Free Energies in the Landau and Molecular Field Approaches

An expression for the entropy as a power series in the order parameter is derived in the context of molecular field theory. The expression is valid both at and away from equilibrium. It is a unique generalization of molecular field theory to non-equilibrium situations. Discrepancies with certain expressions which have appeared in the literature are resolved. Analysis of the radius of convergence of the power series indicates that in certain cases, including the Maier-Saupe model of liquid crystals, molecular field theory and Landau theory cannot be made to agree over the entire range of possible values of the order parameter.     

Study of the molecular tilt angle and the order parameter of a ferroelectric liquid crystal mixture using IR spectroscopy

Abstract

We report measurements of the molecular tilt angle of a ferroelectric liquid crystal mixture (ZLI 3654), using infra-red spectroscopy, and of the optical tilt angle using polarizing microscopy. The molecular tilt angle is found to be approximately the same for different molecular vibrations. The second rank orientational order parameter for the axis of molecular vibrations of different groups of the molecule for homogeneously aligned samples have been determined as a function of temperature. The order parameter depends slightly on the sample thickness and is about 8 per cent higher for a lower thickness (～ 7 μm) compared to a higher thickness (～ 12 μm). The order parameter does not change significantly at the S_C?–S_A transition. The order parameter of S_C? is found to be unaffected by the application of a constant electric field. The order parameter for the alkyl chain is found to be about three times lower than for the molecular core.     

On the transitional properties of rigid oligomers. The orientational order of the monomer 4-n-pentyl-4′-cyanobiphenyl and its platinum dichloride linked dimer

Abstract

We have studied the orientational order of the monomer 4-n-pentyl-4′-cyanobiphenyl (5CB) and of the dimer, [PtCl₂(5CB)₂], formed by linking two cyanobiphenyl units via a platinum dichloride bridge, dissolved in a common nematic solvent, using deuterium NMR spectroscopy. Analysis of the second rank order parameters, obtained from these experiments, in terms of a molecular field theory yields the anisotropic solute-solvent strength parameter responsible for the solute alignment. In the limit of low solvent order the strength parameters for the monomer and dimer differ significantly, in accord with the differing anisotropies of these two solutes. However, as the solvent order increases, so the relative difference in the strength parameters decreases, tending to zero. A possible explanation for this intriguing behaviour is proposed.     

Anomalous density and refractive index variation of a nematic liquid crystal

Abstract

This paper reports the results of the measurement of refractive indices and densities of p-ethoxyphenyl trans-4-butyl cyclohexane carboxylate at different temperatures. The molecular polarizabilities have been calculated from refractive indices using Vuks' formula and orientational order parameters are determined from the polarizability values. The order parameter values have been compared with those obtained from Maier-Saupe theory. The compound shows anomalous behaviour regarding variation of density, ordinary refractive index and order parameter values with temperature. This is consistent with our previous X-ray study of this compound. The possible reason for this peculiar behaviour has been discussed.     

Adenosine A 2A receptor agonists: CoMFA-based selection of the most predictive conformation

A step-wise comparative molecular field analysis (CoMFA)-based procedure was applied to a series of 51 2-oxyadenosines in order to select the most predictive conformation for binding to A 2A adenosine receptor (AR). The highest correlation and predictive power were found for conformers with side chain at 2nd position oriented in the direction opposite to the exocyclic amino group on the adenine ring (torsion N1C2OR=120 ) and fully extended. The interaction of ligand and receptor is under steric and electrostatic control. The steric contribution is of a greater importance for the predictivity than the electrostatic one. Hydrophobicity of the compounds investigated does not affect significantly either the affinity to A 2A AR, nor the predictivity of the models.     

H-shaped liquid crystals inducing nematic order in the isotropic liquid

ABSTRACT

We prepared a homologous series of H-shaped liquid crystals I-n and investigated their phase transition properties using optical microscopy and differential scanning calorimetry. All the compounds exhibited a nematic phase at room temperature. The phase transition behaviour is explained in terms of molecular shape anisotropy. Furthermore, those compounds were found to exhibit electro-optical switching in the isotropic liquid in the vicinity of the nematic–isotropic liquid transition, indicating that the microscopic nematic order with a certain coherence length of the molecules exists in the optically isotropic temperature range.     

