Landau Mean-field Theory Research Articles

Miscibility studies of two twist-bend nematic liquid crystal dimers with different average molecular curvatures. A comparison between experimental data and predictions of a Landau mean-field theory for the NTB-N phase transition.

We report a calorimetric study of a series of mixtures of two twist-bend liquid crystal dimers, the 1'',7''-bis(4-cyanobiphenyl)-4'-yl heptane (CB7CB) and 1''-(2',4-difluorobiphenyl-4'-yloxy)-9''-(4-cyanobiphenyl-4'-yloxy) nonane (FFO9OCB), the molecules of which have different effective molecular curvatures. High-resolution heat capacity measurements in the vicinity of the NTB-N phase transition for a selected number of binary mixtures clearly indicate a first order NTB-N phase transition for all the investigated mixtures, the strength of which decreases when the nematic range increases. Published theories predict a second order NTB-N phase transition, but we have developed a self-consistent mean field Landau model using two key order parameters: a symmetric and traceless tensor for the orientational order and a short-range vector field which is orthogonal to the helix axis and rotates around of the heliconical structure with an extremely short periodicity. The theory, in its simplified form, depends on two effective elastic constants and explains satisfactorily our heat capacity measurements and also predicts a first-order NTB-N phase transition. In addition, as a complementary source of experimental measurements, the splay (K1) and bend (K3) elastic constants in the conventional nematic phase for the pure compounds and some selected mixtures have been determined.

New antiferroelectric liquid crystal for use in LCD

In this work, the physical properties of newly synthesized liquid crystalline compound exhibiting two liquid crystalline phases (ferroelectric and antiferroelectric) were studied. Based on the results of differential scanning calorimetry, polarizing microscopy, and photoelastic modulator methods, the temperature dependences of spontaneous polarization, tilt angle, switching time, and birefringence in the ferroelectric, as well as antiferroelectric phases were determined. Furthermore, the influence of the external electric field on the liquid crystalline textures was studied and the phase sequences at heating and cooling were revealed. The temperature dependence of spontaneous polarization was analysed by means of Landau mean-field theory, and the critical parameter β obtained for ferroelectric liquid crystalline and isotropic liquid transition was 0.21 which is close to 0.25, the value characteristic for tri-critical point.

Step-by-step first order antiferroelectric-paraelectric transition induced by frustration and electric field

We show analytically that even not too strong frustrating next neighbor interaction strongly affects first order antiferroelectric-paraelectric transition in an external electric field. We apply mean-field Landau theory. In the electric field a single phase transition at T0 splits into a step-by-step staircase with a series of intermediate phases. Unexpectedly enough we found that the equilibrium structures of the phases differ substantially from structures formed at low temperature both without field and in field. Polarization of intermediate structures decreases with temperature in a stepwise manner. Similar step-by-step transitions can occur also in magnetic materials with frustrating interaction.

Critical exponents of ferroelectric transitions in modulated SrTiO3: Consequences of quantum fluctuations and quenched disorder

The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, in order to understand the competition among quantum fluctuations (QFs), quenched disorder, and ferroelectric ordering. Two representative systems with sufficiently strong QFs and quenched disorders in competition with the ferroelectric ordering are investigated. We start from non-stoichiometric SrTiO3 (STO) with the Sr/Ti ratio deviating slightly from one, which is believed to maintain strong QFs. Then, we address Ba/Ca co-doped Sr1−x(Ca0.6389Ba0.3611)xTiO3 (SCBT) with the averaged Sr-site ionic radius identical to the Sr2+ ionic radius, which is believed to offer remarkable quenched disorder associated with the Sr-site ionic mismatch. The critical exponents associated with polarization P and dielectric susceptibility ∊, respectively, as functions of temperature T close to the critical point Tc, are evaluated. It is revealed that both non-stoichiometric SrTiO3 and SCBT exhibit much bigger critical exponents than the Landau mean-field theory predictions. These critical exponents then decrease gradually with increasing doping level or deviation of Sr/Ti ratio from one. A transverse Ising model applicable to the Sr-site doped STO (e.g., Sr1−xCaxTiO3) at low level is used to explain the observed experimental data. It is suggested that the serious deviation of these critical exponents from the Landau theory predictions in these STO-based systems is ascribed to the significant QFs and quenched disorder by partially suppressing the long-range spatial correlation of electric dipoles around the transitions. The present work thus sheds light on our understanding of the critical behaviors of ferroelectric transitions in STO in the presence of quantum fluctuations and quenched disorder, whose effects have been demonstrated to be remarkable.

