A NMR STUDY ON ZERO ELECTRIC FIELD GRADIENT NEMATICLIQUID CRYSTALSByThambirajah ChandrakumarB. Sc., University of Peradeniya, Sri Lanka, 1984M. Sc., The University of British Columbia, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHY111THE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CHEMISTRYWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJuly 1994© Thambirajah Chandrakumar, 1994In presenting this thesis in partial fulfilment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of thisthesis for scholarly purposes may be granted by the head of my department or by hisor her representatives. It is understood that copying or publication of this thesis forfinancial gain shall not be allowed without my written permission.Department of ChemistryThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1W5Date:2AbstractThe role of intermolecular forces in describing the orientational nature of liquid crystalsis not well understood. Previous studies using dideuterium as a solute in liquid crystals have demonstrated the importance for orientation of the interaction between thesolute molecular quadrupole moment and the average electric field gradient present inliquid crystals. With the aim of learning aboilt additional orientational mechanisms,we have studied the orientation of solutes in special mixtures of liquid crystals, wherethe contribution from the environment to the average electric field gradient at the 211nucleus of dideuterium is negligibly small. In order to understand the role of short-range forces in such special mixtures, orientational studies have been undertaken in themixtures 55 wt% ZLI- 1132(1132)/N- (-4-ethoxybenzylidene)-4’-butylariiline (EBBA), 56.5wt% 1132/EBBA and 70 wt% 4-n-pentyl-4’-cyanobiphenyl (5CB)/EBBA.As a starting point, the C2v and D2h symmetry solutes meta dichlorobenzene, orthodichlorobenzene, para dichlorobenzene, ortho dicyanobenzene, furan, tetrathiofulvaleneand fiuorobenzene have been studied in the special mixtures 56.5 wt% 1132/EBBA at323K and 70 wt% 5CB/EBBA at 316K, using proton NMR. The measured electric fieldgradient for these two mixtures has been found to be zero. The order parameters obtained from an analysis of the NMR spectra indicate that the solutes experience a similaranisotropic potential in both mixtures. The results are interpreted in terms of a modelfor the short-range anisotropic potentials experienced by the solutes.To further explore the investigation of the short-range forces in zero electric fieldgradient mixtures, the temperature dependence of the solutes meta dichlorobenzene,ortho dichlorobenzene, 1,3-bromochlorobenzene, benzene and 2-butyne has been studied11in the special mixtures 55 wt% 1132/EBBA and 70 wt% 5CB/EBBA, using proton NMR.These solutes vary from each other in symmetry and shape. The aim was to see how thedifferent shaped solutes experience the short-range forces in the liquid crystal mixtures.The results indicate that the solutes experience a similar anisotropic potential in bothmixtures. The biaxial order parameters measured for the solutes meta dichlorobenzene,ortho dichlorobenzene, and 1,3-bromochlorobenzene have also been analysed to magnifythe differences between the mixtures.To extend our understanding on the intermolecular forces among constituent liquidcrystal molecules, a temperature dependence study of the liquid crystal 5CB— d19 as solute has been undertaken in the three liquid crystal mixtures: 55 wt% 1132/EBBA, 56.5wt% 1132/EBBA and 70 wt% 5CB/EBBA, using 2H— NMR. The study of SCB— d19as solute has been used to compare the short-range interactions in these special mixtures.The spectra of 5CB — d19 in the two 1132/EBBA mixtures are equivalent, but are different from those in the 5CB/EBBA mixture. The spectra in 55 wt% 1132/EBBA and70 wt% 5CB/EBBA have been analysed using two different models for the short-rangepotential, and parameters of the models have been used to compare the potentials in thedifferent mixtures. It has been shown that, for a given spectral splitting of the chainC1 deuteron, the reduced short-range potential is the same in all three mixtures studied.The spectral differences observed are a consequence of different nematic-isotropic phasetransition temperatures combined with the effect of trans-gauche isomerization in thehydrocarbon chain.111Table of ContentsAbstract iiList of Tables viiList of Figures xAcknowledgement xiv1 Introduction 11.1 Liquid crystals 11.1.1 General 11.1.2 The Effect of magnetic field 31.1.3 Liquid Crystal Display(LCD) 41.2 NMR and Orientational order 61.2.1 1H—NMR 71.2.2 2H-NMR 81.2.3 The Orientational Distribution Function 101.3 Intermolecular Forces 121.3.1 General 121.3.2 Burnell’s model 151.4 Zero electric field gradient mixtures 221.5 Outline of the thesis 242 Experimental 26ivSample Preparation1H-NMR experiments2HNMR experimentsMicroscopic study262728294 Temperature dependence study of small solutes in the zero efg mixtures4.1 Introduction4.2 Temperature dependence study of trichioro benzene4.3 Structure4.3.1 C3 and higher symmetry solutes4.3.2 C2v and C symmetry solutes4.4 Comparison of short-range interactions4.5 Biaxial order parameter4.6 Summary5 A 211 NMR study of 5CB— d19 in zeromixtures5.1 Introduction5.2 Review of Theoryelectric field gradient nematic6969702.12.22.32.43 Orientation of C2 and D2h symmetry solutes3.1 Introduction3.2 Results3.2.1 Analysis3.2.2 Orientation in Zero efg mixtures3.3 Comparison of short-range interactions3.4 Summaryin zero efg mixtures 3D303131333643444446464647496367V5.3 Results 735.3.1 General. 735.3.2 Analysis of 5CB-d19 spectra5.4 Discussion5.4.1 General5.4.2 RIS parameter and molecular geometry5.4.3 Individual Fit Model parameters5.4.4 Temperature dependence of Individual5.4.5 Global Fit5.5 Summary7 ConclusionBibliographyA TransformationB Dipolar CouplingsC Order Parameters119124129132139Fit model parameters5CB — d19 as a solute77808082858791991011011021101141186 Comparison of short-range interactions using6.1 Introduction6.2 Analysis6.2.1 Individual Fit Parameters6.2.2 Global Fit Parameters .6.3 SummaryviList of Tables3.1 Dipolar couplings obtained from the ‘H-NMR spectra for 02V and D2hsymmetry solutes 323.2 Order Parameters of the solutes in the 70% 5CB/EBBA 333.3 Order Parameters of the solutes in the 56.5% 1132/EBBA 353.4 model parameters for the C2v and D2h symmetry solutes 394.5 TNI values for the solute-liquid crystal mixtures 565.6 Quadrupolar splittings (in kllz) of 5CB-d19 in 55% 1132/EBBA 735.7 Quadrupolar splittings (in kHz) of 5CB-d19 in 70% 5CB/EBBA 755.8 Quadrupolar splittings (in kllz) of 5CB-d19 in 56.5% 1132/EBBA 765.9 Fitted 0 values for different geometries and models 865.10 Fitted values of k0, k0, k0, and Etg using the CZ model 965.11 Fitted values of k0, k0, k0, and using the CI model 975.12 Fitted values of k0, k0, k0 and for PJ9 = 700 cal/mol, using the CZ model. 985.13 Fitted values of k0, k0, k0 and for Etg = 700 cal/mol, using the CI model. 996.14 Temperature scaling factors 114B.15 Dipolar couplings obtained from the ‘H-NMR spectra for the solute orthodichlorobenzene dissolved in 55% 1132/EBBA 133B.16 Dipolar couplings obtained from the1H-NMR spectra for the solute orthodichlorobenzene dissolved in 70% 5CB/EBBA 133viiB.17 Dipolar couplings obtained from the ‘H-NMR spectra for the solute metadichiorobenzene dissolved in 55% 1132/EBBA 134B.18 Dipolar couplings obtained from the ‘H-NMR spectra for the solute metadichlorobenzene dissolved in 70% 5CB/EBBA 134B.19 Dipolar couplings obtained from the ‘H-NMR spectra for the solute 1,3-Bromochlorobenzene dissolved in 55% 1132/EBBA 135B.20 Dipolar couplings obtained from the ‘H-NMR spectra for the solute 1,3-Bromochlorobenzene dissolved in 70% 5CB/EBBA 136B.21 Dipolar couplings obtained from the1H-NMR spectra for the solute Benzene dissolved in 55% 1132/EBBA 136B.22 Dipolar couplings obtained from the ‘H-NMR spectra for the solute Benzene dissolved in 70% 5CB/EBBA 137B.23 Dipolar couplings obtained from the H-NMR spectra for the solute 2-Butyne dissolved in 55% 1132/EBBA 137B.24 Dipolar couplings obtained from the1H-NMR spectra for the solute 2-Butyne dissolved in 70% 5CB/EBBA 138C.25 Experimental order parameters and S for the solute orthodichlorobenzene dissolved in 55% 1132/EBBA as a function of temperature 140C.26 Experimental order parameters S and for the solute orthodichlorobenzene dissolved in 70% 5CB/EBBA as a function of temperature 140C.27 Experimental order parameters and S for the solute metadichlorobenzene dissolved in 55% 1132/EBBA as a function of temperature 141C.28 Experimental order parameters S and S for the solute meta dichiorobenzene dissolved in 70% 5CB/EBBA as a function of temperature 141viiiC.29 Experimental order parameters S, S and S for the solute 1,3- bromochlorobenzerie dissolved in 55% 1132/EBBA as a function of temperature. 142C.30 Experimental order parameters S, S and S for the solute 1,3- bromochlorobenzene dissolved in 70% 5CB/EBBA as a function of temperature. 142C.31 Experimental order parameters Sfor the solute benzene dissolved in 55%1132/EBBA as a function of temperature 142C.32 Experimental order parameters Sfor the solute benzene dissolved in 70%5CB/EBBA as a function of temperature 143C.33 Experimental order parameters Sfor the solute 2-Butyne dissolved in55% 1132/EBBA as a function of temperature 143C.34 Experimental order parameters Sfor the solute 2-Butyne dissolved in70% 5CB/EBBA as a function of temperature 143ixList of Figures1.1 Schematic illustration of the solid, liquid crystal and liquid phases. Thesticks represent molecules 51.2 Energy level diagram showing the effects of the Zeeman and Quadrupolarinteractions on the nuclear states for a spin I = 1 nucleus 111.3 The anisotropic potential given by the CZ model, where Z(c2) is the projection of the molecule onto the director axis, Z. G(f) is the circumferencearound the projection onto the (X, Y) plane 201.4 The anisotropic potential given by the CI model, where Z(Q) is the lengthof the projection of the molecule onto the Z axis. C() is the ‘minimum’circumference obtained by including only the circles formed by the atomswhere they intersect a plane located at Z 213.5 The coordinate system and atom numbering of the solute molecules studied. 343.6 The order parameter ratios, Sb = SZZ/DHH(TCB), of the solutes in 70% 5CB/EBBA against those in 56.5 % 1l32/EBBA 373.7 The order parameter ratios, (S — S)t = (S — S)/DHH(TCB), ofthe solutes in 70 % SCB/EBBA against those in 56.5 % 1132/EBBA. . . 383.8 Calculated versus experimental order parameters S. Open symbols represent 70 % 5CB/EBBA, and filled symbols 56.5 % 1l32/EBBA 403.9 Calculated versus experimental order parameters S-S. Open symbolsrepresent 70 % 5CB/EBBA, and filled symbols 56.5 % 1132/EBBA. . . . 41x3.10 k6/k ratios of the 70% 5CB/EBBA mixture against those of the 56.5%1132/EBBA mixture, where k3 and k are the model parameters for thesolute and for the TCB in the same sample tube 424.11 The order parameter S of TCB vs. reduced temp 454.12 The coordinate system and atom numbering of the solute molecules studied. 484.13 Order parameters vs. DHH(TCB) for BENZENE 504.14 Order parameters vs. DHH(TCB) for 2-BUTYNE 514.15 Order parameters vs. DHH(TCB) for ODCB 524.16 Order parameters vs. DHH(TCB) for MDCB 534.17 Order parameters vs. DHH(TCB) for 1,3- Bromochloro benzene 544.18 Reduced model parameter, k8/T vs. DHH(TCB) for BENZENE 574.19 Reduced model parameter, k/T vs. DHH(TCB) for 2-BUTYNE 584.20 Reduced model parameter, k3/T vs. DHH(TCB) for ODCB 594.21 Reduced model parameter, k5/T vs. DHH(TCB) for MDCB 604.22 Reduced model parameter, k3/T vs. DHH(TCB) for 1,3- Bromochiorobenzene 614.23 Reduced model parameter, k3/T vs. T for all the solutes 624.24 S-S, dependence on for the solute ODCB 644.25 S-S dependence on for the solute MDCB 654.26 S-S, dependence on for the solute 1,3- Bromochioro benzene. . . . 665.27 The coordinate system and atom numbering scheme of the 5CB — d19molecule 715.28 Experimental2H-NMR spectra of 5CB — d19 dissolved in the zero efg mixtures 55% 1132/EBBA, at 307.1K, and 70% 5CB/EBBA at 306.8K. . . 74xi5.29 The quadrupolar splitting Lzi1 versus temperature for the mixtures 55%1132/EBBA, 70% 5CB/EBBA and 56.5% 1132/EBBA 785.30 Quadrupolar splitting ratios Av5/L i versus Lz,’1 of 5CB— d19 in the zeroefg mixtures 55% 1132/EBBA, 70% 5CB/EBBA and 56.5% 1132/EBBA 835.31 RMS (root mean squares deviation) versus temperature of the fits to individual spectra of 5CB in 55% 1132/EBBA for the different geometriesPL-0, PL-4, PERP-0 and PERP-4 at Etg equal 500 cal/mol 885.32 RMS (root mean squares deviation) versus temperature for Ejg equal 700cal/mol 895.33 RMS (root mean squares deviation) versus temperature for Etg equal 900cal/mol 905.34 The reduced model parameter k/T versus reduced temperature 925.35 The reduced model parameter k3/T versus reduced temperature 935.36 The ratio versus reduced temperature 945.37 The ratio ‘ versus reduced temperature 956.38 Reduced model parameter, k/T, against L\v for the Etg = 700 cal/mol 1056.39 Reduced model parameter, k/T, against L\z’1 for the Etg = 700 cal/mol 1066.40 Reduced model parameter, k5/T, against v1 for the Etg = 700 cal/mol 1076.41 Reduced model parameter, k/T, against Lv1 for the Etg = 700 cal/mol. 1086.42 Quadrupolar splitting ratios Lw5/Lv’ versus Av using Individual fit CZmodel parameters 1116.43 Quadrupolar splitting ratios vs//zii versus Av1 using Individual fit CImodel parameters 1126.44 Quadrupolar splitting ratios Lv5/L i versus Av1 using Global fit CZmodel parameters 116xii6.45 Quadrupolar splitting ratios Av5/Azi1versus Av1 using Global fit CI modelparameters 1177.46 Reduced model parameter, k8/T vs. Tr for all the solutes and the liquidcrystal 5CB-d19 122A.47 The angles 0 and represent the transformation between the moleculefixed axis system (x,y,z) and the director-fixed axis system of the nematicliquid crystal. 130xiiiAcknowledgementI would like to thank my supervisor, Prof. Elliott Burnell, for his direction and encouragement to accomplish this thesis. His positive attitude, patience and excellent teachingability certainly helped me to complete this thesis. I should also mention about the coffeemeetings at “Trekkers” and “Expresso”, where we discussed a lot of science in the pastfew years. Certainly, this kind of friendly, informal interaction is an asset to our researchgroup.Secondly, I thank my colleagues Dr. Dan Zimmerman, Leon C. Ter beek and JamesPolson for their useful discussions in the past few years. I should mention particularlyJames Poison, who as a physicist, helped me to understand the fundamentals of NMR.I also thank my former labmates K.Y. Li and Z. Sun. I also like to thank the people inthe electronic shop, NMR lab and mechanical shop.Finally, I must thank my parents in Jaffna, Sri Lanka. Their constant support overthe past few years certainly gave me the strength to complete this thesis. I also thankmy brother, T. Vasanthakumar, and my sisters, Gown, Bavani and Shanthy for theirsupport.xivChapter 1IntroductionSection 1.1 briefly describes the nature of liquid crystals. Section 1.2 introduces theorientational order in liquid crystals and explains how the orientational order can bemeasured using NMR (Nuclear Magnetic Resonance) techniques. Section 1.2.3 brieflydescribes how the orientational order can be related to an orientational potential. Section1.3 deals with the intermolecular forces. The first part of this section describes a fewmodels which have been successful in explaining the intermolecular potential. The secondpart gives the background of models used in this thesis. Section 1.4 describes a particularsystem of liquid crystal mixtures, zero electric field gradient mixtures, where only theshort range potential is responsible for the orienting mechanism. Finally, section 1.5briefly describes an outline of the following chapters of this thesis.1.1 Liquid crystals1.1.1 GeneralSome organic compounds show an intermediate phase when these compounds are heatedfrom the solid phase to the liquid phase. The solid phase starts to turn into a “cloudyliquid”, and as the heating continues this “cloudy liquid” disappears and turns into anordinary liquid. This “cloudy liquid” is known as a liquid crystal, and the phase of“cloudy liquid” is known as a liquid crystalline phase or mesomorphic phase. In 1888,Reinitzer first reported the discovery of liquid crystals [1}.1Chapter 1. introduction 2One of the most obvious characterstics of liquid crystals is that they appear cloudy,whereas isotropic liquids appear clear. The appearance of cloudiness stems from theinteraction of the light with the liquid crystal medium as light passes through. Light, anelectromagnetic wave, propagates in the forward direction as it travels inside a material.Only at boundaries between two different materials can its path be changed.A uniaxial liquid crystal has two principal refractive indices, n and nj. In general,the magnitude of riM is greater than n. The axis along riM is known as the director axis,and I indicates the direction perpendicular to the director. In reality, there exist severaldomains in liquid crystals; in each domain the liquid crystal molecules align in a preferreddirection. When the light passes through the liquid crystal from one domain to another,the director direction also changes. As a result, the refractive indices also change fromone domain to another. Therefore, the original wave can cause a new electromagneticwave to propagate in a direction other than the forward direction. This produces ascattered wave in liquid crystals. It is this scattered light that makes the liquid crystalappear cloudy. The scattering of visible light by nematics is 106 times higher than thatof a conventional isotropic liquid.The liquid crystalline phases can be created either by purely thermal processes (thermotropic liquid crystals) or by the influence of solvents (lyotropic liquid crystals). Thethermotropic liquid crystals are classified into three categories: nematic, smectic andcholesteric. In the nematic phase, the liquid crystal molecules prefer to align parallelto each other, making a small angle from one to another. The molecules diffuse rapidlyand randomly so that there is no positional ordering in the nematic phase. On the otherhand, the smectic phases have layered structures; within layers the molecules tend to lieparallel to each other. Therefore, the smectic phases possess a certain degree of positional order. The cholesteric phase is a special category of the nematic phase, formedby optically active molecules. This thesis deals only with the nematic liquid crystals.Chapter 1. Introduction 3Whenever we use the term liquid crystal in the following text, it always refers to nematicliquid crystals.The liquid crystalline phase is a fluid phase where the liquid crystal flows and takesthe shape of its container. Its cloudiness, however, indicates that the liquid crystal differsfrom ordinary liquids in some fundamental ways. One of the major differences betweenliquid crystals and either solids or liquids is illustrated in Figure 1.1. The molecules insolids have positional order as well as orientational order. When the solid turns into aliquid, both the positional order and orientational order are lost because of the fast motionof the molecules. In nematic liquid crystals, however, the positional order is lost becauseof the diffusion of the molecules, but some orient ational order remains. The orient ationalorder in nematic liquid crystals is not as perfect as in solids. The molecules in nematicliquid crystals align in a preferred direction, known as the liquid crystal director.1.1.2 The Effect of magnetic fieldIn the presence of a strong magnetic field, such as in Nuclear Magnetic Resonance (NMR)experiments, the liquid crystal director aligns either parallel or perpendicular to the fielddirection. When a magnetic field is applied to a sample of liquid crystal, the electronsaround the nuclei precess under the influence of the magnetic field. This leads to aninduced magnetic moment that counteracts the field from which it originates. In aromaticsystems, the ir-electrons in the benzene ring are delocalised and form a ring current.Consequently, when the applied magnetic field is perpendicular to the plane of the ring,a large counteracting magnetic moment in induced.The amount of magnetization depends on the strength of the applied field. A quantitymagnetic susceptiblity is defined as a ratio between the magnetization and the strengthof the magnetic field. The magnetic susceptiblity of a liquid crystal is a tensor property, and it has two independent elements XII, magnetic susceptiblity when the appliedChapter 1. Introduction 4field is parallel to the director, and x±, magnetic susceptiblity when the applied field isperpendicular to the director.Some liquid crystals prefer to align parallel with the magnetic field, whereas othersprefer to align perpendicular to the magnetic field. Liquid crystal molecules havingbenzene rings usually align their director axis parallel to the field since when the fieldis parallel to the plane of the benzene ring the interaction energy is lowered. On theother hand, some liquid crystals do not have benzene rings but do have a CN bond. Inthese liquid crystals, the presence of CN bond along the long axis will have ring currentperpendicular to the long axis [2]. As a result, these liquid crystals prefer to align theirlong axis perpendicular to the magnetic field.The coupling between the induced magnetic moment and the applied field is verysmall. A previous study [3] shows that the coupling energy per molecule is the order ofiO5K which is very small compared to the thermal energy, kBT. For a nematic sample,however, the number of molecules in a nematic domain is the order of 1023. Therefore,the coupling energy is much greater than the thermal energy, kBT. This implies that thedirector axis of the nematic sample will be aligned with the applied magnetic field.This thesis deals only with the liquid crystals where the director aligns parallel tothe field direction. Alignment of the director can also take place in the presence of anelectric field or at the surface of prepared glass plates [3].1.1.3 Liquid Crystal Display(LCD)The alignment of the liquid crystals on the surface of glass plates is widely used inLiquid Crystal Display(LCD) technology, which is a major industrial application of liquidcrystals. This section briefly describes how the Liquid Crystal Display works.Polarization filters are fitted on the outside of two glass plates. The polarizationplanes of the glass plates are turned at 900 to each other. The plates are coated on theChapter 1. Introduction 5/\// \\\ \Solid phase nematic phase Liquid phaseFigure 1.1: Schematic illustration of the solid, liquid crystal and liquid phases. The sticksrepresent moleculesinside with a transparent,conducting material such as indium tin oxide so that they actas electrodes. The inside glass plate surfaces have a molecule-orienting layer. The liquidcrystal material is now placed between the glass plates in such a way that the liquidcrystal molecules on the glass plates lie in the direction of the polarization plane. As aresult, the director of the nematic liquid crystal is forced to twist through an angle of900. This twist is just like the twist of a chiral nematic liquid crystal, so this producesrotation