Equation of state for systems of hard non-spherical molecules

The equation of state for systems of hard prolate spherocylinders has been obtained using a Monte Carlo simulation method. The result in the fluid region are compared with the predictions of scaled particle theory, and are found to agree quite well. The equation of state is significantly different from that for hard sphere molecules, and it is concluded that the effects of non-spherical shape must be explicitly dealt with.     

Structure formation and fractionation in systems of polydisperse attractive rods

Fractionation effects and the formation of structured domains are investigated in polydisperse systems of attractive spherocylinders with the help of Monte Carlo simulations. For sufficiently high attractive interaction strength and pressure, the large rods in the system aggregate and form a highly ordered hexatic monolayer that coexists with an isotropic fluid of smaller rods. Fractionation diminishes with decreasing interaction strength but is still observed for hard rod systems, in which the large rods form a nematic droplet rather than a monolayer. Results for polydisperse systems are accompanied by phase diagrams for monodisperse systems of attractive spherocylinders. Here, the phase behavior is shown as a function of rod length and pressure.     

The equation of state of isotropic fluids of hard convex bodies from a high-level virial expansion

We have calculated virial coefficients up to seventh order for the isotropic phases of a variety of fluids composed of hard aspherical particles. The models studied were hard spheroids, hard spherocylinders, and truncated hard spheres, and results are obtained for a variety of length-to-width ratios. We compare the predicted virial equations of state with those determined by simulation. We also use our data to calculate the coefficients of the y expansion [B. Barboy and W. M. Gelbart, J. Chem. Phys. 71, 3053 (1979)] and to study its convergence properties. Finally, we use our data to estimate the radius of convergence of the virial series for these aspherical particles. For fairly spherical particles, we estimate the radius of convergence to be similar to that of the density of closest packing. For more anisotropic particles, however, the radius of convergence decreases with increased anisotropy and is considerably less than the close-packed density.     

Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)], and we performed a finite size scaling analysis to estimate the location of the critical point. The results are compared with predictions of the free volume theory developed by Lekkerkerker and Stroobants [Nuovo Cimento D 16, 949 (1994)]. We also give estimates for the interfacial tension between the coexisting isotropic phases and analyze its power-law behavior on the approach of the critical point.     

Phase behavior of polarizable spherocylinders in external fields

Applied electric fields are known to induce significant changes in the properties of systems of polarizable molecules or particles. For rod-shaped molecules, the field-induced behavior can be rather surprising, as in the case of the negative electric birefringence of concentrated solutions of rodlike polyelectrolytes. We have investigated the interplay of shape anisotropy and field-induced anisotropy in molecular dynamics simulations of systems of polarizable soft spherocylinders in an electric field, in the limit of infinitely anisotropic polarizability, taking full account of mutual induction effects. We find a novel crystalline structure (K(2)) in the high-field limit, whose formation is driven by interactions between induced dipoles. For high pressures, the phase diagram exhibits a polar nematic phase between the hexagonal close-packed crystal phase and the K(2) phase. We also compare this system with an analogous system of spherocylinders with permanent electric dipoles and find that qualitatively similar behavior is obtained in the limit of strong coupling of the permanent dipoles to the external field.     

The Wolf method applied to the liquid-vapor interface of water

The Wolf method for the calculation of electrostatic interactions is applied in a liquid phase and at the liquid-vapor interface of water and its results are compared with those from the Ewald sums method. Molecular dynamics simulations are performed to calculate the radial distribution functions at room temperature. The interface simulations are used to obtain the coexisting densities and surface tension along the coexistence curve. The water model is a flexible version of the extended simple point charge model. The Wolf method gives good structural results, fair coexistence densities, and poor surface tensions as compared with those obtained using the Ewald sums method.     

Liquid-crystal phase diagrams of binary mixtures of hard spherocylinders

We have built the liquid crystal phase diagram of several binary mixtures of freely rotating hard spherocylinders employing a second-order virial density functional theory with Parsons scaling, suitably generalized to deal with mixtures and smectic phases. The components have the same diameter and aspect ratio of moderate value, typical of many mesogens. Attention has been paid to smectic-smectic demixing and the types of arrangement that rods can adopt in layered phases. Results are shown to depend on the aspect ratio of the individual components and on the ratio of their lengths. Smectic phases are seen not to easily mix together at sufficiently high pressures. Layered phases where the longer rods are the majority component have a smectic-A structure. In the opposite case, a smectic-A(2) phase is obtained where the shorter particles populate the layers and the longer ones prefer to stay parallel to the latter in the interlayer region.     

Hard spherocylinder fluids: a monte carlo study

Fluids of hard prolate spherocylinders of length to breadth ratios 2:1 and 3:1 have been studied using the Monte Carlo method. The equation of state has been calculated at various densities. The effects of density and shape on the structure of the fluid have been observed by using the expansion in spherical harmonics of the pair distribution function.     

