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Ion Sieving Effects in the Electrical Double Layer of Porous Carbon ... Li-ion batteries2 and in electrical double-layer capacitors (EDLC).3 Furthermo...
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J. Phys. Chem. B 2001, 105, 6880-6887

Ion Sieving Effects in the Electrical Double Layer of Porous Carbon Electrodes: Estimating Effective Ion Size in Electrolytic Solutions Linoam Eliad, Gregory Salitra, Abraham Soffer, and Doron Aurbach* Department of Chemistry, Bar-Ilan UniVersity, Ramat-Gan 52900, Israel ReceiVed: January 7, 2001; In Final Form: March 13, 2001

Certain microporous carbons have pores of molecular dimensions, the size of which can be adjusted over a wide range to fit the dimensions of a large variety of molecules. With knowing the dimensions of these molecules, size-calibrated porous carbons can be produced. In this work, we took advantage of the electronic conductivity of carbon in using it as an electrode in electrolytic solutions. By changing the electrode potential, we could induce electroadsorption and electrodesorption of ions of different dimensions into pore-calibrated carbons, thus enabling us to estimate effective ion sizes. A few fundamental questions such as whether ions accommodated in the electrodes’ pores are in a solvated state, which is important for novel electrochemical energy storage devices and for microbiological systems, could be addressed. Analysis of the results indicates that all the cations that are employed are electroadsorbed in the electrode pores in hydrated states. Compared with the monovalent cations, the bivalent cations exhibit dimensions that make them almost twice as big. Monovalent anions are basically adsorbed in a nonhydrated state. The doubly charged sulfate anion is adsorbed in the hydrated state. The nitrate, a multiatom planar anion, has a smaller effective dimension than the monoatomic halogen anions, in accordance with the observation that the pores in many activated carbons are slit-shaped. The analysis of the results enabled us to establish a scale of ionic effective dimensions in aqueous media, as presented below (MTBE stands for methyl tert-butyl ether): cations, [3.62 Å, N2] < Cs+ < K+ < Na+ < Li+ < [4.21 Å, CF4] < [5.05 Å, SF6] < [5.8 Å, MTBE] < Ba2+, Ca2+, and Mg2+; anions, [3.62 Å, N2] < NO3- < Cl- < F- < Br- < [4.21 Å, CF4] < ClO4- < [5.05 Å, SF6] < [5.8 Å, MTBE] < SO2-. We discovered that as long as the pore size is considerably greater than the ion size, the electric double-layer capacity at moderate concentrations is independent of both the size and charge of the ions in solutions.

Introduction Ion size is one of the most fundamental properties of a substance when dealing with the physical chemistry of electrolytic solutions and the electrochemistry of porous electrodes. Ion size has a major influence on the diffusivity and electrical conductivity of solutes, and on the viscosity of electrolytic solutions.1 Pores in carbon and graphite play a very important role in the development of Li-ion batteries2 and in electrical double-layer capacitors (EDLC).3 Furthermore, they play an important role in water treatment and purification by electrochemical means,4 especially in capacitive desalination.5 The relationship between the electrode pore size and the ionic dimension of the solution species is especially important in the case of EDLC that are based on highly porous, large-surface area carbon electrodes. It has been demonstrated6,7 that within the practically pure electric double-layer EDL windows of potentials, upon charging the EDL, the ions enter pores whose size conforms to the hydrated state of the ions (this may be denoted as the effective ion size). We may reasonably assume that for pores that are significantly larger than the effective ion size, the specific EDL differential capacity of porous electrodes (F per gram or F per cubic centimeter, where F is faraday) is proportional to the overall pore surface. The energy density of EDLC devices is estimated on either a weight or volume basis, depending on the particular application being considered. In the case of volume-based optimization, the goal is to attain a larger surface area per volume. This requires as great a subdivision of the solid as possible, resulting in small

pores. In other words, an increasingly larger surface area can be packed into a unit volume of a porous electrode, if the pores are smaller. Obviously, a limit is set to the small size of the pores, related to the accessibility of the pores to the ion from the solution bulk outside the pores. As the average pore size becomes closer to the ion size but remains larger, the electroadsorption kinetics slow. When the average pore size is smaller than the ion size, no ion electroadsorption can take place. As is the case with adsorption from the gas phase,8 an ideal situation can be attained when the average electrode pore size is slightly larger than the ion size, enabling ion interactions with opposite pore walls,8 thus increasing the capacity without slowing the electroadsorption and desorption kinetics. Hence, it is very important to study as precisely as possible ion-electrode pore interaction, using electrolytes that are suitable for EDLC. Recognizing that the effective ion size plays a most important role in determining transport phenomena in bulk electrolyte solutions, we may conclude that the importance of determining the effective ion size extends to bulk electrolyte properties, much beyond the particular issues of porous electrode systems. In fact, consideration of the effective ion size goes back to the early corrections for finite size charge carriers in the Debye-Huckel theory for point charge electrolytes.9 In a previous paper,6 we established a semiquantitative scale of solvated ion dimensions and of micropore dimensions in carbon electrodes based on a single probe, namely, adsorption of N2 molecules. This implies that the established scale had a

