PRISM-Based Theory of Complex Coacervation: Excluded Volume versus Chain Correlation

Abstract

Aqueous solutions of oppositely-charged polyelectrolytes can undergo liquid-liquid phase separation into materials known as complex coacervates. These coacervates have been a subject of intense experimental and theoretical interest. Efforts to provide a physical description of complex coacervates have led to a number of theories that qualitatively (and sometimes quantitatively) agree with experimental data. However, this agreement often occurs in a degeneracy of models with profoundly different starting assumptions and different levels of sophistication. Theoretical difficulties in these systems are similar to those in most polyelectrolyte systems where charged species are highly correlated. These highly-correlated systems can be described using Liquid State (LS) integral equation theories, which surpass mean field theories by providing information * To whom correspondence should be addressed † University of Massachusetts Amherst ‡ University of Illinois Urbana-Champaign 1 on local charge ordering. We extend these ideas to complex coacervate systems using PRISM-type theories, and are able to capture effects not observable in traditional coacervate models, particularly connectivity and excluded volume effects. We can thus bridge two traditional but incommensurate theories meant to describe complex coacervates: the Voorn-Overbeek theory and counterion release. Importantly, we hypothesize that a cancellation of connectivity and excluded volume effects provides an explanation for the ability of Voorn-Overbeek theory to fit experimental data despite its well-known approximations.

50th Anniversary Perspective: A Perspective on Polyelectrolyte Solutions

“…The role of stoichiometry between the polycation and polyanion was addressed by Zhang and Shklovskii 107 based on electrostatics, but without consideration of counterions. Building on the PRISM-type liquid-state theory, Perry and Sing 125 focused on the effects of chain connectivity and excluded volume (which are ignored in the VO theory) and hypothesized that the apparent success of the VO theory is due to cancellation of chain connectivity and excluded volume effects. The role of molecular compactness in terms of the fractal dimension of the polymer was addressed by Qin and De Pablo, 129 by including charge connectivity, although counterion entropy is not included.…”

Charge Correlations for Precise, Coulombically Driven Self Assembly

“…PRISM theory is useful to articulate the molecular features that remain unresolved in field theoretic methods . Figure a demonstrates the results of a PRISM calculation (DHEMSA closure) for a solution of oppositely charged polyelectrolytes with salt, via pair correlations that reveal the molecular correlations in coacervate systems . Similar to the case of counterion condensation, a given charge along the polyelectrolyte backbone must be spatially adjacent to its neighbor of the same charge.…”

“…Therefore, not only is it nearby a charge of the opposite sign, but there is a charge of the opposite sign that is nearby its connected neighbor (see Figure b). This is especially true if the oppositely charged species are connected (the other polyelectrolyte species), as the connectivity correlations persist along the backbone of both species …”

“…a) Pair correlations between species i and j in a coacervate system consisting of cations (+), anions (−), polycations (P+), and polyanions (P−) . Peaks correspond to local charge structure features, schematically shown in panel (b) .…”

“…In this article, charge correlations will be discussed as a powerful motif for self‐assembly and material design. New, underlying principles of their manipulation are beginning to be realized in the literature, in diverse systems such as block copolyelectrolyte melts and aqueous polymer solutions . Electrostatics are simultaneously one of the most challenging interactions in soft material self‐assembly, as well as the interaction with the most remaining potential to truly influence how soft matter can be designed to push the boundaries of materials.…”