Molecular-dynamics study of the nematic-isotropic interface

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.

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.

Rupture mechanism of liquid crystal thin films realized by large-scale molecular simulations

The ability of liquid crystal (LC) molecules to respond to changes in their environment makes them an interesting candidate for thin film applications, particularly in bio-sensing, bio-mimicking devices, and optics. Yet the understanding of the (in)stability of this family of thin films has been limited by the inherent challenges encountered by experiment and continuum models. Using unprecedented large-scale molecular dynamics (MD) simulations, we address the rupture origin of LC thin films wetting a solid substrate at length scales similar to those in experiment. Our simulations show the key signatures of spinodal instability in isotropic and nematic films on top of thermal nucleation, and importantly, for the first time, evidence of a common rupture mechanism independent of initial thickness and LC orientational ordering. We further demonstrate that the primary driving force for rupture is closely related to the tendency of the LC mesogens to recover their local environment in the bulk state. Our study not only provides new insights into the rupture mechanism of liquid crystal films, but also sets the stage for future investigations of thin film systems using peta-scale molecular dynamics simulations.

Coexistence of spinodal instability and thermal nucleation in thin-film rupture: insights from molecular levels

Despite extensive investigation using hydrodynamic models and experiments over the past decades, there remain open questions regarding the origin of the initial rupture of thin liquid films. One of the reasons that makes it difficult to identify the rupture origin is the coexistence of two dewetting mechanisms, namely, thermal nucleation and spinodal instability, as observed in many experimental studies. Using a coarse-grained model and large-scale molecular dynamics simulations, we are able to characterize the very early stage of dewetting in nanometer-thick liquid-metal films wetting a solid substrate. We observe the features characteristic of both spinodal instability and thermal nucleation in the spontaneously dewetting films and show that these two macroscopic mechanisms share a common origin at molecular levels.

Structure and dynamics of interfaces between two coexisting liquid-crystalline phases

A phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid-crystalline phases in two spatial dimensions. Depending on the model parameters, there is a variety of possible coexistences between two liquid-crystalline phases, including a plastic triangular crystal (PTC). Here, we numerically calculate the profiles for the mean density and for the nematic order tensor across the interface for isotropic-PTC and columnar-PTC (or equivalently smectic-A-PTC) phase coexistence. As a general finding, the width of the interface with respect to the nematic order parameter characterizing the orientational order is larger than the width of the mean-density interface. In approaching the interface from the PTC side, at first, the mean density goes down, and then the nematic order parameter follows. The relative shift in the two profiles can be larger than a full lattice constant of the plastic crystal. Finally, we also present numerical results for the dynamic relaxation of an initial order-parameter profile towards its equilibrium interfacial profile. Our predictions for the interfacial profiles can, in principle, be verified in real-space experiments of colloidal dispersions.

Orientational ordering transitions of semiflexible polymers in thin films: a Monte Carlo simulation

Athermal solutions (from dilute to concentrated) of semiflexible macromolecules confined in a film of thickness D between two hard walls are studied by means of grand-canonical lattice Monte Carlo simulation using the bond fluctuation model. This system exhibits two phase transitions as a function of the thickness of the film and polymer volume fraction. One of them is the bulk isotropic-nematic first-order transition, which ends in a critical point on decreasing the film thickness. The chemical potential at this transition decreases with decreasing film thickness ("capillary nematization"). The other transition is a continuous (or very weakly first-order) transition in the layers adjacent to the hard planar walls from the disordered phase, where the bond vectors of the macromolecules show local ordering (i.e., "preferential orientation" along the x or y axes of the simple cubic lattice, but no long-range orientational order occurs), to a quasi-two-dimensional nematic phase (with the director at each wall being oriented along either the x or y axis), while the bulk of the film is still disordered. When the chemical potential or monomer density increase, respectively, the thickness of these surface-induced nematic layers grows, causing the disappearance of the disordered region in the center of the film.

