Equation of State for Parallel Rigid Spherocylinders

The pair distribution function of monodisperse rigid spherocylinders is calculated by Shinomoto’s method, which was originally proposed for hard spheres. The equation of state is derived by two different routes: Shinomoto’s original route, in which a hard wall is introduced to estimate the pressure exerted on it, and the virial route. The pressure from Shinomoto’s original route is valid only when the length-to-width ratio is less than or equal to 0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation of state is shown to agree very well with the results of numerical simulations of spherocylinders with length-to-width ratio greater than or equal to 2.     

An equation of state for hard convex body chains

The thermodynamic perturbation theory of hard sphere chains is generalized to derive an equation of state for hard convex body chains. The hard convex body chain equation of state contains two parameters that are related directly and rigorously to the geometry of the hard convex body. The compressibility factors and second virial coefficients of chains composed of prolate spherocylinders, oblate spherocylinders and doublecones are calculated and compared with hard sphere chain calculations. The comparison indicates that the nature of the hard convex body has a profound influence on the properties of the chain.     

Depletion effects in smectic phases of hard-rod-hard-sphere mixtures

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the τ parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for τ, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the τ parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts τ ∼ d ³. Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for spherocylinders and spheres, the τ parameter should be of order unity as d tends to infinity.     

Depletion Interactions in a Cylindric Pipeline with a Small Shape Change

Stressed by external forces, it is possible for a cylindric pipeline to change into an elliptic pipeline. To expose the effect of small shape change of the pipeline on the depletion interactions, both the depletion potentials and depletion forces in the hard sphere systems confined by a cylindric pipeline or by an elliptic pipeline are studied by Monte Carlo simulations. The numerical results show that the depletion interactions are strongly affected by the small change of the shape of the pipeline in a way. Furthermore, it is also found that the depletion interactions will be strengthened if the short axis of the elliptic pipeline is decreased.     

Entropy-stabilized smectic C phase in a system of zigzag-shaped molecules

We report Monte Carlo simulations of a system of rigid zigzag-shaped molecules that demonstrate that simple excluded-volume interactions are sufficient to produce a fluid tilted lamellar [smectic C (SmC)] liquid crystal phase. The molecules are composed of three rigidly linked hard spherocylinders arranged in a zigzag fashion. By varying the zigzag angle we have mapped out the whole phase diagram as a function of pressure and zigzag angle Psi. For Psi between 35 degrees and 80 degrees our model simulation exhibits the SmC phase. This is the first conclusive evidence where steric interactions arising out of molecular shape alone induce the occurrence of the SmC phase for a wide range of zigzag angles. For smaller Psi, a transition from tilted crystal to crystal is observed.     

Systems of oblate molecules. Monte Carlo study

Monte Carlo (MC) simulations were performed for systems of hard oblate spherocylinders with breadth-to-height ratios φ = 0.5–3.5 and packing fractions y = 0.25–0.45 and for Kihara oblate molecule systems of φ = 1 at reduced temperatures T* = 0.75 and 1.0 and y = 0.05–0.45. The compression factors and the dependence of the average correlation functions on the shortest surface-to-surface distance were determined for the case of hard oblate spherocylinders and the compression factors, residual internal energies and average correlation functions for the case of the generalized Kihara molecule systems. In addition, values of the third virial coefficient of the hard oblate spherocylinders were evaluated in the range of φ = 1–3. Results of the MC simulations for the hard oblate spherocylinders compare well with the available data in the literature and theoretical values; thermodynamic functions of the Kihara molecule systems were determined from the second-order perturbation theory. They agree well with our MC values at lower densities and higher reduced temperatures.     

带电胶体系统中的排空作用

用Monte Carlo模拟研究弱带电胶体系统的性质.在四维超球面欧氏空间中严格表示库仑作用的基础上，通过接受率法计算带电胶球间的排空势和排空力.研究了受限于两块平行带电平板之间、淹没于带电小胶球之中的一个或两个带电大胶球系统的排空作用，并通过与不带电的硬球系统相应结果的分析、对比，发现静电势能增强带电胶球之间的排空作用. 关键词： 超球面法 接受率方法 排空作用 Monte Carlo模拟     

Computer simulation study of a flexible-rigid-flexible model for liquid crystals

Small molecules that form liquid crystals typically consist of a rigid core with flexible tails on one end or on both ends. To date, most computer simulation studies have used completely rigid models such as hard spherocylinders: cylinders, characterized by their length/diameter ratio L/D, with hemispherical end caps. We have studied a model consisting of spherocylinders with L/D = 4, with a flexible tail attached to each end. The tails are ‘ideal’ in the sense that they have no volume. Using Monte Carlo simulations the phase behaviour of this model was studied and, for comparison, the behaviour of hard spherocylinders with L/D = 4 without tails was studied as well. The addition of the tails is found to stabilize the smectic-A phase at a lower pressure, and the nematic phase disappears. In the smectic-A and crystal phases, the smectic layers are further apart when tails are added. The structure of the layers and the smectic-A–crystal transition pressure change only a little. For both models close to melting the crystal consists of ordered layers, but there is almost no correlation between particle positions in neighbouring layers. In fact, the layer coupling is so weak that in a long simulation the layers are found to glide over each other. As the pressure is increased the crystal gradually becomes more ordered and the crystalline layers ultimately ‘lock’ into place.     

Direct measurement of entropic forces induced by rigid rods

We present the first direct depletion potential measurements for a single colloidal sphere close to a wall in a suspension of rigid colloidal rods. Since all particle interactions are as good as hard-core-like, the depletion potentials are of entirely entropic origin. We developed a density functional theory approach that accurately accounts for this experimental situation. The depletion potentials calculated for different rod number densities are in very good quantitative agreement with the experimental results.     

