Strongly entangled system transition point

For the weakly entangled systems, one can expect, that the ratio E/B, that is the parameter of internal viscosity is small. It can be demonstrated in Section 4.2.3, that transition point from weakly to strongly entangled systems occurs at E B. To describe these facts, one can use any convenient approximate function for the measure of internal resistance, for example, the simple formula... 

The transition point can be different, if one uses different modes, but only the transition point for the first mode is considered here. For the strongly entangled systems, according to relation (5.17), ijj = 7t2/x, so that, at %l> 1,... 

One can consider the parameter B to be a function of x and, taking equations (3.17), (3.25) and empirical value 6 = 2.4 into account, finds a solution of the equation, and estimate the value of the transition point between weakly and strongly entangled systems as... 

The results of estimation of coefficient of self-diffusion due to simulation for macromolecules with different lengths are shown in Fig. 12. The introduction of local anisotropy practically does not affect the coefficient of diffusion below the transition point M, the position of which depends on the coefficient of local anisotropy. For strongly entangled systems (M > M ), the value of the index —2 in the reptation law is connected only with the fact of confinement of macromolecule, and does not depend on the value of the coefficient of local anisotropy. At the particular value ae = 0.3, the simulation reproduces the results of the conventional reptation-tube model (see equation (5.21)) and corresponds to the typical empirical situation (M = 10Me). 

The critical value of molecular weight can be identified with the transition point between weakly and strongly entangled systems, the position of which was estimated in Sections 4.2.3 and 5.1.2 as... 

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