Calculation of a generalised smectic–hexatic phase diagram in liquid crystals

This study gives a generalised smectic–hexatic phase diagram calculated by the Landau mean field theory. Our calculated phase line equations are fitted to the experimental phase lines, which represent first-order transition for the liquid crystals studied here. The temperature- and concentration-dependent phase lines calculated in this study describe the observed T–X phase diagram for the smectic–hexatic transitions. This indicates that the method of calculating the phase line equations from the mean field theory is general and it can be applied to other phase transitions in liquid crystals.

Melting of solid nanoscale films with free surfaces

In the framework of the mean-field Landau theory and the Lindemann melting criterion, a novel method has been applied to study the properties of thin solid films. A novel profile of the order parameter in thin solid films of nanoscale thicknesses has been obtained. In terms of this method, it was shown that surface ordering of thin solid films affects their physical properties. A dependence of the order parameter on the reduced film thickness was obtained. It was shown that the melting temperature of a thin film with free surfaces decreases with decreasing film thickness. Nevertheless, it was found that there was no depression of the melting point due to the reduced thickness of films at least down to 15 nm. The results are in good agreement with available experimental data.

A simple electro-optic technique for studying the electroclinic effect in the smectic A* phase

The critical behaviour of the electroclinic response in the chiral smectic A* phase in the vicinity of the second-order smectic A* to smectic C* phase-transition temperature has been investigated using a new electro-optic technique. The temperature variation of the electroclinic coefficient, the relaxation frequency and the coefficient of the quartic term in the tilt angle in the Landau free energy expansion have been studied. The electroclinic coefficient diverges with decreasing temperature as the smectic A* to smectic C* phase-transition temperature is approached with a critical exponent, as predicted in the mean field Landau theory. The measured quartic coefficient varies strongly with temperature, contrary to the usual assumptions of the mean field Landau theory.

Renormalization-group analysis of the RI − RV rotator phase transition

A model for coupled tilt angle and lattice distortion parameter is proposed to describe the R(I)-R(V) transition in n-alkane. The model is treated in the framework of a Landau mean-field theory and renormalization-group theory. The influence of gauche conformations and molecular flexibility on the R(I)-R(V) transition is discussed within the mean-field theory. The fluctuations on the R(I)-R(V) transition are discussed by the renormalization-group theory. Renormalization-group theory predicts that the R(I)-R(V) transition can be driven first order by fluctuations and becomes second order at a tricritical point. Available experimental data are consistent with our model.

The thermodynamic properties of nanoparticles with the characteristic sizes less than 10 nm

In the framework of the Landau mean-field theory, the novel thermodynamic model was developed to describe the behavior of the melting enthalpy and entropy of nano-objects having the characteristic size less than 10 nm. It is implied that nano-objects of the critical sizes undergo the second-order transition instead of usual melting. For the first time it was revealed that the melting enthalpy and entropy of nanoparticles, having the characteristic size less than critical one, increase with decreasing the characteristic size of nanoparticles.

Effective interaction dependence of the liquid–gas phase transition in symmetric nuclear matter

The liquid–gas phase transition for homogeneous symmetric nuclear matter is studied in the mean-field approximation. Critical properties are computed using a comprehensive group of Skyrme and Gogny forces in an effort to elucidate the effective interaction dependence of the results. Analytical models for the thermodynamical and critical properties are discussed and compared to an extensive set of mean-field data. In agreement with these models, a tight correlation is found between the flashing and the critical points. Accurate predictions for the critical temperature, based on saturation properties, can only be obtained after the density dependence of the effective mass is properly taken into account. While the thermodynamical properties coming from different mean-fields do not follow a law of corresponding states, the critical exponents for all the mean-fields have been found to be the same. Their values coincide with those predicted by the Landau mean-field theory of critical phenomena.

Direct Measure of the Tilt Angle in de Vries‐Type Liquid Crystals through NMR Spectroscopy