Helicopter rotation and smectic-isotropic coexistence of strongly attractive rods

Hydrodynamic simulations of strongly attractive rodlike colloids are performed with and without shear flow. In the absence of flow, the isotropic-nematic coexistence becomes isotropic-smectic A, and the interfacial properties clearly vary with increasing attraction strength. In the presence of shear flow, a new collective rotation appears in which the director rotates in the vorticity-flow plane in a similar fashion to the movement of the rotor of a helicopter.

Fundamental measure density functional theory for hard spherocylinders in static and time-dependent aligning fields

The recently developed fundamental measure density functional theory (Hansen-Goos and Mecke 2009 Phys. Rev. Lett. 102 018302) for an inhomogeneous anisotropic hard body fluid is used as a basic ingredient in treating the Brownian dynamics of hard spherocylinders. After discussing the relevance of a free parameter in the fundamental measure density functional for the isotropic-nematic transition in equilibrium, we discuss the equilibrium phase behaviour of hard spherocylinders in a static external potential which couples only to the orientations. For external potentials favouring rod orientations along the poles of the unit sphere, there is a well-known paranematic-nematic transition which ceases to exist above a threshold of the strength V(0) of the external potential. However, when orientations along the equator are more favoured, in the plane of the potential energy V(0) and density, there is a phase transition from paranematic to nematic for any strength, which becomes second order above a critical threshold of V(0). The full equilibrium phase diagram in the V(0)-density plane is computed for a fixed rod aspect ratio of 5. For the equatorial cases, strength V(0) is then oscillating in time and dynamical density functional theory is used to compute the evolution of the orientational distribution. A subtle resonance for increasing oscillation frequencies is detected if the oscillating V(0) crosses the paranematic-nematic phase transition.

Entropic Wetting and the Free Isotropic−Nematic Interface of Hard Colloidal Platelets

We study bulk and interfacial properties of a model suspension of hard colloidal platelets with continuous orientations and vanishing thickness using both density functional theory, based on either a second virial approach or fundamental measure theory (FMT), and Monte Carlo (MC) simulations. We calculate the bulk equation of state, bulk isotropic-nematic (IN) coexistence, and properties of the (planar) free IN interface and of adsorption at a planar hard wall, where we find complete wetting of the nematic phase at the isotropic-wall interface upon approaching bulk IN coexistence. We investigate in detail the asymptotic decay of correlations at large distances. In all cases, the results from FMT and MC agree quantitatively. Our findings are of direct relevance to understanding interfacial properties of dispersions of colloidal platelets.

Perturbative approach to the structure of a planar interface in the Landau-de Gennes model

The structure of nearly static planar interfaces is studied within the framework of the Landau-de Gennes model with the dynamics governed by the time-dependent Ginzburg-Landau equation. To account for the full elastic anisotropy the free energy expansion is extended to include a third order gradient term. The solutions corresponding to the in-plane or homeotropic director alignment at the interface are sought. For this purpose a consistent perturbative scheme is constructed which enables one to calculate successive corrections to the velocity and the order parameter of the interface. The implications of the solutions are discussed. The elastic anisotropy introduces asymmetry into the order parameter and free energy profiles, even for the high symmetry homeotropic configuration. The velocity of the interface with the homeotropic or in-plane alignment is enhanced or reduced, respectively. There is no reorientation of the optical axis in the boundary layer. For the class of nematogens with approximate splay-bend degeneracy the temperature dependence of the interface velocity is weakly affected by the remaining twist anisotropy.

The anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations

We have calculated the interfacial free energy for the hard-sphere system, as a function of crystal interface orientation, using a method that examines the fluctuations in the height of the interface during molecular dynamics simulations. The approach is particularly sensitive for the anisotropy of the interfacial free energy. We find an average interfacial free energy of gamma=0.56+/-0.02k(B)Tsigma(-2). This value is lower than earlier results based upon direct calculations of the free energy [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)]. However, both the average value and the anisotropy agree with the recent values obtained by extrapolation from direct calculations for a series of the inverse-power potentials [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)].

