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The mechanisms of orientational order in nematic liquid crystals Li, Yuzheng 1990

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T H E MECHANISMS OF ORIENTATIONAL ORDER IN NEMATIC LIQUID CRYSTALS By YUZHENG LI B. Sc. (Chemistry) Jilin University A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November 1990 © YUZHENG LI , 1990 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 The University of British Columbia Vancouver, Canada Date •5a 2A illO DE-6 (2/88) Abstract We have analyzed the NMR spectra of a series of 19 di-halobenzenes having C, or C2V symmetry dissolved in a special mixture of nematic liquid crystals, i.e., 55 wt% 1132/EBBA-d 2. This mixture has the unique feature that dideuterium dissolved in it experiences a zero average electric field gradient. Therefore one can assume that for this mixture the contribution to the molecular order due to the interaction between the aver-age electric field gradient and the quadrupole moment of the molecule can be neglected. It has been suggested that the orientational order also depends on the size and shape of the solutes and a model has been used to calculate the order parameters. Another model relates the ordering to the molecular polarizability anisotropy. A description of the ordering of molecules having Ca symmetry requires 3 independent order parameters and thus provides a strong test for the different models of orientational order. Comparisons are made between our experimentally determined order parameters and the theoretical values obtained using the size and shape, and the polarizability models. Very good agree-ment is obtained for the size and shape model. However, it is found that any mechanism, involving a molecular property which is approximately bond additive, can not predict the differences found between the ortho- and meta-dihalobenzenes. Consequently, a poor agreement results from the polarizability model when a bond-additive scheme is used to calculate the molecular polarizability. Further investigation of the correlation between order parameters and solute molecules suggests that the molecular shape dominates the orientational behavior. n Table of Contents Abstract ii List of Tables vi List of Figures vii List of Abbreviations x Acknowledgement xi To my mother xii 1 Introduction 1 1.1 A Short Review . 1 1.2 Objectives of This Thesis 3 2 The Orientational Order in Liquid Crystals 5 2.1 Liquid Crystals 5 2.2 The Nematic Order 6 2.3 Description of the Orientational Order the Order Parameter . . . . 8 2.4 Mean Field Theory the Orientational Potential 10 2.5 High Resolution NMR as a Technique to Study the Orientation in Liquid Crystals 12 2.5.1 The Hamiltonian 12 2.5.2 Dipolar Coupling 13 in 2.5.3 Quadrupole Coupling 13 3 The Two Mechanisms Model 15 3.1 Electric Field Gradient Molecular Quadrupole Moment Interaction . . . 15 3.2 Removing the Electric Field Gradient 17 3.3 Size and Shape Model 17 4 Experimental 23 4.1 Sampling Techniques 24 4.2 NMR Spectroscopy 24 4.3 Spectral Analysis 25 4.3.1 Calculation of a NMR Spectrum 25 4.3.2 Determination of Starting Parameters 26 5 Results 27 5.1 Spectral Parameters of Solutes Oriented in 55 wt% 1132/EBBA-d2 at 304K 27 5.2 Calculation of Order Parameters 30 5.3 Removing the Dependence of Order Parameter on Solute Concentration 36 6 Discussion 39 6.1 Size and Shape Model Comparison between Experimental and Calcu-lated Order Parameters 40 6.2 Nature of the Orienting Forces in Zero-Field-Gradient Nematics . . . . 41 6.2.1 Variation of Molecular Order Parameters with Molecules . . . . 41 6.2.2 Contribution from the molecular polarizability 53 6.3 Determination of Molecular Structure 61 IV 7 Conclusion Appendices A Spectral parameters B Assumed Molecular Structure C Molecular polarizabilities Bibliography List of Tables 5.1 Structural parameters assumed for di-halobenzenes. fAngles are assumed to be in the regular hexagonal model. fThe molecule is assumed to be planar 31 5.2 Experimental and calculated values for the order parameters of di-halobenzenes, dissolved at 1-5 mole percent in the 55 wt% 1132/EBBA-d2 liquid-crystal mixture 33 6.1 Principal values for the order parameters of di-halobenzenes with C, sym-metry, dissolved at 1-5 mole percent in the 55 wt% 1132/EBBA-d2 liquid-crystal mixture 45 6.2 Bond angles and order parameters determined for ortho-dihalobenzenes oriented by the 55 wt% 1132/EBBA-d2 liquid-crystal mixture 62 vi List of Figures 2.1 A schematic representation of the molecular structures that could give rise to the nematic phase, and an example of the nematogen: PA A 6 2.2 (a) Schematic representation of the molecular arrangement in a nematic liquid crystal, (b) The Euler angles required to describe the orientation of a molecule in a nematic liquid 7 2.3 Schematic representation of an ethane solute oriented in a nematic phase 9 2.4 The coordinate system required to describe the interaction between two axially symmetric molecules 10 3.1 Structure of the 5CB molecule 20 3.2 Elastic tube model for the short range interactions 22 5.1 [a]: The proton spectrum of 1,3-fluorobromobenzene partially oriented in the 55 wt% 1132/EBBA-d2 nematic phase, [b]: The computer simulated spectrum 28 5.2 Numbering of the nuclear spins and choice of the coordinate systems used for all calculations in this thesis 29 5.3 Deuteron spectrum of EBBA-d2 contained in the 55 wt% 1132/EBBA-d2 liquid crystal mixture 37 6.1 Size and shape model: Theoretical versus uncorrected experimental values of order parameters Sa& for solutes in 55 wt% 1132/EBBA-d2 42 vii 6.2 Size and shape model: Theoretical versus corrected experimental values of order parameters Sap for solutes in 55 wt% 1132/EBBA-d2 43 6.3 Size and shape model: Theoretical versus corrected experimental order parameters of solutes in 55 wt% 1132/EBBA-d2 44 6.4 Size and shape model: As in Figure 6.9 for diagonal elements St'x< , Sy>y' , and SZIZI of the order matrixes of C, symmetry solutes in 55 wt% 1132/EBBA-d2. Correlation coefficient = 0.985 46 6.5 Size and shape model: Theoretical versus experimental values of the angles rotated clockwise to diagonalize the order matrixes Sap for Cs symmetry solutes in 55 wt% 1132/EBBA-d2. Correlation coefficient = 0.856. . . . 47 6.6 Size and shape model: Theoretical versus experimental values of the asym-metry parameter: rj =(Sn S22 )/Ssa of all solutes in 55 wt% 1132/EBBA-d2 48 6.7 The correlation between the experimental order parameter and molecular dimensions 51 6.8 The additivity of substituent effects on the polarizabilities of ortho- and meta-dihalobenzenes 54 6.9 Polarizability-mean square electric field interaction in 55 wt% 1132/EBBA-d2 56 6.10 Polarizability model: Corrected experimental versus theoretical order pa-rameters of solutes in 55 wt% 1132/EBBA-d2 57 6.11 Polarizability model: Theoretical versus experimental values of the angles rotated clockwise to diagonalize the order matrixes Sap for Cs symmetry solutes in 55 wt% 1132/EBBA-d2. Correlation coefficient = -0.040. . . . 58 6.12 Polarizability model: Theoretical versus experimental values of the asym-metry parameter: 77 =(5n -522 )/S& of solutes in 55 wt% 1132/EBBA-d2. 59 viii 6.13 The deformation [dashed line] of ortho-dihalobenzenes from the hexagonal structure [solid line] ix List of Abbreviations n The director of hquid crystals NMR Nuclear magnetic resonance Order parameters 1132 Merck ZLI 1132 [see chapter 4] EBBA-d2 N-(4-ethoxybenzylidene)-2,6-dideutero-4-n-butylaniline 5CB 4-cyano-4'-n-pentyl-biphenyl PAA P-azoxyanisole U{Q) The orientational potential Q~ zz component of the molecular quadrupole moment tensor efg Electric field gradient Fzz ZZ component of electric field gradient tensor due to hquid crystals Et. The energy difference between the trans and gauche conformations kxr , kzz The elastic force constants <*cx0 Polarizability tensor Ea Electric field x y z Molecule-fixed axis system Molecule-fixed axis system which diagonalizes the order matrix X Y Z Laboratory-fixed axis system MW Microwave ED Electron diffraction X Acknowledgement I wish to give my grateful thanks to Dr. E. E. Burnell for his encouragement, expert advice and guidance, which have been a tremendous help to me throughout the course of this work. I am greatly indebted to those colleagues : Dr. Dan S. Zimmerman, Leon ter Beek, and Chandrakumar T.. Dr. Dan S. Zimmerman's size and shape program gave me a set of intelligent starting parameters, which facilitated the NMR spectral analysis. Leon ter Beek assisted me in the NMR experiments and the use of UNIX operating system. I thank Chandrakumar T. for useful discussions. I benefited a lots from Dr. Burnell's warm and friendly research group. Thanks for everybody's generosity in giving collaboration and support during this project. Many thanks are also extended to Dr. S.O. Chan and the technical staff of the NMR service lab. I should also like to thank the people who synthesised the EBBA-<£2 liquid crystal in Amsterdam. The financial assistance in the form of a teaching and research assistantship is highly appreciated. I reserve my deepest gratitude to my wife, Liu, for her patience and understanding. xi To my mother Deqing Ma xii Chapter 1 Introduction 1.1 A Short Review In the last two decades interest in hquid crystals has strongly increased and we have suc-ceeded in obtaining a phenomenological understanding of their unique optical, electrical, and thermal properties. The situation is quite different when it comes to the molecular physics of liquid crystals. In many cases there is - still little insight into the molecular factors that determine the magnitude and anisotropy of a property. In particular, the mechanism of orientational order, which is the most important characteristic of hquid crystals, is still not well understood. Orientation in hquid crystals is generated by the anisotropic intermolecular forces. Unfortunately, a precise statistical treatment of the molecular interactions is not available for complicated systems like liquid crystals, where the constituent molecules are large and exist in many conformations. A popular choice is to average the physical interactions between one molecule and all others to get a mean single-molecule potential, which serves to orient every molecule in the nematic phase. Although this is quite a big approximation, it turns out that mechanisms, based on this mean field theorydo give a reasonable description of some nematic systems. A mean-field potential for the liquid-crystal molecule then becomes the target of extensive researches. Previous experience concludes that an accurate understanding of the orienting forces will not come about from studies on hquid crystals themselves because 1 Chapter 1. Introduction 2 of their complex structure. Therefore, small rigid and symmetric molecules are used to probe the