Location of the isotropic-nematic transition in the Gay-Berne model

Boltzmann's H-function for molecules with orientational degrees of freedom: Emergence of unique features

Boltzmann's H-function H(t), often regarded as an analog of time-dependent entropy, holds a venerable place in the history of science. However, accurate numerical evaluation of H(t) for particles other than atoms is rare. To remove this lacuna, we generalize Boltzmann's H-function to a gas of molecules with orientational degrees of freedom and evaluate H(t) from the time-dependent joint probability distribution function f(p, L, t) for linear (p) and angular (L) momenta, evolving from an initial nonequilibrium state, by molecular dynamics simulations. We consider both prolate- and oblate-shaped particles, interacting via the well-known Gay-Berne potential and obtain the relaxation of the generalized molecular H(t) from initial (t = 0) nonequilibrium states. In the long-time limit, the H function saturates to its exact equilibrium value, which is the sum of translational and rotational contributions to the respective entropies. Both the translational and rotational components of H(t) decay nearly exponentially with time; the rotational component is more sensitive to the molecular shape that enters through the aspect ratio. A remarkable rapid decrease in the rotational relaxation time is observed as the spherical limit is approached, in a way tantalizingly reminiscent of Hu-Zwanzig hydrodynamic prediction with the slip boundary condition. In addition, we obtain H(t) analytically by solving the appropriate translational and rotational Fokker-Planck equation and obtain a modest agreement with simulations. We observe a remarkable signature of translation-rotation coupling as a function of molecular shape, captured through a physically meaningful differential term that quantifies the magnitude of translation-rotation coupling.

Hidden scale invariance in the Gay-Berne model. II. Smectic-B phase

This paper complements a previous study of the isotropic and nematic phases of the Gay-Berne liquid-crystal model [Mehri et al., Phys. Rev. E 105, 064703 (2022)2470-004510.1103/PhysRevE.105.064703] with a study of its smectic-B phase found at high density and low temperatures. We find also in this phase strong correlations between the virial and potential-energy thermal fluctuations, reflecting hidden scale invariance and implying the existence of isomorphs. The predicted approximate isomorph invariance of the physics is confirmed by simulations of the standard and orientational radial distribution functions, the mean-square displacement as a function of time, and the force, torque, velocity, angular velocity, and orientational time-autocorrelation functions. The regions of the Gay-Berne model that are relevant for liquid-crystal experiments can thus fully be simplified via the isomorph theory.

Hidden scale invariance in the Gay-Berne model

This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity, where we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the mean-square displacement and the reduced-unit time-autocorrelation functions of the velocity, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph-invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the molecules and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation, in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.

Pressure-tensor method evaluation of the interfacial tension between Gay-Berne isotropic fluid and a smooth repulsive wall

The interfacial properties of a confined thermotropic liquid crystalline material are investigated using a molecular dynamics simulation technique. The pairwise interaction among the soft ellipsoidal particles is modeled by the Gay-Berne (GB) potential. The GB ellipsoids are confined by two soft, smooth, repulsive walls defined by the Weeks-Chandler-Andersen (WCA) potential. The aperiodic confinement due to walls makes the system mechanically anisotropic. Hence using the pressure-tensor method, the interfacial tension of an interface between the bulk isotropic (I) phase and WCA wall at various number densities (ρ) is calculated. From the pressure tensor and orientational order profiles, the arrangement of ellipsoids in the bulk and the vicinity of the wall is determined. The effect of system size and the wall-particle interaction strength (ε_W) on is also analyzed by varying the system size and ε_W.

Interfacial stiffness of nematic-smectic B interface in Gay-Berne liquid crystals using capillary wave theory

The interfacial stiffness for nematic-smectic B (nm-smB) interface in a liquid crystalline (LC) material is calculated using Capillary Wave Theory (CWT) and molecular dynamics simulations. The Gay-Berne (GB) pair potential with parameters κ, κ', μ, and ν equal to 3, 5, 2, and 1 is used to model the LC material. Using a smart three-step recipe, we have obtained an nm-smB phase coexistence in our simulations where the nm and smB directors are nearly parallel to each other and perpendicular to the interface normal. The density profiles are used to compute the nm-smB coexisting density range, the interfacial width, and its position. The smectic phase is differentiated from the nematic phase by using the local bond order parameter (q₆q₆), which has helped us to demonstrate that the interface is indeed rough. Finally, the interfacial stiffness of the nm-smB interface is computed by following the CWT analysis and is found to be γ̃_nm-smB=0.39861k_BT/σ_ee ²=0.04429/σ_ss ², where σ_ee and σ_ss are the length and diameter of the GB LC particles.

Molecular-statistical theory of elasticity in nematic liquid crystals composed of polar and nonpolar molecules

A molecular-statistical theory of the orientational elasticity of nematic liquid crystals has been developed employing the orientational deformation tensor which describes the rotation of the director. An explicit expression for the general elasticity tensor of the nematic phase has been obtained and the Frank elastic constants are expressed in terms of the three independent parameters of this tensor. Explicit expressions for the Frank elastic constants have been derived in the molecular field approximation in terms of the orientational order parameters and the corresponding coefficients of expansion of the intermolecular potential in spherical invariants. Frank elastic constants have been calculated numerically for nematic liquid crystals composed of both polar and nonpolar molecules together with the orientational order parameters using the classical Gay-Berne model interaction potential and the two of its popular modifications. The polarity of the uniaxial molecular shape has been directly introduced into the model potential by modifying the distance of closest approach. The elastic constants are presented as functions of temperature for different values of the molecular elongation, the anisotropy of the potential well and the molecular shape polarity. It has been shown that the elastic constants are much more sensitive to the details of the intermolecular interaction potential in comparison with the orientational order parameters. In particular, a relatively weak polarity of the molecular shape may result in an unusual decrease of the splay constant K_{11} which may vanish at some temperature leading to the instability of the homogeneous nematic phase. This may represent a mechanism of the formation of the splay-bend phase.

Dynamics of a binary mixture of non-spherical molecules: Test of hydrodynamic predictions

We consider a new class of model systems to study systematically the role of molecular shape in the transport properties of dense liquids. Our model is a liquid binary mixture where both the molecules are non-spherical and characterized by a collection of parameters. Although in the real world most of the molecules are non-spherical, only a limited number of theoretical studies exist on the effects of molecular shapes and hardly any have addressed the validity of the hydrodynamic predictions of rotational and translational diffusion of these shapes in liquids. In this work, we study a model liquid consisting of a mixture of prolate and oblate (80:20 mixture) ellipsoids with interactions governed by a modified Gay-Berne potential for a particular aspect ratio (ratio of the length and diameter of the ellipsoids), at various temperature and pressure conditions. We report calculations of transport properties of this binary mixture by varying temperature over a wide range at a fixed pressure. We find that for the pressure-density conditions studied, there is no signature of any phase separation, except transitions to the crystalline phase at low temperatures and relatively low pressure (the reason we largely confined our studies to high pressure). We find that for our model binary mixture, both stick and slip hydrodynamic predictions break down in a major fashion, for both prolates and oblates and particularly so for rotation. Moreover, prolates and oblates themselves display different dynamical features in the mean square displacement and in orientational time correlation functions.

Nanodrops of Discotic Liquid Crystals: A Monte Carlo Study

We study the morphologies of nematic nanodrops in a vapor of a discotic nematogen by Monte Carlo simulations. The fluid interactions are modeled by a Gay-Berne model with molecular elongations of κ = 0.3 and 0.5 and different values of the energy anisotropy parameter κ' in the range of temperature T in which the nematic coexists with a vapor phase. We considered nanodrops of N = 4000 and 32 000 particles. For κ > κ', we observe that nanodrops are quite spherical (even for N = 4000 nanodrops), with a homogeneous director field for κ = 0.3 and a bipolar nematic configuration with tangential anchoring for κ = 0.5. By increasing the value of κ', nanodrops change from spherical to lens-shaped for κ = 0.3, and for κ = 0.5, spherical nanodrops with homeotropic anchoring and a disclination ring located on its equatorial plane are observed. Although no radial nanodrops are observed, isotropic liquid nanodrops with a paranematic shell and radial texture are observed for temperatures slightly above the vapor-isotropic-nematic triple point when the vapor-isotropic interface is completely wet by the nematic phase.

