Simulation for memory effect of Fick’s first law
The memory effect of the Fick’s first law, expressed by $\tau(\partial J/\partial t$) = $-J$ - Dgradc, was confirmed by means of the 3D Monte Carlo simulation, where 𝜏 is the relaxation time, 𝐽 is the flux of the diffusing particles, 𝐷 is the diffusion coefficient, and 𝑐 is the concentration of the particles. The delay has been observed by chronoamperometry at a pair electrode. It behaves as if it were due to a slow electron transfer reaction. A diffusion model was composed of two cubic cells with different volumes in contact with each other by their faces, which worked as the boundary for the flux. Each cell contained one diffusing particle and solvent molecules for a given concentration. The particle moved randomly in the 3D lattice until it traversed the boundary. The number of the random steps before the traverse was equivalent to the relaxation time. It was proportional to ca 2/3 powers of the number of solvent molecules or was inversely proportional to 0.63 powers of the concentration. The relaxation time was roughly equivalent to the lapse of taking for the particle to visit every lattice site impartially.
Volume 132, 2020
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