On the Role of Solute Solvation and Excluded-Volume Interactions in Coupled Diffusion

Abstract

Coupled diffusion is observed in multicomponent liquid mixtures in which strong thermodynamic interactions occur. This phenomenon is described by cross terms in the matrix of multicomponent diffusion coefficients. This paper reports a theoretical analysis on the relative role of thermodynamic factors and Onsager crosscoefficients on cross-diffusion coefficients relevant to ternary mixtures containing macromolecules or colloidal particles in the presence of salting-out conditions. A new model based on frictional coefficients between solvated solutes is reported. This model predicts that the Onsager cross-coefficient is negative and contributes significantly to cross-diffusion coefficients even at infinite dilution for solutes with a large difference in size. These predictions are consistent with recent experimental results. The role of preferential solvation and excludedvolume interactions on the thermodynamic factors are also examined. Excluded-volume interactions are introduced through the use of the McMillan-Mayer thermodynamic framework after emphasizing some important aspects of diffusion reference frames and thermodynamic driving forces. Finally, new expressions for cross-diffusion coefficients are proposed.

Amplification of Salt-Induced Polymer Diffusiophoresis by Increasing Salting-Out Strength

“…Since D 12 and D 21 are directly proportional to C 1 and C 2 , respectively, 58 and D 22 − D 11 ≈ D 22 can be roughly regarded as constant, the difference between D 11 and 1 increases with polymer and salt concentrations.…”

Theory of tracer diffusion in concentrated hard-sphere suspensions

“…Batchelor (1976Batchelor ( , 1983Batchelor ( , 1986 solved the hydrodynamic equations describing this system in the dilute limit and obtained expressions for the diffusion coefficients to first order in the particle volume fractions. Later researchers obtained similar results starting from the Smoluchowski and Fokker-Planck equations (Zhang & Nagele 2002;Bruna & Chapman 2012) or by using thermodynamic methods (Vergara et al 2001;Annunziata 2008), while recent efforts have employed Stokesian and molecular dynamics simulations (Wang & Brady 2015;Hannam et al 2017). In many 'crowded' systems the host particles are at non-dilute volume fractions near to and above the glass transition, where long-range viscous effects and nonlinear particle-particle interactions are predominant (Wang et al 2012;Guan et al 2014;Sent-jabrskaja1 et al 2016).…”

“…where k B is Boltzmann's constant, µ 0 i are constants (at constant T, P ) and b ij = (1+λ ij ) 3 (Annunziata 2008;Santos & Rorhmann 2013). Differentiating (2.7) with respect to n i gives…”

“…where Π T ≡ P − p w is the total osmotic pressure of the suspension. Equation (32) is a consequence of the analogy between hard-sphere fluids and hard-sphere suspensions, for which Π T plays the role of pressure (Batchelor 1983;Russel et al 1989;Annunziata 2008). The Gibbs-Duhem equation applied to the reservoir compartment B is…”

“…In (2.1) µ i = µ a i − v i µ a 0 /v 0 are effective (reduced) chemical potentials, where µ a i is the actual chemical potential per particle of component i (0 is the fluid, assumed incompressible, 1 is the host particles and 2 is the tracer particles), and v i = 4 3 πR 3 i is the volume of a particle of radius R i . When the suspending fluid is incompressible and composed of molecules that are much smaller than the hard-sphere particles, the reduced chemical potentials in a hard-sphere suspension are equivalent to the chemical potentials of a hard-sphere gas at the same volume fractions (Russel et al 1989;Batchelor 1983;Annunziata 2008).…”