Thermodynamics of Ion Separation by Electrosorption - Environmental

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Cite This: Environ. Sci. Technol. XXXX, XXX, XXX−XXX

Thermodynamics of Ion Separation by Electrosorption Ali Hemmatifar,†,∥ Ashwin Ramachandran,‡,∥ Kang Liu,† Diego I. Oyarzun,† Martin Z. Bazant,§ and Juan G. Santiago*,† †

Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States Department of Aeronautics & Astronautics, Stanford University, Stanford, California 94305, United States § Departments of Chemical Engineering and Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States ‡

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S Supporting Information *

ABSTRACT: We present a simple, top-down approach for the calculation of minimum energy consumption of electrosorptive ion separation using variational form of the (Gibbs) free energy. We focus and expand on the case of electrostatic capacitive deionization (CDI). The theoretical framework is independent of details of the double-layer charge distribution and is applicable to any thermodynamically consistent model, such as the Gouy−Chapman−Stern and modified Donnan models. We demonstrate that, under certain assumptions, the minimum required electric work energy is indeed equivalent to the free energy of separation. Using the theory, we define the thermodynamic efficiency of CDI. We show that the thermodynamic efficiency of current experimental CDI systems is currently very low, around 1% for most existing systems. We applied this knowledge and constructed and operated a CDI cell to show that judicious selection of the materials, geometry, and process parameters can lead to a 9% thermodynamic ef f iciency and 4.6 kT per removed ion energy cost. This relatively high thermodynamic efficiency is, to our knowledge, by far the highest thermodynamic efficiency ever demonstrated for traditional CDI. We hypothesize that efficiency can be further improved by further reduction of CDI cell series resistances and optimization of operational parameters. In this work, we present an alternative “top-down” theoretical framework that naturally reveals the thermodynamic limits of electrosorption (including supercapacitors, CDI, CAPMIX, etc.), starting from first-principles by variation of the electrochemical free energy functional. Similar variational approaches have been used to calculate electric doublelayer surface forces8−10 and to formulate modified Poisson− Boltzmann models of diffuse charge profiles,11−15 implicit solvent models,16,17 and phase-field models of ionic liquids and solids.18−21 We shall see that the variational approach to electrochemical modeling is also convenient to describe the thermodynamic properties of CDI and yield conclusions applicable across the full range of EDL models and chemistries. One important measure of ion separation in practice is the thermodynamic efficiency of the process (η), defined as the ratio of free energy of separation to the actual work input. Without a careful system design, energy consumption can be more than an order of magnitude larger than free energy of separation (i.e., η ≪ 10%). Various sources of irreversibility include ionic resistive and electronical resistive losses which

1. INTRODUCTION Ion separation (desalination) processes of any type have long been known to require at least a minimum energy equivalent to the (Gibbs) free energy of separation. The minimum energy consumption corresponds to an ideal, extremely slow reversible process free of resistive losses. In systems with electrostatic interactions, such as supercapacitors, capacitive deionization (CDI), and capacitive mixing (CAPMIX),1−4 a common practice to analyze this limit is to start from mechanistic details of electrostatic charge attraction, including specific treatments of the electric double layer (EDL) structure, and then proceed to formulate work integrals to calculate energy.3,5−7 For example, Wang et al.7 showed equivalency of minimum electrical work and the Gibbs free energy of separation in a four-stage electrosorption cycle, although they did not analytically derive this and instead used a numerical approach. A significant limitation of this bottom-up approach is that it cannot be readily generalized to wide range of EDL models, and more importantly, it provides limited insight into the various assumptions and approximations associated with each EDL model. In particular, numerical integration of electrosorptive work generally obscures the effects of compact versus diffuse portions of the EDL structure, effects of finite ion size, and the geometry and relative thickness of EDLs (e.g., whether the EDLs are overlapped or nonoverlapped). © XXXX American Chemical Society

Received: June 1, 2018 Revised: July 16, 2018 Accepted: August 2, 2018

A

DOI: 10.1021/acs.est.8b02959 Environ. Sci. Technol. XXXX, XXX, XXX−XXX

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Environmental Science & Technology

Figure 1. (a) Schematic of an electrochemical desalination system with a pair of porous, conductive electrodes (only one shown) in contact with a reservoir. (b) Solid line is an ion separation cycle (on cions vs c∞ plane) wherein charging and discharging are performed with respect to two reservoirs. Dashed lines depict some arbitrary charging/discharging relative to a time-varying value of reservoir concentration.

