DIFFUSION OF LOW-MOLECULAR-WEIGHT SUBSTANCES INTO A LAMINAR-FILM .1. RIGOROUS SOLUTION OF THE DIFFUSION EQUATION IN A COMPOSITE FILM OF MULTIPLE LAYERS

A rigorous solution of the diffusion of penetrant into a laminar film comprised of multilayers of m components is presented by an orthogonal-expansion method. As the simplest practical cases of m = 2 and m = 3, with stepwise distribution of both diffusion coefficients and solubility coefficients at the boundary between respec tive layers, the diffusion properties in the transient state are analyzed in detail. That is, changes in the penetrant concentration distribution within the laminar film and the total amount of penetrant sorbed within the film both with time after exposing the film to an atmosphere of fixed penetrant concentration are calculated for A-B as well as A-B-A type layer arrangements. The calculation is performed while keeping (L(2)/L(1)) at a constant value of 2.0 but varying the diffusion coefficient ratio of (D-1/D-2) from 10(2) to 10(-2), and/or varying the solubility coefficient ratio of (S-1/S-2) from 1 to 10, where L(1) and (L(2) - L(1)) are the thickness D-1 and D-2 are the diffusion coefficients of penetrant, and S-1 and S-2 are the solubility coefficients in the A-component and the B-component, respectively. The sorption curves deviate considerably from those of Fickian curves of homogeneous film with (D-1/D-2) = 1 in their respective ways. The results obtained here can be applied to the diffusion in a single component polymer film having a surface layer with different diffusion properties from that of the inner side of the film caused by differing distributions in molecular orientation or degrees of crystallinity.