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UBC Theses and Dissertations

Probing anisotropic intermolecular forces in nematic liquid crystals using NMR and computer simulations Syvitski, Raymond Thomas 2000

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P R O B I N G A N I S O T R O P I C I N T E R M O L E C U L A R F O R C E S I N N E M A T I C L I Q U I D C R Y S T A L S U S I N G N M R A N D C O M P U T E R S I M U L A T I O N S By Raymond Thomas Syvitski B.Sc, Lakehead University, 1991 M.Sc, Lakehead University, 1994 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 2000 © Raymond Thomas Syvitski, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Chemistry The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: Abstract Molecules of similar size and shape, but with different electrostatic properties are used to investigate the effects of molecular dipoles, quadrupoles and polarizabilities on the ori-entational ordering of several solutes co-dissolved in nematic liquid crystals. Permanent dipoles have a negligible influence on solute orientational order and effects from molecular polarizability interactions could not be separated from short-range interactions. Order parameters predicted from strong, short-range repulsive forces coupled with interactions between the solute quadrupole and the average electric field gradient felt by the solute (EFG) are consistent with experimental values. For liquid crystals utilized in this study, the calculated values of the (EFGys are the same sign and of similar magnitude to the (_FG)'s determined previously from experiments on D 2 and HD. However, in contradic-tion to these experimental results, the (EFG)'s determined from computer simulations of hard particles with embedded point quadrupoles is found to be very dependent on the properties of the particle. For a particular nematic liquid crystal (55 wt% ZLI 1132 in EBBA), the contribution to solute ordering from long-range electrostatic interactions is found to be negligible. This conclusion is supported by computer simulation studies of hard particles; models for short-range interactions which best fit the NMR experimental solute order parameters ii also best fit the simulation results. Experimentally determined second rank orientational order parameters and structural parameters of solutes are calculated from vibrationally and non-vibrationally corrected nuclear dipolar coupling constants; accurate dipolar couplings are obtained from anal-ysis of the high-resolution nuclear magnetic resonance (NMR) spectra. For the more complicated molecules spectral parameters are first estimated from analysis of multiple quantum NMR spectra. In some cases, a modified version of a least-squares routine which independently adjusts chemical shifts, order parameters, structural parameters and/or dipolar couplings is used. iii Table of Contents Abstract ii List of Tables vii List of Figures ix Acknowledgment xi Dedication xii 1 Introduction 1 1.1 Liquid Crystals 1 1.1.1 General 1 1.1.2 Nematic Liquid Crystals 2 1.2 Orientational Ordering and Anisotropic Intermolecular Interactions . . . 3 1.2.1 Orientational Ordering from Experiments 3 1.2.2 Anisotropic Intermolecular Interactions 5 1.2.3 Calculating Order Parameters from Intermolecular Interactions . 5 1.3 Identifying Intermolecular Interactions that are Important for Orienta-tional Ordering 6 iv 1.3.1 Some Key Experiments and Predictions from Theory/Model . . . 7 1.3.2 Computer Simulations 10 1.4 NMR Experiments and their Relation to Orientational Ordering 11 1.4.1 Dipolar Couplings and Orientational Order Parameters 11 1.4.2 NMR Theory 13 1.4.3 Simplifying NMR Spectra and Analysis by Multiple Quantum NMR 15 1.5 Outline of Thesis 17 2 N M R and Molecular Structure 2 1 2.1 Introduction 21 2.2 Experiment 25 2.3 Spectral Analysis and Strategy 28 2.4 Molecular Structure and Order Parameters 42 2.4.1 Calculations 42 2.4.2 Molecular Structure 46 2.4.3 Order Parameters . . . 47 2.5 Summary 48 3 Dipole-Induced Ordering in Nematic Liquid Crystals 49 3.1 Introduction 49 3.2 Experiments and Results 54 3.3 Mean-Field Models 55 v 3.4 Analysis and Discussion 61 3.5 Conclusions 78 4 Comparative Study Between M C and N M R Experiments 80 4.1 Introduction 80 4.2 Short-range Interactions 82 4.3 Long-range Interactions 88 4.4 Conclusions 95 5 Summary and Future Considerations 96 Bibliography 99 Appendixes 105 A Solutes 106 B Dipolar Couplings 108 C Structural Parameters 124 D Order Parameters 136 E Scaled and Calculated Order Parameters 142 vi List of Tables 2.1 Solute and Solvent Composition of Samples 26 2.2 Selected Dipolar Couplings 42 3.3 Molecular Parameters 63 3.4 Liquid Crystal Parameters 64 3.5 Adjusted Molecular Parameters 76 B.6 Fitting Parameters and RMS Errors from Analysis of High-Resolution and MQ NMR Spectra 109 B. 7 Fitting Parameters and RMS Errors from Analysis of High-Resolution and MQ NMR Spectra of Sample #25 122 C. 8 Molecular Parameters of Fits to Vibrationally Corrected Dipolar Couplings 125 C.9 Structural Parameters of Fits to Dipolar Couplings for chlorobenzene, toluene and 1,3,5-trichlorobenzene 126 C.10 Structural Parameters of Fits to Dipolar Couplings for p-disubstituted benzenes 128 C.ll Structural Parameters of Fits to Dipolar Couplings for o-disubstituted benzenes 130 vii C. 12 Structural Parameters of Fits to Dipolar Couplings for m-disubstituted benzenes 133 D. 13 Order Parameters of Fits to Dipolar Couplings 137 D. 14 Order Parameters for solutes in Sample #25 of Fits to Dipolar Couplings 141 E. 15 Scaled and Calculated Order Parameters 143 viii List of Figures 1.1 Molecular Structure of N-(4-ethoxybenzylidene)-4'-n-butylaniline 3 1.2 An example of angle and axes definitions for order parameters and dipolar couplings . 12 2.3 High-resolution spectrum of acetonitrile, propyne and 1,3,5-trichlorobenzene 30 2.4 High-resolution spectrum of Sample #11 32 2.5 7-quantum spectrum of Sample #11 34 2.6 Expansion of High-Resolution Spectrum of Sample #11 35 2.7 8-quantum spectrum of o-xylene 38 2.8 Spectral analysis strategy 40 2.9 Atom Numbering for p-, m- and o-xylene, and o-chlorotoluene 44 3.10 Coordinate System for Solutes 56 3.11 SaCpled,s for p- and mono substituted benzenes 67 3.12 Sszczaled,s for 1,3,5-trichlorobenzene, acetonitrile and propyne 68 3.13 S^led,s for o- and m-disubstituted benzenes 69 3.14 S^czaled,s for o- and m-disubstituted benzenes 70 3.15 Sscaled,s minus S^'s against Sscaled's 71 ix 3.16 Experimentally determined Fzz's 74 4.17 Order Parameters from MC simulations of hard ellipsoids 85 4.18 Differences between calculated and experimental order parameters . . . . 86 4.19 Relative differences between calculated and experimental order parameters 89 4.20 Experimental and MC FZz's 93 4.21 Relative difference between calculated and NMR solute order parameters 94 A.22 Coordinate System and Atom Numbering of Solutes 107 x Acknowledgment My gratitude goes out to my supervisor Dr. Elliott Burnell for his constant coadjuvancy and encouragement. I thank you for putting up with me and allowing me to redecorate the lab. I thank Dr. Thambirajah Chandrakumar for his useful sug-gestions when I was analyzing NMR spectra and Dr. James Poison who enlightened me about NMR and computer simulations. Dr. Grenfell Patey must be recognized for his stimulating and informative discussions. I congratulate the electronics shop for keep-ing the spectrometers operational; I did my best, but Tom and Milan were still able to fix the spectrometers. Thanks to Dr. Nick Burlinson for helpful discussions re-garding Bruker software. Karen Cheng, Ducky and other fuzzy critters (including my sister Heather) must be acknowledged for their "intellectually stimulating" conversations; sparkles, glow-in-the-dark stars, Teddy, and the couch also helped with our creativity. I must recognize everyone else who kept me (in)sane by either going for coffee, beer, lunch or breakfast with me. Finally, I thank my sister Heather for the interesting if not somewhat odd phone conversations, and my family and my friends for their love, support and encourage-ment. Thanks. xi Dedication To my Grandmother Mary Thomas xii Chapter 1 Introduction 1.1 Liquid Crystals 1.1.1 General In 1888 Reinitzer[l] observed that a turbid liquid was formed when solid cholesteryl benzoate was melted, and that a clear isotropic liquid was produced upon further heating. The turbid liquid was characterized by Lehmann[2] and was found to be birefringent and therefore anisotropic. Phases which are anisotropic and still exhibit some degree of fluidity are described as "liquid-crystalline" or "mesomorphic." Transitions to the liquid-crystalline phase can be induced either by thermal processes (thermotropic liquid crystals) or by the influence of solvents (lyotropic liquid crystals). The main feature of all liquid crystals is the orientational ordering of the component molecules; the molecules of some liquid crystals are also positionally ordered. This study focuses on thermotropic nematic liquid crystals which are the simplest of all the liquid crystals and which are identified by having only orientational ordering. 1 Chapter 1. Introduction 2 1.1.2 Nematic Liquid Crystals Typically, nematogens (the constituent molecules of a nematic phase) are elongated molecules with semi-rigid cores, with flexible alkyl chains, and with polar constituents (see for example Fig. 1.1). The nematic phase is characterized by having no long-range positional ordering, but there are "domains" of long-range orientational ordering which can extend over distances of up to l/xm[3]. Orientational ordering describes the tendency of the nematogen's long axis to be parallel to a common axis; the common axis is defined as the nematic director. In the absence of external fields, the orientations of the nematic directors vary through the sample. Since the dimensions of the domains are on the order of the wavelength of visible light, the turbid appearance of the macroscopic sample arises from the scattering of light as it propagates through the phase. In the presence of a constant magnetic or electric field all the nematic directors align either parallel or perpendicular with the applied field. The direction of the director alignment depends on the magnetic or dielectric susceptibility anisotropy of the domain. The magnetic or electric field has a negligible influence on the relative orientational ordering of individual molecules; the interaction energy for the susceptibility anisotropy coupled with the field is very small compared to the thermal energy [3]. However, over the entire collection of molecules within the domain the energy is sufficient to cause alignment of the directors. Since the current study is concerned with the intermolecular forces that cause alignment of molecules in nematic phases and since the orientational ordering of Chapter 1. Introduction 3 H H 5 C 2 -0 'N Figure 1.1: Molecular Structure of N-(4-ethoxybenzylidene)-4'-r^ butylaniline. A collec-tion of these molecules forms a stable nematic phase from 308 to 352 K. the molecules is determined from analysis of nuclear magnetic resonance spectral data, it is important to realize that the strong magnetic field does not significantly influence the relative orientational ordering of molecules within the phase. For the liquid crystals utilized in this study, the directors are aligned parallel with the main magnetic field. 1.2 Orientational Ordering and Anisotropic Intermolecular Interactions 1.2.1 Orientational Ordering from Experiments The orientational ordering of an inflexible molecule is completely described by the ori-entational distribution function f(Q) where Q, denotes the Eulerian angles that describe the orientations of the molecular fixed axes relative to the nematic director. Since these molecules are in a fluid phase /(fi) is an average over all molecular reorientations arid /(fi)dfi is the probability of finding the molecule in a small solid angle dfi at the direction defined by fi. In principal, the complete distribution function can be assessed by X-ray diffraction techniques[4]. Up to the fourth rank component of the distribution function can be determined from neutron diffraction techniques [5]. However, poor resolution and Chapter 1. Introduction 4 instrumental limitations make these tasks extremely difficult[5]. Nevertheless, the aver-age second rank component S (the second rank orientational order parameter) of /(ft) is readily accessible by analysis of nuclear magnetic resonance (NMR) spectral data (a brief description of N M R theory is given later in this chapter and a detailed description of spectral analysis and determining S from spectral data is the topic of Chapter 2). The relationship between the experimentally determined S and /(ft) is given by: Sa0 = J/(ft) Q cos 9aZ cos 6pZ - dQ (1.1) where a and /3 are the molecular fixed axes (typically defined to be coincidental with symmetry axes of the molecule), Sap is the a(3 component of 5, and 9az and B$z are the angles between the a and /3 axis and the nematic director defined to be parallel to the laboratory fixed Z direction (see Fig. 1.2, page 12 for an example of axis and angle definitions); for the nematic phases utilized in this study the nematic director and magnetic field directions are coincidental with the laboratory fixed Z direction. Since there is no positional ordering of the component molecules, the nematic phase is cylindrically symmetric about the nematic director, and since there is an equal probability of a molecule aligning parallel or anti-parallel with the laboratory fixed Z direction, the nematic phase is apolar. Thus, measured properties are invariant to rotations about the nematic director and all odd components of /(ft) (eg., components that are related to cos 9, cos3 6, etc.) are necessarily zero. The second rank orientational order parameter is Chapter 1. Introduction 5 the leading term in the expansion of the anisotropic components of / ( f i ) . 1.2.2 Anisotropic Intermolecular Interactions Anisotropic intermolecular interactions are responsible for the orientational ordering of liquid-crystal phases. The interactions can be characterized as anisotropic short-range repulsive or as anisotropic long-range. Short-range repulsive interactions depend on the details of the molecular structure, such as size, shape and flexibility. Long-range interactions involve dipoles, quadrupoles, polarizabilities and other properties that describe the distribution of charges over a molecule and can be either attractive or repulsive. 1.2.3 Calculating Order Parameters from Intermolecular Interactions The / ( f i ) and ultimately 5Q /j's can be calculated using statistical mechanics and a mean-field anisotropic orientational interaction potential [/(fi) which is characterized by the short-range repulsive and long-range interactions. It is currently impractical to com-pletely define J7(fi); it would require a detailed understanding of all the interactions present. The form of (7(fi) can be simplified by assuming that it is adequately described either by a pair potential[6, 7] or by the interaction between a molecular property and an average- or mean-field produced from the surrounding liquid crystal medium [8]. For Chapter 1. Introduction 6 relatively inflexible molecules / ( f t ) can be calculated from [/(ft) using exp(-c7(ft)/feT) A ; Jezp( -c7( f t ) /A;T)df t ' 1 Therefore, by defining C/(ft), a second rank order parameter S%$c can be calculated 1.3 Identifying Intermolecular Interactions that are Important for Orienta-tional Ordering It is now recognized that for molecules wi th a high degree of shape anisotropy, the orien-tational ordering mainly arises from anisotropic short-range interactions [8-14]. Contr i -butions from the long-range interactions may have a lesser influence on the orientational ordering[6,15-17]. The importance of various long-range interactions is a matter of cur-rent controversy and is an important topic of this study. A n important means of learning about f/(ft) is to compare real experimental Saps with those calculated (S%$c) from theory or model, or wi th those determined from com-puter simulations. Orientational order parameters of the constituent molecules of a l iquid crystalline phase are difficult to study because these molecules are normally devoid of symmetry and exist in a number of symmetrically unrelated conformers. A proper de-scription involves a plethora of orientational parameters as well as conformer probabilities 5calc _/3 — / (f cos 6aZ cos dffz - \5aP) exp(-U(Q)/kT)dn fexp(-U(n)/kT)dn (1.3) Chapter 1. Introduction 7 and it becomes essential to assume some model for the pair potential in order to relate experimental measurements to single-molecule properties. However, by examining the orientational ordering of small, well-characterized solutes, the role of the various contri-butions to the intermolecular potential can be investigated, for example, by choosing a solute with particular properties [8], by choosing a set of solutes whose properties differ in a well-defined manner[18,19] or by choosing a liquid crystal solvent that may have special properties [8]. 1.3.1 Some Key Experiments and Predictions from Theory/Model D 2 and HD are special solutes; from the NMR spectral data of orientationally ordered D 2 and HD in various liquid crystals, it was determined that the orientational ordering of D 2 and HD is dominated by the interaction between the molecular electric quadrupole and an average electric field gradient due to the liquid crystal environment (EFG)[20\. In addition, the (EFGYs for various liquid crystals, a quantity that is not easily accessible by experimental methods, was determined from the quadrupolar coupling constant of the deuteron BOBS and the dipolar coupling constant between the deuterons DDD (or the deuteron and proton DDH)- The experimentally measured value of BOBS is Bobs = - ^ ( F z z - e q S ) (1.4) Chapter 1. Introduction 8 where eQo is the deuteron nuclear quadrupole moment, Fzz is the ZZ component of (EFG) parallel to the magnetic field direction Z, S is the solute order parameter, and eq is the average electric field gradient due to the intramolecular charge distribution around the deuteron nucleus. eQp was determined from molecular beam experiments and the value of eq determined from quantum mechanical calculations. For the various liquid crystals, the order parameter S of D 2 or HD is directly mea-sured from the DDD or DDH and the vibrationally averaged value of < r - 3 >. The values of the S's are found to be in excellent agreement with the S's calculated from an orienta-tional potential that describes a molecular electric quadrupole moment/Fzz interaction where the Fzz was determined from Eq. 1.4. The calculations incorporated the quantum mechanical nature of D 2 and employed no model or adjustable parameters[21-23]. In other studies acetylene, like D 2 , was found to have a negative order parameter in the nematic solvent N-(4-ethoxybenzylidene)-4'-n-butylaniline (EBBA; see Fig. 1.1, page 3) [24,25]; EBBA is a solvent which was determined (from the D 2 and HD studies) to have a negative Fzz. The counter-intuitive negative order parameter is the predicted result for a positive quadrupole/negative Fzz interaction. Similarly, order parameters for benzene and hexafluorobenzene, molecules with very similar shapes but with quadrupole moments of opposite signs, are in accordance with results predicted from the quadrupole moment/Fzz mechanism[26]. These experiments demonstrated that interactions involv-ing molecular quadrupoles could provide an important orientational mechanism and that for a particular liquid crystal, solutes experience at least the same sign Fzz\ from the Chapter 1. Introduction 9 experiments mentioned above and other similar experiments[8] it was concluded that so-lutes experience roughly the same average environment regardless of the size, shape or electrostatic properties. The concept of a solute independent average environment has been criticized by Photi-nos et. al.[27] and Terzis et. al[Q]. They developed a theory to describe the effects from short-range repulsive and long-range dipole and quadrupole interactions. Effects from dipole-dipole interactions were inferred by comparing order parameters of a,w-dibromo-n-alkanes and n-alkanes[17]. The observed bias on the segmental orientational order of the bromo-alkanes relative to the n-alkanes was ascribed to result from the interaction of the local dipole moment with the local dipoles on the nematogens. The effect was ex-plained qualitatively by the asymmetric arrangement which results from off-center local dipoles on molecules with short-range repulsive cores. This results in strong short-range correlations which contribute significantly to the orientational ordering. They concluded that long-range interactions were comparable in magnitude to short-range interactions and that long-range interactions were highly sensitive to the size, shape and electrostatic properties of the solvent and solute molecules, i.e. solutes do not experience the same environment. Emsley et al. [16] have also examined the importance of dipoles, quadrupoles and the concept of a solute independent average environment. They suggested that there is no contribution to solute ordering from dipole interactions because in apolar nematic phases the first rank order parameter of the liquid crystal is zero (i.e. the mean electric field of Chapter 1. Introduction 10 the nematic phase is zero) and that the F^z's experienced by a solute are dependent on the solvent quadrupole and the distribution of intermolecular vectors about the solute particle; the solute properties influence the distribution of intermolecular vectors and thus the FZz is indirectly influenced by the solute. The distribution of intermolecular vectors is a property which is not easily determined by experimental methods. Nevertheless, the orientational behavior of anthracene and anthraquinone, molecules that are claimed to have similar shapes and polarizabilities but significantly different quadrupole moments, was examined using the theory[28]. The distribution of solvent-solute intermolecular vectors, and consequently the Fzz's, were found to be strongly dependent on both solvent and solute molecular properties. Hence, there is controversy over the importance of dipole and quadrupole interactions and about the concept of a solute-independent average environment. The controversy is an important aspect of this study and is discussed further in Chapters 3 and 4. 