Hard Spherocylinders Research Articles

Ornstein–Zernike equation for the convex molecule fluids

Pair distribution functions yield an important information on the structure of fluids. The general form of the Ornstein–Zernike equation which interrelates the total and direct correlation functions of molecular fluids, h(1, 2) and c(1, 2), respectively, is reformulated for systems of convex molecules. An expression is derived which makes it possible to determine the average correlation function as a sole function of the shortest surface–surface distance between hard cores of a pair of studied molecules. For both h and c, the shape effect is separated from the dependence of these functions on distance. As a result, the total correlation function can be determined from an expression, the convolution integral of which comprises the derivative of the cluster integral (related to the third virial coefficient) for three hard convex bodies. Preliminary results for the average correlation function, gav( = hav + 1), in the system of hard prolate spherocylinders with the reduced core length L = 0.4 and packing fraction y = 0.3142 are presented; values of gav compare well with the corresponding simulation data.

Topological defects in nematic droplets of hard spherocylinders

Using computer simulations we investigate the microscopic structure of the singular director field within a nematic droplet. As a theoretical model for nematic liquid crystals we take hard spherocylinders. To induce an overall topological charge, the particles are either confined to a two-dimensional circular cavity with homeotropic boundary or to the surface of a three-dimensional sphere. Both systems exhibit half-integer topological point defects. The isotropic defect core has a radius of the order of one particle length and is surrounded by free-standing density oscillations. The effective interaction between two defects is investigated. All results should be experimentally observable in thin sheets of colloidal liquid crystals.

Density-functional theory of inhomogeneous systems of hard spherocylinders

The smectic-A phase boundaries of a hard-spherocylinder fluid are calculated using a density-functional theory based on one proposed earlier by Somoza and Tarazona [Phys. Rev. A 41, 965 (1990)]. Our calculations do not employ the translation-rotation decoupling approximation used in previous density-functional theories. The calculated phase boundaries agree well with computer simulation results up to aspect ratios L/D approximately 5 and are in better agreement with the simulations than are previous theories. We generalize the model fluid by including long-range interactions with quadrupolar orientational symmetry, which are taken into account by mean-field approximation. For sufficiently large strength, these interactions produce a smectic-C phase, which undergoes either a continuous or weakly first-order transition to the smectic-A phase. The theory and numerical methods discussed here can be applied to the analysis of interfacial phenomena.

Enhanced stability of layered phases in parallel hard spherocylinders due to addition of hard spheres

There is increasing evidence that entropy can induce microphase separation in binary fluid mixtures interacting through hard particle potentials. One such phase consists of alternating two-dimensional liquidlike layers of rods and spheres. We study the transition from a uniform miscible state to this ordered state using computer simulations, and compare results to experiments and theory. We conclude the following: (1) There is stable entropy driven microphase separation in mixtures of parallel rods and spheres. (2) Adding spheres smaller than the rod length decreases the total volume fraction needed for the formation of a layered phase, and therefore small spheres effectively stabilize the layered phase; the opposite is true for large spheres. (3) The degree of this stabilization increases with increasing rod length.

Computer simulation of the interface between two liquid crystalline phases in rod–plate binary mixtures

Metropolis Monte Carlo NVT computer simulations of 50:50 mixtures of L/ D=5 hard spherocylinders ( N HSC=510) and L/ D=0.12 hard cut spheres ( N CS=510) have been performed. At the start of the simulation, the system is taken as a totally demixed state of pure rods and pure plates. For a packing fraction of 44% the system is found to be a fully mixed isotropic state, while at 48% two ordered phases (one rich in rods and one rich in plates) are found to coexist. In this Letter we examine the stable free interface between the two liquid crystalline phases paying special attention to the orientational order through the interface.

Estimation of the Chemical Potential of the System of Hard Molecules

For the estimation of the chemical potential of the system of hard rod-like molecules, insertion probability of a molecule into the system is obtained through Monte Carlo simulation. The growth probability of a test molecule from one size to the other size is accumulated to give rough estimation of insertion probability of a molecule into the system of hard spherocylinders. The chemical potential is then obtained as a logarithm of the insertion probability.

Simulation study of the phase behavior of a primitive model for thermotropic liquid crystals: Rodlike molecules with terminal dipoles and flexible tails

A primitive model for small mesogenic molecules is proposed, consisting of three elements: (i) a rigid rodlike core, modeled as a hard spherocylinder of length/diameter ratio L/D=5; (ii) a flexible end group, consisting of five segments of length D, which is “ideal” in the sense that it has no volume; (iii) a terminal dipole, located in the end cap opposite the flexible tail. This model is studied using Monte Carlo computer simulation, and the dipolar interactions are evaluated using the reaction field method. The hard spherocylinder model displays four phases: isotropic, nematic, smectic-A and crystal. Previously, it was found that the addition of the terminal dipole to hard spherocylinders without tails greatly enhances the range of stability of the nematic phase, at the expense of the smectic-A phase [McGrother et al., J. Phys.: Condens. Matter 8, 9649 (1996)]. Conversely, adding the flexible tail to hard spherocylinders without dipoles is found to suppress the nematic phase, whereas the smectic-A and crystal phase are little affected. Combining the effects of the terminal dipole and the flexible tail, all four phases survive. Because of the dipoles, the particles prefer to adopt a staggered antiparallel arrangement. In the smectic-A and crystal phases, this gives rise to interdigitation of the smectic layers. In the crystal phase a tendency towards columnar ordering is observed. The results are compared with experimental observations.

