Ising density functional theory for the charge regulation of weak polyelectrolytes

Charge regulation of polymers is an important phenomena that is not well described by conventional methods owing to their mean-field approximations on electrostatic interactions. As a result, the miss the intrachain correlations that lead to unique ionization behavior of polymers compared to their monomeric counterparts. The pH-responsive behavior is advantageous for applications in smart systems to achieve targeted design. We report a theoretical framework for weak polyelectrolytes by combining the polymer density functional theory with the Ising model for charge regulation. The so-called Ising density functional theory (iDFT) provides an accurate description of the effects of polymer conformation on the ionization of individual segments and is able to account for both the intra- and inter-chain correlations due to the excluded-volume effects, chain connectivity and electrostatic interactions. Theoretical predictions of the titration behavior and microscopic structure of ionizable polymers are found in excellent agreement with experiment. Furthermore, we demonstrate unique behavior that results from intrachain correlations that cannot be captured through conventional methods.