cell. The dashed curves in Figure 1b are shown here as a qualitative representation of a more general case. 2.2. Free Energy Functional and Electrical Work of Electrosorption. Our interest is the minimum electrical work required for the ion separation cycle discussed in Section 2.1, which corresponds to the limit of infinitely slow traversal of the charge-voltage cycle with all chemical species in quasiequilibrium. We seek to formulate this from an energetic perspective without assumptions regarding the details of the charge distribution within the pore electrical double layers (EDLs) or the electrode matrix material. We stress that the analysis we present here is applicable in electrosorptive processes such as supercapacitors, CDI, and CAPMIX. The most general starting point is the total Gibbs free energy functional G[{ci},ϕ;ρe,ϕe;{crj }] of a single composite porous electrode, which is an integral over the spatial distributions of ionic concentrations {ci(x⃗,t)}iN= 1 and the electrostatic potential of mean force ϕ(x⃗,t) in the electrolyte-filled pore space; the electronic charge density ρe(x⃗,t) and electrostatic potential (Fermi level per charge) ϕe(x⃗,t) of electrons in the solid electrode matrix; and the concentration profiles {crj (x⃗,t)}j=1Nr of any redox-active chemical species (reactants and/or products) that undergo electrochemical reactions with the ions in the pore space. In general, the redox-active species may be charged or uncharged, resulting from Faradaic, autoionization, or complexation reactions, and may exist anywhere in the porous electrode volume, including dissolved species in the electrolyte filled pores, adsorbed species at interfaces, or inserted species within the electrode solid matrix. Our theoretical development below does not depend on the specific form of G. Various existing mathematical models of electrostatic CDI for flat29 and porous30,31 blocking electrodes as well as Faradaic CDI with redox-active porous electrodes32−34 are included as special cases in our general thermodynamic formalism. In particular, all Poisson−Boltzmann (PB) models (including the classical dilute-solution approximation and various modified PB models13 for thin or thick double layers) correspond to the following form of the free energy functional.

scale with the temporal rate of adsorption/desorption, parasitic losses of Faradaic charge-transfer reactions, dispersion effects and associated flow mixing, and pressure work toward pumping electrolytes. A low resistance and optimized operation design is thus critical for a successful ion separation system. Although numerous studies focus on increasing thermodynamic efficiency of mature technologies such as reverse osmosis (RO)22−24 and thermal desalination,25,26 there have been only a few studies on the thermodynamics of emerging electrosorptive technologies such as CDI. In fact, only a handful of published studies on CDI even report thermodynamic efficiency values.27,28 Further, there has been no overview of the current typical values of CDI thermodynamic efficiency or of methods by which it can be improved.

2. THEORY 2.1. Problem Definition. We introduce our top-down thermodynamic formulation as follows. Consider a pair of identical porous and electrically conductive electrodes which will be used to trap, transfer, and release ions from two reservoirs of fixed volume: a “diluted” solution and a “brine” reservoir. Each of the two reservoirs is filled with a binary symmetric (z:z) electrolyte of initial concentration c0 (Figure 1a). The volume of a single electrode pore space, diluted reservoir, and brine reservoir are respectively vp, vD, and vB. For these, we define water recovery as γ = vD/(vD + vB). Figure 1b (solid lines) shows an example ion separation cycle on cions vs c∞ plane, where we define cions = c+ + c− as total ion concentration trapped by the electrode (c± being pore concentration of cations and anions) and c∞ as the reservoir bulk concentration. The ion separation cycle can be rationalized as four stages: (1) charging stage, which stores charge in the pores and reduces diluted reservoir concentration to cD, (2) exchange of one reservoir for the other, maintaining constant cions value, (3) discharging stage, which releases salt and increases brine reservoir concentration to cB and decreases cions to cB, and (4) a return to the first reservoir at constant cions value. The latter four stages are also discussed in refs 2, 3, 6, and 7 In this construct, mass conservation requires dcions/ dc∞=−vbulk/vp, where vbulk=vD in charging and vbulk=vB in the discharging phase. We stress that ion separation from a single diluted reservoir to a single brine reservoir (solid lines) is an idealized case useful in rationalizing CDI systems. For example, one can envision a process involving multiple intermediate reservoirs (not just two end points). In an actual CDI system with flow from a common source, charging and discharging is performed relative to some time-varying concentration associated with the effective time-varying ion density in the

G=

∫V ijjjkgc + ρp ϕ − 2ε |∇ϕ|2 yzzz{dVp + ∫S qeϕedAe p

e

(1)

Equation 1 expresses the mean-field and local density approximations for a linear dielectric material (neglecting all chemical or electrostatic correlations between ions).14 Here, the integrals are over pore volume and the bounding surface of the solid electrode matrix, respectively; ρp (x ⃗ , t ) = ∑i ziFci is the ionic charge density in the electrode pores; F is Faraday’s B


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Environmental Science & Technology constant (mole of charge); zi is the valence of ionic species i; gc({ci},T) = h − Ts is the chemical portion of the Gibbs free energy density (due to short-range nonelectrostatic interactions) expressed in terms of the enthalpy density h({ci},T) and the entropy density s({ci},T); qe(x⃗,t) is the electronic surface charge density per area of the electrode solid matrix, assumed here to be a metal at constant potential ϕe; and ε(x⃗,t) is the permittivity of the pore solution. The free energy functional is constructed so that the electrostatic potential ϕ satisfies the stationarity condition of vanishing first variation. This construction leads to Poisson’s equation for bulk variations: ij δG yz jj zz = ρ + ε∇2 ϕ = 0 j δϕ z p k {bulk

chemical potential μi = vD δg /δci , is then uniform and constant for each ionic species i. At this point, we can calculate the electrostatic work of the system for the complete ion separation cycle of Figure 1b. Assume a differential electronic charge dqe = ∫ VeδρedVe is injected to the electrodes at fixed electrode potential ϕe, under quasi-equilibrium (μi uniform and constant) exchange with bulk reservoir solution, and results in a change in pore ion concentration of δci(x⃗). This process requires a minimum electrostatic work of −2VTϕ̃ edqe, where ϕ̃ e = ϕe/VT and VT is the thermal voltage. Due to electroneutrality, ionic charge compensates for electronic charge as in ∫ Vpδρp dVp + ∫ Veδρe dVe = 0. Without loss of generality, we take ϕ = 0. The change in free energy of the electrode for this É ÅÄÅ ∼ ÑÑÑÑ process is then vDδg = ÅÅÅÅ∫ ∑i μi δci dVp + ∫ VTδρϕ d V eÑ ÑÑ and e e Ve ÅÅÇ Vp ÑÖ using electroneutrality condition we further simplify to the following:

(2)

and the associated electrostatic boundary condition for surface variations, (δG/δϕ)surface = qe + n̂ · ε∇ϕ = 0. In the mean-field approximation, the force experienced by each individual ion derives from the electric field generated by the mean charge density via Poisson’s equation. This approximation is reflected in the form of the free energy functional by defining the electrochemical potential of any species i as its variational derivative with respect to a localized unit concentration perturbation,20 μi =

δg δG = c + ziFϕ = μiΘ + RT ln ai + ziFϕ δci δci

vDδg =

with dNi = ∫ δci dVp. For a closed loop, we have ∮ δg = 0, and V p

thus the minimum volumetric energy consumption for the cycle Ev,min is as follows:

(3)

Ev ,min = −

where is the standard reference chemical potential and ai is the chemical activity of species i. By setting each electrochemical potential to a constant value, μi = μ∞ i (for exchange with a reservoir “at infinity”), we define the quasi-equilibrium concentration profiles, {cieq(ϕ,μi∞)}. Inserting the quasiequilibrium charge density,

∑ ziFcieq(ϕ , μi∞) i

i ziF(ϕ∞ − ϕ) yz zz zz RT k {

∑ ziFci∞ expjjjjj i

VT vD

∮ 2ϕ∼e dqe =

2 vD

∮ ∑ μi dNi = Δgsep i

(6)

where Δgsep is specific Gibbs free energy of separation. Refer to Section S.1 of the Supporting Information (SI) for details. Equation 6 states that in the absence of chemical (nonelectrostatic) portion of the free energy, Ev,min is equivalent to the Gibbs free energy of separation Δg sep for any thermodynamically consistent electrical double layer (EDL) of arbitrary geometry and thickness (overlapped or nonoverlapped). This includes Poisson−Boltzmann (PB) type EDL treatments such as Gouy−Chapman (GC) model as well as modified Poisson−Boltzmann with finite ion size effects.12,36 We stress that ion size effects do not affect the final result of our thermodynamic analysis here. Inclusion of ion−ion correlation effects changes details of calculations, but the final result in eq 6 holds assuming local thermodynamic equilibrium. EDL descriptions with constant or ci-dependent nonelectrostatic potentials such as modified-Donnan (mD) model31,32 each also respect eq 6 (since the integral of the nonelectrostatic term on a closed path vanishes). Importantly, as noted above, eq 6 is also valid for EDLs with compact layers such as Gouy−Chapman−Stern (GCS) and Gouy−Chapman−Stern−Carnahan−Starling (GCS-CS) models. These conventional electrosorptive desalination EDL models satisfy the free energy formulation results in general, since these models can be derived variationally from the same free energy model. Equation 6 can be further simplified for 1:1 dilute electrolytes (ai = ci) and assuming an idealized instantaneous, quasi-equilibrium ion exchange between reservoir and the pores. Under these conditions and for ϕ = 0 in the reservoir, μi ≈ μi,∞ = RT ln c∞. Moreover, 2dNi = −vbulkdc∞ by mass conservation. The minimum volumetric electrical work then takes the following form:

