^{1,a)}, Hiroshi Shioyama

^{2}, Takushi Sugino

^{1}, Kinji Asaka

^{1}, Yasushi Soneda

^{3}, Kiyoaki Imoto

^{3}and Masaya Kodama

^{3}

### Abstract

The electrochemical thermodynamics of electrolytes in porous electrodes is qualitatively different from that in the bulk with planar electrodes when the pore size is comparable to the size of the electrolyte ions. In this paper, we discuss the thermodynamics of a two component electrolyte in a porous electrode by using Monte Carlo simulation. We show that electrolyte ions are selectively adsorbed in porous electrodes and the relative concentration of the two components significantly changes as a function of the applied voltage and the pore size. This selectivity is observed not only for the counterions but also for the coions.

This work was supported by JSPS KAKENHI Grant No. 24550169. Part of the computation in this work was performed using the supercomputers of Research Institute for Information Technology of Kyushu University and those of Cybermedia Center of Osaka University.

I. INTRODUCTION

II. MODEL

III. MONTE CARLO SIMULATION

IV. RESULTS AND DISCUSSION

A. Surface charge density

B. Ion concentration

C. Ion concentration profile

D. Pressure

V. CONCLUSIONS

## Figures

Schematic picture of the model for porous electrodes used for the Monte Carlo simulation. Six electrode planes are placed parallel to each other. Voltage is applied between three electrode planes on the left and the other three electrode planes on the right. Ions (shown in circles) are inserted into or removed from the regions denoted R 1 and R 2 in this study. W and ΔΦ denote pore size and applied voltage, respectively. The electrode planes are denoted plane 1, plane 2, …, plane 6 from left to right. The corresponding surface charge densities are denoted σ1, σ2, …, σ6, respectively. Reprinted with permission from K. Kiyohara, T. Sugino, and K. Asaka, J. Chem. Phys. 134, 154710 (2011); and K. Kiyohara, H. Shioyama, T. Sugino, and K. Asaka, ibid. 136, 094701 (2012). Copyright 2011 and 2012 AIP Publishing LLC.

Schematic picture of the model for porous electrodes used for the Monte Carlo simulation. Six electrode planes are placed parallel to each other. Voltage is applied between three electrode planes on the left and the other three electrode planes on the right. Ions (shown in circles) are inserted into or removed from the regions denoted R 1 and R 2 in this study. W and ΔΦ denote pore size and applied voltage, respectively. The electrode planes are denoted plane 1, plane 2, …, plane 6 from left to right. The corresponding surface charge densities are denoted σ1, σ2, …, σ6, respectively. Reprinted with permission from K. Kiyohara, T. Sugino, and K. Asaka, J. Chem. Phys. 134, 154710 (2011); and K. Kiyohara, H. Shioyama, T. Sugino, and K. Asaka, ibid. 136, 094701 (2012). Copyright 2011 and 2012 AIP Publishing LLC.

Surface charge density for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e). Surface charge density in the anode (σ1 and σ2 in Fig. 1 ) and that in the cathode (σ5 and σ6) are shown in black circles and red squares, respectively. First order phase transition and hysteresis was observed for W = 1.1.

Surface charge density for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e). Surface charge density in the anode (σ1 and σ2 in Fig. 1 ) and that in the cathode (σ5 and σ6) are shown in black circles and red squares, respectively. First order phase transition and hysteresis was observed for W = 1.1.

Ion concentration in the anode for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e). Red and blue circles denote cation and anion concentrations for component 1, respectively. Orange and cyan squares denote cation and anion concentrations for component 2, respectively.

Ion concentration in the anode for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e). Red and blue circles denote cation and anion concentrations for component 1, respectively. Orange and cyan squares denote cation and anion concentrations for component 2, respectively.

Ion concentration in the cathode for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e). Keys are the same as in Fig. 3 .

Ion concentration in the cathode for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e). Keys are the same as in Fig. 3 .

Density profile in the anode and the cathode for pore sizes W = 1.5, 2.0, 4.0, and 8.0. The results for voltage ϕ = 0.04 are plotted in (a) and (b) for the anode and the cathode, respectively. Those for W = 1.5, 2.0, and 4.0 are shifted upwards by 0.18, 0.09, and 0.04, respectively, for clarity. The results for voltage ϕ = 0.08 are plotted in (c) and (d) for the anode and the cathode, respectively. Those for W = 1.5, 2.0, and 4.0 are shifted upwards by 0.58, 0.24, and 0.07, respectively, for clarity. Red and blue lines denote cation and anion concentrations for component 1, respectively. Orange and cyan lines denote cation and anion concentrations for component 2, respectively.

Density profile in the anode and the cathode for pore sizes W = 1.5, 2.0, 4.0, and 8.0. The results for voltage ϕ = 0.04 are plotted in (a) and (b) for the anode and the cathode, respectively. Those for W = 1.5, 2.0, and 4.0 are shifted upwards by 0.18, 0.09, and 0.04, respectively, for clarity. The results for voltage ϕ = 0.08 are plotted in (c) and (d) for the anode and the cathode, respectively. Those for W = 1.5, 2.0, and 4.0 are shifted upwards by 0.58, 0.24, and 0.07, respectively, for clarity. Red and blue lines denote cation and anion concentrations for component 1, respectively. Orange and cyan lines denote cation and anion concentrations for component 2, respectively.

Pressure in the anode (a) and in the cathode (b). Black circles, red squares, green diamonds, blue up triangles, and brown left triangles denote pore sizes W = 1.1, 1.5, 2.0, 4.0, and 8.0, respectively. For W = 1.1, the results for decreasing the voltage are shown in shaded symbols.

Pressure in the anode (a) and in the cathode (b). Black circles, red squares, green diamonds, blue up triangles, and brown left triangles denote pore sizes W = 1.1, 1.5, 2.0, 4.0, and 8.0, respectively. For W = 1.1, the results for decreasing the voltage are shown in shaded symbols.

Surface charge density for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e) when the cations of component 1 and those of component 2 are indistinguishable. The keys are the same as in Fig. 2 .

Surface charge density for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e) when the cations of component 1 and those of component 2 are indistinguishable. The keys are the same as in Fig. 2 .

Ion concentration in the anode for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e) when the cations of component 1 and those of component 2 are indistinguishable. Red circles denote cation concentration of both components. Blue circles and cyan squares denote anion concentrations for components 1 and 2, respectively.

Ion concentration in the anode for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e) when the cations of component 1 and those of component 2 are indistinguishable. Red circles denote cation concentration of both components. Blue circles and cyan squares denote anion concentrations for components 1 and 2, respectively.

Ion concentration in the cathode for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e) when the cations of component 1 and those of component 2 are indistinguishable. The keys are the same as in Fig. 8 .

Ion concentration in the cathode for pore sizes W = 1.1 (a), 1.5 (b), 2.0 (c), 4.0 (d), and 8.0 (e) when the cations of component 1 and those of component 2 are indistinguishable. The keys are the same as in Fig. 8 .

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