Competition of Desolvation and Stabilization of Organic Electrolytes in

Article pubs.acs.org/JPCC

Competition of Desolvation and Stabilization of Organic Electrolytes in Extremely Narrow Nanopores Tomonori Ohba*,† and Katsumi Kaneko‡ †

Graduate School of Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan Research Center for Exotic Nanocarbons, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan

‡

S Supporting Information *

ABSTRACT: Organic electrolytes are widely used for electric double-layer capacitors. However, the molecular mechanism involved is far from being understood. We demonstrate the structures and stabilities of tetraethylammonium and tetrafluoroborate ions in propylene carbonate solution in carbon nanopores using Monte Carlo simulations. These ions were significantly desolvated at nanopore widths below 1.0 nm. The nanopore potential compensated for the loss of stability of the ions as a result of desolvation for nanopore widths of 0.7−1.2 nm for Et4N+ and 0.6−0.9 nm for BF4−. High-capacitance electrodes can therefore be obtained using such nanoporous carbons.

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INTRODUCTION The serious problems of energy insecurity, climate change, and air and water pollution require innovative concepts and research to provide clean and sustainable energy.1−3 Renewable energy sources such as wind, water, sunlight, and biomass have future growth potential as replacements for conventional energy sources based on oil, coal, and natural gas. These renewable energy sources have to be connected to energy storage systems such as batteries because the outputs of such energy sources fluctuate depending on factors such as the weather and wind speed. Batteries exhibiting high energy power, high power densities, and long lives are therefore necessary. Conventional batteries have high energy densities but inadequate power densities. Electric double-layer capacitors (EDLCs), which are also known as supercapacitors or ultracapacitors, can store electric energy with high power densities.4,5 In addition, EDLCs are durable, have efficient charging and discharging cycles, and contain no heavy metals; these are all advantageous features for relevant applications. EDLCs are also lightweight and have wide thermal operating ranges. As a result, EDLCs have received much attention as environmentally friendly and low-cost electric power capacitors. However, conventional EDLCs have relatively low energy densities and therefore have to be improved to obtain both high power and high energy densities.6−8 This could be achieved by using carbon materials with large surface areas and adaptable nanopore widths and ions as electrodes. As an EDLC is a liquid−solid interface system, the surface area and nanopore width strongly affect the capacitance and cyclability as well as ion concentrations. For this purpose, activated carbons and related materials have been fabricated.9−16 Organic electrolyte solutions are often used as electrolytes. An investigation of suitable nanopore widths with respect to the effective ion size is essential for obtaining highly efficient capacitors. Chmiola and co-workers reported an anomalously high capacitance for nanopore widths less than 1 nm.17 © 2013 American Chemical Society

Chmiola, Largeot, Simon, and co-workers also showed a relationship between ion size and nanopore width; a high capacitance was observed when the ion size corresponded to the nanopore width.18−20 The removal of the solvation shell of the ion is necessary for high capacitance, and the mobility of the ions in nanopores is also significantly affected by the solvent. The effect of the solvent as well as that of the nanopore width is therefore important in elucidating the electric mechanism of EDLCs.21,22 Furthermore, solvents strongly affect the energy and power outputs of capacitors.23 Tetraethylammonium (Et4N+) and tetrafluoroborate (BF4−) ions in propylene carbonate (PC) solvent have been widely used in nonaqueous electrolytes for EDLCs because they are stable and safe and have favorable electrolytic conductivities.24 An understanding of the structures and behaviors of Et4N+, BF4−, and PC adsorbed in carbon nanopores is essential for investigation of the EDLC mechanism. The structures and behaviors of ions have been assumed based on the theories of Helmholtz and the Gouy−Chapman, Gouy−Chapman−Stern, and Debye−Hückel models. Although these models represent the formation of an electric double layer on a surface, there is a lack of knowledge of the structures and behaviors at the molecular level. Structural analyses of electrolytes have shown significantly strong solvation of electrolytes in nanopores.25,26 X-ray diffraction analyses of Et4N+ and BF4− in PC solutions in carbon nanopores indicated that PC molecules were densely packed in those nanopores and took a vertical orientation against the nanopore walls in the narrow nanopores.27 However, detailed structures have been rarely obtained experimentally, and the behavior is still obscure. Molecular simulations can be well-used to evaluate and estimate the behaviors of organic molecules and relatively Received: June 3, 2013 Revised: July 29, 2013 Published: July 30, 2013 17092