1.3.2 Computer Simulations Experimentally determined values of Saps are often difficult to interpret unambiguously. The orientational ordering of a molecule is governed by many interactions and mod-els must be employed to extract the main contributions to the orientational ordering. Computer simulations provide an effective complimentary method to the interpretation of experimental data and can be used to test theories. Specific interactions that are thought to be important for orientational ordering such as short-range size and shape, Chapter 1. Introduction 11 dipole or quadrupole interactions can be incorporated into the simulation algorithm. The effect of each interaction on the ordering can be examined without interference from other ordering mechanisms. A simple but very useful computer simulation method is the Monte Carlo method using the Metropolis algorithm [29]. In this study, a series of micro-states is generated with the probability of a particular state being determined from a Boltzmann distribution. The system is arranged in some initial configuration. One of the particles is randomly chosen, and a repositioning (eg. translation, rotation) is attempted. The energy difference between the initial i and final j states, AE = Ej — E{, is calculated. If AE < 0, then the new position is accepted; if AE > 0, then the new position is accepted with the probability given by Py = e~0AE. The relationship between experiment, model and computer simulations is examined in Chapter 4. 1.4 N M R Experiments and their Relation to Orientational Ordering 1.4.1 Dipolar Couplings and Orientational Order Parameters The second rank orientational order parameters Saps can be determined from analysis of NMR spectral data of orientationally ordered molecules. In particular, dipolar couplings Dy's between spins i and j contain information on the relative orientation of the internu-clear vector between i and j. Unlike NMR spectra of isotropic solutions, the proton NMR spectra of orientationally ordered molecules contain information about nuclear dipolar Chapter 1. Introduction 12 couplings between pairs of spins on the same molecule; random rapid translational mo-tion of the molecules causes intermolecular dipolar couplings to be averaged to zero. The anisotropic molecular reorientation causes the intramolecular dipolar couplings to be av-eraged to a non-zero value. For relatively inflexible molecules with no large amplitude motions, SQ/?'s can be calculated using the relationship n Voftlilj v-^  c j'cos9gcos9P\ i j = — ^ Q/3\—73 / { } where /J,Q is the magnetic permeability of free space, h is Plank's constant, 7J and 7j are the gyromagnetic ratios of spins i and j, rij is the internuclear distance be-tween nuclei i and j, 9a and 9p are the angles between the internuclear vector and the molecular a and j3 axes (see Fig. 1.2 for an example of axis and angle definitions), 1 4 Z _ J Labortroy fixed Z direction Figure 1.2: The nematic director and magnetic field direction are parallel to the labo-ratory fixed Z direction, x, y, z refer to the molecular axis system. As an example, 9xz is the angle between the molecular fixed x axis and the Z direction, and 9X is the angle between the internuclear vector ry- and the molecular fixed x direction. Sa/j's and Di/s are averages over all molecular reorientations and thus 9xz and 9X only represent angles at an instant in time. Chapter 1. Introduction 13 and the angle brackets indicate a statistical average over all intramolecular motions. For isotropic systems Sap = 0 and thus Dij = 0. A detailed description of obtaining Saps from Di/s is given in Chapter 2 and a description of basic NMR theory and the application to oriented systems is given in the next section. 1.4.2 N M R Theory In the high field limit, where the chemical shift, and the direct and indirect dipolar inter-actions are small compared to the principal Zeeman interaction of the bare nucleus with the external magnetic field, the proton (spin I = \) NMR spectrum of orientationally ordered molecules is described by the spin Hamiltonian H, H = HZ + HD + Hj (1.6) where Hz is the Zeeman Hamiltonian, Hj is the scalar coupling and HD is the dipolar coupling Hamiltonian. The Zeeman Hamiltonian is given by N Hz = -^huilf (1.7) i=l where If is the Z-component of the spin operator for the i spin and Vi are the chemically Chapter 1. Introduction 14 shifted frequencies which are given by *i = ^ ( l - * _ _ , , ) • (1-8) H0 is the static external magnetic field, defined to be along the Z-axis. The quantity o~zz,i is the ZZ component of the chemical-shift tensor projected onto the external field for spin i. The indirect or scalar Hamiltonian is approximately given by HJ = YJhJiiIi-h (1-9) i<j —* —* where is the scalar coupling constant between spins i and j, and Ii and Ij are the spin operators for the i and j spins. The general form of this Hamiltonian includes an anisotropic orientationally dependent component; however, for most couplings involving protons, the anisotropy is small and is ignored. The direct dipolar Hamiltonian is given by HD = Y, hDij(3lfl? - h • I,), (1.10) i<j where Dy is the dipolar coupling constant between spins % and j (see Eq. 1.5, page 12). For isotropic systems Dij is zero and only the Zeeman and indirect coupling terms are observed. Chapter 1. Introduction 15 The eigenstates \$A) and eigenvalues EA are obtained from a diagonalization of the Hamiltonian and are parameterized by <7zz,i, Dij and Jy. Thus, the associated spectral transition frequencies and intensities are also a function of the coupling constants. Spec-tra are characterized by transitions between eigenstates \<&A) and |$B) which, in the case of infinitely sharp lines, is given by where UAB — (EA — Eb)/h for eigenvalue energies EA and EB, I+ = Ix + UY, and I~ = Ix - UY. The main NMR selection rule is MA - MB = ±1 where MA and MB are the total angular momenta of eigenstates |$ )^ and |$B). The order oi a particular coherence is given by the value of MA — M B , and the standard high-resolution NMR spectrum (the Fourier transform of the free induction decay acquired after a single pulse) is characterized by transitions of order ±1. 1.4.3 Simplifying N M R Spectra and Analysis by Multiple Quantum N M R For simple molecules with < 7 spins the high-resolution NMR spectrum contains at most a few hundred lines and is usually easy to analyze. For larger spin systems the number of transitions increases dramatically and the high-resolution spectra become extremely difficult to analyze. The analysis of spectra can be simplified by acquiring multiple quantum (MQ) NMR spectra[30-32] (i.e. MA - MB > ±1). The higher order MQ (1.11) A<B Chapter 1. Introduction 16 spectra contain far fewer lines than the high-resolution spectra, but contain the same information about the chemical shifts and coupling constants. A basic 2D pulse sequence that may be used to generate and indirectly observe MQ coherences is given by t2(acquire). (1-12) Prior to application of the pulse sequence the spin system is at equilibrium and only Iz magnetization is present. Application of a 90° Y pulse (for example) converts Iz into Ix. Ix evolves under the spin Hamiltonian into other one-quantum coherences during the preparation time r. The second 90° Y pulse transforms the one-quantum coherences into all possible MQ coherences. The MQ coherences evolve for the evolution time t\. The third pulse partially converts the MQ coherences back into one-quantum coherences which then evolve into the observable Ix which is recorded as a function of i 2- Two-dimensional Fourier transformation and a summed projection onto the / i axis yields a spectrum of MQ transitions which corresponds to the time evolution of MQ coherences during the evolution time t\. During the ti evolution time the chemical shifts are modulated according to their MQ coherence. Therefore, offsetting the carrier frequency from resonance will separate indi-vidual orders. Phase-cycling[33,34] or application of field gradients[35,36] can selectively detect particular orders of MQ spectra. Chapter 1. Introduction 17 Although MQ spectra are easier to analyze and in principal contain the same infor-mation as the high-resolution spectrum, poor signal-to-noise and poor resolution (half-height line-widths of 50Hz) cause the spectral parameters to be somewhat inaccurate. Therefore the spectral parameters determined from MQ spectra are used only as initial guesses when analyzing the well-resolved high-resolution spectra. The spectral analysis using MQ and high-resolution spectra is discussed in Chapter 2. 1.5 Outline of Thesis The understanding of the intermolecular forces within liquid crystals is not complete. Short-range repulsive interactions which are based on the size and shape of the molecules are an important ordering mechanism. Molecular quadrupoles are significant for the long-range contributions, but the form of the quadrupole potential is still much in debate[6,18]. From theory the Fzzs are predicted to be dependent on the properties of the solute, whereas from experimental results it is observed that at least the sign of the Fzz is the same for all solutes in a particular liquid-crystal solvent. The importance of dipoles for the intermolecular potential is still uncertain. One of the objectives of this study is to determine the effects of permanent quadru-poles, dipoles, and molecular polarizabilities on solute ordering. The choice of liquid crystals and solutes is important to the understanding of orientational ordering mecha-nisms. From previous NMR studies of D 2 and HD the Fzz's in ZLI 11321 and EBBA 1 Merck ZLI 1132 is a eutectic mixture of three irons-4-n-alkyl-(4-cyanophenyl)-cyclohexanes and Chapter 1. Introduction 18 were found to be of opposite sign and in the special 55 wt% ZLI1132/EBBA mixture the Fzz is zero. There is evidence that other solutes also experience similar FZz^> m these three liquid crystal mixtures. Since the sign and approximate magnitude of the Fzz's are known for these three liquid crystals, this may help with determining the influence of dipoles and polarizabilities on orientational ordering. Since orientational ordering is dominated by short-range interactions, if probe solutes that have very similar sizes and shapes are compared, differences among orientational order parameters might then reflect the effects of the additional, weak long-range inter-actions. It may therefore be possible to examine effects of long-range interactions on the anisotropic intermolecular potential. Since methyl and chloro constituents have roughly the same size and shape but different electrostatic properties[38], methyl and chloro sub-stituted benzenes (as well as propyne and acetonitrile) can be used to distinguish between steric and electrostatic effects on order parameters. Five sets of similar size and shape molecules have been chosen; the short-range interactions for each set is assumed to be similar but, due to the various constituent substitutions, the long-range interactions for molecules within a set are different. Chlorobenzene and toluene represent a group with dipoles of different magnitudes; p-dichlorobenzene, p-chlorotoluene and p-xylene repre-sent a group in which the chlorotoluene has a dipole and the other two molecules have no molecular dipole; ra- and o-dichlorobenzene, m- and o-chlorotoluene and m- and o-xylene represent two groups where the dichlorobenzenes and xylenes have dipoles that trans-4-7i-pentyl-(4'-cyanobiphenyl)-cyclohexcine. See Ref. [37] for chemical composition. Chapter 1. Introduction 19 are collinear with the z molecular axis while the chlorotoluenes have dipoles that have components along the molecular z and x axes. The last group, acetonitrile and propyne, was chosen because these are small molecules with a large difference in the magnitude of their dipoles; it would be expected that effects on the intermolecular potential from shape anisotropy would be reduced and that the effects from long-range interactions would be enhanced with these two molecules. See Fig. A.22, page 107 for a representation of the molecular structure and axes definitions of the solutes. Chapter 2 focuses on the experimental and analysis methods used to obtain spectral parameters (and ultimately order and structural parameters) from the complicated NMR spectra of the solutes co-dissolved in nematic liquid crystals. The spectra are complicated by having more than one solute dissolved in the sample tube, and methods for disentan-gling spectra from different molecules are discussed. Structural and order parameters are determined from vibrationally and non-vibrationally corrected dipolar couplings. The vibrationally corrected order parameters are utilized in Chapter 3 to examine the effects of size and shape dependent short-range interactions, and dipoles, quadrupoles and polarizabilities on the second rank orientational order parameters of the molecules. The average electric field, average electric field gradient and the average field squared are determined and compared to various theories and models. This is one of a few studies that utilizes a self-consistent set of order parameters and that estimates the sign and magnitude of the FZz$-Chapter 1. Introduction 20 Chapter 4 compares computer simulation results[13,39] with NMR experimental re-sults which were taken from previous studies [8] and from this study. Computer simula-tions which employed only short-range interactions are compared with NMR experiments of solutes dissolved in a special liquid crystal mixture where all long-range interactions seem to be negligible. Results from previous computer simulations using short-range and point quadrupole interactions are compared with NMR results of solutes in liquid crystals where long-range interactions are known to be important. Chapter 2 Multiple Quantum and High—Resolution N M R , Molecular Structure, and Order Parameters of Partially Oriented Solutes Co-dissolved in Nematic Liquid Crystals The material presented in this chapter has either been published in Refs. [40] and [41] or has been submitted for publication[19]. 2.1 Introduction Nuclear magnetic resonance (NMR) spectroscopy of small molecules orientationally or-dered in liquid-crystal solvents can yield precise information about the solute molecular geometry and second rank orientational order parameters[42,43]. NMR spectroscopy is one of the few techniques available for the determination of bond distances and bond angles of molecules in condensed phases, and the method can be used to investigate possible differences between gas and condensed phase structures. In addition, rotational potential barriers in molecules such as butane[44] and biphenyl[45] can be examined. Orientational order parameters are related to anisotropic intermolecular forces and thus have been used to examine statistical theories of liquid crystals[6,8,14,16,18,20,46, 21 Chapter 2. NMR and Molecular Structure 22 47]. Instead of investigating the order parameters of the liquid-crystal molecules them-selves, it is common to examine the orientational ordering of small probe solutes dissolved in the liquid crystal phase; solutes are chosen so as to emphasize specific anisotropic inter-actions^, 17,18, 20]. There is general consensus that molecular size and shape dependent short-range interactions represent the dominant mechanism that is responsible for orien-tational ordering in nematic liquid crystals. However, additional long-range interactions are known to be present and since their precise description is a matter of current con-troversy ,^ 8,14,16,17,27], the order parameters determined in this study for molecules of similar size and shape are quite useful for investigating intermolecular potentials (see Chapter 3 and 4). The differences among order parameters of solutes may be small and thus accurate measurements are required. Order parameters determined for molecules in the same liquid crystal should be measured under identical conditions. Ideally all solutes should be co-dissolved in the same sample tube but, due to overlap of spectral lines, extract-ing information from the resultant NMR spectrum may be impractical. It is common to dissolve solutes in different sample tubes and then to scale the results to account for variation in the solvent orientational order that results from different sample condi-tions^, 17, 27,46,48,49]. In an effort to alleviate the problem of scaling, in this study three or four fully protonated solutes are co-dissolved in the same sample tube. Some interesting NMR and spectral analysis tricks are developed to disentangle the resultant complicated proton NMR spectra. Chapter 2. NMR and Molecular Structure 23 The complexity of high-resolution NMR spectra of partially oriented molecules, and thus the ability to accurately determine spectral parameters such as chemical shifts and nuclear coupling constants from such spectra, depends on the flexibility and symmetry of the molecules and on the number and type of nuclear spins. For example, the proton NMR spectrum of complex liquid crystal molecules is typically broad and featureless and there-fore impossible to analyze accurately; the rolling base line in the experimental spectrum of Fig. 2.3 (page 30) is from the liquid crystal. Unfortunately, even with small solutes that contain « 6 spins, determining spectral parameters from high-resolution spectra can be extremely difficult. In such cases, the use of two-dimensional multiple-quantum (MQ) NMR spectroscopy[30-32] is very helpful since there are comparatively fewer lines in the spectra[44,45,50-53]; for example, compare the high-resolution spectrum of p-xylene (Fig. 2.4C; page 32) with the 7Q spectrum (Fig. 2.5A; page 34). However, the use of MQ spectra is not entirely straightforward; the intensities depend on both spectral and experimental parameters in such a complicated manner that they are unreliable and are not normally used in the analysis. In addition, care must be taken to avoid an incorrect and therefore a meaningless "fit." Nevertheless, the analysis is far easier than for the normal high-resolution spectra. An additional problem with MQ NMR is the technical limitations that lead to spectra with broad peaks and poor resolution. Although the relatively few number of lines in the MQ spectrum can be advantageous, spectral parameters are not determined with high accuracy. Therefore, parameters determined from MQ spectra are used only as a Chapter 2. NMR and Molecular Structure 24 starting point when analyzing high-resolution spectra. Despite the poor resolution of the MQ spectra, often only minor adjustments to parameters determined from such spectra are required in order to obtain a "fit" to the high-resolution spectrum (see Refs. [44,45, 52,53]). High-resolution spectra can have many hundreds of lines and thus obtaining erroneous spectral parameters from a well "fit" spectrum is extremely unlikely. In this chapter, a strategy for the analysis of high-resolution NMR spectra which contain resonances from many partially oriented solutes is developed. In some cases 2D multiple quantum (MQ) NMR spectra are analyzed first. Spectral parameters deter-mined from the analysis of MQ spectra are used as initial estimates in the analysis of the complex high-resolution spectra which contain resonances from other solutes. The resultant analyzed spectrum is subtracted from the experimental one and resonances corresponding to the other solutes are readily visible. From analysis of proton NMR spectra of the partially oriented solutes propyne, acetonitrile, chlorobenzene, toluene, p, m- and o-xylene, p, m- and o-chlorotoluene, and p, m- ando-dichlorobenzene, the chemical shifts, dipolar couplings and for most solutes the indirect scalar couplings were determined. The dipolar couplings were used to calculate molecular order parameters, and internuclear distances including the vibrationally corrected rQ structures. Chapter 2. NMR and Molecular Structure 25 2.2 Experiment The nematic liquid crystal Merck ZLI 1132 (see Ref. [37] for chemical composition) and all solutes were used without further purification. The liquid crystal solvent N-(p-ethoxy-benzylidene)-p'-n-butylaniline (EBBA) was synthesized[54] and purified by recrystalliza-tion from cold methanol. The composition of each sample is given in Table 2.1. Sam-ples #1-3 were prepared by dissolving 1,3,5-trichlorobenzene and acetonitrile in one of the liquid crystal solvents: ZLI 1132; 55 wt% ZLI 1132/EBBA; or EBBA. Approximately 400mg of the mixture was transfered into a medium-walled 5mm o.d. NMR tube and thor-oughly degassed by several freeze-pump-thaw cycles. Propyne was condensed into the NMR tube at liquid nitrogen temperature to achieve approximately 5 mol% of propyne in the mixture. The tube was then flame sealed under vacuum. Samples #4-25 were pre-pared by dissolving three or four solutes in one of the liquid crystal solvents mentioned above. All samples were repeatedly heated to the isotropic phase and thoroughly mixed. The total solute concentration was « 10 mol%. The solute 1,3,5-trichlorobenzene which was added to each sample was used as an internal orientational standard. Proton NMR spectra of Samples #4-25 were acquired at 299.6 ±0.5 K on a Bruker AMX-500 spectrometer. Acetone-d6 in a coaxial capillary provided the deuterium lock. Proton NMR spectra of Samples #1-3 were acquired unlocked at 300 ±1 K on a Bruker CXP-200 spectrometer. For high-resolution proton NMR spectra, 32K point free induc-tion decays were acquired after a single pulse, zero filled to 64K points and processed Chapter 2. NMR and Molecular Structure 26 Table 2.1: Solute" and Solvent Composition of Samples Sample # Solutes6 Liquid Crystal Solvent 1 acetonitrile / propyne ZLI 1132c 2 acetonitrile/propyne 55 wt% ZLI 1132/EBBA 3 acetonitrile/propyne EBBAd 4 chlorobenzene/toluene ZLI 1132 5 chlorobenzene / toluene 55 wt% ZLI 1132/EBBA 6 chlorobenzene / toluene EBBA 7 p-chlorotoluene/p-dichlorobenzene ZLI 1132 8 p-chlorotoluene/p-dichlorobenzene 55 wt% ZLI 1132/EBBA 9 p-chlorotoluene/p-dichlorobenzene EBBA 10 p-xylene / p-dichlorobenzene ZLI 1132 11 p-xylene/p-dichlorobenzene 55 wt% ZLI 1132/EBBA 12 p-xylene/p-dichlorobenzene EBBA 13 o-chlorotoluene / o-dichlorobenzene ZLI 1132 14 o-chlorotoluene/ o-dichlorobenzene 55 wt% ZLI 1132/EBBA 15 o-chlorotoluene / o-dichlorobenzene EBBA 16 o-xylene/o-dichlorobenzene ZLI 1132 17 o-xylene/o-dichlorobenzene 55 wt% ZLI 1132/EBBA 18 o-xylene/o-dichlorobenzene EBBA 19 m-chlorotoluene/m-dichlorobenzene ZLI 1132 20 m-chlorotoluene / m-dichlorobenzene 55 wt% ZLI 1132/EBBA 21 m-chlorotoluene /m-dichlorobenzene EBBA 22 m-xylene/m-dichlorobenzene ZLI 1132 23 m-xylene /m-dichlorobenzene 55 wt% ZLI 1132/EBBA 24 m-xylene /m-dichlorobenzene EBBA 25 o-xylene / o-chlorotoluene / o-dichlorobenzene ZLI 1132 a Total solute concentration is « 10 mol%. 