of the polarization direction as light propagates through the liquid crystal layer.With the correct thickness of the liquid crystal layer and liquid crystal material, therotation of the polarization direction can be made to follow the twist of the director.The polarization direction of the light is therefore rotated through 90° when it strikesthe second polarizer at the second glass plate, which is set at 900 angle with respectto the first polarizer. Therefore, the light passing through the first polarizer can passthrough the second polarizer. There is a reflector, placed behind the second polarizer,which reflects back the light.If an electric field is applied to both electrodes, the polar liquid crystal molecules lineChapter 1. Introduction 6up parallel to this field, and the director of the liquid crystal molecules are not twisted.Therefore, the light passing through the first polarizer can not get through the secondpolarizer. Since no light is passed through the second glass plate, no light is reflected backfrom the reflector. Therefore, the areas with an applied voltage appear dark against thoseareas without an applied voltage which appear silvery clear. When the electric field isswitched off, the elasticity of the molecules makes them return to their helical structure.The major advantage of LCD technology is the low power consumption which is in theorder of 1 A/cm2. Due to the low power consumption of LCD technology, it is possibleto link the LCD with modern electronic components. Further, LCDs are light-weight,flat in design and ideal for portable use.1.2 NMR and Orientational orderThere are several techniques used to study the physical properties of nematic liquidcrystals, including measurement of magnetic susceptiblity [2], measurement of dielectricconstants [2], viscosity measurements and dynamics studies [3]. The orientational orderof liquid crystals can be measured using techniques such as Raman scattering [3], Quasi-elastic scattering of X-rays or neuterons [3] and EPR (Electron Paramagnetic Resonance)[3]. NMR has also been a very useful technique to measure the orientational ordering ofliquid crystals [4, 5, 6, 7]. NMR has also been used to investigate intermolecular forcesamong liquid crystal molecules [5, 7]. Further, NMR studies on relaxation phenomena ofliquid crystals have been useful in understanding the type of motions in liquid crystals[8, 9, 10, 11, 12]. The first two parts of this section deal with the background theory ofProton NMR (1H — NMR) and Deuteron NMR (2H — NMR). The final part brieflydescribes the relationship between the orientational order and orientational potential.Chapter 1. Introduction 71.2.1 ‘H-NMRConsider a pair of protons labelled i and j in a molecule in a nematic phase. In a‘H— NMR experiment, an external magnetic field, H0, is applied along an arbitarydirection Z. Each proton spin is coupled to H0 by the Zeeman interaction, H, whichcan be written as:= —vJz — ‘j1Zj (1.1)where v and v are the resonance frequencies of nuclei i and j. ‘Za are the spin operatorsof these two nuclei along the field direction Z, and a=i, j. The resonance frequencies,v,, depend on the chemical shift, UZZ,a of the nuclei a, the gyromagnetic ratio of theprotons, 7H, and the field strength, H0= ‘YHHo(1—(1.2)In addition to the Zeeman interaction, each nucleus experiences a local magneticfield due to the dipolar field created by the other nuclei. The truncated dipolar-dipolarHamiltonian, Hd, can be written as [13]:Hd= —h2<(3 cos2 °ijZ — 1)> (3IzIz—Ij.Ij) (1.3)where‘,are the gyromagnetic ratios of nuclei i and j, is the internuclear distancebetween nuclei i and j, and 0ijZ is the angle between the interproton vector rj and theexternal magnetic field direction Z. The angular bracket indicates the statistical averageover all possible Oj values. The quantity <(3cos21> is known as the order parameter,3(iJ)• In general, the order parameter is non-zero in the nematic phase. As a result, theorder parameter is measurable for a pair of protons in the nematic phase. In the isotropicphase, however, this quantity vanishes.Although the orientation for a pair of protons can be described by a single orderparameter, 8(ij), the orientation of a molecule, which may have a large number of protons,Chapter 1. Introduction 8in the nematic phase cannot be described by a single order parameter. To describe theorientation of a molecule in a nematic phase, the molecule-fixed axes (x,y,z) are defined,and the order parameters are given by a Saupe ordering matrix S [14]. The matrixelements, S, are given byS = < (3 cos cos—8>, (1.4)where Z is the direction along the external magnetic field, and c, 3 = x,y,z, molecule fixedaxes. The order matrix is real, symmetric and traceless, and thus it has five independentmatrix elements. The number of matrix elements can be reduced, depending on thesymmetry of the molecule. In particular, for molecules with C3v or higher symmetrythere is only one independent order parameter, and C2v and D2h symmetry moleculeshave two independent order parameters. The order parameters, S, of the molecule canbe obtained from the dipolar splittings of a ‘H—NMR spectrum. The dipolar couplings,D3, of the molecule are related to its order parameters, S, by the following equation[4]:877[Szz(3cos2&ijz—1) + (S — Syy)(cos2Oijx — cos2O)) +2S(cos °ijx cos Oijy) + 2Sxz(cos Ojj cos Ojj) + 2S(cos Ojj cos &jj)j (1.5)Although the ‘H — NMR technique is useful in obtaining the order parameters of amolecule with a few spins, the ‘H — NMR spectrum of a molecule with a large numberof spins could be too complicated to analyse. This complexity can be simplified by using— NMR on partially or fully deuterated molecules.1.2.2 2H - NMRDeiiterium nuclei, which have spin I = 1, have electric quadrupole moments. In additionto the Zeeman interaction experienced by deuterium nuclei, the dominant interaction isChapter 1. Introduction 9that between the nuclear electric quadrupole moment of the 2H nucleus and the electricfield gradient experienced by the nucleus. The Quadrupolar Hamiltoriian, HQ, in theprincipal axis system (x’,y’,z’) is given by the following [13]:HQ = — 12) + (V11 — — I,)] (1.6)where V is the electric field gradient tensor component along the principal axis directiona= x’, y’, z’. eQ is the electric quadrupole moment of the 2H nucleus and I, Ii, Iiare spin operators of the 2H nucleus. By defining eq=Vii and i = Vii_V1i equation(1.6) can be rewritten as:HQ= 1(1 1) [(3I- 12) + Q(I, - 1,)] (1.7)Thus, the total Hamiltonian, the Zeeman and Quadrupolar, can be written as:HT = 7D11H01Z + 41(21— 1) [(3I,— 12) + — It,)] (1.8)where Z is the direction of the external magnetic field. For deuterated molecules, the(x’, y’, z’) axes are defined for each C-D bond. The z’ axis is taken to be along the C-Dbond axis, and x’,y’ axes are perpendicular to the C-D bond. Since the spin is quantizedalong the Z direction, the total Hamiltonian is written in the (X, Y, Z) axis system usinga coordinate transformation:HT = 7Dh11O1Z+ 4I( 1)[(31z][(cosO 1)+sin2Ocos2a] (1.9)where 0 is the angle between the C-D bond and the external magnetic field, H0, direction,and a is the azimuthal polar angle.In2H-NMR experiments, the external magnetic field is of the order of i04 gauss;therefore, the quadrupolar Hamiltonian, HQ, can be treated as a perturbation to theZeeman Hamiltonian, H. Using first order perturbation theory [13], the energy levelsChapter 1. Introduction 10of the Quadrupolar Hamiltonian are given by:Em = 81( 1)[(3m2—I(I+1)][(3cos2O—1) +sin2&cos2a] (1.10)where m is the spin quantum number of the Zeeman Hamiltonian. The energy levelsplittings due to Zeeman and Quadrupolar interactions are shown in Figure 1.2.For C-D bonds in methyl groups and methylene groups, the electric field gradienttensor component along the C-D bond is axially symmetric, resulting inThus, the quadrupolar splitting, AvQ, is given by32()<(3cosO—1)> (1.11)where is the order parameter, SGD, of the C-D bond. For C-D bonds inrings, the expression for /vq can be obtained using equation (1.10).For powder samples, 0 takes values ranging from 00 to 3600, and this leads to a powderpattern spectrum [15]. In liquid crystals, however, the SCD is averaged over all motionsto take an absolute value between 0 and 1. Therefore, the 2H— NMR spectrum of adeuterium nucleus in liquid crystals consists of a pair of lines separated by SCD. Notethat <(3co81)> is averaged to zero in isotropic liquids because of the rapid tumblingmotion of molecules.1.2.3 The Orientational Distribution FunctionThe orientation of molecules in a nematic phase can be specified by a singlet distributionfunction, f(), where l denotes the Eulerian angles. The f() can be related to theorientational potential, U(Q), byf() exp(—U(Q)/kT) (1.12)where Z = f exp(—U()/kT)dfZ. U(1) is the mean field potential experienced by asingle molecule, and this potential is responsible for the molecules orienting in a preferredChapter 1. IntroductionFigure 1.2: Energy level diagram showing the effects of the Zeeman and Quadrupolarinteractions on the nuclear states for a spin I = 1 nucleus.direction. Any measurable property, Aav, can be given as a statistical summation of asingle molecular property, A0, byAav = jf0Ad1 (1.13)Therefore, the molecular order parameter, S, can be related to the orientational potential, U(Q), by following equation (see Appendix A for further details):$ — f(3 COS cos — exp(—U()/kT)d 114— 2fexp(—U()/kT)d1The orientational potential, U(), can be investigated in various ways. In some studies,the orientational order of pure nematics are measured to investigate the potential. Inother cases, a probe solute is dissolved in a liquid crystal solvent and the orientationalorder of the probe solute is investigated in terms of the orientational potential. In thisZeemanSplitting11QuadrupolarSplittingm=-1hw03m=O,- -1_AVQ2—v3 Q1—AvQm= 13Chapter 1. Introduction 12thesis, probe solutes are dissolved in liquid crystal solvents to investigate the intermolecular forces.It is assumed that when liquid crystals are used as solvents, the solute concentrationis sufficiently dilute that the solute does not perturb the liquid crystal solvent. In otherwords, the addition of small amount of solute only changes the physical properties ofthe liquid crystal such as nematic-isotropic transition temperature and order parameter,but it does not change the fundamental nature of the liquid crystal. Further, it shall beshown in this thesis that the forces acting on a small solute by the surrounding liquidcrystal molecules are similiar to those acting on a probe liquid crystal molecule by thesurrounding liquid crystal molecules.1.3 Intermolecular Forces1.3.1 GeneralThe investigation of intermolecular forces has been important in understanding the physical nature of liquid crystals. The anisotropic intermolecular forces are often describedby a mean field pseudo potential which is expressed in terms of a long range potentialand a short range potential. The long range force is mainly due to interactions such asdispersion forces and electrostatic interactions. The short range force, on the other hand,is a repulsive interaction which is a consequence of overlap of electron clouds betweentwo neighbouring molecules. The first part of this section describes a few theories whichhave been successful in explaining intermolecular forces. The second part of this sectiondeals with models used in this thesis for the long range forces and the short range forces.Chapter 1. Introduction 13Maier-Saupe modelMaier-Saupe theory [16] was developed to describe a few thermodynamic properties ofnematics. In Maier-Saupe theory, it is assumed that the anisotropic long range forceswere responsible for the existence of the nematic phase. The theory also assumed thatthe constituent liquid crystal molecules are rigid and possess cylindrical symmetry.The anisotropic pair potential between two molecules, Ua, is written asUa(r12,012) = —u(r12)P2(cos012), (1.15)where P2(cos 012) is the second Legendre polynomial, and u(r12) is a proportionalityconstant that depends upon the intermolecular separation. The potential is a function ofthe intermolecular separation, r12, and the angle between the two molecular symmetryaxes, 812. The mean field approximation is implemented by taking three averages of thepair potential to derive the mean field potential: over all orientations of intermolecularvector r12, over all orientations of molecule 2, and over the intermolecular separation r12.The mean field potential, U(0), can be written as:U(O) = — <P2(cos8) >P2(cos0) (1.16)where is an interaction coefficent, < P(cos 0) > is the order parameter of the liquidcrystal. This potential was used to calculate the order parameter of the nematics as afunction of temperature. A prediction of this theory is that a plot of the order parametervs. reduced temperature falls on a universal curve.Emsley - Luckhurst modelThe Maier-Saupe theory assumed cylindrical symmetry for constituent molecules formingliquid crystals. In reality, the constituent molecules do not have this high symmetry.Chapter 1. Introduction 14Luckhurst et. al [17] extended the Maier-Saupe theory for lath-like molecules. Thepotential of the mean torque, U(O, v’), now contains two terms:U(8, b) = —[2,0d(O) +2,d(O) cos 2&] (1.17)where d,0(O) = P2(cos 8) and dg,2(O) = /sin2 0. The 0 and‘/‘ are polar and azimuthalangles respectively, describing the orientation of the director in the molecule-fixed frame.The first term in equation (1.17) is equivalent to the potential given by equation(1.16)derived for cylindrically symmetric molecules. The second term results from molecularbiaxiality.Samuiski’s modelSamulski and coworkers [18, 19, 20] in their study of n-alkanes in liquid crystal solventshave incorporated the molecular shape anisotropy into the intermolecular potential. Thepotential has two terms:N N-iU = —WoP2(s,s)— W1 P2(s,s+1) (1.18)The first term corresponds to alignment of the alkyl chain through aligning of individualC-C bonds in an uncorrelated fashion. Each C-C bond was treated as an independentuniaxial particle whose orientational energy is proportional to < P2(cos O) >, where 0, isthe angle between the C-C bond and the director axis, Z. The second term correspondsto the alignment of midpoints of a pair of adjacent C-C bonds (chord model). Thisterm reflects how the shape of the molecule contributes to the short range part of theintermolecular potential.Chapter 1. Introduction 15Other modelsGilson et. al have studied small solutes dissolved in liquid crystals to investigate theshort range potential [21, 22, 23, 24, 25]. The short range potential is modelled as:U(O, q) = _AS(l)(cos2 0 + B sin2 8 cos 2qf) (1.19)where 0 and g are the polar and azimuthal angles , and S(1) is the solvent order parameter.The parameter A is the potential energy difference between the orientations where thelong molecular axis is parallel and perpendicular to the nematic director. The parameterproduct AB is the potential energy difference between the orientations of the two axes,which are perpendicular to the molecular long axis. This model reflects the size andshape of the solute molecule. Further, Ferrarni et. al have described a shape model forthe short range potential [26].1.3.2 Burnell’s modelIn this section I shall describe how the long range and short range interactions aremodelled by Burnell’s group. The first part deals with the measurement of an averageelectric field gradient in liquid crystals and with the long range interaction in termsof electrostatic interactions. The second part deals with modelling of the short rangepotential.Long range interactionAlthough a liquid crystal molecule generally is an uncharged particle, the presence ofcharge distribution in the liquid crystal molecule induces an electric field, electric fieldgradient and higher order terms at a point, say P, in space. The average electric field,E, experienced at the point P is an average over all the electric fields induced by allChapter 1. Introduction 16the surrounding liquid crystal molecules at the point P. Due to the inversion symmetryand cylindrical symmetry of the nematic phase, it can be shown that the average electricfield, E, vanishes at the point P.Similarly, the charge distribution present in the liquid crystal molecule induces anelectric field gradient at the point P. The average electric field gradient is an averageover all surrounding liquid crystal molecules. The average electric field gradient is atensor property; it has 9 independent matrix elements; and the electric field gradient is atraceless tensor. Further, due to the inversion and cylindrical symmetry of the nematicphase, it can be shown that the off-diagonal matrix elements, F, become zero, wherea, /3 = X,Y,Z, director fixed axes. In addition, the matrix elements Fx and areindistinguishable due to the cylindrical symmetry of the nematic phase. Therefore, theaverage electric field gradient for a liquid crystal can be described by a single parameterThe measurement of the average electric field gradient present in liquid crystals hasbeen achieved by many researchers. Jokisaari et. al have used monoatomic noble gasesdissolved in liquid crystals to measure the average electric field gradient [27, 28, 29, 30].Burnell et. al have used D2 gas dissolved in liquid crystals to measure the average electricfield gradient [31, 32, 33]. The average electric field gradient, , experienced by theD2 gas in liquid crystals can be written as a sum of intramolecular and intermolecularcontributions:= (intermolecular)— eqS (1.20)where eq is the electric field gradient component along the D-D bond and S is the orderparameter of the D-D bond. The 2H— NMR spectrum of D2 gas in a liquid crystalenvironment has been used to obtain the quadrupolar coupling, B0b8, and the dipolarcoupling, DDD. The B0b5 and DDD are then related to obtain the experimental orderChapter 1. Introduction 17parameter S and by the following equations [32]:B06_3e(Fzz(intermolecular)— eqS) (1.21)DDD=DS (1.22)where YD is the gyromagnetic ratio of the deuterons and QD is the electric quadrupolemoment of deuterium nucleus.The presence of an average electric field gradient in liquid crystals suggests that thereis a possiblity of an electrostatic interaction between the average electric field gradient andanother second rank tensor property of the solute molecule. The mean-field electrostaticpotential is described in terms of the average electric field gradient and the electricquadrupole moment of solute molecule, by [34, 35]:U= <( cos cos — co)> (1.23)where O, O are the angles between the c, /3 axes of the solute molecule and the nematicdirector, Z, axis. The term on the right hand side of equation (1.23) is the third termin the multipole expansion of the mean field potential. The first two terms vanish foruncharged solutes in liquid crystals. The higher order terms are neglected.Using the values of and Qn [36] for D2, the order parameter, 5, was recalculatedby using a proper quantum calculation [33]. The calculated order parameter agreedvery well with the experimental order parameter. Furthermore, the studies of smallsolutes 112, HD dissolved in the liquid crystals showed that the calculated order parameteragreed well with the corresponding experimental order parameters. These results showthat the electric field gradient - electric quadrupole interaction is sufficient to explainthe orientation of small solutes such as D2, HD and H2 in liquid crystals. For planarsolutes such as benzene derivatives and for linear molecules, however, the electrostaticpotential was not sufficient to describe their orientation in liquid crystals. In order toChapter 1. Introduction 18describe the orientation of these large solutes in liquid crystals, Burnell and coworkers[38] have included a short range potential, in addition to the long range potential, in theintermolecular potential.Short range potentialThis section describes how the short-range potential is modelled in terms of size andshape of the solute molecule. Van der Est et al. [38] introduced a model for the short-range interaction, wherein the liquid crystal is considered as an elastic tube alignedparallel to the nematic director axis, Z. The introduction of the solute displaces the wallof the elastic tube in the X-Y direction, but keeps the wall parallel to the Z direction.The displacement caused by the presence of the solute molecule leads to a restoring force,which is proportional to the deformation of the elastic tube in the X-Y direction (flooke’slaw). The restoring force, dF(Q), is given by [38, 39]dF() = —kdC(), (1.24)where C() is the circumference of the deformed tube, and k is the force constant, aproperty of the liquid crystal. The potential energy associated with the interaction ofthe solute molecule with the elastic wall is given by [38, 39]:Usr() = F()dC() = kC2() (1.25)The order parameters recalculated using equation (1.25) for a collection of small solutes in the 55% 1132/EBBA mixture agreed well with the experimental order parameters[40]. In this calculation, the experimental order parameters were used to obtain the bestfit model parameter k. When the fit was done for individual solutes, the parameter k wasconsistently smaller for larger solutes such as 2,4-hexadiyne, 1CB (1-cyano biphenyl) and5CB (5-cyano biphenyl) than for smaller solutes. Zimmerman et al. then extended theChapter 1. Introduction 19original short-range potential [38] in two different ways. The first way shall be referredto as CZ model, and the second way shall be referred to as CI model.(a) CZ modelIn the CZ model, the solute is modelled as a cylinder, and the potential energy iseffectively the energy required to displace the liquid crystal solvent molecules upon theintroduction of the cylinder. The modified short range potential is written as [40]Usr(f) 1/2k2C(Q) + 1/2kZ()C(1) (1.26)where k and are the model parameters, Z(1) is the length of the cylinder and C(1)is proportional to the radius of the cylinder as shown in Figure (1.3). The short-rangepotential given by equation (1.26) gave a good and consistent fit for large as well as smallsolutes in the 55% 1l32/EBBA mixture [40]. Equation (1.26) can be rewritten in termsof the model parameters k2 and asUsr() = 1/2kC() + 1/2kz()C() (1.27)where = k/k is dimensionless. Calculations using equations (1.26) or (1.27) for theshort range potential shall be referred to as CZ model calculations in this thesis. In thenotation CZ, the ‘C’ refers to C() term in equations (1.26) and (1.27) the ‘Z’ refers tothe term Z(1).