Randomly charged polymers: An exact enumeration study

We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers ±${\mathit{q}}_0$. Such polymers, known as polyampholytes, are compact when completely neutral and expanded when highly charged. Our exhaustive search includes all spatial conformations and quenched sequences for up to 12-step (13-site) walks. We investigate the behavior of the polymer as a function of its overall excess charge Q and temperature T. At low temperatures there is a phase transition from compact to extended configurations when the charge exceeds ${\mathit{Q}}_{\mathit{c}}$≊${\mathit{q}}_0$/ √N . There are also indications of a transition for small Q between two compact states on varying temperature. Numerical estimates are provided for the condensation energy, surface tension, and the critical exponent ν.