Kinky 2d polymer chain

A long polymer chain consists of N identical units with bonds between each unit, where N is
a very large number. The lowest energy state of the polymer is a straight line where all the
bonds lie along a single line. A ”kink” defect allows the chain to form a right-angled kink as
shown below:

Kink

defect
This kink raises the energy of the chain by an amount or. Use the mierocanonical ensemble to
determine the S(E,N) for the chain where E = M c and M is the number of kinks along the
chain. If the temperature is T, what is the average distance between the ends of the chain (as
a function of N) at temperature T? (Assume the chain is confined to 2D.)
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