(b) CI modelIn an attempt to introduce a better model for the anisotropic short-range interactionbetween the solute surface and the liquid crystal, Zimmermann et al. [41] suggested thatthe short range potential can be writtenUsr(f) = 1/2k8J Cz(Q)dZ, (1.28)Chapter 1. Introduction 20Iz(o)Figure 1.3: The anisotropic potential given by the CZ model, where Z(Q) is the projectionof the molecule onto the director axis, Z. 0(Q) is the circumference around the projectiononto the (X, Y) plane.z0 zlutec(o)Chapter 1. Introduction 21Z(Q)Figure 1.4: The anisotropic potential given by the CI model, where Z(fZ) is the lengthof the projection of the molecule onto the Z axis. Cz(1) is the ‘minimum’ circumferenceobtained by including only the circles formed by the atoms where they intersect a planelocated at Z.zAC(c2)dZ{Chapter 1. Introduction 22where k8 is the model parameter and C(c!) is the circumference of the solute at distanceZ. (see figure 1.4) The potential is obtained by adding contributions from the surfaceelements, where each surface element contributes an amount that depends on its orientation with respect to the director. The short-range potential given by equation (1.28)may be interpreted as an anisotropic surface interaction between the surface of solutemolecule and the surrounding liquid crystals.Combining the solute surface interaction with the liquid crystal medium and theelastic distortion of the liquid crystal (Van der Est’s original model), the short rangepotential is written as:U3(c2) = 1/2kC(c) + 1/2k8 f C(1)dZ, (1.29)where k and k8 are the model parameters, and Cz(Q) is the circumference of the soluteat distance Z (see Fig. 1.4). The first term, as in the case of Van der Est et al. [38],accounts for the elastic distortion of the liquid crystal. This model gave the best fit tothe experimental order parameters of 46 solutes in 55% 1132/EBBA. Equation (1.29)can be rewritten in terms of the model parameters k and ‘ asUsr() = 1/2kC(Q) + 1/2k’ f Cz()dZ (1.30)where ‘ = k/k8 is dimensionless. The calculations using equation (1.28) or (1.29) forthe short range potential shall be referred to as CI model calculations in this thesis. Inthe notation CI, the ‘C’ refers to C(f) term in equations (1.29) and (1.30), and the ‘I’refers to the integral term.1.4 Zero electric field gradient mixturesThis section deals with a system where the long range potential contribution to the intermolecular potential can be eliminated. The long range electrostatic potential dependsChapter 1. Introduction 23on the electric quadrupole moment of solute and the average electric field gradient of theliquid crystal solvent. To remove the long range forces, the system must have either zeroelectric quadrupole moment of the solute or a zero electric field gradient in the liquidcrystal solvent. In reality, it is impossible to find an orienting solute molecule with avanishing electric quadrupole moment. On the other hand, Burnell and coworkers haveshown that a system can be prepared where the average electric field gradient is negligibly small. I shall briefly explain how the system having a zero electric field gradient canbe prepared.The D2 molecule, as a solute, was used to measure the average electric field gradientsof nematic liquid crystal solvents N- (4-ethoxybenzylidene)-4 ‘-n-butylaniline (EB BA) andthe mixture Merck ZLI 1132 [31, 33, 32]. The signs of the electric field gradients in thesetwo liquid crystal solvents are opposite, with the sign in 1132 being positive and that inEBBA being negative. A series of liquid crystal mixtures of EBBA and 1132 were studiedusing D2 to measure the average electric field gradient [32]. The average electric fieldgradient was found to be zero for a particular mixture, 55 wt% 1132/EBBA, at 301.4K.Other studies [37] show that the solute methane also experiences an average zero electricfield gradient in the mixture 55 wt% 1132/EBBA at 301.4K.There are several possiblities in preparing zero electric field gradient mixtures. Oneis to use the same combination of liquid crystals such as 1132 and EBBA, but vary thecomposition. For example, Barnhoorn et al. [42] investigated 56.5 wt% 1132/EBBA usingD2 as a solute and found that the average electric field gradient is zero at 322K. Anotherpossibility is to choose a different pair of liquid crystals which have average electric fieldgradients of opposite sign. For one of the components, it would be interesting to usethe liquid crystal 5CB ((4-n-pentyl)-4’-cyanobiphenyl), a relatively simple nematic liquidcrystal that has received a lot of experimental and theoretical attention from the NMRcommunity [43, 44, 45, 46, 47, 48, 49, 50]. D2 has been used to measure the electricChapter 1. Introduction 24field gradient in this liquid crystal at various temperatures [50]. The magnitude of theaverage electric field gradient in 5CB is found to be 30 per cent as large as that observedin EBBA, but of opposite sign. This suggests that the electric field gradient should bezero in a mixture of 5CB and EBBA. A study of D2 dissolved in the liquid crystal mixture70 wt% 5CB/EBBA shows that its measured electric field gradient is zero at 316K [42].These special mixtures 55% 1132/EBBA, 56.5% 1132/EBBA and 70% 5CB/EBBA,in which the measured average electric field gradient is zero, shall be referred to as zeroefg mixtures in this thesis. Such mixtures experience a zero electric field gradient at aprecise temperature; at other temperatures there exists a small non-zero electric fieldgradient. However, it will be shown in the following sections that this small electric fieldgradient does not significantly affect the resuits. Therefore, throughout this thesis, theterm zero efg mixture will be used to include the nematic temperature range of a mixturethat exhibits a zero electric field gradient at some temperature within this range.1.5 Outline of the thesisOne of the aims of this thesis is to compare the intermolecular forces in three differentliquid crystal solvents. In order to eliminate the long range contribution to the intermolecular potential, zero efg mixtures are used as liquid crystal solvents in this thesis. Threedifferent zero efg mixtures, 55% 1132/EBBA, 56.5% 1132/EBBA and 70% 5CB/EBBAhave been chosen in this study. It is assumed that only short range interactions contribute to the anisotropic potential in the zero efg mixtures. Solutes chosell vary fromhighly symmetric solutes to a large liquid crystal molecule (5CB-d9).Chapter 2 briefly explains the experimental techniques used in this thesis. Chapter 3presents a study of a few solutes with C2v and D2h symmetry using Proton NMR in thezero efg mixtures 70% 5CB/EBBA at 316K and 56.5% 1132/EBBA at 323K. The purposeChapter 1. Introduction 25is to compare the short range potentials experienced by the solutes with C2 symmetryin these two zero efg mixtures. For these solutes, two independent order parameters Sand S—are measured from the experimental spectrum, and these order parametersare related to the short range potential.In Chapter 4, two C3 and higher symmetry molecules, two C2v symmetry molecules,a Cs symmetry molecule and a linear molecule are studied using Proton NMR in the zeroefg mixtures 55% 1132/EBBA and 70% 5CB/EBBA as a function of temperature. Thepurpose is to compare the short range potentials experienced by small solutes of differentsizes, ranging from highly symmetric to linear, in the zero efg mixtures.In Chapters 5 and 6, the molecule 5CB-d19 (perdeuterated 5CB) that by itself forms anematic liquid crystalline phase is studied using2H-NMR in the three zero efg mixtures55% 1132/EBBA, 56.5% 1132/EBBA and 70% 5CB/EBBA as a function of temperature.The purpose here is to compare the short range interactions experienced by a liquidcrystal molecule in zero efg mixtures. This particular system is useful to understand theintermolecular forces existing among constituent liquid crystal molecules in the nematicphase. The spectra of 5CB-d19 in 55% 1132/EBBA and 70% 5CB/EBBA are analysedusing the CZ and CI models. The two-parameter models were chosen for the analysisbecause they gave a very good fit for larger solute 5CB; as well, the choice of twoparameter models allows us to study the temperature dependence of the ratios of themodel parameters, and cs’.Chapter 2Experimental2.1 Sample PreparationThe liquid crystal ZLI-1132, which is an eutectic mixture of alkylcyclohexylcyanobenzeneand alkylcyclohexylcyanobiphenyls, was purchased from Merck and not purified prior touse. The liquid crystal EBBA was synthesized in Amsterdam according to ref. [51]. Theliquid crystal 5CB was purchased from Merck and not purified prior to use. Appropriateweights of liquid crystals 1132, EBBA and 5CB were used to prepare the mixtures 55wt% 1132/EBBA, 56.5 wt% 1132/EBBA, and 70 wt% 5CB/EBBA.The solutes ortho dichlorobenzene (ODCB) meta dichlorobenzene (MDCB), paradichlorobenzene (PD CB), trichlorobenzene (TCB), furan (FUR), ortho dicyanobenzene(ODCyB), tetrathiofulvalene (TTF), fluorobenzene (FB), 1,3-bromochloro benzene (1,3-BrCl), benzene (BENZ) and 2-butyne (2-BUTY) were all commercially available and wereused without further purification. The abbreviations above shall be used throughout thisthesis to refer to the appropriate names of the solutes.For experiments involving the small solutes, the liquid crystal mixtures were placedinto 5mm NMR sample tubes, and 1-5 mol% of the solute was dissolved in each liquidcrystal mixture. In each sample tube, approximately 0.5 mol% of TCB was also dissolvedfor scaling purpose. The mixture was heated to the isotropic phase and mixed using avortex stirrer.The solute 5CB — d19 was synthesized at UBC [52] by Prof. Bates. 1-2 wt% of26Chapter 2. Experimental 275CB— d19 as solute was dissolved in each of the liquid crystal mixtures, 55 wt% 1 132/EBBA,56.5 wt% 1132/EBBA, and 70 wt% 5CB/EBBA. Each mixture was heated to the isotropicphase and mixed using a vortex stirrer. The sample was subjected to freeze-pump-thawcycles until no gas evolved from the liquid crystal mixture. The samples were transferredto NMR tubes, and the tubes were flame sealed under vacuum.2.2 ‘H-NMR experimentsProton NMR experiments were performed on a Bruker Wfl-400 spectrometer, with a highresolution probe having a saddle coil, operating at 9.4T. The proton resonance frequencywas 400 MHz. For the high resolution probe, the 90° pulse length was typically 10-12microsec. The experiment was a single pulse experiment (90x - DE- ACQ), where DE isa delay to compensate for receiver deadtime, and ACQ denotes acquisition time of thefree induction decay (FID). The value of DE was set automatically by the spectrometer.In single pulse experiments the phases of pulse and receiver were cycled through a fourpulse phase cycling scheme X, -X, Y, -Y in order to reduce the effects of pulse and receiverimperfections. Normally 16-32 FID’s were collected using a spectral width of 10 KHz.The accumulated FID was Fourier transformed to obtain the spectrum.In high resolution NMR experiments, the applied magnetic field is along the longaxis of NMR sample tube. This permits the sample to be spinned without destroyingthe orientation of the nematic phase. If spinning is not done, then the magnetic fieldgradient along the X and Y directions would produce broadened peaks. The spinningrate was 30Hz.Shimming the magnet is very important to obtain very narrow peaks in high resolutionNMR spectroscopy. The shimming can be done either by optimising a lock signal or byoptimising the envelope of the FID. Since optimising on the FID was a difficult task inChapter 2. Experimental 28the nematic phase, a field-frequency lock was used to shim the magnet. Acetone-d6waschosen as lock solvent. The lock solvent was filled up to of a capilliary tube, whichwas mounted coaxially inside the 5mm-NMR sample tube using teflon spacers. The Zand Z2 magnetic field gradients were shimmed to obtain an optimum lock signal. Aftershimming, the linewidths of solute peaks in the nematic phase were typically 1-2 Hz fora room temperature spectrum.Temperature of the experiment was controlled by a Bruker temperature control unitusing air flow. The temperature was calibrated against the proton chemical shift difference in an ethylene glycol sample.2.3 2H-NMR experimentsDeuteron NMR experiments were performed on a Bruker CXP-200 NMR spectrometer,with a high power probe having a 1cm-diameter solenoid coil, operating at 4.7T. Thedeuteron resonance frequency was 30.76 MHz. The 900 pulse length was 5sec. TheQuadrupolar echo method (90x- r- 9Oy- r- echo) [53] was used to avoid the effects ofreceiver deadtime. The delay, r, was set to 100tsec, and the recycling time was chosento be 1 sec.The pulses were cycled through a 4-pulse cycling sequence, (XY, -XY, X-Y, -X-Y),and the resulting echoes were alternatively added and substracted from the computermemory. The quadrupolar echo was digitized by a digital oscilloscope. The FID wascollected using a spectral width of 100 KHz. 2048-8096 FID’s were accumulated toobtain a good signal to noise ratio, depending on the temperature of the experiment.The accumulated FID was Fourier transformed to obtain the spectrum.The sample was placed horizontally inside the solenoid coil. The solenoid coil wascovered by a cylindrical teflon chamber (4 cm diameter and 3cm height) for insulation.Chapter 2. Experimental 29The temperature of the experiment was controlled by a Bruker temperature control unit.The temperature control unit was equipped with a heating coil and a thermocouple. Thethermocouple was placed below the solenoid coil, and the voltage from the thermocouplewas compared to a reference voltage corresponding to a “desired temperature” set at thetemperature control unit. If the reference voltage was greater than the thermocouplevoltage, then a voltage proportional to the difference of two voltages was applied to theheating coil. This heating coil was surrounded by a glass tube such that air can bepassed through this flow tube. The heated air was circulated into the sample chamber inorder to heat the sample. Once the thermocouple reached the same temperature as the“desired temperature”, then a constant current was applied to the heating coil.The temperature of the sample was measured using another Copper-Constantan thermocouple, which was placed just above the solenoid coil. The end of this thermocouplewas connected to a digital volt meter (DVM) to measure the voltage. The voltage measured by the DVM was converted into temperature to an accuracy of +0.10 C, using acalibrated conversion table.2.4 Microscopic studySeparate microscope slides were prepared from the pure solvents 55 % 1132/EBBA and70% 5CB/EBBA, and were studied using a Leitz Laborlux 12P0L polarizing microscopeequipped with a Mettler FP-2 heating stage by Dr. Mary E. Neubert at Kent stateUniversity to determine the phase transitions of these zero efg mixtures. It was foundthat TNI, the nematic-isotropic transition temperature, of 55 % 1132/EBBA is in therange 341.8K to 342.4K, and that TNI of 70% 5CB/EBBA is in the range 320.6K to321.4K. It was also found that these two liquid crystal mixtures are in the nematic phaseover the temperature range used for the NMR experiments.Chapter 3Orientation of Gv and D21, symmetry solutes in zero efg mixtures3.1 IntroductionThe study of intermolecular forces in liquid crystals is a complicated problem. A systemof a small solute as a probe molecule dissolved in a liquid crystal can be a good startingpoint to understand the nature of intermolecular forces. The system can be further simplified by choosing zero efg mixtures as liquid crystal solvents, where only the short-rangeinteractions are present to orient the probe solute molecule. In this chapter, several G2vand D2h symmetry solutes are investigated in two zero efg mixtures 56.5% 1132/EBBAat 323K and 70% 5CB/EBBA at 316K. The solutes studied are ortho dichlorobenzene(ODCB), meta dichlorobenzene (MDCB), para dichlorobenzene (PDCB), furan (FUR),ortho dicyanobenzene (OD CyB), tetrathiofulvalene (TTF) and fluorobenzene (FB).Section 3.2.1 deals with how the dipolar couplings, and order parameters, S,can be obtained from ‘H-NMR spectra. Section 3.2.2 compares the orientation of solutesin the zero efg mixtures. Section 3.3 deals with comparison of short range interactionsin the zero efg mixtures in terms of model parameters.30Chapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 313.2 Results3.2.1 AnalysisThe total Hamiltonian, HT, including Chemical shift, Dipolar arid indirect-dipolar Hamiltonians of the solute molecule in the nematic phase can be written as:HT = — VI + i.I) + (3.31)i i j>i i j>i kwhere the first two terms on the right hand side of eqn. (3.31) are the Chemical shift andDipolar Hamiltonians respectively. The third term is the isotropic part of indirect scalarHamiltonian, where the anisotropic contribution to the indirect scalar Hamiltonian isneglected [54]. The programme LEQUOR [55] is used to determine the Dipolar couplings,D’s, and Chemical shifts, zi’s, from the ‘H-NMR spectra, where the indirect scalarcouplings J ‘s are fixed to their isotropic values [56]. The main theme of this programmeis briefly described in next paragraph.Using a suitable set of basis functions, the matrix elements of the total Hamiltonian,HT, are calculated. Then, the Hamiltonian matrix is diagonalised to obtain eigenvaluesand eigenfunctions of the Hamiltonian. These eigenvalues are the energy levels of themolecule. Based on the selection rules and symmetry of the molecule, all possible transition frequencies and their corresponding intensities are calculated. These calculated linefrequencies and intensities are matched with those of the experimental spectrum to assignthe corresponding lines. The sllmmation of squares of differences between experimentaland calculated transition frequencies are minimized by varying the parameters v andD3. The fitted D’s for the C2v and D2h symmetry solutes are reported in Table 3.1.The dipolar couplings of the solutes with C2v and D2h symmetry can be relatedto the solute geometry and orientation by the equation= [S(3 cos2 Oj — 1) + (S — S)(cos26j — cos2 Oj)] (3.32)Chapter 3. Orientation of 02V and D2h symmetry solutes in zero efg mixtures 32Table 3.1: Dipolar couplings obtained from the ‘H-NMR spectra for C2v and D2h symmetry solutes.Solute 70%5CB/EBBA 56.5%1 132/EBBAmetadichlorobenzene D12=D4 -67.79 +0.36 -82.86±0.26D13 -19.52 +0.60 -22.87+0.4623=D34 -725.95 ±0.82 -920.02+0.30D24 -179.7 ±1.2 -225.07 +0.59orthodichlorobenzene 12=D34 -772.76 +0.13 -1023.59 +0.16D13=D24 -97.53 +0.16 -132.28+0.17D14 -46.66 +0.36 -65.33 +0.37D23 -361.81 +0.35 -500.20 ±0.40paradichlorobenzene 12=D34 -1745.74 +0.48 -2320.71 ±0.16D13=D24 -20.98 +0.67 -25.60±0.1914_—D23 74.96 ±0.65 101.05 ±0.19orthodicyanobenzene D12—D34 -807.82 ±0.14 -1028.38 ±0.1213=D24 -108.23+0.14 -124.88±0.14D14 -54.73 +0.34 -57.46 +0.37D23 -423.42+0.33 -441.54 +0.34furan 12=D34 -215.42 +0.24 -249.29 +0.26D13=D24 -74.11+0.28 -88.13 ±0.27D14 -102.92 +0.25 -123.81 +0.27D23 -339.67 +0.42 -409.64 +0.34tetrathiofulvalene 12=D34 338.03 +0.04 470.44 +0.17(TTF) D13=D24 -43.42 +0.05 -55.43 ±0.2014=D23 -56.57 +0.05 -72.30 +0.20fluorobenzene D12=D6 -328.61 +0.41 -491.99 +0.7813=D5 -99.45 +0.43 -139.09+0.78D14 -75.20 +0.23 -105.66 +0.5123=D56 -711.78+0.16 -1020.64 +0.20D24=D46 -116.09+0.26 -169.38 +0.4325=D36 -46.07±0.14 -68.51 +0.19D26 -47.95 ±0.35 -76.10 +0.4634=D45 -363.74±0.33 -539.09 ±0.50D35 -46.79 ±0.32 -72.25 ±0.35Dipolar couplings in Hz for solutes in 70% 5CB/EBBA at 316K and in 56.5% 1132/EBBA at323K obtained from the computer programme LEQUOR.Chapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 33Table 3.2: Order Parameters of the solutes in the 70% 5CB/EBBA70% 5CB/EBBASolute DHH(TCB) /Hz S S, — S RIVIS/Hzmetadichlorobenzene 109.37 -0.1370 0.0954 0.8orthodichlorobenzene 129.51 -0.1619 0.0693 0.9paradichlorobenzene 129.51 -0.1732 -0.2708 1.3orthodicyanobenzene 117.52 -0.1717 0.0637 1.5furan 126.17 -0.0944 0.0239 0.3tetrathiofulvalene 116.43 -0.1906 -0.2794 0.14fiuorobenzene 116.99 -0.1236 -0.0627 0.5Experimental order parameters S and— S of solutes in the zero efg mixture 70%5CB/EBBA obtained from the computer programme SHAPE.where the molecule-fixed axes x, y and z are defined in Figure 3.5. and S-S. are theorder parameters of the solute in the liquid crystal mixture. The angle Oij, represents theangle between the ij direction and the molecule-fixed axis c. The programme SHAPE [58]was used to obtain these order parameters from the dipolar couplings and the geometries[57] of the solutes. These experimental order parameters are reported in Tables 3.2 and3.3.3.2.2 Orientation in Zero efg mixturesThe orientation of the solutes in the zero efg mixtures can be compared at a certainexperimental condition such as a temperature or a given splitting of a reference compound. In this thesis, trichlorobenzene, TCB, is chosen as the reference compound, andTCB splittings are used as a reference point for comparison purpose. It shall be shownin the next chapter that the TCB dipolar coupling in zero efg mixtures can be used asan internal measure of reduced temperature. All samples contain a little TCB, and thedipolar coupling of TCB, DHH(TCB), has been measured from the same spectrum as thesolute. Although all the sample tubes with the same liquid crystal mixture were studiedChapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 34ODCyBH564H_Ø_.F1H3 H2FBH3 H4ci._Ø—ciH2 H1H2 CiH4H CIMDCBH3 H24H_.Ø_H1ODCBH1H1‘H1PDCB2H343H S S H2TTF/1/NH4N FURyzzFigure 3.5: The coordinate system and atom numbering of the solute molecules studied.Chapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 35Table 3.3: Order Parameters of the solutes in the 56.5% 1132/EBBA___________________56.5% 1132/EBBASolute DHiq(TCB) /Hz S S, — S RMS/Hzmetadichlorobenzene 136.39 -0.1717 0.1246 0.21orthodichlorobenzene 171.04 -0.2163 0.0882 1.6paradichlorobenzene 171.04 -0.2290 -0.3614 1.1orthodicyanobenzene 151.21 -0.2104 0.0976 1.6furan 149.03 -0.1119 0.0307 0.5tetrathiofulvalene 148.45 -0.2386 -0.3622 0.17fluorobenzene 167.21 -0.1806 -0.0864 1.3Experimental order parameters S and — S of solutes in the zero efg mixture 56.5%1132/EBBA obtained from the computer programme SHAPE.at the same temperature, there is a slight deviation in the TCB dipolar coupling fromone sample tube to another due to factors such as concentration and nature of the solute.These factors also influence the nematic isotropic transition temperature, TNJ.In order to compare results between the two zero efg mixtures, a new quantity, theorder parameter ratio, S = Sp/DHH(TCB), is defined as a ratio between the orderparameter of the solute, S, and the dipolar coupling of TCB, DHH(TCB), in thesame sample tube. The order parameter ratios, S, of 70 % 5CB/EBBA are plottedagainst those of 56.5 % 1132/EBBA in Figures 3.6 and 3.7. The ratios of the 70% 5CB/EBBA agree very well with those of the 56.5 % 1132/EBBA. Based on thisagreement within experimental error, it can be written for any given order parameter ofany given solutef c’tcb\ — / ctcb’— -3)56.5where the subscripts 70 and 56.5 stand for the liquid crystal mixtures 70% 5CB/EBBAand 56.5% 1132/EBBA. This result is interesting because the order parameter ratiosare found to be equal within experimental error in two different zero efg mixtures. Inother words, as long as the TCB dipolar couplings have been measured in both zeroChapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 36efg mixtures, the order parameters S of any solute with C2v and D2h symmetry canbe predicted in a zero efg mixture if the order parameter of that solute in another zeroefg mixture is known. It is worth while to further analyse the results given by equation(3.33).As described in section 1.2.3, the orientation of a probe solute depends on the meanfield potential experienced by the solute. Therefore, we shall now analyse the potentialin the zero efg mixtures to understand the transferability of the order parameters. In thezero efg mixtures, the intermolecular potential is assumed to be the short-range potential,Usr(1).The orientation of the solute can be related to the short-range potential by equationA.51. The order parameter S is proportional to e_/AT. We shall now analyse thetransferability of the order parameters in the zero efg mixtures in terms of the short-rangepotential, Usr(1).3.3 Comparison of short-range interactionsSince the precise nature of the short-range potential is not well known, a one-parametermodel is used to describe the short-range potential. The reason to choose the one-parameter model is that it can be tested on the two independent experimental orderparameters. We chose the one-parameter model, discussed in Chapter 1, and rewrite as:1 tZmo.rUsr(Q) = J C(1)dZ (3.34)ZmnTo calculate the Cz(t), the solute molecule is taken as a collection of van der Waalsspheres, and van der Waals radii are taken from Bondi et al.