Performance Metrics for the Objective Assessment of Capacitive Deionization Systems

In the growing field of capacitive deionization (CDI), a number of performance metrics have emerged to describe the desalination process. Unfortunately, the separation conditions under which these metrics are measured are often not specified, resulting in optimal performance at minimal removal. Here we outline a system of performance metrics and reporting conditions that resolves this issue. Our proposed system is based on volumetric energy consumption (Wh/m$^3$) and throughput productivity (L/h/m$^2$) reported for a specific average concentration reduction, water recovery, and feed salinity. To facilitate and rationalize comparisons between devices, materials, and operation modes, we propose a nominal standard testing condition of removing 5 mM from a 20 mM NaCl feed solution at 50% water recovery for CDI research. Using this separation, we compare the desalination performance of a flow-through electrode (fte-CDI) cell and a flow between membrane (fb-MCDI) device, showing how significantly different systems can be compared in terms of generally desirable desalination characteristics. In general, we find that performance analysis must be considered carefully so to not allow for ambiguous separation conditions or the maximization of one metric at the expense of another. Additionally, for context we discuss a number of important underlying performance indicators and cell characteristics that are not performance measures in and of themselves but can be examined to better understand differences in performance

Thermodynamics of Ion Separation by Electrosorption

We present a simple, top-down approach for the calculation of minimum energy consumption of electrosorptive ion separation using variational form of the (Gibbs) free energy. We focus and expand on the case of electrostatic capacitive deionization (CDI), and the theoretical framework is independent of details of the double-layer charge distribution and is applicable to any thermodynamically consistent model, such as the Gouy-Chapman-Stern (GCS) and modified Donnan (mD) models. We demonstrate that, under certain assumptions, the minimum required electric work energy is indeed equivalent to the free energy of separation. Using the theory, we define the thermodynamic efficiency of CDI. We explore the thermodynamic efficiency of current experimental CDI systems and show that these are currently very low, less than 1% for most existing systems. We applied this knowledge and constructed and operated a CDI cell to show that judicious selection of the materials, geometry, and process parameters can be used to achieve a 9% thermodynamic efficiency (4.6 kT energy per removed ion). This relatively high value is, to our knowledge, by far the highest thermodynamic efficiency ever demonstrated for CDI. We hypothesize that efficiency can be further improved by further reduction of CDI cell series resistances and optimization of operational parameters

Theory of membrane capacitive deionization including the effect of the electrode pore space

Membrane capacitive deionization (MCDI) is a technology for water desalination based on applying an electrical field between two oppositely placed porous electrodes. Ions are removed from the water flowing through a channel in between the electrodes and are stored inside the electrodes. Ion-exchange membranes are placed in front of the electrodes allowing for counterion transfer from the channel into the electrode, while retaining the coions inside the electrode structure. We set up an extended theory for MCDI which includes in the description for the porous electrodes not only the electrostatic double layers (EDLs) formed inside the porous (carbon) particles, but also incorporates the role of the transport pathways in the electrode, i.e., the interparticle pore space. Because in MCDI the coions are inhibited from leaving the electrode region, the interparticle porosity becomes available as a reservoir to store salt, thereby increasing the total salt storage capacity of the porous electrode. A second advantage of MCDI is that during ion desorption (ion release) the voltage can be reversed. In that case the interparticle porosity can be depleted of counterions, thereby increasing the salt uptake capacity and rate in the next cycle. In this work, we compare both experimentally and theoretically adsorption/desorption cycles of MCDI for desorption at zero voltage as well as for reversed voltage, and compare with results for CDI. To describe the EDL-structure a novel modified Donnan model is proposed valid for small pores relative to the Debye length

Size-based ion selectivity of micropore electric double layers in capacitive deionization electrodes

Capacitive deionization (CDI) is a fast-emerging technology most commonly applied to brackish water desalination. In CDI, salt ions are removed from the feedwater and stored in electric double layers (EDLs) within micropores of electrically charged porous carbon electrodes. Recent experiments have demonstrated that CDI electrodes exhibit selective ion removal based on ion size, with the smaller ion being preferentially removed in the case of equal-valence ions. However, state-of-the-art CDI theory does not capture this observed selectivity, as it assumes volume-less point ions in the micropore EDLs. We here present a theory which includes multiple couterionic species, and relaxes the point ion assumption by incorporating ion volume exclusion interactions into a description of the micropore EDLs. The developed model is a coupled set of nonlinear algebraic equations which can be solved for micropore ion concentrations and electrode Donnan potential at cell equilibrium. We demonstrate that this model captures key features of the experimentally observed size-based ion selectivity of CDI electrodes

Overlimiting Current and Shock Electrodialysis in Porous Media

Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electro-osmotic flow also contribute to ionic fluxes. In this paper, we report experimental evidence for surface-driven over-limiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with 500 nm mean pore size) in an aqueous electrolyte (CuSO$_4$ or AgNO$_3$) passing ionic current from a reservoir to a cation-selective membrane (Nafion). The current-voltage relation of the whole system is consistent with a proposed theory based on the electro-osmotic flow mechanism over a broad range of reservoir salt concentrations (0.1 mM - 1.0 M), after accounting for (Cu) electrode polarization and pH-regulated silica charge. Above the limiting current, deionized water ($\approx 10 \mu$ $M$) can be continuously extracted from the frit, which implies the existence of a stable shock propagating against the flow, bordering a depleted region that extends more than 0.5mm across the outlet. The results suggest the feasibility of "shock electrodialysis" as a new approach to water desalination and other electrochemical separations.Comment: 39 pages, 9 fig

Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes

The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by super-capacitors, water desalination and purification by capacitive deionization (or desalination), and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory in the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) In the "super-capacitor regime" of small voltages and/or early times where the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore. (ii) In the "desalination regime" of large voltages and long times, the porous electrode slowly adsorbs neutral salt, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration