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Investigation of fast Lewis acid-base reactions between copper (II) bis (diethyldithiocarbamate) and… Tapping, Robert Laurence 1972

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\5\SG INVESTIGATION OF FAST LEWIS ACID-BASE REACTIONS BETWEEN COPPER(II) BIS(DIETHYLDITHIOCARBAMATE) AND HETEROCYCLIC BASES USING EPR SPECTROMETRY by ROBERT LAURENCE TAPPING B.Sc. (1967), M.Sc. (1968), University of B.C. A THESIS SUBMITTED IN P.ARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE DEPARTMENT OF CHEMISTRY. WE ACCEPT THIS THESIS AS CONFORMING TO THE REQUIRED STANDARD: THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER, 1972. In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date V^/eu>k. 15. l.ffi-2-~ ABSTRACT Fast Lewis acid-base reactions occur between square planar copper(II) complexes and weak organic bases in non-coordinating sol-vents. An example of such a reaction is that between copper(Il)bis-(diethyl-dithiocarbamate), CuDDC, and a series of pyridines: (1) CuDDC + pyridine CuDDC'pyridine to form a five-coordinate adduct. Such an equilibrium can be treat-ed as a two site exchange process using electron paramagnetic reson-ance (epr) spectrometry, with CuDDC the paramagnetic probe. The situation described by (1) is within the fast exchange approximation for epr. In order to analyse line position epr data for reaction (1) the stoichiometry of the adduct must be established. Using plots of epr line position shift i t was shown that CuDDC forms only 1:1 ad-ducts with pyridine and the methyl-substituted pyridines studied. Knowing this stoichiometry the line position data was analysed using a least squares procedure to obtain the equilibrium, or binding, con-stant, K. Linewidths were analysed as a function of base concentration to obtain the reverse rate constants, k , which were related to the ' r forward rate constants using k^ = Kk^. Both equilibrium and rate constants were studied as a function of temperature using Arrhenius plots in order to obtain thermodynamic parameters. Temperature vari-tions in the epr parameters were included in the analysis of the (ii) linewidth and line position data. Reaction (1) was studied with pyridine as the base in benzene, toluene, and chloroform. Enthalpies of reaction in the reverse direc-tion increased in the solvent order given, and in the forward direc-tion negative activation energies were observed, also increasing in the solvent order shown. Studies of several methyl-substituted pyri-dines in benzene showed a similar behaviour. An isokinetic relation-ship between AH^ and AS^  was observed both for variation of solvent and of base. Such plots emphasise the dominant role solvent inter-actions play in reaction between neutral species in non-coordinating solvents. The results obtained can be consistently and qualitatively in-terpreted in terms of a dynamic solvent structure reorganisation model proposed by Bennetto and Caldin, and are not adequately interpreted in terms of more traditional ideas. ( i i i ) TABLE OF CONTENTS ABSTRACT LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENTS CHAPTER 1: INTRODUCTION CHAPTER 2: FAST EXCHANGE A. AN INTRODUCTION B. A BRIEF SURVEY OF LINESHAPE THEORIES C. THE BLOCH EQUATIONS 13 D. MODIFIED BLOCH EQUATIONS AND FAST EXCHANGE 17 CHAPTER 3: STOICHIOMETRY AND THE DETERMINATION OF FORMATION CONSTANTS 25 A. INTRODUCTION 25 B. THE SATURATION FRACTION 26 C. CONSIDERATION OF POTENTIAL ERRORS 28 D. PRESENTATION OF DATA 31 E. MULTIPLE EQUILIBRIA 35 a) The Binding Model 35 b) Presentation and evaluation of data 38 CHAPTER 4: INFORMATION FROM THE LINEWIDTH 41 A. RELATIONSHIP OF THE LINEWIDTH TO KINETICS 4 1 B. NON-EXCHANGE LINEWIDTHS 43 C. ROTATIONAL EFFECTS AND EXCHANGE 52 i v i v i i i x 1 8 8 (iv) CHAPTER 5: THE SYSTEM: EXPERIMENTAL RESULTS 56 A. LEAST SQUARES ANALYSIS OF THE RESULTS 56 B. DETERMINATION OF STOICHIOMETRY . 66 C. SOLVENT EFFECTS 78 CHAPTER 6: SOLVENT ADD TEMPERATURE EFFECTS ON EPR SPECTRA, AND A COMPARISON WITH OTHER WORK 102 A. SOLVENT EFFECTS ON EPR PARAMETERS 102 B. ULTRA-VIOLET AND VISIBLE SPECTRA 107 C. TEMPERATURE EFFECTS 108 D. COMPARISONS WITH OTHER WORK 110 CHAPTER 7: DISCUSSION OF RESULTS 116 A. SOME THOUGHTS ON THE INTERPRETATION OF EQUILIBRIUM AND RATE DATA 116 a) Introductory Remarks 116 b) Interpretation of Equilibrium Constants 118 c) Interpretation of Rate Constants 122 d) Fast Reactions and Arrhenius/van't Hoff Relation-ships 128 B. THE FORWARD, OR ASSOCIATIVE, REACTION 130 a) Current Ideas, Rate Constants, and Thermodynamic Parameters 130 b) The Bennetto and Caldin Model 138 C. THE REVERSE, OR DISSOCIATIVE, REACTION 151 a) Solvent Effects 151 b) Effects of Varying the Base 157 (v) CHAPTER 8: CONCLUDING REMARKS 163 A. GENERAL CONCLUSIONS 163 B. FUTURE WORK 167 CHAPTER 9: EXPERIMENTAL DETAILS AND ANALYSIS OF DATA 169 A. SAMPLE PREPARATION 169 B. INSTRUMENTAL METHODS 173 C. DATA ANALYSIS 175 REFERENCES 184 APPENDIX 1 195 APPENDIX 2 201 (vi) LIST OF TABLES Table Page 5-1 Parameters obtained from a least squares fit of the line position data and obtained from measurements in neat sol-vents 63 5-2 Parameters obtained from the linewidth data 64 5-3 Parameters obtained from a least squares of the hyperfine parameters 65 5-4 Sample data used to construct Scatchard multiple equili-bria plots. 72 5-5 Parameters obtained from least squares fit of line posi-tion and linewidth for benzene 79 5-6 Parameters obtained from least squares fit of line posi-tion and linewidth in toluene 80 5-7 Parameters obtained from least squares f it of line posi-tion and linewidth for chloroform 81 5-8 Frequency difference and linewidth data for benzene, toluene, and chloroform 82 5-9 Thermodynamic data for various solvents. 86 5-10 Parameters obtained from least squares f it of line posi-tion and lienwidth for 2-picoline in benzene. 90 5-11 Parameters obtained from least squares fit of line posi-tion and linewidth for 3-picoline in benzene 91 5-12 Parameters obtained from least squares fit of line posi-tion and linewidth for 4-picoline in benzene 92 5-13 Parameters obtained from least squares fit of line posi-tion and linewidth for 3,4-lutidine in benzene 93 (vii) Table 5-14 Representative data obtained for 2,6-lutidine in benzene. 94 5- 15 Thermodynamic data for variation of base. 98 6- 1 Temperature and solvent dependence of isotropic epr para- 103 meters for CuDDC. 6-2 Base strengths and aQ for CuDDC in various pyridines 105 6- 3 U.V./visible maxima for CuDDC in various solvents. 108 7- 1 Static (equilibrium) data for a l l systems 117 7-2 Kinetic data for a l l systems. 123 7-3 AH (b.p.) for solvents 145 vap r 7-4 AG° for various solvents and bases for CuDDC 150 7-5 Regression coefficients for isokinetic plots 160 9-1 Effects of modulation on observed linewidth 178 9-2 Effects of different modulation amplitudes on an observed 178 linewidth. 9-3 Comparison of various terms in eq.(9-6) 182 (viii) LIST OF FIGURES Figure Pa 2 4- 1 Mj-dependence of linewidths 50 5- la CuDDC in benzene 57 5-lb CuDDC in IM pyridine in benzene 58 5-2 Concentration dependence of average line position in ben-zene-pyridine solution 59 5-3 Concentration dependence of linewidth in benzene-pyridine solution 60 5-4 Hyperfine splitting of CuDDC in benzene-pyridine solu-tions at low pyridine concentrations ~7 5-5 Scatchard plots of CuDDC with pyridine in solvents indi-cated 69 5-6 Benesi-Hildebrand plots for 3/2 line 70 5-7 Scatchard plots of beenene/pyridine multiple equilibria 73 5-8 Scatchard plots of benzene/pyridine multiple equilibria 74 5-9 Scatchard plots of benzene/pyridine multiple equilibria 7S 5-10 Scatchard plots of benzene/pyridine multiple equilibria 76 5-11 Arrhenius plots for equilibrium constants for solvents indicated 84 5-12 Arrhenius plots for rate constants for solvents indicated 85 5-13 Temperature dependence of CuDDC in toluene-piperidine solutions 89 5-14 Line position vs. concentration for 2,6-lutidine in ben-zene 95 (ix) Figures Page 5-15 Scatchard plots for 2-picoline in benzene 97 5-16 Arrhenius plots of equilibrium constants for various pyridines 99 5-17 Arrhenius plots for several pyridines (forward rate) 100 5-18 Arrhenius plots for several pyridines (reverse rates) 101 6-1 Typical temperature effects on CuDDC in 5-picoline 114 7- 1 Isokinetic plots for solvents 126 7-2 Isokinetic plots for bases 127 7-3 Structural model for a solvated ion 140 7-4 Isokinetic plots for solvents and bases 152 (x) ACKNOWLEDGEMENTS I would like to express sincere gratitude to Dr. F.G. Herring for his guidance, his encouragement, and for many stimulating discus-sions. I would also like to thank Professor J.B. Farmer for his help and interest in this work, and for his advice on several aspects of epr spectrometry. Sincere thanks are due to Professor C A . McDowell for his continued interest throughout this work. I am grateful to Dr. A.G. Marshall for some interesting dis-cussions and comments about certain aspects of this study. Acknowledgements are not complete without thanking Messrs. J. Sallos, T. Markus, and S. Rak for their invaluable technical help, and thanks are due to Dr. J.A. Hebden and Mr. J. Tait for help with various computing problems, and to Dr. N.S. Dalai for useful discus-sions at various times. Finally, I acknowledge the receipt of a Teaching Assistant-ship from the department from 1968 - 1972, and University summer re-search grants to Dr. J.B. Farmer, which enabled me to undertake this work. - 1 -CHAPTER 1  INTRODUCTION Magnetic resonance experiments in solids give results that can, in general, be considered as representative of static molecules. In solu-tion, however, molecular motions, such as random Brownian tumbling, modulate the magnetic properties so as to narrow the observed line-widths and change the overall absorption lineshape. Also, chemical ex-change processes, whereby there is a dynamic exchange between magneti-cally distinct sites, can lead to dramatic changes in magnetic resonance lineshapes*. These effects occur because of a time-dependent averaging over the magnetically distinct sites and their magnetic properties, and are readily distinguished and analysed by magnetic resonance methods. For instance, i f the exchange process is sufficiently rapid between the various sites, coalescence of the magnetic resonance signals will occur, - 2 -because of the uncertainty principle: (1-1) T „ * y where Aui is the frequency separation of the corresponding resonance lines, and x the smallest time for which the separate sites can be dis-tinguished. This time-averaging effect, under conditions of rapid ex-change, leads to the site lifetimes becoming less than the crit ical value of x described by (1-1), and the signals are not resolvable. Under these conditions, the time-averaged line positions and linewidths can be obtained and related to the dynamics of the exchange process, as 2 was first shown by Bloembergen, Purcell, and Pound in 1948 . Today there are available many procedures for analysing chemical exchange data for nuclear magnetic resonance (nmr) or electron para-3 magnetic resonance (epr) experiments , covering a l l ranges from slow to fast exchange rates. For the study of rate processes, nmr and epr techniques complement each other, covering a range for first order pro-cesses of approximately 1 to 10^ sec ^. Epr, in particular, is suitable for fast exchange studies, covering an exchange rate constant range of approximately 10** to 10^ sec -*. The lower rate limit in magnetic reson-ance studies is that due to non-exchange contributions to the absorption linewidth. Linewidth and lineshape studies have been used in epr to 3 6 obtain equilibrium and kinetic data for a large variety of reactions Ion association reactions , electron-transfer reactions , radical 17 18 19 20 association-dissociation processes ' , and ligand exchange ' have a l l been studied, the work referred to giving some useful or historically important examples. - 3 -Many ligand exchange processes are slow^ by epr criteria; rates 3 6 1 being of the order of 10 to 10 sec . Many exchange processes have 36 been observed, the first probably being that of McGarvey , with a more detailed study of ligand exchange between Mn 2 + and various ligands 19 in aqueous solution by Hayes and Myers . The first detailed work in-20 volving neutral species was reported by Walker et al for the follow-ing equilibrium: k f (1-2) V0(acac)2 + pyridine + V0(acac)2'pyridine k r where "acac" means acetylacetonate. This adduct formation equilibrium involves an exchange that averages both the g and hyperfine tensors, and the line broadening and hyperfine splittings were analysed to yield the rate constants k_ and k as lO^imole '''sec-''' and 1.3 x 10^ sec * at f r 300°K, respectively. In general, any equilibrium of the kind: (1-3) ML2 + B j ML2-B 3 4 can be studied by magnetic resonance, using a two site analysis ' . The two site case is simplest and consequently most thoroughly analysed, 3 but in principle any number of sites may be considered . In practice, computer techniques, although straightforward, become quite tedious for multiple site situations. 21 Aasa et al , in 1961, published details of linewidth effects and line position shifts in the epr spectrum of copper(II) bis(diethyldi-thiocarbamate) in benzene upon the addition of pyridine. Although not recognised by the authors as such, this was the first epr detection of fast ligand exchange for a transition metal system. When such Lewis - 4 -acid-base equilibria do occur under fast exchange conditions, the inter-pretation simplifies numerically. It is immediately apparent, at least in retrospect, that copper(II) bis(diethyldithiocarbamate), abbreviated to CuDDC from now on, undergoes weak complex formation with weak Lewis bases in non-coordinating solvents at a fast rate, and hence is a suit-able paramagnetic probe upon which to perform ligand and solvent ex-change epr studies. Before continuing, i t may be useful to note a few facts about CuDDC. CuDDC is a typical square planar copper(II) compound; copper(II) readily forming an unusually stable complex with salts of dithiocar-22 bamic acid . Square planar copper(II) complexes have been extensively 23-25 studied by epr, and a number of thorough reviews are available Copper-nitrogen and copper-oxygen bonding complexes have been most commonly examined; relatively few stable copper(II)-sulfur complexes 25-28 being reported until recently . In fact, copper complexes with sulfur-bonding ligands are usually more stable with the metal in the univalent state"*/ The crystal structure of CuDDC, a dark-green needle-like compound, 7 has been determined , and the structure is schematically shown: In the solid state, CuDDC exists as a bimolecular unit with copper-copper distance approximately 3.5 A. This is close enough that spin-26 spin coupling between the copper atoms can be detected by epr . Mole-C—N o - 5 -cular weight determinations in benzene and chloroform solution, how-31 ever, indicate that CuDDC exists in solution as a monomolecular unit It may be noted that the copper(II) atom is displaced out of the plane o of the four sulfur atoms by 0.26 A. Diethyldithiocarbamate complexes 29 of Ag(II) and Au(II) have also been reported and investigated by epr Hence a well-characterised, stable complex is available for ligand exchange studies. The quite large magnetic moment for copper(II) re--4 suits in a favourable epr signal size for quite dilute solutions ( 10 M), which is useful for epr studies of kinetic processes." Further, and very important, epr spectra of CuDDC in solution are characterised by very narrow linewidths, which allows the experimentalist to distinguish between quite closely spaced epr signals. For the weak complexes formed by equilibrium processes such as those of (1-2) or (1-3), the X-aand frequency separation is quite small: hence the fast exchange con-ditions. A suitable system for ligand exchange is thus available, and studies of CuDDC with various pyridines and in various solvents were carried out. During the course of this work, two similar studies were published. 86 One of these, by Corden and Rieger , studied copper(II) bis(di-n-butyl-dithiocarbamate) in methylcyclohexane with pyridine, n-hexylamine, and piperidine. The fast and intermediate exchange results yielded rate and equilibrium constants. The latter work, however, neglected solvent and ligand effects to a large degree, and contained several important inconsistencies in the treatment of data, which can lead to large errors in the results. Similar criticism can be noted about the work of 109 Shklyaev and Anufrienko on CuDDC with pyridine in toluene. The incon-- 6 -sistencies wil l be discussed later, with an attempt to correct for them, and comparisons made with the results of this thesis. The methods used in both studies reported were similar to those used here. Lately, much interest has surrounded the study of fast metal-com-plex reactions, mainly because l i t t l e kinetic data has been obtained 32 37 for metal ions that are highly labile with respect to substitution ' In general, the purport of most of these studies has been to relate the findings to currently-held ideas about complexation and oxidation-reduc-tion mechanisms. The nmr technique has been used to obtain much of the present data, particularly in aqueous solution. Much of the current 21 33 interpretation is based on a proposal by Eigen ' that dissociative mechanisms dominate the kinetics to date, particularly for divalent 32 transition metal ions . The experimental approach has been to study the rates of solvent exchange with respect to the stability constant, < , o for formation of an outer-sphere complex; in terms of an observed rate, Ic T - K k _» 1 obs o f , ic k_ o f (1-4) M + Lz=± M,L £=— ML r where a l l species are solvated, and L can be solvent, K can be esti-o mated using the ideas of Fuoss and Eigen, as is excellently discussed in 32 33 37 several articles ' ' Reactions of N i 2 + in non-aqueous and aqueous solvents with various 34 neutral bases led Bennetto and Caldin to propose a model involving a concerted rearrangement of solvent molecules to explain their results. The results obtained, they felt, were not consistent with ideas current-- 7 -ly held. In so far as current ideas are concerned, solvent and/or ligand exchange processes involve some sort of pre-equilibrium encoun-ter to form an encounter complex. It can be readily shown that consi-deration of this model cannot adequately explain trends in activation energy due to specific solvent effects, particularly those observed in this work. The negative activation energies observed, in fact, rule out the possibility of any process that is dominated by inner-sphere complex formation, and hence involves breaking and/or reforming metal-ligand bonds. Bennetto and Caldin's concerted model does explain the results of this thesis in a consistent manner, and these results cannot 35 be adequately explained otherwise. Objections by Rorabacher to the Bennetto-Caldin model for N i 2 + exchange processes, with the assertion that inner sphere effects can explain the results, may indeed be valid for that particular situation, but i t seems clear that such ideas are insufficiently concerned with concerted solvent effects to explain very fast reactions between neutral substances in non-coordinating solvents. The ideas necessary to obtain the necessary data for this work are considered in the next three chapters, followed by discussions of the results. Experimental details, which are quite standard, are felt not to contribute to the understanding of the mathematical methods used or the results obtained, and are therefore included at the end of the thesis. - 8 -CHAPTER 2  FAST EXCHANGE A. AN INTRODUCTION: Magnetic resonance methods for measuring fast reaction rates have been applied to a considerable number of simple reactions. Although quite general treatments of the theories of magnetic resonance lineshapes for systems undergoing chemical exchange do exist, i t is only with the use of large computers that full advantage can be made of such theories. Even where the computational facilities do exist, i t may be advantageous to utilise more approximate, therefore simpler, proce-dures. This is the approach to be adopted here, but first a general out-line of some pertinent details will be given. Under conditions of no net chemical reaction, but where a definite chemical equilibrium has been established, there are likely to be sites of different environment which are magnetically distinguishable. Because - 9 -of the establishment of an equilibrium situation, an overall exchange between these environments, or sites, will occur. Magnetic resonance experiments are quite suitable for providing information about very fast reactions in such systems. The intrinsic time scales of nmr and epr can be readily distin-guished by noting that (classically) in a magnetic field of ^10,000 7 gauss (G) protons precess at about 10 Hz. and free electrons at about 10**Hz.. Considering that linewidth measurements are usually employed to obtain rate data from magnetic resonance experiments, any linewidths in excess of those caused by the spectrometer, and those caused by pro-cesses independent of chemical exchange, wil l give information on the rate process under investigation. Nmr spectrometers, for instance, have linewidths less than 1 Hz., and can be used to measure rates from about 10"* to 10^ see"* for diamagnetic systems. Epr methods have a 4 practical lower limit of about 10 Hz. and thus rate processes over the range 10^  to l O * 2 sec * may have observable effects in epr2^. It is instructive to note that since nuclei, and sometimes unpaired electrons, may have weak interactions with their environments, local environmental fluctuations will cause local magnetic field fluctuations which render the precessional frequencies of the nuclei (or electrons) 24 time dependent . This was mentioned briefly in chapter 1, and is caused by the equilibrium or rate process under study. If the rate is sufficiently fast compared to the difference in precessional frequen-cies of a nucleus (or electron) in the various local environments, then the nucleus will see only an overall magnetic field that is a time aver-- 10 -age of the various local fields. This is the fast exchange situation, and results ultimately in only a single resonance absorption, or line. Similarly, for slow exchange rates the nucleus will have time to pre-cess in each environment for a period long enough that several reson-ances due to each local field may appear. If local field differences are very small, then slow exchange processes may have observable ef-24 facts on magnetic resonance spectra B. A BRIEF SURVEY OF LINESHAPE THEORIES: The physical description lead-ing to a l l of the currently available lineshape theories in magnetic 2 resonance is that first proposed by Bloembergen, Purcell, and Pound . 38 In 1953 Gutowsky, McCall and Slichter gave the first method for the calculation of lineshapes in the presence of transfers between various magnetically distinguishable muclei. In their study of relaxation ef-39 fects they used the Bloch equations , suitably modified to account for nuclear transfers. Thus the so-called "modified Bloch equations" 40 were used for the study of various chemical problems , and in 1958 41 McConnelf presented a particularly simple derivation of these modified Bloch equations, with results identical to those of Gutowsky et al , for the case of low radiofrequency power and slow passage (nmr). These 42 equations have been easily adapted to epr , and have been extended to 24 describe the effects of rate processes on spin echo experiments The spirit of McConnell's derivation was similar to that of Bloch1s phenomenological description of nuclear relaxation in the sense that chemical exchange effects were incorporated simply as linear damping terms with coefficients related to the exchange rate. - 11 -A general theory of resonance absorption based on a transfer process being described in terms of Markoffian random modulation was 44-46 derived by Anderson and Kubo . This theory gives formulae for the lineshape of a magnetic resonance spectrum directly, which can be used to obtain rate data, and is rather easily put into a convenient matrix 47 48 form . Recently, Atkins has shown that the Kubo-Anderson-Tomita theory can also account for the fact that some spectra are superposi-26 tions of spectra and thus show an alternation of linewidth , but fails to account for non-secular contributions to the linewidth from degenerate magnetic resonance lines. This latter problem is common to Bloch equation methods and has led to the growing popularity of density matrix methods to describe lineshapes for systems where non-secular contributions may be important. Non-secular transitions in magnetic resonance arise because of relaxation-induced transitions between spin states that are parallel and anti-parallel to the external magnetic f ield. In epr, for instance, the most important effects are usually the secular effects, or those 49 involving no electron-Spin transitions (adiabatic effects). The neg-lect of non-secular effects means that only motions that are not too rapid with respect to the Larmor frequency would be considered. In principle, the density matrix methods have no limitations in exchange situations other than algebraic or computational, and are now routinely used. Bloch^'"^ introduced a detailed treatment of mag-netic relaxation within the framework of the density matrix formalism, 52 using operator techniques, and an equivalent formulation by Redfield - 12 -is commonly used in epr, especially for description of the alternating 26 49 53 linewidth phenomenon ' ' . One of the limitations of the Redfield-Bloch formulation is that because of certain approximations used to evaluate some integrals, the method is restricted to the region of motional narrowing of the lineshape. This is essentially because the evaluation of the integrals requires that the density matrix of the system not change much over the time period over which the integration 54 is defined. A thorough discussion of this is given by Slichter , and by Abragam*, who further gives an excellent account of an operator method for the calculation of mganetic resonance linewidths. Whereas the modified Bloch treatments are limited to secular contributions, but not limited to any exchange rate range, the Redfield theory is limited to the fast motion region, but can be readily generalised to include a l l transitions contributing to any resonance spectrum. Kaplan*^  ^ and Alexander"^, using an exchange operator to des-56 57 cribe the effects of exchange on the density matrix for any system ' , describe a density matrix method that is not restricted to any rate region, and which can include non-secular transitions. Binsch^ has extended these ideas to obtain a general density matrix formalism, suitable for application to intermediate exchange rate situations where computational facilities exist. The spirit of Alexander's modi-fication to the equation of motion for the density matrix is the addi-tion of phenomenological terms to account for intra- and inter-mole-cular exchange, and terms to account for the non-exchange contributions to the lineshape. Thus there is a resemblance to the modified Bloch - 13 -equations, to some extent. In fact, the results of the density matrix treatments are essentially quantum mechanical equivalents to the modi-fied Bloch equations, and in the limit of fast exchange, for instance, 24 the results are identical . The recent modifications to the Kaplan-Alexander theory by Kaplan*^ and Binsch^ also allow for intramole-cular conversion where i t is difficult to explicitly define an exchange operator of the sort used for hindered internal rotation. Examples of the use of various density matrix methods for several problems have 61 63 been published for both nmr and epr exchange studies To end this rather brief survey of lineshape theories, mention should be made of a treatment of chemical exchange mentioned by Ander-son et a l ^ ~ ^ , similar in concept to Sillescu's more general treat-67 ment . In these treatments, molecular reorientation is related to a fluctuating environment (for example, chemical exchange) using probability theory, and the effects upon the molecular motion by the fluctuating process can be described in terms of rotational correla-tion functions of the molecules and a probability function describing the fluctuations. In principle, these ideas can be extended to any exchange process. C. THE BLOCH EQUATIONS: Before proceeding to outline the treatment of chemical exchange used in this thesis, i t is useful to sketch the development of the phenomenological equations proposed by Bloch to describe the behaviour of nuclear magnetic moments in external mag-netic fields. For complete details as to the validity of these equa-39 50 51 tions, the papers by Bloch ' ' should be consulted. - 14 -In a system of weakly interacting spins, Bloch postulated that the magnetization vector per unit volume, M, obeys the equation: where H is the external magnetic field vector and Y the magnetogyric ratio. By simply adding relaxation forces to (2-1) phenomenological-ly i t is possible to describe the behaviour of an isolated group of spins. By resolving into components such that H q is in the z direction, and such that a perpendicular (to z) modulating field is acting to cause the magnetic resonance, one obtains: (2-2) ( H Q = H. H = H,cos wt x 1 H = -H,sin cot y 1 where co is the angular frequency of rotation of about H Q. By adding the rotating terms to the steady state solutions for the motion of M in a static field H the Bloch equations followf^'^ dM M x — + /(M H + M H.sin cut) T„ y o z 1 dt . 