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Orientational ordering of small molecules in nematic liquid crystals Danilovič, Zorana 2004

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ORIENTATION AL ORDERING OF SMALL MOLECULES IN NEMATIC LIQUID CRYSTALS By Zorana Danilovic B . S c , The University of Belgrade, 2001  A T H E S I S S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMISTRY  W e accept this thesis as conformation to the required standard  T H E U N I V E R S I T Y O F BRITISH C O L U M B I A October 2004 © Zorana Danilovic, 2004  JUBCL FACULTY OF GRADUATE STUDIES  THE UNIVERSITY OF BRITISH COLUMBIA  Library Authorization  In presenting this thesis in partial fulfillment 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.  Date (dd/mm/yyyy)  Name of Author (please print)  Title of Thesis:  MJ AM/r?T7C  JjQU/H  QZYSIMS  Year:  Degree:  Department of The University of British Columbia Vancouver, B C  Canada  grad.ubc.ca/forms/?formlD=THS  page 1 of 1  last updated:  20-M-04  Abstract  Orientational ordering in nematic liquid crystal phases arises from the presence of anisotropic intermolecular forces. To date N M R experiments, theory and Monte Carlo simulations indicate the importance of two main contributions to orientational ordering of small solutes in various liquid crystals and liquid crystal mixtures. The first contribution is well defined and involves short-range interactions that depend on the size and the shape of the  solute. The  second contribution,  which  accounts for  long-range  (electrostatic)  interactions, is believed to have lesser impact on the molecular ordering. Which of the electrostatic interactions (induction, electric quadrupole or polarization) are most important is still debated. In order to investigate the impact of electrostatic interactions on molecular ordering, small symmetric molecules with the same size and shape, and therefore the same short-range interactions, but different electrostatic properties were dissolved in various liquid crystals and mixtures of liquid crystals. Second rank orientational order parameters of solutes in various liquid crystal phases are obtained from analysis of high-resolution N M R spectra. For high-spin systems, initial spectral parameters needed to solve very complicated high-resolution spectra are estimated from selective multiple-quantum N M R spectra, collected using a 3D selective M Q - N M R technique. Structural: parameters of the solutes are calculated -using non-vibrationally corrected nuclear dipolar coupling constants accurately obtained from analysis of highresolution N M R spectra. The contribution of the electrostatic interactions to the orientational ordering of small solutes in liquid crystal phases is discussed in terms of different solutes and different types of liquid crystals by comparing experiment with theoretically determined order parameters. Those comparisons seem to suggest that dipoles have the least impact on orientational ordering of small molecules in nematic liquid crystals. Quadrupole contribution results predict opposite signs of the electric field gradient to the one obtained in similar previous studies. Experiments with zero-electric-field-gradient mixtures ('magic mixture') show no significant contributions of the electrostatic long-range interaction to the orientational mechanism in the special mixture. The polarizability effect appears strongly dependent on molecular geometry and in this study appears to be an important electrostatic mechanism of orientation.  Contents  Abstract  ii  Contents  iii  List of Tables  v  List of Figures  vi  List of Abbreviations  vii  Acknowledgement  viii  Dedication  1  ix  Introduction  1  1.1 Liquid Crystals  1  1.2 Nematic Liquid Crystals  2  1.3 Orientational Ordering and Intermolecular Forces in Nematic Liquid Crystals  3  1.4 Orientational Distribution Function and Order Parameter  4  1.5 Orientational Ordering from Experiments  6  1.5.1  N M R Spectra of Oriented Molecules  1.5.2  Solutes as Probes of Orientational Order and Intermolecular Forces 9  1.5.3  Multiple-Quantum N M R  10  1.6 Orientational Ordering from Theoretical Calculation  12  1.6.1  7  Statistical Treatment of Orientational Ordering Using Mean-Field Approach  12  1.6.2  Anisotropic Intermolecular Interactions  14  1.6.3  Molecular Models of Orientational Order  15  A. Short-Range Models  15  B. Long-Range Models  17  Previous Predictions on Orientational Ordering  18  1.6.4  1.7 Outline of the Thesis  19  References  20  in  2  3  4  Experiment  22  2.1 Sample Preparation  22  2.2 Experimental Conditions  24  References  26  Spectral Analysis  27  3.1 Introduction  27  3.2 Spectral Analysis with Aid of MQ N M R  27  3.3 Molecular Structure and Order Parameters  40  3.4 Summary  44  References  44  Orientational Ordering in Nematic Liquid Crystals  45  4.1 Introduction  45  4.2 Determination of a Consistent Set of Order Parameters  47  4.3 Qualitative Comparison between Experimental Order Parameters  50  4.4 Comparison between Experimental and Theoretically Calculated Order Parameters  5  52  A. Short-Range Model Comparison  57  B. Long-Range Model Comparison  58  C. Dipolar Interaction Contribution  62  D. Quadrupolar Interaction Contribution  62  E. Polarizability Interaction Contribution  65  4.4 Summary  67  References  68  Conclusion  69  IV  L i s t of T a b l e s  1.1  Independent Order Parameters as a Function of Molecular Symmetry  1.2  Maximum Number of Transitions in One Quantum Spectrum of a Partially Oriented Molecules as a Function of Number of Spins with / = \  3.1  30  Fitting Parameters from Analysis of M Q and High-Resolution Spectra of DOT in EBBA  3.3  32  Fitting Parameters and R M S Errors from Analysis of High-Resolution Spectra of DOT 6-spin System  3.4  37  Fitting Parameters and R M S Errors from Analysis of High-Resolution Spectra of C L M X 9-spin System  3.5  10  Fitting Parameters and R M S Errors from Analysis of High-Resolution Spectra of T C B 3-spin System  3.2  5  38  Fitting Parameters and R M S Errors from Analysis of High-Resolution Spectra of MESIT 12-spin System  39  3.6  Structural Parameters from Fits to Dipolar Couplings for D C T , C L M X and MESIT  41  3.7  Order Parameters from Fits to Dipolar Couplings  43  4.1  Scaled and Non-Scaled Order parameters  48  4.2  Anisotropy in Scale and Non-Scaled Order Parameters  51  4.3  Molecular Electrostatic Parameters  53  4.4  Adjusted Parameters in the Fitting Procedure  54  V  List of Figures  1.1  Liquid crystal phase on temperature scale  1  1.2  Example of nematic liquid crystal E B B A  2  1.3  Molecular organization in nematic phase  3  1.4  The nematic molecule fixed axis system  5  1.5  Poor resolved high-resolution spectrum of nematogen ZLI 1132  9  1.6  Three pulse sequence use to generate and observe M Q coherences  12  1.7  Elastic model for short-range interaction between solute and liquid crystal  16  2.1  ZLI 1132 liquid crystal  23  2.2  E B B A liquid crystal  23  2.3  Solutes  23  2.4  Single pulse sequence  24  2.5  3D MQ N M R pulse sequence  25  3.1  High-resolution proton N M R spectra of D C T , C L M X and MESIT in ZLI 1132 at 300K  29  3.2  All positive MQ spectra of D C T in E B B A at 300K  33  3.3  Experimental and calculated +5Q spectra of D C T in E B B A  34  3.4  Experimental and calculated +4Q spectra of D C T in E B B A  35  3.5  Experimental and calculated high-resolution proton spectra of D C T in E B B A at 300K  36  3.6  Atom labeling of solute molecules  42  4.1  Chosen set of solutes with same size and shape but different electrostatic properties presented in their coordinate system  46  4.2  Non-scaled (series A) and scaled (series B) experimental order parameters  49  4.3  Anisotropy in scaled order parameters  51  4.4  Differences between S^"' and S^' as a function of S*™' '' for short-range r  models 4.5  4.6  Differences between S^'  57 led  and  as a function of S^'  !ed  for long-range  models  60  Different pair of short- with long-range interaction fits for magic mixture  61  vi  4.7  Differences between . V a n d S%? as a function of S™ c  for dipole interaction  led  contribution 4.8  63  Differences between S™  and S'f  led  as a function of S^"  led  for quadrupole  interaction contribution 4.9  64  Differences between S '"' " and S _ f as a function of s  for  e  AA  XX  polarizability interaction contribution  66  List of Abbreviations  NMR  Nuclear magnetic resonance  MQ  Multiple quantum  Nematogen  Nematic liquid crystal molecule  ZLI 1132  Eutectic (alkyl=propyl,  mixture  of  frans-4-n-alkyl-(4-cyanophenyl)-cyclohexane  pentyl, heptyl)  and  trans—4-n-pentyl-(4'-cyanobiphenyl-4)-  cyclohexane EBBA  N-(p-EthoxyBenzylidene)-p'-n-ButylAniline  TCB  1,3,5 trichlorobenzene  DCT  3,5 dichlorotoluene  CLMX  5 chloro m-xylene  MESIT  1,3,5 trimethylbenzene (mesytilene)  Efg  Electric field gradient  n  The director of liquid crystal  Sap  Order parameter  x,y,z  Molecule fixed axis system  X.Y.Z  Laboratory fixed axis system  VI1  Acknowledgements  I would like to thank my supervisor Prof. Elliott Burnell for his patience, encouragement, superb guidance and support over the past few years. It has been a great pleasure and privilege to work with him. I also wish to thank my colleagues Anand Yethiraj, Joseph Lee, Andrew Lewis, Ray Syvitski, Aman Taggar and Chris Campbell from which I have learned a lot and enjoyed interacting with. Thanks to Dr. Nick Burlinson for enthusiasm, moral support and resourceful discussions. Most of the experimental work wouldn't be possible without the excellent help from the people in the electronic shop, mechanical shop, chemistry store and N M R facility. I would also like to thank Scott Kroeker from University of Manitoba for donating one of the solutes, 3,5-dichlorobenzene. Financial assistance in the form of a teaching and research assistantship is highly appreciated. Special thanks to my family for their love and support, since without their inspiration none of this would have been possible. Finally I would like to express my gratitude to my friends and loved one Ken for their constant support, help and patience.  vni  Dedication  To my lovely parents  Ljiljana and Tetar  IX  1. INTRODUCTION  1.1 LIQUID CRYSTALS The liquid crystal phase is known as a mesophase  (u.eooa  in Greek means middle), a  phase between liquid and solid phases (Fig. 1.1). When heated from the solid phase at the first transition point they appear as a cloudy liquid that upon further heating above the clearing transition point transform into a clear isotropic liquid. Two transitional temperatures define the region in which mesophases are thermodynamically stable. Liquid crystals show the translational and rotational mobility of liquids and the optical properties of solids (like birefringence). They typically consist either of rod like or disk like molecules.  Solid  Liquid Crystal  Melting point  Liquid  Clearing point  TEMPERATURE Figure 1.1 Liquid crystal phase on temperature scale  The main characteristic of liquid crystals is long-range orientational ordering. Some of them display some positional ordering as well. The tendency to align along a preferred direction is caused by intermolecular forces acting between liquid crystal molecules. A s a consequence liquid crystals are categorized as anisotropic phases in which measured properties depend on the direction in which they are measured. The anisotropic nature of liquid crystals is responsible for their unique properties exploited in a variety of applications.  Introduction  Liquid crystals are classified into two main categories: thermotropic and lyotropic. Thermotropic liquid crystals are produced by thermal process as while lyotropic liquid crystal phases depend on solvent composition. The present study focuses only on nematic liquid crystals, the simplest thermotropic liquid crystal that posses only orientational order.  1.2  N E M A T I C LIQUID C R Y S T A L S  Nematic (vefiazoa in Greek means threadlike) liquid crystals are composed of rod-shape molecules with molecular length several times the molecular diameter. These molecules consist of semi-rigid cores like benzene rings with polar and nonpolar flexible ending groups (Fig. 1.2).  Figure 1.2 Example of nematic liquid crystal E B B A (N-(p-EthoxyBenzylidene)-p'-nButyl .Aniline); stable in the,temperature range from 308 to 352 K  Nematic molecules {nematogens) are arranged such that there is no positional order of their centers of mass, meaning that molecules diffuse randomly and rapidly like in isotropic liquids. When a solid melts the thermal energy is sufficient to destroy positional order but not enough to disrupt orientational order. This results in a nematic phase in which molecules group in clusters, and tend to partially align their molecular axes along a preferred direction, called the director n (Fig. 1.3). The cluster size can be as large as 1 fim [1]. In the absence of an external field, the orientation of the director axis in each cluster varies throughout the sample. The cloudy appearance of a macroscopic sample comes from the random scattering of light as it penetrates the sample between the clusters with different directors. In the presence of a magnetic field all clusters' directors reorient along the main magnetic field direction in just a few seconds. For almost all nematics known nowadays, the nematic phase is uniaxial.  