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

The diffusion of linear deuterated polystyrene (DPS) chains into a cross-linked polystyrene matrix has been studied by secondary ion mass spectrometry (SIMS). The cross-linked matrices were prepared by radiation cross-linking with gamma-rays from a Co-60 source. The doses used were 40, 75, and 156 Mrad, which resulted in an approximate network density, N(c) (number of monomer units between cross-linking points), of 9300, 4900, and 2400. The homopolymer DPS chains were of molecular weight M(w) = 85 000, 104 000, 303 000, and 55 0000 (corresponding to degrees of polymerization of N(b) = 759, 929, 2705, and 4910). Diffusion of the linear chains into the cross-linked matrix was observed at all molecular weights and cross-linking densities studied. Diffusion was significantly slower into the cross-linked systems than into the matrix chains before cross-linking (M(w) = 1 030 000). A free energy expression for the system calculated by assuming additivity of Gaussian rubber elasticity and the Flory-Huggins energy of mixing was used in combination with the Hartley-Crank equation to calculate concentration profiles for linear chains diffusing into the matrix. The predictions were then compared with the data obtained by SIMS. The only free parameter used in fitting the data was the relaxed or reference state network volume fraction. Good fits to the data were obtained when the relaxed state of the network accounted for the free sol chains still present after cross-linking. The diffusion of the linear chains became very slow when N(b) almost-equal-to N(c), but no distinct halt to the diffusion was observed at this linear chain length. The tracer diffusion coefficients 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.