10.1021/jp010086y CCC: $20.00 © 2001 American Chemical Society Published on Web 06/28/2001

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TABLE 1: Activation Results for the Various Carbon Samples initial weight (mg) BET area (m2/g) a

TABLE 2: Adsorption Conditions for the Various Adsorbates That Were Used

0.75 ha

1 ha

1.25 ha

3 ha

148.5 340

299 490

342.7 540

158.5 860

Activation time.

single value at 3.62 Å, which is the diameter of the N2 molecule. In this work, we continued our efforts to develop a precise scale of average pore size for large-surface area, activated carbon electrodes for EDLC, as well as a scale of effective dimensions for commonly used ions. We studied the adsorption of a variety of globular molecules of nearly spherical shape, with no or negligible dipole moment, into activated carbons of different, average pore size. These included N2, CF4, SF6, and methyl tert-butyl ether (MTBE). The N2 molecule is an exception to the above list because it is ellipsoidal, rather than spherical, in shape. However, it was repeatedly shown10,11 that the N2 molecule has a cross-sectional diameter that is very similar to that of the truly spherical argon atom, which can be reliably estimated from the density of Ar in the liquid phase. For the sake of simplicity, we preferred to calibrate the carbon pore size by studying molecular probe adsorption from the single-component adsorption, rather than from the liquid solution phase. This is because in the latter case, complexities related to intermolecular interactions within the solution phase and competitive adsorption of the solvent would complicate the adsorbability considerations. The solution phase studies involved cyclic voltammetry applied to the pore size-calibrated carbon electrodes in the presence of the ions whose dimensions were assessed in this work. Since the cyclic voltammograms were recorded within the EDL range of potentials, the electrochemically induced processes are, in fact, the electroadsorption and electrodesorption of ions, which are highly influenced by the relations between the ion and the average pore size. Experimental Section Sample Preparation. Porous carbons were prepared by carbonization of cellulose (cotton cloth). The carbonization were then followed by time-controlled oxidation with CO2 flow at 900 °C. The activation times and resultant properties are given in Table 1 (detail elsewhere6). In our previous work,6 we were not exact in determining the CO2 flow rate over the sample. We only ensured that it was sufficiently higher than the amount needed to effect the weight loss during the time specified in Table 1 above. Later, we found that the extent of activation still depends on flow rate, and therefore, we stabilized it to 15 mL/min. The result was a greater surface area for a given activation time, i.e., 860 m2/g at present rather than 670 m2/g previously.6 As described previously,6 the porosity of the activated (oxidized) electrodes could be modified by changing the activation time at a constant temperature and under CO2 flow at ambient pressure. Surface areas as large as 1500 m2/g could be obtained without any significant changes in the carbon morphology6 on the sub-micrometer scale (i.e., the pores thus formed are all on the nanometer and sub-nanometer scale, as established by SEM and STM measurements).6 The BET area of each activated carbon sample was calculated using standard equipment from Micromeritics Inc. (Gemini 2375 surface analyzer), which employs N2 adsorption at 77 K. For these studies, we produced porous carbons having BET areas

vapor pressure at initial adsorption pressure equilibrium adsorption temperature temperature range pressure (kPa) material bp (K) (K) (kPa) range (kPa) N2 CF4 SF6 MTBE

