Rubber elasticity thermodynamics

Bianchi, U., and E. Pedemonte Rubber elasticity Thermodynamic properties of deformed networks. J. Polymer Sci. Pt A-2, 5039 (1964). 

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. 

This is a theoretical study on the entanglement architecture and mechanical properties of an ideal two-component interpenetrating polymer network (IPN) composed of flexible chains (Fig. la). In this system molecular interaction between different polymer species is accomplished by the simultaneous or sequential polymerization of the polymeric precursors [1 ]. Chains which are thermodynamically incompatible are permanently interlocked in a composite network due to the presence of chemical crosslinks. The network structure is thus reinforced by chain entanglements trapped between permanent junctions [2,3]. It is evident that, entanglements between identical chains lie further apart in an IPN than in a one-component network (Fig. lb) and entanglements associating heterogeneous polymers are formed in between homopolymer junctions. In the present study the density of the various interchain associations in the composite network is evaluated as a function of the properties of the pure network components. This information is used to estimate the equilibrium rubber elasticity modulus of the IPN. 

Rubber Elasticity A Simple Method for Measurement of Thermodynamic Properties 228... 

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... 

With the basic structure of polymers of macromolecules clarified, scientists now searched for a quantitative understanding of the various polymerization processes, the action of specific catalysts, and initiation and inhibitors. In addition, they strived to develop methods to study the microstructure of long-chain compounds and to establish preliminary relations between these structures and the resulting properties. In this period also falls the origin of the kinetic theory of rubber elasticity and the origin of the thermodynamics and hydrodynamics of polymer solutions. Industrially polystyrene, poly(vinyl chloride), synthetic rubber, and nylon appeared on the scene as products of immense value and utility. One particularly gratifying, unexpected event was the polymerization of ethylene at very high pressures. 

Figure 2.29- - An analysis of the thermodynamic equation of state [Eq. (2.69)] for rubber elasticity using a general experimental curve of force versus temperature at constant length. The tangent to the curve at T is extended back to 0°K. For an ideal elastomer, the quantity (dU/df)r is zero, and the tangent goes through the origin. The experimental line is, however, straight in the ideal case. (After Flory, 1953.)...

This equation is sometimes called the thermodynamic equation of state for rubber elasticity. For an ideal elastomer dUjdl )t = 0 Equations (2.63) and (2.69) then reduce to... 

Rubber elasticity and gas pressure arise from the same thermodynamic principle. Corresponding to Eqs. (2.2) and (2.3), we have... 

Finally, it is interesting and helpful to make a comparison between rubber elasticity and gas pressure from the view point of statistical thermodynamics. A gas particle (atom or molecule) has more space to move about in a large container than in a small one. In other words, the total number of the states available for the gas particle to occupy, all having the same potential energy, is proportional to the volume V of the container. Thus, corresponding to Eq. (2.9), the entropy of the gas particle can be... 

Thermodynamics, both classical [Appendix 3.A] and statistical [Appendix 2A], have been applied to many topics in polymer science. The results have provided insights into the origin of rubber elasticity, the nature of polymer crystalline, polymeric heat capacities and the miscibility of polyblends. 

Equations describing rubber elasticity can be derived in a straightforward fashion from classical thermodynamics based on free energy considerations. Free energy in turn can be related to experimentally accessible quantities as shown in the derivation below. 

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