Transport of Ions in Mesoporous Carbon Electrodes during Capacitive

Article pubs.acs.org/Langmuir

Transport of Ions in Mesoporous Carbon Electrodes during Capacitive Deionization of High-Salinity Solutions K. Sharma,† Y.-H. Kim,† J. Gabitto,‡ R. T. Mayes,§ S. Yiacoumi,† H. Z. Bilheux,§ L. M. H. Walker,§ S. Dai,§ and C. Tsouris*,†,§ †

Georgia Institute of Technology, Atlanta, Georgia 30332-0373, United States Prairie View A&M University, Prairie View, Texas 77446-0397, United States § Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6181, United States ‡

ABSTRACT: Desalination of high-salinity solutions has been studied using a novel experimental technique and a theoretical model. Neutron imaging has been employed to visualize lithium ions in mesoporous carbon materials, which are used as electrodes in capacitive deionization (CDI) for water desalination. Experiments were conducted with a flow-through CDI cell designed for neutron imaging and with lithium-6 chloride (6LiCl) as the electrolyte. Sequences of neutron images have been obtained at a relatively high concentration of 6LiCl solution to provide information on the transport of ions within the electrodes. A new model that computes the individual ionic concentration profiles inside mesoporous carbon electrodes has been used to simulate the CDI process. Modifications have also been introduced into the simulation model to calculate results at high electrolyte concentrations. Experimental data and simulation results provide insight into why CDI is not effective for desalination of high ionic-strength solutions. The combination of experimental information, obtained through neutron imaging, with the theoretical model will help in the design of CDI devices, which can improve the process for high ionic-strength solutions.

1. INTRODUCTION With the rapid population growth and expanding industrialization, the scarcity of water resources is one of the major challenges of the present time. Apart from better water management practices, we need to rely on energy-efficient methods for water desalination to increase the supply of available water resources. Since approximately 98% of water on earth is in the form of seawater, desalination is a viable option for obtaining fresh water and adding to the current supply. In addition, water produced from gas and oil operations, such as hydraulic fracturing (fracking), needs to be treated for organics and salts removal prior to recycling and reuse. Thus, desalination processes can be used to produce drinking water and treat gas/oil-produced water for recycling/reuse. The current widely applied desalination technologies are reverse osmosis and thermal desalination. These technologies have some limitations that need to be considered. Thermal desalination is a high-energy-demand process, while membrane fouling and scaling are severe issues in reverse osmosis of fracking water. Capacitive deionization (CDI), which is based on the electrosorption of ions by charged porous carbon electrodes, has attracted interest as an alternative desalination technology, as it has low-energy requirements.1−5 CDI operates at low potentials in the range of 1−1.4 V, and membranes and high-pressure pumps are not required for its operation, so problems of scaling and fouling are avoided. Figure 1 shows © 2014 American Chemical Society

typical adsorption/desorption behavior of ions expected to occur during capacitive deionization of saline water. When an electrical potential is applied across porous electrodes, dissolved ions are adsorbed in the electrical double layer (EDL) formed at the electrode−liquid interface. Regeneration of electrodes is carried out by electrically discharging the electrodes, which leads to the release of ions back into the solution. The electrosorption capacity in this process depends significantly on the physical properties of the electrode material. Porous nanostructured carbon electrodes have been used, as they have a high surface area (400−2000 m2/g) and low electrical resistivity. Many studies have been carried out with the aim of improving the desalination performance of the CDI process, specifically by synthesizing improved carbon electrodes. Various carbon materials have been investigated as electrodes for CDI including carbon aerogel,6,7 activated carbon,8,9 carbon nanotubes,10,11 graphene,12,13 and mesoporous carbon.14−16 The salt removal capacity of carbon electrodes in the CDI process depends strongly on the pore size distribution and surface area of the electrodes. When the electrodes are charged, counterions are adsorbed from solution present in the pores to the surface of the pores, and co-ions are expelled from the Received: November 2, 2014 Revised: December 20, 2014 Published: December 22, 2014 1038

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Figure 1. Adsorption/desorption behavior of ions in capacitive deionization of saline water.

into why the desalination of high-salinity solutions by CDI is challenging and point to a solution for more efficient regeneration.