dx.doi.org/10.1021/jp405479y | J. Phys. Chem. C 2013, 117, 17092−17098

The Journal of Physical Chemistry C

Article

simple molecules in nanopores.28−34 Molecular simulations of inorganic ionic aqueous solutions in nanopores have also been performed to compensate for the lack of available information, and such simulations are a powerful tool for understanding molecular behaviors and structures in nanopores.35−38 However, statistical mechanical simulations of organic molecules are much more difficult because of their complexity, although some previous studies using molecular dynamics simulations have been reported.39−43 The structures of Et4N+, BF4−, and PC molecules adsorbed in nanopores, and their adsorption mechanism, have therefore not been clarified despite their importance. In this study, the molecular structures and solvation numbers of these species in carbon nanopores of width 0.5−2.0 nm are evaluated using canonical ensemble Monte Carlo (CEMC) simulations associated with grand canonical Monte Carlo (GCMC) simulations. In addition, we evaluated stabilized energies of molecules using intermolecular potentials, providing the most effective nanopore width for high capacitance.

the center of the mass of each molecule. We assumed the rigid structure model for each molecule in the simulation. Flexible structure models in nanopores might provide more detailed structure of adsorbed molecules. The interaction potential between an adsorbed molecule and a carbon nanopore wall was described by the Steele 10−4−3 potential model, showing a smooth potential model of a molecule with a carbon wall.49 ϕsf =

i

−

⎤ ⎥ 1.005(zi + 0.20435)3 ⎥⎦ σsfi 4

(2)

Here, A is 76.38πεsfiσsfi2 and z is the vertical distance of the ith atom in a molecule from the center of a carbon atom on one side of a carbon surface. The Steele 10−4−3 potential model is well-used for the adsorption on a solid surface. The potential differences in the smooth Steele 10−4−3 potential and atomistic potential models were trivial for general nanopores, as reported elsewhere.50,51 The difference could be also neglected for nitrogen adsorption in those nanopores in the 0.1 nm unit in our preliminary study, although the difference might be significant for more accurate calculations. σs and εs are the Lennard−Jones parameters for the carbon atom in graphite (σs = 0.3416 nm and εs/kB = 30.14 K).52,53 The GCMC simulations using those potential parameters well describe experimental nitrogen adsorption in carbon nanopores. σfi and εfi are the Lennard−Jones parameters for the ith atom in the molecule. In the case of the carbon nanopore, the interaction of Et4N+, BF4−, or PC with the carbon nanopore was evaluated by the sum of the Steele 10−4−3 potentials of molecules and both carbon walls, as given by eq 3.

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SIMULATION PROCEDURES The potential parameters of BF4− and PC have been reported by Soetens and co-workers.44,45 The structure of Et4N+ was optimized using HF/6-311++g(2d,p) in Gaussian 09, and the potential parameters were determined using the optimized potentials for liquid simulation potential functions.46−48 The partial charges q of Et4N+, BF4−, and PC were evaluated from Mulliken population analysis by the Gaussian 09 program package using HF/6-311++g(2d,p).48 The models of Et4N+, BF4−, and PC were 29-centered, 5-centered, and 13-centered atomistic models, respectively. The simulations using the obtained models of Et4N+, BF4−, and PC gave excellent agreement between the structures and solvation numbers in Figure S1 (Supporting Information) and those using the previously reported models of BF4− and PC, although the same partial charges for Et4N+ were used in the simulations.44,45 This means that the molecular behaviors were rarely affected by the slight difference of those partial charges in the simulations, although the partial charges might not be fully optimized. The comparison of simulated and experimental results is also discussed in this study. Intermolecular interactions of Et4N+, BF4−, and PC were described by the sum of the Lennard−Jones and electrostatic interactions between two atoms of different molecules Φij =

⎡ ⎛ σ ⎞10 ⎛ σ ⎞4 sf i sf ⎟ − ⎜ i⎟ ⎢⎣ 5 ⎝ zi ⎠ ⎝ zi ⎠

∑ A⎢ 2 ⎜

ϕp = ϕsf (z) + ϕsf (H − z)

(3)

