Intra-chain electrostatic correlations govern charge regulation of weakly dissociating polyelectrolytes

Theories for the charge regulation of weakly dissociating polymers that consider both acid-base equilibria and electrostatic interactions are poorly developed. Here, we develop a detailed model that combines an acid-base equilibrium with a random phase approximation (RPA) of electrostatic correlations for a solution containing weak polyacids. We find that charge regulation of a polyacid strongly depends on the polyacid structure: A rodlike polyacid yields the lowest electrostatic repulsions between deprotonated monomers in the chain and protons can easily dissociate from the chain, while in more compact structures, such as Gaussian coil, the polyacids do not easily give up their protons due to the higher electrostatic repulsions that would result. We find that titration of hydrophilic poly(acrylic acid) shows a response similar to our prediction for a rodlike polymer, while a Gaussian coil better models the behavior of hydrophobic poly(acrylamido-2-methyl-1-propanesulfonic acid). Our predictions highlight the significance of inclusion of chain structure in treating electrostatic correlations of polyacids, and suggest the need for self-adjustable polymer structures to obtain realistic a priori predictions.