Variation Of Order Parameter Research Articles

VARIATION OF THE ENTROPY OF THE TRANSITION IN NEMATIC MIXTURES

The temperature variation of orientational order parameter in binary mixtures of two nematic compounds viz P-(p-ethoxy-phenylazo) phenyl Valerate (EPPV) and N-(p-propoxybenzylidene)p-pentylaniline (PBPA) has been estimated using refractive index and density data. The higher order parameter (p4) has been estimated. Employing the Humphries-James-Luckhurst theory the entropy of the transition of the mixtures at different concentrations has been computed. It is observed that the increase in the value of entropy of the transition is associated with the increase in the pair potential of the molecules in the mixtures.

OFF-AXIAL DYNAMIC SYMMETRY BREAKING IN UNIAXIALLY ANISOTROPIC HEISENBERG FERROMAGNET

The dynamics of uniaxially (along the z direction) anisotropic Heisenberg ferromagnets (in three dimensions) in the presence of a magnetic field varying sinusoidally in time (along the x-direction only) is studied by Monte Carlo method using Metropolis rate. The time averaged (over a complete cycle of the oscillating field) value of z component of the magnetization continuously vanishes at a particular transition temperature associated with a dynamic symmetry breaking of mz-hx loop. The temperature variation of dynamic order parameter and the dynamic specific heat for different values of the anisotropy show that the transition temperature increases as the strength of anisotropy increases.

Methods for the exact construction of mesoscale spatial structures in liquid crystal polymers

We examine orientational patterns of liquid crystalline polymers (LCPs) using a mesoscale Doi theory that couples short-range, excluded-volume molecular interactions, rotary molecular diffusion, and the Marrucci–Greco potential for finite-range distortional elasticity. The model is a full tensor, polymeric generalization of small-molecule liquid crystal (Ericksen–Leslie) theory. The symmetric, traceless, rank 2 orientation tensor corresponds to micron-scale, averaged 3D microstructure through an orthogonal frame of eigenvectors (the directors, or principal optical axes) and corresponding eigenvalues (the order parameters) which convey the degrees of orientation with respect to the optical axes. These model quantities are directly related to intensity data from light scattering experiments. We focus on a classical method, separation of variables, to provide an exact construction of spatial patterns, both steady and time-dependent. Our constructions arise from posited tensor representations in spectral variables, separating spatial structure arising from optical axes variations versus order parameter variations. The reduced equations are solved to generate a variety of mesoscale structures, presented both in terms of the geometric content of the orientation tensor and in terms of the light scattering intensity patterns which would result from these exact macromolecular structures.

Improper orientational ordering regime and tricritical behavior in a lyotropic liquid crystal.

Optical microscopy, deuteron quadrupolar NMR, x-ray diffraction, and electrical conductivity techniques have been used to map the phase diagram and to measure the nematic order parameter variation (S) in ternary mixtures of pentadecafluorooctanoate acid ammonium salt (APFO), heavy water (D2O), and ammonium chloride (NH4Cl). A phenomenological model with an isotropic parent phase and a single primary segregation order parameter is elaborated on to describe in consistent terms the linear dependence of S(T) through the whole nematic stability region as well as the existence of a tricritical point at the nematic-to-lamellar phase transition line.

Premartensitic and martensitic transformations in Ti49Ni51 single crystal: Ageing effect

The influence of isochronous annealing on the phase composition, long-range atomic-order parameter S in the B2 phase, premartensitic structure, and martensitic transformation sequence and temperatures in a Ti49Ni51 single crystal was studied by X-ray and neutron-diffraction. Ageing the test alloy was found to bring about concurrent changes in the type of the intermediate shear structure involved and in the sequence of martensitic transormations in the premartensitic temperature range studied. The increase in the order parameter for the B2 phase was most pronounced in passing from the zonal stage of ageing to the growth stage of the Ti3Ni4 precipitates, as revealed by X-ray diffraction. No apparent correlation between the type of the premartensitic structure, R-transformation temperature, and order parameter variations was observed. At the same time, the martensite start temperature into the B19′ phase was directly proportional to variations in S.

