexes in several solvent environments (i.e., vacuum) 328 Table A. 10: Strain-energy contributions for ternary Phe/Cu/L-Pro ligand complexes in several solvent environments 328 Table A. 11: Strain-energy contributions for ternary Val/Cu/L-Pro ligand complexes in several solvent environments 329 X l l LIST OF FIGURES Figure 1.1: Alanine amino-acid enantiomers 1 Figure 1.2: Thalidomide enantiomers 3 Figure 1.3: Chirality of profens 3 Figure 1.4: Copper(II) ion coordination sphere 11 Figure 1.5: Ligand-exchange concept 12 Figure 1.6: Calculated species distribution for a binary Phe/copper mixture. [Phe] = 10 mM, [Cu ] = 5 mM (dashed lines: copper, solid lines: amino acid and water) (7= 0.1 M, 25 °C) 34 Figure 1.7: Two-phase extraction equilibria 37 Figure 1.8: Calculated species distribution for a ternary two-phase Phe, Cu, and Li mixture. [Phe] = 10 mM, [Cu ] = 10 mM, [Li] = 10 mM (solid lines: aqueous phase complexes, dashed lines: organic phase complexes) (1= 0.1 M, 25 °C) 37 Figure 1.9: Enantiomeric hollow-fibre extraction system 46 Figure 2.1: Molecular mechanics energy-potential contributions 63 Figure 2.2: Single-stage two-phase extraction system 77 Figure 2.3: Multi-stage counter-current extraction system 82 Figure 2.4: Counter-current extraction system with mid-stage injection 84 Figure 2.5: Computational flow sheet for the MChemeq2 program 87 Figure 2.6: Solute-concentration profiles across a hydrophilic hollow-fibre membrane.... 88 Figure 2.7: View of a control volume in the CLEC column 92 Figure 2.8: Sketch of an HPLC column 93 Figure 2.9: Computational domain of the chromatography column 96 Figure 2.10: Solute-retention time (r) and column dead volume 97 Figure 2.11: Computational flow sheet for the Chico program 99 Figure 3.1: Sketch of a hollow-fibre cartridge 105 Figure 3.2: Two-phase hollow-fibre extraction setup 108 Figure 3.3: Setup of the potentiometric titration system 116 Figure 4.1: Calculated species distribution of the binary Phe copper complexes formed as a function of equilibrium pH. [Phe] = 10 mM, [Cu] = 5 mM (dashed lines: XU1 complexes involving a copper ion, solid lines: protonated amino acids, dotted line: free-copper concentration) (/ = 0.1 M, 25 °C) 128 Figure 4.2: Calculated species distribution of binary and ternary Phe, copper, L-HyPro complexes formed as a function of pH. [Phe] = 10 mM, [Cu] = 10 mM, [HyPro] = 10 mM (dashed lines: ternary complex for the ternary L- and D-Phe complexes) (7= 0.1 M, 25 °C) 132 Figure 4.3: Change in amino-acid protonation constants with solvent composition. T : Phe, • : Leu, O: L-HyPro (I = 0.1 M, 25 °C). Subscript aq refers to the cosolvent-free system (i.e., pure aqueous phase) 137 Figure 4.4: Change in binary analyte/copper equilibrium formation constants with solvent composition. T : Phe, • : Leu, O: L-HyPro (1= 0.1 M, 25 °C). Subscript aq refers to the cosolvent-free system (i.e., pure aqueous phase) 138 Figure 4.5: Change in the ternary amino-acid (A) equilibrium formation constants (homo-chiral) and selectivities for different solvent compositions. T : Phe, • : Leu (1 = 0.1 M, 25 °C). Subscript aq refers to the cosolvent-free system (i.e., pure water). Subscript aq refers to the cosolvent-free system (i.e., pure aqueous phase) 141 Figure 4.6: Copper partitioning (A) in an n-octanol/water two-phase system containing A-dodecyl-L-hydroxy-proline (LiH) at various aqueous pH values, copper concentrations, and ligand concentrations. Solid line: model regression logioP = -3.11 (7 a q = 0.1 M, 25 °C) 143 Figure 4.7: Copper concentrations (solid lines) and partition coefficient (dashed line) as a function of pH in an n-octanol/water two-phase system containing A-dodecyl-L-hydroxy-proline (LiH). Initial compound concentrations: LiH = 20.0 mM, Cu = 10.0 mM (a = 1.0,1= 0.1 M, 25 °C) 144 Figure 4.8: Experimental values of (A) L- and (O) D-Phe partition coefficients and fitting results (solid lines) in an n-octanol/water two-phase system containing A -^dodecyl-L-HyPro (20.6 mM). Initial aqueous concentrations: D-Phe = 5.97, L-Phe = 5.95 mM, Cu = 20.6 mM (/«, = 0.1 M, 25 °C) 146 Figure 4.9: Experimental values of (A) L- and (O) D-Leu partition coefficients and fitting results (solid lines) in an n-octanol/water two-phase system containing A-dodecyl-L-HyPro (16.3 mM). Initial aqueous concentrations: D-Leu = 4.84 mM, L-Leu = 4.84 mM, Cu = 10.3 mM (7 a q = 0.1 M, 25 °C) 146 Figure 4.10: Experimental values of (A) L- and (O) D-Val partition coefficients and fitting results (solid lines) in an n-octanol/water two-phase system containing A-octyl-L-HyPro (25.58 mM). Initial aqueous concentrations: L-Val = 3.75 mM and D-Val = 3.75 mM, Cu = 12.68 mM (/aq = 0.1 M, 25 °C) 147 Figure 4.11: Experimental values of (A) L-Phe and (•) copper partition coefficients and model predictions (solid and dashed lines) in an n-octanol/water two-phase XIV system containing A-dodecyl-L-HyPro (20.0 mM). Initial aqueous concentrations: L-Phe = 3.14 mM, Cu = 14.73 mM (7aq = 0.1 M, 25 °C) 152 Figure 4.12: Experimental values of (A) L-Phe, (O) D-Phe and (•,•) copper partition coefficients and model predictions (solid and dashed lines) in an n-octanol/water two-phase system containing JV-dodecyl-L-HyPro (20.0 mM). Initial aqueous concentrations: L-Phe = 3.14 mM and D-Phe = 3.14 mM, Cu = 14.73 mM (7aq = 0.1 M, 25 °C) 152 Figure 4.13: Experimental values of (A) L-Phe and (•) copper partition coefficients and model predictions (solid and dashed lines) in an n-octanol/water two-phase system containing 7v-dodecyl-L-HyPro (20.0 mM). Initial aqueous concentrations: L-Phe = 2.86 mM, Cu = 14.66 mM (7aq = 0.1 M, 25 °C) 153 Figure 4.14: Experimental values of L-Phe coefficients (A, A) and model predictions (solid lines) in an n-octanol/water two-phase system containing N-dodecyl-L-HyPro (20.0 mM). Initial aqueous concentrations: L-Phe = 2.86 mM, A: Cu = 7.33 mM, A: Cu = 4.19 mM (7aq = 0.1 M, 25 °C) 153 Figure 4.15: Experimental values of (A) L- and (O) D-Leu partition coefficients and model predictions (solid lines) in an n-octanol/water two-phase system containing N-dodecyl-L-HyPro (16.3 mM). Initial aqueous concentrations: D-Val = 4.84 mM, L-Val = 4.84 mM, Cu = 10.3 mM (/«, = 0.1 M, 25 °C) 154 Figure 4.16: Experimental values of (A) L- and (O) D-Val partition coefficients and model predictions (solid lines) in an n-octanol/water two-phase containing A-octyl-L-HyPro (25.58 mM). Initial aqueous concentrations: D-Val = 3. 93 mM, L-Val = 3. 93 mM, Cu= 12.68 mM (7aq = 0.1 M, 25 °C) 154 Figure 4.17: Calculated species distribution in an n-octanol/water two-phase system containing L-HyPro (10.0 mM) (only complexes with Cu are shown). Initial aqueous phase concentrations: [Cu] = 10.0 mM, [Phe] = 10.0 mM (1= 0.1 M, 25 °C) 155 Figure 4.18: Experimental copper partitioning data (O) in a two-phase system in the presence of the A -^octyl- L-hydroxy-proline ligand (LiH) in n-hexanol at various aqueous pH values, copper, and ligand concentrations. Solid line: model regression log10(3 of-3.15(7) (7aq = 0.1 M, 25 °C) 156 Figure 4.19: Experimental copper partitioning data (O) in an n-octanol/water two-phase system in the presence of the A-octyl-L-hydroxy-proline ligand (LiH) at various aqueous pH values, copper, and ligand concentrations. Solid line: model regression logiop of-3.11(1) (7aq = 0.1 M, 25 °C) 157 Figure 4.20: Experimental partition data (A,0), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing A-dodecyl-L-HyPro (20.45 mM). Initial aqueous concentrations: (O) D-Phe = 5.64 mM and (A) L-Phe = 5.64 mM, Cu = 10. 3 mM(/ a q = 0.1 M, 25 °C) 159 X V Figure 4.21: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing jV-dodecyl-L-HyPro (20.2ImM). Initial aqueous concentrations: (O) D-Phe = 4.36 mM and (•) L-Phe = 4.36 mM, Cu = 17.18 mM(7aq= 0.1 M, 25 °C) 160 Figure 4.22: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing A -^octyl-L-HyPro (20.97 mM). Initial aqueous concentrations: (O) D-Phe = 3.69 mM, (•) L-Phe = 3.69 mM, Cu = 12.64 mM (7aq = 0.1 M, 25 °C) 160 Figure 4.23: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing iV-dodecyl-L-HyPro (19.3 ImM). Initial aqueous concentrations: (O) D-Phe = 0.97 mM and (A) L-Phe = 0.97 mM, Cu = 5.0 mM (7aq = 0.1 M, 25 °C) 161 Figure 4.24: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing N-dodecyl-L-HyPro (19.3 ImM). Initial aqueous concentrations: (O) D-Phe = 0.97 mM and (A) L-Phe = 0.97 mM, Cu = 20.0 mM (7aq = 0.1 M, 25 °C) 161 Figure 4.25: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Leu in an n-octanol/water two-phase system containing TV-dodecyl-L-HyPro (20.2 mM). Initial aqueous concentrations: (O) D-Leu = 4.11 mM and (A) L-Leu = 4.11 mM, Cu = 12.5 mM (7aq = 0.1 M, 25 °C) 162 Figure 4.26: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Leu in an n-octanol/water two-phase system containing 7V-dodecyl-L-HyPro (16.3 mM). Initial aqueous concentrations: (O) D-Leu = 2.54 mM and (A) L-Leu = 2.54 mM, Cu -10.3 mM (7aq = 0.1 M, 25 °C) 162 Figure 4.27: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Val in an n-octanol/water two-phase system containing TV-octyl-L-HyPro (25.58 mM). Initial aqueous concentrations: (O) D-Val = 1.87 mM and (A) L-Val = 1.87 mM, Cu = 12.68 mM (7aq = 0.1 M, 25 °C) 163 Figure 4.28: Predicted complex concentrations for D-Phe in an n-octanol/water two-phase system containing TV-octyl-L-HyPro (20 mM). Initial aqueous concentrations: Cu = 6 mM, Phe: a) 1 mM, b) 10 mM (7aq = 0.1 M, 25 °C) 164 Figure 4.29: Experimental partition data (0,A) and selectivities (•) from Ding (1992) with model predictions (solid and dashed lines) for L- and D-Leu in an n-octanol/water two-phase system containing jV-dodecyl-L-HyPro (20 mM). XVI Initial aqueous concentrations: (O) D-Leu = 0.93 mM, (A) L-Leu = 0.93 mM, Cu = 6.3 mM (G\2 M acetate buffered) 165 Figure 5.1: Structure of the hydrated 6w-L-hydroxy-proline/copper(II) complex determined by molecular mechanics calculations (not all hydrogen atoms are shown).... 169 Figure 5.2: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex in vacuum (L-hydroxy-proline/copper/leucine) 175 Figure 5.3: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex in vacuum (L-hydroxy-proline/copper/valine) 175 Figure 5.4: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex in vacuum (L-hydroxy-proline/copper/phenylalanine) 176 Figure 5.5: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex with water (L-hydroxy-proline/copper/leucine) 176 Figure 5.6: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex with water (L-hydroxy-proline/copper/valine) 177 Figure 5.7: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex with water (L-hydroxy-proline/copper/ phenylalanine) 177 Figure 5.8: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex with methanol (L-hydroxy-proline/copper/leucine) 178 Figure 5.9: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex with methanol (L-hydroxy-proline/copper/phenylalanine) 178 Figure 5.10: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex (/V-octyl-L-hydroxy-proline/copper/leucine) 181 Figure 5.11: Molecular structures of the homo-chiral and hetero-chiral ternary amino-acid complex (Af-octyl-L-hydroxy-proline/copper/Phe) 181 Figure 6.1: Calculated D-Leu partition coefficient (P) in an n-octanol/water two-phase system as a function of copper (Cu ) concentration and equilibrium pH value, /V-alkyl-L-HyPro = 20 mM, L-Leu = 2 mM (7aq = 0.1 M, 25 °C) 192 Figure 6.2: Calculated L-Leu partition coefficient (P) in an n-octanol/water two-phase system as a function of copper (Cu ) concentration and equilibrium pH value, /V-alkyl-L-HyPro = 20 mM, L-Leu = 2 mM (7aq = 0.1 M, 25 °C) 192 Figure 6.3: Calculated D-Phe partitioning (P) in an n-octanol/water two-phase system as a function of copper (Cu ) concentration and equilibrium pH value, yV-alkyl-L-HyPro = 20 mM, L-Phe = 2 mM (7aq = 0.1 M, 25 °C) 193 Figure 6.4: Calculated L-Phe partitioning (P) in an n-octanol/water two-phase system as a function of copper (Cu ) concentration and equilibrium pH value, N-alkyl-L-HyPro = 20 mM, L-Phe = 2mM (7aq = 0.1 M, 25 °C) 193 XVII Figure 6.5: Calculated D-Leu partition coefficient (P) in an n-octanol/water two-phase system as a function of D-Leu concentration and equilibrium pH value, JV-alkyl-L-HyPro = 20 mM, Cu + + = 6 mM (7aq = 0.1 M, 25 °C) 194 Figure 6.6: Calculated D-Phe partition coefficient (P) in an n-octanol/water two-phase system as a function of D-Phe concentration and equilibrium pH value, jV-alkyl-L-HyPro = 20 mM, Cu + + = 6 mM (7aq = 0.1 M, 25 °C) 194 Figure 6.7: Calculated D-Phe partition coefficient (P) in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D-Phe concentration, pH = 3.5, N-alkyl-L-HyPro = 20 mM (7aq = 0.1 M, 25 °C) 195 Figure 6.8: Calculated D-Phe partitioning coefficient (P) in a two-phase system as a function of initial copper (Cu ) and D-Phe concentration, pH = 4.0, jV-alkyl-L-HyPro = 20 mM (7aq = 0.1 M, 25 °C) 195 Figure 6.9: Calculated D-Phe partition coefficient (P) in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D-Phe concentration, pH = 4.5, JV-alkyl-L-HyPro = 20 mM (/«, = 0.1 M, 25 °C) 196 Figure 6.10: Calculated Leu enantioselectivity (a) in an n-octanol/water two-phase system as a function of initial copper concentration (Cu ) and pH, JV-alkyl-L-HyPro = 20 mM, D-Leu = 1 mM, L-Leu = 1 mM (7aq = 0.1 M, 25 °C) 204 Figure 6.11: Calculated Phe enantioselectivity (a) in an n-octanol/water two-phase system as a function of initial copper concentration (Cu ) and pH, TV-alkyl-L-HyPro = 20 mM, D-Phe = 1 mM, L-Phe = 1 mM (7aq = 0.1 M, 25 °C) 204 Figure 6.12: Calculated enantiomeric excess in the aqueous phase (eeaq) of L-Leu in an n-octanol/water two-phase system as a function of equilibrium pH and copper (Cu ) concentration, D-Leu = 1 mM, L-Leu = 1 mM, TV-alky 1-L-HyPro = 20 mM (7aq = 0.1 M, 25 °C) 205 Figure 6.13: Calculated enantiomeric excess in the aqueous phase (eeaq) of L-Phe in an n-octanol/water two-phase system as a function of equilibrium pH and copper (Cu ) concentration, D-Phe = 1 mM, L-Phe = 1 mM, TV-alkyl-L-HyPro = 20 mM (7aq = 0.1 M, 25 °C) 205 Figure 6.14: Calculated enantiomeric excess in the organic phase (ee0Tg) of D-Leu in an n-++ octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Leu concentration, pH = 4.0, iV-alkyl-L-HyPro = 20 mM (7aq = 0.1 M, 25 °C) 206 Figure 6.15: Calculated enantiomeric excess in the organic phase (eeotg) of D-Leu in an n-++ octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Leu concentration, pH = 5.0, TV-alkyl-L-HyPro = 20 mM (7aq = 0.1 M, 25 °C) 206 XV111 Figure 6.16: Calculated enantiomeric excess in the organic phase (eeorg) of D-Phe in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Phe concentration, pH = 4.0, #-alkyl-L-HyPro = 20 mM (7a q = 0.1 M, 25 °C) 207 Figure 6.17: Calculated enantiomeric excess in the organic phase (eeorg) of D-Phe in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Phe concentration, pH = 5.0, 7V-alkyl-L-HyPro = 20 mM (7 a q = 0.1 M, 25 °C) 207 Figure 6.18: Calculated Leu performance factor (pf) in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Leu concentration, pH = 4.0, TV-alkyl-L-FfyPro = 20 mM (7 a q = 0.1 M, 25 °C) 208 Figure 6.19: Calculated Leu performance factor (pf) in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Leu concentration, pH = 5.0, A-alkyl-L-FfyPro = 20 mM (7 a q = 0.1 M, 25 °C) 208 Figure 6.20: Calculated Phe performance factor (pf) in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Phe concentration, pH = 4.0, TV-alkyl-L-HyPro = 20 mM (7 a q = 0.1 M, 25 °C) 209 Figure 6.21: Calculated Phe performance factor (pf) in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Phe concentration, pH — 5.0, N-alkyl-L-HyPro = 20 mM (7 a q = 0.1 M, 25 °C) 209 Figure 6.22: Calculated Leu performance factor (pf) in an n-octanol/water two-phase system as a function of initial D/L-Leu concentration and pH. Cu =10 mM, 7V-alkyl-L-HyPro = 20 mM (7 a q = 0.1 M, 25 °C) 210 Figure 6.23: Calculated Leu performance factor (pf) in a two-phase system as a function of initial D/L-Leu concentration and pH. The copper concentration was adjusted as half of the total ligand and amino-acid concentrations, ZV-alkyl-L-HyPro = 20 mM (7 a q = 0.1 M, 25 °C) 210 Figure 6.24: Calculated Phe performance factor (pf) in an n-octanol/water two-phase system as a function of initial D/L-Phe concentration and pH, Cu =10 mM, 7V-alkyl-L-HyPro = 20 mM (7 a q = 0.1 M, 25 °C) 211 Figure 6.25: Calculated Phe performance factor (pf) in an n-octanol/water two-phase system as a function of initial D/L-Phe concentration and pH. The copper concentration was adjusted as half of the total ligand and amino-acid concentrations, JV-alkyl-L-HyPro = 20 mM (7 a q = 0.1 M, 25 °C) 211 Figure 6.26: Calculated Leu performance factor (pf) in an n-octanol/water two-phase system as a function of pH and copper concentration. TV-alkyl-L-HyPro = 19.31 mM, L-Leu = 0.966 mM, D-Leu = 0.966 mM, acetate-buffer concentration 100 mM (7aq = 0.1 M, 25 °C) 212 X I X Figure 6.27: Calculated Phe performance factor (pf) in an n-octanol/water two-phase system as a function of pH and copper concentration, /V-alkyl-L-HyPro = 19.31 mM, L-Phe = 0.966 mM, D-Phe = 0.966 mM, acetate-buffer concentration 100 mM (7aq = 0.1 M, 25 °C) 212 Figure 6.28: Calculated enantiomeric excess (eeorg) for Phe in an n-octanol/water two-phase system as a function of pH and copper concentration, /V-alkyl-L-HyPro = 19.31 mM, L-Phe = 0.966 mM, D-Phe = 0.966 mM, acetate-buffer concentration 100 mM (7aq = 0.1 M, 25 °C) 213 Figure 6.29: Calculated fraction of Phe extracted into the organic phase (cj>) in an n-octanol/water two-phase system as a function of pH and copper concentration, A-alkyl-L-HyPro = 19.31 mM, L-Phe = 0.966 mM, D-Phe = 0.966 mM, acetate-buffer concentration 100 mM (7aq = 0.1 M, 25 °C) 213 Figure 6.30: Experimental Phe performance factors (pf) in an n-octanol/water two-phase system (O) and model predictions (solid lines) as a function of pH at initial copper concentrations of: a) 5 mM, b) 10 mM, and c) 20 mM with experimental data, Ar-octyl-L-HyPro =19.31 mM, L-Phe = 0.966 mM, D-Phe = 0.966 mM, acetate-buffer concentration 100 mM (7aq = 0.1 M, 25 °C) 214 Figure 6.31: Calculated species distribution for D-Phe as a function of pH in the presence (solid lines) and absence (dashed lines) and of acetate buffer in an n-octanol/water two-phase system, TV-alkyl-L-HyPro = 20 mM, Cu = 11 mM, D-Phe = 2 mM, Ac = 100 mM (only copper complexes are shown) (7aq = 0.1 M, 25 °C) 216 Figure 6.32: Calculated species distribution as a function of pH in the presence (solid lines) and absence (dashed lines) and of acetate buffer in an n-octanol/water two-phase system, TV-alkyl-L-HyPro = 20 mM, Cu = 11 mM, D-Phe = 2 mM, Ac = 200 mM (only copper complexes are shown) (7aq = 0.2 M, 25 °C) 216 Figure 6.33: Calculated copper and D-Phe partition coefficients as a function of pH in the absence (solid lines) and presence of acetate (dashed lines) in an n-octanol/water two-phase system, Af-alkyl-L-HyPro = 20 mM, Cu = 11 mM, D-Phe = 2 mM, acetate-buffer concentration 200 mM (7aq = 0.2 M, 25 °C).. 218 Figure 6.34: Calculated Phe performance factor (pf) in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Phe concentration in the presence of acetate, pH = 4.0, A-alkyl-L-HyPro = 20 mM, acetate buffer = 200 mM (7aq = 0.2 M, 25 °C) 219 Figure 6.35: Calculated Phe performance factor (pf) in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Phe concentration in the presence of acetate, pH = 5.0, W-alkyl-L-HyPro = 20 mM, acetate buffer = 200 mM (7aq = 0.2 M, 25 °C) 219 Figure 6.36: Calculated Leu performance factor (pf) in an n-octanol/water two-phase system as a function of initial copper (Cu ) and D/L-Phe concentration in the presence XX of acetate, pH = 5.0, A-alkyl-L-HyPro = 20 mM acetate-buffer concentration 200 mM (7aq = 0.2 M) 220 Figure 7.1: Experimental benzoic-acid partition coefficients (PBA) m an n-octanol/water two-phase system for several aqueous pH values (7= 0.1 M, 25 °C) 224 Figure 7.2: Overall mass-transfer coefficients (K) for varying lumen velocities and model prediction (dashed line) at different constant shell velocities of: O 0.07, A 0.12 and V 0.19 cm/s, P = 6.0, pH = 5.22, sfp = 42% 227 Figure 7.3: Overall mass-transfer coefficients (K) for varying lumen velocities and shell velocities, and model prediction (dashed line). • : P = 3.0, pH = 5.5, 8fP = 27%; • : P = 6.0, pH = 5.22, efp = 43%, V: P = 0.97, A: pH = 6.08, sfp = 27%. The shell velocity was scaled to be 20% higher than the lumen velocity 227 Figure 7.4: Overall mass-transfer coefficients (K) for varying shell velocities and model prediction (dashed line) at a constant lumen velocities of 0.14 cm/s. P = 3.0, pH = 5.5, = 27% 228 Figure 7.5: Calculated number of transfer units (NTU) as a function of lumen velocities for several constant overall mass-transfer coefficients (K), Zf,bre = 20 cm, a = 200 cm"1 228 Figure 7.6: Experimental aqueous Leu concentrations (A,0) at the reactor outlet in a counter-current hollow-fibre n-octanol/water two-phase extraction system and model predictions (solid lines) containing A-octyl-L-HyPro (10.4 mM). Inlet concentrations: (O) D-Leu = 2.1 mM, L-Leu = 2.1 mM, Cu o r g = 3.6 mM, y = 3.57, pH i n = 4.3, I f i b r e = 22 cm, K= 3xl0"5 cm/s (±25%) (/= 0.1 M) 236 Figure 7.7: Experimental aqueous Phe concentrations (A,0) at the reactor outlet in a counter-current hollow-fibre n-octanol/water two-phase extraction system and model predictions (solid lines) containing A-octyl-L-HyPro (10.4 mM). Inlet concentrations: (O) D-Phe = 2.03 mM, (A) L-Phe = 2.03 mM, Cu o r g = 3.6 mM, y = 3.57, pH i n = 4.3, Z f i b r e = 20 cm, K= 3xl0"5 cm/s (±25%) (1= 0.1 M) 236 Figure 7.8: Experimental aqueous Leu concentrations (A,0) at the reactor outlet in a counter-current hollow-fibre n-octanol/water two-phase extraction system and model predictions (solid lines) containing A-octyl-L-HyPro (9.9 mM). Inlet concentrations: (O) D-Leu =1.53 mM, (A) L-Leu =1.53 mM, Cu o r g = 2.9 mM, Cu a q = 0 mM, y = 2.2, pHin = 3.9 (0.1 M acetate buffered). Zf,bre = 20 cm, K = 3xl0" 5cm/s(±25%)..... 237 Figure 7.9: Experimental aqueous Leu concentrations (A,0) at the reactor outlet of a counter-current hollow-fibre n-octanol/water two-phase extraction system and model predictions (solid lines) containing A -^octyl-L-HyPro (9.9 mM). Inlet concentrations: (O) D-Leu = 1.53 mM, (A) L-Leu = 1.53 mM, Cu o r g = 2.9 mM, Cu a q = 6.68 mM, y = 2.2, pH i n = 3.9 (0.1 M acetate buffered). Z f l b r e = 20 cm, K= 3x\0 5 cm/s (±25%) 237 X X I Figure 7.10: Calculated aqueous Leu and copper concentrations (cf, Figure 7.8) at the reactor outlet in a counter-current hollow-fibre n-octanol/water two-phase extraction system containing A-octyl-L-HyPro (9.9 mM). Inlet concentrations: D-Leu = 1.53 mM, L-Leu = 1.53 mM, Cuorg = 2.9 mM, Cu a q = 0 mM, y = 2.2, pH i n = 3.9 (0.1 M acetate buffered). I f l b r e = 20 cm, K= 3x10 5 cm/s (±25%). 238 Figure 7.11: Calculated aqueous Leu and copper concentrations (cf, Figure 7.9) at the reactor outlet of a counter-current hollow-fibre n-octanol/water two-phase extraction system containing 7V-octyl-L-HyPro (9.9 mM). Inlet concentrations: D-Leu = 1.53 mM, L-Leu = 1.53 mM, C u o r g = 2.9 mM, Cu a q = 6.68 mM, y = 2.2, pHin = 3.9 (0.1 M acetate buffered). Zfibre = 20 cm, K= 3x10 cm/s (±25%). Solid lines: multiple-chemical equilibria model predictions 238 Figure 7.12: Experimental aqueous Phe concentrations (A,0) at the reactor outlet in a counter-current hollow-fibre n-octanol/water two-phase extraction system and model predictions (solid lines) containing A-octyl-L-HyPro (9.9 mM). Inlet concentrations: (O) D-Phe = 1.90 mM, (A) L-Phe = 1.90 mM, C u o r g = 3.0 mM, Cu a q = 0 mM, y = 2, pHin = 3.7 (0.1 M acetate buffered), Z,f,bre = 20 cm, K = 3xl0" 5cm/s(±25%) 239 Figure 7.13: Experimental aqueous Phe concentrations (A,0) at the reactor outlet in a counter-current hollow-fibre n-octanol/water two-phase extraction system and model predictions (sold lines) containing iV-octyl-L-HyPro (9.9 mM). Inlet concentrations: (O) D-Phe = 1.90 mM, (A) L-Phe = 1.90 mM, Cu o r g = 3.0 mM, Cu a q = 4.3 mM, y = 2, pHjn = 3.7 (0.1 M acetate buffered), Z,f,bre = 20 cm, K = 3xl0" 5cm/s(±25%) 239 Figure 7.14: Experimental Aqueous Leu concentrations (A,0) at the reactor outlet in a counter-current hollow-fibre n-octanol/water two-phase extraction system and model predictions (sold lines) containing TV-octyl-L-HyPro (12.95 mM). Inlet concentrations: (O) D-Leu = 0.54 mM, (A) L-Leu = 0.54 mM, Cu o r g = 4.0 mM, Y = 3.0, pHin = 4.4 (0.1 M acetate buffered), If lbre = 20 cm, K = 3xl0"5 cm/s (±25%) 240 Figure 7.15: Calculated species distribution in the organic and aqueous phase over 10 equilibrium stages for D-Leu in a counter-current n-octanol/water two-phase extraction system containing A-octyl-L-HyPro (20.0 mM). Inlet concentrations: D-Leu = 1.0 mM, Cu o r g = 6.0 mM, y = 4.0, pH = 4.0 (7= 0.1 M) 243 Figure 7.16: Calculated species distribution in the organic and aqueous phase over 10 equilibrium stages for D-Phe in a counter-current n-octanol/water two-phase extraction system containing /V-octyl-L-HyPro (20.0 mM). Inlet concentrations: D-Phe = 1.0 mM, Ct io r g = 6.0 mM, y = 2.0, pH = 4.0 (7= 0.1 M) 243 Figure 7.17: Calculated species distribution in the organic and aqueous phase over 10 equilibrium stages for D/L-Leu in a counter-current n-octanol/water two-phase extraction system containing A-octyl-L-HyPro (20.0 mM). Inlet concentrations: X X I I D-Leu = 1.0 mM (solid lines), L-Leu = 1.0 mM (dashed lines), C u o r g = 6.0 mM, y = 4.0, pH = 4.0 (7= 0.1 M) 244 Figure 7.18: Calculated species distribution in the organic and aqueous phase over 10 equilibrium stages for D/L-Phe in a counter-current n-octanol/water two-phase extraction system containing iV-octyl-L-HyPro (20.0 mM). Inlet concentrations: D-Phe = 1.0 mM (solid lines), L-Phe = 1.0 mM (dashed lines), Cu o r g = 6.0 mM, Y = 2.0, pH = 4.0 (1= 0.1 M) 244 Figure 7.19: Experimental aqueous Leu concentrations (A,0) at the reactor outlet of a counter-current n-octanol/water two-phase hollow-fibre two-phase extraction systems (Ding, 1992) and multiple-chemical equilibria multi-staged model predictions (solid lines). The system consists of a fractional extraction setup with two membrane modules (solid symbols: 2x12 cm, open symbols: 2x32 cm -4 -1 hollow-fibre modules). K = 8x10 cm/s, a = 167 cm , (O) D-Leu = 2.45 mM, (A) L-Leu = 2.45 mM, TV-dodecyl-L-HyPro = 20 mM, Cu o r g = 6.3 mM, y = 4, co = 0.1, pH = 4.0 (0.2 M acetate buffered) 247 Figure 7.20: Experimental aqueous Leu concentrations (A,0) at the reactor outlet in a counter-current fractional hollow-fibre n-octanol/water two-phase extraction system and model predictions (solid lines) containing 7V-octyl-L-HyPro (20.0 mM). Inlet concentrations: (O) D-Leu = 2.5 mM, (A) L-Leu = 2.5 mM, Cuorg = 7.56 mM, y = 3.3, co = 0.09, pH = 4.1 (0.1 M acetate buffered), Z f l b r e = 2x20 cm, K= 3x10 5 cm/s (±25%) 248 Figure 7.21: Experimental aqueous Phe concentrations (A,0) at the reactor outlet in a counter-current fractional hollow-fibre n-octanol/water two-phase extraction system and model predictions (solid lines) containing 7V-octyl-L-HyPro (20.0 mM). Inlet concentrations: (O) D-Phe = 2.51 mM, (A) L-Phe = 2.51 mM, Cuorg = 7.56 mM, y = 2.86, co = 0.12, pH = 4.0 (0.1 M acetate buffered), Z f i b r e = 2x20 cm, K= 3xl0"5 cm/s (±25%) 249 Figure 7.22: Calculated species distribution for the organic and aqueous phases over 20 equilibrium stages for Leu enantiomers in a counter-current fractional n-octanol/water two-phase extraction system containing TV-octyl-L-HyPro (20.0 mM). Inlet concentrations: D-Leu = 1.0 mM, L-Leu =1.0 mM, Cuorg = 6.0 mM, y = 4.0, co = 0.1, pH = 4.0 (7= 0.1 M) 251 Figure 7.23: Calculated species distribution for the organic and aqueous phases over 20 equilibrium stages for Phe enantiomers in a counter-current fractional n-octanol/water two-phase extraction system containing A-octyl-L-HyPro (20.0 mM) in n-octanol. Inlet concentrations: D-Phe = 1.0 mM, L-Phe = 1.0 mM, Cu o r g = 6.0 mM, y = 2.0, co = 0.1, pH = 4.0 (I = 0.1 M) 252 Figure 7.24: Calculated performance-factor (pf) contour plots D-Leu as a function of total equilibrium stages (NTU) and phase ratio (y) in a counter-current n-octanol/water two-phase extraction system containing JV-octyl-L-HyPro XX111 (20.0 mM). Inlet concentrations: D-Leu and L-Leu = 1.0 mM, Cu o r g = 6.0 mM, co = 0.1; pH: a) 3.75, b) 4.00, c) 4.25 (7= 0.1 M) 256 Figure 7.25: Calculated performance-factor (pf) contour plots for D-Phe as a function of total equilibrium stages (NTU) and phase ratio (y) in a counter-current n-octanol/water two-phase extraction system containing JV-octyl-L-HyPro (20.0 mM). Inlet concentrations: D-Phe and L-Phe = 1.0 mM, Cu o r g = 6.0 mM, co = 0.1, pH; a) 3.5, b) 3.75, c) 4.0 (/= 0.1 M) 257 Figure 7.26: Calculated performance-factor (pf) contour plot for D-Leu as a function of total equilibrium stages (NTU) and copper concentrations in the organic phase inlet (Cuo rg) in a counter-current n-octanol/water two-phase extraction system containing TV-octyl-L-HyPro (20.0 mM). Inlet concentrations: D-Leu and L-Leu = 1.0 mM, co = 0.1; a) pH = 3.75, y = 5.7; b) pH = 4.00, y = 4.6; c) pH = 4.25, y = 4.0 (7=0.1 M) 258 Figure 7.27: Calculated performance-factor (pf) contour plots for D-Phe as a function of total equilibrium stages (NTU) and copper concentrations in the organic phase inlet (Cuorg) in a counter-current n-octanol/water two-phase extraction system containing 7V-octyl-L-HyPro (20.0 mM). Inlet concentrations: D-Phe and L-Phe = 1.0 mM, co = 0.1; pH: a) 3.5, y = 3.45; b) 3.75, y = 2.3; c) 4.0, y = 1.7 (7 = 0.1 M) 259 Figure 7.28: Calculated performance factor (pf) contour plots for D-Leu as a function of the volumetric injection-phase ratio (co) and copper concentrations in the organic phase inlet (Cuo r g ) in a counter-current n-octanol/water two-phase extraction system containing TV-octyl-L-HyPro (20.0 mM). Inlet concentrations: D-Leu and L-Leu = 1.0 mM; a) pH =3.75, y = 5.7; b) pH = 4.25, y = 4.0 (7 = 0.1 M). 260 Figure 7.29: Calculated feed-stage dependence (Nmf) on the performance factor (pf) over a total of 30 NTUs for Leu in a counter-current fractional n-octanol/water two-phase extraction system containing TV-octyl-L-HyPro (20.0 mM) in n-octanol. Inlet concentrations: D-Leu =1.0 mM, L-Leu =1.0 mM, Cuorg = 6.0 mM, pH = 4.0, y = 4.6, co = 0.1; solid line: Cu a q = 6.0 mM, dashed line: Cu a q = 0.0 mM (7=0.1 M) 262 Figure 7.30: Calculated feed-stage dependence (iVjnj) on the performance factor (pf) over a total of 30 equilibrium stages for Phe enantiomers in a counter-current fractional n-octanol/water two-phase extraction system containing TV-octyl-L-HyPro (20.0 mM) in n-octanol. Inlet concentrations: D-Phe = 1.0 mM, L-Phe = 1.0 mM, C u o r g = 6.0 mM, pH = 4.0, y = 1.7, co = 0.1; solid line: Cu a q = 6.0 mM, dashed line: Cu a q = 0.0 mM (7= 0.1 M) 262 Figure 7.31: Calculated minimum number of equilibrium stages (NTUmm) to achieve a 99% performance factor (pf) in a counter-current fractional two-phase extraction system at optimized phase ratios (y) and pH values as a function of the Gibbs free energy difference (SAG) and enantioselectivity (a) of ternary complexes in xxiv the organic phase. The 8AG values were changed by increasing the equilibrium formation constants of the homo-chiral complex (i.e., PL) at constant PD values (i.e., log10pD-Phe= 6.20, logiopD-Leu= 6.31). 