Statistical theory of the elastic constants of nematic liquid crystals

A statistical mechanical theory of the Frank elastic constants is formulated. The free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients. The Frank constants are expressed in terms of the direct correlation function c(1, 2) and the orientational single particle distribution function. For the example of Onsager spherocylinders three constants K ₁, K ₂ and K ₃ are calculated. The results of these calculations are similar to those given by Priest and by Straley.     

A unified treatment of the equation of state of hard linear bodies

An unified treatment of the equation of state of convex (spherocylinders) and non-convex (dumbells) hard bodies is presented. Comparison of our results with simulation shows very good agreement for diatomics and excellent for triatomics.     

Coupling effects of depletion interactions in a three-sphere colloidal system

In a three-sphere system, the middle sphere is acted upon by two opposite depletion forces from the other two spheres. It is found that, in this system, the two depletion forces are coupled with each other and result in a strengthened depletion force. So the difference of the depletion forces of the three-sphere system and its corresponding two two-sphere systems is introduced to describe the coupling effect of the depletion interactions. The numerical results obtained by Monte-Carlo simulations show that this coupling effect is affected by both the concentration of small spheres and the geometrical confinement. Meanwhile, it is also found that the mechanisms of the coupling effect and the effect on the depletion force from the geometry factor are the same.     

Depletion interactions in cylindric pipeline

In a colloidal system confined by a small cylindric pipeline, the depletion interaction between two large spheres is different to the system confined by two plates, and the influence on depletion interaction from the pipeline is related to both the size and shape of it. In this paper, the depletion interactions in the systems confined by pipelines of different sizes or different shapes are studied by Monte Carlo simulations. The numerical results show that the influence on depletion force from the cylindric pipeline is stronger than that from two parallel plates, and the depletion force will be strengthened when the diameter of the cylinder is decreased. In addition, we also find that the depletion interaction is rather affected if the shape change of the pipeline is slightly changed, and the influence on depletion force from the shape change is stronger than that from the size change.     

Properties of a hard spherocylinder fluid from the blip function theory

Thermodynamic and structural properties of a hard spherocylinder fluid are calculated by means of the blip function theory byAndersen et al. and are compared with Monte Carlo simulation data. It is found that for spherocylinders of length-to-breadth ratio up to 3/2 the theory yields reasonably accurate results while for greater qualitative features of results may be correct only.     

Smectic phases in hard particle mixtures: Koda's theory

Mixtures of parallel linear particles and spheres tend to demix upon compression. The linear species usually concentrates in regular layers, thus forming a smectic phase. With increasing concentration of spheres this ‘smectic demixing’ transition occurs at ever lower packing densities. For the specific case of hard spherocylinders and spheres Koda et al. [T. Koda, M. Numajiri, S. Ikeda, J. Phys. Jap., 65, 3551 (1996)] have explained the layering effect in terms of a second virial approximation to the free energy. We extend this approach from spherocylinders to other linear particles, namely fused spheres, ellipsoids and sphero-ellipsoids.     

Effects of molecular geometry on liquid crystalline phase behaviour: isotropic-nematic transition

The effects of range and geometry of a simple attractive square-well on the phase diagram of hard ellipsoids and hard spherocylinders is systematically studied using a simple van der Waals type theory. The orientational single particle distribution function is approximated using the Onsager trial function. The quantitative errors introduced by this are thought to be considerably smaller than the use of the van der Waals approximation, which has been shown to give qualitatively correct phase diagrams for similar models. The phase diagrams obtained for hard ellipsoids and hard spherocylinders of aspect ratios ranging between 3 and 10 with a variety of square-well attractions are found to fall into three general types. The first type shows liquid-vapour coexistence and an isotropic-nematic transition, which meet at a liquid-vapour-nematic triple point. The second type shows a marked widening of the isotropic-nematic biphasic region which pre-empts the liquid-vapour coexistence. The final phase diagram shows a strong destabilization of the nematic phase with respect to the isotropic, which results in a shift of the phase transition to higher densities and pressures as the temperature is lowered.     

Monte Carlo study of dipolar and quadrupolar hard prolate spherocylinders

Monte Carlo simulations of hard prolate spherocylinders (HPSs) with embedded dipole or quadrupole moment are reported for two elongations (L?=?0.5 and 1) and several values of the packing fraction. The MC values of the residual internal and Helmholtz energy and compressibility factor were determined. Our work represents the first simulation study of dipolar HPSs focused on the determination of the thermodynamic properties. In the case of quadrupolar HPSs, our results enlarge the range of state conditions for which the simulation data are available. The obtained MC data were used for a test of the perturbation theory of polar non-spherical molecule fluids. In order to evaluate the perturbation contributions containing the two-particle integrals, the values of the shape integrals (evaluated recently for dipolar and quadrupolar hard prolate spherocylinders) were employed and we were allowed to avoid the use of the similarity between Kihara and Gaussian overlap models. Fair agreement between the simulation data and the theoretical predictions was reached.     

胶体中排空作用的耦合效应

通过Monte Carlo模拟和接受率方法研究了限制在圆柱形管道中大胶球之间以及大胶球与管壁之间排空作用的耦合效应.研究发现,当两个大胶球靠近时,大胶球之间的排空作用因与大胶球与管道壁之间的排空作用耦合而得到加强,同样当大胶球与管道壁靠近时,大胶球与管道壁之间的排空作用也因与另一大胶球之间排空作用的耦合而得到了加强.此外,研究还发现,随着圆柱形管道直径的减小,胶球之间、胶球与管道壁之间的排空作用的耦合效应是增强的. 关键词： 排空作用的耦合效应 接受率方法 Monte Carlo模拟