Philip J. Camp

THE ISOTROPIC-NEMATIC PHASE TRANSITION IN UNIAXIAL HARD ELLIPSOID FLUIDS :COEXISTENCE DATA AND THE APPROACH TO THE ONSAGER LIMIT

The isotropic–nematic (I‐N) phase transition in hard ellipsoid fluids has been studied by computer simulation, using the Gibbs–Duhem integration technique introduced by Kofke; and theoretically, using Onsager theory and the Parsons–Lee improvement. In the simulations, the I‐N coexistence line is mapped out in the P–x plane, where P is the pressure and x is the elongation, by numerically integrating a Clapeyron‐like first‐order differential equation, using constant‐pressure simulation data for the two coexisting phases. The elongation range 5≤x≤20 has been studied, using independent starting points provided by chemical potential calculations and thermodynamic integration of the equation of state at x=5,20, plus a direct Gibbs ensemble simulation at x=20. The Onsager–Parsons–Lee theory has been applied to the I‐N phase transition for aspect ratios up to x=1000, affording an accurate investigation of the approach to the Onsager limit for this model. This involved the numerical computation of the orientation‐...

Phase diagram of the hard biaxial ellipsoid fluid

The phase diagram of fluids of hard biaxial ellipsoids with c/a=10 and b/a∈{1,10}, where a, b, and c are the semi-axes, has been studied using computer simulation. Four homogeneous phases are in evidence: isotropic (I), nematic (N+), discotic (N−) and biaxial (B). First-order isotropic-nematic and isotropic-discotic coexistence lines have been traced out using Gibbs–Duhem integration of the coexistence pressure with respect to the molecular biaxiality. We conclude that the isotropic-nematic transition is greatly weakened by a modest degree of molecular biaxiality, in agreement with several recent theories. The I–N+ and I–N− lines meet two second-order nematic-biaxial and discotic-biaxial lines at the Landau bicritical point. This point is predicted to occur at around the self-dual particle shape, b/a=c/a, and so extensive simulations have been performed at and around this point. Very sluggish behaviour is expected in this region of the phase diagram and so long simulations were required. An estimate of th...

Applications of Wang-Landau sampling to determine phase equilibria in complex fluids

Applications of the Wang-Landau algorithm for simulating phase coexistence at fixed temperature are presented. The number density is sampled using either volume scaling or particle insertion/deletion. The resulting algorithms, while being conceptually easy, are of comparable efficiency to existing multicanonical methods but with the advantage that neither the chemical potential nor the pressure at phase coexistence has to be estimated in advance of the simulation. First, we benchmark the algorithm against literature results for the vapor-liquid transition in the Lennard-Jones fluid. We then demonstrate the general applicability of the algorithm by studying vapor-liquid coexistence in two examples of complex fluids: charged soft spheres, which exhibit a transition similar to that in the restricted primitive model of ionic fluids, being characterized by strong ion pairing in the vapor phase; and Stockmayer fluids with high dipole strengths, in which the constituent particles aggregate to form chains, and for which the very existence of a transition has been widely debated. Finally, we show that the algorithm can be used to locate a weak isotropic-nematic transition in a fluid of Gay-Berne mesogens.

Spatial Control of Crystal Nucleation in Agarose Gel

Spatial and temporal control of crystal nucleation is demonstrated by nonphotochemical laser-induced nucleation of an aqueous agarose gel prepared with supersaturated potassium chloride. The location of nucleation was controlled by means of an optical mask; crystals were only observed in the area exposed to near-infrared laser radiation. The dependence of nucleation on laser power was measured, and the results suggest that the agarose gel reduces the effective supersaturation of the aqueous potassium chloride.

Demixing in hard ellipsoid rod-plate mixtures

The phase behavior of fluid mixtures of hard uniaxial ellipsoids with elongations e and 1/e, and equal molecular volume, has been studied using constant-pressure Gibbs ensemble Monte Carlo simulations for e = 15 and e = 20. Four distinct phases are observed: isotropic (I), uniaxial nematic (N+and N–) and biaxial nematic (B). The region of stability of the biaxial phase is found to be limited severely by demixing into two coexisting uniaxial phases. This is in agreement with recent theoretical predictions. The theory, however, does not account for the surprising asymmetry of the phase diagram that we find in our simulations.

