Bending Rigidity of Branched Polymer Brushes with Finite Membrane Thickness

Abstract

Nanomechanical properties and, in particular, the bending rigidity of natural and artifficial nanomembranes can be strongly affected by anchored or tethered macromolecules. We present the theory of the induced bending rigidity of polymer brushes symmetrically tethered to both surfaces of the membrane and immersed into the solvent. In contrast to previous works the finite thickness of the membrane was taken into account. The analytical and numerical variants of the self-consistent field approach were used. The mean and Gaussian Helfrich’s bending moduli as functions of the polymerization degree, branching parameter and grafting density of tethered macromolecules were determined both for good and theta solvent conditions. It was shown that the absolute values of the Helfrich’s bending moduli increase with the membrane thickness. The increase of the thickness leads also to the change of the relation between moduli for branched and linear brushes at the same polymerization degree and grafting density. For thin membranes the bending moduli for brushes with linear chains exceed those for branched brushes. However by an increase of the «bare» membrane thickness the moduli for brushes with branched macromolecules can become equal and even exceed those for brushes consisting of their linear analogs.