Here, H is the physical carbon nanopore width, which is the internuclear distance between opposite carbon walls. In the Steele 10−4−3 potential model, a carbon atom in a carbon nanopore wall has a neutral charge, i.e., interaction between Et4N+, BF4−, or PC, and a carbon atom was described by a Lennard−Jones interaction but no electrostatic interaction. The many-body interactions and electron transfer reactions among Et4N+, BF4−, PC, and the carbon wall were neglected here, although potential models including many-body interactions and electron transfer reactions are necessary for more accurate calculations. The Lorentz−Berthelot rules were simply applied for the calculation of Lennard−Jones potentials for different molecules. Software for GCMC simulations of PC and subsequent CEMC simulations of Et4N+, BF4−, and PC was programmed in our laboratory. GCMC simulations of PC in the nanopores were performed with three equivalent trails of creation, deletion, and motion including rotation at 303 K and 0.1 MPa for 5 × 107 steps prior to the above CEMC simulations. PC molecules were replaced with Et4N+ and BF4− molecules and slightly decreased prior to the simulations to achieve the concentration 1 mol L−1 and to maintain density during its replacement. Molecular numbers of Et4N+, BF4−, and PC and those densities are shown in Supporting Information, Table S2. In the bulk Et4N BF4 solutions in PC, the experimental densities of the solutions rarely depended on the Et4N BF4

∑ 4εij[(σij/rij)12 − (σij/rij)6 ] + (1/4πε0)qiqj /rij (1)

Here, σ and ε are the collision diameter and potential well depth of the atoms, respectively. Three-dimensional Ewald summation calculations were adopted for long-range electrostatic interaction. The perpendicular direction against a pore wall is a lack of periodicity in the nanopore system. The extremely long length of the unit cell for the calculations was used to avoid those calculation errors. Rectangular and cubic unit cells of dimensions 5 × 5 × 100 nm3 for nanopores and 3.6 × 3.6 × 3.6 nm3 for the bulk, respectively, were used in the calculations. Periodic boundary conditions were used in two dimensions for nanopores and three dimensions for the bulk. The cutoff lengths for potential calculations in the nanopore and bulk were 2.5 and 1.8 nm, respectively. The potential parameters of Et4N+, BF4−, and PC are shown in Supporting Information, Table S1. Position (X, Y, Z) is the distance from 17093



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concentration (the difference was less than 1%).54 The density of Et4N BF4 solutions in the bulk was very similar to that found in the experimental data. The molecular arrangements after the GCMC simulations were adopted as the initial configurations in the CEMC simulations. Molecular motions, including rotation in the CEMC simulation, were subsequently performed to obtain the adsorbed structures of Et4N+ and BF4− in PC adsorbed in carbon nanopores with pore widths w = 0.5−2.0 nm at 303 K and their stabilized energies, which are defined as the sum of the intermolecular interactions between a molecule and the other molecules and the interactions between a molecule and the pore walls. The calculation cycles in the CEMC simulations were 5 × 107 steps for each pore width and the bulk. Stabilized energies of Et4N+, BF4−, and PC were calculated from the intermolecular interactions among those molecules and from nanopore interactions. Entropic factors could not be directly evaluated in those simulations. However, both energetic and entropic factors contributed to the molecular configurations; thus, the stabilized energy calculated from these molecular configurations is related to the free energy of a molecule in the system.

pore walls in Figure 2. Et4N+ and PC molecules mostly formed mono, double, triple, and quadruple layers in nanopores of

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RESULTS AND DISCUSSION Figure 1 shows the potential profiles of Et4N+, BF4−, and PC molecules in carbon nanopores of different pore widths (see

Figure 2. Molecular distributions of Et4N+, BF4−, and PC in the perpendicular direction against a pore wall for w = 0.7−2.0 nm (left), and snapshots (right).

widths 0.7, 1.0, 1.5, and 2.0 nm, respectively, whereas higherorder layers were observed for BF4− because it has the smallest molecular size. The distances from a pore wall were mostly independent of nanopore width and were 0.31, 0.24, and 0.28 nm for Et4N+, BF4−, and PC, respectively. The BF4− molecules were nearest to a pore wall. The angular distributions of PC, which are defined as the angle between the molecular plane of PC and the nanpore wall, were evaluated from the snapshots, as shown in Figure 3. As the angles of 0° and 90° represent the horizontal and vertical orientations of PC against the nanopore wall, respectively, PC molecules in the 0.6 and 0.7 nm nanopores were highly ordered compared to those in other Figure 1. Potential profiles of Et4N+, BF4−, and PC in carbon nanopores of widths 0.6 (a), 0.7 (b), and 1.0 nm (c) in the perpendicular direction against a pore wall.