Hard ellipsoid rod-plate mixtures: Onsager theory and computer simulations

The liquid crystal phase transitions for a classical fluid mixture of hard ellipsoids with aspect ratios 10 : 1 and 1 : 10, and equal volume, have been studied at two compositions using Onsager theories and by computer simulation. The original Onsager from of the Helmholtz free energy contains the second virial coefficient, but the effect of higher virial coefficients may be taken into account indirectly by resummation theories such as the y-expansion theory of Barboy and Gelbart or by renormalised two-particle theories such as that due to Parsons. A comparison of order parameters and equation of state data calculated by computer simulation and by Onsager, y-expansion-Onsager and Parsons theories shows good qualitative agreement. The resummation of higher virial coefficients is seen to offer improved quantitative agreement with simulation at the level of the second virial coefficient. The predicted phase diagram at this level of approximation is symmetric about the equal mixture of prolate and oblate ellipsoids as a result of the prolate-oblate symmetry of the excluded volume. The direct inclusion of higher virial coefficients has not been attempted but it is anticipated that this would give an asymmetric phase diagram.

Vapor-liquid coexistence in fluids of charged hard dumbbells

Vapor-liquid coexistence in fluids of charged hard dumbbells, each made up of two oppositely charged hard spheres with diameters sigma and separation d, has been studied using grand-canonical Monte Carlo simulations. In the limit d/sigma-->0, and with the temperature scaled accordingly, the system corresponds to dipolar hard spheres. For separations in the range 0.3<d/sigma<or=1 the coexisting vapor phase contains compact clusters. For separations in the range 0.1<or=d/sigma<0.3 the coexistence is between a chainlike vapor and a networklike liquid. Finite-size effects preclude the simulation of the coexistence in systems with d/sigma<0.1, but extrapolations of the results to d/sigma-->0 yield estimates of the apparent critical parameters for dipolar hard spheres.

Coexistence and criticality of fluids with long-range potentials

Using mixed-field finite-size scaling simulations, we have investigated the liquid–vapor critical behavior of three-dimensional fluids with algebraically decaying attractive pair interactions, which vary like −1/r3+σ with σ=3, 1, and 0.1. The finite-size scaling analysis was carried out by matching the critical ordering operator distribution, pL(x), against the limiting Ising form, i.e., Ising criticality was assumed. When the potential is short-ranged (σ=3) the simulation results are entirely consistent with the expected Ising critical behavior. When the potential is long-ranged (σ=1, 0.1), however, marked deviations from Ising behavior are observed, particularly in the form of the critical ordering operator distribution, and in the estimated values of β/ν. The results are consistent with non-Ising criticality which is predicted theoretically in fluids with long-range interactions. Some results from Gibbs ensemble simulations are also provided in order to sketch the shape of the liquid–vapor coexistence ...

Vapour–liquid phase transition of dipolar particles

The question of whether a vapour–liquid phase transition exists in systems of particles with purely dipolar interactions is examined. New Monte Carlo simulation results are presented for the dipolar Yukawa hard sphere (DYHS) fluid with very small values of the attractive Yukawa well depth, almost two orders of magnitude smaller than the characteristic dipolar interaction energy. In this way, it is possible to approach the dipolar hard sphere (DHS) limit. It is found that phase separation is not observable beyond a critical value of the Yukawa energy parameter, even though in thermodynamic and structural terms, the DYHS and DHS systems are very similar. It is suggested that either some very subtle physics distinguishes the DYHS and DHS systems, or the observation of a phase transition in DHSs is precluded by finite-size effects.

Structure and dynamics in a monolayer of dipolar spheres

The structure and dynamics in a monolayer of dipolar soft spheres have been investigated using molecular dynamics simulations. This is a basic model of colloidal ferrofluid monolayers, and other magnetic liquids in planar geometries, which can exhibit self-assembled chainlike aggregates due to strong dipole-dipole interactions. The effects of such chaining on the structure, single-particle translational and rotational motions, and the collective rotational motions are examined. The signatures of aggregation in the various structural and dynamical functions considered in this study could prove useful in experimental investigations of strongly dipolar materials.