Electrical Double-Layer Capacitance in Room Temperature Ionic

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Electrical Double-Layer Capacitance in Room Temperature Ionic Liquids: Ion-Size and Specific Adsorption Effects Y. Lauw,*,†,‡ M. D. Horne,† T. Rodopoulos,† A. Nelson,‡ and F. A. M. Leermakers§ CSIRO Process Science and Engineering, BayView AVenue, Clayton South, Victoria 3169, Australia, Bragg Institute, ANSTO, PMB 1, Menai, NSW 2234, Australia, Laboratory of Physical Chemistry and Colloid Science, Wageningen UniVersity, Dreijenplein 6, Wageningen 6700 EK, The Netherlands ReceiVed: June 9, 2010; ReVised Manuscript ReceiVed: July 29, 2010

The electrical double-layer structure and capacitance in room temperature ionic liquids at electrified interfaces were systematically studied with use of the self-consistent mean-field theory. The capacitance curve departs from symmetry with respect to the point of zero charge when unequal ion-size is implemented or when specific adsorption of ions is introduced. For the case of unequal ion-size, the shape of the capacitance curve is strongly determined by the size of the counterion and only weakly influenced by the co-ion size. When present, specifically adsorbed ions would change the capacitance within a limited range of applied potential from the point of zero charge, which itself varies with the strength of specific adsorption. I. Introduction Room temperature ionic liquids (RTILs) are envisaged to have a prominent role in future energy storage applications, such as high performance batteries and supercapacitors.1 This view is based on several generic features of RTILs. They are typically noncombustible, having good thermal stability and low volatility. These properties make them ideal electrolytes with superior reliability and safety features for energy storage devices. Moreover, RTILs have a relatively wide electrochemical window (up to 6 V), which enables large energy storage. Besides the applied potential, the quantity of the stored energy in RTILs depends on their electrical double-layer (EDL) capacitance, which is determined by the interfacial structure of RTILs at electrified interfaces. The absence of any solvation shells around RTILs reduces the EDL thickness and simultaneously increases their accessibility to penetrate porous electrodes.1,2 These two aspects lead to a large EDL capacitance in RTILs and thus add to their advantage for electrochemical applications. There are many experimental reports on the structure of RTILs at solid-liquid interfaces.3 One of the most interesting findings is that, due to strong steric and electrostatic correlations in RTILs, polar surfaces can induce the formation of an alternating layer of ions through charge overcompensation/ overscreening. A charge overcompensation typically happens when the electrostatic screening length is practically less than the size of the ion.4 This is valid for RTILs, in which the size of each alternate layer is proportional to that of ions. Recently, using the self-consistent mean-field theory (SCMFT), we studied the interfacial structure of RTILs and the corresponding EDL capacitance as functions of the applied electrode potential.5 An alternating layer of ions and camel-shaped capacitance curves (i.e., curves with two maxima) were generated successfully by considering a finite ion-size and an effective (local) polarization. In general, numerical techniques like SCMFT are more realistic to model RTILs than existing analytical approaches. The main reason is that numerical models can accommodate internal * To whom correspondence should be addressed. † CSIRO Process Science and Engineering. ‡ Bragg Institute. § Wageningen University.

degrees of freedom in RTILs and complicated (nonspherosymmetrical) structures of RTILs.6 These aspects are typically not accessible in analytical models.7 In SCMFT, each ion is modeled as a freely jointed chain of segments. To account for local polarization, a higher relative permittivity is assigned to polar (more conductive) components in RTILs, whereas a lower value is designated to apolar (less conductive) components. The value of the effective relative permittivity depends on the local distribution of the polar and apolar components. Due to an accumulation of the polar components of the counterion on the electrode’s surface, the effective relative permittivity is thus higher there than in the bulk. This trend is the inverse of what is typically found in aqueous electrolytes.8 The use of local polarization would further change the shape of the capacitance curve from an inverse parabola to a camel-like curve.5 A similar finding has been reported in the classsical literature for aqueous electrolytes, of which the hump on the corresponding capacitance curves is a direct consequence of nonhomogeneous polarization in the EDL.9 Results from the self-consistent mean-field (SCMF) calculation described in the previous paragraph were based on a uniform dendrimeric model of cation and anion, without taking into account ions of different size and/or with a short-range specific (nonelectrostatic) affinity toward the electrode’s surface. Here, we systematically study the EDL capacitance in RTILs with both features since, in reality, RTILs are typically composed of ions of different size, with a significant specific affinity toward the surface due to the absence of cosolvents. In aqueous electrolytes, specific adsorption is strongly related to the solvation shell of ions. A steric hindrance provided by a thick solvation shell prevents the ions from forming chemical bonds with the surface. However, this is not valid for ions with thin-enough solvation shells since the solvent molecules would be removed from the surface to accommodate adsorption of more ions. This eventually leads to a redistribution of local charges on the surface, changes the surface dipole, and induces a partial charge transfer.10 In the absence of any solvation shells surrounding RTILs, the specific adsorption of ions would arguably occur more strongly than in aqueous electrolytes.11,12 An example of specific adsorption in pure RTILs has been

