Drift-Diffusion Phenomenon in the Presence of Reversible Trapping Reaction

The time evolution of the bulk density of particles in a fixed matrix within a cell in the shape of a slab is investigated in the presence of a reversible trapping reaction. The relaxation times are determined, and their dependence on the trapping parameters is explored. The analysis is performed for both neutral and charged particles. In the case of charged particles, such as ions in a solid electrolyte, ions in hydro-gels, or ions in porous electrodes, we assume that only the ions of a given sign contribute to the conduction current. We demonstrate that, besides the Debye's relaxation time tau(D) = Lambda(2)/D, where Lambda is the Debye length and D the diffusion coefficient, another relaxation time defined by tau = Lambda d/(2D), where d is the thickness of the sample, plays a significant role. The special case in which the exciting electric field is a simple harmonic function is also investigated. In this case, the electric impedance of the cell is determined, and its dc limit, as well as its high-frequency limit, are discussed. We investigate specific cases where the electrodes are blocking, transparent, or one is blocking while the other is transparent. As expected, in the high-frequency limit, the impedance becomes independent of the electrode characteristics. Both the resistance and reactance are bulk properties proportional to the sample's thickness. In contrast, in the low-frequency limit, interface resistance and reactance, localized over a thickness of the order of the Debye length, must be added to the bulk values, which still scale with the cell's thickness. The dependence of the interface properties on the trapping parameters is discussed.