Steric interaction of an incoming particle with grafted rods: Exact solutions and unusual force profiles

We examine the problem of a grafted rod or rods compressed by a sphere, concentrating on the steric force exerted by the rods on the sphere. We show that this problem can be solved exactly to yield simple and nontrivial expressions for the repulsive force. In particular, there are several different regimes and in some of these the force exhibits surprising maxima and minima as a function of compression. This has applications to systems of stiff grafted polymers, particularly biopolymers. One experimental realization of our system might be a rod-coil diblock copolymer with the coil grafted to a solid surface.