The isotropic–nematic transition in hard Gaussian overlap fluids

Density functional theory for dense nematic liquid crystals with steric interactions

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it does not provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature-it vanishes on a nonzero measure set in orientation space.

Nematic-smectic transition of parallel hard spheroellipsoids

Spheroellipsoids are truncated ellipsoids with spherical end caps. If gradients are assumed to change smoothly at the junction of body and cap, the truncation height z0 determines the geometry uniquely. The resulting model particle has only two shape parameters, namely, the aspect ratio c/a of the basic ellipsoid and the cutoff z0/a. These two parameters can be tuned to yield a continuous transformation between a pure ellipsoid and a spherocylinder. Since parallel hard spherocylinders display a nematic-smectic A phase transition, while ellipsoids do not, the influence of the particle shape on the possibility of a smectic phase may be investigated. A density functional analysis is used to detect the dividing line, in the (c/a, z0/a) plane, between the presence and absence of the N-S transition. Since spheroellipsoids may be useful as generic model particles for anisotropic molecules, we provide a computationally efficient overlap criterion for a pair in a general, non-parallel configuration.

Model of hard spheroplatelets near a hard wall

A system of hard spheroplatelets near an impenetrable wall is studied in the low-density Onsager approximation. Spheroplatelets have optimal shape between rods and plates, and the direct transition from the isotropic to biaxial nematic phase is present. A simple local approximation for the one-particle distribution function is used. Analytical results for the surface tension and the entropy contributions are derived. The density and the order-parameter profiles near the wall are calculated. The preferred orientation of the short molecule axes is perpendicular to the wall. Biaxiality close to the wall can appear only if the phase is biaxial in the bulk.

Density functional theory of liquid crystals and surface anchoring: hard Gaussian overlap-sphere and hard Gaussian overlap-surface potentials

This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.

Simulation and theory of hybrid aligned liquid crystal films

We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

Fluids of hard natural and Gaussian ellipsoids: A comparative study by integral equation theories

The hard Gaussian overlap (HGO) model for ellipsoids is compared to the hard ellipsoid of revolution (HER) model, in the isotropic fluid phase and within the framework of the Percus-Yevick (PY) and hypernetted chain (HNC) integral equation theories. The former model is often used in place of the latter in many approximate theories. Since the HGO model slightly overestimates the contact distance when the two ellipsoids are perpendicular to each other, it leads to small differences in the Mayer function of the two models, but nearly none in the integrals of these functions and particularly for the second virial coefficients. However, it leads to notable differences in the pair correlation functions, as obtained by the Percus-Yevick and the hypernetted chain theories, especially at high densities. The prediction of the stability of the isotropic phase with respect to orientational order, at high densities, is notably influenced by these small differences. Both theories predict that, for same aspect ratios, the HGO model overestimates the ordering, when compared to the HER model. This explains why the PY approximation predicts ordering for the HGO model with aspect ratio of 1:3, while it does not for the HER model, in accordance with the very first integral equation results obtained for this system, and at variance with many opposite claims from subsequent publications that used the HGO model in place of the HER model.

Surface tension of the Widom-Rowlinson model

We consider the computation of the surface tension of the fluid-fluid interface for the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] binary mixture from direct simulation of the inhomogeneous system. We make use of the standard mechanical route, in which the surface tension follows from the computation of the normal and tangential components of the pressure tensor of the system. In addition to the usual approach, which involves simulations of the inhomogeneous system in the canonical ensemble, we also consider the computation of the surface tension in an ensemble where the pressure perpendicular (normal) to the planar interface is kept fixed. Both approaches are seen to provide consistent values of the interfacial tension. The issue of the system-size dependence of the surface tension is addressed. In addition, simulations of the fluid-fluid coexistence properties of the mixture are performed in the semigrand canonical ensemble. Our results are compared with existing data of the Widom-Rowlinson mixture and are also examined in the light of the vapor-liquid equilibrium of the thermodynamically equivalent one-component penetrable sphere model.

Smectic, nematic, and isotropic phases in binary mixtures of thin and thick hard spherocylinders

A second-virial Onsager theory, based on Parsons-Lee rescaling and suitably extended to deal with multicomponent systems and smectic phases, has been used to calculate the phase diagram of a collection of binary mixtures of thin and thick hard spherocylinders. In particular, two types of phase diagrams are investigated. First, a number of binary mixtures where the two components have the same total length have been considered; in addition, the phase diagram of a binary mixture where the two components have the same volume has been calculated. For the particles of one of the two components, the length of the cylindrical part and the diameter have always been set equal to 5 and 1, respectively. Spherocylinders of the same total length and different diameter tend to demix considerably as soon as the diameter ratio deviates from unity. This happens especially at high pressures, when at least the phase richer in the thicker component is smectic. In the case where the two components have equal volumes, demixing is further increased due to the disparity not only in particle diameter but also in particle lengths. The incorporation of inhomogeneous layered phases is seen to alter significantly the phase diagrams calculated if only homogeneous phases are allowed, since transitions to a smectic phase often preempt those to a nematic or an isotropic phase. The apparent versatility of the recent experimental techniques suggests that the phase diagram features predicted by the theory might be also observed in real systems.

