M. M. Telo da Gama

The effect of dipolar forces on the structure and thermodynamics of classical fluids

The present understanding of how dipolar forces affect the structure and phase behaviour of classical fluids is reviewed. We focus mainly on the apparent absence of a liquid-vapour phase transition for strongly polar spherical particles, and discuss how the same can be recovered. By concentrating on theoretical and simulation studies of simple models, the roles and interplay of dipolar and Van der Waals interactions and molecular shape can be clearly discerned. Connection is made with experimental work on ferrofluids. Finally, we discuss the theoretical and computational challenges that lie ahead.

The interfacial properties of a model of a nematic liquid crystal

We have developed a statistical-mechanical theory for the interfacial properties of molecular fluids characterized by strongly anisotropic pairwise potentials. The theory, which is a generalization to molecular fluids of the mean-field (or van der Waals) theory for the Helmholtz free energy of non-uniform fluids of spherical molecules, was applied to the nematic-isotropic and nematic-vapour interfaces of a simple model of a nematic liquid crystal. Our model exhibits three fluid phases—a nematic, an isotropic liquid and a vapour—which can co-exist in pairs, and which also simultaneously co-exist at a low temperature triple point, T tr. We present explicit results for the global phase diagram of the model which are in good qualitative agreement with data on real liquid crystals. We have studied in detail the various fluid interfaces occurring in different regions of the phase diagram. We present results of numerical calculations for the density and orientational order parameter profiles of a nematic-isotrop...

A microscopic theory for spherical interfaces: Liquid drops in the canonical ensemble

We have studied the interfacial properties of droplets of (cutoff and shifted) Lennard‐Jones fluids in the canonical ensemble, using mean field theory. We have examined the effects of system size, overall density (supersaturation) and temperature on the density profiles, density and pressure at the center of the droplet, and surface tension. The numerical accuracy of the theory was tested by extensive comparisons of the results with the molecular dynamics simulations of Thompson et al. Good agreement was found. We have used the theory to calculate the energy of formation of a droplet and the stability temperature Ts for droplet formation as a function of the system size and overall density. We find Ts to be lower than the coexistence temperature for the planar surface, and to fall as the drop size falls.

The vapour-liquid interface for a Lennard-Jones model of argon-krypton mixtures

We report a molecular dynamics study of the planar vapour-liquid interface for mixtures of Ar and Kr modelled by truncated Lennard-Jones potentials at 115·77 K and at two compositions. The simulations yield the density profiles, surface tension, surface of tension, adsorption, and normal and transverse components of the pressure tensor. Both the Irving-Kirkwood (IK) and Harasima (H) forms of the pressure tensor are calculated. The values of the surface tension calculated by the thermodynamic and mechanical (for both the IK and H pressure tensors) routes are in agreement, but the IK and H pressure tensors yield different values for the surface of tension, as expected. These results are compared with predictions of the mean field theory (MFT) of the interface. The agreement is generally good, the principal differences being due to the fact that the MFT predicts too low a liquid density. The MFT is also used to predict properties of the mixture interface for the full Lennard-Jones potential. For low concentr...

The structure and surface tension of the liquid-vapour interface near the upper critical end point of a binary mixture of Lennard-Jones fluids

We present the results of calculations of the density profiles, relative adsorption and surface tension of the liquid-vapour interface of a binary mixture of Lennard-Jones fluids on a path of constant temperature and varying composition which passes through the consolute point for liquid-liquid separation but lies entirely in the two phase region. Our calculations are based on a square gradient approximation to the free energy functional of the inhomogeneous fluid. For bulk liquid concentrations x 1≲0·5 the density profile of species 1, the more volatile component, exhibits a maximum in the interface indicating pronounced surface segregation. The relative adsorption Г1,2 is positive for x 1≲0·66 and negative for larger x 1, i.e. the system exhibits an aneotrope. Our analysis suggests that it may be more useful to focus attention on the ratio Г1,2/x 1 than Г1,2 itself. We comment on recent attempts to measure Г1,2 for such interfaces. Our results for the surface tension in the vicinity of the critical end ...

Adsorption and orientation of amphiphilic molecules at a liquid-liquid interface

A generalized van der Walls theory for non-uniform molecular fluids was applied to the (A-rich, B-rich) liquid-liquid interface of a ternary mixture (A, B, C) with one amphiphilic component (C). We have calculated the surface tension, adsorption and density-orientation profiles at the interface at fixed temperature T and pressure p, over the whole range of concentration of C in the two liquid phase region. At fixed pressure this region terminates at a triple point at low T and at a plait point at higher T. The surface tension decreases with the concentration of C and tends to zero as the plait point is approached. At the triple point the surface tension is finite but can be very low. As p and T are varied this interface can exhibit a wetting transition. The dependence of the interfacial properties on the parameters characterizing the potentials (especially those involving C) has been investigated.

Density-functional theory for the interfacial properties of a dipolar fluid

The authors have studied the interfacial properties of a model dipolar fluid using a generalization of the density functional mean-field approximation. The generalization consists in weighting configurations in the mean-field average of the perturbative part of the energy by the low-density approximation of the radial distribution function. This leads to a bulk phase diagram which depends explicitly on the strength of the multipole moments, in contrast with the results of the simpler version of the theory. The calculated surface tension and density-orientational profile are in fair agreement with computer simulation (molecular dynamics) results: the addition of a dipole moment causes the surface tension to increase and there is interfacial ordering induced by purely multipolar forces. An extension of the theory to binary fluid mixtures is also briefly discussed.

Wetting transitions at fluid-fluid interfaces

Using a simple model free energy functional we have shown that the transition from partial to complete wetting which occurs at the αγ interface for a binary mixture of phase separated liquids (β and γ) in equilibrium with their vapour (α) can be a first order surface phase transition, as predicted by Cahn, or a second order surface phase transition. For the single bulk phase diagram that we consider the order of the transition depends on the particular model which is assumed for the attractive part of the intermolecular pairwise potentials. If these potentials decay exponentially with distance the transition is second order and the density profiles at the αγ interface change continuously, i.e. the wetting (β) film grows continuously, at the wetting transition. For inverse sixth power law attractive potentials the transition is first order and the structure of the αγ interface changes discontinuously at the transition—provided the range of the potential between unlike species is longer than that between li...

Theory of the liquid-vapour interface of a binary mixture of Lennard-Jones fluids

We present results of calculations of the equilibrium surface tension and density profiles for the liquid-vapour interface of a binary mixture of Lennard-Jones 12-6 fluids. The calculations are based on a density-functional theory for the Helmholtz free energy of the inhomogeneous mixture. This is a ‘microscopic’ generalization of the van der Waals-Cahn-Hilliard theory for the interface of a binary mixture. Our calculations cover the full range of liquid-vapour coexistence and the whole range of concentration. We find a correlation between the excess surface tension of the mixture and the surface segregation (adsorption) of the species with the lower surface tension. The ways in which segregation and excess surface tension depend on the Lennard-Jones parameters of the pure components are briefly discussed. Our results for the excess surface tension of mixtures of Ar and N2 and Ar and CH4 are compared with experiment; the agreement is reasonable.

Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheims perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a--state-dependent--functionality f and unique bonding probability p. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).