12G THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 



configurational relaxation also occurs for chain lengths greater than 60 

 elements but for chain lengths less than 40 elements this type of relaxa- 

 tion disappears. From the difference between the high frequency shear 

 elasticities measured for polyethylene and nylon 6-6 and those measured 

 for static pulls, it appears that there may be lower frequency relaxations 

 in these materials as well. 



II. METHODS OF MEASUREMENT FOR SOLUTIONS AND PURE POLYMER 

 LIQUIDS 



To measure the mechanical properties of such dilute solutions, shear 

 waves have been used since for longitudinal waves the added stiffness 

 caused by the dissolved polymers is very small compared to the stiffness 

 of the solvent alone. The velocity and attenuation of a longitudinal 

 wave are given by the equations 



= 4/^±^^ ; A = 24! [^ + 2,1 (2) 



where A and /x are the Lame elastic constants, / the frequency, p the 

 density, v the sound velocity, x the compressional viscosity and 77 the 

 shear viscosity. Since for a one percent solution of polyisobutylene in 

 cyclohexane the shear elasticity does not exceed 90,000 dynes/cm^, 

 whereas the value of X is in the order of 2 X 10^" dynes/cm", it is obvious 

 that the longitudinal velocity would have to be measured to an accuracy 

 of 1 part in 100,000 before the presence of polymer molecules could be 

 ascertained. Attenuation measurements give some information on the 

 added viscosity due to the chain molecules but since longitudinal attenu- 

 ations are not easily measured below 1 megacycle, the most interesting 

 frequency range is missed. 



A pure shear wave in a viscous liquid is propagated according to the 

 equation- 



y = yoe-V^(' + '> (3) 



where v is the transverse particle velocity, p the density, / the frequency, 

 r] the shear viscosity, j = y/ — l and z the distance. For typical sol- 

 vents, the attenuation is so high that wave motion cannot be measured. 

 However the viscous wave produces an impedance loading on a crystal 

 generating such a wave which can be measured by the change in the 

 resonant frequency and the change in the resistance at resonance. The 

 mechanical impedance per s(iuare centimeter caused by such a viscous 



