Gerald Rickayzen

Integral equations and the pressure at the liquid-solid interface

The relationship between the pressure in a fluid and the density-functional which controls the density profile of a fluid confined between two walls is examined. As a result, the conditions which must be fulfilled by an approximate density functional to yield a bulk pressure P, a normal pressure, P W at the interface between a hard wall and the fluid, and a fluid density, ρW, adjacent to the wall which satisfy the exact relations P W=P=k B T ρW, are established. The density-functional which yields the HNC closure for a hard-sphere fluid near a hard wall is modified so that the modified functional yields the Carnahan-Starling bulk pressure and hence fulfils the necessary conditions. The density profile to which this gives rise is compared with the results of computer simulation for various bulk densities when the fluid is bounded by two hard walls separated by a distance equal to 8 diameters of the hard sphere. The agreement is found to be very good even at a bulk reduced density of 0·91.

The structure of fluids confined to spherical pores: theory and simulation

A study of the density profiles of a hard sphere and a Lennard-Jones fluid confined to spherical pores has been carried out using both computer simulation and a density functional proposed by Rickayzen and Augousti. For hard sphere fluids very good agreement between the results of theory and simulation are obtained. For the Lennard-Jones fluid, there is reasonable agreement between theory and simulation at the highest temperature studied (T = 2·01 T c) but the agreement deteriorates as the temperature of the fluid is reduced.

Short range solvation forces in fluids

A formalism based on a linearization procedure is used to obtain an expression for the thermodynamic potential of a system of fluid particles in terms of the local particle number density and bulk structure factor. For the case of adsorption of particles at a single impenetrable interface, minimization of the thermodynamic potential yields an integral equation for the number density identical to that obtained by Percus. From the thermodynamic potential for our model we obtain the force/unit area between two plates which is simply related to the surface density of fluids at the plates. The equations are solved numerically for the one-dimensional hard rod fluid and the three-dimensional Percus-Yevick fluid. The resulting density and force show pronounced oscillations in agreement with recent Monte Carlo calculations. The magnitude of the force is comparable to van der Waals interactions and can thus modify significantly forces that exist between colloid particles.

The density profile of a fluid confined to a slit

We report on the application of a density-functional proposed by Rickayzen and Augousti (1984, Molec. Phys., 52, 1355) to the study of a LJ-fluid confined between parallel planar walls. The density profiles obtained are compared with the results of computer simulation obtained by Walton and Quirke (1986, Chem. Phys. Lett., 129, 382) for attractive walls as well as with new results obtained by the authors for hard walls. The agreement is good except at temperatures well below the critical one.

Temperature in the classical microcanonical ensemble

We show that a formula for the temperature of a classical system, originally given by Rugh, can be generalized. The result is that the inverse of the temperature is proportional to the average of the function ∇.(B/B.∇H), where H is the Hamiltonian of the system and B is an arbitrary vector function of the coordinates in phase space. Special cases of the new formula include a number of familiar results including the virial theorem.

Linear and non-linear theories of solvation forces in fluids

From an exact expression for the free energy of a non-uniform classical fluid, due to Saam and Ebner, a closure is used to develop a non-linear theory for the density and solvation force between two planar walls. In the linear limit these expressions reduce to ones used successfully elsewhere. Numerical solution of the equations for a hard sphere fluid shows that while the density profiles predicted by the two theories are markedly different, the solvation forces are similar.

Purely viscous fluids

It is shown that fluids consisting of particles that interact with potentials containing an accessible hard core have elastic moduli at infinite frequency that are infinite in magnitude. A consequence of this is that such a fluid, at any density or temperature, is not viscoelastic as are all real fluids. The viscosity of the fluid, whether shear or bulk, remains finite at all shear rates and the fluid never becomes elastic even for applied stresses at infinitely high frequency. Some care is required, however, in defining what is meant by ‘hard core’ and ‘accessible’. The conclusions are supported by the results of molecular dynamics, calculations of the viscoelastic behaviour of fluids interacting with steeply repulsive pair potentials.

The velocity autocorrelation function and self-diffusion coefficient of fluids with steeply repulsive potentials

We consider the velocity autocorrelation function, vacf, or Cv(t) and self-diffusion coefficients, D, of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, ø (r) = ε(σ/r)n. The Cv(t) are calculated numerically by molecular dynamics simulations. Accurate expressions for the short time expansion of Cv(t) to order O(t4) for n large are derived for this fluid. We propose novel expressions for Cv (t) that, for n large, spans the transition from the short time regime (expandable in even powers of time) and the longer time exponential-like regime characteristic of hard spheres. Inter alia we introduce relaxation times that characterize the duration of a collision and the decay of the velocity correlation within the mean-collision or Enskog-like relaxation time, TE.

Solvation forces in charged fluids: II. A non-linear theory

A formalism based on linear response theory is used to obtain an expression for the free energy of a non-uniform charged fluid in terms of the local ion number density and the bulk direct correlation functions. When the fluid is a restricted primitive model electrolyte the free energy splits into two independent parts, the minimization of which leads to expressions for the equilibrium charge and density distributions. From the free energy an expression for the force between two thick plates immersed in an electrolyte is obtained. In the limit of point ions, the expressions we obtain reduce to those of the Debye-Huckel theory of electrolytes. The equations are solved numerically and at low bulk electrolyte concentrations the monotonically decaying repulsive force of the classic Verwey and Overbeek results is found. But at higher concentrations and larger inverse Debye screening lengths the force displays pronounced oscillations. Correspondingly, the electric potential displays oscillations which have conse...

Forces between surfaces in electrolyte solutions

Abstract Density functional theories of solvation forces in charged fluids are extended to treat electrolytes consisting of finitesized ions and neutral solvent particles. The resulting forces display pronounced oscillations whose magnitude is a strong function of the bulk density of the neutral species.