Maier-Saupe model of polymer nematics: Comparing free energies calculated with Self Consistent Field theory and Monte Carlo simulations

Self Consistent Field (SCF) theory serves as an efficient tool for studying mesoscale structure and thermodynamics of polymeric liquid crystals (LC). We investigate how some of the intrinsic approximations of SCF affect the description of the thermodynamics of polymeric LC, using a coarse-grained model. Polymer nematics are represented as discrete worm-like chains (WLC) where non-bonded interactions are defined combining an isotropic repulsive and an anisotropic attractive Maier-Saupe (MS) potential. The range of the potentials, σ, controls the strength of correlations due to non-bonded interactions. Increasing σ (which can be seen as an increase of coarse-graining) while preserving the integrated strength of the potentials reduces correlations. The model is studied with particle-based Monte Carlo (MC) simulations and SCF theory which uses partial enumeration to describe discrete WLC. In MC simulations the Helmholtz free energy is calculated as a function of strength of MS interactions to obtain reference thermodynamic data. To calculate the free energy of the nematic branch with respect to the disordered melt, we employ a special thermodynamic integration (TI) scheme invoking an external field to bypass the first-order isotropic-nematic transition. Methodological aspects which have not been discussed in earlier implementations of the TI to LC are considered. Special attention is given to the rotational Goldstone mode. The free-energy landscape in MC and SCF is directly compared. For moderate σ the differences highlight the importance of local non-bonded orientation correlations between segments, which SCF neglects. Simple renormalization of parameters in SCF cannot compensate the missing correlations. Increasing σ reduces correlations and SCF reproduces well the free energy in MC simulations.

Doping liquid crystals with nanoparticles. A computer simulation of the effects of nanoparticle shape

Molecular-scale Monte Carlo simulations of liquid crystal-nanoparticle dispersions show the effect on the orientational order and on the clearing temperature of shape and concentration of the dopant nanoparticles.

Calculation of the absolute free energy of a smectic-A phase

In this paper, we provide a scheme to compute the absolute free energy of a smectic-A phase via the "indirect method." The state of interest is connected through a three-step reversible path to a reference state. This state consists of a low-density layer of rods coupled to two external fields maintaining these rods close to the layer's plane and oriented preferably normal to the layer. The low-density free energy of the reference state can be computed on the basis of the relevant second virial coefficients between two rods coupled to the two external fields. We apply this technique to the Gay-Berne potential for calamitics with a parameter set leading to stable isotropic (I), nematic (N), smectic-A (SmA), and crystal (Cr) phases. We locate the I-SmA phase transition at low pressure and the sequence of phase transitions I-N-SmA along higher-pressure isobars and we establish the location of the I-N-SmA triple point. Close to this triple point, we show that the N-SmA transition is clearly first order. Our results are compared to the coexistence lines of the approximate phase diagram elucidated by de Miguel et al. [J. Chem. Phys. 121, 11183 (2004)] established through the direct observation of the sequence of phase transitions occurring along isobars under heating or cooling sequences of runs. Finally, we discuss the potential of our technique in studying similar transitions observed on layered phases under confinement.

Measuring liquid crystal elastic constants with free energy perturbations

A first principles method is proposed to calculate the Frank elastic constants of nematic liquid crystals. These include the constants corresponding to standard splay, twist and bend deformations, and an often-ignored surface-like contribution known as saddle-splay. The proposed approach is implemented on the widely studied Gay-Berne (3, 5, 2, 1) model [J. G. Gay and B. J. Berne, J. Chem. Phys., 1981, 74, 3316], and the effects of temperature and system size on the elastic constants are examined in the nematic phase. The results of simulations for splay, twist, and bend elastic constants are consistent with those from previous literature reports. The method is subsequently applied to the saddle-splay elastic constant k24 which is found to exist at the limits of the Ericksen inequalities governing positive definite free energy. Finally, extensions of the method are discussed that present a new paradigm for in silico measurements of elastic constants.

