Analysis of facilitated transport in solid membranes with fixed site carriers. 1. Single RC circuit model

Abstract A simple mathematical model for facilitated mass transport with a fixed site carrier membrane was derived by assuming an instantaneous, microscopic concentration (activity) fluctuation in the membrane. The concentration fluctuation, developed due to the reversible chemical reaction between carrier and solute, could cause the higher chemical potential gradient and the facilitated transport. For mathematical formulation, the fluctuated concentration profile was assumed to be a sinusoidal, which is analogous to an alternating voltage in electric circuit. An analogy was employed between the mass transfer for the facilitated transport with fixed site carrier membrane and the electron transfer in a single parallel resistor-capacitor (RC) circuit. The current model showed that the facilitation factor, F , increased linearly with the extent of the pressure fluctuation, α p (= p d p o ) , the ratio of the time scales of diffusion to chemical reaction, ψ(= k 2 L 2 D ) , and the ratio of the total carrier concentration to the solute solubility in matrix, γ(= C B O C A ∞ ) . F also increased logarithmically with one plus the combined driving force for facilitation, Δ (= Kp 0 ), i.e. (1+ Δ ). The model was examined against experimental data on oxygen transport in poly(dimethyl siloxane), poly(butyl methacrylate) and poly(methyl methacrylate) with metallo-porphyrin carrier and the agreement was exceptional.