On the Influence of Elastic Modes on the N.M.R. Lineshapes of Polymer Liquid Crystals

Abstract

We have studied the influence of thermally excited orientational fluctuations on the N.M.R. lineshape of a nematic monodomain. The influence is characterized by a static order parameter S _stat whose theoretical expression in terms of viscoelastic parameters is derived. This model is applied to the proton N.M.R. spectrum of a thermotropic main chain polymer. The values of S _stat are deduced from the study of the changes of the N.M.R. lineshape as a function of the angle between the static magnetic field and the nematic director. Good agreement is obtained with theoretical values calculated using estimated values of the Leslie viscosity coefficients and the Frank elastic constants. The importance of an accurate knowledge of S _stat for a number of problems is stressed.     

Proton N.M.R. lineshape in nematic microdroplets

The dependence of the proton N.M.R. absorption spectrum on nematic director configuration and molecular self-diffusion in nematic submicrondroplets is analysed. The lineshape is evaluated numerically for radial and bipolar director configuration. The motional averaging is taken into account by means of a numerical simulation of the molecular diffusion which induces slow molecular reorientations due to non-uniform orientational ordering in the droplet. This diffusion process strongly affects the absorption spectra of the radial configuration, whereas spectra of the bipolar configuration are only slightly influenced. The possibility of determinating the submicrometre nematic droplet structures using the proton N.M.R. lineshape is discussed.     

Proton N.M.R. lineshape in nematic microdroplets

The dependence of the proton N.M.R. absorption spectrum on nematic director configuration and molecular self-diffusion in nematic submicrondroplets is analysed. The lineshape is evaluated numerically for radial and bipolar director configuration. The motional averaging is taken into account by means of a numerical simulation of the molecular diffusion which induces slow molecular reorientations due to non-uniform orientational ordering in the droplet. This diffusion process strongly affects the absorption spectra of the radial configuration, whereas spectra of the bipolar configuration are only slightly influenced. The possibility of determinating the submicrometre nematic droplet structures using the proton N.M.R. lineshape is discussed.     

N.M.R. study of segmental molecular interactions in liquid crystals

A simple statistical model of interacting non-rigid molecules, based on a perturbation expansion of the pair correlation function and the additivity of segmental interactions, is applied to the study of orientational order as measured by N.M.R. in the nematic and S_A phases of 4-n-alkyl-4'-cyanobiphenyls (N-CB, N = 5 to 8), the nematic and S_C phases of 4-n-alkyloxybenzoic acids (N-OBA, N = 7, 8) and the D_h0 columnar discotic phase of hexa-alkyloxytriphenylenes (N-THE, N = 5 to 8). The order parameters of each homologous series are correctly described in terms of two isotropic and two anisotropic segmental coupling constants. The model predicts certain relations among coupling constants pertaining to different homogous series. These predictions are supported by the results obtained for the three types of compounds studied.     

The influence of director fluctuations on molecular reorientation of a small probe molecule in a liquid-crystalline environment

The influence of director fluctuations on a probe molecule dissolved in a nematic liquid crystal is calculated to all orders using the gaussian properties of the director field. Consequences for the N.M.R. spectrum and relaxation through quadrupolar interaction of the probe molecule are indicated. It is found that the equilibrium distribution of molecular orientations, and consequently quadrupolar spectral splittings are virtually unchanged by fluctuations in the director field. The spectral densities are also obtained and it is shown that in addition to J₀₁ also J₀₀ and J₀₂ become frequency dependent in the N.M.R. frequency range. The frequency dependence of J₀₀ and J₀₂ has a logarithmic contribution; the magnitude of the frequency dependent contribution to J₀₂ is, however, insufficient to explain experimental results.     

The effect of molecular biaxiality on the bulk properties of some nematic liquid crystals

The nematic substance 5CB is known from N.M.R. studies to be slightly biaxial, not in the sense that any bulk property measured in a direction at right angles to the director is liable to vary with rotation about the director, but in the sense that there are biaxial terms in the ordering matrix that describes the alignment of individual molecules; (S_xx - S_yy) is non-zero as well as S_zz. We show that the biaxial terms should make a significant contribution to the magnetic anisotropy Δχ^(m) of 5CB, and that the magnitude and temperature dependence of this bulk property, which we have measured, can be understood if, and only if, they are taken into account. The contribution which they make to the optical birefringence term ∑ should, however, be relatively trivial. Although ∑ may in principle be affected by local field corrections of a complicated nature, which do not affect Δχ^(m), a new theory presented in an Appendix to the paper suggests that these too are likely to be relatively trivial. Hence we believe that ∑ is more nearly proportional than is Δχ^(m) to the principal order parameter S_zz.

