Theory of grafted polymer monolayers : chain models with finite extensibility

A theory of polymer monolayers densely grafted to a flat surface was developed within the framework of the mean-field approximation. An arbitrary mechanism for extensibility of the grafted chains was assumed. It was found that, for a layer of monodisperse polymer chains, the self-consistent pseudopotential is controlled only by the mechanism providing chain extensibility and is independent of specific features of interchain interaction ; that is, when interchain interaction varies, the structure of the monolayer changes so as to provide invariability of the self-consistent pseudopotential. A general scheme for calculation of the self-consistent pseudopotential was elaborated. Analytical expressions for the self-consistent pseudopotential were derived for models of monolayers composed of freely jointed chains on square, diamond, and body-centered cubic lattices. Expansions of the self-consistent pseudopotential into series were derived for freely jointed chains on simple cubic and face-centered cubic lattices, a continuum model of freely jointed chains, and lattice models with a banned backward step. The dependences for the self-consistent pseudopotential were used to calculate the structures of the polyelectrolyte monolayers and those of very densely grafted monolayers immersed in a good solvent. The results of the theory show quantitative agreement with previously reported data on numerical calculations of the structure and properties of polymer monolayers.