2 dM M (2-3) ^ _ _ ^  + r(M_H.cos U t - MxHQ) dM (M - M ) * = 2. _ V«(M H,sin cot + M H.cos cot) dt T ' x 1 y 1 where the first terms in each line are those due to relaxation in a static field H , being the transverse or spin-spin relaxation time. - 15 -and the longitudinal or spin-lattice relaxation time, the equilibrium magnetization in the z-direction. clearly governs the rate of approach of the magnetization to an equilibrium value upon the application of a magnetic field. Similarly, T_, usually different from T^, governs the decay of phase coherence of spins in the xy plane, or is the time taken by the spins to dephase once they are in phase. In a liquid, the many rapid fluctuations in local fields (it is these local fields that cause the dephasing of the spins: i f the range of these small fields is 6H then the spins will -1/2 dephase in a time T- ^ (6H) ) during the rotation of a molecule whose spin(s) is(are) precessing at the Larmor frequency will mean that these small local effects are averaged out, and that M and M x y wil l decay in the same manner as M^. Thus T^ - T^. Quantitatively, i f some time x describes the time for molecular rotation, for exam-ple, the rapid fluctuations (compared to the Larmor frequency, I O Q ) are such that: (2-4) C O Q X « 1 and hence T^ = T_. Chemical exchange effects can also interrupt the phase coherence of spins at the Larmor frequency by causing sudden changes in the precession frequency, and this situation would be manifest by change InT_, but not in T^. Under these conditions, T < T 6 9 *2 1 ' The Bloch equations may be simplified by transforming from the fixed laboratory Cartesian axis system to a set of axes rotating - 16 -with the applied field H1 , where the transformation is described by: M = ucostOt - vsinuit (2-5) x M = -us in lit - vcos<it y-Substituting (2-5) into (2-3), and rearranging, gives: du u , rt at * r* K - u)v =0 dM (M - M ) z z o n + - yH v = 0 dt T 1 At steady state, M is constant and the transverse components of M rotate with H^; therefore setting the time derivatives to zero yields: u = M -o 1 + T > o - co)2 + Y H 2 l T l T 2 (2-7) v - -MQ Y H l T 2 1 + ^ ( ^ - W)2 + y2H\T]T2 M =M 1 +  T2^o -z o 1 • T|(a)o - co)2 + y 2 H 2 l T l T 2 In most magnetic resonance experiments, is chosen to be small (yH^ << Y Q^)> therefore the last term in the denominators of (2-7) can be neglected since y 2H 2T^T 2 << 1. This latter condition - 17 -further implies that M 'v- M q . Incorporating this approximation in-to (2-7) yields a Lorentzian form for the lineshape components: u = C2-8) 1 + fo0 - < )^2T2 - ^ H l T 2 M o 1 + (coQ -co)2T2 M = M o z and as (u) - to)T varies from -°° to +°° the resonance absorption goes 24 through a maximum at to = to. The Lorentzian form of the lineshape equation resulting from (2-8) is a limitation of the Bloch treatment, since many lineshapes, especially in solids, are not well-approxi-mated by such a function. For spectra obtained for samples in solu-tion, however, the observed lineshapes are often quite well des-cribed by a Lorentzian lineshape. D. MODIFIED BLOCH EQUATIONS AND FAST EXCHANGE: McConnell's modifi-41 cations to the Bloch equations to allow for reversible chemical exchange processes give the same results as the earlier work of Gutowsky et a l " ^ ' ^ , but because the notation is simpler, only McConnell's treatment will be outlined here. Returning to eqs. (2-6) and recalling that i f H^ is small then M does not change significantly from M q , the first two equations may be written: (2-9) du u ^ ( . n v •* — + — + ( t o - t o ) v = 0 dt T 2 • - 18 -(2-9) to)u = -yH.M J ' 1 o Defining a complex magnetic moment = u.. + l v j > and a com-plex frequency of a- = T * • - i(to- - to), where j refers to the 3 ^»3 3 spin site under consideration, the time dependence of G.. can be written: Now, i f an exchange process is occurring between the j sites, then McConnell proposed that this can be described by assuming that a l l spins be considered to remain in one site until they perform a sudden "jump" to another site. It is assumed that no spin preces-sion occurs during the jump (clearly the sites must be magnetically distinct for the exchange to have an effect). For a spin at some site j , i t is further assumed that there is a constant probability per unit time, 1 /T . , , of the spin jumping to site k. This is the IK same as i f site k becomes site j because of the exchange process, with the spin remaining at the original site j . Since the fraction-al populations of a l l the sites must sum to unity: (2-10) dG. —j + a.G. = - l dt 3 3 iyH M . °3 (2-11) Consideration of a detailed-balancing scheme suggests that: (2-12) k k - 19 -where 1/x., / 0 i f j f k, and 1 /T . v is the probability per unit J k k J k time of the spin at site j going to some other site k. Thus by add-ing on an appropriate exchange term to (2-10) the Bloch equations can be readily modified to include, chemical exchange. For transfers 68 of moments, G. , between i sites the result is : ] ( 2 " 1 3 ) %k • a . G . - -iyH M . + _ £ C ^ 1 G. - T T J G. dt J j j 1 oj 4 j k jk y The steady state solution may be obtained by setting the time derivative of G.. equal to zero, solving the resulting linear equa-tions for Gj and taking the imaginary part of G = EG., since the in-54 tensity of absorption is proportional to the imaginary part of G For many equilibrium situations, and in particular those studied here, only two distinct sites are involved in the exchange process. Although in principle i t is easy to include any number of sites, in practice i t wil l be accompanied by a great deal of algebra. For the two site case, i t is convenient to label the sites A and B, whence the fractional populations of each site, pA and p^, wil l be related to the site lifetimes (inverse of total probability of a jump from that site to the other) as follows: (2-14) pA = ^ f - = 1 - p B A and the modified Bloch equations are: (2-15) dGA/dt • aAGA - -ivH-M • -A - 20 -(2-15) dG3/dt + ctgGg = - i Y H l M o B By defining p M = M , and solving (2-15) for steady state A conditions, one obtains: (2-16) G = Solutions to (2-16) can be obtained over any range of x^ and T g , although a particularly simple result is obtained i f x^ = X g , 24 suitable for fast computer methods . The complete evaluation of (2-16) will not be considered here, but is available in standard texts, for example that of Pople, Schneider and Bernstein^, and references therein. Two limiting cases of (2-16) are commonly used to interpret temperature-dependent magnetic resonance spectra; the slow and fast exchange limits. Slow exchange criteria are satisfied when the separation of the precessional frequencies of the two sites A and B, (co^  - C0g) , is large compared to the inverse of the lifetimes in either site A or site B. Under this condition the magnetic resonance absorption wil l consist of two lines at cu. and coD, and because these signals are A D considered to be completely separated, the assumption is made that when the frequency co is close to co^ , Gg is effectively zero. And vice-versa. Thus: (2-17) G * G, «v» - i H.M P A T A - 21 -with an imaginary part: ?AT2A (2-18) v = -yH M 1 ° 1 + ( T 2 A ) 2 ( u A " 1 0 ) 2 i .e . a signal centered at co, with linewidth ° A (2-19) • T . ; 1 = T - J • T " 1 where T~]' is the linewidth in the absence of exchange. If T * is 2A 2A known, a series of spectra over a known temperature range, in the slow exchange region, wil l give a series of x^* values from (2-19) for the process. In this region, care must be taken not to include spectra where there is any significant overlap of signals. For very fast exchange processes, such as those to be dis-cussed in this thesis, the appropriate approximation to Bloch's equa-tions are obtained when x^ and Xg are short compared to the recipro-cal of the precessional frequency differences: x « (coA - cog)"1 where x = T , T „ / ( T , + x_) is a mean lifetime. In this limit one can A B A B obtain: x + xR iYH,M (2-20) G = -iyHM - l o 1 ° V A + V B PAaA + P B aB by using (2-16) and (2-15). Separating the imaginary part yields: (2-21) v = -yH M T2 1 o • 1 + T2 (PAUA + PBUB " 0 0 ' 22 where T~* is the mean linewidth of a signal centered at the mean frequency: (2-22) <co> = pAcoA + PgU)B T 2 1 = PAT2A + PBT2B Usually the region of complete narrowing in which the ob-served linewidth is a simple weighted mean as in (2-22) is not reached, and the signal is subject to lifetime broadening caused by the fact that the exchange process is not quite fast enough to satisfy T << (co. - coD)~'''. Such lifetime broadening can be taken A D into account by substituting <co> from (2-22) into (2-16), and ex-. . . * • 42,70 panding in powers of T to give ' : V~2V T " 1 =PA T2A + PB T 2B + P i P B < T A + V< wA- UB> 2 This equation can be used to give information about rate processes from fast exchange spectra i f significant lifetime broadening is present. Now, a bimolecular rate process can be described by the following: kA (2-24) A + L ——± B kB where k g =^jj*> since « = k A / k g , k A = K k g . The explicit ligand dependence of k whereas k g is a simple first order rate constant, suggests that numerical analysis of line broadening using (2-23) can be simplified i f the term in i"A + Tg is replaced by a term in - 23 -xD only. For a reaction that is first order in both directions, i t D is unimportant which rate is analysed. It should be made clear that k can be obtained from (2-23), as will be detailed in the next chap-ter, and this is , in fact, a l l that the line position data alone can yield about the rate process. Hence, using (2-14) one can write: (2-25) pB = T B / ( T A • Tg) Hence: (2-26) xB = (xA • Tg)Pg Substituting (2-26) into (2-23) eliminates (T. + xD) and A D gives the useful result: (2-27) T " 1 = p A T" A + p B T"J + PAPBTB(coA -Under certain conditions modifications may be made to (2-27) to extend its application to even slower rates, hence broader lines, 70 by considering more terms in the method of Meiboom et al . These modifications are not large, however, and do not change the ideas involved. In using the fast exchange approximation it must be noted that the two lines involved in (2-22) must not be resolvable, and the linewidths in the absence of exchange must be small compared to the rate of exchange. This latter condition is easily met in this work, but a more general form of (2-27) that is not restricted is - 24 -24 obtainable i f necessary . Thus the conditions imposed by the fast exchange approximations may be conveniently summarised as: (2-28) x |ft). - w R | < 1 T I T~2A - T 2 _ l < 1 ( T " 1 ) * 2,0' < 1 where T_*Q = P ^ 2 A + P B ^ 2 B * knowing the experimentally-determined line positions, (2-22) can be used to obtain equilibrium constants, « , and the frequency difference, (to^  - co_,), from a least squares fit of <<0> to the base concentration. These treatments are detailed in chapters 4 and 9. Potential difficulties that can invalidate the results obtained for and k. are outlined next, before a more l ' detailed treatment of the linewidths is presented. - 25 -CHAPTER 5 STOICHIOMETRY AND THE DETERMINATION OF FORMATION CONSTANTS. A. INTRODUCTION: The determination of formation, or equilibrium, constants, and other thermodynamic parameters for weak complexes has 71-74 been the subject of some controversy , with many authors in the 73 74 past putting undue confidence on unreliable data . Person out-lined the problem by noting that the most accurate values of a for-mation constant are obtained when the concentration of the complex being formed (an adduct, for example) is approximately the same as the unbound concentration of the most dilute component. In epr terms, the most dilute component is invariably the paramagnetic sub-stance, and thus Person's warning suggests that epr measurements of formation constants should bracket = Pg = 0.5 (in terms of nomen-clature introduced in chapter 2). Equivalently, the mole fractions - 26 -of species A and B should be equal. The nmr situation for chemical shift measurements is restricted similarly, although with respect 71 to those species giving rise to nmr signals , but i t may often be impossible to achieve the necessary conditions i f )^  is very small (< 1 M *) or very large (> 10 M~*), or i f solubility problems, for 73 75 instance, prevent attainment of a suitable concentration range ' 12 In epr studies, the very high sensitivity (one can detect ~10 spins for a typical free radical) means that quite low concentra--4 tions (< 10 M) can be used, and hence solubility problems are not usually serious. If experimental formation constant data are assembled, in order to determine if some reaction model is operative, certain anomalies may occur because the data are not collected over a suf-71 85 175 ficiently wide concentration range ' ' . T o ascribe any mean-ing, therefore, to such data invites repudiation of the results at a later date by an experimentalist working in a different concen-tration range. Such instances have been reported, for instance, 73 for some nmr studies of hydrogen bonding in solvents . It is essential, therefore, to decide before assembling the data what con-ditions should be fulfi l led. Surprisingly, this has not been the case often enough in the estimation of formation constants from spectroscopic methods. B. THE SATURATION FRACTION: To introduce the ideas wanted without undue complication, the weak molecular complex to be formed will be considered to have 1:1 stoichiometry with respect to the reac-tants. Thus the system to be considered is : " k f (3-1) A + L V % B ; K = k_/k k f r r Specifically, the copper(Il)bis(diethyldithiocarbamate) "reac-tion" with various pyridines is representable in terms of (3-1) as (3-2) M L 2 + B ^ = = £ M L 2 B Formation constants are generally obtained by keeping the dilute component, A, fixed and "titrating" i t by the addition of vary-ing amounts of L , in a suitable solvent. Thus in terms of eq. (3-1) the formation constant is defined by the expression: (3-3) [ B ] = K [ A ] [L ] = K ( [A q ] - [B])([LQ] - [ B ] ) where [A ] and [ L ] are the fixed concentration of A and the total o L o J concentration of L , respectively. As [ B ] varies from zero to, in principle, [ A q ] , a useful frac-tion of the complex, B , can be expressed as the saturation fraction, s: (3-4) s = [ B ] / [ A Q ] = K[L ] / (1 + K [ L ] ) where 0 < s < 1. The definition in (3-4) is thus the binding probability dis-76 cussed by Weber . Person's requirement for maximum confidence in K can be expressed in terms of (3-4) as s = 0.5, thus [ L ] = 1/K. - 28 -Tacit in the definitions used so far is that al l solutions are ideal, and hence activity coefficients are unity, thus enabling the use of molar concentration in determining K. The solutions generally used are obviously not ideal, and to be correct one should write: (3-5) K' = - — - = _L__ . J _ _ = KK a A a L [A][L] Y A Y L Y where a. are the activities of the various entities in the solvent 1 being used, and a r e t n e corresponding activity coefficients. Thus i f the solutions are non-ideal, the real equilibrium constant, K', is defined as in eq.(3-5),; and not the equilibrium quotient K. Determination of K' is , however, difficult since data are not avail-able for many solvent systems. C. CONSIDERATION OF POTENTIAL ERRORS: It is often possible to arrange conditions experimentally such that the concentration of the adduct, or complex, is almost negligible in comparison to the concentration of the excess ligand (base). In an epr experiment this situation is realised very easily, since the maximum concen-tration of the adduct is that of the unadducted metal compound (for a case similar to the one being considered in this work) which is always very small compared to the base concentration. Therefore substitution of [L] ^ [ L q ] can be made, with an asso-ciated error (3-6) e = JLzJ_t = -s[A o]/[L o] - 29 -where K is the value deduced from setting [ L ] ^ [ L ], and ¥L^ the true value of the equilibrium constant, where [ L ] = [ L q ] - [B]. Because e is always < 0, its value should be very small (consider-ably less than experimental error) for the neglection of [B] to not affect the determined value of K. This error is not a statis-tical error and. must therefore be considered with some care. In the epr experiments performed here the value of [ A Q ] / [ L o ] is a l--3 -4 ways < 5 x 10 and often is < 10 . Since s must < 1, e in these experiments is certainly negligible within experimental error of K, which is ^ + 5%. To determine the minimum error arising in the determination of K under situations in which i t is not possible to separate K easily from some concentration (of base) - dependent parameter (such as optical absorbance, chemical shift, or line position 76 shift) Weber derived the formula, assuming the usual propaga-tion of errors: which is interesting in that i t depends upon s alone, and thus gives an example of the usefulness of using the concept of the saturation fraction. The derivation of (3-7) also assumes that errors in [L q ] and [A q ] be small compared to the error in s. 71 76 A plot of e/As vs. s shows ' that the most accurate values of K wil l be obtained when s lies between about 0.2 and 0.8. 1 1/2 (3-7) (1 - s) 1 2 - 30 -71 Deranleau proceeded further, and using information 77 theory derived the result that s has a maximum information con tent of 83% at s = 0.76. In particular, the region 0 < s < 0.1, although containing 10% of the saturation curve, contains only 4% of the information content. Increasing the number of measure ments in this.region does not alter this situation, since the in formation content is a ratio of theoretically accumulated to total available information, (I/I ). In fact, the rate of ac-' max' ' 71 cumulation of information with respect to s is : <* 3" 8 ' 1 IF— = 1 + s In s + l / s ( l - s ) 2 ln( l - s) max The preceding remarks are not intended to give an authori-tative discussion of experimental validity but only to point out that in order to test any stoichiometric model of weak com-plex formation equilibrium constants the maximum amount of ac-curate information must be obtained. That information is avail-able in the saturation factor region approximately bounded by 0.2 < s < 0.8. Unfortunately much data has been accumulated in the region 0 < s < 0.2, as illustrated in Table I of reference 73, which means that K's determined from such data are unreliabl It is also noteworthy that much of the optical spectroscopy work on weak molecular complexes with Lewis bases has been performed at very low s regions. If i t is impossible, because of experimental limitations, to satisfy the criteria set by Deranleau and Person, then - 31 -an experimental model may be examined using other sources to im-72 prove the results that are available D. PRESENTATION OF DATA: Once the question of a suitable concen-tration range over which to study some reversible process has been established, then a suitable presentation of the data can be made. The information required may be direct or indirect. For instance, the fast exchange situation between two supposed sites may be interpreted using epr data in terms of a two-site model (1:1 binding, say). It would be useful, therefore, to use the ideas of this section to decide upon a means of verifying 1:1 binding without recourse to any but experimentally-determined re-sults. Once 1:1 binding has been, or has not been, established, then the results can be interpreted in terms of the 1:1 model, or some other, respectively. In the case of the present work, parameters available from some plot (in addition to the properties of the plot itself) could also be used to check the results obtained from analysis of the epr data; which was in this case obtained for a 1:1 binding model. The first problem to consider is that for weak complex-es K must be known in order to evaluate the saturation fraction, s (eq.(3-4)). Clearly at some point K must be used to obtain s unless an independent method of measuring the amount of complexed material is available. By noting that s can be replaced with a - 32 -useful experimental parameter, a significant plot may s t i l l be obtained. In an epr experiment, the position of a fast exchange line position for a particular system represents an average ac-cording to (2-22). Rearranging (2-22) one obtains: (3-9) <io> - wA = P B ( W A " wB) and defining 6 = <io> - tuA, 6Q = Wg - toA yields: (3-10) 6 = p B 6 o but i t has been shown previously that Pg = s, hence: (3-11) s = 6/6Q Using these definitions of 6 and 6 q for epr gives the same equation for s as for the nmr case, where 6 is the observed chemical shift, and 6Q the shift of pure complex. Now, to expand Pg in eq.(3-10) in terms of some experi-mentally measurable or known parameters would avoid the problem of having to know 6Q, and further allow the presentation of "raw" data to determine the stoichiometry of complex formation. Thus first the equilibrium constant for the 1:1 process defined by eq.(3-l) is : (3-12) K = [ B ] / ( [ A Q ] - [ B ] ) ( [ L Q ] - [ B ] ) = k /k T 33 Now, as mentioned earlier [ L Q ] > > [ A q ] , hence [L q ] » [B] Therefore (3-12) becomes: (3-13) K = [B]/([AQ] - [ B ] ) [ L Q ] T A Further, p. = = 1 — p_, and T _ = 1/k , T a •= l / k _ [ L ] ' A T a + xD r B ' B ' r ' A ' fL o J A D 1 K t L o ] (3-14) so p = , p = A 1 +K[L ] B 1 + K [ L ] L o J L 0 J Substituting into eq. (3-10) gives: (3-15) 6 = K [ L o ] 6 = K [ L o ] ( 6 o - 6) 1 + K [ L Q ] 0 Since [L q ] is known and 6 can be obtained experiment-ally (there are important considerations about the determined 6 that wil l be considered later, involving the definition of to^), i t is possible to plot the relationships shown in (3-15) in several ways. To satisfy the Deranleau-Person criteria, and hence to plot a l l the theoretically obtainable data, covering the com- plete s range, both origins of any suitable plot must be included. This is to unequivocably determine the quality of the curve. Re-81 ciprocal plots such as the Benesi-Hildebrand (1/[L q] vs. 1/6) 82 or half-reciprocal plots such as the Scott ([L q]/6 vs. [ L 0 D are open-ended on the abscissa, allowing the experimentalist to vary the concentration [ L q ] , and hence the range of s, in a man-- 34 -ner that can often give a straight line simply by distorting 71 low s points with uneven s spacing . Normal errors in small concentration values in the reciprocal plots will become very large errors and thus render such points almost valueless. The higher concentration points, although becoming progressively more reliable, tend to be crowded together. Thus it has been suggested that in order to obtain most confi-dence in plotting (3-15), for the purpose of deciding whether 71 the plot is linear or not, reciprocal-type plots be avoided 79 Plots based on the Bjemim formation function (5 vs. log[LQ]) are curved and symmetrical about s = 0.5 for 1:1 bind-ing, and thus give, in addition to a complete range of the saturation fraction, an easily-recognized plot symmetry for the correct model. A simpler, linear, plot of experimental data giving reliable confirmation of stoichiometry and a presenta-80 tion of the whole s range is the Scatchard plot . This is simply a plot of 6/[L q ] against 6, and one can see from (3-15), by dividing by the constant 6 q, that this plot is equivalent to one of S / [ L q ] vs. s. This plot will be linear, with well-spaced points, over a suitable range of saturation fraction i f the data is correct for the model chosen. Clearly, this plot can be used to obtain estimates for the formation constant and 6q, since it has slope - K and intercept In this work, Scatchard plots of the experimental data were used to establish - 35 -stoichiometry, and the values of K and 6 available from the ' o slope and intercept used only to check the results of least squares fitting procedures. The only exception to this was for the reaction of CuDDC with 2-methylpyridine in benzene, where the least squares fits were inconclusive because of the very small values of K (0.02 < K < 0.08). The Scatchard plots were linear and a reasonable set of values of K and _> obtainable. o These results, and the others, are detailed in chapter 5. 72 Some questions as to the concentration-scale depen-dence of values of K and 6 obtained from Scatchard, Scott, or o ' Benesi-Hildebrand plots clearly do not affect the present work, since the plots were used mostly to check linearity. It is 72 78 worth noting, however, that recent publications ' suggest that the concentration-dependence can be removed by correct interpretation of the equation to be used. In other words, 72 differences in K and 6 values obtained by Hanna and Rose for o concentration scales in molal, molar, and mole fraction do not arise i f donor non-ideality is taken into account. E. MULTIPLE EQUILIBRIA: a) The binding model: The Scatchard presentation was cho-sen for this work because it satisfies the requirements of both convenience and accuracy. A linear Scatchard plot generally confirms the model proposed as long as the saturation fraction range is at least seventy five percent covered. In the - 36 -case of competing or multiple equilibria, for example, small saturation fractions invariably give straight line plots, al-though the slopes and intercepts wil l be different for each case. Also, various combinations of formation constants for several consecutive equilibria can also give rise to linear re-71 lations , add it wil l be shown in this work that this possibi-lity must be considered. Rather than attempt to give a general treatment, which is not particularly difficult but involves considerable algebra, the case to be considered will be that of the possi-bi l i ty of formation of both 1:1 and 1:2 adducts. Chemically, this case has a large number of applications, and can be conven-iently applied to divalent copper. Although there are strong stereochemical and spectroscopic arguments for stating that square-planar copper(il) compounds, such as CuDDC, do not form stable 1:2 adducts with weak bases in solution, the discussion is quite useful. The complex formation process is to be described by the following model: K K (3-16) A B ^=E=S C where for a metal complex, Ml^, interacting with a Lewis base, B: K l (3-17) ML2 + B , ML2B K2 ML2B + B ^ ==± ML B 2 - 37 -This model assumes, for CuDDC specifically, that no for-mation of l-\L^B^ is attained directly by the addition of two mole-cules of base of M L - in a simultaneous process. For epr purposes there is generally no need to restrict the relative rates of formation and dissociation of B and C, in (3-16). However, by restricting the model to the fast exchange region the requirement will be that al l rates are sufficient to maintain overall fast exchange conditions. This allows some simplication as in the two site equilibrium model that describes 1:1 formation, and hence an obvious extension to (2-22) can be , . 