Excess Charge in Polyampholytes

Polyampholytes (PAs) are polymers composed of (quenched) random sequences of positive and negatively charged monomeric groups. We show that the radius of gyration, $R_g$, of a PA strongly depends on its overall excess charge $Q$, and is very weakly influenced by other aspects of the sequence. For $Q<Q_c\approx q_0 \sqrt{N}$, where $N$ is the number of monomers of charge $\pm q_0$, the PA is compact, while for $Q>Q_c$ it is stretched. Some aspects of this behavior can be understood by analogy with the shape instability of a charged drop where the Rayleigh charge plays the role of $Q_c$.