into eq 2 yields a modified Poisson−Boltzmann (PB) equation for concentrated solutions (ai ≠ ci),13 which reduces to the familiar PB equation in the limit of a dilute solution (ai = ci): −ε∇2 ϕ =

(5)

i

μΘi

ρpeq (ϕ , {μi∞}) =

∼

∑ (μi − ziRTϕe )dNi

(4)

Existing models of CDI describe electrosorption of ions in quasi-equilibrium diffuse EDLs via the Gouy−Chapman−Stern (GCS) and modified Donnan (mD) models, which correspond to solutions of the PB equation (eq 4) with the Stern “surface capacitor” boundary condition in the limits of thin and thick double layers, respectively,30,32−34 and are thus included in our thermodynamic framework. More generally, relaxing the quasiequilibrium assumption (by defining mass fluxes in terms gradients of the electrochemical potentials defined by eq 3) leads to modified Poisson−Nernst−Planck equations for diffuse-charge dynamics out of equilibrium,13,17,20 which capture additional effects of nonequilibrium charging and tangential surface conduction.35 Since such nonequilibrium phenomena introduce additional resistance into the system, we will instead focus on quasi-equilibrium electrosorption and derive a thermodynamic bound on the consumed energy. We define the specific free energy g = G/vD (energy per volume of the diluted reservoir) and assume macroscopic quasi-equilibrium across the electrode pores. The electroC


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Environmental Science & Technology Ev,min =

2RT vD

∮ vbulk ln c∞dc∞

reactions that reduce or oxidize the adsorbed ions, either to form new molecules or ions in the pores or on the solid surface18,33,34 or to intercalate ions into an active solid matrix of the porous electrode.40−46 In order to describe such situations, an additional term, GF = ∫ gF ({c jr}, ϕ , ϕe)dVF , must be added to the electrostatic

(7)

For the ion separation cycle of Figure 1b (solid lines), Ev,min can be written in the familiar form ÄÅ ÉÑ Å Ñ c 1 2RT ÅÅÅÅcD ln cD + γ − 1 cB ln cB − γ0 ln c0 ÑÑÑÑ. ÅÇ ÑÖ 2.3. Alternative Approach: Direct Integration of Electrical Work. Alternative to the approach above, for special cases of nonoverlapping (e.g., GCS) and highly overlapped (e.g., mD) double layer models, the equivalency of Ev,min and Δgsep can be shown by explicit calculations (direct integration of electrical work). For example, consider a model including a Stern layer assumption. For the equilibrium condition, the (nondimensional) potential of a single electrode can be written as ϕ̃ e = Δϕ̃ St + Δϕ̃ D where Δϕ̃ St is the Stern layer potential drop and Δϕ̃ D is either the diffuse layer (in GCS model) or Donnan potential drop (in mD model), both normalized by the thermal voltage. A close inspection of the two models reveals that they each obey the following relation between pore ionic concentration cions and pore charge density ρp for 1:1 electrolytes

(

)

1 ρp d jij cions zyz jj n zzz n = F c∞ dΔϕD̃ jk nc∞ {

VF

free energy functional (eq 1). The integral is over the “reactive volume” containing all the active species which undergo chemical or electrochemical reactions involving ions in the pores (with concentration profile {crj (x⃗,t)}), homogeneous free δG energy density gF, and chemical potentials μj (x ⃗ , t ) = δ c rF . In j