83 made, since : (3-18) <to> = / . . Hence, for the three site case described by (3-16), one may write: (3-19) <03>= PAcoA + pBcoB + P c u , c At equilibrium, i t is possible to define the p^ in terms of the base concentration as in the two site case, again requiring [ L ] = [ L q ] . Hence: (3-20) [B] = [A] [ L Q ] [C] = K 2 [ B ] [ L q ] = K ^ - t A H L j 2 - 38 -Defining T c = [A] + [B] + [C] results in: (3-21) pB = K1[\][Lo]/TQ P C = K i V A ] [ L o ] 2 / T c or, using (3-19): (3-22) Tc<u> = [A]coA + K ^ A ] [ L ^ + [A] [L Q] 2CO C but T c = [A] + K [ A ] [ L ] + K K 2 [ L ] 2 [ A ] from (3-20), hence: (3-23) <co> = M A + K 1 [ L 0 K + hK2[Lo]\ 1 + K . [ L ] + K . K _ [ L ] 2 l l o 1 2L o Thus the effects of two competing equilibria can be readily determined from (3-23) for any values of on and and K ^ , over a suitable base concentration range. b) Presentation and evaluation of data: As with the 1:1 binding situation discussed earlier, there are several means of presenting the line position data for an equilibrium process to determine i f multiple equilibria are present to any extent. Also, as before, reciprocal and half-reciprocal plots have the disadvantage of being dependent on the region of the saturation curve over which data is collected. In general, it has been 71 shown, both by Deranleau and by eq.(3-23) that any of the plots considered previously will be curved. The most curved - 39 -plot will be the Scatchard plot, where <S/[Lq] vs. 6 is plotted, since no reciprocal effects will distort the axes. The data collected in this work for a series of to. values and K. and K~ 1 1 2 being consistent with the present experiment, show that the Scatchard plots are indeed curved (see Chapter 5). Some excep-tions occur when K_ < K^. It is again important to note that Scott or Benesi-Hildebrand plots made on restricted regions of the saturation fraction scale (high or low regions, especially) are often quite linear, even when a plot over the whole s range is quite curved. This effect is even apparent for the extremes of the Scatchard-71 type plot. Deranleau's second paper , on multiple equilibria, shows convincing evidence of the fact that only i f a significant percentage (> 75%) of the saturation fraction is measured should any confidence be placed in the results. Even then, special, or circumstantial, combinations of multiple equilibria parameters may result in linear plots. In these situations, checks can be made over a range of expected or known results to see i f , indeed, such cases can occur. This was done in the present work, and the results are available in chapter 5. Finally, the question of possible competing equili-brium processes reemphasises the uncertainty of using isosbes-tic points, as in absorbtion spectroscopy, as proof (or not) of a specific number of species being present. Combined with some other form of confirmation, however, the use of isosbestic - 40 -points can be very informative. It could arise, for instance, that for two competing equilibria = and the absorbtivities of A, B, and C; a^, are al l equal. Under these conditions al l plots of data considered previously will be linear, and the ab-sorbtion spectrum will show an isosbestic point. This argument holds for any number of equilibria as long as the It\ and a^, res-pectively, are equal. This result has been obtained in a differ-84 ent context , and is admittedly rather unlikely to occur, but is included only to demonstrate that often very l i t t le care has been taken to unequivocally establish that only 1:1 binding is 74 71 present. In fact, as noted by Person and Deranleau , few, i f any, of the weak complex formation processes studied spectro-photometrically have been proved to be 1:1 complexes, where per-tinent, unless they were isolable and amenable to chemical ana-lysis. - 41 -CHAPTER 4 INFORMATION FROM THE LINEWIDTH A . RELATIONSHIP OF THE LINEWIDTH TO KINETICS: In the limit of extreme narrowing of a magnetic resonance line, the fast exchange limit, no information about the rate of exchange is available. The linewidth in this limit i s : ^ T2 - P A T 2 A + P B T 2 B and pA = 1 - pB = T A / ( T A + T Q ) = (1 + K f L j ) " 1 , using the nota-tion developed in chapters 2 and 3 . In epr studies of exchanging systems, the limit of fast exchange (k > lO*^ sec"*) is rarely reached, and lifetime broadening contributes to the observed linewidth: ( 4 " 2 ) r2 = PA T 2"1 + P B T 2B + P ^ P B ^ A + T B } ( ( ° A " UB)2 - 42 -For the present study, where the equilibrium process is defined by: k f (4-3) CuL + B -2 —7 CuL0B k 2 r -1 37 k can be equated with T„ , and k. = Kk . Thus, as noted ear-r n B f r l ier , it is more convenient to rewrite (4-2) as: C 4 " 4 ) T 2 1 = PAT_I + PBT2B + PAPBTB ( a JA " W B ) 2 Before considering the non-exchange linewidths, T~^ and T^g, in more detail, i t should be noted that the fast ex-change conditions (2-28) necessary to obtain (4-4) are often not met. For narrow epr lines, the linewidth conditions are usually satisfied, but the line separation condition, T|CO A - C0g| « 1 can easily be unsatisfied. For the reaction of CuDDC with pyri-dines in benzene, for instance, x(co. - to_.) ^0 .8 for some tem-' ' A B preatures. Of course, co^ - co^ is intimately related to the for-mation constant, and as the temperature is decreased, i t is noted that co^ - Ug, and hence K, increases. Clearly, the fast exchange conditions wil l be violated for a certain value of K, no matter what the temperature. In this work, i t appears that 86 K must be £ 2. Corden and Rieger found similar limitations in their work, and to overcome these they expanded the modified Bloch lineshape function in terms of frequency and linewidth to include extra "near fast exchange" terms for the linewidth: 43 (4-5) T"1 = p AT- A + p BT 2 J • P AP B f(A 2-6 2) + (p A-p B)6 (3A 2-6 2) + (5p ApB -l)(A 4-66 2A2 H-6 4)J where 6 = x (T~ A - T ^ ) , A - x (LOa - oig) , r = f /Cp^* + P B T 2 B ) , a n d x = T ^ T B ( T A + Tg) Equation (4-5) was shov • ^ to effectively allow values of x (co - Wg) as large as 0.5 - 0.8, hence extending the fast exchange approximation to slower rates than (4-4), when certain of the terms 6,A or r become large. The inclusion of the extra terms as in (4-5) is usually not necessary in the present work, but where the exchange rate becomes slightly slower, but not slow enough to cause a separation of the lines, the extra terms can become quite large. B. . NON-EXCHANGE LINEWIDTHS: For studies of exchange processes by magnetic resonance, knowledge of non-exchange linewidths is usual-ly necessary. It is usually assumed that the non-exchange line-widths, measured under scr.e condition wherein i t is assumed no ex-change processes are taking place, define the components of the exchanging system equally as well as the non-exchanging one. It is often assumed, also, that the non-exchanging linewidths are temperature-in .lependent. This is rarely, i f ever, the case, and such variation should be taken into account. Similarly for vis-cosity effects, etc.. Two methods commonly prevail for the mea-surement of non-exchange linewidths. One is to measure the line-- 44 -widths of the separated lines in the limit of very slow exchange (i.e. at low temperatures), and the other is to measure the line-widths of the individual species separately in the absence of ex-change conditions. In the former method, the temperature-depen-dence of the non-exchange widths is obscured by the exchange pro-cess, and only in solids is i t likely to be a useful method. In solids, the assumption can often be made that the only tempera-ture-dependent contribution to the linewidth is that of the ex-change process. The second method for measuring T 2 A and T~g does enable the temperature-dependence of the non-exchange linewidths to be observed. For instance, dissolving a metal complex in neat solvent and measuring its temperature dependence in the absence of another solvent or ligand is quite straightforward. However, this latter method suffers from difficulty in being able to de-fine the "end-points" A and B, in solution. The value of A is ideally defined in terms of a completely non-coordinating envir-onment, and B in terms of a completely co-ordinated environment. In solutions, the solvent effects alone render the achievement of these end points experimentally difficult . The approximation that A be defined as the A species in a non-coordinating solvent is , however, a reasonable one for some solvents. It is never possible, however, to obtain 100% co-ordination of some ligand to A in a fast equilibrium process, since the self-concentration of the ligand is usually < 20 M. Hence the value of B obtained from neat ligand solutions may be subject to uncertainty. It - 45 -is useful to keep this in mind when considering fast exchange pro-cesses in solution. It is possible, however, to avoid these difficulties with an appropriate least squares technique, by using the solvent and ligand measurements of A and B as good approximations to (_A, to_,, T~A , and T_g. By allowing the least squares routine to vary over these parameters, as well as K and Xg, respectively, indepen-dent end-points can be obtained, which can then be compared with those measured. This is the procedure used in this work, and is described in more detail in chapter 9. Non-exchange epr linewidths in solution have a tempera-ture dependence defined approximately by the properties of the liquid. Liquid structure fluctuations and collisions, as well as molecular vibrations, give rise to a modulation of electric fields experienced by a nucleus or electron attached to some molecule, and this may cause relaxation. For the doublet state 87 of an ion Kivelson has investigated three major electronic relaxation processes: the direct and Raman processes of Van 88 89 Vleck , and the Orbach process . In the direct process a spin fl ip (absorption of energy) occurs through absorption of a phonon of energy equivalent to the energy required for the f l ip , whereas in the Raman process spin flips are caused by phonons of arbi-trary energy with the emission of phonons with appropriate energy. The Orbach process involves absorption of a phonon of equivalent - 46 -energy, as in the direct process, but involves a simultaneous elec-tronic excitation, hence the overall absorption of energy is higher than in the direct process. These mechanisms were originally pro-posed for the solid state, and are discussed in more detail by Van 88 89 Vleck and Orbach . Kivelson was able to show that none of these electronic relaxation processes is very important in liquids, in comparison to other effects there, although the Orbach process can, 87 in favourable circumstances, be significant . Overall, in fact, it is difficult to separate such electronic relaxation processes from rotational effects, since it is often difficult to study a suitable S=l/2 system over a wide enough temperature range, in a 90 liquid, in order to distinguish the various effects . If the temperature range required was available, however, the electronic and rotational relaxation effects could, in principle, be readily separated since they al l have different temperature coefficients. Kivelson has developed equations describing these temperature 87 relationships 2 + 9 r Specifically, Cu ions (d , equivalent to o=l/2) have very much larger rotational relaxation effects in solution than electronic effects. The rotational, or tumbling, contributions to the linewidth give rise to an m .^-dependence (m^ . is the nuclear spin quantum number in the field direction) which is, in turn, temperature dependent. This m.j.-dependence was first interpreted 102 in terms of a randomly-tumbling microcrystal by McConnell , and - 47 -36 the description was later extended by McGarvery , for several transition metal ions. In effect, the random tumbling of the mlcrocrystal is insufficient to average out the anisotropy in the g- and A-tensors of the central ion, and these incompletely-averaged terms can be shown to contribute to the linewidth. For states of higher multiplicity, anisotropy in the zero-field splitting is generally a predominant contribution to the solution l inewidths 2 6 ' 9 1 ' 92> 1 0 3 . The most comprehensive treatment of the effects of 91 92 tumbling on epr. lineshapes has been given by Kivelson et al ' . 93 Important extensions to this work were developed by McLachlan 94 103 and others ' in addition to those references mentioned in chapter 2, and the ideas overlap considerably with the work of Kivelson, which is based on the Kubo-Tomita-Anderson approach. The results are best summarised in terms of the peak-to-peak linewidth (sec - 1),AH, and the m_ values a particular ion may take (-1 < m_ < +1, I the nuclear spin): 2 3 (4-6) AH(m_) = a' + a" + 3m- + ym^ + 6m_ where: (4-7) a' = (Tc/360)(go3Tr/3/h)"Y8(HoA5)5>-[4-r3(l+w2T2)"1] + 9lCl+l)b 2[3+7(l+co 2T 2) _ 1]J 8 = (T c/15)(g o e T T/3/h)" 1bH oA6[4 +3(l+co 2T 2)" 1] - 48 -(4-7) Y =• ( T c / 4 0 ) ( g o 6 u / 3 / h ) ~ 1 [ 5 - ( l + w \ 2 ) " 1 ] b 2 6 = (x r/10j((g B-n/Z/h)'1^2^ /(t\oj )) and the f o l l o w i n g d e f i n i t i o n s are used: b = 2(k/f + 2A i)/3h, AcU (g„ - g i ) 3 / h a Q = 1/3 (A, + 2A,), g Q = 1/3 (g, + 2 g J . The usual epr nomenclature i s used. (4-7) i s f o r an a x i a l l y - s y m m e t r i c g and h y p e r f i n e tensor, which i s q u i t e common f o r t r a n s i t i o n metal i o n s , and can be e a s i l y g e n e r a l i s e d to an 96 -1 a n i s o t r o p i c case . I t may be noted t h a t the term .(g gTr/3/h) i s the conversion from peak-to-peak ( d e r i v a t i v e ) l i n e w i d t h to ^ 2 > the inv e r s e of the tr u e t r a n s v e r s e r e l a x a t i o n time defined 95 by the h a l f - w i d t h at h a l f - h e i g h t of the abso r p t i o n l i n e . The r o t a t i o n a l c o r r e l a t i o n time, T^, i s th a t time r e q u i r e d f o r a molecule tumbling i n s o l u t i o n to r e g a i n an i n i t i a l o r i e n t a t i o n w i t h respect to i t s environment. The term a" i n (4-6) i s a x^-independent term c o n t a i n i n g a l l c o n t r i b u t i o n s from sources such as s p i n - r o t a t i o n a l r e l a x a t i o n , d i p o l e - d i p o l e r e l a x a t i o n , 98 etc . The form o f (4-7) given i s an approximation r e q u i r i n g a /co be very s m a l l , where co i s the centre of the epr spectrum. 0 0 0 I n c l u d i n g t h i s term generates various cross terms discussed by 96 Wilson and K i v e l s o n , which may c o n t r i b u t e as much as f i f t e e n percent to the l i n e w i d t h under c e r t a i n c o n d i t i o n s ( e s p e c i a l l y - 49 -when ^ C O q ) . The exact form of (4-6) and (4-7) is not impor-tant here; what is important is that the m.-dependence of the linewidth is shown explicitly. The terms a, 8, y and 6 take the form of complicated func-tions of the inner products of the g- and A-tensors, with the 97 linear coefficient, 8, containing a mixed tensor product, g:A Figure (4-1) shows m_-dependences in vanadyl and cupric ion epr spectra. Since the coefficient 6 is usually small, spectra in which y dominates will be symmetric, with respect to the center, and spectra with 8 dominating will show marked asymmetry, broad-ening from one side to the other. Copper(II) B-diketonates (fig. 4-1) and CuDDC are good examples of this asymmetry. Since hyper-fine splittings are often more sensitive to temperature than g values for transition metal chelates, the observed linewidths may show marked temperature effects indicative of increasing sym-metry as temperature increases. Of course, T_. will also decrease as viscosity decreases and this will have some effect in addition to the changes just described. Temperature dependence of the various coefficients in (4-7) is in and epr parameters. It is usually assumed, how-ever, that the hyperfine terms are temperature-independent; values of b and Ay being obtained at 77°K in a frozen liquid, for example, and used for a l l temperatures. This is not neces-sarily a good assumption unless made over a small temperature - 50 -3329 GAUSS U--7/2 M'-V2 M'-V2 U'-l/J I u • 1/2 M-J/2 M-5/2 U-7/2 Vanadyl Acetylacetonate at X-band in Toluene (236 K) 1 I I O O G A U S S U--7/2 M--5/2 M--3/2 U>-l/2 U-l/2 U • 3/Z M-5/2 U-7/Z VOAcac at K-band in Toluene (297 K) M • -3/2 M ' -1/2 M . .1/2 M •. -3/2 CuAcac at X-band in chloroform (331 K) M--3/2 M . - V 2 M - . V 2 M . . J / 2 CuAcac at K-band in chloroform (300 K) F i g 4-1: M r - d e p e n d e n c e of L i n e w i d t h s (from Wilsopand Kivelson, J. Chem.Phys. kk 15^,^5(1966) - 51 -range, since hyperfine splittings in solution are quite strongly temperature dependent. It is difficult to avoid the assumption, though,since very few systems have been studied from very low temperatures to room temperatures in order to evaluate the tem-perature effects. Thus, assuming temperature-independent hyperfine para-meters, a l l the temperature variation is in x .^. Values for the rotational correlation time are usually calculated from the 2 Debye theory of rotational relaxation for a rotating sphere : (4-8) x c = 4Tmr3/3kT where n is the bulk viscosity of the solvent at some temperature T, r the radius of the sphere, and k the Boltzmann constant. Values of r obtained from calculations of xr by means other than (4-8), however, are usually considerably smaller than the mole-cular diameter of the compound being studied"^4. This effect has been corrected-for by Kivelson et a l . 1 ^ ' 1 ^ 6 by introducing an empirical parameter, K , which is unity when Debye theory holds. A quite accurate method of evaluating appears to be that 104 of Burlamacchi , who used the fact that the linewidth passes through a maximum at COQT^ = 1 as the viscosity is increased, for ions possessing zero-field splitting. In conclusion, there must be a temperature dependence of the non-exchange linewidths in an exchanging system, defined ac-cording to the preceding remarks. The various coefficients were not calculated in this work, since they add nothing to the under-- 52 -standing of the basic exchange process; the non-exchange line-widths were simply measured as a function of temperature, in-corporating a l l non-exchange effects implicitly. C. ROTATIONAL EFFECTS AND EXCHANGE: As shown in the preceding section, for transition metal ions the dominant contributions to the linewidths are the anisotropies in the g and hyperfine tensors, coupled to the random (Brownian) diffusion of the metal ion complex. Spin rotational terms are also important, 98 and can be shown to depend on a term T / n , which can be most conveniently included in non-concentration-dependent terms. It is assumed here that the only concentration dependence is the contribution of any exchange process, and indeed a simple test for the presence of an exchange process is a dependence , . 90 on concentration An exchange process will modify the rotational behaviour of the complex by superposing an additional modulation on the components of the anisotropic g and A tensors. In general the relative times and x g x , for reorientation of the complex and exchange with another complex, respectively, can be shown 66 67 to be crit ical in the determination of lineshapes ' . The mathematical treatment of the two competing processes has been described in some detail using reorientation probabilities 67 99 coupled with Redfield theory ' , but the most applicable - 53 -treatment for the present case is that of Atherton and Luckhurst*^. An outline of the treatment follows to illustrate the effects ex-pected. The time-independent Hamiltonian describing the two site situation can be represented as a weighted sum, much as the Bloch lineshapes were: (4-9) iC° = < £ f H S z + <a>I-S where g^> = P^g^ + PgggJ<^ a^ = P^ a A + P B S B an^ w n e r e non-secular terms are not included. The time-dependent Hamiltonian can be written: (4-10) £tiW = e ( g C t ) -<S»HSZ + CaCtD - < a » I.S where^-^(t) arises from modulation of the isotropic parts of the g and A tensors>^_T^2^t-' ^ r o r a modulation of anisotropic ten-sors. The tensor convention of summing automatically over re-peated subscripts is used inp^^C*)* Ing^^(t), g(t) and aft) are randomly fluctuating between g^ and gg, and a^ and ag, respectively, whereas in^^~(t) rota-tion of the complex and ligand exchange give rise to a more com-plicated temporal behaviour. Atherton and Luckhurst found it expedient to evaluate the scalar terms from^^(t) and the - 54 -second-rank tensor temms from^^(t) separately. Since S=l/2 transition metal ions have no degenerate allowed epr transitions, the relaxation matrix can be readily interpreted in terms of the exchange contributions to the linewidth''"'*^^. The pure ex-change (scalar) contribution i s : (4-11) T - 1 = /lg 2B 2H 2 P 2 P 2 ( T a + Tg) + 2AgAaBHp 2p2(T A + + •Ti2 fi 2/2 , ,„ r% , T ^ 2-n 2 2, + Aa £m 2 + 1/2 j I(I + l)-m^ P A P B ( T A + V 2 2 L I + to T o where g =-g A - gg5 a = a A - a g ; T - TA TB T +T A B Equation (4-11) is simply the Bloch equation (4-2) ex-panded to f i r s t order in U K ( E g $H/n + a J T I J ) , plus non-secular contributions. The evaluation of the contribution to the linewidth from jc^2^ * s n o t s t r a i g n t f ° r w a r d , a n d involves probability theory to determine the effects of a random jump between sites, and Brownian motion of the complex i t s e l f . These contributions can be conveniently summarised'''^ to show that the total linewidth is simply that due to ligand exchange plus the weighted mean of the non-exchange linewidths, T~*• As in (4-11) this is simply the Bloch result plus non-secular terms. As w i l l be shown later, the non-secular terms, calculated from (4-11) are very small (< 0.5% usually, often << 0.5%) for the exchange process studied •in this thesis, but were included for completeness. - 55 -The non-secular tumbling terms will become important, and thus invalidate the Bloch treatment, when x^  becomes com-parable to x, or even slower than x. The x^ , dependence here is involved in the^. ( t . j terms, which are not explicitly shown. This limit, x « x^, thus represents a limitation to the applicability of the Bloch equations for exchange process in a liquid medium. The density matrix methods1,*>6-60^ those of Anderson and Si l lescu 6 4 ^ provide means for includ-ing a l l regions of x^_ relative to x. A microscopic analysis of the contributions of x and x^~ to motional narrowing of mag-netic resonance l ines 1 ^ 1 has shown that exchange-narrowed and motional-narrowed lines can be separated by the Fourier trans-forms of the various correlation functions contributing to the lineshape. This is specifically important when a line narrow-ing is present that is not clearly defined to be exchange- or motionally-narrowed. In general, since rotational correlation times are much shorter than most exchange times, the Bloch equations will pro-vide unambiguous and relatively simple interpretations of the exchange process, as long as any motional effects are included in the non-exchange linewidths. In particular, transition-metal complexes reacting reversibly with various ligands to form specific adducts give epr spectra which can often be ana-lysed using the modified Bloch equations. - 56 -CHAPTER 5 THE SYSTEM; EXPERIMENTAL RESULTS A. LEAST SQUARES ANALYSIS OF THE RESULTS: The electron para-magnetic resonance spectrum of copper(II) bis(diethyldithiocar-bamate) in a non-coordinating solvent is typically that shown in fig. 5-la. The effects of chemical exchange, caused by the presence of pyridine at 1 M concentration, are typified by fig. 5-lb. As can be seen the asymmetry of the benzene spectrum can be removed by the chemical exchange contributions to vari-ous lines. Dependence of the line position and linewidth on pyri-dine concentration for benzene/pyridine mixtures at 300°K is illustrated in figs. 5-2 and 5-3. Agreement between experi-mental (circles) and least-squares (solid lines) results is Fig 5-1a: CuDDC in" benzene (300 K) - 58 -\ 59.6 H 58.CH ' i i i « i i \ i i 1 r O 2 4 6 8 IO . 12 [L] (Moles/ l i ter ) Fig 5-2: Concentration dependence of average line position in benzene-pyridine solution (300 K) • 3/2 epr line 0 1/2 epr line 4 0 o 2 4 6 [L] (Mo les / l i t e r ) Fig 5-3: Concentration dependence of linewidth in benzene-pyridine solution. (300 K) - 61 -well within experimental error. The maxima in the linewidth plots are caused by the lifetime broadening contributions to the fast exchange linewidth, and give an empirical evaluation of the exchange rate: the slower the rate, hence the larger Xg becomes, the higher the maximum. The position of the maximum, with respect to base concentration, can be readily shown to be at [L ] = (2K) _ 1, since the lifetime broadening contribution 2 is proportional to PAPg> from (4-4), which has a maximum at PA = 2/3, and PA = d + K [ L o ] ) _ 1 . The least squares fitting routines were allowed to vary over the end points (co^  and tog, or T_A and T_g) as well as the quantity of interest, K or Xg. As noted in more detail in chapter 9, the procedure obviates the need to use neat solvent measurements for the end points, and thus the fitted values of c_A and tog could be associated with solvent-free parameters. This is developed more fully in the next chapter, but for now i t can be stated that a l l least squares-fitted values of the end points are not necessarily the same as those measured in neat solvents. The trends with temperature are preserved, how-ever, and al l results were found to be quite consistent inter-nally. In other words, parameters from the line position data were used without change in the linewidth analyses, allowing a l l data to stand, or f a l l , on their own merit. Several authors - 62 -86 16 ' have not been able to obtain consistent results without applying constraints, however, and i t would seem that this must be due to the data and/or method of analysis. Tables 5-1 and 5-2 give a complete description of the data to be expected for the benzene/pyridine system. In passing, i t should be mentioned that the equilibrium parameters are attainable from an analysis of the hyperfine 107 splittings, using the relationship : ( 5 - 1 ) aQ = pAaA + p B a B for the fast exchange-averaged mean hyperfine splitting. 109 Shklyaev and Anufrienko used this procedure to obtain equil-ibrium constants for CuDDC with pyridine in benzene. Eq. ( 5 - 1 ) was used here for the benzene/pyridine system, the results being the same as analysing the line position itself . Table 5-3 illustrates the data obtained. This method was not used for any other than the benzene/pyridine system, since by using the line positions directly exchange effects on both the iso-tropic and hyperfine values are implicitly included. The line position data, with appropriate units, are readily substituted into ( 4 - 4 ) , ( 4 - 5 ) or ( 4 - 1 1 ) for further analysis. It has beer, noted previously in this work that values of coA obtained from extrapolation of the <co> vs. L q plots to L Q = 0 are consistently higher than those obtained in the cor-TABLE 5-1 Parameters obtained from a least squares f i t of the line position data and obtained from measurements in neat solvents -9 -1 Hyperfine line position (10 sec ) Temperature (°K) +3/2 +1/2 * + * + * + * + u>A coA u,B <_B coA coA COg COg (mole Jl ) 280 59. 612 59.483 59.133 59.196 58.143 58.108 58.010 58.024 0.64 285 59.607 59.478 59.146 59.211 58.143 58.106 58.010 58.029 0.58 290 59.601 59.474 59.156 59.205 58.141 58.105 58.013 58.027 0.53 295 59.594 59.469 59.163 59.232 58.139 58.104 58.015 58.035 0.45 300 59.587 59.465. 59.156 59.223 58.137 58.102 58.013 58.032 0.38 305 59.579 59.460 59.144 59.230 58.135 58.101 58.009 58.034 0.32 310 59.577 59.455 59.158 59.252 58.134 58.099 58.013 58.041 0.30 315 59.569 59.451 59.164 59.255 58.132 58.098 58.015 58.042 0.29 320 59.559 59.446 59.150 59.258 58.129 58.097 58.011 58.042 0.24 325 59.554 59.441 59.145 59.262 58.128 58.096 58.010 58.044 0.23 * value obtained from least squares f i t t value obtained from measurement in neat solvent $ the value of K is the average between the values for the two hyperfine line studies; uncertainty +0.02. TABLE 5-2 Parameters obtained from the line width data Line widths for the +3/2 line CIO"6 sec' 1) Temperature f°IO T T~* T - 1 T - l k Tc 1 J 2A !2A X2B *2B r a i £ TR fx 10" sec"A) C=Kk ) ,f.9 . r.» _i -i CIO sec) (x 10 sec M ) 280 51.27 57.87 63.66 62. 