Segmental friction coefficient

To guarantee the transformational invariance of DG = kBT/(NQ (see Table 4) in the case of Rouse relaxation, the replacement of N by N/A, requires the simultaneous replacement of the segmental friction coefficient by X which is natural, since friction is proportional to the number of segments involved. 

The chemical composition of a polymer described by a Kuhn segment chain (see Fig. 6) is exclusively represented by specific parameters such as the segment friction coefficient and the Kuhn segment length. That is, no information referring to a length scale shorter than the Kuhn segment and, hence, to... 

In this equation, % is a proportionality factor known as the bead-solvent friction coefficient which purports to account in some kind of average way for the complex molecular interactions as the polymer segments (schematized by the bead) move about in the solvent. Following Stokes law of drag resistance, this friction coefficient is usually given as = 67trisa, with a equal to the bead radius. 

An approximate model of the ISE can be developed with the aid of Figure 2.9. This figure shows a schematic cylindrical indenter with a conical tip being pushed into a specimen. The plastic zone is approximated by a segment of a sphere, and the diameter of the indent is 2r. The yield stress is Y, and the friction coefficient is a. 

The contribution of circulation to the frictional coefficient is then obtained by equating the rate of energy dissipation for the chain to the sum of the rates for the individual segments ... 

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