Matrix-theoretical calculation of diffusion parameters for composite membranes with periodic structure

Abstract

Based on the Siegel's theory, the diffusion parameters of steady-stale permeability (P), downstream time Lag(t(L)), forward and backward mean first passage time (<(t)over bar (+)> and <(t)over bar (-)>) fbr absorptive unidirectional permeation for a membrane with n-periodic structure have been calculated from the transmission matrix in the Laplace domain with the help of the Caley-Hamilton theory. The results of calculation give that P = P-(i)/n, t(L) = t(L)((i)) + 1/6(n(2)-1)(<(t)over bar ((i)(+))> + <(t)over bar ((i)(-))>), <(t)over bar (+)> = <n(t)over bar ((i)(+))> + n(2)-n/2(<(t)over bar ((i)(+))> + <(t)over bar ((i)(-))>), <(t)over bar (-)> = <n(t)over bar ((i)(-))> + n(2)-n/2(<(t)over bar ((i)(+))> + <(t)over bar ((i)(-))>), where the diffusion parameter with a superscript (i) denotes its corresponding entity for a single unit period. The consistency with the previous results obtained by repeated integration is also discussed.