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.

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 Simulation of a Binary Mixture of Hard Rods and Hard Spheres

One simple model molecule to examine phase behavior of rod-like molecules is the hard spherocylinder. 1) It is a simple cylinder of diameter d and length l with caps of hemispheres of the same diameter on both ends of the cylinder. Computer simulations have revealed that the system of monodisperse parallel hard spherocylinders shows the nematic and the smectic-A phase as liquid crystalline phases. 2), 3) Computer simulation and mean field theory have also studied a binary mixture of the parallel hard spherocylinders and hard spheres. 4) They have shown that the smectic-A phase of the binary mixture appears as a type of microphase separation. The spheres prefer to stay in the interstitial regions between smectic layers of the spherocylinders. In the present paper, we show an estimation of the Gibbs free energy obtained from isobaric Monte Carlo (MC) simulation for the binary mixture.

Phase diagrams of binary mixtures of hard rods in an external orientational field

We study a binary mixture of hard spherocylinders with the same diameter (D) and different length (L2>L1) in the absence and presence of a static external electric (magnetic) field on the basis of the Onsager theory. In the zero field, we find that the usual isotropic–nematic phase transition takes place only between the length ratio (L2/L1) of 1–2.9, the reentrant phenomenon occurs for L2/L12.7, and the nematic–nematic phase transition starts to be stable for L2/L1>2.9. In the external field, the isotropic–nematic transition is replaced by a weakly ordered nematic–nematic transition. The increasing external field strength shifts the transition towards lower densities and narrows the density gap terminating the first order transition at a critical point. The critical field strength is found to increase rapidly with increasing length ratio.

Theory and computer simulation of bent-core molecules

Fluids of hard bent-core molecules have been studied using theory and computer simulation. The molecules are composed of two hard spherocylinders, with length-to-breadth ratio L/D, joined by their ends at an angle 180°−γ. For L/D=2 and γ=0,10,20°, the simulations show isotropic, nematic, smectic, and solid phases. For L/D=2 and γ=30°, only isotropic, nematic, and solid phases are in evidence, which suggests that there is a nematic-smectic-solid triple point at an angle in the range 20°<γ<30°. In all of the orientationally ordered fluid phases the order is purely uniaxial. For γ=10° and 20°, at the studied densities, the solid is also uniaxially ordered, whilst for γ=30° the solid layers are biaxially ordered. For L/D=2 and γ=60° and 90° we find no spontaneous orientational ordering. This is shown to be due to the interlocking of dimer pairs which precludes alignment. We find similar results for L/D=9.5 and γ=72°, where an isotropic-biaxial nematic transition is predicted by Onsager theory. Simulations in the biaxial nematic phase show it to be at least mechanically stable with respect to the isotropic phase, however. We have compared the quasi-exact simulation results in the isotropic phase with the predicted equations of state from three theories: the virial expansion containing the second and third virial coefficients; the Parsons–Lee equation of state; an application of Wertheim’s theory of associating fluids in the limit of infinite attractive association energy. For all of the molecule elongations and geometries we have simulated, the Wertheim theory proved to be the most accurate. Interestingly, the isotropic equation of state is virtually independent of the dimer bond angle—a feature that is also reflected in the lack of variation with angle of the calculated second and third virial coefficients.

Deviation from Corresponding States for a Fluid of Square Well Spherocylinders

The nonconformal behavior of a fluid of hard spherocylinders with a spherocylindrical square well attraction is examined using a simple perturbation theory in which the thermodynamics of the anisot...

The isotropic–nematic transition and the phase separation of the tobacco mosaic virus particles with polysaccharide

The isotropic–nematic transition of the tobacco mosaic virus (TMV) particles by polysaccharide is related to a high inhibitory activity against TMV infection. We study the process of the isotropic–nematic transition of the TMV particles as a function of the polysaccharide concentration by Monte Carlo simulations in three-dimensional continuous space. In these simulations, we simplify the TMV particles and the polysaccharide molecules as the hard spherocylinders and semirigid chains, respectively, and we assume the simple interactions for the TMV particles and the polysaccharide chains. In our simulation, with increasing concentration of the polysaccharide the homogeneously dispersed TMV particles begin to segregate without orientational ordering, that is isotropic phase separation, and then transform to the nematic state of the TMV particles. The isotropic–nematic transition is caused by simple interactions such as the excluded volume effect, and the complicated biological interaction is not necessary.

