MECHANICAL PROPERTIES OF POLYMERS 139 



stiffness decreases with increase in temperature for a sinji;le frequency 

 measurement. However, when measurements were made at 20, 40, 80 

 and 150 kc it was found that the elasticity was a function of the fre- 

 ([uency, which incHcates the presence of more than one relaxation and 

 complicates the determination of the temperature relationships. Fig. 13 

 shows measurements of the shear elasticity over a frequency range from 

 2.5 kc^" up to 14 megacycles for 25°C. There is a gradual rise up to 

 about 300 kilocj^'les after which there is a sharp break to a stiffness of 

 about 90,000 dynes/cm^ for a 1 per cent solution of the 3,930,000 molecu- 

 lar weight polymer in cyclohexane. If one analyzes the freciuency varia- 

 tion of the elasticity he finds that it can be fitted by three relaxation 

 frequencies, one having a fre(iuency of 230 cycles, one around 66,000 

 cycles and one aroiuid 4 megacycles. A possibility exists for a foiu'th 

 relaxation. The lowest relaxation is thought to be a configurational re- 

 laxation of all the elements of the chain. The highest one appears to be 

 a relaxation of the twisting motion of the smallest segment of the chain 

 such as a Kuhn segment. The intermediate relaxation appears to be due 

 to the motion of the ends of the smallest chain segment from one posi- 

 tion of entanglement to an adjacent position. This interpretation is 

 based partly on the fact that the associated viscosity of the motion is 

 very similar to that for the relaxation of the twisting motion of the 

 smallest chain segment and partly from data presented in the next 

 section on pure polymer liquids which shows a lower frequency relaxa- 

 tion agreeing in frequency assymptotically with this one, which involves 

 chain motions of approximately 30 to 40 chain elements. Temperature 

 variations of these elastic components show that the lowest relaxation 

 mechanism has a stiffness that increases slightly with temperature in 

 agreement with the kinetic theory of elasticity. The corresponding 

 viscosity (172) which comprises most of the viscosity for a solution, when 

 plotted against the reciprocal of the temperature, as shown by Fig. 14, 

 indicates an activation energy of 3.9 kilocalories per mole which is 

 slightly higher than that of the solvent cyclohexane alone, which is 

 about 3.2 kilocalories per mole. This difference of 0.7 kilocalories pre- 

 sumably represents the added energy required to bend the chain in its 

 configurational motion. Measurements with another chain length of 

 1.18 X 10^ molecular weight showed that the stiffness of the lowest (con- 

 figurational) relaxation decreased from 310 to 160 indicating that the 

 stiffness of this motion is approximately proportional to the scjuare root 



'" The lowe.st frequency, 2.5 kc, was measured })y means of a quartz crystal 

 tuning; fork which will be described in another paper. This instrument makes 

 possible the direct measurement of configurational elasticities. 