electrodes. It has been suggested that a typical CDI system can be energy inefficient due to dissolved salt present in the pore volume of the electrodes, and this effect becomes more pronounced at higher electrolyte concentrations.17 To address this issue, Andelman17 suggested a charge barrier to be placed next to the electrode to compensate for losses associated with ions present in the pores of the electrode. Recently, Lee at al.18 developed a membrane capacitive deionization (MCDI) system, in which anion- and cationexchange membranes were placed onto the external surface of the carbon electrodes, and reported a 19% higher salt removal efficiency with the MCDI setup compared to the conventional CDI setup. Motivation for the MCDI system came from the fact that regeneration can occur fast by reversing the polarity of the applied potential. Li et al.19 developed a new MCDI device using ion exchange membranes with carbon nanotubes and nanofibers, and reported that the removal capacity with MCDI was approximately 50% higher compared to the conventional CDI system. In these studies, it has been demonstrated that the MCDI setup can enhance the desalination efficiency. More recently, Biesheuvel et al. presented a theoretical model for the MCDI process, which describes the time-dependent electric current and effluent ion concentration during the sorption and regeneration phases.20 As a desalination method, conventional CDI has not been found to be an energy-efficient method for the treatment of high-salinity solutions when compared to reverse osmosis.4,21 Therefore, the process efficiency of CDI needs to be improved in order to become viable for treatment of high-salinity solutions. Desalination of high-salinity solutions has relevance in the treatment of seawater and water produced in the hydrofracking process, as well as other oil/gas operations. In this context, MCDI technology has the potential for being energy efficient for solutions of high ionic strength. In the present work, neutron imaging of lithium-6 ions was conducted to observe the electrosorption and regeneration behavior during CDI at varying electrolyte concentrations. Neutron imaging reveals the ion-transport behavior during the sorption and regeneration phase in CDI, which can aid in making the CDI process more efficient. Sharma et al.22 conducted neutron imaging of gadolinium nitrate solution in deuterium oxide at a relatively low concentration of 0.00874 M. The effective diffusivity of gadolinium ions was reported at various values of applied potential. Moreover, absorption of counterions was observed during regeneration after removal of applied potential.22 Neutron imaging results provide insight

2. MATERIALS AND METHODS 2.1. Capacitive Deionization Cell for Neutron Imaging. Neutron uptake by various atoms depends on their cross section: atoms with a large cross section can effectively capture neutrons transmitted through a medium, allowing the medium to be imaged.23 In this study, lithium-6 isotope was chosen as the element to absorb neutrons passing through a solution because it has a much greater absorption cross section (940.97 barns) than most of the other elements except gadolinium (259 000 barns).24 Instead of gadolinium(III) used in our previous work,22 LiCl was used because it was desired to use a symmetric 1−1 electrolyte, similar to NaCl. A specially designed CDI cell, containing mesoporous carbon electrodes in electrolyte solution, was used in the study. The cell was filled up with lithium-6 chloride (6LiCl) solution at concentrations much higher than the typical electrolyte concentrations in CDI experiments (∼0.1 M).25 All experiments were conducted in a continuous-flow mode. Deuterium oxide (D2O) was used instead of normal water, as hydrogen has a high neutron total cross-section, which can inhibit the visualization of the lithium ions in the experiments. In terms of physical/chemical behavior relevant to CDI, however, D2O behaves the same way as H2O. 2.2. Electrode Preparation and Characterization. The electrodes used in neutron imaging were composed of monolithic, mesoporous carbon synthesized at the Oak Ridge National Laboratory (ORNL), as previously reported.22 The synthesis method results in a mesoporous carbon material with high porosity. A platinum wire was pressed into the end of each electrode bar for electrical connection and glued at the tip of the electrode. Surface area measurements were performed with a Micromeritics Tristar 3000 at 77 K with nitrogen as the adsorbate. 2.3. Neutron Imaging Principle. Neutron radiography is based on the Beer−Lambert law, which states that radiation passing through matter is attenuated depending on the thickness, structural properties, and density of the material.22 The detector is equipped with a scintillator that converts neutrons to visible light, and the image is then captured by a charge-coupled device (CCD) camera. The attenuation of the beam caused by a uniformly thick, homogeneous sample is given by the Beer−Lambert equation: 1039

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Figure 2. Basic experimental setup for neutron imaging consists of a neutron source, a collimator, which determines the geometric properties of the beam, neutron scintillator screen, and the sample of study (mesoporous carbon electrodes in the present study). The beam is transmitted through the object and recorded by a scintillator-based detector. The detector records a two-dimensional image that is a projection of the sample on the plane. Neutrons are converted to light using a scintillator screen, and the light is captured by the CCD camera.