6 The orientational standard 1,3,5-trichlorobenzene was also co-dissolved in each sample. c See Ref. [37] for chemical composition. d EBBA refers to N-(p-ethoxybenzylidene)-p'-n-butylaniline. Chapter 2. NMR and Molecular Structure 27 using a Lorentzian line broadening of 1.0 Hz. Half height line widths were typically 2-3 Hz. Typical spectra (obtained from Samples #1 and #11) are presented in Figs. 2.3 and 2.4 (pages 30 and 32). An expansion region of Fig. 2.4 is presented in Fig. 2.6 (page 35). For samples which contained p-xylene, two-dimensional selective 7Q and 8Q spectra were acquired whereas for samples which contained m- and o-xylene, only 8Q spectra were acquired using the pulse sequence [33,34] with 1000-1500 increments in t\ and for each ti increment 1024 points were collected in t2; a one dimensional MQ spectrum was produced by zero filling to 2048 in ti, 2D magnitude Fourier transforming and performing a summed projection onto the Fi axis. To selectively detect specific M-quantum coherences, the pulse sequence 2.13 is applied M*2 times for each ti increment with the collected FID's alternately added and subtracted; the phase <j> of the first and second pulse is incremented by (M*2)/360 degrees relative to the third pulse (and receiver) for each application of the pulse sequence[33,34]. For example to selectively detect 8-quantum coherences, the pulse sequence is applied 16 times for each ti increment and the phase of the first and second pulse is incremented by 22.5° after each application of the pulse sequence 2.13. While in principal this pulse sequence also permits detection of ±k * 7-quantum or ±k * 8-quantum spectra, where k = 2,3,..., this was not a problem since for a n-spin-| system, n is the highest attainable MQ order; (2.13) Chapter 2. NMR and Molecular Structure 28 for the MQ spectra which were recorded, only the xylenes possessed > 7 or 8 spins. The intensity of MQ lines is highly dependent on the r value and therefore at least two MQ spectra with two different r values between 10-21 milliseconds were acquired in an attempt to detect all 7- or 8-quantum transitions. The recycling time was 4 seconds. The 7-quantum spectrum obtained from Sample #11 is presented in Fig. 2.5 (page 34). 2.3 Spectral Analysis and Strategy The proton NMR spectrum of orientationally ordered molecules is dependent on the flexibility and symmetry of the molecules and on the number and type of nuclear spins; for example, compare the complexity of the spectra for acetonitrile, propyne, p-dichloro-benzene, p-xylene and the liquid crystal (Fig. 2.3, page 30 and Fig. 2.4, page 32). Spectral parameters of small solutes can be determined accurately by analyzing the experimental spectrum using the spin Hamiltonian (which is equivalent to the Hamiltonian presented in Eqs. 1.6-1.10, pages 13-14) f = - _ > t f + E E [(J«+w*)1?1! + \ v « - Dv)&*7+int)] ( 2 - 1 4 ) i i j>i where IZ,I+ and I~ are the spin operators, Ui is the resonance frequency of nucleus i, and Jij and are the indirect and dipolar coupling constants between nuclei i and j on the same molecule. To analyze experimental spectra, initial estimates of spectral parameters U{, and Chapter 2. NMR and Molecular Structure 29 Dij, either from previous studies or a "best guess," are required. The best guess may be from the D '^s of similar molecules dissolved in the same liquid crystal. From the estimates of the spectral parameters, a trial spectrum is calculated using Eq. 2.14 and the appropriate selection rules for high-resolution or MQ spectra. Experimental and cal-culated spectra are compared and spectral parameters are manually adjusted until the overall structure of the calculated spectrum is similar to the experimental. The calcu-lated frequencies are then assigned to the experimental ones and spectral parameters are adjusted by a least-squares fitting routine. Frequencies are repeatedly assigned and/or unassigned and parameters adjusted until a reasonable fit to the experimental spectrum is obtained; this is the most time consuming portion of spectral analysis. Assignment of calculated to experimental frequencies was performed with the aid of a macro driven graphical interface program SM1. The macro was designed so that experimental frequen-cies could be matched to calculated frequencies using cursor controls. Care was taken to avoid assignment of overlapping or unresolvable lines and experimental frequencies were determined from a five point weighted average about the maximum intensity point. In all cases the frequencies were no more than 0.2 Hz different from a standard Bruker peak picking routine for lines with half height line width < 3 Hz. High-resolution spectra for samples which contained propyne, acetonitrile and 1,3,5-trichlorobenzene (Fig. 2.3) were relatively easy to analyze. The spectrum of 1,3,5-trichlorobenzene 1The back-end graphical interface program SM (Edition 2.2.0. Jan. 1992) is a configurable plotting program written by Robert Lupton (Princeton University) and Patricia Monger (McMaster University). Chapter 2. NMR and Molecular Structure 30 o © CH3-C=N i L-ttjj o o o o © © VJJL-^ © © CH3-C=C-H Jul L i U L l i -5000 5000 104 Frequency Figure 2.3: The experimental high-resolution spectrum (top) is of Sample #1. The main triplet from acetonitrile has been truncated. The calculated spectra of acetonitrile and propyne (values from Table B.6) are in the middle and on the bottom. The two sets of doublets from the coupling to the two C 1 3 nuclei are visible in the experimental and cal-culated (indicated with a o) spectra of acetonitrile and are required in order to determine the absolute sign of DHH- Resonances marked with an * are from 1,3,5-trichlorobenzene and resonances marked with a J and the many low intensity resonances around the center of the spectrum are from unknown impurities. In the experimental spectrum, the rolling base line which is approximately 50 kHz wide is from the liquid crystal molecules. Chapter 2. NMR and Molecular Structure 31 is a triplet with a splitting of 3 x DHH- Thus, the DHH could be determined without the aid of a least-squares fitting routine. For the spectrum of acetonitrile, there is a triplet with a splitting of 3 x DHH and there are two sets of doublets centered around each of the lines of the triplet which are due to the two H 1 -C 1 3 couplings. The splittings are (2 x DHC13 + JHC13), and the H 1 -C 1 3 couplings were required in order to determine the absolute sign of DHH- The spectrum of propyne is slightly more complex and thus, DHH were determined using the least-squares routine. However, it is still quite trivial to analyze and only the proton-proton dipolar couplings were required; the absolute sign of the DHH were defined by setting the initial value of the J coupling to the isotropic value of —3.551 [55] (see Fig. A.22, page 107 for the structure and atom numbering of the solutes and Table B.6, page 109 for the spectral parameters determined from the spectral analysis). Determining spectral parameters from the high-resolution spectra of p-xylene is very difficult; p-xylene has two resonance frequencies and seven independent dipolar couplings. Without accurate estimates of such parameters, it may require months to analyze the high-resolution spectrum (see Fig. 2.4). For a typical spectral analysis method of such complicated spectra, the MQ spectrum is analyzed first to obtain estimates of spectral parameters which are used as initial parameters in the analysis of the high-resolution spectra; accurate spectral parameters are then obtained from the high-resolution spec-trum. Within the least-squares routine, the non-equivalent D^s are adjusted inde-pendently. For p-xylene seven independent D '^s and two resonance frequencies were Chapter 2. NMR and Molecular Structure 32 i i i i i ' ' i i i i i I i i i i I i i i i I 1 1 - l x l O 4 -5000 0 5000 10* Frequency /Hz Figure 2.4: The experimental high-resolution spectrum C is of Sample #11, partially oriented p-xylene, p-dichlorobenzene and 1,3,5-trichlorobenzene (TCB) in 55 wt% ZLI 1132/EBBA at 299 K. Spectrum B is the calculated spectrum of p-xylene from the fit to spectrum C. Spectrum A is a subtraction of the calculated from the experimental spectrum. Since experimental lines had a broad base, the subtraction was performed using a calculated spectrum in which the lineshape is the addition of two Lorentzians with line broadenings of 1 and 4 Hz. Note that resonances corresponding to the external lock signal (acetone-d6 in a capillary tube), TCB and p-dichlorobenzene are clearly visible in the top spectrum. Lines from the 1,3,5-trichlorobenzene (TCB) triplet have been truncated. Chapter 2. NMR and Molecular Structure 33 determined from about 45 lines from the 7Q (Fig. 2.5 and Table B.6, page 109) and 8Q spectra; it must be remembered that intensities in the calculated MQ spectrum are meaningless. There is a chance that the spectral parameters determined from analysis of the MQ spectra are incorrectly determined. However, for p-xylene this was not the case; the agreement between experimental and calculated spectral line positions is excellent. Spectral parameters obtained from the fit to the MQ spectrum were then used to calculate the high-resolution NMR spectrum, and a section of the spectrum from Sam-ple #11 is shown in Fig. 2.6D. Most peaks can be assigned immediately to lines in the experimental spectrum (compare Figs. 2.6C and 2.6D). As has been found for several other complicated spin systems[44,45,52], a correct fit to the MQ spectrum can give a prediction of the high-resolution spectrum that is amazingly close to the experimental spectrum. In the current case, the fit to the high-resolution spectrum is complicated by the presence of lines from the extra two solutes. Once spectral parameters for the MQ spectra were determined, the high-resolution spectra were analyzed within hours and the spectral parameters obtained are given in Table B.6, page 109. The spectrum calculated from the parameters in Table B.6 for Sample #11 is presented in Figs. 2.4B and 2.6B. The excellent quality of the fit to the high-resolution spectrum of p-xylene is demonstrated by subtracting the calculated (Figs. 2.4B and 2.6B) from the experimental (Figs. 2.4C and 2.6C) spectrum, the result being presented as Figs. 2.4A and 2.6A. The experimental p-dichlorobenzene and 1,3,5-trichlorobenzene spectra are readily observed Chapter 2. NMR and Molecular Structure 34 J I I L J I I _ _l I I L_ _L _i i i i_ J 0 10 4 2 x l 0 4 3 x l 0 4 Frequency /Hz 4 x l 0 4 5 x l 0 4 Figure 2.5: The experimental +7-quantum spectrum A is of Sample #11. Only reso-nances from p-xylene are observed; for an n-spin-| system, n is the highest attainable MQ order. Spectrum B is the calculated +7-quantum spectrum of p-xylene. Note the line width in the experimental spectrum is approximately 50 Hz and the intensities of the calculated spectrum do not correspond with those of the experimental. Chapter 2. NMR and Molecular Structure 35 L L J J I I L J I l_ J_ J l_ D J 1000 1500 2000 Frequency/Hz 2500 Figure 2.6: The top three spectra A, B and C are an expansion of Fig. 2.4. Spectrum D is an expansion of the spectrum predicted from the "fit" to the 7-quantum spectrum. Note the line positions and intensities between the 7-quantum prediction and the ex-perimental spectra are in sufficiently good agreement that only minor adjustments to spectral parameters were required in order to "fit" the experimental spectrum. In the experimental spectrum, the average line width at half maximum height is 2-3 Hz. The intensities of the calculated spectrum closely correspond with those of the experimental one. In spectrum A, resonances indicated with an * are from p-dichlorobenzene. Chapter 2. NMR and Molecular Structure 36 and were easily analyzed. For each sample which contained p-xylene, the complete de-termination of the spectral parameters obtained by starting from the MQ spectra and then analyzing the high-resolution spectrum required only a month. Unfortunately, for o- and m-xylene, the sparsity of lines in the MQ spectra and the number of adjustable spectral parameters caused problems when attempting to fit the £>ij's independently; this is not uncommon when analyzing MQ and some simple high-resolution spectra. Spectral parameters may be meaningless even though the spectrum appears to be "fit". The problem can be overcome by realizing that Dy's can be related to molecular orientational order parameters and structural parameters (eg. Eq. 1.5, page 12). The number of adjustable parameters required to analyze the spectrum can be significantly reduced which will greatly simplify the analysis; for example, o-xylene has ten independent A / s but only two independent S^'s and a couple of crucial structural parameters. It should be noted that the calculated frequencies are very sensitive to minor changes in structural parameters and thus reasonably good estimates of proton positions are required for this method to succeed. For the essentially inflexible molecules in this study the Dy's can be calculated from Eq. 1.5 (page 12). The least-squares routine was modified so that 5Q/j's, structural parameters and/or D^ -'s for an arbitrary molecule can be adjusted independently; within the fitting routine Di/s (which are still required for the calculation of the spectrum from Eq. 2.14, page 28) are calculated from 5Q/g's and structural parameters. However, if a Dij is to be adjusted independently, it is not calculated from Saps and structural parameters, Chapter 2. NMR and Molecular Structure 37 but allowed to freely vary. Thus, the dependence of the A / s on 5a/g's is removed; this is useful, for example, if the molecule has internal rotations where the potential barrier is uncertain or if specific structural parameters are not well known. Derivatives of the line positions with respect to the Dj/s are calculated analytically. The derivatives of the line positions with respect to the S^'s and structural parameters are calculated using finite difference and structural data obtained from other studies. This is similar to a fitting method presented in Refs. [45] and [52]; however the fitting routine described in Refs. [45] and [52] was designed for a specific molecule and only allowed for adjustment of Szz and Sxx Syy. Analysis of the very complicated spectra from o- and m-xylene is exemplified with Sample #25 (o-xylene/o-chlorotoluene/o-dichlorobenzene/1,3,5-trichlorobenzene in ZLI 1132). The 8Q spectrum was analyzed first using the modified version of the fitting program. 5a/j's and resonance frequencies were adjusted until a reasonable fit to the 8Q spectrum was obtained. Then using the original version of the MQ analysis program the .Dy's and resonance frequencies were more accurately determined (Fig. 2.7). The values obtained for Sample #25 are presented in square brackets in Table B.6 and in Table B.7 (pages 109 and 122) for the other solute molecules. As was the case for p-xylene, the predicted high-resolution spectrum of o-xylene (Fig. 2.8B) is very similar to the experimental (Fig. 2.8A) and in most cases only minor adjustments to the spectral parameters were required to fit the high-resolution spectrum (Fig. 2.8C). After analysis of the high-resolution spectrum the resultant fitted spectrum of either Chapter 2. NMR and Molecular Structure 38 i i i i I i i i i I i i i i I i i i i I i — i — i — 1 _ 0 5000 10 4 1.5xl0 4 Frequency 2 x l 0 4 2 .5x l0 4 Figure 2.7: The experimental +8-quantum spectrum (top) is of Sample #25. The calcu-lated +8-quantum spectrum of o-xylene (from values in square brackets from Table B.7, page 122) is on the bottom. Chapter 2. NMR and Molecular Structure 39 1 ll 1 ill 11 * LL ill, * 1 1, c * t 1 j 1 1 i i 1 1 1 Exp- ,LlMi I J l l i J i l i l ^ A a^ H 3 (predicted from 8Q analysis) C H i , ig.uJa,,i\i.liliiiLii il ilJiiLJ llilllkJkli JLJLU B C^ CH3 ..i^L., JLAL 11L1IJkllbll,,iii C A - C I JUUi. I j.Mlil|,^ .|,yMll>Mi|Wi J l D 0 / C H 3 (calc.) ^Cl Nilml Llii.L i llill E D - E • *4 <t CI || (calc.) CI F - G * * O 1 t i i i 1 i i i i 1 i i i 1 1 i H -5000 0 5000 -3000 -2000 -1000 Frequency Frequency Figure 2.8: The caption to this figure is on the next page. Chapter 2. NMR and Molecular Structure 40 Figure 2.8: Spectral analysis strategy: Full spectra are displayed on the left and expan-sions are displayed on the right. A is the experimental spectrum of Sample #25. B is the predicted o-xylene spectrum from the parameters determined by analysis of the 8Q spectrum (Fig. 2.7). Spectrum C is calculated from the fit to the high-resolution spectrum of o-xylene. Note that there are only minor differences between spectra B and C. Spectrum D is the difference between A and C. The negative residuals in Spectrum D are due to slight differences between the line shapes of the calculated and experimental spectra. The calculated spectrum of o-chlorotoluene is E and F is the difference be-tween D and E. Spectrum G is the calculated o-dichlorobenzene spectrum and H is the difference between F and G. Note that when calculated spectra are subtracted from ex-perimental, resonances from the.other molecules are readily visible. Resonances marked with an * are from 1,3,5-trichlorobenzene. Resonances indicated with a $ are impurities and the resonance indicated with a o is from the partially protonated acetone used for a field/frequency lock. The calculated spectrum of 1,3,5-trichlorobenzene is not displayed. For high-resolution spectra intensities of the calculated spectrum closely correspond with those of the experimental spectrum. o- or m-xylene was subtracted from the experimental one and resonances from the other solutes could be identified (see Fig. 2.8D). For samples which did not contain o, m- or p-xylene (or acetonitrile and propyne) analysis of the high-resolution spectrum begins with this step in the strategy. The initial dipolar couplings for the o-, m- or p-chlorotoluenes were estimated from the order parameters of o-, m- or p-xylene in the same liquid crystal. The initial estimates for chlorobenzene and toluene were taken from previous studies. For the spectrum of toluene, and o- m- and p-chlorotoluene, there is a group of resonances up frequency (« +4000Hz) from the main portion of the spectrum (for o-chlorotoluene see Figs. 2.8D and E). The fine structure is due to the A / s between methyl and ring protons, and by assigning some of these resonances certain A?'s could be roughly determined which aided with the identification of resonances in the main portion of the spectrum. Chapter 2. NMR and Molecular Structure 41 Once a few resonances within the main portion of the spectrum were correctly assigned the spectrum was analyzed quickly. Again after the high-resolution spectrum of toluene or chlorotoluene was fitted and subtracted from the experimental spectrum, resonances from chlorobenzene or dichloroben-zene were easily identified (eg. Figs. 2.8F and G). In Fig. 2.8H only a few resonances remain after the fitted o-xylene, o-chlorotoluene and o-dichlorobenzene spectra are sub-tracted from the experimental one. The remaining resonances correspond to 1,3,5-trichlorobenzene, acetone-d5 (from lock) and an unknown impurity. The complete anal-ysis of the very complex 8Q and high-resolution spectra of o- and m-xylene was reduced to less than a week. It should be emphasized that one of the objectives of this study is to determine accurate S^'s and structural parameters and thus precise Aj's are required. Due to the poor resolution (line-width « 50Hz), to the possible correlations between some A / s , and to the sparsity of lines in the MQ spectra, Dy's from analysis of the MQ spectra are rather imprecise. Thus it is prudent to analyze the complex high-resolution spectra. Some of the Aj's from the MQ analysis differ significantly from those determined from the high-resolution spectra (refer to Table 2.2 which contains a subset of the data presented in Table B.6). These discrepancies would have a significant effect on the calculated Saps and structural parameters. Chapter 2. NMR and Molecular Structure 42 Table 2.2: Selected Dipolar Couplings" from Table B.6 Value of Du from Sample # Solute Dijc high-resolution multiple quantum 10 p-xylenec Di,2 -2670.51. -2733.9 16 o-xylened Dlt2 -1157.11 -1083.9 16 o-xylened 1508.17 1425.5 17 o-xylened A,3 -140.23 -240.7 17 oxylened £>2,3 -588.10 -505.4 17 o-xylened D2,5 -69.81 13.4 23 m-xylened A,2 -1080.34 -1139.4 23 m-xylened D4,5 -697.73 -744.2 23 m-xylened D5,e 1426.23 1510.8 a For atom numbering refer to Fig. 2.9 (page 44). There are significant differences be-tween the Di/s determined from analysis of the high-resolution and MQ spectra. This will cause large inaccuracies in the calculated molecular parameters. 6 Dipolar couplings are in Hz. c Values determined from the analysis of the 7-quantum specturm. d Values determined from the analysis of the 8-quantum specturm. 2.4 Molecular Structure and Order Parameters 2.4.1 Calculations Except for o-chlorotoluene, relative positions of the nuclei (Tables C.8, C.9, C.10, C.ll and C.12; pages 125-133) and 5Qj3's (Tables D.13, and D.14; pages 137 and 141) were calculated from a simultaneous fit to the Z)y's determined for the solute in all three liquid crystals. Since the spectrum of o-chlorotoluene in EBBA (Sample #15) was of poor quality, molecular parameters for o-chlorotoluene were calculated using A / s Chapter 2. NMR and Molecular Structure 43 from o-chlorotoluene dissolved in ZLI 1132 and 55 wt% ZLI 1132/EBBA. The 5Q/3's of o-chlorotoluene in EBBA were calculated using the structure determined from the other liquid crystals. Calculations were performed using Eq. 1.5 (page 12), a priori estimates[56] and a least-squares minimization routine NL2SNO[57] which minimizes the square of the difference between experimental and calculated D^s. The a priori estimates are values of structural parameters (taken from other studies) that have an associated error and are adjusted in the least-squares routine; large deviations from the a priori estimates are discouraged by the least-squares criteria. Dipolar couplings within the methyl group and between methyl and ring protons are an average over the methyl rotation; -D '^s were calculated for each 15 degree rotation of the methyl group. For o-xylene, the Case II rotational potential and potential parameters reported by Burnell and Diehl[58] was used; the potential was expanded as a Fourier series about the rotation angles OL\ and a.2 of the two methyl groups V — V l^—cos3a+ cos3a_)+\4 cos6a++V^ cos6a_+Vr6(l—cos6a+ cos 6a_)+... (2.15) where a+ = |(ai + 0:2), a_ = \{ai - a2), and V3 = 8.4,14 = 1-21, Vg = 1.55, and 14 = O.OkJ/mol. For o-xylene, the potential minimum (at ai = 0 and a 2 = 0) is where protons 5 and 10 of the methyl groups are in the plane of the benzene ring and adjacent to protons 4 and 1 (see Fig. 2.9 for atom numbering). For o-chlorotoluene only the three fold potential is used; a2, Va, Vg and V& are fixed at zero, V3 is fixed at Chapter 2. NMR and Molecular Structure 44 6 kJ/mol[59,60] and the potential minimum (at cei = 0) is where proton 5 is in the plane of the benzene ring and adjacent to proton 4. For toluene, m- and p-chlorotoluene, and m- and p-xylene, each methyl group was independently modeled with a six fold poten-tial V = VQ(1 — cos6o:)/2 where VE is fixed at 0.060 kJ/mol[59] and the minimum in the potential is where one proton of the methyl group is perpendicular to the benzene ring. In the approximation that a P2(cos0) bond additive interactional] describes the orientational potential, and that the methyl group retains C 3 symmetry upon rotation, the orientational potential is invariant to the methyl rotation. Chapter 2. NMR and Molecular Structure 45 Since the D^s are related to < r - 3 >, molecular vibrations will affect the experimen-tal observations. The effect of vibrations on the experimental data will be different for different experimental techniques. Therefore, to compare data determined from various experimental methods results should be "vibrationally corrected"2. The effect on the dipolar couplings from normal mode vibrations is calculated using a Taylor expansion of Dij about the equilibrium position 6 S where Dfj is the dipolar coupling at equilibrium, 8 is the x', y',and z' internuclear axes, (AS) is the average vibrational amplitude (anharmonic) in the 6 direction and (A52) is the corresponding mean-square amplitude (harmonic). The average structure determined by subtracting the contributions from harmonic vibrations, the rQ structure, has been established as a suitable physical basis for comparing results [66-69]. The average ra structures determined from different techniques are usually in good agreement with each other. A calculation of the ra structural parameters and Sap:s (Tables C.8, C.9, C.10, C.ll and C.12 and Tables D.13 and D.14; ) was performed using a version of the least-squares routine that was modified to include the subroutine VICO[55,70] which corrects 2In this study molecules axe in an anisotropic condensed phase; the anisotropy of the phase affects vibrational motions (orientational-vibrational correlations). Corrections have been calculated for simple molecules such as CH462], acetylene[25], benzene[63], chlorobenzene[63], and CH3F[64]. For molecules with a large Sap's, the orientational-vibrational correlations will have a very small effect ( « 0.2%) on the observed Djj's[63,65]. Normal mode bond vibrations have a larger effect ( « 2.0%) on the observed .Djj's[65] and thus only corrections for these effects have been attempted. Chapter 2. NMR and Molecular Structure 46 for the non-negligible effects of normal mode molecular vibrations using Eq.2.16. Mean square amplitudes (Ao~2) were calculated using the program MSAV[71] from normal mode vibrational analysis using force constants from Refs. [72], [73], [74] and [75]. 