Lipid domains in the exoplasmic and cytoplasmic leaflet of the human erythrocyte membrane: a spin label approach.

The existence of different lipid domains in the monolayers of the human erythrocyte membrane was investigated at 4 degrees C by employing spin-labelled phospholipid analogues. Spectra of analogues located exclusively either in the exoplasmic or in the cytoplasmic leaflet of erythrocyte membranes were recorded. Spectra were simulated by variation of order parameter describing the average amplitude of motion of the long molecular axis of the nitrogen 2 p pi orbital of the spin label and of the respective correlation times. For both leaflets at least three components were required to fit the experimental spectra, differing mainly in the order parameter. While the parameters of each component are not very different between both membrane halves, the relative contribution of each component to the spectrum is different between the exoplasmic and cytoplasmic leaflet. The order parameter of the most fluid component, presumably resembling the lipid bulk phase, is smaller in the cytoplasmic leaflet in comparison to the exoplasmic one. The lateral coexistence of different lipid domains in the human red blood cell membrane is concluded. The molecular nature of those domains is discussed.

Interplay of spin density wave and superconductivity with different pairing symmetry

A model study for the coexistence of the spin density wave and superconductivity is presented. With reference to the recent angle-resolved photo-emission experimental data in high- T c cuprates, presence of the nested pieces of bands is assumed. The single-band Hubbard model, therefore, when treated within the Hatree–Fock mean field theory leads to a spin density wave (SDW) ground state. The superconductivity (SC) is assumed to be due to a generalised attractive potential with a separable form without specifying to any particular origin. It therefore allows a comparative study of the coexistence of superconductivity of different order parameter symmetry with the spin density wave state. We find that the phase diagram, comprising of the amplitudes of the respective gaps (SC and SDW) vs. band filling resembles that of the high- T c cuprates only when the order parameter of the superconducting phase has d-wave symmetry. Thermal variation of different order parameters (e.g., SC and SDW) also shows interesting coexistence and reentrance behaviors that are consistent with experimental observations, specially for the borocarbides.

Study of the Impact of Drops onto Solid Surfaces

In this paper, we report experimental results on the collision dynamics of a water droplet impinging on a rigid surface. The rigid surfaces considered cover a wide range of roughness' and porosities from stainless steel to paper.The experimental method used is based on a highspeed cinematography technique combined with advanced image processing means. The observations are made at ambient pressure, ambient temperature, with an initial droplet diameter of 2 mm.The measurements are performed on a large range of variation of relevant dimensionless parameters in order to determine different thresholds. We show that whatever the operating conditions, the drop spreads and retracts under the action of inertia and capillarity respectively. In the initial stages of impact, the transient evolution of wetted area and spreading rate for a given impact Weber number, appear to be independent of the surface on which the droplet impinges. These results are discussed within the framework of possible physical mechanisms.

Time-Dependent Order-Disorder Change in Alloys

The relaxation of order-disorder transition has been treated. The thermodynamic potential of a non-equilibrium state is discussed, with the affinity of order-disorder change being introduced. Entropy production is written in terms of order parameters. Thus along the line of the Prigogine-de Groot theory in non-equilibrium thermodynamics, time variations of order parameters as well as those of entropies are obtained. It is shown that, in the early stages of both the formation and decay processes of order at constant temperature, the short-range order parameter and the amount of produced entropy vary linearly with time.

Surface-induced nematic ordering and the localization of a twisted distortion in a nematic cell

A Landau--de Gennes phenomenological model is used to analyze the coupling between the surface-induced scalar order parameter variation and the orientational ordering in a nematic slab, considering also nonplanar distortions where the twist angle $\ensuremath{\omega}$ can vary. The results show that a weak variation $\ensuremath{\delta}\ensuremath{\omega}$ additional to that predicted for a pure twist deformation by the Frank elastic theory can appear. This variation can be either globally spread over the whole sample or localized to a subsurface region of thickness comparable to the nematic correlation length. In the former case $\ensuremath{\delta}\ensuremath{\omega}$ results from a global tilt angle variation, while in the latter it is caused by a variation of the scalar order parameter S close to the surface. In contrast to the recently analyzed S variation-induced subsurface deformation of the tilt angle [see, e.g., G. Ska\ifmmode \check{c}\else \v{c}\fi{}ej et al., Phys. Rev. E 57, 1780 (1998)], an intrinsic (chiral nematic) or confinement-induced global twist is needed to yield the localized $\ensuremath{\delta}\ensuremath{\omega}$ effect.

