Role of electrostatic correlations in polyelectrolyte charge association

Abstract

Reversible ion binding equilibria in polyelectrolyte solutions are strongly affected by interactions between dissociated ionic species. We examine how the structural correlations between ionic groups on polyelectrolytes impact the counterion binding. Treating the electrostatic correlation free energy using the classical Debye-Hückel expression leads to complete counterion dissociation in the concentrated regime. This unphysical behavior is shown to stem from improper regularization of the self-energy of dissociated ions and polyions and is mitigated by smearing point-like charges across a finite width. The influence of the self-energy on counterion binding is elaborated on by generalizing the Debye-Hückel free energy to polyelectrolytes with variable fractal dimension and stiffness. In the dilute regime, a greater propensity for binding is found for chains with more compact architectures, which in turn reduces the harsh self-repulsions of tightly packed arrangements of charge. In the concentrated regime, the effects of electrostatic correlations weaken due to screening and the extent of binding is governed by a balance of short-ranged interactions and the translational entropy of ions.

Molecular design of self-coacervation phenomena in block polyampholytes

“…6B), which decreases slightly with block asymmetry. Interestingly, this is the opposite trend of that predicted by RPA, possibly a consequence of miscapturing intramolecular correlations, as has been recently suggested (36,64). However, one should expect ξe to decrease with increasing block asymmetry, as the length of the A block impinges upon the unperturbed lengthscale for electrostatic fluctuations, as seen with the effect of block length.…”

“…Simple analytical theories based on the random phase approximation (RPA) have partially accounted for the phase behavior of sequence-specific electrostatic interactions for a few specific IDP charge patterns (12-14) and other simple patterns (6,7,33), although the RPA is known to break down at low concentration, so it is unable to reliably predict the dilute branch of polyampholyte-phase diagrams. It should also be noted that the widely applied Voorn-Overbeek model of coacervation (34) neglects the connectivity of charges to the polymeric backbone (31,35,36) and thus is not useful for understanding sequence-dependent self-coacervation phenomena.The phase behavior and chain conformations of nearly chargeneutral alternating, random, and diblock polyampholytes have been studied extensively through scaling arguments, RPA, as well as molecular simulations highlighting the attractive electrostatic fluctuations that cause collapse into globular configurations and phase separation at low concentrations (1, 5-9, 19, 33, 37, 38). These approaches have qualitatively matched experiments on synthetic polyampholytes where the overall charge and sequence of charges are difficult to control (3,4,(39)(40)(41)(42), so the accuracy of these approaches is yet unknown.…”

“…Simple analytical theories based on the random phase approximation (RPA) have partially accounted for the phase behavior of sequence-specific electrostatic interactions for a few specific IDP charge patterns (12)(13)(14) and other simple patterns (6,7,33), although the RPA is known to break down at low concentration, so it is unable to reliably predict the dilute branch of polyampholyte-phase diagrams. It should also be noted that the widely applied Voorn-Overbeek model of coacervation (34) neglects the connectivity of charges to the polymeric backbone (31,35,36) and thus is not useful for understanding sequence-dependent self-coacervation phenomena.…”

Recent progress in the science of complex coacervation

“…Zhang and Shklovskii developed an early picture, primarily for complexation between two polymer chains, but including a prediction of bulk coacervation when oppositely-charged polyelectrolytes were near stoichiometric ratios. 29 A more recent approach was used for coacervates by Salehi and Larson (Figure 6c), 97 which has been extended in collaboration with Qin (Figure 6d), 40,154 in which there is a fraction of paired charges between the oppositely-charged chains. These approaches are analogous to the theory developed by Olvera de la Cruz for polyelectrolyte condensation with multivalent ionsessentially coacervation where one species has a very small degree of polymerization -where condensed counterions can be modeled as a a fluctuating 'effective charge.'…”

“…173,174 In all of these efforts, connectivity is implicitly considered via the inclusion of counterion condensation, and is parameterized to match observable phase behavior. 40,97,154 Pairing has also been considered in a model by Adhikari and Muthukumar, 135,175 who model coacervation as the attraction between pairs of complexed polyelectrolytes. The advantage of these ad hoc models is that they do not require an explicit description of the locally condensed charges, and instead only need to be appropriately parameterized.…”