Self Consistent Molecular Field Theory for Packing in Classical Liquids

Building on a quasi-chemical formulation of solution theory, this paper proposes a self consistent molecular field theory for packing problems in classical liquids, and tests the theoretical predictions for the excess chemical potential of the hard sphere fluid. Results are given for the self consistent molecular fields obtained, and for the probabilities of occupancy of a molecular observation volume. For this system, the excess chemical potential predicted is as accurate as the most accurate prior theories, particularly the scaled particle (Percus-Yevick compressibility) theory. It is argued that the present approach is particularly simple, and should provide a basis for a molecular-scale description of more complex solutions.Comment: 6 pages and 5 figure

Equilibrium phase behavior of polydisperse hard spheres

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energy expressions for the fluid and solid phases. Cloud and shadow curves, which determine the onset of phase coexistence, are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation effects. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or re-entrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus only be defined for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find in addition that coexistence of several solids with a fluid phase is also possible

Influence of hydrodynamics on many-particle diffusion in 2D colloidal suspensions

We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective diffusion coefficients $D_T(\rho) / D_0$ and $D_C(\rho) / D_0$, where $D_0$ is the single-particle diffusion coefficient, as a function of the density of the colloids $\rho$. At low Schmidt numbers $Sc={\cal O}(1)$, we find that hydrodynamics has essentially no effect on the behaviour of $D_T(\rho)/D_0$. At larger $Sc$, $D_T(\rho)/D_0$ is enhanced at all densities, although the differences compared to the case without hydrodynamics are minor. The collective diffusion coefficient, on the other hand, is much more strongly coupled to hydrodynamical conservation laws and is distinctly different from the purely dissipative case

Segregation by thermal diffusion of an intruder in a moderately dense granular fluid

A solution of the inelastic Enskog equation that goes beyond the weak dissipation limit and applies for moderate densities is used to determine the thermal diffusion factor of an intruder immersed in a dense granular gas under gravity. This factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, density and coefficients of restitution). The form of the phase-diagrams for the BNE/RBNE transition depends sensitively on the value of gravity relative to the thermal gradient, so that it is possible to switch between both states for given values of the parameters of the system. Two specific limits are considered with detail: (i) absence of gravity, and (ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis extends previous theoretical results derived in the dilute limit case [V. Garz\'o, Europhys. Lett. {\bf 75}, 521 (2006)] and is consistent with the findings of some recent experimental results.Comment: 10 figure

Simple geometrical interpretation of the linear character for the Zeno-line and the rectilinear diameter

The unified geometrical interpretation of the linear character of the Zeno-line (unit compressibility line Z=1) and the rectilinear diameter is proposed. We show that recent findings about the properties of the Zeno-line and striking correlation with the rectilinear diameter line as well as other empirical relations can be naturally considered as the consequences of the projective isomorphism between the real molecular fluids and the lattice gas (Ising) model.Comment: 7 pages, 2 figure

Superdipole Liquid Scenario for the Dielectric Primary Relaxation in Supercooled Polar liquids

We propose a dynamic structure of coupled dynamic molecular strings for supercooled small polar molecule liquids and accordingly we obtain the Hamiltonian of the rotational degrees of freedom of the system. From the Hamiltonian, the strongly correlated supercooled polar liquid state is renormalized to a normal superdipole (SD) liquid state. This scenario describes the following main features of the primary or a-relaxation dynamics in supercooled polar liquids: (1) the average relaxation time evolves from a high temperature Arrhenius to a low temperature non-Arrhenius or super-Arrhenius behavior; (2) the relaxation function crosses over from the high temperature exponential to low temperature non-exponential form; and (3) the temperature dependence of the relaxation strength shows non-Curie features. According to the present model, the crossover phenomena of the first two characteristics arise from the transition between the superdipole gas and the superdipole liquid. The model predictions are quantitatively compared with the experimental results of glycerol, a typical glass-former.Comment: 40 pages, 3 figure

Predicting phase equilibria in polydisperse systems

Many materials containing colloids or polymers are polydisperse: They comprise particles with properties (such as particle diameter, charge, or polymer chain length) that depend continuously on one or several parameters. This review focusses on the theoretical prediction of phase equilibria in polydisperse systems; the presence of an effectively infinite number of distinguishable particle species makes this a highly nontrivial task. I first describe qualitatively some of the novel features of polydisperse phase behaviour, and outline a theoretical framework within which they can be explored. Current techniques for predicting polydisperse phase equilibria are then reviewed. I also discuss applications to some simple model systems including homopolymers and random copolymers, spherical colloids and colloid-polymer mixtures, and liquid crystals formed from rod- and plate-like colloidal particles; the results surveyed give an idea of the rich phenomenology of polydisperse phase behaviour. Extensions to the study of polydispersity effects on interfacial behaviour and phase separation kinetics are outlined briefly.Comment: 48 pages, invited topical review for Journal of Physics: Condensed Matter; uses Institute of Physics style file iopart.cls (included