Stability of Nematic and Smectic Phases in Rod-Like Mesogens with Orientation−Dependent Attractive Interactions

The stability of isotropic (I), nematic (N), smectic A (Sm A), and hexatic (Hex) liquid crystalline phases is studied for a fluid of molecules with a rod-like shape and dispersive interactions dependent on orientation. The fluid is modeled with the spherocylindrical Gay-Berne-Kihara interaction potential proposed in a recent work, with parameters favoring parallel pair orientations. The liquid crystal phase diagram is characterized for different molecular aspect ratios by means of Monte Carlo simulations in the isobaric-isothermal ensemble. Three types of triple points are observed, namely, I-Sm A-Hex, I-N-Sm A, and N-Sm A-Hex, leading to island-shape domains for the smectic A phase. The resulting phase diagrams are compared with those derived previously for prolate fluids of ellipsoidal and spherocylindrical symmetry. It is concluded that the stability of the layered phases with respect to the nematic phase is enhanced in the spherocylindrical fluids due to geometrical constraints. Furthermore, the anisotropy of the dispersive interactions induces a stronger dependence of the overall phase diagram on temperature and aids in the energetic stabilization of the hexatic crystalline phase with respect to the fluid smectic A phase.

Surface ordering and capillary phenomena of confined hard cut-sphere particles

Isothermal-isobaric and Gibbs ensemble Monte Carlo (GEMC) computer simulations of = 1500 and = 3000 hard cut spheres of aspect ratio / = 0.1, respectively, are carried out in order to investigate the effects of confinement on the isotropic (I)-nematic (N) phase transition. We first consider the free system, and confirm the stabilisation of isotropic (I), nematic (N) and columnar (Col) states. We examine in detail the I-N transition and find coexistence densities of =0.355 and =0.368. A slab geometry is then considered for two types of walls: a hard wall, which excludes the particles entirely, and an 'adsorbent' wall which excludes the centre of mass of the particles. The adsorbent wall is found to favour planar (edge-on) alignment, which results in the formation of a first layer of adsorbed molecules, which then acts as a rough hard wall for subsequent particles, and promotes disordered states. Using Gibbs ensemble simulations we determine the capillary phase diagram of the system, and the adsorption as a function of pore width. The capillary phase diagram obtained from Gibbs ensemble simulations corresponds to one with a first-order capillary isotropisation transition, with an associated capillary critical point for a wall separation of ∼3. The hard walls are seen to promote homeotropic (face-on) alignment of the cut spheres, and promote the stabilisation of the nematic phase. In this case the capillary phase diagram obtained from the GEMC simulations exhibits a first-order capillary nematisation transition, and a capillary critical point for a wall separation of ∼4.

Direct correlation functions of binary mixtures of hard Gaussian overlap molecules

We study the direct correlation function (DCF) of a classical fluid mixture of nonspherical molecules. The components of the mixture are two types of hard ellipsoidal molecules with different elongations, interacting through the hard Gaussian overlap (HGO) model. Two different approaches are used to calculate the DCFs of this fluid, and the results are compared. Here, the Pynn approximation [J. Chem. Phys. 60, 4579 (1974)] is extended to calculate the DCF of the binary mixtures of HGO molecules, then we use a formalism based on the weighted density functional theory introduced by Chamoux and Perera [J. Chem. Phys. 104, 1493 (1996)]. These results are fairly in agreement with each other. The pressure of this system is also calculated using the Fourier zero components of the DCF. The results are in agreement with the Monte Carlo molecular simulation.

Lennard-Jones sticks: A new model for linear molecules

We consider the anisotropic interaction between two line segments consisting of a homogeneous distribution of Lennard-Jones centers. The potential energy of such a pair cannot be expressed in closed form. However, we show that it may be approximated in a way that renders this intuitively appealing model competitive both for simulations and theory.

Density functional theory of liquid crystals and surface anchoring

This paper applies the density functional theory to confined liquid crystals comprising ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The restricted orientation model proposed by Rickayzen [Mol. Phys. 95, 393 (1998)] is extended to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the Percus-Yevick DCF for hard spheres; the anisotropy is introduced by means of the closest approach parameter. The average number density and orientational order parameter profiles of a HGO fluid confined in between planar walls are obtained using a hard needle-wall potential to represent the particle-wall interactions. For short and long needle lengths, the homeotropic and planar anchoring are observed, respectively. For the bulk isotropic phase the calculated density and order parameter profiles are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 69, 61705 (2004)]. However, for the bulk nematic phase the theory gives the correct density profile between the walls. The correct order parameters are obtained close to the walls whereas for the region in the middle of the walls, the agreement is less satisfactory.