Liquid-vapor coexistence in fluids of dipolar hard dumbbells and spherocylinders

Fluids of dipolar hard spheres are thought to have rather unusual phase behavior in that liquid-vapor equilibrium has not been observed in computer simulations. Recently, McGrother and Jackson [Phys. Rev. Lett. 76, 4183 (1996)] have reported Gibbs ensemble Monte Carlo (GEMC) results for dipolar hard spherocylinders. At the reduced temperature ${T}^{*}=0.12$ they report liquid-vapor coexistence for aspect ratios $L/D\ensuremath{\gtrsim}0.19,$ but no coexistence was found for smaller values. In the present paper we investigate the phase behavior of dipolar hard dumbbells and dipolar hard spherocylinders using both GEMC and grand canonical Monte Carlo methods. For both models at the same reduced temperature we find liquid-vapor coexistence for aspect ratios as low as 0.1. For aspect ratios $\ensuremath{\lesssim}0.1,$ the strong dipolar interactions create severe sampling problems and reliable results cannot be obtained. This is particularly true for the GEMC method and possibly accounts for the disagreement we find with the earlier simulations.

Anisotropic self-diffusion in colloidal nematic phases

By computer simulation the anisotropic long-time translational self-diffusion coefficients are calculated in the nematic phase of colloidal hard spherocylinders exhibiting Brownian dynamics in a solvent. In particular, the two diffusion coefficients DL i and DL ' , parallel and perpendicular to the nematic director, are obtained for aspect ratios between 4.8 and 16 and for arbitrary densities. Long-time diffusion along the nematic director is nonmonotonic in density: Upon increasing the density, it first increases due to stronger alignment and then decreases due to packing constraints. It is shown that the ratio DL i /DL ' and the orientation flip rate essentially scale with the nematic order parameter. While the ratio DL i /DL ' increases with density in the nematic phase, it decreases dramatically with increasing density in the smectic-A phase. The results are compared to recent experiments. @S1063-651X~99!03602-8#

Phase diagram of tobacco mosaic virus solutions

The phase behavior of an aqueous suspension of rodlike tobacco mosaic viruses is investigated theoretically as a function of the virus density and the concentration of added salt. The total free energy involves ``volume terms'' from the microscopic counter- and co-ions and an effective pair interaction between the colloidal rods described by a Yukawa-segment model according to linear screening theory. Within a thermodynamic perturbation approach, the short-range repulsion between the rods is mapped onto a reference system of effective hard spherocylinders. The free energy of the spherocylinder system is gained from combining a cell model with scaled particle theory, which yields a reasonable phase diagram. The remaining long-range interaction is treated within a mean-field approximation. As a result we find stable fluid, nematic, and smectic phases as well as $\mathrm{AAA}$- and $\mathrm{ABC}$-stacked crystals. For increasing salt concentration at fixed rod concentration, there is a nematic reentrant transition. We finally discuss our results in view of experimental data.

Hard-sphere-chain equations of state for lyotropic polymer liquid crystals

Using Parsons-type scaling, the Onsager theory for the isotropic–nematic (I–N) transition of rigid-rod lyotropic polymer liquid crystals is combined with the equation of state for hard-sphere-chain fluids of Chapman et al. and that of Hu et al. The equation of Hu et al. gives the I–N transition pressure and density in good agreement with computer simulation by Wilson and Allen for a semi-flexible hard-sphere chain consisting of seven segments. For real semi-flexible polymers, we follow the Khokhlov–Semenov theory of persistent chains that introduces chain flexibility into the Onsager theory. Using a consistent procedure to regress the equation-of-state parameters, the equations of Chapman et al. and Hu et al. are also compared with the theory of DuPré and Yang that uses the equation of Lee for hard spherocylinders. These models are compared with experiment for two binary polymer solutions containing poly(hexyl isocyanate) and another solution containing polysaccharide schizophyllan. The concentration of polymer at the I–N transition is predicted as a function of the molecular weight of polymer. All models perform similarly and show semi-quantitative agreement with experiment.

The third cross virial coefficient of hard convex bodies

Third cross virial coefficients of different combinations of hard prolate spherocylinders, hard oblate spherocylinders and hard spheres were calculated employing a simple Monte Carlo method. Obtained results were compared with a semiempirical relation proposed by one of the present authors. Two semiempirical relations devised recently for pure fluids were extended to yield the cross third virial coefficients. Satisfactory agreement was found in the case of moderately non-spherical bodies. For higher non-sphericities, theoretical values differ from Monte Carlo values up to 7%. Considerable regularities were found in series of one combination with an increase of the parameters L and/or D.

The third cross virial coefficient of hard convex bodies

Third cross virial coefficients of different combinations of hard prolate spherocylinders, hard oblate spherocylinders and hard spheres were calculated employing a simple Monte Carlo method. Obtained results were compared with a semiempirical relation proposed by one of the present authors. Two semiempirical relations devised recently for pure fluids were extended to yield the cross third virial coefficients. Satisfactory agreement was found in the case of moderately non-spherical bodies. For higher non-sphericities, theoretical values differ from Monte Carlo values up to 7%. Considerable regularities were found in series of one combination with an increase of the parameters L and/or D.