The Molecular Weight Between Entanglements Me

Table 7.2. Values for the molecular weight between entanglements Me from the equilibrium properties of crosslinked networks... 

As mentioned, the molecular weight between entanglements, Me, or equivalently the entanglement density, ve, is involved in crazing, in craze fibril stability and, thus, in crack formation and propagation. 

Creton et al. [32] used a series ofblock copolymers with different molecular weights to compatibilize blends of PS and poly(2-vinylpyridine) (PVP). Only those copolymers whose PVP block polymerization degree was above 200 were found to be effective in preventing failure at the interface. This critical value corresponded roughly to the molecular weight between entanglements (Me), suggesting therefore... 

Applying the kinetic theory of rubber-like elasticity (62,109) to the entanglement network one can determine the molecular weight between entanglements Me from the plateau compliance Jn or plateau modulus Gn (62) ... 

The properties of styrenic block copolymers are dependent on many factors besides the polymerization process. The styrene end block is typically atactic. Atactic polystyrene has a molecular weight between entanglements (Me) of about 18,000 g/mol. The typical end block molecular weight of styrenic block copolymers is less than Mg. Thus the softening point of these polymers is less than that of pure polystyrene. In fact many of the raw materials in hot melts are in the oligomeric region, where properties still depend on molecular weight (see Fig. 1). 

Swelling data and stress-strain results in SBS have shown that Me is approximately the molecular weight between entanglements. Choudhury and Bhowmick [201] have shown in the case of different NR-based TPEs the following relation ... 

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. 

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... 

Smith, Lemstra and Booij37) developed a similar argument for a gel-spun fibre. The molecular weight between entanglements in the undiluted polymer melt is denoted by Me. The number of statistical chain segments between entanglements is given by... 

The purpose of our study was a rheological evaluation of the effect of composition on the properties of ABS resins in the molten state. Steady-state viscosity was determined over a wide range of temperatures and shear rates. The shear modulus in the molten state was determined by measurement of the diameter of the extrudate. ABS resins in the molten state behaved as an amorphous homophase polymer. The effect of the elastomer phase on the viscoelastic properties which characterize the behavior of the continuous matrix, i.e. monomer friction coefficient and molecular weight between entanglements (Me), was calculated by the application of the molecular theories. The significance of these properties in heterophase systems is discussed. 

Figure 7 The glass-transition temperature as a function of number-averaged molecular weight, M . Left PC. Right PS. Me indicates the molecular weight between entanglements.

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