Thermodynamic cycle analysis for capacitive deionization.

Capacitive deionization (CDI) is an ion removal technology based on temporarily storing ions in the polarization layers of two oppositely positioned electrodes. Here we present a thermodynamic model for the minimum work required for ion separation in the fully reversible case by describing the ionic solution as an ideal gas of pointlike particles. The work input is fully utilized to decrease the entropy of the outflowing streams compared to that of the inflow. Based on the Gouy-Chapman-Stern (GCS) model for planar diffuse polarization layers-with and without including additional ion volume constraints in the diffuse part of the double layer-we analyze the electric work input during charging and the work output during discharging, for a reversible charging-discharging cycle. We present a graphical thermodynamic cycle analysis for the reversible net work input during one full cycle of batchwise operation of CDI based on the charge-voltage relations for different ionic strengths. For the GCS model, an analytical solution is derived for the charge efficiency Lambda, which is the number of salt molecules removed per electron transferred from one electrode to the other. Only in the high voltage limit and for an infinite Stern layer capacity does Lambda approach unity.