Polymer Chain Cross Section and the Mooney-Rivlin Constants. II.
Authors: Boyer R. F. , Miller R. L. 
Published: February 2011

Abstract
We started with a critical examination of published Mooney-Rivlin constants on the common commercial elastomers and some experimental ones. Following a suggestion by Treloar, plots were made of C2/C1 against 2C1 in order to select values of the ratio at constant 2C1 in comparing all elastomers. We found empirically that a log-log plot of C2/C1 against 2C1 seemed to be either linear or slightly concave downwards. This fact facilitated the extrapolation which was necessary in several instances. Cross-sectional areas of elastomer chains in the amorphous state were assumed to be proportional to areas for the same polymers in the crystalline state. (The areas of copolymers were obtained from an averaging process of the areas of the corresponding crystalline homopolymers.) A plot of log C2/C1 against log (area per chain) is linear, as seen in Figure 7, with a slope of about −2. This is, to our knowledge, the first positive correlation of Mooney-Rivlin constants with a specific molecular parameter. It is also one of the first uses of tabulated lattice parameters in structural correlations. Vincent had previously correlated tensile strength of polymers with cross sectional areas per chain. Speculations are presented concerning the implications of the linear relationship in Figure 7. They are divided as between stress-induced local ordering favored by some authors and chain entanglement favored by others. A third possible effect active in readily crystallizable elastomers is strain-induced crystallinity. This paper does not attempt to resolve the conflict between these several alternatives. One by-product of this study is the fact, shown in Figure 9, that C2 at constant C1 increases linearly with molecular weight for cis-trans-vinyl poly-butadienes at low 2C1 but not at high 2C1. This might be consistent with an entanglement mechanism. There is, however, a more important byproduct. Regardless of the molecular interpretation of Figure 7, such a correlation provides a convenient criterion for judging the validity of divergent sets of literature data. Specific examples of this will be discussed in Appendixes 2 to 4. Gaps and scatter in literature data became quite apparent as with butyl rubber and PDMS. Finally, we note the predictive features of Figure 7 in suggesting experiments to carry out on elastomers chosen on the basis of cross-sectional area. Thus, poly(di-n-propylsiloxane) might be expected to show a vanishingly small C2 at any practical level of crosslinking even though, from Vincent's correlation, its strength might also approach zero. In particular, the lower left hand corner of Figure 1 lends itself to such exploration. We obviously could have predicted7 the C2/C1 values later reported by Mark et al. for poly (ethyl acrylate). We have examined most of the available Mooney-Rivlin C1 and C2 values by an objective technique. As a consequence, we are able to pinpoint some unresolved problems which might otherwise not be obvious: many gaps exist in the literature data (for example, it is not possible to prepare a Figure 1 type plot for butyl rubber); many discrepancies remain to be clarified; and key characterization parameters are absent for many elastomers.