10.1021/jp105317e  2010 American Chemical Society Published on Web 08/09/2010

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[

∫ ∑

Figure 1. Schematic of the tetrameric cation (left) and anion (right) used in the model. The cation consists of a positively charged segment P and nA neutral segments A per arm, whereas the anion comprises a negatively charged segment N and nB neutral segments B per arm.

reported by Aliaga et al. for 1-butyl-3-methylimidazolium dicyanamide RTIL on Pt-electrode.12 In this study, we focus on the effect of unequal ion-size and specific adsorption of ions on the EDL capacitance of the modeled RTILs. These two features can occur simultaneously in a real system, and each individual contribution would thus be difficult to distinguish. The SCMFT is used here to investigate each effect separately. Compared to our previous model,5 the SCMFT is now extended to accommodate the two features. The aim is to capture some qualitative changes in capacitance when the ion-size or the affinity of ions toward the surface is systematically varied.

II. Self-Consistent Mean-Field Theory for Room Temperature Ionic Liquids The SCMFT employs an iterative free energy minimization scheme that incorporates a local mean-field approximation in calculating intra- and intermolecular interactions, while implementing the freely jointed chain statistics.13 Hence, results obtained from the SCMF calculation describe a coarsegrained molecular system in equilibrium. Here, we consider a grand canonical ensemble of small systems of cation and anion adjacent to an electrified solid surface. A periodic boundary condition is applied to all sides perpendicular to the surface, whereas a Neumann boundary condition is used on the side opposite to the surface to reflect bulk properties. Each ion is modeled as a chain of charged and uncharged segments which formed a tetramer, as shown in Figure 1. This idealized architecture implies that the charged group is situated at the center, whereas the uncharged segments are located at the arms of the tetramer. For the cation, the positively charged segment P is surrounded by four arms, where each arm is composed of nA neutral segments A. For the anion, the negatively charged segment N is also surrounded by four arms, comprising nB neutral segments B per arm. Each segment is identified by its ranking number s, which marks the position of the segment in the tetramer. This relatively simple molecular architecture is considered adequate to represent RTILs with similar size orders and wellhidden charged groups. In SCMFT, the electrostatic, steric, and specific adsorption terms are deconvoluted in the free energy formulation. The total free energy F per unit volume V of the system reads:

( )

( )

ff+ Vf+ VfF ln + ln + ) VkBT N+ N+Q+ NN-Q1 1 χ φ (r)φj(r) + δ(r - rS) χiSφi(r) dr V 2 i,j ij i i 1 wi(r)φi(r) + λ(r)(1 φi(r)) + V i i 1 eνiφi(r)ψ(r) dr (1) 2 i

[

∑

∫ ∑

∑

∑

]

]

where the first two terms are the translational entropy of ions; the third term is the mixing enthalpy based on the Flory-Huggins formulation;14 the fourth term is the contribution from specific adsorptions; the fifth term comes from the local mean-field interactions; the sixth term is an additional contribution due to an incompressibility constraint of the system; and the seventh term is the electrostatic (Coulombic) contribution. The indices +, -, and S represent the cation, anion, and electrode’s surface, respectively; f+ and f- are the total (volume) fraction of cation and anion; N+ and N- are the total number of segments in cation and anion; Q+ and Q- are the so-called partition function of cation and anion; the indices i and j refer to the segment type, i.e., {i, j} ∈ {A, P, B, N}; χij is the Flory-Huggins interaction parameter between segments i and j; φi(r) and φj(r) are the volume fraction of segments i and j at point r; δ(r - rS) is the Dirac delta function at r ) rS, where rS is the nearest point from the solid surface that can be filled by segments; χiS is the interaction parameter between segment i and the solid surface; wi(r) is the potential of mean-force of segment i at r; λ(r) is the Lagrange multiplier at r; νi is the valence of segment i; and ψ(r) is the electrostatic potential at r. To extremize the free energy F, the first order derivation of the free energy with respect to the order parameters wi(r) and φi(r) are set equal to zero, subject to the incompressibility constraint ∑iφi(r) ) 1 at all r. This leads to a set of governing equations, as described below. The density of segments at point r in the system are quantified by their volume fraction φ(r). The volume fraction of each segment in the cation is determined by the segment-weighting factor q+ (r, s) and its complementary factor q′+(r, s). They quantify the probability to find a given segment in the cation with a ranking number s at point r. The segment-weighting factor q+(r, s) is calculated from the “open-end” of the arm toward the center of the tetramer, whereas the complementary segment-weighting factor q′+(r, s) is calculated from the opposite direction, i.e., starting from the center of the tetramer toward the open-end of the arm. The overall connectivity of segments is governed by the Edwards diffusion equation15