De Vries-type phase transitions in liquid crystalline (LC) smectogens have recently attracted the attention of the liquid crystal community due to their potential in the development of new ferroelectric (FLC) and antiferroelectric (AFLC) electrooptic systems. Indeed, one of the major problems to the application of ferroelectric smectic materials is related to the layer shrinkage at the transition from the not-tilted SmA phase to the polar SmC* phase. This shrinking normally produces zigzag defects due to the opposite distribution of chevron configurations, thus limiting the performance and quality of electrooptic devices. In the last decades, several compounds have been found to behave differently from standard ones. In particular, they do not show any layer shrinkage at the SmA–SmC* transition, and the layer spacing remains substantially constant within the ferroelectric phase. Several models have been proposed to explain such an unconventional feature. The first interpretation, still partially valid, is the one described by the crystallographer de Vries, known as the “diffuse cone model”. 5] He proposed that in these systems LC molecules are tilted, with respect to the layer normal (“l” in Scheme 1), also in the SmA phase, but that the azimuthal angle is randomly distributed within the smectic layer. The SmA–SmC* phase transition is thus seen as a disorder–order transition in the azimuthal directions of the molecular tilt. Several experimental works on different liquid crystals showing de Vries-type transitions, basically confirmed this hypothesis, even though this does not exclude other possible explanations, such as the presence of partially interdigitation among consecutive smectic layers as well as conformational changes at the SmA–SmC* phase transition. For this reason, the nature of the de Vries transition remains a challenging aspect for researchers active in the material science field. However, in the recent years, fundamental progresses have been done in the comprehension of the de Vries -type materials. In addition to layer shrinkage (less than 5%) at the SmA–SmC* transition, the SmA phases formed by de Vries LCs have an uncommonly large electroclinic effect, which is strongly connected to the presence of significant tilt of molecules. The application of external electric fields determines an increase of the induced tilt angle, often defined as “optical tilt” to distinguish it from the molecular tilt, whose temperature dependence is well described by the Landau mean field theory. Moreover, the large soft-mode absorption detected by dielectric measurements, and the high birefringence are additional characterizing features of de Vries SmA phases. To our best knowledge, NMR spectroscopy has never been applied to de Vries-type LC systems, despite its great potential in the determination of both local and molecular properties, namely orientational and conformational ones. Herein, the first H NMR investigation of a de Vries liquid crystal compound [the (S)-hexyl-lactate derivative abbreviated as 9HL] selectively labeled in the aromatic core (Scheme 1), is reported. We monitored the trend of the tilt angle of the deuterated moiety within the SmA and SmC* phases with an NMR study at high magnetic field. This approach, recently used to investigate standard ferroelectric LCs, 28] takes advantage of the ability of high magnetic fields (H) in unwinding the supramolecular heliScheme 1. Molecular structure of the 9HL-d2 sample under investigation. Optimized geometry is displayed with the orientation of the local director of the deuterated phenyl fragment (np) and the layer normal (l) to the SmA planes (p).

Critical behavior from the anomalous Hall effect in (GaMn)As

An unconventional approach to scaling based on the anomalous Hall effect is presented and utilized to demonstrate conclusively that epitaxial (metallic) ${\text{Ga}}_{0.98}{\text{Mn}}_{0.02}\text{As}$ is a mean-field ferromagnet. Such a result provides strong support for the assertion that the underlying interactions can be treated within the framework of Landau mean-field theory, direct support for which had previously been lacking. This scaling approach also provides confirmation---albeit indirect---that the origin of the anomalous Hall effect in this system is intrinsic at the composition studied.

How critical fluctuations influence adsorption properties of a van der Waals fluid onto a spherical colloidal particle

A recently proposed 3rd-order thermodynamic perturbation theory (TPT) is extended to its 5th-order version and non-uniform counterpart by supplementing with density functional theory (DFT) and a number of ansatzs for a bulk 2nd-order direct correlation function (DCF). Employment of the ansatzs DCF enables the resultant non-uniform formalism devoid of any adjustable parameter and free from numerically solving an Ornstein–Zernike integral equation theory. Density profiles calculated by the present non-uniform formalism for a hard core attractive Yukawa (HCAY) fluid near a spherical geometry are favorably compared with corresponding simulation data available in literature, and are more accurate than those based on a previous 3rd + 2nd-order perturbation DFT. The non-uniform 5th-order TPT is employed to investigate adsorption of the HCAY fluid onto a colloidal particle; it is disclosed that a depletion adsorption can be induced when the coexistence bulk fluid is situated in neighborhood of a critical point or near a bulk vapor–liquid coexistence gaseous phase or liquid phase density. A physical interpretation is given for such depletion adsorption and for its connection with parameters of the potential under consideration, which is ascribed to critical density fluctuations existing within a wide region of the bulk diagram. For a large spherical external potential inducing wetting transition, it is found that only round wetting transition is found instead of 1st-order pre-wetting transition in the case of a planar wall external potential, and the wetting transition temperature increases relative to that for the planar wall external potential. The present theoretical results for wetting transitions are supported by previous investigation based on thermodynamic considerations and a phenomenological Landau mean field theory, and are also in conformity with the present qualitative physical interpretation.

