Case II diffusion: effect of solvent molecule size

Rutherford back-scattering spectrometry has been used to examine the detailed composition vs. depth profile for polystyrene exposed at 25°C to the vapour (activity = 0.45) of a series of 1-iodo-n-alkanes ranging from iodopropane ( n = 3) to iodooctane ( n = 8), where n is the number of carbon atoms on the alkane chain. All the iodoalkanes tested exhibit case II diffusion. The velocity V of the case II front decreases exponentially with n. The diffusion coefficient D in the glass, which is determined from the concentration profile of the iodoalkanes ahead of the front using the measured value of V, decreases exponentially with increasing n; D decreases by approximately a factor of 4 for each carbon atom added to the alkane chain. These data are compared with previous studies, which show that D decreases exponentially with the molecular diameter d, calculated from the density of the pure liquid solvent: D = D 0 e − δd , where δ is a constant for spherically symmetric solvent molecules. For the linear iodoalkanes D shows a similar exponential decrease but with a 20% lower value of δ, resulting in D for these non-spherical molecules being as much as three orders of magnitude larger than that for spherical molecules with an equivalent d. At the critical concentration ф c for case II diffusion to begin, the swelling rate dф dt at the surface of the sample also decreases approximately exponentially with increasing n. The swelling rate decreases strongly with the osmotic pressure P os, while P os at ф c decreases with the molecular volume (and thus with n). The change in dф dt with n, inferred from the corresponding change in P os, can account for nearly all of the observed dependence of dф dt on n. The Thomas and Windle model of case II diffusion leads to the following prediction for V: V = [( D ф c )( dф dt )| ф c ] 1 2 . We find that the front velocities derived from this equation using the measured values of D and ( dф dt )| ф c are in quantitative agreement with the experimental values of V for the entire series of iodoalkanes, a result that provides strong confirmation of the Thomas and Windle model.