∂q(r, s) a2 ) ∇2q(r, s) - δi+,swi+(r)q(r, s) ∂s 6

(2)

where q(r, s) here refers to either q+(r, s) or q′+(r, s), a is the size of a segment, δi+, s is a Kronecker delta that equals one if the segment-ranking number s of the cation is of type i+ ∈ {A, P} and zero otherwise. Equation 2 is solved numerically subject to the initial and boundary conditions of the system. Since the open-end of the arm is occupied by an uncharged segment A and the center of the tetramer by the charged segment P, the initial condition at the open-end is q+(r, s0) ) exp(- wA(r)), whereas the initial condition at the center is q′+(r, s0) ) [q+(r, snA)]3. The volume

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fraction φi+(r) of segment i+ in the cation is calculated by convoluting the corresponding segment-weighting factor q+(r, s) with its complementary value q′+(r, s):

φi+(r) )

Vf+ N+Q+

∫0N

+

δi+,sq+(r, s)q
+(r, s) ds

(3)

where Q+ ) ∫q+(r, s)q′+(r, s) dr is the partition function of the cation, which is independent of the segment-ranking number. The volume fraction of segment i- in the anion, where i- ∈ {B, N}, is calculated in a similar fashion as its cation counterpart. The corresponding diffusion equation for the chain connectivity of segments in the anion is

A complete SCMF calculation is conducted in three steps: (i) a set of initial potential of segments is randomly generated; (ii) the corresponding volume fractions of all segments are obtained from eqs 3 and 5 via solving the chain propagators in eqs 2 and 4 by using the Scheutjens-Fleer scheme;19 and (iii) a new set of segment potentials is calculated from eq 6 after solving the corresponding Poisson equation. Steps i-iii are then repeated until the difference between the volume fraction from the previous two iterations at any point r is less than 10-7, which indicates that the free energy converges to an optimum value and the order parameters are self-consistent. Multiple independent calculations were performed with random initial segment potentials to ensure the results satisfy the ergodicity condition. III. Model Parameters

∂q(r, s) a2 ) ∇2q(r, s) - δi-,swi-(r)q(r, s) ∂s 6

(4)

where q(r, s) now refers to the segment-weighting factor in anion, i.e., either q-(r, s) or q′-(r, s), and δi-, s equals one if the segment-ranking number s of the anion is of type i- and zero otherwise. The initial condition at the open-end becomes q-(r, s0) ) exp(-wB(r)), whereas the initial condition at the center is q′-(r, s0) ) [q- (r, snB)]3. The segment volume fraction in anion φi-(r) now reads

φi-(r) )

VfN-Q-

∫0N

-

δi-,sq-(r, s)q
-(r, s) ds

(5)

where Q- ) ∫q-(r, s)q′-(r, s) dr is the partition function of the anion. The local volume fraction φ(r) and the local mean-field potential w(r) depend reciprocally on one another. In a thermodynamical equilibrium, the relationship between these two order parameters can be written based on a so-called saddlepoint approximation, i.e., wi(r) )

∑

χij(φj(r) - φbj ) + χiS

j∈{A,P,B,N},j*i

∫ δ(r - r ) dr + S

1 λ(r) + eνiψ(r) - ε0(εr,i(r) - 1)|∇ψ(r)| 2 2

(6)

where the Flory-Huggins parameter χij in the first term represents the magnitude of the mean-field interaction between segments i and j. A more positive χij indicates a more repulsive interaction, whereas a less positive value means less repulsion. The parameter φbj is the volume fraction of segment j in the bulk. The local electrostatic potential ψ(r) in the fourth term is obtained from the Poisson law, ε0∇(εr(r)∇ψ(r)) ) -∑ieνiφi(r). The last term of eq 6 is a contribution from the polarization charges.16 The permittivity of RTIL, which is a macroscopic property of the medium, is considered a function of the collective permittivity of its constituent segments.17 The local relative permittivity of the system is thus calculated from a linear combination of the local composition of its components, i.e., εr(r) ) ∑iεr, iφi(r), where i ∈ {A, P, B, N, S}. This involves a heuristic approach to assign a specific value of the relative permittivity εr, i to each segment i in the system under a constraint that the overall (bulk) relative permittivity of the RTIL still mimics experimental values.18 We have shown that this seemingly crude approach to account for the local dielectric screening works well within the mean-field Ansatz.5

