Nondraining polymer

A nondraining polymer molecule, also referred to as the impermeable coil, can be represented by an equivalent impermeable hydrodynamic sphere of radius R. The frictional coefficient of this sphere which represents the frictional coefficient of the non-draining polymer coil can thus be written,... 

This equation can be rearranged to give an equation for the hydrodynamic volume of an impermeable (nondraining) polymer molecule in infinitely dilute solution ... 

Ottinger, H. C. Velocity field in nondraining polymer chains. RheoL Acta (1996) 35, pp. 134-138... 

Equations (9.42) and (9.46) reveal that the range of a values in the Mark-Houwink equation is traceable to differences in the permeability of the coil to the flow streamlines. It is apparent that the extremes of the nondraining and free-draining polymer molecule bracket the range of intermediate permeabilities for the coil. In the next section we examine how these ideas can be refined still further. 

In the nondraining limit of Eq. (9.47), the coils are unperturbed in both senses of the word nondraining and 0 conditions. To emphasize the latter we attach the subscript 0 to [r ] when these conditions are met. Thus for high polymers under 0 conditions... 

Next we consider the situation of a coil which is unperturbed in the hydro-dynamic sense of being effectively nondraining, yet having dimensions which are perturbed away from those under 0 conditions. As far as the hydrodynamics are concerned, a polymer coil can be expanded above its random flight dimensions and still be nondraining. In this case, what is needed is to correct the coil dimension parameters by multiplying with the coil expansion factor a, defined by Eq. (1.63). Under non-0 conditions (no subscript), = a(rg)Q therefore under these conditions we write... 

For high molecular weight polymers in good solvents, fo] exceeds fo]0 because of coil expansion under nondraining conditions that is, as more solvent enters the coil domain than would be present under 0 conditions, Equation (92) continues to apply, with R replacing R2gfi. Using Equation (90) to quantify this expansion effect, we obtain... 

What is meant by free-draining model and nondraining model in the case of viscosities of polymer solutions ... 

Two basic theoretical models exist to describe the degree of long-chain branching in dilute solution. According to the nondraining model depicted by Zimm and Kilb (25) and Kilb (26), the ratio of intrinsic viscosities of branched and linear polymers is given by ... 

The second is the hydrodynamic model of Flory and Fox (27) which represents the polymer molecule by an equivalent nondraining hydro-dynamic sphere. Assuming the Flory constant to be the same for linear and branched polymers, the degree of branching is given by the g3/2 rule ... 

Aharoni and coworkers characterized 59 Denkewalter s cascade macromolecules 4 by employing classical polymer techniques viscosity determinations, photo correlation spectroscopy (PCS), and size exclusion chromatography (SEC). It was concluded that at each tier (2 through 10) these globular polymers were, in fact, monodisperse and behaved as nondraining spheres. The purity of these molecules was not ascertained and the dense packing limits were either not realized or simply not noted. 

Based on the Kirkwood-Riseman theory, if polymer chains are nondraining, it follows [Kirkwood and Riseman, 1948 Auer and Gardner, 1955] that intrinsic viscosity data can be related to the radius of gyration, Rg, of flexible polymers. This can be expressed in an equation of the form [Flory and Fox, 1951]... 

We can regard the motion of polymer coils in a dilute solution as in the nondraining mode of spherical particles, which means that a polymer coil moves together with the holding solvent molecules, as shown in Fig. 5.1a. There is no relative velocity for those holding solvent molecules to the polymer, and all the frictional interactions for polymer motions only occur at the surface of the spherical particle. We then have... 

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