34 4.13 2.56 2. 42 285 46.73 58.20 66.19 62. 86 4.76 2.62 2. 10 290 46.76 58.81 61.36 64. 99 5.24 2.52 1. 91 295 47.84 59.67 54.43 67. 31 5.55 2.36 1. 80 300 50.13 60.76 52.25 69. 66 5.85 2.17 1. 71 305 51.86 62.00 50.58 71. 98 6.25 2.13 1. 60 310 51.77 63.56 53.54 74. 31 6.62 1.99 1. 51 315 55.57 63.87 59.80 76. 65 6.99 1.89 1. 43 320 60.86 67,30 57.46 79. 45 7.52 1.88 1. 33 325 66.82 69.48 59.66 81. 31 8.55 1.79 1. 17 * value obtained from the least squares fit t value obtained from measurement in neat solvent TABLE 5-3 Parameters obtained from a least squares f i t of the hyperfine parameters Isotropic Hyperfine constants ( l O ^ s e c " 1 ) Temperature (°K) * A A * A B AA ( 1 0"-1 sec ) K (+0.02) (mole l"1) 280 14.333 13.441 11.063 11.424 3.274 0.62 285 14.283 13.409 11.081 11.531 3.202 0.60 290 14.247 13.378 11.063 11.486 3.184 0.51 295 14.211 13.348 11.207 11.675 3.004 0.47 300 14.175 13.315 11.189 11.612 2.986 0.33 305 14.121 13.283 11.099 11.666 3.022 0.34 310 14.081 13.252 11.153 11.819 2.932 0.30 315 14.040 13.222 11.243 11.837 2.806 0.30 320 13.995 13.189 11.207 11.837 2.788 0.26 325 13.959 13.157 11.225 11.891 2.734 0.24 * value obtained from least squares f i t t values obtained from measurements i n neat solvent - 66 -responding neat solvents. In effect, this is precisely the least squares value of c o ^ , and as will be detailed later, in a l l solvents this "extrapolated" value of t o ^ is the same for a l l solvents studied. Since i t was expected that the differ-ence between icyrCneat solvent) and t o ^ * (extrapolated or least squares result) should reflect some aspect of the solvation of CuDDC in benzene/pyridine mixtures, the benzene/pyridine system was examined at very low pyridine concentrations. The results are illustrated by fig. 5-4. Clearly, a signifi-cant decrease in a 0 , from the trend illustrated by the solid line, occurs at base concentrations approaching that of the metal i tself . B. DETERMINATION OF STOICHIOMETRY: In chapter 3 a discussion of data presentation was outlined. In order to interpret the results of this thesis a knowledge of the adduct stoichiometry was required. The methods quoted in section A of this chapter, and shown to be entirely self-consistent, actually require the results of this section for confirmation. 71 80 Deranleau pointed out that a Scatchard plot of (3-15), represented as 6 / [ L Q ] V S . 6, must be linear over at least seven-ty-five percent of the saturation fraction before confirmation of the stoichiometric model yielding (3-15) can be made. Plots of the data obtained in these experiments, using the Scatchard presentation, are a l l linear over the entire s range, which 81.H Fig 5-4: Hyperfine splitting of CuDDC in benzene-pyridine solutions at low pyridine concentrations 79-j|inert"(solvent free) hyperfine splitting •78.75G co §77H < (3 o < i i 754 73- —r™ .12 0.0 .02 1 1 i .04 .06 .08 Pyridine concentration (moles/litre) .10 - 68 -covers the fraction 0.1 < s < 0.9. Fig. (5-5) illustrates 81 -1 -1 some of these plots. Benesi-Hildebrand plots (6 vs. [L ]~ ) for the same data are also linear, but the rel iabil i ty of the plot is low because of the tendency of a reciprocal plot to 71 crowd the data . This is ably illustrated in fig. (5-6), where the uncertainty problems are also shown. Because of the large uncertainties resulting from taking reciprocals of small numbers, the errors in low concentration data for this type of plot can become absurdly large. The linearity of the plots confirms the 1:1 stoichio-metry model used to derive (3-15). Hence the adduct formation process is describable in terms of: (5-2) CuL2 + B 5 = ± CuL2B Extrapolated values ofto^ were used to define £ , since the neat solvent parameters are lower than the extrapolated ones. Since 6 = co - co^ , values of 6 calculated from to * will always have the same negative sign, since co^ * > co . Values of to t^, however, wil l start out positive and change to negative as co decreases with concentration. Clearly such a situation is unsatisfactory. An important point, in this regard, is that i f neat solvent parameters are used for co^ , and co is not mea-sured down to very low base concentrations, then the difference between co * and co t may not be noticed. Under these conditions, 0.8-1 S OH 1 1 1 1 1 1 1 1 1 O 0.2 0.4 g ° - 6 ° - 8 Fig 5-5: Scatchard plots of CuDDC with pyridine in solvents indicated. - 70 -Fig 5-6: Benesi-Hildebrand plots for 3/2 Line (pyridine in various solvents) T T 1 1 1 1 1 r O 2 4 6 8 i/[|J(L/mole) - 71 -the value of K calculated from (3-15), or equivalent expressions, will be higher from using co^ithan would be obtained by using w ^ * , since co. - co,, is then smaller. A B The question arises: what would be the effect on a Scat-chard plot of the experimental results i f there were several competing equilibria involved rather than the single 1:1 process discussed so far? Although the results obtained confirm the 1:1 binding situation, consideration of the possibility of formation of 1:2 adducts, in addition, presents some interesting informa-tion. The situation to be considered is that discussed in chap-ter 3: K l (5-3) CuL2 + B , v CuL2B K2 CuL2B + B i CuL2B2 It is assumed to be extremely unlikely that only 2:1 adduct species could be formed, and this situation will not be considered explicitly. Using (3-23) values of <co^ > were calculated, assuming reasonable values of co^, co^, co^, and K 2, over a wide base concentration range. Fast exchange con-ditions were assumed throughout. The results are illustrated in figs. (5-7) to (5-10). Fig. (5-7) shows that there is no possibility of K2 > in this work; the Scatchard plot being extremely curved in this case. The other plots demonstrate that for two competing equilibria, no matter what the values - 72 -TABLE 5-4: SAMPLE DATA USED TO CONSTRUCT SCATCHARD MULTIPLE EQUILIBRIA PLOTS; FIGURE 5-7 AS AN EXAMPLE.* Example 1: w A = 59.587 sec"1; tOg = 59.405 sec"1; uQ = 59.223 sec"1 [L] moles/1 AVERAGE FREQUENCY 6 x 10"9sec"1 6/[L] x 10"9sec"1M~1 x 10 sec 0.50 59.521 -0.066 -0.132 1.00 59.468 -0.119 -0.119 2.00 59.397 -0.190 -0.095 3.00 59.355 -0.032 -0.077 5.00 59.311 -0.276 -0.055 7.00 59.288 -0.299 -0.043 9.00 59.274 -0.313 -0.035 12.00 59.262 -0.325 -0.027 Example 2: u>A = 59.587 tOg = 59.405 coc = 59.223 Kx = 0.10 K2 = 0.38 [L] moles/1 AVERAGE FREQUENCY 6 x 10" 9sec - 1 6/[L] x lO s^ec'Hr1 x 10 sec 0.50 59.575 -0.012 -0.024 1.00 59.559 -0.028 -0.028 2.00 59.519 -0.068 -0.034 3.00 59.478 -0.009 -0.036 5.00 59.409 -0.178 -0.036 7.00 59.361 -0.226 -0.032 9.00 59.329 -0.258 -0.029 12.00 59.299 -0.288 -0.024 * Terminology used is that in eq. 3-23. - 73 -Fig 5-7-Hscatchard Plots of Benzene/Pyridine Multiple Equilibria at 300 K Niyi^ in parentheses) 59587x10 (sec1) 59.405 -59.223 -S x lO^sec-1) - 74 -Fig 5-8: Scatchard Plots of Benzene/Pyridine Multiple Equilibria at 300 K ( K J / K J in parentheses) cJA = 59.587 x10 9sec' = 59.223 toc =59.041 04-0 0 2 04 x 10"^(sec-1) 0 6 - 75 -Fig 5-9: Scatchard Plots of Benzene/Pyridine Multiple Equilibria at 300 K (t^/r^in parentheses) .20 .16-To <u .12-.08: .04-.2 Q38/0O «A = 59587x10 sec UJ 8 = 59223 -O J c = 58859 -0.38/10 0.38/0.75 , 0.38/030 Q38/010 038/0.075 038/005 -i r - T — .8 cfxirj^secr1) - 7 6 -Fig 5-10: Scatchard Plots of Benzene/ Pyridine Multiple Equilibria at 300 K ( K j / K ^ in parentheses) <M, = 59.587 xl0*9sec* =59.223 OJc = 5B.495 oa a 4 OB oa -Jxlti^sec1) - 77 -of coD and io„, the plot of 6/[L ] vs. 6 is curved until K >> K_. B L O \ 2. Also, it is clear that a linear Scatchard plot can be obtained where > K^, for the data plotted in the figures. The slopes of the linear Scatchard plots where f 0 are, however, quite different from the 1:1 (K2 = 0) cases. Thus values of K are different. The least squares values of K agree with the 1:1 plots, not the multiple equilibria cases, and hence 1:2 complex formation is unlikely. Even without the epr evidence, the amount of 1:2 adduct formed would be very small, and depends on the formation con-108 stant 6 = K 1K 2 , which will be ^ 0.03 for CuDDC in benzene/ pyridine at 300°K. There will not be enough 1:2 adduct to ren-der the 1:1 assumption inconsistent. Further, the fact that even at quite low temperatures no more than two epr spectra were observed indicates that only 1:1 adduct formation should be considered. Since the 2-picoline results in this thesis in-dicate that formation constants as low as ^ 0.02 can be measured, thus one would expect to observe any 1:2 adducts that might be formed, since it is expected that the hexa-coordinated com-plex would have noticeably different magnetic properties to penta-coordinated ones. 108 Consideration of previous work on copper(II) complexes ' 110,111 indicates that 1:2 adducts of square planar copper(II) compounds are formed rarely; only when the parent complex is i t -- 78 -self unstable. Also, the formation process illustrated by (5-3) would be expected to be a fast equilibrium followed by a slow 1:2 formation step, which would be easily detectable by epr methods. Stereochemical arguments have been invoked to show that in solution the addition of a sixth ligand to square planar -v j 9 . . . ^ . . 110-113 complexes with a d central ion is extremely unfavourable Thus the results of stereochemical and chemical arguments are identical to the conclusions drawn from consideration of Scatchard plots of the epr data, as might be expected, and con-firm that CuDDC forms 1:1 adducts with weak neutral organic bases in inert solvents. C. SOLVENT EFFECTS: The reaction of CuDDC with pyridine was studied in several solvents in order to compare solvent effects. The solvents used were benzene, toluene, and chloroform. The equilibrium and rate constants were determined by the various methods outlined in chapters 3, 4 and 9. Tables 5-5 to 5-8 contain a summary of these results. Table 5-8, for in-stance shows the marked linewidth and co^  - temperature depen-dence. Table 5-5 contains similar information to that in Tables 5-1 to 5-3, but is repeated in the same form as Tables 5-6 and 5-7 for ease of comparisons. The results for the benzene/pyri-dine system were ini t ia l ly analysed at 5°K intervals in order to ensure the accuracy and consistency of the methods of analysis used. Results for other solvents have been analysed at 10°K TABLE 5-5 Parameters obtained from least squares f i t of line Position & linewidth for Benzene (+3/2 line dat« only) Temperature (°K) * Ao (G) (G) u Axl0* 9* (sec) u A x l 0 " 9 + (sec) UgXlO"9* (sec) v 1 0 " 9 + (sec) U/mole) V 1 0 9 (sec) k rxl0- 8 (sec' 1) k f-Klc rxl0" 8 (sec^ r f 1 ) 270 • - - - - -280 -79.70 -74.72 59.612 59.483 59.133 59.196 0.60 2.42 4.13 2.56 290 -79.20 -74.37 59.601 59.474 59.156 59.205 0.53 1.91 5.24 2.52 1 300 -78.74 -74.02 59.587 59.465 59.156 59.223 0.38 1.71 5.85 2.17 -4 <c 1 310 -78.28 -73.67 59.577 59.455 59.158 59.252 0.30 1.51 6.62 1.99 320 -77.80 -73.32 59.559 59.446 59.150 59.258 0.24 1.33 7.52 1.88 1 330 * least squares value t value from measurement 1n neat solvent o $ the K value has an uncertainty of ± 0.02. Uncertainties 1n k. are * 0.12 x 10 , -9 uncertainties In t D are t 0.25 x 10 . TABLE 5-6 Parameters obtained from least squares f i t of line position and linewidth 1n Toluene (+3/2 line data only) Temperature A0* A 0 + ^ x l O " 9 ( d^xlO' 9 w^xlO' 9 w^xlO" 9 K* TgXlO9 k^xlO"8 kf-KI<rxlO' :°K) (G) (G) (sec) (sec) (sec) (sec) (l/mole) (sec) (sec" 1) (sec" 1 270 -80.70 -75.32 59.639 59.498 59.137 59.174 0.92 4.60 2.17 1.99 280 -79.76 -74.96 59.611 59.489 59.146 59.196 0.66 3.70 2.70 1.78 290 -79.14 -74.54 59.591 59.478 59.144 59.205 0.47 2.40 4.18 1.96 300 -78.65 -74.30 59.578 59.472 59.144 59.223 0.36 1.97 5.08 1.83 310 -78.20 -73.96 59.568 59.463 59.144 59.252 0.30 1.65 6.06 1.79 320 -77.76 -73.64 59.561 59.455 59.144 59.258 0.22 1.35 7.41 1.63 330 -77.49 -73.28 59.556 59.446 59.142 59.268 0.18 1.04 9.61 1.73 * value from least squares f i t t value from measurement 1n neat solvent $ the K value has an uncertainty of ±0.02. Uncertainty In k Is *0.12 x 10 , _Q uncertainty 1n T B 1S ±0.25 x 10 . TABLE 5-7 Parameters obtained from least squares f i t of line position and linewidth In Chloroform (+3/2 line data only) Temperature (6K) V (G) V (G) <» A *xlO" 9 (setf « A + x l O " 9 (sec1) ^ • x l O " 9 (sec1) <i)8+xl0"9 (sec1) U/mole) T BX10 9 (see) k xlO* 8 r (sec - 1) k f -Kk r xlO" 8 ( s ec^K 1 ) 270 -80.75 -75.88 59.654 59.514 59.100 59.174 0.60 5.10 1.96 1.14 280 -79.88 -75.51 59.630 59.505 59.091 59.196 0.41 3.90 2.56 1.05 290 -79.11 -75.10 59.604 59.494 59.079 59.205 0.30 2.41 4.15 1.25 300 -78.68 -74.70 59.588 59.484 59.084 59.223 0.24 1.66 6.02 1.42 1 310 -78.19 -74.30 59.582 59.473 59.092 59.252 0.19 1.31 7.63 1.45 OC H» 320 -77.80 -73.94 59.575 59.463 59.104 59.258 0.15 0.99 10.10 1.52 I 330 -77.54 -73.46 59.549 59.451 59.090 59.268 0.12 0.80 12.50 1.50 * value from least squares f i t + value from measurement 1n neat solvent $ uncertainty 1n K t 0.02. Uncertainty In k 1s ± 0.12 x 10 8, uncertainty 1n T B IS ± 0.25 x 10" 9. TABLE 5-8 Frequency difference and line width data (+3/2 line) only for benzene, toluene and chloroform BENZENE Temperature tt T - i . CK) sec l) sec ) (10"6. sec 270 280 0.4793 51.27 57.87 290 0.4443 46.76 58.81 300 0.4312 50.13 60.76 310 0.4190 51.77 . 63.56 320 0.4094. 60.86 67.30 330 -* least squares fitted valves t values measured 1n neat solvents TOLUENE " CHLOROFORM PYRIDINE sec ) *2A sec ) sec ') '2A sec ) <:£>, tt sec ) 0.5024 53.67 55.67 0.5534 47.65 57.60 66.16 60.17 0.4652 54.27 55.91 0.5392 49.45 56.50 63.66 62.34 0.4477 56.62 56.39 0.5250 51.95 56.58 61.36 64.99 0.4344 57.48 57.36 0.5040 58.83 57.99 52.25 69.66 0.4236 62.13 59.20 0.4900 61.54 61.11 53.54 74.31 0.4169 59.14 62.02 0.4715 62.78 66.09 57.46 79.45 0.4134 63.60 66.17 0.4590 62.99 73.26 58.87 84.16 - 83 -intervals. Further, the temperature range over which the inves-tigations were carried out was limited by the boiling and freez-ing points of the solvents, and by the necessity to confine the experiments to the fast exchange region. Hence the temperature range considered was,0°C to 60°C, usually. From the temperature dependence of the equilibrium and rate constants, i t is possible to estimate the thermodynamic parameters characterising the adduct formation process in the various solvents. This was accomplished by using the van't Hoff/Arrhenius law (see Appendix 1 for derivation and use of the relationship), obtaining E, the energy of activation for the process being considered, from a plot of In K (or In k) vs. 1/T. These values are summarised in Table 5-9, along with some values from other work. In figs. 5-11 and 5-12 are shown the Arrhenius plots for equilibrium and rate constants, respectively, for the three solvents. The plots indicate that the results can be confident-ly interpreted in terms of a simple Arrhenius law. Al l thermo-dynamic parameters were calculated for T = 300°K for ease of comparison with the results of other workers. As can be seen in Table 5-9, negative activation ener-gies are obtained for benzene and toluene solvent systems for the adduct formation process. This will be discussed in more detail later, but i t is useful to note here that these nega-tive values were found reproducible and consistent, and are - 84 --Ink 1 /T ( 0 K _ , ) x10 3 Fig 5-11: Arrhenius plots for equilibrium constants for solvents indicated. - 85 -i 1 1 — i 1 3 .0 3.2 3 .4 3.6 3 .8 i / T x I O 3 Fig 5-12: Arrhenius plots for rate constants for solvents indicated. TABLE 5-9: THERMODYNAMIC DATA (Several Cu(II) complexes wi th pyr id ine 1n var ious so lvents) COMPLEX* SOLVENT TEMP K iS° k r k f 4H f# &Hr# C u ( D n - B D c ) ^ C H 3 c 6 Hn C K ) 298 (1/mole) 0.40 (kca ts / mole) - 5 . (e .u . ) -19 ( s e c " 1 x l O - 8 ) 20 • (sec'V 1 x l O " 8 ) ( k c a l s / mole) •vO (e . u . ) • ( kca l s / mole) 5 (e .u . -1 .Cu(D0C)< b ) C H 3 C 6 H 5 298 0.49 -4 .9 - 3.4 - 3.7 - 8.6 -Cu(ODC) | c ) C 6 H 6 300 0.38 -4 .9 -18.3 5.80 2.17 -2 .9 -30 2.1 -11.6 Cu(D0C)jc' CHjCgHg 300 0.36 -5 .4 -20.0 • 5.08 1.83 -1 .0 -24 4.3 - 4.4 Cu(DDC) | c ) CHClj 300 0.24 -5 .2 -20.1 6.02 1.42 0.5 -20 5.7 + 0.6 Cu(t -BuOAc)^ 1 ' C6H12 298 37.7 -7.1 -16.6 - - - - - -C u ( A c a c ) ^ C 6 H 6 303 4.7 -6 .5 -18.1 - - - - - -Cu(3-Metacac)^ e ) C 6 H 6 303 2.0 -3 .0 - 8.6 - - - - - -* Abbrev ia t ions: Cu(Cn-BDC) 2 Copper 51) b is (d l -n-•butyld1th1ocarbamate) Cu(DDC)2 - Copper ( I I ) M s (d iethyld i th locarbamate) Cu(t-Bu0Ac) 2 - Copper ( I I ) b is ( t -buty lacetoacetate) Cu(3-Metacac) 2 - Copper ( I I ) b is (3-methylacetylacetonate) (a) re f . 86 (b) r e f . 109 (c) t h i s work (d) r e f . 132 (e) r e f . 112 - 87 -not the result of experimental error or an artifact of the methods used. Up until now, negative activation energies in solution have been reported only for radical recombination reac-117 tions Other results obtained will be introduced and discussed as they are needed, in order to facilitate certain aspects of the discussion. D. EFFECTS OF VARIATION OF BASE: It was considered important not only to study solvent effects on the equilibrium: (5-4) CuDDC + base * CuDDC-base but also to investigate the effect of variation of the base. In principle, any Lewis base maintaining the equilibrium in (5-4) is suitable, as long as the forward and reverse rates of reac-tion are fast by epr standards. That is , of course, i f the re-sults are to be interpreted within this approximation, as is the case in this work. Relatively small changes in base strength, and hence formation constant, were found to have quite pronounced effects upon the exchange. A quite narrow range of rates is available for study by the fast exchange approximation; perhaps 8 9 -1 10 to 10 sec for the systems studied in this work. Thus i t was found that pyridine and a series of methyl-substituted pyri-dines were the most suitable bases to use. Piperidine, for in-stance, is a strong enough base that many of the spectra ob-- 88 -tained near room temperature were s t i l l in the slow or inter-mediate regions of exchange. Fig. 5-13 illustrates the tem-perature variation of a piperidine/toluene system. The bases chosen for study were 2-, 3-, and 4-picoline (2-, 3-, and 4-methyl pyridine), and 3,4- and 2,6-lutidine (3,4- and 2,6-di-methyl pyridine). These are a l l commercially available in high purity. Al l least squares analysis results, as for the solvents, are most conveniently summarised in tabular form, and are pre-sented in Tables 5-10 to 5-13, along with derived equilibrium and rate constants. The data for pyridine have already been given in Tables 5-1, 5-2, 5-3, and 5-5. Probably because of steric effects caused by the two methyl groups the data for 2,6-lutidine indicate that no adduct formation occurred with this base. In effect, i t behaves as an inert solvent. The experimental data are presented in Table 5-14, and fig. 5-14 illustrates the variation of frequency with base strength for several temperatures. This trend can be seen to be markedly different from that obtained with other bases, as illustrated by fig. 5-2. It was found difficult to dissolve CuDDC in 2,6-lutidine, dissolution being effected after warming to 40°C for 1 - 2 hours. It was also noticeably more difficult to dis-solve CuDDC in 2-picoline than in other pyridines (2,6-lutidine excepted). These facts are reflected in the results, shown in Table 5-10. No equilibrium or rate data could be obtained at - 89 -Fig 5-13: Temperature Dependence of CuDDC in Toluene-TABLE 5-10 Parameters obtained from least squares fit of line position and linewidth for 2-picoline in benzene (+3/2 line data only) Temperature B+ a ' 0 t -9 w 'x 10 A w *x 10~9 A t -9 wB'x 10 y u>B*x 10"9 K* T N x 109 k B r x 10"8 k£= Kk x 10"7 r (°K) (G) (sec ) (sec ) (sec ) (sec ) (1/mole) (sec) (sec-*) (s ec M J 275 -71.25 59.569 59.576 59.394 59.176 0.082 4.27 2.34 1.92 285 -72.07 59.559 59.566 59.415 59.167 0.060 2.50 4.00 2.40 295 -72.75 59.551 59.557 59.432 59.221 0.054 1.45 6.89 3.72 300 -73.00 59.548 59.553 59.439 59.222 0.050 1.07 9.35 4.68 310 -73.45 59.540 59.540 59.450 59.217 0.038 - - -320 -73.75 59.530 59.533 59.457 59.213 0.032 - - -335 -74.00 59.513 59.512 59.462 59.214 0.023 _ +0.05 measured in neat solvent (B refers to 2-picoline, A to benzene) * obtained from least squares fit % maximum errors in K are + 0.02 (from Scatchard plot reproducibility). Uncertainty in k ^ + 0.02 x 10 in T d ^ 0.25 x 10"9. D TABLE 5-11 Parameters obtained from least squares fit of line position and line width for 3-picoline in benzene ( +3/2 line only) Temperature B+ a 0 toA*x 10" Q * coB x 10 9 t -9 y u 'x 10 (wA-toB)*xlO -9 K$ T B x 109 k x 10"8 r k_= Kk x 10 f r (°K) (G) (sec *) (sec - 1) (sec ) (sec ) (1/mole) (sec) (sec"1) (sec^M"1;) 275 -61.60 59.604 59.109 59.145 0.495 1.10 3.64 2.75 3.02 285 -62.60 59.572 59.127 59.164 0.445 0.79 3.25 3.08 2.42 295 -63.50 59.549 59.143 59.195 0.406 0.57 2.47 4.05 2.33 300 -63.90 59.540 59.147 59.206 0.394 0.49 2.20 4.55 2.21 310 -64.75 59.528 59.154 59.228 0.374 0.37 1.79 5.60 2.05 320 -65.50 59.518 59.162 59.247 0.357 0.29 1.50 6.67 1.96 335 -66.44 +0.05 59.508 59.166 59.270 0.342 0.20 1.32 7.58 1.52 ^ measured in neat solvent. B refers to 3-picoline, A to benzene * obtained from least squares fit $ uncertainty in K = + 0.02, in k = + 0. 20 x 108, in V - 0 , 2 5 x 10"? - 8 TABLE 5-12 Parameters obtained from least squares fit of line position and linewidth data for 4-picoline in benzene (+3/2 line only) Temperature B t a 0 * q coA x 10 A * -9 t -9 coB x 10 wB'x 10 ( t V V * x l ° -9 ,$ T B x 109 k x 10"8 r k.= Kk x 10 f r (°K) (G) (sec - 1) (sec ) (sec ) (sec ) (1/mole) (sec) (sec ) (sec M J 275 -61.11 59.613 59.098 59.134 0.515 1.47 5.58 1.79 2.63 285 -61.63 59.576 59.113 59.148 0.463 1.05 4.42 2.26 2.38 295 -62.26 59.547 59.122 59.164 0.425 0.74 3.33 •3.00 2.22 300 -62.58 59.585 59.124 59.172 0.411 0.62 3.05 3.28 2.04 310 -63.25 59.518 59.128 59.190 0.300 0.46 2.42 4.13 1.88 320 -63.96 59.505 59.131 59.208 0.373 0.34 1.87 5.35 1.83 330 -64.71 59.496 59.135 59.227 0.360 0.27 1.48 6.76 1.81 + 0.05 measured in neat solvent. B refers to 4-picoline, A to benzene * obtained from least squares fit $ uncertainty in K ^  + 0.02, in k ^ + 0.20 x 108, in T ^ 0.25 x 10 TABLE 5 - 1 3 Parameters obtained from least squares fit of line position and line width data for 3,4-lutidine in benzene ( + 3 / 2 line only) Temperature aB* 0 * toA x 10 A - 9 * - 9 u„ x 10 t - 9 w 'x 10 D c W * x l° -9 , $ T B x 1 0 9 k x 1 0 ' 8 r k-= Kk x 10" f r (°K) (G) (sec -1) (sec -1) (sec ) (sec - 1) (1/mole) (sec) (sec ) (sec M ) 2 7 5 - 5 9 . 4 8 5 9 . 6 9 8 5 9 . 0 6 6 5 9 . 0 8 8 0 . 6 3 2 2 . 0 2 5 . 7 8 1 . 7 3 3 . 4 9 285 - 6 0 . 9 0 5 9 . 6 3 6 5 9 . 1 0 5 5 9 . 1 2 6 0 . 5 3 1 1 . 5 5 4 . 9 3 2 . 0 3 3 . 1 5 2 9 5 - 6 2 . 2 0 5 9 . 5 8 9 5 9 . 1 3 4 5 9 . 1 6 0 0 . 4 5 5 1 . 1 4 4 . 2 5 2 . 3 5 2 . 6 7 300 - 6 2 . 8 2 5 9 . 5 7 1 5 9 . 1 4 5 5 9 . 1 7 7 0 . 4 2 6 0 . 9 7 4 . 0 4 2 . 4 8 2 . 4 1 310 - 6 4 . 0 0 5 9 . 5 4 5 5 9 . 1 6 4 5 9 . 2 0 8 0 . 3 8 1 0 . 7 1 3 . 3 2 3 . 0 1 2 . 1 2 320 - 6 5 . 0 0 5 9 . 5 2 8 5 9 . 1 8 4 5 9 . 2 3 4 0 . 3 4 4 0 . 5 6 3 . 0 0 3 . 3 3 1 . 8 7 3 3 5 - 6 6 , 4 0 ' + 0 . 0 5 5 9 . 5 1 5 5 9 . 1 8 8 5 9 . 2 7 0 0 . 3 2 7 0 . 3 8 2 . 6 2 3 . 8 2 1 . 4 5 measured in neat solvent. B refers to 3,4-lutidine, A to benzene * obtained from least squares fit $ uncertainty in K ^ + 0 . 0 2 , in k ^ + 0 . 2 0 i n 8 • x 10 , in T D ^ + 0 . 2 5 x 1 0 " 9 TABLE 5-14 Representative data obtained for 2,6-lutidine in benzene Temperature C°K) a 1 * 0 (G) B+ Bo -9 OJ. x 10 A -1 (sec ) co x 10"9 (sec ) (sec ) 275 -78.72 2.04186 59.580 59.585 -0.005 285 -78.35 2.04201 59.567 59.575 -0.006 295 -77.93 2.04215 59.560 59.564 -0.004 300 -77.72 2.04223 59.556 59.559 -0.003 310 -77.30 2.04237 59.546 59.548 -0.003 320 -76.88 2.04258 59.536 59.537 -0.001 335 -76.25 2.04273 59.523 59.521 +0.002 measured in neat solvent. A refers to benzene, B to 2,6-lutidine. Fig 5-14: Line Position va Concentration for 2,6-lutidine in benzene-fa2 I 6 8 10 26-lutidine concentration (moles/1) - • - 96 -al l for 2,6-lutidine, and 2-picoline yielded very small equili-brium constants, the smallest not being obtainable from the least squares analysis of the epr data, but from the Scatchard plots of the data. Fig. 5-15 illustrates these results. It was also found impossible to correlate the linewidths with any reasonable trend above 310°K, for 2-picoline, presumably because K was so small. Results from Arrhenius plots for this case are limited to the range 270-310°K. Thermodynamic results, obtained from Arrhenius plots, are illustrated in figs. 5-16, 5-17, and 5-18, and summarised in Table 5-15. The pertinent base strengths are also given in 5-15. It may be noted that, again, a series of negative activa-tion energies for the forward process in (5-4) is obtained. Fig 5-15: Scatchard Plots for 2-picoline in Benzene ") ' 04 ' ' 08 ' T i ts ' 2J0 cf x l O ^ s e c - O TABLE 5-15 THERMODYNAMIC DATA FOR VARIATION OF BASE (for CuDDC 1n benzene solution at 300°K) BASE pKa K kytlO* 8 k r x l0" 8 M° lS° 4 H f + A S f + t LHf • (i/mole) (sec - 1 n 1) (sec' 1) (kcals/mole) (e.v.) (kcals/mole) (e.u.) (kcals/mole) (e.u.) PYRIDINE 5.22 . 6.38 2.17 5.80 . -5.01 -18.3 -2.85 -29.9 +2.10 -11.6 2-PICOLINE . 5.96 0.05 0.47 9.35 -3.13 -16.6 +5.30 - 5.8 +8.43 +10.6 3-PICOLINE 5.63 0.49 2.21 4.55 -5.18 -18.7 -2.42 -28.5 +2.75 - 9.8 1 4-PICOLINE 5.98 0.62 2.04 3.28 -5.65 -19.8 -1.90 -26.9 +3.76 - 7.1 tc 00 3,4-LUTIDINE 6.46 0.97 2.41 2.48 -5.17 -17.3 -3.29 -31.1 +1.90 -13.8 t Uncertainties In AHO ,N.