molecular interactions in liquid crystals. Due to the anisotropic environment, a solute molecule dissolved in a liquid-crystal solvent will be oriented. That is, different orientations of the molecule relative to an external frame of reference are no longer equally probable. If the solute concentration is small [1 to 5 mole percent] one would expect that the liquid-crystal environment is not strongly perturbed and therefore the solute should experience the same orientational forces as liquid-crystal molecules themselves. Thus studies of the orientational behavior of solutes can be used to elucidate information on the intermolecular forces in nematics. NMR spectroscopy ^ is suited for studying orientational order because quantities such as the dipolar and quadrupolar couplings, and the anisotropy in chemical shifts are known to be functions of the orientation of the molecule with respect to the applied magnetic field direction. For the solute dissolved in a nematic liquid crystal, however, the molecular motion is restricted through interactions with the neighboring liquid-crystal molecules. The NMR spectra are then weighted averages over molecular orientation. As a result, dipolar and quadrupolar couplings, and anisotropics in chemical shifts and indirect couplings appear in the high-resolution spectrum. The observed dipolar and quadrupolar couplings can be used to calculate the degree of average molecular ordering, measured by order parameters ® 5^ . Usually, the liquid-crystal molecule contains large numbers of protons and the signals from it are broad and unresolved. The obtained values of the order parameters Sop can provide information on the phys-ical interaction which leads to molecular orientation. Over the last 30 years, studies have generally centered around correlating the solute order parameters with molecular prop-erties such as moments of inertia'4,5^ the polarizability t6,8', and the molecular shape'7). Such studies have explained the experimental results of some liquid crystals. However, the exact nature of the orienting forces in liquid-crystals is still not well understood '9'. Chapter 1. Introduction 3 Burn ell and coworkers have studied systematically a series of solutes, starting from hydrogen, C^-, C2v-, and D2h-symmetry moleculesl8-10-12-14' as well as the 5CB liquid crystal molecule'16'. A great deal of physical information has been obtained about the mechanisms of orientational ordering [see chapter 3]. Two major orienting mechanisms have been proposed: [1] Electric field gradient molecular quadrupole moment interaction'13'. [2] Short-range size and shape interaction'11'. Since the quadrupole moment is not well determined for large and low-symmetry molecules, we choose to remove the first mechanism by using a liquid-crystal mixture with zero electric field gradient [efg], e.g., 55 wt% 1132 and 45 wt% EBBA-d2. Exper-iments with D2 have shown that this special mixture exhibits zero efg'16', and then for other small solutes dissolved in it at low concentration, we shall assume that they also experience a zero field gradient. In the 55 wt% 1132/EBBA-d2 liquid-crystal mixture, the size and shape mechanism is found to explain the orientational behavior of some high-symmetry solutes, but it was reported that the polarizability mechanism can also reproduce experimental results'14'. In order to test the size and shape model, a logical step is to study a collection of low symmetry molecules, which have three to five inde-pendent order parameters. Because all the order parameters must describe orientation in exactly the same environment, such solutes should constitute a stringent test for any model. 1.2 Objectives of This Thesis The primary goals for this thesis are : [l] To give a stringent test for the size and shape model, [2] To learn the physics of hquid crystals. Chapter 1. Introduction 4 For these purposes, a series of dihalobenzenes having C, or C 2 v symmetry were chosen as solutes. Three order parameters are required to give a complete description of the orientation of C # symmetry molecules. For C2t> molecules, two order parameters are required. The deuteron spectrum of EBBA-d2, contained in the liquid-crystal inixture 55 wt% 1132/EBBA-d2) is used to monitor the liquid-crystal environment between different samples. Thus, our choice of solutes and hquid crystals constitutes a strong test for the, size and shape model. Chapter 2 The Orientational Order in Liquid Crystals In this chapter, we are going to lay out the theoretical background for this thesis. We will describe the orientational order in liquid crystals, and how we are able to measure it using NMR techniques. Because most of the orienting mechanisms make some sort of mean field approximation, the general idea of the mean field theory will also be discussed. 2.1 Liquid Crystals Liquid-crystal molecules can form an intermediate state between the crystalline solid and the isotropic liquid. 0.5% or so of organic substances, on heating, collapse to a turbid melt. If this melt is spread on a flat plate, one can see it is birefringent, showing colored areas under polarized light and having different optical properties parallel and perpendicular to the plate. Further heating of the substance may produce a clear liquid. This type of behavior is called liquid crystalline, and the phases involved are called mesophases. Liquid crystals tend to occur with compounds that are elongated, highly asymmetric in shape, often having well-separated polar and nonpolar portions to the molecule. In the theoretical description of liquid-crystal phases, it is common to model these molecules as rigid rods with complete cylindrical symmetry around the molecular long-axis. Figure 2.1 gives a typical example of their molecular structure. However, at this moment there is no way of predicting with certainty whether or not a given molecule will exhibit liquid-crystal mesophases. 5 Chapter 2. The Orientational Order in Liquid Crystals 6 SUBSTITUENT AROMATIC GROUP LINKAGE GROUP SUBSTITUENT C H 3 0 - ^ O ^ - W » N - ^ O ^ - 0 C H 3 P-AZOXYANISOLE (PAA) Figure 2.1: A schematic representation of the molecular structures that could give rise to the nematic phase, and an example of the nematogen: PAA. 2.2 The Nematic Order In 1922, Friedel proposed a scheme, based primarily on the symmetry of the hquid crystalline phases, to classify them into three basic types'17': smectic, cholesteric and nematic. Most of the work in the liquid-crystal field has been done on nematics because of its simplicity in symmetry and the fact that most of the hquid crystal displays [LCD] rely on nematic liquids. A pictorial representation of the nematic phase is given in figure 2.2. The molecules which form the nematic phase are, in general, long and rod-like, as shown in figure 2.1. When forming the nematic phase, these molecules tend to align with their long axes parallel to each other. Macroscopically a preferred direction is thus defined. That is called the director n of hquid crystal molecules. If this is the only ordering, i.e., partial alignment along the director n, the phase is called nematic. Further experiments showed that there is an infinite rotational symmetry [Dooh] around the direction n, i.e., the phase is uniaxial; and the director n is apolar although the constituent molecules may be polar. Chapter 2. The Orientational Order in Liquid Crystals 7 Figure 2.2: (a) Schematic representation of the molecular arrangement in a nematic liquid crystal, (b) The Euler angles required to describe the orientation of a molecule in a nematic liquid. Chapter 2. The Orientational Order in Liquid Crystals 8 It should be noted that there is no long-range correlation between the centers of mass of the molecules in the nematic phase. The liquid-crystal molecules can translate freely. 2.3 Description of the Orientational Order the Order Parameter The average orientation of a rigid solute molecule in a nematic phase [see figure 2.3] can be described by a traceless, 3x3 symmetric matrix, Sop , introduced by Saupe in 1964.M. Sop = ^ < ZcosBacos8p -6ap> (2.1) where a,3=x, y, or z are axes in the molecule-fixed coordinate system. 6a or Bp is the angle between the director n of liquid crystals and the direction a or 8 in the molecule. Thus cos#a and cosBp specify the instantaneous orientation of the Cartesian frame fixed to the solute relative to the nematic director n. The angle brackets denote that Sap is the time- or ensemble-averaged value of the direction cosines. Sap is called the order parameter and can act as a measure of the time average over orientational fluctuations. This ordering comes from the anisotropic intermolecular forces in liquid crystals. The magnitude and number of independent elements in the ordering matrix Sap depend on the shape anisotropy and symmetry of the solute'2'. For example if a molecule has C 3 or higher symmetry along the z axis, this choice of axis system causes Szz to be the only independent orientation parameter. For Szz =1 the z-axis is parallel to the liquid-crystal director n, and for Szz =-0.5 the z-axis is perpendicular to n. Moreover, if the orientation is entirely random we would have < cos28zz >=l/3 and Szz =0. Thus Sap is a measure of the average alignment. Chapter 2. The Orientational Order in Liquid Crystals Figure 2.3: Schematic representation of an ethane solute oriented in a nematic phase The liquid-crystal molecules are represented by rigid rods in the figure. The long axis z of ethane is preferentially oriented parallel to the nematic director n . The size of ethane molecule is exaggerated in this figure. Chapter 2. The Orientational Order in Liquid Crystals 10 Figure 2.4: The coordinate system required to describe the interaction between two axially symmetric molecules The angles 6 and (f) a r e polar and azimuthal angles with the intermolecular vector r as the common polar axis, respectively. 