Chains molecular weight between entanglements

Comments on Calculated Data. In several studies (13,18,19), G ax has been found to equal, or possibly be somewhat less than, the plateau modulus, G j, of a high molecular weight polymer whose chemical composition is the same as that of the network chains. Although G j for amorphous PPO has not been reported, it can be estimated from Zc, the number of chain atoms per molecule above which the viscosity increases approximately with the 3.4 power of Z. This quantity has been reported (25,26) to be about 400. As the chain atoms between entanglements is commonly about Zc/2, it follows that the molecular weight between entanglement loci is about 3900, and thus G j [ = (p/Me)RT] is about 0.65 MPa at 30°C. 

Chain entanglements are the cause of rubber-elastic properties in the liquid. Below the "critical" molecular mass (Mc) there are no indications of a rubbery plateau. The length of the latter is strongly dependent on the length of the molecular chains, i.e. on the molar mass of the polymer. From the shear modulus of the pseudo rubber plateau the molecular weight between entanglements may be calculated ... 

Smith, Lemstra and Booij developed a similar argument for a gel-spun fibre. The molecular weight between entanglements in the undiluted polymer melt is denoted by M,. The number of statistical chain segments between entanglements is given by... 

One convenient strategy to interpret these results is to review the molecular characteristics of binary blends as extracted from polymer melt rheology [40]. The influence of short chains (M < Me) is to effectively decrease the plateau modulus and the terminal relaxation times as compared to the pure polymer. Consequently, the molecular weight between entanglements... 

The parameter a has been identified as the radius of the tube, and its value is close to the root means square of the end-to-end distance of the chain with molecular weight Mg, that is, the molecular weight between entanglements. 

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