Assessing the Solvation Numbers of Electrolytic Ions Confined in

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Assessing the Solvation Numbers of Electrolytic Ions Confined in Carbon Nanopores under Dynamic Charging Conditions Mikhael D. Levi, Sergey Sigalov, Gregory Salitra, Ran Elazari, and Doron Aurbach* Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel

ABSTRACT We propose herein a new reliable approach to assess solvation numbers of ions confined in carbon nanopores based on dynamic quartz crystal measurements. This was proved for the entire families of alkaline, alkaline-earth cations, and halogen anions. As-assessed hydration numbers appear in the sequence characteristic of a transition from the cosmotropic to a chaotropic-type behavior with the decrease of the ion's charge-to-size ratio. The information on the behavior of ions confined in nanometric space of different (especially charged) carbon materials is in high demand for the development of powerful supercapacitors, nanofiltration membranes, and chemical/biochemical sensors. SECTION Energy Conversion and Storage

T

he ability of electrolytic ions to partially desolvate in a host matrix is a common feature of nanoporous materials of different nature such as high surface area activated carbons and biological membranes. Ionic permeation through phospholipid membranes was shown to strongly depend on the hydrated ions' radii,1,2 which, in turn, define their permeation ability, quantified in terms of the ion hydration dynamic numbers (HDNIs).3 These numbers show how tight the ions are attached to water molecules in their first hydration shell.4 The concept is in good conformity with ab initio quantum mechanical calculations.5 High surface area activated carbons, containing subnanometer size pores, separated by 2-4 graphene layers-thick walls,6 reveal remarkable ion-sieving effect as the size of the solvated ion increases.7,8 Moreover, a partial desolvation of ions confined in subnanometer size carbon pores is believed to be the origin of anomalous increase of the capacitance obtained with different nanoporous carbon materials.9-11 We propose herein a new, reliable method to measure the ability of ions to deform their solvation shells, losing part of the solvent molecules (defined as confined ion solvation numbers, CISNs), during electroadsorption of these ions into carbon nanopores. It was recently shown that a conventional electrochemical quartz crystal microbalance (EQCM) may serve as a true gravimetric probe of the compositional changes in charged nanoporous carbon electrodes,12 and later on reported that, at least for a highly solvated Liþ cation in a typical aprotic solvent such as propylene carbonate (PC), estimation of the partial desolvation of this ion confined in carbon nanopores seems to be plausible.13 This remarkable result inspired us to determine CISNs for three important series of ions using a quartz crystal impedance technique, known for its remarkable ability to characterize both the gravimetric and viscoelastic behavior of conducting polymers14-20 and rough metallic deposits.21

r 2011 American Chemical Society

We employed the same type of nanoporous carbon as in our previous works,12,13 namely, Kuraray YP-17. The porous structure characteristics (see also Figures S1 and S2 of the Supporting Information) and the experimental details are collected in the Experimental Section. Figure S3 of the Supporting Information shows that both cyclic voltammetry (CV) and the resonance frequency curves of the same carbon coating are virtually the same when measured using a Network analyzer station and a simpler research quartz crystal microbalance (RQCM) system. Figure S4 presents quartz crystal admittance (i.e., conductance) spectra of a carbon coating measured at different electrode potentials. The change in the resonance frequency with applied potential was converted into electrode's mass changes according to the Sauerbrey equation: Δf = -CfΔm, where Cf is the sensitivity factor of the crystal equal to 0.056 Hz/ng/cm2, and Δm is the change in mass of the coating per unit area. This equation is valid for the gravimetric limit of the EQCM method,14-21 which implies that coating's rigidity does not change with potential, and hence the width of the resonance peak, fw, remains unchanged. The potential variation of the fw is very small, validating that the crystal admittance data can be translated to gravimetric information. This result is in excellent agreement with an indirect proof of the gravimetric character of the EQCM response from a carboncoated quartz crystal furnished by RQCM: the resonance frequency change is proportional to the carbon coating's mass with a negligible change of the crystal resistance as a function of potential.12 Although we used herein the gravimetric limit of the crystal admittance measurements, application of Received Date: December 15, 2010 Accepted Date: December 29, 2010 Published on Web Date: January 04, 2011

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DOI: 10.1021/jz1016922 |J. Phys. Chem. Lett. 2011, 2, 120–124

