Optimal linearized Poisson–Boltzmann theory applied to the simulation of flexible polyelectrolytes in solution

Optimal linearized Poisson–Boltzmann (OLPB) theory is applied to the simulation of flexible polyelectrolytes in solution. As previously demonstrated in the contexts of the cell model [H. H. von Grünberg, R. van Roij, and G. Klein, Europhys. Lett. 55, 580 (2001)] and a particle-based model [B. Beresfordsmith, D. Y. C. Chan, and D. J. Mitchell, J. Colloid Interface Sci. 105, 216 (1985)] of charged colloids, OLPB theory is applicable to thermodynamic states at which conventional, Debye–Hückel (DH) linearization of the Poisson–Boltzmann equation is rendered invalid by violation of the condition that the electrostatic coupling energy of a mobile ion be much smaller than its thermal energy throughout space, $|ναeψ(r)|≪kBT.$ As a demonstration of its applicability to flexible polyelectrolytes, OLPB theory is applied to a concentrated solution of freely jointed chains. The osmotic pressure is computed at various reservoir ionic strengths and compared with results from the conventional DH model for polyelectrolytes. Through comparison with the cylindrical cell model for polyelectrolytes, it is demonstrated that the OLPB model yields the correct osmotic pressure behavior with respect to nonlinear theory where conventional DH theory fails, namely at large ratios of mean counterion density to reservoir salt density, when the Donnan potential is large.