Effect of Solvent Motion on Ion Transport in Electrolytes

Abstract

We use concentrated solution theory to derive an equation governing solvent velocity in a binary electrolyte when a current passes through it. This equation, in combination with the material balance equation, enables the prediction of electrolyte concentration profiles and species velocities as a function of space and time. This framework is used to predict ion velocities in Li-Li symmetric cells containing a mixture of lithium bis(trifluoromethanesulfonyl)imide and poly(ethylene oxide) (LiTFSI/PEO), for which the cation transference number relative to the solvent velocity, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>,</mml:mo> </mml:math> can be either positive or negative, depending on salt concentration. Accounting for the solvent motion is increasingly important at higher concentrations. Especially for negative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>,</mml:mo> </mml:math> if solvent velocity is set to zero, the cation velocity, based on the electrode-electrolyte interface reference frame, is pointed opposite to the current flow. However, when solvent motion is taken into account, the cation velocity, based on the same reference frame, is in the same direction as the current. This analysis demonstrates the importance of accounting for solvent velocity rigorously in seemingly simple systems such as symmetric cells.