Variation Of Order Parameter Research Articles

Very strong azimuthal anchoring of nematic liquid crystals on uv-aligned polyimide layers

The azimuthal anchoring energy of the nematic liquid crystal 4- n -pentyl- 4' -cyanobiphenyl (5CB) on a uv-aligned polyimide substrate with in-plane order parameter S'=0.2 is measured. The measurements are performed at temperature T=24 degrees C using simultaneously a high accuracy reflectometric method and a high accuracy transmitted light method. With both the methods, we observe an apparent surface director rotation opposite to the orienting torque that would correspond to a negative extrapolation length. It is shown that this unusual behavior is due to the relatively high birefringence of the uv-aligned polyimide layers. Taking into account for this birefringence, we find a small but positive extrapolation length. The experimental results are interpreted in terms of a simple mesoscopic model where the nematic molecules are assumed to be rigidly attached on the polymer surface and the measured extrapolation length is entirely due to the order parameter variation in a thin interfacial layer where the nematic order parameter passes from the surface value to the bulk value within a few nematic correlation lengths. Assuming the surface order parameter is S(0)=0.37 , the correlation length of the nematic liquid crystal is estimated to be xi'(c)=2.4+/-1 nm . The corresponding thermodynamic extrapolation length is de=2.8+/-1.2 nm that corresponds to a very strong azimuthal anchoring.

Plutonium and quantum criticality

The unusual properties of the elemental plutonium have long been a puzzle. It has been suggested that these properties may be related to quantum criticality [G. Chapline, J.L. Smith, LA Sci. 26 (2000) 1]. In this talk we will describe some experimental observations on rare earth and actinide materials which suggest that there are pairing correlations in all f-electron metals, and that the anomalous properties of the actinides in the vicinity of Np/Pu/Am, even at elevated temperatures, is associated with a critical point in the variation of the pair condensate order parameter with atomic number.

Strain effects at the hexatic-B–smectic-Atransition in the 65OBC liquid crystal

We have studied the hexatic-B-smectic-A (HexB-SmA) transition in n -hexyl- 4'-n -pentyloxybiphenyl-4-carboxylate (65OBC) by means of a high-resolution ac photopyroelectric (PPE) calorimetric technique. A procedure for the interpretation of the PPE data, which allows the detection of an internal heating source due to strain annealing and/or latent heat, has been applied. We have found that the strain present in the sample depends on the kinetics of formation of the smectic phase once the sample is cooled from the isotropic one. The strain field keeps memory of this kinetics and can be only partially annealed on decreasing the temperature or cycling it around the Hex-SmA transition. A reversible ordering-disordering process has been found at T(c) and has been explained in terms of the competition between the order parameter variation with temperature and the constraints imposed by the disorder. The results confirm that the transition has a weakly first-order character with a specific heat critical exponent that disagrees with the available theoretical predictions. Our data show the importance of the disorder in 65OBC and we tried to clarify what would be the consequence of this result in theoretical modeling devoted to solving the puzzle of the HexB-SmA transition in this compound.

Generalized cluster variation theory for the isotropic–nematic phase transition

In this study, a cluster variation theory for the Maier–Saupe model of the nematic–isotropic phase transition is generalized by using non-extensive thermostatistics. The variation of long-range order parameter with temperature is investigated and the effect of the possible generalization is shown for some values of the entropic index. The critical value of the long-range order parameter at the nematic–isotropic transition temperature versus the entropic index is also compared with Monte Carlo simulation values and experimental data.

Visualization of liquid crystal director fields within carbon nanotube cavities

Multiwall carbon nanotube cavities were infiltrated with naphthalene polymer which exhibits a discotic nematic liquid crystal phase. The liquid crystal phase is covalently captured by thermal carbonization. High resolution transmission electron microscope images reveal a planar configuration consistent with elastic theory for extreme confinement conditions. Furthermore a spatial variation in order parameter was observed with a surface order parameter S0≈0.92 and an estimated correlation length ξ≈3.5nm.

Fourier transform spectroscopy ofd-wave quasiparticles in the presence of atomic scale pairing disorder

The local density of states power spectrum of optimally doped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+x}$ (BSCCO) has been interpreted in terms of quasiparticle interference peaks corresponding to an ``octet'' of scattering wave vectors connecting $\mathbf{k}$ points where the density of states is maximal. Until now, theoretical treatments have not been able to reproduce the experimentally observed weights and widths of these octet peaks; in particular, the predominance of the dispersing ``${\mathbf{q}}_{1}$'' peak parallel to the Cu-O bond directions has remained a mystery. In addition, such theories predict ``background'' features which are not observed experimentally. Here, we show that most of the discrepancies can be resolved when a realistic model for the out-of-plane disorder in BSCCO is used. Weak extended potential scatterers, which are assumed to represent cation disorder, suppress large-momentum features and broaden the low-energy ``${\mathbf{q}}_{7}$'' peaks, whereas scattering at order parameter variations, possibly caused by a dopant-modulated pair interaction around interstitial oxygens, strongly enhances the dispersing ${\mathbf{q}}_{1}$ peaks.