A series of SCMF calculations is performed using a tetrameric model of cation and anion, as shown in Figure 1. For simplicity, we consider the volume fraction of ions to vary only in the direction perpendicular to the surface. This approximation implies that the volume fractions of ions are homogeneous throughout each plane parallel to the surface. The size of all segments is set equal to 3 Å, which is of a similar order of magnitude to an ethyl chain or a heterocylic polar group in typical RTILs, such as pyrrolidinium and imidazolium rings. The system size is chosen large enough such that the bulk properties are reached within the boundaries of the modeled system. The relative permittivity of segments and electrode’s surface used in the calculation are εr, A ) εr, B ) 10, εr, P ) εr, N ) 30, and εr, S ) 10. These values are chosen such that the relative permittivity of the modeled RTIL in the bulk is realistic, i.e., ∼11-12.18 The interaction parameter χAB ) 1 is chosen to represent an adequate repulsion between uncharged segment A of cation and segmant B of anion. In most RTILs, the anions are relatively smaller than the cations. Here, three size ratios of cation and anion are used to study the effect of ion-size on capacitance. Without losing generality, this is achieved by varying the length of each arm in the anion while keeping the cation size the same. Three ratios of the arm’s length used in this study are nA:nB ) 4:4, 4:3, and 4:2. Note that the unequal ion-size can also be implemented by, e.g., changing the number of arms. Nevertheless, it is not considered here for simplicity. To study the effect of specific adsorption, the affinity of anion toward the electrode’s surface is systematically varied. Three different sets of interaction parameters used here are χBS ) χNS ) 0, -1, and -2. These values are within the typical limit of adsorption energy due to specific interactions, i.e., in the order of a few kBT for each adsorbed ion.20 IV. Results and Discussion The EDL capacitance (C) for three size ratios of cation and anion is plotted as a function of the applied surface potential (ψ0) in Figure 2. The values are calculated from the first derivation of surface charge (σ0) with respect to ψ0, i.e., C ) ∂σ0/∂ψ0. The differential capacitance obtained from an equilibrium model like SCMFT is generally comparable to that measured by impedance spectroscopy at low frequencies. In principle, all differential capacitance curves in Figure 2 have a camel-shaped feature, which is symmetric for RTIL with the same ion-size (nA:nB ) 4:4) and asymmetric for ions with unequal size (nA:nB ) 4:3 and 4:2). It is known that the (local) minimum capacitance is typically reached at the point of zero charge (pzc), where the electrode’s surface charge is practically zero. In our previous publication,5 it was shown that two maxima

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Figure 2. The EDL capacitance (C) and the corresponding surface charge (σ0) as functions of the surface potential (ψ0) of the modeled RTIL with different ratios of nA:nB, as indicated. A symmetric capacitance curve was obtained for RTIL with an equal ion-size, whereas the capacitance curve is asymmetric otherwise. Note that the difference between the three σ0(ψ0) curves is mainly situated at the positive potential.