2.4 Mean Field Theory the Orientational Potential Intermolecular forces determine the orientational ordering because they strongly depend on the relative orientation of adjacent molecules. For example, the rigid rod-like molecules of nematics have the pair interaction potential as follows: U12 =Ul3{r,6ll<i>l,0ai<l>2) (2.2) For axially symmetric molecules, the potential U12 really depends only on r, 6X, 92, and the combination 4>\ — 4>2 [see figure 2.4 ]. The exact nature of the molecular interactions is not specified here. A rigorous molecular theory of the liquid-crystal system based on a pairwise inter-action potential as complicated as equation (2.2 ) is impossibly difficult. A simple but adequate approach is to derive a theory in the mean field approximation'1!. That is, Chapter 2. The Orientational Order in Liquid Crystals 11 we take one single molecule in the nematic phase, and average its interactions with all other surrounding molecules over all possible coordinates. This leads to a single-molecule potential representing [roughly] the mean field of intermolecular forces acting on each in-dividual molecule. To obtain the single-molecule potential from equation (2.2 ), it is necessary to take three successive averages of the function Uu . First, we average Uu over all orientations of molecule 2, i.e., 02. Next, we average U12 over all values of intermolecular separation r. Finally, we average U\2 over all relative combinations <j>i — fa. These three averaging processes provide us with a single-molecule potential which only depends on its own orientation with respect to the director. For the nematic phase with one order parameter., for example, the rod-like molecules, Maier and Saupe(1959, I960)'18' first derived an average single-molecule potential in the mean field approximation: A the strength of the interaction V the molar volume. In practice, A is often taken to be an adjustable parameter to fit the experimental results. This mean potential can in turn be used to calculate order parameters using the Boltzmann expression: S _/(3cos 2fl-l)e*p(-Ml)dcosfl 2 fexp(-¥$-)dcos 6 A comparison between the calculated order parameters and experimental values presents a test for the mean-field potential. In the following section, the principles of determining order parameters by NMR spectroscopy will be demonstrated. Chapter 2. The Orientational Order in Liquid Crystals 12 2.5 High Resolution NMR as a Technique to Study the Orientation in Liquid Crystals 2.5.1 The Hamiltonian The high field spin Hamiltonian for a partially oriented molecule includes four terms'19': chemical shift, spin-spin coupling, dipolar coupling, and for the nuclei with spin greater than one half, nuclear quadrupole coupling. Each of these properties is anisotropic and must be represented by a second rank tensor. H = Hz + Hj + HD + HQ = - E ^ + E ^ i + l W i : - ^ ) + E f fflz-If) (2-5) i ij ij i Vi=—7/1(1 — o~izz)H0: is the resonance frequency of nucleus i. <Tizz is the average ZZ component of the chemical shielding tensor in the lab-fixed frame of reference. H0 is the magnetic field strength 7;: is the magnetogyric ratio of nucleus i Jij: is the isotropic indirect scalar coupling constant between nuclei i and j Dif is the dipolar coupling constant between nuclei i and j B{\ is the quadrupole coupling constant for nucleus i The chemical shift: Hz, is determined by the electronic structure of the molecule and the electric environment in the liquid crystals. The anisotropy of J-coupling has been neglected because spin-spin coupling between protons arises principally from the Fermi contact interaction'20J, which is isotropic. Chapter 2. The Orientational Order in Liquid Crystals 13 2.5.2 Dipolar Coupling Dipolar coupling is a pure magnetic interaction between two magnetic dipoles: Dn = < (3co.2% - l)/2rj > (2.6) iij —distance between nuclei i and j 6ij the angle between the magnetic field H0 (H0 is parallel to the nematic director n here) and the ij direction in the molecule. If averaging over the internal molecular motion and the molecular reorientation can be done separately, equation [2.6] can be written: Ai = - ^ ? < ^ > S i ) (2.7) 5,j = < \cos70ij — \ > the order parameter for the ij direction in the molecule. The proton NMR spectra of solutes in hquid crystal solvents are dominated by dipolar couplings. Due to the relatively rapid molecular tumbling, dipole-dipole splittings get time-averaged and the spectra appear well resolved. The spectral linewidths range from 1 to 5 Hz, but spectral widths are scaled down considerably, compared with solid state NMR spectra, which are of the order of kilohertz. These direct couplings can be used to determine the molecular structure and order parameters. The order parameters can be used to study the liquid-crystal intermolecular forces which lead to the molecular orientation. The structural parameters are not easily available in the hquid state. 2.5.3 Quadrupole Coupling A nucleus with an electric quadrupole moment will interact with the electric field gradient at the site of the spin. For the nucleus with spin 1=1, e.g., deuteron, the term Qi has the Chapter 2. The Orientational Order in Liquid Crystals 14 following form: * = (2.8) eQi is the electric quadrupole moment of nucleus i eqS{is the internal electric field gradient [efg] at nucleus i, averaged over the molecular reorientation, and is assumed to be axially symmetrical Si is the order parameter describing the average orientation in the direction associated with the symmetry axis of the electric field gradient tensor at nucleus i The external efg due to liquid crystals is not included in equation 2.8 and will be discussed in chapter 3. The deuteron quadrupole couplings usually stay within hundreds of kilohertz. We can deuterate liquid crystal molecules and the quadrupole coupling can be obtained directly from the 2 H NMR spectra. Then the average orientation of the deuterated molecular part can be investigated. Chapter 3 The Two Mechanisms Model In this chapter, the studies on orientational mechanisms, performed in E.E. Burnell's laboratory, will be reviewed briefly. The size and shape model will be the main topic in later discussion. 3.1 Electric Field Gradient Molecular Quadrupole Moment Interaction The studies of molecular hydrogen'8,13,16,21' and methane'22' dissolved in nematic liquid crystals, carried out in E. E. Burnell's group seven years ago, gave a great deal of insight into the nature of the physical interactions responsible for orientational ordering. One of the findings is that the ratio of the quadrupolar to dipolar couplings'8', B/D, for HD and D 2 ) is liquid crystal dependent and different from the gas-phase value. This was surprising because one would expect the ratio to be a molecular property. E. E. Burnell et al. explained this variation in B/D by proposing the presence of an average electric field gradient [efg] due to the liquid crystal environment. The total electric field gradient, experienced by each deuteron, is then a sum of an internal contribution due to the electrons and the other nuclei within the molecule, and an external term due to the liquid crystals. Thus the quadrupolar coupling is liquid crystal dependent and is given by. B = < eQD/h > (Fzz - eqSzz ) (3.9) where Fzz is the mean electric field gradient due to the liquid crystal. eqS22 is the 15 Chapter 3. The Two Mechanisms Model 16 intramolecular electric field gradient at the deuteron, averaged over the molecular reori-entation, assuming axial symmetry around the deuteron-deuteron bond direction. The value of Szz can be calculated from the observed dipolar coupling using equation 2.7. Subsequently equation 3.9 can be used to obtain the average electric field gradient Fzz if the intramolecular contribution to the electric field gradient at the site of deuteron is assumed to be the same as that in the gas phase. We treat Fzz a s a property of the hquid crystal itself and assume it is a constant for all solutes. The presence of a non-zero mean electric field gradient gives rise to an orienting mechanism'13'. The interaction of the molecular quadrupole moment, Qajg, with the mean electric field gradient, F^, in the hquid crystal environment is given by. BQ = -\HFafiQc* (3io) where a,0=X, Y, or Z are axes in the lab. frame. Qap is the molecular quadrupole moment. Fa/3 are components of the mean electric field gradient tensor in the hquid crystal. Because of the cylindrical symmetry in nematic phases, the quadrupole Hamiltonian for solute molecules with planar symmetry reduces to: HQ{B,4>) = -Fzz [\Qzz {\cos79 - )^ + ± ( Q „ - Qm )(yin26cos2<f> - \sin26sin2<t>) 2 3 -r-Qxy (-sin26sin<f>cos<j))] (3.11) o & This orientational potential accounts for most of the orientation of hydrogen'13' in sev-eral hquid crystals. For several other small solutes dissolved in 1132 and EBBA, however, the experimental and predicted values of order parameters were not in a good agreement. This difference implies the presence of an additional orienting mechanism. Experiments Chapter 3. The Two Mechanisms Model 17 suggest that the magnitude of order parameters is correlated with the molecular dimen-sions, that is to say, the size and shape is also working to orient the molecules via a steric interaction. 3.2 Removing the Electric Field Gradient In order to investigate the additional size and shape mechanism, a nematic phase with zero electric field gradient would be an ideal solvent. It was found that Fzz has opposite sign in the liquid crystals 1132 and EBBA. In the mixture of 55 wt % 1132 and 45 wt% EBB A the mean electric field gradient was found to be zero in experiments at 301.4K with ZV16'. Therefore we shall assume that for this mixture the interaction between the electric field gradient and molecular quadrupole moment is negligible and that the size and shape interaction is the only orienting mechanism. 3.3 Size and Shape Model It is useful to separate the total orientational potential into two independent portions, that is, the long range interaction between some molecular property and its corresponding mean field in liquid crystals and the short range steric repulsion. U(Q) = U.r(n) + Ulr(Q) (3.12) where Q, represents the angles, 8,<f> and V> between the molecular axes and liquid-crystal director [see figure 2.2 ]. The notation D is meant to describe the orientation of a molecule of any symmetry. The foregoing discussion, given in section 3.1, supports a second order tensorial form of long range interaction, that is, the liquid crystal provides an average electric field gradient which interacts with the molecular quadrupole moment of the solute. Chapter 3. The Two Mechanisms Model 18 For the short-range interaction, the potential imposed by the liquid crystal was as-sumed to be repulsive in nature and was modelled by van der Est et al.