Isotropic-nematic interface and wetting in suspensions of colloidal platelets

We study interfacial phenomena in a colloidal dispersion of sterically stabilized gibbsite platelets, exhibiting coexisting isotropic and nematic phases separated by a sharp horizontal interface. The nematic phase wets a vertical glass wall and polarized light micrographs reveal homeotropic surface anchoring both at the free isotropic-nematic interface and at the wall. On the basis of complete wetting of the wall by the nematic phase, as found in our density functional calculations and computer simulations, we analyze the balance between Frank elasticity and surface anchoring near the contact line. Because of weak surface anchoring, the director field in the capillary rise region is uniform. From the measured rise (6 microm) of the meniscus at the wall we determine the isotropic-nematic surface tension to be 3 nN/m, in quantitative agreement with our theoretical and simulation results.

Isotropic-nematic interface in suspensions of hard rods: mean-field properties and capillary waves

We present a study of the isotropic-nematic interface in a system of hard spherocylinders. First we compare results from Monte Carlo simulations and Onsager density functional theory for the interfacial profiles of the orientational order parameter and the density. Those interfacial properties that are not affected by capillary waves are in good agreement, despite the fact that Onsager theory overestimates the coexistence densities. Then we show results of a Monte Carlo study of the capillary waves of the interface. In agreement with recent theoretical investigations [Elgeti and Schmid, Eur. Phys. J. E 18, 407 (2005)] we find a strongly anisotropic capillary wave spectrum. For the wave numbers accessed in our simulations, the spectrum is quadratic, i.e., elasticity does not play a role. We conjecture that this effect is due to the strong bending rigidity of the director field in suspensions of spherocylinders.

Nematic-isotropic interfaces under shear: A molecular-dynamics simulation

We present a large-scale molecular-dynamics study of nematic-paranematic interfaces under shear. We use a model of soft repulsive ellipsoidal particles with well-known equilibrium properties, and consider interfaces which are oriented normal to the direction of the shear gradient (common stress case). The director at the interface is oriented parallel to the interface (planar). A fixed average shear rate is imposed with moving periodic boundary conditions, and the heat is dissipated with a profile-unbiased thermostat. First, we study the properties of the interface at one particular shear rate in detail. The local interfacial profiles and the capillary wave fluctuations of the interfaces are calculated and compared with those of the corresponding equilibrium interface. Under shear, the interfacial width broadens and the capillary wave amplitudes at large wavelengths increase. The strain is distributed inhomogeneously in the system (shear banding), the local shear rate in the nematic region being distinctly higher than in the paranematic region. Surprisingly, we also observe (symmetry-breaking) flow in the vorticity direction, with opposite direction in the nematic and the paranematic state. Finally, we investigate the stability of the interface for other shear rates and construct a nonequilibrium phase diagram.

Nematic liquid crystals at rough and fluctuating interfaces

Nematic liquid crystals at rough and fluctuating interfaces are analyzed within the Frank elastic theory and the Landau-de Gennes theory. We study specifically interfaces that locally favor planar anchoring. In the first part we reconsider the phenomenon of Berreman anchoring on fixed rough surfaces, and derive new simple expressions for the corresponding azimuthal anchoring energy. Surprisingly, we find that for strongly aligning surfaces, it depends only on the geometrical surface anisotropy and the bulk elastic constants, and not on the precise values of the chemical surface parameters. In the second part, we calculate the capillary waves at nematic-isotropic interfaces. If one neglects elastic interactions, the capillary wave spectrum is characterized by an anisotropic interfacial tension. With elastic interactions, the interfacial tension, i.e., the coefficient of the leading q(2) term of the capillary wave spectrum, becomes isotropic. However, the elastic interactions introduce a strongly anisotropic cubic q(3) term. The amplitudes of capillary waves are largest in the direction perpendicular to the director. These results are in agreement with previous molecular dynamics simulations.

