342 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



molecular coil volume, Ve . This suggests that thermal agitation tending 

 toward a smaller Ve , and excluded volume or repulsions forcing a large 

 one, will cause collisons or entanglements which might last long enough 

 to give a van der Waals cross-bond as denoted by crosses on the ms 

 sketch. (The actual forces in these would somewhat resemble those be- 

 tween different molecules in the concentrated solutions of Ferry .^*' ") 

 This mechanism has the reasonable (based on Ferry's and others' work) 

 relaxation frequency of 8.45 X 10 . A small viscosity, 773 , may comprise 

 friction of slippage at the entanglement points, with both the polymer 

 and associated solvent molecules. 



In Fig. 19, M4 is a relatiA'ely high stiffness presumed to be some average 

 hindrance to rotation of one segment with respect to another. In the 

 sketch, close-packed spheres representing methjd groups in polyiso- 

 butylene are portrayed. Their force fields overlap more in some places 

 than others, in the meandering of the chain to form the molecular coil 

 (of course, some tail-to-tail structures may be important here; they have 

 all been shown head-to-tail in the sketch). Thus, this total internal steric 

 restraint on chain flexibility, with a relaxation frequency of 3.5 X 10 , 

 contributes greatly to the large dispersion of rigidity in the megacycle 

 range noted in Fig. 18. The related viscosity, 774 , is again low. 



There is no doubt a considerable distribution of relaxation character- 

 istics associated with each and all of these mechanisms. 



Physical Properties Per Molecule 



Since the viscosities and rigidities in the dilute solutions indeed seem 

 to be additive with the number of molecules present, values of these 

 properties, for the hypothetical mechanisms, can be expressed per aver- 

 age chain. Of course, the measured quantities are expressed as constants 

 per cc of solution, but it may be useful to think of in terms of one aver- 

 age chain in each cc. Then, the shear deformation of this cham could be 

 denoted by a force constant. The associated viscosities remain, however, 

 dependent on solvent surroundings. Thus, for the polyisobutylene of 

 M„ = 3.9 X 10 , in cyclohexane solution, at 25°C the molecular quan- 



In the section on polj^mer liquids, the high-frequency modulus ^ was 

 attributed to a nearest-neighbor glass or crystal-like mteraction (since 

 the actual values were indeed typical of the hardest organic solids). 



