N. V. Madhusudana

Elastic and Optical Properties of Some 4′-n-Alkyl-4-Cyanobiphenyls

Abstract The bend elastic constants (k 33) and order parameters (S) derived from optical measurements in the nematic phase of pentlyl, hexyl, heptyl and octyl cyanobiphenyls (5CB, 6CB, 7CB and 8CB respectively) are reported. The odd-even effect is clearly seen in the K 33 values of all four compounds and in the S values of the first three. 5CB, 6CB and 7CB show only the nematic mesophase but their elastic constants indicate the existence of smectic-like short range order. For example, even the lowest homologue, 5CB, does not obey the law k 33 ∞ S 2 given by the mean field throry. 7CB, has about the same order parameter as 5CB but a much higher elastic constant. 8CB, which shows a smectic A phase as well, exhibits a lower k 33 than 7CB near the nematic-isotropic transition point but a pronounced pretransitional increase near the A-N transition.

Elasticity and Orientational Order in Some Cyanobiphenyls: Part IV. Reanalysis of the Data

Abstract We present revised absolute values of the elastic constants and order parameters of several cyanobiphenyls. The calculations make use of our earlier measurements of Freedericksz threshold fields and refractive indices, and corrected values of normalizing constants, particularly in respect of the anisotropy of magnetic susceptibility. The new values agree well with some recent measurements.

Elasticity and Orientational Order in Some 4′-n-Alkyl-4-Cyanobiphenyls: Part II

Abstract The splay and twist elastic constants (k 11 and k 22) of pentyl, hexyl, heptyl and octyl cyanobiphenyls (5CB, 6CB, 7CB and 8CB respectively) have been determined by the Freedericksz transition method. The results are compared with the bend elastic constants (k 33) and order parameters (S) of these compounds reported by us in an ealier paper, as also with the heats of transition (δH) determined using a differential scanning calorimeter and the temperatures of transitions (T NI). T NI, and k 33 near T NI, exhibit alternation for all the four compounds. On the other hand, S, δH, and k 11 and k 22, near T NI exhibit alternation only for the first three compounds and increase between 7CB and 8CB. It is concluded that (ζ⊥/ζ∥), the ratio of the transverse to the longitudinal correlation lengths of the smectic A type cybotactic order increases between 7CB and 8CB.

Biaxial smectic A phase in homologous series of compounds composed of highly polar unsymmetrically substituted bent-core molecules

Several compounds belonging to three new series of five-ring banana-shaped esters, which are unsymmetrically substituted with respect to the central phenyl ring, have been synthesised. One of the arms of these bent-core molecules has been terminally substituted with a highly polar cyano group while the other end contains an alkoxy chain. The mesophases exhibited by these compounds have been characterised using a combination of optical polarising microscopy, differential scanning calorimetry and X-ray diffraction studies. These studies indicate that most of the compounds show two smectic A mesophases which have a partial bilayer ordering. Conoscopic experiments clearly reveal that the lower temperature smectic A phase is biaxial in nature. A structural model has been proposed for the lower temperature biaxial smectic A phase. It is argued that quartets of molecules, which are conducive to the formation of the biaxial phase, can form in the layers. The in-layer birefringence of the biaxial smectic A phase has also been measured as a function of temperature for one of the compounds.

Molecular statistical theory of nematic liquid crystals

Assuming a model based on permanent dipole-dipole, dispersion, induction and repulsion forces, the potential energy of a molecule in a nematic liquid crystal is derived as a function of its orientation. Analysis of the temperature variation of the degree of orientational order in p-azoxyanisole (PAA) and p-azoxyphenetole (PAP) indicates that the permanent dipole interactions are relatively unimportant. Making use of a mean field approximation, a statistical theory of long-range orientational order is developed and the thermodynamic properties of the ordered system are derived relative to those of the completely disordered one. Application of the theory to PAA and PAP shows conclusively that a certain degree of short-range orientational order is present in the liquid phase. Using just three parameters for each compound, viz. the two constants of the potential function and a numerical factor to allow for short range order, the following physical properties have been evaluated which are in quantitative agreement with the experimental data: the long-range orientational order parameter, specific heat and compressibility as functions of temperature in the liquid crystalline range, the latent heat and volume change at the nematic-isotropic transition point. The magnetic birefringence of the liquid phase affords an independent estimate of the short range order which supports the previous calculations.