2.4.2 Molecular Structure One of the goals of this study is to report accurate Saps which in turn could be utilized when examining statistical theories. Since D^s are products of order and geometric parameters, it is essential when determining accurate S^'s to carefully consider the molecular structure. Thus, geometric parameters have been determined using a priori estimates and vibrationally and non-vibrationally corrected Z?y-'s. The relative values of the proton coordinates reported in Tables C.8, C.9, C.10, C.ll and C.12 (pages 125-133) are from simultaneous fits to the D^'s obtained in three different liquid crystals for each molecule except for o-chlorotoluene. The use of more than one liquid crystal provides extra independent equations for the fitting procedure. In order to determine the complete molecular structure, it is necessary to fit the proton geometry to the carbon skeleton. The error associated with the resulting structure is difficult to determine. Bond angles are probably not accurate to better than 0.2 of a degree, and CH bond distances to O.OlA. Thus the statistical uncertainties (68% confidence level) for the values reported in Tables C.8, C.9, C.10, C.ll and C.12 are optimistic. Chapter 2. NMR and Molecular Structure 47 Unfortunately rQ structural data for toluene, o- and m-chlorotoluene and o- and m-xylene could not be found in the literature. Even-though the a priori estimates for these molecules were obtained from a combination of data from various other studies, it is noteworthy that most of the calculated structural values (vibrationally and non-vibrationally corrected) do not differ greatly from these a priori estimates. However, there are some exceptions and it is difficult to ascertain the nature of the discrepancies but it is most likely due to the inaccuracies of the a priori estimates. For the other molecules, the calculated structural values are very similar to those previously determined ra values from electron diffraction studies. However, it is well known that proton coordinates are difficult to determine by electron diffraction and the new NMR values for chlorobenzene, p-, o- and m-dichlorobenzene, p-chlorotoluene and p-xylene are taken to be more reliable. 2.4.3 Order Parameters It is generally accepted that anisotropic short-range repulsive forces are primarily respon-sible for the orientational ordering of liquid crystals [9-13,76]. Controversy has arisen over the importance of anisotropic long-range interactions[6,14,16,18]. The spectra in this study have been recorded in such a manner so that the 5Q|a's obtained can be used to ex-plore various models for the anisotropic potential. A detailed quantitative analysis of the anisotropic intermolecular potential using the vibrationally corrected Saps is presented in Chapter 3. Chapter 2. NMR and Molecular Structure 48 2.5 Summary In this study spectral, orientational order, and structural parameters (including vi-brationally corrected molecular parameters) for p-, o and m-disubstituted benzenes, chlorobenzene, toluene, propyne and acetonitrile co-dissolved in various liquid crystals were determined. Resonance frequencies and dipolar couplings for p-xylene were esti-mated by analyzing the 7 and 8Q spectra and adjusting the resonance frequencies and dipolar couplings independently whereas for. o and m-xylene the resonance frequencies and Saps were estimated by analyzing the 8Q spectra using a modified version of the least-squares fitting routine which could adjust Saps, structural parameters, and/or Di/s independently. With this modified version of the program, the time required for analysis was greatly reduced. More accurate resonance frequencies and D^s were then determined with the original MQ program and used as initial estimates when accurately determining spectral parameters from the high-resolution spectra. After the high-resolution spectra were fitted, the calculated spectrum was subtracted from the experimental one and res-onances from the other molecules were identifiable. The spectra of the other molecules were then analyzed one by one and subtracted from the experimental spectrum. This is one of very few studies where many solutes were co-dissolved in a liquid crystal sol-vent and where MQ spectroscopy and analysis of the MQ spectra by adjusting 5Q|g's was utilized in a successful attempt to simplify the analysis of high-resolution spectra. Chapter 3 Dipole-Induced Ordering in Nematic Liquid Crystals: The Elusive Holy Grail The material presented in this chapter has been submitted for publication in Ref. [19]. Analysis of non-vibrationally corrected order parameters of toluene, chlorobenzene, p-dichlorobenzene, p-chlorotoluene and p-xylene have been published in Ref. [18]. 3.1 Introduction Nematic liquid crystals are fluid phases which are characterized by long-range orienta-tional correlations but no long-range positional correlations of the component molecules. The orientational ordering of molecules within liquid-crystal phases mainly arises from size and shape dependent anisotropic short-range interactions[8-14] and to a lesser ex-tent from anisotropic long-range interactions [6,15-17] such as interactions that involve molecular dipoles, quadrupoles and polarizabilities. An important objective when study-ing liquid crystals is to gain a detailed understanding of the effects of the intermolecular potential on the structure of the phase[6,8,14,16,39,76-79]. The roles of the various 49 Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 50 contributions to the intermolecular potential have been investigated by choosing, for ex-ample, solutes with particular properties, or by choosing a liquid crystal solvent that may have special properties [8]. One such liquid crystal with special properties is a mixture of 55 wt% ZLI 1132 (see Ref. [37] for chemical composition) in EBBA (see Fig. 1.1, page 3); from deuterium NMR studies of D 2 and HD, it was determined that for this particular mixture there is no con-tribution to the orientational potential from anisotropic long-range quadrupole interac-tions ]^. From other NMR studies, the orientational order parameters of a wide collection of solutes dissolved in this mixture were very well predicted by various mean-field models that only incorporate the details of the molecular size and shape anisotropy[8]; it was concluded that all solutes experience roughly the same environment, and that size and shape dependent short-range repulsive interactions were the principal factor responsi-ble for the solute orientational ordering. More recently, a computer simulation study of hard ellipsoids [13], undertaken to compliment this experimental work, confirmed the connection between these model potentials and the short-range forces, and provided fur-ther convincing evidence that short-range forces dominate the orientational behavior of molecules in nematic solvents. The choice of probe molecules permits another means of disentangling the many fac-tors that influence the behavior of liquid crystalline systems. Evidence for a solute molec-ular quadrupole-liquid crystal electric field gradient ({EFG)) interaction was obtained from several studies employing D 2 and HD as a solute in nematic liquid crystals[20-23,80]. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 51 In other studies acetylene, like D 2, was found to have a negative order parameter in the nematic solvent EBBA [24, 25]; EBBA is a solvent which was determined from the D 2 and HD studies to have a negative (EFG). The counter-intuitive negative order parameter is the predicted result for a positive quadrupole/negative (EFG) interaction. Similarly, the behavior of the order parameters for benzene and hexafluorobenzene, molecules with very similar shapes but with quadrupole moments of opposite signs, follows the pat-tern predicted from the quadrupole moment/{EFG) mechanism [26]. These experiments demonstrated that interactions involving molecular quadrupoles provide an important orientational mechanism. For a particular liquid crystal, the (EFGYs determined from the dissolved solutes are the same sign and same order of magnitude. Therefore, it was concluded [8] that within a particular liquid crystal all solutes experience roughly the same average environment regardless of the size, shape or electrostatic properties of the solute. The concept of a solute-independent mean-field has been criticized by Photinos et al. [6,17,27]; this type of model was inconsistent with their theoretical calculations. They predicted that short- and long-range interactions were approximately equal in magni-tude, that long-range interactions were mainly from quadrupoles and dipoles and that the long-range interactions were sensitive to the magnitude, position and orientation of the multipole. Emsley, Luckhurst and coworkers have also discussed the significance of the solute-independent (EFG) using a theory for orientational ordering which is closely related to the Maier-Saupe theory of nematics[16,28,81]. In the context of this theory, Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 52 it was shown that the nematogen quadrupole was the lowest order multipole that con-tributed to a non-vanishing (EFG). In an experimental study to compliment the theory, it was concluded that the (EFGYs were strongly dependent on both solvent and solute molecular properties. From recent computer simulations [39] which employed a point quadrupole electro-static model, the sign and magnitude of the (EFG)'s sampled by solutes were also found to be highly sensitive to the shape and electrostatic properties of the solutes. This is in contrast to most experimentally determined (EFGYs; for a particular liquid crystal, solutes experience (EFGYs which are at least the same sign. From the computer simula-tion studies it was also concluded that the origin of the discrepancy was most likely the inadequacy of using point quadrupoles for dense systems and an improved description of molecular electrostatic interactions will likely be essential in order to generate solute orientational behavior consistent with that observed experimentally. Nevertheless, these computer simulations can be used to test the accuracy and reliability of theories; the simulations represent an exact system for the theories of Emsley et al. [16,28,81] and Photinos et al.[6,17,27]. The orientational ordering predicted by the Emsley theory was found to be qualitatively consistent with the computer simulations. However, due to the mathematical approximations and the inadequacy of the electrostatic potential, pre-dictions of the long-range contributions to the orientational ordering were not accurate. For the Photinos theory, the orientational ordering predicted for the hard-body computer simulations were drastically underestimated by the theory. Due to the inadequacy of the Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 53 short-range potential, the long-range electrostatic contributions were not evaluated. Regardless of the inadequacies of the short-range potential with the Photinos et al. theory, they suggested that molecular dipoles are an important orientating mechanism, especially if the dipole is not located at the geometrical centre of the molecule[17,27]. In the context of the Emsley and Luckhurst mean-field theory, for apolar nematic phases the average electric field is necessarily zero and thus the contributions to the orientational potential for dipoles should vanish. An understanding of intermolecular forces within liquid crystals is not complete. There are discrepancies among results from theory, experiment and computer simula-tions. Nevertheless, there is an agreement that short-range repulsive interactions which are based on the size and shape of the molecules are an important ordering mechanism, and that molecular quadrupoles are significant for the long-range contributions; the form of the quadrupole intermolecular potential is still in much debate[6,18]. From theory and computer simulations the sign and magnitude of the (EFG) is found to be dependent on the solute properties whereas from experiments it is observed that at least the sign of the (EFG) is the same for all solutes in a particular liquid-crystal solvent[8,24-26]. The importance of dipoles to the intermolecular potential is still uncertain. The objective of this study is to determine the effects of permanent quadrupoles, dipoles, and molecular polarizabilities on solute ordering. The reasoning for the choice of probe solutes is outlined in Chapter 1, Section 5. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 54 3.2 Experiments and Results A major concern when comparing experimental with theoretical or computer simulation results is the lack of consistent experimental data. Typically, solutes are dissolved in different sample tubes and then results are scaled to account for the variation in the solvent orientational ordering that results from different sample conditions. In an effort to alleviate the ambiguity with the scaling of Sap, molecules were co-dissolved in the same sample tube. However, due to overlap of spectral lines all solutes could not be dissolved in the same tube and thus a method of scaling was still required for different samples. However, 5Qjg's for solutes within the same sample can be directly compared. Sap's were scaled using the equation where Sap and STCB are the order parameters of the solute and 1,3,5-trichlorobenzene (TCB) in the same sample tube and S ' T C B is the order parameter of TCB in the p-dichlorobenzene/p-xylene mixture of the same liquid crystal. The p-dichlorobenzene/p-xylene mixture was arbitrarily chosen as the standard for comparison. Values obtained for scaled, vibrationally corrected order parameters S ^ L E D are given in Table E.15, page 143. In previous studies (see Refs. [8], [14], [17] and [82]) other scaling methods have been 'scaled 'TCB (3.17) Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 55 utilized; for example, spectra were recorded at the same reduced temperature (the ra-tio of the sample temperature to the nematic-isotropic transition temperature) or the orientational potential could be scaled to the ratio of the 1,3,5-trichlorobenzene dipolar couplings. The concerns with scaling of Sap's is part of an ongoing investigation[83]. Nev-ertheless, differences between scaled order parameters for dichlorobenzene in the same liquid crystal but different sample tubes are < 1.7% (see Table E.15, page 143) using this simple method. 3.3 Mean-Field Models For a mean-field orientational potential C/(fi), where fi denotes the Eulerian angles, solute molecular order parameters S^jjj0 are calculated (by taking the appropriate Boltz-mann averages as the molecule is rotated through all possible orientations) using the equation (which is identical to Eq. 1.3, page 6) where 6az and 8pz are the angles between the molecular a and (3 axes (molecular axis are defined in Fig. 3.10) and the nematic director Z (which for the liquid crystals used in this study lies along the magnetic field direction). i7(fi) can be represented as a sum of two terms U(Q)SR and t/(fi)£s; U(Q,)SR accounts for the short-range repulsive inter-actions and U(Q)ES describes the long-range electrostatic interactions. In the context of ocalc °a/3 — /(3cosflaZ cosflflz - Sap) exp(-J7(fi)/fcT)dfi 2fexp(-U(Q)/kT)d£l (3.18) Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 56 Figure 3.10: Coordinate System for Solutes. Ri refers to either a CH 3 or a Cl constituent. When Ri is a CH 3 , R 2 can either be a CH 3 or a Cl constituent. However when Ri is a Cl, R 2 is also a Cl. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 57 this mean-field model, the potentials can be represented by interactions between solute properties (eg. dipoles, quadrupoles, shape anisotropy) and an average field "felt" by the solute due to the solvent[8,18]. This average field is assumed to be a property of the nematic solvent alone, and not significantly influenced by the solute. Due to the presence of various ordering mechanisms, it is difficult to test directly the concept of a solute independent mean-field. However, by utilizing sets of molecules with similar size and shape, it is either assumed that the short-range orientational potential is the same for each set, or that a model for the potential can be used in order to account for the slight differences in molecular size and shape within each set. In both cases, differences among the ordering within each set of molecules should be dominated by the long-range interactions. The short-range potential U(£1)SR is expressed in one of two forms. In the first form the potential t7(ft)|^  is written as an expansion in spherical harmonics and is truncated at the first non-zero term [18]. The mean orientational potential is then U(n)ss% = -^ ( M a^)(3cos^ Q Z cos^ z -M (3.19) a,0=x,y,z where M is a traceless second rank tensor related to the size and shape of the molecule, and kzz is a parameter that depends only on the liquid-crystal solvent. The shape anisotropy of each set of similar size and shape molecules is represented by oneM tensor. The kzz parameter is related to the degree of orientational ordering of the nematogen. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 58 The second short-range potential U(Q)gR is a phenomenological model based on the CI model [8] of Burnell and co-workers where and kzz is the solvent parameter, C(ft) is the circumference of the projection of the solute at orientation ft onto the plane perpendicular to the director, k and ks are constants, and Z is the position along the nematic director bounded by the minimum, Zmin, and maximum, Zmax, points of the orientation-dependent projection of the solute along this axis. C(Z, ft) is the circumference traced out by the solute at position Z along the director. Thus, C(Z,Q)dZ is the area of an infinitesimally thin ribbon that traces out this circumference, and the integral is the area of the full projection of the surface of the solute parallel to the nematic director. For the first term k(C(Q))2, the liquid crystal can be thought of as an elastic continuum and the solute as a distortion on the liquid crystal solvent. The second term can be thought of as an anisotropic interaction between solute surface elements and the liquid-crystal average field[8]. For the long-range electrostatic potential U(£1)ES, the most important contributions are suspected to arise from molecular quadrupoles, dipoles and polarizabilities. The contribution to the potential of a solute quadrupole with an (EFG) felt by the solute is (3.20) a,P=x,y,z (3.21) Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 59 where €Q is the permittivity constant, FZz is the ZZ component of the (EFG) tensor parallel to the nematic director and Qap is the a.0 component of the solute molecular quadrupole tensor. The (EFG) is a traceless, second-rank tensor and for a nematic phase has only one independent term. The interaction of a molecular dipole Jl with an averaged electric field (E) is — fl- (E). However, due to the apolar nature of nematic phases, the average laboratory frame (E) "felt" by the solute must be zero. Thus, if the above approach for short-range and quadrupole effects is used (where the solute is assumed to "see", on average, a field that is constant in the laboratory frame), the dipole interaction is zero. Nevertheless, a permanent dipole can affect the orientational order of a molecule through the field that the solute dipole induces in the surrounding medium. This induced or reaction field in turn interacts with the instigating dipole. The magnitude of the reaction field depends on the solute dipole (E*> = \ E Yl A*cos0Qr (3.22) T=X,Y,Z a-x,y,z where fj,a is the a component of the solute dipole, A and T are the laboratory fixed X, Y or Z direction, R^r is the AT component of the reaction tensor, and (E\) is the reaction field in the A laboratory fixed direction. The potential is then U(n)™fe = -(47rc 0 ) _ 1 ^ ^(Rzz-Rxx)^coaeaZcos0pZ-6af3) (3.23) a,/3=x,y,z Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 60 where Ryy = Rxx a n a > off diagonal elements of the reaction field tensor are zero. Within the liquid-crystal phase there are fluctuating electric fields which can distort the electronic structure of molecules. The distortion of the electronic structures coupled with these electric fields can effect the orientation of the molecules. The potential for such an interaction is ^ M a r i z a b i l i t y = _ ( 4 ? r e o ) - l l £ aa0(Wz -El)(3 COS9aZ COS 9pZ - 5a0). (3.24) where QLa$ is the af3 component of the molecular polarizability tensor and (Ez — E\) is the difference in the average electric field squared between the Z and X laboratory fixed directions. E\ is equal to E\ and off diagonal elements of this tensor are zero for nematic phases. Molecular dipoles, quadrupoles and polarizabilities were calculated1 with respect to the centre of mass using Gaussian 98[84] with RHFS/6-311+-l-G** (theory/basis set). The values obtained (Table 3.3, page 63) are in accordance with other calculations and experiments [85-87]. 