I = I0e−μδ

(1)

where I is the intensity of the neutron beam after attenuation, I0 is the intensity of the incident beam, μ is the attenuation coefficient, and δ is the thickness of the sample. 2.4. Neutron Imaging Experiments. Experiments were conducted at the CG-1D neutron imaging beamline at the High Flux Isotope Reactor at ORNL.26 The experimental setup for neutron imaging is shown in Figure 2. The specially designed flow-through CDI cell was equipped to visualize transport of ions in the electrodes during neutron imaging. The electrodes in the CDI cell were connected to a power supply (HP 3632A; Hewlett-Packard, CO) through platinum wire leads, so that the applied potential could be remotely adjusted away from the beam.

3. THEORETICAL MODEL DEVELOPMENT 3.1. Transport Model. The ion flux of species i in the bulk of the solution filling the pores is given by27 Ni = −Dio{∇ci + (ziFci /RT )∇ϕ}

Figure 3. Porous medium and representative elementary volume (REV).

Here, the thermal voltage (VT) is defined as VT = RT/F. The relationship between liquid-phase potential and the spatial distribution of electric charges in the solution is given by the Gauss electrostatic theorem (Poisson equation):30,31

(2)

where Ni is the ion flux, ci is the ion concentration, ∇ is the nabla operator for one-dimensional variation in the x direction, zi is the ion charge, Doi is the diffusion coefficient of ionic species i, F is the Faraday constant, R is the universal gas constant, and ϕ is the electrostatic potential in the pores. Equation 2 has been derived assuming that the isotropic mobility, ui, is given by the Nernst−Einstein relation28,29 for constant absolute temperature T (ui = Di/RT). We consider a two-phase medium consisting of a phase α (liquid) and a phase β (solid) as shown in Figure 3. The point species molar continuity equation, including the Nernst− Planck expression for the molar flux for the α phase, is given by ∂ci = −∇·Ni ∂t

∇·{ψ ·∇ϕ} = −F ∑ zici

Here, ψ is the permittivity of the electrolyte. Equations 4 and 5 describe ionic transport by concentration and electrical potential gradients at the microscale inside porous media and are referred to as the Poisson−Nernst− Planck (PNP) system of equations.30,31 In order to obtain the macroscopic formulation of the PNP equations, we will use the methodology developed by Whitaker.32 After extensive algebraic manipulations,33 we obtain the following equations: ⎛ ⎧ ∇⟨ϕi⟩α ⎫⎞ ∂⟨ci⟩α α α ⎜ ⎨ ⎬⎟⎟ = ∇·⎜Deff ∇⟨ci⟩ + zi⟨ci⟩ VT ⎭⎠ ∂t ⎝ ⎩

(3)

Substituting eq 2 into 3 yields ⎛ ⎧ ∂ci ∇ϕ ⎫⎞ ⎬⎟⎟ = ∇·⎜⎜Dio⎨∇ci + zici ∂t VT ⎭⎠ ⎝ ⎩

(5)

i

∇·{ψeff ·∇⟨ϕ⟩α } = −F ∑ zi⟨ci⟩α − av⟨q⟩αβ

(4)

i

1040

(6)

(7)

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Langmuir Here, av is the specific effective area of pores, ⟨ϕi⟩α and ⟨ci⟩α are the intrinsic phase averages of the electrostatic potential and the concentration of species i, respectively, which are calculated as ⟨ci⟩α =

1 Vα

∫V ciα dV

⎧ 1 − K e −x ⎫ ⎬ ϕ = 2 ln⎨ ⎩ 1 + K e −x ⎭

Here, x is the dimensionless distance, x = X/λD, X = dimensional distance, K is a dimensionless constant related to the potential (ϕD) at the outer Helmholtz plane and the dimensionless charge density (q*D) in the diffuse layer: K = −tanh[ϕD/4].37 A similar solution can be written for the opposite flat surface. In this case, the solution is a function of a dimensionless distance y that is related to x by

(8)

The effective diffusivity tensor, Deff , and the effective permittivity of the solution in the pores, ψ , are calculated eff

from the solution of the appropriate closure problem plus a spatially periodic porous medium model; ⟨q⟩αβ, the electrode charge density averaged at the interphase area α−β, is calculated by ⟨q⟩αβ

⎧ 1 =⎨ ⎩ Aαβ ⎪

⎪

⎫ q dA ⎬ Aαβ ⎭

∫

y=2

L −x λD

(12)

⎪

⎪

Applying the principle of superposition, the global solution is given by

(9)

By converting eq 7 into a dimensionless form and carrying an order-of-magnitude analysis, one will find that the term on the left-hand-side is negligible compared to the two terms on the right-hand-side. The reason is that the left-hand-side term is multiplied by the square of the ratio of the microscopic over the macroscopic length scales, λα/L. The microscopic length scale (λα) is typically of the order of magnitude of the EDL Debye length, while the macroscopic length scale (L) is estimated by the electrode thickness. In the macroscopic case, the argument for the existence of a matching boundary layer solution34 cannot be made; therefore, we can set the right-hand-side to zero, leading to F ∑ zi⟨ci⟩α + av⟨q⟩αβ = 0 i

(11)

ϕ = A1ϕ(x) + A 2 ϕ(y)

(13)

where A1 and A2 are constants that need to be determined in order to fit the boundary conditions at both flat surfaces, x = 0 and x = 2 L/λD. After some algebraic manipulations, it can be shown that A1 = A 2 =

⎡ (1 − K )(1 − K e−2L / λD) ⎤ ⎥ /ln⎢ 2 ⎣ (1 + K )(1 + K e‐2L / λD) ⎦

ϕD

(14)

Solving for A1 and A2 and introducing the values into eq 13 allows us to determine the electrolyte potential profile inside the slit pore. Summarizing, the electrode charge density is calculated by

(10)

⟨q⟩αβ = ψ (ϕW − ϕD)/λS

Equation 10 describes a macroscopic electroneutrality condition. It states that, at the macroscopic level, the charge on the solid electrode is balanced by the charge in the solution. It is important to notice that this electroneutrality condition results naturally from the different length scales used and not from any arbitrary assumption. Scheiner et al.29 reached a similar conclusion using another averaging technique postulating the presence of a constant charge density on the solid surface. The electrode charge density, ⟨q⟩αβ, is constant within the chosen representative elementary volume (REV). The evaluation of this quantity is important and requires the use of a microscopic EDL model plus assumptions about the microscopic structure of the porous medium. In this work, we used the Gouy−Chapman−Stern EDL model (GCS), which combines a Stern layer of constant capacity with a diffuse layer inside the solution.27 We also assume highly overlapping EDLs in slit-shaped pores following the treatment presented by Yang et al.35 The authors proposed that a representative pore can be viewed as a slit formed by two planar plates with a separation distance 2L between them. The potential profile inside the pore was calculated using a superposition solution based on the numerical solution of the Poisson−Boltzmann equation for a flat plate electrode. The results predicted by the superposition solution were successfully compared to experimental data and Monte Carlo simulation results.35,36 In this work, we propose an analytical version of the superposition solution that agrees well with the aforementioned experimental data and Monte Carlo simulation results. The potential in the electrolyte is given as a function of position by the following analytical solution given by Neumann and Thomas-Alyea:37

(15)

where ϕW and ϕD are the potential values in the solid and the diffuse layer, respectively; and λS is an effective thickness of the Stern layer. The value of ϕD and the pore size allow the calculation of the potential profile using eq 13. Finally, the average potential value in the pore, ⟨ϕi⟩α, is calculated by averaging the calculated potential profile. 3.2. Transport Model for Concentrated Solutions. In order to account for ionic transport in concentrated solutions, we modified our model following Newman and ThomasAlyea.37 The flux equation should be written as Ni = −Dici∇{ln ai + zi(F /RT )ϕ}

(16)

where ai is the activity of ion i in the concentrated solution. The diffusion coefficient (Di) used here has been calculated using an equation proposed by Cervera et al.38,39 These authors introduced a correction to the infinite dilution diffusion coefficient (Doi ) inside micropores using the Renkin equation,40 ⎡ ⎛ R ⎞3 ⎛ R ⎞5 ⎤ R Di = Dio⎢1 − 2.104 i + 2.09⎜⎜ i ⎟⎟ − 0.95⎜⎜ i ⎟⎟ ⎥ ⎢ Rp ⎝ Rp ⎠ ⎝ R p ⎠ ⎥⎦ ⎣ (17)

where Rp is the micropore radius, and Ri is the ionic radius assumed to be the same for all ionic species. Equation 16 has been derived assuming that the gradient in electrochemical potential (∇μi) is the driving force for the ionic transport process, and the gradient of the chemical potential (∇μs) is the driving force for the charge-neutral solvent. 1041

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Figure 4. (a) Nitrogen adsorption isotherms and (b) BJH pore-size distributions for the mesoporous carbon used in neutron imaging experiments.

