Escape Transitions and Force Laws for Compressed Polymer Mushrooms

We describe the behaviour of grafted polymer mushrooms compressed by finite-size particles. Compression of single fixed mushrooms can lead to a first-order escape transition or, in certain circumstances, hysteresis. These transitions or hysteresis can be seen either in the chain radius or in the compressional force law. In the many-mushroom regime the force law is modified by the presence of escaped chains. For surface mobile chains the chains can evacuate from under the particle leading to a force law with a maximum at about 3/4 of a mushroom size. This maximum implies that the system undergoes a collapse transition above a critical pressure or yield stress P c ≈ kT σ 0 R F3 −1 , where σ 0 is the grafting density and R F3 is the unperturbed mushroom size.