Applicability of Generalized Stokes Einstein Relation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Coacervate Solutions

Complex coacervate solutions composed of a blend of oppositely charged polyelectrolytes have recently been observed to exhibit liquid-liquid phase separation upon heating or lower critical solution temperature behavior [1], as found in many water-soluble uncharged polymers. It is interesting to consider whether the dynamic critical phenomena of these phase separating fluids is similar to neutral polymers solutions and blends. Despite the additional complexities due to charge fluctuations and associative behavior, we examine whether the mode-coupling theory of Kawasaki and Ferrell [2,3] can describe the wavevector-dependent collective diffusion coefficient (D_c) in near-critical polyelectrolyte complex coacervate solutions, a framework validated in many uncharged near-critical fluid mixtures. We also test the Generalized Stokes-Einstein relationship predicted by this theory for the collective diffusion coefficient, D_c = k_B T/ 6 π η ξ_s, in the long-wavelength limit where ξ_s is the previously measured static correlation length [1], product of Boltzmann’s constant and temperature (k_B T), and η is the viscosity of the fluid mixture independently measured by capillary rheometry. Our observations show that the critical dynamics are remarkably similar to neutral polymer blends in solution and small molecule mixtures near their critical point for phase separation. We hypothesize that relative simplicity found in the dynamic criticality of the coacervate mixtures might arise from the formation of neutral complexes.

[1] Y. Ma, S. Ali, and V.M. Prabhu, Macromolecules 54, 11338 (2021).

[2] K. Kawasaki, Annals of Physics 61, 1 (1970).

[3] R.A. Ferrell, Phys. Rev. Lett. 24, 1169 (1970).