Two-Dimensional Porous Electrode Model for Capacitive Deionization

Ion transport in porous conductive materials is of great importance in a variety of electrochemical systems including batteries and supercapacitors. We here analyze the coupling of flow and charge transport and charge capacitance in capacitive deionization (CDI). In CDI, a pair of porous carbon electrodes is employed to electrostatically retain and remove ionic species from aqueous solutions. We here develop and solve a novel unsteady two-dimensional model for capturing the ion adsorption/desorption dynamics in a flow-between CDI system. We use this model to study the complex, nonlinear coupling between electromigration, diffusion, and advection of ions. We also fabricated a laboratory-scale CDI cell which we use to measure the near-equilibrium, cumulative adsorbed salt, and electric charge as a function of applied external voltage. We use these integral measures to validate and calibrate this model. We further present a detailed computational study of the spatiotemporal adsorption/desorption dynamics und...

[1]  Volker Presser,et al.  Water desalination via capacitive deionization : What is it and what can we expect from it? , 2015 .

[2]  P. M. Biesheuvel,et al.  Water desalination using capacitive deionization with microporous carbon electrodes. , 2012, ACS applied materials & interfaces.

[3]  P. M. Biesheuvel,et al.  A prototype cell for extracting energy from a water salinity difference by means of double layer expansion in nanoporous carbon electrodes , 2011 .

[4]  M. Bazant,et al.  Electro-diffusion of ions in porous electrodes for capacitive extraction of renewable energy from salinity differences , 2013 .

[5]  P. Długołęcki,et al.  Energy recovery in membrane capacitive deionization. , 2013, Environmental science & technology.

[6]  Hubertus V. M. Hamelers,et al.  Capacitive bioanodes enable renewable energy storage in microbial fuel cells. , 2012, Environmental science & technology.

[7]  P. M. Biesheuvel,et al.  Carbon nanotube yarns as strong flexible conductive capacitive electrodes , 2014 .

[8]  John Newman,et al.  Desalting by Means of Porous Carbon Electrodes , 1971 .

[9]  Onur N. Demirer,et al.  Characterization of Ion Transport and -Sorption in a Carbon Based Porous Electrode for Desalination Purposes , 2013 .

[10]  Peng Liang,et al.  Capacitive deionization coupled with microbial fuel cells to desalinate low-concentration salt water. , 2012, Bioresource technology.

[11]  Y. Jande,et al.  Modeling the capacitive deionization batch mode operation for desalination , 2014 .

[12]  T. Baumann,et al.  Impedance-based study of capacitive porous carbon electrodes with hierarchical and bimodal porosity , 2013 .

[13]  Seung M. Oh,et al.  Complex capacitance analysis on rate capability of electric-double layer capacitor (EDLC) electrodes of different thickness , 2005 .

[14]  Doron Aurbach,et al.  The effect of the flow-regime, reversal of polarization, and oxygen on the long term stability in capacitive de-ionization processes , 2015 .

[15]  Harold L. Weissberg,et al.  Effective Diffusion Coefficient in Porous Media , 1963 .

[16]  H. Gerischer,et al.  Density of the electronic states of graphite: derivation from differential capacitance measurements , 1987 .

[17]  Karel J. Keesman,et al.  Direct prediction of the desalination performance of porous carbon electrodes for capacitive deionization , 2013 .

[18]  R. J. Hunter Zeta potential in colloid science : principles and applications , 1981 .

[19]  F. Béguin,et al.  Saturation of subnanometer pores in an electric double-layer capacitor , 2009 .

[20]  P. M. Biesheuvel,et al.  Membrane capacitive deionization , 2010 .

[21]  R. D. Levie,et al.  On porous electrodes in electrolyte solutions—IV , 1963 .

[22]  H. Hamelers,et al.  CAPMIX -Deploying Capacitors for Salt Gradient Power Extraction , 2012 .

[23]  R. D. Levie,et al.  On porous electrodes in electrolyte solutions: I. Capacitance effects☆ , 1963 .

[24]  C. Tsouris,et al.  Volume Averaging Study of the Capacitive Deionization Process in Homogeneous Porous Media , 2015, Transport in Porous Media.

[25]  Onur N. Demirer,et al.  Energetic performance optimization of a capacitive deionization system operating with transient cycles and brackish water , 2013 .

[26]  Volker Presser,et al.  Carbon flow electrodes for continuous operation of capacitive deionization and capacitive mixing energy generation , 2014 .

[27]  Jeyong Yoon,et al.  Comparison of salt adsorption capacity and energy consumption between constant current and constant voltage operation in capacitive deionization , 2014 .

[28]  G. W. Murphy,et al.  Mathematical theory of electrochemical demineralization in flowing systems , 1967 .

[29]  P. M. Biesheuvel,et al.  In situ spatially and temporally resolved measurements of salt concentration between charging porous electrodes for desalination by capacitive deionization. , 2014, Environmental science & technology.

[30]  P. M. Biesheuvel,et al.  Theory of water desalination by porous electrodes with fixed chemical charge , 2015 .

[31]  P. M. Biesheuvel,et al.  Electrochemistry and capacitive charging of porous electrodes in asymmetric multicomponent electrolytes , 2012, Russian Journal of Electrochemistry.

[32]  Ned Djilali,et al.  Determination of the effective diffusion coefficient in porous media including Knudsen effects , 2008 .

[33]  Meryl D. Stoller,et al.  Review of Best Practice Methods for Determining an Electrode Material's Performance for Ultracapacitors , 2010 .

[34]  P. M. Biesheuvel,et al.  Diffuse charge and Faradaic reactions in porous electrodes. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  John Newman,et al.  Predictions of Specific Energies and Specific Powers of Double‐Layer Capacitors Using a Simplified Model , 2000 .

