144 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



ured values. This equation indicates that when Z = 2,370 or 43 chain 

 elements the viscosity increases only a small amount more by a chain 

 articulation effect and hence in this high frequency range we are dealing 

 with a chain length of about 40 elements or 80 carbon atoms. This is 

 checked also by a comparison of the static and dynamic viscosity. The 

 total dynamic viscosity due to the two relaxation mechanisms compared 

 to the static viscosity does not differ markedly until the number of 

 chain elements is more than 40. Above this value other motions than 

 that of the shortest chain segment can take place and can add to the 

 dynamic viscosity. The static viscosity fits an equation of the same sort, 

 but the indicated chain length for the viscous motion is about -f- times 

 that of the shortest segment. 



When a similar process is carried out over the temperature range the 

 equations of Fig. 16 are obtained. The static viscosity has an activation 

 energy of 16 kilocalories per mole, while the dynamic viscosity has an 

 activation energy of about 11.2 kilocalories per mole. 



The relaxation frequencies for the two components are plotted as a 

 function of the number of chain segments by the solid lines of Fig. 17. 



80 120 160 



NUMBER OF CHAIN ELEMENTS 



Fig. 16 — Triangles are measured static viscosities and circles are dynamic 

 viscosities plotted as a function of molecular weight. Solid lines are a plot of the 

 equations given for static and dj^namic viscosities. 



