ANALYSIS OF FACILITATED TRANSPORT IN SOLID MEMBRANES WITH FIXED SITE CARRIERS .1. SINGLE RC CIRCUIT MODEL

A simple mathematical model for facilitated mass transport with a fixe d site carrier membrane was derived by assuming an instantaneous, micr oscopic concentration (activity) fluctuation in the membrane. The conc entration fluctuation, developed due to the reversible chemical reacti on between carrier and solute, could cause the higher chemical potenti al gradient and the facilitated transport. For mathematical formulatio n, 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 tr ansport with fixed site carrier membrane and the electron transfer in a single parallel resistor-capacitor (RC) circuit. The current model s howed that the facilitation factor, F, increased linearly with the ext ent of the pressure fluctuation, alpha(p)(=p(d)/P-o), the ratio of the time scales of diffusion to chemical reaction, psi(=k(2)L(2)/D), and the ratio of the total carrier concentration to the solute solubility in matrix, gamma(=C-B(0)/C-A(proportional to)). F also increased logar ithmically with one plus the combined driving force for facilitation, Delta(=Kp(o)), i.e. (1 + Delta). The model was examined against experi mental data on oxygen transport in poly(dimethyl siloxane), poly(butyl methacrylate) and poly(methyl methacrylate) with metallo-porphyrin ca rrier and the agreement was exceptional.