Synthesis, antimicrobial evaluation and QSAR studies of 3-ethoxy-4-hydroxybenzylidene/4-nitrobenzylidene hydrazides

A series of 3-ethoxy-4-hydroxybenzylidene/4-nitrobenzylidene hydrazides (1–20) was synthesized and tested for in vitro antimicrobial activity. The results of antimicrobial studies indicated that the compounds having dinitro, methoxy, hydroxy and nitro substituents on phenyl ring of the aromatic acids were most active ones. The QSAR investigation indicated the importance of the topological parameter, third order molecular connectivity index (³χ) in describing the antimicrobial activity of synthesized hydrazides.     

Orientational ordering of nanorods in diblock copolymers

ABSTRACT

Orientational ordering of rod-like nanoparticles in the lamellae phase of diblock copolymers has been considered theoretically using the model of a nanoparticle with two interaction centres. It has been shown that strongly anisotropic nanoparticles order spontaneously in the boundary region between the blocks where the orientational order is induced by the interface and by the interaction with monomer units in different blocks. The nematic order parameter possesses opposite signs in adjacent blocks which means that the nanorods are aligned parallel or perpendicular to the boundary between the blocks on different sides of their interface. Concentration and nematic order parameter profiles have been calculated numerically for different values of the nanoparticle length and compared with the results of recent computer simulations and with the results of the previous molecular theory based on nanoparticles of spherical shape.     

Strain coupling and scaling invariants in search for effective critical parameters of uniaxial ferroelectrics

A scaling equation of state giving a realistic ratio of Curie–Weiss constants and accounting for coupling of the order parameter with a strain (secondary order parameter) is used to describe the temperature dependence of the electric susceptibility in an external biasing field applied in case of uniaxial ferroelectrics. Explicit expressions for the resulting scaling invariants are given. The power laws for the temperature and field dependence of the maxima and of the inflection points of the susceptibility curves are found. The theory is exemplified by the effective critical behaviour of iono-molecular crystals (CH₃NH₃)₅Bi₂Cl₁₁ (MAPCB) and (CH₃NH₃)₅Bi₂Br₁₁ (MAPBB).     

Orientational fluctuations in a nematic liquid crystal as seen by neutron scattering

Abstract

Real time neutron scattering is used in the study of the slow orientational fluctuations of the director in a nematic sample. A statistical analysis of the observed time series gives the Hurst exponent H and β exponent of the frequency power spectrum that satisfy the scaling relationship β = 2H + 1. In the nematic phase, but not in the solid and in the isotropic liquid phases, the exponent values are those expected for a self-organized critical state. When a magnetic field, of the order of the Freedericksz field is applied, the nematic sample is observed to display persistent oscillations of the director. We confront this observation with theoretical predictions.     

Acoustic Nonlinearity Parameter of Liquid Alkanes as a Function of Temperature,Chain Length and Isomerism

Abstract

The acoustic nonlinearity parameter B/A along with intermediate quantities such as the pressure derivative of sound speed and the phase shift were measured in 8 linear alkanes and a series of four isomers of hexane. The influences of temperature and chain length on these quantities were revealed. It was found that the phase shift parameter is more sensitive to molecular structure and temperature than B/A and that the pressure derivative of sound speed.     

Magnetic field effects on atomic and molecular collisions

The full quantal theory of heavy-particle collisions in the presence of a static magnetic field, B, has been formulated. A new mechanism of magnetic field effect was found which depends on the velocity of the molecular center of mass and plays an important role at high-speed collisions. A power series expansion of the cross section as a function of B was obtained, which can be applied to collisions at weak field. It was also found that the differential cross section can become zero due to the magnetic field when a rovibronic energy level of a molecule is in resonance with another energy level.     