The paper includes unpublished data for the magnetic anisotropy and/or the principal refractive indices, n_e and n_o, in a number of other nematics (6CB, 7CB, 8CB, 9CB, 5OCB, 6OCB, 7OCB, 8OCB, 7CCH, MBBA and PAA). Comparison between the temperature dependence of Δχ^(m) and of ∑ suggests that biaxiality is present in all cyanobiphenyls, on much the same scale as in 5CB, and is not affected by the presence of an oxygen atom between the phenyl core of the molecule and its alkyl tail.     

Solute alignment in liquid crystal solvents The Saupe ordering matrix for anthracene dissolved in uniaxial liquid crystals

We have described a theory for U, the potential of mean torque of rigid solutes at infinite dilution in a uniaxial liquid crystal phase; this may be used to calculate (S_xx - S_yy) and S_zz, the principal elements of the Saupe ordering matrix. In its simplest form U(ω) contains only second-rank terms and the dependence of the biaxiality (S_xx - S_yy) is determined by ω, a parameter which describes the departure of the potential of mean torque from cylindrical symmetry, and is predicted to be temperature independent. If dispersion forces are responsible for the magnitude of the orientational order parameter then ω should be independent of the solvent and depend only on the anisotropy in the electric polarizability of the solute. Indeed, this independence should result for any pair potential which can be factorized into a product of solute and solvent properties. These predictions are tested here by determining values of S_zz and (S_xx - S_yy) for anthracene-d₁₀ as a solute in several liquid crystal solvents, from the quadrupolar splittings obtained from the deuteron N.M.R. spectra. It is found that ω has a strong dependence on the nature of the solvent, which demonstrates that the solute ordering cannot be determined primarily by dispersion forces, or by a factorizable potential. There is also a weaker temperature dependence of λ observed for each binary mixture, and we show how this might be caused by a dependence of ω on solvent ordering, or by the inclusion of a fourth-rank term in U(ω).     

Novel glassy nematic and chiral nematic oligomers derived from 1,3,5-cyclohexanetricarboxylic and (1R,3S)-( )-camphoric acids

Novel nematic and chiral nematic liquid crystals capable of vitrification have been synthesized using 1,3,5-cyclohexanetricarboxylic and (1R,3S)-(+)-camphoric acids as the base structures to which cyanotolan, cyanobiphenyl, methoxybiphenylbenzoate nematogenic groups, (S)-(-)-1-phenylethylamine and (S)-(+)-1,3-butanediol chiral moieties are attached. Once the glassy state is induced by quenching or controlled cooling from the isotropic state, these liquid crystals showed no detectable tendency towards crystallization upon heating through the glass transition temperature. In all cases, the ΔC_p and ΔH_c values resulting from the DSC heating scans are comparable to those previously reported for polymer analogues and other low molar mass glassy liquid crystals. In the nematic series with varying spacer lengths, both T_g and T_c are consistently lower than the linear polymer counterparts, in contrast to the siloxane-based systems. It was also demonstrated that cholesteric mesomorphism can be induced following one of the three approaches: chiral nematic mixture, chiral nematic cyclic cooligomer, and pendant nematogenic groups attached to a chiral ring.     

Synthesis and transition temperatures of novel fluorinated chiral liquid crystals containing 1,4-tetrafluorophenylene units

To continue the search for novel series of fluorinated ferroelectric liquid crystals, an additional two series of 4-[(S)-2-methylbutoxy]phenyl 4-[(4-n-alkoxy-2,3,5,6-tetrafluorophenyl)ethynyl] benzoates (C) and 4-(n-alkoxy)phenyl 4-[(4-(S)-2'-methylbutoxy-2,3,5,6-tetrafluorophenyl)] benzoates (D) have been synthesized. Polarizing microscopic textural observations and DSC measurements of the phase transitions of these novel compounds showed that compounds C were liquid crystals with a chiral nematic (N) phase and a monotropic chiral smectic C phase (S_c), and compounds D exhibited a chiral nematic (N) phase.     

