Electrosorption Driven Ion Separation Jorge Gabitto, Costas Tsouris To cite this version: Jorge Gabitto, Costas Tsouris. Electrosorption Driven Ion Separation. 2018. ฀hal-01966598฀ HAL Id: hal-01966598 https://hal.science/hal-01966598 Preprint submitted on 28 Dec 2018 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Electrosorption Driven Ion Separation Jorge Gabitto1* and Costas Tsouris2 1 Department of Chemical Engineering Prairie View A&M University Prairie View, TX 77446 2 Oak Ridge National Laboratory Oak Ridge TN 37831-6181 *Correspondence: jgabitto@aol.com, (936) 261-9409 ABSTRACT The difference in electrosorption capacity of ions of different size, charge, and physical properties can be used for designing a successful electrochemical separation process. In order to properly design such a process, we need a better understanding of the corresponding ion transport processes. Removal of heavy ions from waste streams, for example, is a process where understanding of ion transport is very important. Most theoretical studies available in the literature apply only to symmetric, binary electrolytes. In this work, a model providing the individual ion concentration profiles inside porous electrodes is used to simulate ion transport processes. The model also allows for the calculation of the transport parameters in isotropic porous media. The results calculated using this model are combined with experimental data and 1 literature information to investigate the effect of ion size, charge, and transport parameters on the separation effectiveness. KEYWORDS: electrosorption, heavy ions, charge, size INTRODUCTION Electrosorption, defined as potential-induced adsorption, is an important process taking place in many physical, chemical, and biological systems (Hou et al., 2008). In the case of ion exchange and membrane separation processes, molecular size determines that the larger multivalent ions are more effectively removed than the smaller ones (Gabelich et al., 2002). Early work by Johnson and Newman (1971) using porous carbon electrodes demonstrated preferential electrosorption of divalent ions from mixtures of ions. However, Gabelich et al. (2002), studying the electrosorption capacity of carbon aerogel electrodes, concluded that when multiple ions of varying valences are present, the preferential sorption of the divalent species is limited. Therefore, the authors concluded that this matter required further research and development before this technology could be successfully applied. Taboada-Serrano et al. (2005) used Canonical Monte Carlo (CMC) simulations to study the structure of the electrical double layer (EDL) near discretely charged planar surfaces in the presence of symmetric and asymmetric electrolytes. The authors studied the effects of discrete ion size, strength of surface charge,and charge asymmetry. Taboada-Serrano et al. (2005) reported that the CMC simulation results and the predictions of the classical theory show good agreement for 1:1 electrolytes and low surface charge, at which conditions the Gouy-Chapman model is valid. The authors reported that size plays an important role in determining the species present in the EDL. It was also found that smaller ions with lower valences perform the 2 screening of the charge, resulting in higher local concentrations of small ions close to the surface. Hou et al. (2008) used Grand Canonical Monte Carlo simulations to study the selective electrosorption of ions from a mixture of symmetric and asymmetric electrolytes confined in nanopores. These authors employed the exclusion parameter and selectivity factor to evaluate the selective capacity of pores toward different ionic species under various conditions, and identified the ion charge and effective size as the most important parameters influencing ionic selectivity. The authors reported that, due to asymmetries in charge and size, the electrosorption selectivity of small monovalent over large divalent counterions first decreases with increasing surface charge, passes through a minimum, and then increases with further increase in surface charge. Therefore, electrosorption