^- 1 0' 1 4' 2 3" 2 4! and later modified by Zimmerman and Burnell'11' in the following manner. First, the nematic liquid crystal is regarded as a continuous medium with two force constants, kz and kXy, representing the strength of the interaction parallel and per-pendicular to the director n, respectively. Second, the solute molecule is modelled as a collection of van der Waals spheres centered around the nuclei of their corresponding atoms. When a solute molecule is fit inside the liquid crystal continuum by stretching it along and perpendicular to the director, there is a restoring force acting on the solute. This restoring force is assumed to be an orienting force. In van der Est et al.'s pioneering work'10' , kz was neglected. The restoring force on the solute due to its deformation of the liquid crystal continuum in the XY direction has the form: F(fi) = -kXY <fr(a,Q)da = -kXYC(Q) (3.13) kXY: is a Hooke's law force constant in the direction perpendicular to the director n r(a, fi): is the vector from the origin to the projection of the molecule onto the XY plane, a: is the angle between the lab. X axis and r(a, P.) C(Q): is the circumference around the projection The orientational potential was then: Uer(Q) = -j>F(Sl)d* = kXYC2(Cl)/2 (3-14) Chapter 3. The Two Mechanisms Model 19 12 solutes having C3 or higher symmetry, dissolved in the 55 wt% 1132/EBBA-d2 mixture, were studied by van der Est et al.'10'. The ordering of such molecules is charac-terized by only one independent order parameter, 5 „ , where z is the molecular symmetry axis. Experimental values of Szz for the 12 solutes were compared with those calculated using the size and shape potential [3.14], where only one parameter, the force constant kyy > w as allowed to vary. The results were very encouraging, the force constant kyy=5.0 dyn/cm was determined by a least squares fit with correlation coefficient =0.985. Kok Mei et al.'14' investigated the orientational behavior of 15 C 2 v and D2h molecules in the 55 wt % 1132/EBBA-d2 mixture. They used the size and shape potential [3.14] to predict the order parameters and very good agreement was reached between experimental and predicted values. The temperature dependence of order parameters in 55 wt % 1132/EBBA-d2, and orientation in pure 1132 and pure EBBA, were also successfully described by inclusion of the electric field gradient quadrupole moment mechanism in addition to the size and shape model. The force constant kyy =5.57 dyne/cm was obtained by a least-squares fit to the experimental order parameters of the 27 C 2 v , D2/,, C 3 or higher symmetry, small rigid solutes dissolved in the special mixture. In additional experiments the solute 5CB [see figure 3.1] was used. 5CB is a large and flexible molecule which can exist in many conformations. Its proton spectrum is not well resolved and the deuteron spectrum of perdeuteriated 5CB doesn't give enough quadrupolar splittings to determine unambiguously the orientation of the molecule for every conformation. Thus the size and shape potential [3.14] was used in which the measured quadrupolar splittings serve as constraints for the determination of the model parameters, fcyy and Etg . Etg is the difference between the trans and gauche energies. From such a model order parameters and conformational probabilities are obtained. The resulting values are then used to calculate the quadrupolar splittings. In order to get a good agreement between the calculated and experimental values of quadrupolar splittings, Chapter 3. The Two Mechanisms Model Figure 3.1: The molecular structure of 4-cyano-4'-n-pentyl-biphenyl [5CB]. 20 N E C the value kxy=2.9 dyne/cm was used'16'. This value is lower than the value obtained from fitting the 27 rigid solutes, mentioned above. Also the fit was obtained using Etg =4.45 kJ/mol. This value is much larger than the normally accepted gas phase value Etg =2.09 kJ/mol'25'. Zimmerman et al.'11' tried to solve this problem by proposing a new size and shape potential: U(n) =\k[l-(^}C'(Q) (3.15) where Z(fl) is the length of the projection of the molecule onto the Z axis (see figure 3.5), £k is the strength of the interaction in the direction perpendicular to the director. The equation above can be derived from the following consideration: the interaction depends on the angles between the surface of the solute molecule and the director n of hquid crystals. We model the molecular surface as a cylinder whose long axis is in Chapter 3. The Two Mechanisms Model 21 the direction of the director. It follows that the interaction energy has two terms: one proportional to the surface area of the top and the bottom of the cylinder, and the other proportional to the surface area of the side of the cylinder. U{Q) = 2kXY*r2 + 2kz*rl (3.16) where r and / are the radius and the length of the cylinder. Equation 3.15 is obtained from equation 3.16 using r = C(fi)/(27r) and / = Z(fi) to approximate the dimensions of the cylinder, k = kxy/x, and f = —2irkz/kxy • When this new model is applied to fit the experimental data of the 27 small rigid solutes mentioned before, the optimum values k=3.92 dyne/cm and ^ =5.01 are obtained. These values can reproduce the deuteron spectra of perdeuteriated 5CB with a reasonable value Etg =2.91 kJ/mol. In the spirit of the size and shape model, we will use these values of k and £ as properties of the 55 wt% 1132/EBBA-d2 liquid-crystal mixture and we shall assume that they are independent of the solute. Chapter 3. The Two Mechanisms Model Figure~3.2: Elastic tube model for the short range interactions 22 The potentials given by equations 3.14 and 3.15 depend on the orientation of the molecule through the projections Z(f2) and C(fi) , where Z(Q) is the projection of the molecule onto the space fixed Z axis, and C(U) is the circumference around the projection onto the X Y plane. The Z axis corresponds to the direction of of the liquid-crystal director. The molecule is modelled as a collection of van der Waals spheres. Chapter 4 Experimental The hquid crystal solvent used was a mixture of 55 wt% 1132: Merck ZLI 1132 and 45 wt% EBBA-d2: N-(4-ethoxybenzyhdene)-2,6-dideutero-4-n-butylanihne. The solutes investigated [see figure 5.7] were purchased from a variety of chemical suppliers. All the solutes, 1132 and EBBA-<£2 were used without further purification. The composition of 1132 is given as follows'26': [1]: 24% [2]: 36% [3]: 25% [41: 15% Ri=CsHn Ri=CjHis Ri=C$Hn fl2=Ph-C=N i22=Ph-C=N #2=Ph-C=N 722=Ph-Ph-C=N EBBA-d2 was synthesised in Amsterdam, Prof. C.A. de Lange's Lab. and its molecular structure is: 23 Chapter 4. Experimental 24 The phase transition temperatures have been reported for both 1132 and EBBA: EBBA'27); Crystal Nematic 35i±Vc Isotropic 1132t23l: Nematic34^? Isotropic 4.1 Sampling Techniques 16.07 grams of 1132 and 13.04 grams of EBBA-<£2 were mixed in a 50 ml Erlenmeyer flask by heating the mixture to the isotropic state and vortexing it. After repeating several times, the 55 wt% 1132/EBBA-d2 mixture was ready and stored in a bottle wrapped in aluminum film for latter use. The NMR samples were prepared in 5mm o.d. tubes. The liquid and solid state solutes were directly added to the liquid crystal mixture to produce a concentration of less than 5 mole percent. The tubes were then capped and thoroughly mixed by vortexing the samples in the isotropic phase. All samples were stored in the dark to prevent degradation of EBBA-d2. 4.2 NMR Spectroscopy The proton spectra of the solutes oriented in the 55 wt% 1132/EBBA-d2 mixture were recorded using a Bruker WH-400 FT NMR spectrometer operating at 400.1 MHz, and the deuteron spectra of EBBA-<£2 were recorded immediately following the proton ones without removing the samples from the magnet, both at the same temperature of 304.OK. For the proton spectra and the deuteron spectra: respectively, the frequency range was 9 kHz and 20 kHz; the pulsewidth was 6 to 8 s^ and 30/xs; the number of data points in the FID signal was 32k and 4k; and the number of scans was 32 and 10000. In order to get well resolved spectra, the samples must be homogeneously mixed. Sample spinning was found to reduce the linewidths considerably. About 30 minutes were allowed to reach Chapter 4. Experimental 25 temperature equilibration before the spectra were acquired. 4.3 Spectral Analysis 4.3.1 Calculation of a NMR Spectrum Basically, the NMR spectral analysis means solving the time-independent Schrodinger equation for a nuclear spin system. H9 = EV (4.17) Here H=HZ + Hj + HD -\- HQ [ see section 2.5.1, page 12], $ is the wave function for the spin system. The transition frequencies can then be calculated from the eigenvalues of the Hamiltonian matrix and are functions of chemical shifts and coupling constants. The spectra in this thesis are sufficiently complex that a computer was used to fit them by an iterative procedure. The program LEQUOR'28' has been used to treat the high-resolution spectra of par-tially oriented molecules. To do the analysis, a set of trial input parameters [see below], i.e., chemical shifts and coupling constants, was fed into the LEQUOR program and a trial spectrum was calculated corresponding to the spin system under consideration. Comparing the calculated spectrum with its experimental one, some of the spectral lines were assigned. From the assignment, the program refines some of the starting parame-ters using a least squares method. This process was continued until all the experimental peaks were assigned with acceptable root mean square [RMS] errors between the calcu-lated spectrum and the experimental one. The final spectral parameters are shown in appendix A. Chapter 4. Experimental 26 4.3.2 Determination of Starting Parameters It is important to get a good starting point for the LEQUOR program, so reasonable starting line assignments can be made. For most of the molecules in this thesis, no NMR data have been located in the literature, so the following steps are taken. Initial values for chemical shifts are taken to be the same as the isotropic ones'29'. Indirect coupling con-stants are calculated according to an additive scheme, suggested by S. Castellano'30-33'. It turns out that, compared to fixing these J couplings to the popular values reported, i.e., JOTf/,0=7.549Hz, J m e f a = 1.379Hz and J,xira=0.650Hz for all benzene derivatives, the S. Castellano's predicted J-values can reduce the RMS in LEQUOR by a factor of two and the standard deviation of every spectral parameter decreases too. The size and shape model'11' is used to calculate initial values of order parameters using an ideal molecular geometry based on a regular hexagonal carbon skeleton, with all bond angles 120°, and bond lengths deduced from that of mono-halobenzenes. The force constants used are those obtained from fitting the 27 high-symmetry solutes [see chapter 3.3]. In the cases of 2-fluorobenzonitrile and 3-fluorobenzonitrile, however, the microwave geometry is available'34,35' and is used in the calculations. The choices of structural parameters are presented in table 5.1 and plotted in appendix B. Finally, the starting points for dipolar coupling constants are obtained from those order parameters and our assumption of molecular geometry by a subroutine added to the program LEQUOR. Only the chemical shifts and direct couplings are allowed to vary in the iterative analysis. Chapter 5 Results 5.1 Spectral Parameters of Solutes Oriented in 55 wt% 1132/EBBA-<22 at 304K As an example, Figure 5.1 gives the proton spectrum of 1,3-difluorobromobenzene ori-ented in the 55 wt% 1132/EBBA-d2 mixture together with its computer simulation. For each solute, the total number of lines ranged from 10 to 100, depending on its symmetry and number of spins. Except for ortho- and meta-fluorobromobenzenes '3 6' oriented in a lyotropic mesophase, previous high-resolution NMR studies of solutes in hquid crystals have not, to the au-thor's knowledge, been reported for our choice of molecules [see figure 5.2]. Hence it is worth summarizing the final spectral parameters in appendix A. For every solute, all the observed peaks appeared in the spectrum calculated from the program LEQUOR. The covariance among all dipolar couplings and chemical shifts, as reflected in the small errors reported for these parameters in appendix A, can be neglected. Consequently, all dipolar couplings and chemical shifts are accurately determined. The numbering of the nuclei and the definition of the coordinate systems used for all the solutes are shown in figure 5.2. 