Alignment behaviour of the discotic nematic phase of 2,3,6,7,10,11-hexa(4-n-octyloxybenzoyloxy)triphenylene on polyimide and cetyltrimethylammonium bromide coated substrates

The orientational behaviour of the nematic discotic phase of 2,3,6,7,10,11-hexa(4-n-octyloxybenzoyloxy)triphenylene (C8OBT) on substrates coated with a polyimide or cetyltrimethylammonium bromide (CTAB) was investigated by polarizing optical microscopy. The averaged order parameters and directions of the triphenylene core and the carbonyl groups of C8OBT were evaluated by an infrared dichroic method. The discotic nematic (N_D) phase of C8OBT exhibits a homeotropic alignment on a polyimide film, a typical nematic schlieren texture on a glass substrate, and a tilted or planar homogeneous alignment on a CTAB-coated substrate. The order parameter of the triphenylene core is higher on a polyimide film (S = 0.6) than on a CTAB-coated substrate (S = 0.2), whereas that of the carbonyl groups remains roughly constant at 0.2 to 0.3 independent of the substrate for the N_D phase.     

Orientational ordering of 4-substituted phenylcyclohexanes studied by carbon-13 two-dimensional N.M.R.

An N.M.R. method combining the techniques of separated local field spectroscopy (SLF) and variable angle spinning (VAS) is valuable in the investigtion of nematic liquid crystals. Rapid sample spinning causes the nematic director to align along the spinning axis, resulting in narrow peaks in the C-13 N.M.R. spectrum. SLF is a two-dimensional N.M.R. method which produces a first order splitting pattern for each carbon signal from which C-H dipolar coupling constants can be determined. The order parameters for all segments of the liquid crystal molecule can then be calculated. Results for three 4'-cyanophenylcyclohexanes are considered here. These compounds are trans-substituted at the 4 position of cyclohexane ring with n-pentane (PCH5), 1-pentene (3d₁CP) and 3-pentene (1d₃CP), respectively.     

Ultra-slow director rotation in nematic side-group polymers detected by N.M.R.

A novel N.M.R. method is described in which very high values of the rotational viscosity in nematic liquid crystals are measured with an improved accuracy of several orders of magnitude as compared to conventional N.M.R. methods. It consists of monitoring the deuteron line splitting while rotating the sample in a magnetic field. The rotation speed of the sample container is chosen such that the director orientation follows the container orientation, albeit with a certain phase lag. By synchronizing the data acquisition with the container orientation the phase lag is monitored for several hours. A simple relation, derived from the Ericksen-Leslie-Parodi equations, holds between the rotational viscosity and the phase lag. Frequencies as low as 10^-6 Hz can be measured precisely.     

N.M.R. investigations and the molecular field theory of nematic mixtures

N.M.R. measurements have shown that the mixture E5 can be described by a single order parameter. Based on molecular field theory the nematic-isotropic transition and the temperature dependence of the order parameter in the nematic phase are considered for a binary mixture of nematogens. Guided by the results of the N.M.R. measurements the binary mixture is treated as an effective medium characterized by a single order parameter. Soft attractive forces are taken into account as well as the excluded volume. The coexistence of nematic and isotropic phases in the phase transition region is discussed in detail.     

Solute alignment in liquid crystal solvents The Saupe ordering matrix for perylene and pyrene

The complete second rank ordering matrix for perylene-d₁₂ and pyrene-d₁₀ in four different thermotropic liquid crystals has been determined over large temperature ranges, by interpreting the quadrupolar splittings observed from the deuterium N.M.R. spectra. The dipolar couplings also observed in the spectra were determined by computer simulation for both probes, allowing the commonly made assumptions of rigidity and planarity of these molecules to be tested. It is found that the perylene results are consistent with a non-rigid and non-planar structure with an average twist angle between the napthtalene units of 11.6°, whereas pyrene is rigid and planar within experimental error. It is also observed that both molecules are highly biaxial in their orientational behaviour and therefore another assumption often made especially in fluorescence measurements, that of disc-like cylindrical symmetry, is invalid. The results are interpreted in terms of a molecular field theory which predicts the variation of (S_xx - S_yy) with S_zz by calculating these quantities from the potential of mean torque, U(β, γ), of rigid solutes, expressed solely in terms of one adjustable parameter, the biaxiality parameter, λ. This parameter is predicted by some theories to be both temperature and solvent independent, but our results show that there is a weak temperature dependence and a stronger solvent dependence.     

Study of internal ring rotation and molecular reorientation in the liquid crystal 5O.7 by deuterium N.M.R. spectroscopy

The spectral densities of motion were determined by deuterium N.M.R. relaxation measurements in the nematic, smectic A and smectic C phases of 4-n-pentyloxybenzylidene-d₁-4'-heptylaniline and 4-n-pentyloxybenzylidene-4'-heptylaniline-2,3,5,6-d₄. By examining two atomic sites on a 5O.7 molecule, we were able to gain information on the reorientation motion and internal rotation of the aniline ring. It was also found that director fluctuations make some contribution to the spectral density J₁ (ω). We use the superimposed rotations model to account for the internal ring motion and the small step rotational diffusion model for the molecular reorientation. The derived rotational diffusion constants for the spinning and tumbling motions appear to give physically plausible activation energies in the mesophases of 5O.7.     

