Gay-Berne Model Research Articles

Microscale Normal Compression Behaviors of Clay Aggregates: A Coarse-Grained Molecular Dynamics Study.

Given the limitations of micromechanical experiments and molecular dynamics simulations, the normal compression process of clay aggregates was simulated under different vertical pressures (P), numbers of particles, loading methods, and environments by a Gay-Berne potential model. On the basis of the variations of particle orientation and the distribution of stacks, the evolution of deformation and stresses was elucidated. The results showed that the effects of the pressure level and loading environment on the deformation were significant. In the range of 0.1-10 MPa, the changes in the void ratio were essentially the evolution of the distribution of stacks determined by attractive short-range van der Waals interactions. The deformation under constant pressure was larger than that under step loading. Because the interactions between clay particles were mainly controlled by mechanical force when in the range of 40-100 MPa, the void ratios under various loading conditions were consistent. It was also found that changes in three-dimensional stresses during compression were dependent on those of the distribution of stacks. In the vacuum environment, owing to the lateral movement of interlocked small stacks, the horizontal stress decreased. The lateral pressure coefficients (k) were greater in an atmospheric environment because the anisotropic particle orientation was relatively less obvious. In the range of 10-100 MPa, when the loading path became longer, k was similar in vacuum but became smaller in an atmosphere. If the initial loading pressure was increased, the number of large stacks sharply increased and the anisotropy was significant in a vacuum environment, which was less prone to lateral expansion. In contrast, more consistent particle arrangements were maintained in an atmosphere. This work will be conducive to explaining experimental observations of long-term ripening.

Exploring the interplay of liquid crystal orientation and spherical elastic shell deformation in spatial confinement.

The application of liquid crystal technology typically relies on the precise control of molecular orientation at a surface or interface. This control can be achieved through a combination of morphological and chemical methods. Consequently, variations in constrained boundary flexibility can result in a diverse range of phase behaviors. In this study, we delve into the self-assembly of liquid crystals within elastic spatial confinement by using the Gay-Berne model with the aid of molecular dynamics simulations. Our findings reveal that a spherical elastic shell promotes a more regular and orderly alignment of liquid crystals compared to a hard shell. Moreover, during the cooling process, the hard-shell confined system undergoes an isotropic-smectic phase transition. In contrast, the phase behavior within the spherical elastic shell closely mirrors the isotropic-nematic-smectic phase transition observed in bulk systems. This indicates that the orientational arrangement of liquid crystals and the deformations induced by a flexible interface engage in a competitive interplay during the self-assembly process. Importantly, we found that phase behavior could be manipulated by altering the flexibility of the confined boundaries. This insight offers a fresh perspective for the design of innovative materials, particularly in the realm of liquid crystal/polymer composites.

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.

Effect of molecular aspect ratio on structure, dynamics and phase stability of thermotropic liquid crystals studied by molecular dynamics simulation

Due to the importance of liquid crystals in modern technology and food industry, understanding their structural and dynamical properties are scientifically important. In this study, we applied extensive molecular dynamics simulations to infer the effect of the molecular elongation on the formation, stability and dynamics of liquid crystal mesophases in a system of Gay-Berne model mesogens with parameters GB (k,k′=20,μ=1,ν=1). Four aspect ratio values, k=2,3,4.4 and 5, were studied at pressure P*=4. Thermodynamics properties, the order parameter and pair distribution functions (both translational and positional), helped to identify phases, hysteresis, and consequently phase diagrams. By increasing aspect ratio from 2 to 5, nematic and smectic phases were induced and all transition temperatures were shifted to higher values, hence, the range of stability of the nematic and smectic mesophases became wider. The analysis of the coordination numbers and angular distribution functions showed that the structure of the solid phase of system with k=2 at lowest temperatures was fcc which by increasing the aspect ratio changed to a complete hexagonal in-layer structure. Moreover, by increasing the axial ratio of particles, decoupling between the principal components of diffusion coefficients increased, where it reflects an increase in the molecular orientational order in the system with higher k. The effect of increasing aspect ratio was more pronounced on inter-layers diffusion rather than the in-layers. In all mesophases parallel components of diffusion coefficients were greater than the perpendicular components. We analyzed the results based on the existing theoretical descriptions and experimental observations.