77 145 195 328

77 157 195 298

20-22 21-22.5 21-22.2 5.5

10-23 11-12 13-18 5.1-5.2

100 199.1 44 33

of 340, 490, 540, and 860 m2/g by activating them with CO2 for 0.75, 1, 1.25, and 3 h, respectively. Adsorption. The adsorption temperatures were chosen close to the boiling point of the various substances so that the working pressures fell in the range of tenths of a bar. This enabled appreciable adsorption to take place at pressures that are compatible with the glass-made vacuum/adsorption system. The temperatures employed for each adsorbate, and the initial and final pressures to which the systems were exposed, are given in Table 2. The gas adsorption kinetic method employed in this work is a simplification of the standard volumetric method.12 The system, in which adsorption of gases into the porous carbons was assessed, is shown schematically in Figure 1. It is based on a conventional glass vacuum system with a volumetric branch enclosed among valves 1-3, and including a pressure transducer, as shown. This volume has a known value VP predetermined by means of helium expansion from, or into, the volume standard Vs, employing the ideal gas equation. The adsorption cell volume Vc, which already included the adsorbent, was also predetermined with helium expansion, while immersed in the thermostat bath adjusted at the adsorption temperature, using Vp as a reference (helium is a nonadsorbing gas). An adsorption experiment is carried out by pre-evacuating all volumes, filling a volume Vp with the gas to pressure Pp, disconnecting the volume from the main line (valve l), and then connecting it to the adsorption cell via valve 2. The cumulative adsorbed amount na at any moment is determined by the momentary pressure Pt by means of the equation

na ) [PpVp - Pt(Vp + Vc)]/(RT) Highly pure gases were obtained from the following companies: N2, He, and SF6 from Gordon Gas Inc., CO2 from BOC Gases, Inc., and CF4 from Matheson Inc. MTBE was obtained as a 99.8% pure liquid from Aldrich Inc. For adsorption measurements with this substance, we used its vapor, which was specially cleaned from air as follows. The liquid was cooled to 77 K (with liquid nitrogen), after which the atmosphere above the frozen material was evacuated to 10-6 Torr. The material was then allowed to return to room temperature and was frozen again at 77 K, followed by evacuation to 10-6 Torr. After this procedure had been repeated, we used the (pure) vapor above the liquid at room temperature for the adsorption measurements. The temperatures for the adsorption processes of CF4 (157 ( 5 K) were obtained using a bath of cyclohexane and liquid nitrogen. Electrochemical Measurements. The solution phase studies included essentially cyclic voltammetric measurements applied to the pore size-calibrated electrodes in the presence of the ions whose dimensions had to be assessed. Since the cyclic voltammograms were performed within the EDL range of potentials, the electrochemically induced processes are, in fact, those of electroadsorption and electrodesorption of ions, the extent of

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Figure 1. Scheme of the system used for adsorption of gas molecules into porous carbons.

which reflects the relationship between ion and pore size. Highly pure salts were obtained from the following companies: LiCl, LiClO4, BaCl2, and CaCl2 from Merck, NaCl, KCl, and MgSO4 from Frutarom, MgCl2 from Fluka, CsCl and LiNO3 from Aldrich, and Li2SO4 from Riedel DeHaen. All the electrochemical measurements were performed under a highly pure nitrogen atmosphere. The electrochemical measurements (CV in the EDL potential domains), cells, and equipment were described previously.6 We used two basic reference electrodes: Ag/AgCl/Cl- and Hg/ HgCl2/Cl- (saturated calomel electrode). When the solutions contained anions other than chloride, these reference electrodes (in KCl solutions) were separated from the studied solutions by a fine glass frit. Results and Discussion 1. Calculating the Dimensions of the Reference Molecules. Apart from the molecular dimension of the nitrogen molecule, which was estimated from geometrical considerations assuming a spherocylinder shape,10 the dimensions of the other, globular molecules mentioned above were estimated from the density of the liquefied gas.10,13 This was preferred over several other methods14 because of its simplicity and the similarity of gas adsorption in microporous media to gas condensation in the bulk. The calculated diameters of the various molecules are listed in Table 2. 2. Establishing the Scale of Pore Dimensions of the Carbon Samples. 2.1. Method of Pore Opening. As shown previously,6 the simple and well-known method of activation by burnoff with carbon dioxide at high temperatures leads, in addition to an increase in the surface area, to pore size enlargement. We used this method to obtain activated carbons with different tunable pore size openings. Estimation of the pore size was achieved

by monitoring the kinetics of the adsorption of molecules of different, well-known dimensions from the gas phase. 2.2. Adsorption Conditions. The selected gaseous molecular probes varied considerably from each other in their size and their vapor pressure (PO), and thus, the convenient ranges of working pressures and temperatures had to be different for each molecule. The models of adsorption kinetics that may be applied to interpret the experimental results may differ greatly in their dependence on temperature and pressure. This may make interpreting the adsorption kinetics data of the different molecules very difficult. Fortunately, the extent of accommodation of the molecules of various dimensions in molecular sieve carbons varies greatly. This behavior is typical of carefully developed carbon molecular sieves, as observed in this work and elsewhere.6,15 Therefore, no matter which particular model of adsorption is employed, we can assume a pseudo-first-order reaction between the gaseous substance and the carbon internal surface at the initial stage of adsorption, with the following simple equation:

