Steric interactions between finite objects and end-grafted polymer chains: a two-dimensional mean-field analysis

Abstract

We examine the usefulness of a two-dimensional self-consistent mean-field theory for predicting polymer-induced forces between a finite object and a surface. The predictions are compared with scaling results for the compression of a single, end-grafted chain by a disk and for the compression of a brush with an athermal wall. For the former, the mean-field predictions agree with scaling theory and, in addition, provide the necessary prefactor in the scaling expressions for the Helmholtz potential and force of compression. For the brush, the mean-field results agree with the Alexander–de Gennes scaling result at moderate compressions and also provide an analytical expression for the force without any unknown parameters. We also use the mean-field theory to examine the interaction of a model bacterium with a planar substrate and show that steric interactions due to a single polymer chain alone can dominate van der Waals attraction under typical practical conditions and thus prevent bacterial adhesion to the surface.