Freely jointed chain

This chain is a special case of a random walk, where all of the bonds are of the same length. Then the average of the square of the step lengths can be replaced by l2, leading to

<r2>0 = nl2

The persistence length is l.

The mean square radius of gyration for a freely jointed chain of any length is

<s2>0 = [(n+2)/(n+1)]<r2>0 / 6

which becomes indistinguishable from

<s2>0 = <r2>0 / 6

for long chains. This simple ratio of <s2>0 to <r2>0 is observed with real disordered polymers when they are in their Theta state, unperturbed by long range interaction.

The equivalent chain arises from assignment of n and l so that this simple model will reproduce the mean square unperturbed dimensions of a real chain.

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July 6, 1999
Wayne L. Mattice: wlm@polymer.uakron.edu