Charge Efficiency: A Functional Tool to Probe the Double-Layer

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Charge Efficiency: A Functional Tool to Probe the Double-Layer Structure Inside of Porous Electrodes and Application in the Modeling of Capacitive Deionization R. Zhao,†,‡ P.M. Biesheuvel,*,†,‡ H. Miedema,‡ H. Bruning,† and A. van der Wal§ †

Department of Environmental Technology, Wageningen University, Bomenweg 2, 6703 HD Wageningen, The Netherlands, Wetsus, Centre of Excellence for Sustainable Water Technology, Agora 1, 8900 CC Leeuwarden, The Netherlands, and § Voltea B.V., Wassenaarseweg 72, 2333 AL Leiden, The Netherlands ‡

ABSTRACT Porous electrodes are important in many physical-chemical processes including capacitive deionization (CDI), a desalination technology where ions are adsorbed from solution into the electrostatic double layers formed at the electrode/solution interface inside of two juxtaposed porous electrodes. A key property of the porous electrode is the charge efficiency of the double layer, Λ, defined as the ratio of equilibrium salt adsorption over electrode charge. We present experimental data for Λ as a function of voltage and salt concentration and use this data set to characterize the double-layer structure inside of the electrode and determine the effective area for ion adsorption. Accurate experimental assessment of these two crucial properties of the electrode/solution interface enables more structured optimization of electrode materials for desalination purposes. In addition, detailed knowledge of the double-layer structure and effective area gives way to the development of more accurate dynamic process models describing CDI. SECTION Surfaces, Interfaces, Catalysis

P

orous electrodes are important in many physicalchemical processes such as electrochemical cells, batteries, and supercapacitors.1-3 Another important example is capacitive deionization (CDI),4-16 a water desalination technology based on applying an electrical potential difference between two oppositely placed porous electrodes separated by a spacer compartment that allows solution to flow through; see Figure 1a. In CDI, ions are removed from the aqueous solution and are stored on the internal surface areas inside of the porous electrodes, resulting in an effluent product stream with a reduced ion concentration. Ions can be released back into solution by reducing or even reversing the applied voltage, resulting in a product stream concentrated in ions. CDI is envisioned to be a very energy efficient water desalination technology, especially when the ionic content is relatively low, such as for brackish water. The lower limit of brackish water is on the order of 10 mM, in which case there is only one ion for each 3000 water molecules. Specifically removing these few ions (based on their charge) has the potential to be more energy efficient than technologies where all of the water is removed instead, such as in distillation and reverse osmosis. Recently, it has been discovered that it is possible to reverse this process (“reverse-CDI”) and recoup electrical energy from the salinity difference between sea and river water.17 The ion adsorption capacity of the electrodes used in CDI is directly related to the surface area. Therefore, the electrodes

r 2009 American Chemical Society

typically are made of porous activated carbons with high internal specific surface areas on the order of 103 m2/g. Just as important is the nanoscale structure of the double layers which form at the electrode/solution interface inside of the porous electrode. To elucidate this point, it is helpful to make use of the widely used Gouy-Chapman-Stern (GCS) doublelayer model, which considers an inner, or Stern, layer and a diffuse ion cloud described by the equilibrium Poisson-Boltzmann equation for ions as ideal point charges. According to the GCS model, high Stern layer capacities are advantageous as this allows for a high surface charge and salt adsorption. Previous literature on porous electrode characterization focuses on electrode charge (or capacitance), often only at low cell voltages and for one value of the ionic strength. Though, from such a limited data set, it is in principle possible to simultaneously derive the effective surface area for ion storage, am, and, within the GCS framework, the Stern layer capacity, CSt, this is relatively inaccurate and has not been applied much. Therefore, questions like which part of the activated carbon is actually available for ion and charge storage and do only pores in a certain size range contribute

Received Date: October 17, 2009 Accepted Date: November 9, 2009 Published on Web Date: November 16, 2009

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DOI: 10.1021/jz900154h |J. Phys. Chem. Lett. 2010, 1, 205–210

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Figure 1. (a) Schematic view of one CDI cell. (b) Charge efficiency, Λ, as function of cell potential and ionic strength. Comparison of GCS theory (lines, CSt = 0.1 F/m2) with data.

