Entanglement molar mass table

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. 

The non-uniformity of the molar mass distribution influences polymer properties and their processing (see Table 4.1.5). The distinguishing feature of commercial polymers is that they have molar masses far in excess of the entanglement molar mass of about 10,000 g/mol. From typical industrial synthesis, a fairly broad distribution of molar mass results. The features of this distributicm have dramatic effects on the processability (viscosity) and properties (miscibility, strength and modulus) of plastics. 

Consider tor example, a melt of 1,4-poly butadiene linear chains with M—130000gmol The molar mass of a polybutadiene Kuhn monomer is Mo= I05gmol (see Table 2.1) so this chain has N = MjMo 1240 Kuhn monomers. At 25 °C, this polymer is 124 K above its glass transition and its oscillatory shear master curve is shown in Fig. 9.3. The time scale for monomer motion is tq = 0.3 ns, An entanglement strand of 1,4-polybutadiene has molar mass M — I900gmol (see Table 9.1) and therefore contains N — M jMQ= % Kuhn monomers. The whole chain has N/Ne = MjMs 68 entanglements. The Rouse time of the entanglement strand Te = 0.1 ps [Eq. (9,16)]. 

A critical molar mass (M ) is required in a polymer for chain entanglement s. Polymer materials consisting of macromolecules with molar masses less than this critical value are weak and are readily attacked by appropriate reactants. The melt viscosity of an entangled polymer (M > Me, see Table 4.1.3) strongly depends on the molar mass ( More energy is required for processing and fabrication of polymer materials with large macromolecules. On the other hand, the most mechanical properties increase as the molar masses increases. But, as mentioned above, the most characteristic values asymptotically approach a limit value. 

Table 4.1.3 Molar masses required for entanglements [80Fer] ...

The low molar mass samples display axialitic (sheaf-like) morphology. A relatively high value of n is expected on the basis of the data presented in Table 8.3. The reduction in n for the fractions of intermediate molar mass is consonant with the spherulitic morphology observed in these samples. The crystallization of high molar mass polymers is strongly influenced by chain entanglements and the slow and incomplete crystallization leads to small, uncorrelated crystals, i.e, to a so-called random lamellar structure. A low value of n is expected for such a low-dimensional growth. 

From the value taken by the elastic modulus at the mbbery plateau, the molar mass between entanglements (Me) can be indeed deduced using the relation E=4p RT/5Me, where p is the density. Plotting the variation of the Newtonian viscosity (rio) as a function of the molar mass also gives a critical value (Me) above which entanglements occur (see Figure 13.7), where Me is roughly equal to 10/4 of Mg (see Table 13.1). 

Table 13.1. Critical molar masses between entanglements (Me) determined from viscosity measurements and molar mass between entanglements (Me) drawn from the value of the elastic modulus at the rubbery plateau...

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