[59].The two independent experimental order parameters S22 and S,-S were used toobtain the best fit model parameter k2 for each solute independently. The best fit modelparameter k5 was then used to recalculate the order parameters S22 and TheseChapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 37Nx.0cjSt (in Hz-1)zz 1 132/EBBA—0.002Figure 3.6: The order parameter ratios, S = SZZ/DHH(TCB), of the solutes in 70 %5CB/EBBA against those in 56.5 % 1132/EBBA.C)IC)0NA=MDCB•=ODCB=PDCBS ODCyB•= FURv=TTF=FB—0.002—0.00 15—0.00 1—0.001 —0.0015in 56.5%Chapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 380in 56.5%0.00 11132Figure 3.7: The order parameter ratios, (S — S)t = (S — S)/DHH(TCB), of thesolutes in 70 % 5CB/EBBA against those in 56.5 % 1132/EBBA.0.002‘ I I ‘.- A=MDCB•=ODCB0.001 - •=PDCBLCD =ODCyB- •=FUR0 y=TTFN0- =FB.——N—0.001 —.—..DC)—0.002 ——0.002 —0.001(in Hz—i)0.002/EBBAChapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 39Table 3.4: model parameters for the C2v and D2h symmetry solutes70% 5CB/EBBA 56.5% 1132/EBBASolute k/dyn cm1 k/dyn cm1 k3/dyn cm k/dyn cm1metadichlorobenzene 40 +3 35.62 +0.04 54 +3 48.35 +0.07orthodichlorobenzene 47 +3 44.17 +0.06 71 +3 66.84 +0.13paradichlorobenzene 59 +6 44.17 +0.06 85 +5 66.84 +0.13orthodicyanobenzene 42.4 +0.9 38.96 +0.05 57.8 +0.2 55.75+0.09furan 53.95 +0.13 42.69 +0.05 67.0 +0.5 54.62 +0.09tetrathiofulvalene 53 +11 38.50 +0.05 77 +13 54.31 +0.08fiuorobenzene 46 +3 38.73 +0.05 74 +2 64.57 +0.12Fitted k3 values from equation. 1.28 of the solutes, with the corresponding k’ values oftrichlorobenzene in the same sample tube, in the zero efg mixtures 70% 5CB/EBBA and 56.5%1 132/EBBA.recalculated order parameters are plotted against the experimental ones in Figures 3.8and 3.9. The recalculated order parameters agree well with the experimental ones. Therelative errors are generally less than 10% for all solutes. Therefore, the fits are ofsufficient quality that this one-parameter model is useful for making comparisons betweenmixtures.The one-parmeter model gives the k5 value which is directly proportional to theexperienced by the solute. The fitted k values, along with the short-range potentialparameter of TCB , k, are reported in Table 3.4 for all solutes in both zero efg mixtures.The k was calculated from the TCB dipolar coupling, DHH(TCB), using eqns. (3.32),(A.51) and (3.34). As can be seen in Table 3.4, the k3 values vary among the solutes.To demonstrate the transferability of the short-range potentials between the two zeroefg mixtures, the ratios k8/k for all solutes in the 70% 5CB/EBBA mixture are plottedagainst those in the 56.5% 1132/EBBA mixture in Figure 3.10. The ratios are used toaccount for differences among sample tubes containing the same liquid crystal mixture.The ratios k8/k vary from one solute to another up to 20%. This large difference mainlyChapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 40—0.3—0.2NNU)C)—0.1Filled symb. =Figure 3.8: Calculated versus experimental order parameters Se,. Open symbols represent 70 % 5CB/EBBA, and filled symbols 56.5 % 1132/EBBA.=MDCB=ODCBO=PDCH0= ODCyBQ=FURVv=TTFO=FB0open symb. 70%56.5%one—parameter fit—0.1 —0.2exp.—0.3Chapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 410U)U)0exp. (S—S)Figure 3.9: Calculated versus experimental order parameters Open symbolsrepresent 70 % 5CB/EBBA, and filled symbols 56.5 % 1132/EBBA.L=MDCBEi=ODCBo=PDCB0= ODCyB0= FURANv=TTFØ=FBV0open symb. = 707Filled symb. = 56.5one—parameter fit—0.2Chapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 42<1.4U100N-120-Figure 3.10: k8/k ratios of the 70% 5CB/EBBA mixture against those of the 56.5%1132/EBBA mixture, where k3 and k are the model parameters for the solute and forthe TCB in the same sample tube.11 1.2 1.4k/kof 56.57 1132/EBBAChapter 3. Orientation of C2v and D2h symmetry solutes in zero efg mixtures 43stems from the fact the model fits some solutes better than the other solutes. However,the agreement between the ratios k/k in both mixtures is within 7% for all solutes.This suggests that for a given k the model parameters k8 are transferable from one ofthese mixtures to the other. Therefore, the short-range potentials of these two zero efgmixtures are similiar for a given k.3.4 SummaryFor a given TCB dipolar coupling, the order parameters of C2v and D2h symmetrysolutes are transferable from one zero efg mixture to another. The short-range potentialrepresented by a one-parameter model in eq. (3.34) is quite sufficient to calculate theorder parameters S, which are in good agreement with the experimental order parameters. The one-parameter model k3 values are used to compare the short-range potentialsof the solutes in the two zero efg mixtures. For a given k, the model parameter of TCB,the ratios k5/k in one zero efg mixture are in good agreement with those in the othermixture. This suggests that the form of the short-range potentials experienced by C2and D2h symmetry solutes in the two zero efg mixtures is the same.Chapter 4Temperature dependence study of small solutes in the zero efg mixtures4.1 IntroductionThe temperature dependence study of small solutes in the zero efg mixtures is importantto understand the temperature effect on the short-range interactions. The study is alsoconvenient to compare the short-range potentials in the zero efg mixtures. In this chapter,the temperature dependence of a few small solutes, having different shape and symmetry,is studied in the zero efg mixtures 55% 1132/EBBA and 70% 5CB/EBBA. The one-parameter model (eqn. 1.28) is used to describe the short-range potential. The studyalso focuses on biaxial order parameter, S— S, and on how the model fits to theexperimental order parameters, with the variation of temperature. The solutes studiedare as follows: henzene (BENZ) and 2-butyne(2-BUTY) with C3 and higher symmetry,orthodichloro benzene (ODCB) and metadichloro berizene (MDCB) with C2v symmetryand 1,3- bromochloro benzene (1,3-BrCl) with Cs symmetry.Section 4.2 discusses the temperature dependence of trichloro benzene (TCB) in threezero efg mixtures and in a non-zero efg mixture. Section 4.3.1 briefly describes the geometries of BENZ and 2-BUTY needed to determine the order parameter, S. Similarly,section 4.3.2 briefly mentions the geometries of ODCB, MDCB and 1,3-BrC1. Section4.4 compares the short-range potentials in the zero efg mixtures. Finally, section 4.5discusses the temperature dependence of S-S and S.44Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 45—0.3 I I I I I I I I I I I IIB—0.25 - A ——0.2I_-1A-.0 15!A=55 1132/EBBA—c=70% 5CB/EBBAA=565 1132/EBBA1= Pure 5CB—01I I I I I I I I I I I1 0.95 0.9 0.85TrFigure 4.11: The order parameter S of TCB vs. reduced temp.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 464.2 Temperature dependence study of trichioro benzeneThis section describes how the TCB dipolar coupling in zero efg mixtures can be used asan internal measure of reduced temperature, Tr. To show this, the temperature dependence of TCB was studied in three zero efg mixtures 70% 5CB/EBBA, 56.5% 1132/EBBAand 55% 1132/EBBA and for the pure liquid crystal 5CB. The order parameters ofTCB are plotted against Tr, where Tr is defined as Tr = T/TNI, for the three zero efgmixtures 70% 5CB/EBBA, 56.5% 1132/EBBA and 55% 1132/EBBA and for the pureliquid crystal 5CB. In figure 4.11 it is found that for a given Tr the order parameter Sof TCB for the three zero efg mixtures are equal within experimental error. Therefore,a given DHH(TCB), which is directly proportional to S of TCB, can be used as aninternal measure of Tr in these zero efg mixtures. However, as demonstrated in Figure4.11, this argument is not valid for non-zero efg mixtures such as the pure liquid crystal5CB. Therefore, DHH(TCB) cannot be used as a measure of Tr in non-zero efg mixtures.4.3 Structure4.3.1 03 and higher symmetry solutesAn aromatic planar solute, BENZ, and a non-aromatic molecule 2-BUTY are studiedas a function of temperature. The solute BENZ was chosen for its simple geometricalstructure, and 2-BUTY was chosen because it is a molecule having a different shape fromthe other solutes studied. Due to the higher symmetry of these two molecules, they haveonly one independent order parameter, S, in the nematic phase. The order parameter,can be related to the dipolar couplings by the equation (1.5). The moleculefixed axes x, y and z are defined in Figure 4.12, and D’s were determined using theprogramme LEQUOR [55] and are reported in Appendix B.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 47The programme SHAPE [58] was used to obtain the order parameter, S, fromthe dipolar couplings, D3. The geometry of BENZ and 2-BUTY were taken from ref.[57, 60] respectively, where the geometry of BENZ is a regular hexagon. In 2-BUTY, thetwo methyl groups are separated far enough that the methyl groups undergo free rotationabout the C-C bond [61]. For simplicity, we assume that the 2-BUTY undergoes 18-stepsduring its free rotation (18-site jump). Although the angle a (see Fig. 4.12) determinedby electron diffraction study was found to be 110.9° [60], the RMS error in our studywas the lowest when a was fixed to 109.90. Therefore, we used the value of 109.90 for ato calculate the order parameters. The order parameters S of BENZ and 2-BUTY aretabulated in Appendix C as a function of temperature.4.3.2 C2v and Cs symmetry solutesThe C2v symmetry solutes ODCB and MDCB dissolved in liquid crystals give information about two independent order parameters S and S-S. The solutes ODCBand MDCB have only 4 spin nuclei, therefore, the spectra are not complicated. Thedipolar couplings of ODCB and MDCB in the zero efg mixtures can be related tothe geometry and orientation by the equation (1.5). The molecule-fixed axes x, y and zare defined in Figure 4.12 such that the S is major order parameter. The S-S isthe biaxial order parameter of these two solutes in the nematic phase.The geometries of ODCB and MDCB were taken from ref. [57]. The SHAPE programme was used to obtain the order parameters S and S-S, from the dipolar couplings D3. The order parameters S and S-S as a function of temperature aretabulated in Appendix C.A Cs symmetry solute in a nematic phase gives information about the order parameters, S, S-S and S. The solute 1,3-BrC1 is chosen in this study, and the geometryof 1,3-BrC1 differs from that of MDCB by replacing one of the Cl atoms by a Br atom.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 48.1IxlI4)4)N4)x5III(-)IC)x±1c c,Ia)a)N4)NCs24)N—C)4)0Figure 4.12: The coordinate system and atom numbering of the solute molecules studied.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 49The dipolar couplings of 1,3-BrC1 are related to its geometry and orientation byequation (1.5). The molecule-fixed axes x, y and z are defined in Figure 4.12 . Thegeometry of 1,3-BrC1 is taken from ref [57]. The order parameters S2, S-S and Sas a function of temperature are tabulated in Appendix C.4.4 Comparison of short-range interactionsAll samples contain a little TCB, and the dipolar coupling of TCB, DHH(TCB), hasbeen measured from the same spectrum as the solute. In this section, the short-rangepotentials in the zero efg mixtures are compared at the same TCB splitting.The order parameters S are plotted against DHH(TCB) in Figures 4.13 - 4.17. Theorder parameters S in 70% 5CB/EBBA agree well with those of the 55% 1132/EBBA forall solutes. The agreement between biaxial order parameters, S-S, is close in mixtures55% 1132/EBBA and 70% 5CB/EBBA, but it is not as good as that for S. Althoughthe magnitude of is very small, the agreement between the S in mixtures 55%1132/EBBA and 70% 5CB/EBBA is good. It is interesting to obtain the same magnitudeof order parameters for a solute in the two different zero efg mixtures. What does thisresult tell about the zero efg mixtures? To further understand this, we shall relatethe order parameters to the intermolecular potential and analyse the results in termsof intermolecular potentials of the mixtures. The intermolecular potential is assumedto have only contributions from the short-range potential at all temperatures studied(shall be discussed in Chapter 5). Therefore, to understand the transferability of theorder parameters S, we relate the order parameters to the short-range potential usingequation (A.51). The short-range potential is described by the one-parameter modelgiven by equation (1.28).A least-squares fit is done on the experimental order parameters for each molecule atChapter 4. Temperature dependence study of small solutes in the zero efg mixtures 50I IBA—0.1aNNBENZ AA55%1 132/EBBA•=7075CB/EBBA—02 I I I100 120 140 160DHH(TCB)/HzFigure 4.13: Order parameters vs. DHH(TCB) for BENZENE.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 510.22 I‘- 2-BUTYNEA=55%1132/EBBA A0.2.=7O%5CB/EBBA AA0.18A0.16KA0.14 4?A012—01 I I I100 120 140 160 180DHH(TCB)/HzFigure 4.14: Order parameters vs. DHH(TCB) for 2-BUTYNE.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 520.1 Isyy—sx,cIAAA0 ODCBL=55%1 132/EBBAn =7O%5CB/EBBAFilled symb.=expt.—0. 1 dotted symb.=Caleulatad-AC,—0.2 A —AI I I120 140 160DHH(TCB)/HzFigure 4.15: Order parameters vs. DHH(TCB) for ODCB.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 530.2 I I ISS0.1 AMDCBL=55%1132/EBBACl) D=70%5CB/EBBAFilled symb.=expt.—0.1 dotted symb.=CalcdlÀ.02 S 11.1IIZZI I a100 120 140 160 180DHH(TCB)/HzFigure 4.16: Order parameters vs. DHH(TCB) for MDCB.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 540.2syy—sxx A AA-0.1-1,3—BrC10 A A A AFilled symb.=expt.—0.1 dotted symb.=Calcd_.:,=55%1132/EBBA=70%5CB/EBBA—0.2 AIA A A140 160 180DHH(TCB)/HzFigure 4.17: Order parameters vs. DHH(TCB) for 1,3- Bromochioro benzene.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 55each temperature to obtain the best fit model parameter k3. The k values are reported inAppendix C. The best fit model parameter was then used to obtain the recalculated orderparameters for all solutes. In Figures. 4.13- 4.17, the recalculated order parametersare plotted (open triangles and squares) to see the agreement with the experimental orderparameters. The agreement between the experimental and recalculated order parameterS is very good. Although the recalculated S-S values are close to the experimentalvalues, the agreement is not as good as for S. However, the relative errors betweenthe experimental and calculated order parameters are generally less than 10% for allsolutes. Therefore, the short-range potential, Usr, can well be represented by the modelparameter k3. We shall use the model parameter k to explain the transferability of theorder parameters in the two zero efg mixtures 55% 1132/EBBA and 70% 5CB/EBBA.Based on equations. (A.51) and eq. (1.28), we note that the order parameter Sdepends on k5/T. Thus, S can be written as:= f(k3/T) (4.35)To examine the dependence of the quantity k/T on liquid crystal environment, k/T isplotted against DHH(TCB) for both liquid crystal mixtures in Figures. 4.18- 4.22 for allsolutes. The plots show that there is very good agreement between the k3/T values for55% 1132/EBBA and 70% 5CB/EBBA. Based on this agreement, we write the followingrelationship(k3/T)55 = (k/T)79 (4.36)for a given DHH(TCB), where the subscripts 55 and 70 stand for the liquid crystalmixtures 55% 1132/EBBA and 70% 5CB/EBBA. Sustituting eq. (4.36) into eq. (1.28),we get the relationship(Usr/T)55 = (U3/T)70 (4.37)Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 56Table 4.5: TNI values for the solute-liquid crystal mixtures.TNI valuesSolute 55% 1132/EBBA 70% 5CB/EBBAortho dichlorobenzene 333K 318Kmeta dichlorobenzene 334K 316K1,3-bromochlorobenzene 339K 320Kbenzene 329K 314K2-butyne 333K 313KThe reduced temperatures, Tr, are calculated using the relationship Tr = T/TNI.In order to simplify the notation, new quantities reduced short-range potential, U,and reduced model parameter, k, are defined by U. = Usr/T and k = k8/T. Equations(4.36) and (4.37) suggest that at a given DHH(TCB) the reduced short-range potential,U, and the reduced model parameter, k, are transferable from one of these two mixturesto the other. This explains why the order parameters, S, are transferable from onezero efg mixture to another.We further investigate the temperature dependence of the short-range potentials inthe zero efg mixtures. In figure 4.23, we plot k3/T against Tr for all the solutes. Thereduced temperatures, Tr, are calculated using the relationship Tr = T/TNI, where thenematic - isotropic transition temperatures, TNI, for all sample tubes are tabulated inTable 4.5. The lowest temperature at which the isotropic peak appears is taken to beTNI. The figure shows that the magnitude of the reduced model parameters for all thearomatic solutes are in good agreement within experimental error. The magnitude of thek for the non-aromatic molecule 2-butyne, however, is higher than those of the aromaticsolutes. It should also be noted that the reduced model parameters for a particular solutein the two zero efg mixtures are in good agreement for a given Tr. We shall further discussthe temperature dependence study of the solutes in the Chapter 7.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 570.25 I ‘BENZ•=55% 1132/EBBA0=70% 5CB/EBBA0.2- SHC200.150- 0S001 I I I100 120 140 160 180DHH(TCB)Figure 4.18: Reduced model parameter, k8/T vs. DHH(TCB) for BENZENE.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 580.35I I I2—BUTY•=55% 1132/EBBA0=70% 5CB/EBBA0.3 ...O.25 0.0.20I I I120 140 160 180DHH(TCB)Figure 4.19: Reduced model parameter, k/T vs. DHH(TCB) for 2-BUTYNE.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 59I ‘ I I1132/EBBA ODCB- =7O 5CB/EBBA0.2—H- V‘pp0.1 —I I I I100 120 140 160 180DHH(TCB)Figure 4.20: Reduced model parameter, k3/T vs. DHH(TCB) for ODCB.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 60I I I I•=55% 1132/EBBA MDCBK=7O% 5CB/EBBA0.2—Os0•0•0.1I I I I80 100 120 140 160 180 200DHH(TCB)Figure 4.21: Reduced model parameter, k3/T vs. DHH(TCB) for MDCB.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 610.25I I1,3—BrC1• =55% 1132/EBBA0=70% 5CB/EBBA0.2—000.15I 1o I isoDHH(TCB)Figure 4.22: Reduced model parameter, k3/T vs. DHH(TCB) for 1,3- Bromochiorobenzene.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 620.40.32H0.240.16000=ODCB=MDCB=BrC1= BENZ=BUTY....Tr0.9 1Figure 4.23: Reduced model parameter, k3/T vs. Tr for all the solutes.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 634.5 Biaxial order parameterThe biaxial order parameter, S-S, expresses the asymmetry in the order of the molecular long axis. The temperature dependencies of S-S and have been analysed indetail in the studies [62, 63]. In this thesis, S-S has been measured for the solutesODCB, MDCB and 1,3-BrC1 in the zero efg mixtures. The S-S dependence onshall be compared with that predicted by the model.In Figures. 4.24- 4.26, the variation of S-S with S22 is shown for the solutesODCB, MDCB and 1,3-BrCI in the solvents 55% 1132/EBBA and 70% 5CB/EBBA.The dotted symbols on the figures represent the calculated S-S dependence on S22.In the following, we shall refer to the experimental S-S vs. 522 plots as “experimentalprofile” and those of calculated S-S vs. S22 as “calculated profile”. Figures. 4.24-4.26 show that the “experimental profile” has a weak solvent dependence.The difference between the “experimental proflle”s of the two mixtures is not consistent from one solute to another. The difference is the smallest for the solute MDCB andthe largest for the ODCB. Further, for the solute ODCB the magnitude of the “experimental profile” of 70% 5CB/EBBA is larger than that of 55% 1132/EBBA, whereas itis opposite for the solutes MDCB and l,3-BrCl. If the discrepancies between the “experimental proflle”s of the two mixtllres were systematic for all three solutes, then itcould be argued that there is an additional contribution to the intermolecular potentialin one zero efg mixture, whereas it is absent in the other mixture. Since discrepanciesbetween the “experimental proflle”s for the solutes appear to be random, it is not clearwhy there is a significant difference between the ‘experimental proflle”s of the mixtures55% 1132/EBBA and 70% 5CB/EBBA.The “calculated proflle”s are compared with those of the “experimental profile”s. Itis found that the “calculated proflle”s are always underestimated for all three solutes.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 64AA0.08 AACfAAODCB A=55Z1132/EBBA0.04—s =7o%5c]3/EBBAFilled symb.=expt.dotted symb.=Calcd—0.2szzFigure 4.24: S-S9 dependence on S for the solute ODCB.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 650.2 I I IMDCBL=551 132/EBBA-E:J=70%5CB/EBBA0.16 A A Filled symb.=expLA dotted symb.=CalccA0.12 1AA0.08I I I I—0.24 —0.16szzFigure 4.25: S-S dependence on S for the solute MDCB.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 660.2 IAAAAAI 0.16—Acn1,3—BrC1 AI.- A =55%1132/EBBAD =70%5CB/EBBAFilled symb.=expt.dotted symb.=Calcd.I —0.22 I —0.2 —0.18szzFigure 4.26: S,-S dependence on S for the solute 1,3- Bromochioro benzene.Chapter 4. Temperature dependence study of small solutes in the zero efg mixtures 67This underestimation could be due to two possiblities. First, the model used for theshort-range interaction does not fit the biaxial order parameter, S-S, as well as itdoes to S. This observation was also noted in Figures. 