[36]  C. Huang,et al.  The adsorption of heavy metals onto hydrous activated carbon , 1987 .

[37]  Zhong‐sheng Liu,et al.  Effective transport coefficients in PEM fuel cell catalyst and gas diffusion layers: Beyond Bruggeman approximation , 2010 .

[38]  P. M. Biesheuvel,et al.  Enhanced charge efficiency and reduced energy use in capacitive deionization by increasing the discharge voltage. , 2015, Journal of colloid and interface science.

[39]  Y. Oren,et al.  Capacitive deionization (CDI) for desalination and water treatment — past, present and future (a review) , 2008 .

[40]  R. Brown,et al.  Adsorption of arsenic(V) by activated carbon prepared from oat hulls. , 2005, Chemosphere.

[41]  Doron Aurbach,et al.  A control system for operating and investigating reactors: The demonstration of parasitic reactions in the water desalination by capacitive de-ionization , 2011 .

[42]  Y. Oren,et al.  Water desalting by means of electrochemical parametric pumping , 1983 .

[43]  P. M. Biesheuvel,et al.  Theory of membrane capacitive deionization including the effect of the electrode pore space. , 2011, Journal of colloid and interface science.

[44]  P. M. Biesheuvel,et al.  Energy consumption and constant current operation in membrane capacitive deionization , 2012 .

[45]  Onur N. Demirer,et al.  Macro Analysis of the Electro-Adsorption Process in Low Concentration NaCl Solutions for Water Desalination Applications , 2013 .

[46]  H. Gerischer,et al.  An interpretation of the double layer capacity of graphite electrodes in relation to the density of states at the Fermi level , 1985 .

[47]  B. Kastening,et al.  Properties of electrolytes in the micropores of activated carbon , 2005 .

[48]  Jae-Hwan Choi,et al.  Determination of the electrode potential causing Faradaic reactions in membrane capacitive deionization , 2014 .

[49]  P. M. Biesheuvel,et al.  Charge Efficiency: A Functional Tool to Probe the Double-Layer Structure Inside of Porous Electrodes and Application in the Modeling of Capacitive Deionization , 2010 .

[50]  Mohammad Mirzadeh,et al.  Enhanced charging kinetics of porous electrodes: surface conduction as a short-circuit mechanism. , 2014, Physical review letters.

[51]  Y. Gogotsi,et al.  Materials for electrochemical capacitors. , 2008, Nature materials.

[52]  Wendy G. Pell,et al.  Analysis of power limitations at porous supercapacitor electrodes under cyclic voltammetry modulation and dc charge , 2001 .

[53]  D. Aurbach,et al.  Several basic and practical aspects related to electrochemical deionization of water , 2009 .

[54]  Heidelberg,et al.  Attractive forces in microporous carbon electrodes for capacitive deionization , 2013, Journal of Solid State Electrochemistry.

[55]  P. M. Biesheuvel,et al.  Thermodynamic cycle analysis for capacitive deionization. , 2009, Journal of colloid and interface science.

[56]  Moon Hee Han,et al.  Desalination via a new membrane capacitive deionization process utilizing flow-electrodes , 2013 .

[57]  A. Kornyshev,et al.  Optimized Structure of Nanoporous Carbon-Based Double-Layer Capacitors , 2005 .

[58]  Laurent Pilon,et al.  Accurate Simulations of Electric Double Layer Capacitance of Ultramicroelectrodes , 2011 .

[59]  Volker Presser,et al.  Review on the science and technology of water desalination by capacitive deionization , 2013 .

[60]  P. M. Biesheuvel,et al.  Dynamic Adsorption/Desorption Process Model for Capacitive Deionization , 2009 .

[61]  Juan G. Santiago,et al.  Capacitive desalination with flow-through electrodes , 2012 .

[62]  D. Aurbach,et al.  Assessing the Solvation Numbers of Electrolytic Ions Confined in Carbon Nanopores under Dynamic Charging Conditions. , 2011, The journal of physical chemistry letters.

[63]  B. Conway,et al.  Analysis of non-uniform charge/discharge and rate effects in porous carbon capacitors containing sub-optimal electrolyte concentrations , 2000 .

[64]  T. Baumann,et al.  Characterization of Resistances of a Capacitive Deionization System. , 2015, Environmental science & technology.

[65]  J. Newman,et al.  Porous‐electrode theory with battery applications , 1975 .

[66]  Wayne Moore,et al.  Effect of Pore Structure, Randomness and Size on Effective Mass Diffusivity , 2002 .

[67]  P. M. Biesheuvel,et al.  Optimization of salt adsorption rate in membrane capacitive deionization. , 2013, Water research.

[68]  T. Hirokawa,et al.  Isotachophoretic determination of mobility and pKa by means of computer simulation. V. Evaluation of mo and pKa of twenty-eight dipeptides and assessment of separability. , 1987, Journal of chromatography.

[69]  P. M. Biesheuvel,et al.  Nonlinear dynamics of capacitive charging and desalination by porous electrodes. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  T. Hirokawa,et al.  Isotachophoretic determination of mobility and pKa by means of computer simulation. IV. Evaluation of m0 and pKa of twenty-six amino acids and assessment of the separability. , 1986, Journal of chromatography.

[71]  P. M. Heertjes,et al.  Analysis of diffusion in macroporous media in terms of a porosity, a tortuosity and a constrictivity factor , 1974 .

[72]  T. Yagi,et al.  Table of isotachophoretic indices : I. Simulated qualitative and quantitative indices of 287 anionic substances in the range ph 3–10 , 1983 .