Reformulating the permselectivity‐conductivity tradeoff relation in ion‐exchange membranes

Polymer membranes used in separation applications exhibit a tradeoff between permeability and selectivity. That is, membranes that are highly permeable tend to have low selectivity and vice versa. For ion‐exchange membranes used in applications such as electrodialysis and reverse electrodialysis, this tradeoff is expressed in terms of membrane permselectivity (i.e., ability to selectively permeate counter‐ions over co‐ions) and ionic conductivity (i.e., ability to transport ions in the presence of an electric field). The use of membrane permselectivity and ionic conductivity to illustrate a tradeoff between counter‐ion throughput and counter‐ion/co‐ion selectivity in ion‐exchange membranes complicates the analysis since permselectivity depends on the properties of the external solution and ionic conductivity depends on the transport of all mobile ions within a membrane. Furthermore, the use of these parameters restricts the analysis to ion‐exchange membranes used in applications in which counter‐ion/co‐ion selectivity is required. In this study, the permselectivity‐conductivity tradeoff relation for ion‐exchange membranes is reformulated in terms of ion concentrations and diffusion coefficients in the membrane. The reformulated framework enables a direct comparison between counter‐ion throughput and counter‐ion/co‐ion selectivity and is general. The generalizability of the reformulated tradeoff relation is demonstrated for cation‐exchange membranes used in vanadium redox flow batteries.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/171020/1/pol20210304-sup-0001-Supinfo.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/171020/2/pola30065.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/171020/3/pola30065_am.pd