338 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



40 



5 



O 30 



U 25 



I 20 



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. 15 — Electromechanical interaction of solutions of poh-isobutylene (M, = 

 1.18 X 10^) in cj'clohexane with crj-stal vibrating torsionall}- at 20 kc. 



should for a liciuid having only viscosity. But, apparently as soon as any 

 polymer chains are added, the curves diN'erge. A stiffness coming from 

 separate chain molecules is being displayed. ^° Qualitatively, theoretical 

 expectations of Kuhn ' " and others seem justified, at least that there 

 is a relaxation mechanism for isolated chains. 



The usual question of how best to express the dynamical results arises. 

 The procedure of earlier sections for polymer solids and liquids will be 

 followed. In general, a frequency dependent modified Maxwell element 

 as sketched on Fig. 16 will be used. However, a frequency-independent 

 analysis has also been carried out for one sample system, and, from this, 

 basic mechanical constants of single "average" molecules are obtained, 

 if it is reasonable to relate the mechanical models for the liquid con- 

 tinuum to the discrete chains dissolved in it. 



Fig. 17 shows typical results from the simple scheme of Fig. 16, where 

 the pure solvent viscosity, rjA , has been considered to be in parallel 

 with a Maxwell element. The total shear rigidity of the solution (at a 

 given concentration) is represented by fXB . The viscosity of the polymer 

 molecule coils in solution with the solvent streaming through them is 



i 



Mb = 



(r2-x2) CO 7)2 



a;/?77s-2RX 



Mb\ 



2RX (r2-x2)' 



v.\h v.\h 



r)A = 



top 



COfi 



(0/37)^- 2RX 



Fig. 16 — Relations for calculation of shear stiffness and viscosity of dilute 

 polymer solutions. 