4. RESULTS AND DISCUSSION 4.1. Materials Characterization. From the characterization studies, the pore surface area of the monolithic mesoporous carbon used in this study was determined to be 365 m2/g. Also, the pore volume at P/Po = 0.995 is 0.43 cm3/g, and the average pore size is centered at 15 nm. Figure 4 shows nitrogen sorption isotherms and pore size distributions of mesoporous carbon determined by the Barrett−Joyner− Halenda (BJH) method. 4.2. In Situ Neutron Imaging during CDI of HighSalinity Solutions. In situ measurements of CDI of highsalinity solutions were carried out using the neutron imaging technique. Visualization of ion transport in electrodes via neutron imaging was first performed with 6LiCl solutions at two concentrations, C: 0.26 and 0.73 M. Figure 5 shows

Under those conditions, and using the assumption that the molecular masses of all the ions (M) are the same, Cervera et al.38 proposed the following driving force for the process: ∇μi* = ∇μi − Mi /Ms∇μs

(18)

The advantage of this transformation is that transport equations need to be formulated for the ionic species only, not for the solvent. Making use in eq 16 that ai = γi ci, we obtain ⎧ ⎛ F ⎞ ⎫ ⎟ϕ ⎬ Ni = −Dici∇⎨ln(γici) + zi⎜ ⎝ RT ⎠ ⎭ ⎩

(19)

Following the same procedure used in the case of dilute solutions, we obtain a modified eq 6: ∂⟨ci⟩α /∂t = ∇·(Deff {∇⟨c i⟩α + zi⟨ci⟩α ∇⟨ϕi⟩α /VT} + ∇·(Di⟨ci⟩α ∇ln γi))

(20)

Activity coefficients for concentrated solutions are calculated based upon charge, ionic stength, and ionic size.39−42 The activity coefficients for individual ions based upon charge and ionic strength were calculated using the equation proposed by Bromley.41 This equation is an empirical modification of Guggenheim’s equation42 obtained by fitting of a big set of literature data. Bromley41 observed that experimental values of log(g±)/z+z− were proportional to ionic strength, I, and developed the following equation: log(γ±) =

−A γ |z+z −|I1/2 1 + ρI

1/2

+

(0.06 + 0.06B|z+z −|)I

(

1+

1.5 I |z+z −|

2

+ BI

)

(21)

Here, Aγ = 0.511 and ρ = 1 for 298.1 K. Bromley reported tabulated data of the interaction parameter B and also presented a formula to calculate B from individual ion parameters. The size effect can be described by the equation proposed by Cervera et al.39 used to study electrokinetic flow in cylindrical nanopores representing charged membranes: 1 γi = (1 − ν ∑k ck) (22) 41

Figure 5. Changes in the mean neutron transmission through mesoporous carbon electrodes with 6LiCl solution in D2O at two concentrations, C: 0.26 and 0.73 M. Broken lines in neutron images were drawn to distinguish the electrode-solution boundaries.

changes in the mean transmission and neutron images obtained under various sorption/desorption conditions (Cases 1−5). Neutron images, which were converted to mean transmission according to our previous work,22 represent a relative concentration of 6Li+ ions. Lighter color (or higher mean transmission) means less 6Li+ ions, while darker color (or lower mean transmission) represents a higher concentration of 6Li+ ions. Electrodes used in this experiment were previously submerged in 6LiCl solution of 0.26 M in the preparation stage

where ck is the ionic concentration, and ν is the partial molar volume of both ions assumed to be equal for both ionic species, and calculated using ν = NAVπ (2R i)3 /6

(23)

where NAV is the Avogradro number. 1042

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Figure 6. Time sequences of neutron images of CDI cell with 1.5 M 6LiCl solution in D2O. (a) 1.2 V DC potential applied (the right electrode is negatively charged) and (b) electrodes short-circuited during regeneration.

