Diffusion Dependence from molecular weight

FIGURE 6.5 Dependence of diffusion coefficient on molecular weight for solutes in water and polymer. [Graph reconstructed from data by Haglund et al.,./. Chem. Ed., 73, 889 (1996)]. 

However, the data clearly suggest that the effective diffusion coefficient depends on molecular weight this effect is not predicted by these models of porous structure (i.e., the tortuosity models in Figure 4.18 do not depend on molecular size). The tortuosity for a small water-soluble molecule, the tracer ion TMA, is 2 (Figure 4.22). Large molecules have tortuosity values greater than 2 and the tortuosity increases with molecular size. For larger molecules, this tortuosity —which is estimated from the effective diffusion coefficient— must reflect a decrease in diffusion rate due to actual tortuosity in the extra-... 

Eqn. 5 provides a very clear theoretical basis for the data of Fig. 1 (and similar data on other systems, as we shall see). The measured permeability coefficients for a set of solutes should parallel the measured partition coefficients, if the model solvent corresponds exactly in its solvent properties to the permeability barrier of the cell membrane. In addition, the molecular size of the solute is very likely to be an important factor as it will affect the diffusion coefficients within the membrane barrier phase. Data such as those of Fig. 1 will convince us that we have in our chosen solvent a good model for the solvent properties of the membrane s permeability barrier. We can now calculate values of PLx/K for the various solutes, and obtain estimated values of the intramembrane diffusion coefficient, and are in a position to study what variables influence this parameter. Fig. 3 is such a study in which data from Fig. 1 are plotted as the calculated values of f>n,c,n/A.t (calculated as P/K) against the molecular weight of the permeating solute. The log/log plot of the data has a slope of — 1.22, which means that one can express the dependence of diffusion coefficient on molecular weight (A/) in the form where... 

The diffusivity of DNA in this matrix, measured by both the jump-time distribution and the growth of the mean-squared displacement, indicates an exponential decay with respect to molecular weight, although the amount of data is very limited. If these data are fit by a power law, one obtains D -i i o.7 Although this is very close to inverse dependence on molecular weight predicted by the Rouse model, the dynamics are very different. It is clear from these experiments that direct visualization is necessary to determine the true mode of migration [34]. 

In dilute solutions, tire dependence of tire diffusion coefficient on tire molecular weight is different from tliat found in melts, eitlier entangled or not. This difference is due to tire presence of hydrodynamic interactions among tire solvent molecules. Such interactions arise from tire necessity to transfer solvent molecules from tire front to tire back of a moving particle. The motion of tire solvent gives rise to a flow field which couples all molecules over a... 

Figure C2.1.18. Schematic representation of tire time dependence of tire concentration profile of a low-molecular-weight compound sorbed into a polymer for case I and case II diffusion. In botli diagrams, tire concentration profiles are calculated using a constant time increment starting from zero. The solvent concentration at tire surface of tire polymer, x = 0, is constant.

However, when MAIs are thermolyzed in solution, the role of the cage effect has to be taken into account. The thermolytically formed macroradicals can, due to their size, diffuse only slowly apart from each other. Therefore, the number of combination events will be much higher for MAIs than for low-molecular weight AIBN derivatives. As was shown by Smith [16], the tendency toward radical combination depends significantly on the rigidity and the bulkiness of the chain. Species such as cyclohexyl or diphenylmethyl incorporated into the MAI s main chain lead to the almost quantitative combination of the radicals formed upon thermolysis. In addition, combination chain transfer reactions may... 

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