2  Introduction  Therefore they are cylindrically symmetric and all measured properties are invariant to rotations about the director n . Also the directions -n and ware indistinguishable making the phases apolar.  Director n  Figure 1.3 Molecular organization in nematic phase  1.3 ORIENTATION A L O R D E R I N G A N D I N T E R M O L E C U L A R  F O R C E S IN N E M A T I C  LIQUID C R Y S T A L S  Orientational order is one of the basic characteristics common to all the mesophases. It is a result of anisotropic intermolecular forces acting between liquid crystal molecules. Understanding the relationship between orientational order and anisotropic intermolecular forces that cause the molecular orientation is one of the fundamental questions in the study of liquid crystals that still hasn't been fully answered. Several approaches (experimental, theoretical and computational) have been utilized in order to give some insight into the problem. In this study, N M R was used to extract information about order parameters that were compared with theoretically predicted order parameters calculated from theoretical models (which will be described in 1.6). 3  Introduction  1.4 O R I E N T A T I O N A L DISTRIBUTION F U N C T I O N A N D O R D E R  PARAMETER  /quantitative description of orientational order/  The orientational behaviour of a rigid, axially symmetric nematogen is fully described by the single orientational distribution function f(£l),  where Q. represents the Eulerian angles  (q>,d,\j/) that describe the orientation of the molecule frame system (x, y, z) relative to the nematic director system (laboratory frame system (X, Y, Z)) (Fig. 1.4). Taking into account the cylindrical symmetry and uniaxiality of the phase, the orientational distribution function f(Q), expanded in terms of spherical harmonics, reduces to [2]:  f(Q)=  X ^ ( P ) P ( c o s a ) = l + | < ^ > ^ ( c o s 0 ) + | ( P ) P ( c o s c 9 ) + ... /  / even  ;  4  1 2 .  ^  4  (1.1)  I  where  (/>) = JP, (cos 0)7(0) sin 0</0  (1.2)  0  are called orientational order parameters and P are Legendre polynomials [2]. ;  The same concept can be applied to describe the orientational behavior of an axially symmetric rigid solute molecule dissolved in a liquid crystal. Second rank order parameters also known a s components of the Saupe order matrix represent quantitative measures of average orientational order of rigid molecules of any symmetry in anisotropic systems [3]. The order matrix is a 3x3 symmetric (S  ap  traceless (^S p a  =Sp ) and a  = 0) matrix with five independent components. The matrix elements S p a  a=fi  in the Cartesian coordinate representation are given as  a,f}=x,y,z  .  ^  4  Introduction  where  a and 8  are the molecular fixed axes conveniently chosen as symmetry axes of  the molecule; 6  and 9  a  p  are angles between a and B molecular axis and the nematic  director (which usually coincides with the magnetic field direction) (Fig. 1.4).  n  Z =  y X  Figure 1.4 The nematic molecule fixed axis system The nematic director n and magnetic field B direction are parallel to the laboratory fixed Z 0  direction  Suitably choosing molecular axes, the number of independent order parameters can be reduced depending on the symmetry of the molecule (Table 1.1) [4,5].  Table 1.1 Independent Order Parameters as a Function of Molecular Symmetry  Symmetry point group  C„,C ,,C ,C^ (n m  nh  n  nh  2-5),S ,S  ml  C  = 3-6)  h  D (n =  = 3-6)  h  D ,D ,D„ (n  Independent order parameters  4  h  2 ,D ,D V  2  2h  CCC  $xx'  Syr' S  xy  s s s s ,s XX  5  yy  xy,  xz>  yz  Introduction  (1.4) and for off-diagonal order parameter elements 4S  'V  (1.5)  4  S  When all molecules are oriented parallel to the magnetic field and therefore the nematic director (8 = 0 or 9 = K ), the order parameter is S  aa  = 1 indicating perfect alignment while  for perpendicular alignment (8 = — ), the order parameter becomes S  aa  If molecules  tumble freely and isotropically orientation is totally random, the average value of the cosine squared function is ^ c o s f ^ = j and S 2  aa  = 0 , i.e. the system shows no orientational order  at all.  1.5 O R I E N T A T I O N A L O R D E R I N G F R O M E X P E R I M E N T S  There are many experimental techniques that can provide information about orientational ordering. For example polarized Raman scattering [6], Electron Paramagnetic Resonance (EPR) [7], quasielastic scattering of X-rays [8] or neutrons [9] can give up to fourth rank orientational order parameters. Their instrumental and analytical limitations make this task really difficult and incomplete. N M R has proved to be an excellent non-destructive technique for studying orientational order in anisotropic systems. Its only limitation lies in the fact that only the second rank order parameters can be extracted from experimental N M R spectroscopic data therefore giving a slightly modest representation of the orientational distribution function. The theoretical background and the relationship between order parameters and accessible spectral parameters will be described in the following section 1.6.1. Spectral step by step analysis and determination of order parameters will be covered in Chapter 3.  6  Introduction  1.5.1  NMR S P E C T R A OF ORIENTED MOLECULES  In the high-field limit* the spin Hamiltonian for a collection of spins ( / = | ) in a uniaxial anisotropic environment is given as:  H = H + Hj + H 7  where H  z  (1.6)  D  is the Zeeman, Hj is the scalar (indirect) coupling and H  D  is the direct dipolar  Hamiltonian. The Zeeman Hamiltonian represents the interaction between nuclei and the main external magnetic field. Expressed in Hz units, it takes the following form  H  z  =-_>,7,,  z  ^ - ^ 7 , ( 1 - 0 - , ^ ) / , ,  (1.7)  where v are the chemically shifted frequencies of the /' spin, B j  7  magnetic field defined to be along the Z-axis, l  i7  for the /'spin, and a  i 7 7  is the static external  is the Z-component of the spin operator  is the ZZ-component of the chemical shift tensor for spin /'.  The scalar coupling Hamiltonian has the general form  where the scalar coupling constant J  v  is a second-rank tensor that describes the indirect  interaction between spins defined through spin operators 7. and 7.. (  Another approximation is applied here: for most protons the anisotropy in the J  i}  tensor is  small and is ignored.  * T h e high-field limit approximation takes into account that the Z e e m a n term in the Hamiltonian dominates over other terms in the Hamiltonian; for example the Z e e m a n term in a 100 M H z field is of order ~10 and quadrupolar contributions do not exceed 10  4  8  H z while dipolar  Hz; this simplifies the expression for the Hamiltonian.  7  Introduction  The direct dipolar Hamiltonian  ^=X^(3/,Az-A-^-)  <-> 19  '</  takes into account the interaction between magnetic dipoles of spins / and j through the dipolar coupling constant D  tJ  given as  _Kfir,rj(i«»'o,*-,  D=  )  8*  where  u.  Q  (  r]  \  2  1  1  0  )  I  is the magnetic permeability of vacuum, ft is Planck's constant, y is the  gyromagnetic ratio of the spin and G  ijZ  is the angle between the internuclear vector r and jj  the external magnetic field defined along the Z-axis. For rigid molecules (i.e. ignoring vibrations and taking r fixed instead of using the averaged values for l—j)) ij  expression  (1.10) can be rewritten as  D  where  „ = - ¥ T T  S  ap  L  S  S^COS^COS*,  are the order matrix elements and  axes and the internuclear vector r  jy  study of orientational information  (1.11)  order.  are angles between a , j3 molecular  Equation (1.11) is the basis for the experimental N M R  It gives a direct relation between extractable spectral  (D, ) and second-rank orientational y  order parameters as a measure of  orientational order of the molecule in anisotropic media. In isotropic media, rapid translational motion and random reorientation cause intermolecular and  intramolecular dipolar interactions to average out ( £ ^ = 0 ) , due to which isotropic  spectra look less complicated and give no information about orientational order. 8  Introduction  The eigenstates and eigenvalues are obtained from a diagonalization of the Hamiltonian. They are characterized by spectral parameters (o~, J Z ) ) in the Hamiltonian. On the other (y  jy  side eigenvalues and eigenstates govern spectral frequencies and intensities and make the connection between accessible spectral parameters and actual spectra.  1.5.2  S O L U T E S A S P R O B E S O F ORIENTATIONAL O R D E R A N D I N T E R M O L E C U L A R FORCES  Increasing the number of spins in a molecule causes the number of dipolar couplings to rise which results in very complex, poorly resolved high-resolution spectra that are hard to analyze and extract spectral information from. That kind of situation is present in highresolution spectra of nematogens, since individual molecules might have more than 20 proton spins (Fig. 1.5).  —i— -40000  .  1 -20000  ,  i 0  ,  i 20000  L  i_ 40000  Frequency (Hz)  Figure 1.5 Poor resolved high-resolution N M R spectrum of nematogen ZLI 1132 Spectral lines marked as (*) belong to impurities used to stabilize the system 9  Introduction  A very useful alternative for studying orientational order in nematic liquid crystals is to use solutes as probes of orientational order. Usually small, rigid symmetric molecules are used to simplify spectral analysis. They are dissolved in the liquid crystal in small concentrations to avoid any strong perturbations in the liquid crystal environment. Addition of small amounts of solutes only changes physical properties of the liquid crystal (such as the nematic-isotropic transition temperature) but the fundamental  nature of liquid crystals stays unchanged. Also solutes feel the same  orientational forces as liquid crystal molecules themselves. Another important reason why this approach of using small, symmetric molecules is very useful is that by choosing certain types of molecules it is possible to explore the role of particular intermolecular forces in orientational ordering mechanisms. This can be achieved by choosing a solute with a particular property [10], or by choosing a set of solutes whose properties vary in a well-characterized way [11,12], or by choosing a liquid crystal solvent that has special properties [10].  1.5.3  MULTIPLE Q U A N T U M N M R  -  /spectral simplification and analysis of high-resolution N M R spectra/  High-resolution proton N M R spectra (AM = ±1) of low spin systems are relatively solvable without too much trouble. They might have hundreds of lines. The number of single transitions for an N spin system that has 2 distinct eigenstates and eigenvalues can be N  calculated as  (2 AO! Number of  transitions =  .  C-12)  (N -\)\(N + \)\ Table 1.2 Maximum Number of Transitions in One Quantum Spectrum of a Partially Oriented Molecule as a Function of Number of Spins with I - \  Number of spins  1  2  3  4  5  6  7  8  Number of transitions  1  4  15  56  210  792  3003  11000  10  For systems that have some degree of symmetry (Table 1.1) many energy levels with the same M quantum number are degenerate which automatically reduces the possible number of transitions and therefore simplifies the spectra. Many spin systems with N>8 have a complex Hamiltonian and high-resolution N M R spectra which are challenging to analyze even for symmetric molecules. For these systems which have so closely packed spectra, quite accurate initial spectral parameters are required in order to solve the spectrum. In that case known spectral parameters ( J '  v  and  cr,) of  molecules with similar size and shape for the same liquid crystal are used as starting parameters in spectral analysis. In most cases this does not lead to a satisfactory solution so multiple quantum N M R is used. Multiple quantum spectra involve transitions between energy levels with the difference in M quantum numbers A M = 0,±\,....±(N-\),±N.  