selectivity of ions from a mixture of electrolytes could be achieved by tuning the operating variables of the process to the different ion properties. Zhao et al. (2012) studied experimentally and theoretically ion selectivity of the electrical double layer (EDL) formation in porous carbon electrodes. The authors concluded that capacitive charging of porous electrodes in multicomponent electrolytes may lead to the phenomenon of time-dependent ion selectivity of the electrical double layers (EDLs) in the electrodes. Zhao et al. (2012) experimentally found that, in experiments on capacitive deionization of water containing 5:1 NaCl/CaCl2 mixtures, first the majority of monovalent Na+ cations are preferentially adsorbed in the EDLs, and later, they are gradually replaced by the minority, divalent Ca 2+ cations. A nonlinear time-dependent analysis of capacitive charging was performed for both porous and flat electrodes. The authors attributed time-dependent ion selectivity to the interplay between the transport resistance for the ions in the aqueous solution outside the EDL and the voltage-dependent ion adsorption capacity of the EDLs. 3 Most studies of ion transport in porous media have been carried out using the assumption of binary, symmetric electrolytes (Bazant et al., 2004; Chu and Bazant, 2007; Biesheuvel and Bazant, 2010, Gabitto and Tsouris, 2015 and 2016; among others). This assumption leads to a single equation for the salt concentration instead of dealing with several equations for multiple ions of different charges and diffusivities (mobilities). Biesheuvel at al. (2012) presented a porous electrode theory for the general situation of electrolytes containing mixtures of mobile ions of arbitrary charges and diffusion coefficients. The authors focused on porous electrodes comprising solid particles that are porous themselves, and proposed that the macropores operate as transport pathways, while the ionic species are stored inside the micropores. The potential and ion concentrations between the macro and microscales are related by a modified Donnan model. This phenomenological formulation led to a set of individual ion concentrations plus equations to calculate ion charges and potentials. Schmuck and Bazant (2014) derived effective PoissonNernst-Planck (PNP) equations for macroscopic ion transport in charged porous media, and performed a homogenization analysis of a two-component periodic porous medium consisting of a dilute electrolyte and a continuous dielectric matrix impermeable to the ions and carrying a given surface charge. The transport coefficients in the macroscopic PNP equations were calculated from periodic reference cell problems. Sharma et al. (2015) studied desalination of high-salinity solutions using a neutron imaging experimental technique and a theoretical model. The authors presented a new model that computes the individual ion concentration profiles inside carbon electrodes to simulate the CDI process. This theoretical model can be used to simulate ion transport inside pores of any size, from macro to micropores. As part of the volume averaging technique used by Sharma et al. (2015) the effective transport parameters in isotropic porous media can be calculated. 4 Chen et al. (2015) studied the capacitive deionization (CDI) performance of activated carbon electrodes and competitive electrosorption of various anions, and found that the electrosorption capacity was strongly dependent on the ion charge and hydrated radius. The order of normalized equivalent capacity show trivalent anion > divalent anion > monovalent anion. Li et al. (2016) found that the hydration ratio, i.e., the ratio of hydrated radius to ion radius, significantly affects the electrosorption capacity and selectivity. The hydration ratio and valence affect the ions’ electrostatic attraction to the electrodes, determining the electrosorption capacity and selectivity of ions in capacitive deionization. The authors reported that monovalent ions absorbed first to be displaced at longer times by ions with smaller hydration ratio or higher valence. The goal of the present research is to study ionic