The anatomy of the double layer and capacitance in ionic liquids with anisotropic ions: Electrostriction vs. lattice saturation

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Abstract

We investigate the basic mechanisms of the electrical double layer formation in ionic liquids near a flat charged wall, by performing Monte Carlo simulations of several model liquids with spherical and elongated ions that contain charged ‘heads’ and neutral ‘tails’. We analyze the structural transitions in response to the variation of the voltage across the double layer and their effects on the formation of the characteristic ‘camel shape’ capacitance recently observed in experiments [1], [2]. The camel shape was predicted earlier by the mean-field theory [3] for the case of an ionic liquid with large percentage of voids which allowed for substantial ‘electrostriction’ and thereby increase of the local charge density in the double layer. However, we show that in contrast to a liquid composed of spherical ions, in a liquid with anisotropic ions the double-hump ‘camel shape’ of the capacitance curve does not require high compressibility of the liquid. Many ionic liquids have elongated shape of ions, with charged ‘heads’ and neutral ‘tails’. We show that these neutral tails play a role of space fillers, or ‘latent voids’ that can be replaced by charged groups, following rotations and translations of ions. This feature allows an electric field-induced increase of the counter charge density without a substantial compression of the liquid. It causes rising branches of capacitance at small positive and negative electrode polarizations. However, we show that at large positive and negative voltages it has to be inevitably replaced by the ‘lattice saturation’, a universal effect, which does not depend on the model, in which the capacitance decreases inversely proportional to the square root of the voltage. This conclusion is supported by our analysis of the experimental results of Lockett et al. (2008) [1] that appear to follow this law staring from the potentials ∼±0.7–0.9 V. The competition between the two trends, one prevailing at low voltages and the other one at high voltages, results in the camel shape of capacitance, seen in our simulations.

Introduction

The rediscovery of room temperature ionic liquids (RTILs) of the last 15 years comprised a major breakthrough in chemistry. With RTILs and their mixtures, we have now practically unlimited number of solvents that can be synthesized and blended. Hundreds of them are already known [4]; the structure and dynamics of many of them is currently under investigation [5]. The wave of interest to RTILs has reached electrochemistry and electrochemical engineering [6], [7], [8], [9], [10], [11], because RTILs as electrolytes are nonvolatile, can sustain substantially higher voltages in electrochemical cells without decomposition, and many RTILs are environmentally friendly. At ambient temperatures, however, RTILs have high viscosity, and the diffusion and conductivity of ions is normally lower in RTILs than in aqueous electrolyte solutions. At a first glance, this limits applications of RTILs as solvent-free electrolytes in supercapacitors and batteries. But nowadays we witness an intensive search for new architectures and new effects in templated nanoporous electrodes that may help to overcome those limitations [12], [13]. Such search would be facilitated by unraveling the fundamentals of the double layer structure and capacitance on flat electrodes, as a reference base for the effects emerging in nanoporous electrodes. Note, that from the fundamental point of view, the high electrochemical window of RTILs opens doors to experimental investigations of interesting high-voltage regimes of the capacitance which were inaccessible in aqueous electrolytes. Investigating these regimes has also great practical importance for understanding of performance of supercapacitors at full load.

The interest to the double layer in RTILs at electrified interfaces, has triggered a wave of new theoretical [3], [14], [15], experimental [1], [2], [16], [17], [18], [19], [20], [21] and simulation [22], [23], [24], [25], [26], [27], [28], [29] studies of the capacitance in ionic liquids at different electrodes in a range of electrode potentials. One group of simulations [23], [24], [28] deliberately did not mimic the force-field patterns of real ionic liquids. Instead, these works have dealt with a dense mixture of positively and negatively Lennard-Jones charged spheres, in order to reveal the anatomy of the double layer formation as a function of electrode potential. The focus was on the interplay between the effect of electrostriction with overscreening, which dominates at small voltages and the excluded volume effect, which governs the ion packing at large voltages. Whereas in Ref. [23] the ions were of identical size, Ref. [24] analyzed the effect of difference in size of cations and anions. The prediction of Ref. [3], that for cations larger than anions a maximum of capacitance will be shifted towards negative potentials, was reproduced.

In the present study we investigate the influence of the cation shape asymmetry, using again deliberately a similarly idealized approach. Indeed, a detailed atomistic model of an ionic liquid would – at least at the present level of our understanding of the double layer and capacitance – would make it more difficult to distinguish the pure effect of molecular size and shape. However, a simplistic model, lacking all molecular details except for the excluded volume and shape asymmetry, would allow tracing the consequences of these two features in their pure form.

