William van Megen

The grand canonical ensemble Monte Carlo method applied to the electrical double layer

The grand canonical ensemble Monte Carlo method is applied to the electrical double layer, using a discrete surface charge distribution and the restricted primitive model for the electrolyte. A systematic examination of the effects of the dimensions of the basic Monte Carlo cell shows that the usual minimum image technique, for determining the potential energy of the system, must be supplemented by long range corrections. Alternatively, very large dimensions or numbers of ions must be employed. The calculated ion distribution functions are compared with the Gouy–Chapman theory for bulk electrolyte concentrations up to 0.2 C/m2. The Gouy–Chapman theory compares very well with the Monte Carlo results for electrolyte concentrations up to 0.1 mole/dm3, but quantitatvive differences appear at 1 mole/dm3. These differences are more pronounced at 2 mole/dm3 for which the Monte Carlo results indicate an inversion of the positive and negative charge distribution functions.

Structure of dense liquids at solid interfaces

Detailed calculations of dense fluids of hard spheres, soft repulsive spheres and Lennard‐Jones molecules between hard, soft repulsive and attractive solid walls reveals a pronounced stratification of the fluid’s density profile. The calculations have been performed using the NVT Monte Carlo method with about 200 fluid molecules. The results indicate that a very significant role is played by the attractive component in the intermolecular potentials, which suggests that the usual hard‐sphere perturbation theories are not applicable in their present form.

Comparison of Brownian dynamics with photon correlation spectroscopy of strongly interacting colloidal particles

The Brownian dynamics computer simulation method is applied to a dilute system of charged spheres dispersed in a very dilute electrolyte. The parameters of this model system are chosen to match those of an aqueous dispersion of highly charged and strongly interacting polystyrene spheres, on which a number of photon correlation spectroscopy studies have recently been made. The structure factor and the electric field autocorrelation functions calculated by the Brownian dynamics method agree with the experimental data provided that allowances are made for the effects of polydispersity and multiple scattering. A few commonly used approximations for analyzing the dynamic properties of many particle systems are also examined.

Statistical mechanical approaches to phase transitions in hydrophobic colloids. I. effects of electrolyte concentration

Abstract First-order perturbation theory and the cell model are used to determine excess pressures and the discorder-order phase transition in hydrophobic colloids. The results of these apprxoimate methods compare well with those of exact Monte Carlo calculations. Particular regard is paid to the effect of the electrolyte concentration on the calculated properties.

Structure and ordering in dilute dispersions of spherical particles

The Monte Carlo method is used to determine the structure of a very dilute colloid electrostatically stablized in a dilute aqueous electrolyte. The colloidal system is treated as a monodisperse collection of structureless spherical particles embedded in a continuous background. The calculated radial distribution functions are converted into structure factors which are subsequently compared with the corresponding quantity determined from laser light scattering experiments.

Effect of polydispersity on the crystallization kinetics of suspensions of colloidal hard spheres when approaching the glass transition

We present a comprehensive study of the solidification scenario in suspensions of colloidal hard spheres for three polydispersities between 4.8% and 5.8%, over a range of volume fractions from near freezing to near the glass transition. From these results, we identify four stages in the crystallization process: (i) an induction stage where large numbers of precursor structures are observed, (ii) a conversion stage as precursors are converted to close packed structures, (iii) a nucleation stage, and (iv) a ripening stage. It is found that the behavior is qualitatively different for volume fractions below or above the melting volume fraction. The main effect of increasing polydispersity is to increase the duration of the induction stage, due to the requirement for local fractionation of particles of larger or smaller than average size. Near the glass transition, the nucleation process is entirely frustrated, and the sample is locked into a compressed crystal precursor structure. Interestingly, neither polydispersity nor volume fraction significantly influences the precursor stage, suggesting that the crystal precursors are present in all solidifying samples. We speculate that these precursors are related to the dynamical heterogeneities observed in a number of dynamical studies.

Solvent structure and solvation forces between solid bodies

The canonical ensemble Monte Carlo method has been used to determine the structure of dense Lennard-Jones fluids in the vicinity of a rigid solid. From these results the adsorption excesses and solvation forces have been calculated. The solvation force is very significant when compared with the van der Waals force between the solid bodies at short surface to surface separations.

A hard sphere model for order—disorder transitions in colloidal dispersions

Abstract Use of a hard sphere model and the concept of an effective hard sphere diameter of a colloidal particle with its associated double layer is reported. This method allows rapid determination of the order-disorder transition in colloidal dispersions and yields reasonable estimates of the osmotic pressures compared with “exact” Monte Carlo calculations.

Microscopic approach to colloid stability

Abstract Use is made of the well-known Monte Carlo technique to calculate some of the observed properties of stable colloid suspensions. Using a very simple form for the interparticle potential the results are at least in qualitative agreement with some recent experimental data.

Finite ion size effects in the electrical double layer—A Monte Carlo study

The grand canonical ensemble Monte Carlo method is applied to monovalent and divalent symmetric primitive model electrolytes between plane charged surfaces. Results for continuous and discrete surface charge distributions are compared with the Gouy–Chapman theory.