(565h) Charge Regulation of Weak Polyelectrolytes in Inhomogeneous Solutions

Weak polyelectrolytes exhibit electrostatic charges dependent on the solution pH and local chemical environment (e.g., salt concentration). This pH-responsive behavior instills weak polyelectrolytes great versatility in their practical use as a smart system to achieve specific functions such as targeted drug delivery and controlled release, but a quantitative description of such behavior remains a challenge. In contrast to their isolated monomeric counterparts, the ionization of a monomer within a polymer chain is highly dependent upon the charge status of other monomers particularly those that neighbor it. The importance of these intramolecular correlations leads to a unique step-like titration curve that results from the polymer favoring the ionization of only every other site to avoid repulsive interactions between adjacent sites. The conventional approach to describe weak polyelectrolytes in bulk solution is through the site-binding model which accounts for the work to ionize an isolated site as well as the additional work to ionize two adjacent sites. This method works quite well at moderate to high salt concentrations despite its inherent simplicity (e.g., no account for conformation of the polymer). However, its two parameters (the apparent equilibrium constant and the interaction energy between two charged sites) must be determined through correlation with experimental data and they are dependent on the solution conditions because of changes in inter- and intramolecular interactions. We recently demonstrated that by incorporating a molecular model for weak polyelectrolytes into the site-binding model to account for this thermodynamic non-ideality, we can quantitatively capture the titration behavior of various weak polyelectrolytes using only the thermodynamic equilibrium constant and size of the monomers. Thus, we are able to predict the ionization behavior of weak polyelectrolytes at different solution conditions. However, this site-binding model is limited to studying bulk solutions and thus cannot explore the broad uses of weak polyelectrolytes. The standard approach to study weak polyelectrolytes in inhomogeneous fluids (e.g., near an interface) typically involves a description of electrostatics at the mean-field level (i.e., through the Poisson equation) and accounting for the connectivity of sites within a polymer chain (e.g., tangent chain or gaussian). While this has provided some valuable insights on the adsorption characteristics of these polymers or how the swelling/collapse of polymer brushes varies with solution conditions, the mean-field description cannot account for the important intramolecular correlations that govern the ionization behavior of weak polyelectrolytes. This leads to a qualitative disagreement between the titration curves predicted by conventional methods versus experiments. In addition, these methods often neglect intermolecular correlations (e.g., electrostatic correlations) that can promote or inhibit the ionization of individual sites. An accurate description of weak polyelectrolyte ionization relies on a correct description of the intrachain correlations; however, this requires knowledge of the multibody state of the polymer (i.e., the states of all monomers). By coupling a molecular thermodynamic model for chemical reactions with the polymer density functional theory, we are able to incorporate both intra- and intermolecular correlation effects into the conventional models. This so-called Ising density functional theory accounts for both the multibody state and position of the polymer in the inhomogeneous fluid. It well describes the interfacial behavior of weak polyelectrolytes in good agreement with experimental data. The theoretical model has been used to study the surfaces forces mediated by a confined weak polyelectrolyte solution to generate insight into the design of bioadhesives such as those mimicking marine animals.