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this technique in the foreseeable future may be decisive in understanding the nature of charge-induced deformations of carbon nanopore walls (especially, in the range of high electrode surface charge densities) with the goal of improving the existing and designing new generations of carbonbased supercapacitors. Typical CVs of carbon-coated quartz crystals in aqueous solutions of alkaline and alkaline-earth cations are shown in Figure 1A,C whereas the related charge-density dependent changes in the amounts of the adsorbed ions, ΔΓ, are presented in Figure 1B,D, respectively. The values of ΔΓ were calculated from the experimentally measured electrode's mass change, Δmexp (g cm-2): ΔΓ = Δmexp /Mtheor where Mtheor stands for the dehydrated ion's molecular weight. The above equation is valid for a particular case of ideal permselectivity of an electroactive coating, whereas analysis of a more general case (e.g., failure of permselective behavior or coupling between the insertion of ionic and solvent species) is complicated by the fact that the population changes of three species (i.e., anion, cation, and solvent) have to be measured and monitored using only two experimentally measured quantities (Δmexp and Q). This problem was rigorously formulated and successfully solved by Bruckenstein and Hillman et al. for the ions and solvent transport during charging of conducting polymer film electrodes.14-16,18-20 The treatment of EQCM responses of nanoporous carbons is greatly facilitated by the fact that (as reported below in this communication and earlier for aprotic organic solutions)13 a broad variety of relatively large ions (except for the bulkiest tetraalkylammonium cations) exhibit experimental ΔΓ/Q ratios that perfectly match the theoretical ones at moderate electrode charge densities (i.e., far from both the potential of zero charge (pzc) and from the extreme vertex potentials of highamplitude charging-discharging potential scans). This points to the permselective behavior of the carbon coating used, and thereby to the absence of any accompanying flux of solvent molecules. The thermodynamic origin of the solvent transfer in electroactive polymer films has been carefully studied by Bruckenstein and Hillman22 who came to an important conclusion that bathing solutions defined solvent activity in the bulk of the polymer films, independent of their redox composition, thus demonstrating a large variety of particular cases for the ratios of the inserted ions and solvent fluxes.15,18-20 The difference in the behavior of both types of host materials can be easily rationalized in terms of a higher rigidity of activated carbon as compared to the majority of polymeric matrices (the important argument of free-volume constraint in carbon coatings was considered elsewhere).13 Since a permselective behavior, by definition, does not involve a co-ion ejection mechanism,15 any deviation of the experimental ΔΓ/Q beyond the theoretical one can be translated into the accompanying insertion of solvent molecules, which directly leads to determination of a quantity, called CISN. The calculations were adopted from the routine proposed for electroactive polymers to separate between fluxes of ionic species and solvent molecules.18-20 Although EQCM measures changes in populations of the species involved and is not able to indicate any possible link between them,16 the idea of equating the experimentally found ΔΓion/ΔΓsolvent


Figure 1. CVs (A and C) and the related ΔΓ versus Q plots of the carbon electrode in 0.1 M solutions of alkaline and alkaline-earth metal chlorides, respectively (as indicated). The dotted lines at the most negative charge densities are extrapolations of the linear portions of the experimental curves, compared with the theoretical straight line based on the Faraday law (the dashed black lines). The values of the CIHN are calculated from the slopes of these dotted lines.

ratio to the CISN stems from a consideration of the elementary stages of adsorption processes of ions into any confined (or semiconfined) space: prior to being adsorbed, the ion (naturally) should leave part of its solvation shell to an extent dependent on the pore size and the ion's characteristic charge per size ratio. Similar logic is used in the ion size exclusion chromatography method,3 and is even reflected in classical EDL models for ions specifically adsorbed at the inner Helmholz

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Table 1. Solvation Numbers of Ions Confined in Carbon Nanopores (CIHN) Obtained from EQCM.a CIHN (this paper)

hydrated ion radius/nm 1

Liþ

2.6

0.382

22

Naþ

2.2

0.358

13

Kþ

1.3

0.331

7

Csþ Mg2þ

0.5 5.8

0.329 0.428

6 36

Ca2þ

3.7

0.412

29

Ba2þ

2.8

F-

1.4

0.352

6.7

Cl-

0.6

0.332

6.4

Br-

0.05

0.330

5.9

I-

0

0.331

5.8

ion

bulk solution hydration number26,27

a

Hydrated ions' radii and hydration numbers in bulk solution are given for comparison.

Figure 2. CVs (A) and the related ΔΓ versus Q plots of the carbon electrode in 0.025 M solutions of potassium halogenides (the designations are similar to those used in the legend to Figure 1).

water molecules to the smaller anions. Smearing of the V-shape feature on the CVs near the pzc and flattening of the ΔΓ versus Q curves close to Q = 0, when going from F- to I-, is another consequence of the ability of large ions (chaotropes) to disturb water structure in their close vicinity, resulting in the appearance of the so-called “water structure enforced ion pairing”:23,24 for the relatively wide pores, the (water) structure-breaking ions tend to partition into carbon micropores (for slightly charged electrode surfaces) in the form of ion pairs with the co-ions, resulting in the breakdown of carbon's permselectivity.12,13 Our recent study of carbon electrodes using EQCM revealed a dramatic breakdown of the carbon electrodes' permselectivity (extending from the pzc toward relatively high cathodic polarizations) for very bulky tetraalkylammonium cations,25 which are typical and quite efficient water-structure breakers. At higher Q, the co-ions are electrostatically excluded from the carbon pores, supporting their permselectivity.12,13,25 Attributing the difference between the experimental value of Mexp and the theoretical one, Mtheor, to the stacked water molecules from the first hydration shell of the ions, we come to a simple equation for the confined ion hydration number (CIHN): n = (aexp - atheor)Mtheor/atheorMH2O, where aexp and atheor stand for the experimental and theoretical values of the slopes of the ΔΓ versus Q plots in Figures 1B,D and 2B (similar arguments were used to separate ionic and solvent fluxes in conducting polymers).18-20 As-obtained values of n for alkaline, alkaline-earth, and halogen ions are listed in Table 1. It is seen that identification of the Liþ, Naþ, all the double-charged alkaline-earth cations, F- anion with typical cosmotropic, and the rest with chaotropic ions, is in good agreement with the change in their hydrated ionic radii.1 Comparison between thus obtained values of n and the solvation numbers of these ions in bulk solutions26,27 (Table 1) gives a sense of the extent of dehydration of the ions confined in carbon nanopores, in qualitative agreement with the HDNI numbers obtained by ion exclusion chromatography.3 Exact coincidences are not expected as a general rule because both hydration numbers may depend on the pore widths and the difference