also Supporting Information, Figure S2). An Et4N+ molecule was intensively stabilized in the 0.7 nm nanopore, and the BF4− and PC molecules were also strongly stabilized in narrow 0.6 and 0.7 nm nanopores. As Et4N+ is larger than the other molecules, the 0.6 nm carbon nanopore repelled Et4N+. The adsorbed structures of the molecules are clearly observed from the molecular distributions of Et4N+, BF4−, and PC against the

Figure 3. Angular distribution of PC molecules in nanopores. 17094



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although the distance in the simulation was slightly longer than that in the experiment. The slight difference is a result of the inclusion of intermolecular distances between an adsorbed molecule and the carbon walls for the experimental intermolecular distance and the assumption of a rigid structure of adsorbed molecules in the simulation. The nearest neighbor distances of Et4N+−PC, BF4−−PC, and PC−PC were only 70, 65, and 64% of the corresponding intermolecular distances of 0.88, 0.73, and 0.85 nm, respectively, evaluated based on the molecular sizes. Here, the molecular sizes of Et4N+, BF4−, and PC molecules are 0.90, 0.61, and 0.85 nm, respectively, based on the assumption that they are spherical. The shortest PC−PC intermolecular distance is the result of planar stacking of PC molecules. However, the Et4N+−PC and BF4−−PC intermolecular distances, especially that of BF4−−PC, were also rather short despite the roughly spherical shapes of Et4N+ and BF4−. This indicates that these organic electrolytes were strongly solvated by PC molecules. The distribution of Et4N+ and BF4− was scarce because the molecular numbers of Et4N+ and BF4− were significantly smaller than that of PC in each nanopore. The solvation numbers of Et4N+ and BF4− in Figure 5 were evaluated from the distribution in the range of the nearest

nanopores and took relatively vertical and horizontal orientations against the nanopore walls, respectively. The tendency observed for the 0.6 nm nanopore agrees well with the experimental structure of PC molecules in nanopores of activated carbons having an average pore width of 0.7 nm.27 The slight difference of nanopore widths is caused by the pore size distribution of activated carbons. In any case, PC molecules were strongly aligned by the 0.6 and 0.7 nm nanopores Figure 4 shows the radial distribution functions of Et4N+, BF4−, and PC. The nearest neighbor distances of Et4N+−PC,

Figure 5. Solvation numbers of Et4N+ and BF4− as a function of nanopore width. Dashed lines represent solvation numbers in the bulk.

neighbor distances (Figure 4). The solvation numbers of Et4N+ and BF4− were 14.5 and 9.0 in the bulk, respectively, and were slightly decreased in the 1.5 and 2.0 nm nanopores. The solvation numbers decreased significantly in nanopores narrower than 1.0 nm; the solvation numbers of Et4N+ and BF4− were 12 and 7, respectively, in 1.0 nm nanopores and 7 and 5, respectively, in nanopores of widths 0.6−0.8 nm. In other words, nanopores of width less than or equal to 1.0 nm induce desolvation of these ions. Desolvation of ions plays a very important role in high capacitance, as reported elsewhere.18,20 Highly concentrated ions in nanopores or a high capacitance density can be achieved in such desolvated ion systems because desolvated ions can directly contact charged nanopore walls. However, desolvation reduced the stabilized energy of the ions in the nanopores. The stabilized energies of the Et4N+, BF4−, and PC molecules were evaluated from the intermolecular interactions among these molecules and interactions with the carbon nanopores (Figure 6). The interactions with nanopore walls, which were rather smaller than the corresponding stabilized energy, are also shown in Supporting Information, Figure S3. However, the repulsive interaction dominated the overall interaction of Et4N+ in the nanopores narrower than 0.7 nm. The intermolecular interaction of adsorbed molecules was predominant for the stabilized energy. The stabilized energies in nanopores larger than 0.6 nm were similar to those in the bulk. The stabilized energy of PC was 90 kJ mol−1 and was independent of

Figure 4. Radial distribution functions for Et4N+−PC (a), BF4−−PC (b), and PC−PC (c).

