Internal energy and specific heat of an isolated polymer chain

8 Internal energy and specific heat of an isolated polymer chain 

The free energy of a chain is the sum of a regular part which is proportional to S (to the number of links), and of a singular part F 

From the free energy of the chain, we can deduce the internal energy and the specific heat of the chain. Let E(S, P) be the singular part of the internal energy and C(S, ft) the singular part of the specific heat. These quantities are given by 

The last term is a regular term and we may drop it. Thus, taking into account (14.6.36) and the equality z = 6Si/2(2jt) 3/2, we find that the singular part of C at the tricritical point is given by 

We see that, at a tricritical point, the specific heat per chain length becomes infinite when S/s0 - oo. The dependence with respect to S is in agreement with Duplantier s findings12 (though he used somewhat different assumptions to calculate C). 

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