Scaling Theory for Compressed Polymer-Brush Bilayers

We present a novel scaling theory to describe the interaction free energy within a compressed polymer-brush bilayer. For semidilute brushes at intermediate and strong compressions, we predict that the interaction free energy scales with distance, D, between the grafting surfaces as A(D) similar to D-2.5; i.e., the repulsive force, f(D) similar to D-3.5, measured at the surfaces increases more strongly upon compression than predicted by the classical theory of Milner, Witten, and Cates. We find good agreement with experimental data and excellent agreement with numerical results, which follow our analytical predictions over a wide range of surface separations. The theory is based on the assumption of a strong correlation of the repulsive force and the interpenetration between the brushes. Using our numerical data, we can demonstrate this correlation with great precision.