7V-octyl-L-HyPro = 20.0 mM, inlet concentrations: D- and L-amino acid = 1.0 mM, Cuorg = 8.0 mM, co = 0.1 (7 = 0.1 M) 265 Figure 8.1: L-Leu chromatograms calculated with Chico for a CLEC column containing TV-n-dodecyl-L-HyPro (12 mM) as a function of control volume numbers (CVN) (D = 10"9 m2/s, pH = 4, L = 15 cm, Q = 1.0 ml/min, s = 0.71, F i n j = 5 pl) 270 Figure 8.2: Experimental Leu and Phe chromatograms using the CLEC column containing TV-n-dodecyl-L-HyPro (12 mM). Cu = 1.0 mM, acetate buffered, a) Leu: pH 4.64, b) Leu: pH 5.44, c) Phe: pH 4.64, d) Phe: pH 5.44, L = 15 cm, Q = 1.0 ml/min, s = 0.71, F i n j = 5 pl (7 = 0.1 M, 20% MeOH, 25 °C) 271 Figure 8.3: Experimental Leu enantiomer elution times from the CLEC column containing 7V-n-dodecyl-L-HyPro (12 mM) at different acetate-buffer concentrations. pH = 5.44 (•, • ) ; pH = 4.64 (O, ), L-Leu = 0.5 mM, D-Leu = 0.5 mM, Cu = 1.0 mM, L = 15 cm, Q = 1.0 ml/min, E = 0.71, VH = 5 pl (7= 0.1 M, 20% MeOH, 25 °C) 272 Figure 8.4: Experimental Phe enantiomer elution times from the CLEC column containing 7V-n-dodecyl-L-HyPro (12 mM) at different acetate-buffer concentrations. pH = 5.44 (•, A); pH = 4.64, pH = 5.44 (0,A); pH = 4.64 ^) , L-Phe = 0.5 mM, D-Phe = 0.5 mM, Cu = 1.0 mM, L = 15 cm, Q = 1.0 ml/min, 8 = 0.71, Vm] = 5 pl (/= 0.1 M, 20% MeOH, 25 °C) 273 Figure 8.5: Experimental Leu enantiomer chromatogram using a CLEC column (O) containing jV-n-dodecyl-L-HyPro (12 mM) and model prediction (solid lines) using equilibrium formation constants measured in 20% methanol. Initial aqueous concentrations: L-Leu = 0.5 mM, D-Leu = 0.5 mM, Cu = 1.0 mM, acetate buffer 50 mM, pH = 4.64, WL-Leu = 12.7, wo-Leu = 17.9 s, Z = 15 cm, Q = 1.0 ml/min, s = 0.71, VH = 5 pl (7= 0.1 M, 20% MeOH, 25 °C) 277 Figure 8.6: Experimental Phe enantiomer chromatogram using a CLEC column (O) containing TV-n-dodecyl-L-HyPro (12 mM) and model predictions (solid lines) using equilibrium formation constants measured in 20% methanol. Initial aqueous concentrations: L-Phe = 0.5 mM, D-Phe = 0.5 mM, Cu = 1.0 mM, acetate buffer 50 mM, pH = 4.64, WL-phe = 22.2 s, wD-phe = 29.4 s, L = 15 cm, Q = 1.0 ml/min, e = 0.71, VH = 5 pl (7= 0.1 M, 20% MeOH, 25 °C) 277 Figure 8.7: Experimental Leu elution times (0,A) and model regression (solid lines) using the CLEC column containing TV-n-dodecyl-L-HyPro (12 mM). (O): D-Leu -0.5 mM, (A): L-Leu = 0.5 mM, Cu = 1.0 mM, acetate buffer 50 mM, L=\5 cm, (9=10 ml/min, 8 = 0.71, VH = 5 ul (7= 0.1 M, 20% MeOH, 25 °C) 280 Figure 8.8: Experimental Phe elution times (0,A) and model regression (solid lines) using the CLEC column containing jV-n-dodecyl-L-HyPro (12 mM). (O): D-Phe = X X V 0.5 mM, (A): L-Phe = 0.5 mM, Cu = 1.0 mM, acetate buffer 50 mM, L = 15 cm, Q=l.O ml/min, s = 0.71, Vmi = 5 ul (1= 0.1 M, 20% MeOH, 25 °C) 280 Figure 8.9: Experimental Leu enantiomer chromatogram using a CLEC column (O) containing A-n-dodecyl-L-HyPro (12 mM) and model prediction (solid lines) using regressed equilibrium formation constants. L-Leu = 0.5 mM, D-Leu = 0.5 mM, Cu = 1.0 mM, acetate buffer 50 mM, pH = 4.64, L = 15 cm, 0=1.0 ml/min, s = 0.71, F i n j = 5 ul (7= 0.1 M, 20% MeOH, 25 °C) 281 Figure 8.10: Experimental Phe enantiomer chromatogram using a CLEC column (O) containing A-n-dodecyl-L-HyPro (12 mM) and model predictions (solid lines) using regressed equilibrium formation constants. L-Phe = 0.5 mM, D-Phe = 0.5 mM, Cu = 1.0 mM, acetate buffer 50 mM, pH = 4.64, L = 15 cm, 0=1-0 ml/min, e = 0.71, K i n j = 5 ul (/= 0.1 M, 20% MeOH, 25 °C) 281 Figure 8.11: Experimental Leu and Phe elution times from the reverse-phase column in the absence (open symbols) and in the presence of the JV-n-dodecyl-L-HyPro ligand (12 mM) (closed symbols) at different pH values. (A): Phe = 0.5 mM, (•): Leu = 0.5 mM, Cu = 1.0 mM, acetate buffer 100 mM, L = 15 cm, Q = 1.0 ml/min, s = 0.71, Vm] = 5 ul (/= 0.1 M, 20% MeOH, 25 °C) 285 Figure 10.1: Continuous hollow-fibre extraction system for enantioseparation (dashed lines: aqueous streams, solid lines: organic streams) 292 Figure A. l : Chemical structures (hydrogen atoms and charges are not shown) 316 Figure A.2: Experimental aqueous Phe concentrations (A,0) at the reactor outlet in a counter-current hollow-fibre n-octanol/water two-phase extraction system and model predictions (solid lines) containing A-octyl-L-HyPro (12.95 mM). Inlet concentrations: (O) D-Phe = 0.51 mM, (A) L-Phe = 0.51 mM, Cuor„ = 4.0 mM, -5 y = 3.0, pHjn = 4.3 (0.1 M acetate buffered), Zf,bre = 20 cm, K- 3x10 cm/s (±25%) 330 ABBREVIATIONS A amino acid Asn asparagine cis cis configuration CLEC chiral ligand-exchange chromatography CMPA chiral mobile phase additives CSP chiral stationary phase Cu copper ion D dextro rotary form of the enantiomer DOPA 3,4-dihydroxyphenylalanine H proton HyPro hydroxy-proline L levo rotary form of the enantiomer Leu leucine Li ligand MeOH methanol Met methionine MHis A-methyl histidine Phe phenylalanine Pro proline SMB simulated moving bed trans trans configuration xxvn ACKNOWLEDGMENTS I am very grateful to my supervisor Dr. Charles Haynes (alias Chip) for giving me the opportunity to pursue this interesting and challenging work as well as for his support. In particular, I would like to acknowledge Dr. Louise Creagh for her help, fruitful discussions, and the never-ending patience she showed in organizing the lab. In addition, I would like to thank all my colleagues at the Biotech Lab for their contributions and friendships. The summer students Andrea Roche and Collin Mui are greatly acknowledged for supporting some of the experimental measurements. I am also very grateful to the Akzo Nobel Faser company in Germany for providing me with the hollow-fibre membranes. Finally, I would like to dedicate this work to my loving parents (Lore and Wolfgang) that never doubted my decision to spend so many years at universities. I am grateful for their love and support during my stay in Canada. Irticrjt J&unst un5 TJDissensCrjaft aflein, W e c a n '* depend alone on science or on art, 6e6u(b" wifT bet 5em XDerRe setn. T h e w o r k d e m a n d s a d e a l of patience too. J.W. von Gothe (Faust, 1808) 1 CHAPTER I 1 Introduction An enantiomer (Greek: enantio, opposite) is a molecule that is not superimposable on its mirror image (reflection). Enantiomers occur in molecules that are chiral (Greek: cheir, hand). The simplest type of chiral molecule contains a single tetrahedral carbon where four different atoms or groups are attached. These four atoms or groups can be connected to the chiral carbon atom in two distinct arrangements, resulting in two enantiomeric forms of the molecule. Figure 1.1 shows a sketch of two alanine enantiomers. The chiral flag (*) indicates the asymmetric carbon centre of the molecules. mirror plane H 3 C COOH V N F L S(L) Figure 1.1: Alanine amino-acid enantiomers. COOH H.N \ 2 CH. R(D) The first method to distinguish between enantiomers was the sign of optical rotation (i.e., d- and /-, or (+) and (-)-forms). In 1919, Emil Fisher introduced a new convention for defining optical conformations. He arbitrarily decided to name the (+)-glyceralaldehyde enantiomer D-(+)-glyceralaldehyde according to his nomenclature convention. Accordingly, all chiral molecules that could be chemically related to D-(+)-glyceralaldehyde were assigned 2 the D-configuration, while molecules related to L-glyceralaldehyde became the L-series. This Fisher convention is still widely used in sugar chemistry and for labeling a-amino acids. In 1951, X-ray crystallography showed that Fisher's guess was correct. However, an unambiguous rule to label enantiomer was introduced by Cahn Ingold and Prelog (Sheldon, 1993) which labels enantiomers by hierarchical assignment of substituents at any chiral centre. The counting priority of the atoms is established by differences in the atomic numbers closest to the asymmetric centre. Chirality plays a very important role in biological systems. The high specificity of the catalytic domain of enzymes is a direct consequence of its three-dimensional structure, which in turn depends on an exclusively L-amino-acid sequence. Therefore, nature discriminates the chiral character of molecules. Many drugs, vitamins, flavors and fragrances, herbicides and pesticides contain a chiral centre. Often only one enantiomer is responsible for the desired response, while the other is either ineffective or toxic. The classic and most tragic example of the different effects of chiral enantiomers, in this case a drug, occurred in the early 60s. The sedative thalidomide (cf, Figure 1.2) was discovered to cause serious malformations in newborns of women during early pregnancy (Allenmark, 1988). Later it was determined that the toxic effect (teratogenicity) was caused exclusively by the iS-enantiomer of thalidomide. The i?-enantiomer, responsible for the sleep-inducing effects, had no side effects. More recently it was shown that thalidomide is optically unstable and will racemise by opening its phthalimide ring in less than 10 minutes in blood (Caldwell, 1995). Therefore, it is not possible to determine if the tragedy could have been prevented by marketing the drug in an enantiomerically pure form. Until thalidomide, drug researchers had been content to develop racemic forms of chiral drugs, assuming that either both enantiomers were equally active, or one enantiomer was inactive and inert. 0 H o ' - N ' o o H (S^-N-phthalylglutamic acid amide (teratogenic form) Figure 1.2: Thalidomide enantiomers. 9 H (,K)-jY-phthalylglutamic acid amide (therapeutically-active form) A better justification for enantiomerically pure drugs is given by 2-arylpropionic acids (profen), which belong to the class of non-steroidal anti-inflammatory drugs (NSAIDs). The molecules in this family contain only a single chiral centre (cf, Figure 1.3). The active S-enantiomer inhibits cyclooxygenase, an enzyme that converts arachidonic acid into prostaglandins and other mediators of an inflammatory response. However, in vivo, the i?-enantiomer is metabolically inverted into the active S-enantiomer. It is therefore difficult to correctly dose the racemic mixture because the amount of the active S-enantiomer is constantly changing. In addition, some inactive i?-enantiomer can accumulate in fat tissues before inversion. Several other profens were withdrawn from the market since the chiral counterparts were toxic (e.g., benoxaprofen, indoprofen, suprofen) (Caldwell, 1995). R\ R' COOH 'Me COOH •H active S-enantiomer Figure 1.3: Chirality of profens. inactive /^-enantiomer 4 In 1992, the Food and Drug Administration (FDA) adopted new legislation regarding chiral drugs (FDA's Policy Statement, 1992). It is now required that in vitro pharmacological testing of both enantiomers be carried out independently. These studies are designed to address issues like chiral form stability, interconversion, pharmacokinetic properties, and dosage equivalence. A similar but weaker statement has been announced by the Committee for Proprietary Medicinal Products of the European Medicines Evaluation Agency (Persidis, 1997). As the FDA begins to distinguish between racemates and enantiopure drugs, industries are focusing more closely on enantioseparations (Stinson, 1993, 1994, 1997; Richards and McCague, 1997). It is obvious that the enantiomeric ballast taken or released into the enviromnent should be reduced to the minimum possible level. Crosby (1991) summarized the reasons for producing enantiomerically pure molecules into different groups: (1) biological activity is associated with only one enantiomer; (2) enantiomers exhibit very different types of activity, both of which may be beneficial or one may be beneficial and the other undesirable; (3) the unwanted isomer is at best 'isomeric ballast' for the environment; (4) the optically pure compound may be significantly more active due to the absence of antagonistic effects (/'. e., the presence of the inactive enantiomer inhibits the activity of the therapeutic counterpart); (5) the unwanted enantiomer could be considered an impurity during drug registration; (6) where the switch from a racemate to the enantiomeric pure substance is feasible, there is an opportunity to double the capacity and efficiency of an industrial process; and (7) the physical characteristics of enantiomers versus racemates may confer processing or formulation advantages. 5 The market for enantiopure drugs has reached many billions of dollars per annum (cf, Table 1.1). It is predicted that by the year 2000 the sale of chiral pharmaceuticals will exceed the 100 billion dollar barrier (Cannarsa, 1996). In addition, another 20 billion dollars will be generated in the sale of chiral intermediates used in the synthesis of chiral drugs (Persidis, 1997). Therefore, a strong interest exists in the development and improvement of enantiomeric separation techniques. In particular, there is a need for processes that allow continuous operation and uncomplicated system scale-up. Table 1.1: Sales of chiral therapeutics in 1995 (in millions of US dollars). Category Total Sales Chiral Sales Antibiotics 25,000 17,380 Cardiovascular 30,000 15,345 Hormones 12,000 6,655 Cancer 8,000 5,200 Hematology 11,000 4,245 Central nervous system 26,000 3,330 Vaccines 4,000 3,800 Respiratory 18,000 1,230 Organ rejection 1,400 1,290 Anti-inflammatories 11,000 895 Total 146,400 59,370 Source: Persidis (1997) 6 The agrochemical sector is another important field where chiral molecules are used. Total production levels are nearly an order of magnitude higher than in the pharmaceutical industries and the majority of these products are sold as racemic mixtures (Ariens, 1988). As in the therapeutic case, a switch to enantiomerically pure products would not only increase specificity, but also decrease the total amount released into the environment. Due to their identical chemical formula, molecular weight and shape, enantiomers are indistinguishable with respect to most physico-chemical properties. For instance, they share identical melting and boiling points. An exception is the direction in which they rotate plane-polarized light. This fact is the basis of the L- and D- nomenclature often used to define enantiomers. In conventional chemical syntheses, (almost) equal amounts of enantiomers are generally produced. This 50/50% composition is referred to as a racemic mixture. The similarity of the enantiomer molecules makes it difficult to separate them by physical methods. Therefore, enantioseparations are among the most difficult separation problems in the chemical and pharmaceutical industries. In 1848, Louise Pasteur reported the first chiral separation of tartaric acid into two enantiomeric structures (Pasteur, 1848). Based on the visually distinguishable appearance of sodium-ammonium tartrate crystals, he was able to separate the two enantiomers by hand. In general, only a very limited number of enantiomers can be separated by such crystallization techniques (Armstrong, 1987). This thesis is concerned with new methodologies for separating enantiomers. 7 1.1 Chiral Synthesis In some cases, enantiomerically pure products can be produced by stereoselective synthesis. If, during the individual reaction steps, the optical orientation of the molecules is preserved, a chiral separation is not required. For example, protease inhibitors are synthesized from the "chiral pool" of L-amino acids via stereoselective reactions (Cannarsa, 1996). Benzamide-type neuroleptics and meteneprost (abortion drug) are other examples where direct chiral synthesis schemes have been successfully developed (Federsel, 1993). In many cases, however, a chiral separation step is required during synthesis since intermediate molecules, or reactions of intermediates are often not enantiopure. Chiral enantiomers can also be produced by asymmetric synthesis, where an achiral molecule is converted more or less exclusively into a particular isomer. Depending on the degree of the reaction specificity, a chiral separation step may still be required. Examples are the production of Naproxen (anti-inflammatory drug), the Monsanto L-Dopa (3,4-dihydroxyphenylalanine) production process which uses an asymmetric hydrogenation reaction, and the asymmetric isomerization of diethylgeranylamine for the synthesis of L-menthol (Sheldon, 1993). 1.2 Racemic Resolution Techniques 1.2.1 Crystallisation Crystals of racemic mixtures can be divided into two major classes: conglomerates and racemic crystals. The latter is the most often encountered (>90%). Racemic crystals consist of perfectly ordered arrays of R or S molecules such that each individual crystal contains equal amounts of each enantiomer. Conglomerates consist of a mechanical mixture 8 of enantiomerically pure crystals. A conglomerate is optically neutral although individual crystals contain only one enantiomer. In a conglomerate, the racemic mixture is eutectic, exhibiting a lower melting point than either one of the pure enantiomers. Racemates that form conglomerates can therefore be easily separated by crystallization techniques. For example, an intermediate for oc-methyl-dopa, is successfully separated by a direct crystallization process (Rheingold etal., 1968). This process, used by Merck, is carried out on a scale of several hundred tons per annum. Other examples are the separation of chloramphinol intermediates and the large-scale separation of L-glutamic acid (recently replaced by more economical fermentation processes). 1.2.2 Enzymatic Transformations Enzymes are components of living cells, which catalyze and regulate most biochemical reactions. Like all catalysts, they can accelerate progress towards chemical equilibrium. Enzymes have the advantage of very high substrate specificity and stereoselectivity. They also work under very mild conditions. However, the costs of enzymes, particularly those used for the production of chiral molecules, can be substantial. Therefore, their application to the field is limited. An important exception is the use of hydrolases in the production of L-amino acids and other chiral compounds. The majority of chiral separation techniques utilizing enzymes are based on kinetic resolutions, i.e., the enzyme has a larger activity for one of the enantiomers. More recently, enzymes have been applied in chiral separations (Akiyama et al. 1988; Lewis, 1997). It is expected that chiral separations utilizing enzymes will expand in the near future, given the exquisite selectivity of enzymes. In addition, progress in enzyme-reactor 9 engineering is leading to new systems for chiral resolution (Bednarski et al. 1987; Lopez and Matson, 1997). 1.3 Chromatographic Chiral Separation Methods Chromatography has long been the most powerful and common method for separating mixtures, including chiral compounds. The chromatographic separation relies on the distribution of a compound or compounds between two phases: a stationary phase that is usually attached to a support matrix, and a mobile phase (liquid or gas). The advantage of chromatography lies in the simplicity of the system and the large number of equilibrium stages that can be obtained in a column. The various operating modes of a chromatographic separation depend on the nature of the two phases. In the following sections a brief description of the most common chromatography phases used for chiral separations is given. Essential to all stationary phases used in chiral chromatography is a reversible interaction of both enantiomers with the chiral selector to form diastereoisomeric complexes that possess distinct physical properties. The more pronounced these differences, the higher the enantiomeric resolution. In general, however, these differences are small due to the similarity of the enantiomers. Therefore, a large number of equilibrium stages is often required for a successful enantioseparation on chiral columns. The chiral selectivity of an affinity ligand can be utilized in two different ways in chromatographic systems. Either the selector is continuously added to the mobile phase (CMPA, chiral mobile phase additives) or is fixed to the chromatographic support matrix (CSP, chiral stationary phase). The first method has the advantage that ligand 10 immobilization to the column matrix is not required, and a conventional, inexpensive achiral (e.g., reverse-phase) column is therefore sufficient for the enantioseparation. However, large amounts of ligands are typically required, increasing costs and potential for the ligand to interfere with enantiomer detection. In addition, product recovery is complicated by the presence of the CMPA, making an additional separation step necessary (Armstrong, 1997) . Therefore, mobile-phase additives are generally used in analytical-scale assays for enantiopurity, but rarely for large-scale separations of enantiomers. 1.3.1 Chi ra l R e c o g n i t i o n M e c h a n i s m s A widely accepted theory to rationalize the chiral discrimination of stationary phases is the "three-point contact rule". This rule was originally proposed by Easson and Stedman (1933) when discussing the interactions of racemic drugs with receptors. Dalgliesh (1952) was the first to apply this rule to enantiomeric amino-acid separations on TLC (thin layer chromatography) plates. The rule requires that at least three interaction or contact points have to be present between the solute and the chiral phase for an enantiomeric discrimination to occur. The energy difference between the two diastereoisomers (/. e., complexes) provides the driving force for the separation. The interactions can be very different in origin, e.g., steric, ionic, non-covalent, hydrogen bonding as well as dipole-dipole stacking. The three-point rule was extensively used by Pirkle and House (1979) in explaining chiral separation mechanisms and in the design of new stationary phases. Under certain conditions, a two-point interaction can be sufficient for chiral discrimination if an achiral matrix is involved in the interaction by providing an additional interaction site (Davankov et al, 1990). 11 1.3.2 Ligand-Exchange Phases Any solutes that contain electron-donating hetero-atoms (e.g., nitrogen, oxygen, sulfur) or 7t-electron-donating double bonds, can participate in the formation of complexes with transition-metal ions. The electrons are incorporated into the metal-ion coordination sphere to complete its inner unfdled J-shell up to the stable structures characteristic of the noble gases (Comba and Hambley, 1995). In particular, the bivalent cations of copper, zinc, and nickel are most suitable for complexation reactions due to the fast reaction kinetics (Laurie, 1987). Figure 1.4: Copper(II) ion coordination sphere. The ground electronic configuration of nonlinear copper(II) complexes (d9) is degenerate and distorts to remove the degeneracy to achieve a lower energy state (Jahn-Teller effect). An octahedral complex is degenerate because the odd electron can occupy either the or the d^ orbital, and a tetragonal distortion lowers the energy of the latter (Shriver etal., 1994). Therefore in solution, copper(II) ions have a distorted octahedral structure. Four of the octahedral coordination sites are in a square plane about the central copper ion (cf, Figure 1.4). The two apical coordination sites are at a greater distance from the central axis, and are perpendicular to the square plane. When complexed, copper(II) ions have a strong preference for square planar structures (Freeman, 1967). Therefore, strong 12 donor atoms are bound in the tetragonal plane of the copper ion. The two distal coordination sites are often occupied by solvent molecules. The basis behind ligand-exchange separations is the formation of labile ternary complexes between a ligand and solutes that are centred around a transition-metal ion (cf., Figure 1.5). The formation of such complexes typically requires concurrent proton-displacement reactions of participating amino and carboxy groups. Thus, the separation involves complicated reaction equilibria. The stabilization of the copper complex by donated electrons can influence chiral selectivity. In addition, it is assumed that solvent molecules (i.e., water) can stabilize the complex by coordination in axial position (cf, Figure 1.5). In this way, the solvent molecules can also affect chiral selectivity. Therefore, the stability and the selectivity of the complex depends on ligand and enantiomer geometry, which affect solvent participation. homo-chiral complex hetero-chiral complex Figure 1.5: Ligand-exchange concept. Helfferich (1961) was the first to report a ligand-exchange-based separation. In the presence of transition-metal ions, an ion-exchange column was successful in separating a range of compounds which could complex with the metal ion (e.g., organic amines, polyhydric alcohols, olefins, organic amines, polyhydric alcohols, and ions of organic acids 13 and amino acids). Helfferich also was the first to recognize the possibility of predicting solute retention times from chemical-reaction-equilibrium data. Chiral ligand-exchange chromatography (CLEC) is a method that is frequently applied in the separation of enantiomers. Ternary complexes are formed with bidentate ligands that can donate electrons into the unfilled inner -^orbitals of transition metal ions (e.g., amino, oxygen, sulfur groups). These complexes form very well defined geometries, such that ligands can only occupy a distinct spatial position. The chiral separation of two enantiomers is based on the difference in thermodynamic stabilities of the complexes formed between the ligand, metal ion, and the amino-acid enantiomers (cf, Figure 1.5). In general, copper(II) ions form the most stable complexes. The pioneering work of CLEC in the application for chiral separation was carried out by Davankov and coworkers beginning in the late 60s (Rogozhin and Davankov, 1968). An optically active amino-acid ligand (L-proline) was immobilized at polystyrene beads and used, through the formation of ternary complexes in the presence of copper(II) ions, to separate amino-acid enantiomers. Gubitz and coworkers (Giibitz etal., 1981) improved the separation performance by developing silica-bonded stationary phases based on a number of amino-acids ligands. Davankov etal. (1988) have shown that cyclic L-amino acids such as L-proline are among the most efficient chiral selectors for amino-acid enantiomers. The development of CMPA (chiral mobile phase additives) came a decade later. LePage etal. (1979) and Lindner etal. (1979) studied complexation of triamine additives (CMPA) with zinc and other transition-metal ions for the separation of dansyl-derivatives of amino acids on reverse-phase columns. Gil-Av etal. (1980) developed optically active Cu-proline additives (CMPA) for the separation of free amino-acid enantiomers on an ion-14 exchange column. In both cases, chiral discrimination was based on hydrophobic and ionic interactions of the two diastereoisomers with the stationary phase. Recent advances in ligand design include the work of Remelli et al. (1991) , who designed a new CLEC ligand by alkylating histidine amino acids at the imidazole ring. Enantioselectivity was investigated on TLC plates for several amino-acid racemates. Remelli et al. (1993) also adsorbed the iV'-alkylated histidine ligand to a reverse-phase column and showed a high affinity to non-polar amino-acid enantiomers. Enantioselectivities were similar to values reported by Davankov for the L-hydroxy-proline ligand. Hyun et al. (1993) dynamically coated norephedrine derivatives onto a reverse-phase column and studied the CLEC separation of amino-acid enantiomers as a function of pH and organic modifier concentration. Results indicated an insignificant stereoselectivity dependence on acetonitrile concentrations in the eluent solvent. However, solute-retention times increased at higher pH values and lower acetonitrile concentrations. The authors proposed a structure of the ternary diastereoisomeric complex formed between the ligand, copper(II) ion and enantiomers interacting with the alkyl-chains of the stationary phase (Lam, 1989; Golkiewicz and Polak, 1994). However, the possible participation of the acetonitrile solvent in the formation of the complex was not addressed. Galaverna etal. (1993) investigated the performance of iVx-alkylated L-amino acid amides added to the eluent for CMPA enantioseparations. Non-polar amino acids were successfully separated using dimethyl-L-phenylalanine-amide and L-proline-amide, whereas polar amino acids were separated by L-phenylalanine-amide and methyl-L-phenylalanine ligands. Later, Galaverna etal. (1996) successfully adsorbed octyl derivatives of these ligands to reverse-phase columns and investigated the enantioseparation performance. High 15 separation factors were reported for most of the investigated amino acids. However, the ligands were not able to separate histidine enantiomers. Belov etal. (1996) used phosphorus analogous of amino acids (i.e., a-aminoalkylphosphonic acids) to separate valine enantiomers by CMPA. The ligand was added to the eluent buffer. Results indicated that solute retention times and selectivities were very sensitive to pH and copper(II)-ion concentrations. Higher enantioselectivities were measured at lower pH values, where solutes showed lower retention times. An alkylated penicillamine-based CLEC ligand (N, S-dioctyl-D-penicillamine; cf, Appendix A.3) was developed by 6i etal. (1992). Miyazawa etal. (1997) reported successful enantioseparation of a wide range of underivatized non-protein amino acids using this ligand. By adjusting the organic modifier (2-propanol), nearly all amino-acid enantiomers were resolved. The authors also noted a peculiar copper(II) ion dependence, i.e., decreased copper-ion concentrations resulted in slightly reduced retention times (i.e., k values), but considerably increased the enantioseparation. 1.3.3 Protein Phases Due in part to their exclusive L-amino-acid architecture, proteins are chiral and able to discriminate between enantiomeric structures through surface interactions. It is believed that the dominating contributions to the enantioselective interactions are electrostatic (ionic) and hydrophobic in nature. The multiplicity of binding interactions causes the net affinity of each enantiomer for the protein to also depend on steric factors. However, the complex nature of the protein-enantiomer interactions makes column properties difficult to predict. Elution profiles from immobilized protein-phase chiral columns often show very broad 16 peaks, and the columns typically contain a low number of theoretical plates. In addition, variations in buffer conditions and pH have a strong influence on retention times and stereoselectivity (Allenmark, 1986). The advantages of a protein-immobilized stationary phase lies in the broad spectrum of enantiomeric compounds that can be separated on a single column. Although the early examples of protein-bound phases showed a lack of reproducibility and a tendency to deteriorate with use, recent commercially available columns are more reliable (Taylor and Maher, 1992). The enantioselectivity of these phases seems restricted to solutes which contain aromatic and polar groups (Stewart and Dohery, 1973). Major contributions to this field were made by Allenmark and coworkers (Allenmark et al., 1982), who developed chiral stationary phases of albumin immobilized to porous silica beads. The human-serum transport protein a racid glycoprotein shows good stability and selectivity for many pharmacologicals, e.g., ketamine, disopyramide, mepivacaine, etc. (Taylor and Maher, 1992). Recently, Ekelund etal. (1995) showed that a glycoprotein HPLC column possesses similar resolution performance to cellulose matrices for the chiral resolution of beta-blocking drugs (propranolols). 1.3.4 Polymer Phases Polysaccharide phases, in particular cellulose or amylose and their derivatives are readily available and have a long history of industrial applications. Hesse and Hagel (1973) developed the first microcrystalline cellulose triacetate column. The mechanism of chiral recognition for cellulose-based phases remains largely unknown. It is believed that the helical polymer structures and the associated multi-point interactions contribute to the chiral 17 recognition. In general, however, enantioselectivity and column loading are relatively low, making large-scale applications expensive. Molecular imprinting technology was first developed by Curti and Colombo (1952) and later continued by Wulff etal. (1973, 1980). This technology has recently found new applications in chiral separations. An imprinted three-dimensional network is formed by casting a polymer matrix in the presence of enantiopure molecules. Molecular recognition is governed by multiple interactions, including ionic, hydrogen bonding, n-n, and hydrophobic forces, as well as solvent effects. The advantage of molecular imprinting is the high specificity that can be achieved since the matrix mimics an artificial antibody. Unfortunately, this also makes the matrix very specific and expensive, since a fair amount of the enantiomerically pure molecule must be available for the creation of the chiral template. In addition, the active-site density within the polymer matrix is often low, resulting in low column loadings compared to conventional stationary chiral packing materials. New tailor-made imprinted polymers have been reported by Mosbach and coworkers (Kempe and Mosbach, 1995; Mosbach and Ramstrom, 1996) for the enantiomeric separation of amino-acid derivatives, peptides, and some drugs (nonsteroidal anti-inflammatories, and ephedrine). A remarkable enantioselectivity (17.8) was reported by Ramstrom (1994) for the separation of a dipeptide (A-acetyl-Trp-Phe-OMe). However, these columns are still under development and no imprinted-polymer chiral columns are currently available commercially or in industrial use. 18 1.3.5 Chiral Cavity Phases Chiral cavity, phases can be divided into two major groups. The first one includes all chiral cavity-based columns formed from cyclodextrins, which are oligosaccharides containing six to twelve D-glucopyranose units, bonded in a ring through a-(l,4) linkages. Cyclodextrins form hollow truncated cone-like structures. The second group includes all crown-ether-type phases. Crown ethers are macrocyclic polyethers with a crown-like shape. Solutes form inclusion complexes within the cavities of either cyclodextrins or crown ethers. The difference in the formation energy of the 'guest-host' complexes results in a chiral separation. The size of the cavity relative to the size of the enantiomer determines in part, the chiral selectivity. Major contributions to this field were achieved by Armstrong and co-workers (Armstrong and DeMond, 1984; Armstrong, 1987; Hilton and Armstrong, 1991), who separated amino acids and barbiturates as well as several drug stereoisomers. Crown ethers have the ability to form strong inclusion complexes with metal- and substituted ammonium-ions by forming multiple hydrogen bonds between the ammonium group and the oxygen of the ether groups (Allenmark, 1988). The chiral discrimination is due to steric interactions, resulting in a higher stability of one enantiomer. Cram and coworkers (Sousa etal., 1974; Dotsevi etal., 1975) achieved optical resolution of racemic amino-acid enantiomers by the use of a liquid chromatography column containing a chiral crown ether matrix. The phases require low operating pH values for resolving enantiomers with a primary amine group close to the chiral centre (Clark, 1994). Recent applications of chiral crown ether phases include the separation of phenylglycine (Zulkowski etal., 1991). However, due to the toxicity and the limitations of these phases, applications are decreasing in favour of less toxic cyclodextrin phases (Taylor and Maher, 1992). 19 1.3.6 Charge-Transfer Phases Charge-transfer or brush-type chiral phases are often referred to as donor-acceptor or Pirkle-type phases in recognition of William Pirkle, who has developed a range of useful ligands of this type (Pirkle and House, 1979). Pirkle-type chiral selectors are characterized by the formation of %-n bonding interactions as an essential part of the retention process. Typically, they are amino-acid based and contain additional 7i-donor-acceptor interactions. For example, Pirkle-type ligands usually contain rc-basic derivatives (e.g., naphthyl groups) (Pirkle etal., 1979) or 7t-acidic aryl groups (e.g., 3,5-dinitrobenzoyl moiety) (Pirkle etal., 1987). The simultaneous electron stacking and hydrophobic interactions between the enantiomer and ligand result in chiral discrimination (Pirkle et al., 1980). It should be noted that the enantiomers must also contain a 7i-electron acidic and/or a basic moiety. Otherwise, a chemical modification of the enantiomer must occur prior to the enantioseparation. Columns have also been designed which contain both ligand types (Hyun and Min, 1994), making it possible to resolve a wider range of enantiomers. Newer Pirkle type selectors include derivatives of Naproxen, a non-steroidal anti-inflammatory drug (Hyun and Lee, 1995). Other constructed selectors include binaphthyl and dinitrobenzoyl substituted amino-acid derivatives (Bojarski, 1997). Peterson etal. (1997) showed a wide application range of a Pirkle-Type CSP phase for the enantioseparation of beta-blockers. By varying the alcohol modifier in the mobile phase, a total of fifteen of the eighteen investigated enantiomers were successfully separated. 