Thermodynamics of rubbers

Rubber elasticity is strikingly similar to the behavior of a gas. A gas is characterized by three independent variables, P, V, and T, as has been discussed in Chapter 4. In addition to P, V, and T, rubber elasticity is characterized by two more independent variables the stretching force / (also called the tensile force) and the length L. For a rubber, the volume is virtually constant during the deformation. A comparison can be made, therefore, between a gas and rubber in terms of three independent variables PVT for gas and T for rubber. The similarity consists of the following If Yis kept constant, P is directly proportional to T for a gas, whereas if L is kept constant,/is directly proportional to T for rubber. For this reason, we can treat rubber in thermodynamics in a similar way that we treat gas. Our attention is consequently focused on the influence of temperature on the elasticity of rubber. The first law and the second law remain the same  

Here dw is no longer the same. We have to add the term/dL, that is, 

To derive measurable thermodynamic quantities such as dH/dL)j.p and pf/AT)p, we need the four exact differentials together with the Maxwell 

Since the quantity (0V/0L) p is negligible, V being nearly constant, we can write the equation of state for elasticity (or for rubber) as 

This is almost identical with the equation of state for gas. 

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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. 

G. Gee, Thermodynamics of rubber solutions and gels, in Advances in Colloid Science, Vol. 2, Interscience, New York (1946). 

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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