INTERACTION OF POLYMKHS AND M KCIIAXK AL WAVKS 



31 



the ''plastics" range is approached; a relaxalioii region is implied. Figs. 

 1 to 4 show the dispersion of rigidity with fretiuency in moi-(> detail. 

 Especially striking in Figs. 1 and '2 is the small lemperature dependence 

 (at least between 27° and ()()°C) of /x- Jiecanse of experimental uncer- 

 tainty, M cannot be said to be actually higher at the higher temperatures 

 in accord with straight kinetic theory, but at least it is strongly tencHng 

 that way, as also noted for lower freciuencies studies on natural rubber. 

 Nothing like this appears for the plastics; in plasticizcd nitrocellulose 

 the 100-cycle rigidity decreases lO-fold from 27° to GG°C. This is, then, 

 the second general dynamic (|uality which reflects the low van der Waals' 

 (dipole, dispersion and induction) forces in hevea rubber and polydi- 

 methyl siloxane, as well as their intrachain flexibility. Interchain forces 

 in polyisobutylene (Butyl rubber) are low too, but barriers to flexibility 

 because of sterically hindered-CHs groups come in. Table I and Fig. 3 



KELVIN-VOIGT 

 MAXWELL I 



da 



Jt 



IdS S 

 fj. dt T] 



»S = 5oe " = aSoc ^ 



(7 = strain 



*S = stress 



t = time 



T = relaxation time 



T = retardation time 



jj. = G = modulus 



yu' = 17 = viscosity 



dt t] 



S 



M< 



(T = - ( I — e '' ) = (Toe 



For const. S, 



da S 



dt 



= - ov r] = 



s_ 



da 

 dt 



There is same stress on each ele- 

 ment ; the total strain = sum of 

 single strains. 



T = - 

 M 



There is same strain in each ele- 

 ment; the total stress = sum of 

 single stresses. 



