Non‐fickian diffusion with reaction in glassy polymers with swelling induced by the penetrant—effects of consecutive and parallel reactions

Abstract

AbstractA mathematical model is presented for non‐Fickian diffusion of a penetrant A into a granular glassy polymer containing a reactive group B, resulting in the desired product P. Further, both a consecutive reaction between A and P (producing X) and a parallel reaction between A and C (producing Y) are incorporated, with C initially present in the particle. The swelling of the polymer, induced by the penetrant, is described by power‐law kinetics for the velocity of the swelling front. Kinetics are considered to be first order in each of the two reactants. Concentration profiles in the particle and selectivity to desired product are calculated as function of the swelling behavior of the polymer grain. In case of a consecutive reaction the local concentration of P reaches a maximum value independent of the swelling rate. However, the position of the maximal concentration of P moves towards the center of the grain with a rate depending on the kinetics of swelling. For Case II diffusion this velocity equals the velocity of the advancing front between glassy and rubbery polymer. The selectivity of the desired reaction decreases with decreasing swelling rate. A low swelling rate also results in an inhomogeneous product distribution within the granule. A criterion is derived predicting under what conditions the consecutive reaction can be neglected and a pure product is obtained. The analysis further reveals that both a more homogeneous product and a higher selectivity toward a desired product can be obtained by realizing preswelling of the polymer with an inert swelling agent. For Case II diffusion the concentration profiles of the side product of the parallel reaction, Y, are flat in the rubbery part of the polymer. This is caused by the relatively low swelling rate allowing Y to redistribute in the swollen polymer. If additional C is continuously supplied from the gas phase, then the selectivity decreases continuously with increasing conversion of B.