±0.2 kcals/mole, In aS'vtl.2. e .v . ; values for these parameters derived from temperature dependence of equilibrium constant. - 99 -- 100 -- 1 0 1 -- 102 -CHAPTER 6 SOLVENT AND TEMPERATURE EFFECTS ON EPR SPECTRA, AND A COMPARISON WITH OTHER WORK A. SOLVENT EFFECTS ON EPR PARAMETERS: The effects on copper(II) epr parameters of varying the solvent have been studied quite ex-tensively for copper(II) bis(acetylacetonate) and various substi-23 130-132 tuted derivatives ' . No previous work on solvent effects has been published for CuDDC, however. The results obtained in this work show a definite solvent (and temperature) dependence of the isotropic hyperfine splitting and g value. Table 6-1 sum-marises these results. Now it may be remembered that in chapter 5 mention was made * of the fact that extrapolated values of to^, coA , were consistent-ly higher than those measured in neat solvent, w^T It may also be noted that for a l l three solvents, benzene, toluene, and - 1U3 -T A B L E 6-1 TEMPERATURE AND SOLVENT DEPENDENCE OF ISOTROPIC EPR PARAMETERS FOR CUDDC* TEMPERATURE(°K) 270 280 290 300 310 320 330 benzene -75.06 -74.72 -74.37 -74.02 -73.67 -73.32 -72.97 2.04540 2.04544 2.C4544 2.04545 2.04546 2.04547 2.04548 toluene -75.32 -74.96 -74.54 -74.30 -73.96 -73.64 73.28 2.04503 2.04483 2.04500 2.04525 2.04556 2.04600 2.04604 cTiloroform -75.88 -75.51 -75.10 -74.70 -74.30 -73.94 -73.46 2.04643 2.04628 • 2.04650 2.04666 2.04682 2.04640 2.04647 cyclohexane -79.25 -78.88 -78.50 -78.13 -77.75 -77.37 -77.00 2.04200 2.04206 2.04213 2.04224 2.04237 2.04260 2.04300 carbon tetrachloride -79.30 -78.93 -78.56 -78.18 -77.80 -77.43 -77.05 2.04230 2.04209 2.04206 2.04210 2.04217 2.04227 2.04242 pyridine -62.58 -55.30 -63.85 -64.55 -65.15 -65.78 -66.50 2.05518 2.05650 2.05622 2.05514 2.05435- 2.05360 2.05295 piperidine -54.75 -55.30 -55.92 -56.60 -57.22 -57.80 -58.30 2.05977 2.05940 2.05860 2.05823 2.05800 2.05750 2.05690 * Quoted are ( °) values, a 1n Gauss. - 104 -* chloroform, the to values are equal within experimental error. The extrapolated values (least squares fitting of the results defines as that value obtained by extrapolating the w vs. L q curve to L q = 0) can evidently be associated with a "pure-solvent" situation. The equivalence of the extrapolated values on al l solvents at a l l temperatures is illustrated in Tables 5-5 to 5-7. Consider-ing the values of the hyperfine splitting associated with the ex-* trapolated value of co^ , a^ , i t is clear from Table 6-1 that only measurements made in neat cyclohexane and carbon tetrachloride * approach a^ , which averages to -78.70 + 0.15 G at 300 K. In a l l other solvents, the values of a are lower than this value. ' o It was found difficult to dissolve CuDDC in both cyclohexane and carbon tetrachloride, a fact that suggests that these two sol-vents can be regarded as quite inert or non-coordinating. It may also be noted that the value of aQ for 2,6-lutidine at 300°K was -77.70 G, and great difficulty in dissolving CuDDC in this solvent has already been reported in this thesis (or see chapter 9). The presence of methyl groups adjacent to the nitro-gen nucleus evidently prevents interaction between 2,6-lutidine and copper(II), hence the non-coordinating nature of this solvent, which behaves much like cyclohexane and carbon tetra-chloride with respect to CuDDC. Further, the known co-ordinating solvents, piperidine and the pyridines, a l l have values of aQ that increase (become less negative) as the base strength in-- 105 -creases. Table 6-2 gives the base strengths and aQ values at 300°K: TABLE 6-2: BASE STRENGTHS AND VALUES OF a FOR CuDDC IN VARIOUS o PYRIDINES Base pK 3 (G) Dipole Moment (D) 1 7 2 Pyridine 5.22 -64.5 2.33 2- Picoline 5.96 -73.0 1.93 3- Picoline 5.63 -63.9 2.54 4- Picoline 5.98 -62.6 2.75 3,4-Lutidine 6.46 -62.8 1.87 2,6-Lutidine 6.72 -77.7 1.66 Piperidine 11.28 -56.7 1.29 There is clearly a correlation between decreasing co-ordin-ating ability of the base, taking into account steric hindrance, and more negative, or increasing values of aQ. There is appar-ently no significant correlation with dipole moment unless only the picolines are considered. Thus i t seems that the extra-polated values of a^ and OJ^ can be regarded as solvent-interac- tion-free parameters, and hence define a level of inertness. The deviation of most solvents from this inert value indicates a small degree of co-ordination by the solvent. Adding very . small amounts of pyridine then must disturb this co-ordination - 106 -in some manner that does not lead to co-ordination of the pyri-dine, but a simple clustering of molecules of solvent and base about the copper(II) nucleus. This would be an inert or non-coordinating situation, and hence the value of OJ^, or a^, in-creases to that expected from smooth extrapolation of vs. L to low L . Then as more pyridine is added the magnitude of o o aQ decreases with increasing pyridine concentration as coordina-tion occurs. The remarkable consistency, at a l l temperatures in-vestigated, of the fitted values of for the three solvents is rather strong evidence that these values do indeed represent an inert solvent, since there are noticeable differences in the values ofm obtained in the neat solvents. A general trend of a0 suggests a decreasing level of inertness in the order (300°K): (6-1) CC1. > C,H > CHC1, > CH,C,HC> C.H. > C,-HCN > C CH 1 1N ^ J 4 6 l£ 3 3 6 5 6 6 55 5 11 This seems intuitively reasonable, apart from details about benzene and toluene, perhaps, and agrees with the findings of 134 Selbin on the donor properties of various solvents. 133 The conclusions of Antosik et al , confirmed by Adato and 131 Eliezer for copper(II) acetylacetonate, is that as solvent interactions along the axial direction increase, the g value will increase and the a value decrease (if a < 0, magnitude o o ' " 141 of aQ decreases). Kuska and Rogers earlier concluded simi-larly for the interaction of copper(II) acetylacetonates with basic solvents. The trends, in fact, are predicted to hold for - 107 -both a and A. o An unusual exception to the trends noted above is given in 132 the work of Libutti et al . , who investigated the variation of the epr parameters for copper(H) t-butylacetoacetate with vari-ous solvents. They found that aQ increased, relative to cyclo-hexane (-70.0 G)jfor the series: carbon tetrachloride (-71.3 G), benzene (-72.4 G), and chloroform (-74.8 G). This trend is oppos-ite to that obtained here, and that expected, and Libutti et a l . interpreted i t as evidence that aQ values increase (become less negative) as inertness increased. It is not likely that copper t-butylacetoacetate solvates differently from copper acetylace-tonate and CuDDC, but that is the only conclusion available from * - i , -P +-V. * v A «-!, 131,133,141 comparison of the results of this work, and others, ' ' 132 with that of Libutti et a l . B. ULTRA-VIOLET AND VISIBLE SPECTRA: Libutti et a l ! 3 2 supported their epr findings by noting a shift in the visible region for copper t-butylacetoacetate in cyclohexane, compared to chloroform. Thus UV and visible spectra were examined in this work in several solvents and pyridines to determine whether or not the epr para-meters are sensitive to coordination effects. One would expect . shifts in the UV and visible spectra upon co-ordination, the mag-nitude of the shift perhaps reflecting something of the degree 135 of co-ordination. Vanngard and Pettersson measured such shifts for various divalent coinage metal dialkyldithiocarbam-- 108 -ates, with results agreeing essentially with those obtained here. Table 6-3 illustrates these findings: TABLE 6-3: UV/VISIBLE MAXIMA FOR CuDDC IN VARIOUS SOLVENTS AT 298°K solvent visible 1 X ( a n ) max1- 7 U V -1 X (cm L) max •* cyclohexane 23,030 34,020 benzene 22,980 34,145 chloroform 22,940 34,350 pyridine 21,740 33,100 2,6-lutidine 22,960 33,175 The shifts here are smaller than those obtained by Vann-gard and Pettersson, but the trend is the same. The combina-tion of epr and UV/visible absorption results indicate that more coordination does take place between CuDDC and benzene, and chloroform, than in cyclohexane, and the pyridine results substantiate this. The UV results for 2,6-lutidine and pyri-dine appear to be somewhat out of place, in comparison to epr and visible spectra results, probably because of other elec-tronic effects associated with these bases. C. TEMPERATURE EFFECTS: Table 6-1 indicates that the isotrop-- 109 -ic epr parameters of CuDDC in solution are highly temperature dependent. Temperature dependence of the hyperfine splittings 136 of copper(II) complexes in solution has been noted before , and these authors ascribed the dependence to a vibrational ef-fect wherein the motion of the copper atom and its nearest neigh-bours is described in terms of Boltzmann distributions: a (6-2) a = — o + Z ia iexp (-AE^/kT) 1 + E exp (-AEi/kT) where aQ is the hyperfine splitting in the vibrational ground state, a. that in the i ' th vibrational state, and AE. the ener-i i gy difference between the ground and i ' th vibrational levels. Eq.(6-2) has been reasonably successful in interpreting temper-ature dependences for proton hyperfine splittings in simple 137 organic free radicals , where only one excited vibrational 136 state is considered in the calculation. Luckhurst and Falle obtained reasonable agreement with the experimentally-observed trend using (6-2) in the same fashion, but pointed out that i t is unreasonable, with the amount of data presently available, to attempt to interpret the right hand side of (6-2) with res-pect to epr parameters. No attempt will be made here to give a quantitative interpretation of the temperature dependence, but i t has been reported^ 9 ' that a decrease of |aQ| with increasing temperature points to an increase of covalent bond-ing as the temperature is increased. Non-coordinating solvents - 110 -do behave in this fashion, 2 ,6- lut idine included, in this work. The trends for co-ordinating solvents are exactly opposite to this, leading to the suggestion that covalency decreases with increasing temperature for a co-ordinating solvent. Thus i t is unlikely that a simple covalency argument is sufficiently gener-al to explain these opposite trends with temperature, and that the explanation lies in a combination of vibrational and co-valency effects. An important ramification of the temperature dependence of hyperfine parameters is that the commonly used assumption: (6-3) a = 1/3(A + A + A ) v J o xx yy zz is valid only at the temperature at which a l l parameters are measured. In other words, i t is commonplace in epr studies for measurements of a to be made in solution, and either A , . o ' * ( = A , for an axial case) or A . ( = A = A ) to be measured v zz' J -L xx yy in frozen solution. The other parameter, A _ L or k0> is often difficult to measure and is estimated from aQ and or A^ using ( 6 - 3 ) ; for example: (6-4) A± = (3aQ - kg)/2 Admeasured in this fashion will certainly be subject to 138 error D. COMPARISONS WITH OTHER WORK: Although it may seem out of place at this point, a comparison with the only other work pub-- I l l -lished on CuDDC interacting with Lewis bases in inert solvents is useful here because of the close connection with the temper-ature dependence of epr parameters just mentioned. 86 Very recently, Corden and Rieger and Shklyaev and Anu-109 frienko , published studies on fast exchange equilibria invol-ving Lewis acid-base adduct formation, with copper(II) dialkyl-86 dithiocarbamates as the Lewis acid. Corden and Rieger studied the system copper(II) bis(di-n-butyldithiocarbamate) with pyri-dine, piperidine, and n-hexylamine in methylcyclohexane, ana-lysing the results in a fashion similar to that employed here. A direct comparison of these results is not possible, although the thermodynamic parameters for pyridine (see Table 5-9) seem reasonable. The lifetimes, however, are quite different to those obtained here. Close examination of their work reveals several quite important inconsistencies. For the study with pyridine, these authors found i t necessary to both (i) con-strain oo^ - cjg to be temperature independent, and (ii) to use the piperidine value of to^ - w ,^ since they found i t impossible to obtain consistent values of k^ otherwise. It may be noted further that the concentration range covered (0 - 2.5 M) is in-sufficient to obtain reliable results for K and k (see discus-sion in chapters 3 and 5), and that only three temperatures were measured. The limited amount of data taken thus renders the pyridine results subject to uncertainty. Constraining co - co R to be temperature independent will - 112 -116 introduce large errors , and means that values of Xg will be too high when uj^ - oig is less than the "temperature-independent" value, and too low when otherwise. This, in turn, will lead to errors in AH^. Increasing the value of - Wg to that for piperidine (for CuDDC this represents a 30% increase) will simi-larly lead to smaller values of Xg than should be the case. Both these constraints are arbitrary and not difficult to avoid, as demonstrated in this work, and lead to serious limitations upon the conclusions that may be inferred by Corden and Rieger. 109 The more recent study by Shklyaev and Anufrienko in-volved reaction between CuDDC and pyridine in toluene. Values of K obtained are in good agreement with those obtained here, but discrepancies exist in the evaluations of AH^. Once again, these authors make the assumption that aQ and g , and the neat solvent parameters, are temperature independent. Tables of data given by these authors indicate that this is not so, as stressed here earlier, and to make use of this assumption invites large errors 1 1^. Examination of their data (not a l l the necessary data is provided so exact reconstruction of their results is not possible) shows that C J ^ - Wg should change by 30% over the temperature range they consider. Appropriate corrections to xn and hence k then indicate that AH^ should B r r be ^ 5 kcals/mole, rather than the value 8.6 kcals/mole ob-tained. This would be in agreement with that obtained here, and would yield a similar value of AH^ to that quoted in this - 113 -work. The method used by Shklyaev and Anufrienko is that of Dye and Dalton^^^, which is based on determining the m^-depen-dent coefficients of the linewidths (eqs.(4-6) and (4-7)), and which is equivalent to that used here, with one caution. To extract the linewidth coefficients from only a four line epr spectrum, as is the case with copper(II) complexes in solution, is a difficult task at low or moderately low tempera-tures (T < 280°K). At these temperatures the two low field lines become quite broad, often broad enough to overlap. Line-width measurements on such lines are subject to large errors, and extraction of m .^-dependent coefficients is likely to be subject to equally large uncertainty. Fig. 6-1 illustrates typical CuDDC broadening. The vanadyl eight-line spectrum is not subject to such uncertainties, for instance, since i t is relatively easy to least-squares analyse the linewidths ob-served for the parameters a, 8, y, and 6. A final point with respect to the study of Shklyaev and Anufrienko is that the equilibrium constants were measured over a wide pyridine concentration range, but rate constants were evaluated only at 0.475 M pyridine in toluene. This may not, cause any increase in error in the results, but it is clear that this region is not the most sensitive to the effects of exchange. The maximum exchange effects occur at pyridine con-centrations > 1 M for the temperature range 0 - 60°C, and i t would be expected that in order to minimise any possible errors, - 114 -,25 6 , Fig 6-1: Typical Temperature Effects on CuDDC in 4-Picoline, as an example. - 115 -measurements of the exchange rate should be made over a reason-able concentration range, including very carefully the region of maximum exchange. Regions not in a sensitive part of the con-centration range will be relatively insensitive to small changes in Tg. These qualitative considerations, coupled with those of 71 Deranleau for instance, suggest that a l l rate processes should be studied not only over a reasonable range of temperature, but also over a range of concentration sufficient to include a l l ef-fects of exchange. It is also unnecessary, as well as unwise, to assume that epr parameters are temperature independent in or-der to evaluate rate and equilibrium data. When such assump-tions are made, i t is impossible to treat the results in strict-est confidence. Since insufficient fast exchange data are avail-able for study, the rejection of some data as unreliable is un-fortunate. - 116 -CHAPTER 7 DISCUSSION OF RESULTS A. SOME THOUGHTS ON THE INTERPRETATION OF EQUILIBRIUM AND RATE DATA. a) Introductory Remarks: The results quoted in chapter 5 demonstrated that the various pyridine adducts with CuDDC in the solvents studied are of 1:1 stoichiometry. The mechanism leading to the observed rate constants, and hence thermodyna-mics, wil l be discussed as a function of solvent. These con-siderations will be shown to ^ consistent with the results ob-tained in benzene with various pyridines. Table 5-9, repeated here as Table 7-1, shows that the process: k f (7-1) CuDDC + B v CuDDC-B k TABLE 7-1 Static (Equilibrium) Data for al l Systems (300°K) System P^a^ Dipole (of base) Moment (D) Benzene/Pyridine 5.22 2.33 Toluene/Pyridine 5.22 2.33 Chloroform/Pyridine 5.22 2.33 Benzene/2-picoline 5.96 1.93 Benzene/3-picoline 5.63 2.54 Benzene/4-picoline 5.98 2.75 Benzene/3,4-lutidine 6.46 1.87 K AH0 AS° AG0 (1/mole) (kcals/mole) (e.u) (kcals/mole) 0.38 -4.9 -18.4 +0.5 0.36 -5.4 -19.7 +0.6 0.24 -5.2 -20.1 +0.8 0.05 -3.7 -16.4 +1.7 0.49 -5.2 -18.7 +0.4 0.62 -5.7 -19.8 +0.3 0.97 -5.2 -17.4 +0.0 - 118 -where B is a suitable base and K = ^^/k^, is highly solvent depen-dent. That is , examination of rate constants and thermodynamic parameters reveals a solvent dependence of some sort. It was es-tablished that the values of ! „ , and hence k , were not themselves B' r concentration dependent. Some studies of the effects of solvent on equilibrium constants of adducts formed from a Lewis acid-base reaction of square planar copper(II) complexes writh organic bases 1, u * ,112,114,132 , ^  ^ , . . ,. . have been reported , but theoretical and/or experiment-al studies of the rates and mechanisms of fast equilibria involv-ving neutral species are nonexistent. It may be noted also that the concept of equilibrium is difficult to discuss for processes with 153 low or negative energies of activation b) Interpretation of Equilibrium Constants: Table 7-1 shows the variation of equilibrium constant with solvent. Immediately obvious is that the formation (equilibrium) constants are uni-formly much smaller for CuDDC than for copper(II) bis(8-diketon-ates). This is presumably because the g-diketonate complexes are less stable than CuDDC in inert solvents, and this suggests that CuDDC is a much weaker Lewis acid than the 3-diketonate complexes. As already noted, few studies have been reported on sol-vent effects on equilibrium constants for Lewis acid-base equili-bria involving square planar copper(II) complexes in non-coordin-. , 112,114,132,145 ., , , • J * • atmg solvents . Many have been carried out in , 146-148 „, .„ , , . , 132 fc . fc benzene . The results here, and elsewhere , suggest that - 119 -benzene is not a good example of an inert solvent, as often sup-posed, and may interact considerably with the ligand or chelate structure of the metal complex. 112 132 Previous work has established ' that for copper(II) 3-diketonates the adduct formation constants decrease in the order: benzene > toluene > chloroform. The results here, at a l l temperatures from 270 - 330°K, agree with this order. Heats of 132 solvation have been measured for pyridine in various solvents , and these are as follows: benzene = -0.01 kcal/mole, chloroform = -1.82 kcals/mole, cyclohexane = +1.84 kcals/mole, and carbon tetrachloride = +0.17 kcal/mole. These results suggest a strong interaction between pyridine and chloroform, presumably via hydro-149 gen bonding. It is known, for instance , that pyridine and car-bon tetrachloride form weak adducts. The near zero heat of sol-vation of pyridine in benzene reflects the similar structure of these two solvents. Thus the lower heat of formation for CuDDC and pyridine in chloroform, compared to benzene, reflects the fact that the heat evolved in solution of pyridine in chloroform would have to be at least partially restored in the process of ad-112 duct formation , thus leading to lower formation constants. This statement is actually an empirical assessment of a more de-tailed consideration of the formation process to be discussed shortly. The similarity of formation constants for benzene and toluene simply reflects the lack of differentiation by pyridine between the two similar structures. The temperature dependence - 120 -of K in both solvents points out, however, that only near room temperature is the similarity as strong as just quoted. At low-er temperatures toluene becomes progressively more ordered (epr measurements at X-band become impossible at ^-30°C due to ab-sorption of microwave energy by toluene. Dielectric relaxation measurements show a maximum at this temperature for X-band fre-quencies. Hence the implication is that toluene becomes an or-dered array of oriented dipoles) raising the temperature tends to destroy this , and the values for K become as much as 50% larger than for benzene. It is also evident that the overall enthalpies and en-tropies of formation are reasonably similar, leading one to sus-pect that changing the solvent, does not have a dramatic effect on the overall process. The value of faH°, ^ -5 kcals/mole, is within the range, -2 < AH° < -10 kcals/mole, thought to typify 114 formation of a Cu-N bond . This value can be compared to that suggested for the Cu-0 bond in bis(2,4-pentanedione)-copper(II) of 48.7 kcals/mole''^. The Cu-N bond formed is hence relatively weak. Table 7-1 also contains the data for several bases in ben-zene solution. The variation of formation constant can be sum-marised for a l l temperatures studied as decreasing in the order: (7-2) 3,4-lutidine > 4-picoline > 3-picoline > pyridine pyridine » 2-picoline - 121 -2,6-Lutidine presumably formed an even weaker bond than 2-picoline, to the extent that i t was not measurable. The base strengths quoted in Table 6-1 are in the same order as the K values, except for the sterically-hindered 2-picoline and 2,6-lutidine. The same trends with variation of base have been 86 noted by other workers studying copper(II) bis(3-diketonates) ' 112,114,132,146-148,173-178 _ , „ 148 . . ' . Also, Graddon and Hsu obtained a low value of K, about half that for 2-picoline, for 2,4,6-collidine. Thus steric effects are quite pronounced for substi-tuents at the 2- or both 2- and 6- positions of pyridine, pre-suming similar solvent interactions, for nucleophilicity towards copper(II). That the base strengths in aqueous solution do not reflect this hindrance is due simply to the small size of the proton. Changing the reference acid to progressively larger species leads to a regular change in the observed order of base 179 strengths in the series: pyridine, 2-picoline, and 2,6-lutidine Obviously 2,6-lutidine fails to form a bond, in any measurable sense, to copper(II), but 2-picoline can presumably approach the bonding site in a configuration suitable for some bond formation. This bond formation would be expected to require more solute-base encounters for 2-picoline than for an unhindered pyridine. Hence the overall enthalpy of formation is considerably lower for 2-picoline.. The trend in overall enthalpy of formation is: (7-3) 4-picoline > 3,4-lutidine > 3-picoline > pyridine - 122 -(7-3) pyridine » 2-picoline and that for entropy of formation is : (7-4) 4-picoline > 3-picoline > pyridine > 3,4-lutidine 3,4-lutidine > 2-picoline The trends are the same as formation constant and base strength (neglecting 2-picoline) except for the anomalous posi-tion of 3,4-lutidine. It has been noted that in aqueous solu-tion the enthalpy" and entropy of ionization for 2,6-lutidine 166 178 are lower than expected ' , considering the trend observed in the picolines. Ionisation effects are not important here, but the lower values of AH° and AS° may reflect an inability to form a bond at every encounter with the metal, due to repulsion and hindrance effects caused by adjacent methyl groups, but that once a favourable encounter has occurred, a strong Cu-N bond results, hence the higher value of K (and lower value of c) Interpretation of rate constants: Solvent variation of the rates, as well as base variation, is shown in Table 7-2. For the three solvents, benzene, toluene, and chloroform, a de-crease in forward rate over the series is noted; there is an especially noticeable decrease in chloroform. In constrast, the rates for the various bases in pyridine are reasonably con-20 sistent, except for 2-picoline. Walker et al obtained a sim-TABLE 7-2 Kinetic Data for a l l Systems (300°K) System pK 2 r a Dipole Moment (D) g k^lO sec M k xlO" 8 r -1 sec kcals/mole AS^ e.u. r kcals/mole AS^  r e.u. Benzene/pyridine 5.22 2.33 2.17 5.8 -2.9 -30.0 2.1 -11.6 Toluene/pyridine 5.22 2.33 1.83 5.08 -1.0 -24.1 4.3 - 4.4 Chloroform/pyridine 5.22 2.33 1.45 6.02 0.5 -19.5 5.7 + 0.6 Benzene/2-picoline 5.96 1.93 0.47 9.35 +5.3 - 5.8 8.4 + 10.6 Benzene/3-picoline 5.63 2.54 2.21 4.55 -2.4 -28.5 2.7 - 9.8 Benzene/4-picoline 5.98 2.75 2.04 3.28 -1.9 -26.9 3.8 - 7.1 Benzene/3,4-lutidine 6.46 1.87 2.41 2.48 -3.3 -31.1 1.9 -13.8 - 124 -i lar forward rate at 300°K to that obtained here,for the reac-tion of vanadyl acetylacetonate with 2-picoline. Noting that for bases other than 2-picoline the forward rates are not ligand base-strength-dependent in benzene, one might summarise the find-ings by asserting that the forward rate process is not ligand de-pendent, but insolvent dependent. Reverse rates, however, are very much ligand dependent, whereas solvent dependence remains the same. Such conclusions, at 300°K, might appear to be sound. However, to interpret such relationships amongst rates in terms of some specific mechanism can be dangerous. That this is so can be shown after consideration of the temperature variation of the rate constants. As with the equilibrium constants, the temperature depen-dence of the rate constants can be related to enthalpies and en-tropies of reaction by the Arrhenius/van*t Hoff relationship discussed in Appendix 1. These parameters are tabulated in Table 7-2. The overall negative entropy changes reflect the simple disorder argument that two molecules are forming one com-plex, and thus losing some disorder. The negative entropy of formation in each case is relatively large, as expected. The negative entropies of dissociation, however, presumably reflect the fact that there must be solvent participation and steric effects involved also in the formation/dissociation process. Clearly the. dissociation of the complex is highly favoured for 2-picoline, compared to the other bases. On the other hand, - 125 -chloroform, known to react quite strongly with pyridine, has a lower A S ^ than the other solvents. The negative values of A S ^ , apart from solvent and steric effects, do not follow directly the order-disorder argument, although the A S ^ values are markedly decreased i n the reverse direction. Possibly the remaining con-tribution is from the fact that many copper(II) square planar complexes, and CuDDC in particular, in solution prefer to be four-coordinate. A close look at the entropies and enthalpies of reaction 164 reveals a compensation, or isokinetic, effect . In other words, a plot of V S . A S ^ wil l be linear with slope T^, the isokine-t ic temperature. This temperature is that for which the rates are equal. The isokinetic plots are shown in figures 7-1 and 7-2 for the solvents and bases, respectively. Such a correlation relates an isoequilibrium set of reactions to an isoequilibrium temperature, Z H / A S , and a condition for the existence of the ef-163 feet is a common mechanism . Steric interactions might cause restrictions of motion or reaction in the reacting molecules of some process and must be accounted for in any isokinetic plot. More detail about the isokinetic behaviour will be given later, but for now the important point to note is its existence in pro-cesses dominated by solvation changes, and having common mechan-. 