Rubber elasticity entropy change

According to the theory of rubber elasticity, the elastic response of molecular networks is characterized by two mechanisms. The first one is connected with the deformation of the network, and the free energy change is determined by the conformational changes of the elastically active network chains. In the early theories, the free energy change on deformation of polymeric networks has been completely identified with the change of conformational entropy of chains. The molecular structure of the chains... 

In non-polymeric materials the entropy change on deformation is minimal so that the intrinsic and stored elastic energies are the same at least for rapidly occurring events - but in polymers not only may the entropy contribution predominate but for large strains in rubbers the internal energy term is nearly negligible (but not at small strains where it may amount to 20% of the free energy). 

Before developing the entropic, or statistical, theory of rubber elasticity in a quantitative way, it is important to be sure that this really is the most important contribution, i.e. to be sure that any contribution to the elasticity due to changes in the internal energy on stretching is very small compared with the contribution due to changes of entropy. This is shown to be so in the following section. 

An elastomer may be defined as a crosslinked polymer network whose temperature is above its glass transition temperature. The molecular mechanism responsible for rubber elasticity is based on changes in chain conformation brought about by the overall strain (see Figure 1.13). Clearly, the number of possible chain conformations must be fewer in case (c) than in case (a), resulting in a reduction of entropy (Flory, 1953, Chapter 11). Statistically all possible chain conformations are equally likely, assuming negligible... 

The discussion of the chain statistics permits one, thus, to have a more quantitative description of a flexible, linear macromolecule. The random coil of a sufficiently long molecule can be compared in mass-density and randomness to an ideal gas at atmospheric pressure. The elastic compression and expansion of gases are caused by changes in entropy. It will be shown below that corresponding behavior exists for the extension and contraction of random-coil macromolecules (entropy or rubber elasticity, see Sect. 5.6.5). Combining many random coils into a... 

Why is the high elasticity of the rubber mainly sourced from the entropy change ... 

The idea was developed, in accordance with the second law of thermodynamics, that the retractive stress of an elastomer arises through the reduction of entropy rather than through changes in enthalpy. Thus long-chain molecules, capable of reasonably free rotation about their backbone, and joined together in a continuous, monolithic network are required for rubber elasticity. 

Rubber elasticity of a polymer network is one of the most distinctive features of long polymer chains. The elastic force of such a network is mainly due to, the change of conformational entropy of network strands which are connected to other strands by chemical linkages or topological constraints. The theoretical models to clarify the relationship between... 

The entropy changes that give rise to rubber elasticity may be modeled in terms of the chain statistics introduced in Section 14.1.2. For a chain whose end-to-end vector is fixed and equal to R, the number of conformations, il(R), that the chain can adopt is proportional to P(R, N). From Eq. (3), one thus obtains Eq. (20), where k is Boltzmann s constant and S is a constant. 

In the 1930 s several scientists presented evidence showing that rubber elasticity is essentially an entropy phenomenon, related to the change in randomness of location of the rubber segments when the material is extended. On this basis they derived relationships between the initial elastic modulus, the average chain length between network junctions, etc. The basic idea-appealed to me. It was a natural extension of my 1922 theory of conformations in simple molecules. 

The classical statistical theory of rubber elasticity1) for a Gaussian polymer network which took into account not only the change of conformational entropy of elastically active chains in the network but also the change of the conformation energy, led to the following equation of state for simple elongation or compression 19-2,1... 

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