20 1.3.7 Novel Developments A new class of chiral selectors is based on antibiotics. Armstrong and coworkers (Armstrong etal, 1995; Berthold etal, 1996; Nair etal. 1996) report excellent chiral resolutions and a broad application range for immobilized macrocyclic glycopeptides such as teicoplanin and vancomycin phases. Successful enantiomeric separations included amino acids, some A-blocked amino acids, a-hydroxycarboxyacids, small peptides, and cyclic amines. Solute retention and chiral separation in antibiotic phases are influenced by solution pH, organic modifier concentration and, to a lesser extent, the nature of the buffer ions and temperature. The mechanism for the chiral discrimination is still not understood. It is assumed that complexation occurs in the inner basket-like structure of the antibiotics. 1.4 Continuous Chiral Separation Systems A major disadvantage of conventional liquid chromatographic systems is the batch-type operation. Solutes are injected into the column and separation is achieved by the differential migration of the solute molecules through the packed bed. Therefore, at any given time, only a small fraction of the bed participates in the separation, leaving the rest inactive. Column wash and regeneration steps further decrease the efficiency of the separation process. The scale-up of chromatographic columns is another technical challenge, in part due to the rapid increase in back pressure with increasing column length. Several new separation systems have been designed to overcome the limitations associated with chromatography. In most, the stationary phase is either presented in a manner which effectively simulates the continuous movement of the selection media (e.g., 21 simulated moving-bed chromatography), or replaced by a second liquid phase containing the chiral selector. Liquid-phase systems have the advantage that flow can be easily achieved by pumping, in contrast to solid-particle phases. Therefore, continuous separation systems can be designed by using conventional liquid-phase extraction systems. 1.4.1 Simulated Moving-Bed Chromatography Recently, simulated moving-bed (SMB) chromatography has been successfully applied to chiral separations (Schulte etal, 1996; Strube et al, 1997). Cavoy et al. (1997) reported that a separation of Tramadol enantiomers was ca. three-times more economical than an SMB consisting of 12 chiral columns. The product purity and yield had the same values in comparison to the conventional chromatographic method. Francotte and Richert (1997) showed a reduction of mobile phase consumption of over 80% for the separation of Formoterol (anti-asthmatic agent) and Guaifenesin (anti-tussive agent) enantiomers with a SMB consisting of 16 chiral columns in series. Along with providing a continuous mode of operation and a substantial reduction of solvent waste, SMB offers the advantage of traditional chromatography, namely, a high number of theoretical plates. However, the technology is complex, relying on precise control of a sequence of injection and sampling valves. It is also expensive and relatively difficult to scale. 1.4.2 Two-Phase Liquid Partition Systems In chromatographic systems, the ligand is usually immobilized onto a stationary porous matrix. However, scaleable continuous separation systems require the simultaneous 22 movement of both phases. The design of a continuous counter-current chromatographic separation system therefore requires a method for continuous ligand regeneration. Two-phase liquid extraction systems are an established method in the chemical industries for achieving this goal. Instead of attaching ligands at a porous matrix, they are solubilized in a second fluid phase. Solute-ligand interactions are then established through the phase boundaries of the two (immiscible) fluids. Operating properties such as volumetric flow rates can be regulated easily, and complicated switch valve procedures, necessary in SMBs, are avoided. Moreover, the systems scale linearly, making them applicable to large-scale separations. Staged extraction systems usually consist of a sequence of mixers and settlers. After the two phases are mixed and equilibrium is reached in each stage, the phases are separated in the settler. This simple approach can be highly efficient if a separation can be achieved in only a few stages. The method is, however, not appropriate for separations requiring a large number of equilibrium stages. Moreover, strong mixing required for rapid mass-transfer and approach to equilibrium can lead to emulsification. Therefore, phase separation requires long settling times. These limitations can be overcome by using a differential extraction system, where two liquid phases continuously flow past one another but equilibrium is never completely achieved. In general, a large contact area between the phases is required in differential extraction systems. Suitable devices for such operations include hollow-fibre membrane reactors. A hollow-fibre reactor consists of a bundle of membrane fibres that are potted together at each end of a shell housing, similar to a conventional heat-exchanger system. The 23 fibres are composed of a porous membrane that allows rapid solute transport. Operating conditions and geometrical dimensions determine mass transfer across the phases, which can be adjusted to optimize the extraction performance. It is, however, the large surface-to-volume ratio which makes these systems very attractive for liquid-liquid extraction applications. The greatest challenge in two-phase extractions utilizing hollow-fibre membrane modules is the reduction of phase leakage or dispersion due to convective transport through the porous membrane material. The transport of solute from one phase to the other should occur only by diffusive transport through the membrane layer. Typically, convective transport is reduced by applying a positive pressure on the non-wetting membrane phase. A positive pressure is required over the full fibre length to ensure that the membrane wetting fluid is retained in the porous membrane structure. Since a pressure drop also occurs down the fibre length, care must be taken in setting the inlet pressure of the non-wetting phase. An excessive inlet pressure will lead to breakthrough, i.e., the non-wetting phase will push the liquid through the membrane pores. For a single reactor, an acceptable positive pressure difference can be reasonably well established by controlling the flow and pressures at every inlet and outlet. However, for a series of modules, the procedure is very difficult, since a large number of valves and gauges are required to control the pressure distribution. Ding and Cussler (1991) reported a different approach to avoid emulsification in two-phase hollow-fibre extraction systems. The reactor lumen was filled with a polyvinyl-alcohol solution that penetrated into the porous membrane-fibres. The lumen was flushed and a polymerization reaction initialized to create a hydrophilic gel layer in the fibre membrane structure. They reported that no phase dispersion occurred between the two 24 phases separated by the gel/membrane structure. Also, mass-transfer coefficients of the treated and untreated membrane modules were not significantly influenced by the applied gel, indicating the low impact of the hydrogel structure on small solute transport. When properly designed, two-liquid phase extraction systems also offer a large number of equilibrium stages for continuous separation of enantiomers. However, relatively little attention has been paid to the application of such systems to chiral separations (Takeuchi etal, 1990; Ding etal, 1992; Leloux and Keurentjes, 1995; Keurentjes etal, 1996). A goal of this work therefore is to explore the potential of liquid-liquid extraction systems in chiral separations through systems design, characterization, and model development. 1.5 CLEC-Ligand Development The development of chromatographic ligand-exchange-type ligands for chiral separations was initiated by Rogozhin and Davankov (Rogozhin and Davankov, 1968 and 1970). They successfully separated amino-acid racemates by coupling L-proline at its amino group to chloromethylated polystyrene beads (Rogozhin and Davankov, 1970, 1971). Since then, improvements in alkylation chemistry have allowed a wide range of synthetic and natural ligands to be coupled to polymeric chromatographic resins (Lefebvre etal, 1977; Gubitz et al, 1979; Lindner, 1983; Yamskov et al, 1981; Watanabe et al, 1981). Polystyrene-based columns developed by Davankov and coworkers (Davankov et al, 1988) are not easily scaleable due to the tendency of polystyrene to swell, thereby increasing column back-pressure to high levels. Gtibitz et al. (1979) overcame the problem by linking L-proline to micro-porous silica particles, which are suitable for analytical to preparative-25 scale separations. In recent years, a number of other ligands have been chemically or physically linked to silica gels (Davankov et al., 1980; Roumeliotis et al, 1983; Saigo et al. 1988; Remelli etal, 1993; Wan etal, 1997a). These studies have revealed a number of features of CLEC ligands which can be used as a basis for designing large-scale chiral separations systems. For example, CLEC ligands derived from cyclic amino acids tend to have a higher resolving power than those from non-cyclic amino acids. The copper(II) ion is an ideal chelation centre for resolving enantiomers which form bidentate interactions in the ternary complex. For solutes containing a larger number of groups capable of interacting with the chelating ion, transition-metal ions with higher coordination numbers (e.g., nickel) show better selectivities. However, much of what is known about chiral ligands is derived from on-column experiments. In general, these results do not provide direct insight into the thermodynamics of ligand-binding interactions resulting in enantiomer separation. Moreover, bidentate and higher coordinated complexes are sufficiently complex to make de novo design a difficult prospect. For example, the introduction of a hydroxy group at the P-carbon atom of the L-proline ligand (i.e., trans L-hydroxy-proline; cf, Appendix Figure A. 1) resulted in a decrease in elution times but an increase in enantioselectivities (Davankov etal., 1978a, 1978b). The impact of the hydroxy group on the complexation reaction is unclear, since for spatial reasons the hydroxy group is not able to interact directly with the copper ion (Davankov etal., 1978b). Nor is it clear why the ligand's resolving power is amino-acid specific. Enantioselectivities are high for most amino acids, in particular phenylalanine and proline, but lower for amino acids containing polar side-chains (e.g., lysine, glutamine, glutamic acid). Reversed enantioselectivities (i.e., higher retention time of homo-chiral 26 complexes) were reported for amino acids forming tridentate complexes (e.g., histidine, glutamic acid, aspartic acid). On columns, a number of non-specific interactions can contribute to chiral recognition. The size of linker between the L-hydroxy-proline ligand and the support matrix was found to significantly influence retention times as well as chiral selectivities (Davankov etal., 1980). Enantioselectivities calculated from solute-retention times increased when shorter alkyl spacers were used (Davankov etal., 1980). This indicates that non-specific amino-acid interactions with the reverse-phase column can contribute to column performance. Wan etal. (1997a) investigated the enantiomer-separation performance of TV-substituted L-phenylalanine chiral ligand-exchange selectors coated on porous graphitic carbon (PGC). PGC has the advantage that it is free of any ionizable groups and therefore offers few sites for non-specific complex formation at the particle surface. In agreement with Davankov etal. (1980), they reported that the alkyl-chain length influences the solute retention times on the column, whereas the stereoselectivity remained relatively unchanged. Longer retention times were measured for shorter tether lengths. An increase in retention times and a reversal in elution order was reported when alkyl chains were replaced by aromatic linkers (i.e., methoxybenzyl-, naphthylmethyl-, and anthrymethyl-groups). The stereoselectivity for non-polar amino acids was lower for the aryl-substituted phenylalanine selectors. The methoxybenzyl linker showed (with some exceptions) the highest amino-acid retention times, whereas the enantioselectivity remained nearly unchanged by the linker type. Wan etal. (1997b) continued the previous studies with L-proline. Results indicated that the linker type did not change the amino-acid elution order (i.e., the hetero-chiral 27 complex was always favoured). When aromatic linkers were used, both the retention times and the enantioselectivities decreased as the aryl substituent size increased (i.e., from naphthyl to anthryl). L-Proline selectors with longer alkyl chains resulted in substantially decreased retention times but increased enantioselectivities. The retention behaviours and enantioselectivities were explained by hydrophobic interactions with the linker as well as changes in chelating properties of the selector by the linker type. However, the authors did not correct the reported retention times for non-specific binding of the amino-acid enantiomers to the column (i.e., the absence of copper ions). Therefore, it is difficult to distinguish between the different effects resulting in retention-time changes. The column-retention times of enantiomers can be significantly affected by the addition of organic modifiers (i.e., cosolvents). Enhanced enantioselectivities have been reported for separations in which acetonitrile has been added to the mobile phase. Moreover, a reversed elution order was found upon the addition of tetrahydrofuran (Lam, 1989). Like water, tetrahydrofuran contains a lone electron pair that can occupy the distal coordination sites of copper ions. In general, organic modifiers will significantly reduce hydrophobic interactions of analyteS at reverse-phase columns. A higher organic modifier content will therefore lead to shorter retention times. 1.5.1 CLEC-Ligand Evaluation A number of new and highly specific CLEC ligands have been developed since the pioneering work of Davankov (Rogozhin and Davankov, 1970). Brookes and Pettit (1974) investigated the enantioselectivity of histidine in aqueous solution by potentiometric titration. Equilibrium formation constants were determined for different enantiopure L- and D-amino 28 acids with the L-histidine ligand in the presence of copper(II) ions. Enantioselectivities were highest for phenylalanine and tryptophan enantiomers, and a reasonable level of discrimination was observed for nearly all amino acids. Several other amino acids investigated for the use as chiral ligands showed very little or no stereoselectivity with the known exception of L-proline, which had good selectivities towards many amino acids. The impact of substituents on histidine ligands was investigated by Brookes and Pettit (1976). They showed that the highest stereoselectivity was found when very bulky groups were attached. This suggests that the chiral selectivity of histidine-based ligands is dominated by steric effects. It should be noted that histidine possesses a nitrogen on the imidazole ring which can participate in the complex formation. Davankov et al. (1981) A-alkylated L-histidine at the primary amine and adsorbed it on a reverse-phase column. Relative to the L-hydroxy-proline column, measured retention times increased for most amino acids, whereas the enantioselectivities showed reduced values. Borghesani etal. (1990) measured equilibrium formation constants for ternary complexes of D- and L-histidine ligands with several enantiopure L-amino acids in aqueous solution. Additional formation-enthalpy measurements allowed them to separate enthalpic and entropic contributions to ligand-exchange complexes. Measurements revealed that ternary complex formations are entropically as well as enthalpically favoured. They concluded that both histidine enantiomers are tridentate ligands. These findings were supported by solid-state crystal structure results. A mechanistic model for complex formation was proposed. Equatorial binding occurs with the amino group and nitrogen atom of the imidazole ring at the copper(II) ion. Chiral recognition of L- and D-histidine is 29 therefore mainly governed by the carboxyl group, which interacts with the metal ion at the axial (distal) sites. It should be noted that such structural models are unproven, and therefore give only limited insight into the actual forces that govern the complex structures. L-Alanine showed nearly identical ternary equilibrium formation constants with either form of the histidine ligand. This suggests that the presence of the short alkyl side-chain in alanine is insufficient for chiral discrimination in aqueous solution. The investigated D-histidine complexes were enthalpically favoured over the L-forms for aromatic-side-chain containing L-amino acids (i.e., L-phenylalanine, L-tryptophan). An opposite behaviour was found for amino acids with aliphatic residues (i.e., L-leucine, L-valine). Remelli etal. (1991) investigated the chiral separation performance of L-histidine-based ligands bearing different aliphatic linkers. The amino acid was alkylated at the pyrrole nitrogen on the imidazole ring (N\ cf, Appendix Figure A.l) to facilitate adsorption on thin layer chromatography plates. Unlike earlier results when the hydrophobic tail was attached at the carboxyl group (Davankov etal., 1981; Watanabe et al., 1981, Watanabe et al., 1983), alkylation at the pyrrole nitrogen resulted in good chiral resolution of phenylalanine and tryptophan enantiomers. Remelli etal. (1993) adsorbed their Ax-n-decyl-L-histidine ligand on a reverse-phase column to investigate retention times and separation factors as a function of ligand loading. Results indicated increased column-retention times for higher ligand loadings, but no significant change in chiral selectivities compared to thin-layer chromatography systems. The retention data were not corrected for non-specific amino-acid retention, making the values of the reported reduced plate heights questionable. The highest enantiodifferentiation was reported for valine and proline. 30 The impact of alkyl-tails on the performance of histidine ligands was studied by Remelli etal. (1994) by using a water-soluble analogue with a short alkyl (methyl) group attached at the Nz nitrogen. Findings indicated that the equilibrium formation constants and the chiral selectivities in aqueous systems were not significantly affected by the methyl-tail. Derivatives of the chiral selector containing the alkyl-tail on the Nn nitrogen showed no stereoselectivity, indicating that the molecular position of the tail has a strong effect. The chiral selectivity of L-spinacine (cf, Appendix Figure A. 1), a cyclic homologue of histidine, was also investigated by Remelli etal. (1995). The authors were not able to detect any enantioselectivity for amino-acid enantiomers by means of potentiometric titrations. These findings are surprising, since the orientation of the carboxy and amino group is similar to that in proline, which shows excellent enantiomeric selectivities for a wide range of amino acids. Dallavalle etal. (1996) studied the chiral selectivity of amino-acid amides (i.e., L-phenylalanine-amide, L-proline-amide and L-tryptophan-amide) in aqueous solution by potentiometric titrations. Whereas all ligands showed good stereoselectivities for histidine enantiomers, only the bidentate selectors (i.e., L-phenylalanine-amide and L-proline-amide) showed a good chiral resolution of tryptophan enantiomers. The authors found that the measured equilibrium formation constants do not sufficiently account for the enantiomeric separation performance reported on chromatographic columns utilizing these ligands. For example, an inverted stereoselectivity was found for tyrosine enantiomers in aqueous solution compared to the chromatographic elution results. The application of A""-alkylated amino-acid amides for chiral ligand-exchange chromatography adsorbed on reverse-phase columns was studied by Galaverna et al. (1996). 31 Results indicated that the measured enantioselectivities for 7V-alkyl-leucine amide and TV-alkyl-phenylalanine were not significantly different. However, the retention times showed higher values for the latter ligand. Strongly decreased enantioselectivities and retention times were measured after the hydrophobic tail of L-phenylalanine-amide was increased from an octyl to a dodecyl group. Phenylalanine enantiomers showed such high column-retention times that a separation was not possible. However, by lowering the copper-ion concentration in the aqueous buffer solution Galaverna et al. (1996) were able to decrease the enantiomer retention and successfully separated the enantiomers. Prelog etal. (1982, 1983) solubilized tartaric acid esters in organic solvents and investigated the enantiomeric-extraction performance of norephedrine ammonia salts in two-phase systems. Partition coefficients and enantioselectivities strongly depended on the concentration and type of the phase-transfer catalyst (i.e.,NaPF6,NaBF6). Chiral discrimination was explained by hydrogen bonding interactions in theorganic phase between the solute and the tartaric acid ionophore. Increased stereoselectivities were reported at lower temperature. 1.5.2 Theoretical Characterization of Chiral Ligands Computational calculations of chiral recognition using molecular mechanics, molecular dynamics, or quantum-mechanical calculations are limited. This is mainly due to the very small energy differences between the enantiomer complexes required for chiral discrimination. In ternary ligand-exchange complexes, chiral resolution is based on multi-point binding loci involving many different forces. Subtle differences in the spatial alignment of the chiral selector and the enantiomers in each complex result in a small energy 32 difference responsible for chiral recognition. Thus, quantitative molecular modelling of these complexes must be based on accurate calculations of excluded-volume effects and complex force fields in a multi-component system. Lipkowitz et al. (1989) calculated chiral selectivities of Pirkle-type ligands adsorbed to chromatographic columns. Analytes were rolled over the van der Waals surface of the phases using a molecular mechanics program (MOPAC) to determine free energies of the transient diastereomeric complexes. This allowed determination of the lowest energy state(s) for a given configuration. Solvent and non-specific stationary-phase interactions were not included in the calculations. The computed chromatographic separation factors agreed well with experimental values reported in the literature. In addition, the authors confirmed that the dinitrobenzyl and naphthylamine groups are most responsible for solute binding at Pirkle-type phases. Bernhardt et al. (1992) applied a molecular mechanics approach to predict the isomer distributions of quadridentate-amine ligands in ternary complexes with bidentate enantiomers. The chiral ligand-exchange complexes were formed in aqueous solutions containing nickel or cobalt ions and analyzed for their enantiomer compositions. Molecular mechanics calculations showed excellent agreement with experimentally determined enantiomer distributions. Hanai etal. (1996) used a molecular mechanics approach to predict the chiral recognition of Pirkle-type ligands (naphthyl amino acids). The steric and electrostatic effects of stationary silica phases were also considered in the calculations. Results indicated that the ligand-packing density and the silanol groups influence the chiral separation significantly. In particular, large solutes may form complexes that are not in a 1:1 ratio with the ligand. 33 Predicted elution orders for high-density chiral phases showed reasonable agreement with the experimental values. 1.6 C h e m i c a l E q u i l i b r i a 1.6.1 Chemical Equilibria In Single-Phase Systems Amino acids are known to complex with transition-metal ions through their electron rich carboxylic and primary amino groups. In such complexes, the amino acids are usually referred to as the ligands (electron donor, Lewis base) and the metal ion as the central atom (Lewis acid). For example, copper(II) ions can form the following equilibrium complexes with an amino acid (A) in solution at high pH values: Cu + ++A~ <-*CuA+ C u + + + 2 A " **CuA 2 ' Both complexes are referred to as binary amino-acid copper complexes to reflect the fact that only two molecule types participate. The strong influence of solution pH on the formation of binary complexes is not directly evident from these equations. Amino acids have at least two protonatable groups (i.e., -COO" and -NH2). Therefore, depending on the solution pH, several protonation states may exist. For amino acid A containing two protonation sites (e.g., Phe), the following equilibrium reactions and equilibrium formation constants (i.e., p, and p2) can be defined: A-+FT A H A " + 2 H + < - ^ - ^ A H ; ' For amino acids having more protonation sites, additional equilibrium reactions must be defined (e.g., glutamine, histidine, etc.). Therefore, the number and distribution of binary 34 complexes formed are dependent on the amino-acid protonation states. Rewriting the binary complex formation reactions in terms of the neutral amino acid AH makes this dependence more obvious: Cu + + + AH <-» CuA+ + H + Cu + + +2AH <-> CuA2 + 2H + ' 1 2 3 4 5 6 7 8 9 10 PH Figure 1.6: Calculated species distribution for a binary Phe/copper mixture. [Phe] = 10 mM, [Cu ]^ = 5 mM (dashed lines: copper, solid lines: amino acid and water) (1= 0.1 M, 25 °C). Figure 1.6 shows the distribution of binary complexes of phenylalanine and copper(II) as a function of equilibrium pH values. The details of these calculations will be described later in section 2.3. At low pH values, most amino acids molecules are fully protonated with a net-charge of +1, making it energetically (electrostatically) unfavourable for the amino acids to participate in binary complexes with positively charged copper(II) ions. At elevated pH values, the amino acid exists as a zwitterion and binary complex 35 concentrations increase until all copper ions are saturated with Phe. The presence of copper-hydroxide complexes (/. e., Cu(OH)n, n = 1 to 4) is not considered in this plot, since significant amounts are only formed at pH values higher than 10 (Creagh et al., 1994). If two analytes are present in solution (A and Li), both will compete for binding sites at the copper ion. Therefore, an additional ternary amino-acid complex can form in solution: A" + Cu + + + Li" <^  ACuLi. Extending this to a racemic mixture of amino acid A (i.e., LA and DA) leads to the formation of two additional ternary complexes with ligand Li and Cu+ +: L A~ + Cu + + + Li~ <-> LACuLi D A " +Cu + + +Li" <-> D ACuLi If the ligand Li is stereoselective, one of these ternary complexes will reach a lower energy state at equilibrium. The ratio of the equilibrium formation constants of the two ternary complexes is therefore an appropriate measure of the enantioselectivity of Li, often referred to as the chiral selector. 1.6.2 Chemical Equilibria In Two-Phase Systems Solute complexation can also be linked with partitioning between two liquid phases. These systems have recently been used for the extraction of metal ions from an aqueous phase into an organic phase containing a metal selector (Lee and Yang, 1995; Daiminger etal., 1996; Alonso and Pantelides, 1999; Akakabe etal., 1995). The extraction equilibria involving metal-chelate ions can be described by linked chemical and phase equilibria (Freiser, 1988a). Furthermore, by solubilising a chiral selector in an organic phase or by 36 immobilizing it onto a matrix, a two-phase separation system can be designed for chiral separations. Highly alkylated amino-acid derivatives are only soluble in hydrophobic solvents. In such an aprotic solvent (e.g., n-octanol), the ligand is largely present in its charge-neutral form (i.e., LiH). Speciation reactions with copper ions must therefore occur at the phase boundary. Electroneutrality permits only the formation of neutral binary ligand complex in the organic phase (i.e., Li2Cu), which require the release of proton(s) into the aqueous phase, i.e., 2 LiH" r £+^Cu+ + ^ " r gCuLi 2 +2 aqH+ . In the presence of other complex-forming solutes (i.e., amino acid A), additional neutral ternary complexes are formed in the organic phase (i.e., Li.CuA), i.e.: L i H < " s + « / C u + + + aqA- <-> '^'ACuLi + "*H+ . If two amino-acid enantiomers are present, both can form a ternary complex in the organic phase. However, if the ligand (Li) is chiral selective, one of these ternary complexes will be preferentially formed in the organic phase. This difference in equilibrium formation constants can be utilized for a chiral separation scheme as indicated in Figure 1.7. Chemical-equilibria reactions for ligand-exchange-type two-phase separations can result in very complex solute chemistry (cf, Figure 1.8 for a single enantiomer). Previous investigations of ligand-exchange systems for chiral separation have not fully accounted for the presence of these complex solution equilibria. A central objective of this work is to apply multiple-chemical equilibria theory to chiral separation systems and to determine its role in process performance. 37 Aqueous Phase Phase Boundary A- + FT <-» A H A"+2H + AH^ A~+Cu + + e C u A + 2A~+Cu + + ±+ CuA, 2 LiH Li 2Cu LiH Li-Cu-AD LiH Li-Cu-AL Organic Phase Figure 1.7: Two-phase extraction equilibria. CO ' - J 1 1 1 • 1— • C u A \ L i H \ x -• HPhe \ \ PheCuLi " / \ \ _ _ - - _ " " x \ \ v .AH 2Phe + \ \ \ • \ PheCu^X< Li^Cu •<^^plie^Cu, 1 ' " * i • T'" • t ~? i ~ ~« PH Figure 1.8: Calculated species distribution for a ternary two-phase Phe, Cu, and Li mixture. [Phe] = 10 mM, [Cu ] = 10 mM, [Li] = 10 mM (solid lines: aqueous phase complexes, dashed lines: organic phase complexes) (1= 0.1 M, 25 °C). 38 1.7 C a l c u l a t i o n o f M u l t i p l e - C h e m i c a l E q u i l i b r i a Several programs have been reported for the general calculation of multiple-chemical equilibria in liquid systems. A brief summary is given of the most recent advances in the field, which primarily involves programs for determining equilibrium formation constants in aqueous solutions. 1.7.1 Aqueous Systems LETAGROP was one of the first programs reported for the determination of equilibrium formation constants from potentiometric titration data (Meloun etal., 1988). The program was developed in the early sixties by Sillen and coworkers (Sillen, 1962; Ingri and Sillen, 1962). Memory limitations and restricted computation power allowed only a limited set of data points to be handled. The programs, GAUSS (Tobias and Yasuda, 1963) and SCOGS (Sayce, 1968; Sayce, 1971; Sayce and Sharma, 1972) allowed for larger data sets by calculating the independent variable with respect to the fitting parameters by numerical differentiation. A decade later Sabatini and coworkers introduced the programs LEAST (Sabatini etal., 1972) and MINIQUAD (Sabatini etal., 1974). These programs included an improved parameter refinement algorithm (Gauss-Newton) as well as improved statistical data handling. The refinement algorithm minimized the residuals of the mass-balance equations at each titrant addition. These derivatives, required for the Gauss-Newton method, were calculated directly from mass-balance equations. This indirect method greatly improved the computation speed since the gradient matrix (derivatives) could be calculated analytically. 39 None of the previous programs directly minimized the residual of the free-species concentration, which is usually the experimental measurement in a titration (i.e., pH, recorded with an ion-selective electrode). The non-linearity of the multiple-chemical-equilibria equations does not allow one to write the free-species concentration in an explicit form. Nagypal and Paka (1978) solved this problem by implicit differentiation of the multiple-chemical-equilibria equations. The method allowed the numerical calculation of any derivative, and hence opened a new area of multiple-chemical-equilibria programs. The resulting direct parameter minimization on the measured data allowed incorporation of sound weighting schemes that accounted for random errors in the titrant volume and potential readings. Newer programs such as TITFIT (Zuberbtihler and Kaden, 1982), SUPERQUAD (Gans etal., 1985), and ESTA (May etal., 1988) incorporated the implicit differentiation algorithm by Nagypal and Paka. The SUPERQUAD program was an improved version of the previously released MINIQUAD. Both programs included a very effective Gauss-Newton algorithm using the Levenberg-Marquardt technique to improve convergence. In addition, SUPERQUAD allowed the minimization of data from two electrodes. De Stefano etal. (1989) developed the ES4ECI program, which was further developed in 1993 (De Stefano et al., 1993) to include an algorithm to estimate ion-activity coefficients from potentiometric titration data using the Debye-Htickel theory. The structure of the minimization routine is very similar to SUPERQUAD. Similarly, Barbosa et al. (1996) reported the development of the program PKPOT. This program only crudely corrected for ion-activity coefficients at constant ionic strengths. However, both programs suffer from the lack of experimental activity-coefficient data required to verify the accuracy of the calculated values. 