Figure 2. (a) Equilibrium electrode charge as a function of cell potential and ionic strength. Comparison of the GCS model (lines) with data (am = 720 m2/g, CSt = 0.1 F/m2). (b) Total equilibrium salt adsorption, data, and GCS model (same parameters).

to the adsorption process are still a matter of debate. Related to that, available experimental data can hardly be used to accurately validate models for the double-layer structure of porous materials. Obviously, the current situation hampers the design and effective optimization of (the structure of) electrode materials, for instance, for desalination purposes. In this Letter, we introduce an alternative procedure, alternative in respect to considering data for charge Σ only. The procedure combines data for Σ with data for the equilibrium salt adsorption from solution into the double layers inside of the electrode, Γsalt; see Figure 2. Importantly, even though Σ and Γsalt are recorded simultaneously, the measurement of each is entirely independent. At first sight, one may have the impression that measuring Γsalt simultaneously with Σ will be superfluous. This idea may arise from the assumption that each electron charge will be fully charge-balanced by counterion adsorption. If so, this would imply indeed that the transfer of one electron from one to the other electrode is accompanied by the removal of precisely one salt molecule out of the bulk solution. This is however not the case because, simultaneously with counterion adsorption, co-ions are excluded from the double layer.5-7,14-18 The effect of co-ion exclusion reduces the ratio of Γsalt over Σ, a ratio which we call the charge efficiency, Λ. Theoretically, for low potentials across the diffuse layer (the Debye-H€ uckel limit), counterion


adsorption and co-ion desorption are actually of equal importance, that is, for each electron transferred, there is half of a cation adsorbed and half of an anion desorbed and thus Λ will be zero, while for very high potentials, the limit is approached where counterion adsorption fully compensates the electron charge and Λf1. As we will show, data for Λ as a function of voltage and ionic strength are an excellent probe to test models for the structure of the double layer inside of the porous electrode, without a-priori knowledge of the effective area for ion adsorption; see Figure 1b. Actually, after having established that a certain double-layer model accurately describes data for Λ, the effective surface area am per gram of electrode can be directly determined from a simple fit to the full data sets of both Γsalt and Σ. The use of Λ to determine double-layer properties points to the fact that salt adsorption is a basic characteristic of double layers, as much as electrode charge. Therefore, just as with Σ, Γsalt follows from any quantitative model that describes double-layer structure.14,18 Thus, the objective of the present work is to show that both am and CSt of porous electrodes can be accurately derived experimentally from two independently obtained data sets for equilbrium salt adsorption and electrode charge, both assessed as a function of ionic strength and cell potential. These two parameters, in turn, are used as input parameters in an electrokinetic CDI process model15 and are compared

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with data for current and effluent ionic strength, obtained as a function of voltage, ionic strength, and flow rate; see Figure 3. We model the ion distribution in the porous electrode according to the GCS model, which describes a planar double layer as a combination of a Stern layer and a diffuse, GouyChapman, layer. In the GCS model, the surface charge density σ is given by14-18 σ = 4λDc sinh(Δφd/2), where λD is the Debye length, λD = (8π 3 c 3 Nav 3 λB)-1/2, λB the Bjerrum length (λB = 0.72 nm in water at room temperature), Nav Avogadro's number, Δφd the potential difference over the diffuse layer, and c the ionic strength (in mM). The voltage difference over the Stern layer ΔφSt relates directly to σ according to Gauss's law, CSt 3 ΔφSt 3 VT = σ 3 F, where CSt is the Stern layer capacity. Potentials Δφd and ΔφSt are dimensionless and can be multiplied by the thermal voltage VT = RT/F to result in the dimensional voltage. At equilibrium, the sum of Δφd and ΔφSt (times VT) equals half of the applied cell potential, Vcell, as we assume that Vcell equally distributes over the two CDI electrodes. The surface charge Σ per gram of total electrode mass is given by multiplying σ by the factor 1/2 3 am, where am is the specific electrode area available for ion adsorption (in m2/g), while the salt adsorption Γsalt is given by multiplying the salt adsorption surface density,14,18 w = 8λDc sinh2(Δφd/4), by the same factor. Finally, the charge efficiency is given by14,15,18 Λ = Γsalt/Σ = w/σ = tanh(Δφd/4). Figure 1b shows measured values for Λ based on data for equilibrium charge Σ and salt adsorption Γsalt, as function of cell voltage and ionic strength (shown in Figure 2). These experimental findings confirm the behavior of Λ predicted by GCS theory in that Λ increases with increasing cell voltage and, in addition, that at each potential, Λ is higher when the ionic strength is lower. Figure 1b shows that by using an optimized value of CSt = 0.10 F/m2, the only adjustable parameter in the GCS model, a fairly well model fit is obtained. Applying the GCS model with the value CSt = 0.10 F/m2 now immediately results in the effective electrode area am by fitting to the full data sets of Σ and Γsalt, which are well described using a value of am ∼ 720 m2/g, which is ∼55% of the measured BET area of this material (∼1330 m2/g). Note that if we would have fitted to the data for charge of Figure 2a only, quite different values would have been obtained, namely, CSt ∼ 0.25 F/m2 and am ∼ 320 m2/g. With those parameter settings, however, salt adsorption would be predicted to be independent of ionic strength (which is not the case; see Figure 2b), with values predicted ∼15% too high. In Figure 2, both data and theory show how for a given applied cell voltage, and when the ionic strength is reduced, we require less charge but still we adsorb more salt (i.e., Λ is higher at lower ionic strength). This conclusion exemplifies why CDI is expected to be most promising for aqueous solutions of relatively low ionic strength. The dashed line in Figure 2a identifies the differential capacitance in the lowvoltage limit, CD,Vf0, which is ∼52 F/g when defined per single electrode mass and based on half of the cell voltage, as usual in the literature of electrodes for supercapacitor batteries. This result is in the range of reported literature values.1,2 Furthermore, Figure 2a shows that CD,Vf0 is an underestimate of CD values at higher voltages (which are up to a factor of ∼2 higher at 1.0 V) and is a function of ionic