in the capacitance curve mark the saturation of the Helmholtz layer by cation (on the left-hand side of pzc) or anion (on the right-hand side of pzc). The relationship between σ0 and ψ0 is nearly linear in the region between these two maxima and nonlinear elsewhere. We refer to these regions as quasilinear and nonlinear regimes, respectively. The quasilinear regime for the modeled RTIL with nA:nB ) 4:4 is located within -0.63 V < ψ0 < 0.63 V. This regime expands further for RTILs with unequal ion-size, i.e., -0.73 V < ψ0 < 0.83 V for nA:nB ) 4:3, and -0.83 V < ψ0 < 1.19 V for nA:nB ) 4:2. The complete list of the pzc, location of both maximum potentials (ψ0max- and ψ0max+), and the extrema of the capacitance curves (Cpzc, Cmax-, and Cmax+) are shown in Table 1. From Figure 2, the impact of smaller anions on capacitance becomes more significant with an increasingly positive potential, as also shown by a more prominent deviation of σ0(ψ0) there. Figure 2 also suggests that the shape of the capacitance curve is strongly influenced by the size of the counterion, whereas the effect of co-ion size seems to be limited. In general, smaller ions have a larger packing density and screen electrostatic potential more effectively. For smaller anions, these two factors cause a positive shift in ψ0max+ and, to a lesser extent, a negative shift in ψ0max-. The positive shift is needed to accommodate the increasing number of anions required to saturate the Helmholtz layer, whereas the negative shift would counter the increase in screening effect of anions in the EDL. A slightly negative pzc found for smaller anions is a result of the size mismatch between anion and cation, which triggers a population inbalance of ions near the surface. At zero surface charge (pzc), this inbalance results in a slightly nonzero (negative) excess charge in the Helmholtz layer, which is then overcompensated by opposite charges in subsequent layers. Besides causing the shift in critical potentials, less bulky anions raise the capacitance value at ψ0 > 0.63 V and lower it in -0.83 V < ψ0 < 0.63 V. The former occurs due to the formation of more compact alternate layers by smaller anions,21 as illustrated in Figure 3a; the latter is a result of less polarized alternate layers, as the screening effect of smaller anions dampens the potential field more effectively. To illustrate the last point, the mole fraction profile of ions at this region (ψ0 ) -0.6 V) is shown in Figure 3b. The changes in capacitance described here are in a good agreement with previous findings reported in the literature, e.g., those obtained from a molecular dynamics simulation,22 and spectroscopic study of RTILs composed of imidazolium-based cations and Cl or BF4 anions on glassy carbon, gold, or mercury electrodes.23

Lauw et al. For RTILs, the scaling of capacitance with applied potential at both potential “wings” is a good indication of the extent of electrostriction in the EDL. For the case of nA:nB ) 4:4 (cf. Figure 2), the scale is identical in the first nonlinear regime (ψ0 < ψ0max-) and the second nonlinear regime (ψ0 > ψ0max+), i.e., C ∝ |ψ0|-0.82. For asymmetric capacitance curves, this scale persists in the first nonlinear regime and becoming more pronounced in the second regime, i.e., C ∝ |ψ0|-1.04 for nA:nB ) 4:3, and C ∝ |ψ0|-1.32 for nA:nB ) 4:2. Each scaling exponent corresponds to the change in thickness of alternate layers with electrostatic potential since the capacitance in the nonlinear regime is mainly determined by the size of these layers.5 In principle, less bulky anions are geometrically more susceptible to variation in potential field by forming thicker (thinner) alternate layers at a more (less) positive applied potential. This explains a more rapid decay of the capacitance in the second nonlinear regime for smaller anions. It is interesting to note that all scaling exponents obtained here are considerably less than -0.5,7 which is the value predicted analytically by Kornyshev based on the Poisson-Fermi distribution of spherical ions at a charged interface.24 As highlighted in our previous publication,5 this discrepancy originates from different underlying assumptions in our model, such as the use of effective relative permittivity and chain flexibility of nonspherical ions. Kornyshev incorporated the excluded volume term by introducing a fixed lattice saturation parameter into the Boltzmann distribution of ions. In SCMFT, the lattice saturation parameter would not be homogeneous throughout the system since the ions are modeled as flexible chain molecules and their compression or relaxation within the EDL would depend on the local electrostatic potential field. This makes the EDL structure more responsive to the applied potential, which results in a more rapid decay of C(ψ0) than analytically predicted. Asymmetric capacitance curves in RTILs do not only occur when the corresponding ions have different size. They also happen for same-size ions with different nonelectrostatic (specific) affinity toward the electrode’s surface, as shown in Figure 4a. Here, the surface affinity of the anion was systematically varied by assigning different interaction parameters between the anion’s segments and the electrode’s surface, i.e., χBS ) χNS ) 0, -1, and -2. The more negative the interaction parameters, the stronger the specific affinity of anion toward the surface. All the critical values for capacitance curves in Figure 4a are listed in Table 2. It appears that a stronger specific adsorption of anion increases the capacitance value at -1.2 V < ψ0 < -0.3 V and decreases it at -0.3 V < ψ0 < 1.2 V. The trend is reversed when the specific adsorption of cation is stronger, i.e., for χBS ) χNS > 0 (results are not shown). The physical interpretation of these trends is that the amount of energy to bring one counterion from the bulk to the surface would be either reduced by the presence of specifically adsorbed co-ion, or increased when some counterion is already specifically adsorbed on the surface. It is known that the impact of specific adsorption is typically confined within a limited range of applied potential from the pzc.25 For our case, this ψ0-zone is located in -1.2 V < ψ0 < 1.2 V (cf. Figure 4a). As discussed above, specifically adsorbed ions tend to increase the gradient of C(ψ0) in the ψ0-zone. Such a steep capacitance curve is typically caused by partial charge transfers at a nonideally polarized surface, which can be induced by specifically adsorbed ions.10,26 Beyond the ψ0-zone, the longrange electrostatic interaction overcomes the short-range effect of specific adsorption to diminish the amount of adsorbed anion on the surface (φanion) at negative potential, as illustrated in