166,167 istic pathways ' As the name implies, an isokinetic plot means a tempera-ture exists at which all rates are equal, for some formation or - 126 -A benzGne B toluene C chloroform AH (kcals/mole) A -AS(eu) Fig 7-1: Isokinetic plots for solvents o forwards * reverse - 127 -AH (kcals/mole) Fig 7-2: Isokinetic plots for bases. o forwards A reverse - 128 -dissociation process. Clearly, on either side of this tempera-ture the order of rate constants must exactly be reverse to the other. Hence, studies made at one temperature based on a series of ordered reaction rates are incomplete. The mechanism proposed for any isokinetic series of reactions must be able to justify this reversal. A recent theory of concerted solvent interaction in labile metal complex reactions proposed by Bennetto and Cal-34 din takes such behaviour into account. The work of Rorabacher et a l " ^ ' ^ \ however, is performed at room temperature only. Hence conclusions drawn from such results must be subject to the limitation that they are valid only on one side of the isokinetic-temperature and hence remain somewhat incomplete. It is d i f f i -cult to envisage, in fact, how solvent structure effects could be taken into account adequately through measurements made at o n -ly one temperature, in light of available information on isokin-etic reactions1^^ ) and the implications of the work of Bennetto 34 and Caldin d) Fast Reactions and Arrhenius/van't Hoff relationships: As a final point in this section, i t might be useful to reiterate a few cautionary remarks about the use of Arrhenius plots for fast 124-129 processes . For more details on the derivation of Arrhenius relationships, Appendix 1 and standard texts are available. The Arrhenius activation energy, described by: (7-4) k = Aexp(-EA/RT) - 129 -is usually interpreted as the difference between the average ener-gy of the reacting complexes and the average energy of a l l the 153 colliding pairs of reactant molecules present . Several distinct contributions make up this activation energy, usually considered to be bond energies, repulsion forces, electrostatic interactions and reorganisation of solvent molecules. This sort of interpretation of usually assumes that this value is temperature independent and can be associated with its value at absolute zero temperature. Hence no account of thermal energy is included. Linear Arrhenius plots, as obtained in this work, for reactions involving no change in ionic charge are justifiable evidence for the temperature inde-153 pendent approximation to E^, however , and E^ can be reasonably associated with the height of the potential energy barrier to the transition state. Success in its application tends to alleviate any fear of the potential errors involved. Fast reactions clearly have a low energy of activation (hence a high collision or encounter rate), and are not always well described by transition state theory. Gas phase reactions, in particular, have been shown to not maintain an equilibrium dis-153 tribution of energy for low energy barriers (E/RT £ 5) . I n solution, however, i t is likely that solvent molecules will tend to maintain an equilibrium distribution, and not be subject to large deviations from transition state theory. Also, the small values of K observed in this work indicate that products and reac-tants are depleted and replenished at fairly fast rates, and equi-- 130 -librium is maintained. The negative activation energies are not simply related to traditional ideas, and, in fact, staying within transition state theory means that at least a two step process 117 must be involved, the first of which is reversible Thus the interpretation of the results will be kept with-in the bounds of transition state theory, but precise definition of the transition state will prove to be difficult. It would ap-pear, however, that very fast reactions that are more than uni-molecular, ana reversible, must always be subject to similar lim-itations. B. THE FORWARD, OR ASSOCIATIVE, REACTION: a) Current Ideas, Rate Constants, and Thermodynamic Para- meters : A brief description of the solvent effects on forward, or associative, rates has already been given. Several recent reviews have discussed fast metal-complex formation reactions 32,37,151,152 _ ^ , 152-157 ^. . . ' ' ' The accepted consensus that solvent or ligand exchange at a metal ion in solution often proceeds via a dissociative interchange mechanism incorporating a rapid pre-equilibrium invokes the formation of an outer-sphere complex, and may be illustrated as follows; for an octahedrally solvated metal ion, (7-5) MS*+ L q " o where is some incoming ligand species. The ligand does not have to be charged, necessarily. The overall process may be re-- 131 -presented as: (7-6) MS z + L(S) [MS ...L(S) ] L n n J z + MLS z + + • v n m k m+n-p 21 where p represents the number of solvent molecules returned to the bulk solvent. Solvent exchange can be incorporated as a t r iv ia l extension, replacing ligand with solvent. This scheme was in i t i a l -ly proposed by Eigen'''''''', along with several other mechanisms, to explain a series of experimental results involving metal ions. One important assumption is inherent. That is , that the solvation shell of the ligand is several orders of magnitude more labile 37 than that of the metal . Such an assumption is reasonable for most ion pair and metal complex reactions, but fast Lewis acid-base reactions involving neutral molecules may not always be with-in such an assumption. It is known, for instance, that the high 7 -1 rate constants (> 10 sec ) observed for the replacement of sol-. u • J • 151,153 „ . vent by incoming ligand in some reactions mean that loss of solvent from the coordination sphere of the metal ion is very easy, and consequently ligand attack is the rate-determining step. As noted earlier with respect to equilibria^and activation ener-gies, very fast reactions are perhaps not entirely within the framework of conventional mechanistics. forward rate constant is second order, first in metal and first in ligand, and (ii) that the rate of complex formation is usually simi-Much evidence in favour of (7-6) is (i) that the observed - 132 -lar to the rate of solvent exchange. There will be l i t t le or no ligand dependence (not concentration dependence, but dependence on the coordinating or attacking properties of the ligand) in such a mechanism^^, in the sense that there is only partial involve-152 ment of the ligand, with outer sphere complexes as precursors 154 Langford and Muir have shown the importance of this kind of mechanism for complex formation with inert ions such as cobalt(III) A study of adduct formation between various amines and nickel(II) B-diketonates^"^'has also concluded that the important process in the formation is the nickel-amine bond breaking step, although when uncomplexed amine is present in large excess, then pseudo first order kinetics may be the true description, owing to prefer-ential solvation of the adduct by the amine. Consideration of a purely dissociative mechanism: k u k A ab cd (7-7) MSZ ; = - ± MSZ+ + LS * MLSZ+ v J m k m n k m+n-p-l ba dc involves an intermediate of reduced co-ordination number, and one would expect some dependence on ligand for the rates. This mech-anism is expected to show larger rate constants the weaker the 37 metal-solvent bond , irrespective of the nature of a particular ligand. It has been argued that reaction through a reduced-coor-180 dinate intermediate is energetically unfavourable , but i t would appear that the purely dissociative mechanism may be fav-oured for strongly co-ordinating so lvents *^ '^ * . Solvent effects must be considered, therefore, as - 133 -part of the dissociative mechanisms, and both inner sphere and , outer sphere effects need to be discussed. Rorabacher"^ 'has proposed a model to explain certain solvent effects within the framework of the dissociative mechanism, based on studies made in mixed solvents^ 1 . It is reasonable to assume that i f a dissocia-tive process is found for individual solvents, then the same mech-anism should hold in mixtures of these solvents. With this in mind, Rorabacher proposed1^ that a "pure solvent of strong coor-dinating nature results in a more stable five-coordinated metal ion transition state relative to its six-coordinated ground state than does a pure solvent of weaker coordinating ability", based on results obtained for N i 2 + in water, methanol, and ammonia sol-utions. This leads, when mixed solvents are considered, to the conclusion that substitution of weaker co-ordinating ligands in the inner solvation sphere decelerates the metal bond rupture rate for al l other ligands in the inner sphere. In other words, the five co-ordinate transition state is destabilised relative to the hexa-coordinate ground state. Thus i f no steric effects occur, as might with multidentate ligands, the reaction rate of a solvated metal ion should reflect the rupture rate of the weak-est metal-solvent bond in the inner solvation, or coordination, complex. This rate can be modified quite markedly by the varia-tion in donor strength of other ligands (solvents) in the complex. Solvent mixture results should then reflect the balance between weak and strong bonding species present in a particular metal - 134 -inner sphere. These inner sphere considerations apply particular ly well to ligand exchange in fairly strong solvents such as water or methanol, where a highly solvated metal ion is usually considered. By reducing the inner sphere effects (with a quinque 35 dentate ligand) at Ni(II) Rorabacher also managed to show that outer sphere effects are important in exchange processes. The similarity of this restricted inner sphere complex situation to the CuDDC case studied here is notable. Rorabacher's proposal was put forward to explain the fact that when inner complex ef-fects are minimised, both formation and dissociation rates for am monia exchange are increased as the methanolic content of the sol vent is increased. This effect is opposite that for which the in ner sphere effects were discussed, whereby as inner-coordinated solvent molecules changed from water to methanol the weaker metal methanol bonds tended to lower the bond-breaking rate for metal-water bonds. For pure solvents, this leads to slower ammonia ex-change rate in methanol than in water. Thus Rorabacher's outer sphere mechanism to explain the opposite effect was that methanol is more effective in "pulling" an ammonia molecule from the coor-dinating site than is water. The affinity of a particular leav-ing group for a particular solvent molecule is expected to be ref lected as trends in dissociation rate constants as a function of solvent composition. Effects such as hydrogen bond formation would be expected to contribute. It is clear, therefore, that the proposals put forward by - 135 -Rorabacher, which evidently consistently interpret ammonia ex-change rates in various solvents with Ni(II) ions, may explain the results obtained here. First, it is useful to note that a solvent pre-equili-brium process: (7-8) B + Solvent * B(Solvent) Cul^ + Solvent ^ CuL.2 (Solvent) CuL2(Solvent) + B(Solvent) s N (CuL2'B)(Solvent) cannot explain the observed solvent trends in forward enthalpies. That this is so can be seen by considering that the overall en-thalpy change may be expressed as: (7-9) AH° = AHj - AHj + A H S Q 1 V where H , represents some sort of contribution from the sol-solv r vent pre-equilibrium. Rearranging, one obtains: (7-10) AH^ = AH° " A H s o l y + AH* Now AH , for the solvent/ligand interaction is variable solv " with varying solvent, and i t may be assumed that a constant con-tribution is made by the solvation of the metal complex. So noting that AH , for benzene/pyridine is % 0 kcals/mole, and 6 solv r 132 for chloroform/pyridine is -1.86 kcals/mole , it would appear that AH .^, from (7-10) does indeed increase on going from benzene - 136 -to chloroform, as observed. However, this model cannot include the changes in A H ^ , which are observed to increase from benzene to chloroform, but which ( 7 - 1 0 ) predicts wil l decrease in the same order using the values for A H s q ^ v just quoted. Both trends in A H ^ and AH^_ require information about the other, and hence pre-equilibrium arguments can be used to qualitatively rational-ise solvent trends, but cannot be very specific. Rorabacher's results were obtained for ^ 3 0 0 ° K , so i t wil l be fruitful to see whether or not his inner sphere and outer sphere solvation models can definitely reproduce the trends ob-served. As noted already the forward rates for CuDDC in various solvents with pyridine decrease from benzene to chloroform, and the enthalpies of formation increase over the same order. Schem-atically this may be represented as: (__ DPC //» Cu-BDC • benaeng / / ' / oi LU where the arrows represent the various A H ^ . to be expected. The fact that A H ^ is negative for benzene and toluene is not impor-tant in the present discussion, so only the trends in rates will be considered. In terms of Rorabacher's*^ proposals for inner sphere effects, then, one would expect the reduced-coordinate transition state, designated CuDDC, to be less stable relative - 137 -to benzene than chloroform, and the forward rate to be faster in benzene than in chloroform as observed. Such a description relies, of course, on the fact that chloroform is known to hydrogen bond to various ligands, and might be expected to form a stronger inner sphere complex than benzene or toluene. The trends observed in both rates and enthalpies are as the model would predict. Trends in forward AS* values are observed to increase in the same order, perhaps reflecting the situation that chloroform forms a stiffer solvent structure than toluene or benzene through hydrogen bonding. Although the rate trends are neatly explained at 300°K, a flaw in Rorabacher's argument becomes apparent when the Arr-henius plots for the solvents are examined (fig. 5-12). As the isokinetic relationship would predict (fig. 7-1), above "o 340°K, the observed order of the forward rates reverses itself . In effect, according to Rorabacher's arguments, above this tempera-ture the solvents behave oppositely to that at lower temperatures. Invoking various thermal effects is not a consistent approach, and i t would appear that these inner sphere effects discussed by Rorabacher are unable to include isokinetic behaviour. The consistency of the forward rates for various pyridines in the same solvents is strong evidence that a solvent effect dominates the adduct formation process. In other words, i t would appear that the solvents used in this work do not co-ordinate to the metal, but instead form some sort of outer sphere complex. - 138 -The replacement of a solvent molecule by the base would then depend only on the solvent structure, and not on the formation of metal-ligand bonds. An inner sphere complex formation cannot be the complete explanation, even using the ideas of Rorabacher just outlined, since negative acitvation energies are observed for the process. The breaking of a metal-solvent bond would re-quire a positive activation energy. Thus although inner sphere effects may be present, outer sphere effects are more dominant. This point will be elaborated and established shortly. b) The Bennetto and Caldin Model: It is appropriate at this point to extend the discussion to another dissociative in-terchange solvent model, designed to explain certain trends in Ni(II)-bipyridyl reaction with solvent composition. This model, 43 the Bennetto and Caldin model , hereafter referred to as the 35 BC model, has been criticised by Rorabacher as being insuf-ficient in its consideration of inner sphere effects. It is Rorabacher's contention that, although outer sphere effects are present, they are different from those proposed by Bennetto and Caldin in mixed solvents, and inner sphere effects are sufficient to explain the trends in the work of Bennetto and Caldin. It would appear that Rorabacher's inner sphere and outer sphere pro-posals, as outlined above, do explain previous results in the Ni(II) system reasonably well, but do not include isokinetic be-haviour. For the reaction of CuDDC with pyridines in non-coor-- 139 -dinating solvents, however, i t has already been shown that the isokinetic behaviour should be included. This behaviour is in-cluded in the BC model, and a discussion of the model follows. 162 An ion solvation model first proposed by Frank and Wen was adapted by Bennetto and Caldin to explain certain trends in activation parameters for the Ni(H)-bipyridyl system 1^. The model is illustrated in fig. 7-3. The central metal ion is surrounded by an inner solvation shell, A, in which i t is considered that solvent-solvent forces are defeated by ion-solvent forces. In this respect the "bond-ing" is considered to be more akin to adsorption of gas mole-cules than to a crystallisation of solvent about M. The region immediately beyond A, designated B in the figure, is a disordered: region of high energy and entropy, relative to the bulk solvent, wherein the solvent molecule may have escaped from the force field of its bulk solvent neighbours, but has not yet penetrated the inner shell, A. The lifetime of a molecule in this disor-dered region will be short, and the boundaries not well-defined. The outer sphere, C, is composed of bulk solvent when solvent-solvent forces predominate. A solvent exchange process (ligand exchange or ligand sub-stitution can be considered in an analogous manner) can be readi-ly described in terms of this model. First, a solvent molecule must overcome solvent-solvent forces and escape from C to B (pro-cess 1 in the figure). This step can be envisioned as requiring - 140 -Fig7-3: S t ruc tura l M o d e l for a S o i v a t e d Ion ( a f t e r Frank and W e n ) E m p l o y e d by B e n n e t t o and C a l d i n (C) .(B) (A) CB) (C) A = First So iva ted L a y e r B s In termedia te D i s o r d e r e d Reg ion C = Bulk Solvent - 141 -an energy comparable to the heat of evaporation, AH^ , for the liquid. A molecule in region B can enter into region A i f there is an empty position in A (process 2), which can be created by process 3 in which the inner sphere molecule has overcome the ion-solvent interaction. The "hole" in the bulk solvent is re-placed by process 4, which can be regarded as a condensation with energy release -AHv . The overall free energy of forma-tion, AG°, will have varying contributions from all four pro-cesses, and i t should be recognized that processes 1 and 4 wil l be interdependent (process 5) through solvent-solvent interac-tions and reorganisations. Process 5 can clearly contribute to the energy of the transition state, and i t will be shown that this proces^ s can, in fact, determine the differences in a common reaction taking place in different solvents. The energies of the various processes can be identified as follows. If the enthalpy associated with breaking a metal-solvent bond is Alt^,, then process 3 refers to A H ^ . Processes 1, 4 and 5 can be related to the enthalpy change associated with structural reorganization of the solvent, AH ^. It is useful to a ' st associate these processes in this manner, but i t is difficult to isolate the different contributions to AH s t at present, although qualitative assignments of the overall enthalpy change can be made. The overall relationship for solvent exchange may be ex-pressed as: (7-11) AH* = AH^ + AH s t - 142 -Hence a variation in AH* can arise through variation of AH g t, assuming for the moment that remains constant for a series of similar solvents. Variation in AH ^ is caused by a s t balance between processes 1 and 4, whence process 5 is also im-plicated. If, for example, the structural contributions to AG* from processes 1 and 4 are approximately equal then no net work is done when molecules enter or leave region C. Under these cir-cumstances AH g t =0. Consequently the reaction is dominated by the dissociative process 3, which can be associated with a metal-ligand bond rupture, as noted earlier. The structure of the bulk solvent remains largely unaffected. If, now, a solvent is considered whose bulk structure is such that i t cannot readily adapt to accomodate the molecule leaving region B (and entering C), then it may be stated that net work must be done on the bulk solvent. This is equivalent to saying that process 1 is contributing to the formation of the transition state. In other terms,, the co-operativity (process 5) in the solvent is such that the leaving group cannot enter the bulk solvent (process 4) before an incoming molecule enters B (process 1). Overall, this is tantamount to saying that work has to be done and AH g t will be positive. Alternatively, pro-cess 1, being akin to evaporation, is an endothermic one and hence AH . > 0. st In contrast, i f the bulk solvent molecules can readily adapt (through, presumably, reorientation and rotation) so that - 143 -leaving molecules (process 4) are easily reaccomodated with no work having to be done on the bulk solvent, then AH „_ will be st negative. That is , process 4, the exothermic condensation pro-cess, wil l dominate AH ' st The considerations outlined above have been for pure sol-vents; the effects of mixed solvents or solvent-ligand mixtures may now be mentioned. Obviously the contributions to AH from st processes 1, 4 and 5 will now be modified because of the pre-sence of the ligand (or other solvent molecule). Solvent struc-tures wi l l be modified since a ligand which is not i tsel f the solvent will produce local changes in the liquid structure. These changes will depend on factors like dipole moment and polarisability of the ligand molecule. In other words, factors that may contribute to intermolecular forces. A rough measure 34,158 q £ ^ese intermolecular forces is the enthalpy of vapor-isation, AH v ap, and one might expect that the greater the dif-ference between AH for the solvent and that for the ligand, vap ' the greater the local changes in solvent-ligand mixtures. This fact can be rationalised by noting that a high value of AHv suggests strong intermolecular forces. Interspersing a solvent or ligand into this structure will change the intermolecular forces considerably. The degree to which the bulk solvent (or solvent mixture) readmits a molecule is its cooperativity. Thus i f processes 1 and 5 remain the same for some sol-vent, addition of a ligand with a value of AHyap higher than - 144 -that of the solvent will lead to a more negative value of AH 6 st since less work is done on the solvent in process 4. This is because the ligand will promote a more ordered and open struc-ture in the solvent. Hence i f AH , in this example, is more negative (than in the case of solvent exchange) then AH* will be smaller. If AH g^ is smaller than AH , then AH* will be negative. The more open structure of the solvent will lead to partly com-pensating effects in AS and AS*. It may be considered, then, that the effective AH of the solvent-ligand mixture is some-vap 6 where between the values for pure solvent and pure ligand. Now i f the addition of the ligand also reduces the abil i-ty of the solvent to accomodate a leaving solvent molecule (pro-cess 4) then work must be done on the bulk solvent. In other words, process 1 (which is endothermic) and process 5 (which is also endothermic and relates the degree of cooperativity of the solvent to the exchange process) contribute to the formation of the transition state. Hence AHv effects may be negated by the presence of solvent properties that lead to a low degree of co-operativity. Hydrogen-bonded solvents might be expected to de-monstrate these effects. Discussion of the processes just mentioned in terms of the solvents used in this study requires knowledge of AH^ . This is given in Table 7-3. - 145 -TABLE 7-3: AH (b.p.) FOR SOLVENTS —vap—i—z—L : benzene 7.55 kcals/mole toluene 8.00 kcals/mole chloroform 7.02 kcals/mole pyridine 8.37 kcals/mole Before considering the benzene/pyridine system, i t should be reemphasised that the solvents used here are essentially non-coordinating. Because of this, i t is expected that AH g^ be small, and certainly smaller than AH^> where L refers to the base in question. Although this latter point is perhaps intuitively ob-vious, i t can also be deduced from the fact that AH^ > AH .^. Since ' r f AH . may be assumed the same for both forward and reverse direc->t tions, for any given ligand, then from 7-11 AH^ > ^H^g* 132 Now. for benzene/pyridine mixtures i t is known that AH r soln for pyridine in benzene is ^ 0 kcals/mole. It would appear then that very l i t t l e structure change takes place when pyridine mole-cules replace benzene molecules. This suggests in turn that for ligand exchange the benzene molecule displaced from the metal ion by the incoming pyridine (processes 3 and 2, respectively) mole-cule is easily readmitted to the bulk solvent. Process 4, akin to condensation, tends to dominate in this system. Further, AH is ' vap greater for pyridine than benzene, and one therefore expects A H s t to be small, or negative. If A H s t is much more negative than Arl^  - 146 -is positive, then AH* will be negative. This is the observed result shown in Table 7-2. Toluene/pyridine systems are subject to the same criteria, except that now AHy for toluene is nearer that of pyridine. In this case, one would expect AH* for toluene to be larger than that for benzene, assuming similar values of AH^g. This conclu-sion is further supported by noting that toluene and pyridine are not as similar as benzene and pyridine, hence more work will be required to return toluene to the toluene/pyridine mixture. Thus process 4 will be less exothermic. Overall, Table 7-2 shows AH* (toluene) > AH* (benzene), supporting these conclusions, The pyridine/chloroform case exhibits some interesting ap-plications of the Bennetto/Caldin model. From Table 7-3 it may be noted that the difference in heats of vaporisation for chloro-form and pyridine is the largest of the three solvents studied. From the experience gained with toluene and pyridine, then, one expects AH g t to be lowest, or most negative, and hence AH* to be smallest. However, this conclusion would be wrong, as Table 7-2 indicates. The extra factor to be accounted for here is the 132 strong hydrogen bonding known to exist in chloroform and chloroform/pyridine mixtures. This leads to a large contribu-tion from processes 5 and 1 to the enthalpy of formation of the transition state, since a returning solvent molecule has to do work on the solvent to be reaccomodated. The overall endothermic - 147 -contributions from processes 1 and 5 evidently just balance, or slightly outweigh, the contributions from process 4, resulting in chloroform/pyridine mixtures having the largest A H ^ , as ob-served. The fact that the values of A H ^ remain in the same or-r der is further evidence for the concerted processes involved in the mechanistics of ligand exchange or solvent exchange situa-tions, although in this case inner sphere effects are very im-portant. This will be discussed in more detail shortly. The solvent variation data can be discussed in a slightly different way to that just given, although in terms of the BC model the descriptions are equivalent. For the solvents, the existence of negative activation energies, and the relationship (7-11) allow some qualititive conclusions to be drawn about AH^,. Although one might expect some sort of variation of AH^ with solvent, it is not possible at present to evaluate i t . As just discussed, this is not really needed since AH considerations vap are more important. Because the solvents studied here are non-coordinating, as opposed to the quite highly coordinating sol-vents studied by Bennetto and C a l d i n ^ ' a n d Rorabacher'^*''^^] AH ,^, is expected to be small. Because of the small variations in coordinating ability for benzene, toluene, and chloroform, one might expect AH g^ to show small variations with solvent, but variations negligible compared to AHy , perhaps. The small, almost constant, value of AH g^ is therefore a large contributor to the overall negative activation energy for the forward pro-- 148 -cess: k f CuDDC + Base > CuDDC-Base It can also be mentioned that the evaporation/condensation processes could be likened to an expansion/contraction descrip-tion of the gas-like region. Such a process would involve en-tropy differences, and i f likened to the gaseous model, a con-traction process wil l be accompanied by a decrease in entropy of the bulk solvent. On an overall basis, passage from processes 1 to 5 in the BC model requires less work to be done against the bulk solvent to reincorporate a solvent molecule than to reincor-porate a larger ligand molecule. In the reverse, or dissocia-tion of adduct, direction, the reincorporation of a ligand into the solvent wil l require more energy than the incorporation of a solvent, leading to an entropy change that should be more posi-tive for reverse reactions than forward ones. This is because the expansion of the outer sphere to reincorporate a ligand mole-cule is more than that required for a solvent molecule, and a more disordered solvent results. This is the observed trend in these experiments. For the variation of bases in benzene, examination of base-solvent structure within the BC model would be expected to re-veal a trend in AH* that reflects the interaction between ligand and solvent. The equality of rates is expected since the same solvent, benzene, is involved and the loss of benzene from the - 149 -metal ion is expected to dominate the ligand approach. Trends in AH^ would be expected, therefore, to reflect steric effects rather than basicity. The most symmetrical base, 4-picoline, wil l form a better, or tighter, structure with benzene than the other pyridines. A minor contribution from the basicity can be noted in that AH^ for 4-picoline is greater than that for pyri-dine. The other picolines show a decreasing AH^ as the steric effects, represented by the methyl groups, increase. The small variation in rate is also explained (although this variation is not much more than experimental uncertainty) qualitatively in terms of stiffness of solvent structure. Clearly, a fairly bulky 3,4-dimethyl substituent will interfere with the solvent organisation ability, making the benzene/3,4-lutidine more sus-ceptible to the concertion process than the benzene/4-picoline system. The more disordered liquid structure leads to a higher AS5* for 