Comment on: "Na-Ion Desalination (NID) Enabled by Na-Blocking Membranes and Symmetric Na-Intercalation: Porous-Electrode Modeling" [J. Electrochem. Soc., 163, A530 (2016)]

In the original paper a uniform, one-dimensional superficial velocity u_s was used to model the flow of electrolyte through porous electrodes. Pore-scale mean velocities were also reported for several different current and flow conditions. The values presented for each of these parameters were correct, but the relationship between the pore-scale mean velocity and the superficial velocity was stated incorrectly as "the product of porosity and superficial velocity." Pore-scale mean velocity is equal to superficial velocity divided by porosity, not multiplied by it.

Numerical predictions for several limiting cases were compared to analytical models for validation. The analytical expression predicted by Faraday's Law for the average effluent concentration of a membrane-based cell with superficial velocity u_s contained an erroneous factor of electrode porosity ε shown. The correct expression takes the following form: , where cⁱⁿ_e, i, L, w, and F are the inlet concentration, space-averaged applied current-density, current-collector length, electrode thickness, and Faraday's constant, respectively. Numerical predictions were compared with the correct expression for average effluent concentration, and, thus, no corrections of the results presented are required.

The energy consumed per unit volume of desalinated water E_d was defined with an erroneous factor of electrode porosity ε shown. The correct expression takes the following form: , where L, V_cell, i, u_s,d, w, and Δt are the current-collector length, cell voltage at time t, space-averaged applied current density, superficial velocity in the desalinating electrode, electrode thickness, and the total elapsed time for the desalination process, respectively. The correct expression was used to obtain all values of energy consumption presented in the original paper, and, thus, this error has no impact on the original results.

The equations for the membrane potential of an anion-exchange membrane were written with two sign errors in the original paper (p. A532). We emphasize here that the electrostatic potential ϕ_ES and the solution-phase potential ϕ_e are different quantities. The electrostatic potential ϕ_ES is defined as the reduced electric potential in the solution, while the solution-phase potential ϕ_e is defined as the reduced electrochemical potential of Na⁺ in solution.¹ The corrected electrostatic potential drop across a membrane with ideal anion permselectivity is expressed for NaCl electrolyte with unit activity coefficients as (Ref. 2, p. 375),

We note that the membrane-potential model presented in the reference originally cited³ reproduces this potential drop in the limit of high ion-exchanger capacity. As described in our original paper, membrane polarization can also be addressed in terms of the solution-phase potential ϕ_e according to its definition as the reduced electrochemical potential of Na⁺,¹

Solving Eq. 2 for ϕ_ES and substituting into Eq. 1 we find the correct expression for solution-phase potential drop across the membrane,

The correct expressions were implemented in the original model, and, thus, these corrections do not impact the original results.

Throughout the paper, the term "intercalant" was used inaccurately to describe intercalation host compounds, when in fact "intercalant" refers to the species undergoing intercalation (which was Na⁺ in the modeled device). In addition, the terms "cathode" and "anode" were used, respectively, to refer to the positive and negative terminals across which cell voltage was measured. This is conventional nomenclature used in the rechargeable Li-ion and Na-ion battery communities, but, strictly speaking, these designations are consistent with the defintions of cathodic and anodic processes only during cell discharging (i.e., when current flows from the negative to the positive electrode) and not during cell charging. Finally, in several instances the terms "charge cycle," "discharge cycle," and "charging cycle" were used to describe either a charge or discharge step in a complete charge/discharge cycle. In these respective instances the correct terminology is "charge process," "discharge process," and "charging process."