Effect of Finite Extensibility on the Equilibrium Chain Size

We investigate the finite-extensibility effect on the equilibrium size of a single polymer chain by using a Flory-type calculation. The finite extensibility of the chain is effectively taken into account by modifying the Gaussian stretching energy to a non-Gaussian form which recovers the harmonic spring behavior in the limit of weak stretch and diverges when the chain extension approaches the total contour length. In general, the finite extensibility decreases the equilibrium size of the chain compared to that obtained from Flory's classic theory, due to a steeper free energy or effective potential of the chain generated by the finite-extensibility effect. It is illustrated clearly that, for a chain with a short contour length and/or with strong repulsions between monomers, the finite-extensibility correction is important and necessary to be taken into account. A typical system where the finite extensibility plays an important role is suggested to be the highly charged and highly crosslinked hydrogel.