Parallel Hard Spherocylinders Research Articles

Phase behaviour of polarizable colloidal hard rods in an external electric field: a simulation study.

We present a double-charge model for the interaction between parallel polarizable hard spherocylinders subject to an external electric field. Using Monte Carlo simulations and free-energy calculations, we predict the phase behaviour for this model as a function of the density and electric field strength, at a fixed length-to-diameter ratio L/D = 5. The resulting phase diagram contains, in addition to the well-known nematic, smectic A, ABC crystal, and columnar phases, a smectic C phase, and a low temperature crystal X phase. We also find a string fluid at low densities and field strengths, resembling results found for dipolar spheres.

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.

Non-Gaussian dynamics in smectic liquid crystals of parallel hard rods

Using computer simulations, we studied the diffusion and structural relaxation in equilibrium smectic liquid-crystal bulk phases of parallel hard spherocylinders. These systems exhibit a non-Gaussian layer-to-layer diffusion due to the presence of periodic barriers and transient cages and show remarkable similarities with the behavior of out-of-equilibrium supercooled liquids. We detect a very slow interlayer relaxation dynamics over the whole density range of the stable smectic phase which spans a time interval of four time decades. The intrinsic nature of the layered structure yields a hopping-type diffusion which becomes more heterogeneous for higher packing fractions. In contrast, the in-layer dynamics is typical of a dense fluid with a relatively fast decay. Our results on the dynamic behavior agree well with that observed in systems of freely rotating hard rods but differ quantitatively as the height of the periodic barriers reduces to zero at the nematic-smectic transition for aligned rods, while it remains finite for freely rotating rods.

Ordering of biaxial solutes in a smectic solvent

The positional–orientational probability distribution function of a number of hard-body biaxial solute particles, treated in the Zwanzig approximation and dissolved in the smectic A phase of parallel hard spherocylinders, has been calculated using a second-virial theory. It is found that the tendency of a solute to be partitioned between intra- and inter-layer regions, each one associated with a different degree of solute orientation, exhibits a non-monotonic behavior with the geometrical parameters defining its shape and size. These results, compared with the available experimental and numerical data, could be of help in qualitatively interpreting ordering phenomena of interest in both material and biological sciences.

Smectic Ordering of Parallel Hard Spherocylinders: An Entropy-Based Monte Carlo Study

We investigated the nematic to smectic transition undergone by parallel hard spherocylinders in the framework provided by the residual multi-particle entropy (RMPE) formalism. The RMPE is defined as the sum of all contributions to the configurational entropy of the fluid which arise from density correlations involving more than two particles. The vanishing of the RMPE signals the structural changes which take place in the system for increasing pressures. Monte Carlo simulations carried out for parallel hard spherocylinders show that such a one-phase ordering criterion accurately predicts also the nematic-smectic transition threshold notwithstanding the almost continuous character of the transition. A similar quantitative correspondence had been already noted in the case of an isotropic fluid of freely rotating hard spherocylinders undergoing a transition to a nematic, smectic or solid phase. The present analysis confirms the flexibility of the RMPE approach as a practical and reliable tool for detecting the formation of mesophases in model liquid-crystal systems.

Test of the scaled particle theory for aligned hard spherocylinders using Monte Carlo simulation

We obtained the chemical potential of a system of parallel hard spherocylinders by calculating the insertion probability of the particle. As a technique to obtain the insertion probability, we used a gradual insertion method together with Monte Carlo simulation. The simulation results provide a test of the scaled particle theory, suggesting a better approximation of the equation-of-state of the nematic phase of aligned long hard spherocylinders compared to the original scaled particle theory.

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.

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.

Effect of Addition of Hard Spheres to the Smectic-A Phase of Parallel Hard Spherocylinders

Constant pressure Monte Carlo simulation is used to discuss the structure of binary mixtures of parallel hard spherocylinders and hard spheres. Results of the simulation indicate that, the smectic layer periodicity is stretched when we add the spheres to the smectic-A phase of the spherocylinders.

Smectic-A Phase of a Bidisperse System of Parallel Hard Rods and Hard Spheres

A binary system of parallel hard spherocylinders and hard spheres are considered to examine influence of addition of spherical molecules to the pure system of rod-like molecules, especially the influence on the structure of the smectic-A phase. Free energy of the system is calculated through the second virial approximation, and nematic–smectic-A transition is estimated by stability analysis of nematic state with sinusoidal density fluctuation. Constant pressure Monte Carlo simulation is also used to confirm a prediction of the stability analysis which prediction indicates that the addition of spherical molecules induces a smectic-A phase as a microphase separation between the spheres and the spherocylinders.