minutes),43,44 the LiCl concentration in the electrode pores of Case 3 was initially higher than that of Case 1. After the negative potential was applied, the surfaces of the electrodes became charged and interacted with counter- and co-ions existing in the pores and in the bulk solution. In comparison with Case 1, more counterions were rapidly adsorbed on the electrodes through electrostatic attraction and more co-ions were quickly released into the bulk solution via electrostatic repulsion. Thus, the initial adsorption/desorption rate of ions in Case 3 was higher than that in Case 1. In particular, the fast desorption of co-ions from the electrodes might influence the effluent concentration of ions from the CDI cell at the initial stage of Case 3. Although a relatively large reservoir was used in this study to continuously circulate 6LiCl solution at a relatively constant concentration, it was observed in neutron images that the 6Li+ concentration of the circulating solution of Case 3 slightly increased, after applying a negative potential (result not shown), and then within a short time, the steady-state concentration was recovered. A similar observation was reported in CDI experiments using NaCl solution.43 In those experiments, zero-voltage operation followed by the application of a positive potential slightly increased the effluent NaCl concentration during the initial stage of a typical CDI cycle. After sorption/desorption of ions in Case 3 reached equilibrium, the 6LiCl concentration in the bulk solution was increased about three times (Case 4: C = 0.73 M, V = −1.2 V). Then, the 6Li+ concentration was observed to increase significantly in both electrodes. Since the system was at equilibrium prior to increasing the 6Li+ concentration in the bulk solution, accumulation of 6Li+ ions in both electrodes in Case 4 has to be associated with accumulation of Cl− ions at similar concentrations to achieve electroneutrality. When the applied potential was set to zero again (Case 5: C = 0.73 M, V = 0.0 V), rapid adsorption of counterions and the fast desorption of co-ions caused by electrostatic interactions occurred in both electrodes during the initial period of regeneration. However, similarly to Case 2, the electrodes in Case 5 were not fully regenerated, although the regeneration time was much longer than a typical CDI operational period. To further investigate the sorption/desorption behavior of ions in CDI of high-salinity solutions, a sorption/regeneration experiment (Cases 6 and 7) was separately carried out with 1.5 M 6LiCl in D2O and clean electrodes. Figure 6 shows timedependent changes in neutron images during capacitive

of neutron imaging, thereby leading to initial neutron absorption. Cl− ions do not contribute significantly to neutron absorption and can be considered transparent for all practical purposes. As the potential, V, was applied (Case 1: C = 0.26 M, V = +1.2 V), 6Li+ ions were rapidly adsorbed by the right electrode, while they were desorbed from the left electrode. Thus, the sorption/desorption behavior of 6Li+ ions shows that the right electrode was negatively charged, attracting 6Li+ ions, while the left electrode was positively charged, attracting Cl− ions. When the applied potential was set to 0 V (Case 2: C = 0.26 M, V = 0 V), the right electrode lost 6Li+ ions, while the left electrode gained 6Li+ ions in comparison with Case 1. This sorption/desorption behavior of ions is the result of electrostatic interactions between ions in the electrodes and in bulk solution. When the surface charge was set to zero, the left electrode which was loaded with Cl− ions in Case 1 simultaneously lost Cl− ions and gained 6Li+ ions in order to become neutralized. At the same time, the right electrode lost 6 + Li ions and gained Cl− ions in order to become neutralized. The rapid adsorption of 6Li+ ions observed on the left electrode at the beginning of regeneration reveals a strong electrostatic attraction between Cl− and 6Li+ ions. Similarly, the fast desorption of 6Li+ ions from the right electrode reveals electrostatic repulsion generated among co-ions. Thus, in Case 2, the charge in the electrodes was dissipated by simultaneous adsorption of counterions and desorption of coions. Similarly, in our previous work,22 using solutions of low concentration gadolinium(III) nitrate, it was observed that, during discharging at 0 V, Gd3+ ions were adsorbed on an electrode initially loaded with NO3− ions. However, while the uptake of Gd3+ ions by the electrode was stopped after approximately 1.5 h, 6Li+ ions in this study were continuously adsorbed on the left electrode for 8 h. This behavior is due to the higher concentration of 6LiCl compared to the concentration of Gd(NO3)3 in previous experiments. The negative potential applied after regeneration (Case 3: C = 0.26 M, V = −1.2 V) resulted in an initially rapid change in 6 + Li concentration of the electrodes. The significant change of the ion concentration is attributed to the previous history of the CDI cycle (Cases 1 and 2), which led to the accumulation of many ions in the electrode pores. Because regeneration was not completed despite the zero-voltage operation for a much longer period than a typical CDI operation time (e.g., a few 1043

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Langmuir ⎛ 1 Deff = εαDi ⎜⎜I + Aαβ ⎝