There are already first experimental data to refer to in this context. Several experimental groups [1], [2], [17], [18] independently observed the peculiar double-hump camel-like shape of differential capacitance in different RTILs at different electrodes. Lockett et al. [1] have measured capacitance curves in a series of ionic liquids with a common anion with the cations that differ in the length of the alkyl chain: 1-ethyl-3-methylimidazolium chloride [emim][Cl], 1-butyl-3-methylimidazolium chloride [bmim][Cl], 1-hexyl-3-methyl-imidazolium chloride [hmim][Cl]. The obtained capacitance curves exhibited two local maxima, which vary in height and position with the length of the alkyl chain. These results suggest that longer alkyl chains have the tendency to decrease the capacitance, with an exception for [bmim][Cl]. The latter was attributed to the possible lack of equilibrium, because this liquid has higher freezing temperature, very close to the temperature at which the observations were performed. It remained open to understand how the excluded volume of the alkyl chains, the cation shape asymmetry and other details of molecular structure affect the features of the observed capacitance. The present work is targeted to answer this question.

The excluded volume and shape asymmetry of the cation are incorporated in our model via linear two- or three-bead rigid chain. We choose the radius of beads close to typical values for RTILs. As we will see, the model – although a cartoon-like – catches the qualitative features of the experimental data. This is not too surprising. The differential capacitance is determined by the position of the center of mass of the distribution of the additional charge induced by an extra charge on the electrode [30]. In this quantity molecular details are largely ‘integrated out’. This advocates the use of a simplified model as a reference base.

A preliminary account of this work has been reported [28]. In this paper we present a detailed analysis of the results as well as investigate a set of important new questions not considered in Ref. [28], such as the interplay between the electrostriction and the lattice saturation regimes.

Section snippets

Model and methods

We consider an ionic liquid slab of thickness L confined between two oppositely charged electrodes. The distance between the electrodes is sufficiently large so that the electric field in the middle of the slab (call it ‘bulk’) is practically zero, i.e. this region is electroneutral. Using the obtained equilibrium Monte Carlo configurations, for each value of surface charge density σ on one of the electrodes, we calculated the charge distributions ρ(z) averaged over z-crosssection, using a

Differential capacitance of the double layer

Fig. 1 shows the charge density as a function of the potential for all three models.

Differentiating the fitted σ(U)-functions in Fig. 1 the capacitance profiles for all three systems were obtained as shown in Fig. 2, together with the experimental capacitance curve for [hmim][Cl] [1]. As in our previously used models [23], [24], [28] we do not introduce any potentials that could be responsible for the specific adsorption of ions on the electrode, the PZC for all three models is close to zero

Conclusions

Because a great number of known cations as well as some large anions of ionic liquids have inhomogeneous structure and shape anisotropy, consisting of charged heads and neutral ‘bodies’ or ‘tails’, the revealed camel shape profile is likely to be a common feature of the double layer capacitance. We note, however, that the exact positions of the peaks will be structure specific, and some may not be accessed experimentally, if shifted beyond the range of ideal polarisability of the electrode.

This

Acknowledgements

A.A.K. acknowledges the financial support of EPSRC-NSF project through the EPSRC Grant EP/H004319/1. We are thankful to Vera Lockett, Rossen Sedev and John Ralston for the experimental data of their work provided in a digital form. We thank Eckhard Spohr, Philippe Bopp and Genady Chuev for discussions of the simulations setup. We acknowledge the help of Rainer Kleineresing and Ronald Kriemann with technical aspects of supercomputing calculations.

References (42)

  • M.T. Alam et al.

    Phys. Chem. C

    (2007)
    M.T. Alam et al.

    Electrochem. Commun.

    (2007)
  • M. Drueschler et al.

    J. Phys. Chem. C

    (2010)
  • G. Feng et al.

    J. Phys. Chem. C

    (2009)
  • A.A. Kornyshev et al.

    Electrochemical interfaces: at the border line

  • V. Lockett et al.

    J. Phys. Chem. C

    (2008)
  • M.T. Alam et al.

    J. Phys. Chem. C

    (2008)
  • A.A. Kornyshev

    J. Phys. Chem. B

    (2007)
  • T. Welton

    Chem. Rev.

    (1999)
  • Special issue on ionic liquids. J. Phys. Chem. B 111 (2007)...
  • M.C. Buzzeo et al.

    Chem. Phys. Chem.

    (2004)
    D.S. Silvester et al.

    Z. Phys. Chem.

    (2006)
  • F. Endres, D. MacFarlane, A. Abbott (Eds.), Electrodeposition from Ionic Liquid, Wiley-VCN,...
  • W. Freyland

    Phys. Chem. Chem. Phys.

    (2008)
  • M. Armand et al.

    Nat. Mater.

    (2009)
  • D.R. MacFarlane et al.

    Phys. Chem. Chem. Phys.

    (2010)
  • L. Hongtao et al.

    Phys. Chem. Chem. Phys.

    (2010)
  • J. Chmiola et al.

    Science

    (2006)
  • C. Largeot et al.

    J. Am. Chem. Soc.

    (2008)
  • M. Kilic et al.

    Phys. Rev. E

    (2007)
  • K.B. Oldham

    J. Electroanal. Chem.

    (2008)
  • Yu.-Zh. Su et al.

    Angew. Chem. Int. Ed.

    (2009)
  • S. Baldelli

    Acc. Chem. Res.

    (2008)
  • Cited by (0)

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