Theory of polymer brushes grafted to finite surfaces

Abstract

In this work, a model based in strong-stretching theory for polymer brushes grafted to finite planar surfaces is developed and solved numerically for two geometries: stripe-like and disk-like surfaces. There is a single parameter, R∞*, which represents the ratio between the equilibrium brush height and the grafting surface size, that controls the behavior of the system. When R∞* is large, the system behaves as if the polymer were grafted to a single line or point and the brush adopts a cylindrical or spherical shape. In the opposite extreme when it is small, the brush behaves as semi-infinite and can be described as a planar undeformed brush region and an edge region, and the line tension approaches a limiting value. In the intermediate case, a brush with non-uniform height and chain tilting is observed, with a shape and line tension depending on the value of R∞*. Relative stability of disk-shaped, stripe-shaped, and infinite lamellar micelles is analyzed based in this model.