27 Chapter 5. Results 28 Figure 5.1: [a]: The proton spectrum of 1,3-fluorobromobenzene partially oriented in the 55 wt% 1132/EBBA-d2 nematic phase, [bj: The computer simulated spectrum ! [a] i • i - i set -mi [b] tooo -2000 Solute concentration = 1-5 mole percent; temperature = 304K Chapter 5. Results 29 cC cC cC " a * v . cC V CM cC CC . XT Br 9 I I 9 9 Figure 5.2: Numbering of the nuclear spins and choice of the coordinate systems used for all calculations in this thesis. Chapter 5. Results 30 5.2 Calculation of Order Parameters The expression of the dipole-dipole coupling between spins i and j can, for the Cs sym-metry molecules in the coordinate system shown in figure 5.2, be written as'19': 2Sxy{cosdijxcos6ijy)} (5.18) This equation is correct under two assumptions: [1] the anisotropy of the indirect coupling Jt°n"° is negligible, [2] equation (5.18) refers to a system of static nuclei. The first assumption is justified for proton-proton couplings (see chapter 2, pagel2 ). The assumption [2] may be argued in the following way: our experiments were carried out at room temperature. The nuclear vibrational motion is usually much faster than the molecular reorientation. Then the average over the vibrations and reorientations can be done separately and a least squares fit of the average nuclear coordinates to the dipolar couplings is done by a computer program SHAPE'37', based on equation (5.18). Experimental order parameters Sa$ for an assumed geometry are then obtained and shown in table 5.2. For our choice of solutes, their microwave (MW) or electron diffraction (ED) geometry has not been located in the literature. However, as far as order parameters are concerned, the geometry assumed [see table 5.1] is accurate enough for the purpose of comparing the values of experimental and calculated order parameters. Two indications to support the assumed geometrical coordinates can be drawn here: Qualitatively, by simply looking at the molecular shape [appendix B], plotted according to the assumed structural parame-ters, we see that the van der Waals radii of all non-bonding hydrogen and halogen atoms do not overlap. This is consistent with the idea of van der Waals volume, i.e., the area Chapter 5. Results 31 Table 5.1: Structural parameters assumed for di-halobenzenes. fAngles are assumed to be in the regular hexagonal model. fThe molecule is assumed to be planar. MOLECULE STRUCTURAL PARAMETER Bond Length(A) Van der Waals Radii(A) rC-H=1.084 rc-c=1.397 RB=1.01 rc-ci=1.711 Rc=i.n rC-Br=1883 RF=\A1 rc_/=2.08 Rci=l-77 rc_F=1.324 #Bp=1.92 For all rc-jv = 1.1581 i2/=2.06 Dihalobenzenes l 3 8 , 3 9 ' rC-cJV=l-4509 RC(N)=l.7& rc_c=1399 r c _H = 1084 rc-jv = 1.159 rc_F=1.308 Fluorobenzonitrile t34'35' rc-cAr=l-433 impenetrable for other molecules with thermal energies at ordinary temperatures. For ortho-dihalobenzenes, the two halogens' van der Waals spheres overlap. The possibility of this fact leading to structural distortion will be discussed in section 6.3. Quantita-tively, experimental order parameters for different solutes can be fitted with reasonable RMS values using the assumed geometry [see table 5.1 ]. The internuclear distances, and consequently the experimental and calculated dipolar couplings, are internally consistent for those molecules. These facts suggest that the assumed hexagonal symmetry is a good approximation. Equation (5.18) is also true for para-dihalobenzenes, except that the last term vanishes (5^=0 here). This sort of difference in the mathematical formulae will not be given in the following discussion, because the problem of high symmetry molecules can always be treated as a special case of that for lower symmetry molecules. Theoretical values of order parameters were obtained without any adjustable param-eters from the nuclear coordinates and van der Waals radii shown in table 5.1, used as Chapter 5. Results 32 input data into the size and shape program. The values used for the force constants k and ( are those from the fit, described in section 3.3, to the 27 high-symmetry, rigid solutes. Order parameters are also calculated from the polarizability mechanism using the assumed hexagonal carbon skeleton [see section 6.2.2 for details]. All the calculated values are listed in table 5.2. A discussion regarding the relationship between the order parameters and molecular structure will be given in section 6.1 and section 6.2. Chapter 5. Results 33 Table 5.2: Experimental and calculated values for the order parameters of di-halobenzenes, dissolved at 1-5 mole percent in the 55 wt% 1132/EBBA-d2 liq-uid-crystal mixture. SOLUTE ORDER PARAMETERS W RMSW (Hz) ExptW ExptW CalcW CalcW 1,2- chlorobromobenzene Sxx 0.1459 0.1536 0.1641 0.2041 szz -0.2113 -0.2225 -0.2003 -0.2081 2.13 Sxy 0.0125 0.0131 0.0298 0.0444 1,2- chloroiodobenzene Sxx 0.1532 0.1566 0.1718 0.2247 szz -0.2234 -0.2283 -0.2048 -0.2412 1.35 SXy 0.0428 0.0437 0.0610 0.0462 2- chlorobenzonitrile Sxx 0.1688 0.1737 0.1830 0.1576 SZ2 -0.2292 -0.2359 -0.2140 -0.1811 1.48 s -'ni 0.0693 0.0713 0.0708' -0.0101 1,2-bromoiodobenzene Sxx 0.1362 0.1446 0.1739 0.2571 szz -0.2119 -0.2250 -0.2097 -0.2511 1.67 SXy 0.0267 0.0283 0.0324 0.0000 2-bromobenzonitrile s 0.1640 0.1727 0.1845 0.1903 szz -0.2340 -0.2465 -0.2180 -0.1952 1.06 Sxy 0.0595 0.0627 0.0428 -0.0539 2-fluorobenzonitrile s x x 0.1690 0.1740 0.1800 0.1134 szz -0.2148 -0.2212 -0.2042 -0.1535 0.55 SXy 0.0968 0.0997 0.1176 0.0391 1,3-chlorobromobenzene s •Jxx 0.1984 0.2027 0.2345 0.2041 szz -0.2225 -0.2273 -0.2052 -0.2081 0.189 Sxy 0.0117 0.0119 0.0210 0.0444 1,3-chloroiodobenzene sxx 0.1966 0.1985 0.2527 0.2247 szz -0.2124 -0.2145 -0.2103 -0.2412 0.64 Sxy 0.0289 0.0292 0.0417 0.0462 3-chlorobenzonitrile Sxx 0.2336 0.2381 0.2616 0.1576 szz -0.2398 -0.2444 -0.2203 -0.1811 0.65 Sxy 0.0746 0.0760 0.0536 -0.0101 1,3-bromoiodobenzene SXX 0.1956 0.2062 0.2750 0.2571 Szz -0.2099 -0.2212 -0.2152 -0.2511 0.54 Sxy 0.0179 0.0189 0.0207 0.0000 3-bromobenzonitrile Sxx 0.2310 0.2366 0.2835 0.1903 Szz -0.2337 -0.2393 -0.2250 -0.1952 0.54 Sxy 0.0599 0.0613 0.0332 -0.0539 Chapter 5. Results Table 5.2 Continues SOLUTE ORDER PARAMETERS <l> RMS<2> (Hz) Expt<3> ExptW Calc<6> Calc*6) 1,3-fluorobromobenzene s x x 0.1664 0.1692 0.1929 0.1605 szz -0.2026 -0.2060 -0.1946 -0.1847 0.91 Sxy 0.0486 0.0494 0.0684 0.0930 3-fluorobenzonitrile Sxx 0.1906 0.2060 0.2161 0.1134 szz -0.2139 -0.2312 -0.2092 -0.1535 0.95 Sxy 0.0977 0.1056 0.0996 0.0391 1,4-chlorobromobenzene Sxx -0.0812 -0.0840 -0.1421 -0.0856 0.69 szz -0.2330 -0.2410 -0.1995 -0.2179 1,4-chloroiodobenzene Sxx -0.1051 -0.1073 -0.1603 -0.0771 0.001 Szz -0.2427 -0.2479 -0.2041 -0.2497 4- chlorobenzonitrile Sxx -0.1179 -0.1209 -0.1649 -0.0388 0.429 szz -0.2507 -0.2571 -0.2132 -0.1866 1,4-bromoiodobenzene s '-'XX -0.1048 -0.1138 -0.1761 -0.1178 3.60<"> szz -0.2205 -0.2395 -0.2081 -0.2643 1,4-fluorobromobenzene Sxx -0.0342 -0.0359 -0.0944 -0.0420 11.06^ szz -0.2091 -0.2195 -0.1925 -0.1869 4-fluorobenzonitrile Sxx -0.0751 -0.0775 -0.1179 0.0042 1.84<"> szz -0.2290 -0.2366 -0.2063 -0.1547 Chapter 5. Results Note: (1): The axis system is chosen such that: z is perpendicular to the ring plane of the solute molecule, x and y are in the plane [see figure 5.2 ]. (2) : R M S is the error of the fit of the experimental dipolar couplings to the assumed molecular geometry by the program S H A P E . (3) : Uncorrected experimental order parameters are obtained from the observed dipolar coupling constants. (4) : Corrected experimental order parameters are obtained by removing the dependence of order parameter on solute concentration [see section 5.3]. (5) : The order parameters are calculated using the size and shape program with the molecular structure in table 5.1 as input. The force constants used are k=3.92dyne/cm, and £ =5.01. They are obtained from a least squares fit of 27 other small rigid solutes to the size and shape model'11'. (6) : The order parameters are calculated using the interaction between the molecular polarizability of the solute and the mean squared electric field EQE^ due to the liquid-crystal environment. The anisotropy in the mean squared electric field has been obtained by a least squares fit of the calculated order parameters Sa/3 for Chapter 5. Results 36 all solutes to the experimental values. See section 6.2.2 for discussion. (*) The large RMS values arise from the fact that their experimental spectra are not satisfactorily resolved. See the corresponding large RMS values from LEQUOR in appendix A. 5.3 Removing the Dependence of Order Parameter on Solute Concentration Generally, the orienting potential for every individual molecule is slightly different be-cause each sample is not measured under identical conditions. A change in temperature and solute concentrations always makes a contribution to the potential energy. It was found that the deuteron spectrum of EBBA-d2, which is a measure of the ordering of the hquid crystal molecules, depends on temperature and solute concentration too. It should be possible to remove the influence of solute concentration on experimental order parameters using the deuteron spectra of EBBA-d2. x X An example of the deuteron spectra of EBBA-rf2 is shown in figure 5.3. It consists of four lines which arise from the quadrupolar couplings of the deuterons and the dipolar Chapter 5. Results 37 Figure 5.3: Deuteron spectrum of EBBA-d2 contained in the 55 wt% 1132/EBBA-d2 hquid crystal mixture. Chapter 5. Results 38 couplings between the deuterons and the adjacent ring protons'46'. The quadrupolar splittings were within the range of 16.52 to 17.77 kHz and dipolar couplings range from 679 to 819 Hz. The linewidth lies between 800 and 900 Hz. In the 55 wt % 1132/EBBA-d2 mixture without solutes at 304 K the value obtained for the quadrupolar coupling, Bp, is 17.94 kHz, and for dipolar coupling, D^D , is 774 Hz'23'. Because of the relatively large errors in DHD> only the the quadrupolar coupling, BD , was used to correct the order parameters ' 2 4'. •Sexp. [corrected ] = ~T X Sexp. (5.19) Where Au^e is the quadrupolar splitting of EBBA-d2 in the pure 55 wt % 1132/EBBA-d2 mixture, and Avtoiute is the quadrupolar splittings of EBBA-d2 in the sample contain-ing the solute. This set of corrected order parameters is presented in table 5.2. Chapter 6 Discussion In this chapter, the relationship between molecular structure and orientational order will be explored. We start by comparing the experimental order parameters with the theo-retical values calculated from the size and shape model. Then we search for more general correlations between the order parameters and molecular properties. It is hoped that ex-tra evidence in support of the size and shape mechanism will be found. In addition, the low-symmetry molecules are also used to test another model, the interaction of the mean squared electric field with the molecular polarizability. Finally, the structural parameters of ortho-dihalobenzenes in the 55 wt% 1132/EBBA-d2 solvent will be determined from the measured dipolar couplings. In this thesis, a homologous series of benzene derivatives, i.e. di-halobenzenes, are chosen as solutes. The di-halobenzenes are known to be planar molecules. When the two halogen substituents are different, ortho- and meta-dihalobenzenes have C, symmetry, and para-dihalobenzenes have C2v symmetry. For C, symmetry molecules, the choice of a molecule-fixed coordinate system [see figure 5.2] with the x and y axes in the plane requires three independent order parameters SXi, S« and S^ j, to describe the orientation. Since C2v molecules have two perpendicular planes of symmetry, the choice of a molecule-fixed coordinate system [see figure 5.2] with the x axis in the ring plane and the y axis in both planes leaves only Sxx aad S« to be independent. 