Optical and dielectric properties of the mesogen 4-cyano-4′-n–octyl biphenyl as a function of temperature

The effect of temperature on certain optical and dielectric properties of one member, namely 4-cyano-4′-n–octyl biphenyl (8CB) of the mesogenic series 4-cyano-4′-n–alkyl biphenyl (nCB), is reported. The dependence of the ordinary and extraordinary components of polarisability, αo and αe, on temperature is studied using a He–Ne laser beam, and the variation of orientational order parameter with temperature in the entire mesogenic phase determined from the optical studies. The dependence of the effective molecular dipole moment, μeff, in the liquid-crystal phase, and the angle of inclination, β, of the dipole moment with the preferred direction have been investigated. An experimental estimate of the correlation factor ‘g’, which is indicative of the nature of the molecular association in the mesophase, has been obtained.

Mesoscale structures in flows of weakly sheared cholesteric liquid crystal polymers

We revisit the permeation flow issue in weakly sheared cholestericliquid crystal polymers in plane Couette and Poiseuille flowgeometries using a mesoscopic theory obtained from the kinetictheory for flows of cholesteric liquid crystal polymers [2]. Wefirst present two classes of equilibrium solutions due to the orderparameter variation and the director variation, respectively; then,study the permeation mode in weakly sheared flows of cholestericliquid crystal polymers employing a coarse-grain approximation. Weshow that in order to solve the permeation flow problem correctlyusing the coarse-grain approximation, secondary flows must beconsidered, resolving a long standing inconsistency in the study ofcholesteric liquid crystal flows [7]. Asymptotic solutions aresought in Deborah number expansions. The primary and secondary flow as well as the director dynamicsare shown to dominate at leading order while the local nematic orderfluctuations are higher order effects. The leading order solutionsare obtained explicitly and analyzed with respect to thecholesteric pitch and other material parameters. The role of theanisotropic elasticity in equilibrium phase transition andpermeation flows is investigated as well.

Predicting internal protein dynamics from structures using coupled networks of hindered rotators

Internal motions in proteins, such as oscillations of internuclear vectors u(N(i)H(i) (N)) of amide bonds about their equilibrium position, can be characterized by a local order parameter. This dynamic parameter can be determined experimentally by measuring the longitudinal and transverse relaxation rates of (15)N(i) nuclei by suitable NMR methods. In this paper, it is shown that local variations of order parameters S(ii) (2) can be predicted from the knowledge of the structure. To this effect, the diffusive motion of the internuclear vector u(N(i)H(i) (N)) is described in a potential that takes into account the deviations of the angles theta(ij) between u(N(i)H(i) (N)) and neighboring vectors u(N(j)H(j) (N)) from their average value and similarly of deviations of the angles subtended between u(N(i)H(i) (N)) and u(X(j)Y(j)), where X(j) and Y(j) are heavy atoms in the vicinity of the u(N(i)H(i) (N)) vector under investigation. It is shown how the concept of vicinity can be defined by a simple cutoff threshold, i.e., by neglecting vectors u(X(j)Y(j)) with distances d(N(i),X(j))>7.5 A. The local order parameters S(ii) (2) can be predicted from the structure using a limited set of coordinates of heavy atoms. The inclusion of a larger number of heavy atoms does not improve the predictions. Applications to calmodulin, calbindin, and interleukin 4 illustrate the success and limitations of the predictions.

