INTERACTION OF POLYMERS AND MECHANICAL WAVES 343 



However, in polyisobutyleiie (and to some degree in poly-a-methyl 

 styrene), it is espeeiall}' difficult to distinguish inter-chain from inira- 

 cliain crowding of metliyl groups. Tfius, while average center-to-center 

 separation of methyls is '^4 A in adjacent chains, it is <2.5 A within 

 chains, in polyisobutylene. This crowding is apparently strong; tlic ob- 

 served AHp^n is only 12.8 kcal per mole instead of the 19.2 expected.^"^' ''' 

 The energy of steric hindrance thus amounts to almost half of the actual 

 heat of polymerization. It is reasonable that a large part of the hardness 

 of a mass of polyisobutylene chains, such as in the liquids, should there- 

 fore reflect the same mechanism as that for ^4 (Fig- 19) in the dilute 

 solutions. A rough check on this can be made. A polyisobutylene having 

 considerably lower molecular weight than 3.9 X 10*^ and thus inter- 

 mediate between the "liquid" and "solid" ranges, had a Maxwell shear 

 modulus in the megacycle region (14 mc) of /x = 5.3 X 10 , at 25°C. 

 The number of molecules/cc, with individual [/4] given above, necessary 

 to give the observed density of this polymer was multiplied by [/4], giving 

 M = 2.8 X 10^ dynes/cm . Accordingly, about half of the observed high 

 frequency rigidity of polyisobutylene, at 25°C, may be calculated from 

 a "molecular constant" embodymg mtra-chain stiffness. 



jMuch more refined and detailed treatments are requu-ed to generalize 

 these "molecular constants" which are after all, as shown below, de- 

 pendent on using a thermodynamically "inert" solvent. However, much 

 as structurally significant dipole moments can be derived from measure- 

 ments in dilute solutions, it seems hopeful that macromolecular me- 

 chanics can be so elucidated. Also additional structures, such as poly- 

 propylene and polj^dimethyl siloxane compared to polyisobutylene, are 

 currently being studied. 



Temperature Variation 



Some further behaviour at different temperatures and solubihties of 

 separate chains in dilute solution may now be considered against this 

 background of possible mechanisms. Practically, these studies will bear 

 on processing and properties, lacquers, paints, and casting solutions of 

 polymers, as well as on the other qualities outlined in the introduction. 

 Results may be conveniently discussed in terms of the modified Max- 

 well single element, with factors va , Vb , and mb (Fig. 16). Mostly, the 

 kilocycle range, reflecting molecular coil changes, will be of interest. For 

 comparison, it may be noted that at 20 kc, the polyisobutylene whose 

 fiB = 1061 dynes/cm in 1 per cent solution in cyclohexane receives 889 

 dynes, cm" of this from /xo , the retarded configurational mechanism; 169 