40 1.7.2 Two-Phase Systems Whereas several programs exist for chemical-equilibria calculations in aqueous solutions, programs for calculating equilibrium formation constants from two-phase equilibrium data are very limited. Rydberg etal. (1959) applied a power series approximation to solve the nonlinear overall mass-balance equations for simple extraction systems. Liem etal. (1971) modified the LETAGROP program, initially developed for aqueous phase titrations, to determine equilibrium formation constants in liquid two-phase systems (LETAGROP-DISTR). Finally, the program EXLET was developed by Havel and Meloum (1985b) for the regression of equilibrium formation constants from spectrophotometric data of liquid two-phase systems. In these programs, two-phase extraction equilibrium was applied to simple systems, with only a few species and complexes present. The model equations (usually mass balances) were linearized to simplify computation of the equilibrium formation constants (Aguilar, 1988). Most of these algorithms have been applied to systems for metal-ion extraction (e.g., Cu, Ni, etc.) and to determine the solubility of acids in organic solvents (Freiser, 1988b; Hogfeld, 1988). A program implementing a sophisticated nonlinear regression algorithm to determine equilibrium formation constants in a two-phase extraction system is not available. 1.8 Chiral Extraction Systems 1.8.1 Liquid-Liquid Chiral Extraction Newcomb etal. (1979) investigated enantiomeric differentiation in a chloroform-water two-phase system. The chiral selectors (optically active derivatives of dinaphthyl 41 units) were solubilized in a chloroform phase that was placed between two aqueous phases. Ion-pair equilibrium enabled the transport of the enantiomers through the chloroform phase. The selective n-n interactions between the ligand and the enantiomer resulted in enantiomeric recognition. In addition, it was shown that mechanical mixing controlled solute transport across the interface. Takeuchi etal. (1984a) investigated the chiral selectivity of an alkylated L-proline ligand in an aqueous-organic two-phase system. The amino-acid-based ligand was previously applied to ligand-exchange chiral separations on stationary HPLC phases in aqueous solutions (Davankov etal., 1980; Davankov etal., 1983; Gtibitz etal. 1981), allowing a direct comparison to be made. Partitioning experiments were conducted for different amino-acid racemates in an aqueous/butanol two-phase system in the presence of copper(II) ions. The reported enantioselectivities in a single-stage extraction setup were higher than those reported for multi-staged chromatographic systems. Surprisingly, in the non-aqueous extraction system, the enantioselectivity of the ligand was opposite that in the aqueous chromatographic systems, indicating the importance of solvent and matrix effects in chiral recognition. Enantiomeric selectivities for aliphatic amino acids (e.g., Leu, Val) were higher than for aromatic (e.g., Tyr, Phe). In addition, the authors performed the first continuous two-phase enantiomeric extraction by utilizing a droplet-based counter-current liquid chromatography system. Analysis of fractions collected at the column outlet indicated that a baseline separation of the D/L isoleucine was achieved. Takeuchi etal. (1984b) investigated the two-phase chiral extraction of amino acids with the yV-alkylated L-proline and L-hydroxy-proline ligands. A critical chain length of six to seven alkyl groups was required to localize the ligand completely in the organic phase. In 42 butanol-water two-phase systems, the L-hydroxy-proline ligand showed lower amino-acid partition coefficients but higher enantioselectivities in comparison to the proline ligand. These findings were consistent with results reported in chromatographic systems by Davankov etal. (1988). Results indicated significant amino-acid partitioning into the butanol phase in the absence of copper. Takeuchi et al. (1990) extended their single-stage separation studies (Takeuchi et al, 1984a, 1984b) by utilizing the ligand-exchange separation concept in a continuous two-phase system. The fractional extraction system consisted of two rotating columns. The ligand (/V-n-dodecyl-L-hydroxy-proline) was solubilized in an organic phase (n-butanol), which was flowing in counter-current direction to an aqueous phase. By appropriate adjustments of the aqueous-phase conditions and flow-rate ratios, valine enantiomers were separated to a purity of higher than 99.5%. The authors estimated an efficiency of 24 theoretical equilibrium stages in the extraction system. A chiral aqueous two-phase extraction system was reported by Ekberg and Sellergren (1985). Bovine serum albumin was used to separate tryptophan enantiomers in a counter-current distribution apparatus containing 60 cavities. Enantioseparation results showed a higher selectivity of the protein-phase for the L-enantiomer. However, a complete chiral separation was not achieved, presumably because capacity factors of protein ligands are very low. Pirkle and Doherty (1989) designed a simple liquid-liquid extraction system by wrapping silicon-rubber tubing around two spools and immersed each in a separate bath containing a water-methanol mixture. An alkylated Pirkle-type chiral selector (naphthyl-leucine octadecyl-ester) was solubilized in the organic (decane) phase, which was pumped 43 through the lumen side of the tubing. Methyl- and butyl-esters derivatives of enantiomeric amino-acid mixtures were supplied in the first vessel (source-phase). After the amino acids associated with the ligand in the organic phase, they were transported downstream into the second vessel (scrubbing section). Results indicated very high enantioselectivities for the extraction system. Transport rates increased with the lipophilicity of the analytes. Increased enantioselectivities were reported at reduced operating temperatures (0 °C). However, a relatively high temperature was required in the scrubbing vessel (50 °C) to increase back-extraction into the receiving phase. This resulted in increased partition coefficients which compromised the enantiomeric separation performance. Therefore, methanol was added into the aqueous source phase to reduce partitioning and increase enantioselectivity. The reported enantioselectivity for the separation system exceeded the performance of aqueous-based chromatographic system utilizing the chiral selector. They speculated that the reduced enantioselectivity in the chromatographic system was due to unfavourable effects of the silica-particle environment close to the ligands. However, no substantive investigations on the effects of the non-aqueous environment on the increased ligand selectivity were initiated. Subsequently, Pirkle and Bowen (1994) improved this simple extraction system (Pirkle and Doherty, 1989) by utilizing two hollow-fibre reactors. The organic solvent (hexane), containing the chiral selector (naphthyl-leucine fatty acid ester), was recycled in the fibre lumina. In the first module (extraction section), the racemic analyte mixture (dinitrobenzoyl leucine) was circulated in the shell side where it interacted with the chiral carrier phase via a phase-transfer catalyst (tetrahexylammonium chloride). After the enantiomers associated with the ligand, they were transported into the second module 44 (scrubbing section) where a receiving phase stripped the solutes from the carrier stream. The transient enantiomer concentrations of the source and receiving vessel indicated that the L-enantiomer was initially extracted at a much higher rate. Therefore, the highest enantiomeric separation was achieved in the first ten hours. The enantiomeric-separation performance then showed an exponential decline until a steady state was reached at ca. 4 days. Emulsification of the organic and aqueous phases was prevented by applying only low flow rates and pressures. Pickering and Chaudhuri (1997a) continued the work of Takeuchi etal. (1984b) by using A-n-decyl-L-hydroxy-proline ligand to separate phenylalanine enantiomers in a two-phase system consisting of an aqueous acetate buffer and a decane/hexanol mixture. A model that described copper partitioning into the organic phase in the presence of acetate-buffer ions was reported. Much of the complex chemical equilibria, including amino-acid speciation, was neglected in this model. Binary equilibrium formation constants in the aqueous and organic phase were measured. Transient extraction studies were performed to determine the forward-reaction rates for the individual enantiomers. The authors concluded that differences in the kinetic constants are responsible for the enantioselectivity of the ligand. Kellner el al. (1997) studied the enantioselective two-phase extraction of L- and D-A-(3,5-dinitrobenzoyl)-leucine with a Pirkle-type chiral selector (octadecyl carbamoylated quinine) in different organic solutions. By replacing the dinitrobenzoyl moiety of the amino acid with different structures, they observed total or substantial reduction of enantioselectivity. Therefore, the electron-rich dinitrobenzoyl group must be present in non-aqueous solution for Pirkle-type ligand chiral separations. The primary driving forces for the 45 extraction are intermolecular association and ion-pair formation between the amino acids and the chiral selector. The authors noted that enantioselectivity in ion-pair extraction is not expected because the presence of additional molecular interactions is required for chiral recognition. These interactions include hydrogen bonding, dipole-dipole interactions, n-n interactions, hydrophobic van der Waals-type interactions, and steric attraction/repulsion. It should be noted, however, that chiral recognition has been observed in ion-exchange chromatography (Davankov, 1980). 1.8.2 Chiral Extraction with Membranes Masawaki etal. (1992, 1994) prepared enantioselective membranes by linking L-phenylalanine and L-phenylglycine via glutaraldehyde to porous membrane structures. The optical resolution of the system was investigated under diffusive and convective transport conditions for racemic mixtures of phenylalanine and phenylglycine. The membranes showed selectivities for the homo-chiral complex. The influence of the linker and support material on the chiral selectivities was not addressed. However, the authors reported that increased selectivities were found for lower solute fluxes and for membranes with lower hydraulic permeabilities. Ding etal. (1992) attempted to improve the continuous chiral extraction system developed by Takeuchi et al. (1990). Phase emulsification during extraction in hollow-fibre modules was prevented by creating a polyvinyl-alcohol gel inside the micro-porous membrane structure. The hydrogel filling procedure was previously reported by Ding and Cussler (1991) for the fractional extraction of benzoic acid and nitrobenzoic acid in a two-phase system. 46 Applying the A-n-dodecyl-L-hydroxy-proline ligand to this system, Ding et al. (1992) measured the fraction of enantiopure leucine extracted into an n-octanol organic phase (cf., Figure 1.9). Results indicated that complete enantiomeric separations could be obtained over a range of flow rates. A comparison with conventional extraction equipment indicated superior performance of the hollow-fibre membrane system. These improvements were mainly attributed to the high surface-to-volume ratio. Wash Stage Extraction Stage • Q. •• • V A Hollow-Fibre Modules Racemic Mixture Figure 1.9: Enantiomeric hollow-fibre extraction system. mm wrnm** Organic Phase with Selector 47 Bryjak etal. (1993) measured the transport of amino-acid enantiomers through supported chiral liquid membranes. Two different chiral alcohols, nopol (+6,6-dimethyl bicyclo [3.1.1] hept-2-ene-2-ethanol) and methyl-1-butanol, were immobilized in the pores of polyethylene films. The enantiomeric flux was determined for salts of several amino acids. A high chiral selectivity was reported for phenylalanine, whereas for other amino-acid salts significantly lower selectivities were found. An attempt was made to correlate the measured stereoselectivity to the hydrophobicity, polarity, and molecular volume of the studied amino acids. Results, however, are unconvincing due to the excessive scatter in the correlation. Keurentjes and coworkers (Keurentjes, 1994; Keurentjes etal, 1996) applied analogues of Prelog's (1982, 1983) tartaric acid (i.e., dihexyltartrate and dibenzoyltartaric acid) and a polylactic acid chiral selectors to a continuous supported liquid-membrane two-phase enantiomer extraction system. The organic extraction and raffinate phases containing the opposite chiral form of the selector flowed counter-currently through the lumen and shell side of the hollow-fibre modules. Mixing of the organic phases was avoided by entrapping water in the porous membrane structure. The high lipophilicity of the chiral selectors ensured that no permeation through the aqueous membrane barrier occurred. The racemic compounds (i.e., cc-hydroxy-amines, amino acids, and other chiral components) were solubilized in the organic phase through the presence of phase-transfer ions (Na-hexafluorophosphate or Na-tetraphenylborate). Results indicated that the dihexyltartrate ligand showed the highest enantioselectivity, which also increased at decreased solvent temperatures. Single-stage extraction experiments indicated only very low enantioselectivities for the tartaric-acid ligand (Keurentjes, 1994). Optical-purity results for the separation of a 48 racemic mirtazapine mixture in a hollow-fibre module showed an enantiomeric excess of ca. 20%. Nevertheless, over 99% resolution of norephedrine was demonstrated using a bench-scale setup consisting of seven hollow-fibre modules with an overall length of 7 meters. This experiment demonstrated that even for ligands with low selectivities, a complete enantioseparation is feasible. By increasing the total length of the extraction column, additional equilibria stages were created to facilitate chiral separation. A novel membrane-based chiral separation system was recently reported by Lakshmi and Martin (1997). An enantioseparation of racemic phenylalanine was performed by immobilizing an apoenzyme (D-amino-acid oxydase) in a porous membrane structure. Apoenzymes lack the cofactors required for biological activity, and are therefore not able to convert substrates to product. Higher enantioselectivities were reported for membranes with smaller pore sizes. The authors speculated that the smaller pores reduced non-specific amino-acid transport through the membrane. 1.8.3 Micellar Systems Creagh and coworkers (Creagh etal., 1994) investigated a micellar-enhanced ultrafiltration system for large-scale chiral separations of amino acids. A non-ionic surfactant was used in the presence of a ligand-exchange cosurfactant (L-glutamic acid y-cholesterol ester) to form mixed micelles. Equilibrium formation constants were determined by potentiometric titrations using a water-soluble analogue (L-glutamic acid y-methyl ester) of the cholesterol-based ligand. The single-stage extraction system showed high stereoselectivity for a ligand/amino-acid ratio of 2:1 (pH = 11). Enantioselectivities determined by potentiometric titrations of the micelle-free ligand were significantly lower. 49 This suggested that the chiral selectivity was partly due to: (1) steric restrictions on the cholesterol ligand because of its position in the micelle and (2) the absence of binary copper-glutamate complexes in the micellar environment. Pickering and Chaudhuri (1997b) proposed an emulsion liquid-membrane system for chiral extractions. A racemic amino-acid mixture was extracted from a source phase through a thin liquid membrane into an inner micelle environment. The alkylated L-hydroxy-proline ligand was solubilized in the liquid membrane in the presence of a surfactant to facilitate enantiomer transport. The previously developed kinetic model (Pickering and Chaudhuri, 1997a) was extended to describe the transient enantiomer uptake in an agitated vessel. Whereas experimental results indicated relatively slow enantiomer uptake in the source phase, the model predicted a nearly instantaneous equilibrium. Mass-transfer limitations, which could have been responsible for the deviations, were not addressed. The published data suggest that diffusional resistances in the micellar environment are limiting in the extraction system. 1.9 Modelling of Chiral Separation Systems 1.9.1 Two-Phase Systems Takeuchi et al. (1984b) were the first to develop a model for amino-acid partitioning in a two-phase system in the presence of copper(II) ions: PLID =Pa(l + RKUD), (1.1) where P is the partition coefficient of the enantiomer, R is the ratio of free to complexed ligand in the organic phase, and K is the equilibrium formation constant for the L- or D-enantiomers. The partition coefficient P0 is that for the enantiomer in the absence of 50 binding. The model was developed under the limiting assumption that the ligand is in large excess relative to the enantiomers and there are no enantiomer complexes formed in the aqueous phase. In the low concentration range, measured partition coefficients for the amino-acid enantiomers showed a linear trend for several i?-values. Partition measurements were only performed with enantiopure analytes, and model validation in the presence of both enantiomers was not reported. In addition, the pH dependence of the copper-ion partitioning as well as binary complex formation of the enantiomer with copper ions (in the aqueous phase) was not included in the modelling approach. Takeuchi et al. (1990) used a rotating column setup to purify valine enantiomers in a counter-current two-phase extraction system. The number of equilibrium stages was estimated by an equation by Alders (1955) for staged equilibrium extractions under the assumption of constant partition coefficients and the absence of mass-transfer resistances, /. e., where (j) is the fraction of solute extracted into the organic phase, m and n are the number of transfer stages in the extraction and stripping section, respectively, and E, is the extraction factor for species 1 and 2, defined by Pi is the partition coefficient and Q0!& and are the volumetric flow rates of the organic and aqueous phase, respectively. Using this simple model, Takeuchi estimated that a total of at least 25 stages was required to obtain ca. 99% pure valine enantiomers. (1.2) (1.3) 51 Ding and Cussler (1991) applied a differential mass-balance on the lumen- and shell-side of a hollow-fibre membrane to describe their fractional solute-extraction system (cf., Figure 1.7). The equations were integrated and an analytical solution was presented to calculate the fraction of solute extracted into the organic phase (<)>), i.e., E - exp r - ^ - ' W i 2E E exp 2 £ -1 (1.4) where NTU is the total number of transfer units in the extraction system. The equation was derived under the assumption that each solute has a constant partition coefficient and no competitive solute interactions exist. Additionally, it should be noted that for large number of transfer units the differential model (cf, equation 1.4) and the stage model (cf, equation 1.2) yield identical results. Ding etal. (1992) used this equation to model enantiomeric leucine extractions in hollow-fibre modules. The partition coefficients were measured independently in a single-stage extraction system for the individual L- and D-amino-acid enantiomers. The data indicated that a nearly 100% enantiomeric separation could be obtained by adjusting flow rates to optimal settings. The model predictions were in reasonable agreement with the experimental data. However, only very limited data were reported at higher flow rates settings, where low NTUs are expected. Keurentjes and coworkers (Keurentjes, 1994; Keurentjes etal., 1996) applied the same modelling approach as Ding and Cussler (1991) for the characterization of hollow-fibre extraction systems. The equation was defined in terms of enantiomeric selectivity a in the outflow, /. e., 52 E2 exp V 2E2 _ o E2 -1 p J^2 J [L] £, f 2£, exp V (1.5) where [L] and [ D ] are the concentrations of the L- and D-enantiomer, respectively (provided the feed stream consists of a 1:1 racemic mixture). The equation was subsequently used to calculate enantiopurities as a function of number of NTUs and selectivities. The plots indicate that a large number of NTUs is required for low ligand selectivities. It should be noted that this analysis can be misleading since the selectivity (a) depends not only on the partition coefficient ratio but also on the initial partition-coefficient values. Therefore, the analysis would benefit by calculating enantiomeric purities for different initial partition coefficients. Pickering and Chaudhuri (1997a) developed a model to describe transient amino-acid extraction in a two-phase partitioning system (Lewis-type cell). Based on this model, first-order reaction constants for L- and D-phenylalanine enantiomers were reported. Back-extraction reactions were assumed to be non-limiting and hence excluded in the model. The ratio of the reaction rates agreed reasonably well with the measured enantioselectivities. However, the data showed large scattering, making the validity of the model assumptions questionable. Moreover, the authors did not show whether the system was reaction or diffusion controlled. Pickering and Chaudhuri (1997b) extended their kinetic model, despite its potential inappropriateness, to describe transient chiral extraction results in an emulsion hexanol/decane-membrane system. The chiral ligand (TV-n-decyl-L-hydroxy-proline) was solubilized in the organic membrane phase. The extended model included single amino-acid 53 protonation constants, but neglected binary complex formation and acetate-buffer ions in the aqueous phase. In addition, competitive ternary complex formation in the organic phase was not addressed. The transient extraction data for varying solvent conditions were in poor agreement with the model predictions. For example, the model calculations predicted that a nearly instantaneous equilibrium exists, which was not observed experimentally. These and all other previously reported models do not, or only partially, address the complicated chemical equilibrium that governs ligand-exchange-type chiral extractions. Simplified equations, like those reported by Takeuchi etal. (1984b) and Pickering and Chaudhuri (1997a), are only valid for infinitely dilute enantiomer concentrations. This thesis is concerned with the development of a comprehensive model, which accounts for all chemical species free in solution and involved in complexation reactions. This multiple-chemical-equilibria model is then combined with multi-staged equations to describe chemical equilibria and phase equilibria in chiral extraction systems. 1.9.2 Chromatographic Separations Sanders etal. (1988) reported the first program to include multiple-chemical equilibria in ion-exchange chromatographic separations. In the model, the column is divided into a series of equilibrium stages. Applications of the model to ion-exchange separations of amino-acid mixtures allowed the study of activity-coefficients and temperature influences on solute-elution profiles. In a related study, Theis (1988) modeled trace-metal transport and partitioning in soils. The multiple-chemical-equilibria equations were simplified to a set of Langmuir-type equations. This allowed the use of a simplified numerical approach to calculate the 54 continuity equations that govern species transport through the packed porous soil bed. The model was subsequently used to predict breakthrough curves at constant pH values. A model including a first-order reversible reaction for every complex formed was also presented which is valid for Damkohler numbers greater than 100, where chemical equilibrium is established nearly instantaneously. The only attempt to include multiple-chemical equilibria in the modelling of chiral chromatography separations is the work of Seidel-Morgenstern and Guiochon (1993). They modeled elution profdes of Troger's base enantiomers on a microcrystalline cellulose triacetate column. Troger's bases are chiral molecules due to the blocked conformation of the nitrogen atoms of the diazocine cycle (no inversion is possible). The binding isotherms for each enantiomer were measured independently on the column by frontal analysis. The data were then fit to a standard Langmuir-type adsorption isotherm for the (-) enantiomer. A quadratic term had to be added to the Langmuir equation to account for the observed non-ideality of the (+) enantiomer. The isotherm equations were subsequently used in a transient equilibrium-dispersive chromatography model, solved numerically by an orthogonal collocation method. Model results were reported for non-competitive binding and for competitive adsorption where the ideal adsorbed solution theory (IAS) was applied. Modelling results using the IAS theory were in better agreement with experimental data than those where the non-competitive isotherms were applied. The IAS theory was originally developed by Prausnitz and coworkers for gas-phase adsorption (Myers and Prausnitz, 1965) and later extended to ideal dilute solutions (Radke and Prausnitz, 1972). 55 1.10 Research Objectives This thesis focuses on the development of new methods for separating single-centre chiral enantiomers by the ligand-exchange principle, and the derivation of a model for such systems. The model explicitly accounts for all speciation and associated chemical equilibria within each phase of the separation system. Equilibrium formation constants required for the model are determined by potentiometric titration experiments when the phase is aqueous and by partition experiments in the two-phase system. The nonlinear nature of the large set of equations that describes the chemical equilibria requires the development of a robust least-squares minimization program. Current models of ligand-exchange based separations do not fully address the complicated solution equilibria in such systems (Pickering and Chaudhuri, 1997; Takeuchi etal, 1984b). The most advanced model (Seidel-Morgenstern and Guiochon, 1993) calculates binding equilibria with linearized multi-component Langmuir-type isotherms that are only applicable at low solute concentrations and do not account for solute-solute interactions. Consequently, the thermodynamic description of the system is incomplete and such models camiot be effectively used to predict, and thereby optimize, solute speciation as a function of operating conditions. The multi-stage multiple-chemical-equilibria model developed here allows one to predict separation performance as a function of pH, temperature, solvent-composition, ligand and solute concentrations, and chelating metal concentration. Therefore, the model provides a powerful approach to the design and optimization of chiral separation systems, where subtle changes in system conditions can lead to significant changes in enantiopurity and 56 yield. However, the model could be applied to any separations governed by multiple-chemical equilibria, including single and multi-staged extraction systems. The work focuses mainly on the separation of two distinct model solutes (the amino acids leucine (Leu) and phenylalanine (Phe)). Frequently, L-amino-acid enantiomers serve as precursors for the synthesis of chiral pharmaceuticals (i.e., protease inhibitors, DOPA, ibuprofen) or food additives (i.e., aspartame), making their separation an ideal model system. Leu and Phe enantiomers were chosen since these two amino acids have distinct chemical structures and physico-chemical properties (i.e., hydrophobicities). The model is tested by applying it to the description of two schemes for separating racemic mixtures of amino-acid enantiomers. The first is a liquid-liquid extraction system operating either in a single-stage mode, or through the use of hollow-fibre modules, in a multi-stage mode in which water-soluble enantiomers are selectively extracted into an organic phase by the presence of a lipophilic chiral ligand. The second scheme is a more conventional chiral ligand-exchange chromatography system in which the chiral selector is immobilized at the surface of a porous solid matrix. Finally, the model is combined with experiments to investigate the role of solvent, and solute and ligand chemistry in chiral recognition. In particular, Chapter V explores the influences of water on chiral selectivity arising from its ability to occupy the apical coordination sites of the chelating metal. This thesis is divided into ten Chapters. Chapter II provides a description of multiple-chemical-equilibria theory and its application to aqueous-phase speciation. The theory is then used to develop models for single and multi-staged chiral extraction systems. In addition, a transient multiple-chemical equilibrium model is developed to calculate elution 57 profiles from chiral chromatography columns. Chapter III describes the methods and materials used for the performed experiments. Chapter IV reports measured equilibrium formation constants for complexes in the aqueous phase and within the organic phase of a two-phase extraction system. Chapter V reports formation energies and enantioselectivities for selected ligands calculated by molecular mechanics simulations. Comparisons with experimental values are made as a basis for determining the potential of molecular modelling in ligand design. In Chapter VI , the developed multiple-chemical-equilibria model is used to investigate enantiomeric solute partitioning and enantioselectivity in single stage two-phase extractions. Chapter VII investigates multi-staged chiral extraction systems utilizing hollow-fibre membrane separators. Chapter VIII focuses on modelling of chromatographic chiral ligand-exchange separations. In Chapter IX, final conclusions are drawn and suggestions for further research are proposed in Chapter X . 