Influence of docosahexaenoic acid and cholesterol on lateral lipid organization in phospholipid mixtures.

We investigated lateral lipid organization in membranes with a lipid composition relevant to neural and retinal membranes [phosphatidylcholine (PC)/phosphatidylethanolamine (PE)/phosphatidylserine (PS)/cholesterol, 4/4/1/1, mol/mol/mol/mol]. The mixed-chain phospholipids contained saturated stearic acid (18:0) in the sn-1 position and the monounsaturated oleic acid (18:1) or polyunsaturated docosahexaenoic acid (22:6) in sn-2. Lateral lipid organization was evaluated by 2H NMR order parameter measurements on stearic acid of all individual types of phospholipids in the mixture and, through a novel approach, two-dimensional NOESY 1H NMR spectroscopy with magic angle spinning (MAS). The docosahexaenoic acid chain order was evaluated from 1H NMR chain signal MAS-sideband intensities. Averaged over all lipids, the cholesterol-induced increase in sn-1 chain order is 2-fold larger in monounsaturated than in polyunsaturated lipids, and the order of both saturated and polyunsaturated hydrocarbon chains increases. Addition of cholesterol increases lipid order in the sequence 18:0-18:1 PE > 18:0-18:1 PC > 18:0-18:1 PS for the monounsaturated and 18:0-22:6 PC >> 18:0-22:6 PE > 18:0-22:6 PS for polyunsaturated mixtures. The variation of order parameters between lipid species suggests that cholesterol induces the formation of lipid microdomains with a headgroup and chain unsaturation-dependent lipid composition. The preferential interaction between cholesterol and polyunsaturated 18:0-22:6 PC, followed by 18:0-22:6 PE and 18:0-22:6 PS, was confirmed by 1H MAS NOESY cross-relaxation rate differences. Furthermore, cholesterol preferentially associates with saturated chains in mixed-chain lipids reflected by higher saturated chain-to-cholesterol cross-relaxation rates. We propose that cholesterol forms PC-enriched microdomains in the polyunsaturated 18:0-22:6 PC/18:0-22:6 PE/18:0-22:6 PS/cholesterol membranes in which the saturated sn-1 chains are preferentially oriented toward the cholesterol molecules.

Diffraction Gratings in a Nematic Cell Due to Spatial Variation of Surface Order Parameter

The influence of a periodical spatial modulation of a surface order parameter on the distribution of the order parameter in a nematic liquid crystal bulk is studied. The problem is treated in the framework of the Landau - de Gennes theory with an anchoring energy in the form F S ∼ (S-Q)2, where S is the NLC order parameter and Qis the surface order parameter. It is shown that the order parameter grating, which damps exponentially with the distance to the cell plates, appears in the cell bulk. The damping coefficient is inversely proportional to the coherence length ξ of the nematic-isotropic phase transition. Diffraction efficiency of this grating is proportional to (ξΔQ)2, where ΔQ is an amplitude of the order parameter modulation, and is sufficient for experimental observations.

