Coils rate dependence

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

For polymer melts or solutions, Graessley [40-42] has shown that for a random coil molecule with a Gaussian segment distribution and a uniform number of segments per unit volume, a shear rate dependent viscosity arises. This effect is attributed to shear-induced entanglement scission. 

Intcrmolecular Contributions. Increasing concentration reduces the effects of excluded volume and intramolecular, hydrodynamic on viscoelastic properties (Section 5). Internal viscosity and finite extensibilty have already been eliminated as primary causes of shear rate dependence in the viscosity. Thus, none of the intramolecular mechanisms, even abetted by an increased effective viscosity in the molecular environment, can account for the increase in shear rate dependence with concentration, e.g., the dependence of power-law exponent on coil overlap c[r/] (Fig. 8.9). Changes in intermolecular interaction with increased shear rate seems to be the only reasonable source of enhanced shear rate dependence, at least with respect to the early deviations from Newtonian behavior and through a substantial portion of the power law regime. 

The inside convective heat transfer coefficient h, is the only element of the overall heat transfer coefficient U that varies with the agitation speed N. If heat is removed from an agitated reactor using an internal coil or external jacket, the overall heat transfer rate depends on the rotation speed of the agitator N and if the process side offers the major resistance. This is expressed by... 

Morris, E. R., Cutler, A. N., Ross-Murphy, S. B., Rees, D. A., and Price, J. (1981). Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions. Carbohydr. Polym. 1 5-21. 

The concept of polymer entanglements represents intermolecular interaction different from that of coil overlap type interaction. However, it is difficult to define the exact topological character of entanglements. The entanglements concept was aimed at understanding the important nonlinear rheological properties, such as the shear rate dependence of viscosity. However, viscoelastic properties could not be defined quantitatively as is possible with the reptation model. Because an entanglement should be... 

This first CPC model was devised in an effort to improve the efficiency of lymphocyte separation which was conventionally performed in a short centrifuge tube. If a long tubing is wound into a coil and rotated in a centrifugal field, the particles present in the tube would travel through the tube from one end to the other at a rate depending on their size and density. This idea was implemented in the designs of the first device named the CPC. ... 

Strain Rate Dependence. The outline given above is, however, an oversimplification, because it has been implicitly assumed that the flow would not affect orientation or conformation of the polymer coil. This is not true. It is always observed that r, and thus [ /], is affected by the shear rate applied. As discussed in Section 5.1.1, various types of flow can occur and, more generally, we should say strain rate or velocity gradient, rather than shear rate. However, we will restrict the discussion here to simple shear flow. 

The coil length depends primarily on the speed of reaction and the sample plus reagent flow-rates, and varies considerably in different applications. However, extremely long reaction coils create excessive impedance, as well as carry-over problems in the... 

Fig. 3 Schematic view of the human vimentin protein and force-strain curves of coiled-coil intermediate filament under tensile loadings, (a) Schematic representation of vimentin structure, (b) Force-strain behaviors of a coiled-coil a-helical structures revealing the loading rate dependency of the molecular-level stiffness under tensile loading. (Reprinted from [66], with kind permission from Springer Science and Business Media), (c) a-p secondary structural transition of coiled-coil a-helix under tensile loading. (Reprinted from [67])...

First, we measured the flow rate dependent relative retention [(Co — C)/Co] of hyperbranched polystyrene fractions by gradually increasing the flow rate. Figure 5.9 shows that (Co — C)/Co decreases as the flow rate increases but not as sharp as the first-order coil-to-stretch transition of linear chains observed before [38, 43]. Presumably, this is because even for a given overall molar... 

Experiments carried out at different polymer concentrations yielded the same halflife of the intensity change. This result is clear evidence that the process observed in the range of several hundred microseconds is an intramolecular reaction. The rate of coil contraction depended on temperature 13 /2 10 s at 25 C and 10 ... 

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