INTERACTION OF POLYMERS AND MECIIANK'AL WAVES 



339 



taken to be tjb . Tims, tlie stead}' flow viscosity, r/, = r;,, + Vn . Also, 



V.i + Vb 



= Vr Ol 



Vb 



V'P 



Va n.i 



under steady flow, or, allernati\ely, approximately a "dynamic intrinsic 

 viscosity" 



LVa C. 



can be written for any given freqneney. 



The curves in Fig. 17 are frequency dependent, however, although it 

 turns out that t?/, is only slightly so. Nevertheless, the considerable rise 

 of 7? -1 al)o\'e the piu'e solvent viscosity, as the concentration is increased, 

 indicates other mechanisms are being lumped into tja . As usual, some 



0.03 O 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



^ CONCENTRATION IN GRAMS (PER 100 ML. OF SOLUTION) 



Fig. 17 — Rigidity and viscosities of polj'isobutj'lene (M, = 1.18 X 10* 

 clohexane, at 25°C and 20 kc. 



in cy- 



extensive distribution of relaxation times is probably responsible. How- 

 ever, from the chemical point of view, it is best to see if some principal 

 mechanisms related to known structures can be identified. If so, they 

 could be associated with new ideas about the details of polymer intrinsic 

 viscosities, as well as the form of isolated molecules. ' ' ' 



First, the frequency dependence of the hb of the model of Fig. 16 is 

 as shown on Fig. 18. Striking regions of dispersion appear, although 

 more points are needed to define the 10 cycle zone. Actually, many sets 

 of data have been obtained in the 10 cycle zone. Recently, an immersed 

 (luartz tuning fork has given the approximate value shown for 2300 

 cycles. The experiments of Fig. 18 were on a polyisobutylene having 

 M, = 3.9 X 10 , dissolved in cyclohexane. Values of 77.4 and tjh were, 

 of course, also obtained. The results were then analj'zed for a system of 