Calibration of excess thermodynamic properties and elastic constant variations associated with the alpha <-->beta phase transition in quartz

Spontaneous strains for the a ↔ b transition in quartz were determined from lattice parameter data collected by X-ray powder diffraction and neutron powder diffraction over the temperature range ;5‐1340 K. These appear to be compatible with previous determinations of the order parameter variation in a quartz only if there is a non-linear relationship between the individual strains and the square of the order parameter. An expanded form of the 2-4-6 Landau potential usually used to describe the phase transition was developed to account for these strains and to permit calculation of the elastic constant variations. Calibration of the renormalized coefficients of the basic 2-4-6 potential, using published heat capacity data, provides a quantitative description of the excess free energy, enthalpy, entropy, and heat capacity. Values of the unrenormalized coefficients in the Landau expansion that include all the strain-order parameter coupling coefficients were used to calculate variations of the elastic constants. Values of the bare elastic constants were extracted from published elasticity data for b quartz. Calculated variations of C11 and C12 match their observed variations closely, implying that the extended Landau expansion provides a good representation of macroscopic changes within the (001) plane of quartz. Agreement was not as close for C33, suggesting that other factors may influence the strain parallel to [001]. The geometrical mechanism for the transition involves both rotations and shearing of SiO4 tetrahedra, with each coupled differently to the driving order parameter. Only the shearing part of the macroscopic distortions appears to show the same temperature dependence as other properties that scale with Q 2 . Coupling between the strain and the order parameter provides the predominant stabilization energy for a quartz and is also responsible for the first-order character of the transition.

Molecular dynamics simulations of flexible liquid crystal molecules using a Gay-Berne/Lennard-Jones model

Molecular dynamics simulations are described for liquid crystal molecules composed of two Gay-Berne particles connected by an eight-site Lennard-Jones alkyl chain. Calculations have been carried out for 512 molecules in the NVE and NPT ensembles for simulation times of up to 6.4 ns. The system exhibits the sequence of phases: isotropic liquid, smectic-A, smectic-B, and the simulations demonstrate the spontaneous growth of a smectic-A liquid crystal over a period of approximately 6 ns on cooling from the isotropic liquid. Model molecules are seen to remain flexible and able to change conformation in the smectic-A phase. As temperature is reduced molecules become elongated as the number of gauche conformations drops, leading to a small increase in the spacing of smectic layers. The latter is seen through the temperature dependence of the Gay-Berne radial distribution function resolved parallel to the direction of orientational order. Results are presented which show an odd–even variation of orientational order parameters for bonds in the alkyl chain, and a change in effective torsional potentials as the system is cooled from isotropic liquid to a smectic-A phase.

A phenomenological approach to ordering kinetics for partially conserved order parameters

The kinetics of cation ordering in complex crystal structures, such as minerals and ceramics, is discussed with regard to the applicability of time-dependent Ginzburg - Landau theory (TDGL). Deviations from the predictions made by TDGL may arise due to partial conservation of continuous and non-uniform order parameters at low temperatures. Under these conditions the movement of areas with large order parameter gradients (`walls') provides a local alternative to the continuous ordering kinetics described by TDGL. A simple phenomenological description of order parameter kinetics taking these constraints into consideration can be obtained. The underlying assumption is that the geometry of spatial order parameter variation close to equilibrium resembles that of a phase-separated system. The resulting kinetics differs substantially from the predicted TDGL behaviour.

Quasicritical heat capacity at a smectic-A–hexatic-Bphase transition

High-resolution ac calorimetry has been used to characterize the excess heat capacity $\ensuremath{\Delta}{C}_{p}(T)$ associated with the smectic-$A$ $(\mathrm{Sm}A)$ --hexatic-$B$ $(\mathrm{Hex}B)$ transition in $n$-hexyl-${4}^{\ensuremath{'}}\ensuremath{-}n$-pentyloxybiphenyl-4-carboxylate (65OBC). For temperature oscillations in the investigated frequency range 1.42--400 mHz, the $\ensuremath{\Delta}{C}_{p}$ data reveal no frequency dependence and correspond to static thermodynamic values. The present data resolve several discrepancies in previously reported ${C}_{p}$ values. This transition is very weakly first order, but power-law fits could be made to $\ensuremath{\Delta}{C}_{p}.$ Such fits yield an effective critical exponent ${\ensuremath{\alpha}}_{\mathrm{eff}}=0.65\ifmmode\pm\else\textpm\fi{}0.05,$ which agrees quite well with values of $\ensuremath{\sim}0.6$ reported by Huang and co-workers [Phys. Rev. Lett. 46, 1289 (1981); Phys. Rev. A 28, 2433 (1983); Phys. Rev. Lett. 56, 1712 (1986)]. Such an exponent value disagrees strongly with the theoretically predicted three-dimensional $\mathrm{XY}$ value ${\ensuremath{\alpha}}_{\mathrm{XY}}=\ensuremath{-}0.007.$ It is proposed that this ${C}_{p}$ behavior and also the reported order parameter variation, which yields an effective critical exponent ${\ensuremath{\beta}}_{\mathrm{eff}}$ of $\ensuremath{\sim}0.2,$ are consistent with quasitricritical or quasitetracritical (strain-smeared, very weak first-order) behavior arising from a coupling between the amplitude of the bond-orientational order and the in-plane positional strain.

