Small-molecule translational diffusion in polymer solutions

3 Small-molecule translational diffusion in polymer solutions 

We now turn from solvent and small-molecule mohon in simple solvents to mohon in polymer soluhons. Translahonal diffusion of solvent molecules through polymer solutions has been studied extensively. Correlations were obtained 

D being a prefactor not necessarily equal to at any concentration at which Eq. 5.3 applies. The stretching exponent v is in the range 2.4-3.8. The concentration dependence seen here is quite different from that found for polymer self-diffusion, as seen in Chapter 8, which in most cases follows a single stretched exponential in c extending from pure solvent out to the largest polymer concentrations studied. However, polymer self-diffusion measurements in solution almost never extend above 400 g/1 of polymer, so one cannot absolutely reject the possibility that the transition represented by Eqs. 5.2 and 5.3 corresponds to a transition also found for polymer self-diffusion. Indeed, results of Tao, etal.(34) suggest such a possibility. 

Kosfeld and Zumkley(31) report Ds of benzene in benzene 110 kDapolystyrene at eight temperatures 25 T 100 and polymer volume fractions up to 0.75. 

The effect of a somewhat different phase transition, namely the gelation of photographic gelatin, was studied by Mel nichenko, et a/.(24). Neutron transmission was used to observed the diffusion of H2O into gelatin gels saturated with D2O at various gel concentrations. The value of Dg depended on gel concentration as Dg 4 ) = D o(l — for gel volume fractions as large as 

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Translational motions of solvent and other small molecules in polymer solutions are quite different from their behaviors in viscous liquids. The self-diffusion coefficient of the solvent has a transition at a polymer volume fraction 0.4. At smaller (j), Ds follows a simple exponential exp(-a) in polymer concentration, but at larger Ds(c) follows a stretched exponential with large exponent. The exponential factor a is independent of polymer molecular weight, while rj depends strongly on M, so Ds and A must be nearly independent of solution rj. Probes somewhat... 

Local motions which occur in macromolecular systems can be probed from the diffusion process of small molecules in concentrated polymeric solutions. The translational diffusion is detected from NMR over a time scale which may vary from about 1 to 100 ms. Such a time interval corresponds to a very large number of elementary collisions and a long random path consequently, details about mechanisms of molecular jump are not disclosed from this NMR approach. However, the dynamical behaviour of small solvent molecules, immersed in a polymer melt and observed over a long time interval, permits the determination of characteristic parameters of the diffusion process. Applying the Langevin s equation, the self-diffusion coefficient Ds is defined as... 

Chapter 5 considers translation and rotation by solvent molecules in small-molecule liquids and polymer solutions. Correlations between solution properties are already more complex than might have been expected. At small rj, the diffusion coefficient and equivalent conductance of small-molecule probes in simple liquids scale as At larger rj, D and A are instead The boundary between small and large t] seen in the literature is uniformly near 5 cP. It is unclear why this particular value of r should not be system-specific. In contrast to smaU-molecule probes, mesoscopic probes such as polystyrene latex spheres in potentially highly viscous mixed solvents such as water glycerol retain D T/ri behavior over three or more orders of magnitude in rj. 

The addition of a polymeric solute to a small-molecule solvent affects translational diffusion, viscosity, and rotational diffusion of solvent and other small molecules in solution. For polymer concentrations 4> < 0.4, the solvent selfdiffusion coefficient follows D exp(—a). The constant a is linear in the probe s molecular volume but is independent of polymer molecular weight. At larger concentrations (/) > 0.4, the simple-exponential dependence of D on concentration is replaced by a stretched-exponential concentration dependence, D and dD/dc both appearing continuous through the transition. The effects of added polymer on solvent self-diffusion and on the diffusion of small-molecule probes are clearly not the same. 

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