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Based on classical statistical mechanics, we calculate analytically thelength extension and the fluctuations, under a pulling force, of a polymermodelled as a freely jointed chain with extensible bonds, the latter consideredas harmonic springs. We obtain an analytical formula for the partitionfunction, and derive both the extension curve of the chain and the fluctuationsas a function of the force. An independent high force approximation has beenalso evaluated. The analytical formulas have been validated by analysing theexactness of their fit on data obtained from Langevin simulations, and comparedwith the phenomenological expressions largely used in the past literature.

Analytical results of the extensible freely jointed chain model