competition inside charged porous media. A modified version of the model presented by Sharma et al. (2015) plus experimental data and theoretical results taken from the literature are used to determine the effects of ion size, charge, and operating conditions on ion selectivity. The closure problem derivation, which was omitted in the Sharma et al. (2015) article is presented along with the solution of the closure problem. THEORETICAL SECTION Closed Equations Section Potential Using a volume averaging technique (Whitaker, 1999), Sharma et al. (2015) derived the following equation for the electrostatic potential:   {    }  av     F   z i ci   eff i 5 (1) Here, ci is the ion concentration,  is the nabla operator, zi is the ion charge, av is the specific area ( A /V), A is the interface area between the solid (-phase) and the liquid (-phase), V is the representative elementary volume (REV), is the volume fraction given explicitly by  = V /V with V the liquid-phase volume inside the REV, F is the Faraday constant, and  is the electrostatic potential in the pores. The ion concentration intrinsic phase average ci is given by:  ci    1 ci dV V V (2) The effective permittivity tensor (  eff    (1  1 V ) can be expressed as: eff  n gdA) , (3) A where n is the normal vector pointing from the phase into the phase, and  is the permittivity of the electrolyte. The average surface charge density    is defined as:   αβ  1   dA Aαβ A (4) αβ Sharma et al. (2015) solved the corresponding potential closure problem (Whitaker, 1999) to calculate the g vector field and evaluate the effective permittivity tensor ( ) using eq. (3). eff Species Concentration Sharma et al. (2015) derived the following closed equation for the species concentrations:    ci      D i ,eff  ci    z i U i ,eff  ci      t 6  (5) Here,  is the dimensionless potential (=  F/ R /T), R is the gas constant, T is temperature, and Di is the diffusion coefficient of ionic species i. The effective diffusivity tensor ( D eff ) and the effective mobility tensor ( U eff ) are given, respectively, by:  D i ,eff  Di   ( I   U i ,eff  Di   ( I  1 V 1 V  n f dA) , (6)  n gdA) . (7) A A Sharma et al. (2015) solved the corresponding species concentration closure problem (Whitaker, 1999) to calculate the f vector field and evaluate the effective diffusivity tensor ( D eff ) using eq. (6). RESULTS Ion charge and size are the two most important properties determining electrosorption selectivity. The effect of ion size is represented by an effective ion size given by the value of the hydrated ion radius, not by the actual ion radius (Gabelich et al., 2002; Taboada-Serrano et al. (2005); Hou et al., 2008; Zhao et al., 2012; and Li et. al., 2016). The simulation results of Taboada-Serrano et al. (2005) showed that the hydrated radius ( rH ) significantly affects the electrosorption capacity and ion slecivity. Experimental data from Li et al. (2016) showed that in a mono-ionic solution, ions with low hydrated radius exhibit high electrosorption capacities. The authors also reported that in a multi-ionic solution, tri- and divalent ions adsorb more easily inside the electrode pores than monovalent ions do, resulting in increased electrosorption selectivity. In Table I, we include a list of ionic properties relevant to the calculations performed in this work. 7 Table I. Ionic Properties Ion Radius Hydrated Radius Diffusivity (×10-10m)1 (×10-10 m)1 (× 10-9 m2/s)2 H+ 1.2 9.0 9.31 Na+ 1.2 3.6 1.33 Li+ 0.9 6.0 1.03 K+ 1.6 3.3 1.96 NH4+ 1.5 3.3 1.98 Ca2+ 1.0 4.1 0.79 Cu2+ 0.6 6.0 0.73 Mg2+ 0.7 8.0 0.71 Ni2+ 1.0 6.0 0.68 La3+ 2.0 9.0 0.62 Fe3+ 1.0 9.0 0.61 Cr3+ 0.6 9.0 0.59 Al3+ 0.8 9.0 0.56 Cl- 1.9 3.3 2.03 Br- 2.0 3.3 2.01 I- 2.1 3.0 2.00 NO3- 1.8 3.4 1.91 OH- 1.3 3.0 1.73 8 HCO3- --- 3.8 1.18 MnO4- --- 4.5 0.99 SO42- 2.9 3.8 1.07 PO43- --- 4.0 1.00 CO32- --- 4.5 0.96 1 from Kielland (1937), Conway (1981), and Nightingale (1959) 2 from Lerman (1979), Samson et al. (2003), and Li et al. (2016) The model used in this work is based on the continuum approximation; therefore, we cannot directly determine the effect of effective ion size. The concept that ionic diffusivity is related to the hydrated radius, however, is a logical one. In this work we assume the hydrated radius to be representative of the effective ion size in dilute electrolyte solutions. This assumption is verified by plotting the values of infinite dilution diffusivities versus hydrated radius. The following empirical correlation can be calculated by curve-fitting: Di  0.3776  rH rH  2.6806 (8). In Figure 1, we include the data shown in Table I, except for H+ and OH-. The results in Figure 2 show that there is a strong correlation between ionic diffusivity and hydrated radius. 