39 Chapter 6. Discussion 40 6.1 Size and Shape Model Comparison between Experimental and Cal-culated Order Parameters The order parameters for all solutes are given in table 5.2. Figure 6.1 shows a plot of all the experimental values of order parameters against the calculated results from size and shape potential equation 3.15 [see page 20]. As can be seen, the agreement between experimental and calculated values is very good. This supports the claim that in this mixture the ordering of solutes is dominated by the size and shape interaction and the electric field gradient in the hquid crystal mixture is negligible. As in figure 6.1, figure 6.2 shows a plot for the corrected order parameters Sexp.[corrected]-Comparing figure 6.1 with figure 6.2, we notice that the correction is too small to see any significant difference. This fact suggests that for small amounts of impurities, like the solutes here, dissolved in the hquid crystals, the liquid-crystal environment is not strongly perturbed, as indicated by the almost constant values of Avtoiute in appendix A. To emphasize the differences between experimental and theoretical values, figure 6.3 is a plot for the four elements of the order matrix: Szz , Sxx , Syy , and Sxy [for C 2 v solutes, Sxy =0]. It can be seen that the calculated order parameters, according to the orienting potential equation 3.15, have small but systematic deviations from the experi-mental values. Szz , the order parameter perpendicular to the benzene ring, are overes-timated; Sxx are overestimated for ortho- and meta-dihalobenzenes and underestimated for para-dihalobenzenes; Syy are underestimated for ortho- and meta-dihalobenzenes and overestimated for para-dihalobenzenes. is predicted well. A new attempt to refine the size and shape potential has been made by D.S. Zimmerman and much better fit has been obtained'40'. The order matrix Sa$ for a C, symmetry molecule has three independent elements. Chapter 6. Discussion 41 In order to facilitate the comparison, it is useful to diagonalize 5 a£ . This can be done through rotation of the x and y axes around the z axis, leaving only two independent non-zero elements, Sx>x> and Syiy> (in the principal axis systems;', y', z'). Sz>x> stays unchanged under the coordinate transformation. The results are presented in table 6.1 and are plotted in figure 6.4. As can be seen, the agreement between experimental and calculated values is quite good. Comparison is also made between the diagonalization angles $ of experimental and calculated order matrixes. The results are presented in table 6.1 and plotted in figure 6.5. In addition, let the asymmetry parameter 77 be defined as: 77 = { S n g " 5 " } (6.20) 033 S33 , S22 > o r "^ii *s t n e diagonal element of order matrix with the largest, inter-mediate and smallest absolute value respectively. The ratio 77 and the diagonalization angle <$ are expected to be, to a good approximation, independent of small changes in the liquid-crystal environment. A comparison between the values of experimental and calculated 77, and $ should reveal how closely the model follows the variation in solute molecules. The two parameters $ and 77 are severe tests for any model as they are differ-ences in two large numbers. Thus the correlations for the size and shape model, shown in figures 6.5 and 6.6, are very good. 6.2 Nature of the Orienting Forces in Zero-Field-Gradient Nematics 6.2.1 Variation of Molecular Order Parameters with Molecules Now let's discuss how the order parameters are related to molecular properties. It is helpful to consider the di-halobenzenes Listed in appendix B from two distinct points of Chapter 6. Discussion 42 Figure 6.1: Size and shape model: Theoretical versus uncorrected experimental values of order parameters 5^ for solutes in 55 wt% 1132/EBBA-d2 -0.2 -0. 0 Sop(exp.) 0.2 0.4 The calculated order parameters, also shown in tables 5.2, are obtained using size and shape potential 3.15. For solutes with Cs symmetry the values of Sxx , Syy , Szz , and Sxy are plotted. For solutes with C2V symmetry the values of Sxx , Syy , and Szz are plotted. The definitions of the axes, x, y, and z are given in figure 5.7. The type of the points refers to molecules listed in appendix B. The force constants k=3.92dyne/cm and 4=5.01, are used and these values are obtained from a least squares fit to potential equation 3.15 for other 27 rigid solutes'11'. T=304.0K, and the concentration of solutes in each sample is 1 to 5 mole percent. The correlation coefficient is 0.983. Chapter 6. Discussion 43 Figure 6.2: Size and shape model: Theoretical versus corrected experimental values of order parameters Sop for solutes in 55 wt% 1132/EBBA-d2 0.4 0.2 e •J) 0 -0:2 i r V. L 1 J L J L 0.2 J I 0 x 0.2 Sa/S(exp.) As in Figure 6.9 for corrected experimental values of order parameters So& • Correlation coefficient = 0.983. 0.4 Chapter 6. Discussion 44 Figure 6.3: Size and shape model: Theoretical versus corrected experimental order pa-rameters of solutes in 55 wt% 1132/EBBA-d2 S^exp.) (c) Vexp.) (d) As in Figure 6.10 for individual elements of the ordering matrix: (a) Szz , correlation coefficient = 0.473; (b) Sxx , correlation coefficient = 0.995; (c) Syy , correlation coefficient = 0.994; (d) , correlation coefficient = 0.930. Chapter 6. Discussion 45 Table 6.1: Principal values for the order parameters of di-halobenzenes with Ct symmetry, dissolved at 1-5 mole percent in the 55 wt% 1132/EBBA-d2 liquid-crystal mixture. SOLUTE ORDER PARAMETER Rotation Angle (exp./cal.) Experimental Calculated 1,2-chlorobromobenzene Sx'x' 0.1477 0.1707 Sy'y' 0.0636 0.0295 $= -8.60 /-12.46 Sz'x' -0.2113 -0.2003 1,2-chloroiodobenzene Sx'x' 0.1714 0.1948 Sy'y' 0.0521 0.0100 $=-22.94 /-20.67 Sz'z' -0.2234 -0.2048 2-chlorobenzonitrile Sx'x' 0.2026 0.2108 Sy'y' 0.0266 0.0031 $=-26.00 /-21.47 Sz'z' -0.2292 -0.2139 1,2-bromoiodobenzene Sx'x' 0.1463 0.1811 Sy'y' 0.0656 0.0286 $=-20.72 / -12.59 Sz'z' -0.2119 -0.2097 2-bromobenzonitrile Sx'x' 0.1928 0.1958 r Sy'y' 0.0412 0.0222 $=-25.87 / -14.76 Sz'z' -0.2340 -0.2180 2-fluorobenzonitrile Sx'x' 0.2227 0.2432 Sy'y' -0.0095 -0.0390 $=-28.03 /-28.24 Sz'z' -0.2132 -0.2041 1,3- chlorobromobenzene Sx'x' 0.1992 0.2362 Sy'y' 0.0233 -0.0310 $=-3.81/-4.53 Sz'z' -0.2225 -0.2052 1,3- chloroiodobenzene Sx'x' 0.2011 0.2585 Sylyl 0.0113 -0.0482 $=-8.87 /-7.89 Sz'z' -0.2124 -0.2103 3-chlorobenzonitrile Sx'x' 0.2559 0.2708 Sy'y' -0.0161 -0.0505 $=-16.63 /-9.75 Sz'z' -0.2398 -0.2203 1,3-bromoiodobenzene Sx'x' 0.1974 0.2763 Sy'y' 0.0125 -0.0611 $=-5.59 /-3.53 Sz'z' -0.2099 -0.2152 3-bromobenzonitrile Sx'x' 0.2458 0.2867 Sy'y' -0.0121 -0.0617 $=-13.83 /-5.49 Sz'z' -0.2337 -0.2250 1,3-fluorobromobenzene Sx'x' 0.1886 0.2149 Sy'y' 0.0203 -0.0203 $=-18.01 / -17.79 Sz'z' -0.2088 -0.1946 3-fluorobenzonitrile Sx'x' 0.2418 0.2541 Sy'y' -0.0189 -0.0449 $=-23.10 / -20.89 Sz'z' -0.2229 -0.2092 Chapter 6. Discussion 46 - 0 . 2 0 0.2 0.4 SP(exp.) Figure 6.4: Size and shape model: As in Figure 6.9 for diagonal elements Sx>x* , Sy'y> , and Sz>zi of the order matrixes 5^ of C, symmetry solutes in 55 wt% 1132/EBBA-d2. Correlation coefficient = 0.985. Chapter 6. Discussion 47 Rotation angle(exp.) Figure 6.5: Size and shape model: Theoretical versus experimental values of the angles rotated clockwise to diagonalize the order matrixes 5^ for Cs symmetry solutes in 55 wt% 1132/EBBA-d2. Correlation coefficient = 0.856. Chapter 6. Discussion 48 Figure 6.6: Size and shape model: Theoretical versus experimental values of the asym-metry parameter: TJ =(Sn -S 2 2 )/£;» of all solutes in 55 wt% 1132/EBBA-d2. Chapter 6. Discussion 49 view. The three molecules in each row have the same constituent atoms but different geometric shape. The molecules along each column have almost the same shape but composite atoms are different. Because all these solutes are closely related, it is thus hoped that specific conclusions would be possible when the effects on the orientational behavior are correlated with molecular size and shape. Variation of Order Parameters with Atoms It's interesting to look at the order parameters Sap for the molecules in each column, that is, the ortho-, meta-, and para-dihalobenzenes, respectively [See figure 5.2 and figure 6.7]. All of them are roughly the same magnitude and exclusively the same sign although the two substituent groups have changed from F, to CI, to Br, to I and to CN. Molecular properties such as the dipole moment and moment of inertia will vary significantly among these molecules. The fact that there is no large change in the orientational order suggests that these two properties have no important contribution to determining the molecular orientation. The contribution from the permanent dipole moment is negligible because molecules are tumbling very rapidly on the NMR time scale and the dipole moments are not oriented, so the permanent dipole -permanent dipole interaction averages to zero. The relatively constant value of order parameters can be easily understood using the idea of the size and shape model, which predicts similar order matrices for all the molecules in a column. This is because the ortho-, meta-, or para-dihalobenzenes are similar in molecular shape. This fact supports the idea that the repulsive force, closely related to the size and shape of the interacting objects, is playing a major role in orienting the solute molecules here. Chapter 6. Discussion 50 Variation of Order Parameters with Atomic Positions The order parameter is to a good approximation proportional to the orientational potential U(Q) , on the condition that U(Cl) / & B T <C 1. is in turn dependent upon the product of two factors given as follows: 0 1 ~k^T~ K TBT • ( 6 ' 2 1 ) G is some property of the hquid crystal B is some property of the solute The corrected values of order parameters can be regarded as only dependent on the solute properties because they are obtained in the same liquid-crystal environment. Soft [cc^ etecf] * B ( 6 22) The subscript -[corrected] will be omitted in the following discussion. So the problem remaining now is how to correlate the values of order parameters from some molecular property. In the spirit of the size and shape model, the following equation is used to make the discussion easier. Where D|| is the molecular dimension along the p direction in the molecule-fixed axis Dj_, and Dj_3 are the molecular dimensions perpendicular to the p direction. Of course, this is not the right expression for calculating order parameters [i.e., it is not traceless]. But, on a qualitative level, it can be used to rationalize the experimental order parameters. For example, the three molecules in each row, i.e., ortho-, meta-, and para-dihalobenzenes, have identical size. Proceeding along the three isomers, significant change can occur to the geometrical shape, i.e., the ratios of molecular dimensions. Chapter 6. Discussion 51 Figure 6.7: The correlation between the experimental order parameter and molecular dimensions Halogen 1 Sxx: Halogen 1 i t Halogen 2 Halogen 1 Halogen 2 Halogen 2 The value of order parameters Sxx Increases in this direction. The molecular dimension in the x direction increases in this direction. -0.2 ^' ' 1 ' 1 1 1 ' 1 1 1 1 1 1 1 1 1 • 1 1 1 1 • 1 " -0.2 -0.1 0 0.1 0.2 0.3 Sxx(exp.) In this figure, open n sided polygons [n=2-8] are for ortho-dihalobenzenes, skeletal poly-gons [center connected to vertices] for meta-dihalobenzenes, and solid polygons for para-dihalobenzenes. Appendix B gives the type of points for every individual molecule. Chapter 6. Discussion 52 Figure 6.15: continues. 0 4 ' i n - i - i i i i i i i r Syy: 0.3 -0^ 2 o "to CJ e f t 0 -0.1 i — r T " I i i -r-i - l I I I I I I I I I I • l • • -0.1 0 0.1 0.2 0.3 0.4 STO(exp.) (c) Halogen 1 Halogen 1 Halogen 2 Halogen 1 ogen2 Halogen 2 The value of order parameters Syy increases in this direction. The molecular dimension in the y direction increases in this direction. Because the dimensions perpendicular to the ring plane, i.e., z direction in the molecule, are the same, Dz can be omitted when comparing order parameters and only two dimensions Dx and Dy are competing to orient the molecule with x or y parallel Chapter 6. Discussion 53 to the nematic director, i.e., the order parameter along x or y direction will have larger positive value. The result is that the more elongated direction in the molecule, the larger the order parameter along that direction. Figure 6.7 presents a qualitative picture of this idea. This agreement is very good if we notice that equation 6.23 is a very rough correlation under the mean field approximation. 6.2.2 Contribution from the molecular polarizability The foregoing discussion supports the idea that size and shape dependent forces are the main orientational mechanisms in nematic liquid crystals. However, it seems that any model, if roughly related to the size and shape of the molecule, can give a rea-sonable description of the orientational ordering in liquid crystals. For example, the interaction between the molecular polarizability and the squared electric field EQE^ has been suggested as being responsible for orientation of solutes dissolved in nematic mesophases I6,41'42'. The electric polarizability is to a good approximation bond additive and therefore closely related to the size and shape of the molecule. The experimental results for low-symmetry solutes may help to distinguish between the size and shape model and this polarizability mechanism. It turns out that the ortho- and meta-dihalobenzenes will have identical values of polarizabilities if bond additivity is used, because under the exchange of the positions of the carbon-halogen (2) and the carbon-H bonds the total molecular polarizabilities stay unchanged according to the second-order tensor transformation [see figure 6.8]. Appendix C shows all the values of polarizabilities calculated using the bond-additivity scheme. Then the polarizability mechanism will predict the same order parameters for ortho-and meta-dihalobenzenes. Of course, this is not true experimentally [see table 5.2]. We can further state that any orienting mechanism, based on any property which can Chapter 6. Discussion 54 Figure 6.8: The additivity of substituent effects on the polarizabilities of ortho- and meta-dihalobenzenes X Halogen 1 ( i) Halogen 2 Hajogen i Exchange Halogen 2 and H g^^^^f Ju) _ Halogen 2 P o l a r i z a b i l i t y "^ changed The halogen-carbon bond at position (2) or at position (1) makes the same contribution to the molecular polarizability tensor axx , ctyy , and azz : axx =ait cos230° + att sin230° otyy -au sin230° + att cos230° a-zz =avv <*xv =(au -«« )cos30°sin30° <*u , cttt , or Qvv is the element of the halogen-carbon bond polarizability tensor. 1 is in the direction parallel to the bond, t and v are both perpendicular to the bond direction with t in the ring plane and v perpendicular to the plane'45'. An hexagonal structure for dihalobenzenes is assumed here. Chapter 6. Discussion 55 be approximated as being bond additive, will fail to predict the subtle differences in orientational order for ortho- and meta-dihalobenzenes. The interaction energy between the polarizability anisotropy and the anisotropy in the mean squared electric field is given by: U(Cl) = -^(< El > - < El >)[<*„ (Zcos29 - 1) + axx (Zsin26cos2<l> - 1) + 6 1 ayy (3sin26sin7<f> — 1) + 2axy (3sin28sin<f>cos(f))] (6.24) The polarizability tensor for the C, symmetry molecules has four independent ele-ments, axx , Qyy , azz and . The C2v solutes have three independent elements with zero. Order parameters calculated using the potential energy [6.24] are presented in table 5.2 and are plotted in figures 6.9-6.12. As can be seen, the agreement between the ex-perimental and calculated values is much worse than for the size and shape model in figures 6.1-6.6. Especially in figure 6.11, we get a -0.040 correlation between the experi-mental diagonalization angles and the values predicted from the polarizability model. It should be noted also that, for the size and shape model, the calculated order parame-ters are obtained without any adjustable parameter; but for the polarizability case, the anisotropy in the mean squared electric field is used as an arbitrary parameter in fitting the experimental order parameters of all solutes to equation [6.24]. The resulting value of (< E\ > -< El > ) is 1.94±0.01xl0 1 5 V2cm"2, which is quite close to 2.27 xlO 1 5 V 2 cm - 2 , obtained previously from 12 C3 or higher symmetry solutes by van der Est'23'. It is found that when both the size and shape and the polarizability models are included together in the calculation of order parameters, the anisotropy in the mean squared electric field goes down to 0.10 xlO 1 5 V2cm~2, which is only 5 % of the value mentioned above, and the resulting force constants are: k =3.39 dyne/cm and f=4.68, Chapter 6. Discussion 56 Figure 6.9: Polarizability-mean square electric field interaction in 55 wt% 1132/EBBA-d2 0.4 0.2 o o e n co u 0.2 1 " |— ' 7" 1 T 1- 1 1 ' ' 1 • —I 1 7 x / / * • o / o o /*• X -o / D E K a / o o ' D • X D X* *x o o y o o j/ -A / - /"k r. -1 1 - J i i_ 1 , , , 1 , J I , 0.2 Corrected experimental versus theoretical order parameters Sa0 for solutes in 55 wt% 1132/EBBA-d2- The calculated order parameters, also shown in tables 5.2, are obtained using the interaction between the polarizability tensor of the solute [ given in appendix C], and the mean squared electric field due to the liquid-crystal environment. The definitions of the axes, x, y, and z are given in figure 5.3. The anisotropy in the mean squared electric field is obtained from a least squares fit to the line of slope 1. (< f?jj > — < E\ >)= 1.94±0.01 x lO^V^cm"2. The correlation coefficient is 0.938. Chapter 6. Discussion 57 Figure 6.10: Polarizability model: Corrected experimental versus theoretical order pa-rameters of solutes in 55 wt% 1132/EBBA-d2. S n(exp.) (c) S^exp.) (d) As in Figure 6.17 for individual elements of the ordering matrix: (a) Szz , correlation coefficient = 0.261; (b) Sxx , correlation coefficient = 0.881; (c) Syy , correlation coefficient = 0.927; (d) S^ , correlation coefficient = 0.04 . Chapter 6. Discussion 58 Rotation angle(exp.) Figure 6.11: Polarizability model: Theoretical versus experimental values of the angles rotated clockwise to diagonalize the order matrixes for C5 symmetry solutes in 55 wt% 1132/EBBA-d2. Correlation coefficient = -0.040. Chapter 6. Discussion 59 Figure 6.12: Polarizability model: Theoretical versus experimental values of the asym-metry parameter: 77 =(Sn -S22 )/<Ss3 of solutes in 55 wt% 1132/EBBA-d2. 7?(exp.) Chapter 6. Discussion 60 which are almost the same as those obtained when the size and shape model is used alone to predict order parameters [k =3.92 dyne/cm and £=5.01, in page 35]. The fact that the inclusion of the size and shape model reduces the contribution of the polarizability model to a negligible level strongly supports the dominance of size and shape interactions. Chapter 6. Discussion 61 Figure 6.13: The deformation [dashed line] of ortho-dihalobenzenes from the hexagonal structure [solid line]. The C-H bond is assumed to bisect the C-C-C angle. The deviation is exaggerated for halogens. 6.3 Determination of Molecular Structure The RMS values from SHAPE for ortho-dihalobenzenes are consistently higher than those for the meta- and para-dihalobenzenes (see table 5.2 ). This difference may result from the assumption of an ideal geometry based on a regular hexagonal carbon skeleton [see appendix B]. A departure from the ideal geometry could account for the unusual behavior. Thus it is worth while determining the molecular structure from the NMR results on these oriented molecules. The molecular geometry can be calculated from the dipole coupling constants accord-ing to eq. (5.18) but, since only information about the interacting nuclei appears in the NMR spectra, in order to construct a complete molecular structure other sources have to be used. The molecular structure determined by electron diffraction (ED) and the moments of inertia from microwave experiments (MW) provide information about the bond lengths. Therefore, the NMR results will be used to determine the molecular shape, i.e. the bond angles. Because ortho-dihalobenzenes have six different dipolar couplings, Chapter 6. Discussion 62 Table 6.2: Bond angles and order parameters determined for ortho-dihalobenzenes ori-ented by the 55 wt% 1132/EBBA-tJ2 liquid-crystal mixture.  