Friction between Polymer Brushes

By solving the equilibrium equations for a polymer in a neutral polymer brush, the degree of interpenetration of two polymer brushes in contact and near contact is calculated. These results are used to calculate values of the force of static friction in agreement with recent friction measurements for polymer brush lubricated surfaces. It is shown that at sufficiently light loads polymer brush coated surfaces can slide, with the load supported entirely by osmotic pressure, at a sufficiently large spatial separation so as to avoid entanglement, and hence static friction.