The melting temperature of the most common models of water

The melting temperature of ice I(h) for several commonly used models of water (SPC, SPC/E,TIP3P,TIP4P, TIP4P/Ew, and TIP5P) is obtained from computer simulations at p = 1 bar. Since the melting temperature of ice I(h) for the TIP4P model is now known [E. Sanz, C. Vega, J. L. F. Abascal, and L. G. MacDowell, Phys. Rev. Lett. 92, 255701 (2004)], it is possible to use the Gibbs-Duhem methodology [D. Kofke, J. Chem. Phys. 98, 4149 (1993)] to evaluate the melting temperature of ice I(h) for other potential models of water. We have found that the melting temperatures of ice I(h) for SPC, SPC/E, TIP3P, TIP4P, TIP4P/Ew, and TIP5P models are T = 190 K, 215 K, 146 K, 232 K, 245 K, and 274 K, respectively. The relative stability of ice I(h) with respect to ice II for these models has also been considered. It turns out that for SPC, SPC/E, TIP3P, and TIP5P the stable phase at the normal melting point is ice II (so that ice I(h) is not a thermodynamically stable phase for these models). For TIP4P and TIP4P/Ew, ice I(h) is the stable solid phase at the standard melting point. The location of the negative charge along the H-O-H bisector appears as a critical factor in the determination of the relative stability between the I(h) and II ice forms. The methodology proposed in this paper can be used to investigate the effect upon a coexistence line due to a change in the potential parameters.

Monte Carlo simulations of liquid crystals near rough walls

The effect of surface roughness on the structure of liquid crystalline fluids near solid substrates is studied by Monte Carlo simulations. The liquid crystal is modeled as a fluid of soft ellipsoidal molecules and the substrate is modeled as a hard wall that excludes the centers of mass of the fluid molecules. Surface roughness is introduced by embedding a number of molecules with random positions and orientations within the wall. It is found that the density and order near the wall are reduced as the wall becomes rougher, i.e., the number of embedded molecules is increased). Anchoring coefficients are determined from fluctuations in the reciprocal space order tensor. It is found that the anchoring strength decreases with increasing surface roughness.

Using particle shape to induce tilted and bistable liquid crystal anchoring

We use Monte Carlo simulations of hard Gaussian overlap (HGO) particles symmetrically confined in slab geometry to investigate the role of particle-substrate interactions on liquid crystalline anchoring. Despite the restriction here to purely steric interactions and smooth substrates, a range of behaviors are captured, including tilted anchoring and homeotropic-planar bistability. These macroscopic behaviors are all achieved through appropriate tuning of the microscopics of the HGO-substrate interaction, based upon nonadditive descriptions for the HGO-substrate shape parameter.

Computer simulation of a liquid-crystal anchoring transition

We present a study of the effects of confinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential. Using geometrical arguments to calculate the molecular volume absorbed at the substrates, we show that both planar and homeotropic arrangements can be obtained using this model. Monte Carlo simulations are then used to perform a systematic study of the model's behavior as a function of the system density and the hard-needle-wall interaction parameter. As well as showing the homeotropic to planar anchoring transition, the anchoring phase diagrams computed from these simulations indicate regions of bistability. This bistable behavior is examined further through the explicit simulation of field-induced two-way switching between the two arrangements.

Orientational orders of small anisotropic molecules confined in slit pores

Based on a constant-pressure Monte Carlo molecular simulation, we have studied orientationally ordered transitions of small anisotropic molecules confined in two parallel hard walls. These molecules are modeled by the hard Gaussian overlap model. The molecular elongations of the chosen molecules are so small that the molecules cannot form stable liquid-crystal (LC) phases in the bulk. But in the slit pores, we found, while the distance between two walls of the pores decreases to the molecular scale, an orientationally ordered phase can form. It shows that even hard confining surfaces favor the alignment of the small anisotropic molecules. Thus we conclude that the required molecular elongation for forming LC phases will decrease in confinement. Our results indicate that some non-LC small molecules may form stable LC phases due to the inducement of confining surfaces.

Orientational order in binary mixtures of hard Gaussian overlap molecules

Based on a standard constant-pressure Monte Carlo molecular simulation, we have studied liquid crystal phases of binary mixtures of nonspherical molecules. The components of the mixtures are two types of hard Gaussian overlap (HGO) molecules. The first type of molecule has a small molecularelongation parameter (short HGO molecules) and cannot form stable liquid crystal phase in the bulk by themselves. The second type of molecule has a large elongation parameter (long HGO molecules) and can form a liquid crystal phase easily. In the mixtures, the short HGO molecules can form an orientationally ordered phase because the long HGO molecules form confining surfaces to induce the alignment of the short molecules. We also study the isotropic-nematic phase transition in different mixtures composed of short and long HGO molecules with different elongations and concentrations. The obtained result implies that small anisotropic molecules can show liquid crystal behavior.

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.