strength. The data of Figure 2b can be recalculated to obtain the volumetric salt concentration in the electrode. For example, by taking the value of 0.2 mmol/g at Vcell = 1.4 V, this recalculates with an electrode density of 0.72 g/cm3 and porosity of 55% into an effective concentration of removed salt of 250 mM, that is, we have in the open volume of the electrode an excess salt concentration which is ∼40% of the salt concentration of seawater (∼600 mM). The dynamic ion adsorption/desorption model15,18 includes the GCS model as well as an Ohmic resistance across the spacer region. These are valid simplifications when the double-layer structure responds quickly to a varying surface charge and bulk ion concentration, when ion concentration variations across the spacer layer are small, and when we can assume local electroneutrality outside of the double layer.18 We then neglect a resistance within the porous electrode. These assumptions will be relaxed in future work. During ion adsorption, the applied cell voltage Vcell is no longer equal to Δφd þ ΔφSt (as it is for equilibrium), but instead, Vcell/(2 3 VT) = Δφtr þ Δφd þΔφSt, where Δφtr is the potential drop over half of the spacer layer. The current, or charge transport rate, Jcharge, defined per unit electrode area A (i.e., the projected area), relates to Δφtr according to Jcharge = k 3 c 3 Δφtr where k is an inverse specific resistance. Implementing this expression, the charge density per unit specific area, σ, is given by dσ/dt = A/(am 3 m) 3 Jcharge, where t is time and m is the mass of all electrodes of one bias (half the total electrode mass), while the salt adsorption w relates to the salt removal rate Jsalt according to dw/dt = A/(am 3 m) 3 Jsalt. The CDI cell overall salt balance is v 3 dc/dt = Φ(c0 - c) - Jsalt 3 A, where c0 is the inlet salt concentration, c the effluent concentration, and v the spacer open volume. Here, we describe the CDI cell as a single ideally stirred volume. In the ion release step, we set Vcell equal to 0, upon which the current direction is reversed and salt is released from the electrodes back into solution. For the CDI stack, consisting of the eight cells, values for A and v are measured as A = 270 cm2 and v = 70 mL. Figure 3 compares calculations with experimental data for the effluent salt concentration and electrical current. All calculations are based on a single set of input parameters as defined above (v, A, CSt, and am), both for ion adsorption and for ion release. The inverse resistance factor, k, is the only remaining free parameter and can be fitted quite successfully to the data as a single constant, except for an apparent ionic strength dependence, which can be described empirically by k (μm/s) = 1/2 þ 10/c0 (mM), that is, k is higher at lower ionic strength. That k depends on ionic strength (instead of only depending on ion mobility) remains an inconsistency of the model which might relate to the influence of nonconstant ion profiles across the spacer channel,18 dispersion effects in the spacer channel, and/or resistances to ion transport within the electrode.5 For comparison, for 5 mM, the value of k recalculates to a volumetric resistance of 10.6 kΩ 3 cm (∼6 times that of a 5 mM aqueous solution) and an overall resistance for all eight cells together of 1.57 Ω. With an applied voltage of 1.0 V, this implies that the initial current must be 0.63 A (because at time 0, the double layers have not yet been formed), a number which can indeed be read off from Figure 3d.

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Figure 3. CDI process data (left column) and theory (right column) as a function of cell potential V (a-d), flow rate Φ (e, f), and ionic strength of the inlet solution c0 (g, h). At time zero, a positive voltage is applied, which is reduced to zero halfway through the cycle.


