310 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



This sums up to mean that the chemical interpretation of basic poly- 

 mer mechanics recjuires shear wave measurements. Nevertheless, fas- 

 cinating evidence of the existence of fine-structure rehixations in polymer 

 solid has come from longitudinal wave investigations. ' " ' ' " ' Also, 

 the pioneering shear wave studies of Ferry and collaborators" ' " on con- 

 centrated solutions of polymers have suggested intrinsic relaxations of 

 the chain molecules in a highly plasticized "semi-solid" state. 



The more simplified findings cited below will be seen to luiify ap- 

 proaches in this field. Comment must first be made, however, on formu- 

 lation of experimental results in dynamics of polymers. 



Expression of Dynamic Properties 



Alternate and equi^'alent expressions have been thoroughly surveyed;" 

 all represent combinations of either Maxwell (series) springs and pistons 

 (elasticity and viscosity) or Voigt (parallel) springs and pistons. Obvi- 

 ously, there is no physical separation of elastic and viscous elements in 

 a polymer molecule, so the irrelevance of the detail of the model need 

 not be emphasized. However, the models lead to convenient formulation 

 of relaxation times which dielectric studies, in particular, have shown 

 have clear connections with chemical structure. In this chapter, some- 

 times one and sometimes the other model, or combination, will be used, 

 with the symbols shown on the next page. 



Other symbols are sometimes used, but should be easily identified 

 in terms of the above. 



Rubbers and Soft Plastics 



In Table I, the shear moduli of rigidity, n, and of viscosity, ij.', are 

 shown as calculated for the Kelvin-Voigt model, for polymers having 

 the indicated units of structure. The freciuencies are from a few hundred 

 to a few thousand cycles, hence, in the range of much technical use, 

 (flexing of tires '~300 cps) and rates of shear during processing. ' Data 

 are from a general study by I. L. Hopkins of the Bell Laboratories, 

 based on a tuning fork transducer introduced by Rorden and Grieco. 

 The strains employed were always small, in the range 0.3 to 1.5 per 

 cent; ^l and /x' were essentially independent of strain, except for some 

 loaded rubber stocks. The /x values clearly trace the magnitudes to be 

 expected in going from the most typical rubber (hevea) to the semi- 

 rigid plastics (vinyl chloiide-acetate copolymer and plasticized cellulose 

 nitrate). As anticipated from steady-stress observations the "plastics" 

 have /I > 10' dynes /cm". Increase of ijl with fre(iuency is also greater as 



