Viscoelasticity of Adsorbed Polymer Layers

Abstract

We discuss theoretically dynamic measurements with a surface force apparatus composed of a plane and a sphere coated with adsorbed polymer layers in a good solvent. The hydrodynamics are studied within a simple two fluids model where the friction between polymer and solvent is described by the so-called Brinkman approximation. In a steady compression experiment the distance between the sphere and the plane varies at a constant velocity and the polymer layers have a hydrodynamic thickness f?H of the order of their radius of gyration. In a periodic compression experiment, the distance has a periodic modulation of small amplitude at a finite frequency; the results are recast in terms of a complex modulus G. At a low frequency, the modulus has the standard Maxwell behavior (G' N w2, = w). The contribution of the polymer to the loss modulus is small when the polymer layers do not overlap; it is of the same order of magnitude as the pure solvent contribution when they do overlap. The elastic modulus increases with the thickness of the adsorbed layers. At a high frequency, the complex modulus increases as G = u2/3 and is independent of the thickness of the polymer layers. When the adsorbed polymer layers overlap, there is an intermediate regime where the elastic part of the modulus increases as G' = w4I3.