In energy devices, such as batteries and liquid thermoelectric converters, electron transfer occurs between ions dissolved in the electrolyte and the electrodes. For current to continue flowing in such devices, new ions must be supplied continuously to the electrode surface from the bulk region of the electrolyte. This is because ions that have undergone electron transfer cannot undergo further electron transfer. The driving force for mass transfer is the concentration difference ΔC between the electrode surface and the bulk region.

When an electric current I is passed through the electrolyte, ions are consumed at the electrode surface; hence, the ion concentration at the electrode surface decreases compared with the bulk region. The resulting concentration difference ΔC drives the diffusion of new ions to the electrode surface. Eventually, the concentration distribution near the electrode reaches a steady state. The concentration distribution at the steady state is usually approximated with a linear function (diffusion layer approximation), i.e., the concentration increases proportionally with distance from the electrode surface and becomes constant when it reaches the value of the bulk region. The distance δ at which the concentration reaches the bulk value is called the “thickness” of the diffusion layer. In the steady state, the current (= AFDΔC/δ, where A, F, and D are electrode area, Faraday constant, and diffusion constant, respectively.) caused by diffusive mass transfer matches I. The mass transfer is observed as diffusion resistance R_dif. R_dif can be considered the equilibrium potential shift resulting from ΔC divided by I. If ΔC/C (C is the concentration in the bulk region) is sufficiently small, R_dif becomes 2k_BT/eI ×ΔC/C, where k_B and T are the Boltzmann constant and temperature, respectively.

In this study, the relationship between the diffusive mass transfer and the diffusion layer was clarified using the rotating disk electrode method, in which centrifugal force causes the electrolyte near the electrode to flow outward, and convection occurs from the bulk region toward the electrode to compensate for this. With increasing angular velocity ω of the rotating electrode, the flow velocity toward the electrode increases. It was found that R_dif decreased sharply with increasing ω. Detailed analysis revealed that R_dif is proportional to ω^-1/2 with a proportionality constant of 43.5 Ωs^-1/2. In the diffusion layer approximation, δ in the rotational electrode method is proportional to ω^-1/2. Then, R_dif (= 2k_BTδ/eAFDC) is expected to be proportional to ω^-1/2. From the parameters of the electrolyte and electrodes, the proportionality constant is calculated as 30.9 Ωs^-1/2. The calculated value ​​showed good agreement with the observed value, demonstrating that R_dif can be understood quantitatively in terms of the diffusion layer.

(Written by Yutaka Moritomo on behalf of all authors.)

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