1 Geometry optimized molecular coordinates and electrostatic properties were also calculated using G98[84]. These properties varied by no more than 5% between non-optimized and optimized calculations. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 61 3.4 Analysis and Discussion Intermolecular potential parameters were determined by a series of non-linear least squares minimizations to S^led,s using Eq. 3.18 and the / i Q , Qap and OLap values de-termined from G98. The values of the intermolecular potential parameters from several "fits" are presented in Tables 3.3 and 3.4. When analyzing short-range interactions with the minimization routine, either Eq. 3.19 or Eq. 3.20 was utilized. For the short-range interaction described with Eq. 3.19, MQ|g's and kzz were adjusted, whereas with Eq. 3.20, kZz was adjusted keeping ks and k fixed at 48.0 x 10~9 Jm~2 and 2.04 x 10~9 Jm - 2 . The ks and k values were taken from a previous NMR study of 46 solutes dissolved in the liquid crystal mixture of 55 wt% ZLI 1132/EBBA for which D 2 and HD experience a zero (EFG) [8]. From examination of the RMS errors reported in Table 3.4, the short-range models U(£l)gR (Fit #1) and 11(0,)^ (Fit #2) are approximately equivalent and account for most of the orientational ordering. This is consistent with previous experiments[8,14,18, 88] and computer simulation results[39,76-79,89,90]. As expected, the fits to the long-range interactions alone U(Q)^ole (Fit #3) and [/(fi)^^ 0 1 6 (Fit #4) are significantly poorer. The RMS from the f/(fi)^ a r i z a b i l i 1 y (Fit #5) model is the same order of magnitude as the RMS of the short-range models. However, when the long-range (7(fi)^5 a r i z a b l h t y interaction is coupled with a short-range potential, the RMS is virtually the same as Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 62 for the short-range potential alone, and the potential parameters for the short-range interaction are rendered meaningless (eg. Fit #6): the kzz parameter for EBBA is 0.18 and for ZLI 1132 is 1.81. In the context of the model presented the degree of orientational ordering within EBBA would be 10 times smaller than the degree of ordering within ZLI 1132 for short-range effects alone; this discrepancy is unreasonable. Thus, with the molecules chosen for this study it is difficult to separate the effects of short-range size and shape from long-range polarizability interactions; this is not surprising since to a large extent the anisotropy in the polarizability tensor is related to the anisotropy in the molecular dimensions. From previous studies[88,91] it has also been noted that the effects of size and shape and polarizability could not be separated. Since polarizabilities are expected to make a small contribution to the anisotropic intermolecular potential[6] and since short-range interactions are thought to be very significant, the polarizability interactions will not be utilized further. Short-range interactions which are related to the size and shape of the molecule are an important ordering mechanism; the longer-range interactions are more subtle. From ex-amination of the S%pled,s of acetonitrile and propyne, and of the mono and p-substituted benzenes (Figs. 3.11 and 3.12), dipoles that are collinear with the symmetry axis of the molecule have little or no influence on the orientational ordering of the molecules. The value of U(Q)SR is similar for each set of molecules and for all liquid crystals; thus if U(CI)ES is dominated by a solute dipole interacting with a reaction field there should be a correlation between the solute dipole moments and the S^led,s for a particular set of Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 63 © CO ^ s o -a CO 03 s, >H CH .2 c SH 05 " o Cu 3 O IC? 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Dipole-Induced Ordering in Nematic Liquid Crystals 64 e co S-i CD CD a SH tf PH " t f 4 J CO SH o 3 cr T f CO •CD SH O • SH fa GO CD 4 J o CD fa S i tf cr & ^ tf TJ CD "OJ • ^ G CD ST1 o fa tf *H CD r>5 bO ^ £ "O CD CD > o It, 1 s 3^ | CD • — bO fa IN! tf (S) t> — (-1 CD CD «8 3 -« t-i <tf fa I S-l CO SH u • i-H cr CD SH 4 J X L O CN T f CO CO L O T f to co o o o O O O o o o O O © o o o o d d fa < m m CM CO i-H CN 1 — 1 CO v o s ^  < 3 L O m CS! L O fa *<-. o o o o d d o o o o o o o o o o d d 00 L O co co cd t>- CO M CN r l o co co CN >—I i—I o o o o d d o o o o d d O O) s w ^ CO CO L O co oi co CM i — I T—I o o o o d d o o o o d d co co o o d d ^ co co Oi L O L O t d N CO C71 N N O O O o d d o © © o d d < PQ pq fa CN co < pq pq fa CN CO < m pq fa CN CO CN co & pq L O CQ L O fa fa T f < pq J L O CQ X N io H fa L O < pq pq NI L O a fa < pq pq fa CN CO i—I CN 1 — 1 CO v o 3 ^ < M £ CQ 3 L O m N L O fa to co 0 3 i > 52 1 ffi ^ ^ T f 92 ^ co " ^ ^ o o o o d d •*-. •*-. o o o o d d T F T f eo" co" " L O " O cn O © O o © © T f cn O O O ^ d d d d o O o O O o o o o d L O CO CO CO d d d d d d d d d H T—5 CN O i CM O i O i CO 1—5 d i—1 d d 1—H L O T f CO CO fa < pq pq fa CN CO i—l CM r _ l co S ^ < & CQ J L O CQ CS] L O fa Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals o LO o o o o d d •*-. •<-. o o o o d d o ; ic ^ d d d o o oq N W CN LO Tf . O ) . O O O O C O T-H Q O C N O i < PQ PQ fa C M co fa C M CO Tf C O *-> **-> 0 0 0 o d d 0 0 0 o d d CO CM <=> ~ o . OS O O O o ~—' Tf r-H CO CM O O T-H PQ ^ LO ffl •S LO fa fa HH5 is «< CQ CQ fa CM co T-H CM T — l 2 ^ <J K H is PQ N LO H 00 0 0 0 o d d o T o T o T 00" 00S o T d ^ d _ d d d d LO co 0 LO CO CO d d 06 1 T-H 0 0 0 o d d CM o CM CM CM 0 o C O O i 01 O i d d < PQ PQ fa CM CO O i 2 b < _ is CQ 13 LO m N LO H SH 3 o3 -O cu CG • i-H 13 • i-H 3 CU HH5 O a coco T^ CU xi 00 =tt= 3 «3 I> co" 3 co cu LO co CM * T-T CO +3 • I—1 fa SH 1 - O a 3 o CJ . "0 CO o H a d O l t l s g CXcoO O cu ^  — S3 cu D 2 s X X £ •-! co >—1 co ,,. 1 a 3 03 HHJ SH o a --a CJ 3 - o o SH OH CU HJ 3 CO o3 cu CO SH 03 LO SH T -H CU SH «3 O G § Xi O IM 'a a w S O b CD g 3 8 8 o o 2 « CO rr- ."tin < .t3 D a fa -a •p -p '6 o ? > .—I -H o o T-H T-H <+H <+H o o co co • i-H -i-H J cu SH o 22 tin 3 -5" cu s3 H-> SH H-= ° 9 C H Cl £ CO ^ 03 .22 iS SH CU CU H O 2 -03 is EH 3 cu SH 3 -O + i CU X a is SH O SH SH CU CU o a CO 03 S 03 Cti fa 3cu CO cu SH OH CU SH LO 03 LO CO CD CU H3 d 4 3 3 s > H-H U Co Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 66 molecules. However, the S^led,s of p-chlorotoluene (dipole moment of 7.17 x 1 0 - 3 0 Cm) are intermediate between those of p-xylene and p-dichlorobenzene (dipole moment = 0) (Fig. 3.11). Chlorobenzene and toluene have very similar order parameters (Fig. 3.11) but very different molecular dipole moments (Table 3.3). The 5 z s f ' e d ' s of propyne, a molecule with a small dipole, decreases significantly between ZLI 1132 and E B B A whereas the S^led,s of acetonitrile, a molecule with a large dipole, remains virtually unchanged (Fig. 3.12; Table 3.3). If dipoles were important then it would be expected that the gscaiedis 0 f a c e ton i t r i l e would change significantly and the S^led:s of propyne would remain virtually unchanged. For the molecules with dipoles along a symmetry axis there is no correlation be-tween order parameters and dipoles. This simple observation is also evident for the sets of molecules which have dipoles along the molecular z and x axes. The m- and o-chlorotoluenes have dipole components along the z and x axis directions. The m- and odichlorobenzenes and xylenes have dipole components along the z axis direction only. If dipoles were important to the orientational potential, the Ss^led values (particularly the S*cxaled,s of the chlorotoluenes) should be substantially different from those of the dichlorobenzenes and xylenes. However, as is the case for the p-disubstituted molecules, the diagonal order parameters of the chlorotoluenes are intermediate (except for the ^scaled Q f o-chlorotoluene in E B B A ) to those of the dichlorobenzenes and the xylenes (Figs. 3.13 and 3.14; Table 3.3). The conclusion that dipoles have little or no effect on the orientation of solutes is also evident by examination of Table 3.4; the RMS error Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 67 Figure 3.11: S^led,s (values taken from Table E.15, page 143) for p- and mono substi-tuted benzenes are represented by A and correspond with the axis labeling in Fig. 3.10. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 68 -0.1 p •0.15 T -0.2 "r •0.25 fc\ -0.3 -0.35 I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 J — trichlorobenzene _L i i i i i i i i | i i i | i i i J 0.25 acetonitrile : - 0.2 i i i i _L 20 40 60 80 wt% EBBA 100 20 40 60 80 1o8 wt% EBBA Figure 3.12: Experimental order parameters for 1,3,5-trichlorobenzene in samples con-taining p-dichlorobenzene and p-xylene, and S^led,s (values taken from Table E.15, page 143) for acetonitrile and propyne are represented by • and correspond with the axis labeling in Fig. 3.10. of Fit #7, which includes the U(Q)1% and [/(Q)^|ole interactions, and Fit #1, which includes only t/(£2)f|[, are identical. The (Rzz — Rxx) is zero within the calculated errors. Thus, within the context of this theory, dipoles are of minimal importance in the anisotropic part of the electrostatic potential and have no influence on solute ordering. When the Vr(STj££adrupole interaction is included with one of the short-range potentials the RMS significantly decreases compared to the RMS of the short-range interactions alone (in Fig. 3.15 compare A l , 2 and 3 to B l , 2 and 3 and in Table 3.4 compare Fits #8 and #9 to #1 and #2). This is not surprising since quadrupole interactions are known to be important to the orientational potential. The S%pc values for Fits #8 and #9 are presented in Table E.15, page 143. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 69 Figure 3.13: S^fled,s (values taken from Table E.15, page 143) for o- and nvdisubstituted benzenes are represented by A and correspond with the axis labeling in Fig. 3.10. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 70 0.1 0.05 -0.05 1 I 1 1 1 I 1 1 1 I ' 1 ' I 1 1 1 m— dichlorobenzene m— chlorotoluene m —xylene ± _L 20 40 60 80 wt% EBBA 100 I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 'J0.1 o—dichlorobenzene o—chlorotoluene o-xylene • • • • • _L I i i i I • • • 0.05 to 20 40 60 80 wt% EBBA 100 -0.05 Figure 3.14: S£f icd's (values taken from Table E.15, page 143) for o- and m-disubstituted benzenes are represented by A and correspond with the axis labeling in Fig. 3.10. The calculated Fzz& change sign between ZLI 1132 and EBBA. This is most evi-dent from the S^led,s of the p- and m-disubstituted benzenes, and propyne and ace-tonitrile (Figs. 3.11, 3.12 and 3.13). For the -^substituted benzenes in ZLI 1132 the trend of Szz^led is: Szz(xylene) > Szz(chlorotoluene) > Szz(dichlorobenzene). For the m-disubstituted benzenes the trend of the Szzaled is: Szz (xylene) < Szz (chlorotoluene) < Szz(dichlorobenzene), and for propyne and acetonitrile the trend of the Szzaled is: Szz(propyne) > Szz(acetonitrile). However, in EBBA these trends are reversed. Since U(Q)SR is similar for the individual sets of molecules there must be a change in sign of C/(ft)^adrupole between ZLI 1132 and EBBA. The 55 wt% ZLI 1132/EBBA mixture is where [/(ft)^adrupole happens to be » 0. The change in sign of f/(n)g^drupole is due to Fzz changing sign. The trend in the observed order parameters is most evident with these molecules because there is a relatively large difference among their QZZ values. The Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 71 ZLI 1132 _ i TT' | 1 ' I ' I I -0.1 A1 -1 o CO -1 A A A 0 4 a ft -I! CO _ --0.1 — — - i D Q D > l l h 3.75; A - 2.76 i I i i i i i i i I i-ZLI1132/EBBA i i i I i i i I i i i I i i i I i. r_ A2 1 *B A -m 6—r BUS: • - 0.58; A - 0.91 •I I I I I I I I I I I I I I I I I ' U A3 EBBA I I | I I I | I I I | I I I | dh & 1 RHS: • - 3 .32; A - 3.54 i i i I i i i I i i i I i i i I i-0.1 h co CO -0.1 .1 1 1 I . 1 | 1 1 1 | 1 1 1 | - B1 -8 4 6 * - 1 _ - • -- RHS: • = 1.82; A s 1.39 -• • 1 i • 1 • , • 1 i • • 1 J : B2 I H A RHS: Q = 0.54; A s 031 11 i i I i i i I t i i I i i i I IT ri j i I I I - B3 — A * ^ A : s u a -- RMS: • = -1 1 1 1 1 2.10; A H 2.69 i 1 i i i 1 i i i 1 i-0.1 h CO CO -0.1 1 1 1 I 1 1 ' I 1 1 1 I 1 ' 1 I ' C1 (- RHS: • - 1JS8; A - 0.91 i i I i i i I i i i I i i i I i -0.4 -0.2 0 0.2 0.4 gsealed 1 1 I 1 1 1 I 1 1 1 I C2 RHS: • - 0.48; A - 0.82 • • • I • • • I • • • I • • • I •-! -0.4 -0.2 0 0.2 0.4 Cj scaled I 1 1 1 I I I I I I C3 • A h RUB: • - 138; A - 2.23 i i I . . . I i i . I . . . I -0.4 -0.2 0 0.2 0.4 gsealed Figure 3.15: Sscaled,s minus S^'s results (values are taken from Table E.15, page 143) are plotted against Sscaled,s. The principal (largest absolute diagonal value) order parameter element is represented. Note that the vertical scale is expanded by three compared to the horizontal scale. Series A is the results from Fit #1 (•) and Fit #2 (A) and series B is the results from Fit #8 (•) and Fit #9 (A). Series C is the results from the fits where by the parameters of Fit #8 (•) and Fit #9 (A) were fixed and the origin of the quadrupole tensor was allowed to vary. RMS errors (xlO - 2 ) between Sscaled,s and 5ca'c's are reported within the graphs. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 72 difference among Q22's for the ortho and mono substituted benzenes is smaller and thus the trend is not as evident. In all cases (including the Sszczaled of o-chlorotoluene in EBBA) the trends are consistent with the signs of the molecular quadrupoles. For the 55 wt% ZLI 1132/EBBA mixture, the Fzz's determined from D 2 and HD studies were « 0. Within the reported error of our calculated values, the Fzz's in the 55 wt% ZLI 1132/EBBA mixture is also « 0 (Table 3.4). The value of the FZz can be rationalized by examining the 5^a'ed's; since the molecules of similar size and shape, have similar Ssafed in the 55 wt% ZLI 1132/EBBA mixture (Figs. 3.11, 3.12, 3.13 and 3.14), all long-range electrostatic contributions (not only the FZz) to the potential are essentially zero. Only short-range interactions are important in the 55 wt% ZLI 1132/EBBA mixture. The Fzz's determined from D 2 and HD studies were «s 6.11, « 0.0 and « -6.41 x 1011 esu (18.44, 0.0 and -19.16 x 1017 volt-m-2)[20] for ZLI 1132, 55 wt% ZLI 1132/EBBA and EBBA. In this study the calculated F z z ' s are « 7.0, « 0.8, and -7.7x 1017 volt-m~2. The discrepancy between the calculated Fzz's of D 2/HD and the much larger molecules in this study may have several causes, including: the approximations involved with the G98 calculations of molecular quadrupole tensors; the differences in sample conditions between the D 2/HD and the present experiments; or the assumption that the (EFG) is a property of only the liquid crystal. Our calculated Fzz's presented above are from a global fit to all the molecules. In an attempt to minimize the inadequacies of the short-range potentials, to minimize the Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 73 ambiguities with the scaling of the experimental Sap, and to test the concept of a solute-independent Fzz, individual FZz values were determined for each set of similar size and shape molecules (Fig. 3.16). Regardless of the size, shape or electrostatic properties of these solutes, all calculated Fzz's for a specific liquid crystal have the same sign and have approximately the same magnitude. The calculated values of the Fzz* in ZLI 1132 and EBBA are the same sign but smaller in magnitude than the FZz's determined from the D 2 / H D experiments. Both theory[16] and computer simulations[39] predict that the Fzz's are very sensitive to solute molecular properties. In fact, from computer simula-tions, the FZz for a particular liquid crystal changes sign depending on the size, shape and quadrupole moment of the solute particle (see Chapter 4). While the experimental Fzz* do depend on solute molecular properties, this discrepancy is far less than that predicted by either computer simulations or the theory. The rationalization of these different dependencies represents an interesting problem to both theory and computer simulations. In the case of the m-chlorotoluene, the trend in the S™lc,s is incorrectly predicted (Table E.15, page 143). Also, from examination of Fig. 3.15, Al , 2 and 3, and Bl, 2 and 3, the inclusion of the [/(ft)^™1™1 6 interaction decreases the difference among Sscaled,s and Sca'c's for the liquid crystal ZLI 1132 more than for EBBA. Also the difference is much smaller for the 55 wt% ZLI 1132/EBBA mixture then for the component liquid crystals. It is interesting to ask: to what extent are the disparities due to inaccuracies with the calculation of the quadrupole tensor? For molecules that possess a molecular Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 74 Figure 3.16: Graph (A) is the individually and globally determined field gradients for the molecules in this study from least-squares fits using Eq. 3.20 coupled with Eq. 3.21. Graph (B) is the field gradients from least-squares fits using Eq. 3.19 coupled with Eq. 3.21. Regardless of the size, shape or electrostatic properties of the solute, all calculated field gradients (units of 1017 volt m - 2) for the same liquid crystal are the same sign and roughly similar in magnitude. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 75 dipole, one simple method to help compensate for these inaccuracies is to adjust the origin at which the quadrupole is calculated (the value of the first non-zero multipole is origin independent). The center of mass has been chosen as the origin but this may not be an appropriate choice. The origin dependence of the new quadrupole component Q'a/3 for a neutral molecule is Q'a0 = Qap + 3/2(/iaA/J + Hf)&a) - (/xA)5Q/3 (3.25) where QQ/? is the original quadrupole component, ft is the dipole and A is the difference in distance between the original origin and the new origin. Another series of least-squares minimizations was performed whereby the short-range parameters and the Fzz& were fixed to the values determined from Fit #8 and the origin of the quadrupole was adjusted in the z direction (Table 3.5 and Figure 3.15 Cl, 2 and 3). The adjustments in the z direction reported in Table 3.5 seem unreasonably large. However, the quadrupole tensor components of the molecules are still within reasonable values; the magnitudes and not the signs of most of the quadrupole components were altered. The Qzz values of acetonitrile and p-chlorotoluene, and the Qxz value of m-chlorotoluene, did change sign. Since acetonitrile has a large dipole moment, the choice of origin is particularly impor-tant, and only a slight shift of the origin is required to change the sign of the quadrupole component. With the origin shift, the difference between the Szzaled,s and Szzlc's is smaller. However, the difference between the quadrupole components is not significant Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 76 Table 3.5: Adjusted Molecular Parameters" Solute Qzz Quadrupole Component6 Qxx Qyy Qxz Adjustment0 in z axis origin A 2 acetonitrile propyne 0.356 3.727 -0.178 -1.863 -0.178 -1.863 0.000 0.000 0.41 (0.13) 2.74 (0.59) chlorobenzene toluene 0.719 0.709 1.979 1.503 -2.698 -2.212 0.000 0.000 -0.24 (0.31) -2.52 (1.18) p-dichlorobenzene p-chlorotoluene p-xylene -2.301 -1.013 1.826 3.681 2.662 0.792 -1.379 -1.649 -2.619 0.000 0.000 0.000 0.0d -1.01 (0.25) 0.0d o-dichlorobenzene o-chlorotoluene o-xylene 0.736 0.957 0.547 1.372 1.376 1.459 -2.108 -2.333 -2.006 0.000 -1.196 0.000 0.59 (0.22) 0.18 (0.4.3) -1.45 (0.74) m-dichlorobenzene m-chlorotoluene m-xylene 2.335 2.209 2.130 -0.819 0.480 0.967 -1.516 -2.689 -3.097 0.000 0.588 0.000 0.61 (0.36) -1.70 (0.38) 3.45 (1.21) 1,3,5-trichlorobenzene 0.492 0.492 -0.974 0.000 0.0d a For axis definitions see Fig. A.22. Fit performed by fixing the parameters from Fit #8 and adjusting the origin of the quadrupole in the z direction. RMS error is 1.23 x 10-2. 6 Units of IO - 3 9 coulomb-m2. c Units of A. c Quadrupole components are origin independent. Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 77 enough to suggest an inconsistency with the current theory or to suggest a poor G98 calculation. For p-chlorotoluene it is expected that the value of Qzz be between the value of the Qzz components of p-dichlorobenzene and p-xylene. The original Qzz value, as well as the Q'zz value, is in-between the Qzz values of p-dichlorobenzene and p-xylene. Thus it is difficult to discount the sign change in the adjusted Qzz. It could be due to the difficulty in calculating the electronic charge density around a chlorine constituent. With a positive Q'xz for m-chlorotoluene, the trend in S^.fc is correctly predicted. However, since there is a large negative charge distribution around the chlorine, the Qxz is expected to be negative (as was calculated by G98). It is difficult to suggest, within the context of the current mean-field model, an interaction which could account for the trend in Slczled of m-chlorotoluene and correctly predict the trend for all other order parameters. It is noted that the values of the Sxzaled,s are small and, even with the somewhat crude mean-field model, the trends with all other order parameters are correctly predicted. For the fit in EBBA the difference between the Sscaled,s and Scalc,s slightly decreases. However, the fit is still somewhat poorer than the fit in ZLI 1132. For the 55 wt% mixture all long-range interactions are minimal and the F'zz's are almost zero; thus the adjustment of the quadrupole tensor has a small effect on the RMS error. For the component liquid crystals, there may be other interactions (other than dipole, quadrupole or polarizability) which are important. It is also possible that this mean-field model is Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 78 too crude and that individual molecules (not just individual sets) experience slightly different average environments. Nevertheless, the quadrupole interactions are important for the long-range potential. 