NON-FICKIAN DIFFUSION WITH CHEMICAL-REACTION IN GLASSY-POLYMERS WITH SWELLING-INDUCED BY THE PENETRANT - A MATHEMATICAL-MODEL

A mathematical model is presented which describes non-Fickian diffusion with chemical reaction of a penetrant A with some reactive group B of a granular glassy polymer. The diffusion process cannot be described by Fick's law due to the swelling of the glassy polymer grain caused by the penetration of the diffusing species. Therefore, the kinetics of swelling must be taken into account. A new model is presented, allowing for mass transfer with chemical reaction whilst assuming power-law kinetics for the velocity of the swelling front: dr0/dt = - K(c(a,r = r0) - c(a)*)n where c(a)* is the threshold concentration for swelling, c(a,r = r0) the concentration of penetrant A at the position r0 of the swelling front and K a constant independent of the penetrant concentration. Two cases of reaction kinetics am analysed: first order in A only and first order in both A and B (overall second order). Criteria for the occurrence of homogeneous addition and for a shrinking core type of reaction are given. For a low conversion of B, the reaction can be pseudo-first-order in A. Both Fickian diffusion (high K, n > 0 and c(a)* = 0) and the so-called case II diffusion (low K, n > 0) are shown to be asymptotic solutions of the model. It is also shown that in some cases an excellent agreement can be obtained between the numerical unsteady-state solution and the so-called pseudo-steady-state solution in which the accumulation term of the mass balance of A is neglected. This PSS-solution could be obtained analytically. Both the case without reaction and with first-order kinetics in A are analysed. The approximation is rather good for high first-order reaction rates, short diffusion times and if case II diffusion is approached.