9 2.5 y = 1.0073x R² = 0.9683 Dcalc (m2/s x 10-9 2 1.5 1 0.5 0 0 0.5 1 1.5 Dexp (m2/s x 10-9) 2 2.5 Figure 1. Relationship between diffusion coefficient and hydrated radius. This approach is not valid for very small pores where the hydrated radius and the pore diameter are comparable (Hou et al., 2008). The highest hydrated radius values used in this work are approximately 9×10-10 m; therefore, the diffusivity will represent acceptably ionic size for pores larger than 10-8 m. The experimental data and simulation results from Hou et al. (2008) support this conclusion. The results reported by Sharma et al. (2015) showed that the effective diffusivity is a function of the electrode geometrical properties and the charge density. Jardat et al. (2017) in a study using Brownian dynamics simulations reported similar conclusions. In the next sections, we study the effect of charge and size on ion selectivity. Charge In a mixture of several electrolytes, the selectivity factor ( ) and the exclusion parameter () can be used to characterize the electrosorption behavior of counterions and coions, respectively (Hou et al., 2008). 10  ci / c j , (23) cio  ci .  cio (24) cio / c oj Here, c i and c j represent the average concentrations of ions i and j inside the electrode, cio and c 0j are the concentrations of ions i and j in the external solution. The effect of ionic charge is shown in Figures 2, 3, and 4. For the calculations used in these figures, we used a porous electrode with a void fraction ( ) equal to 0.5, specific surface area (av) equal to 2×108 (m-1), corresponding to mesopores with diameter equal to 10 -8 m. The dimensionless time is given by t/tc, with t c  L2e / Do equal to 1000 s. Le is the electrode thickness assumed equal to 0.001 m, and Do is a reference diffusivity equal to 1×10-9 m2/s. In Figure 3, we plot the time variation of ion selectivity factor for mixtures of 1-2 (NaClCaCl2), 1-3 (NaCl-AlCl3), and 2-3 (CaCl2-AlCl3) valence cations. In all cases, Cl- was the anion and the selectivity was calculated using the higher valence cation in the numerator of eq. (23), e.g., selectivity for the 1-2 mixture represents the selectivity of the +2 ion, 2-3 is the selectivity of the +3 ion, etc. 11 5 Selectivity, a (dimensionless) 4.5 4 3.5 3 2.5 2 1.5 1 Na/Ca/Cl 0.5 Na/Al/Cl Ca/Al/Cl 0.6 0.8 0 0 0.2 0.4 1 Time (dimensionless) Figure 2. Time variation of the selectivity for several ionic mixtures. In Figure 2, we can see that the selectivity of the highest charged counterion increases continuously with time. There is a higher increase during the supercapacitor regime (short times) than during the desalination regime (long times). The selectivity is higher for trivalent counterions than for divalent counterions. The lowest selectivity values were calculated for mixtures of divalent and trivalent ions. These conclusions agree with the findings of several authors (Gabelich et al., 2002; Hou et al., 2008; Zhao et al., 2012; Cheng et al., 2015; and Li et al., 2016). The results depicted in Figure 3 show that the exclusion factor for the coion Cl- increases continuously at short times for all the cation systems, but slowly decreases at long times for all the mixtures. In Figure 4, we studied the effect of the externally applied voltage on the selectivity of the higher charge counterion. A dimensionless voltage is plotted in the figure (V *). We can see that 12 the selectivity of the higher charge ion increases continuously with the applied voltage. The dimensional voltage can be calculated by multiplying the dimensionless value by the thermal voltage (VT = 0.025 volts at 25 oC). These results agree well with results reported by Hou et al. (2008), and they are very important for practical applications. Exclusion Factor,  (dimensionless) 0.6 0.5 0.4 0.3 0.2 0.1 Na/Ca/Cl Na/Al/Cl Ca/Al/Cl 0 0 0.2 0.4 0.6 0.8 1 Time (dimensionless) Figure 3. Time variation of the exclusion factor for several ionic mixtures. 