Onset of Transition Zone on Frequency Scale

Butyl rubber is cross-linked to give an equilibrium shear modulus of 4.0 X 10 dynes/cm. What is the longest relaxation time in the transition zone, T,r, and at what frequency will the onset of the transition zone be encountered as defined by Fig. 14-1, at 25°C  

The relaxation time r,r can be calculated from equation 37 of Chapter 10 with p =. The average degree of polymerization of a strand. Pc = Mc/Mq, is obtained from equation 33 of Chapter 10 with g = 1, noting that Me = p/v, as 100. The friction coefficient fb and characteristic length a are obtained from Table 12-III. The result is log Ttr = -3.0. The onset frequency for the beginning of the transition zone is approximately the reciprocal in accordance with equation 9 of Chapter 12, log (jitr = 2.9 or v,r = 130 Hz. The experimental value from Fig. 14-1 is log j, r = 2.4. 

Terminal Relaxation Time (Low Mtriecular Weight) and Its Dependence on Temperature and Pressure 

For a sample of poly(vinyl acetate) with uniform molecular weight 1.1 X 10 , whose viscosity at 76°C is 6.1 X 10 poises, what is the terminal relaxation time (controlling stress relaxation in a mold, approach to steady-state flow, etc.) What increase of temperature is needed to decrease it by a factor of 10 At what confining pressure would it be increased by a factor of 10  

The terminal relaxation time t can be roughly estimated from equation 7 of Chapter 10, derived from the Rouse theory it may be expected to be nearly correct since the molecular weight is only moderately greater than that for onset of entanglement coupling effects. The result is ti = 1.2 X 10 sec, which happens to be very close to the observed value of 1.3 X 10 sec. 

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