Chasset-Thirion equation

Figure 5-16. Physical stress relaxation at 25 °C in a crosslinked network made by a zinc oxide cure of a halobutyl rubber. The elastomer has been soaked in oil to speed the relaxation. The line is the fit to the data using the Chasset-Thirion equation with E =0.018 MPa, t= 1.04 s and m = 0.31. The nature of the polymer and the cure makes for a chemically stable structure otherwise, the plot would begin to curve downward at long time.

Computer) (a) Compare the Chasset-Thirion equation with an exponential relaxation to equilibrium such as... 

Oscillatory shear rheology of EPDM plasticized with resol was used to determine an equilibrium shear modulus Ge), relaxation in compression and strain recovery. Ge was analysed with consideration of crosslink density and permanent entanglements, including evaluation of plasticizer and soluble polymer fraction. Relaxation data were modelled with the empirical Chasset-Thirion equation and it was proposed that longer relaxation times were associated with chains pendant from the network. Relaxation times increased with crosslink density. When the crosslink density was low and pendant chains were longer and more numerous, relaxation times were increased and elastic recovery diminished. ... 

Relation [1] Is the frequency-dependent analogue of a formula proposed by Chasset and Thirion (2, 3) which has since been applied very frequently to relaxation measurements on cured rubbers. The next three equations are Inspired by similar relations In dielectrics (they are not derived from these) Equation [2] by the Cole-Cole and Equation [3] by the Davidson-Cole relation (15, 16). Both are special cases of the most general Equation [4] which contains five parameters (17). 

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

The earliest published analysis of stress relaxation in cross-linked rubbers was performed by Chasset and Thirion [43], They established the following empirical equation ... 

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