BF4−−PC, and PC−PC in the bulk were 0.62, 0.46, and 0.56 nm, respectively, which were very similar to those in the nanopores except for the PC−PC distance in the nanopores narrower than 1.0 nm. The PC−PC nearest neighbor distance was 0.52 nm in the narrow nanopores. The shorter distance between PC molecules in the narrow nanopores compared to that in the other nanopores is due to a strong condensation effect in such nanopores. The experimental nearest neighbor distances of molecules in the bulk and in the nanopores were 0.53−0.54 and 0.48 nm, respectively.27 Here the experimental nearest neighbor distance was mainly dominated by the PC− PC intermolecular distance. Therefore, PC−PC intermolecular distances in both the simulation and the experiment were shortened when those molecules were adsorbed in the nanopores. The intermolecular distances and the trend of decreasing distance in the narrow nanopores in the simulation and in the experiment correspond well with each other, 17095



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respectively. The energy differences between the 0.8 nm nanopore and larger nanopores were 16 kJ mol−1 for Et4N+ and 22 kJ mol−1 for BF4−, indicating a remarkable stabilization in comparison with the thermal energies of 2.5 kJ mol−1. The electrolyte stabilities were therefore significantly affected by the nanopore width. Furthermore, Et4N+ suddenly became unstable in nanopores narrower than 0.7 nm. BF4− should be unstable in nanopores of widths less than 0.5 nm. Therefore, the suitable nanopore widths with small solvation numbers and highly stabilized energies were 0.7−1.2 nm for Et4N+ and 0.6−0.9 nm for BF4. In summary, organic electrolyte structures and stabilities in noncharged carbon nanopores of widths 0.5−2.0 nm were evaluated from CEMC simulations associated with GCMC simulations. Et4N+ and BF4− molecules were significantly stabilized by solvation with PC molecules even in an unstable state for Et4N+ or BF4− molecules. Significant desolvation was observed for the organic ions in nanopores narrower than 1.0 nm. However, those ions were still stabilized, except for Et4N+ in the nanopores narrower than 0.7 nm. The stability of ions is inherently important for high ionic concentration and superior capacitance properties, as well as for desolvation of ions. The most suitable nanopore widths for the above purposes evaluated based on the above considerations were 0.7−1.2 nm for Et4N+ and 0.6−0.9 nm for BF4−. Therefore, tuning of the above nanopore widths of carbon nanoporous media is crucial for EDLC applications. Pore size dependence of organic electrolyte in nanopores was the focus of this paper. Surface area and surface chemistry are important factors for the EDLC performance as well.55 Mesoporous carbons also have high capacitance, as reported elsewhere.56−58 Further study of these simulations during charged and discharged cycles as well as in mesopores is necessary to evaluate actual EDLC systems.

Figure 6. Stabilized energy of each molecule and total stabilized energy in the nanopores. Dashed lines represent values in the bulk.

nanopore widths of 0.6−2.0 nm. The stabilized energies of Et4N+ and BF4− decreased at nanopore widths less than 1.0 nm: 300 kJ mol−1 to negative values for Et4N+ and 220 to 170 kJ mol−1 for BF4−. Et4N+ and BF4− were sufficiently stabilized even in 0.7−1.0 nm nanopores, despite being desolvated to some extent. This is a result of compensation of stabilization by nanopore potential fields. Et4N+ was unstable in the 0.6 nm nanopores because its molecular size was larger than the pore width, but the other molecules were stabilized even in the narrow nanopores. The overall stabilized energies changed from 600 to 110 kJ mol−1 in the 0.6 nm nanopore; these values were simply obtained from the sum of the stabilized energies of Et4N+, BF4−, and PC. The electrolyte solutions were therefore stabilized even in the 0.6 nm nanopores. The nanopores narrower than 1.0 nm imposed desolvation on the ions, playing an important role in providing high capacitance, but decreased the stabilities of the ions, resulting in a decrease in the amount of adsorbed species. These opposing properties result in complicated behaviors in EDLCs, that is, narrow nanopores are not simply suitable for high capacitance. We have to determine the nanopore widths that achieve conditions under which ions are both less solvated and highly stabilized or, in other words, under which conditions the ions have small solvation numbers and high stabilized energies. The highest stabilized energies of Et4N+ and BF4− per solvation number indicate the best conditions for both small solvation number and high stabilized energy (Figure 7). Here, the relative

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ASSOCIATED CONTENT

S Supporting Information *

Potential parameters, molecular numbers, densities in carbon nanopores, and potential profiles. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the JGC-S Scholarship Foundation, Promotion of Ion Engineering, Murata Science Foundation, Nippon Sheet Glass Foundation, and the Global COE Program, MEXT, Japan.

Figure 7. Relative stabilized energies of Et4N+ and BF4− per solvation number as a function of nanopore width. Dashed lines represent values in the bulk.

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