(58c) Thermodynamic Modeling of Ion Adsorption in Capacitive Deionization Cell Units with Enrtl Model | AIChE

(58c) Thermodynamic Modeling of Ion Adsorption in Capacitive Deionization Cell Units with Enrtl Model


Yu, Y. - Presenter, Texas Tech University
Chen, C. C., Texas Tech University
Hossain, N., Texas Tech University
Capacitive deionization (CDI) is a technology to remove salts from low salinity brine solution with electrical cell units. The two electrodes in each cell unit adsorb opposite charged ions in the brine water when charged and release them when discharged. Modified Donnan’s theory has been used to model the electrical double layer surrounding electrodes. However, non-ideality of ions adsorbed to the electrodes has yet to be adequately accounted for. [1]

Our previous work established a thermodynamic model for polyelectrolyte solutions by extending Manning’s limiting law with eNRTL model representing short range interactions. For a polyion that has a charge density larger than a certain critical value, the counterions in the polyion solution are condensed on the surface of the polyion to reduce the charge density. Manning first described the limiting law for calculating counterion activity coefficients in polyelectrolyte solutions [2]. Our model extended the concentration range of salts so that it offers a comprehensive thermodynamic formulation to correlate and extrapolate thermodynamic behavior of all aqueous polyelectrolyte systems, including ion exchange membranes or resins.

The CDI units at equilibrium have the electrodes with counterions electrically attached to the surfaces. The scenario is very similar to the counterion condensation process of polyions. We apply the extended Manning’s model to explain the amount of adsorbed salt in a CDI unit. We consider the electrodes as polyions. The polyions and adsorbed ions form a separate phase separated from the bulk brine solution. This polyions phase is then treated as the polyelectrolyte-water binary.

The activity coefficient of counterions on electrodes is calculated with the extended Manning model. From the equality of chemical potential of solute NaCl in the bulk solution and in the electrode polyion phase, we relate concentrations of bulk solution, amount of adsorbed salt, and charge density of the electrodes. Both the sodium cation and chloride anion are considered as counterions because the two electrodes attract oppositely charged ions at the two ends.

Predictions of salt concentrations in the electrodes at different bulk solution concentrations are generated and compared with experimental data. Future works include investigating the relationship between the model parameters and the cell voltage and finding optimal working conditions for a given desired separation.


  1. P. M. Biesheuvel, et al., "Attractive forces in microporous carbon electrodes for capacitive deionization." Journal of solid state electrochemistry 18.5 (2014): 1365-1376.
  2. Gerald S. Manning, "Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties." The journal of chemical Physics 51.3 (1969): 924-933.