4.13 - 4.17.The other possiblity is that if there still exists a residual electric field gradient presentat temperatures other than 301K for 55% 1132/EBBA and 316K for 70% 5CB/EBBA,then the residual electric field gradient— electric quadrupole moment interaction contributes to the potential. If this is the case, there should be a much better agreementbetween the experimental and calculated order parameters at temperature 301K for 55%1132/EBBA and 316K for 70% 5CB/EBBA than that at other temperatures. However,the quality of agreement between the “experimental profile” and the “calculated profile”at all temperatures is more or less the same. This suggests that the same type mechanismis responsible for the intermolecular potential in the zero efg mixtures at all temperaturesstudied and that the temperature effect on the electric field gradient is negligibly smallin the zero efg mixtures. Therefore, it must be concluded that the discrepancies betweenthe “experimental profile” and the “calculated profile” is mainly due to the fact that themodel does not fit the biaxial order parameter, S-S, very well. The temperature effecton the residual electric field gradient shall be investigated further in the next chapter.4.6 SummaryThe TCB dipolar coupling is a good measure of reduced temperature, Tr, in zero efgmixtures. The order parameters, S, are in good agreement in the two zero efg mixturesfor a given TCB splitting. The origin of this transferability of the order parametersbetween the two mixtures comes from the short-range potential. It has been found thatreduced short-range potentials in the two zero efg mixtures 55% 1132/EBBA and 70%5CB/EBBA are the same. The short-range potential is quite sufficient to describe theChapter 4. Temperature dependence study of small solutes in the zero efg mixtures 68orientation of the solutes having different shape and symmetry in the zero efg mixtures55% 1132/EBBA and 70% 5CB/EBBA at all temperatures studied.Chapter 5A 211 NMR study of 5CB — d19 in zero electric field gradient nematic mixtures5.1 IntroductionThe nature of intermolecular forces among constituent liquid crystal moledilles is a fascinating problem. As a starting point, it is convenient to use small solutes as probesto understand the intermolecular forces. In Chapter 3, small C2v symmetry solutes asprobes were studied in the zero efg mixtures 56.5% 1132/EBBA and 70% 5CB/EBBAat certain temperatures. As an extension to this study, the temperature dependence ofdifferent-shape-solutes were undertaken in the zero efg mixtures 55% 1132/EBBA and70% 5CB/EBBA in Chapter 4. To further extend the understanding of intermolecularforces among liquid crystal molecules, it is appropriate to study a liquid crystal as aprobe molecule.In this chapter, the molecule 5CB— d19 (Figure 5.27) is studied in the three zero efgmixtures 55% 1132/EBBA, 56.5% 1132/EBBA and 70% 5CB/EBBA. 5CB is interestingbecause it exhibits a nematic phase, and is in fact one of the components of one of themixtures used. The spectra of 5CB— d19 at the same temperature are not the same inthe different mixtures. To understand the differences, a model is used for the short-rangeinteractions to calculate the spectrum. Two different models, CZ and CI, are used forthe calculation. The reason to use two different models is to confirm the experimentalresults independent of model. The calculations are also repeated for different Ejg valuesto choose an appropriate trans-gauche energy difference, E9, value.69Chapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematic mixtures7OSection 5.2 briefly reviews the theory needed to calculate the quadrupolar splittingsof 5CB— d19 in the zero efg mixtures. Section 5.3 describes the spectral analysis of the5CB— d19 spectra. Section 5.4.1 discusses the temperature effect on residual electricfield gradient in the mixtures 55% 1132/EBBA and 56.5% 1132/EBBA. Section 5.4.2mainly deals with the geometry of the 5CB— d19 molecule. Section 5.4.3 describes thecalculation of quadrupolar splittings using the CZ and CI models at each individualtemperature (Individual Fit). In these calculations, the model parameters are obtained ateach temperature. Section 5.4.4 discusses the temperature dependence of the individualfit model parameters. Section 5.4.5 describes how the parameters Etg and the ratios ofthe model parameters, and ‘, can be calculated for a particular mixture in a single fit,where the quadrupolar splittings of all temperatures are included.5.2 Review of TheoryThe solute 5CB — d19 has a rigid ring part and a flexible chain part. According to theRIS approximation [64], each C-C bond has three discrete rotational states: trans, t, andtwo gauche, g+ and g—. Thus, there are 27 conformer states for 5CB — d19. The totalenergy, UT,1(Q), of conformer i in orientation is a sum of two terms [65]:UT,() = + U(1) (5.38)which is assumed to be independent of orientation [66], describes the internal energyof conformer i. U() is an orientation dependent part of the interaction potential. Theinternal energy, is given by:Uint,i = ngEtg + 7gg_Egg_ (5.39)where E9 is the trans-gauche energy difference, n9 is the number of gauche rotations andg+g— is the number of gauche+ followed by gauche— rotations in the conformer. TheChapter 5. A 211 NMR study of 5CB — d19 in zero electric field gradient nematic mixtures’71,. I —III —DD D‘IC3’%C..’0’DDDzFigure 5.27: The coordinate system and atom numbering scheme of the 5CB — d19molecule.© ya;Chapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematic mixtures72energy Eg+g._ is the additional energy required to inhibit successive gauche+ gauche—bonds which include large steric interactions. Egg_ is taken as 1.5 kcal/mol [52, 64].The probability of conformer i, p, is given by:/ \ r / (0)— exp kT ) j exp kT— —u,,_______>j exp( kT ) f exp( )d1where the integration is over all orientations ft For a nematic liquid crystal with thedirector aligned parallel to the magnetic field direction the Quadrupolar splitting of adeuteron in conformer , VQ,, is given by:l”Q,i = (5.41)where eQ is the quadrupole moment of the 2H nucleus, and qp,j are the a3 components of the order matrix and the electric field gradient of the deuteron nucleus in aconformer coordinate frame. The components of the order matrix for conformer i,are given by:— f(3 cos cos —6,3)exp(—Uj(f)/kT)d1 (5 42)— 2fexp(—U(1)/kT)dwhere cos cos are the direction cosines of the c, /3 axes with respect to the Z,director, axis. The calculated quadrupolar splitting, AL’Q, is then:AVQ—VQ,iPi (5.43)The principal axes, a, b, c, of the intramolecular electric field gradient tensor of thering deuterons have axis b along the C-D bond and axis a in the plane of the ring. Thequadrupolar splitting of conformer i, VQ,j, is then written in terms of the quadrupolar coupling constant, e2Qg and the asymmetry parameter,= (qaa — qcc)/qbb. Thequadrupolar coupling constant for ring deuterons is 185 KHz, and i is 0.04 [67]. For theflexible chain part, the quadrupolar coupling constant is taken as 168 KHz and is takenas zero [68].Chapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematicmixtures73Table 5.6: Quadrupolar splittings (in kllz) of 5CB-d19 in 55% 1132/EBBA.Temp./K Lv1‘2 Lv3 iv4 Lv5 Ring A Ring B251.4 77.782 63.768 65.233 49.559 35.790 21.728 17.577256.1 77.050 62.255 63.719 47.899 34.569 21.435 17.430261.1 75.878 60.887 62.597 46.142 33.446 21.240 17.236265.3 75.048 59.569 61.327 44.823 32.568 20.946 17.040270.7 74.267 58.251 59.960 43.066 31.396 20.946 16.893275.8 73.974 57.177 58.739 41.747 30.663 20.702 16.699281.5 72.314 55.028 56.688 39.745 29.199 20.263 16.161285.3 70.898 53.319 55.077 38.329 28.173 19.725 15.721292.1 68.309 50.438 52.489 35.936 26.366 18.896 14.941296.4 66.796 48.730 50.634 34.520 25.292 18.310 14.501302.1 64.697 46.337 48.339 32.616 23.827 17.577 13.818307.1 62.743 44.189 46.239 30.858 22.606 16.698 13.232312.7 59.911 41.308 43.456 28.612 20.995 15.770 12.352317.0 57.079 38.768 41.014 26.757 19.579 14.843 11.572323.1 53.368 35.448 37.646 24.218 17.724 13.524 10.497327.0 49.316 32.079 34.276 21.776 15.917 12.255 9.325332.6 42.333 26.806 28.661 18.017 13.182 10.156 7.567334.6 38.622 24.315 25.927 16.307 11.962 9.130 6.7865.3 Results5.3.1 GeneralFigure 5.28 shows the spectra of 5CB — d19 in 55 % 1132/EBBA at 307.1 K and in70% 5CB/EBBA at 306.8 K. The quadrupolar lines are broadened due to the dipoledipole coupling between deuterons. Quadrupolar splittings were measured in a mannerconsistent with line shape simulations. Measurements were carried out at temperaturesranging from 250K to the isotropic temperature on the mixtures 55% 1132/EBBA, 70%5CB/EBBA and 56.5% 1132/EBBA. Measured line positions are tabulated in Tables 5.6to 5.8. Spectral line assignments are discussed in detail in section 5.3.2.As the temperature approaches TNI, the spectra begin to appear as a superpositionChapter 5. A 2H NMR study of5CB — d19 in zero electric field gradient nematic mixtures7455% 1132/EBBAL_—50I50Frequency! KHzFigure 5.28: Experimental2H-NMR spectra of 5CB — d19 dissolved in the zero efg mixtures 55% 1132/EBBA, at 307.1K, and 70% 5CB/EBBA at 306.8K.70% 5CB/EBBAI I I—25 0 25Chapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematicmixtures75Table 5.7: Quadrupolar splittings (in kHz) of 5CB-d19 in 70% 5CB/EBBA.Temp./K Lti1 L\v2 Lzi3 Lv4 Lv5 Ring A Ring B251.9 72.509 57.812 59.569 44.140 32.031 19.725 15.966255.9 70.702 55.663 57.958 42.626 30.956 19.189 15.526261.2 69.579 53.564 55.712 40.233 29.345 18.652 14.940265.3 68.163 52.148 54.101 38.720 28.271 18.212 14.550271.1 65.868 49.511 51.513 36.230 26.513 17.528 13.963276.1 64.550 47.704 49.755 34.569 25.438 17.040 13.524281.9 62.108 44.921 46.972 32.177 23.827 16.258 12.841285.9 60.399 43.017 45.116 30.517 22.704 15.721 12.352292.1 57.861 40.331 42.626 28.319 21.044 15.038 11.766296.6 56.298 38.671 40.819 26.854 20.018 14.452 11.425302.0 53.906 36.620 38.573 24.999 18.700 13.866 10.937306.8 51.563 34.570 36.524 23.438 17.480 13.232 10.400308.8 49.462 32.909 34.813 22.118 16.551 12.597 9.764310.8 46.728 30.859 32.714 20.702 15.477 11.816 9.130312.7 42.968 28.026 29.736 18.700 14.013 10.595 8.153313.7 40.624 26.464 28.075 17.578 13.134 10.008 7.616314.7 37.646 24.608 25.976 16.210 12.059 9.228 6.982315.7 34.130 21.678 22.704 14.404 10.839 8.104 6.201Chapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematic mixtures76Table 5.8: Quadrupolar splittings (in kHz) of 5CB-d19 in 56.5% 1132/EBBA.Temp./K LzJ1 Av2 Lv3 Lv4 Lv5 Ring A Ring B261.4 75.927 61.156 62.987 46.569 33.691 21.239 17.211266.1 75.255 59.997 61.827 45.349 32.714 20.995 16.966271.7 74.340 58.287 60.180 43.334 31.616 20.812 16.783276.0 73.791 57.311 59.143 42.236 30.821 20.751 16.722281.9 72.630 55.480 57.067 40.160 29.479 20.201 16.234286.1 71.044 53.649 55.541 38.695 28.441 19.713 15.929292.5 69.029 50.963 53.222 36.620 26.854 19.042 15.075296.7 67.321 49.133 51.390 35.095 25.634 18.432 14.587302.0 65.123 46.813 48.889 33.080 24.169 17.638 13.915307.1 63.415 44.615 46.752 31.372 22.887 16.844 13.304312.6 60.851 41.870 44.249 29.235 21.362 15.990 12.511317.1 58.226 39.489 41.869 27.403 20.018 15.075 11.718323.1 54.686 36.376 38.513 24.963 18.249 13.854 10.742327.6 50.963 33.263 35.522 22.704 16.600 12.633 9.764328.6 50.109 32.653 34.972 22.277 16.234 12.389 9.459330.1 48.095 31.127 33.202 21.117 15.360 11.779 8.971330.6 47.057 30.089 32.226 20.446 14.892 11.413 8.666332.6 44.799 28.502 30.517 19.286 14.037 10.802 8.056333.6 43.578 27.648 29.601 18.676 13.610 10.436 7.812334.6 42.296 26.732 28.747 18.065 13.183 10.070 7.507335.1 40.526 25.573 27.465 17.272 12.572 9.642 7.140336.1 38.207 23.864 25.817 16.112 11.718 8.971 6.591337.1 36.193 22.460 23.925 15.075 11.046 8.300 6.163338.1 33.019 20.263 21.422 13.732 10.009 7.446 5.553Chapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematicmixtures77of nematic and isotropic peaks. The lowest temperature at which the isotropic peakappears is taken to be TNI. The TNI of 55% 1132/EBBA and 56.5% 1132/EBBA are337K and 339K respectively, and the TNI of 70% 5CB/EBBA is 316K. These numbersdiffer slightly from those of the microscopic study (Chapter 2) because the samples usedfor NMR contain deuteriated materials.The measured quadrupolar splittings at position 1, Lv1, are plotted against temperature in Figure 5.29. The curves corresponding to 55% 1132/EBBA and 56.5%1132/EBBA are similar. However, the curve corresponding to the mixture 70% 5CB/EBBAappears to have a break at 307K(see Figure 5.29). Below this temperature the quadrupolar splitting changes linearly with temperature. However, the microscope study indicatesthat there is no phase transition taking place near 307K in this mixture. Thus, the liquidcrystal mixtures are nematic for all points given in Figure 5.29.5.3.2 Analysis of 5CB-d19 spectraThe2H-NMR spectrum of 5CB-d19 in the nematic phase has 7 pairs of quadrupolarlines, each pair corresponding to its C-D bond site. The assignment of each pair to itscorresponding site is described below.As described in section 1.2.2, the quadrupolar splitting, LI/Q, depends on the orderparameter, SCD, of the C-D bond. In other words, the quadrupolar splitting depends onthe angle between the C-D bond and the director axis, Z. In order to relate the quadrupolar splitting to the geometrical features of 5CB-d19 molecule, it is convenient to describethe quadrupolar Hamiltonian in terms of an intermediate frame. The intermediate frameis usually chosen such that the long molecular axis is one of the axis in the intermediateframe. For 5CB-d9 molecule, the para axis, the axis connecting two phenyl group, ischosen as one of the axis in the intermediate frame.Chapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematic mixtures7880 I I I I I I I—I..•7QB.60- II<50 II40—= 55% 1132*= 56.5% 1132-1= 70% 5CB30 I I I I260 280 300 320 340Temperature/KFigure 5.29: The quadrupolar splitting Lv1 versus temperature for the mixtures 55%1132/EBBA, 70% 5CB/EBBA and 56.5% 1132/EBBA.Chapter 5. A 2H NMR study of 5CB— d19 in zero electric field gradient nematic mixtures79To a good approximation, the quadrupolar splitting, /1JQ, can be described as3e2qQ (3cos2O’— 1) (3cos28”— 1)L1/Q= 4h < 2 >< 2 > (5.44)(3cos20fl_1)where the term < 2 > is the transformation from the principal axis system ofthe C-D bond to the intermediate frame of the molecule. The term < (3cos28_1) > is thetransformation from the intermediate frame to the lab-fixed axis system of the molecule.Since 0’ is the angle between the para axis of 5CB-d19 molecule and the lab-fixed axis,Z, the term < (3c0s7_1) > is the same for all 7 different sites of the C-D bond. On theother hand, the term < (3co8”—1) > varies from one C-D bond to another due to thegeometrical features.We shall now correlate the assignment of the quadrupolar splitting to its C-D bondsite based on the angle 0”. First, we look at the quadrupolar splitting corresponding to C1position (Figure 5.27). Since the bond attaching C1 with aromatic ring is fixed, the angle,,, .. (3cos 6 —1)O is very close to 109 . This causes the term < 2 > to have a large magnitude.As a result, the quadrupolar splitting at C1 position has the largest magnitude.Next, we assign the quadrupolar splitting due to the methyl group. The methylgroup of the alkyl chain undergoes a fast free rotation along the C4-C5 bond. Due tothis extra motion, the quadrupolar splitting needs to be described in two intermediateframes. As a result, the expression for the quadrupolar splitting (eq. 5.44) has an extraterm < (3cos2I31) >, , where 3 is the angle between C4-C5 bond and C-D bond in theo (3cos23—1)methyl group. The angle 3 takes a value of 70.5 . Consequently, the term < 2 >reduces the magnitude of the quadrupolar splitting of the methyl group. Therefore, thequadrupolar splitting of the methyl group is the narrowest among chain deuterons.The rotation along the C-C bonds of C1-C2,02-C3 and C3-C4 leads to 27 conformational states. This extra motion causes an additional motional narrowing. As a result, thequadrupolar splittings at the C2, C3 and C4 positions are smaller in magnitude than thatChapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematic mixtures8Oat 01 position, but larger than at 05 position. In general, the magnitude of quadrupolar splittings has the tendency to decrease towards the end of the chain since the orderdecreases from rigid ring part to the tail chain part. Due to the odd-even effect [69],however, the quadrupolar splitting at 03 position has a larger magnitude than that at02 and 04 positions. The spectral line assignments for the chain deuterons agree exactlywith the previous work [70]. The assignment of the quadrupolar lines corresponding tothe ring deuterons is described in the next paragraph.In order to assign the quadrapolar lines corresponding to Ring A and Ring B (seeFigure 5.27), the experimental quadrupolar splittings for the flexible chain were assignedfirst for the room temperature spectrum. These assigned experimental quadrupolar splittings were fitted to calculate the quadrupolar splittings at all 7 different sites, using theCZ model for the short-range potential. (calculation shall be described in sections 5.4.2and 5.4.3). These calculated quadrupolar splittings for ring deuterons are matched withthe experimental ones to assign the experimental quadrupolar lines of Ring A and RingB.The assignment of ring deuterons shows that the two inner pairs of quadrupolarlines correspond to the aromatic deuterons. This can be understood in terms of the 0”angle. The angle 0” between aromatic C-D bond and the molecular para axis is close to600. Therefore, < > term becomes very small. As a result, the quadrupolarsplittings of aromatic deuterons are small.5.4 Discussion5.4.1 GeneralThe purpose of this section is to examine several zero efg mixtures. One way of emphasizing small differences among the zero efg mixtures is to plot ratios of the quadrupolarChapter 5. A 2H NMR study of 5GB — d19 in zero electric field gradient nematic mixtures8lsplittings, such as /.vs/Avi, against LS1. These plots shall be referred to as ratio plots.Ratio plots for 5CB — d19 were previously used to illustrate differences among the liquidcrystals 1132, EBBA, 5GB and 55% 1132/EBBA [52]. In that study, the differences wereascribed to the presence of a non-zero electric field gradient in the various liquid crystals.A plot of i.’5/v1 against is shown in Figure 5.30. Intuitively, one might expect that ratio plots for all zero efg mixtures would be similar. However, the differencesbetween 55% 1132/EBBA and 70% 5CB/EBBA are large and comparable to those between the liquid crystals 1132 and EBBA in ref [52]. On the other hand, the ratio plots of5CB — d19 in 55% 1132/EBBA and in 56.5% 1132/EBBA are superimposable. This latter fact allows us to evaluate the effect of a small residual electric field gradient presentin the mixtures 55% 1132/EBBA and 56.5% 1132/EBBA at temperatures other than301.4K and 322K where the electric field gradient is zero.In such zero efg mixtures, the average electric field gradient measured using D2changes sign and magnitude with changing temperature. At any given temperature,the average electric field gradient in the 55% 1132/EBBA mixture differs from that inthe 56.5% 1132/EBBA mixture. If these small efg’s made a significant contribution to theanisotropic orientational potential, the 2H spectra of 5GB — d19 should differ between thetwo mixtures. However, the ratio plots in Figure 5.30 show that the quadrupolar splittingratios zz’s/Lvi are identical for the two mixtures over the temperature range 250K-337K.This result, together with the equivalence of the ZXv1 for the two 1132/EBBA mixturesin Figure 5.29, shows that the small electric field gradients present in these mixtureshave a negligible effect on the spectra. The quadrupole moment - electric field gradientmechanism can be neglected as an important orientational mechanism in these mixtures.Thus, when we refer to a zero efg mixture, we include the entire nematic range of amixture that has a precisely zero efg at one specific temperature. Note that van der Estet al. [71] have reported a quantitative temperature dependence study of the efg in theChapter 5. A 211 NMR study of 5CB — d19 in zero electric field gradient nematicmixtures8255% 1132/EBBA mixture, and found that the magnitude of the measured electric fieldgradient does not change much with temperature.We shall also assume that the contribution of the electric field gradient-electric quadrupolemoment interaction to UT,(f) is negligible throughout the nematic range of the zero efgmixture 70% 5CB/EBBA. Thus the differences in Figure 5.30 between 70% 5CB/EBBAand the other zero efg mixtures do not arise from the electric field gradient- molecularquadrupole moment mechanism. Do these differences imply that the details of the short-range potential are liquid crystal dependent? We shall attempt to answer this questionbelow.To proceed, it is useful to introduce a model for the short-range potential, Usr,j(Q). Itseems sensible to choose a model that provides a successful fit to the orientational orderparameters measured for a range of rigid solutes in a zero efg nematic solvent [39, 40, 41].Because we wish to draw meaningful conclusions from our work, we shall investigate twodifferent models, CZ model and CI model, for the short-range potential in an attemptto come up with a comparison among mixtures that is independent, as far as possible,of the model chosen. Since no significant differences between the zero efg mixtures55% 1.132/EBBA and 56.5% 1132/EBBA are observed, only the zero efg mixtures 55%1132/EBBA and 70% 5CB/EBBA shall be compared in the following sections.5.4.2 RIS parameter and molecular geometryOne of the complexities of the 5CB — d19 molecule is the presence of the flexible hydrocarbon chain which introduces the additional parameter, E9, the trans-gauche energy difference. Since Etg is an intramolecular property, it should be independent of temperatureand environment. Etg values have been measured for n-butane in isotropic solvents and itwould seem reasonable to use these values for 5CB— d19 in zero efg mixtures. Literaturevalues of Ejg for n-butane vary from 400 to 900 cal/mol [64, 72, 73, 74, 75, 76, 77, 78].Chapter 5. A 2H NMR study of 5GB— d19 in zero electric field gradient nematicmixtures83I I Iz= 55% 11320.45.