Relaxation Processes in Amorphous Polymeric State

The amorphous or molten polymer is a conglomeration of badly packed interlacing chains, and the extra empty space caused by this random molecular arrangement is called the free volume, which essentially consists of all holes in the matrix. When sufficient thermal energy is available, the vibrations can cause a segment to jump into a hole by cooperative bond rotation and a series of such jumps will enable the polymer chain eventually to change its position. 

While the 1.0 power dependence in Eq. (2.67) represents the simple increase in viscosity as the chain gets longer, the dependence of the viscosity on the 3.4 power of the chain length as shown in Eq. (2.68) arises from entanglement and diffusion considerations. 

Problem 2.33 A certain extruder for plastics was found to work best at a melt viscosity of about 20,000 poises. The vinyl polymer of DP , = 750 and Tg — 80°C usually used with this extruder had this viscosity at 150°C. However, a batch of the same polymer received subsequently has DP, = 500. At what temperature should the extruder now be run so that the viscosity remains at optimum conditions  

For a vinyl polymer, Z = 2(DP ). Since both samples have Z 700, Eq. (2.68) can be used for both. 

Since at high molecular weight Tg is essentially constant, both the polymer samples may be assumed to have the same Tg. Therefore, 

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