Isobars and pitch of cholesteric phases for a chiral Gay-Berne fluid by molecular dynamic simulations

In this work, we explore using molecular dynamics simulations, the isobars and the behaviour of the pitch as a function of temperature and density for a chiral Gay-Berne model using different parametrisations. We present two alternative and consistent methods to calculate the pitch whose dependence on temperature may increase or decrease depending on the parameters of the model. This agrees with experimental results of cholesteric liquid crystals where both positive and negative slopes have been found in the pitch versus temperature curves. We propose a qualitative explanation of this behaviour in terms of the thermal expansion and average angle between the particles.

Beyond Bulk Gay-Berne fluids: An outlook on mesogenic mixtures with molecular dynamics simulations

In this review, we focus on heterogeneous, thermotropic liquid crystal (LC) mixtures our group has studied with molecular dynamics (MD) simulations. Systems considered include: (1) binary LC mixtures, (2) colloidal inclusions in a mesogenic solvent, and (3) confined mesogenic samples. An extension of the Gay-Berne model is provided to treat the mixtures investigated. Our findings are contextualized to calamitic and discotic LC systems. Structural properties of the mesogenic solvent are probed using the Maier-Saupe (nematic) order parameter. Representative snapshots from MD simulations are used to corroborate phase phenomenology. Topological defects are treated in the presence of colloidal inclusions and in confined samples. The effect of solvent flow on the behavior of topological defects is also assessed. These LC mixtures are of interest in the area of applied materials: aside from their rich mesophase behavior, these systems provide a promising platform for molecular self-assembly and organization.

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.

Lines of invariant physics in the isotropic phase of the discotic Gay-Berne model

The Gay-Berne model is studied numerically with a choice of parameters allowing for the formation of a discotic liquid crystal at low temperatures. We show that the model has strong virial potential-energy correlations in the isotropic phase at high temperatures, i.e., it obeys the criterion for the existence of isomorphs, which are curves of approximately invariant structure and dynamics. These properties are demonstrated to be approximately invariant in reduced units along the isomorph studied. The isomorph is described well by the constant density-scaling exponent 11.5, a number that is significantly larger than the density-scaling exponents of various Lennard-Jones models that are always below 6.

Density Scaling of Translational and Rotational Molecular Dynamics in a Simple Ellipsoidal Model near the Glass Transition.

In this paper, we show that a simple anisotropic model of supercooled liquid properly reflects some density scaling properties observed for experimental data, contrary to many previous results obtained from isotropic models. We employ a well-known Gay–Berne model earlier parametrized to achieve a supercooling and glass transition at zero pressure to find the point of glass transition and explore volumetric and dynamic properties in the supercooled liquid state at elevated pressure. We focus on dynamic scaling properties of the anisotropic model of supercooled liquid to gain a better insight into the grounds for the density scaling idea that bears hallmarks of universality, as follows from plenty of experimental data collected near the glass transition for different dynamic quantities. As a result, the most appropriate values of the scaling exponent γ are established as invariants for a given anisotropy aspect ratio to successfully scale both the translational and rotational relaxation times considered as single variable functions of densityγ/temperature. These scaling exponent values are determined based on the density scaling criterion and differ from those obtained in other ways, such as the virial–potential energy correlation and the equation of state derived from the effective short-range intermolecular potential, which is qualitatively in accordance with the results yielded from experimental data analyses. Our findings strongly suggest that there is a deep need to employ anisotropic models in the study of glass transition and supercooled liquids instead of the isotropic ones very commonly exploited in molecular dynamics simulations of supercooled liquids over the last decades.

Equilibrium phases and domain growth kinetics of calamitic liquid crystals.