Higher order multiple quantum spectra are  quite simple containing fewer transitions than lower quantum ( A M < ±(N - 2)) spectra and therefore easier to analyze. Transition frequencies are governed by the same spectral parameters as conventional highresolution spectra. In principle analyzing the N, N-1 and N-2 multiple quantum spectra is sufficient enough to gather all spectral parameters. The limitation of M Q N M R lies in the fact that multiple quantum spectra are much broader and less resolved than single quantum spectra leading to less precise spectral parameters. That is why spectral parameters determined from MQ experiments are used as initial spectral parameters in analysis of highresolution spectra. Generally M Q coherences are created and observed using a three pulse sequence (Fig. 1.5) [13]. Before firing the first pulse the spin system is in equilibrium and only longitudinal magnetization I  7  is present. The first pulse flips I  7  magnetization into the x-y plane, which  evolves in preparation time % (fixed) among one-quantum coherences. The second pulse transforms one-quantum coherences into all possible MQ coherences that evolve in t1 evolution time under the internal spin Hamiltonian (direct dipolar, indirect scalar) and finally the third pulse partially converts M Q coherences back into observable one-quantum coherences that evolve in time t2.  11  l  7  Introduction  nil*  nil.  n!2  r  ACQUIRE/t  2  Figure 1.6 Three pulse sequence used to generate and observe MQ coherences  More on how different MQ coherences are selectively detected using phase cycling and how MQ spectra are transformed will be explained in Chapter 2.  1.6 O R I E N T A T I O N A L O R D E R I N G F R O M T H E O R E T I C A L  1.6.1  CALCULATION  STATISTICAL T R E A T M E N T O F ORIENTATIONAL O R D E R I N G USING  MEAN-  FIELD A P P R O A C H  The orientational distribution function f(Q.) fully describes the orientational order of a rigid solute in the nematic liquid crystal as well as the connection with experimentally measurable spectral parameters. Using statistical mechanics, the orientational distribution function f(Q)  can be expressed as a singlet distribution function, that is  kT  (1.13) kT dQ.  In the mean-field approximation all interactions in the system can be represented as interactions between a single molecule and the average field, i.e t / ( Q ) i s the mean-field potential that governs the orientational order of.the molecule..  12  Introduction  The physical picture behind this simple philosophy is that interactions between the solute and the liquid crystal environment (solvent) are described as interactions between a solute property (such as dipole) and the averaged field of the solvent, so that  V(0) = A , (0)-F So!u e  Liquicl  .  ,  co skd  (1.14)  The assumption that the averaged field is not influenced by the solute presence means that there is a clear and distinct separation of both solute and solvent contributions to the potential (no correlations between the two contributions). Statistically speaking, any measurable property taken as an average (for example S p ) can a  be then expressed a s  ^=J/(Q).(Acos0 cos0 ,-^)-dQ. a  /  (1.15)  Combining E q . 1.3, 1.13 and 1.15 gives  >~>„a  kr  J(-f c o s 0 cos 6^ a  Qcalc —  -t/(Q)  dQ.  (1.16)  dQ  Equation 1.16 is the basis for the statistical treatment of the orientational ordering, because it connects the intermolecular potential with the orientational  ordering. It gives the  opportunity to investigate various intermolecular potentials, by comparing calculated and experimental order parameters and therefore create a better picture of the orientational behavior of molecules in nematic liquid crystals. Representation of the intermolecular interactions can be done either using statistical theories'(Maier-Saupe [14,15], Onsager [16]), simulation'methods [17-25] or phehomenological models [10-12,26-29]. In the present study the simple phenomenological approach will be utilized.  13  Introduction  1.6.2  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 INTERACTIONS  Anisotropic intermolecular interactions are responsible for the orientational ordering of the solutes in the liquid crystal systems. The effective orienting mean-field potential can be divided into two contributing terms; one that presents short-range interactions and the other that presents long-range interactions, so that  LR  (1.17)  Short-range interactions consist of both an attractive and repulsive part. At short distances, the attractive part is ignored. Only the dominant repulsive part that is a consequence of overlapping of the electron clouds between neighbour molecules is considered. Short-range interactions are considered as interactions that are highly affected by the molecular structure. Long-range interactions-involve distances much larger that the molecular dimensions. They are attractive or repulsive interactions that depend on electrostatic properties of the molecules.  1.6.3  , .  •  M O L E C U L A R M O D E L S O F ORIENTATIONAL O R D E R  A. S H O R T - R A N G E M O D E L S  A1. CI model One of the short-range potentials used is a phenomenological model called C l by Burnell and co-workers [10], a combination of a circumference (C) model and an integral (I) model [26, 27] in which  (1.18)  14  Introduction  where k  7Z  and k  s  is a solvent parameter that determines the mean field influence on the solute, k  are proportionality constants; C(Q) is the circumference of the projection of the  solute at orientation Q. onto a plane perpendicular to the director (that is along the Z axis in the laboratory frame) and C(Q,Z)  is the circumference of the projection of the solute at  position Z and orientation Q onto a plane perpendicular to the director; so that C(Q,Z) dZ is an infinitesimal thin ribbon that traces out the molecule at position Z and orientation Q . The first term in Eq. 1.18 (C model) can be interpreted as a Hooke's elastic law where the liquid crystal is treated as an elastic continuum and the solute as its distortion. The second term (I model) can be seen as an anisotropic interaction between solute surfaces and solvent averaged field. The presented model treats molecules as a collection of van der Waals hard spheres placed at the atomic sites (Fig. 1.7).  A2. SS model Another type of short-range potential written as an expansion in spherical harmonics truncated at the first non-zero term [11] is  ^(M k )(3cose cos -d ) ap  77  a  p  (1.19)  ap  a.fi=x,y,z  where M  a j 3  are the traceless tensor components related to size and shape, and k  77  is the  same as in the previous model, a liquid crystal parameter related to the degree of orientation of the nematogen.  15  Introduction  Figure 1.7 Elastic model for short-range interaction between solute and liquid crystal The potential described by E q . 1.18 depends on the orientation  Q of the molecule  throughout C(Q) and C ( Z , Q ) ; C ( O ) is the circumference of the projection of the solute at orientation Q. onto a plane perpendicular to the director; C(Z,Q)  is the circumference of  the projection of the solute at position Z and orientation Q onto a plane perpendicular to the director. The Z axis corresponds to the direction of the liquid crystal director. The molecules are modeled as a collection of van der Waals hard spheres.  16  Introduction  B. L O N G - R A N G E M O D E L S  For long-range models only dipoles, quadrupoles and polarizabilities are suspected to be the most important contributors to orientational ordering and therefore will be utilized.  B1. Dipole model The dipole interaction in the mean-field approximation, defined as an interaction between a permanent solute dipole moment and the averaged electric field of the liquid crystal, would be zero due to the apolar nature of the liquid crystal, i.e (is) = 0 . Nevertheless, the permanent dipole moment can induce a dipole moment in the liquid crystal, creating the so called reaction field (in the liquid crystal) that will in return react with the permanent dipole. The magnitude of this kind of interaction is proportional to the magnitude of the created field as can be seen from:  tf(")£U=-;r-7 where }i ,jip (R  -RXX^J  77  (1.20)  are dipole moments of the solute along the a,B molecule fixed directions  a  and  S ^ ^ - ^ X S c o s ^ c o s ^ - ^ )  is the average value of the difference in the electric field between the Z  and X laboratory directions [11,12].  B2. Quadrupole model The quadrupole interaction, an interaction between the quadrupole moment of the solute and the electric field gradient of the liquid crystal {efg), is given by  m)t^ -rr\ =1  where Q  ap  is the afi  Sca^xscose.cose, -s  ali)  '  0.21)  quadrupole tensor component of the solute and F  77  is the Z Z  component of the electric field gradient, traceless second-rank tensor parallel to the nematic director [11]. 17  Introduction  B3. Polarizability model The local electric fields within the liquid crystals could change the electronic charge distribution in the solute molecules that could lead to a change in their orientation. The potential corresponding to this kind of interaction is:  UMZor**!*, =~T—T  77  -d ) ap  (1.22)  cu  is the a/3 molecular polarizability tensor component of the solute and  -Elx^  is the average value of the squares of the electric field between the Z and X  where (E  S«^.(^ - ^ ^ c o s ^ c o s ^  a/3  laboratory directions [11].  1.6.4 P R E V I O U S P R E D I C T I O N S O N ORIENTATIONAL O R D E R I N G  Some important experiments and predictions from theory/models over the course of the past few decades will be presented so as to gain a better perspective on where the science stands on the fundamental question of orientational ordering. Phenomenological investigation of orientational ordering  has been developed in two  different ways. One in which interactions between solutes and liquid crystals are described as mean-field interactions meaning that all solutes feel the same averaged liquid crystal field [12, 30-36]. The other states that the mean-field picture is too simple and that there are correlation effects between solutes and liquid crystals leading to the fact that different solutes feel different liquid crystal fields [37-39]. This is supported by the possibility that one solute molecule could spend more time on average in the aromatic regions of the liquid crystals while the other solute would prefer more the hydrocarbon chain region of the liquid crystals. Burnell and co-workers have utilized the mean-field approach and investigated the orientational behaviour of small symmetric molecules D  2  and HD [30-33] and methane  [34-36] in a special mixture called magic mixture of 55 wt% 1132/EBBA and its pure components. From magic mixture experiments it was determined that there is no long-range 18  Introduction  interaction contributions to the ordering, leaving the short-range interaction as the dominant contribution. The same results were obtained studying a whole range of small molecules dissolved in the magic mixture [12]. A computer simulation study of hard ellipsoids was performed to test the previously stated findings, and confirmed that short-range interactions indeed have a dominant effect on the orientational ordering of molecules in liquid crystals [19]. Studies of D  2  and HD in pure component liquid crystals show some evidence of  quadrupole-liquid crystals efg interactions. The determined electric field gradient of E B B A was shown to be negative not only from D and HD but also from benzene and benzene 2  derivatives studies [12]. The sign of the efg of E B B A is the same as one predicted from the mean-field quadrupole moment/efg model demonstrating that the quadrupole interaction is an important orientational mechanism. Photinos et al.  [37-39] on the contrary predicted theoretically that short- and long-range  interactions contribute equally to the orientation and that long-range interactions arise mainly from dipoles and quadrupoles. Emsley, Luckhurst and co-workers have shown, using the statistical Maier-Saupe theory of nematics [40-42] that the quadrupole is the lowest order multipole that contributes to a nonvanishing efg and that the efg strongly depends on solute and solvent molecular properties. Overall agreement of different results from experiments, theories and computer simulations is that short-range interactions, size and shape dependent, are the dominant orientational mechanism. The importance of different electrostatic interactions is still an open question and is the main object of the presented study. 1.7 T H E O U T L I N E O F T H E THESIS  In order to gain a better understanding about anisotropic intermolecular forces within liquid crystals, small molecules were dissolved in liquid crystal solvents and used to probe the anisotropic intermolecular forces. Chosen solute molecules have the same size and shape, same short-range contribution to the ordering but different electrostatic properties that enable testing of the effects of the additional long-range interactions. Also, the choice of liquid crystals is important in the sense of separately exploring the effects of different electrostatic effects. In magic mixture liquid crystals it was found [30-33] that the efg is zero, i.e. quadrupole interactions are annulled and therefore other electrostatic effects (like dipole and polarizability) if effective should clearly be visible. 