Entanglement overlap parameter

Figure 4-6 Illustration of Dilute and Concentrated Regimes in Terms of Log c[tj (coil overlap parameter) against Log t)sp = [( o >ls)l>ls] (Vsp = specific viscosity) slope of 3.3 for entangled polysaccharide chains dissolved in good solvents and 4.1 for polymers with specific intermolecular associations.

It is obvious from these results that the parameter essentially describes the frictional contribution of the contacts between the chains and the frictional resistance of single chains. This can be seen even more clearly by plotting the ratio of the entanglement contributionri j at zero shear rate and ofrij, . versus the coil overlap parameter hie C2 in Fig. 9... 

F. 9. Ratio of the entanglement part of the shear viscosity (cf. Eq. (14)) at zwero shear rate and the frictional part of the viscosity as a function of the coil overlap parameter... 

This number appears to be constant for flexible polymers, with the average value = 20.6( 8%). Table 25.1 shows data for polyolefin melts listing density p, plateau modulus Ge, melt chain dimensions from SANS o/M, entanglement molar mass Me calculated from Eq. (25.6), Kuhn length b, packing length p, tube diameter a, and the overlap parameter for entanglement P, all at temperature T. 

In relation [2], [r ] is the intrinsic viscosity expressed in mL/g and C[ti] is the overlap parameter when C[ri] is iarger than 1, the semi diluted regime starts followed by entanglements. For perfectly water soluble polymers, the Huggins constant is generally of the order of 0.4 and the exponent a is around 3.4-4. 

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