STATISTICAL THERMODYNAMIC THEORY OF GRAFTED POLYMERIC LAYERS

We present a theoretical approach to study the conformational and thermodynamical properties of grafted polymer layers. The theory is based on the generalization of a mean-field approach previously used to treat chain packing in amphiphilic aggregates. The theory can be used for any chain model, for any mixture of grafted chains and for any quality and type of solvent. The theory is based on finding the probability distribution function (pdf) of chain conformations that is shown to depend on the local osmotic pressure. The equations needed to find the osmotic pressures (and thus the pdf) are a set of nonlinear equations with the chain conformations, surface coverage, and surface geometry as input parameters. The theory is applied to off-lattice and lattice chain models. For the former, excellent agreement is found with molecular dynamic simulations. For the latter, we look at the effect of chain branching on the spatial structure and thermodynamic properties of the grafted layer.