19  Introduction  Chapter 1 contains all the theory basics needed to understand the experimental and theoretical determination of the spectral and order parameters and how valuable information about intermolecular forces that causes the orientational behavior of the molecules in liquid crystals can be extracted from those parameters. Chapter 2 presents the technical aspect of experiments while Chapter 3 focuses on analysis methodology and determination of spectral and structural parameters from non-vibrationally corrected dipolar couplings. A set of self-consistent order parameters is obtained in Chapter 4 and it was used to examine the effects of various short- and long-range interactions models on the ordering by comparing them with the calculated order parameters from those models. Chapter 5 summarizes the important results of the presented study with future work proposal.  References: [1] de Gennes, P. and Prost, J . , 1993, The Physics of Liquid Crystals, Claredon Press, Oxford, 2  n d  edition.  [2] Emsley, J . W., 1985, Nuclear Magnetic Resonance of Liquid Crystals, C. Riedel Press [3] Saupe, A., 1964, 2. Naturforsch.,  19, 161.  [4] Diehl, P., Khetrapal, C. I., 1969, NMR Basic Principles and Progress, Vol. 1, SpringerVerlag, Berlin. [5] Bunnell, E. E., de Lange, C. A., 2003, NMR of Ordered Liquids, Kluwer Academic Publishers. [6] Vartogen, G . and de Jeu, W . H., 1988, Thermotropic Liquid Crystals,  Fundamentals,  Springer-Verlag. [7] Berliner, L. J . , 1976, Spin Labelling:Theory  and Application, Academic Press, London.  [8] Zannoni, C. and Guerra, M., 1981, Mol. Phys., 44, 849. [9] Leadbetter, A., 1979, The Molecular Physics of Liquid Crystals, Academic Press. [10] Burnell, E. E. and de Lange, C , 1998, Chem. Rev., 98, 2359. [11] Syvitski, R. and Burnell, E. E., 1997, Chem. Phys. Letters, 281, 199. [12] Syvitski, R. and Burnell, E. E., 2000, J. Chem. Phys., 113, 3452. [13] Syvitski, R., Burlinson; N., Burnell, E. E. and Jeeiier., J . , 2002, J.Mag. [14] Maier, W. and Saupe, A., 1959, Z. Naturforsch. A, 14, 287. 20  Res., 155, 251.  Introduction  [15] Maier, W. and Saupe, A., 1960, Z. Naturforsch. A, 15, 882. [16] Onsager, L , 1949, N.Y. Acad. Sci., 51, 627. [17] Hashim, R., Luckhurst, G . R. and Romano, S., 1985, Mol. Phys., 56, 1217. [18] Luzar, M. Rosen, M. E. and Caldarelli, S., 1996, J. Phys. Chem., 100, 5098. [19] Poison, J . M. and Bunnell, E. E., 1996, Mol. Phys., 88, 767. [20] Poison, J . M. and Burnell, E. E., 1997, Phys. Rev. E, 55, 4321. [21] Syvitski, R. T., Poison, J . M. and Burnell, E. E., 1999, Int. J. Mol. Phys. C, 10, 403. [22] Burnell, E. E., Berardi, R., Syvitski, R. T. and Zannoni, C , 2000, Chem. Phys. Letters, 331,455. [23] Celebre, G., 2001, Chem. Phys. Letters, 342, 375. [24] Celebre, G., 2001, J. Chem. Phys., 115, 9552. [25] Lee, J . ' - S . J . , Undergraduate thesis, Department of Chemistry, University of British Columbia, 2001. [26] van der Est, A. J . , Kok, M. Y. and Burnell, E. E.,1987, Mol.Phys., 60, 397. [27] Zimmerman, D. S. and Burnell, E. E., 1990, Mol. Phys., 69, 1059. [28] Zimmerman, D. S. and Burnell, E. E., 1993, Mol. Phys., 78, 687. [29] Ferrarini, A., Moro, G . J . , Nordio, P. L. and Luckhurst, G . R., 1992, Mol. Phys., 77,1. [30] Burnell, E. E., de Lange, C. A. and Snijders, J . G., 1982, Phys. Rev., A25, 2339. [31] Burnell, E. E., van der Est, A. J . , Patey, G. N., de Lange, C. A. and Snijders, J . G., 1987, Bull. Mag. Reson., 9, 4. [32] van der Est, A. J . , Burnell, E. E. and Lounila, J . , 1988, J. Chem. Soc. Faraday Trans. 2, 84, 1095.  [33] Burnell, E. E., de Lange, C. A., Serge, A. L., Capitani, D., Angelini, G., Lilla, G . and Barnhoorn, J . B. S., 1997, Phys. Rev., E55, 496. [34] Snijders, J . G . , de Lange, C . A. and Burnell, E. E., 1983, Israel. J. Chem., 23, 269. [35] Snijders, J . G., de Lange, C. A. and Burnell, E. E., 1982, J. Chem. Phys, 77, 5386. [36] Snijders, J . G., de Lange, C. A. and Burnell, E. E., 1983, J. Chem. Phys, 79, 2964. [37] Terzis, A. and Photinos, D., 1994, Mol. Phys., 83, 847. [38] Photinos, D., Poori, C , Samulski, E. and Toiumi, H., 1992, J. Phys. Chem, 96, 8176. [39] Photinos, D., Poon, C , Samulski, E., 1993, J. Chem. Phys., 98, 10009. [40] Emsley, J . , Palke, W. and Shilstone, G., 1991, Liquid Crystals, 9, 643. [41] Emsley, J . , Heeks, S., Home, T., Howells, M., Moon, A., Palke, W., Patel, S., Shilstone, G. and Smith, A., 1991, Liquid Crystals, 9, 649. [42] Emsley, J . , Luckhurst, G . and Sachdev, H., 1989, Mol. Phys., 67, 151. 21  2. E X P E R I M E N T  2.1 S A M P L E P R E P A R A T I O N  The nematic liquid crystals used as solvents are: - ZLI-1132, a eutectic mixture of  frans-4-n-alkyl-(4-cyanophenyl)-cyclohexane  (alkyl=propyl,  pentyl, heptyl) and rrans-4-n-pentyl-(4'-cyanobiphenyl-4)-cyclohexane (Fig. 2.1) purchased from Merck.  :  .  ,  '•  ~ E B B A (N-(p-EthoxyBenzylidene)-p'-n-ButylAniline) (Fig. 2.2) synthesized according to a reference book [1] by Ray Syvitski - a mixture 55 wt% ZLI-1132/EBBA called 'magic mixture' a nematic phase that has zero external electric field gradient (efg) at approximately 301.4 K [2,3] prepared from pure liquid crystals The solutes 1,3,5-trichlorobenzene (TCB), 3,5-dichlorotoluene (DCT), 5-chloro m-xylene (CLMX) and mesytilene (MESIT) (Fig. 2.3) were commercially available except 3,5dichlorotoluene, which was donated by Scott Kroeker from the University of Manitoba. All liquid crystals and solutes were used with no further purification. 3,5-dichlorotoluene, 5-chloro m-xylene and mesytilene were dissolved in liquid crystal solvents in about - 5 % mol concentration in 5 mm outer diameter N M R tubes. In each sample - 1 % mol concentration of T C B was added as an internal orientational standard for scaling purposes. The mixtures were then heated to the isotropic phase and mixed thoroughly on a vortex stirrer repeatedly until samples became homogeneous. The N M R tubes were equipped with a capillary tube filled with acetone-d6, centered in the middle using teflon spacers. The acetone-d6 was used as a deuterium lock (signal).  22  Experiment  H  trans-4-n-propyl-(4-cyanopheny)-cyclohexane 24%  H  trans-4-n-pentyl-(4-cyanophenyl)-cyclohexane 36%  NC-  C  5 11 H  H ^  trans-4-n-heptyl-(4-cyanophenyl)-cyclohexane 25%  15o/ trans-4-n-pentyl-(4'-cyanobiphenyl-4)-cyclohexane C  5 11 H  0  Figure 2.1. ZLI 1132 liquid crystal  H H  5  C —  O-  \  //  X  ^ C  4  H  9  Figure 2.2 E B B A liquid crystal ( N-(p-EthoxyBenzylidene)-p'-n-ButylAniline )  Cl  C |  '  "ci TCB  cr  CH.  CH.  CH  " Cl  Cl'  DCT  ^CH CLMX  Figure 2.3 Solutes  23  3  CH  CH  3  MESIT  Experiment  2.2  experimental conditions  Proton high-resolution and multiple-quantum N M R experiments were performed on a Bruker AMX-500 spectrometer equipped with a high resolution probe operating at 11.75 T (corresponding to a proton resonance frequency of 500 MHz). The temperature in the probe was calibrated using the difference in the proton chemical shifts of 80% EthyleneGlycol/DiMethylSulfOxide-d6 and it was controlled by a Bruker temperature unit using airflow. The dial temperature of 300.7 K was calibrated to 300.0 K +/_ 0.1 K. All samples were heated up to the isotropic phase and vortexed thoroughly before placing in the N M R probe. They were let to sit in the probe for half an hour in order for them to reach equilibrium. High-resolution proton N M R spectra were acquired using a simple one pulse sequence (Fig. 2.4) with 32K data points that are zero filled to 64K points in the ^dimension. The phase of the pulse (0) and the receiver (6) were cycled according to the cycling scheme in Fig. 2.4 in order to reduce the effects of pulse and receiver imperfections. The 90° degree pulse width varied between 11 u.s and 13 u,s; recycle delay was 2 s; spectral width varied from 13 kHz to 20 kHz depending on the sample, and the number of scans was 100.  FID  Phase  4  e  Phase cycling 0, n, n, 0, n/2,  3n/2,  3TT/2, n/2  0, JI, 7 i , 0. n/2,  3TC/2, 3TX/2, n/2  Figure 2.4 Single pulse sequence 24  Experiment  All multiple quantum (MQ) spectra were acquired simultaneously as separate slices of a three-dimensional spectrum using the 3D M Q - N M R pulse sequence (Fig. 2.5) [4]. MQ coherences excited by the second pulse evolve in variable time t and are converted {  into observable one-quantum coherences by the third pulse. Individual echoes S(t ) are 2  acquired a s a function of time /, and phase <p that is incremented by 360°/n (n is an arbitrary intiger that should be at least 2N+1) n times for each /, value. This gives rise to a 3D interferogram where the signal is a three-dimensional function After Fourier transformation with respect to t  ]t  <p and t  2  S(t ,(/),t ). {  2  for each value of FT-ed 0  dimension the M Q spectrum was extracted a s the summed projection of the Fourier transforms of the echo signal S(t ) onto the /, dimension. 2  nil.  Till,  ,n/2.  ACQUIRE  t1  \  ,  FID  i  11  aA  x  multiple quantum coherence evolve  2  „  II l/\/VWwwwwv\  II \i •-'  echo S( t )  Phase <|) 0  Phase cycling 0,2rc/n, 2*2jr/n, 0  ,(n-l)*2jt/n  Figure 2.5 3D M Q N M R pulse sequence  25  AAA  A A A ,  Experiment  The experiment time varied between 9 hours for D C T (6 spin) and 36 hours for MESIT (12 spin system). Recycle delays were in the range between 1.3 s and 2 s; preparation T time ranged between 9 ms and 12 ms (it was chosen so as to produce visible intensities of higher MQ coherences). In both the r, and t  2  dimensions, 1024 points were acquired and zero filled to 2048 points.  In the <p dimension 16 points (a multiple of 2) for D C T and 32 for C L M X and MESIT were collected. In order to get rid of coherent noise, the processing parameter F C O R was set to 1 (default value was 0.5 [5]). The F C O R parameter defines that the first point in the real FID was multiplied with its value in order to overcome the rolling baseline caused by the nonsimultaneous acquisition of the  real and the  imaginary  signals. In  high-resolution  experiments the rolling baseline is annulled by setting F C O R to 0.5. On the other hand FCOR=0.5 creates a systematic coherent noise in the 3D MQ experiment.  References: [1] Keller, P. and Liebert, L. (1978), Solid State Phys. Supplemental,  14, 19.  [2] Barker, P.B, Van der Est, A . J . , Burnell, E.E., Patey, G.N., de Lange, C A . and Snijders, J . G . , 1984, Chem. Phys. Lett, 107, 426. [3] Van der Est, A . J . , Barker, P.B., Burnell, E.E, de Lange, C A . and Snijders, J . G . , 1985, Mol. Phys., 56, 161. [4] Syvitski, R.T., Burlinson, N., Burnell, E.E and Jeener.J., 2002, J. Magn. Res., 155,251. [5] XWIN-NMR Software Manual, Bruker Analytik GmbH, 2000.  26  3. SPECTRAL ANALYSIS  3.1 I N T R O D U C T I O N  The N M R experiment for ordered systems provides valuable and precise information such as dipole-dipole and spin-spin interactions, anisotropies in chemical shifts and quadrupole coupling constants. From dipolar couplings, information about relative molecular geometries and conformations as well as second rank order parameters can be easily extracted (Eq. 1.11, page 8). This chapter explains how spectral parameters were extracted from complex high-resolution proton N M R spectra of small solutes with the help of MQ N M R , as well as how spectral parameters are used to obtain the solute molecular geometry and its second rank orientational  order  parameters. Those orientational  order  parameters  are important  information that will be used later to examine which mechanisms of ordering are dominant in liquid crystal systems.  3.2 S P E C T R A L A N A L Y S I S W I T H T H E A I D O F M Q N M R  High-resolution spectra of small solutes dissolved in liquid crystal solvents are determined by the spin Hamiltonian (equivalent to the Hamiltonian in section 1.5.1):  +2^)/,, /.  " = -!>,/,•./ *  '"  /  /  '/  z +  |(.y,  ;  - o , ) ( / , / - + /,/;)]  (3.1)  j>i  where /"*" and I~ are raising and lowering spin operators, v, is the resonance frequency of nucleus /'; and J  i}  and Z X are the indirect and dipolar coupling constant between nuclei /  and j in the molecule. The eigenstates and eigenvalues that govern spectral frequencies and intensities can be calculated from diagonalization of the Hamiltonian for a given set of spectral parameters. Therefore an initial set of spectral parameters is needed to simulate the experimental spectrum.  27  Spectral analysis  One way of choosing an appropriate initial set of parameters for a molecule is the choosing a set for the same liquid crystal solvent from a molecule with similar size and shape. This approach is only successful in a small number of simple cases (like low-spin symmetrical systems). For more complicated cases (Fig. 3.1) MQ spectra were analyzed first. Due to the poor resolution of M Q spectra (up to 100 Hz) the obtained set of spectral parameters is rather imprecise but it serves as a good starting point for analysis of the high-resolution spectra (where observed line widths were of the order of a few Hz) (see Table 3.2). Using the initial set of spectral parameters a trial spectrum was calculated. Calculated frequencies were then assigned to the experimental ones using cursor control in the graphical program called S M [1] with macros written by Ray Syvitski and spectral parameters were adjusted in a least-square fitting routine. Assignment and reassignment of frequencies and adjustment of spectral parameters were repeated until a reasonable fit was achieved (a fit that is of the order of the digital resolution of the experimental spectra). During the assignment process non-resolvable and low intensity  spectral lines were  assigned last to avoid a misleading and meaningless fit. The program used to calculate spectra and iteratively adjust spectral parameters was- L E Q U O R [2] for spectral analysis and its modified version for MQ analysis [3].  