Michael Plischke

Pair correlation functions and density profiles in the primitive model of the electric double layer

In the primitive model of the electric double layer an electrolyte near a charged surface is modeled by an assembly of charged hard spheres in a medium of dielectric constant e. We solve numerically the inhomogeneous Ornstein–Zernike equation for the pair correlation functions in the hypernetted chain and mean spherical approximations together with the Lovett–Mou–Buff–Wertheim equation for the density of the ions near a charged surface. For highly charged surfaces the profiles display layering and charge reversal. The density profiles and diffuse layer potential are generally in excellent agreement with Monte Carlo data. The pair correlation functions at small separation are significantly different from correlation functions in the bulk and at larger separation have the well‐known power law decay (r−3) as function of separation when both hard spheres are kept at constant distance from the surface.

Density profiles and pair correlation functions of Lennard‐Jones fluids near a hard wall

We numerically solve the inhomogeneous Percus–Yevick equation for a system of particles interacting with each other through a Lennard‐Jones potential in the vicinity of a flat impenetrable wall. The density profile and pair correlation function are determined self‐consistently. We obtain density profiles which are, at least close to the wall, in good agreement with Monte Carlo results for low to intermediate densities. In one case for which a comparison of the entire profile with a Monte Carlo calculation is possible, we also obtain encouraging results.

Scaling of Growing Surfaces with Large Local Slopes

The Wolf-Villain model for growing surfaces is investigated using the height-height correlation function and the structure factor. Both functions show an unusual scaling behaviour that can be attributed to the time dependence of the average step size and is characterized by a new exponent. A modified scaling law is introduced which may describe quite generally the crossover behaviour in models of this kind. It leads to a very different classification of the model than has been inferred from the exponents obtained by measuring the width of the surface as a function of time and system size.

The primitive model of the electric double layer: Nonsymmetric electrolytes

We solve the inhomogeneous Ornstein–Zernike equation for the pair correlation functions together with the Lovett–Mou–Buff–Wertheim equation for the density profiles for charged hard spheres in the vicinity of a charged hard wall. This constitutes the so‐called primitive model of the electric double layer. In this article, we consider 2‐1 electrolytes (doubly charged positive ions and singly charged negative ions) near both positively and negatively charged surfaces. We use the hypernetted chain approximation to close the Ornstein–Zernike equation. Except for very high surface charge densities and low bulk concentrations, we obtain excellent agreement with the Monte Carlo data.

Viscoelasticity near the gel point: a molecular dynamics study.

We report on extensive molecular dynamics simulations on systems of soft spheres of functionality f, i.e., particles that are capable of bonding irreversibly with a maximum of f other particles. These bonds are randomly distributed throughout the system and imposed with probability p. At a critical concentration of bonds, p(c) approximately 0.2488 for f=6, a gel is formed and the shear viscosity eta diverges according to eta approximately (p(c)-p)(-s). We find s approximately 0.7 in agreement with some experiments and with a recent theoretical prediction based on Rouse dynamics of phantom chains. The diffusion constant decreases as the gel point is approached but does not display a well-defined power law.

Force between colloidal particles in a Lennard‐Jones fluid

We calculate the force between hard spheres of several diameters at infinite dilution in a Lennard‐Jones fluid on the basis of the Percus–Yevick solution of the Ornstein–Zernike equation. In particular, we study the region of the phase diagram near the critical point of the solvent. We find, in contrast to recent results for sticky spheres, that the solvent mediated force is attractive and monotonically increasing in the critical region. At high solvent density the force, while still attractive, oscillates as function of separation.

CONTRASTS BETWEEN COARSENING AND RELAXATIONAL DYNAMICS OF SURFACES

We discuss static and dynamic fluctuations of domain walls separating areas of constant but different slopes in steady-state configurations of crystalline surfaces both by an analytic treatment of the appropriate Langevin equation and by numerical simulations. In contrast to other situations that describe the dynamics in Ising-like systems such as models A and B, we find that the dynamic exponent z=2 that governs the domain wall relaxation function is not equal to the inverse of the exponent n=1/4 that describes the coarsening process that leads to the steady state.

Some comments on the self-consistency of the Poisson-Boltzmann theory for inhomogeneous coulomb systems

The Gouy-Chapman profile and linearized Poisson-Boltzmann pair correlation function are found to be self-consistent solutions to the Ornstein-Zernike equation coupled with the Lovett et al., Lebowitz-Percus, and Blum et al. sum rules.

Model for gelation with explicit solvent effects: Structure and dynamics

We study a two-component model for gelation consisting of f-functional monomers (the gel) and inert particles (the solvent). After equilibration as a simple liquid, the gel particles are gradually cross linked to each other until the desired number of cross links have been attained. At a critical cross-link density, the largest gel cluster percolates and an amorphous solid forms. This percolation process is different from ordinary lattice or continuum percolation of a single species in the sense that the critical exponents are new. As the cross-link density p approaches its critical value p(c), the shear viscosity diverges: eta(p) approximately (p(c)-p)(-s) with s a nonuniversal concentration-dependent exponent.

Rigidity transition in polymer melts with van der Waals interaction.

We study the onset of rigidity near the glass transition (GT) in a short-chain polymer melt modelled by a bead-spring model, where all beads interact with Lennard-Jones potentials. The properties of the system are examined above and below the GT. In order to minimize high-cooling-rate effects and computational times, equilibrium configurations are reached via isothermal compression. We monitor quantities such as the heat capacity CP, the short-time diffusion constants D, the viscosity eta , and the shear modulus; the time-dependent shear modulus Gt is compared with the shear modulus mu obtained from an externally applied instantaneous shear. We give a detailed analysis of the effects of such shearing on the system, both locally and globally. It is found that the polymeric glass displays long-time rigid behavior only below a temperature T1 , where T1 < TG. Furthermore, the linear and nonlinear relaxation regimes under applied shear are discussed.