= 56.5% 1132••= 70% SCE•0.4 1tf).L.I0.35 1*I• L*I.11.ttI I I I0.3 40 60 80&‘1/kHzFigure 5.30: Quadrupolar splitting ratios Lvs/Lvi versus Lv1 of 5GB— d19 in the zeroefg mixtures 55% 1132/EBBA, 70% 5CB/EBBA and 56.5% 1132/EBBA.Chapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematicmixtures84Most of the literature values of liquid n-butane are close to 500 cal/mol [74, 75, 76, 77].However, one study [73] reports a value of 966 cal/mol for gaseous n-butane. Since thereare a range of Eg values in the literature, we shall explore calculations using Etg valuesof 500, 700 and 900 cal/mol.In addition, the geometry of 5CB — d19 must be known in order to calculate thequadrupolar splittings. The parameters C and Z in the equations for Usr () depend onthe bond lengths, and the quadrupolar splittings depend on the bond angles. We assumethat the benzene rings are regular hexagonal, and that the angle between the normals tothe two benzene rings is 30° [45]. In addition, we assume that all the methylene groupsare described by the CCC and CCD bond angles 112.5° and 108.82°. The DCD plane ineach CD2 group is assumed to bisect the CCC angle. The dihedral angle for a trans —gauche conformational change is 112.00.Two additional unknowns in the molecular geometry of 5CB— d19 are the angles0’ (see Figure5.27) and °d, where °d is the dihedral angle between the C12 bond andthe plane of benzene ring A. Most studies of 5CB assume that the angle 0’ is 120°.However, Photinos et al. [43] used the value 124° from X-ray studies on 5-OCB fortheir calculations of N-CB and N-OCB liquid crystals. While 5-OCB aild 5-CB will havedifferent geometries, it nevertheless seems worthwhile to explore the possibility of a valueof 0’ different from 120° for 5CB. Of the many possibilities, we perform four differentcalculations corresponding to four different geometries: the four geometries are (1) 0’ =120°, 0d = 00 (the bond C12 is coplanar to the benzene ring A — this geometry shallbe referred as PL-0); (2) 0’ = 124°, 0d = 00 (this geometry shall be referred as PL-4); (3) 0’ = 120°, 0d = 90° (the ring-C1 bond lies along the para axis of ring A and thebond C12 is perpendicular to the benzene ring A— this geometry shall be referred asPERP-0); (4) 0’ = 124°, °d = 900 (starting from the PL-4 geometry, the hydrocarbonchain is rotated 90° about the para axis of ring A — this geometry shall be referred asChapter 5. A 2H NMR study of 5CB— d19 in zero electric field gradient nematicmixtures85PERP-4).5.4.3 Individual Fit Model parametersA least squares minimization routine was used to obtain best fit model parameters foreach experimental spectrum from a minimization of the differences between experimentaland calculated quadrupolar splittings of 5CB — d19 as solute in the zero efg mixtures 55%1132/EBBA and 70% 5CB/EBBA. The quality of the fit is judged mainly from RMS(root mean square deviation) values— i.e. the lower the RMS the better the quality ofthe fit. We find that the quality of the fit depends on the parameters U (see Figure 5.27)and Etg. When the angle U was varied, the calculated quadrupolar splittings agreed verywell with the experimental quadrupolar splittings at the ring positions. However, thevariation of U did not change much the calculated quadrupolar splittings at the chainpositions. Hoatson et al. [52] also allowed 0 to vary and obtained a good fit for the ringdeuterons in their study of 5CB — d19 in liquid crystals. When the parameter Etg wasvaried for each individual temperature, the fitted E9 values varied with temperature.This contradicts the fact that the intramolecular property Etg should be independentof temperature. Therefore, we decided to fix the parameter Etg to certain values, 500,700 and 900 cal/mol, at all temperatures. These values span the range of literature Etgvalues [64, 72, 73, 74, 75, 76, 77, 78]Separate calculations were performed for both the CZ and CI models for the fourgeometries PL-0, PL-4, PERP-0 and PERP-4 and for the three E9 values 500, 700and 900 cal/mol. The model parameters k, and 0 were fitted in the CZ modelcalculations. The CI model calculation gives k, k and 0 values. Therefore, we obtain 12sets of (ks, 0) and of (k, k3, 0) values for each spectrum. The fitted 0 value rangesare reported in Table 5.9. The 0 values obtained are consistent with the value reportedin reference [70]. In order to reduce the number of possible calculations in the following,Chapter 5. A 211 NMR study of 5CB— d19 in zero electric field gradient nematic mixtures86Table 5.9: Fitted 0 values for different geometries and modelsModel and Geometry Et9cal moM 0/deg of 55% 1132/EBBA 0/deg of 70% 5CB/EBBACOZ 500 118.88 117.48 118.70 117.48700 118.96— 117.90 118.80 118.00PERP-0 900 119.02 118.28 118.90- 118.44COZ 500 119.00 — 117.48 118.80- 117.48700 119.14 — 118.04 118.96— 118.18PERP-4 900 119.26— 118.58 119.14— 118.78CAl 500 119.76— 122.20 119.94 122.68700 119.60 121.00 119.72 121.06PERP-0 900 119.38 119.52 119.42 119.00COZ 500 120.38 123.26 120.62 123.82700 120.18 121.88 120.34 122.00PERP-0 900 119.88— 120.12 119.90 120.04Fitted ranges for 0 of 5CB (Figure 5.27) in 55% 1132/EBBA and 70% 5CB/EBBA.we shall examine the quality of these fits and choose one set of k, and one set of k,k3 values. We shall choose the geometry and Etg values that fit best the experimentalquadrupolar splittings as the most appropriate basis.The quality of the fit (RMS) to the 55% 1132/EBBA mixture for the four differentgeometries using the two different models and three different Etg values is shown in Figure5.31- 5.33. While some fits are obviously much better than others, most of these fitsare acceptable considering the many assumptions involved in the modelling process. Itis unfortunate that the parameters are correlated such that it is not possible to choose adefinitive value of from these calculations. However, calculations that use a value ofEtg of order 500 cal/mol are generally considered preferable [43]. In all cases for the CImodel, the PERP-4 geometry gives the best fit. For the CZ model, the PERP-0 geometrygives the best fit except for Etg of 900 cal/mol at low temperatures, where the PERP4 geometry gives the best fit. Similar results were obtained for the 70% 5CB/EBBAChapter 5. A 2H NMR study of 5CB— d19 in zero electric field gradient nematic mixtures87mixture. Based on these plots, we decided to choose the PERP-0 geometry for the CZmodel and the PERP—4 geometry for the CI model. Henceforth, whenever we refer toCZ model parameters, it implies the parameters calculated with the CZ model using thePERP-0 geometry. Similarly, any reference to the CI model parameters implies that theparameters are calculated with the CI model using the PERP-4 geometry.5.4.4 Temperature dependence of Individual Fit model parametersThe temperature dependence of the short-range potential is described by the temperaturedependence of the CZ and CI model parameters. We use the parameters k and k tocharacterize the magnitude of the short-range potentials. The parameters and ‘ areratios of model parameters. If all contributions to the potential scale the same way withtemperature, these ratios would be independent of temperature. First, we shall analysethe temperature dependence of the model parameters k and k. Then, we shall examinethe temperature dependence of the ratios and ‘.k and k8Our main interest here is to see how the model parameters k and k8 depend on factorssuch as liquid crystal mixture, Etg and temperature. The fitted k and k6 values obtainedfor each experimental temperature and for Etg of 500, 700 and 900 cal/mol are plottedas reduced model parameters, k/T, against reduced temperature, Tr = T/TNI, in Figure5.34- 5.35. We use reduced model parameters because in the calculation of quadrupolarsplittings the k are always divided by temperature; we use reduced temperature becausethe liquid crystal mixtures 55% 1132/EBBA and 70% 5CB/EBBA have different TNIvalues.As temperature increases towards TNJ, the reduced model parameters decrease. Thek/T values of 55% 1132/EBBA are higher than those of 70% 5CB/EBBA at reducedtemperatures less than 0.95, and this is true for all three E9 values. The k8/T values areChapter 5. A 2H NMR study of 5CB — d19 in zero electnc field gradient nernatic mixtures881600Cl)Temperature/KFigure 5.31: RMS (root mean squares deviation) versus temperature of the fits to individual spectra of 5CB in 55% 1132/EBBA for the different geometries PL-0, PL-4,PERP-0 and PERP-4 at E9 equal 500 cal/mol.2400‘ IEtg=SOO cal/mol_II••I55% 1132/ERBAI IAAA AAAt*.AA..L2••. .. .00 O000800OOü 000=00:PL—O,CZPL—4,CZPERP—O,CZPRP—4,CZ1.=000PL—O,CIPL—4,CIPERP—O,CIPRP-4,CI I260 280 300 320 340Chapter 5. A 211 NMR study of 5CB— d19 in zero electnc field gradient nematic mixtures8955% 1132/EBBAI I IEtg=700 cal/mol A PLO,CI•= PL—4,CI*= PERP—O,CI2400 = PERP-4,C1•.a... •.-N X!*AAAfrIA*1600••••.••••..o_200.1-gi000000800 L= PL—O,CZu= PL—4,CZ0= PERP—O,CZ9= PRP-4,CZ1 I I260 280 300 320 340Temperature/KFigure 5.32: RMS (root mean squares deviation) versus temperature for E9 equal 700cal/mol.Chapter 5. A 2H NMR study of 5CB — d19 in zero electnc field gradient nematicmixtures9O55% 1132/EBBA‘ I I I IEtg=900 cal/mol A PL—O,CI•= PL—4,CI= PERP—O,CI2400= PERP-4,CI= PL—O,CZD= PL—4,CZ0= PERP—O,CZ0= PERP—4,CZN*D AA1600ii’OO... •00000,,•800I I I I I260 280 300 320 340Temperature/KFigure 5.33: RMS (root mean squares deviation) versus temperature for E equal 900cal/mol.Chapter 5. A 2H NMRstudyof5CB — d19 in zero electric field gradient nematicmixtures9lquite similar in both mixtures. However, the break observed in Figure 5.29 for the 70%5CB/EBBA mixture is also apparent in Figures 5.34- 5.35.and ‘The ratios and ‘ are plotted against reduced temperature in Figures 5.36 and 5.37.The similar result obtained for both mixtures, independent of model used, is striking.Thus the form of the short-range potential appears to be the same in both mixtures.The temperature dependence of c depends on Etg. The ratio has a large temperaturedependence for the Etg value 500 cal/mol, is less dependent on temperature for theEtg value 700 cal/mol, and is almost independent of temperature for the E9 value 900cal/mol. On the other hand, the ratio ‘ is small and has no significant temperaturedependence for all Etg values. Except for the CZ calculations at 500 and 700 cal/mol,these results are consistent with all terms in the potential having the same temperaturedependence.The small value of ‘ suggests that using oniy the second term of equation 1.28 or 1.29would provide an excellent fit to the experimental results. It is precisely this term thatprovides the best one parameter fit to a collection of 46 solutes in the 55% 1132/EBBAmixture [40].5.4.5 Global FitIn section 5.4.3, we have seen that the ratio is independent of temperature for Etgvalues close to 900 cal/mol, and ‘ is independent of temperature for Etg values of 500to 900 cal/mol. Constant values of and ‘ are consistent with the reasonable guessthat all contributions to the short-range anisotropic potential have similar temperaturedependence. In such a case, it is possible to calculate the parameters and ‘ in a singleleast squares fit to all the experimental quadrupolar splittings at all temperatures for agiven liquid crystal mixture. In addition, it is possible to determine the E9 value in theChapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematic mixtures92C)H 0.01NEl*ElL1OCZ model, PERP—0 geom.0.030.02AAA’ I ‘A.AAI A.•• AEl*AI*— L=Etg:SOOEl =Etg:?OOO=Etg:900- A=Etg:SOO• =Etg:?OOEl* ElAAElEl0of 70%of 70%of 70%A0Aof 557of 55%of 550.8 0.9 1TrFigure 5.34: The reduced model parameter k/T versus reduced temperature.Chapter 5. A 211 NMR study of 5CB — d19 in zero electnc field gradient nematicmixtures93C-)HU)odel, PERP—4Aeom.Ls=Etg:5OO(7O%)n =Etg:700(70%)0tg9(7)AA0.50.250I.’ L+L0*0*A=Etg:500(5570)• =Etg:700(55%)*=Etg:900(5157o)0.8 0.9Tr1Figure 5.35: The reduced model parameter k3/T versus reduced temperature.Chapter 5. A 2H NMR study of 5CB — d19 in zero electnc field gradient nematic mixtures94CZ model, PERP—O geom.I I I00000*c...- *))AAAE—10— —AzIL=Etg:5OO c/mol A=E 700 c/mol—20 tg0=Etg:900 c/molI I I0.8 0.9TrFigure 5.36: The ratio versus reduced temperatureChapter 5. A 2H NMR study of 5GB — d19 in zero electnc field gradient nematic mixtures95CI model, PERP—4 geom.I I IAAAA A- I R—0.04- 0000000- =Etg:5OO c/mol 0—0.08=Etg:?OO c/mol- O=Etg:9pO c/rnol0.8 0.9TrFigure 5.37: The ratio ‘ versus reduced temperatureChapter 5. A 211 NMR study of 5CB— d19 in zero electric field gradient nematic mixtures96Table 5.10: Fitted values of k0, k0, k0, and Etg using the CZ model.Fitted parameters 55% 1132/EBBA 70% 5CB/EBBAk0 /dyne cm 0.94 ±0.06 1.11 ±0.03Ic1 /dyne cm1 -2.28 ±1.04 -1.05 ±1.07Ic2 /dyne cm1 7.47 ±0.50 5.41 ±0.38-2.20 ±0.23 -2.73 ±0.32Etg /cal ‘nol’ 952 +19 911 +210 /deg 118.94 ±0.03 118.74 +0.03RMS/Hz 1089 968Fitted parameters of the CZ model using the PERP-0 geometry and varying Etg. For a givenliquid crystal mixture, the fit is to all experimental quadrupolar splittings at all temperatures.The k describe the temperature dependence of the model parameter k according to eq. 5.45.same fit, since E9 is independent of temperature. To reduce the number of adjustableparameters in such a fit it is useful to choose some functional form for the temperaturedependence of k and Ic8. The variations of k and k3 from the individual fits to eachtemperature above resemble parabolas. To an excellent approximation, these k and Ic8can be approximated bykiko+ki*(lTr)+k2*(lTr)”. (5.45)Using this functional form in a fit to all experiments for a given sample at all temperaturesgives the fitted parameters Ic0, Ic1 and Ic2, (or ‘), Etg and 0 in Table 5.10 for the CZmodel and in Table 5.11 for the CI model.Global Fit Model ParametersIt is instructive to compare the fitted parameters k (k3), (a’) and E9 to those fromprevious studies. First, we compare the parameters (ks, ) and (Ic3, ) to the valuesobtained from a study of 46 solutes in 55% 1132/EBBA at 301K [40]. The k value forthe 55% 1132/EBBA at 301K in our study is 3.13 dyn/cm, which is close to the valueChapter 5. A 211 NMR study of 5CB— d19 in zero electnc field gradient nematicmixtures97Fitted parameters 55% 1132/EBBA 70% 5CB/EBBAk0 /dyne cm1 -5.34 +1.48 -5.57 +2.00k1 /dyne cm’ 30.68 +8.27 18.63 +6.73k2 /dyne cm1 -35.13+9.39 -21.84+7.71‘ -0.16+0.05 -0.19±0.08Etg /cal mo11 1001+23 972+230 /deg 119.68 +0.05 119.58 +0.08RMS/Hz 946 1006Fitted parameters of the CI model using the PERP-4 geometry and varying For a givenliquid crystal mixture, the fit is to all experimental quadrupolar splittings at aM temperatures.The k describe the temperature dependence of the model parameter k3 according to eq. 5.45.3.92 dyn/cm found in the study of 46 solutes in 55% 1132/EBBA at 301K [40]. However,the ratio is -2.20 in our study and -5.01 for the 46 solutes [40]. Although the k valuesin these two studies are close, the ratio in our study is of much smaller magnitude thanthat for the 46 solutes [40]. Similarly, the fitted k and k8 values are 2.22 and 6.08 in ourstudy compared to 2.04 and 48.4 for the 46 solutes in 55% 1132/EBBA at 301K [41].Next, we compare the fitted PJ9 values to those in the literature. The fitted valuesfor 55% 1132/EBBA are 952 and 1001 cal/mol and those for 70% 5CB/EBBA are 911and 972 cal/mol using the CZ (Tab.5.10) and CI (Tab.5.11) models. These Etg valuesare high compared to most accepted literature values [64, 74, 75, 76, 77] which are closeto 500 cal/mol. However, we note that one study reports the value 966 cal/mol for Etgof gaseous n-butane [73].Since the fitted Etg values are high compared to commonly accepted literature values(400— 700 cal/mol), we shall explore the possibility of using a more acceptable value.For this purpose, we consider the RMS plots given in Figures 5.31- 5.33. For the CImodel, the Etg value 700 cal/mol gives acceptable fits, although larger Etg values givebetter fits. Moreover, ‘ is independent of temperature when Etg takes the value 700Table 5.11: Fitted values of k0, k0, k0, and Etg using the CI model.Chapter 5. A 2F1 NMR study of5CB— d19 in zero electnc field gradient nematicmixtures98Fitted parameters 55% 1132/EBBA 70% 5CB/EBBAIc0 /dyne cm1 0.83 +0.12 1.08 +0.05k1 /dyne cm1 1.66 +1.96 2.29 +1.30Ic2 /dyne cm1 9.25 +1.07 6.39+0.59-4.02 ±0.11 -4.79 +0.14Etg /cal mot’ 700.00 700.000 /deg 119.38 ±0.04 119.27 +0.04RMS/Hz 1594 1405Fitted parameters of the CZ model using the PERP-0 geometry and fixing Etg at 700 cal/mol.For a given liquid crystal mixture, the fit is to all experimental quadrupolar splittings at alltemperatures. The k, describe the temperature dependence of the model parameter k accordingto eq. 5.45.cal/mol. For the CZ model, the ratio is independent of temperature for high E9values. However, the Etg value 700 cal/mol gives acceptable fits, and the ratio is lessdependent on temperature than for Etg of 500 cal/mol. As a result, we choose the Etgvalue 700 cal/mol, which is also the upper limit of the acceptable E9 range, and repeatthe least squares minimization keeping the Eg value fixed at 700 cal/mol and adjustingthe parameters Ic0, Ic1, Ic2, 0, and orThe fitted values of Ic0, Ic1, Ic2, 0, and or are reported in Table 5.12 or Table 5.13for the Etg value 700 cal/mol. The RMS deviation in these fits is larger than when Etgwas varied, but the fits are still quite acceptable. We again compare the fitted valueswith those from the study of 46 solutes in 55% 1132/EBBA. The k and values are 4.03and -4.02 in our study, whereas these values are 3.92 and -5.01 in the study of 46 solutes[40]. This is excellent agreement. In addition, the fitted Ic and Ic3 values in our study are-0.80 and 76.4 compared to 2.04 and 48.0 in ref [41]. However, the Ic3 value 76.4 dyn/cmis very close to the Ic8 value 76.7 dyn/cm [41] obtained for the 46 solutes when the shortrange potential, Usr,j(I), is expressed only in terms of k3 (i.e. k=0). This is consistentTable 5.12: Fitted values of Ic0, Ic0, Ic0 and for E2 = 700 cal/mol, using the CZ model.ChapterS. A 2H NMR study of 5CB— d19 in zero electric field gradient nematic mixtures99Fitted parameters 55% 1132/EBBA 70% 5CB/EBBAk0 /dyne crn1 -25.27 +1.49 -28.55 +1.28k1 /dyne cm1 115.05 +16.67 78.05 +15.46k2 /dyne cm1 -147.87+10.39 -102.59+8.15‘ -0.013+0.002 -0.013+0.002/cal mol’ 700.00 700.000 /deg 120.50 +0.04 120.74+0.06RMS/Hz 1390 1464Fitted parameters of the CI model using the PERP-4 geometry and fixing Etg at 700 cal/mol.For a given liquid crystal mixture, the fit is to all experimental quadrupolar splittings at alltemperatures. The k describe the temperature dependence of the model parameter k3 accordingto eq. 5.45.with the separate fits at each temperature of k and k3, section 5.4.3, where it was foundthat the k8 term dominates the potential.5.5 SummaryThe quadrupolar splittings of 5CB — d19 in the zero efg mixtures 55% 1132/EBBA and56.5% 1132/EBBA are almost equal at any given temperature. Therefore, the short-rangepotentials in these two mixtures are the same. However, the quadrupolar splittings of5CB— d19 in the zero efg mixture 70% 5CB/EBBA are different from those of 55 %1132/EBBA at any given temperature. These differences at a given temperature aredue to the different magnitudes of the short-range potentials in these mixtures. The CZand CI models describing the short-range potentials are both successful in calculatingthe quadrupolar splittings of 5CB— d19 in the mixtures 55 % 1132/EBBA and 70%5CB/EBBA. In both cases the trans-gauche energy difference is consistent with the upperrange of acceptable values, 700 kcal/mol. The model parameters k and of the CZmodel and k and k of the CI model are useful in comparing the short-range potentialsTable 5.13: Fitted values of k0, k0, k0 and for Etg = 700 cal/mol, using the CI model.Chapter 5. A 2H NMR study of 5CB — d19 in zero electric field gradient nematic mixtureslOObetween these two mixtures. The values obtained agree quite well with those obtainedfrom a study of 46 solutes in a zero efg nematic solvent.Chapter 6Comparison of short-range interactions using 5CB — d19 as a solute6.1 IntroductionIn the preceding chapter the perdeuteriated molecule 4-n-pentyl-4’-cyanobiphenyl, 5-CB,was studied as solute in three zero efg mixtures. The spectra at a given temperature,however, were not the same in the different mixtures. Do the differences imply thatthe nature of the short-range potential is liquid crystal dependent? In this chapter weshall demonstrate that the short-range potential is the same in all three mixtures thespectral differences arise from the differing effects of temperature on the different partsof the potential.A convenient way to understand the spectral differences is to calculate the NMRspectrum using a potential and to analyse the differences in terms of the potential. Thequadrupolar splittings observed in the NMR spectrum are calculated using the equations(5.40), (5.41) and (5.42). The probablity, p, of each conformer i is rewritten as(—Uint,i‘\ f 1Usr,i (i) ‘d2— exp kT ) , exp kT——Ufl —Uexp( kT ) f exp( . )dIn equation (6.46) we note that all potential terms are divided by T. A simple MaierSaupe mean field theory of nematics [79] would predict a unique value for Usr,j(l)/Tat the nematic-isotropic phase transition temperature, TNI. As TNJ varies for differentliquid crystals, and as is a constant for a given conformer, the Ut,j/TNI part ofthe potential for the solute 5CB at the nematic-isotropic transition will vary inverselywith TNI. The simple Maier Saupe potential predicts the same reduced temperature,101Chapter 6. Comparison of short-range interactions using 5CB — d19 as a solute 102Tr = T/TNI, dependence of the order parameter. Thus differences at TNI are expectedto propagate throughout the nematic temperature range. Could this variation with TNIof the part of the potential account for the observed spectral differences? Toexamine this possibility in terms of the intra- and inter-molecular potentials acting on5CB as solute in the nematic mixtures that we are investigating here, we need to analyzethe results in terms of the parameters on which these potentials, and thus the quadrupolarsplittings, depend.6.2 AnalysisIn section 5.4.3 of the preceding chapter we saw that fits to the spectrum obtained ateach individual temperature using the Etg value 700 cal/mol give very good agreementbetween the experimental and calculated quadrupolar splittings. In section 5.4.5 we foundthat the global fit calculation using the value 700 cal/mol gives very good agreementbetween the fitted model parameters in our study and the parameters found in a studyof 46 solutes in the 55% 1132/EBBA zero electric field gradient nematic mixture [40, 41].Therefore, an appropriate choice of Etg for comparison of the short-range potentials inthe zero electric field gradient mixtures is 700 cal/mol. The model parameters k areand for the CZ model, and k and k3 for the CI model. Therefore, the quadrupolarsplitting of deuteron j, can be writtenk Etg= f(j, , -i-, i- (6.47)for the CZ model with a similar equation for the CI model.To compare the potentials in the various liquid crystals, it is instructive to plot thecalculated k/T values versus Li’1. The choice of /v as a plotting parameter requiressome explanation. In the quadrupolar splitting vs. temperature plot in Figure 5.29 andthe k/T vs. reduced temperature plots in Figures 5.34- 5.35 an unusual temperatureChapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 103dependence was observed for the 70% 5CB/EBBA mixture. Therefore we wish to choosea quantity, other than reduced temperature, for comparison. The first quantity thatcomes to mind is the order parameter for the sample. However, this quantity is difficultto define, especially for the liquid crystal mixtures used in this work. In addition, aMaier Saupe mean field theory for binary mixtures of axially symmetric nematic liquidcrystals gives the anisotropic part of the mean-field intermolecular potential for particlei as [80, 81, 82]U(1) = [pUS + pUS]P2(cosQ) (6.48)where p is the number density of component i, U is the anisotropic interaction strengthbetween components i and j, and S is the order parameter of component i. Note that it iseasy to extend equation (6.48) to multicomponent mixtures by adding a term for eachcomponent. This potential predicts in general different values for the order parameters ofcomponents i and j. In addition the value of U()/T for a given liquid crystal i will notnecessarily be the same at a given reduced temperature in different mixtures; this couldexplain some of the difference between mixtures observed in Figures 5.34- 5.35. As wewish to compare the intermolecular potential acting on our solute 5CB in the differentliquid crystal mixtures, it would make sense to choose for comparison situations wherethe order parameter of the solute is the same. In terms of equation (6.48) for an axiallysymmetric nematic, this would require that U(Q)/T be the same in both mixtures. Inthe real case, 5CB is not axially symmetric, and exists in many conformations. Thusthe test for similar potentials would be that the various contributions to the potential,i.e. the two terms in equations (1.26) and (1.29) or the terms in equation (6.48), dividedby temperature, give equal contributions to the total potential. Fortunately the lackof symmetry in 5CB allows us to fit our spectral results to potentials with more thanone parameter: the comparison between mixtures then involves comparison of theseChapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 104parameters.As an aside, equation (6.48) has also been used to describe mixtures of a nematicliquid crystal with a solute that does not itself exhibit a liquid crystalline phase [831.Thus, for all solutes i to experience the same anisotropic potential in different liquidcrystal mixtures, in terms of equation (6.48) it is required that Uk = Ckj X U with Ckj aconstant depending only on liquid crystal components j and k, but being independent ofsolute i. Note that the requirement for a zero field gradient mixture is that for all solutesthe anisotropic components of the field gradient cancel when terms for all componentliquid crystals are added.Because of the lack of symmetry and intramolecular motions in 5CB, the choice ofits order parameter for comparison purposes presents a problem. A more convenientchoice would be the quadrupolar splittings Lw of 5CB — d19 which are related to thisorder parameter. But which splitting is the best to use? Note that we are interestedin separating the temperature effects of the and Usr,j(). In a calculation of thequadrupolar splittings of 5CB— d19 at two different temperatures having the same k/Tvalues, we found that Lv1 is the least dependent of the quadrupolar splittings on theE9/T term. Thus it is appropriate to use Lv for comparing the liquid crystal mixtures.To examine the liquid crystal mixture dependence of the k parameters, we plot k2/T,k/T, k8/T and k/T vs.zv1 in Figures 6.38 to 6.41. The k, values in these plots arethose that were obtained in the preceding chapter from a separate least squares fittingfor each spectrum at each different temperature. The plots in these figures show that fora given Z\z-’ the k/T values of 55% 1132/EBBA are in excellent agreement with thoseof 70% 5CB/EBBA. Based on this agreement, we can write for a given Lv1:(k/T)55 = (k/T)70 (6.49)where k/T can be k2/T, k/T, k/T or k/T. The subscripts 55 and 70 stand for theChapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 105CZ model, PERP—O geom.0.02 I II 1:1Etg=?OO cal/mciL1IC)Q)IIH N= 70% 5CB/EBBA•= 55% 1132/EBBA0 I I I I I I40 60 80tv1/kHzFigure 6.38: Reduced model parameter, k/T, against v1 for the E9 = 700 cal/mol.Chapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 106CZ model, PERP—O geom.I I I I I I.L10.07 Etg=700 cal/mol0.06 I•00.05H L1u‘Ij= 70% 5CB/EBBA0.04.