  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.
