MECHANICAL PHOPKRTIES OF POLYMERS 



U9 



quite well for frequencies much lower than the relaxation frequencies 

 of the smallest chain segment, but as the frc(iuency approaches these 

 relaxation frequencies, the stitYness of these polymers increases as the 

 temperature decreases. 



A fair approximation to these measured values is obtained by assum- 

 ing one more "contigurational" relaxation frequency in addition to the 

 two smallest segment relaxations discussed previously. Fig. 21 shows 

 calculations of the ratio of dynamic to static viscosity and the shear 

 stiffness for 65°C and 25°C. The lowest relaxation frequency is assumed 

 to have a stiffness of G.3 X 10*^ dynes/cm^ and a viscosity of 20 poises 

 at 65°C. For 25°C the stillness of 2 X 10 dynes/cm is assumed and an 

 activation energy of 17.3 kilocalories gives the component a viscosity 

 of 607 poises at 25°C, and a relaxation frequency of 5,250 cycles. The 

 average value of IG kilocalories for the static viscosity is a result of the 

 sum of the variation due to the two components. Although the agree- 

 ment can be improved by assuming distributions of relaxation fre- 

 quencies centered around these three primary frequencies, there does 

 not seem to be much doubt of the existence of these primary relaxation 



in 



iDtr 



Zuj 



Q lU 



_2 



i-(n 



PRODUCT OF FREQUENCY TIMES STATIC VISCOSITY 



Fig. 20 — Plot of ratio of dynamic to static viscosity and the corresponding 

 intermediate frequency shear stiffnesses as a function of temperature and prod- 

 uct of frequenc}' times static viscosity. 



