Single-chain diffusion concentration dependence

Chapter 8 treats single-chain motion including measurements of polymer self-diffusion and tracer diffusion, and measurements that track the motions of individual polymers. It is almost uniformly found that a stretched exponential in polymer concentration and a joint stretched exponential in c, P, and M describe how the single-chain diffusion coefficient depends on matrix concentration and molecular weight and on probe molecular weight. On log-log plots, these functions appear as smooth curves that almost always agree with measurements of D (c, P, M) at concentrations extending from dilute solution to the melt. 

The objective here is to identify features characteristic of single-chain diffusion by an ideal polymer in solution, following which it becomes possible to identify specific chemical effects in particular series of measurements. As discussed below first, the functional forms of the concentration and molecular weight dependences of the self- and tracer diffusion coefficients are found. Second, having found that Ds almost always follows a particular functional form, correlations of the function s phenomenological parameters with other polymer properties are examined. Third, for papers in which diffusion coefficients were reported for a series of homologous polymers, a joint function of matrix concentration and matrix and probe molecular weights is found to describe Ds. Fourth, a few exceptional cases are considered. These cases show that power-law behavior can be identified when it is actually present. Finally, correlations between Ds, rj, and Cp are noted. In more detail ... 

Phillies, etal. (77) re-examined results of Brown and Zhou(78) and Zhou and Brown (79) on probe diffusion by silica spheres and tracer diffusion of polyisobutylene chains through polyisobutylene chloroform solutions. These comparisons are the most precise available in the literature, in the sense that all measurements were made in the same laboratory using exactly the same matrix polymer samples, and were in part targeted at supporting the comparison made by Phillies, et al.(Jl). Comparisons were made between silica sphere probes and polymer chains having similar Dp and Dt in the absence of polyisobutylene. For each probe sphere and probe chain, the concentration dependence of the single-particle diffusion coefficient is accurately described by a stretched exponential in c. For large probes (160 nm silica spheres, 4.9 MDa polyisobutylene) in solutions of a small (610 kDa) polyisobutylene, Dp c)/Dt(c) remains very nearly independent of c as Dp c) falls 100-fold from its dilute solution limit. 

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