the case of Faradaic reactions with different redox species in each electrode, the open circuit voltage is generally nonzero. The transient voltage under general nonequilibrium conditions is determined by a stoichiometric sum of the chemical potentials of the reactive ions and reduced/oxidized species (defined variationally from the total free energy functional according to the general thermodynamic framework of electrochemical kinetics).20 As with electrostatic adsorption in the diffuse EDLs described above, the free energy change of any charge/ discharge cycle is minimized when Faraday reactions are also in quasi-equilibrium. In presence of chemical surface charge, a suitable adsorption isotherm governs the thermodynamics. For Faradaic reactions, the quasi-equilibrium charge-voltage relation is derived from a generalized form of the Nernst equation,20 such as the Frumkin isotherm (or regular solution model) for ion intercalation.46 In this limit of “fast” reactions, there is no net change in total chemical potential from reactants to products, and the total free energy is the same as in the original electrostatic adsorption model, at the same state of charge. Moreover, since the additional contribution to the energy only depends on the state of charge (assuming quasiequilibrium reactions), it vanishes under any closed charging cycle, ΔGF = vD ∮ δgF = 0. Therefore, our main result, eq 6, is unchanged by the presence of any chemical or electrochemical reactions in the electrodes. 2.5. Thermodynamic Efficiency of Electrosorption in Practice. Having established a general theory of minimum energy consumption, we now focus on practical relevance of this analysis in CDI cycles. First, we highlight the importance of series resistance (an important cell design parameter and fabrication challenge), and then we focus on effects of flow rate and ion separation rate (operational parameters) on thermodynamic efficiency, η. In CDI, the (ionic and electronic) resistances and Faradaic reactions are two main sources of energy loss.47,48 The pumping energy is usually insignificant,47 except perhaps for flow-through CDI designs at very high flow rates. We make the effort to reduce Faradaic losses as much as possible by limiting the voltage window to 0.4 to 1 V range. The existing models that quantify Faradaic energy loss mechanisms are overly complex.32,49−51 We strive for simplicity, and thus in the current work, we consider a regime where Faradaic losses are negligible and focus instead on resistive losses in quantifying the thermodynamic efficiency of CDI operation. Such an estimate provides a simple yet useful lower bound for η. Motivated by this, we later show in Section 4.2 that simple reduction of series resistance can lead to significant increase in η. In its simplest form, the volumetric resistive consumption Ev,resist for constant current operation can be estimated as RsI2/

(8)

where n = 1/2 and 1 for GCS and mD models, respectively. Using this ad-hoc relation, the electroneutrality condition (qe + vpρp = 0), and mass conservation (dcions/dc∞=−vbulk/vp), the electrical work can be written (see Section S.2 of the SI for details) as follows: Ev , min = 2 F

Ä VT ÅÅÅÅ Å− vD ÅÅÅÇ

∮ Δϕ∼St dqe −∮ d[qeΔϕ∼D + Fvp(1/n − ln c∞)cions] + ÑÉÑ

∮ vbulk ln c∞dc∞ÑÑÑÑÑÑÖ

(9)

or again simply Ev,min = Δgsep. Importantly, note the electrical work of the Stern layer ESt (the first term on the right-hand side) vanishes on a closed loop for the classical surfacecapacitor approximation introduced by Grahame,37 where Δϕ̃ St is solely a function of surface charge density qe (equal to the total nearby pore charge density by macroscopic electroneutrality). We can thus write the integrand as a total differential dESt, where Δϕ̃ St = dESt/dqe, whose integral around a closed loop must vanish. The second integral must also vanish for any closed loop. In the classical picture, the Stern layer charge and discharge dissipates no energy in a cycle, since its capacitance depends only on charge, and not voltage. In contrast, diffuse layer charging cycles consume energy, since EDL capacitance is inherently voltage dependent, except in the limit of small EDL voltage drop (Debye−Hückel theory), where linear response again yields a constant capacitance, independent of voltage. 2.4. Effect of Electrochemical Reactions. Although the preceding analysis is based on the electrostatic free energy functional (eq 1) for electrosorption of ions in the diffuse double layers of a porous electrode, it also applies to processes involving chemical or electrochemical reactions. A simple extension would include regulation of surface chemical charge of the porous electrode, e.g., by pH-dependent deprotonation or hydroxyl dissociation reactions.38,39 A broader class of reactive systems include Faradaic CDI, where significant electro-sorption is mediated by reversible electron transfer D


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Figure 2. (a) Schematic of embedded titanium mesh sheet into the activated carbon electrode using 100 °C hot press. Images of (b) electrode side, (c) titanium mesh side, and (d) cross-section side views after hot press step. (e) Cyclic voltammetry (CV) test of the assembled cell at 0.2 mV/s scan rate and 20 mM NaCl electrolyte solution with −0.6 to 0.6 V voltage window. CV test shows about 17 F cell capacitance or ∼60 F/g specific capacitance. (b) Electrochemical impedance spectroscopy (EIS) test of the assembled cell again with 20 mM NaCl electrolyte solution. The setup resistance (ionic resistance in separators, electric resistance of current collectors and wires) is only 0.33 Ω and the contact resistance is negligible.

