Characteristics of macromolecular monolayers grafted onto an impermeable boundary calculated by the self-consistent field method

Abstract

The mean thickness and its fluctuation have been calculated by means of the self-consistent field lattice model for monolayers formed by flexible polymer chains grafted onto a planar insert surface at different graft densities σ −1. At σ⪆4 the mean layer height z̄ obeys the relationship z ̄ ≌0·52 Nσ −0·38 where N is the number of repeat units in the chain), in close agreement with the result of the scaling theory. Deviations from this formula appear in densely grafted systems, i.e., when the distance between the neighbouring chains drops below the length covered by two or three monomer units. Tke fluctuations in monolayer height are described by ( z ̄ 2- z ̄ 2) 1 2 ≌0·18 Nσ −0·325 a nd substantially exceed the fluctuations in size of an isolated macromolecule.