Grand canonical investigations of prototypical polyelectrolyte models beyond the mean field level of approximation

Understanding the chemistry and physics of polyelectrolyte systems challenges scientists from a wide spectrum of research areas, ranging from colloidal science to biology. However, despite significant progress in the past decades, the calculation of large open polyelectrolyte systems on a detailed level remains computationally expensive, due to the highly polymeric nature of the macromolecules and/or long-range character of the intermonomer interactions. To cope with these difficulties, field-theoretic methodologies based on the mean-field approximation have emerged recently and have proven to provide useful results in the regime of high polyelectrolyte concentration. In this paper we present applications of a low-cost field-theoretic calculation approach based on the method of Gaussian equivalent representation, which has recently been proven useful for delivering accurate results in case of polymer solutions beyond the mean field level of approximation. Here we demonstrate its effectiveness on the example of a Gaussian effective potential, mimicking the effective interactions between weakly charged polyelectrolyte coils, and a screened Coulomb model, describing the effective intermonomer interactions of Debye-Hückel chains. Moreover, we show that the approach opens perspectives to extend the range of applicability of the grand canonical ensemble to dense liquid and solid phases of more sophisticated polyelectrolyte models. Finally, we demonstrate that our approach is also much more reliable for determining the phase boundaries of these models than conventional mean field and grand canonical Monte Carlo approaches.