used. We ultrasonically cleaned titanium meshes of 250 μm thickness (uncompressed) and used them as current collectors. Each current collector was square shaped with 5 × 5 cm2 size and had a tab section (1 × 3 cm2) for connection to external wires. To enhance electrical contact between current collectors and electrodes, we embedded the titanium meshes intro the electrodes using a hot press at 100 °C temperature. A schematic of a single current collector with compressed thickness of 170 μm embedded into carbon electrode is shown in Figure 2a. The compressed thickness of the stack was 300 μm. Electrode side, titanium mesh side, and cross-section views are shown in Figure 2b−d, respectively. Polypropylene meshes of 30 μm thickness (McMaster-Carr, Los Angeles, CA) acted as spacers between the electrode pairs. The assembly was then sealed with gaskets and fastened by C-clamps. 3.2. Cell Characterization. We characterized the cell assembly by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) tests. The CV test in Figure 2e was performed at 0.2 mV/s scan rate with 20 mM NaCl solution and showed cell capacitance of about 17 F (or ∼60 F/ g specific capacitance). The EIS measurements in Figure 2f show 0.33 Ω (or 16.5 Ω cm2 area-normalized) setup resistance (ionic resistance of the solution in the separators, electrical resistance of current collectors, and resistance of connecting wires). The contact resistance, usually associated with a semicircle feature in the EIS Nyquist plot, is almost completely eliminated, as shown in the inset of Figure 2f. 3.3. Experimental Procedure. The experimental setup consisted of our fbCDI cell, a 3 L reservoir filled with 20 mM NaCl solution, a peristaltic pump (Watson Marlow 120U/DV, Falmouth, Cornwall, U.K.), a sourcemeter (Keithley 2400, Cleveland, OH), and a flow-through conductivity sensor (eDAQ, Denistone East, Australia). We operated our cell at constant current (CC) charging and discharging and studied the effect of flow rate and current on the thermodynamic efficiency of the CDI desalination process. We used flow rates varying between 0.22 and 3.47 mL/min, and current densities

γQ where Rs, I, and Q are respectively the effective series resistance, current magnitude, and flow rate of the solution from reservoir to the cell. We show in Section S.3 of the SI that the minimum energy of ion separation (Δg) can be well approximated as Δg/c0 ≈ a (Δc/c0)n, where a and n depend only on the recovery ratio γ, and Δc (= c0−cD) is the desalination depth. The values of a and n versus the recovery ratio are given in Section S.3 of the SI. Importantly, the exponent n is close to 2 (between 1.5 and 2.5) for all recovery ratios. The thermodynamic efficiency η can thus be estimated as follows: η≈

Δg Ev , resist

γ Λcyclea ij Δc yz jj zz ≈ FIR s jjk c0 zz{

n−1

(10)

In eq 10, we have used the relation Δc = IΛcycle/FQ, where Λcycle is the cycle charge efficiency. The cycle efficiency Λcycle is defined as the ratio of moles of removed salt (calculated using the effluent concentration data) to the moles of electronic charge passed through the electrodes (calculated using the electrical current data). Also, note that the exponent n − 1 is positive (close to 1). Thus, for a given recovery ratio (i.e., fixed γ, a, and n), thermodynamic efficiency of a desalination cycle can be increased by (i) decreasing the series voltage drop IRs, (ii) increasing cycle charge efficiency, and (iii) larger desalination depths, Δc/c0. Motivated by this, as we will see in Section 3, we fabricate a low resistance CDI cell and optimize the thermodynamic efficiency of CDI by careful choice of operational parameters (such as flow rate, current, and voltage window).

3. EXPERIMENTAL SECTION 3.1. Cell Design. The cell assembly was similar to that in ref 48 with a radial flow structure. Two pairs of square shaped activated carbon electrodes (Materials and Methods, PACMM 203, Irvine, CA) with 5 × 5 cm2 size and initial (uncompressed) thickness of 270 μm and total dry mass of 1.14 g was E


