Phase Separation of Polyelectrolytes: The Effect of Charge Regulation.

Bin Zheng,David Andelman,Yael Avni,Rudolf Podgornik

doi:10.1021/acs.jpcb.1c01986

Abstract

Complex coacervation, known as the liquid–liquid phase separation of solutions with oppositely charged polyelectrolytes, has attracted substantial interest in recent years. We study the effect of the charge regulation (CR) mechanism on the complex coacervation by including short-range interactions between the charged sites on the polymer chains as well as an association–dissociation energy parameter in the CR mechanism. We investigate the phase diagrams of two CR models: (i) the hopping CR model (HCR) and (ii) the asymmetric CR model (ACR). It is shown that during the phase separation that the polymers in the condensed phase are more charged than those in the dilute phase, in accordance with Le Chatelier’s principle. In addition, secondary CR effects also influence the change in the volume fraction of the two phases. The latter can cause the charge difference between the two phases to change nonmonotonically as a function of the CR parameters.

Highlights

Solutions of oppositely charged polyelectrolytes under certain conditions can undergo a liquid−liquid phase separation, resulting in a condensed phase coexisting with a dilute one
The VO model largely captures the phenomenology of coacervate phase behavior, the model neglects the connectivity of the polymer chains, and its validity conditions are limited by DH theory to low salt concentrations
We investigate the effects of charge regulation (CR) on the polyelectrolyte phase diagram and analyze the variation of the polymer charge for the hopping CR model (HCR)/asymmetric CR model (ACR) models

Summary

INTRODUCTION

Solutions of oppositely charged polyelectrolytes under certain conditions can undergo a liquid−liquid phase separation, resulting in a condensed phase coexisting with a dilute one. Salehi and Larson[15] studied a more complex system and considered three different types of short-range electrostatic effects In their study, they included the association/ dissociation of the CR counterions and ion pairing of charges on oppositely charged polyelectrolyte and based their model on an extended version of the VO free energy. We consider the asymmetric CR model (ACR), where the B sites on the polyanion are fully dissociated such that there is only one relevant chemical reaction for the A sites (see Figure 1b), This corresponds to the limit α− → −∞, where the n polymers have a constant charge on their chain, z− = z0, and z+ is an annealed thermodynamic variable that can be adjusted on the p polymers. As our main focus is to show clearly the effects of the charge-regulation parameters on the phase diagram, the addition of salt is neglected

RESULTS AND DISCUSSION

CONCLUSIONS

■ ACKNOWLEDGMENTS

■ REFERENCES