Molecule Bond Angles (in Degrees) Order Parameters RMS (Hz) 1,2-chlorobromobenzene a 120.47 0 120.09 S x x 0.1461 Szz -0.2123 Sxy 0.0128 0.28 1,2- chloroiodobenzene a 120.50 0 116.35 Sxx 0.1418 Szz -0.2129 Sxy 0.0403 0.56 2-chlorobenzonitrile a 120.52 0 118.62 S x x 0.1639 Szz -0.2253 0.0690 1.35 1,2- bromoiodobenzene a 120.49 0 117.18 S x x 0.1281 Szz -0.2050 5^ 0.0256 0.60 2-bromobenzonitrile a 120.53 0 117.56 Sxx 0.1558 S« -0.2269 5^ 0.0578 0.46 2-fluorobenzonitrile a 120.48 0 118.60 S x x 0.1641 5„ -0.2107 S^ 0.0962 0.49 of which three define the molecular orientation, only three structural parameters can be determined independently. Assuming that the structural distortion arises from the steric repulsion between the two neighboring halogens [see appendix B], it is sensible to adjust the two bond angles as drawn in figure 6.13. Because the anisotropy in J J J F ' 1 9 ' has a value about 1 % of the dipolar couplings and introduces small but systematic errors into structures determined by the NMR technique, all the proton-fluorine couplings are excluded from the calculation of order parameters and molecular structure. Table [6.2] gives the structural and orientational parameters calculated with the iter-ative least squares program SHAPE, when the two bond angles a and 0 [see figure 6.13] Chapter 6. Discussion 63 are allowed to vary, together with three order parameters 5TC , Szt , and . It can be seen that deviations in the ring structure, reflected by bond angles a [close to 120 de-grees], are quite small. The obtained bond angles 8 show larger deformations. However, the important thing is that order parameters differ, by about 5 %, from those calculated using the ideal hexagonal geometry [see table 5.2]. This value is within the relative errors between the calculated and the experimental order parameters. Chapter 7 Conclusion The starting point of this thesis was to test the size and shape model. As we have seen the results of 19 dihalobenzene molecules having C, or C 2 v symmetry support the idea that the size and shape of a solute dominates its orientational behavior in the liquid-crystal mixture: 55 wt% 1132/EEBA-rf2. The orienting potential based on size and shape interactions provides excellent fits between the experimental and calculated values of order parameters. Other mechanisms, involving molecular properties which are approximately equal to the sum of contributions associated with each bond, will fail in distinguishing the orientational order between ortho- and meta-dihalobenzenes. This fact implies that the orienting potential must be derived by treating the molecule as an entity which then interacts with the Liquid-crystal mean field. Our treatment of the size and shape model and the molecular quadrupole moment electric field gradient interaction is performed this way. 64 Appendix A 65 Appendix A. Spectral parameters 66 Spectral parameters These are spectral parameters for di-halobenzenes dissolved in the 55 wt% 1132/EBBA-d2 Liquid-crystal mixture, obtained by NMR Spectroscopy. SOLUTE SPECTRAL PARAMETERS ( 1 , 2 ) Dipolar Couplings (Hz) Du D1Z Du Du D23 D24 D25 2DHDW(Ez) 2B0(4)(kHz) £ 4 5 RMS<5) (Hz) J-couplings (6> (Hz) Jl2 Jl3 Jl4 JlS J23 J24 J2S J34 ^35 J45 Chemical Shifts ™ (Hz) V\ v2 v3 1/4 1,2-chlorobromobenzene -1082.7 (1.0) -147.5 (3.1) -67.2 (0.3) 1436 -514.9 (1.3) -116.5 (1.8) 17.04 -911.7 (0.7) 0.1 8.3 1.3 0.6 t43l 7.5 1.6 8.3 16.1 (0.3) 22.6 (0.3) 83.7 (0.5) 0.0 (0.5) Appendix A. Spectral parameters Appendix A Continues SOLUTE SPECTRAL PARAMETER 1,2-chloroiodobenzene -1344.6 (0.1) -195.9 (0.2) -71.9 (0.1) 1475 -551.9 (0.2) -85.0 (0.1) 17.56 -756.4 (0.03) 0.1 7.7 1.8 0.4 W 7.6 2.1 7.9 60.5 (0.02) -7.7 (0.02) 151.5 (0.02) 0.00 (0.02) 2-chlorobenzonitrile -1585.8 (0.4) -235.5 (2.2) -60.6 (0.9) 1523 -469.8 (2.0) -44.5 (0.7) 17.43 -641.8 (0.3) 0.6 7.7 1.6 0.4 7.6 1.0 8.2 214.9 (0.3) 99.7 (0.3) 260.6 (0.6) 0.00 (0.5) 1,2-bromoiodobenzene -1143.4 (0.1) -175.0 (0.1) -77.8 (0.1) 1470 -598.3 (0.1) -106.0 (0.1) 16.90 -776.6 (0.04) 0.0 7.9 1.6 0.3 '311 7.4 1.5 8.0 51.8 (0.1) -7.3 (0.1) 89.5 (0.1) 0.00 (0.1) Appendix A. Spectral parameters Appendix A Continues SOLUTE SPECTRAL PARAMETER 2-bromobenzonitrile -1509.8 (0.1) -221.7 (0.2) -71.4 (0.1) 1489 -547.0 (0.2) -65.7 (0.1) 17.03 -699.1 (0.03) 0.1 7.7 1.7 0.4 7.6 1.0 8.2 209.7 (0.2) 140.9(0.2) 230.1(0.1) 0.0 (0.1) 2-fiuorobenzonitrile -1741.5 (0.02) -244.2 (0.01) -46.5 (0.1) 5.2 (0.2) -358.0 (0.1) 7.5 (0.1) -45.8 (0.2) 1404 -426.2 (0.02) -207.3 (0.03) 17.42 -1456.1 (0.03) 0.1 7.6 1.7 0.4 6.9 7.5 1.0 -0.6 8.4 4.9 8.9 207.3 (0.2) 50.4 (0.2) 315.7 (0.03) 0.0 (0.03) 1,3-chlorobromobenzene -118.7 (0.3) -23.9 (0.1) -88.5 (0.3) 1480 -1144.1 (1.2) -303.1 (0.2) 17.56 -1307.1 (0.9) 0.1 2.0 0.2 1.9 8.0 0.9 8.0 0.0 (0.04) 321.7 (0.2) 173.8 (0.1) 311.3 (0.2) Appendix A. Spectral parameters Appendix A Continues SOLUTE SPECTRAL PARAMETER 1,3-chloroiodobenzene -130.5 (0.1) -15.8 (0.1) -55.9 (0.1) 1441 -998.2 (0.6) -299.3 (0.2) 17.77 -1401.4 (0.3) 0.04 2.1 0.2 1.7 8.0 0.9 7.9 0.0 (0.04) 376.6 (0.08) 148.5 (0.1) 355.9 (0.2) 3-chlorobenzonitrile -193.3 (0.1) -5.5 (0.1) 1.7 (0.2) 1518 -880.7 (0.5) -355.9 (0.3) 17.60 -1897.2 (0.2) 0.2 2.2 0.4 1.5 8.2 1.0 7.7 0.0 (0.1) 380.7 (0.1) 102.9 (0.3) 276.3 (0.3) 1,3- bromoiodobenzene -113.6 (0.2) -14.3 (0.1) -67.7 (0.2) 1416 -1065.8 (1.1) -298.2 (0.3) 17.02 -1317.9 (0.8) 0.2 1.9 0.2 1.7 8.0 0.9 7.9 0.0 (0.1) 431.1 (0.2) 154.4 (0.2) 416.4 (0.4) Appendix A. Spectral parameters Appendix A Continues SOLUTE SPECTRAL PARAMETER 3-bromobenzonitrile -169.1 (0.1) -2.5 (0.1) -11.8 (0.1) 1583 -959.7 (0.3) -351.6 (0.1) 17.52 -1744.9 (0.1) 0.1 2.1 0.4 1.5 8.2 1.0 7.7 0.0 (0.1) 452.9 (0.1) 117.8 (0.1) 340.7 (0.2) 1,3-fluorobromobenzene -167.6 (0.1) -34.6 (0.1) -42.0 (0.1) -1188.4 (0.1) 1542 -718.5 (0.5) -252.2 (0.3) -189.2 (0.1) 17.64 -1383.6 (0.2) -37.1 (0.2) 0.2 -77.2 (0.2) 2.5 0.2 1.9 8.4 [32] 8.3 0.8 8.3 7.9 6.0 -0.5 0.0 (0.1) 149.3 (0.1) 128.0 (0.1) 138.8 (0.1) 3-fluorobenzonitrile -226.1 (0.1) -20.4 (0.1) 28.2 (0.1) -1552.4 (0.04) -498.2 (0.9) -289.9 (0.7) -53.27 (0.04) 1475 -1830.1 (0.1) 21.9 (0.4) 16.60 -54.7 (0.4) 0.1 2.7 0.4 1.5 8.4 8.4 1.0 8.3 7.8 6.0 -0.5 0.0 (0.04) 165.6 (0.04) 62.1 (0.3) 121.7 (0.3) Appendix A. Spectral parameters Appendix A Continues SOLUTE SPECTRAL PARAMETER 1,4-chlorobromobenzene 1477 17.34 0.1 -2490.9 (0.03) -18.6 (0.03) 124.4 (0.03) 124.4 (0.03) -18.6 (0.03) -2490.9 (0.03) 8.6 0.3 2.5 M 2.5 0.3 8.6 46.0 (0.04) 0.0 (0.04) 0.0 (0.04) 46.0 (0.04) 1,4-chloroiodobenzene 1456 17.56 0.2 -2757.0 (0.1) -8.1 (0.1) 160.3 (0.1) 160.3 (0.1) -8.1 (0.1) -2757.0 (0.1) 8.4 0.4 2.4 '441 2.4 0.4 8.4 46.0 (0.1) 0.0 (0.1) 0.0 (0.1) 46.0 (0.1) 4-chlorobenzonitrile 1638 17.49 0.6 -2897.6 (0.2) -4.4 (0.3) 178.7 (0.3) 178.7 (0.3) -4.4 (0.3) -2897.6 (0.2) 8.4 0.9 2.1 I44' 2.1 0.9 8.4 46.00 (0.81) 0.00 (0.81) 0.00 (0.81) 46.00 (0.81) Appendix A. Spectral parameters Appendix A Continues SOLUTE SPECTRAL PARAMETER 1,4-bromoiodobenzene -2579.8 (0.2) 3.0 (0.2) 157.2 (0.2) 1358 157.2 (0.2) 3.0 (0.2) 16.52 -2579.8 (0.2) 0.6 8.6 0.3 2.4 '4 4' 2.4 0.3 8.6 46.0 (0.3) 0.0 (0.3) 0.0 (0.3) 46.0 (0.3) 1,4-fluorobromobenzene -1912.8 (0.3) -36.8 (0.3) 32.8 (0.3) 262.2 (0.4) 72.7 (0.3) -36.8 (0.3) 304.5 (0.4) 1470 -1912.8 (0.3) 304.5 (0.4) 17.09 262.2 (0.4) 1.6 8.9 0.2 2.6 4.2 3.2 0.2 8.0 8.9 8.0 4.2 84.1 (0.4) 0.0 (0.4) 0.0 (0.4) 84.1 (0.4) 4-fluorobenzonitrile -2385.2 (0.2) -22.2 (0.2) 115.6 (0.2) 236.0 (0.3) 113.8 (0.2) -22.2 (0.2) 311.9 (0.3) 1524 -2385.2 (0.2) 311.9 (0.3) 17.37 236.0 (0.3) x 1.2 8.6 0.4 2.2 4.2 2.7 0.4 8.0 8.6 8.0 4.2 84.1 (0.3) 0.0 (0.3) 0.0 (0.3) 84.1 (0.3) Appendix A. Spectral parameters Note: (1) : The numbering of the nuclear spins is shown in figure 5.2 (2) : The numbers in brackets refer to standard deviations, e.g. -2385.2 (0.2) means -2385.2±0.2 (3) : DtfD is the dipolar coupling between the deuterons and the adjacent protons of the EBBA-d2 contained in the 55 wt% 1132/EBBA-d2 mixture, plus solute (see figure 5.3 ). (4) : Bx> is the quadrupolar coupling average of the two deuterons ortho to the nitrogen in the EBBA-d2 contained in the 55 wt% 1132/EBBA-d2, plus solute, mixture (see figure 5.3 ). (5) : RMS is the final error of the fit of the experimental spectrum to the calculated spectrum by the program LEQUOR'28'. (6) : The J-couphng constants are calculated from an additivity scheme, proposed by S. Castellano'31-33', except the cases specified there. They are kept constant in the iterative spectral analysis by LEQUOR program. (7) : The reference of chemical shifts for every individual molecule is that proton with i>i=0. Appendix B Assumed Molecular Structure 74 Appendix B. Assumed Molecular Structure 75 3 0 -t5 0)20 o in 10 0 1,2-chloTobromobentene 1,3-chlorobromobeiuene 1,4-chlorobrojnobeueoe ~ J I I L J I I L J ' ' J L 0 10 2 0 X Scale (A) 30 This is a plot directly from the assumed molecular structure [shown in table 5.1] These nuclear coordinates and van der Waals radii are used as input for the size and shape program to calculate order parameters. The ring carbon van der Waals spheres are omitted here because they don't contribute to the solute circumference, described in chapter 3. See table 5.2 for calculated order parameters and section 6.1 and 6.2 for discussion. Appendix B. Assumed Molecular Structure 76 D X • 1,2-chlorobeoionitrile 1^ -chlorobeaxonitrile 1,4-chlorobenxonitrile 0 ' 1 1 • 1 1 i i i i I i i i i — L — i — L 0 10 '"" 2 0 3 0 X Scale (A) Appendix B continues Appendix B. Assumed Molecular Structure 77 Appendix B continues Appendix B. Assumed Molecular Structure 78 Appendix B continues Appendix C Molecular polarizabilities The values of following polarizability tensors are calculated according to bond additivity '4 5' and the assumed hexagonal geometry. MOLECULE Polarizability (cm 3) Ctxx Qyy a z z axy 1,2- or 1,3-chlorobromobenzene 18.74 15.72 9.75 0.67 1,4-chlorobromobenzene 14.21 20.26 9.75 0.00 1,2- or 1,3-chloroiodobenzene 21.64 18.62 10.85 0.67 1,4-chloroiodobenzene 17.11 23.16 10.85 0.00 2- or 3-chlorobenzonitrile 16.66 14.59 9.30 -0.16 4-chlorobenzonitrile 13.56 17.70 9.30 0.00 1,2- or 1,3-bromoiodobenzene 23.26 19.46 11.55 0.00 1,4-bromoiodobenzene 17.56 25.16 11.55 0.00 2- or 3-bromobenzonitrile 18.27 15.43 10.00 -0.83 4-bromobenzonitrile 14.01 19.70 10.00 0.00 1,2- or 1,3-fluorobromobenzene 15.93 13.81 8.55 1.45 1,4-fluorobromobenzene 12.75 17.00 8.55 0.00 2- or 3-fluorobenzonitrile 13.85 12.68 8.10 0.62 4-fluorobenzonitrile 12.10 14.44 8.10 0.00 79 Bibliography [1] E.B. Priestley, P.J. Wojtowicz, and P. 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