Statistical physics of the freely jointed chain

Using the method of constraints proposed by S. F. Edwards and A. G. Goodyear [J. Phys. A 5, 965 (1972); 5, 1188 (1972)], we do a complete calculation of the canonical partition function of a freely jointed chain (FJC) from its classical Hamiltonian. We show how the constraints reduce the phase space of an ideal gas of monomers to the phase space of a FJC, and how they permit one to find the canonical partition function. By using this function, it is possible to study thermodynamical properties of FJC’s and to build other thermodynamical ensembles via Laplace transforms. Thus we define a grand canonical ensemble where the monomer number of the FJC can fluctuate; in this ensemble, the FJC of infinite length is the asymptotic state at low and high temperatures. The critical exponents γ and ν for FJC’s are calculated and found to be equal to the Gaussian polymer exponents. Connections between the properties of FJC’s and random walks on regular lattices are also discussed. © 1996 The American Physical Society.