Let’s say we are concerned with the special case in which all segments of the chain has the same length although their orientations differ. For a random chain, bond vector  can assume any orientation independent of , so that the result  vanishes. In other word only the diagonal terms remain which equals . Then a chain with random orientation obeys,
                                                        

(35.4)

Furthermore using , we obtain

(35.5)

which is similar to equation 14.35 for , with being replaced by .

Chain configurations and elasticity:

The tangent correlation function or the end-to-end distance does not really give the complete picture of the configuration of the chain, the probability distribution of its end-to-end distance. These distributions confirm that it is highly unlikely that a random chain will remain in a fully stretched condition, because the most likely value of  for a freely jointed chain is not far from the value of . Basically there are far more configurations available for than available for . Because of this when an external load is applied to straighten a chain its entropy decreases, i.e. the chain behaves elastically because of its entropy.