Test-area simulation method for the direct determination of the interfacial tension of systems with continuous or discontinuous potentials

A novel test-area (TA) technique for the direct simulation of the interfacial tension of systems interacting through arbitrary intermolecular potentials is presented in this paper. The most commonly used method invokes the mechanical relation for the interfacial tension in terms of the tangential and normal components of the pressure tensor relative to the interface (the relation of Kirkwood and Buff [J. Chem. Phys. 17, 338 (1949)]). For particles interacting through discontinuous intermolecular potentials (e.g., hard-core fluids) this involves the determination of delta functions which are impractical to evaluate, particularly in the case of nonspherical molecules. By contrast we employ a thermodynamic route to determine the surface tension from a free-energy perturbation due to a test change in the surface area. There are important distinctions between our test-area approach and the computation of a free-energy difference of two (or more) systems with different interfacial areas (the method of Bennett [J. Comput. Phys. 22, 245 (1976)]), which can also be used to determine the surface tension. In order to demonstrate the adequacy of the method, the surface tension computed from test-area Monte Carlo (TAMC) simulations are compared with the data obtained with other techniques (e.g., mechanical and free-energy differences) for the vapor-liquid interface of Lennard-Jones and square-well fluids; the latter corresponds to a discontinuous potential which is difficult to treat with standard methods. Our thermodynamic test-area approach offers advantages over existing techniques of computational efficiency, ease of implementation, and generality. The TA method can easily be implemented within either Monte Carlo (TAMC) or molecular-dynamics (TAMD) algorithms for different types of interfaces (vapor-liquid, liquid-liquid, fluid-solid, etc.) of pure systems and mixtures consisting of complex polyatomic molecules.

Isotropic-nematic interfacial tension of hard and soft rods: Application of advanced grand canonical biased-sampling techniques

Coexistence between the isotropic and the nematic phase in suspensions of rods is studied using grand canonical Monte Carlo simulations with a bias on the nematic order parameter. The biasing scheme makes it possible to estimate the interfacial tension gamma(IN) in systems of hard and soft rods. For hard rods with LD=15, we obtain gammaIN approximately 1.4kBT/L2, with L the rod length, D the rod diameter, T the temperature, and kB the Boltzmann constant. This estimate is in good agreement with theoretical predictions, and the order of magnitude is consistent with experiments.

Interfacial tension of the isotropic-nematic interface in suspensions of soft spherocylinders

The isotropic to nematic transition in a system of soft spherocylinders is studied by means of grand canonical Monte Carlo simulations. The probability distribution of the particle density is used to determine the coexistence densities of the isotropic and the nematic phases. The distributions are also used to compute the interfacial tension of the isotropic-nematic interface, including an analysis of finite size effects. Our results confirm that the Onsager limit is not recovered until for very large elongation, exceeding at least L/D=40 , with L the spherocylinder length and D the diameter. For smaller elongation, we find that the interfacial tension increases with increasing L/D , in agreement with theoretical predictions.

Molecular dynamics study of then-hexane–water interface: Towards a better understanding of the liquid–liquid interfacial broadening

By molecular dynamics simulations, we have studied the hydrophilic-hydrophobic interface between water and n-hexane liquid phases. For all temperatures studied our computed interfacial tension agrees very well with the experimental value. However, the interfacial width calculated from capillary wave theory systematically overestimates the width obtained from fitting either the total density or composition profile. We rationalize the applicability of capillary wave theory for our system by reconsidering the usual value taken for the correlation length. This is motivated by the presence of order at the interface. Possible implications for recent experimental studies on the structure of model alkane-water interfaces are discussed, including the significance of the intrinsic width parameter.

Density-functional study of the nematic-isotropic interface of hard spherocylinders

The Somoza-Tarazona density-functional theory is applied to the isotropic-nematic interface of hard spherocylinders with length (L)-to-diameter (D) ratios in the range L/D=5-20. Properties such as the density and orientational order-parameter profiles and the variation of interfacial tension with bulk nematic tilt angle agree qualitatively with results of previous studies at larger values of L/D using both computer simulation and the Onsager second-virial approximation. The minimum interfacial tension is obtained at a tilt angle of 90 degrees. For values of L/D approximately 5, it is found that the Onsager approximation predicts a spurious minimum in the interfacial tension at small tilt angles.