Simple Approach for Charge Renormalization in Highly Charged Macroions

We revisit the notion of renormalized charge, which is a concept of central importance in the field of highly charged colloidal or polyelectrolyte solutions. Working at the level of a linear Debye-Hückel-like theory only, we propose a versatile method to predict the saturated amount of charge renormalization, which is, however, a nonlinear effect arising at strong electrostatic coupling. The results are successfully tested against nonlinear Poisson-Boltzmann theory for polyions of various shapes (planar, cylindrical, and spherical), both in the infinite dilution limit or in confined geometry, with or without added electrolyte. Our approach, accurate for monovalent microions in solvents such as water, is finally confronted against experimental results on charged colloids and B-DNA solutions.