Tracer diffusion probe concentration

The literature on self-diffusion of polymers in solution, and on tracer diffusion of probe polymers through solutions of matrix polymers, is systematically reviewed. Virtually the entirety of the published experimental data on the concentration dependence of polymer self— and probe- diffusion is represented well by a single functional form. This form is the stretched exponential exp(—ac"), where c is polymer concentration, a is a scaling prefactor, and is a scaling exponent. 

If Dp depends significantly on Cp, extrapolation to Cp 0 must be performed. The initial slope of the dependence of Dp on probe concentration, and the slope s dependence on matrix concentration, have been measured in some systems and should be accessible to theoretical analysis. In this review If the probe and matrix polymers differ appreciably in molecular weight or chemical nature, the phrase probe diffusion coefficient is applied. If the probe and matrix polymers differ primarily in that the probes are labelled, the phrase self diffusion coefficient is applied. The tracer diffusion coefficient is a single-particle diffusion coefficient, including both the self cind probe diffusion coefficients as special cases. The interdiffusion and cooperative diffusion coefficients characterize the relaxation times in a ternary system in which neither m lcrocomponent is dilute. 

Although cannot be measured in DLS, a closely related tracer diffusion coefficient Dj can be measured. In the tracer diffusion, the motion of a labeled solute called a probe or a tracer is traced selectively. A second solute called a matrix is added to the solution and its concentration is varied, whereas the concentration of the probe molecules is held low. The matrix must be invisible, and the probe must be visible. We can give a large contrast between the matrix and probe by choosing a pair of solvent and matrix that are nearly isorefractive, i.e., having the same refractive index. Then, the light scattering will look at the probe molecules only. For instance, we can follow the tracer diffusion of polystyrene in a matrix solution of poly(dimethyl siloxane) in tetrahydrofuran. 

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. 

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. 

As part of a study of probe diffusion and tracer chain diffusion in dextran solutions, Furukawa, et al. report the viscosity of 40 and 150 kDa dextrans in aqueous solution(20). Viscosities measured with Ubbelohde viscometers reached 100 cP concentrations extended up to 400 g/1. Their measurements and functional fits appear as Figure 12.4. While t (c) is described reasonably weU by stretched exponentials in c, for solutions of the 150 kDa dextran at small concentrations the measured viscosities clearly lie below the stretched-exponeniial fit. 

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