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.