∆ni dni ) kiPio ) kiPi w dt ∆t initial

(1)

where ni is the concentration of molecules adsorbed (translated into pressure at the constant temperatures of the process), Pi is the adsorbate pressure, and ki is the pseudo-first-order rate constant. Hence, ki can be obtained by dividing ∆ni/∆t, measured at the initial step of adsorption, by Pio, the initial adsorbate pressure. Therefore, the ki values calculated for the different adsorption processes of the various molecules that were studied can be taken as comparative parameters with which the kinetics of these processes can be compared. The rationale behind this comparison at the beginning of the adsorption processes is the absence of any significant pressure inside the pores (the carbon

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Figure 2. Amount of nitrogen adsorbed per square meter BET unit area at 77 K vs time into a carbon cloth activated by CO2 at 900 °C for 0.75 h (assigned as C3.6).

Figure 4. Same as Figure 3. The carbon cloth that was used was activated by CO2 at 900 °C for 1.25 h (assigned at C5.1).

Figure 3. Amount adsorbed per square meter BET unit area vs time, of N2 at 77 K, CF4 at 156 K, SF6 at 196 K, and MTBE at 197 K, into a carbon cloth activated by CO2 at 900 °C for 1 h (assigned as C4.2).

Figure 5. Same as Figures 3 and 4. The carbon cloth used was activated by CO2 at 900 °C for 3 h (assigned as C5.8).

samples are initially under vacuum), which could impede the driving force for adsorption and which, in any event, would be unknown. In several cases, the adsorption rate was faster than the time needed to open the valve, which led the gas to the adsorbent. In such cases, it was experimentally difficult to determine both the adsorption rate (∆ni/∆t) and the initial adsorbate pressure (Pio). Fortunately, the difference in adsorbability of the various adsorbates that are employed, in the various carbon molecular sieves that are chosen, is very significant. Therefore, a quantitative estimate of the initial adsorption kinetics was not required for estimating the average pore size of the carbons, as seen in the subsequent presentation of the Results and Discussion. 2.3. Estimating the Pore Size. In Figure 2, the adsorption level-time curve for adsorption of N2 into the carbon activated for 0.75 h (340 m2/g) is plotted. This carbon could not adsorb CF4, SF6, or MTBE. Therefore, we conclude that its pore openings are smaller than 4.21 Å, which is the dimension of the CF4 molecule, and larger than 3.62 Å, the dimension of the nitrogen molecule. Figure 3 shows the adsorption kinetics curves for adsorption of all four gases onto carbon activated for 1 h. The results show that adsorption of nitrogen and adsorption of carbon tetrafluoride occur at significant adsorption rates, while SF6 and MTBE are scarcely adsorbed. This implies that the average pore size of the carbon activated for 1 h falls between that of CF4 and SF6, namely, 4.21-5.1 Å. The difference in the kinetics of adsorption between the two groups of molecules was so apparent that there was no need to employ eq 1 for a more quantitative interpretation. Figure 4 shows the adsorption level-kinetic curves for all four gases on carbon activated for 1.25 h. As seen from these curves, this activation time created a carbon that can significantly adsorb all the gases except for MTBE, which remained practically unadsorbed. We therefore conclude that the average pore size of the carbon activated for 1.25 h is smaller than MTBE, but larger than SF6. Here again, the initial adsorption rate and the quantities of any adsorbed MTBE are so small that

TABLE 3: Different Carbon Electrodes Used in Terms of the Size of the Largest Molecule Adsorbed, the Activation Time, and Their BET Surface Area activation BET surface carbon largest adsorbed calculated time (h) area (m2/g) assignment molecule diameter (Å) 0.75 1 1.25 3