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TABLE 1: List of Critical Values and Scaling Parameters for Differential Capacitance Curves in Figure 2a nA:nB

pzc (mV)

ψ0max- (V)

ψ0max+ (V)

Cpzc (µF/cm2)

Cmax- (µF/cm2)

Cmax+ (µF/cm2)

R-

R+

4:4 4:3 4:2

0 -6 -12

-0.63 -0.73 -0.83

0.63 0.83 1.19

23.30 22.46 21.60

24.85 24.40 23.80

24.85 26.42 29.39

-0.82 -0.82 -0.82

-0.82 -1.04 -1.32

a The indices max- and max+ indicate values at the maximum capacitance on the left-hand and right-hand sides of pzc, respectively. Parameters R- and R+ are the exponents from the scaling of the capacitance with respect to each surface potential “wing” in the nonlinear regime, i.e., C ∝ |ψ0|R- for ψ0 < ψ0max- and C ∝ |ψ0|R+ for ψ0 > ψ0max+.

Figure 3. Profile of the mole fraction (x) of cation and anion at the interface for the modeled RTIL with different ratios of nA:nB at (a) ψ0 ) 3 V and (b) ψ0 ) -0.6 V. Here, z indicates the distance from the electrode’s surface.

Figure 4b. There are two additional trends observed by increasing the specific affinity of anion. First, the φanion curve shifts to the left, indicating an increasing presence of anion on a negatively charged surface. Second, the pzc and both saturation limits (ψ0max- and ψ0max+) shift to more negative values since, in principle, a more negative surface is needed to counter the increasing amount of specifically adsorbed anion. The pzc is one of the most robust parameters to detect the existence of specific adsorption in RTILs. Compared to the change in pzc for unequal ion-size, the shift of pzc due to specific adsorption is relatively larger (cf. Tables 1 and 2). The relationship between the pzc and the strength of specific adsorption is depicted in Figure 5. Here, the pzc varies steadily in the R-zone (|χBS| ) |χNS| j 6) and goes to asymptotic values at the limit of extreme adsorption in the β-zone (|χBS| ) |χNS| J 6). The gradient of the pzc curve in the R-zone is ∼2kBT per ion for each unit of interaction parameter (χBS ) χNS). In the β-zone, the gradient is close to zero, indicating the saturation of the Helmholtz layer by specifically adsorbed ions. The shift in the pzc can be used as a qualitative tool to predict, e.g., the type of RTIL-metal species specifically adsorbed on the electrode’s surface during metal electrodeposition, provided that each species has a distinct size but similar affinity toward the surface. The trends in capacitance curve and pzc presented in this study are generally useful to assist in the choice of RTILs for specific electrochemical applications, and in the design of new RTILs with tailored electrochemical properties. V. Concluding Remarks The impact of unequal ion-size and specific adsorption on the EDL structure and capacitance in RTILs are systematically

Figure 4. (a) The EDL capacitance of the modeled RTIL with nA:nB ) 4:4 and χBS ) χNS ) 0, -1, and -2, as indicated. The capacitance curve is asymmetric with respect to the pzc when the specific adsorption of anion is present. The impact of specific adsorption is limited within the ψ0-zone marked by the arrow. (b) The volume fraction of anion on the electrode’s surface (φanion). When specific adsorption of the anion is present, a significant amount of anion can still be found at negative potentials.

studied with SCMFT. The introduction of unequal ion-size leads to asymmetric capacitance curves. The shape of these curves is strongly determined by the size of the counterion and only weakly influenced by co-ion size. In general, smaller ions have a higher packing density and screen the electrostatic potential more effectively. These two factors cause a shift in critical values of the capacitance curves. The presence of a nonelec-

Figure 5. The point of zero charge (pzc) as a function of the strength of specific adsorption of ion (nA:nB ) 4:4). For χBS ) χNS < 0, the anion is adsorbed specifically to the surface, whereas for χBS ) χNS > 0, the cation is specifically adsorbed. In the β-zone, i.e., |χBS| ) |χNS| J 6, the Helmholtz layer is saturated with specifically adsorbed ions and the pzc curve reaches a plateau.

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Lauw et al.

