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3.1 Polymer Chain in Tension

For example, in elongation of a polymer chain due to tension, we may assume these blobs are more or less lined-up along the direction of deformation. The number of blobs is (N∕g) so that the extension R ≈ ξ (N∕g). From this, we see that

ξ ≈ N b2∕R g ≈ N 2b2∕R2 (8)

The free energy of the chain is increased in tension due to the restriction of the degrees of freedom of the blobs - each blob in this case contributes kT and so

2 F ≈ kT N∕g ≈ kT R--- Nb2

If we consider the force required to stretch the polymer coil

∂F- -R-- f = ∂R ≈ kTN b2 ≈ kT ∕ξ
(9)

we see that the blob defines a length scale over which the elastic energy is ≈ kT. That is, under an external force, the polymer will be unperturbed on length scales smaller that that for which the corresponding ‘thermal forces’ are kT or larger.

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