NONEQUILIBRIUM PHASE TRANSITIONS IN MODEL FERROMAGNETS: A REVIEW

The thermodynamical behaviors of ferromagnetic systems in equilibrium are well studied. However, the ferromagnetic systems far from equilibrium became an interesting field of research in last few decades. Recent exploration of ferromagnetic systems in the presence of a steady magnetic field are also studied by using standard tools of equilibrium statistical physics. The ferromagnet in the presence of time-dependent magnetic field, shows various interesting phenomena. An usual response of a ferromagnet in the presence of a sinusoidally oscillating magnetic field is the hysteresis. Apart from this hysteretic response, the nonequilibrium dynamic phase transition is also a very interesting phenomenon. In this chapter, the nonequilibrium dynamic phase transitions of the model ferromagnetic systems in presence of time-dependent magnetic field are discussed. For this kind of nonequilibrium phase transition, one cannot employ the standard techniques of equilibrium statistical mechanics. The recent developments in this direction are mainly based on numerical simulation (Monte Carlo). The Monte Carlo simulation of kinetic Ising model, in presence of sinusoidally oscillating (in time but uniform over space) magnetic field, is extensively performed to study the nonequilibrium dynamic phase transition. The temperature variations of dynamic order parameter, dynamic specific heat, dynamic relaxation time etc. near the transition point are discussed. The appearance and behaviors of a dynamic length scale and a dynamic time scale near the transition point are also discussed. All these studies indicate that this proposed dynamic transition is a nonequilibrium thermodynamic phase transition. The disorder (quenched) induced zero temperature (athermal) dynamic transition is studied in random field Ising ferromagnet. The dynamic transition in the Heisenberg ferromagnet is also studied. The nature of this transition in the Heisenberg ferromagnet depends on the anisotropy and the polarisation of the applied time varying magnetic field. The anisotropic Heisenberg ferromagnet in the presence of elliptically polarised magnetic field shows multiple dynamic transitions. This multiple dynamic transitions in anisotropic Heisenberg ferromagnet are discussed here. Recent experimental evidences of dynamic transitions are also discussed very briefly.

Multicritical behavior of the antiferromagnetic [formula omitted] Blume–Emery–Griffiths model

The multicritical behavior of the antiferromagnetic spin- 3 2 Blume–Emery–Griffiths model in an external magnetic field is studied within the lowest approximation of the cluster variation method. We have investigated the thermal variations of order parameters for different values of interaction parameters and external magnetic field and constructed the resulting phase diagrams. The model exhibits distinct critical regions, including the first-order, second-order tricritical point, double critical point and zero critical point. Comparison of the phase diagrams with closely related systems is made.

Solid–plastic and plastic–isotropic liquid phase transitions on molecular crystals

Crystalline solid–plastic solid and plastic solid–isotropic liquid phase transitions are studied using a modified Pople and Karasz model. The thermodynamic properties of the model are evaluated by the cluster variation method. The variation of positional and orientational order parameters with temperature is studied. We have also obtained theoretical isotherms, volume and entropy changes of transitions at zero pressure and theoretical phase diagrams at high pressures. The results are compared with the original Pople and Karasz theory and the other by a modified Pople and Karasz theory which was done by Chandrasekhar et al.

Influence of finite size and wetting on nematic and smectic phase behavior of liquid crystal confined to controlled-pore matrices

The high-resolution calorimetric study was carried out on octylcyanobiphenyl liquid crystal (LC) confined to various controlled-pore glass (CPG) matrices with silane-treated surface. The diameter of the voids cross section ranged between 23.7 and 395 nm. The results are compared to those obtained previously on CPG voids nontreated with silane. We found a striking similarity between the shifts in the isotropic to nematic and nematic to smectic-A phase transition temperatures as a function of the void radius in which order parameter variations at the LC-void interface play the dominant role. Weaker temperature shifts are observed in silane-treated samples, where surface ordering tendency is larger. In nontreated samples, a finite-size scaling law in the maximum value of the heat capacity at the nematic to smectic-A transition was observed for void diameters larger than 20 nm. In silane-treated samples, this behavior is considerably changed by surface wetting interactions.

Three‐dimensional polymer flow in the calender bank

AbstractThe velocity and pressure field that forms within the gap of a calender is numerically calculated. The numerical calculations are based on a decoupled calculation method for the free surface of the bank. The transport equations for mass and momentum are solved numerically. The position of the free surface of the bank is determined by shifting it until it matches a streamline. The resulting three‐dimensional velocity field gives the vortex patterns within the volume of the bank for fluids with non‐Newtonian and Newtonian rheological behavior. The shape of the free surface of the bank and its position are determined by the gap height, the circumferential speed of the rolls, the speed ratio, the feed mass flow into the gap and the rheological behavior of the polymer. Additionally, there are special requirements to be considered that determine the product quality, such as the thickness of the produced sheet, its uniformity and surface appearance, air inclusions and the mixing of the polymer. The calendering process itself requires limited operating windows for the variation of the process parameters in order to meet the product quality requirements. These operating windows are discussed and graphically plotted. Polym. Eng. Sci. 44:1642–1647, 2004. © 2004 Society of Plastics Engineers.

Nematic-isotropic phase transition in diblock fused-sphere chain fluids.

A density-functional theory for the isotropic-nematic phase transition in fluids of rigid or semiflexible fused hard-sphere chains, developed previously by the authors, is extended to diblock chains each consisting of both a rigid and a flexible part. The theory is compared with recent Monte Carlo simulation results of McBride et al. The theoretical results for the variation of pressure and nematic order parameter with density agree well with the simulation data over density ranges where the simulations find isotropic and nematic phases.