Splay elasticity in an oligomeric liquid crystal

A magnetically-induced Freedericksz transition was used in conjunction with capacitance techniques to determine the splay elastic constant of the 4,4'-dialkoxyphenylbenzoate monomer '5OO5rsquo; [C₅H₁₁OC₆H₄COOC₆H₄OC₅H₁₁] and its dimer. As a function of reduced temperature in the nematic phase, it was found that K₁₁ of the dimer is only about 20 per cent larger than that of the monomer. Moreover, the values of K₁₁/S² versus reduced temperature, where S is the scalar order parameter, are equal to within experimental noise. These results suggest that for short oligomers Meyer's entropic model for splay elasticity in polymer liquid crystals is not applicable. A lowest order correction to the entropic model is suggested, which partially accounts for excluded volume and dispersive effects.     

Liquid crystalline compounds in the thiophene series. VIII. Synthesis and characterization of liquid crystalline vinylenes with thiophene moieties and carbaldehyde groups

New thermotropic liquid crystal compounds, with one and two mesogenic groups, have been synthesized and characterized. The structural elements of the compounds consist of thiophene ring systems, vinylene units and, for some compounds, carbaldehyde groups. Mesogenic groups involving three thiophene ring systems are normally not liquid crystalline. Only in the case of E,E-5-[5-(5-butyl-2-thienylvinyl)-2-thienylvinyl]-2-thiophenecarbaldehyde could a monotropic nematic phase be easily observed. By replacing thiophene ring systems in the core with a benzene ring system, or by attaching one carbaldehyde group at the moieties, or by doubling the mesogenic groups via an alkylene spacer, the temperature ranges of the mesophases of the compounds with thiophene ring systems can be enlarged or liquid crystal phases induced. The small values for δS_NI, which have been observed for the low molecular weight compounds, indicate a very low order in the nematic phases.     

A study on the relaxation phenomena of nematic polymers after cessation of shear flow

A viscoelastic model, composed of the Ericksen and Landau-de Gennes nematic continuum theories, is used to study numerically the relaxation phenomena after cessation of simple shear flow for a model rigid rod uniaxial nematic polymer. This model predicts that under certain conditions the relaxation of stored molecular and coupling elastic free energies due to periodic fluctuations in the scalar order parameter results in a transient periodic distortion of the director field. These conditions are that: (1) the ratio of the wavelength scales of the initial periodic spatial variation in the scalar order parameter k_s to the initial periodic planar director orientation fluctuation kφ (i.e. k_S/kφ) and the amplitude of the initial S spatial variation exceed certain minimum values, and (2) kφ is not zero. It is shown that the wavelength selection mechanism is controlled by the director reorientation-induced backflows. The digitized optical patterns of the transient periodic director field show transient periodic optical patterns similar to the transient banded texture nematic polymers exhibit after cessation of shear flow when observed between crossed polars. The numerical results and digitized optical patterns replicate frequently reported experimental observations.     

CNDO/2 study of the mechanism and kinetics of the CIS-trans isomerization of N2F2(g) using the activated-complex theory

Complete optimization of the molecular geometry of N₂F₂ confirmed the two previously assumed activated complexes (AC's) for the title reaction. The contributions of both AC's were precisely weighed up in terms of the activated-complex theory. The possibility of an autocatalysed chain mechanism is discussed because of the disagreement of theoretical and experimental ΔH^‡_T and ΔS^‡_T values.     

Photochemical E/Z isomerization of aryl-substituted methanimines. AM1-CI potential energy curves along the CN double bond twisting and the N atom in-plane inversion

Potential energy curves of aryl-substituted methanimines along the C = N bond twisting and the in-plane inversion of the N atom were obtained by AM1-SDCI calculations, and the photochemical E/Z isomerization paths were elucidated. An aromatic group introduced at the C atom of the C = N group has little effect on the S₀ surface for the inversion and rotation paths, while it has a significant effect on the shape of the T₁ curve along the rotation path. It is suggested that phenylmethanimine and 2-anthrylmethanimine undergo photoisomerization by the rotation mechanism. The methoxy group introduced at the N atom raises the inversion barrier on the S₀ state, while it lowers the 90°-twistedT₁ energy. TheT₁ potential energy curves of N-methoxy-1-phenylethanimine and N-methoxy-1-(2-anthryl)ethanimine indicate that the former undergoes a two-way isomerization and the latter a one-way isomerization by the rotation mechanism, which is in accordance with experiment.