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THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



in the kilocycle range with shear waves generated by torsional crystals 

 and in the megacycle region by shear waves with tiie reflectance method 

 and by longitudinal (ultrasonic) waves from a pulse i^ropagation tech- 

 nique. The results have been expressed in two ways. Fu'st, hi earlier 

 reports, " a trend corresponding with experiment was given by two 

 Maxwell elements arranged in parallel. This result is too simple com- 

 pared to the distributions of relaxation times pre\'iously proposed for 

 high molecular weight polymers to reproduce detailed observation. 

 Nevertheless, perhaps because of the smaller molecules involved, there 

 seems to be clear indication that two principal relaxations predominate 

 the mechanical reactions of these liciuids over the range of frequencies 

 of present interest, 10" to 10' cps. For example, for polymer D, these are: 



(In accounting for the second main relaxation, a hysteresis component 

 had to be introduced whose significance has been suggested. ') 



Second, specific values of shear rigidity /x (Maxwell) and m (Voigt), 

 shear viscosity n' (Maxwell) and m' (^ oigt) as well as the constants for 

 related compressional wave systems, X -|- 2/x (elastic) and X' + 2^' 

 (viscous) have been calculated for particular frequencies. Unlike in the 

 first way of expression, these latter quantities are all highly frequency 

 dependent. However, they describe conditions at various frequencies of 

 interest, and are thus often worthwhile. 



Both ways of looking at the data lead, as implied by the figures above, 

 to the proposal that typical polymer stiffness (shear rigidity of '^10 

 dynes/cm") is present at M, '^ 1600, ^\ith DPr, '^ 30, or an average 

 chain length of about 60 carbon atoms. This appears when the straining 

 is done in 10~ to 10~ sec. In the 10~ to 10~ sec range, rigidity occurs 

 for even an average chain length of 20 atoms as shown in Table IV. 



STRUCTURAL FACTOR IN LIQUID MECHANICS 



The mam relaxations in the kilocycle range in polyisobutylene liquids 

 seem to lead to quasi-configurational elasticity. This is where the kinetic 

 theory tendency for a most probable separation of chain ends is retarded 

 by viscous interaction of segments between and within the chains. Hence, 

 the middle dashed curves of Fig. 5, showing shear elasticity for some of 

 the polymers of Table IV, decrease e.xponentially with increasing tem- 