13 6 5 Selectivity 4 3 2 1 V*= -20 V*= -10 V*= -5 0 0 0.2 0.4 0.6 0.8 1 Time (dimensionless) Figure 4. Influence of dimensionless applied voltage on selectivity (1-3 mixture). The influence of size is studied in Figures 5, 6, and 7. The value of the diffusion coefficient was used as representative of the effective ion size. An equivalent mesopore value of 10 -8 m was selected to minimize the restriction effects imposed by the ratio of the hydrated radius and the pore diameter, as shown by Hou et al. (2008). 14 Selectivity, a (dimensionless) 1.4 1.3 1.2 1.1 1 Cu/Ca/Cl Na/K/Cl Na/Cl/HCO3 0.9 0.8 0 0.2 0.4 0.6 0.8 1 Time (dimensionless) Figure 5. Influence of different ion sizes on selectivity. In Figure 5, we studied the size effect on monovalent cations (K/Na/Cl), divalent cations (Cu/Ca/Cl), and anions (Na/Cl/HCO3) by plotting the selectivity of the smallest size counterion versus time. We used the fact that the hydrated radius of: K+< Na+, Ca2+< Cu2+, and Cl-<HCO3-, see Table I. We can see that at short times (supercapacitor regime) the selectivity of the smaller ion increases sharply, and slowly decreases during the desalination regime. The same effect is observed for cations and anions mixtures. We explored this matter further in Figure 6 by plotting the value of average concentration inside the electrode versus time for the mixture K/Na/Cl. We can see in Figure 6 that, during the supercapacitor regime, there is a fast increase in the concentration of the counterions and decrease of the coion concentration. The concentration of the smaller counterion, however, increases faster than the one of the bigger counterion. During the desalination regime, this trend is reversed and slowly both concentrations tend to the same value. This finding is explained by considering that there are two main mechanisms for mass transport in and out the electrodes, migration and diffusion. At short times (supercapacitor 15 regime), migration predominates as the EDLs are charged. During the desalination regime, ion diffusion is the main mechanism due to concentration gradients, which tends to restore equilibrium. Electroneutrality between the solid electrode and the electrolyte solution should be preserved and, if the concentration of one counterion decreases, the concentration of the other should increase. It is shown in Figure 7 that, during the supercapacitor regime, the liquid phase charge density increases rapidly as the EDLs are charged. After the EDLs are charged in the desalination regime, the charge density remains mostly constant. Ionic Concentration (dimensionless) 3.5 3 2.5 2 1.5 Na+ K+ Cl- 1 0.5 0 0 0.5 1 1.5 2 Time (dimensionless) Figure 6. Variation of average ionic concentration in the electrode with time. 16 Charge Density (dimensionless) 3 2 Na/K/Cl 1 Na/Cl/HCO3 0 0 0.5 1 1.5 2 -1 -2 -3 Time (dimensionless) Figure 7. Variation of liquid phase charge density with time. In Figure 8, we applied a negative half voltage of 0.5 V (-20) to mixtures of a monovalent cation, divalent cation, and a monovalent coion. Figure 8 shows the influence of divalent cations of different sizes (Mg2+ < Ca2+ < I2+) on the divalent/monovalent selectivity. In order to expand the size range, we ran simulations using an imaginary divalent cation (I 2+) with a diffusivity equal to 10-9 m2/s. We can see in the figure that the selectivity increases as the hydrated radius decreases. This result agrees with the findings of Hou et al. (2008) using Monte Carlo simulations and the experimental data from Li et al. (2016). These authors concluded that smaller ions can displace bigger ions of the same charge. However, it is important to state that the charge effect takes precedence over the size effect. 