Phase behavior of hard colloidal platelets using free energy calculations

We investigate the phase behavior of a model for colloidal hard platelets and rigid discotic molecules: oblate hard spherocylinders (OHSC). We perform free energy calculations using Monte Carlo simulations to map out the phase diagram as a function of the aspect ratio L∕D of the particles. The phase diagram displays a stable isotropic phase, a nematic liquid crystal phase for L∕D≤0.12, a columnar phase for L∕D?0.3, a tilted crystal phase for L?0.45, and an aligned crystal phase for L∕D?0.45. We compare the results to the known phase diagram of hard cut spheres. Thin cut spheres are almost cylinder-shaped, while the interactions between real discotic mesogens and colloidal platelets are more consistent with the toroidal rims of the OHSC. Since the shapes of the OHSC and the cut spheres are otherwise similar, the phase diagrams of the two types of particles are quite akin. However, the tilted crystal phase for OHSC, which is of a crystal type that is frequently found in experiments on disklike molecules, has not been found for hard cut spheres. Furthermore, although we have found a cubatic phase, it was shown to be definitely unstable, whereas the stability of the cubatic phase of cut spheres is still disputed. Finally, we also show that the phase boundaries differ significantly from those for cut spheres. These are remarkable consequences of a subtle change in particle shape, which show that for a detailed comparison with the phase behavior of experimental particles, the OHSC should be used as a model particle.     

Revisiting the Frenkel-Ladd method to compute the free energy of solids: the Einstein molecule approach

In this paper a new method to evaluate the free energy of solids is proposed. The method can be regarded as a variant of the method proposed by Frenkel and Ladd [J. Chem. Phys. 81, 3188 (1984)]. The main equations of the method can be derived in a simple way. The method can be easily implemented within a Monte Carlo program. We have applied the method to determine the free energy of hard spheres in the solid phase for several system sizes. The obtained free energies agree within the numerical uncertainty with those obtained by Polson et al. [J. Chem. Phys. 112, 5339 (2000)]. The fluid-solid equilibria has been determined for several system sizes and compared to the values published previously by Wilding and Bruce [Phys. Rev. Lett. 85, 5138 (2000)] using the phase switch methodology. It is shown that both the free energies and the coexistence pressures present a strong size dependence and that the results obtained from free energy calculations agree with those obtained using the phase switch method, which constitutes a cross-check of both methodologies. From the results of this work we estimate the coexistence pressure of the fluid-solid transition of hard spheres in the thermodynamic limit to be p*=11.54(4), which is slightly lower than the classical value of Hoover and Ree (p*=11.70) [J. Chem. Phys. 49, 3609 (1968)]. Taking into account the strong size dependence of the free energy of the solid phase, we propose to introduce finite size corrections, which allow us to estimate approximately the free energy of the solid phase in the thermodynamic limit from the known value of the free energy of the solid phase with N molecules. We have also determined the free energy of a Lennard-Jones solid by using both the methodology of this work and the finite size correction. It is shown how a relatively good estimate of the free energy of the system in the thermodynamic limit is obtained even from the free energy of a relatively small system.     

Dichroism in dye-doped colloidal liquid crystals

Nematic liquid crystals were obtained in sterically stabilized suspensions of rodlike particles of sepiolite clay, with an average length up to 900 nm and aspect ratio up to 40. In agreement with computer simulations for hard spherocylinders, the isotropic-nematic transition shifted to lower volume fractions with increasing aspect ratio. However, the coexistence gap was broadened noticeably due to particle polydispersity. The sepiolite crystal structure includes channels filled with zeolitic water, which can be replaced by indigo dye molecules. The indigo molecules are constrained inside the zeolitic channels to be aligned along the long axes of the rods. As a result, the colloidal nematic phase showed a marked dichroism, with an order parameter up to 0.5 for magnetically aligned samples, similar to typical values for dye-doped thermotropic liquid crystals.     

Shape factors in equations of state. Part II. Repulsion phenomena in multicomponent chain fluids

An equation of state for the multicomponent fluid phase of nonattracting rigid particles of arbitrary shape is presented. The equation is a generalization of a previously presented equation of state for pure fluids of rigid particles; the approach describes the volumetric properties of a pure fluid in terms of a shape factor, zeta, which can be back calculated by scaling the volumetric properties of pure fluids to that of a hard sphere. The performance of the proposed equation is tested against mixtures of chain fluids immersed in a "monomeric" solvent of hard spheres of equal and different sizes. Extensive new Monte Carlo simulation data are presented for 19 binary mixtures of hard homonuclear tangent freely-jointed hard sphere chains (pearl-necklace) of various lengths (three to five segments), with spheres of several size ratios and at various compositions. The performance of the proposed equation is compared to the hard-sphere SAFT approach and found to be of comparable accuracy. The equation proposed is further tested for mixtures of spheres with spherocylinders. In all cases, the equation proved to be accurate and simple to use.     