58 CHAPTER II 2 Theory and Model Development 2.1 Nonlinear Regression The method of least-squares consists of finding those parameters that minimize the error in a function or a set of functions when applied to a defined set of experimental data (Gans, 1992). For a given set of m experimental observations, one can construct a vector y o b s of measured values for a vector x of the independent variables. The objective is to best fit a function ycal to this set of n experimental observations. The function (or set of functions) is defined such that for each observed valueyfs, a valuey.alcan be calculated, i.e., where the terms ei define the associated experimental errors. Implicit in this model is the assumption that y™' is error free and that the calculated values depend only on the parameter vector p and the independent variable X; , i. e., For a given parameter vector p, one can calculate the corresponding vector yca!. The objective is to find a set of parameters which minimizes the difference between the vectors y c a landy o b s. The most common form of an objective function to minimize is the sum of squared-weighted residuals, U, (Edgar and Himmelblau, 1988), i.e., the least-squares method: / = !,..., n, (2.1) y?' = f M - (2.2) 59 U = YJ^=YW,rl = r\^, (2.3) where the vector r contains the residual between the observed and calculated values, i.e., r = y"fa-y"". (2.4) Since the measured observations are subject to errors (a), a weight matrix W is introduced in equation 2.3 (Bard, 1974). The set of weighting factors reduces the statistical significance of experimental observations which may be less accurate or reliable than others. The weight matrix then emphasizes the more reliable members of y°bs in the analysis. A linear approximation of the model function can be obtained from a truncated Taylor series expansion around an arbitrary set of m initial parameter values p, i.e., 7=1 or in matrix notation: \dP.U Ap,, (2.5) y c a ' « y " " + J A p , (2.6) where the vector J represents the Jacobian matrix, i. e., bycal J ( 2 - 7 ) 8Pj The goal is to minimize the objective function (cf, equation 2.3) by appropriate adjustment of the parameters p. The minimum of U can be found by differentiation, where the value of each derivative is then set to zero (Beck and Arnold, 1977), i.e., 60 8U — = -2J T Wr = 0. (2.8) dPi By substituting the residual r and the Taylor series expansion (neglecting higher order derivatives) into the above equation, one can write: J T w ( y o b s - y i n i - J Ap) = 0, (2.9) which is equal to: J T W J A p = J T W r . (2.10) This equation is generally referred to as the Gauss-Newton method (Leggett, 1985) and is frequently used to solve sets of nonlinear equations. Initially, the residual r vector is calculated with the initial parameter estimates. Equation 2.10 is solved for the new correction vector Ap, which is then used to calculate an improved parameter estimate p'+1, i.e., p/+1-= p'+Ap . (2.11) The new parameter set p will result in a reduction of the objective function U. The procedure is repeated until no further reduction is achieved or a given convergence criteria is satisfied. It should be noted that, unlike with a linear function, the scheme is iterative and the new (refined) initial parameters have to be recalculated. Since the Taylor expansion was truncated, the final solution is obtained after successive approximations. Therefore, the success of the scheme depends on a good guess of the initial parameters; otherwise divergence can occur and no solution is found. A modification to overcome convergence problems was proposed by Levenberg (1944) and Marquardt (1963). They proposed to rewrite equation 2.10 in the following form: 61 ( j T W J +A,l)Ap = J t Wr, (2.12) where the parameter A. is multiplied by the identity matrix I. If AI becomes larger than J W J , the correction vector Ap will point in the direction of steepest descent. The direction of steepest descent is perpendicular to the contour lines of U. Therefore, U is guaranteed to decrease in this direction. The steepest descent method is usually not a good choice for least-squares minimization, because the minimum is not usually in that direction. However, for parameters far from the minimum, a rotation of the correction vector into the direction of steepest descent was found to be a good minimization strategy. An effective strategy for adjusting A, was reported by Fletcher (Adby and Dempster, 1974) and is used in this work. 2.2 M o l e c u l a r M o d e l l i n g 2.2.1 Introduction to Molecular Mechanics Modelling Molecular mechanics is a technique that is widely used for the computation of molecular structures and relative stabilities (Comba, 1993). The advantages of molecular mechanics over quantum chemical methods are mainly based on the computational simplicity of empirical force field calculations, leading to a comparatively small computational effort for molecular mechanics calculations. Molecular mechanics calculations assume that the motions of the molecular nuclei are independent of electron motions. The arrangement of the electrons is fixed and the positions of the nuclei are calculated. By accounting for all forces that can exist between the atoms, the spatial positions of the atoms of a molecule or complex are calculated using a mechanical approach. Bonded atoms are assumed to be held together by mechanical springs and non-bonded interactions can be attractive or repulsive in nature. The most likely spatial 62 arrangement of atoms is then calculated by minimizing the total energy of the molecule or complex of molecules. An empirical set of potential functions and the corresponding parameters are used to calculate the atomic interactions. The total strain energy is a sum of all the atomic potential energy functions for the molecule. This energy depends on the compounds stoichiometry, connectivity, and geometry, and the force field (potential energy functions between atoms). Minimization of the strain energy by rearrangement of the atoms ultimately yields a structure of lowest energy. Different approaches are used to specify the potential functions in the molecular mechanics approach (Comba, 1996). In general, the total strain-energy function (£10,ai) in a molecules is represented by a sum of individual energy functions, i.e., These include bonding (EH), valence angle (EQ), torsional angle (£<,), and non-bonded van der Waals interactions (£ n b). Various additional interaction terms can be added, e.g., hydrogen bonding ( E b b ) , electrostatic interactions (£E), out-of-plane bending (EB), and twist angle deformation (E¥). Figure 2.1 shows a ternary copper complex indicating several strain-energy contributions. The bond-formation term (EB) is a two-body interaction and accounts for the deformation energy associated with stretching or contracting a bond. The valence angle (EE) and torsional (E$) interactions belong to three-body and four-body interactions, respectively. The plane twist potential function (E¥) is used to enforce a square planar geometry over a tetrahedral geometry. These energies are associated with the three-dimensional geometry (2.13) molecule 63 around the metal centre. The van der Waals energy (£ n b) term describes the various contributions to atomic attraction and repulsion. Repulsive forces increase exponentially but are often described by other functions (e.g., Lennard-Jones potential, Buckingham potential, etc.), whereas attractive forces are usually modeled by a 1/r6 term. The required force-field parameters are obtained by fitting the strain-energy function to experimental data, such as X-ray structures or spectrographical measurements (Comba and Hambley, 1995). Figure 2.1: Molecular mechanics energy-potential contributions. The molecular modelling of transition-metal ion complexes is complicated by the partially filled inner <i-orbitals of the chelating ion. These orbitals are responsible for the multiple coordination geometries that can arise when complexes are formed. The coordination geometry is always a compromise between the size and electronic structure of the metal ion type, and the size, and geometric requirements of the coordinated ligand(s). Environmental effects such as solvation are often neglected in such calculations. 64 2.2.2 The P r o g r a m MOMEC MOMEC is a molecular modelling program based on strain-energy minimization. It was originally developed by Hambley (1987) for the calculation of transition-metal compounds. The program was further developed by Comba and his group and the present release is the MOMEC97 software package (Comba etal., 1997). Minimization of the potential-energy functions is achieved by conjugate gradients (first derivative), by full-matrix Newton-Raphson refinement, or by a combination of both methods. Molecular modelling of metal complexes is not as precise a science as is the modelling of simple organic compounds. However, it is capable of yielding useful and informative results. The major impediment to achieving successful modelling of metal-ion complexes is the inherent difficulty of describing the multiple number of oxidation states, coordination numbers, and coordination geometries of the transition-metal ions. Also, there is frequently interplay between steric and electronic factors that is not rigorously accounted for in molecular mechanics. Thus, it is unclear whether such programs can provide useful information for chiral ligand design and analysis. 2.3 M o d e l l i n g o f M u l t i p l e - C h e m i c a l E q u i l i b r i a For any chemical species or complex A aB b... in equilibria, one can write an overall equilibrium formation constant pab... as follows: R - [ A A - ] (2 14) where A, B,... identify the reactants, [A], [B],... are the associated free species concentrations (i.e., uncomplexed concentrations), and the subscripts a, b, ... identify the 65 stoichiometric coefficients (charges omitted). Activity coefficients are omitted in the above equation, and it is therefore implicitly assumed that they remain constant at the high-ionic-strength conditions used in these studies (Meloun etal., 1988). The concentrations of each species in equilibria is constrained by component mass-balance equations, e.g., for species A: ^ A = [ A ] + i : « / k B v . . ] , (2.15) ./=1 where xA represents the total concentration of species A (mol/1) and there are Nc complexes present in solution. The previous equation can be rewritten in terms of the free-species concentrations by defining an equilibrium formation constant (3, for every complex present, i.e., * A - [ A ] + t a A M ' W ' - - ( Z 1 6 ) 7=1 The general mass-balance equation for any species i in solution can therefore be expressed as follows: 7=1 k=l,N, (2.17) when Ns species are present and a,j is the stoichiometric coefficient matrix. A more detailed mass-balance example for an amino-acid/copper mixture is included in Appendix 3. In addition, the application of the Gibbs phase rule in an aqueous multi-species mixture is included in Appendix 4. 66 2.3.1 Determination of Equilibrium Formation Constants by Potentiometry Titrations allow one to measure changes in chemical equilibria in response to the addition of defined amounts of a species to a system. In potentiometric titrations, a base or an acid is titrated to the solution, and changes in the free-proton concentration are measured by a pH electrode. For an ideal pH electrode, the electrode response is given by the Nernst equation, which relates the measured potential (E) to the free proton concentration, i. e., E = E° + S,ln[n+], (2.18) where E° is the standard potential of the electrode, and the theoretical electrode slope SL is given by: nF where 91 is the gas constant, T is the absolute temperature, n is the number of electrons transferred (n is equal to one for protons), and F is the Faraday constant. Electrode non-idealities are often accounted for in equation 2.19 by multiplying the theoretical slope SL by a correction factor. At 25 °C, SL has a value of 25.69 mV, or 59.16 mV if the proton concentration is expressed in log10 values. The total concentration of species x, after each volume addition v from the burette can be calculated by: x"" vmi + x"v x = , (2.20 v""+v 67 where x"" is the initial concentration of species i present in the initial sample volume v"", and x- is the concentration of species / in the burette. The titration data required to determine equilibrium formation constants (P) are obtained as follows. A defined amount of titrant of known concentration is added to the sample volume. The free-species concentration in the sample solution is determined by an ion-sensitive electrode (which is most often a pH electrode) by equation 2.18. The measurements are repeated after each addition of titrant creating a titration curve, i.e., a pH response curve. Regression of the set of species mass-balances equations and the Nernst equation to this data, according to the computational approach described in the following section, then yields the desired equilibrium formation constant(s). 2.3.1.1 Computational Approach The calculated free-species concentrations in the solution at each titration point are obtained by solving the set of nonlinear of mass-balance equations (cf, equations 2.17) with a modified Newton-Raphson method (Gans, 1992). The relative shift vector AC (i.e., Ac/c) in free-species concentrations c, (i.e., [H], [B],....) is calculated according to the following equation: where J is the Jacobian matrix, and Ax is the residual vector of the total species concentrations: J AC = - Ax, (2.21) (2.22) 68 The shift vector (Ac) is then used to calculate the new set of free species concentrations (c" e w ), i.e., c"ew= c + A c . (2.23) These equations are iteratively solved until convergence occurs (i.e., E A C = 10"3). In matrix form, equation 2.21 can be written as follows: [A] & A d[A] [B]d[B] [A] &* [ B ] & B S[A] 3[B] A [ A J [A] A N [B] A x , A x c (2.24) This symmetric matrix can be efficiently decomposed numerically (Gans, 1992). The derivatives are calculated by defining the elements of the coefficient matrix as multiples of the complex concentrations, e.g., [B] ^ = [ A ] ^ = | ^ P , [ A ] M B ] ^ . . . = | « A (2.25) The diagonal matrix terms are then calculated as, e.g., for species A W ^ ] = W + f X P, WW. . . = [A] + ta) [ A „ B , . . . (2.26) 7=1 7=1 The stoichiometric coefficients for the complexes present in the system are specified in matrix form. The matrix then consists of Ns columns for each free species and /Vc rows for each complex. During the computation, the matrix is continuously used to calculate the mass-balance equations and the Jacobian matrices. 69 The program incorporates a new computational method that reduces redundant computations if matrix factors are zero, i.e., if species are not present in a given complex. Vectors are set up after the program is initialized to determine the sparseness of the complex matrix. Hence, species multiplications are reduced to a minimum. This method has two advantages: (1) it reduces round-off errors due to redundant additions and/or multiplications, and (2) it speeds up the calculation procedure. In particular, in the two-phase extraction system where a large number of complexes can be present, this approach significantly reduces the computational time. 2.3.1.2 Regression of Equilibrium Formation Constants The equilibrium formation constants ((3) defined in the chemical-equilibria model are regressed by minimizing the sum of squared-weighted residuals (U, equation 2.3) between the observed and calculated electrode potentials, E°bs and E?^, respectively, (Meloum etal, where G\ is the estimated error (standard deviation) of the observation i and W, is the weighting factor (1/a^). In the experimental system, only uncertainties in the measured electrode reading (CTe) and added titrant volume (av) are considered as a source of error. Since these errors are uncorrelated, the estimated variance (a2) can be calculated from the error-propagation formula (Gans, 1992), i.e., 1988), i.e., (2.27) 70 dV o i - (2.28) The first derivative of the electrode potential with respect to the titrant volume is calculated from the experimental data by spline interpolation. A three-point quadratic interpolation method (Hyman, 1982) is then used to compute the local derivative estimates (i.e., dEldV) associated with each data point. A Hermite interpolant of the derivative estimates preserves monotonicity of the data. Note that although a E and a v are constant, the weights are not. In particular, in the end-point region, the electrode potential may change very rapidly and a volume error can have large effects on the measurement. Updating of the estimated model parameters p in equation 2.10 requires the calculation of the derivatives within the Jacobian matrix J . The parameters to be determined are not explicit in the expression for the measured potential (cf., equation 2.18). This problem can be overcome by implicit differentiation, i.e., 3E dE 5[H] SL a[H] P—=P-r-i—= ^ 7 ^ — • (2.29) dp *5[H] dp [H] dp The partial derivatives of the free-proton concentration [H] with respect to the fitting parameter cannot be obtained directly from the mass-balance equations. However, Nagypal and Paka (1978) noted that if one has a set of functions F that depend on p, and another function u(p) of the following form: ¥[u{p),p] = Q, (2.30) the total differential can be written as follows: 71 d¥ d¥du dF , du n — + = — + J — = 0. dp du dp dp dp (2.31) Applying this method to the chemical equilibrium mass-balance equations (cf, Appendix 2) one can write: [H]-^n [H] 9 X » [pi dXH a[H] 1 Ja[B] [pi d*B a[H] 1 J5[B] \ 1 »5M [ < dp - 77 — 5p 1 5[B] [B] ^ (2.32) Therefore, any derivatives of the free-species concentrations with respect to the fitting parameter (p) can be calculated by solving equation 2.32. After having determined the partial derivatives with respect to each fitting parameter at every titration point the Jacobian matrix, J (cf, equation 2.10) can be calculated. By solving equation 2.10 the improved set of parameters is obtained that minimizes the squared-weighted residuals. The process is repeated until convergence occurs to yield the equilibrium formation constants for the investigated complex(es). In certain cases, convergence does not occur due to initial parameters estimates that are too far from the optimum values. Therefore, good initial parameter estimates are often necessary. The ratio of the ternary equilibrium formation constants is the enantioselectivity a, a PD PL (2.33) and is a direct indicator of the quality of the enantiomeric discrimination. For an efficient separation, a should be greater or smaller than one. The calculated homo- and hetero-chiral 72 equilibrium formation constants (PL and po or, log10pL and log,opD) of the amino-acid/copper/ligand complexes can be used to calculated the difference in Gibbs free energy (8 AG),/-*, SAG =-RT In R T x 2.3026 x[log10PD - log I 0 p j = -i?7Tn(a). (2.34) V r L J 2.3.1.3 Statistical Data Analysis Shifts in proton titration curves resulting from formation of equilibrium complexes are often subtle, particularly when the solubility of the components or complexes is low. In addition, differences in equilibrium formation constants for homo- and hetero-chiral complexes are small, reflecting the chemical similarity of the enantiomers. Therefore, successful regression of equilibrium formation constants from potentiometric titration data requires careful analysis of the model fit. The goodness-of-fit of the model-parameter adjustment to the experimental data can be assessed quantitatively by applying statistical moments analysis to the residuals (r, equation 2.4) (Meloun etal, 1988) . The first moment mx is the arithmetic mean of the residuals, i.e., ™,= — fw,r,, (2.35) HDF ;=i and should be close to zero for data well described by the model. The degree of freedom nDT is defined as the number of observations (n) minus the number of parameters regressed (np), i.e., 73 nDF=n-np, (2.36) The second moment m2 is the variance, i.e., ™2=s2=~fj{Wlrl)\ (2.37) nDF i=\ and its square root is the residual standard deviation (5), which should be numerically similar to the error of the instrument used to measure the dependent variable. The third moment m3, the coefficient of symmetry (skewness), gives information about the shape of the error-distribution curve. • (2-38) m2 For a normal Gaussian distribution, m3 has a value of zero. The fourth moment m4> the coefficient of kurtosis, also characterizes the shape of the error distribution curve, mA = 4 2 (2.39) If the errors are normally distributed, m4 should have a value of 3. The goodness-of-fit statistic x 2 (Pearson test) is derived from differences between the observed («!"") and the expected probabilities of the residual frequencies ntxp (Spiegel, 1961). The residuals are divided into eight classes, for which there is a normal probability that each class contains 12.5% (i.e., nxv = «/8) of every residual. The classes are defined by the limits -oo < -1.15-5, -1.15-5 < -0.675-5, -0.675-5 < -0.319-5, -0.319-5 < 0.0, 0.0 > 0.319-5, 0.319-5 > 74 0.675-5, 0.675-5 > 1.15-5, 1.15-5 > oo (Meloun etal, 1988). The %2 value is calculated from the sum of the individual classes, i.e., x 2 = E 8 (nfm -nexpJ 1=1 (2.40) Since the residual standard deviation s is calculated from the residuals themselves (i.e., equation 2.27), there are six degrees of freedom. At a 95% confidence level a fit can be accepted if the experimental value of %2 is less than 12.6. The Hamilton T?-factor (i?„„„,) is another test for model adequacy (May etal, 1988) and is defined by: (2.41) The calculated i?Ham is compared to its limiting value R lim Ham n l i m _ 1 YWE2 . / i ; exp,; (2.42) which should be less than i?Ham-It should be noted that none of these statistical requirements provide a definitive gauge of the goodness-of-fit when analyzing a nonlinear, multi-parametric set of functions. However, the statistical analysis described above provides a sound basis for determining the model accuracy and the quality of associated regressed parameters (Havel and Meloun, 1985a). 75 Other concerns are the errors and the uniqueness of the regressed parameter set. The covariance matrix C (or error matrix) can be calculated from the inverse of the design matrix B of equation 2.10 after the parameter X has been set to zero, i.e., The square roots of the diagonal elements can be used to calculate the 95% confidence interval (perr) for each parameter, i.e., where t is the value for the Student's -^Test at a 95% confidence level and degree of freedom. Since individual errors from repeated observations are unknown, p e r r is multiplied by the standard deviation s (Massart et al, 1988). This approach provides a good estimate of the parameter errors if the model does not show any lack of fit. The partial correlation coefficients (r,y) give a measure of the interdependence between two constants,/?, and pj, assuming that all other constants have fixed values: Similarly, the total correlation coefficients (Sy) provide a measure of the interdependence between two constants when the other constants are regarded as fitted parameters: C = B 1 = ( j T Wj) - i (2.43) (2.44) (2.45) (2.46) Finally, the multiple correlation coefficients (R,) give a measure of the independence of a given constant from all others: 76 *--fic-.-  {2A7) Each of these correlation coefficients can have a value between 0 and 1. A value close to zero implies total independence of the two parameters, and a value close to one means complete correlation, indicating that the two parameters cannot be regressed simultaneously (Zekany and Nagypal, 1985). It should be noted that a good data fit does not necessarily indicate correct model parameters. The correlation coefficients must be investigated carefully after regression to ensure that the fitted parameters (i.e., equilibrium formation constants) are uncorrelated. In this work, a model fit was accepted when the statistical moments indicated a good fit of the model to the data. In particular, the residual standard deviation (s) had to be less than the instrumental error of the pH electrode (i.e., 0.2 mV) and the residual frequencies % had to be lower than 12.6. Increased %2 values (> 20) were a good indicator that the pH electrode was in need of cleaning or replacement. In addition, to ensure uncorrelated equilibrium formation constants the correlation matrix was evaluated. Finally, the reported equilibrium formation constants are expressed in log)op values, where the 95% confidence region is indicated by last digit (in parentheses), i.e., log,op = 9.12(1). 2.3.2 Modelling of Two-Phase Multiple-Chemical Equilibria In the previous sections, a multiple-chemical-equilibria model applicable to a single aqueous-phase system was developed. In the following sections, the model is extended to a two-phase system, consisting of an aqueous phase in equilibrium with an immiscible organic phase, where speciation and complexation reactions are allowed to occur in both phases. The 77 model is then extended further to staged multiple-chemical-equilibria separations and is applied to two different separation schemes. The first is a cascade of perfectly mixed reactors where equilibrium is established at every reactor stage. The second describes the transient separation performance of a liquid chromatography system. 2.3.2.1 Single Stage Two-Phase Extraction Systems Consider an organic phase of volume V0Tg in equilibrium with an aqueous phase of volume Vaq (cf, Figure 2.2). Species in both phases are in chemical equilibria and can form complexes in each phase. Each phase is open with respect to the other and some free species (e.g., Cu++) can cross the phase boundary to form complexes with species in the other phase. Figure 2.2: Single-stage two-phase extraction system. At equilibrium, a mass-balance equation can be written for each species present in the two-phase system (shown schematically in Figure 2.2) as follows: x - x " " + y y - Y y » " ' = 0. (2.48) Here x and y are the total species concentration vectors at equilibrium in the aqueous and organic phase, respectively, and xIm and y"" are the initial total species concentration vectors prior to equilibrium. The volumetric phase ratio y in the system is defined as: 78 "1 In the organic/aqueous two-phase systems under consideration, each free species is soluble in one of the phases, but not in both. This allows one to write simplified free-species mass balance equations. The total concentration of species / in the aqueous (x() or organic phase (yi), respectively, can be expressed in terms of the free species and complexes formed, i.e., *i=S? c, +XS,*jA f lB 4 yCC y...] 1 r 1, (2-50) y i = Q - O c , +2a -^)« f f |A f lA c «>-J j where the index j runs over all complexes present and the solubility index t\, determines the solubility of the jth complex. The solubility index £° indicates the solubility of free species i. It should be noted that the solubility index £, can only take on values of 0 or 1, since a free species or complex is either insoluble or soluble in a phase. Assigning an equilibrium formation constant (P) to each complex formed, the previous equations can be rewritten in terms of the free-species concentrations, i.e., y,=<X-%)c, +X ( 1 - ^ K P , l[cka k=\,N, (2.51) Equations 2.51 and the overall mass-balance equations 2.48 define the set of nonlinear equations that were solved for the free-species concentrations by using a Newton-Raphson method (cf, section 2.3.1.1). The partition coefficient P{ for each species / can be calculated by: 79 P = y, k=\,N, (2.52) k=l,N, Each species partition coefficient is therefore a complex function of the free-species concentrations present in each phase. The ratio of the D- and L-enantiomer partition coefficients (i.e., P D and PL) defines the enantioselectivity (a) in a two-phase system: a PL (2.53) The enantiomeric excess (ee) in the organic or aqueous phase at the outlet stream can be calculated by the following formula: ee = [D]-[L] [D] + [L] (2.54) where [D] and [LJ are the concentration of the D- and L-enantiomer, respectively, in the aqueous phase (i.e., eeaq) or organic phase (i.e., eeots). By taking the absolute enantiomeric excess, we ensure positive values in either phase. The enantiomeric excess in the aqueous and organic phase can also be expressed in terms of enantiomer-partitioning coefficients PD and PL (cf, equation 2.52) by the following equations: ee aq 1 + p 1 + PR i~[D]"" ! - [ L j r> L J 1 . n L -I l + P, M"" + -V[L} (2.55) l + P, and 80 P, D lini P, [L] lint l + P D l + P, ee (2.56) l + P, [Lj L where [D]'ni and [L]"" are the initial phase concentrations of the D- and L-enantiomers, respectively. It should be noted that these initial concentrations cancel from the above equations for a racemic mixture. An example mass-balance calculation for a ternary two-phase mixture is presented in Appendix 3 and the application of the Gibbs phase rule for this example is included in Appendix 4. 2.3.2.2 Regression of Equilibrium Formation Constants in Two-Phase Systems In the aqueous single-phase system, equilibrium formation constants were regressed from potentiometric data. In the two-phase system, ternary equilibrium formation constants are regressed from measured species partition coefficients at different solution conditions (i.e., pH and species concentrations), i.e., where ' Pkohs and' Pkcal are the measured and calculated partition coefficients, respectively, for species k. The computer program Chemeq2 was developed to minimize the above equation by adjustment of the ternary equilibrium formation constant in the organic phase. The minimization routine is based on the same algorithm introduced in section 2.1. After the mass-balance equations 2.51 are solved for the free-species concentrations, each partition coefficient'P™' is calculated by equation 2.52. (2.57) 81 Gauss-Newton minimization of equation 2.10 requires the first derivative of the objective function (e.g., enantiomer partition coefficient'P™') with respect to the regressed parameter variables (i.e., P) for the Jacobian design matrix (J). This derivative can be easily obtained by realizing that the only amino-acid complex present in the organic phase is the ternary complex formed with the ligand (i.e., LiCuA). This is a good assumption, as will be addressed in the experimental section, since the partitioning of free amino acids into a hydrophilic phase (i.e., n-octanol) is negligible. Hence, after some algebra, one can write the first derivative of the partition coefficient function (cf., equation 2.52) with respect to the ternary complex formed (i.e., PL-ACL; or PD-ACUU) in the organic phase as follows: 8 d ([LiCuA]" a fp[Li][Cu][A]^ K XA J I X A J K  X A J [Li][Cu][A] . P ACuLi 5P ACuLi 5P ACuLi P^ ACuLi dP ACuLi X A X A (2.58) where xA and vA are the D- or L-species concentration in the aqueous or organic phase, respectively. Indices, specifying the i-fh experimental conditions are omitted for simplicity. However, the above expression can be easily extended to account for more complex speciation reactions, if required. 2.3.2.3 Fractional Extraction with Two Moving Phases Due to their chemical and structural similarities, enantiomers can rarely be separated in a single equilibrium stage. Therefore, multi-stage purification systems are usually required. Here, the equations describing single-stage two-phase extraction are extended to multi-staged systems. The system consists of N stages of two phases flowing in counter-82 current directions (cf., Figure 2.3). All stages are assumed to be perfectly mixed and in instantaneous equilibrium, and there is no mass-transfer resistance for any species crossing the phase boundaries. fi aq jn+ \ _ n+\ Figure 2.3: Multi-stage counter-current extraction system. N 1 fi org Assuming that the phases are immiscible and there is no change in fluid densities, one can write a total mass-balance equation for a species i at stage n as follows: Xr-Xnt =yYr-yYi" (2.59) where r : =y>sorg{y':-y"~xy and y is the phase ratio, now defined as: (2.60) Y = fi org Qaq ' (2.61) where Qox% and Q a q are the volumetric flow rates for the organic and aqueous phase, respectively. In equation 2.60, saq and sorg are the back-mixing coefficients for the aqueous and organic phase, respectively. The boundary conditions for each species are defined as follows: 83 Xf =xf where x"1 and v™ are the phase concentrations entering the first stage of the aqueous and organic streams {i.e., 1 and N), respectively. The equations derived are similar to the ones by Mecklenburgh and Hartland (1975) for partitioning of uncomplexed components. Here, however, the mass-balance equations are defined for each species present in each phase. Consequently, an analytical solution cannot be obtained since the species partition coefficients are now complex functions defined by the multiple-chemical-equilibria equations at each stage (cf., equation 2.52). As in the single stage system, the total concentrations x, and yt can be defined in terms of the free-species concentrations (cf, equations 2.51). These are then substituted into the overall mass-balance equations 2.59 for every stage. This results in a large set of nonlinear equations with Ns x Nstages unknown free-species concentrations. Chiral separations have also been achieved in more complex extraction systems where the solutes are injected at an intermediate stage n (cf, Figure 2.4). This arrangement is often referred to as a "double-counter-current", "centre-feed" or "fractional" extraction system. The concentrated solutes are injected at the intermediate stage and stripped in the stages to the left of the feed-inlet stage n (cf, Figure 2.4). Refinement and purification of the solutes is achieved in the stages to the right of the feed inlet. This extraction approach results in both high yields and high product qualities (Belter et al, 1988). The model equations developed for the counter-current extraction with end-point feed remain valid, but their solution requires proper indexing of stages upstream and downstream 84 of the feed-inlet stage n. In addition, the feed-inlet boundary condition for the species concentrations xm,d has to be incorporated into the equations at stage n as follows: 1 co 1 xr +- x'r -y y y « _ v"+l V " (2.63) The aqueous-injection-phase ratio (co) is defined by: co = Qa (2.64) where g i n j is the volumetric injection flow rate at the inlet stage n. The phase-ratio coefficient y* accounts for the additional fluid stream Qmi and can be expressed as follows: 1 _ Qaa + Q i n j _ (l + co) fi org For stages n > Nini the phase ratio y is equal to y*. (2.65) n-l Qin 17/1+1 x"< JV-1 rN-\ N 17/V+l org Y* x i n i Figure 2.4: Counter-current extraction system with mid-stage injection. 2.3.2.4 Numerical Solution Methods The set of model equations defining multiple-chemical equilibria in a multi-stage two-phase extraction system (cf, equations 2.51 and 2.59 or 2.63) are nonlinear and require 85 numerical solution techniques. Therefore, the program MChemeq2 was developed (source code listed in Appendix 7). Solute transport to or from stage / occurs only through stages in direct contact with stage /', i.e., i+\ and z'-l. Therefore, the species mass-balance equations result in a banded block-diagonal matrix with a bandwidth of H-species and A-stages. Banded block-diagonal matrices can be efficiently decomposed and therefore do not require an iterative solution method (Fletcher, 1991). After initializing the routine with an initial guess of the free-species concentrations (i.e., a fraction of the inlet concentrations), the new free-species shift vector is obtained and the updated species concentrations are calculated according to equation 2.21. In addition, overall mass-balances for every species at the stage inlets and outlets are calculated to ensure mass-conservation, i.e., y y) + (1 + co)*," = y yf+l + x,° + co xf . (2.66) Initial estimates for the free-species concentrations at each stage are required to initialize each mass-balance equation for the Newton-Raphson method (i. e., a fraction of the initial species concentration). In particular, for a large number of stages where a substantial number of unknown free-species concentrations need to be determined, a "good" initial estimate is required, otherwise convergence is not guaranteed. This problem was avoided by solving the equations for a small number of stages (e.g., 1 or 2) and then progressively increasing the number of stages by using the previously calculated free-species concentrations as initial estimates (cf., Figure2.5). This solution method proved very effective and the free-species concentrations at each stage were found within a few iterations. The fraction of solute /' extracted (<(>j) into the organic phase can be calculated as follows: 86 , y, Qor8 —yy, ( 2 6 7 ) Finally, the product of the fraction extracted (())) and the enantiomeric excess ee (cf., equation 2.54) defines the performance factor (pfi), i.e., pf^ee-^. (2.68) A performance factor close to unity indicates a high enantiomeric purity in both outlet streams. 87 Initialize - NTU = NTU+ 1 Calculate Mass Balances Solve Nonlinear Equations new shift in solution vector convergence yes Check Mass Balances Terminate yes yes *- Terminate no NTU-NTU+ 1 Figure 2.5: Computational flow sheet for the MChemeq2 program. 