Mooney-Rivlin softening

A totally different approach to rubber elasticity has been developed by Stepto and co-workers [15, 16], which also accounts for the Mooney-Rivlin softening. Their approach is not phenomenological, but is based on structural considerations that give an accurate description of the moleeular eonformational states of the units in the polymer chains as the network is stretched. They have proposed a method for calculating the free energy of a stretched molecular network based on the rotational isomeric state of the network chains, with conformational energies determined from observations of conformational properties. 

The Mooney-Rivlin equation is frequently used to interpret experimental results related to stress softening ... 

The nonlinear elastic properties can be described by both the Mooney-Rivlin model and the molecularly based slip-tube model. Both of these models stress the fact that the low-strain modulus of the adhesives is controlled by the entanglement structure of the isoprene -i- resin phase, while the high-strain modulus is controlled by the physical crossHnk structure. The incorporation of diblocks in the adhesive dramatically reduces the density of crossHrrks and causes a more pronounced softening in the high-strain part of the stress-strain curve. 

The predictions of the classical models of rubber elasticity correspond to horizontal lines in a Mooney-Rivlin plot (C2 = 0). Plots for experimental data show a positive slope (C2 > 0). This indicates a stress softening with increasing deformation (as the reciprocal deformation 1 /X decreases). A comparison of (4) and (6) shows that, for the classical models, the Mooney-Rivlin coefficient 2Ci, corresponds to the shear modulus G given by (5), and the Mooney-Rivlin plot presents another method to determine crosslink density Vc or the average molecular mass of a network chain Me ... 

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