Pressure exerted by a grafted polymer: Bethe lattice solution

Resumo: We solve the problem of a chain, modeled as a self-avoiding walk (SAW), grafted to the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point. The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walks on regular lattices and gaussian walks. The adsorption transition, which is discontinuous, and its influence on the pressure are also studied.