Thermodynamic non-ideality in charge regulation of weak polyelectrolytes.

Polymer ionization differs from that for their monomeric counterparts due to intramolecular correlations. Such effects are conventionally described in terms of the site-binding model that accounts for short-range interactions between neighboring sites. With an apparent equilibrium constant for each ionizable group and the nearest-neighbor energy as adjustable parameters, the site-binding method is useful to correlate experimental titration curves when the site-site interactions are insignificant at long ranges. This work aims to describe the electrostatic behavior of weak polyelectrolytes in aqueous solutions on the basis of the intrinsic equilibrium constants of the individual ionizable groups and solution conditions underlying the thermodynamic non-ideality. A molecular thermodynamic model is proposed for the protonation of weak polyelectrolytes by incorporating classical density functional theory into the site-binding model to account for the effects of the local ionic environment on both inter-chain and intra-chain correlations. By an extensive comparison of theoretical predictions with experimental titration curves, we demonstrate that the thermodynamic model is able to quantify the ionization behavior of weak polyelectrolytes over a broad range of molecular architectures and solution conditions.

Ising density functional theory for weak polyelectrolytes with strong coupling of ionization and intrachain correlations.

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 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 interchain 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 to be in excellent agreement with the experiment.

Modeling Surface Charge Regulation of Colloidal Particles in Aqueous Solutions.

Colloidal particles are mostly charged in an aqueous solution because of the protonation or deprotonation of ionizable groups on the surface. The surface charge density reflects a complex interplay of ion distributions within the electric double layer and the surface reaction equilibrium. In this work, we present a coarse-grained model to describe the charge regulation of various colloidal systems by an explicit consideration of the inhomogeneous ion distributions and surface reactions. With the primitive model for aqueous solutions and equilibrium constants for surface reactions as the inputs, the theoretical model is able to make quantitative predictions of the surface-charge densities and zeta potentials for diverse colloidal particles over a wide range of pH and ionic conditions. By accounting for the ionic size effects and electrostatic correlations, our model is applicable to systems with multivalent ions that exhibit charge inversion and provides a faithful description of the interfacial properties without evoking the empirical Stern capacitance or specific ion adsorptions.

Mapping the phase behavior of coacervate-driven self-assembly in diblock copolyelectrolytes.

Oppositely-charged polymers can undergo an associative phase separation process known as complex coacervation, which is driven by the electrostatic attraction between the two polymer species. This driving force for phase separation can be harnessed to drive self-assembly, via pairs of block copolyelectrolytes with opposite charge and thus favorable coulombic interactions. There are few predictions of coacervate self-assembly phase behavior due to the wide variety of molecular and environmental parameters, along with fundamental theoretical challenges. In this paper, we use recent advances in coacervate theory to predict the solution-phase assembly of diblock polyelectrolyte pairs for a number of molecular design parameters (charged block fraction, polymer length). Phase diagrams show that self-assembly occurs at high polymer, low salt concentrations for a range of charge block fractions. We show that we qualitatively obtain limiting results seen in the experimental literature, including the emergence of a high polymer-fraction reentrant transition that gives rise to a self-compatibilized homopolymer coacervate behavior at the limit of high charge block fraction. In intermediate charge block fractions, we draw an analogy between the role of salt concentration in coacervation-driven assembly and the role of temperature in χ-driven assembly. We also explore salt partitioning between microphase separated domains in block copolyelectrolytes, with parallels to homopolyelectrolyte coacervation.