28  high-resolution  Spectral analysis  .  ,  .  i  -5000  ,  .  .  .  i  .  0  ,  .  i  5000  Frequency (Hz)  Figure 3.1 High-resolution proton N M R spectra of D C T (A), C L M X (B) and MESIT (C) in ZLI 1132 liquid crystal at 300 K with total number of calculated spectral lines of 69, 782 and 3819. Spectral lines marked with an (*) belong to the internal standard T C B . The rolling baseline is the unresolved spectrum of the ZLI 1132 liquid crystal. 29  Spectral analysis  The high-resolution spectrum of T C B (3-spin system) is a 1:2:1 triplet with a splitting of 3-D  HH  and chemical shift that corresponds to the position of the middle peak (Table 3.1).  Table 3.1 Fitting Parameters and R M S Errors from Analysis of High-Resolution Spectra of T C B 3-spin System  Solutes  Liquid Crystal  Parameter  a  ZLI 1132  T C B with D C T  R M S error T C B with C L M X °n R M S error  55 wt%  1132/EBBA  EBBA  -199.68(01)  -171.92(02)  -138.19(03)  3536.85(02)  1875.15(04)  3920.67(06)  0.020  0.045  0.064  -208.27(04)  -163.52(04)  -144.15(05)  2187.67(09)  2590.95(10)  3783.51(11)  0.095  0.099  0.113  -212.13(04)  -167.65(00)  -144.14(02)  2586.97(10)  2528.62(00)  2740.47(05)  0.097  0.001  0.051  b  T C B with MESIT OH"  R M S error a  Parameter in Hz  b  Frequency is referenced to an arbitrary zero. Spectra were acquired at 500.13 MHz.  Determination of spectral parameters of D C T (6-spin system) is a challenging task since DCT has 3 different chemical shifts and 5 independent dipolar coupling constants. In this case an initial set of spectral parameters was obtained from the (N-1) and (N-2)Q spectra (Fig. 3.2). First the (N-1)Q spectrum was fitted using a modified version of the program L E Q U O R that allows either independent adjustment of 5 . and/or D within the fitting (>  30  tj  Spectral analysis  routine. Knowing the geometry of the molecule and the relation between Sy and ZX (Eq. 1.11), by adjusting the Sy,  D.  tj  is adjusted automatically. In some cases varying order  parameters is an advantage since a smaller number of parameters are fitted to and therefore the spectral analysis is simplified. In the case of the +5Q spectrum of DCT, instead of fitting to 5 independent dipolar coupling parameters only two independent order parameters (S  zz  and S  xx  - order parameters in the plane of the benzene ring (Fig. 3.6)) were  adjusted within the fitting routine. Since the geometry of D C T hasn't been determined previously, the known geometry of T C B a molecule with similar size and shape, taken from ref. [4] was used as an initial geometry needed to calculate independent / ^ p a r a m e t e r s . The +5Q and +4Q spectra were easily fitted (Fig. 3.3 and Fig. 3.4) with a R M S error of 4 Hz and the set of spectral parameters obtained (Table 3.2) were then used to simulate the highresolution spectrum. A total of 68 lines were assigned in the high-resolution spectrum of DCT in E B B A with a R M S error of 0.343 Hz. The fitted high-resolution spectrum is shown in Fig. 3.5 and fitting parameters are presented in Table 3.3. In the calculated spectrum a Lorentzian line broadening of 2 Hz was used to incorporate the natural line broadening effect due to motion and collision in the system. Similar spectral strategy was applied in solving the high-resolution spectra of C L M X and MESIT molecules. Fitted spectral parameters of those molecules are presented in Tables 3.4 and 3.5.  31  Spectral analysis  Table 3.2 Fitting Parameters and R M S Errors from Analysis of M Q and High-Resolution Spectra of D C T in E B B A  Parameter  a  EBBA  EBBA  EBBA  +5Q  +4Q  +1Q  spectrum  spectrum  spectrum  -120.94  -123.95  -126.39(17)  -153.60  -157.74  -157.90(17)  - 399.42  -396.10  -394.60(08)  -63.18  -63.15  -63.58(043)  A»  1161.58  1174.49  -" 1173.95(08)  01  3861.57  3831.77  3836.03(20)  3913.77  3882.17  3891.44(23)  1686.31  1706.67  1710.42(15)  3.092  4.094  0.343  6  14  70  D  l2  5  6  R M S error (Hz) Number of assigned lines  a  Parameter in Hz  b  Frequency is referenced to an arbitrary zero. Spectra were acquired at 500.13 MHz.  32  Spectral analysis +6Q  +5Q  +4Q  +3Q  +2Q  +1Q  +0Q  20000  10000 .  0  10000  20000  Frequency (Hz)  Figure 3.2 All positive M Q spectra of D C T (6-spin system) in E B B A liquid crystal at 300 K With T =12 ms, recycle delay of 2 s, two scans for e a c h n=16 phase increments per r,, 1024 t  x  increments, F  2  spectral width of 25 k H z and F  l  spectrum strong central line w a s cut off for clarity  33  spectral width of 50 kHz. The +0Q  Spectral analysis  10000  12000  14000  16000  18000  20000  Frequency (Hz)  Figure 3.3 Experimental (top) and calculated (bottom) +5Q spectra of D C T in E B B A Line width in the experimental spectrum is approximately 80 Hz. Two lines around 12000 Hz in calculated spectrum are not visible separated. The intensities of the-calculated spectrum do not correspond with those of the experimental spectrum  34  Spectral analysis  I  I 5000  I  L  . ...  I  ,, I  I  I  I  10000  I  I  . .  I  I  I  I  15000 .  Frequency (Hz) '  Figure 3.4 Experimental (top) and calculated (bottom) +4Q spectra of D C T in E B B A Line width in the experimental spectrum is approximately 70 Hz and the intensities of the calculated spectrum do not correspond with those of the experimental spectrum  35  Spectral analysis  Figure 3.5 Experimental (top) and calculated (bottom) high-resolution proton spectra of D C T in E B B A at 300 K. Spectral lines marked with an (*) belong to the internal standard T C B and resonances marked with an  (•) are from unknown impurities (the D C T solute is an old  sample that has probably degraded a little bit over a long period of time); less intense resonances (+) belong to the lock solvent (acetone-d6 in a capillary tube); the rolling base line is the unresolved spectrum of E B B A liquid crystal. In the experimental spectrum the line width at half-maximum height varied between 2-8 Hz. Lorenzian line broadening used in the calculated spectrum is 2 Hz. The intensities of the calculated spectrum closely correspond with those of the experimental spectrum. 36  Spectral  analysis  Table 3.3 Fitting Parameters and R M S Errors from Analysis of High-Resolution Spectra of D C T 6-spin System  Solute  DCT  ZLI1132  Liauid Crystal 55 wt% 1132/EBBA  EBBA  D  -255.66(19)  -201.31(19)  -126.39(17)  D  -176.15(21)  -162.89(21)  -157.90(17)  -493.48(08)  -440.10(08)  -394.60(09)  -56.26(36)  -56.39(36)  -63.58(44)  1030.85(08)  1039.46(09)  1173.95(08)  -  -  -  2.06(44)  1.85(40)  2.20(32)  -0.70(14)  -0.95(14)  -0.72(17)  -0.38(65)  -0.85(69)  -0.50(84)  O",  3569.70(21)  1862.77(23)  3836.03(20)  0-3  3411.09(24)  1787.45(27)  3891.44(73)  1534.72(15)  -266.03(16)  1710.41(15)  Parameter  a  n  n  A.4 °12  J  n  R M S error  0.327  Number of  68  .  0.546  0.343  61  70  assigned lines a  Parameter in Hz  b  J  l2  0  *  coupling constant was not determined due to insensitivity of the fitting process  Frequency is referenced to an arbitrary zero. Spectra were acquired at 500.13 MHz.  37  Spectral analysis  Table 3.4 Fitting Parameters and R M S Errors from Analysis of High-Resolution Spectra of C L M X 9-spin System  ZLI1132  Liquid Crystal 55 wt% 1132/EBBA  EBBA  -160.34(11)  -144.20(10)  -167.69(09)  -70.42(05)  -59.49(07)  -61.95(09)  -659.22(05  -495.41(07)  -403.10(07)  D 34  -414.89(07)  -374.65(08)  -439.08(06)  D  1292.43(03)  1089.89(03)  1141.24(03)  D,  -60.26(03)  -54.35(03)  -63.74(03)  J ,2  1.99(18)  1.97(18)  2.01(18)  J ,3  1.53(10  1.75(13)  1.37(15)  -0.51(10)  -0.43(14)  -0.78(17)  -0.66(11)  -0.69(16)  -0.53(17)  J 34  -0.75(13)  -0.76(17)  -0.77(14)  J 47  -0.18(06)  -0.22(06)  -0.21(06)  2099.63(09)  2497.30(10)  3675.27(10)  2214.41(12)  2546.08(13)  3657.00(13)  91.23(05)  422.84(06)  1578.88(06)  R M S error  0.560  0.401  0.453  Number of  445  396  379  Solute  Parameter'  CLMX 0,2  0,4 0,7  H,  H  H.  H.  H. Cl  45  O", O-3 O-4  assigned lines  a  Parameter in Hz  b  Frequency is referenced to an arbitrary zero. Spectra were acquired at 500.13 MHz. 38  Spectral analysis  Table 3.5 Fitting Parameters and R M S Errors from Analysis of High-Resolution Spectra of MESIT 12-spin System  Solute  D  l 2  0,4 0,7  H,  H, 9,  8  044  9 047  S  H. H  12  EBBA  -220.49(06)  -179.26(06)  -168.75(06)  -571.94(03)  -465.51(03)  -439.58(03)  -82.99(06  -67.583(07)  -63.79(07)  1518.15(02)  1234.96(03)  1166.50(03)  -82.97(02  -67.53(02)  -63.82(02)  1.72(11)  1.57(13)  1.76(12)  -0.71(05)  -0.66(07)  -0.67(07)  -0.44(10)  -0.41(01)  -0.45(14)  -0.22(04)  -0.19(05)  -0.22(05)  2510.77(08)  2420.58(10)  2592.37(09)  492.02(05)  367.53(07)  537.91(06)  0.341  0.371  355  381  1  MESIT  H H  ZLI1132  Liquid Crystal 55 wt% 1132/EBBA  Parameter  H  H„  AI *^47  0-4  R M S error Number of  0.474 . 494  assigned lines  a  Parameter in Hz  b  Frequency is referenced to an arbitrary zero. Spectra were acquired at 500.13 MHz.  39  Spectral  3.3  analysis  M O L E C U L A R STRUCTURE AND ORDER P A R A M E T E R S  The relative positions of nuclei and order parameters for a given solute were calculated from a simultaneous fit to the dipolar couplings obtained for all three liquid crystals. For this purpose a slightly modified version of a program called S H A P E [3] was used. The program calculates the dipolar couplings according to E q . 1.11 using initial inputted geometry and it performs the least-square minimization routine N L 2 S N O [5] that minimizes the difference between calculated and experimentally determined dipolar couplings (which are part of the input data). The exact geometry of solutes used in this study, except T C B , hasn't been measured yet so the initial geometry used in the fitting routine was chosen to be geometry of the molecule with similar size and shape (such as T C B (ref. [4])). For molecules with rotating groups, such as a methyl group, dipolar interactions must be averaged over a whole rotation. Each methyl group was modeled with a potential function  V - i;(l~cos6a)/2  .  '  (3.2)  where V is fixed at 60 J/mol [6]. The potential minimum corresponds to the position of the 6  proton in a methyl group that is perpendicular to the benzene ring. Each methyl group is rotated independently through 360° in 10° steps. For each position dipolar couplings between hydrogens were calculated and averaged over all possible ~ /v  conformations, with each conformation weighted by the Boltzman factor (~ e  ).  /kT  A s a result of the minimization routine, relative structural parameters and order parameters of the studied solutes DCT, C L M and MESIT were successfully determined and are presented in Tables 3.6 and 3.7. Order parameters were determined with high accuracy. That is quite important since the values of the order parameters of a solute may be quite small and the prime goal of this study is to explore various models for the anisotropic potential.  40  Spectral  analysis  Table 3.6 Structural Parameters from Fits to Dipolar Couplings for DCT, C L M X and M E S I T  Parameter  TCB  3  DCT  d  CLMX  e  MESIT  e  e  1.3908  1.3920(05)  1.3870(19)  1.3861(37)  r(C -C )  1.3908  1.3898(08)  1.3922(20)  1.3861(37)  r(C -C )  1.3908  1.3890  1.3919  1.3861(37)  r(C -H)  1.0940  1.0893(14)  1.0865(24)  1.0881(18)  r(C -H)  1.0940  1.0914(14)  1.0903(25)  1.0881(18)  r(C -X )  1.7326  1.5283(18)  1.7326  1.5267(27)  r(C -X )  1.7326  1.7326  1.5218(30)  1.5267(27)  r(C-H)  -  1.0997(13)  1.1114(19)  1.1056(22)  -  1.7326  f  1.5281(30)  1.5267(27)  Z(C,C C )  122.00  121.77  9  Z(C C C )  118.00  118.01(07)  118.22(12)  118.36(14)  Z(C,C C )  122.00  122.21(15)  121.72(12)  121.64(14)  *(C C C )  118.00  117.78  118.13  118.36(14)  Z(C C X )  121.00  119.00'  118.90(12)  119.18(07)  Z(C C H)  121.00  120.77(05)  121.35(13)  120.82  9  120.82  9  r(C -C ) x  2  3  4  4  3  x  5  c  2  h  4  mulhyl  (C  — C  r  6  methy  2  2  3  4  4  5  i)  3  4  5  6  h  5  4  (  3  '  Z(C C H) 4  5  Z(C C X") X  ^(  2  CC  R M S error  6  melhyl  H  methyl  )  121.00  9  •'  121.'11  f  9  9  121.98  9  f  121.64(14)  9  9  ' 120.93 ' " 9  119.00  119.11(05)  119.01(12)  119.18(07)  -  110.47(07)  111.22(16)  110.94(14)  -  0.321  0.548  0.566  41  a  Spectral  3  analysis  See figure 3.6 for structure and atom labeling of molecules. Bond distances are in (A) bond angles in degrees and errors are in Hz  b  X=CI for TCB and CLMX; X=CH  3  0  X=C/ for TCB and DCT; X=CH  3  d  for DCT and for CLMX  and  MESIT MESIT  Geometry taken from Ref. [4]  e  Initial a priori geometries are TCB geometries taken from Ref. [4]  1  Parameter not varied during fit  9  Parameter calculated from the bond angles and lengths of the carbon skeleton z  CLMX  "  i  MESIT  Figure 3.6 Atom labeling of solute molecules 42  Spectral analysis  Table 3.7 Table of Order Parameters from Fits to Dipolar Couplings  Liauid Crystal 1132  55wt% 1132/EBBA  EBBA  0.13480(01)  0.11606(01)  0.09329(02)  -0.26960(01)  -0.23212(03)  -0.18658(04)  0.13480(01)  0.11606(01)  0.09329(02)  0.14060(03)  0.11039(03)  0.09731(03)  -0.28120(05)  -0.22078(05)  -0.19462(05)  0.14060(03)  0.11039(03)  0.09731(03)  0.14321(00)  0.11318(00)  0.09731(01)  -0.28641(00)  -0.22635(00)  -0.19462(03)  0.14321(00)  0.11318(00)  0.09731(01)  0.17265(80)  0.13162(50)  0.08347(50)  -0.27022(11)  -0.23001(82)  -0.19459(86)  s  0.09757(31)  0.09838(32)  0.11112(36)  s,.  