The anisotropic shape of calamitic liquid crystal (LC) particles results in distinct values of energy when the nematogens are placed side by side or end to end. This anisotropy in energy which is governed by a parameter κ^{'} has deep consequences on equilibrium and nonequilibrium properties. Using the Gay-Berne (GB) model, which exhibits the nematic (Nm) as well as the low-temperature smectic (Sm) order, we undertake large-scale Monte Carlo and molecular dynamics simulations to probe the effect of κ^{'} on the equilibrium phase diagram and the nonequilibrium domain growth following a quench in the temperature T or coarsening. There are two transitions in the GB model: (i) isotropic to Nm at T_{c}^{1} and (ii) Nm to Sm at T_{c}^{2}<T_{c}^{1}. κ^{'} decreases T_{c}^{1} significantly but has relatively little effect on T_{c}^{2}. Domain growth in the Nm phase exhibits the well-known Lifshitz-Allen-Cahn (LAC) law, L(t)∼t^{1/2} and the evolution is via annihilation of string defects. The system exhibits dynamical scaling that is also robust with respect to κ^{'}. We find that the Sm phase at the quench temperatures T (T>T_{c}^{1}→T<T_{c}^{2}) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers (SmB-H phase). Coarsening in this phase exhibits a striking two-timescale scenario: First, the LC molecules align and develop orientational order (or nematicity), followed by the emergence of the characteristic layering (or smecticity) along with the hexatic bond-orientational-order within the layers. Consequently, the growth follows the LAC law L(t)∼t^{1/2} at early times and then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest that L(t)∼t^{1/4} in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes and the scaling function is universal. The dynamics is also robust with respect to changes in κ^{'}, but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to the Sm phase even with other kinds of local order within the Sm layers.

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.

Chiral Gay–Berne model for molecular dynamics computer simulations

We have extended the chiral Gay–Berne (GB) pair potential of Memmer and co–workers [Liq. Cryst. (15), 345 (1993)] to the general case of biaxial ellipsoids, and we provide explicit expressions for the gradient and the torques to be used in molecular dynamics (MD) codes. To test our results against published results we have performed MD simulations of samples formed by N = 1024 uniaxial GB ellipsoids with constant volume, and we have studied how the thermotropic behavior is affected by particle chirality. We have run temperature scans starting from isotropic samples and found clear signatures of the spontaneous formation of both lower temperature blue and cholesteric phases.

An evaluation of contact models for particle-scale simulation of clay

Geotechnical engineers are well aware that the particle surface chemistry and the pore fluid composition can significantly influence the mechanical behaviour of clay. Reference is often made to the Derjaguin-Landau-Vervey-Overbeek (DLVO) theory, which enables the electrochemical interactions between charged particles to be estimated. Hitherto, the absence of an effective framework for particle-scale simulation of clay has inhibited a direct link between these electrochemical interactions and clay behaviour (e.g. load:deformation response) or fabric (i.e. the development of a disperse or flocculated fabric). Ebrahimi [1] demonstrated the viability of using molecular dynamics simulations where the clay grains are simulated as ellipsoidal particles whose interactions are described by an analytical expression called the Gay-Berne (GB) potential. While promising when compared to other approaches documented in the literature, Ebrahimi's work considered only a single clay mineralogy and did not explicitly account for the pore fluid composition. This paper considers the use of the Gay-Berne potential in particle-scale modelling of clay from a more general perspective. Calibration of the GB model parameters to predict kaolinite particle interactions reveals a lack of generality in Ebrahimi's approach. The Gay-Berne potential cannot simulate situations in which attractive and repulsive interactions co-exist, which lead to the classical “cardhouse” fabric, as is the case of kaolinite particles interacting via an acidic pore fluid.