17 Selectivity, a (dimensionless) 7 6 5 4 3 2 Na/Ca/Cl 1 Na/Mg/Cl Na/I2+/Cl 0.6 0.8 0 0 0.2 0.4 1 Time (dimensionless) Figure 8. Influence of different divalent cations size on selectivity. Exclusion Factor, b (dimensionless) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 Na/Ca/Cl 0.1 Na/Mg/Cl Na/I2+/Cl 0.6 0.8 0 0 0.2 0.4 1 Time (dimensionless) Figure 9. Influence of different divalent cation size on the exclusion factor. 18 The influence of ion size on the coion exclusion factor is shown in Figure 9. The exclusion factor of the Cl- coion decreases as the ion size increases. Ionic Concentrations (dimensionless) 2.5 2 1.5 Na+ 1 Ca2+ Cl- 0.5 0 0 1 2 3 4 5 Time (dimensionless) Figure 10. Time variation of average ionic concentrations inside the electrode. In Figure 10, we reproduce qualitatively the case studied of Zhao et al. (2012). These authors studied theoretically and experimentally the competition between a mixture containing Na + and Ca2+ counterions for a 5:1 concentration ratio. Zhao et al. (2012) concluded that, due to charge differences, the Ca2+ selectivity will increase as time increases. In a long time experiment, due to selectivity, the Ca2+concentration inside the electrode eventually will be higher than the Na + concentration despite the big initial Na/Ca ratio. All concentrations in Figure 10 have been made dimensionless with reference to the ionic strength of the free solution. The results shown in Figure 10 confirm qualitative the picture reported by Zhao et al. (2012). At short times both counterions adsorbed inside the electrode. The smaller one adsorbed faster than the bigger one. Due to the charge difference, however, the counterion with the biggest 19 charge displaced the other continuously until equilibrium is achieved at very long times, 5 hours in their experiments. CONCLUSIONS A model based upon the volume averaging method has been used to study ion selectivity in charged porous electrodes. The solution of the closure problem for isotropic porous media has been presented. The effective diffusivities in isotropic porous media are a function of the void fraction and the solid-liquid surface charge density. Ion selectivity depends upon ion charge and effective ion size (Gabelich et al.. 2002; Hou et al., 2008; Zhao et al., 2012; Chen et al., 2015; and Li et al., 2016). The effective ion size is represented by the hydrated ion radius. In this work, we represented effective ion size using the values of the effective diffusivity. This assumption is acceptable for porous media with pore diameters greater than 10 nm. Our results support the Zhao et al. (2012) conclusion that there is a time-dependent selectivity effect during capacitive charging of porous electrodes. We also found that as the applied voltage increases, the ion selectivity of the higher charge ions over the lower charge ions increases. Experimental data from literature (Gabelich et al.. 2002; Hou et al., 2008; Zhao et al., 2012; Chen et al., 2015; and Li et al., 2016) and our calculations show that the charge effect is the most important. Ions with higher valence displace ion with lower valences. Small hydrated ions displace bigger hydrated ions of the same valence. At short times, the higher-diffusivity ions adsorb faster than the lower-diffusivity ones. During the desalination regime (at long times), transport of same-charge ions from the bulk solution to the electrode is determined by ion 20 concentrations. Our results support this conclusion for pore diameters bigger than 10 nm, but the Hou et al. (2008) data suggest that this conclusion also applies for smaller pore diameters. Experimental data from literature (Gabelich et al.. 2002; Hou et al., 2008; Zhao et al., 2012; Li et al., 2016) and our calculations show that ions of different charges and sizes can be separated using capacitive charging/discharging processes. This important finding can be used to design effective ion separation processes. ACKNOWLEDGMENTS Notice: This manuscript has been authored by UT-Battelle, LLC under Contract No. DEAC05-00OR22725 with the US Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. 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