Theory of birefringence of nematic liquid crystals

A theory of the birefringence of nematic liquid crystals is de- veloped taking into account the intermolecular potential energy arising from dipole-dipole, anisotropic dispersion, induction and repulsion inter- actions. The potential energy exhibits a dependence on molecular orientation and is expressible ae - (uo + u1 cost9 + uz cosat9 + u4 cos48 + u6 cosee + ...) where t9 is the angle which the long axis of the molecule makes with the uniaxial direction of the liquid crystal. The birefringence of the medium is evaluated in terms of the Boltzmann distribution of the oriented mole- cules. The theory explains the experimentally observed result that the temperature coefficient of the extraordumy index is large and negative whereas that of the ordinary index is small and positive. Analysis of the data on p-azoxyanisole and p-azoxyphenetole shows that dispersion and repulsion forces play a predominant role in determining the temperahre variation of the birefringence. Assuming that the molecular librations in the liquid crystal can be represented by a system of harmonic oscillators, the rn librational mnpli- tude is evaluated for p-azoxyaniaole from recent measurements of the ultrasonic velocity. The increase in the rn amplitude With temperature in the nematic range is found to be in good agreement with that obtained directly from the experimental data on birefringence.

Statistical theory of orientational order in nematic liquid crystals

Assuming a model based on dispersion and repulsion interactions, it is shown that the orientational potential energy of a molecule in a nematic liquid crystal is expressible as, where U i = −(u 0 + u 2 cos 2 θ i + u 4 cos 4 θ i + u 6 cos 4 θ i + ....), u 0 = w 00 + w 02 cos 2 θ + w 04 cos 4 θ + .... u 2 = w 20 + w 22 cos 2 θ + w 24 cos 4 θ + ...., etc., W mn = W nm , and θ is the angle which the long axis of the molecule makes with the uniaxial direction of the medium. Using a slightly simplified form of this function, a statistical theory of long range orientational order in the nematic state is developed. The thermodynamic properties of the ordered system are evaluated relative to those of the completely disordered one, and the conditions of equilibrium are discussed. The constants of the potential function are determined for p-azoxyanisole that lead to a theoretical curve for the degree of orientational order and a volume change at the nematic-isotropic transition point in good agreement with observations. However, the predicted latent heat of the nematic-isotropic transition is significantly higher than the experimental value suggesting that a certain degree of short range order persists in the liquid phase. The calculated latent heat of transition as well as the specific heat and the compressibility of the liquid crystal fit the experimental data when a correction factor is included in the theory to allow for the effect of short range order. The magnetic birefringence of the liquid phase gives an independent estimate of the short range order which confirms the previous calculations.

A simple molecular theory of double reentrance exhibited by highly polar compounds

Abstract We show by simple model calculations that dipole-induced dipole and interchain interactions lead to a parallel alignment of molecules with strong longitudinal dipoles for intermolecular separations below a certain value. On the other hand an antiparallel alignment is favoured for larger separations because of dipole-dipole interactions. We incorporate this change in the intermolecular configuration, which naturally leads to two ‘lengths’ in the problem, in developing a simple McMillan type molecular theory of the double reentrance phenomenon in which the following phase sequence is observed on cooling the sample: isotropic-nematic-smectic Ad-reentrant nematic-smectic A1. The calculated properties including the phase diagram are in broad agreement with experimental trends.

Experimental determination of the flexoelectric coefficients of some nematic liquid crystals

Abstract We report measurements of the temperature variation of the flexoelectric coefficient (e 1–e 3) of a number of nematic liquid crystals like phenylcyclohexanes, cyanobiphenyls, etc. We have also measured (e 1+e 3) of a few systems using appropriate methods of applying an electric field gradient to the sample. In most of the systems, (e 1–e 3)/k, where k is a curvature elastic constant, is found to be positive and independent of temperature, as expected. However, in 4-heptyl-1-(4-cyanocyclohexyl)cyclohexane and a few other compounds with relatively flexible parts, |(e 1–e 3)/k| increases with temperature. We discuss the possible molecular origin of the sign and temperature dependence of the flexoelectric coefficients of the systems studied.

Short range orientational order in nematic liquid crystals

The different approximations that have been used in applying Bethe’s cluster model to the nematic-isotropic phase transition are examined. It is shown that the introduction of a higher order term in the mean field potential of an outer molecule of the cluster improves the consistency of the theory considerably. In particular, the importance of satisfying Chang’s relation is emphasized. Calculations are presented of the long and short range order parameters, heat of transition and specific heat for different values ofz, the number of nearest neighbours around any given molecule, for both nonpolar and antiparallel near neighbour correlations. Even the new mean field potential appears to be inadequate forz=3.