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Recent advances in single macromolecule experiments have sparked interest inthe ensemble dependence of force-extension relations. The thermodynamic limitmay not be attainable for such systems, that leads to inequivalence of thefixed-force and the fixed-extension ensemble. We consider an ideal Gaussianchain described by the Edwards Hamiltonian with one end tethered to a rigidplanar substrate. We analytically calculate the force-extension relation in thetwo ensembles and we show their inequivalence which is caused by theconfinement of the polymer to half space. The inequivalence is quite remarkablefor strong compressional forces. We also perform Monte-Carlo simulations of atethered wormlike chain with contour length 20 times its persistence lengthwhich corresponds to experiments measuring the conformations of DNA tethered toa wall. The simulations confirm the ensemble inequivalence and qualitativelyagree with the analytical predictions of the Gaussian model. Our analysis showsthat confinement due to tethering causes ensemble inequivalence, irrespectiveof the polymer model.

Inequivalence of fixed-force and fixed-extension statistical ensembles for a flexible polymer tethered to a planar substrate