A density functional study of nematic-smectic A-solid transitions of parallel hard spherocylinders

A density functional theory is formulated to study the nematic, smectic A and solid phases and phase transitions of a system of parallel hard spherocylinders (PHSC). For the direct correlation function the analytic expression suggested by Pynn is employed and an effective liquid approach is proposed to calculate the excess free energy of the inhomogeneous (smectic and solid) phases. The nematic-smectic A transition is found to be second order. The first-order nematic-solid and smectic A-solid transitions are calculated. As a function of the elongation of the spherocylinders, the phase behaviour and coexistence data obtained from the theory are in reasonable agreement with the available computer simulation results.

Relative stability of columnar and crystalline phases in a system of parallel hard spherocylinders.

We report a computer-simulation study of the stability of the columnar phase in a system of parallel spherocylinders with aspect ratios L/D=5 and \ensuremath{\infty}. It is found that the range of stability of the columnar phase is strongly dependent upon the system size. In particular, for particles with an aspect ratio L/D=5, the columnar phase that is observed in small systems (N=90) disappears for a system of N=1080 particles. In its place, a simple hexagonal crystal (``AAA stacking'') appears. On the basis of our present simulations, we cannot tell whether the latter phase is truly crystalline or possibly a smectic-B phase. For particles with an aspect ratio L/D=\ensuremath{\infty}, similar behavior is observed, although in this case a stable columnar ``pocket'' remains, even for the largest systems we studied. We have computed the locations of all phase transitions involving the new hexagonal phase.

Nematic to smectic-A transition of parallel dipolar hard spherocylinders and ellipsoids, a hypernetted chain equation study

The thermodynamic, dielectric, and structural properties of systems of dipolar hard spherocylinders and ellipsoids with perfect nematic order are investigated by means of the hypernetted chain (HNC) equation. The density, temperature domain for which the HNC equation admits a stable solution is determined. For spherocylinders a large increase of the main peak of the total structure factor in the vicinity of the stability limit of the HNC equation is, tentatively, associated with the onset of a nematic–smectic-A transition. The situation seems less clear for dipolar ellipsoids, though the results are in many aspects qualitatively similar to the spherocylinder case. The pair structure near the transition is analyzed. It is not characteristic of any of the smectic-A phase structures typical of strongly polar liquid crystals. This is probably a consequence of the highly symmetric nature of the model.

Columnar liquid crystal of parallel hard spherocylinders.

We study the columnar phase in a system of parallel hard spherocylinders, using the density-functional model that we have proposed and used recently for the description of nematic and smectic liquid crystals. We obtain a first-order transition between the smectic A and the columnar phases, in good agreement with the computer-simulation results. However, the analysis of the correlation structure shows that our approximation may break down for the crystal phase.

Equation of state for parallel hard spherocylinders.

A recent model for positional ordering in systems of monodisperse parallel hard spherocylinders is used to calculate the pressure over the entire range of densities and cylinder axial ratios. Reasonable quantitative agreement with Monte Carlo data is obtained for the full spectrum of nematic, smectic, columnar, and crystalline order. Analytical expressions are also given for the characteristic lengths of the ordering in these phases.

Density functional approximation for hard-body liquid crystals

We present a density functional approximation for the free energy of a system of hard bodies with arbitrary shape and orientational distribution. For systems with homogeneous density it reduces to existing treatments, which describe the isotropic liquid and the nematic liquid crystal. The treatment of the inhomogeneous density allows the study of smectic and crystal phases. We applied the approximation to a system of parallel hard spherocylinders, for which we compare the nematic to smectic-A phase transition with recent computer simulation data. We also study a system of oblique cylinders and show that smectic-C phase may appear as the result of packing effects in systems of hard bodies.

Integral equation study of parallel hard spherocylinders

The hypernetted chain (HNC) and Percus–Yevick (PY) integral equations are solved numerically for parallel hard spherocylinders of length-to-width ratios L/σ ranging from 0.5 to 5.0. The PY virial pressure is in excellent agreement with Monte Carlo data. The HNC equation gives evidence for the existence of a nematic to smectic-A phase transition at densities which compare reasonably well with the Monte Carlo (MC) estimates, whereas the PY equation gives stable nematic solutions for densities beyond the MC transition densities. For a given packing fraction η, pressure and pair correlation functions (properly scaled) depend very little on the elongation L/σ in the range 3–5.

Computer simulation of crystal nucleation of parallel hard spherocylinders

We report a molecular dynamics study of homogeneous nucleation in a fluid of parallel hard spherocylinders. It is found that the rate of nucleation of the crystal depends strongly on the presence of a nearby metastable smectic phase.

Theory of Ordered Phases in a System of Parallel Hard Spherocylinders

Theory of Ordered Phases in a System of Parallel Hard Spherocylinders

Theory of ordered phases in a system of parallel hard spherocylinders.

Theory of ordered phases in a system of parallel hard spherocylinders.