Ordering in spinels—A Monte Carlo study

We have extended a recently developed Monte Carlo technique which includes explicit exchange as well as movement of ions to systems involving heterovalent exchange. These Monte Carlo computer simulations, based on analytical inter-atomic potentials, are capable of providing detailed quantitative information concerning the thermodynamics of ordering of spinel (MgAl 2 O 4 ), gahnite (ZnAl 2 O 4 ), hercynite (FeAl 2 O 4 ), NiAl 2 O 4 , and magnesioferrite (MgFe 2 O 4 ) over a range of pressures and temperatures. At all temperatures and pressures ionic relaxation, lattice vibrations, and pressure are explicitly taken into account. Each compound has a larger expansion coefficient and smaller bulk modulus in the normal than in the inverse spinel structure. We predict only a small variation of order parameter with pressure, and that this will be more pronounced for inverse than normal spinels. We examine, briefly, the consequences of our results for the kinetics of cation ordering in these solids.

Depth-resolved X-ray residual stress analysis in PVD (Ti, Cr) N hard coatings

Abstract Physical vapour deposition (PVD) of thin hard coatings on TiN basis is usually performed at rather low temperatures (TD < 500°C) far from thermal equilibrium, which leads to high intrinsic residual stresses in the growing film. In contrast to the extrinsic thermal residual stresses which can easily be estimated from the difference of the coefficients of thermal expansion between the substrate and the coating, a theoretical prediction of the intrinsic residual stresses is difficult, because their amount as well as their distribution within the film depend in a very complex way on the deposition kinetics. By the example of strongly fibre-textured PVD (Ti, Cr)N coatings which have been prepared under defined variation of the deposition parameters in order to adjust the residual stress distribution within the coatings, the paper compares different X-ray diffraction techniques with respect to their applicability for detecting residual stresses which are non-uniform over the coating thickness.

Production-scale processing of a new intermetallic NiAl–Ta–Cr alloy for high-temperature application: Part I. Production of master alloy remelt ingots and investment casting of combustor liner model panels

Several master alloy remelt ingots of about 100 kg each with nominal composition 45 at.% Ni, 45 at.% Al, 7.5 at.% Cr and 2.5 at.% Ta were produced by vacuum induction melting. These ingots were used for a series of investment castings with variation of casting parameters in order to develop and optimise the investment casting process for this new intermetallic NiAl-based alloy. The microstructures of the remelt ingots and of various investment castings were characterised by light optical and scanning electron microscopy (SEM). The compositions of the constituent phases were determined by energy dispersive and wavelength dispersive analysis. The 0.2% yield stress, secondary creep rates and oxidation rates were determined and compared with those of materials produced on laboratory scale. Except of a decreased toughness of the production scale material the properties were otherwise comparable to those of the laboratory scale material. Though properties of the cast alloys are found not to be sensitively affected by impurities such as oxygen, carbon, iron, hafnium and zirconium, silicon was found to promote segregation during casting which is believed to result in embrittlement of the production scale material. Silicon contaminations could be avoided by usage of a ceramic-free cold-wall induction melting aggregate, but due to the coarse resulting microstructures this did not improve toughness of the production scale material.

Dynamic phase transitions in the anisotropic XY spin system in an oscillating magnetic field.

The Ginzburg-Landau model for the anisotropic XY spin system in an oscillating magnetic field below the critical temperature T(c), psi;(r,t)=(T(c)-T)psi-/psi/(2)psi+gammapsi(*)+ nabla (2)psi+h cos(Omegat) is both theoretically and numerically studied. Here psi is the complex order parameter and gamma stands for the real anisotropy parameter. It is numerically shown that the spatially uniform system shows various characteristic oscillations (dynamical phases), depending on the amplitude h and the frequency Omega of the external field. As the control parameter, either h or Omega, is changed, there exist dynamical phase transitions (DPT), separating them. By making use of the mode expansion analysis, we obtain the phase diagrams, which turn out to be in a qualitative agreement with the numerically obtained ones. By carrying out the Landau expansion, the reduced equations of motion near the DPT are derived. Furthermore, taking into account the spatial variation of order parameters, we will derive the analytic expressions for domain walls, which are represented by the Néel and Bloch type walls, depending on the difference of the coexistence of phases.

Magnetic properties of the mixed spin- [formula omitted] and spin-1 Ising ferromagnetic system

The magnetic properties of the mixed spin- 1 2 and spin-1 Ising ferromagnetic system with a crystal–field interaction in the absence and presence of an external magnetic field are studied by using the cluster variation method. Thermal variations of order parameters are investigated and the metastable and unstable branches of the order parameters are obtained besides the stable states. We also investigate the nonequilibrium properties of the model by the path probability method in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. The metastable phase diagram in addition to the equilibrium phase diagram and only the metastable phase diagram are presented in the absence and presence of the external magnetic field, respectively. The influence of the external magnetic field on the system is also examined.