0.10627(40)  0.09565(35)  0.11186(39)  -0.28468(03)  -0.22793(83)  -0.21573(79)  0.17841(63)  0.13228(48)  0.10387(40)  0.14467(66)  0:11770(54)  0.11117(51)  -0:28935(32)  -0.23541(08)'  -0.22234(02)  0.14467(66)  0.11770(54)  0.1117(51)  Order Parameter  Solute  TCB/DCT "  s  zz  TCB/CLMX ~  s  zz  TCB/MESIT ~  s  zz  DCT  zz  CLMX  s  zz  MESIT ~  s  zz  +  * Order parameter that is perpendicular to the benzene ring +  s +s +s_.=o xx  vy  AX  yy  43  Spectral analysis  3.4 SUMMARY In this study spectral, structural and orientational order parameters for T C B , DCT, C L M X and M E S I T dissolved in three different liquid crystals were determined. An initial set of spectral parameters, used in the analysis of the high-resolution spectrum, was estimated from the analysis of the (N-1) and (N-2)Q spectra adjusting either S  y  or D  tj  independently.  With this approach analysis was simplified and therefore analysis time was significantly reduced. Highly accurate spectral parameters were extracted by analyzing the highresolution spectrum. Accurate order parameters and relative positions of nuclei were obtained by simultaneously fitting to all dipolar coupling parameters of the solute in all liquid crystals.  .  ,  :  References:  [1] Graphical Interface program S M , Edition 2.2.0. J a n . 1992, Lupton, R. and Monger, P. [2] Diehl, P., Kellerhals, H. and Niederberger, W., 1971, J. Magn. Resonance, 4, 352. [3] Syvitski, R. and Burnell, E.E., 2000, J. Chem. Phys., 113, 3452. [4] Almenninbgen, A. and Hargittai, I., 1984, J. Mol. Struct., 116, 119. [5] Dennis, J . E., Gay, D. M. and Welsch, R. E., 1981, ACM Trans. Math. Software, 7, 3. [6] Lister, D., MacDonald, J . and Owen, N., 1978, Internal Rotation and Inversion, Academic Press, London.  44  4. ORIENTATIONAL ORDERING IN NEMATIC LIQUID CRYSTALS Investigation of different contributions to the orientational mechanisms in  nematic liquid  crystals  4.1 INTRODUCTION  Previous studies on orientational mechanisms in nematic liquid crystals gave great insight into the nature of the physical interactions responsible for orientational behaviour in these phases. Generally they show that the main orientational ordering mechanism comes from short-range interactions [1-7], i.e. the repulsive interactions that are closely correlated with the size, shape and flexibility  of the molecules. Contributions from the  long-range  interactions, interactions that are due to properties that describe the distribution of the charge over a molecule (like dipole, quadrupole, polarizability) seem to have a less dominant effect on the orientational ordering [8-11]. To what extent each electrostatic longrange interaction contributes to the orientational mechanisms is still an open debate. The purpose of this study is to determine the effects of permanent dipoles, quadrupoles and molecular polarizabilities on orientational ordering. In order to reduce the effect of dominant short-range interactions and to emphasize different electrostatic interactions, solutes with similar size and shape but different electrostatic properties are chosen as probe solutes in various liquid crystals. The set of chosen solutes with similar size arid shape (Fig. 4.1) have either C 2 or C 3 type symmetry. If they had the same size and shape and if the size and shape is the only orientational mechanism then the anisotropy of the experimentally determined order parameters (S -S__ xx  ) would be zero due the same symmetry. And if any other  orientational mechanisms beside size and shape also contributes to the orientational ordering then the anisotropy in the order parameters would be influenced by them, and they should differ from zero. Particularly the anisotropy in the order parameters in the magic mixture  (zero electric field gradient and quadupole interaction)  manifestation of dipole and polarizability effects.  45  will allow the clear  Orientational ordering in nematic liquid crystals  Comparing the anisotropy of the experimentally determined order parameters (S  XX  -S- ) Z  in  a series of solutes with the same size and shape but different electrostatic properties, a qualitative  picture  about  long-range  electrostatic  contributions  to  the  orientational  mechanisms can be drawn. It should be stressed that behind this way of examining the experimental results is the assumption that all solutes have the same size and shape. A more quantitative approach to learning about intermolecular interactions is to compare the experimental order parameters with calculated order parameters from theory or models, or those determined from computer simulations. A s described in the introductory chapter two short-range potential (Cl and size and shape) models and three long-range potential (dipole, quadruple and polarizability) models were utilized to investigate the orientational mechanism in nematic liquid crystals. H  CLMX  .  •  H  MESIT  ~x Figure 4.1 Chosen set of solutes with the same size and shape but different electrostatic properties presented in their coordinate system 46  Orientational ordering in nematic liquid crystals  4.2 D E T E R M I N A T I O N O F A C O N S I S T E N T S E T O F O R D E R P A R A M E T E R S  When solutes are dissolved in liquid crystal solvents they tend to slightly perturb the liquid crystal environment. The perturbation effect depends on solute properties and solute concentration in a given sample. If one needs to compare the solute orientational order parameters in different samples then all the above mentioned factors must be compensated for. In other words a consistent set of order parameters must be obtained. That can be done in a few different ways [1,7,11-13].  T For example, spectra can be recorded at the same reduced temperature (T =  , where  R  • ' T  N1  '  "  '  T  N1  is the nematic-to-isotropic phase transition temperature) or order parameters of each  solute in the liquid; crystal can be measured a s a function of concentration and then extrapolated to zero concentration. In the present study a constant real temperature scaling approach, shown to give the most consistent results, [13] is utilized. Order parameters were scaled using the internal standard T C B and the simple equation:  c r. scaled  _  ^ ij (solute) ~  ij( solute) „  '  (4-1)  ij (TCB-reference)  ^ij(TCB)  where S  !J(sulule)  and S  iJ(TCB)  are the order parameters of the solute and internal standard T C B  in the same sample tube and S  _  ij(TCIS  re/erence)  is the order parameter of internal standard T C B  used as a reference tube (arbitrarily chosen to be T C B with MESIT sample tube) in the same liquid crystal. The set of scaled and non-scaled order parameters is presented in Table 4.1. Differences between scaled and non-scaled values of order parameters of different solutes (DCT, C L M X and MESIT) in the same liquid crystal are less then 6 % using this scaling method (see Fig. 4.2). Also comparing scaled and non-scaled values of order parameters of T C B coodisolved with various solutes for the same liquid crystal the discrepancies are less than 6% (Table  47  Orientational ordering in nematic liquid crystals 3.7). Both discrepancies imply that the main contribution to the difference comes from solute properties since the concentration of solutes is very small and roughly the same.  Table 4.1 Scaled and Non-Scaled Order Parameters  Liauid Crystal  Scaled/ Non-scaled Solute TCB  1132  55wt% 1132/EBBA  EBBA  0.14321/0.14321  0.11318/0.11318  0.09731/0.09731  -0.28642/-0.28642  -0.22636/-0.22636  -0.19462/-0.19462  S^'"" IS  0.14321/0.14321  0.11318/0.11318  0.09731/0.09731  g scaled j Q  0.18342/0.17265  0.12835/0.13162  0.08707/0.08347  -0.28707/-0.27022  -0.22429/-0.23000  -0.20297/-0.19459  0.10365/.09757  0.09594/0.09838  0.11590/0.11112  Order Parameter'  +  C< scaled j r t  1  ZZ  DCT  o scaled *yy  i rt '^yy  £ i scaled j Q  CLMX  g scaled j  g  0.10824/0.10627  0.09807/0.09565  0.11185/0.11186  ri scaled  / rt  -0.28996/-0.28468  -0.23369/-0.22793  -0.21572/-0.21572  ITI scaled j <ri  0.18172/0.17841  0.13562/0.13228  0.10387/0.10387  JTI scaled j Q  0.14467/0.14467  0.11770/0.11770  0.11117/0.11117  -0.28934/-0.28934  -0.23540/-0.23540  -0.22234/-0.22234  ^  MESIT  o scaled yy  b  '^yy  i rt '^yy  £ scaled j <^  0:14467/0.14467  0.11770/0.11770 ""  0.11117/0.11117  * Order parameters were scaled to order parameters of internal standard TCB in the sample of TCB with MESIT for each liquid crystal +  TCB codissolved with MESIT sample  48  Orientational ordering in nematic liquid crystal  Figure 4.2 Non-scaled (series A) and scaled (series B) experimental order parameters / taken from Table 4.1 / • TCB  T DCT  • CLMX  49  MESIT  Orientational ordering in nematic liquid crystal 4.3 Q U A L I T A T I V E C O M P A R I S O N B E T W E E N E X P E R I M E N T A L O R D E R P A R A M E T E R S  An intuitive picture about electrostatic interactions that are a consequence of the electrostatic distribution in the molecules can be obtained by examining the relationships between experimental order parameter (or their anisotropies) and molecular properties (or their anisotropies). Starting with the relationship between order parameters with potential Eq. 1.16 (page 13) and long-range potentials with molecular properties Eq. 1.20-22 (page 16-17) , a connection between order parameter and molecular properties can be derived. For the dipole potential model that correlation presented in the simplified fashion (in the high-temperature limit)*:  (4.2)  If the dipole interaction is important in the orientation then from E q . 4.2 the order parameter anisotropy would behave linearly with the anisotropy of the squared dipole moment. For the two polar molecules D C T and C L M X the anisotropies of the squared dipole moment (see Table 4.3) have the same sign but the anisotropies in their order parameters have opposite sign (Table 4.2 or Fig. 4.3). This seems to indicate that dipoles do not play a role in the orientation of these solutes in the liquid crystals. In the magic mixture it is expected that only dipole and polarizability effects can be seen. Since dipoles are of no importance let's see if there is a correlation between polarizabilities (their anisotropies) and anisotripies in the order matrix. Following the same rationale as for dipoles, the polarizability (anisotropy) correlation with order-parameter anisotropy should be linear with appropriate sign if polarizability has an effect on the orientation:  LR  (4.3)  * In the high temperature limit potential energy is much smaller then thermal energy kT, so the exponential function can be expanded and truncated at the first non-zero term as  e ~\-x. x  50  Orientational ordering in nematic liquid crystal  The anisotropies in the polarizabilities for D C T ( a (a  o  -a.. =- \  \^Cm  1  -oc =1.922• 1 0 '^'Cm 1V) and C L M X 2  r v  ::  IV) (taken from Table 4.3) are similar, with opposite signs and  they linearly follow the anisotropies in the order parameters (Table 4.2 or Fig. 4.3), i.e. the anisotropies in the order parameters also have opposite signs, implying that polarizability may have an important role in the orientational ordering of the solutes.  Table 4.2 Anisotropy in Scaled and Non-Scaled Order Parameters  Anisotropy in Scaled and Non-Scaled Order Parameters"  Solute  TCB  <  4£ scaled  +  -s  zz  DCT  ^  scaled  Q scaled  -S  ZZ  CLMX  rt scaled  <ri scaled  Liquid Crystal 55wt% 1132/EBBA  1132  EBBA  0.00000  0.00000  0.00000  0.00000  0.00000  0.00000  0.07977  0.03241  -0.02883  0.07509  0.03324  -0.02764  -0.07347  -0.03755  0.00799  -0.07214  -0.03662  0.00799  0.00000  0.00000  0.00000  0.00000  0.00000  0.00000  °v.v  -S  ZZ  MESIT  Q scaled  ^scaled  -S  ZZ  * Order parameters were scaled to order parameters of internal standard TCB in the sample of TCB with MESIT for each liquid crystal; TCB codissolved with MESIT sample +  Figure 4.3 Anisotropy in scaled order parameters / values taken from Table 4.2 / o.oo  9-  • DCT • CLMX  -0.02 -0.04 H -0.06 • I -0.08 -0.10 -  40  60  30  wt % EBBA  51  T C B , MESIT  Orientational ordering in nematic liquid crystals  4.4 C O M P A R I S O N B E T W E E N E X P E R I M E N T A L A N D T H E O R E T I C A L L Y C A L C U L A T E D ORDER PARAMETERS  / quantitative approach I  Different combinations of a short-range model (Cl or S S ) with or without long-range contributions (dipole and/or quadrupole and/or polarizability) were used in a minimization fitting routine. The routine calculates order parameters with E q . 