Liquid-crystal mediated nanoparticle interactions and gel formation

Colloidal particles embedded within nematic liquid crystals exhibit strong anisotropic interactions arising from preferential orientation of nematogens near the particle surface. Such interactions are conducive to forming branched, gel-like aggregates. Anchoring effects also induce interactions between colloids dispersed in the isotropic liquid phase, through the interactions of the pre-nematic wetting layers. Here we utilize computer simulation using coarse-grained mesogens to perform a molecular-level calculation of the potential of mean force between two embedded nanoparticles as a function of anchoring for a set of solvent conditions straddling the isotropic-nematic transition. We observe that strong, nontrivial interactions can be induced between particles dispersed in mesogenic solvent, and explore how such interactions might be utilized to induce a gel state in the isotropic and nematic phases.

Nematic-field-driven positioning of particles in liquid crystal droplets

Common nematic oils, such as 5CB, experience planar anchoring at aqueous interfaces. When these oils are emulsified, this anchoring preference and the resulting topological constraints lead to the formation of droplets that exhibit one or two point defects within the nematic phase. Here, we explore the interactions of adsorbed particles at the aqueous interface through a combination of experiments and coarse-grained modeling, and demonstrate that surface-active particles, driven by elastic forces in the droplet, readily localize to these defect regions in a programmable manner. When droplets include two nanoparticles, these preferentially segregate to the two poles, thereby forming highly regular dipolar structures that could serve for hierarchical assembly of functional structures. Addition of sufficient concentrations of surfactant changes the interior morphology of the droplet, but pins defects to the interface, resulting in aggregation of the two particles.

Modeling the polydomain-monodomain transition of liquid crystal elastomers

We study the mechanism of the polydomain-monodomain transition in liquid crystalline elastomers at the molecular scale. A coarse-grained model is proposed in which mesogens are described as ellipsoidal particles. Molecular dynamics simulations are used to examine the transition from a polydomain state to a monodomain state in the presence of uniaxial strain. Our model demonstrates soft elasticity, similar to that exhibited by side-chain elastomers in the literature. By analyzing the growth dynamics of nematic domains during uniaxial extension, we provide direct evidence that at a molecular level the polydomain-monodomain transition proceeds through cluster rotation and domain growth.

Molecular theory of smectic ordering in liquid crystals with nanoscale segregation of different molecular fragments

A molecular statistical theory of the smectic A phase is developed taking into account specific interactions between different molecular fragments which enables one to describe different microscopic scenario of the transition into the smectic phase. The effects of nanoscale segregation are described using molecular models with different combinations of attractive and repulsive sites. These models have been used to calculate numerically coefficients in the mean filed potential as functions of molecular model parameters and the period of the smectic structure. The same coefficients are calculated also for a conventional smectic with standard Gay-Berne interaction potential which does not promote the segregation. The free energy is minimized numerically to calculate the order parameters of the smectic A phases and to study the nature of the smectic transition in both systems. It has been found that in conventional materials the smectic order can be stabilized only when the orientational order is sufficiently high, In contrast, in materials with nanosegregation the smectic order develops mainly in the form of the orientational-translational wave while the nematic order parameter remains relatively small. Microscopic mechanisms of smectic ordering in both systems are discussed in detail, and the results for smectic order parameters are compared with experimental data for materials of various molecular structure.

Molecular model of biaxial ordering in nematic liquid crystals composed of flat molecules with four mesogenic groups

Relative stability of uniaxial and biaxial nematic phases is analyzed in a model nematic liquid crystal composed of flat molecules of C2h symmetry with four mesogenic groups rigidly linked to the same center. The generalized effective quadrupole mean-field potential is proposed and its constants are evaluated numerically for the pair intermolecular potential based on Gay-Berne interaction between mesogenic groups. The dependencies of the constants on molecular shape parameters are systematically analyzed. Order parameters of the uniaxial and biaxial nematic phases are evaluated by direct minimization of the free energy at different temperatures. The corresponding phase diagrams are obtained enabling one to study the effects of molecular model parameters on the stability regions of uniaxial and biaxial phases. The results are used to clarify the nature of experimentally observed biaxial ordering in nematic liquid crystals composed of tetrapode molecules with the same symmetry.

The Percus-Yevick approximation for quadrupolar molecular fluids

The Percus-Yevick integral equation theory has been solved to study the equilibrium and structural properties of quadrupolar Gay-Berne fluids. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to 6 have been considered. Molecules with length-to-breadth ratios 3.0 and 4.0 have been considered and results are reported for different densities, temperatures, and quadrupole moments. The values of pair correlation functions have been compared with the available computer simulation results.