Isotropic-nematic phase transition of nonaqueous suspensions of natural clay rods

A novel model system for studying the behavior of hard colloidal rods is presented, consisting of sterically stabilized particles of natural sepiolite clay. Electron microscopy and scattering results confirmed that the organophilic clay particles were individual, rigid rods when dispersed in organic solvents. With a length-to-diameter ratio of approximately 27, the particles showed nematic ordering for volume fractions phi > 0.06. Polarizing microscopy revealed that the phase separation process involved nucleation, growth, and coalescence of nematic domains. The phase volumes and particle concentrations in the coexisting phases were determined. The dependence of these quantities on the total concentration of the suspension agrees well with Onsager's [Ann. N. Y. Acad. Sci. 51, 627 (1949)] isotropic-nematic phase transition theory extended to bidisperse and polydisperse rod systems, and with previous experimental results for rigid rodlike particles. Particle size distributions were obtained by analyzing transmission electron microscopy images. A significant fractionation with respect to rod length (but not diameter) was observed in the coexisting isotropic and nematic phases. The relative polydispersity of both daughter phases was distinctly smaller than that of the parent suspension. The phase behavior of these daughter fractions agrees well with the predictions for hard spherocylinders of corresponding aspect ratios. An isotropic-nematic-nematic phase equilibrium was seen to develop in phase separated samples after 1 month standing and is ascribed to the effect of polydispersity and possibly gravity. The second nematic phase appearing is dominated by very long rods.     

Phase behavior of colloidal hard tetragonal parallelepipeds (cuboids): a Monte Carlo simulation study

The impact of particle geometry on the phase behavior of hard colloidal tetragonal parallelepipeds (TPs) was studied by using Monte Carlo simulations in continuum space. TPs or "cuboids" of aspect ratios varying from 0.25 to 8 were simulated by approximating their shapes with multisite objects, i.e., via rigid clusters of hard spheres. Using equation of state curves, order parameters, radial distribution functions, particle distribution functions along three directions, and visual analysis of configurations, an approximate phase diagram for the TPs was mapped out as a function of aspect ratio (r) and volume fraction. For r > 3 and intermediate concentrations, the behavior of the TPs was similar to that of spherocylinders, exhibiting similar liquid crystalline mesophases (e.g., nematic and smectic phases). For r = 1, a cubatic phase occurs with orientational order along the three axes but with little translational order. For 1 < r < 4, the TPs exhibit a cubatic-like mesophase with a high degree of order along three axes where the major axes of the particles are not all aligned in the same direction. For r < 1, the TPs exhibit a smectic-like phase where the particles have rotational freedom in each layer but form stacks with tetratic order. The equation of state for perfect hard cubes (r = 1) was also simulated and found to be consistent with that of the rounded-edge r = 1 TPs, except for its lack of discontinuity at the cubatic-solid transition.     

Estimating the sizes of small single crystals satisfying the Wolf theorem

Geometric estimates of the characteristic sizes of simple single crystals with tetragonal, cubic, and octahedral shapes of the surface are obtained. The Wolf theorem with independent contributions from each face to the surface tension can be applied to these if the edge size is at least ~53 lattice constants. Energy estimates of the individuality of free energy contributions from each face are consistent with this estimate. The resulting minimum edge sizes also agree with an independent estimate obtained earlier using the contributions from fluctuations in the near-surface region of the phase.

     

Centrifugation equilibrium for spheres and spherocylinders

The centrifugation equilibrium problem is formulated and solved using a new procedure in which the specified variables are the temperature, system volume, particle dimensions and concentrations, angular speed, cell length, and cell distance from the rotation axis. As a result, we obtain the concentration profiles for all types of particles present in the system, which are considered to be immersed in a fluid. The particles are modeled as hard nonattractive spherocylinders using an equation of state, but the procedure is not restricted to any geometrical shape, and can be used with any equation of state available. The fluid is treated as a continuous medium, responsible for centrifugal buoyancy. We make calculations for colloidal suspensions of silica, often used for separations in biotechnology. Results are in good agreement with experiments and show excellent agreement in comparison with Monte Carlo simulations. Our calculations also predict focusing and shifting phenomena that have been experimentally observed in separations of fine particles.     

Application of the Wolf damped Coulomb method to simulations of SiC

A multibody interatomic potential is developed for bulk SiC using a modification of the Wolf et al. summation technique [D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)] for the electrostatic interaction. The technique is modified to account for the short-range nonpoint charge effect. The nonelectrostatic interaction is modeled by a simple Morse-stretch term. This potential is then applied to beta-SiC to calculate various bulk properties using molecular dynamics simulations. The simulated x-ray diffraction pattern, radial distribution functions, lattice constant, elastic constants, and defect energy agree well with experimental data.     

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.     

Constant pressure molecular dynamics simulations of the crystal–smectic transition in systems of soft parallel spherocylinders as a model for liquid crystals

Abstract

We present the results of constant pressure molecular dynamics simulation under hydrostatic pressure for soft parallel spherocylinders. A clear first order transition from crystal to smectic phase is observed. The anisotropy of the molecular volume plays an important role in this transition. We study the anisotropy of the diffusion process in the smectic phase by the mean-square displacement in each direction. Also the structures before and after the transition are analysed by means of the pair distribution functions.     

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.