INTERACTION OF POLYMERS AND MECHANICAL WAVES 347 



This seems to take place, as indicated by the lower compared to the 

 upper curve on Fig. 23. Here, the /xs of the usual modified Ma.wvell 

 model, at 20 kc, is plotted against c for the polyisobutylene of M, = 

 3.9 X 10 . Also, the middle curve shows hb for a polymer of about a 

 tiiird of this molecular weight; while there is a small reduction in hb 

 with il/, in this range, it is much less than the reduction caused by 

 tightening up the polymer coil. 



Tiie M« N'alues per average molecule, [fa], fall from 18 X 10~ ' dyne 

 cm in cyclohexane to 7 X 10 ' in benzene. (Of course, [Jb] for the inter- 

 mediate molecular weight polymer in cyclohexane is only 5 X 10~ be- 

 cause so many more molecules are present in solution.) 



The temperature dependence of /xb ^ilso becomes nearly zero at least 

 o^•er the narrow range from 25 to 50°C, in benzene compared to cyclo- 

 hexane. This seems to accord with the indications pre\'iously, from Fig. 

 20, for a lower molecular weight polymer, that different mechanisms are 

 competing. These may be the configurational, with fi cc T, and relaxa- 

 tion, witli M \'arying in some complicated way with T. Thus [ry] increases 

 markedly with T, and presumably denotes an expandmg molecular coil 

 tending toward the "normal" configuration in cyclohexane. At the same 

 time, the relaxation processes with rising temperature tend to cause the 

 decrease in yus typical of the upper, solid, curves on Fig. 24. In engineer- 

 ing use, often times poorly compatible plasticizers give compounds 

 which stiffen more gradually with temperature than do "solvent" plas- 

 ticized ones. 



For similar reasons, the dynamic molecular coil viscosity, rji? , ought 

 to vary less with temperature in thermodynamically poor than in good 

 solvents. This is indeed seen in Fig. 25. On the other hand, tia for the 

 modified ^laxwell element has been described as the solvent viscosity 

 with segment hindrance and restricted rotation terms from the polymer 

 molecules lumped in with it. These latter terms are presumably little 

 affected by over-all configiu'ation (n-i term; the ms mechanism will be 

 somewhat affected, but not the m4 , on Fig. 19). Thus, tja should have 

 comparable temperature dependence in both good and bad solvents, as 

 seems to be indicated by Fig. 26. 



Microgel Molecule Solutions 



The statistical coil of linear polymer molecules may be replaced by a 

 chemically fixed, cross-linked network in microgel molecules. ' These 

 may be made completely rigid, like Einstein spheres, or highly swell- 

 able. The latter are hj^brids between rigid spheres and coiled chains. In 