Effect of Central Longitudinal Dipole Interactions on Chiral Liquid-Crystal Phases

Monte Carlo simulations of chiral liquid-crystals, represented by a simple coarse-grained chiral Gay–Berne model, were performed to investigate the effect of central longitudinal dipole interactions on phase behavior. A systematic analysis of the structural properties and phase behavior of both achiral and chiral systems, with dipole interactions, reveals differing effects; strong dipole interactions enhance the formation of layered structures; however, chiral interactions may prevent the formation of such phases under certain conditions. We also observed a short-ranged smectic structure within the cholesteric phases with strong dipole interactions. This constitutes possible evidence of presmectic ordering and/or the existence of chiral line liquid phases, which have previously been observed in X-ray experiments to occur between the smectic twisted grain boundary and cholesteric phases. These results provide a systematic understanding of how the phase behavior of chiral liquid-crystals changes when alterations are made to the strength of dipole interactions.

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.

Computer simulation study of the nematic–vapour interface in the Gay–Berne model

ABSTRACTWe present computer simulations of the vapour–nematic interface of the Gay–Berne model. We considered situations which correspond to either prolate or oblate molecules. We determine the anchoring of the nematic phase and correlate it with the intermolecular potential parameters. On the other hand, we evaluate the surface tension associated to this interface. We find a corresponding states law for the surface tension dependence on the temperature, valid for both prolate and oblate molecules.

1PA04 末端双極子と末端側鎖をもつGay-Berneモデルを用いた5CBのMD計算

1PA04 末端双極子と末端側鎖をもつGay-Berneモデルを用いた5CBのMD計算

Elastic properties of common Gay–Berne nematogens from density of states (DOS) simulations

ABSTRACTA free energy perturbation method is used to systematically study the elastic properties of four common Gay–Berne nematogenic models; two with a length-to-diameter ratio κ = 3 [(3, 5, 1, 2) and (3, 5, 1, 3)], a model with κ = 4.4 parameterised for p-terphenyl (4.4, 20, 1, 1), and a discogen with κ = 0.345 (0.345, 0.2, 1, 2). In accordance with previous measurements, we find that for κ = 3, models, . We additionally find the latter two models in particular accurately capture the experimentally measured elastic ratios in apolar achiral systems. The (4.4, 20, 1, 1) model reproduces the elastic constant ratios of p-azoxyanisole remarkably well, and maps to within 30% of the absolute. The (0.345, 0.2, 1, 2) model elastic constants exhibit an unusual temperature dependence similar to recent experimental studies. Here we find , in line with theoretical predictions. All models deviate from the mean-field expectation kii ∝ S2. These results represent a crucial first step towards quantitatively accurate coarse-grained liquid crystalline models of self-assembly and response, enabling one to choose a Gay–Berne model based on its measured elastic ratios rather than just its shape and energy anisotropy.

Dissipative particle dynamics thermostat: a novel thermostat for molecular dynamics simulation of liquid crystals with Gay-Berne potential

The Gay-Berne (GB) model has been proved to be highly successful in the simulation of liquid crystal phases via both molecular dynamics (MD) and nonequilibrium molecular dynamics (NEMD). However, the conventional thermostats used in the simulations of GB systems, such as Nose-Hoover and Langevin thermostats, have serious shortcomings especially in NEMD simulations. Recently, dissipative particle dynamics (DPD) has established itself as a useful thermostat for soft matter simulations, whereas the application of DPD thermostat in (NE)MD simulations is limited to the spherically isotropic potential models, such as the Lennard-Jones model. Considering the virtues of the DPD thermostat, that is, local, momentum conserved, and Galilean invariant, we extend the DPD thermostat to the non-spherical GB model. It is interesting to find that the translational DPD and rotational DPD thermostats can be used in the GB system independently and both can achieve the thermostatting effects. Also, we compared the performance of the DPD thermostat with other commonly used thermostats in NEMD simulations by investigating the streaming velocity profiles and the dynamics of phase separation in a typical but simple binary GB mixture under shear field. It is revealed that the known virtues of DPD thermostats, such as Galilean invariant, shear velocity profile-unbiased, and unscreened hydrodynamic interactions, are still intact when applying to GB systems. Finally, the appropriate parameters for the DPD thermostat in the GB system are identified for future investigations.

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.