TABLE 2: List of Critical Values for Differential Capacitance Curves in Figure 4a

113, 4549. Trulsson, M.; Algotsson, J.; Forsman, J.; Woodward, C. E. J. Phys. Chem. Lett. 2010, 1, 1191. (7) Kornyshev, A. A. J. Phys. Chem. B 2007, 111, 5545. Oldham, K. B. J. Electroanal. Chem. 2008, 613, 131. (8) James, R. O.; Healy, T. W. J. Colloid Interface Sci. 1972, 40, 65. Teschke, O.; de Souza, E. F. Appl. Phys. Lett. 1999, 74, 1755. (9) MacDonald, J. R. J. Chem. Phys. 1954, 22, 1857. Parsons, R. AdVances in Electrochemistry and Electrochemical Engineering; Delahay, P., Ed.; Interscience Publishers: New York, 1961; Vol. I, Chapter 1. MacDonald, J. R.; Barlow, C. A., Jr. J. Chem. Phys. 1962, 36, 3062. (10) Lorenz, W.; Salie, G. G. J. Electroanal. Chem. 1977, 80, 1. Lipkowski, J.; Shi, Z.; Chen, A.; Pettinger, B.; Bilger, C. Electrochim. Acta 1998, 43, 2875. Magnussen, O. M. Chem. ReV. 2002, 102, 679. (11) Gale, R. J.; Osteryoung, R. A. Electrochim. Acta 1980, 25, 1527. (12) Aliaga, C.; Baldelli, S. J. Phys. Chem. B 2006, 110, 18481. (13) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at interface; Chapman and Hall: London, UK, 1993. Leermakers, F. A. M.; Eriksson, J. C.; Lyklema, J. Fundamentals of Interface and Colloid Science; Lyklema, V. J., Ed.; Elsevier: Amsterdam, The Netherlands, 2005; Chapter 4. (14) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: New York, 1953. (15) Edwards, S. F. Proc. Phys. Soc., London 1965, 85, 613. (16) Feynman, R. P. Lectures on Physics II; Feynman, R. P., Leighton, R. B., Sands, M., Eds.; Addison-Wesley Publishing Company: Reading, MA, 1964. (17) Bohmer, M. R.; Evers, O. A.; Scheutjens, J. M. H. M. Macromolecules 1990, 23, 2288. Reis, J. C. R.; Iglesias, T. P.; Douheret, G.; Davis, M. I. Phys. Chem. Chem. Phys. 2009, 11, 3977. (18) Krossing, I.; Slattery, J. M.; Daguenet, C.; Dyson, P. J.; Oleinikova, A.; Weingartner, H. J. Am. Chem. Soc. 2006, 128, 13427. Koeberg, M.; Wu, C. C.; Kim, D.; Bonn, M. Chem. Phys. Lett. 2007, 439, 60. (19) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1979, 83, 1619. Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1980, 84, 178. (20) Parsons, R. Trans. Faraday Soc. 1955, 51, 1518. Nikitas, P. J. Phys. Chem. B 1994, 98, 6577. Lyklema, J. Fundamentals of Interface and Colloid Science II; Lyklema., J., Ed.; Elsevier: Amsterdam, The Netherlands, 1995; Chapter 3. Lamperski, S. J. Electroanal. Chem. 1997, 437, 225. (21) The alternating layer of ions is formed when the surface charge is overscreened by counterions in the Helmholtz layer and the resulting net charge is further overcompensated by co-ions in the subsequent layer, and so on. One can assume the alternating layer of ions as a series of capacitors, in which the overall capacitance C is obtained from 1/C ) ∑l1/Cl, where Cl is the capacitance of layer l. On the basis of this interpretation, the capacitance would be determined by a balance between the thinning (thickening) of each layer and the decreasing (increasing) polarization. (22) Fedorov, M. V.; Kornyshev, A. A. J. Phys. Chem. B 2008, 112, 11868. (23) Lockett, V.; Sedev, R.; Ralston, J.; Horne, M. D.; Rodopoulos, T. J. Phys. Chem. C 2008, 112, 7486. Alam, M. T.; Islam, M. M.; Okajima, T.; Ohsaka, T. J. Phys. Chem. C 2007, 111, 18326. Alam, M. T.; Islam, M. M.; Okajima, T.; Ohsaka, T. J. Phys. Chem. C 2008, 112, 16600. (24) Bikerman, J. J. Philos. Mag. 1942, 33, 384. Freise, V. Z. Elekrochem. 1952, 56, 822. Kilic, M. S.; Bazant, M. Z.; Ajdari, A. Phys. ReV. E 2007, 75, 021502. Bazant, M. Z.; Kilic, M. S.; Storey, B. D.; Ajdari, A. New J. Phys. 2009, 11, 075016. (25) Graves, A. D. J. Electroanal. Chem. 1970, 25, 349. (26) Parsons, R. Can. J. Chem. 1981, 59, 1898.

