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



Yuanchi Ma, Steven D. Hudson, Paul Salipante, Jack F. Douglas, Vivek Prabhu


We examine whether the mode-coupling theory of Kawasaki and Ferrell1,2 (KF) can describe the wavevector-dependent collective diffusion coefficient in near-critical polyelectrolyte complex coacervate solutions that have previously been shown to exhibit lower critical solution temperature phase separation and static critical behavior consistent with a Fisher-renormalized value of correlation length critical exponent . Good qualitative agreement is observed with the GSE relation predicted by KF for the collective diffusion coefficient, Dc = kB T/ 6 pi eta xi_s, in the long-wavelength limit where xi_s is the previously measured static correlation length and eta is the viscosity of the fluid mixture measured by capillary rheometry. We also find that the wavevector-dependent collective diffusion coefficient Dc (q) measured by varying the scattering angle in the dynamic light scattering measurements is well-described by the Kawasaki and Ferrell theory. Remarkably, this accord is much better than found for the corresponding mode-coupling theory and Dc (q) measurements on dilute and semi-dilute polymer solutions in good to marginal solvents, and we suggest a modification of the polymer solution theory based on our observations. In particular, we suggest that the viscosity in the GSE relation for polymer solutions should be identified with the solution viscosity rather than the solvent viscosity at non-vanishing polymer concentrations as in the KF theory of near-critical fluid dynamics.
ACS Macro Letters


polyelectrolyte complex, critical fluid, dynamic light scattering, Generalized Stokes-Einstein Equation, mode-coupling theory, dynamic critical phenomena, static and dynamic correlation lengths, universal scaling


Ma, Y. , Hudson, S. , Salipante, P. , Douglas, J. and Prabhu, V. (2023), Applicability of Generalized Stokes Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions, ACS Macro Letters, [online],, (Accessed June 15, 2024)


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Created February 10, 2023, Updated February 24, 2023