Unifying Weak and Strong Charge Correlations within the Random Phase Approximation: Polyampholytes of Various Sequences

We consider the problem of charge correlations in self-coacervate phases of polyampholytes and disordered proteins with different monomer sequences. An analytical approach consistently describing both weak and strong correlations is proposed, which is based on the improvement of the random phase approximation (RPA) by taking into account (i) discreteness of charges in polymer chains and (ii) a finite number of wave modes of the charge density fluctuations. These modifications are an essential element of the particle-to-field transformation. For strong Coulomb interactions, the generalized RPA reproduces the free energy of the strongly correlated Wigner liquid of disjointed charges. The developed theory is applied to describe coil-to-globule transitions in single-chain polyampholytes as a function of the monomer sequence. Comparison with results of molecular simulations confirms that the theory reproduces the observed scaling laws for globule size at weak charge correlations, and in addition, it provides a quantitative description of electrostatic interactions when correlations are strong.