3,4-lutidine, compared to 4-picoline, also. These solvent compensation effects, as mentioned earlier, should lead to an isokinetic relationship. The BC model, i f correct, should lead to an isokinetic relationship, on the basis of evidence so far. This is hence the evidence for the model for a series of ligand exchange or solvent exchange reactions. The review by Ritchie and Sager**^ presents a thorough summary of the factors behind an isokinetic relationship, and wil l not be repeated here, except to note that processes domin-ated by solvation effects commonly, i f not invariably, show an - 150 -isokinetic behaviour . This is because changes in solvent structure demonstrate a balance between entropy and enthalpy such that a change in the structure leads to a compensation in entropy and corresponding compensation in enthalpy. It is not expected, therefore, that AG should reveal very much about solvent, or steric effects, since AG is defined by: (7-12) AG = AH - TAS A compensation effect, as we11-demonstrated by figs. 7-1, 7-2 for the present case, will lead to AG values being almost con-stant. It then follows that the equilibrium constant, defined as: (7-13) K = exp(-AG°/RT) is a somewhat insensitive, or blunt, tool for studying solvent o r ligand effects. Table 7-4 illustrates the values of AG*obtained. TABLE 7-4: AG FOR VARIOUS SOLVENTS AND BASES FOR CuDDC AG0 AG* AG* System f r (kcals/mole) (kcals/mole) (kcals/mole) pyridine/benzene 0.5 6.1 5.6 pyridine/toluene 0.6 6.2 5.6 pyridine/chloroform 0.8 6.3 5.5 benzene/2-picoline 1.7 7.0 5.3 benzene/3-picoline 0.4 6.1 5.7 benzene/4-picoline 0.3 6.2 5.9 benzene/3,4-lutidine 0.0 6.0 6.0 - 151 -As can be seen, there is remarkably l i t t l e variation, ex-cept for 2-picoline, in the forward direction. There is more variation in the reverse direction, and this point will be re-considered shortly. Figure 7-4 shows the correlation between AH and AS for both solvents and bases. The forward correlation is quite sig-nificant on several points. First, i t establishes that solvent effects do, indeed, dominate the forward formation process, to the extent that even 2-picoline falls on the line. The solvent effects are so well correlated that the BC model is to be con-sidered an excellent description of the mechanistics of ligand and solvent exchange, especially for the forward reaction. Clearly the presence of a common isokinetic temperature means that Rorabacher's inner sphere model must be expanded to include outer sphere effects, otherwise i t is incapable of explaining the isokinetic behaviour. Similar tests of the current theories can be made for the data obtained in the reverse, or dissociative, direction of the reaction between CuDDC and Lewis bases in inert solvents, and conclusions discussed. This will be done now. C. THE REVERSE, OR DISSOCIATIVE, REACTION: a) Solvent Effects: The reaction to be considered, common for both solvents and bases, is described by the following: k (7-14) CuDDC-base —^>• CuDDC + base - 152 -A benzene B toluene C chloroform 1 3,4-lutidine 2 pyridine 3 3-picoline 4 4-picoline 5 2-picoline AH [kcals/mole] A •33 -27 AS[eu] Fig 7-4: Isokinetic plots for solvents and bases. o;» forwards *A reverse - 153 -and clearly involves the breaking of a metal-nitrogen bond, and the dissociation of the adduct, presumably accompanied by resol-vation of the CuDDC complex. As Tables 7-1 and 7-2 show, there is not a simple correlation of k with solvent, but AH* and AS* r r ' r r both increase from benzene to toluene. On the basis of Rorabacher's inner-sphere and outer-sphere mechanisms for a reaction such as (7-14), the solvent molecule must assist in removing the base from the metal. The replace-ment of the base by a solvent molecule must be determined by the labil ity of the solvent in the outer sphere. This lability is more enhanced the greater the total solvation energy. Or, the more stable the solvent structure, as for extensive hydrogen bonding solvents, the more likely is a molecule from that solvent 35 to replace the departing ligand . For CuDDC, inner sphere ef-fects are minimised by the bidentate ligands, leaving one site, most probably, for solvent or ligand co-ordination. Two weak bonds may be formed with solvents, but i t seems well established, from the remarks in chapter 5, that only one co-ordinating mole-cule need be considered. This situation is similar to that 35 wherein Rorabacher used a quinquedentate ligand to leave ac-cessible only one co-ordinating site on the Ni(II) ion. Since chloroform is known to form hydrogen-bonded struc-tures, as does water, i t might be expected from Rorabacher's model that the rate of reverse reaction in benzene should be slower than in chloroform. Toluene would be intermediate - 154 -because its dipole moment will stiffen the solvent structure somewhat. Table (7-2) indicates that this is the case at 300°K. The presence of an isokinetic plot for the reverse thermodynamic parameters, albeit not as consistent as the forward one, suggests that Rorabacher's prediction will not hold at some other tempera-ture. This is amply illustrated by fig. 5-12. In the reverse direction, Att^, the enthalpy for breaking a a metal-ligand bond, is expected to contribute to the overall enthalpy. For pyridine in various solvents, this value should be constant and the trends in AH* should reflect AH ^ from (7-11). r st The trend observed is that AH* increases from benzene to chloro-r form. Hence it would be reasonable to assume that AH . increas-st es from benzene to chloroform. This is explained in terms of the BC model by the fact that pyridine does less work in enter-ing the solvent structure of the benzene/pyridine mixture than it does to reenter the chloroform/pyridine structure, but the energy required for a chloroform molecule to leave the strongly interacting pyridine-chloroform solvent structure outweighs the entering process by an amount sufficient to make the process in benzene a lower energy process. The apparent contradiction on the basis of AH is that the rate is faster in chloroform, vap This can be rationalised by noting that pyridine dissolves readily in chloroform (AH , = -1.8 kcals/mole), much more so } solv than benzene. Data is not available for toluene, unfortunately, for, on the basis of this discussion, AH 1 for pyridine in - 155 -toluene should be less favourable than benzene. The easier sol-vation of pyridine in chloroform would tend to accelerate the leaving of the pyridine molecule more so than for benzene (pro-cess 3 in the BC model), on the basis of energetics alone. How-ever, as soon as the pyridine molecule reaches region B a chloro-form molecule must replace i t (process 1 is s t i l l dominant). Similarly for benzene. It is this latter process that is ener-getically less favourable, leading to the observed trend in en-thalpies. The rate in chloroform, however, is s t i l l slightly faster than in benzene because for benzene the in i t i a l process 3 is the more important in the concerted scheme. One would there-fore expect toluene to be resistant, at 300°K, to acceptance of the leaving pyridine molecule, but process 1 in pyridine/toluene to be relatively easy. It is not easy to see how Rorabacher's outer sphere model 35 might be applied in this case. His associative "push" mech-anism, whereby the solvent l i teral ly "pushes" the ligand from the inner sphere and replaces i t with i t se l f is not likely to occur with the bulky solvents and ligands used here. This is , 35 in fact, an objection of his own for methanol . The dissocia-tive, or "pulling", process mentioned earlier suggests that the more basic solvent will be best at removing the ligand. In this case, the more basic solvent is difficult to ascertain. The criterion that the more labile species in replacing the departed ligand is that with the most solvation energy apparently deter-- 156 -mines chloroform as the fastest rate process in the reverse direc-tion, as mentioned before. Rorabacher's work, however, was for co-ordinati-ng solvents, and although his ideas predict the fast-est rate, it is difficult to see how non-coordinating solvents, such as those used here, can participate in the enhancement of the leaving rate of a ligand. These bulky solvents could not interact with the nitrogen nucleus, which must be in a sterically crowded environment: and i t is unlikely that chloroform, the most active chemically, could exert a signigicant "pul l " on the ligand. The outer sphere presentation of the BC model seems more likely, based on solvent-ligand and solvent-solvent interactions, as i t also explains al l the thermodynamic trends, and is apparently more suitable to non-182 coordinating solvents . The BC model, moreover, allows the equivalence of saying that i t is difficult for the ligand to get into the solvent structure, or that the solvent structure is not helpful in removing a ligand. 35 Disagreements arise , because the BC model predicts that the rate of removal of ammonia from Ni(II) in water should be - 157 -faster than in methanol, because of the fact that AH _ > 0 for st 34 methanol and this indicates that methanol wil l tend to inhibit cooperativity in the transition state. The hydrogen bonding will tend to prevent the ammonia molecule from entering the bulk sol-vent (processes 4 and 5) before process 1 occurs. Water tends to favour concerted mechanisms, the molecules undergoing highly co-operative molecular motions. Repulsive and attractive intermole-cular forces are so strong that as soon as a molecule escapes from the structure, there is a high probability that i t wi l l soon return to the structure. Water is unique in that i t possesses high stiffness, open-ness and order3^, and overall is small. Hence, i t would appear that ammonia exchange must be faster in water than in methanol, for instance. Such a prediction is op-posite to Rorabacher's f i n d i n g s ^ ' 1 ^ , and Rorabacher's outer sphere model can explain the results in terms of increased abil-ity for methanol in removing ammonia from Ni(II). That the BC model was postulated on the basis of results for Ni(II)-bipyri-dyl reactions may have been unfortunate for the application to some other systems. b) Effects of Varying the Base: With the results of this section, i t wil l be seen that the BC model provides a coherent and consistent interpretation of the results. Referring once again to Table 7-2, the trend of rate constants with base for the reverse direction is seen to follow the order of base - 158 -strengths, i f it is accepted that 2-picoline is a weaker base than pyridine in benzene for reaction with CuDDC. The trend ob-served in rates is that expected for the metal-ligand bond breaking order: the stronger the base the harder i t is to break the bond, hence the slower the reverse rate. Since the solvent is a common one, AHgt is expected to be reasonably constant, ex-cept perhaps for small changes caused by interaction of solvent with base. As in the forward direction, process 1 is s t i l l a major step in the exchange process, although for solvents en-tering its contribution is small, energy-wise. For co-ordinat-ing ligands, on the other hand, AH^ will be larger, and posi-tive, and so will contribute to the energetics of the reverse process in a more noticeable fashion. The trends in AH5* show a distinct solvent interaction be-r tween benzene and the pyridines. In terms of AH^ g alone, i t would be expected that variation of AH^  would be with base strength. This is not the case, and the observed trends point out that solvent-ligand structure is important, although AH^ contributions are present. The observed trends indicate that 4-picoline forms a stiffer structure with benzene than do the other pyridines, and hence the work required to remove a sol-vent from the benzene/4-picoline structure is more than for a more open structure like 3,4-lutidine. The position of pyri-dine in the trend presumably reflects the fact that pyridine/ benzene structures are ordered but not too s t i f f , thereby per-- 159 -mitting easy removal of solvent and easy re-entry of ligand. The base strength, and hence AH^> is lowest, and so pyridine occu-pies an "anomalous" place in the trend. 2-Picoline, because of steric inhibitions involved with co-ordinating at copper(II) ap-parently has the highest value of A H ^ . This seems certainly anomalous, and may reflect an enhanced solvent-ligand interaction, and hence restrictions on the "concerted-ness", or expansion/con-traction, of the overall mechanism. Fig.(7-2) shows the isokinetic plot for bases alone, and fig. (7-4) shows that for al l bases and solvents. For the re-verse parameters, i t is clear that the variation in AFL^ must be causing the AH/AS compensation effects to be slightly disturbed. In other words, outer sphere effects alone are not totally suf-ficient to describe the results, but the labil ity of the ligand must be included when i t is bonded ot the metal. It is inter-esting to note that since 2-picoline behaves approximately like a solvent, an isokinetic line through the points for benzene, toluene, chloroform, and 2-picoline has a better regression co-efficient* (0.9996) than the line through the bases alone (0.9979), or the solvents and bases (0.9976). In fact, 2-picoline is on * the regression, or correlation, coefficient is defined by: ^(x i - x) (y. - y) R = -—^ 2 v /^(x i - x) ( y i - y) where x indicates the arithmetic mean. - 160 -the line through the solvents since the regression coefficient for the three solvents alone (0.9997) is almost unchanged from that including 2-picoline. In contrast, the regression coeffi-cients for the forward plots are much better (see Table 7-5). TABLE 7-5: REGRESSION COEFFICIENTS FOR ISOKINETIC PLOTS System R (forward) R(reverse) solvents only 0.99999 0.99972 bases only 0.99995 0.99788 solvents and bases 0.99988 0.99764 solvents and 2-picoline 0.99986 0.99957 The solvent-like behaviour of 2-picoline is expected on the basis of the very slow forward rate and small equilibrium constant. It is perhaps the reason for the large positive value for AH*, which then indicates that large (compared to other pyridines) energies are required to remove solvent from benzene/2-picoline mixtures and to reintroduce a 2-picoline molecule. This pseudo-solvent behaviour should also be reflec-ted by an increase in entropy in the reverse direction, since more disorder is created in both reactants and solvent struc-ture. This is indeed the observation. With respect to the order of bases on the isokinetic plot, - 161 -there is correlation between the dipole moment of the base (Table 7-1) and the order. The isokinetic, hence AH, or AS, order is : (7-15) 3,4-lutidine < pyridine < 3-picoline < 4-picoline 4-picoline < (2-picoline). The dipole moment order is : (7-16) 3,4-lutidine < (2-picoline) < pyridine < 3-picoline 3-picoline < 4-picoline Using the BC model, the dipole moment would be expected to reflect solvent structure for a common solvent; the more ordered structure arising from interaction of benzene with the strongest dipole. This correlation is excellent, and is an additional confirmation of the dominance of solvent effects in these reactions. The emphasis on isokinetic plots here, and by Bennetto and Caldin3^'160^ Reserves some remarks before conclusions are drawn and discussed. It has been pointed out by Ritchie and Sager1^^ that simultaneous Hammett (linear free energy relationships, see Appendix 2 for details) and isokinetic behaviour in a series of reactions is rare, and perhaps non-existent. In fact for both relationships to hold there is a quite stringent requirement, that "free energy, entropy and enthalpy must al l be separately correlated with the Hammett equation". Laidler's work 1^ also suggests that these conditions are difficult to meet. Reaction series giving separate isokinetic or Hammett plots are, of course, - 1 6 2 -numerous ' . In this work isokinetic plots have been ob-tained for the complete system. This infers, then, that no Ham-mett relationship should be observed. In other words, because AG" is small, AG^ being almost constant, the Hammett equations: ( 7 - 2 0 ) log K = log K q + cp ( 7 - 2 1 ) log k = log kQ + ap should not describe any of the results of this work. This is in-deed the case, calculations being performed for pyridine as the 1 2 7 "parent" compound, using a values for m- and p-methyl groups on pyridine. - 163 -CHAPTER 8 CONCLUDING REMARKS A. GENERAL CONCLUSIONS: In describing fairly detailed studies and results for the overall reaction: (8-1) CuDDC + B ^ ^ CuDDC-B in various solvents and with various bases, a number of conclu-sions have been made. Before detailing these, i t might be well 183 to requote J^rgensen's warning, noted by Langford and Sten-181 gle , that " . . . kinetics is like medicine or linguistics - i t is fascinating, i t is useful, but i t is too early to hope to understand much of i t . " Since 1967, however, a great deal of work has been done, and the understanding encompasses a rather larger share now. - 164 -Fast exchange processes undoubtedly s t i l l pose problems for the kineticist, but i t is in the area of neutral molecules and non-coordinating solvents that a great deal of interesting work has yet to be done. As far as is known, this study is the first to be reported in detail for the latter situation. Different theories or interpretations of the results may be applied to future studies. Even with the pronounced agreement between the BC model and this w;ork, questions remain about detailed solvent interactions. For example, in the BC treatment, a "solvent-modi-34 + 4 fied dissociative process" , low values of AH and AS can be obtained only i f the condensation process dominates. In other words, a negative value of A H s t is required, as already discussed?, to obtain overall negative values of AH^, which may be associated;; with a simultaneous passage of solvent from B to C (in fig. 7-3). Low values of entropy, and corresponding compensating changes in enthalpy, are to be associated with the condensation of a gas. Why does the condensation process dominate for such reac-tions? The rationale, assuming this fact, explains the results. Its justification is that process 5 in fig. 7-3 links regions A and C effectively through long range solvent structure, and the vaporisation process is energetically less favourable. Thus one can imagine that process 4 is followed by processes 5 and 1 to complete the solvent, or ligand, exchange. The fact that the for-ward rate is ligand independent supports the idea that processes 3 and 4 dominate. For very low, for instance negative, AH^ values - 165 -process 5 obviously does not have much effect and processes 3 and 4 dominate 1 and 2 even more. This explanation is s t i l l a rationale. It remains that the condensation process, assumed equal in magnitude but oppo-site in sign, to the vaporisation process in setting up the BC model, dominates for these results. The quantitative reason is not really known at present. It can easily be seen that similar considerations might apply to a l l phases of the solvent contribu-tion to the solvent/ligand exchange situation, depending on the reaction. General conclusions are, however, very useful. 35 Rorabacher's ideas cannot explain the reversal of rates at the isokinetic temperature. It is evident, also, that CuDDC does not form strong bonds, i f any, to the non-coordinating sol-vents used and therefore whatever inner coordination sphere ef-fects are present are likely to be small. This has been shown to be true for the forward rate, resulting in an excellent iso-kinetic relationship. For the reverse process small variations in A H J ^ are noted when the base is varied and some inner sphere effects contribute. This is reflected in the poorer isokinetic plot for the bases in the reverse direction. Overall, however, the evidence has been shown to overwhelmingly involve outer sphere effects. Thus the Bennetto and Caldin model is most ap-plicable. The Bennetto/Caldin treatment was derived to account for solvent structure changes, in addition to the breaking of a - 166 -metal-solvent, or metal-ligand even, bond, as contributions to 34 the free energy of activation . Earlier studies have largely 34 35 managed to avoid this ' . In applying this model, non-aqueous solvents must be considered in addition to water. The BC model effectively accounts for large variations in enthalpy and en-tropy. In this work, negative enthalpies of reaction are ex-plained within the framework of the model. Ligand modifications to the solvent can be accounted for and the results obtained here suggest that related series of ligands will stiffen a com-mon solvent proportionately to the dipole moment of the ligand. Steric effects that lead to very low values of AFL^ wil l result in a ligand behaving more as a solvent than a ligand. This is amply illustrated by the behaviour of 2-picoline towards CuDDC in benzene. The concerted nature of the BC model is a major factor in being able to explain the results of equilibria involving fast processes in non-coordinating solvents. Situations involving , , . ,. . 34,35,160-162 charged species in coordinating solvents are not as sensitive to concerted solvent effects, and it is usually expected in these situations that inner sphere effects are more important In concluding the remarks about the Bennetto and Caldin model, i t is sufficient to note that this model completely and consistently explains the results obtained for the process de-fined by (8-1). Other ideas recently proposed"^ do not explain - 167 -these results sufficiently, and conventional ideas involving solvation pre-equilibria have been shown to be inadequate for 182 this situation. In fact, it has been recently observed , that the reaction mechanism: 1 K o , . (8-2) MS" + L ; ? = ± MS.L ; " M S c - L l n _ m J + + xS 6 % IT 6 5 x fast is of questionable validity in non-aqueous solvents. It should be added that (8-2) may have questionable validity in non-coor-dinating solvents. The results obtained in this work certainly support this view. B. FUTURE WORK: Application of line broadening effects in epr or nmr spectra to obtain rate constants has been fruitful. Es-pecially so in this work. Further work, however, is limited to relatively few systems i f the fast exchange method of analysis 177 is to be employed . Because this method of analysis is con-venient, i t would seem that future epr work is limited to CuDDC 86 and related dialkyldithiocarbamates . If means are available for the analysis of any range of exchange rates, then clearly these studies could be extended to any paramagnetic system with 5 12 -1 exchange rates between ^ 10 and 10 sec . At the upper limit of exchange rates, consideration of non-secular effects would have to be made1^, since exchange rates and rotational reorien-tation times would be similar. Nmr studies might be useful to evaluate some of the unknown solvent effects involved in the - 168 -model of Bennetto and Caldin. Nmr studies were attempted on CuDDC in benzene/pyridine and mixed non-coordinating solvents, but chemical shifts observed were very small, and the results inconclusive. This should not deter attempts, using nmr, to study these systems. In terms of the BC model, i t would be instructive to evalu-ate additional thermodynamic data for several more solvents. Cyclohexane, predicted here earlier to be inert, should yield very low AH* values, smaller or more negative than for benzene. The loose solvent structure and the value of AH (7.2 kcals/ vap mole) suggest this. Acetone, on the other hand, should yield larger AH* values than chloroform, since i t is a coordinating solvent. CuDDC is soluble in both these solvents, but not in methanol or water. Variation of the base to include a few more points would be useful, though not as interesting in terms of the BC model as solvent variations. To test the various sol-vent-solvent and solvent-ligand interactions best, however, a series of experiments on mixed solvents and mixed ligands should be performed. In this way definite statements about the AH^ jg and terms may be forthcoming, which would shed considerable light on the significance of liquid structure in fast reactions in non-coordinating solvents. - 169 -CHAPTER 9 EXPERIMENTAL DETAILS AM) ANALYSIS OF DATA A. SAMPLE PREPARATION: The analysis of epr line positions and linewidths for copper in solution is often severely complicated by the presence of two isotopes in naturally-abundant copper. Copper-63 and copper-65 isotopes are present in a 70%:30% ratio, respectively. For samples showing narrow linewidths, resolu-tion of the two isotopes is readily achieved in many solutions. CuDDC epr spectra show these effects, and hence it was decided to perform the experiments with 99%+ copper-63. The isotopical-ly pure metal was obtained from A.E.R.E. , Harwell, England. Pure copper metal was converted to copper(II) nitrate in reagent-grade nitric acid. The nitrate anions were replaced with chloride anions by repeated reaction with hydrochloric acid. - 170 -The cupric chloride so obtained was washed repeatedly with de-ionized water, and green-blue crystals of Cu^C^^h^O obtained. This product was reacted with a slight excess of sodium diethyl-dithiocarbamate (Eastman) in absolute ethanol. The resultant dark green, almost black, precipitate was filtered, washed with ethanol and ether, dried, and recrystallised several times from benzene. This procedure yields shiny dark green needles of cop-per(II) bis(diethyldithiocarbamate) in high yield (^  92%). Ana-lysis showed (theoretical percentages in parentheses) the follow-ing percentage composition: C - 33.26 (33.43), H - 5.87 (5.57), and N - 7.78 (7.80). 