Rubber, thermodynamics

To make the flaw grow, say by 1 mm, we have to tear the rubber to create 1 mm of new crack surface, and this consumes energy the tear energy of the rubber per unit area X the area of surface torn. If the work done by the gas pressure inside the balloon, plus the release of elastic energy from the membrane itself, is less than this energy the tearing simply cannot take place - it would infringe the laws of thermodynamics. 

The value of AG° at various reaction temperatures and corresponding Kp values are reported in Table 2. It can be understood from Table 2 that the formation of hydrogenated nitrile rubber from nitrile rubber is thermodynamically feasible. 

A compatibilizer is sometimes used to overcome the interfacial tension between the two phases of dissimilar polymers. It enables a fine dispersion of highly cross-linked rubber particles. The function of the compatibilizer is to provide greater, but not total, thermodynamic compatibility between the two polymers [8]. 

This thermodynamic behaviour is consistent with stress-induced crystallisation of the rubber molecules on extension. Such crystallisation would account for the decrease in entropy, as the disorder of the randomly coiled molecules gave way to well-ordered crystalline regions within the specimen. X-Ray diffraction has confirmed that crystallisation does indeed take place, and that the crystallites formed have one axis in the direction of elongation of the rubber. Stressed natural rubbers do not crystallise completely, but instead consist of these crystallites embedded in a matrix of essentially amorphous rubber. Typical dimensions of crystallites in stressed rubber are of the order of 10 to 100 nm, and since the molecules of such materials are typically some 2000 nm in length, they must pass through several alternate crystalline and amorphous regions. 

Frenkel R., Duchacek V., Kirillova T., and Kuz min E. Thermodynamic and structural properties of acrylonitrile butadiene rubber/polyethylene blends, J. Appl. Polym. Sci., 34, 1301, 1987. 

Lord Kelvin s close associate, the expert experimentalist J. P. Joule, set about to test the former s theoretical relationship and in 1859 published an extensive paper on the thermoelastic properties of various solids—metals, woods of different kinds, and, most prominent of all, natural rubber. In the half century between Gough and Joule not only was a suitable theoretical formula made available through establishment of the second law of thermodynamics, but as a result of the discovery of vulcanization (Goodyear, 1839) Joule had at his disposal a more perfectly elastic substance, vulcanized rubber, and most of his experiments were carried out on samples which had been vulcanized. He confirmed Gough s first two observations but contested the third. On stretching vulcanized rubber to twice its initial length. Joule ob-... 

These deductions from basic facts of observation interpreted according to the rigorous laws of thermodynamics do not alone offer an insight into the structural mechanism of rubber elasticity. Supplemented by cautious exercise of intuition in regard to the molecular nature of rubberlike materials, however, they provide a sound basis from which to proceed toward the elucidation of the elasticity mechanism. The gap between the cold logic of thermodynamics applied to the thermoelastic behavior of rubber and the implications of its... 

These conclusions have been confirmed by Wood and Roth, who carried out measurements at both constant lengths and at constant elongations using natural rubber vulcanized with sulfur and an accelerator. Their results at constant elongation, to be considered later in connection with the thermodynamics of rubber elasticity at higher elongations, are summarized in Fig. 89. 

The formal thermodynamic analogy existing between an ideal rubber and an ideal gas carries over to the statistical derivation of the force of retraction of stretched rubber, which we undertake in this section. This derivation parallels so closely the statistical-thermodynamic deduction of the pressure of a perfect gas that it seems worth while to set forth the latter briefly here for the purpose of illustrating clearly the subsequent derivation of the basic relations of rubber elasticity theory. 

The molecular models of rubber elasticity relate chain statistics and chain deformation to the deformation of the macroscopic material. The thermodynamic changes, including stress are derived from chain deformation. In this sense, the measurement of geometric changes is fundamental to the theory, constitutes a direct check of the model, and is an unambiguous measure of the mutual consistency of theory and experiment. 

Thermodynamic Analysis. As reported previously, the storage modulus G of PDMS networks with tetrafunctional crosslinks is independent of frequency between 10 3 and 1 Hz (21). This behaviour which is entirely different from that of vulcanized natural rubber or synthetic polyisoprene networks, was attributed to the lack of entanglements, both trapped and untrapped, in these PDMS networks. Figure 4 shows that G of a network with comb-like crosslinks is also frequency independent within an error of 0.5%. For comparison, two curves for PDMS having tetrafunctional crosslinks are also shown. The flat curves imply that slower relaxations are highly unlikely. Hence a thermodynamic analysis of the G data below 1 Hz can be made as they equal equilibrium moduli. 

---