deionization of the 1.5 M 6LiCl solution. Images in Series (a) were obtained during electrosorption (Case 6: C = 1.5 M, V = +1.2 V), while images in series (b) were obtained during regeneration (Case 7: C = 1.5 M, V = 0 V). During electrosorption, 6Li+ ions transferred from the left electrode to the solution and from the solution to the right electrode. It is also observed that 6Li+ ions on the right electrode were adsorbed throughout the width of the electrode. In the images of series (b) of Figure 6, similarly to Cases 2 and 5, as soon as the electrodes were discharged, the left electrode, which was loaded with chloride ions, adsorbed 6Li+ ions to neutralize the charge of the Cl− ions. The right electrode, which was loaded with 6Li+ ions, remained dark with time, indicating that the majority of 6Li+ ions were not released. Instead, the right electrode adsorbed Cl− ions to neutralize the charge of the 6Li+ ions. Another interesting observation is that, even after a period of approximately 10 h, both electrodes were very dark, which means that regeneration has not been completed and the concentration of 6Li+ ions remains above the value in the bulk of the solution. In situ measurements performed in this study have been focused on visualizing transport of ions in CDI of high-salinity solutions. It has been shown that electrostatic interactions of ions play a major role in CDI of concentrated solutions, leading to accumulation of counterions in electrodes when the applied potential is set to zero, which in our setup is same as shortcircuiting the electrodes. In contrast to the sorption process under an applied potential, the regeneration process of electrodes in high-salinity solution was much slower than that in low-salinity solution. 4.3. Simulation Results. The system of equations defined by eq 20 for positive and negative ions plus the aforementioned procedure to calculate a relationship between the average ionic concentration, ⟨ci⟩α, and the average potential were implemented into a numerical computer code using an explicit finite differences methodology. The system converged to a smooth solution as long as the time step was small enough. In order to study the time evolution of ionic charge and potential inside the electrode, we calculated an average value for the whole porous electrode. We used eq 22 based on ions of finite size to calculate the activity coefficients. We rejected the equations based upon ionic strength39 because they were determined from experimental data measured under conditions of solution electroneutrality. Inside mesopores and micropores there is a net charge in the solution balancing the charge on the solid matrix. In all our calculations we used a value of the effective diffusivity tensor (Deff) calculated using the closure procedure described by Ryan et al.45

∇̲ 2 f ̲ 1 = 0

(24)

− n̲ αβ·∇̲ f ̲ 1 = n̲ αβ , in A αβ

(25)

∫A

⎞ n̲ αβ f ̲ 1 dA⎟⎟ αβ ⎠

(27)

Here, I is the unit tensor, and εα is the void fraction. The closure problem given by eqs 24−26 was solved using a spatially periodic unit cell corresponding to an isotropic porous medium. Ryan et al.45 showed that, for isotropic porous media, only one component of the effective diffusivity tensor is relevant to the transport process and that the geometry influence is successfully described by the value of the void fraction (εα). The value of the only Deff component used (Deff) was calculated by numerical integration along the liquid−solid interphase area (Aαβ). The isotropic effective diffusivity was given by Deff /Dio = εα3 − 0.7548εα2 + 0.7452εα

(28)

where εα is the void fraction. The dimensionless time (τ) appearing in Figures 7 and 8 was calculated by τ = L2/Di, where L is the electrode thickness used as macroscopic length scale, and t is the dimensional time.

Figure 7. Time evolution of average ionic concentration inside the porous electrode during a typical charging/discharging cycle.

Typical results for the variation of ionic concentrations ⟨ci⟩α versus time are shown in Figure 7. The results were calculated using typical experimental values for the CDI process: electrode thickness (L) = 0.001 m, Doi = 1.5 × 10−9 m2/s, pore diameter = 7.5 nm, void fraction = 0.5, salt concentration = 0.5 M,

For spatially periodic porous media: f ̲ 1(r ̲ + 1̲ i ) = f ̲ 1(r)̲

(26)

Here, r is the position vector, 1i represents the three nonunique lattice vectors that are needed to describe a spatially periodic porous medium, f1 is the closure variable used to calculate Deff using

Figure 8. Time variation of diffuse layer potential, ϕD, (PhiD) and average solution potential, ⟨ϕi⟩α (Phisol). Results corresponding to δ = 1. 1044