88 2.4 M a s s T r a n s f e r in H o l l o w - F i b r e M e m b r a n e s The overall mass-transfer coefficient consists of three resistances {cf., Figure 2.6; Yang and Cussler, 1986). The first is due to solute transport across the hydrodynamic boundary layer at the inner membrane wall (region I). The solute must then pass through the porous membrane material (region II) before crossing a second boundary layer at the outer membrane surface (region III). Concentration Profile i u t I • d-JJJ JJ J Membrane Structure Lumen Shell Organic Aqueous Phase Phase Figure 2.6: Solute-concentration profiles across a hydrophilic hollow-fibre membrane. In analogy to an electrical circuit, the overall mass-transfer resistance (Kin) can be calculated by the summation of the inverse of the individual resistances (Prasad and Sirkar, 1987), i.e., J L = J _ J L L K,.. L. + k + P k (2.69) in m 89 where km, km and A:out are the individual mass-transfer coefficients at the inner fibre surface, within the fibre membrane and at the outer fibre surface, respectively. The overall mass-transfer coefficient (Kin) in equation 2.69 is expressed with respect to the solute concentration at the fluid surface at the inner-membrane boundary layer. Since the solute partitions into the organic phase at the outer fibre surface, the mass-transfer coefficient koM is multiplied by the solute partition coefficient P. If the organic phase flows in the fibre lumen and wets the membrane, equation 2.69 is rewritten as follows: 1 = _ L 1 1 K k,„ + Pk + Pk (2.70) Individual mass-transfer coefficient correlations for hollow-fibre membranes are available in the literature (Prasad and Sirkar, 1988; Yang and Cussler, 1986). Dahuron and Cussler (1988) reported the following correlation for the mass-transfer coefficient at the inner fibre membrane (km) under laminar flow conditions (Re < 2000), i.e., M =*inA = 1.5 D Sn = 1.5 fp, A (2.71) where Sh is the Sherwood number, Dm is the solute diffusivity in the lumen fluid, um is the lumen velocity, d\ is the inner fibre diameter, Pem is the inner Peclet number and L is the effective fibre length over which mass transport occurs. The same authors also reported a correlation for the mass-transfer coefficient at the outer membrane (koul) for laminar flow conditions (Re < 2000), i. e., V ^ J u . d out e V V o u t J 1/3 = 8.8 f A \ (2.72) 90 where uout and vout is the velocity and kinematic viscosity of the fluid at the shell side, respectively, Re is the Reynolds and Sc is the Schmidt number. The equivalent hydraulic diameter at the shell space (de) is calculated from the following equation (Prasad and Sirkar, 1988): d. = id)-nfdl) (2.73) where, ds is the inner shell diameter, nt is the number of fibres, and d0 is the outer fibre diameter. Prasad and Sirkar (1988) reported a correlation for the outer mass-transfer coefficient that contained a nonlinear velocity dependence for laminar flow conditions (Re < 2000), i.e., ShM = 6.1 ,1/3 V ^ J V V o u t J = 5.9 Reou,  SCou, • (2.74) The mass-transfer coefficient in the membrane can be expressed as the ratio of the solute diffusion coefficient to an effective membrane thickness (Prasad and Sirkar, 1988), i.e., T5 ' (2.75) where D is the diffusion coefficient, T the membrane tortuosity, 8 the membrane thickness, and sm the membrane porosity. It should be noted that the product of x and 8 can be considered as an effective length. In most applications, the membrane resistance does not influence the overall mass-transfer resistance because the membrane is usually very thin and diffusive transport occurs quite rapidly. However, under certain operating conditions (i.e., high fluid velocities) this resistance can be limiting. It should be noted here that these correlations were derived for modules containing low fibre packing densities. For higher densities, where fibres are tightly packed, the overall mass-transfer coefficient can become independent of fluid velocity. In such cases, diffusional transport between the fibres dominates since fluid flow channels around the packed fibres (Yang and Cussler, 1986). The overall mass-transfer coefficient can be used to calculate the height of a transfer unit (HTU) through the following relationship (Prasad and Sirkar, 1990): 'HTU = - U Ka (2.76) where a is the ratio of membrane area to volume. The number of equilibrium stages (NTU) can be determined from the length of the extraction device (L), i.e., NTU = — — . (2.77) HTU The NTU concept has been used for over 50 years in the design and evaluation of separation equipment, i.e., distillation and extraction (Treybal, 1980). The NTU number describes the difficulty of a separation, and the HTU estimates the efficiency of the separation equipment (Cussler, 1994). 2.5 M o d e l l i n g o f L i g a n d - E x c h a n g e C h r o m a t o g r a p h y In this section, a model is derived to Calculate multiple-chemical equilibria in an unsteady-state chromatographic system. In chiral ligand-exchange chromatography (CLEC), 92 the ligand is immobilized on a support matrix. The solvent flowing through the porous column contains a mixture of enantiomers, copper, and buffer ions that will participate in complexes formed in the mobile phase and with the stationary ligand (cf., Figure 2.7). Enantiomer binding to ligand and complex formation is dictated by multiple-chemical equilibria (cf, equations 2.51). control-volume boundary Figure 2.7: View of a control volume in the CLEC column Figure 2.7 shows a schematic of a control volume in the CLEC column. A control volume is a column segment over which the species concentrations are uniformly averaged. The ligand is adsorbed to the silica bead (containing grafted hydrophobic tethers) through its hydrophobic tail. For simplicity only copper (Cu++), protons (H+), and amino-acid 93 enantiomer (A) are identified in the fluid phase, since they are the dominant species forming complexes with the ligand. It should be noted that Figure 2.7 is a simplified sketch and the actual silica bead is a micro-porous particle. Therefore, the ligand is not only attached to the outer bead surface, but also to the inner pore structure of the silica particles. The transient solute (enantiomer) transport model in an HPLC column filled with a matrix consisting of porous silica particles (cf., Figure 2.8) is developed as follows. The axial-symmetric column is assumed to be uniformly packed with a constant hydraulic conductivity where Darcy's law applies. Since the column has a large aspect ratio (Lid > 50), radial velocity and concentration gradients can be neglected and the column can be treated as one-dimensional with a uniform constant axial velocity profile (Giddings, 1965). - L -Figure 2.8: Sketch of an HPLC column. The general continuity equation for any species / present in the system can be written as (Bird etal, 1960): s ^ = 9 - ( D ^ ] - u ^ , (2.78) dt dzy dz J dz where xx is the total concentration of species / in the aqueous phase, t is time, z is the coordinate in the axial direction, D is the solute diffusion coefficient, s is the column-bed 94 porosity, and u is the average superficial fluid velocity of the mobile phase in the packed column. It should be noted that the diffusion coefficient D in equation 2.78 is a scalar, since any variations in the species diffusion coefficients are neglected. This assumption is valid for high Peclet numbers (Pe = u LID > 100), where convective transport dominates mass transfer. The appropriate boundary conditions for each species x{ are defined as follows: 1) x,(z), v,(z)=0 at 0<z<L, t =0, i= sample 2) x, (z) = cf at z = 0, 0<t< tin, i = sample 3) x,.(z) = c;B at z = 0, t>0, i = buffer dx (z) 4) — ^ = 0 atz=L, 0<r<r„, i = sample, buffer (2.79) dz 5) y. (z) = cf at 0 < z < L, t > 0, / = ligand 6) xi (z)=cf at 0 < z < X, t = 0, i = buffer 7) x(^) = ^ /" «^  0<z<L, t=0, /= buffer The first boundary conditions indicate that prior to sample injection, solute concentrations in the mobile phase as well as adsorbed to the ligand are zero. Sample injections occur over a defined time interval (/in) at the column inlet (2). Boundary condition (3) indicates a constant buffer concentration in the mobile phase. The Danckwerts' boundary conditions (4) express flux continuity at the column outlet for all species present. Boundary condition (5) assumes that the ligand is homogeneously distributed in the column. Conventionally, the column is equilibrated with a buffer solution prior to sample injection. Therefore, there will be a defined and constant buffer concentration in the column (6). Boundary conditions (7) define 95 the concentration of the buffer species that will bind to the ligand after the column has been equilibrated. The continuity equations 2.78 determine the transient total-equilibrium concentration Xi of species i through the column. Since the ligand is stationary, 7YS-1 nonlinear partial differential equations are linked together and must be solved simultaneously. The nonlinearity arises from the chemical-equilibria equations (cf, equations 2.51) which determine the amount of species bound to the ligand in every column control volume. To solve this coupled set of nonlinear equations, the following simplifying assumptions were made. 1) There is no mass-transfer resistance between the bulk fluid phase and the ligand at the porous support material. 2) Chemical equilibria are established instantaneously in every column control volume. 3) Finally, the ligand concentration at the porous beads is averaged over the column volume accessible to the mobile phase. 4) In addition, due to the high Pe numbers in the column, solute transport is governed by convection. Therefore, diffusive transport does not influence the concentration profile. However, the diffusive transport term was maintained in the computational procedure to ensure numerical stabilty (Anderson et al. 1984). 2.5.1 Numer i ca l S o l u t i o n The set of coupled transport equations 2.78, which are linked via the chemical equilibria equations 2.51, were solved numerically by a finite-difference method. In the finite-difference approach, the column is sectioned into n equally spaced grid points of length Az where locally averaged species concentrations x,. and y: exist (cf, Figure 2.9). The averaging is performed over half a length of Az in each grid direction to define a local control 96 volume (cf, Figure 2.9). The spatial derivatives in all equations were discretized using a first and second order accurate Taylor series expansion of the spatial derivatives for the convective and diffusive terms, respectively (Patankar, 1980). These equations resulted in sets of tri-diagonal matrices. A first-order upwind corrected "power-law scheme" (Patankar, 1980) was applied to create an artificial diffusivity to ensure diagonal dominant matrices at high cell Peclet numbers (u Az/D). control volume z Az • <—• column Tl >• grid points X X ; , y{ Figure 2.9: Computational domain of the chromatography column. Since the complexity of the governing equations is high due to the presence of many interacting species, a simplified solution method was applied. At each time increment, the species transport equations were decoupled and solved individually, i.e., apseudo steady-state situation was assumed. The nonlinear chemical-equilibria equations were then solved to obtain new estimates of species concentrations bound to the ligand (x() and free in solution ( _y;) at any axial position. The transport equations were resolved with the new local species concentrations and the procedure was repeated until convergence. This solution method has the advantage that the set of finite-difference equations that result from the discretized form of the transport equations (2.78) are linear and tri-diagonal. The iteration procedure at each time step requires only a few iterations for convergence since the time increments used were small. In general, the time increments (At) were chosen as a 97 fraction of the injection time. The injection time (/in), at which the solute boundary conditions were applied at the column inlet, was calculated from: (2.80) where Via is the sample volume and Q is the volumetric flow rate. The time domain of equation 2.78 (left-hand-side) was discretized by a 2nd order accurate Crank-Nicolson scheme to calculate the species concentrations at each new time (Patankar, 1980). The calculation proceeded until all injected species were completely eluted from the column. A mass balance was performed to ensure that the calculations were mass-conservative. For each enantiomer, the time when the concentration peak height at the column outlet occurred was defined as the total elution time (rtot) (cf, Figure 2.10). This time was corrected by the column dead-volume time (4) and reported as the elution time (t). solute injection Figure 2.10: Solute-retention time (t) and column dead volume. The program code (Chico) was written in the FORTRAN77 programming language. It is listed in the Appendix and was executed on an IBM compatible Pentium 120Mhz computer. An axial grid of 101 nodes showed good numerical peak resolution. It should be noted that a larger number of grid points did not significantly alter the location of the 98 maximum peak height or elution time, but did affect the peak shape (i.e., sharper elution peaks were obtained with more axial nodes). The last boundary conditions (6 and 7) in equations 2.81, specifying the column equilibria prior to the solute injection, need to be addressed further. Experimentally, column equilibration is achieved by flowing buffer solution through the column until a stable baseline is obtained. The numerical equivalent of this process would require solving the steady-state form of the transport equation 2.78 with the buffer-species concentrations as constant boundary conditions. This time consuming procedure was not applied in favour of an easier solution procedure (described below). Since the ligand is distributed homogeneously in the column, no axial concentration gradients exist after buffer equilibration. Therefore, equations 2.78 are uncoupled from the mass-balance equations 2.51 and one can treat the entire column as a single-stage unit. The mass-balance equations 2.51 are solved until the aqueous species concentrations entering the stage (i.e., boundary conditions 6, in equation 2.82) are equal to the concentrations leaving the stage. This vector of equilibrium concentrations (x and y) is then mapped into each column control volume. It should be noted that this procedure is only applicable for a constant ligand concentration and the absence of any concentration gradients in the column. Otherwise, the transient form of equation 2.51 needs to be solved. Figure 2.11 shows a computational flow sheet of the applied solution procedure. 99 Initilize program Equilibrate Column t = t + At Increment time Solute Transport Equations Multiple Chemical Equilibria Equations —<^^^^^ convergence of mass balances yes — a l l solutes eluted yes Terminate program Figure 2.11: Computational flow sheet for the Chico program. 100 CHAPTER III 3 Materials and Methods If not otherwise stated, all chemicals were purchased from the Aldrich Chemical Company Inc. (Milwaukee, WI) or ICN Pharmaceuticals Canada Ltd. (Montreal, PQE). The chemicals were always of the highest available purity (>99%) and were used without further purification. For the preparation of all aqueous solutions, water was first distilled and then treated with a NANOpure® II ultrafiltration system (Barnstead; Dubuque, IW). All aqueous solutions were maintained at an ionic strength of 0.100 M by appropriate additions of KN0 3. The ionic strength I was calculated from: / = ^ I > , 2 , (3-83) where c{ is the concentration of ion / and z, is its charge (Meloun et al., 1988). 3.1 Buffer Preparation Acetate-buffer solutions were prepared from aqueous stock solutions of 0.200 M sodium acetate and 0.200 M acetic acid (Fasman, 1996). Depending on the required pH, different volumes of each stock solution were mixed and further diluted with water to obtain a final buffer concentration of 0.100 M. 101 3.2 p H M e a s u r e m e n t s The pH of the aqueous phase was routinely determined with a Corning bench-top pH meter (Aldrich, WI). The pH electrode was an Ingold microelectrode type D402-M3-S7/60 (Aldrich, WI). The pH electrode was calibrated daily with at least four pH stock solutions (2, 4, 5 and 6 or 7). 3.3 L i g a n d S y n t h e s i s The alkylated L-hydroxy-proline ligands required for the two-phase experiments were synthesized in the lab. The synthesis procedure was identical to that reported by Ding et al. (1992). Briefly, the A-n-dodecyl-L-hydroxy-proline ligand is synthesized by dissolving 0.15 mol of decanal in 100 ml absolute ethanol and adding 0.1 mol of L-hydroxy-proline (250 ml round flask). In another flask, 1.5 g of 5% palladium on activated carbon is suspended in 50 ml absolute ethanol. This suspension is carefully added to the reactants. The solution is stirred magnetically for ca. 3-4 days under constant hydrogen gas sparging. L-Hydroxy-proline has a very low solubility in ethanol, while the product is soluble. The progress of the reaction can therefore be monitored by observing the disappearance of the white suspended L-hydroxy-proline crystals in the solution. After the reaction was completed, the activated carbon particles were retained on filter paper (Whatman Inc.; Rockland, MA). The filter cake was then washed several times with small amounts of ethanol, which is removed later by vacuum. The product residue was washed with ether and then recrystallized from water to obtain white crystals. The measured melting point was in close agreement with the one reported by Ding et al. (1992). 102 For the synthesis of A-n-octyl-L-hydroxy-proline, the dodecyl-aldehyde was replaced by decanal. Otherwise, the experimental procedures were identical to the one described above. 3.4 H o l l o w - F i b r e M e m b r a n e S y s t e m The hollow-fibre membranes were a gift from Akzo Nobel Faser AG, Membrana (Wuppertal, Germany) and are made from regenerated cuprophan type RC55. The physical dimensions and membrane properties were kindly supplied by the manufacturer and are listed in Table 3.1. The manufacturer included a detailed pore-size distribution and reported that molecules with a molecular weight lower than 2000 Dalton do not experience any significant hindrance in the membrane. The specific weight of a single fibre (82.9 u.g/cm) was determined by counting 100 fibres and weighing. Membrane-tortuosity estimates for the cellulose-fibre membrane were taken from Prasad and Sirkar (1988). 103 Table 3.1: Hollow-fibre membrane parameters. Parameter Value units Inner fibre diameter (d{) Membrane thickness (8) Outer fibre diameter (d0) Membrane cut-off Pore volume fraction Membrane porosity Membrane bound water fraction Membrane tortuosity Pore radii Min. Max. Average Specific dry fibre weight Prasad and Sirkar (1988) 3.4.1 Design of Hollow-Fibre Modules The assembly of hollow-fibre modules used in this work involved testing of many different system components to identify an adequate reactor. An important design criterion was that the fibres were completely embedded in the potting material to prevent phase leakage. Also, the potting material was not allowed to penetrate through the membranes where it could cause plugging of the fibre lumia. In addition, the potting material had to be 200 (±15) um 8 (±1) um 216 (±15) pm 10,000-13,000 Dalton 0.20 0.80 0.35 6 I. 76 II. 18 2.55 82.9 nm nm nm tig/cm 104 resistant to organic solvents. The epoxy encapsulating resin SEALTRONIC 21AC-7V (Industrial Formulators of Canada LTD, Burnaby BC, Canada) was used since it showed excellent resistance, negligible amounts of swelling in organic solvents, and was easy to handle during the curing process. The shell housing for the fibre bundle consisted of standard plexi-glass tubes. The tubes were cut with a saw to a length (Z*) of ca. 21 cm. After cartridge assembly, the modules had an effective fibre length (L) over which mass transport occurred of ca. 19.5 cm. Slight variations in the length existed in each module assembly. However, these were in general less than 5%. The membrane-packing density (sfp) in the cartridge was varied by using plexi-glass tubes of different inner diameters or by changing the amount of fibres potted into the shell housing. The binding strength of the adhesives to the shell walls was improved by treating the inlet of the inner tube with sandpaper. As shown in Figure 3.1, two holes were drilled at each end of the plexi-glass shell and short pieces of glass tubes (ID =1.5 mM, OD = 3 mM) were inserted. The connections were sealed by applying a layer of adhesive at the outer circumference. These inserts were used as inlet and outlet flow channels to the shell side of the reactor module. A defined number of fibres was gently inserted into the shell. Small pieces of silicon tubing were wrapped around each end of the fibre bundle and carefully pushed into the shell housing (ca. 3-4 mM). These rubber inserts ensured that the liquid potting material did not penetrate beyond a defined point into the module (cf, Figure 3.1). 105 Figure 3.1: Sketch of a hollow-fibre cartridge. The handling of the two component potting adhesive required a very strict timing schedule. After vigorously mixing the two components in a 1:2 ratio, the paste was placed in an oven at 60 °C for 30 minutes. The heat treatment reduced the viscosity of the liquid and therefore improved the transfer of the adhesive into the interstitial fibre space in the shell housing. After filling the potting adhesive into one reactor end, the module was put back into the oven (60 °C) to shorten the curing time. The opposite reactor end was filled by the same procedure. After ca. 4 hours, the module was taken from the oven and the excess potting material at each side of the module was cut with a sharp razor blade to obtain a smooth surface. Finally, plastic connectors were attached to the shell ends to join the lumen inlet and outlet feed tubes. A cut section of the fibre potting was visually inspected under a light microscope to confirm that the adhesive did not penetrate into the lumen side of the cellulose fibre membrane material during the curing process, that the fibres were homogeneously distributed in the potting material, and that they showed no clogging or dimensional changes. Also, when an aqueous fluid stream was pumped through the lumen side of the module, a uniform 106 fluid distribution in the fibre bundle was observed. The dimensions of the manufactured hollow-fibre membrane cartridges are listed in Table 3.2. Table 3.2: Hollow-fibre membrane cartridge dimensions. Properties Value Units Overall cartridge length, L* 21-22 cm Effective fibre length, L 19.5 cm Inner shell diameter, Ds 0.635 or 0.476 cm Number of fibres in the shell 166-230 -Fibre-packing densities (efp) 27-44 % 3.4.2 Hollow-Fibre Membrane Two-Phase Extractions In all experiments, the aqueous phase was pumped through the lumen side of the membrane modules. The aqueous and organic solvent streams were delivered by Gilson Miniplus 3 peristaltic pumps (Mandel Scientific, Guelph, ON). Digital control of the step motor allowed accurate and reproducible non-pulsing flow rates. The pumps and the hollow-fibre modules were connected using Tygon tubing (Cole-Palmer, Vernon Hills, IL), which resisted swelling or solubilization in the organic solvent. The startup procedure for an extraction experiment was as follows. Distilled water was slowly pumped through the fibre lumia to wet the fibres, which resulted in the white fibre membranes becoming translucent due to the penetration of water into the porous 107 cellulose membrane material. The reactor was tilted upwards during this procedure to allow gas bubbles entrapped in the fibre lumen to escape. After establishing the lumen flow, the aqueous pump was shut off and the organic phase was pumped slowly into the reactor shell. Again, the reactor was tilted upwards to remove gas bubbles entrapped between the fibre bundle. The gas bubbles had the tendency to adhere at the wet fibres. However, by rapidly changing the pump speed, these bubbles were successfully removed. The organic phase containing the chiral selector was equilibrated with copper solution prior to the chiral extractions. Saturation of the organic ligand-containing phase with copper ions was performed in a shake flask in the presence of an acetate-buffered copper solution. The phases were mixed, vigorously shaken and the copper concentration in the organic phase was measured by EDTA titration (described later in section 3.5.3) after equilibration. 3.4.3 Measuring Hollow-Fibre Mass-Transfer Coefficients Overall mass-transfer coefficients for the hollow-fibre modules were determined by extraction experiments. An acetate-buffered (0.1 M) benzoic-acid solution was pumped through the lumen side of the fibre membranes (cf., Figure 3.2). The organic phase (n-octanol) was pumped in counter-current direction through the shell side of the module. Volumetric flow rates were determined by gravimetric measurements at defined time intervals. At each operating flow rate, ca. 3 hollow-fibre dead volumes were pumped through the reactor to ensure steady-state conditions before solute samples were taken and analyzed. 108 z = 0 z = L aqueous phase organic phase Figure 3.2: Two-phase hollow-fibre extraction setup. The overall mass-transfer coefficient K was calculated using the correlation of Ding and Cussler (1991): La E-l In ,."1 _ Cz=0 Lz=0 H r»rg aq _ <-\z=/, Z-L H -^xNTU, La (3.1) where «,u is the aqueous lumen velocity in the fibres, L is the length of the fibre that is in contact with the organic phase, a is the specific surface area, ca:l0, c"J0 and c°lL , c°JL are the aqueous phase and organic phase concentrations at the fibre inlet and outlet. The extraction factor E is defined by: E = P Q o r s Q (3.2) aq where P is the partition coefficient, g o r g and Qiq are the volumetric flow rates of the organic and aqueous phase, respectively. The specific surface area is defined as the surface area per module volume and can be calculated by: 109 izd} d: a = — ^ = — . (3.3) where dx is the inner fibre diameter. Benzoic-acid concentrations in the aqueous stream were determined spectro-photometrically. By applying a solute mass balance, it was possible to determine the concentration of benzoic acid in the organic outlet stream, i.e., Cz=L = Cz=0 + Qo M<£o-<£j , (3-4) The fluid and solute properties required for the mass-transfer calculations are listed in Table 3.3. The benzoic-acid diffusivity in the aqueous solution was taken from Cussler (1997). This value was subsequently used in estimating the diffusivity in the n-octanol phase by applying the Stokes-Einstein equation (Cussler, 1997). The density of the n-octanol solvent was taken from Smith and Srivastava (1986) and the viscosity from Reid etal. (1987). Table 3.3: Fluid and solute properties (25 °C). v [cm2/s] H [g/cm-s] P [g/cm3] D [cm2/s] aqueous phase 8.93xl0"3 8.91xl0"3 0.998 l.OxlO"5 n-octanol phase 72.1xl0"3 59.2xl0"3 0.824 *1.5xl0-6 estimated value 110 3.5 A n a l y t i c a l M e t h o d s 3.5.1 HPLC System All chromatographic separations were performed on a Waters™ HPLC system (MILLIPORE Waters Chromatography; Milford, MA). The system consisted of a Waters™ 717 plus auto-sampler, a Waters™ 600s controller, a Water™ 486 tunable absorbence detector, and a Waters™ 626 pump. The control of the instrument was performed using the Waters™ Millenium software (version 2.1). The software also performed peak integration and analysis. A solvent flow rate of 1.00 ml/min was used for all HPLC experiments and the analyte absorbence was detected at a wavelength of 254 nm. 3.5.2 Measuring Amino-Acid Concentrations Separation and characterization of enantiomers was performed on a chiral ligand-exchange chromatography column (CLEC) (4.0 x 150 mm) containing a D-penicillamine selector. The CLEC QA-5000 column was supplied by YMC Inc. (Wilmington, NC). The aqueous mobile phase contained 1 mM Cu(SO)4 and small amounts of 2-propanol to decrease enantiomer retention times in the column. For leucine and valine, a 2-propanol concentration of 1-2% was used, while for phenylalanine a higher amount of 5-7% (v/v) was required. Under these conditions, a baseline separation of all enantiomers was obtained. Depending on the amino-acid concentrations, sample volumes between 10-20 pi were injected into the column. The measurements were repeated at least in duplicate for each sample. Standard absorbence versus concentrations curves for each enantiomer were prepared from concentrated racemic amino-acid stock solutions. Calibration curves of the peak area versus enantiomer concentrations showed excellent linearity (r > 0.99). I l l 3.5.3 Measuring Copper Concentrations Copper(II)-ion concentrations in the aqueous phase were determined by volumetric titration with EDTA using l-(2-pyridylazo)-2-naphthol (PAN) indicator dye. A defined volume of the copper containing sample was diluted in 5.0 ml de-ionized water and a small amount of nitric acid was added (ca., 200 uX of 0.1 M HN03). Then, 2-3 drops of PAN (3% solution in methanol) were added. Under the slow addition of the EDTA-stock solution, the copper solution was titrated to equivalence, which was indicated by a colour change (from a light purple to a light gray). The copper concentration in the organic n-octanol phase was determined by diluting the sample with ca. 5.0 ml of ethanol instead of water. The colour change was then from purple to a light yellow. It should be noted that the colour change for this titration was not as fast as in the aqueous-phase titration, requiring the EDTA to be added very slowly. EDTA solutions were prepared from a stock solution supplied by Aldrich. When further dilutions were necessary, the EDTA titer was determined by titration against a defined solution of copper(II) prepared from 99.999% pure Q1CI2. All copper titrations were performed with a 10.00 ml (± 0.01ml) volumetric burette (Cole-Parmer, Vernon Hills, IL). The sample volumes were chosen such that a volume of ca. 2-4 ml of EDTA had to be added to reach the equivalence point. The distribution of copper(II) ions in two-phase systems was measured by volumetric titrations in which the phase containing the higher copper-ion concentration was analyzed. Since the total moles of copper present are known (nmi), the concentration in the remaining phase can be calculated from a mass balance, i.e.: nm. = V"rc"r + V^c'"1, (3.5) 112 where V" , and c \ cq are the volumes and the copper(II) concentrations in the organic and aqueous phases, respectively. Occasionally, both phases were analyzed to ensure that the copper mass balance closed. These results showed deviations of less than 5%. 3.5.4 Measuring Benzoic-Acid Concentrations The concentrations of benzoic acid in the aqueous phase were determined by measuring the absorbence at 280 nm with a Milton Roy Spectronic 601 (Rochester, NY) spectrophotometer. At each buffer pH, a benzoic-acid standard curve was established with at least four sample points (measured in duplicate) which fell in the linear range (OD280 < 1.2). 3.6 Molecular Mechanics Calculations Molecular mechanics calculations were performed with the program MOMEC (97) (Chemische Verfahrens- & Software-entwicklung Heidelberg, Germany). MOMEC accepts input files created by HyperChem®, a molecular modelling program developed by Hypercube Inc. (Waterloo, ON). Both programs were executed under Windows 95 on an IBM compatible Pentium 120 MHz computer with 32 Mbytes of RAM. MOMEC changes the force field parameters used by HyperChem® to allow calculation of transition-metal containing complexes. Occasionally, MOMEC was not able to find the minimum energy configuration for a complex structure because the initial complex structure was too far from equilibrium. In such instances, the optimization was restarted after the initial complex structure was altered. This procedure was also used to ensure that the equilibrium structure corresponded to a 113 global energy minimum. Further information about the programs is provided in the MOMEC user's guide and the HyperChem® manuals. 3.7 P a r t i t i o n E x p e r i m e n t s All partition experiments were performed at a room temperature of ca. 25 °C. Partition coefficients for enantiomers were determined from a mass balance and measurements of the aqueous phase concentration using HPLC. Partition coefficients were determined for each enantiomer over a range of different solution conditions, e.g., pH, concentration. 3.7.1 Copper Par t i t ion ing The amount of base or copper solution added was varied to achieve different copper distributions between the two phases. A defined volume of the ligand-containing organic solution was injected into a 2 ml Eppendorf tube using a 2.5 ml Hamilton syringe. A defined volume of copper-nitrate solution (stock) was then added. The organic phase instantaneously changed colour from transparent to a deep blue, indicating a fast complexation reaction. The Eppendorf tube was vortexed and equilibrated for ca. 5 minutes. Defined amounts of 0.1 M base (KOH) and 0.1 M background electrolyte solution (KN03) were then added to the two-phase system. The sample was vortexed and mixed with a mechanical rotator for ca. 30 minutes to equilibrate. Afterwards, the tube was centrifuged to accelerate phase separation. The organic and aqueous phases were then carefully removed with an pippetor and analyzed. The pH of the aqueous phase and the copper concentration in the aqueous and organic phases were measured. 