1.16 (page 13) using various potential functions by performing the non-linear least square fits to experimental order parameters while varying potential parameters. Potential functions for short- and long-range interactions utilized in the calculation were described earlier in the introductory chapter (Eq. 1.18-22, page 14-17). Molecular properties such as molecular dipoles, quadrupoles and polarizability factors used in long-range models were calculated with respect to the center of mass using Gaussian 98 [14] with B3LYP/6-311++G** (theory/basis set). Obtained values are reported in Table 4.3. Geometries used in the G98 input file are the geometries obtained from spectral analysis of high-resolution spectra (Table 3.6) which are then converted into the center of mass coordinate system. Intermolecular potential parameters obtained for various combinations of potential models are presented in Table 4.4. For the C l potential model the k  77  were fixed at 4&.0 • \0~ Jm~ 9  2  parameter was adjusted while the k and k parameters s  and 2.04 1 0 J w " ( E q . 1.18). The k and k parameters were -9  2  s  taken from the N M R study of 46 solute molecules dissolved in 55 wt%'1132/EBBA [1]. For the S S potential model M  a / 3  (reported in Table 4.4) and k  ?7  independently.  52  parameters were varied  Orientational ordering in nematic liquid crystals  Table 4.3 Molecular Electrostatic Parameters  Component  Polarizability Tensor  Quadrupole Tensor  Dipole Moment  Solute  Component  b  a  Component  c,f  °>  d,g  a  Qxx  Qyy  -0.017 "  0.349'  -0.690  0.341 '  21.634'  9.438  21.663  zz  TCB  0.025  DCT  0.147"  -7.188  -1.555  -1.407  2.962  22.225  10.131  20.303  CLMX  0.011 *  7.024  2.418  -1.973  -0.445  20.342  10.909  21.799  MESIT  0.125"  -0.021 "  1.139'  -2.146  1.007'  20.883'  11.529  20.515  a  h  Values calculated with respect to the center of mass using Gaussian 98 with B3LYP/6-311++G** (theory/basis set). Axis labeling is shown in Figure 4.1.  "Units of 1(T Cm (\ Cm = 2.99793- \Q" esu ). 30  c  Units of 1 0 "  39  "Units of K T e  1 0  2  For all solutes the fi  h  13  2  Cm V-\  ' For all solutes the Q 9  1 C• m = 2.99793-10 esu • cm ).  C-m\  1 C - m • F" = 8.9878 • 10 cm ). 2  1  15  3  component is zero. and Q , y  components are zero.  For all solutesi the a vi, and oc components are zero. Values taken as zero (by symmetry) in the fitting routine.  ' Due to a D type symmetry, xx and,zz tensor components of molecular parameters should be 3h  the same. Therefore their averaged values were used in the fitting routine.  53  Orientational ordering in nematic liquid crystals Table 4.4 Adjusted Parameters in the Fitting Procedure  a/ C l model combined with/without long-range models Cl fitting Liquid crystal  parameter k  Dipole { 7,7. R  R  \ \ }"  3  parameter  Polarizability  Quadrupole F  SS fitting M  c  parameter  paramater  a  SS fitting  »  8  M  parameter  SS fitting  M  a  Error'  B  parameter  parameter  Fit #1 1132 MM EBBA  1.46 (05)  e  6  9  e  e  e  e  e e  ~  0.96 (03)  e  e  _e  e  0.84 (03)  e  e  e  e  e  1.32  Fit #2 1132 MM EBBA  1.46 (05) 0.96 (04) 0.83 (03)  e  e  e  _ e  e  1.7 (8.5)  _e  _e  _e  e  e  8.4 (8.7)  e  _ e  e  e  e  -2.9 (8.0)  1.29  Fit #3 1132 MM EBBA  1.48 (03)  e  0.96 (02)  e  0.80 (02)  e  -2.4 (0.7)  e  e  e  e  -0.1(0.7)  e  e  e  e  4.0 (0.7)  _ e  e  e  e  0.86  Fit #4 1132 MM EBBA  1.07 (12)  e  e  1.02 (11)  e  e  1.58 (12)  e  e  68.9 (19.9)  e  e  e  -9.9 (20.4)  e  e  e  -135.3(21.0)  e  e  e  0.79  Fit #5 1132 MM EBBA  1.48 (04) 0.96 (03)  1.9 (5.8) 2.1 (6.2)  -2.4 (0.7)  e  __ e  e  e  -0.1 (0.8)  e  e  e  e  4.0 (0.8)  e  e  e  e  0.80 (02)  0.5 (6.3)  1.07 (13)  1.1 (5.3)  e  0.86  Fit #6 1132 MM  1.01 (12)  1.2 (5.6)  _e  EBBA  1.57 (13)  . 1.1 (5.7)  e  69.9 (21.5) 8.8 (22.1)  e  e  e  _e  e  e  e  _ e  e  e _e  ..  e  0.79  e  -134.4(22.6)  Fit #7 e  -11.5(9.8)  -289.5(103.6)  2.95 (40)  _e  -33.0 (6.7)  -340.5(69.1)  _e  _e  2.83 (38)  _ e  -7.1 (2.1)  -348.7 (65.5)  _ e  _  1132  3.31 (60)  3.8 (3.1)  -12.5 (3.2)  MM  3.03 (40)  4.7 (3.3)  -11.6 (2.2)  1132  3.18 (61)  MM EBBA  e  0.46  e  Fit#8  EBBA  2.88 (38)  3.5 (3.3)  _ e  e  e  -354.6 (67.8)  _e  _e  _e  -358.6 (64.6)  e  e  e  -312.8(102.2)  -7.6 (3.0)  54  0.42  Orientational ordering in nematic liquid crystals  bl S S model combined with/without long-range models  Cl fitting Liquid crystal  parameter  Quadrupole  Dipole (*,/ * , v ) parameter  9  F  Polarizability  SS fitting  M  0  a xx  parameter  paramater  SS fitting  M  SS fitting Error'  a yy  parameter  parameter  parameter  -628 (27)  1257 (56)  -630 (29)  1.62  -628 (27)  1256(60)  -628 (33)  1.60  -643 (12)  1298 (25)  -655 (13)  0.66  -467 (48)  942 (97)  -475 (49)  0.72  -648 (12)  1294 (26)  -646 (14)  0.61  -466 (51)  931 (103)  -465 (51)  0.70  -1018 (159)  2058 (320)  -1039 (162)  0.52  -1095 (132)  2189 (263)  -1093(132)  0.40  Fit m e  e  e  e  e  0.89 (06)  e  e  _ e  1132  1.49 (10)  -3.1 (1.3)  e  e  MM  1.00  1.2 (11.8)  e  e  7.5 (11.8)  _ e  e  1132  1.48 (09)  MM  1.00  EBBA  e  Fit #10  EBBA  0.88 (06)  Fit #11 1132  1.51 (04)  e  -6.2 (0.6)  e  MM  1.00  e  -2.6 (0.6)  e  0.83 (02)  e  1.9 (0.6)  1.04 (15)  e  e  1.00  e  _e  44.8 (13.4)  1.53 (19)  e  e  -47.2 (13.6)  EBBA  e  Fit #12 1132 MM EBBA  126.0 (13.1)  Fit #13 1132  1.51 (04)  -8.6 (5.3)  -6.2 (0.6)  _ e  MM  1.00  6.6 (4.9)  -2.7 (0.6)  _e e  EBBA  0.83 (02)  4.6 (4.9)  1.9 (0.6)  1132  1.04 (16)  4.0 (5.3)  _ e  MM  1.00  4.0 (5.5)  e  45.8 (14.1)  1.54 (20)  5.6 (6.2)  _ e  -46.0 (14.1)  1132  1.03 (26)  _ e  -6.9(2.7)  -19.3 (58.2)  MM  1.00  e  -7.1 (1.9)  -97.1 (38.4)  0.95 (19)  e  -3.3(1.8)  -110.6(36.5)  Fit #14  EBBA  134.6(13.7)  Fit #15  EBBA Fit #16 1132  1.12 (23)  10.5 (3.8)  -9.1 (2.4)  -63.6 (50.8)  MM  1.00  10.4 (3.7)  -8.2(1.7)  -114.5(33.8)  EBBA  0.94 (16)  8.9 (3.7)  -4.1 (1.5)  -124.8(30.8)  55  . Orientational ordering in nematic liquid crystals  cl long-range models alone and combined  Cl fitting Liquid crystal  parameter kr/.  Dipole  (E?.z- xx)"  ( zz - xx ) " R  E  R  8  K  Polarizability  Quadrupole  parameter  parameter  paramater  SS fitting M  a M  SS fitting M  SS fitting Error'  3 vv  parameter  parameter  parameter  Fit #17 1132  e  MM  e  EBBA  _ e  e  e  e  e  e  133.5 (108.6)  _e  e  e  e  e  130.0 (108.8)  e  e  e  e  _ e  _ e  167.1 (106.9)  16.41  Fit #18 1132  e  _ e  27.3 (9.3)  e  e  e  MM  e  e  23.4 (9.4)  e  _e  _e  EBBA  e  e  24.5 (9.6)  e  e  e  e  _ e  e  246.4 (15.8)  e  _ e  e  169.4 (12.1)  e  _e  e  146.2 (10.9)  e  _ e  e  e  13.98  _ e  Fit #19 1132 MM  e  _e  e  EBBA  e  _ e  e  1132  e  56.8 (124.0)  MM  e  EBBA  e  1132  2.81  Fit #20 25.0 (11.1)  e  _ e  _ e  21.8 (11.2)  _e  e  e  31.0 (118.6)  23.2 (11.3)  e  e  12.1 (17.4)  _ e  245.8 (16.2)  MM  e  12.5 (18.1)  _e  168.4 (12,5)  e  EBBA  e  18.5 (18.6)  _ e  144.5 (11.3)  _ e  36.8 (121.9)  _  e _  e  e  e  e  _ e  _e  e  e  e  _ e  e  13.89  Fit #21 _ e  2.72  Fit #22 1132  _ e  e  5.6 (1.0)  252.8 (8.5)  _ e  e  MM  e  e  5.3 (1.0)  166.0 (6.0)  e  e  EBBA  e  _ e  .8.6(1.0)  .,137.8(5.7)  _ e  8  0.44 (8.2)  5^6 (1.1)  252.8(9.0)  _ e  e  0.7 (8.7)  5.3(1.1)  166.0 (6.4)  e  e  e  137.8 (6.0)  e  e  _ e  fif#23 1132  e  EBBA  e  -0.6 (8.9)  8.6 (1.1)  Units of 10~ J. Unitsof 10 V/Cm . Units of 10 V/m . " Units of 10 V /m . Parameter was not adjusted. Units of 10' . a  c  23  36  2  17  17  2  2  2  e  f  _e  1.22  _ e  "  MM  b  _  e  2  56  _ e  1.22  Orientational  ordering in nematic liquid crystal  A. Short-Range Model Comparison  Examining the difference between  and S" order  S^"  scaled  parameters as a function of  C  HL1  X  (Fig. 4.4, Fit #1 and Fit#9) that result from fits to short-range models alone it can be stated that in magic mixture the C l model is excellent (Fig. 4.4, A , with errors up to 5-6%) while the 2  S S model is less satisfying (Fig. 4.4, B , with errors up to 14%). 2  ZLI 1132  008  010  012  0.06  CO  012  014  EBBA  55 wt% 1132/EBBA  016  0 16  0 20  022  0 16  0.18  0 20  0 22  008  010  0 12  0.14  0 16  0 18  0 20  0 22  008  010  0 12  0 14  0 16  0 18  0 20  0 22  0.06  0.10  012  0.14  0 16  0 18  0 20  0.22  _  scaled  CO  u  0 14  „  0.06  0 10  0.12  0.14  0.16  016  0.20  0.22  „ seated  scaled  Figure 4.4 Differences between . V a n d  S^' ' 1  as a function of  S[:"  HJ  for short-range  models alone. Series A are results from Fit #1 (Cl model) with RMS= 1.32-10 a n d 2  series B are results from Fit #9(SS model) with RMS=1.62 10" . 2  • TCB  T DCT  • CLMX  57  MESIT  Orientational ordering in nematic liquid crystal The Cl model uses geometries determined individually for each solute from high-resolution spectral analysis. On the contrary the S S model assumes that all solutes have the same geometry, and it doesn't take into account that D C T and C L M X geometries slightly deviate from D  3 h  symmetry. That could explain why the Cl model fits better than the S S model and  therefore in the following investigations only the Cl model in combination with long-range models will be considered. Not surprisingly the fits for pure liquid crystals are poorer (Fig. 4.4  A , Eh, B )) (with 3  3  discrepancies up to 30%, see D C T in A , or B ^ . The same trends are seen for S ^ ' a n d 3  gscaled j ^ j  s  a  ||  0 w s  f  or  investigation of what other contributions to the short-range interaction  might improve the fit and to what extent they might contribute to the  orientational  mechanism. In that manner of thinking different long-range contributions will be additively combined with short-range ones and their combined contributions will be examined in part C-E.  B. Long-Range Model Comparison  Although short-range models reasonably well describe the orientational mechanism, especially in the magic mixture, let's see what information we can get if we assume that the orientational mechanism can be described with only long-range electrostatic interactions. Judging by the R M S of the Fits #17-19 (Table 4.4) that belong to various electrostatic models alone and by comparing the differences between experimental and calculated order parameters, dipole (Fit #17) alone (Fig. 4.5, series C) and quadrupole (Fit #18) alone (Fig. 4.5, series D) are significantly worse than short-range (Fit #1) (Fig. .4.5, series A). The Fit #19 (Fig. 4.5, series E) that accounts for polarizability effects alone with R M S of 2.8110" is 2  qualitatively and quantitatatively better than other long-range fits alone but still worse than short-range fits alone.(RMS(Fit#1)=l.32lO- rRMS(Fit#9)=l.62lO- ). 2  2  Almost the same R M S and fitted potential parameters are reached when the Fits #17-19 were repeated only for the magic mixture. The anisotropy in the polarizability tensor is strongly affected by size and shape anisotropy. That connection between polarizability with size and shape is even more stressed by the fact that the polarizability fit alone, although worse than the size and shape model, explains relatively well the experimental results. More about polarizability effects to the 58  Orientational ordering in nematic liquid crystal orientational ordering mechanism will be discussed later when comparing short-range with long-range contributions in an additive manner. Although Fits #22 and #23 (combination of two/three long-range models) show small R M S the fits are meaningless since fitted F  77  values have very large associated errors due to the  large number of adjusting parameters and possible correlation between potential models. Therefore those fits won't be taken into consideration. Using only magic mixture spectral parameters in the fitting routine where the quadrupole contribution is expected to be zero, the aim was to investigate the effects of other longrange potentials like dipole and polarizability. Fig. 4.6 contains fits of different pairs of shortrange with long-range interactions only for the magic mixture. Fit F belongs to short-range (Cl) model alone, fit G is combination of C l model with dipole model, fit H is Cl model with quadrupole model and fit I is Cl model with polarizability model. The equality of the Fits A and H indicates that the quadrupole interaction in magic mixture is annulled and that potential parameter F  77  ~0.  It is also obvious that overall all fits look the same (Fig. 4.6)  with the same RMS=0.94 10~ , the same k 2  Z7  and zero F  zz  , (R  ZZ  -RXX)  and (E  -E ^ 2  77  parameters. From all of the above, we can say that in magic mixture long-range interactions do not play an important role in the orientational mechanism and that short-range interactions are the only dominant contributor to the orientational ordering.  