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Langmuir average ion size = 2 × 10‑10 m, and half-electrode potential = 0.3 V. The ratio of the diffuse-layer and Stern-layer capacitances (δ), used as an adjustable parameter in the model, was assumed to be equal to one, and τ was equal to 11 min. It is shown in Figure 7 that the counterion concentration increases very fast at short times during the charging step. At longer times, the average counterion concentration increases slowly and eventually reaches an equilibrium value. The co-ion average concentration decreases very fast at short times until it eventually reaches a low equilibrium value. Figure 7 also shows that, as soon as the electrodes are discharged, the counterion concentration decreases rapidly while the co-ion concentration increases fast. Compared to the changes in concentration of counter- and co-ions observed in CDI of high-salinity solution with various concentrations (Cases 1−7), it is found that prediction results of the individual ionic concentration profiles inside the electrodes showed similar tendencies. For all cases shown in Figures 5 and 6, the rapid uptake of counterions and the fast release of co-ions were observed in both electrodes during the charging step. Case 3 also showed that the concentration of counter- and co-ions inside the electrodes reached equilibrium after about 12 h. In the case of the discharging of the electrodes, the changes in concentration of counter- and co-ions observed in Cases 2 and 7 showed a similar tendency to those of the simulation results. Thus, the developed model was used to further explain the transport of ions inside electrodes, which can give valuable insights into the actual electrode charging/ discharging mechanism. As shown in Figure 7, it is important to note that within a short period of time the co-ion concentration reaches a value higher than the bulk solution value. This behavior is produced by the high value of the migration flux term in eq 19. At longer times, the migration term decreases and the process becomes more and more diffusive in nature. The point where the migration term becomes zero is reached when both the average concentration values are equal. The results presented in Figure 7 show that both average concentration values are above the bulk concentration value at this point. After this critical point, the decrease in ionic concentrations occurs only by diffusion and, therefore, it is a very slow process. The interpretation of the results presented in Figure 7 is confirmed by Figure 8, which depicts the time variation of the averaged solution potential inside the electrode. At lower times, the diffuse-layer potential decreases as time increases until reaching an equilibrium value. The same behavior is observed for the average solution potential in the electrode. The difference between the absolute value of both potentials is determined by the value of the δ dimensionless parameter that represents the ratio of the diffuse-layer and Stern-layer capacitances. This group acts as an adjustable parameter in the model. After discharge, the potential in the solution changes sign and increases in absolute value until decreasing to zero. A zero potential value means that further ion transport can only proceed by diffusion. Some calculations (not shown here) also raise the possibility that diffusion transport out of the porous electrode can be further slowed down by a negative activity gradient. In concentrated solutions, the diffusion process is controlled by the gradients of activities (eq 19), and not by gradients of concentrations. Under certain circumstances, a pseudoequilibrium state can be reached where the concentration inside the electrodes has a value above the concentration in the bulk of

the solution. Slow diffusion process and pseudoelectrochemical equilibrium can explain the fact that the 6Li+ ion concentration remains above the solution values for very long periods of time. It should be noted that the phenomenon of counterion adsorption for neutralization after electrode discharging was also observed in the case of gadolinium nitrate in our previous work.22 Thus, the commonly accepted behavior during the regeneration cycle, where the adsorbed ions are simply expected to diffuse out of the electrodes into the solution seems not to be accurate. Instead, counterions first diffuse into the electrode pores, overshooting the bulk solution concentration. In the case of low salt concentration in the original solution, it was observed that after a certain period of counterion diffusion into the electrode pores, both types of ions diffuse back from the electrodes into the solution.22 However, in the case of high salt concentration, as is the case of seawater or fracking water, as counterions diffuse into the electrode pores during regeneration, the temporally high concentration of positive and negative ions in the pores persists for a long time due to slow diffusion. The result of this behavior is that the CDI cycle becomes very slow and cannot operate as planned. Neutron imaging experiments and simulation results indicate that ion accumulation in electrode pores during regeneration can cause capacitive deionization to be ineffective in desalinating high-salinity solutions. As discussed in the Introduction, ion-exchange membranes can be used to hinder accumulation of counterions in electrode pores during regeneration. A membrane-capacitive-deionization system can significantly enhance the desalination efficiency of seawater.46 Furthermore, desorption of ions from mesoporous carbon electrodes during regeneration can be facilitated by applying a pulsed potential of small amplitude, on the order of ±100 mV.47 Thus, desalination efficiency of high-salinity solutions in capacitive deionization may be improved by employing ionselective membranes and applying a low-amplitude AC electrical signal.

5. CONCLUSIONS Experimental and theoretical studies of the CDI process at high electrolyte concentrations have been carried out. We observed that, at high concentrations, the discharge process involves very fast ion transport inside the electrode that can produce concentration values of both ions to be higher than in the bulk solution. These values appear as dark areas inside the electrodes in neutron imaging experiments. This transport process will switch off ion electromigration and leave only diffusion transport as a mechanism for ion discharge. The diffusion process can be further slowed down by negative differences in the activity coefficients. These mechanisms greatly decrease the efficiency of the CDI process for high saline concentrations.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Telephone: 865-241-3246; Fax: 865-241-4829. Notes

This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. 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 nonexclusive, paid1045

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up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was partially supported by the Laboratory Director’s Research and Development Seed Program of ORNL. ORNL is managed by UT-Battelle, LLC, under Contract DE-AC05-0096OR22725 with the U.S. Department of Energy. A portion of this research at the Oak Ridge National Laboratory’s High Flux Isotope Reactor was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Partial support to S.Y., K.S., and Y.-H.K. was provided by the National Science Foundation, under Grant No. CBET-0651683. The authors are thankful to Jean Bilheux for his help with the neutron image analysis.

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