Thermodynamics of rubber elasticity

The rst law of thermodynamics states that the change in internal energy (At/) of an isolated system is equal to the total heat (0 absorbed by the system less the work (W) done by the system  

If the work is done on the system, such as when a gas is compressed or an elastomer is deformed by applying force, the corresponding equation is 

According to the second law of thermodynamics, the heat absorbed by the system dQ at temperature T is related to the increment of entropy dS by 

If the length of an elastic specimen is incieased a small amount dl by a tensile force / then the amount of work fdl will be done on the system (i.e., the specimen). There is also a change in volume dV during elastic deformation. So if a hydrostatic pressure P is acting in addition to the tensile force /, the work PdV is done by the system against the pressure, P. The total work done on the system is therefore 

One experimental observation which allows the analysis to be simpli ed is that the deformation of elastomers takes place approximately at constant volume, i.e., the deformation is nearly isovolume. For such a deformation at ambient pressure (F = 1 atm), the contribution of PdV to dW will be small and so the work done on the system in creating an elongation dl is 

Elastic properties of rubbers and gels are markedly different from those of metals, ceramics, and glasses. The properties of rubbers may be summarized as follows  

rubbers seem to be peculiar materials. We can, however, understand these unique properties very naturally if we consider that the main cause of the elasticity comes not from the interaction energy of the constituent molecules but from the conformational entropy of the chain segments, which are free to move. 

Perhaps the most striking difference between rubbers and other materials is their capacity for large reversible or nearly reversible deformations at their service temperature, and it is this aspect of their behavior that will be described here. The commercial exploitation of natural rubber developed rapidly with the discovery that crosslinking greatly improves its mechanical properties, giving the first of what is now a broad class of materials often referred to as elastomers . Elasto- 

Although E drops significantly as T is raised above Tg, K changes relatively little, so that K E and, from Eq. (9), v 0.5. Volume changes may hence be considered negligible compared with other types of deformation. This justifies the use of the Helmholtz free energy in the thermodynamic analysis of rubber elasticity, defined by Eq. (11). 

The work done when a specimen subject to a force / undergoes an incremental elongation dl is dW = fdl. The corresponding change in free energy is given by Eq. (14), from which Eq. (15) follow. 

Another characteristic of elastomers is that their temperature increases during rapid deformation, for which dQ x 0. In this case, one can show that Eq. (19) applies, where Q is the specific heat at fixed 1. 

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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. 

Allen,G., Kirkham,M.J., Padget,J., Price,C. Thermodynamics of rubber elasticity at constant volume. Trans Faraday Soc. 67, 1278-1292 (1971). 

In this chapter, we first discuss the thermodynamics of rubber elasticity. The classical thermodynamic approach, as is well known, is only concerned with the macroscopic behavior of the material under investigation and has nothing to do with its molecular structure. The latter belongs to the realm of statistical mechanics, which is the subject of the second section, and has as its... 

James HM, Guth E (1953) Statistical thermodynamics of rubber elasticity. J Chem Phys 21 1039-1049... 

In order to determine the nature of the force generated by a polymer gel, one must consider all the relevant interactions that contribute to the force or displacement. We learned from the thermodynamics of rubber elasticity that the molecular mechanism of force generation in the network chains is made up of two different contributions. In general, energetic and entropic effects must be taken into account ... 

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