Entropy random coil

This thermodynamic behaviour is consistent with stress-induced crystallisation of the rubber molecules on extension. Such crystallisation would account for the decrease in entropy, as the disorder of the randomly coiled molecules gave way to well-ordered crystalline regions within the specimen. X-Ray diffraction has confirmed that crystallisation does indeed take place, and that the crystallites formed have one axis in the direction of elongation of the rubber. Stressed natural rubbers do not crystallise completely, but instead consist of these crystallites embedded in a matrix of essentially amorphous rubber. Typical dimensions of crystallites in stressed rubber are of the order of 10 to 100 nm, and since the molecules of such materials are typically some 2000 nm in length, they must pass through several alternate crystalline and amorphous regions. 

The reversible recovery of a deformed elastomer to its original (undeformed) state is due to an entropic driving force. The entropy of polymer chains is minimum in the extended conformation and maximum in the random coil conformation. Cross-linking of an elastomer to form a network structure (IX) is... 

The distortion of a random-coil unit to the a-helical conformation should bring the unit up to a state of lower entropy. Hence, if the interactions with the solvent are weak, it is expected that Shc < 0. Naturally, HB must be negative. Thus, if Hfo is not too large to suppress HB, then A H and A S become negative, and we ought to observe a normal thermal transition. The observation of inverse... 

More quantitative chemical evidence for random coil configuration comes from cyclization equilibria in chain molecules (49). According to the random coil model there must be a very definite relationship among the concentrations of x-mer rings in an equilibrated system, since the cyclization equilibrium constant Kx should depend on configurational entropy and therefore on equilibrium chain and ring dimensions. Values of /Af deduced from experimental values on Kx for polydimethylsiloxane, both in bulk and in concentrated solution, agree very well with unperturbed dimensions deduced from dilute solution measurements(49). 

The change in configurational entropy, AS g, on forming a loop of n residues from an open random coil has been estimated from simple polymer theory and the probability that the two points where the loop in the random coil is linked lie simultaneously within a defined volume element V. Thus, equations of the form... 

For a constant polysaccharide mass, an extended (random) coil exposes more surface area than does a helix, and a single helix exposes more than a double helix. The energy content of a polymer molecule is a property of its surface area. Thus, one consequence of a coil-to-helix transition is a diminution of the macromolecular exposed surface area and energy in compliance with the law of entropy. An increase in viscosity coincides with an increase in surface, inasmuch as the resistance to motion covers a wider area. 

Several general requirements must be met for a polymer to be elastic—that is, to stretch under the application of force but return to its original shape when the force is released. The polymer should be predominantly amorphous so that its Tg is below room temperature. The individual molecules of an amorphous polymer are not in fully extended, anti conformations instead, they have random, coiled conformations. When a force that pulls on opposite ends of the molecules is applied, the molecules assume an anti conformation about more bonds and thus they become longer that is, they stretch. Although the stretching tends to arrange the molecules in extended, zigzag conformations that are favorable for crystallization, the overall shapes of the elastomer molecules are such that crystallization does not readily occur. Furthermore, most elastomers Eire nonpolar, so only weak attractive forces exist between chains. Therefore, when the force is removed, the molecules tend to return to their initial random conformations because these random shapes are favored by entropy (disorder). 

The basic unit of elastin structure is tropoelastin, which has a molecular weight of about 72,000 and contains 800-850 amino acid residues. It has been proposed that tropoelastin units are present in the random coil conformation and are extensively cross-linked. This makes such a network kinetically free free to stretch and to recoil. It is the entropy effects that permit the stretched elastin... 

There is a very substantial loss of conformational entropy accompanying the conversion of a protein molecule to its native conformation from a random-coil structure limited only by primary valence bonds. This entropy loss makes a large contribution to the destabilization of the native conformation. However, if the assumption is made that the random-coil form has a similarly large conformational entropy in different solvents, this entropy change should not be much influenced by a change of solvent, and is therefore not considered further at this point. 

---