340 490 540 860

C3.6 C4.2 C5.1 C5.8

N2 CF4 SF6 MTBE

3.6 4.21 5.1 5.8

there was no need for the semiquantitative treatment based on eq 1. We can therefore conclude that the average pore size of the carbon activated for 1.25 h ranges between 5.1 and 5.8 Å. Figure 5 shows that the carbon activated for 3 h significantly adsorbs MTBE, as well as the other three smaller molecules. We may, therefore, estimate that the average pore size of this carbon is larger than 5.8 Å. As described above, we produced, from the same batch of carbon cloth, four different carbons with different average pore sizes that can be tested as electrodes for EDL capacitors, in the electrical double-layer region of potentials. In terms of the amount and type of surface groups, the activated carbons that were prepared should be considered identical, since they received the same treatment at 900 °C, where surface groups on carbons are not stable. We assign these carbon samples according to the size of the largest molecule that they could adsorb. These assignments, related to activation times, are summarized in Table 3. It should be mentioned that the various activated carbon cloths could be used as are, with no need for a current collector and a binder.6 3. Assessing Effective Ion Dimensions. 3.1. Differences between Alkaline Metal Cations. Figure 6 shows typical CVs for the alkali chloride solutions at the same scanning rate, 0.2 mV/s, with carbon electrodes of different activation times, as indicated. The potential range was chosen to be negative to the potential of zero charge (pzc)6 so that mainly cation absorption would affect the voltammetric behavior of these systems. The differences between the various cations are most evident with the C3.6 carbon (Figure 6a) and become smaller for the carbons with more opened pore structures. In general, we see two groups

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Figure 6. CV curves obtained at 0.2 mV/s with various carbon cloth electrodes in Li+, Na+, K+, and Cs+ chloride 0.1 N solutions, as indicated. (a) A C3.6 carbon electrode: 0.75 h activation time; BET surface area, 340 m2/g; (b) A C4.2 carbon electrode; 1 h activation time; BET surface area 490 m2/g; (c) A C5.1 carbon electrode; 1.25 h activation time; BET surface area 540 m2/g; (d) A C5.8 carbon electrode; 3 h activation time; BET surface area 860 m2/g. The currents are normalized per m2 BET unit area. In the right axis, the current densities are translated into EDL capacities (microfarads/cm2) by dividing the current density by the potential scan rate.

Figure 7. Apparent specific capacities of the various activated carbon electrodes in the four alkali ion salt solutions that were studied, calculated from the CV curves in Figure 8a-c.

of curves: the CVs related to the Li+ and Na+ salt solutions, which reflect slow charging rates, and the CVs related to the K+ and Cs+ salt solutions, which reflect quicker charging rates. This division in the voltammetric behavior of the various solutions is very pronounced with the C3.6 carbon electrodes (Figure 6a) and much less pronounced with the C4.2 carbon electrodes (Figure 6b), and in fact, it does not exist at all with the C5.8 carbon electrodes (Figure 6d), whose average pore size is the largest of all the activated carbon electrodes tested in this study. We may therefore conclude that the ionic size of K+ and Cs+ is within the range of 3.62-4.2 Å, while the solvated Na+ and Li+ ions are larger than 4.21 Å. Of special interest is the dependence of the EDL capacity on the average pore size of the various activated carbon electrodes (Figure 7). The specific EDL capacity of the carbon electrodes was derived from the currents in the middle of the cyclic voltammograms shown in Figure 6a-d for all four alkali cation salt solutions. As can be seen in Figure 6, the C5.8 carbon exhibits no selectivity at all, while the C3.6 carbon exhibits the highest selectivity. However, the most interesting feature in Figure 7 is the maximum in the specific EDL capacity obtained

with all the cations when the C4.2 activated carbon electrodes were used. This is due8 to the optimal fitness of the pore dimension to the (hydrated) cation size, and correlates with the above conclusion that the size of all these cations is in the range of the C4.2 pore dimensions of the C4.2 carbon (e.g., ∼4.21 Å). This issue was previously discussed in detail.6 3.2. Ion SieVing Effects with BiValent Cations. Figure 8 presents a series of cyclic voltammograms obtained with the various carbon electrodes in the bivalent, alkaline earth metal chloride solutions at relatively large potential windows (≈0.5 V), negative to the pzc. Figure 8a presents cyclic voltammograms of the alkali metal chloride solutions with the C3.6 activated carbon electrode, at this wide potential range. Therefore, the CVs of Figure 8a, which demonstrate a clear sieving effect of the carbon electrode for the alkaline ions, can be regarded as reference curves with which the CVs of the bivalent cation salt solutions should be compared. Figure 8b presents CVs of the same C3.6 carbon electrodes, but for the chlorides of the bivalent alkaline earth cations (Mg, Ca, and Ba salt solutions, as indicated). The difference between the monovalent and bivalent ions is dramatic. It can be seen that all the bivalent cations are excluded from the pores of this carbon electrode. The same dramatic difference is also observed in Figure 9 for the C4.2 carbon, and in Figure 10 for the C5.1 carbon. It is noteworthy that while the bivalent ions are totally excluded from carbons C4.2 and C5.1 the monovalent ones are adsorbed in these carbons to full capacity. In the case of C5.8 carbon electrodes (Figure 11), the effect of sieving out the doubly charged cation disappears, and the cyclic voltammograms retain their rectangular shape. Moreover, the CV curves for the bivalent and monovalent cations become practically identical when the C5.8 carbon electrodes are used, indicating that for the potential range and electrolyte concentrations that is employed, the electrical double layer on carbon