Order-disorder molecular model of the smectic-A-smectic-C phase transition in materials with conventional and anomalously weak layer contraction

We develop a molecular-statistical theory of the smectic-A-smectic-C transition which is described as a transition of the order-disorder type. The theory is based on a general expansion of the effective interaction potential and employs a complete set of orientational order parameters. All the order parameters of the smectic-C phase including the tilt angle are calculated numerically as functions of temperature for a number of systems which correspond to different transition scenario. The effective interaction potential and the parameters of the transition are also calculated for specific molecular models based on electrostatic and induction interaction between molecular dipoles. The theory successfully reproduces the main properties of both conventional and so-called "de Vries-type" smectic liquid crystals, clarifies the origin of the anomalously weak layer contraction and describes the tricritical behavior at the smectic-A-smectic-C transition. The "de Vries behavior," i.e., anomalously weak layer contraction is also obtained for a particular molecular model based on interaction between longitudinal molecular dipoles. A simple phenomenological model is presented enabling one to obtain explicit expressions for the layer spacing and the tilt angle which are used to fit the experimental data for a number of materials.

Pair correlation functions and a free energy functional for the nematic phase

In this paper we have presented the calculation of pair correlation functions in a nematic phase for a model of spherical particles with the long-range anisotropic interaction from the mean spherical approximation (MSA) and the Percus-Yevick (PY) integral equation theories. The results found from the MSA theory have been compared with those found analytically by Holovko and Sokolovska [J. Mol. Liq. 82, 161 (1999)]. A free energy functional which involves both the symmetry conserving and symmetry broken parts of the direct pair correlation function has been used to study the properties of the nematic phase. We have also examined the possibility of constructing a free energy functional with the direct pair correlation function which includes only the principal order parameter of the ordered phase and found that the resulting functional gives results that are in good agreement with the original functional. The isotropic-nematic transition has been located using the grand thermodynamic potential. The PY theory has been found to give a nematic phase with pair correlation function harmonic coefficients having all the desired features. In a nematic phase the harmonic coefficient of the total pair correlation function h(x1,x2) connected with the correlations of the director transverse fluctuations should develop a long-range tail. This feature has been found in both the MSA and PY theories.

Characteristic behavior of short-term dynamics in reorientation for Gay-Berne particles near the nematic-isotropic phase transition temperature

A specific transition behavior was found in the tumbling motion near the nematic-isotropic phase boundary using molecular dynamics simulations of the Gay-Berne mesogenic model under isobaric conditions at a reduced pressure P* of 2.0. The relaxation time for the motion obtained from the second-rank orientational time correlation function and the rotational diffusion coefficient showed a clear jump at the nematic-isotropic phase transition temperature. Regardless of the temperature dependence of the relaxation time, the change in the rotational diffusion coefficient evaluated from the orientational order parameters and the relaxation time agreed qualitatively with that of real mesogens. The rotational viscosity coefficients gamma(1) and gamma(2) were obtained from the simulation data for the relaxation time for the short-term dynamics and for the rotational diffusion coefficients. gamma(1) was proportional to <P2>(2), where <P2> is the second-rank orientational parameter. Furthermore, the rotational behavior of the model was compared with that of the Debye approximation in the isotropic phase.

The nature of the calculation of the pressure in molecular simulations of continuous models from volume perturbations

We consider some fundamental aspects of the calculation of the pressure from simulations by performing volume perturbations. The method, initially proposed for hard-core potentials by Eppenga and Frenkel [Mol. Phys.52, 1303 (1984)] and then extended to continuous potentials by Harismiadis et al. [J. Chem. Phys. 105, 8469 (1996)], is based on the numerical estimate of the change in Helmholtz free energy associated with the perturbation which, in turn, can be expressed as an ensemble average of the corresponding Boltzmann factor. The approach can be easily generalized to the calculation of components of the pressure tensor and also to ensembles other than the canonical ensemble. The accuracy of the method is assessed by comparing simulation results obtained from the volume-perturbation route with those obtained from the usual virial expression for several prototype fluid models. Monte Carlo simulation data are reported for bulk fluids and for inhomogeneous systems containing a vapor-liquid interface.

Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid

We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 < or = x(0) < or = 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x(0) considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x(0). The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.

Discrimination in isotropic, nematic, and smectic phases of chiral calamitic molecules: a computer simulation study

Racemic fluids of chiral calamitic molecules are investigated with molecular dynamics simulations. In particular, the phase behavior as a function of density is examined for eight racemates. The relationship between chiral discrimination and orientational order in the phase is explored. We find that the transition from the isotropic phase to a liquid crystal phase is accompanied by an increase in chiral discrimination, as measured by differences in radial distributions. Among ordered phases, discrimination is largest for smectic phases with a significant preference for heterochiral contact within the layers.

In search of temporal power laws in the orientational relaxation near isotropic–nematic phase transition in model nematogens

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.

Stability of smectic phases in the Gay–Berne model

We present a detailed computer simulation study of the phase behavior of the Gay-Berne liquid crystal model with molecular anisotropy parameter kappa=4.4. According to previous investigations: (i) this model exhibits isotropic (I), smectic-A (Sm-A), and smectic-B (Sm-B) phases at low pressures, with an additional nematic (N) phase between the I and Sm-A phases at sufficiently high pressures; (ii) the range of stability of the Sm-A phase turns out to be essentially constant when varying the pressure, whereas other investigations seem to suggest a pressure-dependent Sm-A range; and (iii) the range of stability of the Sm-B phase remains unknown, as its stability with respect to the crystal phase has not been previously considered. The results reported here do show that the Sm-A phase is stable over a limited pressure range, and so it does not extend to arbitrarily low or high pressures. This is in keeping with previous investigations of the effect of molecular elongation on the phase behavior of Gay-Berne models. A detailed study of the melting transition at various pressures shows that the low-temperature crystalline phase melts into an isotropic liquid at very low pressures, and into a nematic liquid at very high pressures. At intermediate pressures, the crystal melts into a Sm-A liquid and no intermediate Sm-B phase is observed. On the basis of this and previous investigations, the reported Sm-B phase for Gay-Berne models appears to be a molecular solid rather than a smectic liquid phase.

Computer simulations of hard pear-shaped particles

We report results obtained from Monte Carlo simulations investigating mesophase formation in two model systems of hard pear-shaped particles. The first model considered is a hard variant of the truncated Stone-expansion model previously shown to form nematic and smectic mesophases when embedded within a 12-6 Gay-Berne-like potential [R. Berardi, M. Ricci, and C. Zannoni, ChemPhysChem 7, 443 (2001)]. When stripped of its attractive interactions, however, this system is found to lose its liquid crystalline phases. For particles of length to breadth ratio k=3, glassy behavior is seen at high pressures, whereas for k=5 several bi- layerlike domains are seen, with high intradomain order but little interdomain orientational correlation. For the second model, which uses a parametric shape parameter based on the generalized Gay-Berne formalism, results are presented for particles with elongation k=3, 4, and 5. Here, the systems with k=3 and 4 fail to display orientationally ordered phases, but the system with k=5 shows isotropic, nematic and, unusual for a hard-particle model, interdigitated smectic A2 phases.

Structure and freezing of fluids interacting via the Gay-Berne (n-6) potentials

We have calculated the pair-correlation functions of a fluid interacting via the Gay-Berne (n-6) pair potentials using the Percus-Yevick integral equation theory and have shown how these correlations depend on the value of n that measures the sharpness of the repulsive core of the pair potential. These results have been used in the density-functional theory to locate the freezing transitions of these fluids. We have used two different versions of the theory known as the second order and the modified weighted-density-functional theory and examined the freezing of these fluids for 8< or =n< or =30 and in the reduced temperature range lying between 0.65 and 1.25 into the nematic and the smectic A phases. For none of these cases smectic A phase was found to be stabilized though in some range of temperature for a given n it appeared as a metastable state. We have examined the variation of freezing parameters for the isotropic-nematic transition with temperature and n. We have also compared our results with simulation results wherever they are available. While we find that the density-functional theory is good to study the freezing transitions in such fluids the structural parameters found from the Percus-Yevick theory need to be improved particularly at high temperatures and lower values of n.