plane on metallic electrodes (meaning a partial desolvation of such ions from the electrode surface side). The almost identical CVs for the alkaline and alkaline-earth cations imply that most of the carbon nanopores have widths larger than the ions sizes (no sieving effect). The CVs reflect the electronic current passing through the carbon electrode, and appear to be insensitive to the ion's nature. By contrast, the ΔΓ versus Q plots obtained from EQCM measurements show remarkable selectivity for the cations (Cl- was the common anion to these series of cations, thus the ΔΓ vs Q plots are almost identical at Q > 0). The theoretical ΔΓ versus Q plots calculated from the Faraday law are designated by the black broken lines in Figure 1B,D. For the smallest, highly hydrated cations, the slope of the experimental ΔΓ vs Q plots at Q , 0 is the largest, decreasing down to the theoretical value for the bulkier cations. The apparent mass of the highly hydrated cations in the carbon nanopores, Mexp, is higher than Mtheor, in contrast to the larger, less hydrated cations, with their Mexp closely approaching the theoretical (anhydrous) ones. This finding correlates well with the size exclusion chromatography data revealing that, e.g., LiCl had an apparent molecular weight larger than its anhydrous molecular weight due to the tight attachment of water molecules to Liþ ions.3,4 This correlation implies the ability of the EQCM method to approach the CISNs in nanoporous carbons. From Figure 1 it can be concluded that, in accordance with refs 3 and 4, Cl- anion with its Mexp value close to Mtheor (derived at moderate charge densities of the electrode) should be considered as a typical chaotropic ion. Prior to quantification of the CISNs, we characterized the desolvation ability of the halogen anions, choosing dilute solutions of potassium halogenides (0.025 M) because of the stronger adsorption and limited anodic stability of I- on the carbon electrode surface. The related CVs and the Γ versus Q plots are shown in Figure 2A,B, respectively. Again, smaller anions have Mexp higher than Mtheor, suggesting sticking of


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in the ion-pore wall interactions. Interestingly, the Al3þ ion (hydrated radius 0.48 nm),1 with the expected value of n higher than that of Mg2þ, actually demonstrates the opposite behavior (Figure S5). This shows that our approach to CIHN in activated carbons based on EQCM measurements cannot be extended to ions prone to bulk hydrolysis. The resulting protonation of the oxygen-containing functionalities on the carbon surface decreases its negative charge and, hence, diminishes the Al3þ cations flux. We recently reported a similar effect on a carbon electrode when CsCl solution was acidified with HCl, which dramatically suppresses the insertion of Csþ cations, replacing it by electrically equivalent desorption of Cl- co-ions.28 The assessment of the CIHNs with the use of EQCM reported herein is a promising tool for screening entire families of electrolytic ions to partially desolvate and permeate inside the nanometer size pores of different membrane materials. Understanding the phenomena of partial desolvation of ions confined in nanometric space of different nanoporous hosts is critically important for the development of high-energy and high power density supercapacitors,10,11 desalination technologies,29 and natural and artificial biochemical membranes.30

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EXPERIMENTAL METHODS We used activated carbon powder Kuraray YP-17 with a Brunauer-Emmett-Teller (BET) surface area of 1600 m2g-1, average particle size around a few micrometers, about 50% of the total pore volume related to the micropores, and narrower than 1.1 nm. Details of its porous structure and the mode of composite carbon coatings preparation are presented in the Supporting Information as well as in refs 9 and 10. A Maxtek 1-in.-diameter Au-coated AT-cut quartz crystal with a fundamental frequency at 5 MHz was used as previously reported.9,10 The quartz crystal impedance measurements were carried out with the use of an E5100A High-Speed Network Analyzer in combination with a Schlumberger's 1287 electrochemical interface driven by Lab-View 9.0 software employed for data acquisition and processing. The control experiments were carried out using the Maxtek RQCM system combined with Autolab PGSTAT20 for simultaneous EQCM and CV measurements.9,10 All the potentials were measured with respect to Ag/AgCl/0.5 M CsCl reference electrode separated from the working compartment by a Vycor membrane.

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SUPPORTING INFORMATION AVAILABLE Experimental procedures and materials' characterization. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

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Corresponding Author: *To whom correspondence should be addressed. E-mail address: [email protected]. (18)

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Assessing the Solvation Numbers of Electrolytic Ions Confined in

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