Rubber entropy changes

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). 

Derive a formula for the entropy change for stretching an ideal rubber for which... 

From Eq. (3.14), the entropy change of the chain, when the rubber is sheared, is... 

According to Equation (11-33), the entropy change of a rubber on stretching is not due to a particular chemical structure, but simply to the number of chains and hence the number of cross-linking points linking the chains. 

The above examples are related to the concept of the one-dimensional solubility parameter. However the effects of specific interactions between some functional groups can change compatibility of the system. ChloroaUcanes compared with esters are known to be better solvents for polymethylmethacrylate. Aromatic hydrocarbons although having solubility parameters much higher than those of alkanes, dissolve some rubbers at least as well as alkanes. Probably it is related to increase in entropy change of mixing that has a positive effect on solubility. 

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

The entropy change of the rubber sample under a constant pressure is given by... 

Flory has derived the entropy change for the isotropic swelling of a rubber network ... 

For an ideal rubber a change in L causes no change whatsoever in . There are, however, changes in the entropy S. (cSjdL)jy is negative so that an... 

While the entropy change is zero for either system during the reversible adiabatic steps (see Rgures 9.12c and 9.13c), it must be emphasized that the entropy change is greater than zero for an irreversible adiabatic process. An example for an elastomer is letting go of a stretched rubber band. 

The remaining five polymers have extremely low values of ASc. These values can be related to some element of disorder within the crystal structure. The low value of ASc per bond found for poly(tetrafluoroethylene) can be attributed to the room temperature polymorphic transition and the associated entropy change.(233,234) On the other hand, poly(cis-l,4-isoprene), natural rubber, is not known to undergo any polymorphic transitions at atmospheric pressure. Yet ASc per bond is only 0.43 e.u. There is, however, some disagreement in interpreting the x-ray diffraction pattern of this polymer. Nyburg has concluded that the crystal structure is statistically... 

In a cross-linked rubber the network prevents total solution of the polymer, the polymer swelling instead to an equilibrium value. In this case the total energy of dilution, AG, will be the sum of two terms, AGm, the free energy of dilution in the state prior to cross-linking and AGe, which takes into account the entropy changes caused by expansion of the polymer network, i.e. 

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. 

---