Ion Sieving Effects

Figure 8. CV curves of the C3.6 activated carbon electrodes (determined by dividing the current density by the potential scan rate): activation time of 0.75 h, BET surface area of 340 m2/g, and scan rate of 0.2 mV/s. (a) Li, Na, K, and Cs chloride solutions. (b) Mg, Ca, and Ba chloride solutions. On the right axis, the current densities are translated into EDL capacities.

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Figure 10. Same as Figure 8, but C5.1 carbon electrodes.

Figure 11. Same as Figure 8, but for the C5.8 carbon electrodes. The CV curves related to the solutions of all seven cations that were studied, with chloride as the common anion, are plotted together.

Figure 9. Same as Figure 8, but C4.2 electrodes.

electrodes is indifferent to the cation valency as long as the pore size does not come close to the hydrated ion size. These results enable us to approximate the size for the doubly charged alkaline earth cations; i.e., between 5.1 and 5.8 Å. They are significantly larger than that of the alkaline metal cations. 3.3. SieVing Effects for Anions. Figure 12 presents cyclic voltammograms of the C3.6 activated carbon electrodes in four Li salt solutions with the following anions: Cl-, NO3-, ClO4-, and SO42-. Since the purpose of these measurements was to study the sieving effects of these electrodes for the anions, a

symmetrical potential range as wide as 1 V around the pzc (ca. -0.15 vs SCE6) was chosen. Note that at the potentials negative to the pzc, pronounced currents can be measured, although it was concluded in the previous section that the C3.6 carbon has a pronounced sieving effect for the Li+ ions (see Figures 6 and 7). The relatively high currents in the cathodic branch of the CVs in Figure 12, although relating to adsorption of Li+ ions, are, because of the pronounced driving forces for adsorption, applied in the experiments related to Figure 12 (0.8 V compared with tens of milivolts in the experiments to which Figures 6 and 7 relate). Therefore, the pronounced sieving effect of the C3.6 carbon electrodes for the Li ions could be clearly seen in Figures 6 and 7 but not in Figure 12. The anodic branch (positive to the pzc) of the CVs of Figure 12 also shows a very pronounced sieving effect of the sulfate ion. It can be concluded that the sulfate ion cannot penetrate the pores in the C3.6 activated carbon electrodes. However, it is significant that the ClO4- anion, which apparently has a similar structure, can be significantly adsorbed into this carbon. This may indicate that the sulfate ion is strongly hydrated. In contrast to both the SO42- and ClO4- ions, Figure 12 shows that the Cl- and NO3- ions can easily penetrate the majority of

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Figure 12. CV curves of Li salts of different anions as indicated with C3.6 carbon electrodes. The scan rate was 0.2 mV/s. Electrolyte concentrations were 0.1 N.

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Figure 14. Same as Figure 12, with C5.1 carbon electrodes.

Figure 15. Same as Figure 12, with C5.8 carbon electrodes. Figure 13. Same as Figure 12, with C4.2 carbon electrodes.