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flow rate), the data organize fairly well near and just above the line set by the resistive limit Ev = Ev,resist line. This shows our simple estimate of Ev,resist correctly predicts an approximate minimum for Ev in practice. Further, it confirms that work toward decreasing series resistance is essential to the improvement of thermodynamic efficiency η of CDI cells. Also, we note that for cells with low series resistance, the Faradaic losses can contribute to most of the energy loss. The spread of our experimental data and their distance from the dashed line (red, filled circles in Figure 3) indicates that our cell has sufficiently minimized resistance losses such that now Faraday losses are very important. As a result, remedies for further reduction of Faradaic losses (e.g., further limiting maximum voltage) can also greatly improve the energy performance of CDI. 4.2. Operation for High Thermodynamic Efficiency. Consistent with the importance of series resistance, slow ion separation processes are often more thermodynamically efficient than faster processes. However, slower processes are not always superior because of the effects of Faradaic losses. We explore and demonstrate this in Figure 4. Shown is data given our low-resistance CDI cell for CC operation with current densities in 1−26 A/m2 (equivalent to 2.5−65 mA) and flow rates in 0.22−3.47 mL/min range. Figure 4a−c shows the respective volumetric energy consumption Ev, energy consumption per ion and per salt removed (note two ordinates), and thermodynamic efficiency η, all plotted versus applied current density. The voltage windows were 0.4−1 V to ensure high charge efficiency.56,57 For a given flow rate, operation at high currents is limited by resistive losses as expected.48 However, at overly low applied current, performance is limited by Faradaic losses since the cell spends overly long times near the high voltage limit.48 This trade-off between two very different energy loss mechanisms results in pronounced optima in η. Similarly, exceedingly low flow rate operation (e.g., 0.22 mL/min) suffers from dispersion and mixing inefficiencies associated with incomplete removal of desalted water or brine during charging and discharging, respectively.58 Instead of a monotonic trend, we see that midrange values of current and flow rate (4 A/m2 and 0.44 mL/min in this case) results in thermodynamic efficiency of about 9% and energy consumption of about 4.6 kT/ion. This thermodynamic efficiency is unprecedentedly high for traditional CDI designs (i.e., with no membranes, no ion intercalation, no inverted operation, etc.). We note that energy consumption per removed ion, unlike thermodynamic efficiency, is not a fundamental property. Such high thermodynamic efficiency is a result of low resistances and careful choice of operation parameters, such as voltage window, current, and flow rate. We predict that even higher η can be achieved using optimized operation and highperformance electrodes with low electrical resistance. 4.3. Trade-Off between Thermodynamic Efficiency and Throughput. Lastly, for completeness, we stress that the energy-efficient ion separation of our cell comes at a price. Any practical operational design is a trade-off between throughput and energy efficiency.48,59 Figure 5a shows thermodynamic efficiency of ion separation versus desalination depth (Δc) for our cell and published CC cell data.47,48,52−56 Figure 5b shows the main trade-off for this thermodynamic performance is a mediocre value for productivity (defined as volume of treated solution per unit time per cell area) at around 3 L/h/m2.56 Clearly, at a given desalination depth Δc, one can achieve

between 1 to 26 A/m2 with closed-loop circulation in all of our experiments (flow from reservoir to cell and back to reservoir). For all experiments, we charged (at current I) and discharged (at current − I) the cell between 0.4 to 1.0 V voltage window. Further, we performed at least three complete charge/ discharge cycles for each experiment to ensured dynamic steady state (DSS) operation, in which salt adsorption during charging is equal to desorption during discharging. We recorded external voltage and effluent conductivity using a Keithley sourcemeter and an eDAQ conductivity sensor (with ∼93 μL internal channel volume). Conductivity was converted to salt concentration using a calibration curve for NaCl. In Section S.4 of the SI, we present voltage and concentration measurements versus time for our experiments.

4. RESULTS AND DISCUSSION 4.1. Importance of Series Resistance Energy Loss. To put the energetic performance of current CDI technology into perspective, we show in Figure 3 experimental performance

Figure 3. Measured volumetric energy consumption (Ev) versus estimated resistive energy consumption (Ev,resist) for a wide variety of CDI and membrane-CDI cell designs operated under constantcurrent (CC) operation. Ev,resist provides a very good estimate of minimum Ev observed in practice, as all data points lay near and above the line set by the resistive limit Ev = Ev,resist. This shows decreasing series resistance is essential for improvement of thermodynamic efficiency η.

data for variety of reported CDI cells. The figure shows experimental volumetric energy consumption Ev versus Ev,resist for various CDI and membrane-CDI systems under constantcurrent (CC) operation.47,48,52−56 We here focus on CC operation, since the energy recovery during discharge step results in a lower energy per removed ion compared to shortcircuit discharge at 0 V.27 Particularly, Ev here is calculated based on the measured voltage and current as ∫ VIdt with the integral over a full cycle (charge and discharge). In addition to published data, we include measurements from a cell which we constructed specifically for the current study. As discussed in Section 3.1, our CDI cell here features a low-resistance (for each electrode pair) design which we realized by pressing into and embedding titanium mesh current collectors into 270 μm thick commercially available porous carbon electrodes. We also lowered series resistance by using 30 μm spacers. We observe that despite the wide variation in CDI cell materials, geometry, and operational parameters (including applied current, maximum and minimum voltage settings, and F