59  Orientational  ordering in nematic liquid crystal  55 wt% ZLI 1 1 3 2 / E B B A  0.3  03  Xi <D  0 0  O  .01  *o W  • -01  5  -U2  Al  D.tO  0.1!  0 14  QIC  0.18  0.20  -0.3  0 22  O.OB  a io  :  * *  a  12  12  0.14  018  0.12  OH  010  0 12  0 14  0  18  0 20  0 22  03 0.2  •  0  T  «  0 •  •  -OJ  Dl  D  «B  2  000  ow  OS U2 01  CO •  t3  01  0  •  • El  oot  aio  on  on  Q»  014  o»  0 22  •  -Ul  T  * ^1  E  •03 act  oio  a i2  o i»  o 16  o is  020  0.08  022  0 10  3  0.16  scaled Figure 4.5 Differences between S ~  and S™  !c  as a function of  5 ™  Series A are results from Fit #1 (Cl model) used for comparison; Series C are results from Fit #17 (Dipole model); Series D are results from Fit #18 (Quadrupole model); Series E are results from Fit #19 (Polarizability model). • TCB  T DCT  • CLMX  60  MESIT  Orientational  ordering in nematic liquid crystal  TO CU  0.08  010  0.12  0.14  0.16  0.18  0.20  008  010  012  014  0 16  0.18  0.20  0.22  0.10  012  0.14  0.16  0.18  0.20  0.22  CO  ro  0 08  0.22  010  scaled  012  014  0 16  0.18  0.20  0.22  scaled  Fig 4.6 Different pairs of short with long-range interaction fits when only magic mixture order parameters were used Fit F is C l model alone, Fit G is C l with Dipole, Fit H is C l with Quadrupole and Fit I is C l with Polarizability model • TCB  • DCT  • CLMX  61  MESIT  Orientational ordering in nematic liquid crystal C. Dipolar Interaction Contribution  The qualitative picture drawn earlier shows that dipoles have no noticeable effect on the orientation of the solutes. The same conclusion is evident by examining the R M S values (Table 4.4) and Fit #1 (Cl model) and Fit #2 (Cl+Dipole) or Fit #9 (SS model) and Fit #10 (SS+Dipole)(Fig. 4.7, compares series A with J and/or series B with K) for molecules with dipoles. Both fits with or without dipole contribution are the same, with the same fitting parameters and R M S errors. Also the dipole potential fitted parameters  (R Z~^XX)  k  77  A  R  E  Z  zero within the calculated errors (see Table 4.4). Within the context of the results, dipoles are not an important factor in the orientation of the solutes (also in agreement with previous studies [15]) and won't be taken into account further.  D. Quadrupolar Interaction Contribution  Previous studies characterized the quadrupolar interaction as an interaction with a significant contribution to the orientational mechanism. Comparing the Fit #1 (Cl model) with Fit #3 (Cl+Quadrupole) and/or Fit #2 (Cl+Dipole) with Fit #5 (Cl+Dipole+Quadrupole), i.e comparing series A with L and/or series M with N shown in Fig. 4.8, the same conclusion follows. The significant drop in R M S between fits with the quadruple contribution as opposed to only short-range contributions implies that this might be attributed to the effect of the quadrupole interaction. It should also be pointed out that the quadrupole potential parameter F  77  does change sign  from ZLI 1132 to E B B A , being almost zero for the magic mixture 55 wt% 1132/EBBA. The sign obtained for F  in E B B A is positive (F  77  (F  77  =-2.4  10 l /Cm ). 17  /  2  = 4 . 0 - 1 0 V / C m ) and in 1132 is negative n  77  2  This is not consistent with the signs of the electric field gradients  in the component liquid crystals determined from molecular hydrogen experiments [16] and mono- and di- substituted benzene molecule experiments [15]. This difference opens a new question that needs to be investigated. Maybe our assumption of using a mean field approach is too simple. Running Monte Carlo simulations (as part of future work) that employs the quadrupole interaction can be used to test the validity of the mean-field  62  Orientational ordering in nematic liquid crystal  approach, a s well as gain a better picture as to what extent the quadrupole interaction contributes to the orientational mechanism. EBBA  55wt%ZLI 1132/EBBA  ZLI 1132  GO B  co  4  •  EH not  am  on  o14  a IB  ois  a 30 ti7>  OB  Q1D  012  014  0*6  OIG  Q3D  co •tj'  #  m  K1  K 008  scaled  scaled  010 012 014  3  018 018 030 o n  o scaled  Fig 4.7 Differences between Stf''" and S^f as a function of S ™ J  s  ,ed  Series A and B are results from Fit #1 (Cl model) and Fit #9 (SS model); Series J and K are results from Fit #2 (Cl+Dipole) and Fit #10 (SS+Dipole) • TCB  VDCT  • CLMX  63  MESIT  Orientational ordering in nematic liquid crystal 55wt%2LI 1132/EBBA  EBBA  m  005  •  V _  •  •  O  o  ••  • T  •0  one  oio  gti  OH  010  010  0 20  05  -OOS  0.10 0.20 022  G1C  0 22  ooe  a 10  012  a 4  010  0  10  020  012  a 4  0  10  0  10  020  0.22  005  005  .  •  o  •  _  ...»  M oat  010  G12  OH  L UC  010  ooe  ..1.  .  v  o  • y  ... M  000  0.10 012 O H ftlfl  • 10  .•  OtS  022  0.1S  o  3  DOS  Jf  ¥  M  2  0.20 0 22  oos  •  3  022  0.06  oos  m  aia  -  o  .  •  o  • -005  -ace  N  Nl OOt 0.10  012  014  O.ie CO  0 20  0.22  o.oo  oto 0.12 an  scaled  gto  0.1C  N  2  020 022  0 00  scaled  Fig 4.8 Differences between M  0 10  0  3  12 u  scaled  and S ' f as a function of XX  XX  XX  Series A and L are results from Fit #1 (Cl model) and Fit #3 (Cl+Quadrupole); Series M and N are results from Fit #2 (Cl+Dipole) and Fit # 5 (CI+ Dipole+Quadrupole) • TCB  T DCT  • CLMX  64  MESIT  Orientational ordering in nematic liquid crystal Certain Fits (#7, #8, #15, #16) that contain a quadrupole contribution in combination with other long-range interactions are discarded as meaningless, since the potential parameters F  77  obtained have large calculated errors. The explanation for this finding might be the  existence of a correlation between the different potential models. The reason for getting a good R M S in these cases is the fact that by adding another potential more available fitting parameters are introduced into the fitting routine.  E. Polarizability Interaction Contribution  Comparing the R M S errors of Fits #1, #4 and #6 or Fits #9, #12 and #14 significant change is noticed when the polarizability interaction is added to the fitting. This is more obvious when comparing series A (Cl model), O (Cl with Polarizability) and P (Cl with Dipolar and Polarizability model) (see Fig. 4.9). In the magic mixture the polarizability parameters (E ,— 2  7  E^ 2  potential  are zero within the calculated errors (Table 4.4), once more  agreeing with the results found in magic mixture fits (section B, page 59, 61), i.e. that in the magic mixture long-range interactions are not affecting the ordering mechanism since the C l short-range model so wonderfully explains the experimental results. In the component liquid crystals the polarizability model significantly improves the fit. All this indicates that the polarizability effect could be considered as one of the contributors to the orientational ordering mechanism.  65  Orientational ordering in nematic liquid crystal  ZLI 1132  55 wt% ZLI 1132/EBBA  EBBA  0.05  0.05  • o  o  •  •  • -0.05  •0.05  Al  A 006  010  012  0.14  0.16  018  0.20  008  0.22  0.05  0 10  0 12  0 14  0.12  0.14  016  016  0 20  3  0 22  0.05  O  •  •  " • *  4  • •  • •0.05  •0.05  Oi 0.06  0.10  0 12  •  0 14  0 16  Q. 16  o •  0  0 22  0 20  0.06  010  012  014  0.16  0.18  0.10  0 12  0 14  2  008  0.22  0.05  0.05  am  CLOG  -0.05  -0.05  0 10  0.16  0.18  0.20  0.22  T  Pi 0.08  0.20  0.16  0.18  0.20  0.22  P2 II  if  010  012  Q.14  0.16  0.16  P3  0.20 C.22  0 06  010  012  0.14  0 16  018  0.20  022  o scaled  ^ scaled  o scaled  Fig 4.9 Differences between S^** and S™' as a function of C  Series A, O and L are results from Fit #1 (Cl model), Fit #4 (Cl+Polarizability) and Fit #6 (Cl+Dipole+Polarizability); • TCB  T DCT  • CLMX  66  MESIT  Orientational ordering in nematic liquid crystal  4.5 SUMMARY Short-range interactions  are the dominant  orientational  mechanism in liquid  crystal  environments. The importance of various electrostatic contributions to the orientational mechanism is still not completely understood. The role of various electrostatic interactions in the orientational mechanism is investigated using small and symmetric molecules with the same size and shape, therefore the same short-range interactions but different electrostatic properties. According to the R M S and differences in experimental and calculated order parameters of different fits to different combinations of long-range and short-range models, the dipole interaction  appears to be least important.  On the contrary,  results for  quadrupole  interactions imply that improvement of the fits could be attributed to the effect of the quadrupoles on the orientational mechanism; however, predicted signs of the electric field gradients F  77  for 1132 and E B B A contradict previous F  77  study results for component  liquid crystals. This interesting observation needs future investigation possibly using the Monte Carlo simulation method. Single potential fits for all liquid crystals show that the Cl model alone accounts the best for the orientational ordering. In the magic mixture polarizability, alone explains the experimental results better than the other elecrostatic interactions alone but still not as good as does the C l model alone. Combined short and long range potential investigations show that in the magic mixture not only is the quadrupole interaction annulled but also the other long-range interactions as well. The polarizability effect appears not to be easily separated from short-range interactions since they both strongly depend on the size and the shape of the molecule. However, examining additive contributions of short-range models with and without the polarizability effect, the polarizability contribution should be considered as an important electrostatic effect in the orientational mechanism.  67  Orientational ordering in nematic liquid crystal  References: [1] Burnell, E. and de Lange, C , 1998, Chem.Rev., [2] Gelbart, W., 1982, J.Phys.Chem.,  98, 2359.  86, 4289.  [3] Frenkel, D., 1989, Liq. Crystals, 5, 929. [4] Vertogen, G . and de Jeu, W., 1989, Thermotropic Liquid Crystals, Springer, Heidelberg, 2  n d  Fundamentals,  edition.  [5] Vroege, G . and Lekkerkerker, H., 1992, Rep. Prog. Phys,, 55, 1241. • [6] Poison, J . and Burnell, E., 1996, Mol. Phys., 88,767. [7] Terzis, A., Poon, C , Samulski, E., Luz, Z., Poupko, R., Zimmermann, H., Muller, K., Toriumi, H. and Photinos, D., 1996, J. Am. Chem. Soc, 118, 2226. [8] Terzis, A. and Photinos, D., 1994, Mol. Phys., 83, 847. [9] Photinos, D., Samulski, E. and Toriumi, H., 1990, J. Phys. Chem., 94, 4694. [10] Emsley, J . , Palke, W . and Shilstone, G., 1991, Liquid Crystals, 9, 643. [11] Photinos, D., Poon, C , Samulski, E. and Toriumi, H., 1992, J. Phys. Chem., 96, 8176. [12] Celebre, G., de Luca, G., Longeri, M. and Ferrarini, A., 1994, Mol.Phys.,  83, 309.  [13] Syvitski, R., Pau, M. and Burnell, E., 2002, J. Chem. Phys., 117, 376. [14] Gaussian 98, Revision A.9, M. J . Frisch, G . W . Trucks, H. B. Schlegel, G . E. Scuseria, M. A. Robb, J . R. Cheeseman, V. G . Zakrzewski, J . A. Montgomery, Jr., R. E. Stratmann, J . C. Burant, S. Dapprich, J . M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J . Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, Adamo, S. Clifford, J . Ochterski, G . A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J . B. Foresman, J . Cioslowski, J . V. Ortiz, Baboul, B. B. Stefanov, G . Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J . Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J . L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle, and J . A. Pople, Gaussian, Inc., Pittsburgh PA, 1998. [15] Syvitski, R. and Burnell, E., 1997, Chem. Phys. Letters, 281, 199. [16] Patey, G., Burnell, E., Snijders, J . and de Lange, C , 1983, Chem. Phys. Letters, 99, 271.  68  5. C O N C L U S I O N S  Extensive  comparison  analysis of  parameters for a series of C  2 v  and D  3 h  experimental  and  theoretically  calculated  order  type symmetry molecules in a magic mixture support  the conclusion that orientation of these solutes is dominated by short-range hard body interactions. In pure liquid crystal components the results suggest that additional long-range interactions might play a role. The dipole interaction appears to be the least important while the quadrupole interaction fits predict different signs of electric field gradient than previous studies [15, 16]. The ambiguity associated with the quadrupole findings should be tested by using computer simulations (MC simulations) as well as checking the validity of statistical approximations employed in the theory. Finally, the trends among experimental order parameters are the most consistent with the polarizability/short-range model implying that polarizability effects should be taken as an important electrostatic orientational mechanism.  69  

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