Elasticity of a Single Molecule

The essential requirement for a substance to be rubbery is that it consist of long flexible chainlike molecules. The molecules themselves must therefore have a backbone of many noncolinear single valence bonds, about which rapid rotation is possible as a result of thermal agitation. Some representative molecular subunits of rubbery polymers are shown in Fig. 1 thousands of these units linked together into a chain constitute a typical molecule of the elastomers listed in Fig. 1. Such molecules change their shape readily and continuously at normal temperatures by Brownian motion. They take up random conformations in a stress-free state but assume somewhat oriented conformations if tensile forces are applied at their ends (Fig. 2). One of the first questions to consider, then, is the relationship between the applied tension / and the mean chain end separation r, averaged over time or over a large number of chains at one instant in time. 

Chains in isolation take up a wide variety of conformations, governed by three factors the statistics of random processes a preference for certain 

Flory [1] has argued that the occupied-volume exclusion (repulsion) for an isolated chain is exactly balanced in the bulk state by the external (repulsive) environment of similar chains, and that the exclusion factor can therefore be ignored in the solid state. Direct observation of single-chain dimensions in the bulk state by inelastic neutron scattering gives values fully consistent with unperturbed chain dimensions obtained for dilute solutions in theta solvents [2], although intramolecular effects may distort the local randomness of chain conformation. 

If the real molecule is replaced by a hypothetical chain consisting of a large number n of rigid, freely jointed links, each of length I (Fig. 3), then 

In this case rl is independent of temperature because completely random fink arrangements are assumed. The tension/in Eq. (1) then arises solely from an entropic mechanism, i.e., from the tendency of the chain to adopt conformations of maximum randomness, and not from any energetic preference for one conformation over another. The tension / is then directly proportional to the absolute temperature T. 

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