Isotropic-nematic phase transition of uniaxial variable softness prolate and oblate ellipsoids.

Onsager's theory of the isotropic-nematic phase separation of rod shaped particles is generalized to include particle softness and attractions in the anisotropic interparticle force field. The procedure separates a scaled radial component from the angular integral part, the latter being treated in essentially the same way as in the original Onsager formulation. Building on previous treatments of more idealised hard-core particle models, this is a step toward representing more realistic rod-like systems and also allowing temperature (and in principle specific chemical factors) to be included at a coarse grained level in the theory.

The second virial coefficient and critical point behavior of the Mie Potential.

Aspects of the second virial coefficient, b2, of the Mie m : n potential are investigated. The Boyle temperature, T0, is shown to decay monotonically with increasing m and n, while the maximum temperature, Tmax, exhibits a minimum at a value of m which increases as n increases. For the 2n : n special case T0 tends to zero and Tmax approaches the value of 7.

Binary mixtures of asymmetric continuous charge distributions: molecular dynamics simulations and integral equations.

An investigation is carried out of the association and clustering of mixtures of Gaussian charge distributions (CDs) of the form ∼Qexp(-r(2)/2α(2)), where Q is the total charge, r is the separation between the centers of charge and α governs the extent of charge spreading (α → 0 is the point charge limit). The general case where α and Q are different for the positive and negatives charges is considered. The Ewald method is extended to treat these systems and it is used in Molecular Dynamics (MD) simulations of electrically neutral CD mixtures in the number ratios of 1:1 and 1:4 (or charge ratio 4:1).

Continuous distributions of charges: extensions of the one component plasma.

The electrostatic interaction between finite charge distributions, ρ(r), in a neutralizing background is considered as an extension of the one component plasma (OCP) model of point charges. A general form for the interaction potential is obtained which can be applied to molecular theories of many simple charged fluids and mixtures and to the molecular dynamics (MD) simulation of such systems. The formalism is applied to the study of a fluid of Gaussian charges in a neutralizing background by MD simulation and using hypernetted-chain integral equation theory.

The force distribution probability function for simple fluids by density functional theory.

Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids.