Studies of cyclic and linear poly(dimethyl siloxanes): 5. Diffusion behaviour in dilute solution

The diffusion coefficients of cyclic and linear oligomeric and polymeric dimethyl siloxanes, containing number-average numbers of skeletal bonds in the range $\text{6 <}\text{n}\text{?}{}_{\mathrm{n}}\text{< 650}$, have been measured in toluene solution at 298K. Impermeable diffusion behaviour was observed for all the siloxanes studied, in agreement with previous findings for ethylene oxide and hexamethylene oxide oligomers and polymers. The ratio of the friction coefficients $\text{f}{}_{\mathrm{r}}\text{f}{}_{\mathrm{l}}$ for the ring (r) and linear (l) dimethyl siloxanes was found to be $\text{8}\text{3κ}$ (within the limits of experimental error) over the whole range of molecular weights studied. Values of the expansion factor α_f for the linear poly(dimethyl siloxanes) (obtained from the diffusion measurements) were found to be approximately equal to the corresponding values for α_η (found previously by viscometric studies) for small values of the excluded volume parameter z; and α_f was larger than α_η for large z, as predicted by first-order perturbation theory. Mean-square radii of gyration 〈s²_G〉 were calculated from the diffusion data for both cyclic and linear poly(dimethyl siloxanes) assuming Gaussian statistics, and found to be in good agreement with the corresponding values obtained by neutron scattering. However, the values of 〈s²_G,l〉 for the short chain poly(dimethyl siloxanes) did not agree with the corresponding values of 〈s²_O,l〉, calculated using the rotational isomeric state model of Flory, Crescenzi and Mark. This discrepancy is thought to arise from deviations from Gaussian behaviour, and considerably better agreement between experiment and theory was achieved by using appropriate values of a function ψ_l(x), which relates radii of gyration and impermeable hydrodynamic diffusion radii.