Effects of Cross-Linking in the Transition Zone

The onset of the transition zone on the frequency scale can be defined as in Fig. 12-9 except that for a cross-linked polymer the left side of the curve for G goes into the equilibrium modulus Ge instead of the plateau G% (except for the very lightly cross-linked systems discussed in Section B4 below). The boundary frequency (j tr is given by equation 9 of Chapter 12 according to the Rouse-Mooney theory. Various cross-linked rubbery polymers show similar frequency dependences of G as the transition zone is entered, as shown in Fig. 14-1 if the logarithmic scales are arbitrarily shifted to make Gg and o),r coincide for all four polymers shown, the curves nearly coincide.  

From the low-frequency region of the transition zone where the corresponding relaxation spectrum has a slope of — on the logarithmic scales, as in Fig. 12-4, the monomeric friction coefficient fb can be calculated by equation 1 of Chapter 12. If the cross-linking process is not accompanied by side reactions which significantly alter the chemical nature of the polymer, the effects on fo and the position 

Logarithmic plots of G against radian frequency at 25 C for four cross-linked polymers showing the onset of the transition zone. (NR) natural rubber (PB) 1,4-polybutadiene, about 50% trans (SBR) styrene-butadiene rubber with 23.5% styrene (Butyl) butyl rubber. All cross-linked with sulfur except SBR by dicumyl peroxide. (A) Plotted directly (B) with scales shifted to make C, and to, coincide with the values for natural rubber (indicated by cross). Reproduced by permission, from Science and Technology of Rubber, edited by F. R. Eirich, Academic Press, New York, 1978. 

The origin of the change is not certain, but it may be associated with a decrease in average fractional free volume associated with the formation of a cross-link (in the case of dicumyl peroxide, believed to be a carbon-carbon bond between two 

Dependence of diffusion coefficient of n-hexadecane on the degree of cross-linking in three polymers in the rubberiike state at 25°C. (PB) 1,4-Polybutadiene, cis trans vinyl = 40 53 7 (NR) natural rubber (pips denote four different initiai molecular weights before cross-linking, from 2.3 to 7.7 X 10 ) (SBR) styrene-butadiene random copolymer, 23.5% styrene. Abscissa is moles effective network strands per cubic centimeter estimated from swelling measurements. (Chen. ) 

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