Diffusion of the dicumyl peroxide in molten polymer probed by rheology
Résumé
The mutual coefficient of diffusion of the dicumyl peroxide (DCP), which diffuses into an ethylene-octene copolymer above its Tg was measured from an innovative rheological experiment. The experiments were carried out on a parallel plate geometry rheometer. The method is based on the cross-linking of a two-layer sample; the upper layer contains 2 wt% of DCP, and the lower layer is free of DCP. Actually, this experiment is based on the competition between the reaction of cross-linking and the diffusion of DCP in the lower layer. Comparing this rheological behavior with the rheological kinetic of cross-linking of an homogeneous sample with 1 wt% DCP, we are able, from an inverse fitting procedure, to calculate the mutual coefficient of diffusion. Our hypothesis is that the diffusion of DCP in the copolymer above Tg, can be described by Fick's classical law. Using Fick's law, the concentration of the DCP was established for any given point of the thickness of the two-layer sample at any time. Using a one-dimensional grid to solve continuous equations that describe the different rheological contributions of each abscissa, we determined the linear viscoelastic response of the whole sample. Comparing the experimental storage modulus of the two layer sample to the values measured from an homogeneous sample, we found the values of the mutual coefficient of diffusion. Finally, a simple relation, which describes the mutual coefficient of diffusion of DCP into melt ethylene-octene copolymer was established according to an Arrhenius law as: D12 = 1.25 x 102exp(-70.0 × 103 /RT)m2/s Moreover, this work clearly shows how a reaction in molten media can be controlled by the diffusion process of small reactive molecules.