This paper presents an approach to modeling a binary mixture near a surf ace. The approach used is based on statistical mechanics. The Cluster Variation (CV) method is used to solve an Ising-like model with a cluster size of two (neighboring lattice points). The free energy of the system is expressed in terms of the probabilities of occurrences of particular clusters. The CV method is first developed for a homogeneous system which leads to a set of three non-linear partial differential equations. The surface boundary is then introduced and the CV method is developed for this system which leads to a set of seven non-linear partial differential equations for each layer. In the calculations, the Natural Iteration (NI) method is introduced as a method of solving these non-linear partial differential equations. The steps involved in implementing the NI method are outlined. The number of layers is chosen to be 32. Concentration profiles are calculated for the binary system using the NI method and the results are discussed.

Graduation date: 1994