3.5 Conclusions Short-range interactions account for most of the solute orientational ordering in l iquid crystalline solvents. The relative importance of various electrostatic interactions on or-der parameters is demonstrated by using solute molecules of similar sizes and shapes. W i t h i n the reported errors the reaction field anisotropy (Rzz — Rxx) is zero and thus for these molecules interactions involving the solute dipole moment have litt le influence on ordering. In addition, the effects between polarizabili ty anisotropy and short-range in-teractions cannot be distinguished. However, it is expected that polarizabili ty anisotropy interactions are minor. Trends among experimental order parameters (except for the very small ' e d ' s of m-chlorotoluene) are consistent wi th a short-range interaction coupled wi th a quadru-pole/ (EFG) interaction. The trend for the Ssxzaled of m-chlorotoluene is correctly pre-dicted when the origin of the quadrupole is shifted which may suggest that for a dense system the center of mass is not an appropriate choice for the origin. The sign of Fzz$ in al l l iquid crystals is in accordance wi th previous results from D 2 and H D experiments. However, since values of Fzz change by approximately a factor of two between the very small solute D 2 and the larger benzene derivatives, the assumption that a l l solutes feel Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals 79 essentially the same average environment may not be completely valid. Nevertheless, the signs and relative magnitudes of all the Fzz's calculated for the larger molecules are consistent among the various sets of similar size and shape molecules; at least the larger molecules seem to experience similar average environments. This study presents the analysis of a self consistent set of order parameters and is one of a small number of studies that provide an estimate of the sign and magnitude of the (EFG). It has been demonstrated that the average electric field gradient (EFGYs felt by solutes in the 55 wt% ZLI 1132/EBBA mixture are « 0. Not only are the (EFG)-quadrupole interactions « 0 in this special mixture, but other long-range interactions appear to be negligible as well. Chapter 4 Intermolecular Potentials in Liquid Crystals: Comparison Between Simulations and N M R Experiments The material presented in this chapter has been published in Ref. [76]. 4.1 Introduction Current thinking is that short-range interactions dominate the anisotropic intermolecu-lar potential which is responsible for the partial orientational order in liquid crystalline phases. However, it is recognized that longer-range electrostatic interactions are also important. These long-range interactions are often expressed in terms of molecular elec-trostatic multipoles and polarizabilities. An important means of learning about the intermolecular potential is to compare results obtained from real experiments with those predicted by theories, models or sim-ulations. In this chapter second-rank orientational order parameters obtained by NMR experiments on small probe molecules dissolved in nematic liquid crystalline phases are compared with those obtained from Monte Carlo (MC) simulations. Results for two particular sets of experiments are utilized. 80 Chapter 4. Comparative Study Between MC and NMR Experiments 81 The first set of experiments involves published work on a series of 46 solutes which was studied in a special mixture of nematic liquid crystals for which the nuclei of the so-lute dihydrogen are known to experience a zero average electric field gradient {EFG)[8\. In this special mixture experimental results for other solutes such as methane [92] and substituted aromatics[18,19,40,41] (Chapter 3) have been interpreted to mean that these molecules also experience a zero (EFG); the orientational ordering is purported to arise mainly from short-range repulsive forces[8, 26,46]. The NMR results are compared with MC simulations of hard ellipsoids. The comparison is performed with the aid of phe-nomenological models for short-range interactions. The second set of NMR experiments (results taken from Chapter 3) was designed to probe long-range electrostatic interactions by using molecules of essentially the same size and shape but different electrostatic multipole moments as solutes in several different nematic liquid crystal solvents. It was concluded that permanent molecular dipoles have a negligible effect on solute orientational order, while order parameters obtained for solutes in the various liquid crystal solvents are consistent with an anisotropic interaction that involves the solute molecular quadrupole. In order to make comparisons, MC simulations with point quadrupoles placed at the centre of hard ellipsoids are employed (results taken from Ref. [39]). Chapter 4. Comparative Study Between MC and NMR Experiments 82 4.2 Experiments for which short-range interactions are thought to dominate the intermolecular potential Dideuterium experiences a zero (EFG) in the nematic liquid crystal mixture of 55 wt% ZLI 1132/EBBA. This has been taken as evidence that long-range electrostatic interac-tions can be neglected in this special mixture [8]. The second-rank orientational order parameters SQp obtained from NMR measurements for a series of 46 solutes dissolved in this mixture have been fit previously to several phenomenological models for a short-range interaction[46]. In one of these, model C[26], the solute exerts an elastic distortion on the liquid crystal solvent, where C(Q) is the circumference of the projection of the solute at orientation Q, (which refers to the polar angles 9,4>) onto the plane perpendicular to the director, and k is a (Hooke's law) constant. Model I [46] is one of several basically equivalent [88] models which assume that the anisotropic intermolecular potential can be written in terms of an anisotropic interaction between solute surface elements and the liquid crystal average field [46,47]. The potential used for model I is where Z is the position along the nematic director bounded by the minimum, Zmin, and U(Q) = \k(C(Q))2 (4.26) (4.27) Chapter 4. Comparative Study Between MC and NMR Experiments 83 maximum, Zmax, points of the orientation-dependent projection of the solute along this axis. C(Z, Q) is the circumference traced out by the solute at this position along the director. Thus, C(Z, Vt)dZ is the area of an infinitesimally thin ribbon that traces out this circumference, and the integral is the area of the full projection of the surface of the solute parallel to the nematic director. A third model, model CI (described in Chapter 3, Eq. 3.20, page 58), is a two-parameter model formed by combining Eqs. 4.26 and 4.27. The reasonable fits obtained for these three models (see below) were taken as an indication that in this special liquid-crystal mixture the anisotropic intermolecular potential is dominated by short-range repulsive terms that depend on the solute size and shape. The same models C, I and CI are used to fit order parameters from MC simulations of hard cylindrically symmetric ellipsoidal solutes of various dimensions and aspect ratios in a collection of 95 or 239 hard cylindrically symmetric ellipsoidal solvent particles of aspect ratio 5:1 (Fig. 4.17). The simulations for single prolate solutes in 95 solvent particles have been presented previously[13], while the simulations for oblate ellipsoids in 239 solvent particles are new for this study; the simulation program that was utilized for this study is described in Ref. [13]. Constant-volume simulations were performed using a reduced density p*=Ni>0/V=0.488, where N is the number of particles confined to the cell, v0 is the volume of a solvent ellipsoid, and V is the volume of the cell. Particles were randomly chosen for an attempted repositioning, which consisted of a simultaneous translation and rotation, the maximum magnitudes of which were chosen so that the translation and Chapter 4. Comparative Study Between MC and NMR Experiments 84 rotation would contribute about equally to the likelihood that the new position would be rejected. Solute orientational order was monitored by measuring the second-rank order parameter Szz — (P2(cos6)), where 6 is angle between the solute symmetry axis and the nematic director. Models C and I both involve a single adjustable parameter, and both fit the MC results reasonably well (short dash (C) and dotted (I) curves in Fig. 4.17). However, the difference between fit and simulation is consistently in opposite directions for the two models. Thus, it is not surprising that the two-parameter CI model provides a particularly good fit (solid curves in Fig. 4.17). The value 38.1 obtained for the ratio of the two parameters ^  compares with the value 23.5 realized from fitting experimental Sap from NMR experiments[46]. More important, when this ratio is fixed to the NMR value of 23.5, the agreement between model and simulation (long dashed curves in Fig. 4.17) is essentially equivalent to that found when the two parameters are adjusted independently (solid curves in Fig. 4.17). In order to investigate to what extent the same phenomenological models rationalize both NMR and MC results, we compare in Fig. 4.18 the difference between SQpS recalcu-lated from the fits to the three models and the experimental values. Circles are used for principal (largest absolute value) solute Sap's determined by NMR measurements, and filled squares are used for the MC values. The fits of the models to both the NMR and MC results show quite similar trends. Model C (Fig. 4.18a) tends to overestimate the orientational order of more asymmetric Chapter 4. Comparative Study Between MC and NMR Experiments 85 co 0.5 h Oh -0.5 ~i—i—i—i—i—i—i—i—i—r . . o 0 U V J I I I I I I I CO CO oh -0.5 h - | — i — i — i — | — i — i — i — | — i — r w=1.25 h loooO J I L 1 J L 1 0 2 4 length i — i — i — i — i — i — i — I — i — r 7 w=0.5 o 0 oO J i i_ J I L J L i — i — i — i — i — i — i — i — i — r 7 w=1.0 -I h - o O O O J I L 1 J I L 0 2 4 length M o d e l C M o d e l I - C o m b i n e d CI — C o m b i n e d CI w i t h k / k f i x e d Figure 4.17: Solute order parameters S's versus solute length from MC simulations (•) for various width (w, indicated within the graph) and length particles. Solute shapes are represented at the bottom of the graph; they are not directly in line with their corresponding points. The liquid-crystal is represented by the shaded particle. The model used for each fitted curve is indicated at the bottom right. Chapter 4. Comparative Study Between MC and NMR Experiments 86 0 4 ( c ) 0.1 m I 3 0 -0.1 -o.2 r-~\—i—I—i—i—i—r t _ i i i i i i i i • i . -0.5 0 0.5 S r ( b ) ~ l — I — I — I — I — I — I — I — I — I — I — I — I — r q • • _ • • t _ l I I I I I I I I I I I I l_ Figure 4.18: The 5calc's from fits to various models minus S's from NMR[46] (O) or MC (•) results are plotted against S's. The principal (largest absolute diagonal value) Sap element is used for the NMR results. Note that the vertical scale is expanded by three compared to the horizontal scale. Graph (a) is a fit from Model C, graph (b) from Model I, graph (c) from the combination CI model adjusting both k and ks, and graph (d) is a fit where the ratio of y for the MC results is fixed to the value 23.5 obtained from the fit to the NMR data. Chapter 4. Comparative Study Between MC and NMR Experiments 87 solutes (i.e. those with the most positive or most negative Sap), while model I (Fig. 4.18b) tends to do the opposite. Combining both potentials in a two-parameter fitting (model CI, Figs. 4.18c and d) produces an excellent fit to both NMR and MC results. As was the case with Fig. 4.17, the two-parameter fit of the MC simulation results (Fig. 4.18c) is only marginally better than the one-parameter fit (Fig. 4.18d) with the ratio y fixed to the NMR value 23.5. The similar trends found for fits to both NMR and MC results is an indication that the same anisotropic intermolecular potential applies in both cases. This is further evi-dence that in the special 55 wt% ZLI 1132/EBBA liquid-crystal mixture the anisotropic intermolecular potential is dominated by short-range forces that depend on molecular size and shape. While the C and I models were developed with specific physical interactions in mind (an elastic distortion of the nematic solvent and an anisotropic surface interaction), they are also phenomenological descriptions of the anisotropic potential. The C and I models were based on an elastic continuum model. As the molecule reorients the continuum exerts an elastic restoring force on the molecule. The MC calculations involve only excluded volume effects, and hence the intuitive picture of the C and I models do not necessarily apply in this case. Nevertheless, the fact that the combination CI model does such and excellent job in fitting both NMR data for solutes in the special liquid crystal mixture and MC simulations of hard ellipsoidal particles is strong evidence that in both cases the anisotropic intermolecular potential is dominated by short-range repulsive Chapter 4. Comparative Study Between MC and NMR Experiments 88 forces. It must be noted that attempts to generalize this notion to arbitrary nematic phases are fraught with difficulty. A most dramatic example is the negative S^'s found for both acetylene[24,25] and hydrogen[93] in EBBA. To emphasize the difficulty, we plot in Fig. 4.19 the relative difference between experimental and fitted S^c,s for least squares fits to the CI model. Fig. 4.19a gives the results presented before in Fig. 4.18d (for the 55 wt% ZLI 1132/EBBA mixture and the MC hard ellipsoids). Most relative differences are less than 20%. Fig. 4.19b gives the fit obtained for a collection of solutes in EBBA[91]. Huge relative differences (the largest being -225% for acetylene, 127% for iodomethane and 88% for propyne) are noted, especially for solutes with small S^'s (such solutes do not in general have a large shape anisotropy). These results are completely contrary to the notion that short-range repulsive interactions alone determine the solute orientational behavior. 4.3 Experiments for which long-range electrostatic interactions are thought to contribute significantly to orientational ordering The previous section focused on the effects of short-range interactions on solute ordering. The MC simulations only incorporated hard-body interactions and the experimental solute SQ/3's were determined using a liquid crystal for which all long-range interactions seem to be minimized. However, for most liquid crystals long-range interactions are not negligible. Chapter 4. Comparative Study Between MC and NMR Experiments 89 1 -0.5 Figure 4.19: Relative difference between calculated and experimental solute principal Sa/g's; AS = Scalc—S. (a) is a different representation of the results presented in Fig. 4.18d. (b) is a fit of the two-parameter CI model to Sa^s from NMR experiments of solutes in the nematic liquid crystal EBBA[91]; the fitting parameters obtained are k — 2.4 ± 1.0 dyne cm - 1 and ^ = 11 ± 9. Chapter 4. Comparative Study Between MC and NMR Experiments 90 Quadrupole interactions are commonly utilized in the description of the orientational potential[8]. From the NMR experiments of D 2 and HD, the value of the (EFG) in ZLI 1132 was determined to be positive whereas in EBBA it was negative. If as assumed in the previous section all solutes experience essentially the same average environment, the negative Szz's found for acetylene and dihydrogen dissolved in EBBA can be easily rationalized by the interaction between the positive solute quadrupole and the negative (EFG) in EBBA[20]. However, Emsley et al. have developed a theoretical model for describing the orientational ordering of solutes in a uniaxial nematic solvent and con-cluded that the (EFG) should in fact be dependent on the solvent as well as the solute quadrupole [7] (discussed in Chapters 1 and 3). In this section we compare (EFGYs determined from previous MC simulations[39] and NMR experiments (from Chapters 2 and 3) to test the assumption that all solutes experi-ence the same average environment. The MC simulations[39] employed hard-body inter-actions together with point quadrupoles at the center of the particles. Only quadrupoles were used because the quadrupole moment is the lowest order electrostatic multipole moment that the theory by Emsley et al. predicts to contribute to a non-vanishing Fzz-Nematogens were modeled as axially symmetric hard ellipsoids with an aspect ratio of 5:1 and with a fixed value of the reduced quadrupole moment Q*zznem^ = — \/2T5. Solutes were modeled as axially symmetric hard ellipsoids with varying lengths and quadrupole moments. The (EFGYs were determined at the center of the solute using Chapter 4. Comparative Study Between MC and NMR Experiments 91 Fr A = V R £ A = -VRVA</> = -g [ - 2 C # A + 2^ 1 0 < 3TA r r r r + 10Qrr r r r A T=x,y,z r=x.y,z + £ 5QSm)^r*o-rA - £ 35QSm)^r$rr A], (4.28) where f is a unit vector describing the orientation of the displacement between the quadrupole pair, and QrvT™^ is the solvent quadrupole moment in the laboratory frame. The dimensionless F*zz is then defined as \Qzz I From the NMR experiments, the Fzz's were determined from a combination of the potentials presented in Eqs. 3.20 (page 58) and 3.21 (page 58) (Fig. 4.20; the FZz's for acetonitrile and propyne are not displayed); k and ks (the ratio of f^- was fixed to the value from previous studies [46]) and Fzz$ were determined by a least-squares fit to the non-vibrationally corrected S^s presented in Table D.13, page 137. Note, Fig. 3.16 (page 74) presents results from fits to the vibrationally corrected SQ/j's. In Fig. 4.20a the Tzz's calculated from the fits to Eqs. 3.20 (page 58) and 3.21 (page 58), and the Fzz§ determined from D 2 experiments[21], are shown. The signs of the calculated Fzz's are the same as those determined from the deuterium experiments. However, the magnitudes in ZLI 1132 and EBBA are approximately 1/3 the magnitudes determined from D 2. Nevertheless, the approximately zero value for Fzz$ in the special 55 wt% ZLI 1132/EBBA mixture is predicted by both the D 2 and the substituted benzene results. The size, shape and electrostatic properties of the solute seem to have a small effect on Chapter 4. Comparative Study Between MC and NMR Experiments 92 the magnitude, but have no effect on the sign of the F zz's In Fig. 4.20b we show the Fzz,s determined from the MC simulations. The F zzs for a given solute ellipsoid is very dependent on its quadrupole moment and also on its size and shape. Thus, in agreement with Emsley et al.[7], the solutes in MC simulations do not seem to experience the same average environment. In the case of non-spherical solutes, the (EFG) experiences a concomitant change in sign with the solute quadrupole moment. This result is in sharp contradiction with the experimental NMR results for which it was found that the S%jjc,s of several molecules conform to the mean-field model where the solutes interact with an (EFG) which, at the very least, has the same sign. To emphasize this point the relative differences be-tween calculated and experimental NMR or MC order parameters are shown in Fig. 4.21. Most of the predicted S%pc,s from the NMR studies are within 20% of the experimentally determined 5Q|g's whereas most of the predicted order parameters from the MC simu-lations are > 20%. The origin of the discrepancy between NMR experiments and MC simulations is very likely the inadequacy of using point quadrupoles for dense systems for which the convergence of the multipole expansion at short distances becomes an impor-tant consideration. Thus, an improved description of molecular electrostatic interactions will likely be essential in order to generate solute orientational behavior consistent with that observed experimentally. It is most likely that small, almost spherical solutes are the best choice for investigating long-range interactions since the influence of size and shape on their Saps is Lilliputian. Chapter 4. Comparative Study Between MC and NMR Experiments 93 Figure 4.20: Graph (a) is field gradients F z z ' s (in units of 1017 volt m - 2) for dideu-terium[20] and for the substituted benzenes from least-squares fits to SQpS obtained from NMR experiments. Regardless of the size, shape or electrostatic properties of the solute, all determined Fzz§ for the same liquid crystal are the same sign and roughly similar in magnitude. Graph (b) is Fzzs taken from MC simulations for various shape solute particles with various point quadrupole moments [39]. The solute ellipsoid dimen-sions are: A 0.65:1; • 1:1; and • 2:1. The quadrupole of the nematogen Q z i n e m ^ was fixed at — \/2T5. Note that this graph represents one liquid crystal mixture and thus all the points in this figure can be compared with the points in (a) for either 0% or 100% EBBA. For these MC simulations, the Fzz is not a solute independent property, which is contrary to the experimental NMR results of graph (a). Chapter 4. Comparative Study Between MC and NMR Experiments 94 1 1 | 1 1 1 1 | 1 1 1 1 | 1 1 0.5 • • • CO — CO 0 — < -- 0 . 5 1 1 • • • — 1 I l l l 1 I I I I 1 I l - 0 . 