DIFFUSION OF LINEAR DEUTERATED POLYSTYRENE CHAINS IN CROSS-LINKED POLYSTYRENE NETWORKS

The diffusion of linear deuterated polystyrene (DPS) chains into a cro ss-linked polystyrene matrix has been studied by secondary ion mass sp ectrometry (SIMS). The cross-linked matrices were prepared by radiatio n cross-linking with gamma-rays from a Co-60 source. The doses used we re 40, 75, and 156 Mrad, which resulted in an approximate network dens ity, N(c) (number of monomer units between cross-linking points), of 9 300, 4900, and 2400. The homopolymer DPS chains were of molecular weig ht M(w) = 85 000, 104 000, 303 000, and 55 0000 (corresponding to degr ees of polymerization of N(b) = 759, 929, 2705, and 4910). Diffusion o f the linear chains into the cross-linked matrix was observed at all m olecular weights and cross-linking densities studied. Diffusion was si gnificantly slower into the cross-linked systems than into the matrix chains before cross-linking (M(w) = 1 030 000). A free energy expressi on for the system calculated by assuming additivity of Gaussian rubber elasticity and the Flory-Huggins energy of mixing was used in combina tion with the Hartley-Crank equation to calculate concentration profil es for linear chains diffusing into the matrix. The predictions were t hen compared with the data obtained by SIMS. The only free parameter u sed in fitting the data was the relaxed or reference state network vol ume fraction. Good fits to the data were obtained when the relaxed sta te of the network accounted for the free sol chains still present afte r cross-linking. The diffusion of the linear chains became very slow w hen N(b) almost-equal-to N(c), but no distinct halt to the diffusion w as observed at this linear chain length. The tracer diffusion coeffici ents for the linear chains, which were measured separately, were found to be independent of the cross-linking density and to scale with M(w) -2.0, in agreement with the reptation model prediction.