The Green-Tobolsky limit

Let us next consider the special case where the chain dissociation rate (r) is a constant. This limit is called the Green-Tobolsky limit (GT limit). Since r)= o iP ir) = 0), we And from (9.70a,b) 

The dissociation rate per unit time takes the activation form 

Temperature dependence of the rheological time scale in temporal networks is different from that of uncross-linked polymer melts. In the latter systems, both Rouse relaxation time and the reptation time are virtually proportional to T apart from the indirect dependence through the friction coefficient. 

Upon substitution of (9.82) into the moduli (9.68), we find the frequency-temperature superposition principle such that a modulus-frequency curve at any temperature T can be superimposed onto a single curve at the reference temperature 7b, if it is vertically and horizontally shifted properly. Such construction of the master curve is described by the equation 

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