5 0 0.5 Figure 4.21: Relative difference between calculated and NMR (A = solutes in ZLI 1132 and • = solutes in EBBA) or MC (•) order parameters; AS = S c a l c - S. S$c's for both the NMR and MC results are calculated from a global fit to all solutes in a particular liquid crystal using the CI model (Eq. 3.20, page 58; with the ratio of ^ fixed to 23.5) coupled with Eq. 3.21, page 58. Chapter 4. Comparative Study Between MC and NMR Experiments 95 4.4 Conclusions Figs. 4.18 and 4.19a demonstrate that 5Qjg's from both NMR experiments in special liquid crystal mixtures (such as 55 wt% ZLI 1132/EBBA) for which dideuterium experiences zero (EFG) and MC simulations can be rationalized in equivalent ways. This is strong evidence that the anisotropic intermolecular potential is dominated by short-range inter-actions in such liquid crystals. Fig. 4.19b demonstrates that results for arbitrary liquid crystals such as EBBA cannot be rationalized in a similar manner. In such cases long-range electrostatic interactions must be considered. MC simulations of hard ellipsoids containing point quadrupoles at their centres yield average electric-field gradients that depend on solute size, shape and quadrupole moment. This result agrees with theory[7], but is not consistent with NMR experimental results (Fig. 4.20a) which indicate that, solutes experience at least the same sign Fzz-Chapter 5 Summary and Future Considerations Accurate spectral parameters for orientationally ordered p-, o- and m-disubstituted ben-zenes, chlorobenzene, toluene, propyne and acetonitrile co-dissolved in various liquid crystals were determined from analysis of high-resolution NMR spectra. For the more complex molecules, initial estimates of the spectral parameters were determined by anal-ysis of MQ spectra. For o- and m-xylene, resonance frequencies and 5Qja's were esti-mated by analyzing the 8Q spectra using a modified version of the least-squares fitting routine which could adjust 5Q|g's, structural parameters, and/or Di/s independently; once a reasonable fit to the MQ spectrum was obtained, the original version of the MQ analysis program was used to determine the Aj's and resonance frequencies. The es-timates of spectral parameters from the MQ analysis were used as initial parameters when analyzing the high-resolution spectra. After the high-resolution spectrum was fit-ted, it was subtracted from the experimental one and resonances from the other solutes could be easily identified and spectral parameters for those molecules were determined. After spectral parameters from the high-resolution spectra were determined, S^ /j's and molecular structural parameters were calculated from vibrationally and non-vibrationally 96 Chapter 5. Summary and Future Considerations 97 corrected D^s. From analysis of the experimental SQ^'S, it was determined that short-range interac-tions account for most of the solute orientational ordering in liquid crystalline solvents. It has been demonstrated that the (EFGYs felt by solutes in the 55 wt% ZLI 1132/EBBA mixture are « 0. Not only are the (E'FG)-quadrupole interactions « 0 in this special mixture, but all other long-range interactions appear to be negligible as well. This was supported by Monte Carlo computer simulation results. Models for short-range inter-actions which best fit the NMR experimental solute order parameters also best fit the simulation results. For the molecules in this study, interactions involving the solute dipole have little influence on ordering. In addition, the effects of polarizability could not be separated from short-range interactions. However, it is expected that polarizability interactions are minor. Trends among experimental order parameters are consistent with (a model for) a short-range interaction coupled with a quadrupole/(EFG) interaction. The sign of Fzzs in all liquid crystals is in accordance with previous results from D 2 and HD experiments. However, values of Fzz change by approximately a factor of three between the very small solute D 2 and the larger benzene derivatives; the assumption that all solutes feel essen-tially the same average environment may not be completely valid. Nevertheless, the signs and relative magnitudes of all the Fzz,s are consistent among different sets of similar size and shape molecules. MC simulations of hard ellipsoids containing point quadrupoles Chapter 5. Summary and Future Considerations 98 at their centres yield average electric-field gradients that depend on solute size, shape and quadrupole moment. The correct prediction of the NMR results could constitute an interesting challenge for computer simulation studies. At close distances, the point quadrupole is a very poor approximation of the charge distribution of a molecule. An atomistic type calculation which includes a more realistic charge distribution and pos-sibly the flexibility of liquid crystal molecules may be required in order to rationalize orientationaL ordering that is consistent with experiments. It has been demonstrated that effects from long-range interactions are relatively small. Therefore, it is important to determined a self-consistent set of order parameters either by co-dissolving many solutes in the same sample tube, or by scaling order parameters among different samples. The effects of relative solute concentration and temperature on the orientational ordering of solutes is an important question which requires investigation[83]. Effects from long-range interactions should be more prevalent with small, almost spherical solutes. One such study would involve trichloroethane, 2,2-dichloropropane and 2-chloro-2-methylpropane. 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[94] K. Cheng and R.T. Syvitski and E.E. Burnell, study currently in progress. [95] Cheng, K. W. Y. A., 1999, In Search of Dipole Ordering in Nematic Liquid Crystals, Honour's thesis, University of British Columbia. Bibliography 104 [96] Diehl, P., Jokisaari, J., and Amrein, J., 1982, J. Mag. Res., 48, 495. [97] Cradock, S., Liescheski, P. B., and Rankin, D. W. H., 1991, J. Mag. Res., 91, 316. [98] Diehl, P. and Moia, F., 1981, Organ. Mag. Res., 15, 326. [99] Diehl, P. and Bosiger, H., 1977, J. Mol. Struct, 42, 103. 100] Diehl, P., Heinrichs, P., and Niederberger, W., 1971, Mol. Phys., 20, 139. 101] Diehl, P. and Bosiger, H., 1977, Org. Magn. Reson., 9, 98. 102] Yamamota, O., Hayamiza, K., Sekine, K., and Funahira, S., 1972, Anal. Chem., 44, 1974. 103] Almenningen, A. and Hargittai, I., 1984, J. Mol. Struct, 116, 119. 104] Chen, P. C. and Wu, C. W., 1995, J. Phys. Chem., 99, 15023. 105] Domenicano, A., Schultz, G., Kolonits, M., and Hargittai, I., 1979, J. Mol. Struct, 53, 197. 106] Richard, E., Walker, R., and Weisshaar, J., 1996, J. Chem. Phys., 104, 4451. 107] Gough, K., Henry, B., and Wildman, T., 1985, J. Mol. Struct, 124, 71. 108] Anderson, D., Cradock, S., Liescheski, P., and Rankin, D., 1990, J. Mol. Struct, 216, 181. [109] Lu, K., Weinhold, F., and Weisshaar, J., 1995, J. Chem. Phys., 102, 6787. Appendixes 105 Appendix A Solutes 106 Appendix A. Solutes 107 Appendix B Dipolar Couplings 108 Appendix B. Dipolar Couplings 109 Table B.6: Fitting Parameters and RMS Errors from Analysis of High-Resolution and MQ NMR Spectra0 Solute Parameter6 Liquid Crystal ZLI 1132 55 wt% 1132/EBBA EBBA acetonitrile DHC(methyl) DHc {JHC'{methyl))0 (JHCY Md RMS Error Number of lines assigned propyne DH (methyl) H (methyl) DHH(methyl) JHH(methyl) {vH(methyl))d RMS Error Number of lines assigned 1,3,5-trichlorobenzenee Md RMS Error Number of lines assigned Sample #1 1342.01(15) 915.69(61) -269.16(61) 135.7 -9.94 1859.34(38) 1.28 15 2200.24(30) -310.03(40) -2.848(74) 1820.88(63) 1460.8(10) 1.83 15 190.85(08) 2748.95(19) 0.20 #2 1206.45(14) 836.29(70) -240.92(57) 135.7 -9.94 2350.32(38) 1.17 13 1475.25(09) -207.58(11) -2.28(21) 2318.98(18) 2091.79(29) 0.54 15 166.25(08) 3251.12(19) 0.20 #3 1077.56(27) 777.6(10) -214.9(11) 135.7 -9.94 1904.00(66) 2.08 15 602.91(12) -84.02(15) -2.36(28) 1878.27(26) 1811.65(45) 0.73 13 144.93(12) 2808.05(31) 0.31 Appendix B. Dipolar Couplings 110 Sample #4 #5 #6 chlorobenzene toluene 01,2 -1862.92(07) -1282.57(06) -1506.95(06) 01,3 -280.89(16) -187.54(21) -199.17(46) 01,4 -80.45(06) -45.04(06) -12.39(05) ^1,5 -43.01(24) -9.12(36) 72.60(64) 02,3 -624.69(18) -352.96(24) -99.53(40) 02,4 -42.53(21) -8.57(33) 71.44(67) 7.608 7.608 7.608 ( W 1.451 1.451 1.451 0.864 0.864 0.864 1.781 1.781 1.781 7.280 7.280 7.280 (J*AY 1.301 1.301 1.301 -3851.15(02) -3976.17(03) -2895.17(07) -3870.82(02) -3973.60(03) -2880.10(07) -4019.38(01) -4071.38(01) -3011.00(01) RMS Error 0.298 0.330 0.289 Number of assigned lines 39 39 35 01,2 -1870.33(08) -1262.18(02) -1491.20(10) 01,3 -279.68(13) -186.31(03) -206.09(18) 01,4 -81.16(07) -50.01(01) -32.58(09) 01,5 -46.31(13) -21.90(03) 28.07(22) 01,6 -617.57(05) -407.24(01) -426.78(09) 02,3 -635.73(13) -394.32(03) -262.45(25) 02,4 -46.37(14) -21.76(03) 27.67(22) 02,6 -176.35(06) -118.11(02) -134.67(11) 03,6 -133.58(13) -90.26(03) -106.39(22) 06,7 2464.93(03) 1662.25(01) 1963.05(04) ( * , 2 ) h 8.00 8.00 8.00 0.92 0.92 0.92 «A,4 0.94(16) 0.49(44) 0.37(25) Appendix B. Dipolar Couplings 111 1.86 1.86 1.86 «A,6 -0.72(08) -0.69(02) -0.58(13) ^2,3 7.28(20) 7.46(05) 7.27(48) (J2A)h 1.11 1.11 1.11 ^2,6 0.57(09) 0.34(03) 0.36(17) ^3,6 -1.28(27) -0.56(08) -0.54(43) ( l^)fl -3813.17(01) -3912.96(01) -2782.23(02) (^)9 -3869.13(01) -3969.34(01) -2840.32(02) -3971.21(02) -4025.51(01) -2927.76(02) K ) S -1669.00(01) -1681.38(01) -562.88(01) RMS Error 0.510 0.110 0.660 Number of assigned lines 171 151 149 chlorobenzenee DHH 213.59(08) 147.67(06) 151.55(04) (VH)9 -3707.32(02) -3816.21(01) -2689.23(01) RMS Error 0.199 0.136 0.109 Number of assigned lines 3 3 3 Sample #7 #8 #9 p-dichlorobenzene 01,2 -2411.29(07) -2255.46(17) -3035.20(15) 01,3 -49.89(08) -24.02(19) 27.68(16) 01,4 56.36(08) 99.98(19) 254.98(15) 8.55 8.55 8.55 0.39 0.39 0.39 2.57 2.57 2.57 (»i)9 -2621.48(09) -2699.33(25) -3058.53(22) RMS Error 0.186 0.620 0.531 Number of assigned lines 8 10 10 Appendix B. Dipolar Couplings 112 p-chlorotoluene 0 1 , 2 0 1 , 3 01 ,4 A , 5 0 2 , 3 0 2 , 5 0 5 , 6 Jl,2 ^2,5 (^ ) s RMS Error Number of assigned lines 1,3,5-tr ichlor obenzene6 DHH RMS Error Number of assigned lines -2596.80(06) -2323.54(07) -2901.55(09) -41.16(06) -23.24(08) 11.83(08) 83.51(16) 102.78(20) 211.14(23) -707.50(07) -605.32(09) -673.78(11) 83.30(17) 102.21(21) 210.49(23) -231.75(06) -204.91(09) -248.26(10) 3424.82(04) 3063.94(04) 3828.14(05) 8.52 (22) 8.42(66) 8.49(41) 0.39 0.39 0.39 2.58 2.58 2.58 -0.64(08) -0.58(12) -0.64(13) 2.58 2.58 2.58 0.28(09) 0.36(13) 0.45(13) -2537.69(17) -2606.36(21) -2934.16(26) -2605.87(18) -2688.29(24) -3045.33(26) -482.12(07) -502.43(09) -849.59(09) 0.563 0.612 0.688 132 100 111 203.29(01) 165.53(10) 156.51(01) -2580.31(02) -2664.43(25) -3058.21(01) 0.024 0.245 0.013 3 3 3 Appendix B. Dipolar Couplings 113 Sample #10 #11 #12 p-dichlorobenzene 01 ,2 -2403.92(05) -2189.81(15) -2702.88(14) 0 1 , 3 -49.35(06) -22.61(16) 23.80(16) 01 ,4 57.21(06) 97.13(16) 225.83(16) (Jl*Y 8.55 8.55 8.55 0.39 0.39 0.39 2.57 2.57 2.57 -837.52(07) -908.56(22) -2755.40(21) RMS Error 0.196 0.531 0.521 Number of assigned lines 12 10 10 p-xylenefc 01 ,2 -2670.51(04) -2229.24(08) -2369.51(04) [-2733.9] [-2269.0] [-2386.7] 0 1 , 3 -39.60(05) -27.47(08) -8.58(04) [-39.8] [-28.0] [-4.6] 0 1 , 4 87.97(05) 85.13(09) 131.66(04) [92.6] [91.2] [134.55] 0 1 , 5 -714.82(03) -585.03(06) -580.35(03) [-727.1] [-593.3] [-582.6] 0 1 , 8 -235.24(03) -195.37(07) -203.74(04) [-241.4] [-201.7] [-204.0] 0 5 , 6 3472.13(04) 2896.91(10) 3076.68(02) [3495.2] [2908.2] [3088.7] 0 5 , 8 -121.38(25) -101.24(05) -107.58(02) [-124.2] [-102.9] [-109.9] 7.93(14) 8.16(47) 7.59(20) Jlfi 0.40(15) 0.85(39) 0.64(18) J\A 2.04(19) 1.57(45) 1.49(21) J\,b -0.61(06) -0.68(12) -0.79(06) Jl,8 0.36(07) 0.42(13) 0.36(07) 0.56(05) 0.57(10) 0.60(05) (»i)9 -756.80(05) -826.20(10) -2662.65(05) Appendix B. Dipolar Couplings 114 RMS Error Number of assigned lines 1,3,5-trichlorobenzenee DHH M9 RMS Error Number of assigned lines o-dichlorobenzene 01,2 01,3 01,4 02,3 (»i)9 ; RMS Error Number of lines assigned o-chlorotoluene 01,2 01,3 01,4 [-756.7] [-826.1] [-2662.6] 1307.29(06) 1293.08(13) -537.47(05) [1299.3] [1291.9] [-538.07] 0.485 0.780 0.522 [5.113] [4.303] [9.636] 210 172 275 [44] [34] [30] 202.66(01) 160.76(15) 139.70(01) -795.85(01) -873.33(38) -2745.15(03) 0.008 0.385 0.033 3 3 3 Sample #13 #14 #15 -1182.09(05) -887.83(02) -791.22(03) -161.98(06) -113.68(03) -68.16(03) -84.41(11) -55.62(06) -16.93(18) -643.54(12) -427.11(06) -135.99(18) 8.06 8.06 8.06 1.52 1.52 1.52 0.35 0.35 0.35 7.45 7.45 7.45 -2160.66(15) -2334.90(08) -2436.27(23) -2245.63(14) -2373.25(08) -2476.69(23) 0.230 0.125 0.103 19 20 14 -1124.97(05) -910.64(05) -950.84(05) -166.82(09) -122.84(10) -91.58(28) -92.91(07) -59.00(09) -20.37(28) Appendix B. Dipolar Couplings 115 A,5 -100.78(04) -68.02(05) -44.95(27) 02,3 -712.98(06) -452.76(07) -153.44(27) 02,4 -168.91(10) -110.81(10) -60.99(29) 02,5 -82.72(04) -61.45(05) -56.53(27) 03,4 -1159.40(06) -866.88(06) -810.02(06) 03,5 -142.29(03) -113.15(03) -120.61(28) 04,5 -705.83(03) -573.11(03) -628.72(04) 05,6 1510.26(02) 1121.67(02) 1031.86(02) Jl,2 8.24(08) 7.86(10) 8.15(31) (Ji,s)m 1.64 1.64 1.64 0.29 0.29 0.29 (Ji,s)m 0.40 0.40 0.40 7.54 7.54 7.54 <72,4 1.62(11) 1.32(12) 2.04(20) (^2,5)TO -0.60 -0.60 -0.60 •^3,4 7.58(07) 7.55(09) 7.54(11) (^3, 5) m 0.40 0.40 0.40 -0.83(05) -0.97(06) -0.77(07) [vxy -2139.28(09) -2301.41(12) -2371.73(70) -2206.71(09) -2333.93(12) -2420.63(69) -2234.88(06) -2365.16(06) -2457.61(08) -2157.64(06) -2289.40(07) -2339.36(08) -19.02(03) -106.06(04) -193.17(04) RMS Error 0.309 0.337 0.379 Number of lines assigned 220 200 156 chlorobenzene6 DHH 195.81(04) 148.90(05) 131.33(01) M9 -2084.23(09) -2232.41(13) -2317.31(01) RMS Error 0.091 0.131 0.002 Number of lines assigned 3 3 3 Appendix B. Dipolar Couplings o-dichlorobenzene 01,2 01,3 01,4 02,3 ( W ( W RMS Error Number of lines assigned o-xylenen 01,2 01,3 01,4 01,5 01,8 02,3 02,5 02,8 05,6 Sample #16 #17 #18 -1208.43(03) -987.27(06) -877.21(08) -165.02(04) -124.94(07) -74.47(09) -85.64(07) -60.29(15) -18.97(55) -655.06(07) -464.04(16) -143.58(54) 8.06 8.06 8.06 1.52 1.52 1.52 0.35 0.35 0.35 7.45 7.45 7.45 -2562.42(09) -3495.31(19) -3682.95(68) -2651.38(09) -3552.21(19) -3744.86(68) 0.154 0.246 0.248 20 17 12 -1157.11(03) -979.16(03) -968.23(03) [-1083.9] [-987.9] [-967.2] -177.32(04) -140.23(04) -116.66(04) [-177.0] [-240.7] [-115.2] -102.07(05) -76.60(06) -54.33(07) [-90.8] [-53.0] [-62.2] -103.89(03) -83.42(04) -72.64(04) [-79.6] [-90.5] [-69.8] -716.87(02) -619.37(03) -641.37(03) [-696.6] [-616.0] [-638.2] -780.36(05) -588.10(06) -419.47(05) [-705.7] [-505.4] [-419.8] -82.70(03) -69.81(04) -68.71(04) [-58.6] [13.4] [-76.4] -141.16(03) -121.96(04) -125.94(04) [-156.3] [-189.6] [-118.4] 1508.17(01) 1271.18(01) 1247.47(01) [1425.5] [1284.2] [1245.3] Appendix B. Dipolar Couplings 117 £>5j8 -252.05(01) -184.40(01) -117.93(01) [-237.4] [-183.0] [-119.5] Ji, 2 7.50(06) 7.77(07) 7.44(08) Ji, 3 1.50(06) 1.41(07) 1.37(07) J M 0.54(09) 0.57(11) 0.27(11) Ji, 5 0.44(05) 0.43(06) 0.61(08) Ji, 8 -0.69(04) -0.73(05) -0.74(05) J 2 ) 3 7.39(09) 7.50(10) 7.46(10) J 2 l 5 -0.86(06) -0.69(07) -0.56(09) J 2 , 8 0.37(06) 0.37(07) 0.26(08) J 5 ) 8 0.42(02) 0.40(03) 0.44(03) (vxy -2534.15(05) -3429.84(05) -3557.98(06) [-2533.7] [-3429.7] [-3556.7] (v2y -2603.67(05) -3500.48(05) -3649.12(05) [-2592.6] [-3507.6] [-3641.0] (i/8)» -377.71(02) -1236.73(03) -1376.92(03) [-369.7] [-1232.8] [-1373.6] RMS Error 0.377 0.413 0.403 [9.18] [14.88] [3.02] Number of lines assigned 501 427 374 [22] [22] [24] 1,3,5-trichlorobenzenee DHH 200.07(07) 164.55(01) 145.88(02) (pHy -2486.79(17) -3396.67(01) -3566.11(04) RMS Error 0.174 0.011 0.038 Number of lines assigned 3 3 3 Sample #19 #20 #21 m-dichlorobenzene D 1 | 2 -1342.52(05) -1122.42(05). -1095.21(05) £>i>3 -318.61(11) -275.317(11) -296.046(12) Di, 4 -144.36(07) -99.39(07) -37.55(07) Appendix B. Dipolar Couplings 118 02,4 -56.33(09) -26.31(10) 32.63(10) 8.10 8.10 8.10 2.00 2.00 2.00 UM)0 1.80 1.80 1.80 (J2,4)° 0.40 0.40 0.40 -2339.57(08) -2435.74(08) -3850.49(09) -2240.18(14) -2328.10(14) -3677.43(14) (1 /4 ) ' -2022.961(10) -2137.61(11) -3453.63(11) RMS Error 0.265 0.262 0.270 Number of lines assigned 28 26 26 Dtoluene 01,2 -1559.065(23) -1247.31(56) -1144.35(36) 01,3 -339.72(10) -287.14(14) -303.61(12) 01,4 -103.68(10) -80.27(18) -54.05(11) 01,5 -90.38(06) -77.53(10) -83.24(07) 02,3 -1249.99(30) -1079.54(68) -1157.04(35) 02,4 -44.05(07) -22.98(09) 19.81(08) 02,5 -72.88(07) -59.46(10) -50.72(14) 03,4 -168.14(09) -116.83(18) -54.63(12) 03,5 -177.47(10) -118.44(12) -12.42(12) 04,5 -919.22(03) -770.59(18) -798.88(04) 05,6 1655.06(02) 1426.57(10) 1531.65(03) Ul,2)P 8.09 8.09 8.09 1.10 1.10 1.10 (JIAY 2.71 2.71 2.71 0.00 0.00 0.00 (J2,*y 7.53 7.53 7.53 ( W 0.39 0.39 0.39 2^,5 -0.05(14) -0.02(20) 0.57(27) (^ 3,4)P 1.65 1.65 1.56 3^,5 -1.10(20) -0.75(27) -0.50(27) 4^,5 -0.84(06) -0.42(09) -0.47(08) -2277.75(13) -2375.82(22) -3775.89(19) Appendix B. Dipolar Couplings 119 ( i / 4 ) » RMS Error Number of lines assigned l,3,5-trichlorobenzenee DHH RMS Error Number of lines assigned m-dichlorobenzene 0 1 , 3 01 ,4 02 ,4 (Jl,2)° VIA)0 (J2A)° (»l)9 RMS Error Number of lines assigned m-xylenen 01 ,2 0 1 , 3 -2198.39(10) -2290.13(14) -3620.80(12) -2322.36(12) -2377.84(23) -3715.48(20) -2005.36(07) -2106.64(09) -3397.48(08) -54.42(04) -91.77(06) -1401.47(06) 0.350 0.426 0.409 159 134 146 205.51(02) 165.28(06) 142.13(06) -2137.15(05) -2234.33(14) -3586.12(15) 0.046 0.148 0.158 3 3 3 Sample #22 #23 #24 -1288.85(03) -1029.43(02) -1151.31(05) -305.41(07) -252.94(05) -311.24(11) -139.17(04) -90.88(03) -39.17(06) -54.49(07) -23.63(04) 34.71(09) 8.10 8.10 8.10 2.00 2.00 2.00 1.80 1.80 1.80 0.40 0.40 0.40 -3057.83(06) -3684.85(04) -3842.65(08) -2962.75(09) -3583.56(06) -3661.69(13) -2757.10(07) -3417.19(04) -3419.55(10) 0.198 0.127 0.240 31 -1382.31(04) [-1372.0] -334.82(27) 28 -1080.34(03) [-1139.49] -263.28(21) 26 -1211.96(07) [-1204.28] -308.63(53) Appendix B. Dipolar Couplings 120 [-323.3] 01,4 -128.69(04) [-120.4] 01,5 -99.84(04) [-118.4] 01,8 -225.32(03) [-198.9] 02,4 -38.93(07) [-44.4] 02,5 -89.22(04) [-97.9] 04,5 -884.83(01) [-885.2] 05,6 1827.38(01) [1825.2] 05,8 -127.65(01) [-126.7] •A ,2 7.69(20) 1.03(12) JlA 1.70(08) Jl,5 -0.55(08) Jl,& -0.70(06) J2A 0.53(13) ^2,5 0.30(06) ^4,5 -0.77(02) •^ 5,8 -0.22(02) -2975.53(03) [-2975.4] Md -2907.24(07) [-2917.5] (^Y -2711.86(04) [-2708.1] {vsY -767.40(02) [-770.8] [-284.55] [-313.64] -95.53(03) -77.29(06) [-96.28] [-76.55] -78.03(03) -87.66(11) [-82.87] [-87.67] -159.57(04) -80.20(10) [-155.71] [-79.16] -25.50(06) 0.45(09) [-21.86] [1.31] -67.51(03) -62.34(04) [-68.98] [-61.60] -697.73(01) -821.09(01) [-744.20] [-820.94] 1426.23(01) 1596.53(01) [1510.85] [1597.69] -100.66(01) -118.42(01) [-107.32] [-118.43] 7.24(17) 7.06(40) 0.87(08) 0.72(99) 1.87(07) 1.76(11) -0.48(07) -0.20(22) -0.70(08) -0.97(24) 0.46(11) 0.63(17) 0.32(05) 0.31(08) -0.71(02) -0.73(02) -0.22(01) -0.30(02) -3571.06(03) -3647.19(06) [-3571.1] [-3647.2] -3536.71(05) -3571.89(07) [-3561.6] [-3579.3] -3353.38(04) -3352.63(05) [-3352.1] [-3361.7] -1336.21(02) -1395.72(02) [-1358.2] [-1400.0] Appendix B. Dipolar Couplings 121 RMS Error 0.304 0.305 0.384 [5.85] [10.01] [11.48] Number of lines assigned 402 501 440 [24] [25] [22] 1,3,5-trichlorobenzene6 DHH 197.80(04) 151.74(05) 149.66(07) M9 -2860.41(11) -3497.34(13) -3565.45(18) RMS Error 0.119 0.132 0.186 Number of lines assigned 3 3 3 Q For atom numbering refer to Fig. A.22. Numbers in round brackets are errors (68% confidence) in the last two reported digits of varied parameters. 6 Dipolar couplings, J couplings, chemical shifts and RMS Errors are in Hz. Unless otherwise specified, dipolar couplings, J couplings and chemical shifts are for protons. c Parameters not varied during analysis of spectrum. Values taken from Ref. [96]. d Frequency is referenced to an arbitrary zero and is increasing to high field. Spectra were acquired at 200.05 MHz. e 1,3,5-trichlorobenzene is an internal orientational standard. f Parameters not varied during analysis of spectrum. Values were determined from a separate analysis of chlorobenzene dissolved in the nematic phase of ZLI 1132. 9 Frequency is referenced to an arbitrary zero and is increasing to high field. Spectra were acquired at 500.13 MHz. h Parameters not varied during fitting of spectrum. Values taken from Ref. [60] 1 Parameters not varied during fitting of spectrum. Values taken from Ref. [97] J Parameters not varied during fitting of spectrum. Values taken from Ref. [98] k Values in square brackets are from analysis of the 7-quantum spectrum. J couplings were set to zero for the MQ analysis. ' Parameters not varied during analysis of spectrum. Values taken from Ref. [99]. m Parameters not varied during analysis of spectrum. Values taken from Ref. [100]. n Values in square brackets are from the analysis of the 8-quantum spectrum. J couplings were set to zero for the MQ analysis. 0 Parameters not varied during analysis of spectrum. Values taken from Ref. [101]. p Parameters not varied during analysis of spectrum. Values taken from Ref. [102]. Appendix B. Dipolar Couplings 122 Table B.7: Fitting Parameters and RMS Errors from Analysis of High-Resolution and MQ NMR Spectra of Sample #25° Parameter6 o-dichlorobenzenec o-chlorotoluened o-xylenee Di > 2 -1200.30(09) -1145.14(06) -1147.51(03) [-1157.53] L>i,3 -163.97(11) -169.31(10) -175.93(04) [-169.98] Di | 4 -84.76(21) -94.01(07) -101.17(06) [-101.20] £>i|5 -102.17(04) -103.08(02) [-108.11] Difi -710.74(02) [-711.40] L>2,3 -649.78(21) -720.68(06) -774.72(05) [-789.86 ] £>2,4 -170.79(11) D 2 ) 5 -83.95(04) -82.10(03) [-80.59] D2,8 -139.95(03) [-144.10] £>3i4 -1177.36(06) L>3,5 -144.66(03) £ 4 , 5 -718.62(03) L>5,6 1533.32(01) 1495.65(01) [1507.09] Ji, 2 8.06 7.93(09) 7.52(07) Ji, 3 1.52 1.64 1.29(08) J 1 > 4 0.35 0.29 0.55(10) J 1 ) 5 0.40 0.47(05) J 1 ; 8 -0.66(04) J 2 > 3 7.45 7.54 7.20(10) J2,4 - - - 1-47(11) J 2 , 5 -0.60 -0.57(06) J 2 , 8 0.27(06) J 3 ) 4 7.57(09) J3,5 0.40 J 4 ) 5 -0.82(05) Appendix B. Dipolar Couplings 123 J 5 , 8 0.48(02) {uxy -2392.96(27) -2371.91(09) -2363.55(05) [-2363.6] (v2y -2480.69(29) -2441.83(09) -2432.16(06) [-2432.2] (u3y -2470.72(06) (u4)f -2391.22(06) - - -(v5)f 258.00(03) -204.36(02) [-207.5] RMS Error 0.421 0.301 0.419 [7.79] Number of lines assigned 18 188 437 [23] a For atom numbering refer to Fig. A.22. Numbers in round brackets are errors (68% confidence) in the last two reported digits of varied parameters. 6 Dipolar couplings, J couplings, chemical shifts and RMS Errors are in Hz. Dipolar couplings, J couplings and chemical shifts are for protons. c J couplings are not varied during analysis of spectrum. Values taken from Ref. [99]. d Some J couplings are not varied during analysis of spectrum. Values taken from Ref. [100]. e Values in square brackets are from the analysis of the 8-quantum spectrum. J couplings were set to zero for the MQ analysis. •f Frequency is referenced to an arbitrary zero and is increasing to high field. Spectra were acquired at 500.13 MHz. 9 Resonance frequency, dipolar coupling and RMS error for 1,3,5-trichlorobenzene was determined to be -2317.02(02), 198.59(01) and 0.028 Hz. Appendix C Structural Parameters 124 Appendix C. Structural Parameters 125 Table C.8: Molecular Parameters" from Fits to Vibra-tionally Corrected Dipolar Couplings Molecular Parameter Solute6 r(C-H(methyl)){ r (C-C (methyl)){ r(N=C or C=C){ r(C-H){ <(C-C-H (methyl))/ RMS' acetonitrile0 Propyne" fitted 1.0994(71) 1.1030(05) a priori* 1.1044(15) 1.1010(10) fitted 1.4634(91) 1.4703(06) a priorf 1.4596(15) 1.4710(10) fitted 1.2066(06) a priorf 1.1627 1.2073(10) fitted 1.0593(06) a priori6 1.0600(10) fitted 110.025(22) 109.977(42) a priorf 109.994(150) 110.251(100) 3.74 0.25 a Numbers in round brackets are standard deviations in the last reported digits of varied parameters. Bond distances (r) in A and bond angles (<) in degrees. In the least squares fit to experimental dipolar couplings the weight given to each dipolar coupling is ^ error ) where the errors are reported in Table B.6. 6 For axis definitions see Fig. A.22 c a priori estimates were taken from the ra structure reported in Ref. [74] d a priori estimates were taken from the ra structure reported in Ref. [75] e a priori estimates[56] are values of structural parameters (taken from other studies) that have an associated error and are adjusted in the least-squares routine; large deviations of the a priori estimates are discouraged by the least-squares criteria. For the least squares fitting routine the weight associated with the a priori estimates is ( e r r x > r) where the errors are reported in brackets. 