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Figure 4. (a) Measurements of volumetric energy consumption Ev, (b) energy consumption per ion and salt removed in units of kT/ion and kJ/ mol, and (c) the thermodynamic efficiency η for CC operation and 0.4−1 V voltage window at various currents and flow rates. Midrange values of current density (4 A/m2) and flow rate (0.44 mL/min) result in thermodynamic efficiency of up to 9%, unprecedentedly high for traditional CDI designs.

Figure 5. Thermodynamic efficiency versus (a) average effluent concentration reduction Δc and (b) productivity (in units of L/h/m2) for our cell and selected published CDI cells under constant current charge/discharge. The thermodynamic efficiency generally correlates with high Δc and low throughout productivity.

significantly higher η by sacrificing productivity (low flow rates). Finally, we present practical considerations for efficient CC operation based on observations in Figure 5. The following considerations can ensure good overall performance:

5. IMPLICATIONS We presented a top-down approach to calculate minimum energy requirement of electrosorptive ion separation using variational form of free energy formulation. The advantage of our formulation is its generality; it is free of any assumptions about the charge distribution in the EDLs or the profile of Faradaic reaction products, since all such processes occur in quasi-equilibrium (without internal resistance to transport or reactions). We showed, analytically, the minimum energy required for most known EDLs (irrespective of EDL geometry or thickness) is indeed equivalent to free energy of separation. These include (but not limited to) Poisson−Boltzmann type models such as GCS, GCS-CS, and mD. We focused on thermodynamic efficiency η of CDI systems as an example of electrosorptive ion separation method. We then discussed practical considerations in CDI cell design and operation and showed cell series resistance, Faradaic losses, and optimization of operational parameters such as flow rate and current are contributing factors to practical values of η. To reduce Faradaic losses, we suggested careful choice of the operation conditions so as to carefully manage the maximum voltages (and times near maximum voltages) experienced by the CDI cell (e.g., see He et al.,60 Tang et al.,49 and

(a) Choice of current and f low rate: the flow rate and current can be determined based on throughput and salt removal (Δc = IΛcycle/FQ) requirements. (b) Choice of voltage limits: the maximum voltage (after accounting for series resistance voltage drop) strongly influences the extent of Faradaic losses. The minimum voltage can be chosen so that least 4−5 cell volumes are flowed during charging. This ensure efficient recovery of fresh water at the effluent (high flow efficiency) and high cycle charge efficiency as a result.56 (c) Avoiding extremities: Extreme operations such as (i) very low operating currents wherein the operating current is comparable to the leakage current, (ii) very low flow rates wherein dispersion and mixing inefficiencies are important, and (iii) very high operating voltages wherein Faradaic losses dominate can all adversely affect overall performance. G


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Environmental Science & Technology Hemmatifar et al.48). However, we suggested to reduce resistive losses by both operating conditions (see for example Qu et al.,61 Dykstra et al.,52 and Ramachandran et al.56) and hardware design changes. Examples of important design components include spacer geometry, electrode material, and geometry, the electrical contact between current collector and electrode,62 and the shape of the cell’s flow channels (e.g., to minimize dispersion). As a comparison to published studies, we fabricated and tested a cell with reduced cell resistance. We used variations in operation to identify Faraday losses, resistive losses, and flow efficiency losses as primary irreversible loss mechanisms. Our cell demonstrated an unprecedented 9% thermodynamic efficiency and only 4.6 kT energy requirement per removed ion (NaCl solution), but we show that this achievement comes at the cost of productivity. Overall, the study identifies fundamental limits for CDI as an energy efficient desalination technology as well as the significant challenges associated with approaching this limit.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.est.8b02959. Details of derivations, supplementary measurements of concentration and voltage, and cell performance data (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (J.G.S.). ORCID

Ali Hemmatifar: 0000-0001-6716-3144 Juan G. Santiago: 0000-0001-8652-5411 Author Contributions ∥

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.H. gratefully acknowledges the support from the Stanford Graduate Fellowship program of Stanford University. A.R. gratefully acknowledges the support from the Bio-X Bowes Fellowship of Stanford University. We acknowledge the support from the California Energy Commission grant ECP16-014 and thank Dr. Michael Stadermann of LLNL for fruitful discussions.

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Thermodynamics of Ion Separation by Electrosorption - Environmental

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