Abstract
The temperature functions of the elastic modulus K2 and of the stress-optical constant K1 or its reciprocal 1/K1 were investigated for several elastomers. In the case of a hypothetical rubber which we have called “ideal” rubber—in analogy to gases—theory requires a direct proportionality between K2 or 1/K1 and the absolute temperature. The temperature functions of K2 and 1/K1 which we found by experiments with “real” elastomers show characteristic negative and positive deviations Δa2 and Δa1 from “ideal” values. When we put these values of Δa2 and Δa1 into a coordinate system, we find a certain orderly arrangement of the different elastomers, which allows us to picture a relationship between molecular structure and the values of Δa2 and Δa1. This brings up the possibility of explaining the experiments with the help of already known molecular-physical concepts. Although other explanations are conceivable the attempt is made to develop the simplest and most obvious ideas. It is conjectured that negative values of Δa2 and Δa1 come about from a loosening of secondary valence bonds—in certain ways, like crystal bonds— between neighboring molecules. Negative Δa1 values were found only in the crystallizable elastomers. It is further conjectured that positive values of Δa2 and Δa1 may result from the liberation by heat, of blocked, bulky molecular segments. These molecular segments can then contribute to the entropy elasticity only at higher temperatures. Positive Δa2 and Δa1 values are found chiefly in strongly crosslinked elastomers. Brief attention is given to the physical processes which are responsible for the elongation—double refraction and the entropy-elasticity. From this, it seems that the stress-optical constant and its temperature function are connected with properties of the molecular chains and on their orientability and crystallizability. The elastic modulus and its temperature function are strongly affected by the structure of the network and the molecular cohesive forces. Worthwhile hints about crystallization tendency, polarity and degree of symmetry of the different systems are given by the Δa1 and Δa2 values in the above mentioned coordinate systems. Natural rubber was tested in different recipes. The results of milling, of sulfur and accelerator additions, of time and temperature of vulcanization, on the values of K2, 1/K1, Δa2 and Δa1 were all investigated. The values of 1/K1 are at their highest level for dried latex films (unvulcanized). Milling and vulcanization, particularly the use of rather long periods and high temperatures, lower the value of 1/K1. A drop in the value of 1/K1, which regularly appears with a reduction of the negative Δa1 value, is explained as a loosening of secondary valence molecular couplings. According to this, natural rubber in the latex state is most strongly associated. According to this explanation, stretching in the unvulcanized condition is sufficient to loosen the secondary valence molecular bonds. Milling and vulcanization also act to loosen the linkages. Secondary valence bonds which are loosened by warming, as a general rule, are reestablished by prolonged cooling. It is to be supposed that the secondary valence molecular bonds under consideration are limited to small regions, somewhat comparable to the ordering in liquids. With an increasing degree of vulcanization, the Δa2 values go through a maximum which perhaps coincides with the condition of optimum vulcanization. This is explained as a maximum of the entropy-elasticity. In the case of slightly milled natural rubber which is appropriately vulcanized, the value of Δa2 can become practically zero. The change of the elastic modulus with temperature then is “ideal.” Nevertheless, no “ideal” rubber exists here, for Δa1 is less than zero.
Mass‐Temperature Relation of Galaxy Clusters: Implications from the Observed Luminosity‐Temperature Relation and X‐Ray Temperature Function