1 RMS error in Hz between vibrationally corrected and calculated dipolar couplings. Appendix C. Structural Parameters Table C.9: Structural Parameters from Fits to Dipo-lar Couplings for chlorobenzene, toluene and 1,3,5-trichlorobenzenea Parameter6 chloro-benzene toluene 1,3,5-tri-chlorobenzenec r(C2-Hl) { n V 1.0812(04) 1.0819(02) 1.0838(15) 1.0831(15) 1.094 r(C3-H2) | n V 1.0803(05) 1.0791(02) 1.0824(14) 1.0792(14) r(C4-H3) { n V 1.0803(04) 1.0808(02) 1.0742(17) 1.0778(17) 1.094 r(C7-H6) { n V 1.0983(10) ) 1.0929(11) ) r (Cl-C7) { n V 1.4896(51) 1.5044(46) Z(C3C2H1) { n V 121.53(08) 121.30(04) 120.11(09) 120.27(09) 121.0 Z(C4C3H2) { n V 121.04(07) 120.66(03) 120.53(10) 120.41(10) Z(C2C1H6) { n V 110.49(17) 111.42(17) Z(C2C1C7) { n V 120.85 120.85 R M S Error d R M S Error 6 0.3098 0.1601 0.3150 0.3111 a priori estimates 1 r(C2-Hl) r(C3-H2) r(C4-H3) r(C7-H6) r (Cl-C7) Z(C3C2H1) 1.0823(02) 1.0787(02) 1.0808(02) 120.89(05) h 1.077(02) 1.076(02) 1.076(02) 1.113(02) 1.516(05) 119.70(05) c 1.094 1.094 .121.0 Appendix C. Structural Parameters 127 Z(C4C3H2) 120.56(05) 120.10(05) Z(C1C7H6) 110.00(05) Z(C2ClC7)i — — 120.70(-) — — — Fixed Parameters 9 h c r(Cl-C2) 1.389 1.388 1.3908 r(C2-C3) 1.394 1.388 1.3908 r(C3-C4) 1.393 1.383 1.3908 r(Cl-Cl) 1.739 1.7326 Z(C1C2C3) 119.04 120.90 118.0 Z(C2C3C4) 120.06 120.20 122.0 Z(C3C4C5) 120.23 119.50 118.0 Z(C3C4H3) 119.89 120.30 121.0 Z(C2C1C1) 119.27 119.0 a Refer to Fig. A.22 for structure and atom numbering of molecules. Bond distances r in A and bond angles Z in degrees. In the least squares fit to experimental dipolar couplings the weight given to each dipolar coupling is ^ error j where the errors are from Table B.6. Numbers in round brackets are statistical errors (68% confidence) in the last two reported digits of varied parameters. 6 Parameters which are indicated with "n" are calculated with no vibrational correc-tions to dipolar couplings whereas parameters indicated with "v" are calculated with vibrational corrections and are the rQ structural parameters. c Structural parameters not adjusted. From Ref. [103]. 1,3,5-trichlorobenzene is an internal orientational standard. d RMS Error in Hz between calculated and experimental dipolar couplings. e RMS Error in Hz between vibrationally corrected and experimental dipolar couplings. ' a priori estimates are from Ref. [63] and [104] and the weight associated with the estimates is (error) w n e r e the errors are reported in brackets. 9 ra structure determined from liquid-crystal NMR data which has been corrected for normal mode vibrations and orientational-vibrational correlations [63]. h From molecular orbital calculations using Gaussian 92 and HF/6-31G* theory/basis set [104]. 1 no error is associated with this parameter. This is adjusted so the C1-C7 (and C4-C8) bond directions are collinear with the z axis of the molecule. Appendix C. Structural Parameters Table C.10: Structural Parameters from Fits to Dipolar Couplings for p-disubstituted benzenes" Parameter6 p-dichloro- p-chloro- p-xylene benzene toluene r(C2-Hl) { n V 1.0760(04) 1.0760(03) 1.0792(53) 1.0806(04) 1.0914(11) 1.0890(14) r(C3-H2) { n V 1.0760(04) 1.0760(03) 1.0737(63) 1.0749(05) 1.0914(11) 1.0890(14) r(C7-H5) | n V 1.1032(04) 1.0986(04) 1.1038(08) 1.0988(11) r(Cl-C7) { n V 1.4898(06) 1.4892(05) 1.5066(16) 1.5109(22) Z(C3C2H1) { n V 120.58(01) 120.58(01) 118.84(05) 119.31(04) 119.67(01) 119.78(01) Z(C4C3H2) { n V (119.99)c (119.95)c 120.27(07) 120.41(05) (118.93)c (118.82)c Z(C1C7H5) { n V 110.12(05) 111.50(04) 109.84(08) 111.12(11) Z(C2C1C7) { n V 120.90 120.88 121.4 121.4 RMS Errord 0.3121 0.2949 0.3867 RMS Errore 0.2195 0.2335 0.4795 a priori estimates ^ r(C2-Hl) r(C3-H2) r(C7-H5) r(Cl-C7) Z(C3C2H1) Z(C4C3H2) Z(C1C7H5) Z(C2C1C7)J 9 1.076(02) 1.076(02) 120.05(05) (120.48)c h 1.0811(02) 1.0745(02) 1.0989(02) 1.4891(02) 118.90(05) 120.40(05) 111.17(05) 120.91(-) 1.076(02) 1.076(02) 1.113(02) 1.512(02) 120.80(05) (117.8)c 110.30(05) 121.4(-) Appendix C. Structural Parameters 129 Fixed Parameters 9 h i r(Cl-C2) 1.395 1.406 1.405 r(C2-C3) 1.391 1.404 1.392 r(C3-C4) 1.395 1.400 1.405 r(C4-Cl) 1.729 1.72 Z(C1C2C3) 119.47 121.52 121.40 Z(C2C3C4) 119.47 118.64 121.40 Z(C3C4C5) 121.06 121.48 117.10 Z(C3C4C1) 119.47 119.26 a Refer to Fig. A.22 for structure and atom numbering of molecules. Bond distances r in A and bond angles Z in degrees. In the least squares fit to experimental dipolar couplings the weight given to each dipolar coupling is ( e r r o r ) where the errors are from Table B.6. Numbers in round brackets are statistical errors (68% confidence) in the last two reported digits of varied parameters. 6 Parameters which are indicated with "n" are calculated with no vibrational correc-tions to dipolar couplings whereas parameters indicated with "v" are calculated with vibrational corrections and are the ra structural parameters. c Parameters are calculated from Z(C1C2C3) and Z(C3C2H1). d RMS Error in Hz between calculated and experimental dipolar couplings. e RMS Error in Hz between vibrationally corrected and experimental dipolar couplings. * a priori estimates are from Ref. [97], [98] and [105] and the weight associated with the estimates is ( e r r 0 r ) w h e r e the errors are reported in brackets. 9 ra structure from a joint analysis of liquid-crystal NMR, electron diffraction and rota-tional spectroscopy data [97]. h ra structure from liquid-crystal NMR data which has been corrected for normal mode vibrations [98]. 1 ra structure from electron diffraction data [105]. J no error is associated with this parameter. This is adjusted so the C1-C7 (and C4-C8) bond directions are collinear with the z axis of the molecule. Appendix C. Structural Parameters Table C.ll: Structural Parameters from Fits to Dipolar Couplings for o-disubstituted benzenes" Parameter6 o-dichloro-benzene o-chloro-toluene o-xylene r(Cl-C2) { n V 1.3799(15) 1.3793(13) 1.3849(30) 1.3839(34) 1.3751(59) 1.3764(62) r(C2-C3) | n V 1.4025(15) 1.4001(13) 1.3982(23) 1.3938(26) 1.3820c 1.3820c r(C3-C4) { n V 1.3799(15) 1.3793(13) 1.3890(30) 1.3909(33) 1.3751(59) 1.3764(62) r(C4-C5) { n V 1.3822(16) 1.3826(14) 1.3840(30) 1.3836(34) 1.3771(58) 1.3764(62) r(C5-C6) { n V (1.4050)d (1.4054)d (1.3850)d (1.3839)d (1.3880)d (1.3924)d r(C6-Cl) { n V 1.3822(16) 1.3826(14) 1.385c 1.385c 1.3771(58) 1.3764(62) r(Cl-Hl) { n V 1.0819(15) 1.0826(13) 1.0754(30) 1.0753(33) 1.0732(18) 1.0726(19) r(C2-X) { n V 1.0890(15) 1.0883(13) 1.0830(36) 1.0842(39) 1.0912(59) 1.0944(60) r(C3-H3) { n V 1.0890(15) 1.0883(13) 1.0909(35) 1.0909(39) 1.0912(59) 1.0944(60) r(C4-X) { n V 1.0819(15) 1.0826(13) 1.0733(19) 1.0726(21) 1.0732(18) 1.0726(19) r(C5-X) { n V 1.733c 1.733c 1.5202(48) 1.5250(53) 1.5288(20) 1.5294(21) r(C6-X) { n V 1.733c 1.733c 1.751c 1.751c 1.5288(20) 1.5294(21) r(C7-H5) { n V 1.1051(18) 1.1037(20) 1.1054(20) 1.1045(18) <(C1C2C3) { n V 119.54(07) 119.65(06) 119.10(26) 118.69(34) 118.97(13) 118.97(14) Appendix C. Structural Parameters 131 <(C2C3C4) { n V <(C3C4C5) { n V <(C4C5C6) { n V <(C5C6C1) { n V <(C6C1C2) { n V <(C2C1H1) { n V <(C3C2X) { n V <(C2C3H3) { n V <(C3C4X) { n V <(C4C5X) { n V <(C1C6X) { n V <(CXC7H5) { n V RMS Error6 RMS Error' a priori estimates 9 r(Cl-C2) r(C2-C3) r(C3-C4) r(C4-C5) r(C5-C6) r(C6-Cl) r(Cl-Hl) r(C2-X) r(C3-H3) 119.54(07) 119.65(06) 121.01(12) 120.86(10) (119.43)d (119.48)d (119.43)d (119.48)d 121.01(12) 120.86(10) 121.10(14) 120.99(12) 120.46(12) 120.33(10) 120.46(12) 120.33(10) 121.10(14) 120.99(12) 118.99c 118.99c 118.996 118.996 0.5630 0.4914 h 1.3760(02) 1.3960(02) 1.3760(02) 1.3850(02) 1.4078(02)'' 1.3850(02) 1.0870(02) 1.0840(02) 1.0840(02) 118.94(19) 119.57(30) 122.00c 122.006 117.506 117.50c 121.406 121.406 (121.04)d (120.83)d 121.86(48) 121.50(54) 119.96(33) 119.72(43) 119.65(24) 118.71(36) 119.64(12) 119.69(13) 118.88(14) 118.65(16) 116.90c 116.906 110.48(23) 111.73(26) 0.5148 0.5667 1.38200(025) 1.38500(025) 1.38300(025) 1.39300(025) 1.38990(025)d 1.385c 1.08000(025) 1.0800(03) 1.0800(03) 118.97(13) 118.97(14) 122.24(15) 122.35(16) (118.78)d (118.67)d (118.78)d (118.67)d 122.24(15) 122.35(16) 120.00(48) 120.36(50) 118.82(19) 118.85(20) 118.82(19) 118.85(20) 120.00(48) 120.36(50) 119.94(24) 119.03(25) 119.94(24) 119.03(25) 110.21(23) 111.53(24) 0.7022 0.7337 3 1.38700(015) 1.3820c 1.38700(015) 1.38800(015) 1.3978(03)d 1.38800(015) 1.0820(01.) 1.0820(01) 1.0820(01) Appendix C. Structural Parameters 132 r(C4-X) 1.0870(02) 1.08000(016) 1.0820(02) r(C5-X) 1.7330c 1.5100(04) 1.5260(015) r(C6-X) 1.7330c 1.751c 1.5260(015) r(C7-H5) 1.09600(025) 1.0960(01) <(C1C2C3) 120.30(05) 119.65(05) 119.60(05) <(C2C3C4) 120.30(05) 119.75(05) 119.60(05) <(C3C4C5) 119.90(02) 122.0C 121.20(01) 120.00(05)d <(C4C5C6) 119.80(05)" 117.50c <(C5C6C1) 119.80(05)d 121.40c 120.00(05)d <(C6C1C2) 119.90(02) 119.70(05)d 121.20(01) <(C2C1H1) 120.28(02) 120.15(05) 119.50(03) <(C3C2X) 120.10(05) 120.18(05) 120.40(05) <(C2C3H3) 120.10(05) 120.13(05) 120.40(05) <(C3C4X) 120.28(02) 119.40(01) 119.50(03) <(C4C5X) 118.99c 119.90(05) 120.00(05) <(C1C6X) 118.99c 116.90c 120.00(05) <(CXC7H5) 111.00(04) 110.90(02) a Refer to Fig. A.22 for structure and atom numbering of molecules. Bond distances (r) in A and bond angles (<) in degrees. In the least squares fit to experimental dipolar couplings the weight given to each dipolar coupling is ^error) where the errors are reported in Tables B.6 and B.7. 6 Parameters which are indicated with "n" are calculated with no vibrational corrections to dipolar couplings and parameters indicated with "v" are calculated with vibrational corrections. c Parameter not adjusted during fit. d Dependent parameter is calculated from the bond angles and lengths of the carbon skeleton. e RMS Error in Hz between calculated and experimental dipolar couplings. f RMS Error in Hz between vibrationally corrected and experimental dipolar couplings. 9 For the least squares fitting routine the weight associated with the a priori estimates is ^ e r r 0 r ) where the errors are reported in brackets. h ra structure from Ref. [99]. * Structure from Ref. [100] and [106]. j Structure from Ref. [58] and [107]. Appendix C. Structural Parameters 133 Table C.12: Structural Parameters from Fits to Dipolar Couplings for m-disubstituted benzenes0 Parameter6 m-dichloro-benzene m-chloro-toluene m-xylene r(Cl-C2) { n V 1.4039(05) 1.4041(06) 1.3846(12) 1.3857(14) 1.3991(42) 1.4013(34) r(C2-C3) { n V 1.4039(05) 1.4041(06) 1.3818(12) 1.3830(14) 1.3991(42) 1.4013(34) r(C3-C4) { n V 1.3921(06) 1.3920(06) 1.3880(12) 1.3889(15) 1.3884(23) 1.3896(22) r(C4-C5) { n V (1.3872)c (1.3872)c 1.3901(12) 1.3904(15) (1.3941)c (1.3930)c r(C5-C6) { n V (1.3872)c (1.3872)c (1.3860)c (1.3870)c (1.3941)c (1.3930)c r(C6-Cl) { n V 1.3921(06) 1.3920(06) 1.382d 1.382" 1.3884(23) 1.3896(22) r(Cl-Hl) { n V 1.0846(05) 1.0847(06) 1.0860(12) 1.0886(14) 1.0793(41) 1.0776(33) r(C2-X) { n V 1.0913(06) 1.0912(06) 1.0898(12) 1.0899(14) 1.0898(44) 1.0916(36) r(C3-H3) { n V 1.0846(05) 1.0847(06) 1.0838(12) 1.0845(14) 1.0793(41) 1.0776(33) r(C4-X) { n V 1.7355" 1.7355* 1.5096(22) 1.5140(26) 1.5139(20) 1.5193(20) r(C5-X) { n V 1.0911(06) 1.0910(06) 1.0860(12) 1.0915(15) 1.0913(22) 1.0883(21) r(C6-X) { n V 1.7355d 1.7355d 1.746d 1.746d 1.5139(20) 1.5193(20) r(C7-H5) { n V 1.1014(07) 1.0942(09) 1.1083(09) 1.1006(09) <(C1C2C3) { n V (120.59)c (120.65)c 120.77(10) 120.85(12) (121.02)c (120.84)c Appendix C. Structural Parameters <(C2C3C4) j * <(C3C4C5) { J <(C4C5C6) { * <(C5C6C1) { 1 <(C6C1C2) { J <(C2C1H1) { J <(C3C2X) { * <(C2C3H3) { J <(C3C4X) { * <(C4C5X) { J • <(C1C6X) { J <(CXC7H5) { J RMS Error6 RMS Error' a priori estimates r(Cl-C2) r(C2-C3) r(C3-C4) r(C4-C5) r(C5-C6) r(C6-Cl) r(Cl-Hl) r(C2-X) r(C3-H3) 118.40(06) 118.37(06) 122.40(11) 122.34(11) (117.80)c (117.89)c 122.40(11) 122.34(11) 118.40(06) 118.37(06) 120.67(06) 120.83(07) 119.70(03) 119.67(03) 120.67(06) 120.83(07) 118.75d 118.75d (121.09)6 (121.05)c 118.75d 118.75d 0.2372 0.2385 h 1.4040(02) 1.4040(02) 1.3920(02) 1.3873(02)c 1.3873(02)c 1.3920(02) 1.0850(02) 1.0910(02) 1.0850(02) 119.63(13) 119.84(15) 119.67(19) 119.55(22) (118.72)c (119.06)6 121.50d 121.50d 119.69(16) 119.16(19) 120.33(17) 120.61(22) 118.78(11) 118.61(12) 121.30(11) 121.29(13) 120.34(13) 120.55(15) 120.43(19) 120.09(22) 119.30d 119.30d 110.67(09) 111.78(11) 0.2989 0.3466 1.38500(025) 1.38300(025) 1.39000(025) 1.39000(025) 1.38510(025)c 1.3820d 1.08500(025) 1.0910(02) 1.08500(025) 118.75(28) 119.17(23) 121.34(26) 120.19(22) (118.78)6 (120.42)c 121.34(26) 120.19(22) 118.75(28) 119.17(23) 120.43(80) 120.32(62) 119.48(45) 119.57(35) 120.43(80) 120.32(62) 119.50(27) 119.96(21) (120.60)c (119.78)c 119.50(27) 119.96(21) 110.98(12) 111.73(15) 0.2204 0.2281 j 1.40400(015) 1.40400(015) 1.39200(015) 1.3873(02)c 1.3873(02)c 1.39200(015) 1.08500(015) 1.0910(01) 1.08500(015) Appendix C. Structural Parameters 135 r(C4-X) r(C5-X) r(C6-X) r(C7-H5) <(C1C2C3) <(C2C3C4) <(C3C4C5) <(C4C5C6) <(C5C6C1) <(C6C1C2) <(C2C1H1) <(C3C2X) <(C2C3H3) <(C3C4X) <(C4C5X) <(C1C6X) <(CXC7H5) 1.7355 1.0910(02) 1.7355d 121.10(05)c 118.10(05) 122.30(05) 118.10(05)c 122.30(05) 118.10(05) 120.70(05) 119.45(05) 120.70(05) 118.75d 120.95(05)c 118.75d 1.51200(045) 1.09100(025) 1.7460d 1.09880(025) 121.100(055) 119.000(055) 119.000(055) 118.570(055)c 121.50d 120.23(04) 120.700(055) 119.450(055) 120.700(055) 121.100(055) 120.950(055) 119.30d 111.120(025) 1.51200(025) 1.0910(01) 1.51200(025) 1.09880(015) 121.100(025)c 118.100(025) 122.300(025) 118.100(025)c 122.300(025) 118.100(025) 120.700(025) 119.450(025) 120.700(025) 121.100(025) 120.950(025)c 121.100(025) 111.12(01) a Refer to Fig. A.22 for structure and atom numbering of molecules. Bond distances (r) in A and bond angles (<) in degrees. In the least squares fit to experimental dipolar couplings the weight given to each dipolar coupling is (error) where the errors are reported in Table B.6. 6 Parameters which are indicated with "n" are calculated with no vibrational corrections to dipolar couplings and parameters indicated with "v" are calculated with vibrational corrections. c Dependent parameter is calculated from the bond angles and lengths of the carbon skeleton. d Parameter not adjusted during fit. e RMS Error in Hz between calculated and experimental dipolar couplings. ' RMS Error in Hz between vibrationally corrected and experimental dipolar couplings. 9 For the least squares fitting routine the weight associated with the a priori estimates is (error) w n e r e the errors are reported in brackets. h ra structure from Ref. [108]. 1 Structure taken from Ref. [109] and m-dichlorobenzene[108]. J Structure taken from ra-dichlorobenzene[108]. Appendix D Order Parameters 136 Appendix D. Order Parameters 137 Table D.13: Order Parameters from Fits to Dipolar Couplings0 Order Solute Parameter b Liquid Crystal ZLI 1132 55 wt% 1132/EBBA EBBA Sample #1 #2 #3 acetonitrile V 0.1305(24) . 0.1174(22) 0.1049(19) propyne Szz V 0.2162(01) 0.1449(01) 0.0592(01) 1,3,5-trichlorobenzene Szz n -0.2576 -0.2244 -0.1956 Sample #4 #5 #6 chlorobenzene <? / n 0.23724(26) 0.16334(18) 0.19191(21) &zzS V 0.23921(14) 0.16469(09) 0.19355(11) q Q ) n 0.29192(15) 0.17442(10) 0.09667(13) '-'xx ^yy 1 V 0.29559(08) 0.17661(06) 0.09767(07) toluene n 0.23233(35) 0.15668(23) 0.18503(28) V 0.23539(35) 0.15874(23) 0.18747(28) C C J n 0.29035(20) 0.18412(12) -0.14883(23) &xx ^yy | V 0.29427(20) 0.18652(12) -0.15017(24) 1,3,5-trichlorobenzene SZz n -0.28838 -0.19938 -0.20462 Sample #7 #8 #9 p-dichlorobenzene <? / n 0.30854(20) 0.28860(19) 0.38838(25) V 0.31062(13) 0.29055(12) 0.39099(16) C Q ) n 0.23495(07) 0.15805(17) 0.05427(16) >Jxx ^yy \ V 0.23654(04) 0.15915(10) 0.05469(10) p-chlorotoluene <7 / n 0.32950(20) 0.29479(13) 0.36830(22) V 0.33489(16) 0.29961(14) 0.37432(18) c c / n 0.21944(13) 0.16033(13) 0.09268(18) iJxx ^yy | V 0.22247(10) 0.16259(10) 0.09416(14) Appendix D. Order Parameters 138 1,3,5-trichlorobenzene Szz n -0.27447 -0.22350 -0.21132 Sample #10 #11 #12 p-dichlorobenzene <7 / n 0.30761(12) 0.28021(11) 0.34586(14) V 0.30967(12) 0.28209(11) 0.34818(14) q Q ) n 0.23307(04) 0.15293(11) 0.05006(09) " i i ^yy I V 0.23465(04) 0.15399(11) 0.05044(09) p-xylene <7 1 n 0.33637(43) 0.28066(36) 0.29811(38) °zzS V 0.34157(59) 0.28500(49) 0.30272(52) q q j n 0.21971(14) 0.16824(15) 0.12447(15) ^ I I ^yy | V 0.22495(19) 0.17226(21) 0.12756(21) 1,3,5-trichlorobenzene Szz n -0.27362 -0.21705 -0.18862 Sample #13 #14 #15 o-dichlorobenzene <7 / n 0.17132(67) 0.13099(50) 0.12676(45) ^ZZ] V 0.17232(59) 0.13180(44) 0.12773(39) C C J n 0.34056(38) 0.24319(25) 0.16231(12) &xx ^yy I V 0.34343(33) 0.24525(22) 0.16369(11) o-chlorotoluene <? / n 0.16600(56) 0.13327(45) 0.14387(50) ozzs V 0.16984(64) 0.13654(51) 0.14767(56) q q / n 0.34678(39) 0.24827(27) 0.18577(39) ^ I I ] V 0.35486(64) 0.25419(31) 0.19101(44) <? / n -0.00037(16) 0.00468(15) 0.01128(25) JxzS V -0.00125(67) 0.00363(59) 0.00949(78) 1,3,5-trichlorobenzene n -0.26436 -0.20103 -0.17730 Sample #16 #17 #18 o-dichlorobenzene <7 / n 0.17527(69) 0.14611(56) 0.14081(50) '-'zz 1 V 0.17630(60) 0.14702(49) 0.14189(44) C C / n 0.34743(38) 0.26802(30) 0.17843(14) &xx ^yy | V 0.35038(33) 0.27028(26) 0.17995(12) Appendix D. Order Parameters 139 o-xylene <? { n 0.16646(71) 0.14369(61) 0.14859(61) Jzz 1 V 0.16956(76) 0.14637(65) 0.15138(66) c c / n 0.35394(46) 0.28468(34) 0.24869(22) ^xx ^yy I V 0.35912(49) 0.28877(36) 0.25212(24) 1,3,5-trichlorobenzene n -0.27012 -0.22217 -0.19696 Sample #19 #20 #21 m-dichlorobenzene <? / n 0.05755(18) 0.02678(16) -0.03363(16) '-'ZZ 1 V 0.05809(18) 0.02702(17) -0.03399(16) C C / n 0.48431(25) 0.39784(22) 0.36841(22) ^ I I ^yy \ V 0.48777(25) 0.40067(22) 0.37099(23) m-chlorotoluene <? 7 n 0.04365(20) 0.02255(17) -0.01916(17) ^ z z | V 0.04561(25) 0.02374(21) -0.01930(20) c c J n 0.48878(33) 0.40026(28) 0.38199(29) L^ XX 2/2/1 V 0.49674(40) 0.40663(33) 0.38766(34) <? / n 0.02617(30) 0.01539(28) 0.00259(35) '-'xz'l V 0.02632(35) 0.01583(32) 0.00369(41) 1,3,5-trichlorobenzene n -0.27747 -0.22314 -0.19190 Sample #22 #23 #24 m-dichlorobenzene n 0.05581(14) 0.02422(10) -0.03567(15) >->zz1 V 0.05633(15) 0.02444(10) -0.03605(15) C C / n 0.46513(24) 0.36476(19) 0.38717(23) *^ £x *^ 2/2/ 1 V 0.46846(24) 0.36740(20) 0.38989(24) m-xylene n 0.03912(46) 0.02550(35) -0.00036(34) «->zzl V 0.03921(37) 0.02557(28) -0.00047(28) C C / n 0.48225(64) 0.37482(51) 0.41029(61) '-'yy | V 0.49831(55) 0.38034(44) 0.41663(52) 1,3,5-trichlorobenzene Szz n -0.26706 -0.20488 -0.20207 Appendix D. Order Parameters 140 a For axis definitions see Fig. A.22. For corresponding structural parameters refer to Tables C.8, C.9, CIO, C.ll and C.12. Numbers in round brackets are standard deviations in the last two reported digits of varied parameters. 6 Order parameters which are indicated with "n" are calculated with no vibrational corrections to dipolar couplings and parameters indicated with "v" are calculated with vibrational corrections. Appendix D. Order Parameters 141 Table D.14: Order Parameters for solutes in Sample #25 from Fits to Dipolar Couplings" Order o-dichloro- o-chloro- o-xylene 1,3,5-tri-Parameter6 benzene toluene chlorobenzene <? J n 0.17412(69) 0.16894(57) 0.16503(71) -0.26812 V 0.17514(60) 0.17286(65) 0.16811(76) c c J n 0.34494(42) 0.35172(40) 0.35116(46) '-'xx ^yy | V 0.34785(37) 0.35990(65) 0.35628(49) <? / n -0.00017(16) V -0.00108(69) 0 For axis definitions see Fig. A. 22. For corresponding structural parameters refer to Table C.l l . Numbers in round brackets are standard deviations in the last two reported digits of varied parameters. 6 Order parameters which are indicated with "n" are calculated with no vibrational corrections to dipolar couplings and parameters indicated with "v" are calculated with vibrational corrections. Appendix E Scaled and Calculated Order Parameters 142 Appendix E. Scaled and Calculated Order Parameters 143 Table E.15: Scaled and Calculated Order Parameters Liquid Crystal ZLI 1132 55 wt%1132/EBBA EBBA Oscaled I1 cca,lc\b It Qcalc\c qscaled 11 ccalc\b It ccalc\c cscaled 11 qcalc\b 11 qcalc\c da0 /{°a0 ) A D a/3 )  Da0 I Wa0 ) I \°a0 ) °aQ I \Da0 ) I \Ja0 ) acetonitrile S2 2 0.1386/0.1371/0.1258 0.1135/0.1187/0.1087 0.1012/0.1419/0.1305 propyne S22 0.2296/0.1861/0.1983 0.1402/0.1233/0.1308 0.0571/0.0827/0.0895 chlorobenzene S22 0.2269/0.2136/0.2195 }yy -0.2537/-0.2376/-0.2452 0.0267/0.0239/0.0257 0.1792/0.1769/0.1812 -0.1857/-0.1865/-0.1930 0.0064/0.0095/0.0118 0.1783/0.1839/0.1879 -0.1341/-0.1586/-0.1655 -0.0441/-0.0252/-0.0223 toluene S22 0.2233/0.2351/0.2255 -0.2512/-0.2392/-0.2398 0.0279/0.0040/0.0143 0.1728/0.1789/0.1699 -0.1879/-0.1866/-0.1863 0.0151/0.0077/0.0163 0.1728/0.1593/0.1495 -0.1556/-0.1561/-0.1552 -0.0171/-0.0032/0.0056 p-dichlorobenzened (with p-chlorotoluene) S2 2 0.3096/ / 0.2821/-S r o -0.2727/ / -0.2183/--0.0638/--0.0369/ /-7-0.3489/ / --0.1989/ /--0.1500/ /-p-dichlorobenzene (with p-xylene) S22 0.3096/0.3011/0.3007 -0.2721/-0.2651/-0.2649 -0.0375/-0.0359/-0.0357 yy 0.2820/0.2836/0.2817 -0.2180/-0.2246/-0.2234 -0.0640/-0.0589/-0.0582 0.3481/0.3592/0.3539 -0.1993/-0.2268/-0.2240 -0.1488/-0.1324/-0.1298 p-chlorotoluene S22 0.3338/0.3518/0.3391 S w -0.2777/-0.2760/-0.2715 Sxx -0.0560/-0.0757/-0.0676 0.2909/0.2884/0.2758 -0.2244/-0.2259/-0.2202 -0.0665/-0.0625/-0.0556 0.3340/0.2987/0.2836 -0.2090/-0.2074/-0.2000 -0.1250/-0.0912/-0.0835 p-xylene SZ2 0.3415/0.3777/0.3549 Syy -0.2832/-0.2803/-0.2713 S x x -0.0583/-0.0974/-0.0836 0.2850/0.2910/0.2689 -0.2286/-0.2264/-0.2160 -0.0563/-0.0645/-0.0528 0.3027/0.2664/0.2417 -0.2151/-0.2005/-0.1879 -0.0875/-0.0659/-0.0538 Appendix E. Scaled and Calculated Order Parameters 144 o-dichlorobenzened (with o-chlorotoluene) S22 0.1783/ / 0.1423/-Syy -0.2669/ / -0.2035/-0.0885/ /--/--/-0.0612/ /-0.1358/ / --0.1550/ /-0.0191/ / -o-dichlorobenzene (with o-xylene) S22 0.1785/0.1919/0.2078 0.1436/0.1458/0.1582 Syy -0.2667/-0.2601/-0.2701 Sxx 0.0881/0.0682/0.0623 0.2038/-0.2089/-0.2186 0.0602/0.0630/0.0604 0.1358/0.1224/0.1351 -0.1541/-0.1820/-0.1928 0.0182/0.0595/0.0577 o-chlorotoluene SZ2 0.1757/0.1799/0.1830 yy -0.2715/-0.2588/-0.2638 Sxx 0.0957/0.0789/0.0808 Sxz -0.0013/-0.0237/-0.0132 0.1474/0.1447/0.1474 -0.2109/-0.2087/-0.2135 0.0635/0.0640/0.0660 0.0039/-0.0021/0.0063 0.1570/0.1365/0.1393 -0.1801/-0.1846/-0.1897 0.0230/0.0480/0.0503 0.0101/0.0268/0.0353 o-xylene S22 0.1717/0.1838/0.1755 S w -0.2677/-0.2583/-0.2584 Sxx 0.0960/0.0744/0.0828 0.1429/0.1450/0.1386 -0.2125/-0.2087/-0.2084 0.0695/0.0636/0.0698 0.1449/0.1320/0.1253 -0.1932/-0.1850/-0.1843 0.0482/0.0529/0.0590 m-dichlorobenzened (with m-chlorotoluene) S2 2 0.0572/ / 0.0262/-}yy -0.2691/-0.2118/-7" 7 --0.2080/-0.1817/- 7--0.0334/ /--0.1656/ /-0.1990/ / -m-dichlorobenzene (with m-xylene) S22 0.0577/0.0637/0.0595 0.0258/0.0265/0.0240 Syy -0.2688/-0.2543/-0.2649 -0.2075/-0.2092/-0.2190 S x x 0.2111/0.1906/0.2054 0.1816/0.1827/0.1949 -0.0336/-0.0342/-0.0367 -0.1651/-0.1970/-0.2071 0.1988/0.2312/0.2438 m-chlorotoluene Szz 0.0449/0.0299/0.0237 0.0230/0.0235/0.0201 Syy -0.2674/-0.2597/-0.2649 -0.2093/-0.2099/-0.2142 S x x 0.2224/0.2297/0.2411 0.1862/0.1863/0.1941 S I 2 0.0259/-0.0222/-0.0064 0.0154/-0.0020/0.0104 -0.0189/0.0021/-0.0004 -0.1810/-0.1873/-0.1919 0.2000/0.1852/0.1924 0.0036/0.0251/0.0376 Appendix E. Scaled and Calculated Order Parameters 145 m-xylene SZ2 0.0401/0.0178/0.0176 0.0270/0.0225/0.0232 -0.0004/0.0152/0.0163 Syy -0.2707/-0.2616/-0.2617 -0.2150/-0.2101/-0.2090 -0.1942/-0.1837/-0.1819 S I X 0.2305/0.2438/0.2441 0.1879/0.1876/0.1858 0.1946/0.1685/0.1655 1,3,5-trichlorobenzene S w -0.2736/-0.2550/-0.2818 -0.2170/-0.2143/-0.2403 -0.1886/-0.2087/-0.2353 a For axis definitions see Fig. A.22. 6 Sffi values are predicted using potential parameters from Fit #8 (see Table 3.3 and 3.4). ° Softf v a m e s a r e predicted using potential parameters from Fit #9 (see Table 3.4). d Order parameters were not used when determining potential parameters and thus S^c are not reported. The S^led are shown for comparison. 

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