the pores in the C3.6 carbon electrodes. Taking into account the fact that the hydrated Li ions cannot easily penetrate the pores of this carbon, we can conclude that both the Cl- and NO3- ions are smaller than the highly hydrated Li+ ion (as well as the hydrated Na+ ion), and are thus closer in size to the K+ cations. The fact that the highest capacitive currents with the C3.6 activated carbon electrodes were obtained with the NO3salt solution is also significant. This should be attributed to its planar geometry and to the special shape of the pores in these carbons. From previous work,16 it is frequently recognized that porous carbons develop flat, slit-shaped pores through mild oxidation. Hence, the flat NO3- anion, which is significantly larger than the Cl- ion in its bulk size,16 can be adsorbed more easily than the other ions, whose structure is more bulky. Since we have shown that the Cl- ion enters the pores when it is nonhydrated, we can assume, likewise, that the nitrate anion is not adsorbed in a hydrated state. The C4.2 activated carbon electrodes (Figure 13) also show pronounced sieving effects for the SO42- and ClO4- ions, like the C3.6 carbon electrodes (Figure 12). The difference in the sieving effects of these two types of carbon is that the C4.2 carbon allows for better adsorption of the ClO4- ions than the C3.6 carbon. However, the similarity in the sieving effects of these two carbons may indicate that their pore distribution is quite wide. From these measurements and from the above discussion, it can be concluded that the size of the sulfate ions is greater than 4.21 Å, while the size of the ClO4- ion ranges between 3.62 and 4.21 Å [a significant adsorption of the ClO4- ions into the C4.2 carbon takes place (Figure 12)]. Figure 14 depicts cyclic voltammograms related to anion adsorption into the C5.1 carbon electrodes. Comparing the CVs in Figure 14 with the CVs in Figure 13 (which relate to the C4.2 carbon), we see that the level of electroadsoption of the chlorate is increased significantly and approaches that of the smaller Cl- anion when the C5.1 carbon electrodes are used. On the other hand, that of the sulfate basically remains negligible. This should imply that, parallel to the electroadsorption of doubly charged cations, the sulfate is larger than

Figure 16. CV curves (0.2 mV/s), obtained with 0.1 N MgSO4 solutions, using C5.8 and C5.1 carbon electrodes, as indicated. For a comparison, CV curves (0.2 mV/s) for 0.1 N Li2SO4 and MgCl2 solutions measured with C5.1 carbon electrodes are also presented. The currents are normalized per square meter BET unit area.

5.1 Å and should appreciably contribute to the EDL capacity only at larger pores, as is, in fact, seen in Figure 15, which relates to the C5.8 carbon electrodes. Here, the CVs measured with sulfate solution do not show any sieving effect. Moreover, the fact that the cyclic voltammograms of the bivalent and monovalent anions are practically identical indicates that the EDL capacity is independent of ion charge at least at the concentration and voltage range that are employed (as was shown for the cations in Figure 11). 3.4. BehaVior of the 2-2 Electrolyte, MgSO4. The conclusion that doubly charged ions exhibit uniquely large dimensions has been demonstrated with 1-2 or 2-1 electrolytes. We interpreted the triangular shape of the CV obtained in these cases as being the result of the adsorption of the smaller ion into the pores, at one side of the pzc, and the result of the absence of adsorption of the bivalent, large ions at the other side of the pzc. Strong and impressive evidence of this interpretation is found in Figure 16. This figure compares CVs measured with C5.1 and C5.8 carbon electrodes in Li2SO4 and MgCl2 solutions. While the currents in the CV measured in a MgSO4 solution with the C5.1 carbon electrodes are negligible, a maximal EDL capacity is reflected by the CV measured with the C5.8 carbon electrodes in the same solution. For comparison, Figure 16 also demon-

Ion Sieving Effects strates the sieving effect of the C5.1 carbon electrodes for both the bivalent anion and cation in 2-1 and 1-2 electrolyte solutions (MgCl2 and LiSO4, respectively). Conclusion The effective size of various aqueous ions was estimated from the sieving effects of microporous carbon electrodes, whose average pore size was determined by absorption studies of globular molecules of known size in the gas phase. We were able to develop carbons having pore dimensions whose size was of known values, i.e., 3.62, 4.21, 5.1, and 5.8 Å. Using cyclic voltammograms of pore-size calibrated carbons in aqueous solutions of various electrolytes, we obtained rectangular-shaped voltammetric curves when the pore size was significantly larger than the ion size. The rectangular CVs are changed to triangular ones at potentials when the ions studied were larger than the pore dimensions, and could therefore not be electroadsorbed into the pores to balance the charge of the electrical double layer. Following this procedure, we could establish a scale of dimension of the different ions. The electrolytes used in comparative series were Li, Na, K, Mg, Ca, and Ba chlorides at potentials negative to the pzc, and nitrate, chloride, perchlorate, and sulfate of Li at potentials positive to the pzc. The results indicate that the sizes of all four alkali cations fall between 3.62 and 4.21 Å, where the lighter the ion, the larger its size. Taking into account the fact that the bare ion diameter values obtained from the crystal parameters17 are only 1.21, 1.92, 2.66, and 3.312 Å for Li+, Na+, K+, and Cs+, respectively, we can conclude that the alkali ions in aqueous solutions can be adsorbed into pores together with a sizable hydration sheath having a diameter between 3.62 and 4.21 Å. The bivalent alkaline earth cations are clearly larger than 4.21 Å, but smaller than 5.8 Å. This, as expected, indicates that the hydration sheath of the bivalent ions cannot be stripped of the ions when they are forced to penetrate the carbons’ pores at the negative potentials. The hydration shell of the alkaline earth cations is obviously much thicker than that of the monovalent alkaline ions. With regard to the anions, it was found that NO3- is slightly smaller than Cl- and that they both are approximately 3.624.21 Å in size. When comparing perchlorate and chloride anions, we found that ClO4- definitely exhibits limited electroadsorption into the C3.6 carbon, easier electroadsorption into the C4.2 carbon, and further, greater electroadsorption in the case of the C5.1 carbon. When the fact that the pore system in each of the activated carbon samples that were studied has a significant size distribution is taken into account, this places the perchlorate’s ion size in the 4.21-5.1 Å range. More accurate estimates of