114 The equilibrium partitioning reaction of copper ions can be written as follows: 2 LiH o r g + Cua +; L Li 2 Cu o r g + 2 H ; + . (3.6) which shows that for every copper ion partitioned into the organic phase, two protons are released into the aqueous phase. The equilibrium formation constant for the above reaction is defined as follows: _ [H]2 [Li2Cu] P [LiH] 2[Cu]' { } where charges and phase indices are omitted. The partition coefficient of copper is expressed as the ratio of total copper concentration in the organic phase (yCu) to that in the aqueous phase (xCa), i.e., X C u [Cu] • At low pH values, which is the preferred operating range, the total copper concentration in the aqueous phase is essentially equal to the free-copper concentration (i. e., [Cu ]^) in that phase. Substituting equation 3.7 into equation 3.8 yields after some algebraic modifications: log(PCu) = log(p) + 2(log[LiH]+pH) . (3.9) The equilibrium concentration of ligand (i.e., [LiH]) can be calculated from a mass balance, i.e., [LiH] F o r g =[LiHf V°rs - 2 [Li2Cu] V0T& = [LiH]"" Vor& - 2 [Cu]org V0Tg, (3.10) 115 where [LiH]'"' is the initial uncomplexed ligand concentration present in the organic phase, and [Li2Cu] is binary copper-ligand complex concentration, which is equal to the equilibrium copper concentration in the organic phase, i.e., [Cujor8. The equilibrium formation constant P for the copper-ligand complex is then calculated from the experimental data by plotting log10[LiH] + pH versus log,aPcu (cf, equation 3.9). A linear regression on the data will yield a slope of 2 and a y-intercept of log,o(P). 3.7.2 Amino-Acid Partitioning The preparation of two-phase samples for amino-acid partition-coefficient measurements was similar to that described for copper partitioning. A defined amount of an enantiopure amino acid (stock solution, 1= 0.1 M) was added with the copper solution to the ligand-containing organic phase. After a defined amount of base and background electrolyte were added, the solution was equilibrated for ca. 1 hour under constant mixing. The amino-acid concentration and solution pH were measured after the equilibrium aqueous phase was recovered. The amino-acid concentration in the organic phase was calculated from the aqueous phase concentration using an overall mass balance. Ternary equilibrium formation constants for the L- and D-amino acids in the organic solution were then regressed to the two-phase multiple-chemical-equilibria model described in section 2.3.2 (cf, equations 2.51). 116 3.8 P o t e n t i o m e t r i c T i t r a t i o n s Potentiometric titrations were performed with a Schott Titronic Tl 10 automatic titrator (Schott Instruments, Germany). The titration vessel was water jacketed and maintained at 25.0 °C (±0.1) with a recirculating constant-temperature water bath (Julabo, Germany). Constant-speed magnetic stirring was applied throughout the experiments. Carbon-dioxide-free nitrogen gas was continuously sparged through a saturated 0.1 M KN0 3 solution and then passed through the headspace of the titration vessel to prevent carbonate formation. Aliquots of the base titrant solution were delivered into the titration vessel by a Schott TA01 automatic burette with a stroke capacity of 1.0 ml and an accuracy of 2.0 ul. pH electrode N 2 stream • 1 3 stirrer A Computer control burette O . I M K N O 3 water jacket analyte solution recirculation bath Figure 3.3: Setup of the potentiometric titration system. Potential readings were measured by a Metrohm micro-combination pH glass electrode (Brinkmannn Instruments Ltd., Mississauga, ON), which combines a glass indicator electrode and a reference electrode in the same shaft. An IBM-compatible 117 computer controlled the titration procedure (i.e., titrant additions and electrode equilibrations) as well as recorded the electrode-potential readings and titrant additions by running the Schott TR600 titration software (cf, Figure 3.3). 3.8.1 Electrode Calibration Electrode calibrations were carried out daily to determine the standard-electrode potential (E°). An acid stock solution was prepared by adding KN0 3 as background electrolyte into a standard 10 mM HN0 3 solution such that the solution had an ionic strength of 0.1 M. The electrode was calibrated by titrating 5.000 ml of this HNO3 solution with a standard 0.1 M KOH solution. The titration data were analyzed by the nonlinear regression program Chemeq. A listing of the FORTRAN source code (Chemeq) is given in the Appendix. Chemeq was used to determine E° as well as the initial total proton concentration in the vessel. Electrode calibration was also carried out to obtain the standard electrode potential in mixed water/methanol solutions. In this case, methanol was added to the acid and base stock solutions to ensure a constant methanol concentration during the titration. When a new 0.1 M KOH base stock solution was prepared, the concentration was tested by titrating against a potassium hydrogen phthalate (KHP) primary standard. A 5 ml solution of 10 mM KHP (I = 0.1 M) was titrated with the new base-stock solution. The titration data were regressed with Chemeq to obtain the base concentration. For aqueous stock solutions, the calculated base concentration was always very close to the value given by the supplier (error < 0.1%). The electrode was periodically cleaned by soaking it in 0.1 M nitric-acid solution for two minutes to dissolve precipitates formed on the electrode membrane. In addition, the 118 electrode was regenerated whenever necessary by dipping it in a cleaner solution (Radiometer Copenhagen Renovo-X, distributed by Bach-Simpson Ltd., London, ON) for ten minutes, then into acidic and basic buffer solutions (pH = 2.0 and 10.0) for two minutes each. 3.8.2 Titration Procedure All titrations were performed at a constant ionic strength of 0.100 M, using KNO3 as background electrolyte. The concentrations of amino acids and ligands in the samples were determined by gravimetric analysis, and the concentrations of HN0 3 and Cu(N03)2 were determined from the standardized stock solutions. For amino-acid titration experiments, samples were prepared by adding solid amino acid and standard HNO3 in nanopure water such that the concentrations of HNO3 and amino acid were ca. 10 mM. Appropriate amounts of K N 0 3 were added to achieve a total ionic strength (I) of 0.100 M. For binary complex titrations, solutions containing ca. 10 mM amino acid, 10 mM HNO3 and 5 mM Cu(N03)2 were prepared (i.e., [amino acid] : [Cu] = 2:1). By applying the law of error propagation (Andraos, 1996) the maximum error in the concentration was estimated to be less than ±1%. For ternary complex titrations, equimolar solutions of ca. 10 mM ligand, amino acid, HNO3 and Cu(N03)2 were used. For non-aqueous titrations, HPLC-grade methanol was added to the sample solutions to achieve the desired concentrations. A defined titrand volume (2.000 or 5.000 ml) was added into the titration vessel using a volumetric pipette. The pH electrode was carefully inserted into the sample and equilibrated until the electrode potential for 2-3 consecutive readings deviated less than 0.1 mV. The base injection tip was carefully inserted into the vessel to ensure the absence of 119 gas bubbles in the tubing. The presence of a gas bubble will show up as a discontinuity in the titration data, and hence these data cannot be used. The Schott TR600 computer titration program recorded the titration data (electrode potential and base volume), and controlled the addition of base. The titration protocol was set up such that the titration was initiated after the standard deviation from 10 consecutive electrode readings was less than ±0.1 mV. During the electrode potential readings, the magnetic stirrer was shut off. Afterwards, a new base solution was added and the solution stirred for 1-2 minute in order to equilibrate and mix the solution. This procedure was repeated until a defined solution pH was reached or a precipitate was noticed. Copper-complex precipitations can occur at the base injection tip where locally high base concentrations exist. Depending on the system investigated, the titration pH ranged from 2 to 10. In general, the added base aliquots were defined to ensure ca. 30-50 electrode-potential measurements during a titration experiment. 3.8.3 Titration-Data Analysis Equilibrium formation constants were obtained sequentially for every investigated system. First, the protonation constants for each amino acid were determined. These constants were combined with a second set of titrations to determine binary amino-acid/copper equilibrium formation constants. Finally, the protonation and binary equilibrium formation constants for two enantiomers were combined with a third set of titrations to determine the mixed (ternary) equilibrium formation constants. The data for each titration were analyzed by the program Chemeq. Total concentrations of the components were measured gravimetrically. For each system 120 investigated, multiple titrations (in general, 5-8) were performed to ensure reproducibility. The set of titration data for each system were then combined and regressed by Chemeq to get a best fit value of the equilibrium formation constants (i.e., P) as the final result. 3.9 Chiral Column System Chiral ligand-exchange chromatography studies were performed on a modified reverse-phase column (BetaBasic-18, KeyStone Scientific Inc.; Bellefonte, PA). The column contained porous particles of 5 pm diameter, packed into a stainless steel shell of length L = 150 mm, and an inner diameter d\ = 4.6 mm. Prior to column modification, the overall column porosity (s) was measured by injecting a non-absorbing solute into the column and recording the elution profile. In measuring the overall bed porosity, it is assumed that the sample concentrations in the mobile phase and within the voids of the porous particles are identical. This assumption is reasonable, since the elution peak shapes were symmetric and very sharp, indicating that for the investigated flow rates, diffusional transport into the particle void space is not limiting. The manufacturer reported average-pore-size of 150 A is more than an order of magnitude larger than the size of a ternary amino-acid/copper complex (10 A) . Therefore, steric hindrances should not significantly effect solute transport. All experiments were performed at a volumetric buffer flow rate of 1.00 ml/min. The tubing between the auto sampler and the column creates a dead space, and thus a short lag time follows sample injection. In order to determine this dead volume of the HPLC injection system (Vjfj!fc), 1 pl of sample solution was injected into the system in the absence of the column. Sharp elution peaks were recorded after 0.20 ml or a lag time (^dead) of 0.20 min. 121 The void volume of the column was determined by injecting 2 pl of a non-adsorbing solute (2-propanol) and measuring the elution peak maximum. The void fraction (e) of the column was then calculated by dividing the elution volume (minus the dead volume) by the empty column volume. All column parameters are reported in Table 3.4. Amino-acid retention times (t"™) were also determined for different buffer conditions in the absence of the ligand. These values were used to correct the retention times on the activated (i. e., ligand containing) column. The corrected enantiomer elution time (^ ret) was then calculated from: Ket = flu ~ Kbs ~ 1'dead ' (3 • 1 1) where is the measured retention time on the ligand containing column. Table 3.4: HPLC and column properties. Parameter Value Units column-free dead volume 0.2 ml column porosity 0.714 -inner diameter 4.60 mm length 150 mm empty column volume 2.49 ml average bead size 5.00 (am average bead pore size 150 A 122 3.9.1 Chiral Column Preparation The /V-n-dodecyl-L-hydroxy-proline ligand was adsorbed on a BetaBasic-18 reverse-phase column by pumping a 5.9 mM solution (95% methanol and 5% water) through the column at a flow rate of 0.20 ml/min. The solvent absorbence at the column outlet was continuously measured until ligand breakthrough occurred. The average ligand concentration cL in the column was calculated from a solute mass balance, i. e.: where V is the interstitial column volume, Q is the volumetric flow rate, th is the breakthrough time, and cini is the initial concentration of ligand in the injected solution. By using this equation, it was assumed that ligand binding is instantaneous and uniform in the column. These assumptions appear valid since a sharp break-through confirmed the high affinity of the N-n-dodecyl-L-hydroxy-proline ligand for the hydrophobic C-18 residues on the column matrix. The concentration of cL was determined to be 12 mM. 123 CHAPTER IV 4 Equilibrium Formation Constants The multiple-chemical-equilibria model developed in section 2.3 requires equilibrium formation constants for every complex formed in solution. These protonation, binary and ternary copper equilibrium formation constants dictate ligand enantioselectivity and determine solute partition coefficients in a multi-phase system. Protonation constants of amino acids and equilibrium formation constants for binary amino-acid/copper and ternary amino-acid/copper/ligand complexes in aqueous solution and in mixed solvent were determined in this study by potentiometric titrations. The nonlinear (least-squares) multiple-chemical-equilibria program Chemeq, described in section 2.3.1, is applied to the regression of protonation and equilibrium formation constants from the experimental potential readings. Ternary equilibrium formation constants in organic-aqueous two-phase extraction systems are calculated from partition experiments using the Chemeq! program, described in section 2.3.2.2. The regressed data are then used to generate speciation plots, which are a convenient way to present chemical equilibria and phase equilibrium as a function of system variables such as pH. The reported equilibrium formation constants are always expressed as the logarithmic value to base ten (i.e., log10) and represent the simultaneous fitting results of multiple titration experiments. In particular, for systems where differences in the ternary equilibrium formation constants are small, 10 to 15 titrations were performed to achieve a high confidence in the reported values. The 95% confidence intervals are reported in round brackets after each equilibrium formation constant, and refer to the deviation of the last 124 reported figure. The subscripts associated with each beta value ((3) indicate the stoichiometric coefficients for the complex formed. It should be noted that a negative stoichiometric index for the proton (in the aqueous phase) specifies a hydroxy-ion in water, e.g.,H., = OH". 4.1 A q u e o u s P h a s e 4.1.1 Protonation Constants Before investigating new systems it was necessary to validate the experimental titration protocol and the multiple-chemical regression program Chemeq. Table 4.1 compares measured protonation constants with those reported in the literature for a range of analytes. It should be noted that the charges on each species are not shown in the tables for simplicity. 4.1.2 Binary Equilibrium Formation Constants Measured binary copper/amino-acid equilibrium formation constants are reported in Table 4.2 and Table 4.3. Where available, literature values are also shown to determine the accuracy of the experimental and regression protocols. In general, the measured values are in excellent agreement with literature. Equilibrium formation constants for several iw-copper amino-acid complexes show slightly reduced values in comparison to the published data. It is believed that these deviations are due to less accurate experimental systems and less sophisticated regression programs when these literature values were reported ca. 20 years ago. 125 Table 4.1: Amino-acid equilibrium protonation constants in water (7=0.1 M, 25 °C). System Logio Literature this work OH, water P-io 13.74 -H, hydroxy-proline (HyPro) Pn 9.47 9.46(2) P21 11.27 11.28(2) H, proline (Pro) Pn 10.47 10.50(2) P21 12.37 12.38(2) H, Tmethyl-histidine (MHis) Pn 9.16t 9.18(1) P21 15.031 15.04(1) P31 16.73f 16.73(2) H, phenylalanine (Phe) Pn 9.09 9.09(1) P21 11.26 11.24(1) H, leucine (Leu) Pn 9.59 9.61(1) P21 11.89 11.91(2) H, valine (Val) Pn 9.49 9.51(1) P21 11.75 11.83(1) H, asparagine (Asp) Pn 8.72 8.72(1) P21 10.87 10.83(1) H, acetate (Ac) Pn 4.56 4.56(1) H, methionine (Met) Pn 9.06 9.06(1) P21 11.16 11.24(1) H, dihydroxy- P.. 13.40 13.40(1) phenylalanine (DOPA) P21 23.21 23.25(1) Psi 31.96 32.02(1) B41 34.16 34.22(1) * Smith and Martell (1989), * Remelli et al. (1994) 126 Table 4.2: Binary amino-acid/copper equilibrium formation constants in water (7=0.1 M, 25 °C). System Logio Literature this work H, HyPro, Cu Pon 8.38 8.46(1) P021 15.42 15.54(1) H, Pro, Cu Pon 8.83 8.84(1) P021 16.40 16.25(4) H, Val, Cu Pon 8.09 8.01(1) P021 14.90 14.76(1) H, Leu, Cu Pon 8.25 8.20(1) P021 15.20 15.09(1) H, Phe, Cu Pon 7.80 7.76(3) P021 14.70 14.52(4) H, Val, Cu Pon 8.09 8.01(1) P021 14.90 14.76(1) H, Asn, Cu Pon 7.83 7.81(1) P021 14.36 14.26(1) H, Met, Cu Pon 7.86 7.81(1) P021 14.60 14.37(1) H, Leu, Cu Pon 8.25 8.20(1) P021 15.20 15.09(1) H, Ac, Cu Pon 1.82 1.74(1) P021 2.80 -'Smith and Martell (1989) Table 4.3: Binary amino-acid/copper equilibrium formation constants in water (7=0 .1 M, 25 °C). System Logio Literature this work H, MHis, Cu P m 14.07f 14.15(2) Poii 10.22f 10.21(2) P221 27.10f 27.27(5) Pl21 23.87* 24.01(3) P021 18.38f 18.53(4) H, DOPA, Cu P211 30.74* 30.72(1) Pill - 23.96(.l) P011 - 19.66(1) P421 60.72* 60.58(1) P321 53.97* 53.97(2) P221 45.57* 45.39(2) Pl21 35.97* 35.77(2) P021 • 25.67* 25.55(2) ' Smith and Martell (1989), Remelli et al. (1994) 128 Figure 4.1 shows a speciation distribution for a binary phenylalanine (Phe)/copper mixture in aqueous solution at an ionic strength of 0.1 M and a temperature of 25 °C. At low pH values, the amino acid exists in two protonated forms (210 and 110). The presence of the positive charge greatly reduces the formation of copper amino-acid complexes. By increasing the equilibrium solution pH, the formation of copper amino-acid complexes is increasingly favoured. Initially, a complex involving one amino acid is formed (i.e., Oil). At higher pH values, the concentration of the to-copper complex (i.e., 021) increases and it ultimately becomes the dominant complex in solution. P H Figure 4.1: Calculated species distribution of the binary Phe copper complexes formed as a function of equilibrium pH. [Phe] = 10 mM, [Cu] = 5 mM (dashed lines: complexes involving a copper ion, solid lines: protonated amino acids, dotted line: free-copper concentration) (/= 0.1 M, 25 °C). In general, binary amino-acid/copper complexes are always formed at higher pH values. However, the detailed structure of the speciation diagram shown in Figure 4.1 129 depends on the amino acid equilibrium formation constants, which are specific for the analytes involved. Phenylalanine has two protonation sites. Analytes with additional protonation sites (e.g., His, DOPA) can form additional binary copper complexes, resulting in speciation distributions which are significantly more complex. 4.1.3 Ternary Equilibrium Formation Constants In the separation systems under consideration, chiral discrimination is achieved through differences in the energetics of the ternary complexes formed with the copper(II) ion and the chiral selector. These differences in energetics arise from subtle changes in the spatial geometry of the complex, which can lead to changes in either the enthalpy or entropy of complex formation (Borghesani etal., 1990). The interactions of the electron donating ligand atoms with the metal ion take place at precise angles and over well-defined distances. Densely packed solvent molecules (e.g., water), present at the outer coordination sphere of the metal ion, can mediate interactions through direct contact with the ligand atoms or via other solvent molecules (Davankov, 1980). Tables 4.4 - 4.7 report measured ternary equilibrium formation constants for several L- and D-amino acids binding with either L-hydroxy-proline (L-HyPro), L-proline (Pro), or L-methyl-histidine (L-MHis) ligand. The tables indicate the differences in the formation energies (8AG) of the homo-chiral and hetero-chiral ternary complexes, as well as the enantioselectivity (values in squared brackets). 130 Table 4.4: Ternary amino-acid/copper equilibrium formation constants, differences in the formation energies (5AG), and enantioselectivities containing L-hydroxy-proline (L-HyPro) in water (/= 0.1 M, 25 °C). System Logio Log10p Log10p 5AG L D [J/mol] H, HyPro, Cu, Phe Pon l 15.59(1) 15.49(1) 571 [0.79]' H, HyPro, Cu, Leu Pom 15.73(1) 15.76(1) -171 [1.07]* H, HyPro, Cu, Val Pon l 15.61(1) 15.57(1) 228 [0.91]* H, HyPro, Cu, Pro Pom 16.34(1) 16.39(1) -285 [1.12]* H, HyPro, Cu, Asn Pom 15.26(1) 15.21(1) 285 [0.89]' H, HyPro, Cu, DOPA Pun 31.88(3) 32.08(3) P2111 38.86(1) 38.54(3) -1827 [2.09]* * enantioselectivity Table 4.5: Ternary amino-acid/copper equilibrium formation constants, differences in the formation energies (8AG), and enantioselectivities containing L-proline (Pro) in water (1= 0.1 M, 25 °C). System Logio Log10p Log.op SAG L D [J/mol] H, Pro, Cu, Phe Pom 15.87(1) 15.80(1) 400 [0.85]* H, Pro, Cu, Leu Pom 16.12(1) 16.10(1) 114 [0.95]* enantioselectivity 131 Table 4.6: Proton-corrected ternary amino-acid/copper equilibrium formation constants for the Pro and L-HyPro ligand in water (7= 0.1 M, 25 °C). System LogI0p Log10p 8AG L D [J/mol] Pro, Cu, Phe -3.72 -3.79 400 [0.85]* Pro, Cu, Leu -3.99 -4.01 114 [0.95]* HyPro, Cu, Phe -2.96 -3.06 571 [0.79]* HyPro, Cu, Leu -3.34 -3.31 -171 [1.07]* enantioselectivity Table 4.7: Ternary amino-acid/copper equilibrium formation constants, differences in the formation energies (5AG), and enantioselectivities containing yVx-methyl-L-histidine (MHis) in water (7=0.1 M, 25 °C). System Logio Log10p LogloP SAG L D [J/mol] H, MHis, Cu, Phe Pom 17.63(1) 17.79(1) -913 [1.45]* Pll.l 21.37(1) 21.34(1) H, MHis, Cu, Leu Pom 18.00(1) 18.03(1) 171 [1.08]* Pun 21.88(1) 21.98(1) H, MHis, Cu, Pro Pom 18.57(1) 18.56(1) -57 [0.98]* Pi i n 22.72(2) 22.68(2) enantioselectivity 132 The enantioselectivity of the L-HyPro ligand is highest for Phe and DOPA (cf., Table 4.4). Negative 8AG values indicate a higher stability of the homo-chiral complex. The results for the DOPA and Phe systems show that the presence of the hydroxy group on L-HyPro tends to increase chiral discrimination, particularly for more hydrophobic solutes such as Phe and DOPA. This suggests that the hydroxy group participates favourably in the homo-chiral complex and that size and chemistry of the side-chain play a central role in the enantiomeric discrimination. 2 3 4 5 6 7 8 P H Figure 4.2: Calculated species distribution of binary and ternary Phe, copper, L-HyPro complexes formed as a function of pH. [Phe] = 10 mM, [Cu] = 10 mM, [HyPro] = 10 mM (dashed lines: ternary complex for the ternary L- and D-Phe complexes) (/= 0.1 M, 25 °C). In Figure 4.2 a calculated speciation diagram of a ternary phenylalanine (Phe)/copper/ligand system is shown in the presence of copper ions. For clarity, only the complexes involving copper ions are plotted. The system includes a racemic Phe mixture 133 complexing with the L-hydroxy-proline ligand (L-HyPro). Due to the presence of both L-and D-enantiomers, the number of binary complexes has been doubled, making speciation in the system rather complex. To simplify the presentation, only binary complexes with L-Phe are shown. The homo-chiral ternary complex (0111) containing L-Phe and L-HyPro is formed in large quantities at higher pH values. The plot also shows the concentration of the hetero-chiral ternary complex, indicating the higher affinity of L-Phe to L-HyPro. . The stereoselectivity values of the L-HyPro ligand for Leu and Val amino acids are fairly low in the aqueous system. Although the difference in the ternary formation energies (SAG) is small, these structurally related amino acids show opposite stereoselectivity for the L-HyPro ligand (cf., Table 4.4). This suggests that in the presence of water molecules the short alkyl side-chains participate in the stereoselective discrimination by altering the packing of water molecules in the first solvation shell in subtle and different ways. The chiral discrimination of the Pro ligand is reported in Table 4.5. The absence of the hydroxy group on the ligand significantly influences the strength of the formed complexes and the stereoselectivity. For example, the 8AG for Phe is reduced by 171 J/mol, indicating a strong reduction in enantioselectivity. In some cases the change is more striking; Leu undergoes an inversion as well as a reduction in enantioselectivity. The absence of the hydroxy group on the Pro ligand also results in lower equilibrium formation constants and hence reduced ternary complex concentrations. This is not directly evident from the data reported in Table 4.4 and Table 4.5 since the formation of ternary complexes depends not only on ternary equilibrium formation constants, which are defined with respect to the free species concentrations (cf, section 1.6), but also on the amino-acid protonation constants. At pH values of 3-8, most amino acids are present in their 134 zwitterionic forms. Therefore, the true tendency for a given ternary complex to form is determined by subtracting the amino-acid protonation constant (pn in Table 4.1) from the ternary equilibrium formation constant. The corrected values shown in Table 4.6 indicate that the L-HyPro ligand has a higher affinity for both Phe and Leu enantiomers as well as a higher enantioselectivity. These findings are in agreement with retention times reported by Davankov and Zolotarev (1978a, 1978b), and Giibitz etal. (1981) for enantioseparations utilizing these ligands attached to stationary chromatographic phases. The ternary equilibrium formation constants for the JVT-methyl-L-histidine (MHis) ligand (cf., Table 4.7) agree well with limited data reported by Remelli etal. (1994). The ligand shows good stereoselectivity towards Phe, but lower selectivity to Leu and nearly none to Pro. Because of its additional protonation site, the MHis ligand forms two different ternary complexes with amino-acid enantiomers, i.e., (0111) and (1111). The fully protonated complex (1111), however, is present only at very low concentrations and does not significantly influence chiral selectivity. Therefore, 8AG and stereoselectivity values reported in Table 4.7 are those for the unprotonated (0111) complexes only. Unlike proline, the histidine ligand does not show a reversal in stereoselectivity for Leu and Val. This may be attributed to the presence of the aromatic imidazole group which enables histidine to coordinate like a tridentate ligand, resulting in higher thermodynamic stabilities (Laurie, 1987). 135 4.2 M i x e d S o l v e n t S y s t e m Water molecules can participate as electron donors in copper complexation reactions. As a result, reduction of water activity through the introduction of a non-aqueous cosolvent can have a strong effect on complex stabilities and possibly on enantioselectivities. Titrations were performed in a mixed-solvent environment by successively replacing water with methanol (MeOH). Protonation constants and binary and ternary equilibrium formation constants were measured at methanol concentrations up to 40% (v/v). Higher methanol concentrations (> 40%) were not possible due to decreased amino-acid solubilities resulting in precipitation of the complexes. 4.2.1 Protonation Constants Measured protonation constants for several analytes are shown in Table 4.8 for three methanol concentrations. The shifts in the protonation constants are plotted in Figure 4.3. One can notice that the logBn values for the first protonation site do not change significantly with increased methanol concentration. However, the second protonation constants (P21) increase with % methanol at a nearly constant rate for all analytes studied. Similar results were reported by Azab etal. (1994) for amino-acid protonation constants in mixed-solvent systems. 136 Table 4.8: Solute protonation constants in water/methanol (MeOH) mixtures (7=0.1 M, 25 °C). System Logio 0% 20% 40% MeOH MeOH MeOH H, HyPro Pn 9.46(2) 9.47(1) 9.45(1) P21 11.28(2) 11.49(1) 11.71(1) H, Phe Pn 9.09(1) 9.03(1) 8.97(1) 11.24(1) 11.46(1) 11.66(1) H, Leu Pn 9.61(1) 9.53(1) 9.48(1) P21 11.91(1) 12.13(1) 12.35(1) H, Ac Pn 4.56(1) 4.79(1) -An increase in methanol concentration lowers the dielectric constant of the solvent, thereby increasing the electrostatic forces which contribute to formation of complexes with copper ions. Free protons (H+) become less soluble in the presence of organic modifier, due to unfavourable hydrogen-ion/co-solvent interactions, resulting in higher proton activities which further increase the P21 equilibrium formation constant (Azab et al, 1995). The dependence of p2i on solvent composition can be further understood by considering the charge distribution on the amino-acid molecules. A neutral amino-acid having a non-protonatable side-chain (/'. e., the 11 species) exists in aqueous solution in the zwitterionic form: the number of charges on the molecule is therefore twice that when the molecule is fully protonated (i.e., the 21 species) (Harris, 1987; Lehninger, 1993). A decrease in solvent polarity by the addition of methanol will result in a shift in the equilibrium from the 11 complex to the 21 complex, or to the uncharged R-CH-COOH-NH2 137 moiety, since the concomitant reduction in charge is energetically favourable in the more hydrophobic environment (Burgess, 1988). Methanol Concentration [%] Figure 4.3: Change in amino-acid protonation constants with solvent composition. T : Phe, • : Leu, O: L-HyPro (/ =0.1 M, 25 °C). Subscript aq refers to the cosolvent-free system (i.e., pure aqueous phase). 4.2.2 Binary Equilibrium Formation Constants Equilibrium formation constants for binary copper/analyte complexes in mixed solvents are presented in Table 4.9. As shown in Figure 4.4, the values of both equilibrium formation constants log10B011 and loglop02i increase linearly with % methanol for each analyte studied. The increase in the 6w-complexes (i.e., 021) is nearly twice that of the mono complexes (i.e., Oil), indicating that the effect is additive on a per analyte basis. 138 Table 4.9: Binary amino acid/copper complex equilibrium formation constants in water/methanol (MeOH) mixtures (7= 0.1 M, 25 °C). System Logio 0% 20% 40% MeOH MeOH MeOH H, HyPro, Cu Pon 8.46(1) 8.72(1) 9.09(1) Po21 15.54(1) 16.09(1) 16.77(1) H, Phe, Cu Pon 7.76(1) 8.11(1) 8.45(1) P021 14.52(4) 15.23(1) 15.82(1) H, Leu, Cu Pon 8.20(1) 8.46(1) 8.82(1) Po21 15.09(1) 15.65(1) 16.43(1) H, Ac, Cu Pon 1.74(1) 1.96(1) 1.50-. cr ro 1.25-c a o T— 1.00-CD O • _ l 0.75-c a o 0.50-D) • O _ ! 0.25-0.00-10 20 30 40 Methanol Concentration [%] Figure 4.4: Change in binary analyte/copper equilibrium formation constants with solvent composition. T : Phe, • : Leu, O: L-HyPro (I = 0.1 M, 25 °C). Subscript aq refers to the cosolvent-free system (i.e., pure aqueous phase). 139 Increased equilibrium formation constants in methanol solutions were also reported for 6/s-amino-acid complexes by Davankov etal. (1975) and Malini-Balakrishnan (1985). A reduction in the dielectric constant of the solvent (Bates and Robinson, 1964) favours the formation of the electroneutral complex. In addition, methanol binding at the two apical copper-ion coordination sites can result in increased complex hydrophobicity (Davankov etal., 1975). Therefore, increased methanol concentrations favour binary amino-acid complex formation, resulting in higher equilibrium formation constants. 4.2.3 Ternary Equilibrium Formation Constants Ternary equilibrium formation constants for homo-chiral and hetero-chiral complexes utilizing the L-hydroxy-proline ligand are reported in Table 4.10 as a function of methanol concentration. The results were used to calculate differences in the formation energies of the two enantiomeric complexes as well as enantioselectivities (cf, Table 4.11). Figure 4.5 shows that the equilibrium formation constants of the ternary homo-chiral complexes increase nearly linearly up to 40% methanol. The enantioselectivities for the ternary complexes (cf, Figure 4.5) indicate that the Phe complex is less affected by the increased methanol concentrations than the Leu complex. In particular, an inversion in enantioselectivity is observed at a methanol concentration of ca. 20% for leucine. These results agree with Davankov etal. (1975), who reported that solvent conditions influence the magnitude of the selectivity, as well as the sign. 140 Table 4.10: Ternary amino-acid/copper equilibrium formation constants containing L-hydroxy-proline (L-HyPro) in water/methanol (MeOH) mixtures (7=0.1 M, 25 °C). System Logio 0% 20% 40% MeOH MeOH MeOH H, HyPro, Cu, L-Leu Pom 15.73(1) 16.22(1) 16.65(1) H, HyPro, Cu, D-Leu Pom 15.76(1) 16.22(1) 16.62(1) H, HyPro, Cu, L-Phe Pom 15.59(1) 16.13(1) 16.70(1) H, HyPro, Cu, D-Phe Pom 15.49(4) 16.02(1) 16.61(1) Table 4.11: Difference in formation energies (5AG) and enantioselectivities for ternary complexes containing L-hydroxy-proline (L-HyPro) in water/methanol mixtures (7=0.1 M, 25 °C). System 0% MeOH 20% MeOH 40% MeOH [J/mol] [J/mol] [J/mol] H, HyPro, Cu, Leu 5AG (a) -117 [1.07]' 0 [1.0]* 117 [0.93]* H, HyPro, Cu, Phe 5AG (a) 571 [0.79]* 628 [0.78]* 514 [0.81]* enantioselectivity 141 These results again point to the involvement of the side-chain in stabilizing ternary complex structures. The electron-rich phenyl-ring of Phe can participate in the complex at the apical copper coordination sites. Consequently, solvent participation in the complex is reduced, resulting in a weak dependence of the enantioselectivity on solvent composition. The side-chain of leucine enantiomers is too short and constrained to interact directly with the apical copper coordination sites. Therefore, methanol will compete with water molecules for these sites, resulting in different complex energies and steric hindrances. 2.00 I-1.00 CO I-0.75 r F H A C u . H y P r o , 0.50 4" 0.25 0.00 10 ~2D 30 40 Methanol Concentration [%] Figure 4.5: Change in the ternary amino-acid (A) equilibrium formation constants (homo-chiral) and selectivities for different solvent compositions. T : Phe, • : Leu (I = 0.1 M, 25 °C). Subscript aq refers to the cosolvent-free system (i.e., pure water). Subscript aq refers to the cosolvent-free system (i.e., pure aqueous phase). 