Phase Behavior of Partially Charged Polyelectrolyte Solutions with Salt: A Theoretical Study

Abstract

Weakly (or partially) charged polyelectrolytes represent an important subset of the polyelectrolyte family. For instance, polycarboxylate-based superplasticizers, or PCEs, are comb-shaped polyelectrolytes possessing anionic backbones grafted with neutral side chains. PCEs play an important role in modern concrete production. However, their behavior in salt solutions remain poorly understood. The present work builds upon a recently developed liquid-state theory for fully charged polyelectrolyte solutions and extends it to describe the phase behavior and salt partitioning of PCEs in a 2:1 salt solution. Previous studies have shown that there can be an additional short-range attraction, often referred to as the "calcium-binding" interaction between calcium ions and the negatively-charged carboxylate groups of PCEs. Such a calcium-binding interaction and how its strength affects the phase behavior are investigated. It is found that increasing the calcium-binding strength expands the phase-separated region and increases the critical extra salt concentration, and it also leads to a wider phase-separated region for salting-out and salting-in phenomena. The structural parameters of PCEs also affect the phase behavior. Increasing the side-chain length shrinks the phase-separated region, while increasing the acid-to-ether ratio expands the phase-separated region. Those results may find applications in molecular design of weakly charged polyelectrolytes like PCEs.

Phase Behavior of Ion-Containing Polymers in Polar Solvents: Predictions from a Liquid-State Theory with Local Short-Range Interactions

“…As the results show, the larger the k value, the smaller the critical Bjerrum length. The effect of the N 1 -parameter has also been discussed in our recent work [91], increasing N 1 without changing other parameters will increase the electrostatic contribution to the excess Helmholtz free energy density and hence promotes phase separation. We have also varied the valency of the charged groups, and as is shown in Figure 10, increasing the valency of the charged groups of the polymer or the counterions also lowers the critical Bjerrum length.…”

“…The detailed numerical procedure was explained in an earlier work [91]. The globally convergent Newton method [119] is also employed to minimize the errors (tolerance < 10 −12 ) when solving the system of nonlinear equations.…”

“…where N T is the total number of segments of the polymer. Note that it is possible to consider beads of different sizes, as was done in our recent work [91], and to consider bead diameter as a function of temperature, as was described in the PC-SAFT literature [99] and a recent work by Xu et al [63]. However, since the theoretical formulation presented in this section is already complicated, in pursue of a minimalist model, such detailed factors are not included in this study, and we do not expect qualitative differences from the results presented in this work when those factors are included.…”

“…In a recent work [91], the LS theory of Zhang et al [44] was applied to study the phase behavior of partially charged ionic polymers, both in the salt-free case and with added 2 : 1 salt. Previous studies have shown that there can be an additional short-range attraction, often referred to as the "calcium-binding" interaction [92][93][94][95][96][97] between calcium ions and the negatively-charged carboxylate groups of polycarboxylate-based superplasticizers (PCEs) [13].…”

“…In the present work, we consider a linear polymer consisting of two types of monomers, A (charged) and B (neutral), in a polar solvent. The counterions released are referred to as type C. In a recent work of Qiu et al [91], we considered only dispersion interactions between A and C, which are often referred to as the specific ion binding interactions. In the present work, dispersion interactions between A and A and between B and B are considered.…”