Charge Regulation of Weak Polyelectrolytes: A New Predictive Model from Classical Poisson-Boltzmann Theory

We develop a new predictive model for the degree of ionization of weak polyelectrolytes based on the classical Poisson-Boltzmann theory. Through asymptotic analysis, we identify three distinct regimes, and derive new analytical approximations and scaling laws for the degree of ionization as functions of pH, salt concentration, and polymer concentration. By explicitly resolving inter-monomer electrostatic interactions, our model overcomes limitations of classical approaches such as the Donnan approximation and effective pK concept, achieving quantitative agreement with molecular dynamics simulations and experimental data. Our findings bridge gaps between theory, simulations and experiments, offering predictive insights for charge-responsive materials and biomolecules.