Modelling of kinetics of solidification of intermetallic compounds

Rapid solidification of an intermetallic compound can be associated with a reduction in the chemical long-range order in the solid at the solid/liquid interface. This reduced degree of order can result in unique kinetic effects such as marked interfacial undercoolings, anomalous partitioning behaviour and disorder trapping. The kinetic effects can be predicted by modelling of solidification kinetics incorporating variations of order parameter. This work presents an example of such modelling. The predictions are in the form of relations between explicit processing variables (such as melt composition and undercooling) and growth rate; thus, they can be tested against experiments concerning direct kinetic measurements. This is done by modelling of dendritic growth into an undercooled melt, taking account of displacements of the phase boundaries due to non-equilibrium effects. In contrast to the conventional analysis of the dendritic growth in intermetallics, growth of both the ordered and the disordered versions of the solid is treated in a single kinetic model and disorder trapping transitions are not excluded from the predictions.

Polarizabilities and Related Properties of Azo Benzene Liquid Crystal Compounds

AbstractA novel method, molecular vibration approach is presented and used to evaluate polarizabilities, polarizability anisotropies and diamagnetic susceptabilities of Azo Benzene liquid crystal compound. In this approach vibrational frequencies are used to calculate the force constants, mean amplitude of vibrations and bond polarizabilities. In addition, the variation of order parameter with temperature is also studied. The results are compared and discussed with the literature values.

Variations of order parameter and bias current distribution with time in thin film superconducting lines

We study variations of the order parameter and the vector potential with time using the rescaled time-dependent Ginzburg - Landau (TDGL) equation. Computer simulations for several conditions are performed to discuss the bias current distribution and the time necessary for the transition from the normal state to the superconducting state for the superconducting narrow line. As a result, we have found that the time necessary for the transition from the normal state to the superconducting state is an important factor to explain the I - V characteristics due to the vortex motion in superconducting narrow lines.

Elastic energy anisotropy effects on antiphase boundaries

The effect of elastic energy on the anisotropy of antiphase boundary (APB) interfacial energy has been studied theoretically. The model used, a generalization of one developed by Kikuchi and Cahn, treats composition and atomic ordering as local variables defined on each of the atomic planes parallel to the APB. The equilibrium APB structure is found as the set of planar variables that minimizes the free energy. A strain energy term involving an orientation-dependent stiffness parameter and a phenomenological law giving lattice constant as a function of local composition and order parameter is included in the definition of the free energy. Elastic effects in APBs in B2 ordered FeAl alloys with 0.2 – 0.3 atomic fraction Al were investigated. It was found that, despite the high elastic anisotropy of FeAl alloys, elastic effects would not result in any substantial anisotropy in APB interfacial energy. This is because in FeAl alloys the variation in lattice constant due to order parameter variation at the APB is almost completely cancelled out by the variation in lattice constant due to compositional variation. In a hypothetical model with physically reasonable parameters, APB energies were found to vary by up to 9% with orientation, purely as a result of elastic effects. It was concluded that elastically induced APB anisotropy would be observable in alloys such as FeSi in which lattice constant variations due to order parameter variation are cooperative with those due to compositional variation.