Flow models intrinsic viscosity

According to this model, intrinsic viscosity depends not only on the molecular weight but also on the specific volume of the macromolecule and the shielding ratio, de Gennes considered this a model of porous sponge with uniform density. The monomers inside the sponge are screened from the flow. Only those on the surface are subject to friction. 

For poly electrolyte solutions with added salt, prior experimental studies found that the intrinsic viscosity decreases with increasing salt concentration. This can be explained by the tertiary electroviscous effect. As more salts are added, the intrachain electrostatic repulsion is weakened by the stronger screening effect of small ions. As a result, the polyelectrolytes are more compact and flexible, leading to a smaller resistance to fluid flow and thus a lower viscosity. For a wormlike-chain model by incorporating the tertiary effect on the chain... 

C0Pi6 (137) was the first to give an expression for the contribution of the form birefringence to the Maxwell constant. His theory is based on the elastic dumb-bell model, which has been used in early theories on flow birefringence and viscosity and which is identical with the model used in Sections 2.6.1 and 2.6.2. The ratio of Maxwell constant to intrinsic viscosity is probably unaffected by this simplification, when also the viscosity is calculated with the same model, as Copi6 did. For the absence of the form effect, this has strictly been shown in the mentioned Sections. In fact, in the case of small shear rates the situation is rather simple To a first approximation with respect to shear rate, the chain molecules are only oriented, their intramolecular distances which are needed for the calculation of form birefringence, being unaffected. 

Imai (56) constructed a theory fear the intrinsic viscosity and sedimentation constant of ring polymers using the Fixman method shown in 2.3.2 for a model similar to the Hearst-Harris model which will be described in 4.2.2. This model reduces to the Rouse model in a limiting case. The excluded volume potential is included in the form of Eq. (2.26) and the same type of calculation as described in 2.3.2 was performed for a steady shear flow. Dynamic mechanical properties were not treated, although the extension to include this case is only a matter of tedious calculations. 

To estimate the intrinsic viscosity in the bead-spring model, we need to find how much the stress tensor in the flowing fluid changes when a unit amount of the polymer is added. At low concentrations, the increase in the stress tensor (a, /3 = x, y, z) due to the presence of bead-spring chains is given as... 

Rouse assumed the molecule to he freely draining, i.e., that the effect of the flow of solvent past one part of the molecule has no effect on another part. Another way of saying this is that he assumed no hydrodynamic interaction. As is noted in Section 2.5 on intrinsic viscosity, this led to predictions that were not in accord with observations for dilute polymer solutions. Zimm later developed a model that took into account hydrodynamic interaction, but it is not necessary to consider this here, as it is not relevant to our discussion of melt behavior where there is no solvent. 

The predictions of the Zimm model for a Gaussian chain have a very simple interpretation the Zimm limit is a non-draining limit, the solvent flow does not penetrate into the polymer chain and, as far as hydrodynamic properties are concerned, a polymer chain can be considered as a hard sphere. The diffusion constant is then given by Stokes law, and the intrinsic viscosity by the Einstein equation for dilute solutions of hard spheres, the only difference being in the numerical factors. 

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