Mooney-Rivlin constants, dependence

Mooney-Rivlin constants obtained from strain dependent measurements at 298 K... 

Figure 9. Dependence of the Mooney-Rivlin constant on extent of cross-linking. Mn is 21,600 PDMS. Key , 2C, X, 2CS (3).

The results of stress-strain measurements can be summarized as follows (1) the reduced stress S (A- A ) (Ais the extension ratio) is practically independent of strain so that the Mooney-Rivlin constant C2 is practically zero for dry as well as swollen samples (C2/C1=0 0.05) (2) the values of G are practically the same whether obtained on dry or swollen samples (3) assuming that Gee=0, the data are compatible with the chemical contribution and A 1 (4) the difference between the phantom network dependence with the value of A given by Eq.(4) and the experimental moduli fits well the theoretical dependence of G e in Eq.(2) or (3). The proportionality constant in G for series of networks with s equal to 0, 0.2, 0.33, and 0. Ewas practically the same -(8.2, 6.3, 8.8, and 8.5)x10-4 mol/cm with the average value 7.95x10 mol/cm. Results (1) and (2) suggest that phantom network behavior has been reached, but the result(3) is contrary to that. Either the constraints do survive also in the swollen and stressed states, or we have to consider an extra contribution due to the incrossability of "phantom" chains. The latter explanation is somewhat supported by the constancy of in Eq.(2) for a series of samples of different composition. 

Related problems which have received more interest recently are the swelling dependence of the C2 term in the Mooney-Rivlin equation, and the swelling dependence of the product of the dilation ratio and of the elastic contribution to the chemical potential of the solute in a swollen network. Classical network theories predicted either constant or monotonically increasing values, whereas the experiments give a sharp and pronounced maximum ... 

Again by analogy with the treatment of cross-linked polymers, the dependence of Ea on X at constant time can be fitted to the Mooney-Rivlin equation " ... 

In Figure 1.10 the typical dependences corresponding to Equations 1.22 and 1.23 for PC (testing temperature T = 403 K) and HOPE (T = 293 K) are shown. As one can see, the Mooney-Rivlin equation is applicable to both amorphous glassy PC and semi-crystalline HDPE and gives reasonable 2Cj and 2C values. The latter statement is based on the following observation. As it is known [58], the 2Cj constant can be expressed as follows ... 

Figure 1.11 The dependence of the molecular weight of the chain part between clusters on the Mooney-Rivlin equation constants ratio ICJIC for (1) PC (2) poly(arylate sulfone) (PAS) and (3) HOPE [56]...

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