= 55% 1132/EBBAI I I I I I I40 60 80&‘1/kHzFigure 6.39: Reduced model parameter, k/T, against Lv1 for the Fi9 = 700 cal/mol.Chapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 107CI model, PERP—4 geom.I I I IEtg=?OO cal/mol.DRkL.l_IaC.)IDIDH D5CB/EBBA•E1D I=55 1132/EBBA0.1 —40 I 60 Izv1/kHzFigure 6.40: Reduced model parameter, k/T, against iv1 for the Eg = 700 cal/mol.Chapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 108CI model, PERP—4 geom.—0.003 I IEtg=?OO cal/mol-L1C)—0.002>0HQ =7O% 5CB/EBBA•=55% 1132/EBBA0.001 40 I 60 I 80tv1/kHzFigure 6.41: Reduced model parameter, kIT, against v1 for the Ejg = 700 cal/mol.Chapter 6. Comparison of short-range interactions using 5CB — d19 as a solute 109liquid crystal mixtures 55% 1132/EBBA and 70% 5CB/EBBA. This demonstrates thatthe choice of zv1 (as a parameter proportional to the 5CB order parameter) for comparison purposes was a good one. Because the two parameters describing the potential scalein the same way, Figures 6.38 to 6.41 demonstrate that the anisotropic short-range potentials in 55% 1132/EBBA and 70% 5CB/EBBA are the same. Substituting eq. (6.49)into eq. (1.26) and eq. (1.29), we obtain for a given Lv1(Usr/T)55 = (Usr/T)70. (6.50)Thus, for a given zv1, the experimental results of the preceding chapter are describedby the same reduced short-range potentials and reduced model parameters for both zeroelectric field gradient mixtures. This conclusion is independent of the model chosenfor analysis. Note that by a reduced quantity we mean the actual quantity divided bytemperature.As the purpose of this chapter is to examine several zero electric field gradient mixtures and to investigate to what extent the description of the anisotropic short-rangepotential is similar in the various mixtures, it is worthwhile analyzing equations (6.49)and (6.50) further. As pointed out in the preceding chapter, one way of emphasizing smalldifferences among zero electric field gradient mixtures is to plot ratios of the quadrupolarsplittings, such as Lv5/L i, against In Figure 5.30 we chose the ratio L\r15/L\v1for comparison because the quadrupolar splittings at the 5 position are more difficultto fit than the quadrupolar splittings at other positions of the chain. This is becausethe methyl deuterons are sensitive to all internal chain motions. However, qualitativelysimilar results are obtained for other chain positions.Chapter 6. Comparison of short-range interactions using 5CB — d19 as a solute 1106.2.1 Individual Fit ParametersIn Figs 6.42 and 6.43 we compare experimental ratios from Fig. 5.30 (filled symbols)with those recalculated from the best-fit parameters obtained from separate fits to eachexperimental spectrum in section 5.4.3 of the preceding chapter(dotted symbols). Fig6.42 presents results for the CZ model, and Fig 6.43 for the CI model. Although thereis a deviation between the calculated and experimental quadrupolar splitting ratios, thegeneral experimental trends are observed with both models. More important, the differences between the liquid crystal mixtures are well predicted. The deviation betweenexperiment and theory is mainly due to the inadequacy of the models.We now turn to the question “If the intermolecular potential is the same, why do thequadrupolar splitting ratios Av5/L1 differ with liquid crystal solvent in the ratio plotsof Figures 6.42 and 6.43?” Equation. (6.47) tells us that there is another parameter,on which the quadrupolar splitting iu depends. The value of Etg is constant,and is set to 700 cal/mol throughout this chapter. However, the temperature at whicha given v1 is observed in the 55% 1132/EBBA mixture, T55, is different from that inthe 70% 5CB/EBBA mixture, T70. As a result, the Etg/T term is different for the twomixtures. Therefore, the differences in quadrupolar splitting ratios /z’s/Lv1must be dueto the different temperatures (T55 and T70) associated with the different liquid crystalmixtures 55% 1132/EBBA and 70% 5CB/EBBA.Of course the above analysis is based on independent fits of spectra in the differentmixtures. Perhaps a better demonstration that the spectral differences are due to thetemperature dependence of the conformational averaging would be to predict the spectrum of one mixture from the k, parameters of the other mixture. We shall call thequadrupolar splittings of these predicted spectra “scaled quadrupolar splittings”.In this study, we shall start from the reduced model parameters of 70% 5CB/EBBAChapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 111ir)I I I II I I I60&‘1/kHzFigure 6.42: Qtiadrupolar splitting ratios i.vs//.S.iii versus v1 using Individual fit CZmodel parameters.CZ model, PERP—0 geom.0.50.4A= exp 55%.= exp 70%-.:.=ca155%cal 70%thick line = Scaled AAAAAAAAAA0.3AA AA40 80Chapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 112IDI I I I40 60zv1/kHzFigure 6.43: Quadrupolar splitting ratiosv5/v1 versus v1 using Individual fit CImodel parameters.CI model, PERP—4 geom.I I0.50.4A= exp 55%.= exp 70%-.:.=cal55%cal 70%thick line=ScaledAA-AAAAA.AAAII AIAA0.3A A80Chapter 6. Comparison of short-range interactions using 5CB — d19 as a solute 113and shall predict the quadrupolar splittings of the 55% 1132/EBBA mixture. In orderto predict the quadrupolar splittings in 55% 1132/EBBA, it is necessary to use the appropriate temperatures in the Etg/T term; the temperature in the Etg/T term has to bescaled by a factorT55/T70. In order to simplify the notation, we define this factorT55/T70as the Temperature Scaling Factor (TSF). The TSF values are calculated from the resultsof the preceding chapter for a given Lv1 and tabulated with the corresponding temperatures of the 70% 5CB/EBBA mixture in Table 6.14. For each entry in Table 6.14, thereduced short-range potentials Usr,j(Q)/T along with U,/(T70 x TSF) are used to calculate the “scaled quadrupolar splittings”. If we are correct that the spectral differencesarise from the temperature effect on the conformational averaging, these scaled splittingsshould equal the recalculated splittings of 5CB — d19 in the 55% 1132/EBBA mixture.To demonstrate that this is indeed the case, we plot “scaled” along with experimentaland recalculated quadrupolar splitting ratios Lz/5/Lv1 in Figures 6.42 (CZ model) and6.43 (CI model). The agreement between the “scaled” (thick lines, predicted from theresults of the 70% 5CB/EBBA experiments) and recalculated (dotted lines, fits to the55% 1 132/EBBA experiments themselves) quadrupolar splitting ratios is excellent forthe CZ model. This agreement confirms that the differences in the quadrupolar splittingratios Lzis/Lv1 come from the different temperatures T55 and Tm of 55% 1132/EBBAand 70% 5CB/EBBA for a given Lv1. For a given value of Usr,j()/T, the differenttemperatures affect the quadrupolar splittings via the effect of the different onthe conformational averaging.In section 5.4.5 of the preceding chapter the results were analysed by fitting all spectraat all temperatures in a given liquid crystal solvent to a set of global parameters. In thesefits the ratio between the k, values, or ‘, were kept constant for a given solvent. Abovewe have seen that, for a given experimental Lzi1, the reduced model parameters aretransferable from one zero electric field gradient mixture to another and the reducedChapter 6. Comparison of short-range interactions using 5CB — d19 as a solute 114Table 6.14: Temperature scaling factorsT70/K of 70% 5CB/EBBA TSF251.9 1.114255.9 1.117261.2 1.107265.3 1.108271.1 1.106276.1 1.097281.9 1.094285.9 1.092292.1 1.082296.6 1.077302.0 1.069306.8 1.061308.8 1.058310.8 1.058312.7 1.062313.7 1.061314.7 1.065315.7 1.065TSFaverage 1.083Temperature scaling factors, TSF (see text).short-range potentials of the two zero electric field gradient mixtures are equal. Theglobal fit parameters can be tested in a similar analysis.6.2.2 Global Fit ParametersFirst, we shall examine the fitted parameters in Tables 5.12 and 5.13 of the precedingchapter corresponding to Etg of 700 cal/mol. Based on eq. 6.49, we intuitively expectthat the ratios = k/k or = k/k3 should be the same in all zero electric field gradientmixtures. The values are -4.02 and -4.79 and the ‘ values are -.013 and -.013 for theliquid crystal mixtures 55% 1132/EBBA and 70% 5CB/EBBA. The and ‘ values ofthese two liquid crystal mixtures are in excellent agreement. Thus, the ratios and ‘Chapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 115are transferable from one zero electric field gradient mixture to another.As was the situation above, a most useful comparison is to check the transferability ofreduced model parameters by calculating the “scaled quadrupolar splittings”. We startwith the reduced model parameters k0/T70,k1/T70 and k2/T70 of 70% 5CB/EBBA. Thenwe use T = T70 X TSFaverage (see Table 6.14) in the calculation of U/T to calculate the“scaled quadrupolar splittings”.The “scaled”, experimental and recalculated quadrupolar splitting ratios zi5/v1are plotted against Luz’1 in Figs 6.44 (CZ model) and 6.45 (CI model). The agreementbetween the “scaled” (solid line, predicted from the results of the 70% 5CB/EBBA experiments) and recalculated (dotted line, fits to the 55% 1132/EBBA experiments themselves) quadrupolar splitting ratios is excellent for the CI model. In addition, the fits arein reasonable agreement with the experimental results, and the general features of theexperimental quadrupolar splittings are predicted. In this case a temperature independent ‘ seems the correct choice. For the CZ model, however, the fits are not as good.This is because the parameter was kept constant with temperature. In the precedingchapter it was shown for this model with Etg 700 cal/mol that the best results areobtained with a temperature dependent . This is evident from the deviation betweenthe experimental and recalculated quadrupolar splitting ratios in Fig. 6.44. The “scaledquadrupolar splitting” ratios agree well with the recalculated quadrupolar splitting ratios at high temperatures. However, the deviation is large for low temperatures. Thisdeviation is partly due to the fact that the TSF ratios, T55/T70 at low temperaturesare very different from the TSFaverage (1.083), whereas these ratios are very close to theTSFaverage at high temperatures.Chapter 6. Comparison of short-range interactions using 5CB — d19 as a soluteIC).1ACZ model, PERP—O geom.zv1/kHz116AA-AAAAFigure 6.44: Quadrupolar splitting ratios Z115/Lvi versus u1 using Global fit CZ model0.5—A= exp 55%0.4.= exp 70%-.:.=ca155%cal 70%thick line = ScaledSAAAAAIS0.340I I I I60 80parameters.Chapter 6. Comparison of short-range interactions using 5CB — d19 as a solute 117CI model, PERP—4 geom.I I I0.5—A= exp 55%•= exp 70%- .:.=ca155%:= cal 70% :..:,‘:: Athick line = Scaled0.4- •. AAAAA.:--. A..•I AAA A0.3I I40 60 80v1/kHzFigure 6.45: Quadrupolar splitting ratios zvs/.v1 versus zzi1 using Global fit CI modelparameters.Chapter 6. Comparison of short-range interactions using 5CB— d19 as a solute 1186.3 SummaryIn this chapter we have demonstrated in several different ways that for a given experimental t1v the reduced model parameters k/T of 55 % 1132/EBBA are the same as thoseof 70% 5CB/EBBA. That is, irrespective of the model used for analysis, the reducedshort-range potential appears to be the same in all zero electric field gradient nematicmixtures. In other words, the quadrupolar splittings of 5CB — d19 in one zero electricfield gradient mixture can be predicted knowing the reduced model parameters of anotherzero electric field gradient mixture. The differences in spectra between mixtures resultfrom the temperature dependence of the internal energy contribution to the conformerprobabilities.Chapter 7ConclusionIntermolecular forces play an important role in understanding the orientational natureof liquid crystals. Due to the different strengths of intermolecular potentials, the onentational properties of liquid crystals differ from one liquid crystal to another. Theonientational differences among pure liquid crystals such as 1132, EBBA and 5CB can beexplained by the presence of long range intermolecular forces. In the absence of the longrange forces, such as in the special mixtures 55 wt% 1132/EBBA, 56.5 wt% 1132/EBBAand 70 wt% 5CB/EBBA, one expects that the orientation would be negligibly small.However, the orientational studies of small solutes show that there exists short-rangeforces which orient the solutes in these special mixtures. In order to understand the roleof short-range forces in zero efg mixtures, the orientational studies were undertaken inthe zero efg mixtures.The study of C2v symmetry solutes in mixtures 56.5 wt% 1132/EBBA at 323K and70 wt% 5CB/EBBA at 316K, using proton NMR, shows that the solutes orient in thesame way, upon scaling for the different nematic-isotropic transition temperature values,TNI, of the two mixtures. The experimental order parameters were related to the shortrange potential with the aid of a model. It has been found that the short-range potentialsexperienced by the solutes are similiar in both mixtures.The temperature dependence of the solutes meta dichlorobenzene, ortho dichlorobenzene, 1,3-bromochlorobenzene, benzene and 2-butyne in the special mixtures 55 wt%1132/EBBA and 70 wt% 5CB/EBBA shows that the solutes orient in the same way in119Chapter 7. Conclusion 120both mixtures. The results were analysed to compare the short-range interactions inthese two mixtures. It is found that the reduced short-range potentials are the samein both mixtures. The analysis of biaxial order parameters shows that the temperatureeffect on the electric field gradient is small.Although the study of small solutes as probes in liquid crystals gives a starting point,the temperature dependence study of a liquid crystal, 5CB-d19 in the zero efg mixtures55 wt% 1132/EBBA, 56.5 wt% 1132/EBBA and 70 wt% 5CB/EBBA gives a better understanding about the intermolecular forces among constituent liquid crystal molecules.The flexible chain part of the constituent liquid crystal molecule plays an important rolein orienting the liquid crystal molecules. The free rotation along the C-C bond leadsto several conformations for the constituent liquid crystal molecule. The probability ofeach conformer depends on the internal energy, of the constituent liquid crystalmolecule.The temperature dependence study of 5CB — d19 as solute in the mixtures 55 wt%1132/EBBA, 56.5 wt% 1132/EBBA and 70 wt% 5CB/EBBA indicates that the solute5CB— d19 experiences the same reduced potential in all three mixtures. These resultshave been confirmed using two independent models for the short-range interactions. Sincethe solute 5CB — d19 experiences the same reduced potential in the special mixtures, onewould expect that the2H-NMR spectra of the liquid crystal 5CB— d19 in the specialmixtures be identical. However, the spectra in the mixtures 55 wt% 1132/EBBA and70 wt% 5CB/EBBA are different, and the spectral differences are explained in termsof different nematic-isotropic transition temperature, TNI, values. As TNI varies fordifferent special mixtures, the part of the potential for the solute 5CB — d9 willvary inversely with TNT. Thus differences at TNI propagate throughout the nematictemperature range. This variation with TNT of the !I1 part of the potential explainsthe observed spectral differences of 5CB— d19 in these special mixtures.Chapter 7. Conclusion 121Other useful information which can be obtained from our study is the value of forthe flexible chain part of the 5CB— d19 molecule. Although the E9 values for the flexiblechain molecules in isotropic solvents are available, the E9 value in the nematic phase isnot available. We have used the values of 500, 700 and 900 cal/mol for the Etg in Chapter5 and Etg = 700 cal/mol for the analysis in Chapter 6. To obtain an estimate for theEtg value, we shall now compare the temperature dependence study of 5CB — d19 withthat of small solutes (Chapter 4), where the extra complexity due to Etg does not exist.In figure 7.46, we plot the reduced model parameter, k/T, against Tr for both the smallsolutes and the liquid crystal 5CB — d19. The figure suggests that the k5/T values for allaromatic solutes are in good agreement with those of 5CB — d19 at Etg = 700 cal/mol.It should be noted that the k3 values for 5CB— d19 are slightly underestimated becausethe 5CB — d19 data were fitted using the two-parameter model (equation 1.29), having k3and k terms (with k being very small), whereas the order parameters of the small soluteswere fitted using the one-parameter model (equation 1.28), only the k term.For the linear molecule, 2-butyne, however the k3/T values are close to those of5CB— d19 at Etg = 500 cal/mol. Although we expected that the k3/T vs. T plots for allthe small solutes would behave similiarly, the different behavior for the linear molecule,2-butyne, from the aromatic solutes is not understood well. It should, however, be notedthat k3/T values for 2-butyne is close to 500 cal/mol, which is the most commonlyaccepted literature value. Based on agreement between the temperature dependencestudies of small solutes and of liquid crystal 5CB— d19, we report the E9 value as 700cal/mol although an exact estimate can not be predicted from our study.Having studied the three zero efg mixtures 55 wt% 1132/EBBA, 56.5 wt% 1132/EBBAand 70 wt% 5CB/EBBA, it is interesting to see whether we can extend our results to otherpossible zero efg mixtures. Some other possible zero efg mixtures are: PCH-7/EBBA,PCH-7/MBBA and 5CB/MBBA, where the measured electric field gradient has beenChapter 7. Conclusion 1220.480.40.320.240.160.080Figure 7.46: Reduced model parameter, k3/T vs. Tr for all the solutes and the liquidcrystal 5CB-d19Filled =Open =70% =MD,cBo=BENZQ=BUTYA•1.•\10.8 0.9 1TrChapter 7. Conclusion 123found to be opposite in sign in the liquid crystals PCH-7 and MBBA [84]. For example,a study of a solute in the zero efg mixtures 70 wt% 5CB/EBBA and x wt% 5CB/MBBA,where x has to be determined experimentally, may lead to an understanding how thatparticular solute prefers to orient with a particular liquid crystal site.Another interesting aspect in the zero efg mixtures is the ability to determine thequadrupole moment of a solute. For example, to determine the quadrupole momentof the solute benzene, the following methods could be used. The orientational study ofbenzene dissolved in pure 5CB, pure EBBA and 70 wt% 5CB/EBBA could be undertaken,using proton NMR. The short-range potential, which can be be determined in the zeroefg mixture 70 wt % 5CB/EBBA, could be transfered to the pure liquid crystals 5CBand EBBA. Having known the short-range potential contribution to the intermolecularpotential, the long-range potential can be determined for the pure liquid crystals 5CBand EBBA. Note that the long-range potential is decribed in terms of electric quadrupolemoment - electric field gradient interaction. The electric field gradient has already beenmeasured in the pure liquid crystals EBBA and 5CB [32, 50]. Hence, it may be possibleto determine the electric quadrupole moment of the benzene.Bibliography[1] F. Reinitzer, 1888, Monatsh. Chem., 9, 421[2] de Jeu, W.H., “Physical Properties of Liquid Crystalline Materials”, 1980, Gordonand Breach, Science Publishers, Inc.[3] deGennes, P.G., “The Physics of Liquid Crystals”, 1974, Cambridge UniversityPress.[4] Emsley, J.W., and Lindon, J.C., “NMR Spectrosocopy using Liquid Crystal Solvents”, 1975, Pergamon Press.[5] Emsley, J.W., “Nuclear Magnetic Resonance of Liquid Crystals”, 1985, Reidel Press.[6] Diehi, P., and Khetrapal, C.L., “NMR Basic Principles and Progress”, 1969, Vol.1.[7] Dong, R.Y., “ Nuclear Magnetic Resonance of Liquid Crystals”, 1993, Springer-Verlag Press.[8] Dong, R.Y., and Richards, G.M., 1992, J. Chem . Soc. Faraday Trans., 88, 1885.[9] Dong, R.Y., 1991, Phys. Rev. A, 43, 4310.[10] Dong, R.Y., and Richards, G.M., 1990, Chem. Phys. Lett., 171, 389.[11] Beckmann, P.A., Emsley, J.W., Luckhurst, G.R., and Turner, D.L., 1986, Mol.Phys., 59, 97.[12] Beckmann, P.A., Emsley, J.W., Luckhurst, G.R., and Turner, D.L., 1983, Mol.Phys., 50, 699.[13] Slichter, C.P., “Principles of Magnetic Resonance”, 1989, Springer-Verlag Press.[14] Saupe, A., Molecular Crystals., 1966, 1, 527.[15] Pake, A., J. Chem. Phys., 1948, 16, 327.[16] Maier, W., and Saupe, A., Z. Naturforsch., 1958, A 13, 564; 1959, A 14, 882; 1960,A 15, 287;[17] Luckhurst, G.R., Zannoni, C., Nordio, P.L., and Segre, U., 1975, Mol. Phys., 30,1345.124Bibliography 125[18] Photinos, D.J., Samuiski, E.T., and Toriumi, H., 1991, Mol. Crst. Liq. Crst., 204,161.[19] Photinos, D.J., Samuiski, E.T., and Toriumi, H., 1990, J. Phys. Chem., 94, 4688.[20] Photinos, D.J., Samuiski, E.T., and Toriumi, H., 1990, J. Phys. Chem., 94, 4694.[21] Yim, C.T., and Gilson, D.F.R., 1991, J. Phys. Chem. , 95, 980.[22] Yim, C.T., and Gilson, D.F.R., 1990, Can. J. Chem. , 68, 875.[23] Yim, C.T., and Gilson, D.F.R., 1989, Can. J. Chem. , 67, 54.[24] Yim, C.T., and Gilson, D.F.R., 1988, Can. J. Chem. , 66, 1749.[25] Yim, C.T., and Gilson, D.F.R., 1987, Can. J. Chem. , 65, 2513.[26] Ferrarini, A., Moro, G.J., and Nordio, P.L., 1992, Mol. Phys. , 77, 1.[27] Jokisaari, J., Ingman, P., Lounila, J., Pulkkinen, 0., Diehi, P., and Muenster, 0.,1993, Mol. Phys. , 78, 41.[28] Ingman, P., Jokisaari, J., Pulkkinen, 0., Diehi, P., and Muenster, 0., 1991, Chem.Phys. Lett., 182, 253.