Phase diagrams of cholesteric liquid crystals obtained with a generalized Landau-de Gennes theory

Abstract

Phase diagrams of chiral nematic liquid crystals are studied within the framework of a generalized Landau-Ginzburg-de Gennes theory. Using the parametrization of Grebel, Hornreich, and Shtrikman for the tensor order parameter Q, all relevant elastic terms are included for the helicoidal phase and the blue phases of chiral nematic liquid crystals up to fourth order in Q and its gradient ?Q. The influence of the additional elastic terms on the phase diagrams of the chiral nematic phases is then investigated. The theory correctly describes the variation of the pitch with temperature and the induced biaxiality of the cholesteric phase. The results resolve the discrepancies encountered by Hornreich and Shtrikman in the comparison of experiment and theory. New features in the topology of the phase diagrams of blue phases, like re-entrant phase transitions, are predicted.     

Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices

Probabilistic evolution theory (PREVTH) is used for the solution of initial value problems of first order explicit autonomous ordinary differential equation sets with second degree multinomial right hand side functions. It is an approximation method based on Kronecker power series: a rewriting of multivariate Taylor series using matrices having certain flexible parameters. Kronecker power series have matrices which are called telescope matrices: \(n \times n^{j+1}\) matrices where j is the index of summation. The additive terms of each telescope matrix is formed through Kronecker product from both sides by Kronecker powers of identity matrices. Recently, squarification is proposed in order to avoid the growing of the matrices in size at each additive term of the series. This paper explains the squarification procedure: the procedure used in order to avoid Kronecker multiplications within PREVTH so that the sizes of the matrices do not grow and so that the amount of necessary computation is reduced. The recursion between squarified matrices is also given. As a numerical application, the solution of a Hénon–Heiles system is provided.     

Modeling Investigation of Volume Variation Kinetics of Fast Response Hydrogels

Abstract

Fast response hydrogels have attracted great attention recently. Three kinds of models with different complexity are available in the literature to investigate their volume variation kinetics. A phenomenal model based on second‐order reaction kinetics provides a simple method to correlate the experimental kinetic data. A power law model can be employed to evaluate different volume variation mechanisms according to the diffusion exponential coefficient. The multi‐field model incorporates mechanical deformation with the diffusion of ion species. The volume variation rate is dependent on both hydrogel molecular design and operation conditions.     

Determination of the orientational ordering of 4′-cyanophenyl-4-alkylbenzoates by 13C NMR

Abstract

The orientational ordering of three 4′-cyanophenyl-4-alkylbenzoates (with number of carbons in the alkyl chain, n = 6,7 and 8; hereafter abbreviated as n-CPBs) has been investigated by ¹³C NMR. The order parameters of different molecular segments in the nematic phase of the n-CPBs were determined by the two-dimensional technique of separated local field (SLF) spectroscopy combined with off-magic-axis, variable-angle spinning (VAS) of the sample. The carbon-13 chemical shifts for each carbon nucleus in these compounds were determined by slowly spinning the sample parallel to the applied magnetic field. The order parameters obtained from SLF/VAS studies are linearly related to the corresponding anisotropic carbon-13 chemical shifts. These results provide a convenient way to obtain the order parameters for other homologous members of this liquid crystal series by direct measurement of only their carbon-13 chemical shifts in conjunction with the observed linear relationship between order parameters and chemical shifts.     

A re-examination of the justification of neglect of differential overlap approximations in terms of a power series expansion inS

Neglect of differential overlap methods are treated as approximations to calculations in a symmetrically orthogonalized basis. The accuracy of this approximation is investigated in terms of a power series expansion of the overlap matrix. TheS-matrix can be transformed into a matrix which will give a convergent series, and this series is used in the examination. The only approximation having any justification from this point of view is the NDDO method and even this neglects certain important three-electron integrals. Corrected expressions for the repulsion integral scaling factors introduced by Chandrasekharet al. are also derived. On leave from The Chemistry School, University of Western Australia.