J. Phys. Chem. B, Vol. 105, No. 29, 2001 6887 ion dimensions may be obtained if the carbon pore size distribution function were narrower. However, progressive activation of carbon materials that makes them more porous should limit their ability to produce pores at a narrow size distribution. Like Mg2+, SO42- exhibits extra large dimensions, in tandem with a large, strongly bound hydration sheath. This leads us to conclude that it should be relatively easy to prepare electroadsorption-selective porous carbon electrodes for the separation of monovalent and multivalent ions. Acknowledgment. Partial support for this work was obtained from the BSF, Israel-U.S. Binational Science Foundation, and from ECR-AVX (Israel) Inc. We thank Dr. Shifra Hochberg for editorial assistance. References and Notes (1) Harned, H. S.; Owen, B. B. Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold Publishing Corp.: New York, 1958; pp 283285. Gorin, M. H. J. Chem. Phys. 1939, 7, 405. (2) Winter, M.; Besenhard, J. O. In Lithium-ion Batteries, Fundamentals and Performance; Wakihara, M., Yamamoto, O., Eds.; Wiley VCH: New York, 1998; Chapter 6. (3) Kinoshita, K.; Chu, X. In Electrochemical Capacitors; Delnick, F. M., Tomkievicz, M., Eds.; Proceedings Volume; The Electrochemical Society Inc.: Pennington, NJ, 1996. (4) Oren, Y.; Tobias, H.; Soffer, A. Bioelectrochem. Bioenerg. 1984, 411, 347. Oren, Y.; Soffer, A. Electrochim. Acta 1984, 28 (11), 1649. Tobias, H.; Taragan, E.; Oren, Y.; Soffer, A. Nucl. Technol. 1987, 77, 46. (5) Oren, Y.; Soffer, A. J. Appl. Electrochem. 1983, 13, 473, 489. Farmer, J. C.; et al. J. Electrochem. Soc. 1996, 143 (1), 161; J. Appl. Electrochem. 1996, 26, 1007. (6) Salitra, G.; Soffer, A.; Eliad, L.; Aurbach, D. J. Electrochem. Soc. 2000, 147, 2486. (7) Koresh, J.; Soffer, A. J. Electroanal. Chem. Interfacial Electrochem. 1983, 147, 223. (8) Everett, D. H.; Powl, J. C. J. Chem. Soc., Faraday Trans. 1 1976, 72, 619. (9) Grunwall, T. H.; Lamer, V. K.; Sancved, K. Phys. Z. 1928, 29, 358. LaMer, V. K.; Grunwall, T. H.; Grieff, L. J. Phys. Chem. 1931, 35, 2245. (10) Koresh, J. E.; Soffer, A. J. Chem. Soc., Faraday Trans. 1 1980, 76, 2472. (11) Koresh, J. E.; Soffer, A. Sep. Sci. Technol. 1983, 18 (8), 723. (12) Ross, S.; Olivier, J. P. On Physical Adsorption; Interscience: New York, 1964. (13) Brunauer, S.; Emmet, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309. (14) Israelachvili, J. Intermolecular and surface forces, 2nd ed.; Academic Press: New York, 1995; Chapter 7. (15) Sutt, Jr.; Robert, F. Use of carbon molecular sieves for separating gas or liquid mixtures. U.S. Patent 4,594,163, June 10, 1986. (16) Koresh, J. E.; Soffer, A. J. Chem. Soc., Faraday Trans. 1 1980, 76, 2457; J. Colloid Interfacial Sci. 1980, 75 (1), 34. (17) Pauling, L. The Nature of the Chemical Bond; Cornell University Press: Ithaca, NY, 1939; Chapter 10.