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Accepting for now the empirical relation for k(c0), Figure 3 shows the correspondence between the data and theoretical prediction. In general, the model reproduces the data very well, notably the difference in the sharply spiked upward trace of ceffluent versus time during ion release, compared to the more shallow downward trace during ion removal. This difference is due to the lower resistance in the spacer channel when ions are released from the electrode, and the ion concentration in the spacer is therefore higher (and vice versa). Even the rather unexpected nongradual decline of current with time during ion removal at 1.0 V, where a rapid decay of current up to ∼100 s is suddenly followed up by a period of a much slower decay of the current (panels c and d), is observed both in the data and in the theory. The present study significantly extends the work reported in ref 15, where only a single experiment was analyzed based on a higher value of CSt. In addition, in ref 15, we did not succeed in describing both ion removal and ion release with a single set of parameters. Interestingly, in the present work, this inconsistency has disappeared, which suggests that with correct values of CSt and am implemented, both ion removal and ion release can be described by the same parameters. Experimental data were obtained in a laboratory-scale CDI stack with eight unit cells consisting of graphite current collectors (Cixi Sealing Spacer Material Factory, Ningbo City, China; thickness δ = 250 μm), porous carbon electrodes (type CR-B, Axion Power Intl., Delaware, U.S.A.; δ = 270 μm, 2 3 m = 10.6 g total mass), and a polymer spacer (Glass fiber prefilter, cat no. AP2029325, Millipore, Ireland; δ = 400 μm). The graphite current collectors were alternatively positively or negatively biased. All materials were cut into pieces of 6 6 cm2 dimension and assembled, after which the entire stack of all layers was firmly pressed together and placed in a Teflon housing. An aqueous NaCl solution was pumped through a small hole (1.5 1.5 cm2) located in the exact middle of the stack radially outward through the spacer layers; see Figure 1a. The current and voltage were measured online as well as the ion conductivity of the influent and effluent streams, which was converted to ionic strength. The experiment was run sufficiently long (1-2 h) for the current to drop to 0 (except for a leakage current) and for the effluent ionic strength to return to the inlet value. In this way, we ascertained that the double layers everywhere within the electrodes were at equilibrium with the bulk salt solution, of which we know the ionic strength. We calculated Λ from the independent measurement of the equilibrium salt adsorption, Γsalt, and equilibrium charge Σ. The salt adsorption can be calculated from integrating (c0 - ceffluent) with time (e.g., Figure 3a) and multiplying with the solution flow rate Φ. Obviously, the amount of salt adsorbed must equal the amount of salt released, a condition which we checked to hold during our experiments. The current signal (Figure 3c) was integrated with time to obtain the electrode charge, Σ. Here, a leakage current, observed as a constant small current (of the order of 10 mA) in the ion removal step, was subtracted from the data. This procedure ensured that the total charge transferred in one direction during ion removal equaled the charge transferred in the opposite direction during ion release.


In conclusion, the charge efficiency Λ of two oppositely positioned porous electrodes can be determined from the total salt adsorption and electrode charge as reached at equilibrium. A data set for Λ as a function of cell potential and ionic strength can be used to validate models of ion distribution within the electrical double layers which form inside of porous electrodes without a priori knowledge of the effective area for ion storage. We find that the classical GCS model in which only the Stern layer capacity CSt is a freely adjustable parameter describes our present data well. On the basis of the validated GCS model, we can derive that per gram of electrode material, the effective use of the electrode area is am ∼ 720 m2/g, which is ∼55% of the BET area of this material, suggesting that quite a significant portion of the BETarea is used for ion adsorption. Our analysis points out that apart from the surface area, the Stern layer capacity is an equally important parameter to characterize (and optimize) the capacity of the porous electrode for salt storage. We have shown how optimized values for equilibrium properties of the porous electrodes are essential elements of a dynamic electrokinetic process model for capacitive deionization. Such models are instrumental for system design and cost optimization of future energy-efficient water desalination technologies using electrical fields.

AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. E-mail: maarten. [email protected]. Tel: þ31 6 46 193949. Fax: þ31 317 48 21 08.

ACKNOWLEDGMENT This work was performed in the TTIWcooperation framework of Wetsus, Centre of Excellence for Sustainable Water Technology (www.wetsus.nl). Wetsus is funded by the Dutch Ministry of Economic Affairs, the European Union Regional Development Fund, the Province of Friesland, the City of Leeuwarden, and the EZ/Kompas program of the “Samenwerkingsverband NoordNederland”.

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Charge Efficiency: A Functional Tool to Probe the Double-Layer

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