[29] Ingman, P., Jokisaari, J., and Diehi, P., 1991, J. Magn. Res., 92, 163.[30] Jokisaari, J., 1994, Progress in Nuclear Magnetic Resonance Spectroscopy, 26, 1.[31] Burnell, E.E., de Lange, C.A., and Snijders, J.G., 1982, Phys. Rev. A, 25, 2339.[32] Barker, P.B., van der Est, A.J., Burnell, E.E., Patey, G.N., de Lange, C.A., andSnijders, J.G., 1984, Chem. Phys. Lett., 107, 426.[33] Patey, G.N., Burnell, E.E., Snijders, J.G., and de Lange, C.A., 1983, Chem. Phys.Lett., 99, 271.[34] Stone, A.J., 1979, The iVlolecular Physics of Liquid Crystals, edited by Luckhurst,G.R., and Gray, G.W., (Academic Press), Chapter 2.[35] Buckingham, A.D., 1970 An Advanced Treatise in Physical Chemistry, 4, 349.[36] Code, R.F., and Ramsey, N.E., 1971, Phys. Rev. A, 4, 1945.[37] van der Est, A.J., Barker, P.B., Burnell, E.E., de Lange, C.A., and Snijders, J.G.,1985, Mol. Phys., 56, 161.Bibliography 126[38] van der Est, A.J., Kok, M.Y., Burnell, E.E., 1987, Mol. Phys., 60, 397.[39] van der Est, A.J., 1987, Ph. D. thesis, University of British Columbia.[40] Zimmerman, D.S., and Burnell, E.E., 1990, Mol. Phys., 69, 1059.[41] Zimmerman, D.S., and Burnell, E.E., 1993, Mol. Phys., 78, 687.[42] Barnhoorn, J.B.S., de Lange, C.A., and Burnell, E.E., 1993, Liq. Crystals., 13, 319.[43] Photinos, D.J., Samuiski, E.T., and Toriumi, H., 1991, J. Chem. Phys., 94, 2758.[44] Samulski, E.T., and Dong, R.Y., 1982, J. Chem. Phys., 77, 5090.[45] Sinton, S.W., Zax, D.B., Murdoch, J.B., and Pines, A., 1984, Mol. Phys., 53, 333.[46] Emsley, J.W., Luckhurst, G.R., Gray, G.W., and Mosley, A., 1978, Mol. Phys., 35,1499.[47] Emsley, J.W., Lindon, J.C., and Luckhurst, G.R., 1975, Mol. Phys., 30, 1913.[48] Sinton, S.W., and Pines, A., 1980, Chem. Phys. Lett., 76, 263.[49] Emsley, J.W., Luckhurst, G.R., and Stockley, C.P., 1982, Proc. R. Soc. A, 381, 117.[50] Weaver, A., van der Est, A.J., Rendell, J.C.T., Roatson, G.L., Bates, G.S., andBurnell, E.E., 1987, Liq. Crystals., 2, 633.[51] Keller, P., and Liebert, L., 1978, Solid State Phys. Suppi., 14, 19.[52] Hoatson, G.L., Bailey, A.L., van der Est, A.J., Bates, G.S., and Burnell, E.E., 1988,Liq. Crystals., 3, 683.[53] Davis, J.H., Jeffrey, K.R., Bloom, M., Valic, M.I. and Riggs, T.P., 1976, Chem.Phys. Lett., 42, 390.[54] Lounila, J., and Jokisaari, J., 1982, Progress in Nuclear Magnetic Resonance Spectroscopy, 15, 249.[55] Diehl, P., Kellarhals, H., and Lusting, E., “NMR Basic Principles and Progress”,1972, 6, 1.[56] Kok, M.Y., 1986, M. Sc. thesis, University of British Columbia.[57] Harmony, M.D., Laurie, V.M., Kuczkowski, R.L., Schwendeman, R.H., Ramsay,D.A., Lovas, F.J., Lafferty, W.J., and Maki, A.G., 1979, J. Phys. Chem. Ref. Data,8, 619.Bibliography 127[58] Diehi, P., Henrichs, P.M., and Niederberger, W., 1971, Mol. Phys., 20, 139.[59] Bondi, A., 1964, J. Phys. Chem., 68, 441.[60] Tanimoto, M., Kuchitsu, K., and Morino, Y., 1969, Bull. Chem. Soc. Japan, 42,2519.[61] Buckingham, A.D., Burnell, E.E., and de Lange, C.A., 1968, Mol. Phys., 15, 285.[62] Bos, P.J., Pirs, J., Ukieja, P., and Doane, J.W., 1977, Mol. Cryst. Liq. Cryst., 40,59.[63] Emsley, J.W., Hashim, R., Luckhurst, G.R., Rumbles, G.N., and Viloria, F.R., 1983,Mol. Phys., 49, 1321.[64] Flory, P.J., 1969, “Statistical Mechanics of Chain Molecules “.[65] Emsley, J.W., and Luckhurst, G.R., 1980, Mol. Phys., 41, 19.[66] Burnell, E.E., de Lange, C.A., and Mouritsen, O.G., 1982, J. Magn. Reson., 50,188.[67] Diehl, P., and Reinhold, M., 1978, Mol. Phys., 36, 143.[68] Davis, J.H., and Jeffrey, K.R., 1977, Chemistry and Physics of Lipids, 20, 87.[69] Marceija, 1974, J. Chem. Phys., 60, 3599.[70] Emsley, J.W., Luckhurst, G.R., and Stockley, C.P., 1981, Mol. Phys., 44, 565.[71] van der Est, A.J., Burnell, E.E., and Lounila, 1988, J. Chem. Soc., Faraday Trans.2, 84, 1095.[72] Sheppard, N., and Szasz, G.J., 1949, J. Chem. Phys., 17, 86.[73] Verma, A.L., Murphy, W.F., and Bernstein, H.J., 1974, J. Chem. Phys., 60, 1540.[74] Bradford, W.F., Fitzwater, S., and Bartell, L.S., 1977, J. Mol. Struct., 38, 185.[75] Colombo, L.,and Zerbi, G., 1980, J. Chem. Phys., 73, 2013.[76] Kint, S., Scherer, J.R., and Snyder, R. 0., 1980, J. Chem. Phys., 73, 2599.[77] Rosenthal, L., Rabolt, J.F., and Hummel, J., 1982, J. Chem. Phys., 76, 817.[78] Wiberg, K.B., and Murcko, M.A., 1988, J. Am. Chem. Soc., 110, 8029.[79] Maier, W., and Saupe, A., 1959, Z. Naturf. (a), 14, 882.Bibliography 128[80] flumphries, ILL., James, P.G., and Luckhurst, G.R., 1971, Symp. Faraday Soc., 5,107.[81] Paiffy-Muhoray, P., de Bruyn, J.R., and Duilmur, D.A., 1985, Mol. Cryst. LiquidCryst., 127, 301.[82] Bates, G.S., Beckmann, P.A., Burnell, E.E., Hoatson, G.L., Palify-Muhoray, P.,1986, Mol. Phys., 57, 351.[83] Bates, G.S., Burnell, E.E., Hoatson, G.L., Palify-Muhoray, P., Weaver, A., 1987,Chem. Phys. Letts., 134, 161.[84] Ter Beek, L.C., Private communication.Appendix ATransformationThe order parameter S is related to the intermolecular potential by:f(3 cos cos — exp(—U()/kT)dfZ= 2fexp(—U()/kT)d (A.51)where a, /3 x,y,z, molecule fixed axes and the angle denotes the Eulerian angle(q,O,&) that transform from the molecule-fixed axis system to director-fixed axis system.Since the nematic phase is an uniaxial phase, the transformation needs only two anglesO and 5. The angle 0 is the angle between the director axis and the molecule-fixed z axis(see Figure A.47), and the angle g5 is the angle between the projection of the director, ,on the xy plane and the molecule-fixed axis x.The order parameters S, S and for a solute molecule dissolved in a uniaxialnematic phase can be expressed in terms of 0 and 4 as:— ff(3cos2O— l)exp(—U(0,b)/kT)sinOd0dqA 522ffexp(—U(O,q)/kT)sin0dOdqS—f f(3 sin2 0 cos2 g — l)exp(—U(0, /)/kT) sin 0dOdq A 53— 2ff exp(—U(0, ç)/kT) sin 0d0dq— ff(3sin20sinq— 1)exp(—U(0,ct)/kT)sinOd0dq AM—2ff exp(—U(O, )/kT) sin OdOdqSimliarly, the off-diagonal matrix elements S, S and S can be described in termsof 0 and q. If the molecule-fixed axis system (x,y,z) is the principal axis system, thenthe orientation of the solute in the nematic phase can be described by two independent129Appendix A. Transformation 130yxFigure A.47: The angles 0 and g5 represent the transformation between the molecule-fixedaxis system (x,y,z) and the director-fixed axis system of the nematic liquid crystal.nz0Appendix A. Transformation 131order parameters since the order matrix is a traceless tensor. If two or more orderparameters are needed to describe the orientation of a solute molecule in the nematicphase, then the solute is referred to have biaxiality. If a solute molecule has a 3-fold orhigher symmetry, the U(q, 0) is invariant of the angle q. Therefore, it can be shown thatthe order parameters S. and become equal for these higher symmetry solutes. Theorientations of a 3-fold or higher symmetry solute in the nematic phase can he describedby a single order parameter.A Appendix BDipolar Couplings132Appendix B. Dipolar Couplings 133Temp / K D12 = D34 D13 = D24 D14 D23301 -1036.32 ±0.04 -132.30 ±0.01 -64.49 ±0.02 -494.85 ±0.05305 -996.55 ±0.05 -128.31 ±0.02 -63.11 ±0.02 -484.58 ±0.06310 -945.08 ±0.03 -122.93 ±0.08 -61.05 ±0.09 -469.47 ±0.04315 -886.20 ±0.10 -116.50 ±0.29 -58.46 ±0.22 -450.11 ±0.13320 -817.69 +0.16 -108.92 +0.39 -55.20 ±0.44 -424.28 ±0.19322 -799.08 +1.11 -106.65 +0.33 -54.79 ±0.46 -417.20 ±1.28325 -747.60 +0.46 -99.74 +1.01 -51.64 +1.48 -394.86 ±0.66327 -710.45 ±0.70 -95.73 ±0.21 -49.01 +0.29 -379.39 ±0.80330 -643.93 ±1.02 -87.12 ±0.32 -43.87 +0.43 -349.43 ±1.17J12 = = 8.00 J13 J24 = 1.50 J14 = 0.30 J23 = 7.40Table B.15: Dipolar couplings obtained from the ‘H-NMR spectra for the solute orthodichlorobenzene dissolved in 55% 1132/EBBA.Temp / K D12 = D34 D13 = D24 D14 D23294 -987.28 +0.15 -119.75 +0.38 -55.50 +0.54 -422.13 +0.19302 -895.03 +0.02 -110.30 +0.09 -51.77 +0.02 -396.67 +0.07304 -879.09 +0.04 -108.66 +0.10 -51.13 +0.03 -392.03 +0.08305 -865.92 +0.09 -107.26 +0.02 -50.69 +0.03 -387.92 +0.11306 -848.48 +0.12 -105.47 +0.03 -49.97 +0.05 -382.62 +0.14311 -766.75 +0.28 -96.28 +0.68 -46.57 +0.87 -354.58 +0.35313 -715.33 +0.36 -90.26 ±1.03 -43.47 +0.94 -335.75 +0.42315 -661.30 +0.18 -84.37 ±0.44 -40.69 +0.56 -314.04 +0.23316 -606.30 ±0.64 -77.70 ±1.77 -37.00 +1.40 -293.59 ±0.75J12 = = 8.00 J13 = = 1.50 J14 = 0.30 J23 = 7.40Table B.16: Dipolar couplings obtained from the ‘H-NMR spectra for the solute orthodichlorobenzene dissolved in 70% 5CB/EBBA.Appendix B. Dipolar Couplings 134Temp / K D12 = D14 D13 D23 D34285 -114.72 +0.20 -30.71 +0.30 -1280.81 +0.15 -314.09 +0.34292 -110.92 +0.03 -29.68 +0.04 -1244.09 +0.02 -305.45 +0.04301 -105.26 +0.09 -27.72 +0.14 -1184.33 +0.07 -290.71 +0.15305 -101.47 +0.03 -26.69 +0.04 -1143.91 +0.02 -281.08 +0.05310 -96.69 ±0.02 -25.54 ±0.03 -1089.42 ±0.01 -267.52 ±0.03315 -90.48 +0.02 -24.17 ±0.05 -1015.79 +0.02 -249.21 ±0.05320 -85.83 ±0.16 -23.12 ±0.25 -961.63 ±0.11 -235.87 ±0.26325 -80.40 +0.14 -21.94 +0.26 -893.69 +0.16 -218.90 +0.25333 -61.68 +0.33 -16.90 +0.72 -665.52 +0.35 -161.67 +0.52J12 = = 1.97 J13 = 0.36 J23 =J34 = 8.10 J24 = 0.89Table B.17: Dipolar couplings obtained from the ‘H-NMR spectra for the solutemetadichlorobenzene dissolved in 55% 1132/EBBA.Temp / K D12 = D14 D13 D23 = D34 D24290 -106.31±0.28 -31.04 ±0.50 -1122.60 ±0.27 -272.06 ±0.59295 -99.77±0.24 -29.85 +0.39 -1063.15 ±0.17 -258.17 ±0.48297 -95.52±0.01 -28.91 +0.02 -1018.82 ±0.01 -247.81 ±0.03299 -92.82±0.03 -28.00 ±0.05 -991.35 ±0.02 -241.22 ±0.06303 -88.39+0.04 -26.54 ±0.06 -945.86 ±0.03 -230.10 ±0.09305 -85.92±0.06 -25.70 ±0.08 -922.39 ±0.05 -224.44 ±0.15309 -80.19±0.06 -23.86 ±0.10 -860.27 +0.05 -209.50 ±0.13311 -75.49+0.05 -22.51 +0.07 -810.48 ±0.04 -197.29 +0.09315 -60.42±0.34 -15.28 ±0.65 -631.39 ±0.36 -151.58 ±0.66J12 = J14 = 1.97 J13 = 0.36 J23 =J34 = 8.10 J24 = 0.89Table B.18: Dipolar couplings obtained from the ‘H-NMR spectra for the solutemetadichlorobenzene dissolved in 70% 5CB/EBBA.Appendix B. Dipolar Couplings 135Temp D12 D13 D14 D23 D24 D347K294 -124.24 -25.04 -90.25 -1175.89 -313.29 -1357.82+1.12 +0.28 ±1.25 +5.31 +0.82 +4.37301 -118.24 -24.03 -86.92 -1133.45 -298.57 -1287.84±0.97 ±0.19 +1.08 +4.19 +0.59 ±3.56305 -114.99 -23.50 -86.69 -1111.64 -293.89 -1266.44±0.70 +0.13 +0.78 +3.24 +0.47 +2.74310 -111.18 -23.05 -85.81 -1085.06 -286.90 -1235.71+0.99 +0.20 +1.11 +4.83 +0.70 ±4.05315 -105.03 -22.75 -86.80 -1045.72 -280.03 -1208.34+1.68 ±0.42 +1.96 +10.32 ±1.74 +8.50318 -103.69 -22.39 -83.20 -1026.77 -269.52 -1163.15+2.27 +0.44 +2.53 +11.72 +1.70 +9.98323 -95.41 -21.22 -81.70 -954.00 -254.79 -1095.39±2.50 +0.55 ±2.94 +16.28 ±2.73 +13.53J12 = 2.00 J13 = 0.20 J14 = 1.90 J23 = 8.00 J24 = 0.90 J34 = 8.00Table B.19: Dipolar couplings obtained from the ‘H-NMR spectra for the solute 1,3-Bromochlorobenzene dissolved in 55% 1132/EBBA.Appendix B. Dipolar Couplings 136Temp / K D12 D13 D14 D23 D34300 -109.46 -25.61 -81.68 -985.12 -263.45 -1156.86+0.77 +0.17 +0.88 +3.91 +0.70 +3.17301 -109.02 -25.33 -77.35 -978.18 -256.68 -1123.12+1.56 +0.26 +1.71 +6.47 +0.94 +5.44302 -106.89 -24.73 -78.15 -963.61 -253.84 -1113.89±1.68 +0.29 +1.87 +7.57 +1.19 +6.29305 -104.66 -24.35 -75.03 -944.14 -246.76 -1077.95+2.36 +0.38 ±2.60 +9.70 +1.36 +8.23306 -101.51 -23.87 -75.87 -928.19 -243.34 -1067.15+0.93 +0.16 +1.04 ±4.21 ±0.63 ±3.54307 -100.45 -23.53 -74.98 -919.89 -241.32 -1051.19+1.75 +0.31 +1.95 +7.78 +1.14 +6.55J12 = 2.00 J = 0.20 J14 = 1.90 J23 = 8.00 J24 = 0.90 J34 = 8.00Table B.20: Dipolar couplings obtained from the ‘H-NMR spectra for the solute 1,3-Bromochlorobenzene dissolved in 70% 5CB/EBBA.Temp / K D12 = D16 = D23 D13 = D15 = D24 D14 D25 = D36= D4 =D45 = D56 =D26 =D35 =D46306 -624.04 +0.01 -120.77 +0.01 -78.65 +0.01309 -596.57 +0.00 -115.44 +0.00 -75.17 +0.01314 -558.20 +0.02 -107.98 +0.02 -70.32 ±0.02320 -512.80 +0.03 -99.18 +0.03 -64.58 +0.04325 -457.03 +0.03 -88.45 +0.04 -57.58 +0.04328 -373.43 ±0.22 -72.56 +0.13 -46.99 ±0.17J12 = J6 = J23 J13 = J15 = J24 J14 = J25 = J36 =0.65J34 J45 = = 7.55 =J26 =J35 =J46 = 1.38Table B.21: Dipolar couplings obtained from the ‘H-NMR spectra for the solute Benzelledissolved in 55% 1132/EBBA.Appendix B. Dipolar Couplings 137Temp / K D12 = D16 = D23 D13 = D15 = D24 D14 = D25 = D36= D3 —D45 = D56 =D26 =D35 =D46300 -565.83 +0.02 -109.51 +0.03 -71.35 ±0.04305 -516.40 +0.01 -99.99 +0.01 -65.13 +0.01307 -491.57 ±0.02 -95.11 +0.03 -61.95 +0.04309 -461.94 ±0.01 -89.43 +0.02 -58.24 +0.02311 -417.48 +0.03 -80.78 +0.04 -52.59 +0.05312 -398.03 +0.06 -76.72 +0.08 -50.08 +0.09313 -357.22 +0.12 -68.87 +0.14 -44.79 +0.15J12 = J16 = J23 J13 = J15 = J24 J14 = J25 =J36=0. 5J34 J15 = = 7.55 =J6 =J35 =J = 1.38Table B.22: Dipolar couplings obtained from the ‘H-NMR spectra for the solute Benzenedissolved in 70% 5CB/EBBA.Temp / K D11 = D22 D12300 2066.07 +0.04 -163.94 +0.04305 1958.81 +0.02 -155.51 +0.02310 1838.25 +0.04 -146.05 +0.04315 1705.11 +0.04 -135.55 +0.03320 1560.53 +0.10 -124.26 +0.07322 1559.38 +24.85 -119.94 +0.04325 1352.55 +40.46 -112.37 +0.08327 1315.09 +37.91 -107.64 +0.08329 1398.75 +51.04 -101.17 +0.09J12_= 2.70Table B.23: Dipolar couplings obtained from the1H-NMR spectra for the solute 2-Butynedissolved in 55% 1132/EBBA.Appendix B. Dipolar Couplings 138Temp / K D11 = D22 D12300 1606.40 ±0.02 -127.37 ±0.02301 1564.18 ±0.01 -124.05 ±0.01305 1439.99 ±0.03 -114.16 ±0.03307 1350.21 ±0.07 -107.20 ±0.07309 1247.35 ±0.04 -98.95 ±0.03312 992.09 ±34.09 -81.22 ±0.06J12_=_ .70Table B.24: Dipolar couplings obtained from the ‘H-NMR spectra for the solute 2-Butynedissolved in 70% 5CB/EBBA.Appendix COrder Parameters139Appendix C. Order Parameters 140Temp / K DHH(TCB) S k3301 -172.970 -0.21801 0.06337 67.53812305 -167.165 -0.21037 0.06202 64.82430310 -159.503 -0.20034 0.06007 61.37217315 -150.443 -0.18868 0.05757 57.28411320 -139.527 -0.17489 0.05430 52.47647322 -136.508 -0.17111 0.05338 51.33454325 -128.217 -0.16042 0.05044 47.64440327 -122.103 -0.15282 0.04849 45.04757330 -111.752 -0.13894 0.04459 40.37634Table C.25: Experimental order parameters S and S for the solute orthodichlorobenzene dissolved in 55% 1132/EBBA as a function of temperature.Temp / K DHH(TCB) S294 -160.958 -0.20354 0.05414 60.46520302 -147.713 -0.18569 0.05084 54.43857304 -145.327 -0.18259 0.05024 53.53156305 -143.330 -0.18001 0.04971 52.69720306 -140.632 -0.17660 0.04903 51.47000311 -128.517 -0.16031 0.04540 46.04045313 -120.278 -0.14995 0.04294 42.52127315 -111.610 -0.13898 0.04023 38.90255316 -102.083 -0.12783 0.03750 35.24450Table C.26: Experimental order parameters S and S for the solute orthodichlorobenzene dissolved in 70% 5CB/EBBA as a function of temperature.Appendix C. Order Parameters 141Temp / K DHH(TCB)285 -188.590 -0.23853 0.03197 73.47398292 -183.035 -0.23137 0.03057 72.40457301 -174.340 -0.22006 0.02881 69.91814305 -168.393 -0.21242 0.02763 67.70210310 -160.598 -0.20234 0.02637 64.56969315 -150.162 -0.18890 0.02494 59.93653320 -142.450 -0.17895 0.02379 56.80786325 -132.707 -0.16673 0.02274 52.69603333 -99.620 -0.12530 0.01864 37.97432Table C.27: Experimental order parameters S and S for the solute metadichiorobenzene dissolved in 55% 1132/EBBA as a function of temperature.Temp / K DHH(TCB) S290 -168.690 -0.21281 0.03363 63.15729295 -159.695 -0.20104 0.03110 59.84965297 -153.107 -0.19260 0.02973 57.08479299 -149.018 -0.18732 0.02879 55.48940303 -142.245 -0.17864 0.02735 52.99610305 -138.642 -0.17404 0.02641 51.67089309 -129.542 -0.16233 0.02464 48.02930311 -122.123 -0.15290 0.02317 44.95268315 -95.548 -0.11994 0.01929 33.95981Table C.28: Experimental order parameters S and S for the solute meta dichlorobenzene dissolved in 70% 5CB/EBBA as a function of temperature.Appendix C. Order Parameters 142Temp / K DHH(TCB) S S3294 -182.595 -0.23221 0.02546 -0.01318 70.43817301 -174.883 -0.22172 0.02447 -0.01154 67.96272305 -171.878 -0.21795 0.02392 -0.01113 67.41445310 -167.900 -0.21284 0.02345 -0.01049 66.47770315 -163.525 -0.20751 0.02306 -0.00939 65.37035318 -159.245 -0.20097 0.02279 -0.00907 63.29045323 -149.897 -0.18936 0.02158 -0.00763 59.65535Table C.29: Experimental order parameters S, S and S for the solute 1,3- bromochlorobenzene dissolved in 55% 1132/EBBA as a function of temperature.Temp / K DHH(TCB) S S300 -157.755 -0.19965 0.02605 -0.01175 58.40745301 -154.538 -0.19534 0.02576 -0.01111 56.96485302 -152.912 -0.19299 0.02519 -0.01102 56.38040305 -149.010 -0.18789 0.02478 -0.01031 55.03480306 -147.177 -0.18528 0.02431 -0.01007 54.30561307 -145.388 -0.18331 0.02395 -0.00966 53.79278Table C.30: Experimental order parameters S, S and S for the solute 1,3- bromochlorobenzene dissolved in 70% 5CB/EBBA as a function of temperature.Temp / K DHH(TCB)306 -160.738 -0.15838 66.05761309 -154.227 -0.15141 63.06516314 -145.058 -0.14167 59.10931320 -133.790 -0.13015 54.43838325 -119.867 -0.11600 48.30814328 -98.610 -0.09486 38.82091Table C.31: Experimental order parameters Sfor the solute berizene dissolved in 55%1132/EBBA as a function of temperature.Appendix C. Order Parameters 143Temp / K DHH(TCB) S k3300 -144.465 -0.14361 57.39262305 -132.525 -0.13107 52.31176307 -126.790 -0.12476 49.68468309 -119.402 -0.11724 46.47961311 -108.560 -0.10596 41.69242312 -103.712 -0.10101 39.60073313 -93.460 -0.09066 35.22472Table C.32: Experimental order parameters Sfor the solute benzene dissolved in 70%5CB/EBBA as a function of temperature.Temp / K DHH(TCB) S300 -175.418 0.20608 95.12899305 -169.237 0.19538 91.64436310 -161.773 0.18336 87.40088315 -153.080 0.17008 82.37475320 -143.097 0.15566 76.63711322 -139.210 0.15070 74.66101325 -132.395 0.14118 70.65552327 -127.438 0.13524 68.10666329 -120.798 0.12711 64.47373Table C.33: Experimental order parameters Sfor the solute 2-Butyne dissolved in 55%1132/EBBA as a function of temperature.Temp / K DHH(TCB) S300 -145.760 0.16023 73.90833301 -142.678 0.15602 72.22457305 -133.440 0.14363 67.42133307 -126.613 0.13468 63.70778309 -118.320 0.12442 59.28707312 -99.097 0.10204 49.24637Table C.34: Experimental order parameters Sfor the solute 2-Butyne dissolved in 70%5CB/EBBA as a function of temperature.
- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- A NMR study on zero electric field gradient nematic...
Open Collections
UBC Theses and Dissertations
Featured Collection
UBC Theses and Dissertations
A NMR study on zero electric field gradient nematic liquid crystals Chandrakumar, Thambirajah 1994
pdf
Page Metadata
Item Metadata
Title | A NMR study on zero electric field gradient nematic liquid crystals |
Creator |
Chandrakumar, Thambirajah |
Date Issued | 1994 |
Description | The role of intermolecular forces in describing the orientational nature of liquid crystals is not well understood. Previous studies using dideuterium as a solute in liquid crys- tals have demonstrated the importance for orientation of the interaction between the solute molecular quadrupole moment and the average electric field gradient present in liquid crystals. With the aim of learning aboilt additional orientational mechanisms, we have studied the orientation of solutes in special mixtures of liquid crystals, where the contribution from the environment to the average electric field gradient at the ²H nucleus of dideuterium is negligibly small. In order to understand the role of shortrange forces in such special mixtures, orientational studies have been undertaken in the mixtures 55 wt% ZLI- 1132(1132)/N- (-4-ethoxybenzylidene)-4’-butylariiline (EBBA), 56.5 wt% 1132/EBBA and 70 wt% 4-n-pentyl-4’-cyanobiphenyl (5CB)/EBBA. As a starting point, the C2v and D2h symmetry solutes meta dichlorobenzene, ortho dichlorobenzene, para dichlorobenzene, ortho dicyanobenzene, furan, tetrathiofulvalene and fiuorobenzene have been studied in the special mixtures 56.5 wt% 1132/EBBA at 323K and 70 wt% 5CB/EBBA at 316K, using proton NMR. The measured electric field gradient for these two mixtures has been found to be zero. The order parameters ob tained from an analysis of the NMR spectra indicate that the solutes experience a similar anisotropic potential in both mixtures. The results are interpreted in terms of a model for the short-range anisotropic potentials experienced by the solutes. To further explore the investigation of the short-range forces in zero electric field gradient mixtures, the temperature dependence of the solutes meta dichlorobenzene, ortho dichlorobenzene, 1,3-bromochlorobenzene, benzene and 2-butyne has been studied in the special mixtures 55 wt% 1132/EBBA and 70 wt% 5CB/EBBA, using proton NMR. These solutes vary from each other in symmetry and shape. The aim was to see how the different shaped solutes experience the short-range forces in the liquid crystal mixtures. The results indicate that the solutes experience a similar anisotropic potential in both mixtures. The biaxial order parameters measured for the solutes meta dichlorobenzene, ortho dichlorobenzene, and 1,3-bromochlorobenzene have also been analysed to magnify the differences between the mixtures. To extend our understanding on the intermolecular forces among constituent liquid crystal molecules, a temperature dependence study of the liquid crystal 5CB — d19 as so lute has been undertaken in the three liquid crystal mixtures: 55 wt% 1132/EBBA, 56.5 wt% 1132/EBBA and 70 wt% 5CB/EBBA, using ²H — NMR. The study of SCB — d19 as solute has been used to compare the short-range interactions in these special mixtures. The spectra of 5CB — d19 in the two 1132/EBBA mixtures are equivalent, but are dif- ferent from those in the 5CB/EBBA mixture. The spectra in 55 wt% 1132/EBBA and 70 wt% 5CB/EBBA have been analysed using two different models for the short-range potential, and parameters of the models have been used to compare the potentials in the different mixtures. It has been shown that, for a given spectral splitting of the chain C1 deuteron, the reduced short-range potential is the same in all three mixtures studied. The spectral differences observed are a consequence of different nematic-isotropic phase transition temperatures combined with the effect of trans-gauche isomerization in the hydrocarbon chain. |
Extent | 2179604 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
FileFormat | application/pdf |
Language | eng |
Date Available | 2009-04-09 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0061706 |
URI | http://hdl.handle.net/2429/6997 |
Degree |
Doctor of Philosophy - PhD |
Program |
Chemistry |
Affiliation |
Science, Faculty of Chemistry, Department of |
Degree Grantor | University of British Columbia |
GraduationDate | 1994-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
Download
- Media
- 831-ubc_1994-953233.pdf [ 2.08MB ]
- Metadata
- JSON: 831-1.0061706.json
- JSON-LD: 831-1.0061706-ld.json
- RDF/XML (Pretty): 831-1.0061706-rdf.xml
- RDF/JSON: 831-1.0061706-rdf.json
- Turtle: 831-1.0061706-turtle.txt
- N-Triples: 831-1.0061706-rdf-ntriples.txt
- Original Record: 831-1.0061706-source.json
- Full Text
- 831-1.0061706-fulltext.txt
- Citation
- 831-1.0061706.ris
Full Text
Cite
Citation Scheme:
Usage Statistics
Share
Embed
Customize your widget with the following options, then copy and paste the code below into the HTML
of your page to embed this item in your website.
<div id="ubcOpenCollectionsWidgetDisplay">
<script id="ubcOpenCollectionsWidget"
src="{[{embed.src}]}"
data-item="{[{embed.item}]}"
data-collection="{[{embed.collection}]}"
data-metadata="{[{embed.showMetadata}]}"
data-width="{[{embed.width}]}"
async >
</script>
</div>
Our image viewer uses the IIIF 2.0 standard.
To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0061706/manifest