χBS ) χNS

pzc (mV)

ψ0max(V)

ψ0max+ (V)

Cpzc (µF/cm2)

Cmax(µF/cm2)

Cmax+ (µF/cm2)

0 -1 -2

0 -52 -95

-0.63 -0.66 -0.77

0.63 0.61 0.60

23.30 22.27 20.76

24.85 26.45 27.86

24.85 23.67 23.03

trostatic (specific) affinity of ions toward the electrode’s surface also leads to asymmetric capacitance curves. The impact occurs only within a limited range of applied potential from the pzc. Besides changing the capacitance values, specifically adsorbed ions shift the pzc and both saturation limits of the capacitance curves to one direction, depending on the type of their charge and the strength of specific adsorption. Acknowledgment. We thank Dr. Bart Follink and Dr. Luuk Koopal for helpful discussions in this work. References and Notes (1) Endres, F. Chem. Phys. Chem. 2002, 3, 144. Sato, T.; Masuda, G.; Takagi, K. Electrochim. Acta 2004, 49, 3603. Ohno, H., Ed. Electrochemical aspects of ionic liquids; John Wiley & Sons, Inc.: Hoboken, NJ, 2005. Endres, F.; MacFarlane, D.; Abbott, A., Eds. Electrodeposition from Ionic Liquids; Wiley-VCH: Weinheim, Germany, 2008. Simon, P.; Gogotsi, Y. Nat. Mater. 2008, 7, 845. Arbizzani, C.; Biso, M.; Cericola, D.; Lazzari, M.; Soavi, F.; Mastragostino, M. J. Power Sources 2008, 185, 1575. Armand, M.; Endres, F.; MacFarlane, D. R.; Ohno, H.; Scrosati, B. Nat. Mater. 2009, 8, 621. (2) Largeot, C.; Portet, C.; Chmiola, J.; Taberna, P. L.; Gogotsi, Y.; Simon, P. J. Am. Chem. Soc. 2008, 130, 2730. Chmiola, J.; Largeot, C.; Taberna, P. L.; Simon, P.; Gogotsi, Y. Angew. Chem., Int. Ed. 2008, 47, 3392. (3) Horn, R. G.; Evans, D. F.; Ninham, B. W. J. Phys. Chem. 1988, 92, 3531. Rivera-Rubero, S.; Baldelli, S. J. Phys. Chem. B 2004, 108, 15133. Santos, V. O., Jr.; Alves, M. B.; Carvalho, M. S.; Suarez, P. A. Z.; Rubim, J. C. J. Phys. Chem. B 2006, 110, 20379. Atkin, R.; Warr, G. G. J. Phys. Chem. C 2007, 111, 5162. Baldelli, S. Acc. Chem. Res. 2008, 41, 421. Mezger, M.; Schroder, H.; Reichert, H.; Schramm, S.; Okasinski, J. S.; Schoder, S.; Honkimaki, V.; Deutsch, M.; Ocko, B. M.; Ralston, J.; Rohwerder, M.; Stratmann, M.; Dosch, H. Science 2008, 322, 424. Mezger, M.; Schramm, S.; Schroder, H.; Reichert, H.; Deutsch, M.; De Souza, E. J.; Okasinski, J. S.; Ocko, B. M.; Honkimaki, V.; Dosch, H. J. Chem. Phys. 2009, 131, 094701. Yuan, Y. X.; Niu, T. C.; Xu, M. M.; Yao, J. L.; Gu, R. A. J. Raman Spectrosc. 2010, 41, 516. (4) Stillinger, F. H.; Kirkwood, J. G. J. Chem. Phys. 1960, 33, 1282. Outhwaite, C. W.; Bhuiyan, L. B.; Levine, S. J. Chem. Soc., Faraday Trans. 1980, 76, 1388. Parsons, R. Chem. ReV. 1990, 90, 813. (5) Lauw, Y.; Horne, M. D.; Rodopoulos, T.; Leermakers, F. A. M. Phys. ReV. Lett. 2009, 103, 117801. (6) Urahata, S. M.; Ribeiro, M. C. C. J. Chem. Phys. 2004, 120, 1855. Lynden-Bell, R. M.; Del Popolo, M. Phys. Chem. Chem. Phys. 2006, 8, 949. Qiao, B.; Krekeler, C.; Berger, R.; Site, L. D.; Holm, C. J. Phys. Chem. B 2008, 112, 1743. Feng, G.; Zhang, J. S.; Qiao, R. J. Phys. Chem. C 2009,

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