142 4.3 O r g a n i c S o l v e n t s Equilibrium formation constants for ternary amino-acid complexes were also determined in a pure organic solvent (i.e., n-octanol). For this study, the chiral selector (L-HyPro) was made soluble in the organic phase by attaching a hydrophobic tail (alkyl chain) at the amino group. A solvent phase ratio (y) of unity, indicating identical organic and aqueous phase volumes, was used for all partition experiments. 4.3.1 B inary E q u i l i b r i u m Fo rma t ion Cons tan ts The equilibrium formation constant for the binary Z/w-A-dodecyl-L-hydroxy-proline/copper complex (i.e., Li2Cu) in the organic n-octanol phase was determined from partition-coefficient measurements (cf, section 3.7.1) by utilizing equation 3.9. A log,0p value of -3.11(1) (cf, Table 4.12) was found from a global fit of all experimental data (cf, Figure 4.6). Experimental measurements at pH values higher than 6 were omitted since precipitation of the copper complexes was observed. The L-hydroxy-proline ligand (L-HyPro) in the organic phase has a higher affinity to copper(II) ions than in the pure aqueous phase, where the log,0p equals -3.38 (cf, Table 4.12). In the aqueous phase, two binary copper/analyte complexes can be formed; whereas in the organic phase, only the bis-amino-acid complex exists. Therefore, one would expect the binary equilibrium formation constant in the organic phase to be higher. The absence of water molecules in the organic phase may further enhance the stability of the binary complex in the organic phase since the iw-complex is electroneutral. A species distribution plot of the total copper concentration in the aqueous and organic phases is shown in Figure 4.7. The plot also includes copper partition coefficients as 143 a function of the solution pH. The concentration of copper in the aqueous phase decreases sharply at a pH value of 2.5. At pH > 6, copper is partitioned quantitatively into the organic phase, indicating that the aqueous solution pH can be used to tune copper-ion partitioning and thus separation efficiency in a chiral separation system. o CD O 0.5 1.0 1.5 pH + log10[LiH] 2.0 Figure 4.6: Copper partitioning (A) in an n-octanol/water two-phase system containing A-dodecyl-L-hydroxy-proline (LiH) at various aqueous pH values, copper concentrations, and ligand concentrations. Solid line: model regression log10p = -3.11 (7aq = 0.1 M, 25 °C). 144 P H Figure 4.7: Copper concentrations (solid lines) and partition coefficient (dashed line) as a function of pH in an n-octanol/water two-phase system containing N-dodecyl-L-hydroxy-proline (LiH). Initial compound concentrations: LiH = 20.0 mM, Cu = 10.0 mM (a = 1.0,1 = 0.1 M, 25 °C). 4.3.2 Ternary Equilibrium Formation Constants Table 4.12 reports measured log10B values for ternary complexes in n-octanol at 25 °C containing copper(II) ions, the alkylated L-hydroxy-proline ligand, and an amino-acid enantiomer. In each case, the log10p value was regressed by fitting the two-phase chemical equilibria model Chemeq2 to experimental partition-coefficient data for the enantiomer over a range of pH values. The accuracy of the model fit was generally excellent, as illustrated in Figure 4.8 for partitioning of L-Phe and D-Phe, in Figure 4.9 for L-Leu and D-Leu, and in Figure 4.11 for L-Val and D-Val enantiomers. 145 Table 4.12: Measured binary and ternary equilibrium formation constants in the n-octanol phase containing N-dodecyl-L-hydroxy-proline (LiH) (7aq = 0.1 M, 25 °C). System log.op log10p 8AG L D [J/mol] 2 LiH + Cu » Li 2Cu + 2H -3.11 ** water -3.38 LiH + Cu + Phe » LiCuPhe + H 5.99(1) 6.20(1) -1198 (1.62)* water 6.13 6.03 571 (0.79) LiH + Cu + Leu LiCuLeu + H 6.01(1) 6.31(1) -1712(2.0)* water 6.27 6.30 -171 (1.07)* LiH + Cu +Val « LiCuVal + H 5.33(3) 5.71(1) -2170 (2.40)* water 6.15 6.11 228 (0.91)* 'enantioselectivity, ** L-HyPro without the alkyl tail Table 4.13: Corrected ternary equilibrium formation constants from Table 4.12 (I = 0.1 M, 25 °C). System logiop log10p L D LiH + Cu + HPhe <=> LiCuPhe + 2H -3.10 -2.90 water -2.96 -3.06 LiH + Cu + HLeu « LiCuLeu + 2H -3.60 -3.30 water -3.34 -3.31 LiH + Cu + HVal LiCuVal + 2H -4.19 -3.82 water -3.36 -3.40 146 r-;-, 1-50 c 1.25J Figure 4.8: Experimental values of (A) L- and (O) D-Phe partition coefficients and fitting results (solid lines) in an n-octanol/water two-phase system containing /V-dodecyl-L-HyPro (20.6 mM). Initial aqueous concentrations: D-Phe = 5.97, L-Phe = 5.95 mM, Cu = 20.6 mM (7aq = 0.1 M,25 °C). 1.50 Figure 4.9: Experimental values of (A) L- and (O) D-Leu partition coefficients and fitting results (solid lines) in an n-octanol/water two-phase system containing TV-dodecyl-L-HyPro (16.3 mM). Initial aqueous concentrations: D-Leu = 4.84 mM, L-Leu = 4.84 mM, Cu = 10.3 mM(/„ = 0.1 M, 25 °C). 147 1.50 c CD "O CD O O o cc Q_ Figure 4.10: Experimental values of (A) L- and (O) D-Val partition coefficients and fitting results (solid lines) in an n-octanol/water two-phase system containing TV-octyl-L-HyPro (25.58 mM). Initial aqueous concentrations: L-Val = 3.75 mM and D-Val = 3.75 mM, Cu = 12.68 mM (/aq = 0.1 M, 25 °C). Table 4.12 also reports differences in equilibrium formation energies 5AG of ternary homo- and hetero-chiral complexes in water and in the n-octanol organic phase. Data reported for the aqueous phase are for a water-soluble analogue (2S-4R, 4-hydroxy-2-pyrrolidine-carboxylic acid) of the iV-alkyl-L-hydroxy-proline ligand. Relative to that in water, the homo-chiral ternary complex formed with L-Phe is significantly destabilized in n-octanol, while the hetero-chiral complex is stabilized. Thus, solvent effects appear to make a substantial contribution to complex energetics, either through direct participation in the complex or by modifying the activities of the complex-forming components. The latter solvent contribution is reflected, in part, by the observed shift in the log10p value for the binary complex formed between copper(II) ions and the L-hydroxy-proline ligand, which indicates that the presence of n-octanol (in place of water) strongly stabilizes the complex. 148 More energy is therefore required to liberate ligand molecules from to-binary complexes for formation of ternary complexes. As a result, the transfer of a ternary complex from water to n-octanol is energetically unfavourable, as observed for all three homo-chiral complexes. A more accurate gauge of the strength of each ternary complex relative to the binary copper/L-hydroxy-proline complex can be obtained by subtracting the protonation constant for the carboxylic group of the amino acid from the log10p value for the ternary complex. This normalizes the reaction stoichiometry for all complexes such that two protons are released during complex formation. As shown in Table 4.13, the converted equilibrium formation constants for the ternary complexes are similar to those for the binary copper/L-hydroxy-proline-ligand complex, supporting the argument that the increased stability of the binary complex in n-octanol leads to a decrease in stability of the homo-chiral ternary complex. Table 4.12 shows that in certain cases (e.g., Phe), hetero-chiral complexes are more stable in the n-octanol phase, indicating that the increased energetic penalty of breaking the binary complex in the n-octanol phase can be overcompensated if formation of the ternary complex is sufficiently favourable. This suggests that the nature of solvent effects, particularly those due to direct participation in the ternary complex, depends on the geometry of the complex. The binding of water molecules in the apical coordination sites appears to stabilize both ternary complexes, but reduces, often greatly, chiral discrimination. A consequence of this is the tendency for the absolute value of SAG to be much greater in non-aqueous systems. For example, the absolute value of SAG increases by a factor of two for Phe, and a factor of ten for Leu and Val. This can result in a dramatic improvement in the 149 enantioselectivity of the L-hydroxy-proline ligand (cf., Table 4.12), and therefore a reduction in the number of equilibrium stages required for separation. Table 4.14 lists hydrophobicity values (n-values) of several amino-acid side-chains based on the n-octanol/water partitioning system (Tayar El etal., 1992). Hydrophobicity increases with increasing rc-values. Thus, of the three amino acids studied, Phe is the most hydrophobic, followed by Leu and Val. Comparison of this hydrophobicity index with the measured ternary equilibrium formation constants shows a direct correlation between the stability of the ternary complex in the organic phase and the side-chain hydrophobicity (cf, Table 4.14). Solubilities of ternary complexes involving hydrophobic amino acids are therefore enhanced in n-octanol. As a result, the concentrations of both L- and D-enantiomers in the organic phase tend to be high, causing |8AG I to be relatively low (cf, Table 4.14). Table 4.14: Amino-acid side-chain hydrophobicity (rr) values (Tayar El et al., 1992), corrected ternary equilibrium formation constants, and Gibbs free energy values SAG for the A-alkyl-L-hydroxy-proline ligand in the n-octanol phase (I- 0.1 M, 25 °C). amino acid 71 logioP log10p 5AG L D [J/mol] Phe 1.56 -3.10 -2.90 -1198 Leu 1.28 -3.60 -3.30 -1712 Val 0.71 -4.19 -3.82 -2170 150 In addition to its hydrophobic nature, n-octanol differs from water as a solvent by its bulky asymmetric structure. As a result, dense packing of n-octanol molecules around a binary or ternary chiral complex is more difficult, particularly when the energetic constraint is imposed that the hydroxy oxygens of two octyl chains be correctly positioned at the distal coordination sites of the copper(II) ion. Therefore, steric effects may also make significant contributions to chiral recognition, and to observed changes in enantioselectivity, in the n-octanol system relative to the aqueous phase. In total, changes in solvent-packing effects, solvent and side-chain hydrophobicity, and the unique energetics of water binding at the apical copper(II) coordination sites, contribute to the often dramatic changes in enantioselectivity observed in Table 4.12. For example, the chiral recognition of L-hydroxy-proline ligand for Phe enantiomers is inverted in the organic phase: the hetero-chiral complex is strongly favoured in the n-octanol phase, while the homo-chiral complex is more stable in the aqueous phase. To test the accuracy of the model, the regressed equilibrium formation constants were used to predict partition coefficients of amino acids in two-phase systems where the concentrations of the analytes, particularly copper(II) and the ligand, differ from those used for parameter regression. For example, Figure 4.11 to Figure 4.14 compare predicted copper(II) and Phe partition coefficients in n-octanol/water two-phase systems at 25 °C with experimental values as a function of system pH. Up to the solubility limit of the complex (near pH 4.5), which is not accounted for in the model, the calculations are in excellent agreement with experimental measurements. Similar model-prediction results are shown in Figure 4.15 and Figure 4.16 for Leu and Val enantiomers, respectively. 151 A species distribution plot for L-Phe in an n-octanol/water two-phase system is presented in Figure 4.17. The graph shows only complexes involving copper ions. In addition, the pH dependence of the ternary D-Phe enantiomer complex in the organic (org) phase is plotted (other D-enantiomer complexes are not shown). One can notice that a large number of complexes are formed in varying concentrations over the plotted pH range. At higher pH values, the ternary amino-acid ligand complex increases in concentration in the organic phase. Substantial amounts of binary amino-acid/copper complexes are formed in the aqueous phase at all equilibrium pH values. Previous simplified models that neglect the speciation in the aqueous and organic phases insufficiently describe this multiple-chemical equilibria and partitioning. For example, the model of Takeuchi etal. (1984b) and that by Pickering and Chaudhuri (1997a) were developed for low amino-acid ligand ratios, and therefore neglect binary complexation reactions in the aqueous phase. These models are not capable of describing the dependence of partitioning on species concentrations as well as equilibrium pH values. Later, it will be shown that increased copper/amino-acid complexation reactions at higher amino-acid concentrations are, in part, responsible for the model deviations published by Pickering and Chaudhuri (1997a). In addition, under such low amino-acid ligand ratios, enantioseparations are not practical. If optimum operating and separation conditions are required, the model must include all speciation reactions that can occur in both the aqueous and organic phases. 152 1.50 Figure 4.11: Experimental values of (A) L-Phe and (•) copper partition coefficients and model predictions (solid and dashed lines) in an n-octanol/water two-phase system containing iV-dodecyl-L-HyPro (20.0 mM). Initial aqueous concentrations: L-Phe = 3.14 mM, Cu = 14.73 mM (/„ = 0.1 M, 25 °C). Figure 4.12: Experimental values of (A) L-Phe, (O) D-Phe and (•,•) copper partition coefficients and model predictions (solid and dashed lines) in an n-octanol/water two-phase system containing iV-dodecyl-L-HyPro (20.0 mM). Initial aqueous concentrations: L-Phe = 3.14 mM and D-Phe = 3.14 mM, Cu = 14.73 mM (/„ = 0.1 M, 25 °C). 153 1.50 Figure 4.13: Experimental values of (A) L-Phe and (•) copper partition coefficients and model predictions (solid and dashed lines) in an n-octanol/water two-phase system containing iV-dodecyl-L-HyPro (20.0 mM). Initial aqueous concentrations: L-Phe = 2.86 mM, Cu = 14.66 mM (7aq = 0.1 M, 25 °C). _ 1.50 c CD "O i t CD O o c o CO Q_ 1.25-1.00-0.75-0.50-0.25-0.00-Cu = 7.33 mM Figure 4.14: Experimental values of L-Phe coefficients (A,A) and model predictions (solid lines) in an n-octanol/water two-phase system containing /V-dodecyl-L-HyPro (20.0 mM). Initial aqueous concentrations: L-Phe = 2.86 mM, A: Cu = 7.33 mM, A : Cu = 4.19 mM (7aq = 0.1 M, 25 °C). 154 Figure 4.15: Experimental values of (A) L- and (O) D-Leu partition coefficients and model predictions (solid lines) in an n-octanol/water two-phase system containing 7V-dodecyl-L-HyPro (16.3 mM). Initial aqueous concentrations: D-Val = 4.84 mM, L-Val = 4.84 mM, Cu = 10.3 mM (/„ = 0.1 M, 25 °C). Z7 1.25J 2 3 4 5 6 P H Figure 4.16: Experimental values of (A) L- and (O) D-Val partition coefficients and model predictions (solid lines) in an n-octanol/water two-phase containing A-octyl-L-HyPro (25.58 mM). Initial aqueous concentrations: D-Val = 3. 93 mM, L-Val = 3. 93 mM, Cu = 12.68 mM(7aq = 0.1 M, 25 °C). 155 p H Figure 4.17: Calculated species distribution in an n-octanol/water two-phase system containing L-HyPro (10.0 mM) (only complexes with Cu + + are shown). Initial aqueous phase concentrations: [Cu] = 10.0 mM, [Phe] = 10.0 mM (/= 0.1 M, 25 °C). 4 .3 .3 Solvent and Ligand Effects on the Equilibrium Formation Constants The effect of solvent chemistry on the equilibrium formation constant of the binary copper-ligand complex was studied by changing the n-octanol solvent to n-hexanol, i.e., reducing the solvent hydrophobicity and size. The measured copper partitioning data are plotted in Figure 4.18 along with the fitted equilibrium formation constant logi06 of -3.15(7). This value is close to the previously determined value of -3.11 in n-octanol and indicates that the reduced solvent hydrophobicity does not significantly effect the binary/ligand copper equilibrium formation constant. Attempts to use other organic solvents to measure the copper partition data in a two-phase system were not successful. The modified ligand was insoluble in chloroform, ethylether, toluene, and butyronitrile. 156 Pickering and Chaudhuri (1997a) determined a higher equilibrium formation constant for the binary to-copper/L-hydroxy-proline ligand complex in a hexanol/dodecane 50/50% (vv) solvent mixture (logi0(3 = -2.51). This result is somewhat surprising since one would expect a reduced value based on the data shown in Table 4.13 and the increased hydrophobicity of the solvent mixture. However, it should be noted that the authors measured partitioning only at limited solute concentrations. In addition, at higher pH values and copper-ion concentrations, the data showed strong deviations from the model regression, indicating the potential of a poor parameter estimate. pH + log10[LiH] Figure 4.18: Experimental copper partitioning data (O) in a two-phase system in the presence of the ./V-octyl- L-hydroxy-proline ligand (LiH) in n-hexanol at various aqueous pH values, copper, and ligand concentrations. Solid line: model regression log,0p of -3.15(7) (7aq = 0.1 M, 25 °C). Replacement of the dodecyl chain on the L-hydroxy-proline ligand to an octyl chain does not change the equilibrium formation constant in the n-octanol phase for the binary ligand-copper complex. The copper-partitioning data shown in Figure 4.19 indicate that the 157 data are well described by the previously determined equilibrium formation constant loglop of -3.11. An independent fit of the data resulted in an identical equilibrium formation constant value. These results agree with the findings by Takeuchi etal. (1984b), who reported that an alkyl chain length of greater than six resulted in no measurable change in partitioning in an n-butanol/water two-phase system. - o . ^ i 1 1 1 1 1 1 1 1 0.0 0.5 1.0 1.5 2.0 pH + log[UH] Figure 4.19: Experimental copper partitioning data (O) in an n-octanol/water two-phase system in the presence of the A-octyl-L-hydroxy-proline ligand (LiH) at various aqueous pH values, copper, and ligand concentrations. Solid line: model regression log,0f3 of -3.11(1) (4, = 0.1 M, 25 °C). 4.4 E n a n t i o m e r P a r t i t i o n i n g in T w o - P h a s e S y s t e m s When combined with measured protonation constants and equilibrium formation constants for all binary and ternary complexes present, the two-phase multiple-chemical 158 equilibria model Chemeq2 derived in Chapter II (section 2.3.2) provides a rigorous method for predicting enantiomer partition coefficients and degree of racemic mixture resolution in n-octanol/water two-phase systems as a function of system composition and pH. To verify the accuracy of the model predictions, amino-acid racemates were partitioned in an n-octanol/water two-phase system over a range of compositions and pH values. Figure 4.20 to Figure 4.27 report experimental results in terms of measured partition coefficients for each enantiomer of the racemic amino-acid mixture and the associated enantioselectivity (cf, equation 2.53). Partitioning of Phe enantiomers was particularly well studied, thereby providing a reasonable database for model comparison. For each system investigated, predicted enantiomer-partition coefficients and enantioselectivities are compared to the experimental data. In all cases, model predictions are in good agreement with experiments. Model deviations from the experimental selectivities are observed in some systems at very low pH, where both enantiomers partition almost exclusively into the aqueous phase. Since the experimental selectivity (open squares) is calculated from partition-coefficient data for each enantiomer, which has a high degree of error when partitioning is extreme, these deviations are almost certainly due to errors in the experimental data. Comparison of Figure 4.21 and Figure 4.23 for partitioning of Phe enantiomers shows that enantiomer-partition coefficients and, to a lesser extent, enantioselectivity depend on the system composition, particularly the molar concentration of copper(II) ions relative to the ligand. The model predicts this effect quantitatively. Although partitioning decreases dramatically at sub-saturating copper concentrations (relative to the ligand concentration), selectivity increases under such conditions due to the preference of the ligand to form the hetero-chiral complex. When the concentration of copper(II) ions is increased, the 159 concentrations of active (copper-bound) ligand increase proportionally. When it becomes in excess, active ligand is available for complexation with both enantiomers and, although partitioning is increased, enantioselectivity is diminished. Figure 4.20: Experimental partition data (A,0), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing A/-dodecyl-L-HyPro (20.45 mM). Initial aqueous concentrations: (O) D-Phe = 5.64 mM and (A) L-Phe = 5.64 mM, Cu = 10. 3 mM (/„ = 0.1 M, 25 °C). 160 Figure 4.21: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing TV-dodecyl-L-HyPro (20.2ImM). Initial aqueous concentrations: (O) D-Phe = 4.36 mM and (A) L-Phe = 4.36 mM, Cu = 17.18 mM (/„= 0.1 M, 25 °C). P H Figure 4.22: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing iV-octyl-L-HyPro (20.97 mM). Initial aqueous concentrations: (O) D-Phe = 3.69 mM, (A) L-Phe = 3.69 mM, Cu = 12.64 mM (7aq = 0.1 M, 25 °C). 161 2.5 c 2.04 CD ' o ! £ 1.5-1 c: o 1.0J Q_ 0.0 o • "CT D-Phe 2.0 H.5 I-1.0 < •e-L-Phe h0.5 0.0 Figure 4.23: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing vV-dodecyl-L-HyPro (19.3 ImM). Initial aqueous concentrations: (O) D-Phe = 0.97 mM and (A) L-Phe = 0.97 mM, Cu = 5.0 mM (7aq = 0.1 M, 25 °C). 2.5 CD ' O o 1.0J 0.0. 1 ' 1 • 1 " 1 1 • • • O D-Phe" 1 — I ' 1- • i L-Phe - « — i — > -1.5 2.0 i — * -0.5 HI 0.0 P H Figure 4.24: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Phe in an n-octanol/water two-phase system containing JV-dodecyl-L-HyPro (19.31mM). Initial aqueous concentrations: (O) D-Phe = 0.97 mM and (A) L-Phe = 0.97 mM, Cu = 20.0 mM (/„ = 0.1 M, 25 °C). 162 fZ CD "O E rz o •E 03 C L Figure 4.25: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Leu in an n-octanol/water two-phase system containing N-dodecyl-L-HyPro (20.2 mM). Initial aqueous concentrations: (O) D-Leu = 4.11 mM and (A) L-Leu = 4.11 mM, Cu = 12.5 mM (/„ = 0.1 M, 25 °C). Figure 4.26: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Leu in an n-octanol/water two-phase system containing /V-dodecyl-L-HyPro (16.3 mM). Initial aqueous concentrations: (O) D-Leu = 2.54 mM and (A) L-Leu = 2.54 mM, Cu = 10.3 mM (7aq = 0.1 M, 25 °C). 163 1.00 Figure 4.27: Experimental partition data (0,A), selectivities (•) and model predictions (solid and dashed lines) for racemic Val in an n-octanol/water two-phase system containing TV-octyl-L-HyPro (25.58 mM). Initial aqueous concentrations: (O) D-Val = 1.87 mM and (A) L-Val = 1.87 mM, Cu = 12.68 mM (7aq = 0.1 M, 25 °C). Effects that are more dramatic are observed when the amino acid is present at higher concentrations. Figures 4.28a and 4.28b show a species distribution plot at a low D-Phe (0.1 mM) and a high D-Phe enantiomer (10 mM) concentration, respectively. The plot shows that an increase in Phe concentration results in higher aqueous and organic phase complex concentrations. Only the binary to-Phe/ligand complex decreases in concentration since at higher concentrations Phe competes for copper ions in the organic phase to form the mixed ternary complex. It should be noted that for clarity the plots do not include hydroxy ion and free-species concentrations. 164 a ) 10, 2 1 0 0 org -• Li wCu xPhe yH z \ 0120 a nl \ aq • Figure 4.28: Predicted complex concentrations for D-Phe in an n-octanol/water two-phase system containing TV-octyl-L-HyPro (20 mM). Initial aqueous concentrations: Cu = 6 mM, Phe: a) 1 mM, b) 10 mM (7aq = 0.1 M, 25 °C). 165 The accuracy of the Chemeq! model was further tested by comparing model predictions with partitioning data measured independently by Ding etal. (1992) and Ding (1992) for Leu enantiomers in an n-octanol/water two-phase system containing the ./v-dodecyl-L-hydroxy-proline ligand (cf., Figure4.29). The pH in the aqueous phase was controlled by an acetate buffer. Prior to the enantiomer partitioning, the ligand was saturated with the acetate buffer containing only copper(II) ions. Model predictions therefore had to include the binary equilibrium formation constants for the acetate/copper complex. Figure 4.29: Experimental partition data (0,A) and selectivities (•) from Ding (1992) with model predictions (solid and dashed lines) for L- and D-Leu in an n-octanol/water two-phase system containing A-dodecyl-L-HyPro (20 mM). Initial aqueous concentrations: (O) D-Leu = 0.93 mM, (A) L-Leu = 0.93 mM, Cu = 6.3 mM (0.2 M acetate buffered). The calculated partition coefficients show good _ agreement with the published data. Although the measured enantioselectivity values are scattered, the model is capable of 166 predicting the measured data well. It should be noted that the ionic strength of the Ding et al. (1992) system was not 0.1 M. The regressed equilibrium formation constants are exact only for solutions with an ionic strength of 0.1 M. The model does not include changes in ion and complex activity coefficients, and therefore model predictions at ionic strengths away from 0.1 M may be in error. The results shown in Figure 4.29 suggest that these model deviations are small, which is not surprising since each equilibrium formation constant is defined in terms of a ratio of activities. The presented data indicate that the Chemeq and Chemeq2 models are powerful tools for the calculation of solute partition coefficients in one-phase and two-phase systems, respectively, exhibiting complex chemical equilibria. When equilibrium formation constants for all complexes present in solution are provided, Chemeq2 can quantitatively predict solute partitioning and enantioselectivities at various system conditions and solute concentrations. The model can thus be used for the optimization of enantiomer partitioning and enantioselectivities. The model is highly flexible, allowing for instance additional interactions due to buffer ions (e.g., acetate ions) to be included. In addition, the model can be extended to include temperature effects as well as varying ionic strength. 167 CHAPTER V 5 Molecular Modelling Calculations The calculations in Chapter IV verified that the two multiple-chemical equilibria models Chemeq and Chemeq2 accurately predict species distributions and phase equilibria in aqueous solutions and in aqueous/organic two-phase partition systems, respectively. However, determination of the required set of equilibrium formation constants for all binary and ternary complexes is time consuming and, at present, the necessary database is lacking. Therefore, it would be desirable to establish a method for predicting equilibrium formation constants from the chemistry (i.e., molecular structure) of each component in a given complex. This chapter explores the potential of applying molecular mechanics simulations to such calculations. In addition, molecular mechanics calculations are used as a basis of ligand design by computing simulated equilibrium formation constants for selected ternary complexes. Molecular mechanics calculations are performed in this work with the MOMEC (v97) program (Chemische Verfahrens- & Software-entwicklung Heidelberg, Germany) to determine the total strain energies of ternary amino-acid/copper/enantiomer complexes. It should be emphasized that the parameterization of the potential-energy functions is, in general, performed on solid crystal structures (Comba and Zimmer, 1996). Therefore, solvation effects may not be properly accounted for in the refined molecular structures of transition metal-ion complexes (Comba, 1993). As a first order correction, we have included the presence of solvents in the calculations by connecting, for instance, water and methanol molecules at the apical copper-ion coordination sites. After successful energy minimization, 168 the molecular structures are exported into ISIS™ Draw (MDL Information Systems INC., San Leandro CA) for graphical presentation. For each ternary enantiomer complex investigated, both stereoisomers (i.e., cis and trans) were simulated to determine the configuration with the lower strain energy. For a hetero-chiral complex in the cis configuration, the side-chains are oriented in the same coordination plane, whereas for the trans complex the side-chains are on opposite sides of the plane (Gillard, 1967). The configurations are reversed for homo-chiral complexes. 5.1 Solvation Effects on Complex Stability and Enantioselectivity Strain-energy minimization results for Phe, Leu, and Val ternary enantiomer complexes with the L-HyPro ligand are reported in Table 5.1 for several solvation environments. A comprehensive listing of the individual strain-energy contributions to the Leu, Val and Phe structures is given in Appendix 5. Initially, calculations were performed in the absence of solvent molecules to simulate low-dielectric phase conditions (i.e., solvent-free). Solvent molecules were then added at the apical coordination sites of the copper ion to investigate the associated changes in complex stability and stereoselectivity. As part of this study, an attempt was made to include long-chain alcohols (i.e., n-octanol) at the distal coordination sites. However, the relatively high number of degrees of freedom of these molecules increased the complexity of the calculations such that the program was not able to find a local or global minimum. Therefore, simulations of complexation in non-aqueous phases were carried out in the presence of a short chain alcohol (i.e., methanol). 169 Relatively few structures of ternary chiral complexes have been solved experimentally (Comba etal, 1990; Bernhardt etal, 1992). Carrondo et al. (1990) investigated the crystal structure of the to-L-hydroxy-proline/copper hydrate complex by X-ray diffraction and found that the structure exists in the cis configuration. Figure 5.1: Structure of the hydrated to-L-hydroxy-proline/copper(II) complex determined by molecular mechanics calculations (not all hydrogen atoms are shown). A molecular mechanics calculation of the hydrated to-L-hydroxy-proline/copper(II) complex was performed with MOMEC. The calculated strain energies of the to-L-hydroxy-proline complexes (£°1S = 50.7 kJ/mol, 7ftrans = 54.63 kJ/mol) are in agreement with Carrondo's experimental results and show that the cis configuration is energetically preferred over the trans. The calculated cis structure, shown in Figure 5.1, indicates that the pyrrolidine rings are aligned on both sides of a square planar configuration. It should be noted that, for clarity, the hydrogen atoms are partially omitted. The hydroxy groups are oriented outward away 170 from the metal-ion centre and therefore do not directly participate in the complex. This calculated structure agrees with that determined by Carrondo etal. (1990) and confirms that the molecular mechanics program MOMEC can be successfully applied to the modelling of chiral complexation reactions around a copper(II) ion, at least in the absence of solvent molecules. 5.1.1 Absence of Solvent The strain-energy minimization results for ternary Leu, Phe, and Val enantiomer complexes reported in Table 5.1 predict that the hetero-chiral D-amino-acid complex is more stable in the absence of solvent molecules. The electron-poor hydrophobic side-chain of Leu and Val cannot neutralize charge at the copper(II) ion, and therefore it is energetically unfavourable for them to occupy the distal coordination site (cf, Figure 5.2 and Figure 5.3). Table 5.1: Molecular modelling energy-minimization results of ternary complexes formed with the L-HyPro ligand in different solvation environments. £ t o t a i [kJ/mol] L-Leu D-Leu L-Val D-Val L-Phe D-Phe vacuum 57.57c 53.20° 52.lT 48.05° 58.69° 45.94° water 46.64' 46.54' 41.94' 42.16' 39.57° 40.49° methanol 44.18' 44.35c 39.29' 39.25° 43.73° 43.10° c = cis, t = trans The D-enantiomer can rotate the side-chain away from the copper(II) ion into a position where valence- and torsion-angle deformation, as well as non-bonded energy contributions, 171 are lower. The side-chain of the Val enantiomers is reduced by a methyl-group and therefore the hydrophobic isopropyl group is closer to the copper ion (cf., Figure 5.3). This results in increased repulsion for the L-enantiomer and hence increases the energy difference between the homo- and hetero-chiral structures. The electron-rich phenyl-ring of Phe can establish n-n (i.e., electron stacking) interactions (Sigel, 1975) at the apical coordination sites of the copper ion to occupy unfilled inner ^ -orbitals (cf, Figure 5.4). As a result, the relative stability of homo- and hetero-chiral ternary Phe complexes is governed by the coordination reaction of the amino-acid side-chain. The calculated structures in Figure 5.4 show that the electron-rich hydroxy group of the L-HyPro ligand is pointing towards the phenyl-ring of D-Phe to establish additional electron-stacking interactions. Steric and bond-angle restrictions prevent the L-enantiomer from positioning the phenyl-ring near the hydroxy group of L-HyPro. As a result, Lewis-base-type stacking interactions result in significantly lower energy values for the D-enantiomer and favour the formation of the hetero-chiral complex. It should be noted here that these molecular mechanics calculations were performed in the absence of solvent molecules interacting with the complex or participating in the complex formation by competing for the distal coordination sites. The calculated energy values are those in vacuum. In the next section, the effect of solvent molecules on the ternary complex structure will be investigated. 5.1.2 Presence o f So lven t In the absence of solvent, maximum stability of the ternary copper(II) complexes involving amino-acid-based ligands is achieved when both ligands assume a cis 172 configuration. When water is present, Gillard (1967) and Davankov (1988) have argued that the trans configuration becomes more stable due to favourable molecular packing and decreased repulsion between oxygen atoms in the coordination shell. The distal coordination sites of the copper(II) ion can participate in complexation reactions with free-electron pairs on solvent molecules such as water or alcohols. MOMEC simulations indicate that the presence of such solvent molecules reduces the total strain energies of ternary complexes and therefore stabilizes both homo- and hetero-chiral complex formation (cf, Table