Temperature evolution of the ferroelastic order parameter of Li2TiGeO5

The temperature dependence of the order parameter of Li2TiGeO5 ferroelastic was determined on the basis of several independent measurements: specific heat, birefringence and IR spectroscopy. The estimated temperature evolution of order parameter is in very good agreement with mean field Landau theory in temperature range 40 < T < 233.5 K. The character of the above mentioned dependence unequivocally confirms the second-order phase transition in Li2TiGeO5 at 233.5 K.

Landau Mean‐Field Approximation of Percolation in Conductive Polymer Composites

AbstractSummary: A novel approach of the percolation behavior in conductive composites was proposed on the basis of Landau mean‐field theory. The percolation transition is treated as a concentration‐derived phase transition of conductive particles from dispersion to flocculation so as to form a dissipative percolating network. A formulation of conductivity as a function of filler volume fraction in the percolation transition region was established, which was validated in high‐density polyethylene/carbon black (HDPE/CB) composites from two different laboratories and also in cured epoxy/CB composites of Fournier et al. At high CB concentrations above the percolation threshold, the conductive behavior in HDPE/CB composites follows the statistical percolation theory.

The anisotropic Heisenberg ferromagnet in a magnetic field

The one- and two-dimensional spin S = 1 2 anisotropic Heisenberg ferromagnet model is studied by the double-time Green's function method within the random phase approximation. The magnetization, susceptibility and transverse correlation functions are found to be dependent on the anisotropy. Our result shows that the position and height of maximum of the susceptibility yields the power-law behaviors with respect to the magnetic field. It does not support the 2 3 power law which is obtained from the mean-field Landau's theory. For the isotropic case, our results are in agreement with the results obtained by other theoretic techniques. For S = 1 2 ferromagnetic chain system (C 6H 11NH 3)CuBr 3, the crossover of the anisotropic system to XY-kind behavior is expected at low temperature T ≈ 5.5 K , which agrees with experiment results and theoretical calculations.

Field dependence of the susceptibility maximum in the anisotropic Heisenberg ferromagnet

The location and height of the susceptibility maximum for anisotropic one and two-dimensional spin S = 1 2 Heisenberg models are investigated by using the Green's function treatment within the random phase approximation. The results are fitted to the power law behaviors, T m χ - T 0 = ah γ and χ ( T m χ ) = bh - β , in the high field. And the exponents γ , β are found to be dependent of the anisotropy. Our results do not support the 2 3 power laws which are obtained from the mean-field Landau's theory. For the isotropic and Ising cases, the exponents γ , β which are in agreement with the results by other theoretic techniques.

Superconductors with two critical temperatures

We propose a simple model for superconductors endowed with two critical temperatures, corresponding to two second-order phase transitions, in the framework of the Ginzburg–Landau mean-field theory. For very large Cooper pair self-interaction, in addition to the standard condensation occurring in the Ginzburg–Landau theory, we find another phase transition at a lower temperature with a maximum difference of 15% between the two critical temperatures.

Electrooptic study of antiferroelectric mixtures for display application

AbstractThe aim of this paper is to study the influence of electric field on alignment of para-, ferro- and antiferroelectric phases in the vicinity of SmA* — SmC* or SmC* — SmCA* phase transitions as to obtain mono-domain cells. Four mixtures studied (W-193B, W-193B-1, W-201, W-204D) show the SmCA* phase in a wide room temperature range. Measurements of the spontaneous polarization versus temperature by using reversal current method give an answer to the question, what kind of the transitions take place between para-, ferro- or antiferroelectric phases using the Landau mean field theory. Optimal electrooptic parameters for different compositions of the mixtures such as tilt angle, spontaneous polarization and saturation voltage have been measured to compare parameters of the mixtures studied.

Studies of the effects of ion irradiation on ferroelectric domains of triglycine sulfate single crystals on a nanometer scale

The effects of low dose (10 9/cm 2) ion irradiation on the ferroelectric domains and on the ferroelectric↔paraelectric phase transition of triglycine sulfate (TGS) single crystals has been studied by using variable temperature dynamic contact electrostatic force microscopy. The evolution with temperature of ferroelectric domains of virgin and ion irradiated samples was observed in situ. In general, the phase transition of ion unirradiated samples is similar to that of virgin samples, which can be well described by Landau's mean field theory. However, on ion irradiated samples, there is a strong asymmetry of spontaneous polarization P for positive and negative domains. This asymmetry is due to the defects produced by ion implantation.