Diffusion coefficients of polymer

If no entanglements are present, the diffusion coefficient of polymer molecule is, according to Beuche (7 ), given as... 

It has long been a mystery why diffusion coefficients of polymer-diluent systems, especially when the diluent is a good solvent for a given polymer, exhibit so pronounced a concentration dependence that it looks extraordinary. Several proposals have been made for the interpretation of this dependence. Thus Park (1950) attempted to explain it in terms of the thermodynamic non-ideality of polymer-diluent mixtures, but it was found that such an effect was too small to account for the actual data. Fujita (1953) suggested immobilization of penetrant molecules in the polymer network, which, however, was not accepted by subsequent workers. Recently, Barrer and Fergusson (1958) reported that their diffusion coefficient data for benzene in rubber could be analyzed in terms of the zone theory of diffusion due to Barrer (1957). Examination shows, however, that their conclusion is never definitive, since it resorted to a less plausible choice of the value for a certain basic parameter. 

Let us now analyze the concentration dependence of the diffusion coefficient of polymer solutions. By using the methods outlined above, we find that... 

Equation 5.9 has been derived from a correlation of data obtained with compounds with molecular weights between 100 and 500, and it does not give good estimates of the diffusion coefficient of polymers, especially proteins. Nevertheless, as the specific volume of proteins is nearly constant, around 0.73 [17], their molecular volume is proportional to their molecular weight, and Eq. 5.9 predicts values of the diffusion coefficient between 0.5 and 1 x 10 ... 

Evidently, Dj depends on the second derivative of the free energy, which in turn can be expressed in terms of the self-diffusion coefficients of polymers 1 and 2, as well as to the... 

The characteristic feature for the motions of chain-like molecules is that, the Brownian motion of the whole chain is integrated by the Brownian motion of all the monomers. Since the motion of each monomer is restrained by the chain coruiection of other monomers, the Brownian motion of the polymer as a whole is slower than the small monomer molecules under comparable conditions. In other words, the diffusion coefficient of polymers strongly depends on the chain length. 

Evidently, Dm depends on the second derivative of the free energy, which in turn can be expressed in terms of the self-diffusion coefficients of polymers, D and D2, and the (70-distance from spinodal. The method of determining Dm is presented in Fig. 2.22, whereas its dependence on T across the spinodal is shown in Fig. 2.23. From Dm, one may calculate the binary interaction parameter and. 

Dynamic light-scattering, sometimes called quasi-elastic light scattering or photon correlation spectroscopy, can be used to measure the diffusion coefficients of polymer chains in solution and colloids, a kind of Doppler effect see Section 3.6.6. In a dilute dispersion of spherical particles, the diffusion coefficient D is related to the particle radius, a, through the Stokes-Einstein equation. 

Apart firom the scaling of the diffusion coefficient of polymer chains with concentration, the dependency on their molecular weight is of high interest. For PS in the good solvent toluene, a scaling of and for dilute and... 

E. D. von Meerwall, E. J. Amis, and J. D. Ferry. Self-diffusion in solutions of polystyrene in tetrahydrofuran Comparison of concentration dependences of the diffusion coefficient of polymer, solvent, and a ternary probe component. Macromolecules, 18(1985), 260-266. 

ABSTRACT. Over the past 15 years, a number of transient optical grating techniques have been developed for measurements of the transport properties of materials. Such methods have been used to measure the tracer diffusion coefficients of polymer molecules which have been labeled with photochromic or fluorescent dyes. The present paper describes the common features of these techniques, and gives an example of how Fluorescence Redistribution After Pattern Photobleaching has been used to study the diffusion of polymer molecules in the melt. 

BD calculation for the diffusion coefficient of polymer chains in solute... 

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