6 3 Cu DDC was kept dry in a dessiccator during the investi-gation, although it has been noted^"^ that copper(II) B-diketon- • ates and related compounds are normally obtained anhydrous and show no tendency to coordinate atmospheric moisture. No differ-ence in the epr signal was noted in this work between the dry CuDDC and that which was left exposed to air for several weeks. CuDDC prepared from naturally-occurring CuC^*2^0 was 6 3 prepared in the same manner as Cu DDC, and used for situations where the presence of the two isotopes was unimportant. Reso-lution of the high-field epr line into two peaks confirmed the presence of the two isotopes in a 2.3:1 ratio. Al l solvents used in this work: benzene, toluene, chloro-form, carbon tetrachloride, cyclohexane and acetone were of spectroscopic grade quality (Fisher), which were kept sealed - 171 -before use. After opening, the solvents were stored under dry nitrogen and over Linde 4A molecular sieves, i f they were to be reused. Attempts were made, in a l l cases, to use opened bottles, only for a day or less, so as to minimise any absorption of at-mospheric impurities. Nmr spectra of benzene, toluene, and chloroform indicated no appreciable impurity content. Al l organic bases used; piperidine, pyridine, 2,6-lutidine, 2,4-lutidine, 2-, 3-, and 4-picoline were of highest available purity. Gas chromatographic analysis failed to show any impuri-ties in the lutidines and picolines, although it must be noted that these isomers are difficult to resolve amongst themselves, and the gas chromatographic separation might not reveal isomeric impurities. The presence of an appreciable amount of impurity that might interfere in the exchange process should be resol-vable by epr spectra taken of CuDDC in the neat solvents. In al l cases, high gain epr spectra failed to show any sign of im-purity, although they did partially show hyperfine splittings from sulfur-33 (0.7% natural abundance). As with the solvents, the bases were kept cool and dry before use, at which time they were resealed under nitrogen with an appropriate drying agent (see, for example, L.E. Tenenbaum, in "The Chemistry of Heterocy-clic Compounds", Interscience, New York (1961), volume 14, sec-tion 2) . All solutions prepared from CuDDC in the various solvent/ base mixtures were stable once prepared and degassed, and showed - 172 -no tendency to precipitate. The least squares analysis used in.: this work required a range of concentrations of base in any par-ticular solvent usually calculated as a minimum of three times-the number of variables used in the least squares f i t . Since three parameters were varied, on average, at least nine concen-trations were prepared for each system. Once the range of con-centrations to be covered was determined, solutions were made up individually, CuDDC dissolved in them, and a sample transferred to a s i l ica epr tube. This solution was freeze-thaw degassed a number of times on a vacuum system, and then dry nitrogen intro-duced to approximately atmospheric pressure to maintain normal boiling and freezing points of the solvent mixtures. Epr spec-tra were then recorded over a range of temperatures. Al l spec- . tra were recorded within a similar period of time to ensure con-sistency. No decomposition over a period of several days was noted in any of the samples mentioned so far. Decomposition, or reaction, did occur in piperidine and piperidine/solvent systems, and in the carbon tetrachloride/pyri-^- : dine system. The result was a diamagnetic pale green solution in a l l cases (CuDDC in solution is normally yellow-brown in colour). In a piperidine/benzene system that was being recorded; by epr it was noted that during the decomposition, whilst no solution colour change was yet discernible, a free radical spec-trum of several lines was observed, coincident with the much broader and larger high field line of the CuDDC spectrum. As - 173 -the solution decomposed further and changed colour, a l l epr sig-nals decayed. This free radical spectrum was then obtained inde-pendently by reacting piperidine with AlCl^ in a n appropriate: solvent, and it could be observed to consist of eleven lines. The interpretation is not entirely clear, but the spectrum ap- . pears to be due to hyperfine splittings from a nitrogen nucleus: and four equivalent protons. ^ -4 Al l epr solutions were prepared to be between 10 and 3, x -4 10 M in CuDDC. No broadening due to dipolar effects is discer-118 nible in this region , and strong epr signals are readilyj'at-tained. Solutions for UV spectroscopy were prepared using natural-ly-occurring copper(II), and oxygen removed by bubbling nitrogen through for a reasonable period. Matched quartz cells of 1 cm pathlength were used throughout. B. INSTRUMENTAL METHODS: Epr spectra were recorded on a Varian E-3 spectrometer equipped with a four inch magnet and using 100 KHz field modulation. For a l l spectra recorded the same X-band cavity was used, and al l Fieldial , modulation amplitude and scan time settings were the same. Field calibration was by means of a proton magnetometer manufactured in this department. The probe for the magnetometer was connected to an oscillator which sup-plied a variable frequency of ^ 14 MHz (X-band fields), modulated at 20 Hz. After beating with a signal generator the proton re-- 174 -sonance frequency was monitored on a Hewlett Packard 5425L fre-quency counter equipped with a 3-12 GHz plug-in unit to measure microwave frequency. Microwave frequency was monitored several times during each scan, so as to be able to reject any spectra '>. recorded during unstable conditions. Absolute field measure-ments to + 0.2 gauss and frequency measurements to + 20 KHz were i made. Temperature control was effected using a Varian V6040 con-trol unit, with a special dewar containing the sensor and heater. This device was calibrated with a copper-constantan thermocouple. Al l samples were continuously monitored for temperature fluctua-tions, the thermocouple junction being placed beside the sample, tube and as far into the cavity as was possible without inter-fering with the cavity tuning. It was found impossible to place the thermocouple junction at the center of the cavity with the sample, so the temperature difference between the center and the junction was measured before and after a scan to correct the ac- > tual sample temperature. This temperature difference was a near-ly constant 0 .5 °C. Checks were made on the difference between the sample temperature measured in the liquid itself , and outside at the wall of the s i l ica tube. No appreciable difference was found. During an actual scan temperature fluctuation was never more than + 0 .2 °C, and absolute thermocouple measurements were determined, by comparison with boiling and slush points of water, - 175 -to be accurate to at least + 0.05°C. UV spectra were recorded on a Cary 14 instrument equipped with an R-213 phototube. Concentrations are subject to weighing and volumetric•er-rors . Neighing errors are ^ + 0.01 mg, causing essentially neg-ligible error in weighings of ^ 3 - 5 mg. Volumetric measure-metns were made wholly with graduated pipettes which can be con-119 sidered accurate to ~* 0.4% or better . Concentrations of var-ious samples should therefore be subject to an uncertainty ^ 1% or less. Since al l concentrations were calculated for room tem-perature densities and volumes, corrections for temperature, on the basis of density changes alone, were calculated. Over the range 0 - 60°C, used here, the temperature corrections are neg-ligible for very low concentrations, but become significant for higher concentrations. An 8M solution of pyridine, in benzene, for example, is in reality 7.7M at 60°C. When significant,cor-rections were made to the concentrations, although i t was found* that the least squares results were not overly sensitive to such changes, since the analysis is , in effect, similar to an aver-aging over a series of concentrations. C. DATA ANALYSIS: Various steps in the analysis procedure were: al l carried out using a series of least squares fitting routines and the U.B.C. IBM 360/67 computer. The least squares fitting program involves an appropriate routine containing the differen-- 176 -tials of the function to be analysed, and the least-squares vai5~; iation is carried out using a fast iterative matrix inversion and diagonalisation procedure to obtain the variables and stan-i-dard deviations. Iteration continues until the standard devia-tions are reduced to an appropriate tolerance. The four epr line positions for each spectrum were fitted 120 to Bleaney's equation , to second order in aQ and gQ: g a 2 (9-1) H(m ) = - a M - ^ — I (I + 1) - m 2 I 1 go 0 0 1 2H(mx) ( 1 ) where the various terms have their usual meaning'*'2^. Because there are four lines and only two variables a con-sistent f it was obtained very rapidly, with deviations in gQ and aQ being + 0.0001 and + 0.05, respectively. Since the whole spectrum shows the effects of chemical ex-change, any one of the four lines could be analysed for the ex-change parameters. In practice, however, only the +1/2 and +3/2 lines are narrow enough to satisfy the linewidth criteria of (2-28). Both lines were analysed for the benzene/pyridine sys-tem, to establish the procedure, and also for the other two sol-vents with pyridine, although in these latter examples only the results for the +3/2 line are quoted. The results are essential-ly equivalent for both lines, the equilibrium constants being identical, for instance. Because the non-exchange widths for the +1/2 line are broader than for the +3/2 line, however, i t was - 177 -noted that the least squares fitting procedure was not as consis-tent in the +1/2 case as the +3/2 case. This was especially true at low temperatures. Thus i t was decided to carry out the analy-sis for the +3/2 line in al l cases. This means that the larger ~ ^B ^ o r t n ^ s l i - n e might cause additional problems, leading to a larger exchange effect on the +3/2 line compared to all others, however. Careful application of the fitting procedure, however,, revealed that overall the +3/2 line data gives most consistent results and is most consistently within the fast exchange limita-tions outlined in (2-28). Measured peak-to-peak linewidths, AH, were corrected for possible modulation broadening using an iterative procedure based 121 on an equation developed by Wahlquist . The modulation-broad-ened linewidth, AH, is related to the true linewidth, AH^, by: (9-2) AH = AH | R 2 + 5 - 2(4 + R 2 ) 1 / 2 } 1 / 2 where R = H /AH„. and H is the amplitude of the modulation field., . m t m r 95 A useful rule of thumb is that to avoid broadening,H should bet.' less than one tenth AH, although for this work H < AH/3 appears to be sufficient for most cases. A modulation amplitude of 1 G was used throughout this work and no significant corrections using (9-2) were found for widths above 5 G. Tables 9-1 and 9-2 illustrate the corrections calculated. The 100 KHz modulation frequency associated with Hm contributes a constant broadening of; + 35 mG, or 70 mG overall, to the epr spectra. - 178 -TABLE 9 -1: EFFECTS OF MODULATION ON OBSERVED LINEWIDTH, FROM WAHLQUIST 73 AH PPobs CG) AHppCG) AH (G) PPobs AH (G) PP 1.0 0.67 6.0 5.96 2.0 1.87 7.0 6.96 2.5 2.40 8.0 7.97 3.0 2.91 9.0 8.97 3.5 3.43 10.0 9.97 4.0 3.94 15.0 14.98 5.0 4.95 20.0 19.99 TABLE 9 -2: EFFECTS OF DIFFERENT MODULATION AMPLITUDES ON AN OBSERVED LINEWIDTH OF: (i) 3.0 G (ii) 5.5 G Ci) H J m (G) AH (G) PP (ii) Hm(G) A V G ) 0.2 3.00 0.2 5.50 0.4 2.99 0.4 5.49 0.6 2.97 0.6 5.48 0.8 2.95 0.8 5.47 1.0 2.91 1.0 5.45 2.0 2.63 2.0 5.31 3.0 2.00 3.0 4.0 5.0 5.07 4.68 4.09 - 179 -The line positions obtained from (9-1) were analysed using: (9-3) <to> = 'A + 1 + K [ L ] L o J 1 + K [ L 1 L o J by least squares fitting the observed line positions,<w> , to those calculated from (9-3). K, GJ^ and tOg were allowed to vary, with [L q ] the independent variable, until a consistent fit was obtained. Initial estimates of to. and toD were those values mea-A D sured in neat solvents. Since both gQ and aQ are temperature de-pendent, values of to^ and tOg were, as measured in neat solvents. The difference is also temperature dependent. This dependence was included in the least squares procedure in the in i t i a l esti-mates of co^ and tOg, and fitted values of these parameters re-flected these findings, although it was noted that fitted values of toD were almost temperature-independent in some cases. This-D is undoubtedly because these fitted tOg values represent an extra-polation of <to> to infinite base concentration, whereas the neat solvent values are obtained in concentrations of base ^ 12 M, where 100% adduct formation is never attained. This large extra-; polation would be expected to render the Wg's relatively insensi-tive to temperature. This is not the case with to^ values. From the standard deviations in the fitted results, uncer-tainties in K can be estimated to be + 0.02 1/mole and in to. as l + 0.0005 sec Standard deviations are calculated according to 122 123 usual methods ' - 180 -The temperature dependence of K, as discussed earlier and in Appendix 1, is described by the Arrhenius relationship: (9-4) K = exp(-E,/RT) cl A straight line obtained from a plui. of In K vs. 1/T w i l l have slope -E /R, and errors associated with the slope, inter-a cept, and any point on the line can be evaluated by standard 122 procedures . In this work i t was assumed that the temperature was subject to much smaller error than K, or k, and hence was regarded as measurable without error. This results in a simpli-122 fication of the error analysis , and standard deviations of any point Y q on the straight line at X = can be calculated from: , < X 0 - x ) J \ 1 / 2 where s is the standard deviation of the- parameters subject to error, y^, x is the mean of the x values, JI tlie number of points on the line. By using (9-5) errors in In k , for instance, can be estimated, and typical standard deviations are a- 0.1. - 0.14, 8 -1 which, at 300°K, lead to uncertainties :i n k '\- + 0.2 x 10 sec r -Tlris is of the order of the experimental error in k resulting from uncertainties involved in measuring i„. Experimentally-obtained linewidths were least squares f i t -ted to the expression: - 181 -(9-6) T"1 = p A T " A + p B T ~ J + P ^ P B r B C a ) A - t o B ) 2 + T ( l V P B ) ( S ( 3 A 2 - 6 2 ) + ( 5 p A P B - D ( A 4 - 6 6 2 A 2 + 6 4 ) B + P/vPl^B 2 I(I+l)-m* 2 2 2 1 +^o TBPA ( a A - a B ) 2 where the f i r s t l i n e i s the usual modified Bloch r e s u l t f o r f a s t exchange, (4-4), the second l i n e theslow exchange c o r r e c t i o n s of Corden and Rieger, (4-5) , and the t h i r d l i n e the non-secular con-t r i b u t i o n s c a l c u l a t e d from r e l a x a t i o n - m a t r i x theory, (4-11) . The l a s t two terms i n (9-6) are u s u a l l y very much s m a l l e r than the f i r s t , i n the experiments performed her;-. Exceptions could occur at low temperature and/or high base s t r e n g t h or f o r -mation const;.it (K ^ ' • ) . Table 9-3 i l l u s t r a t e s the comparison. Using values o f K and ^ - tog obtained from the l i n e p o s i -t i o n f i t t i n g procedure, a l e a s t squares f i t of observed t o c a l -c u l a t e d l i n e w i d t h s using (9-6) was made using l i n e w i d t h s measured i n neat s o l v e n t s , at each temperature, as i n i t i a l estimates of T 1 and T 1 . Free v a r i a t i o n of T 1 , T 1 and T„ allowed k = T * 2A 2B 2A' 2B B r B and k_ = Kk t o be c a l c u l a t e d . Trends i n the f i t t e d l i n e w i d t h s , f r T 2 A and T^g, r e f l e c t e d those of the observed values, but these parameters were not used f o r any other s p e c i f i c c a l c u l a t i o n s , and hence are not considered i n any d e t a i l . Maximum u n c e r t a i n t i e s i n Xg were found to a, + 0.15x10 sec, leading to experimental uncer-t a i n t y i n k % + 0.2xl0^sec \ U n c e r t a i n t i e s i n various d e r i v e d TABLE 9-3 Comparison of various terms in Equation (9-6) DATA FOR BENZENE/PYRIDINE 300°K (3/2 line) Base Concentration (M) Ordinary Bloch Term Extended Bloch Term Non-Secular Term (observed) 1.03 1.38 2.77 3.55 6.20 7.79 12.41 1.198 x 108sec" 1.156 x 108sec" Q 1.036 x 10 sec" 0.887 x 10 sec" o 0.762 x 10 sec" Q 0.736 x 10 sec" 0.717 x 108sec" 0.418 x 10 sec" 3.046 x 10 sec" 2.060 x 10 sec" 0.457 x 10 sec" 0.012 x 10 sec" -0.006 x 10 sec" -0.011 x 10 sec" 0.171 x 10 sec 0.233 x 10 sec 0.364 x 10 sec 0.588 x 10 sec 0.950 x 10 sec 1.086 x 10 sec 1.067 x 10 sec 1.202 x 108sec 1.187 x 108sec 1.056 x 108sec 0.891 x 108sec Q 0.762 x 10 sec 0.736 x 108sec 0.717 x 108sec - 183 -parameters are as shown in tables of results, unless otherwise stated. - 184 -REFERENCES 1. A. 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Tweedale, Adv. Chem. Phys. 21_ 113 (1971). 126. K.J. Laidler, "Theories of Chemical Reaction Rates", McGraw-H i l l , New York (1969). 127. K.J. Laidler, "Chemical Kinetics", McGraw-Hill, New York (1965). 128. H. Eyring, J. Chem. Phys. 3 107 (1935). - 191 -129. I. Amdur and G.G. Hammes, "Chemical Kinetics: Principles and Selected Topics", McGraw-Hill, New York (1966). 130. K.-E. Falk, E. Ivanova, B. Roos, and T. Vanngard, Inorg. Chem. 9_ 556 (1970) . 131. I. Adato and I. Eliezer, J. Chem. Phys. 54 1472 (1971). 132. B.L. Libutti, B.B. Wayland, and A.F. Garito, Inorg. Chem. 8 1510 (1969). 133. S. Antosik, N.M. Brown, A.A. McConnell, and A.L. Porte, J. Chem. Soc. (A) 545 (1969). 134. J. Selbin, Chem. Rev. 65_ 168 (1965). 135. R. Pettersson and T. Vanngard, Arkiv. Kemi. 17 249 (1961). 136. H.R. Falle and G.R. Luckhurst, Mol. Phys. j_0 598 (1966). 137. R.E. Moss, Mol. Phys. 10_ 339 (1966). 138. H.R. Gersmann and J.D. Swalen, J. Chem. Phys. 36_ 3221 (1962). 139. 0. Matumura, J. Phys. Soc. Japan 1£ 108 (1959). 140. J.S. Van Wieringen, Disc. Faraday Soc. 1_9 118 (1955). 141. H.A. Kuska and M.T. Rogers, J. Chem. Phys. 43_ 1744 (1965). 142. A.H. Maki and B.R. McGarvey, J. Chem. Phys. 29_ 35 (1958). 143. C P . Keijzers, H.J. De Vries, and A. van der Avoird, Inorg. Chem. U 1338 (1972). 144. E. Buluggiu, A. Vera, and A.A. Tomlinson, J. Chem. Phys. 56 5602 (1972). 145. W. Partenheimer and R.S. Drago, Inorg. Chem. 9_ 47 (1970). 146. W.R. May and M.M. Jones, J. Inorg. Nucl. Chem. 25 507 (1963). 147. D.P. Graddon and R.A. Schulz, Aust. J. Chem. 18 1731 (1965). - 192 -148. D.P. Graddon and various authors, Aust. J. Chem. 24 1781, 2077, 2267, 2509 (1971). 149. Morcom and D.N. Tr avers, Trans. Faraday Soc. 62_ 2063 (1966) . 150. M.M. Jones, B.J. Yow, and W.R. May, Inorg. Chem. j_ 166 1515 (1962). 151. M. Eigen and R.G. Wilkins, Adv. Chem. Ser. 49 55 (1965). 152. A. McAuley and J. H i l l , Quart. Rev. 2_3 18 (1969). 153. E.F. Caldin, "Fast Reactions in Solution", Blackwell, Ox-ford (1964), chapter 12. 154. C H . Langford and W.R. Muir, J. Am. Chem. Soc. 89 3141 (1967) . 155. R.W. Kluiber, R. Kukla, and W. De W. Horrocks, J r . , Inorg. Chem. 9 1319 (1970). 156. T.R. Stengle and C H . Langford, Coord. Chem. Rev. 2_ 349 (1967). 157. C H . Langford, J . Chem. Ed. 46 557 (1969). 158. G.N. Lewis and M. Randall, "Thermodynamics", 2nd. ed., re-vised by K.S. Pitzer and L. Brewer, McGraw-Hill, New York (1961), chapter 33. 160. H.P. Bennetto and E.F. Caldin, J. Chem. Soc. (A) 2191, 2207 2211 (1971). 161. W.J. Mackellar and D.B. Rorabacher, J. Am. Chem. Soc. 93 4379 (1971). 162. H.S. Frank and W.Y. Wen, Disc. Faraday Soc. 24 133 (1957). - 193 -163. D.P. Graddon and K.B. Heng, Aust. J. Chem. 24 1781 (1971). 164. J .E. Leffler, J. Org. Chem. 20 1202 (1955). 165. CD. Ritchie and W.F. Sager, Progr. Phys. Org. Chem. 2_ 323 (1964). 166. K.J. Laidler, Trans. Faraday Soc. 55_ 1725 (1959) and fol-lowing papers. 167. H.S. Venkatavaman and C. Hinshelwood, J. Chem. Soc. 4977, 4986 (1960). 168. A.D. Buckingham, Adv. Chem. Phys. 1_2 107 (1968). 169. L.S. Frankel, Inorg. Chem. 1_0 814 (1971). 170. S. Carter, J.N. Murrell, and E.J. Rosch, J. Chem. Soc. (A) 2048 (1965). 171. R.L. Scott, J. Phys. Chem. 75 3843 (1971). 172. L.E. Tenenbaum, "The Chemistry of Heterocyclic Compounds", vol. 14, part 2, chapter 5 (Interscience, New York, 1961). 173. A.F. Garito and B.B. Wayland, J. Am. Chem. Soc. 91_ 866 (1969). 174. R.W. Kluiber, F. Thaller, R.A. Low, and W. De W. Horrocks, Jr . , Inorg. Chem. 9_ 2592 (1970). 175. P.E. Rakita, S.J. Kopperl, and J.P. Fackler, Jr . , J . Inorg. Nucl, Chem. 30 2139 (1968). 176. J.A. Happe and R.L. Ward, J. Chem. Phys. 39 1211 (1963). 177. . F.A. Walker, R.L. Carlin, and P.H. Rieger, J. Chem. Phys. 45 4181 (1966). 178. C.T. Mortimer and K.J. Laidler, Trans. Faraday Soc. 55 - 194 -178. 1731 (1959). 179. H.C. Brown and B. Kanner, J. Am. Chem. Soc. 88^ 986 (1966). 180. F. Basolo and R.G. Pearson, "Mechanisms of Inorganic Reac-tions", 2nd. ed., Wiley, New York (1967), pp. 132 - 136. 181. C H . Langford and T.H. Stengle, Ann. Rev. Phys. Chem. 19 193 (1968). 182. D.J. Benton and P. Moore, Chem. Comm. 717 (1972). 183. CK. J^rgensen, Struct. Bonding (Berlin) 3 106 (1967). - 195 -APPENDIX 1: The Arrhenius Law: 1 2 Basically, Arrhenius' Law states ' that only activated (or energised) molecules undergo chemical change. Formulation of this principle requires two experimental relationships, de-fined at equilibrium: one, (Al-1) K = k x /k 2 where K is the equilibrium constant, k^ and k^ the forward and reverse rate constants, for a simple process, and, ,2/ (Al-2) AH = RT' where AH° is the overall heat of reaction, R the gas constant, and the subscript p denotes constant pressure. Combining Al-1 and Al-2 yields: ( A 1_ 3) ( R T 2 ( ^ . ) = R T 2 ^ l ) - R T 2 ^ ) (or, more simply, AH° = E. 1 - E where the E. . are the apparent activation energies for the pro-A , l cess. Combining Al-3 and Al-2 gives further: (Al-4) " ^  - ^ 2 ( ^ ) i / d l n k A V d T 2 ) E A , 1 ] " P " [RT 2 (^-2] - E A 2] P Now the LHS is zero, by definition. Arrhenius' contribu-- 196 -tion was that each of the bracketed terms on the RHS is also zero, and so the forward and reverse reactions can be considered separately. One thus obtains: (Al-5) E A = R T 2 ( ^ - j which is the form most often seen. If, in fact, the activation energy EA is considered constant over the temperature range be-ing studied, Al-6 may be integrated to give: (Al-7) k = A exp(-EA/RT) This form is thus more restricted than that of Al-6, and 3 is the form originally proposed by van't Hoff , based on experi-4 mental results of Hood , who proposed the empirical law: (Al-8) log k = B - A ' /T , A1 and B being constants. The integrated form of Al-7 is , in fact: (Al-9) Ink = A - EA/RT where A is a constant often called a frequency factor (although it has units of frequency only for a first-order reaction). Hence a plot of Ink vs. 1/T will be linear with slope -E /R and - 197 -intercept A (at T = 0) i f the reaction being considered has Arrhenius' temperature-dependence. The law is obeyed for many chemical reactions. Sometimes the more general law: (Al-10) k = A T n e " E a / R T is invoked, where n has any value dictated by experiment. The Arrhenius law finds wide application in chemistry and is quite successful. Several unusual applications of the law have been 7 given by Laidler . Frequently it is convenient, in solution especially, to express the experimental, or Arrhenius, energy of activation in terms of thermodynamical functions. This is accomplished by first noting that the activated complex (the energy of activa-tion is that required to go from the in i t i a l state to the acti-vated state) is in equilibrium with the reactants. In other words: (Al-11) A + B X* where X* represents the activated complex. Thus an equilibrium constant K* can be defined for Al-11, and the overall forward rate of the reaction: i k (Al-12) A + B X * C can be shown1 to be related to K* by: V I T -4 (Al-13) k = -V- K - 198 -where k'T/h represents a Boltzmann population constant. Now, from thermodynamics, the equilibrium constant K* can be related to the Gibbs free energy increase in going from the in i t i a l state to the activated stated (Al-14) K* = e~AG*/RT so one may write: (Al-15) k = kJT e-AG*/RT Since i t is now possible to write: (Al-16) AG* = AH* - TAS* then (Al-17) k = ^ 1 e - ^ / R T e A S ^ R -which is that of Wynne-Jones and Eyring^. For unimolecular reactions, or reactions in solution, i t can be assumed that there is no change in the number of mole-cules as the activated complex is formed, and the experimental energy of activation may be written: (Al-18) E = AH* + RT J exp Hence knowing the value of E from a simple Arrhenius exp r plot (eq. Al-9), AH* is available. The Boltzmann constant term in eq. Al-17 can be evaluated next at some desired temperature, and hence AS* derived at that temperature. AG* is then avail-- 199 -able from Al-16. Although the Arrhenius equation is largely successful in explaining the temperature dependence of equilibrium and rate constants, there are many potential exceptions, one of which is fast reactions. The temperature independence of the activation energy is clearly useful only when E g X p » RT in eq. Al-18. g Many of these objections are thoroughly discussed by Caldin . 9 Also, Labhart points out that for E ^ RT, conclusions as to ' r exp ' what E defines cannot be made, although i f a linear Arrhenius exp ' plot is obtained, and if E is not close to RT, then careful r exp ' interpretation of E does yield useful results. To consider exp a "break" in the Arrhenius plot as evidence for the superposi-tion of two mechanisms with different activation energies is an interpretation that may be wrong in these low energy regions. References: 1. K.J. Laidler, "Chemical Kinetics", McGraw-Hill, New York (1965), chapters 1-3. 2. E.A. Moelwyn Hughes, "The Chemical Statics and Kinetics of Solutions", Academic Press, New York (1971). 3. J.H. van't Hoff, "Etudes de Dynamique Chimique", Muller, Amsterdam (1884). 4. J.J. Hood, Phil. Mag. 20 323 (1885). 5. W.F. Wynne-Jones and H. Eyring, J. Chem. Phys. 3_ 492 (1935). 6. D.M. Golden, J. Chem. Ed. 48 235 (1971). - 200 -7. K.J. Laidler, J. Chem. Ed. 49 343 (1972). 8. E.F. Caldin, "Fast Reactions in Solution", Blackwell, Oxford (1964), chapter 12. 9. H. Labhart, Chem. Phys. Letters 1 263 (1967). - 201 -APPENDIX 2: Linear Free Energy Relations and Isokinetic Plots. A number of quantititive relationships have been suggested in connection with the effects of substituents on the rates of reactions. These are well documented by Ritchie and Sager^. For the present very brief discussion, the derivation of Hammett' 3 will be outlined . The relationship applies to a series of aromatic compounds with a reactive side chain and a substituent m- or p- to i t . Ortho substituents are not considered because of steric interac-tions. For example, a group of substituted benzoic esters is often used. Accordingly, a rate or equilibrium constant for reaction of any of these compounds is related to the value for an unsubstituted (parent) member of the series in terms of two parameters: the substituent parameter a and the reaction con-stant p, which depends on external conditions, such as the sol-vent. Thus one usually writes: (A2-1) log k = log kQ + OQ or (A2-2) log K = log K q + ap By arbitrarily assigning p for benzoic acid to be unity, for the ionization equilibrium constant in aqueous solution, and for the substituted benzoic acids, a is the logarithm of the - 202 -ratio of the ionization constant of a substituted benzoic acid to that of benzoic acid itself . Thus a series of a values can be determined from this control series, and they have been large-1 3 ly successful when applied correctly ' . Now the Hammett relationships can be shorn to be equivalent to linear relationships between the free energies of reaction or activation for different series of reactions. As noted in Appendix 1, one may write: ( A 2_ 3) k = ! £ . e~AG*/RT so that taking natural logarithms yields: (A2-4) Ink = In _ _ ^ Substituting into A2-1 gives: (A2-5) AG* = AG* - RTpa Eq. A2-5 applies to any reaction involving a reactant hav-ing a series of substituents, and a particular value of p can be assigned. Now for a second series of homologous reactions, having a different reaction constant p 1 , 9A2-6) AG1 * = AG^* - RTp'a Dividing eqs. A2-5 and A2-6 by p and p 1 , respectively, then subtracting, yields: r A 2 71 — — * = ^ o P " P 1 ~P° ~ P 7 0 - 203 -or (A2-8) AG^ - AG , ? i = constant Equation A2-8 is a linear relationship between the free energies of activation for two homologous series of reactions. These linear relationships have been observed for a large num-• i 3 ber of examples ' . Now, i t has often been argued that the presence of a l in-ear free energy relationship was associated with a linear rela-tionship between the enthalpies of activation and energies of reaction, the entropies remaining constant. It is now esta-13 4 blished ' ' that, on the contrary, the free energies are much simpler functions thai\ the enthalpies and entropies, which are more sensitive to external factors (i.e. solvent). Many exam-ples are known that exhibit linear free energy relationships, but no clear enthalpy and entropy relationships. This is pos-sible because of a "compensating effect", or isokinetic rela-tionship, wherein the entropy and enthalpy change so as to com-pensate each other. Plots of TAS^ against AH^, where such an effect holds, yield straight lines of slope approximately unity. Or, as is often done, plots of AS5* against AH^ yield a slope known as the isokinetic temperature, T. These isokinetic relationships are only very rarely, i f at a l l , observed when there is a linear free energy relation-ship, and are most often noted for a given reaction in a series - 204 -of solvents, or for homologous reactions in which substituents 3 are introduced into a reactant . It actually follows that i f there is a linear relationship between AH^ and AS^, then, since AG*" = -TAS^ + AH^ there can be no linear free energy relation-ship. Those reactions that have been claimed to exhibit both relationships are most likely the result of experimental error*! When isokinetic relationships are found for overall pro-cesses in solution, the explanation cannot be explained in terms of purely kinetic effects, but solute-solvent interactions 13 4 3 must play a large part ' ' . For example, Laidler states that any effect leading to stronger solvent-solute interaction will lower the enthalpy, and also, by restricting solvent vibrational and rotational freedom, lower the entropy. A very small effect on AG usually results. References 1. CD. Ritchie and.W.F. Sager, Progr. Phys. Org. Chem. 2_ 323 (1964) . 2. L.P. Hammett, "Physical Organic Chemistry", New York (1955), pp. 184 - 419. 3. K.J. Laidler, "Chemical Kinetics", McGraw-Hill, New York (1965) , pp. 246 - 249. 4. K.J. Laidler, Trans. Fara. Soc. 55 1725 (1959). 


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