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.

[1]  Eishun Tsuchida,et al.  Effect of polymer matrix and metal species on facilitated oxygen transport in metalloporphyrin (oxygen carrier) fixed membranes , 1988 .

[2]  Wolf R. Vieth,et al.  A model for diffusion in a glassy polymer , 1965 .

[3]  N. Ogata,et al.  Transport of halogen ions through synthetic polymer membranes containing pyridine moieties , 1986 .

[4]  H. Kawakami,et al.  Facilitated transport of molecular oxygen in the membranes of polymer-coordinated cobalt Schiff base complexes , 1987 .

[5]  R. Probstein,et al.  Similarity considerations in facilitated transport , 1973 .

[6]  Eishun Tsuchida,et al.  Effect of polymer matrix on the oxygen diffusion via a cobalt porphyrin fixed in a membrane , 1991 .

[7]  Richard D. Noble,et al.  Facilitated transport mechanism in fixed site carrier membranes , 1991 .

[8]  R. M. Barrer.  Diffusivities in glassy polymers for the dual mode sorption model , 1984 .

[9]  W. Koros,et al.  Effect of partially immobilizing sorption on permeability and the diffusion time lag , 1976 .

[10]  R. Wessling,et al.  Oxygen/nitrogen transport in glassy polymers with oxygen-binding pendent groups , 1990 .

[11]  Wolf R. Vieth,et al.  Dual sorption theory , 1976 .

[12]  Richard D. Noble,et al.  Generalized microscopic mechanism of facilitated transport in fixed site carrier membranes , 1992 .

[13]  H. Bohlen,et al.  Polymeric schiff's base chelates and their precursors, 7. Dioxygen binding and catalytic oxidation of 2,6-di-tert-butylphenol† , 1984 .

[14]  R. Noble.  Analysis of facilitated transport with fixed site carrier membranes , 1990 .

[15]  Rutherford Aris,et al.  On the limits of facilitated diffusion , 1989 .

[16]  Jae-Min Hong,et al.  Analysis of facilitated transport in polymeric membrane with fixed site carrier 2. Series RC circuit model , 1996 .

[17]  John W. Cahn,et al.  Phase Separation by Spinodal Decomposition in Isotropic Systems , 1965 .

[18]  J. A. Quinn,et al.  The prediction of facilitation factors for reaction augmented membrane transport , 1979 .

[19]  D. Wöhrle,et al.  Polymeric schiff's base chelates and their precursors, 9. Synthesis of covalently and coordinatively bound polymeric chelates and their dioxygen binding in the solid state†‡ , 1986 .

[20]  G. M. Ginley,et al.  Facilitated transport of CO2 in ion exchange membranes , 1987 .

[21]  J. L. Duda,et al.  A Deborah number for diffusion in polymer‐solvent systems , 1975 .

[22]  N. Ogata,et al.  Active transport of organic acids through poly(4-vinylpyridine-co-acrylonitrile) membranes , 1986 .

[23]  H. Nishide,et al.  Dual-mode transport of molecular oxygen in a membrane containing a cobalt porphyrin complex as a fixed carrier , 1987 .

[24]  W. Koros,et al.  Effect of structural symmetry on gas transport properties of polysulfones , 1992 .

[25]  R. M. Barrer,et al.  Sorption and diffusion in ethyl cellulose. Part III. Comparison between ethyl cellulose and rubber , 1958 .