(516h) Thermodynamic Modeling of Electrodes and Mobile Ions in Capacitive Deionization Cell Units with Enrtl Model

Capacitive deionization (CDI) is a technology to purify brine water of low concentration with cell units. The two electrodes in classical CDI unit attract opposite charged ions in the brine water when charged and release them when discharged. Using electrodes modified with immobile chemical charge, inverted CDI units take in ions when not charged while release them during charging. Biesheuvel et al. put forward a dynamic model of the electrical double layer and electrodes, however, thermodynamic activity of ions in the electrodes was not considered. [1,2]

We have established a thermodynamic framework for polyelectrolyte solutions by introducing Manning’s limiting law to the eNRTL model. For a polyion that has a charge density larger than certain critical value, the counterions in the polyion solution will condense on the surface of the polyion to reduce the charge density. The degree of the condensation is positively related to the charge density of the polyion. Manning first described the counterion condensation phenomenon by integration of the potential between mobile ions and polyions as the limiting law. [3] The eNRTL short-range equations are used to describe the interactions between particles in their immediate neighborhood. [4] Our model is a comprehensive one that works not only in the limiting case but also any multi-component system containing polyelectrolytes with high accuracy, including ion exchange membranes and resins.

The classical and inverted CDI units at equilibrium have the electrodes with counterions electrically or chemically attached to the surfaces. The scenario is very similar to the counterion condensation process of polyions. We are applying our thermodynamic framework to calculate the equilibrium adsorption capacity of CDI systems. Consider the electrodes and attached ions as polyions. The polyions form separate phases from the bulk simple salt solution. These polyions phases can be treated as the polyelectrolyte-water binary cases.

By equality of chemical potential of solute (NaCl) in the bulk solution and the electrode phase, we have

m_Na^-bulkγ_Na^+bulkm_Cl^-bulkγ_Cl^+bulk=m_{Na^-electrode}γ_{Na^+electrode}m_{Cl^-electrode}γ_{Cl^+electrode}

where m is the molality of species; γ is the activity coefficient.

With this equation, we are able to relate concentrations of bulk solution, amount of adsorbed salt and charge density of the electrodes. The activity coefficients in the bulk solution can be calculated with the original eNRTL model while the ones in the electrode phase need to be computed with the eNRTL model modified with Manning’s limiting law to account for the “point-to-line” electrostatic potential. In the electrode phase, the two types of ions are both considered as counterions since oppositely charged ions are attracted at the two electrodes. Equilibrium salt adsorption and cell voltage data are used to fit the charge density of the electrodes as the parameter in Manning’s limiting law. The short-range interaction parameters between water and the charged segments on the electrodes also need to be regressed from data.

Modeling results show that higher charge density on the electrode will improve the performance of CDI units. We are also interested in the relationship between the cell voltage and the polyion charge density value, and finding the working condition of the best performance given certain brine concentration.

Reference

1. Biesheuvel, P. M., et al. "Attractive forces in microporous carbon electrodes for capacitive deionization." Journal of solid state electrochemistry 18.5 (2014): 1365-1376.
2. Biesheuvel, P. M., H. V. M. Hamelers, and M. E. Suss. "Theory of water desalination by porous electrodes with immobile chemical charge." Colloids and Interface Science Communications 9 (2015): 1-5.
3. Manning, Gerald S. "Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties." The journal of chemical Physics 51.3 (1969): 924-933.
4. Song, Yuhua, and Chau-Chyun Chen. "Symmetric electrolyte nonrandom two-liquid activity coefficient model." Industrial & Engineering Chemistry Research 48.16 (2009): 7788-7797.