A Comparison of Bead-Spring and Site-Binding Models for Weak Polyelectrolytes

Understanding states of weak polyelectrolytes is essential for designing advanced materials in biological and industrial applications. However, predicting their ionization states in aqueous solutions with added salt remains challenging due to the interplay between long-range Coulomb interactions, conformational degrees of freedom and chemical equilibria. While flexible bead-spring models with an explicit ion treatment provide accurate results, they are computationally expensive. In contrast, Ising-like site-binding models can often be solved in a matter of seconds and a further speed-up is possible using exact reweighting techniques. Notably, these models neglect conformational degrees of freedom and rely on an implicit salt description. To address the question under which circumstances these approximations are justified, we compare a site-binding model to bead-spring models with implicit and explicit ion treatments. Our results show that under strong electrostatic coupling, an explicit ion treatment is critical for accurately capturing ionization behavior. In particular, both, the site-binding model, and the bead-spring model with implicit ion treatment, strongly overestimate correlations between monomers in this regime, leading to significant deviations from the explicit bead-spring model. Conversely, under weak coupling, which is realized in aqueous environments in the presence of monovalent salts, all three models yield reasonable ionization curves. Minor differences arise, with the implicit bead-spring model showing slightly stronger suppression of ionization, while the site-binding model aligns more closely with the explicit bead-spring model due to compensating errors in ion treatment and conformational flexibility. In summary, while all models are effective under weak coupling, the explicit ion treatment within the bead-spring model is essential for capturing accurate ionization behavior under strong coupling.