Surface Specific Mixing Rule for Ionic Diffusion Coefficients at Infinite Dilution in Polymer/Water Mixtures

Abstract

It has recently been shown that the viscosity of polymer/water mixtures can be accurately predicted with an ideal linear mixing rule based on molecular van der Waals surfaces. Because of the Stokes-Einstein relation, a similar mixing rule may also be applicable to ionic diffusion coefficients at infinite dilution in polymer/water mixtures. This assumption is confirmed for the example system KDP/polyol/water at various temperatures. Moreover, the impact on electrolyte concentration is calculated and shows that the surface-based mixing rule can also be used as a good approximation for the ionic diffusion coefficient for finite electrolyte concentrations. IntroductionDiffusion of ions through a solution is a complicated process since long-range coulomb forces, electrophoresis and dissociation have to be additionally considered when compared to diffusion of uncharged molecules. Circumstances become highly complicated when the aqueous solution contains organic or, even worse, polymer admixtures which affect dielectricity, viscosity and ion dissociation. However, at infinite dilution, ions can be treated like molecular species. In this case, diffusion of molecules or ions may be treated like macroscopic particles within the framework of the Stokes law and a direct relation to viscosity is given according to the Stokes-Einstein equation [1] 1) :In a recent paper, linear ideal mixing rules for calculating mixture viscosities for binary mixtures containing polyol (index 2) and water (index 1) have been discussed. From Eyrings theory [2] the following mixing rule based on segment fractions n t was derived [3]: lng = lng 1 (1 -n t,2 ) + ln g 2 n t,2Van der Waals (VdW) surface fractions n q have been shown to be a good approximation for the segment fractions n t which can currently only be derived from experiments for complex polymers like polyols [3]. This way, viscosities of several binary mixtures containing different polyols with water could be reliably calculated with this entirely predictive VdW surface-based mixing rule [4]. Eq. (1) is equivalent to:A similar mixing rule may therefore also be applicable to ionic diffusion coefficients at infinite dilution:whereThe VdW molecular surfaces for any kind of organic species can be approximated from functional group contributions published elsewhere [5].This work focuses on an example electrolyte system containing potassium dihydrogen phosphate (KDP), water and a polyol admixture. Diffusion coefficients at infinite dilution are calculated from experimental limiting equivalent conductivities and compared to Eq. (4). The impact of electrolyte content on the ionic diffusion coefficient up to saturation is calculated from a rigorous physical model in order to assess deviations from Eq. (4) for finite electrolyte concentrations. -1) List of symbols at the end of the paper.