Different statistical mechanical ensembles for a stretched polymer

Imposing to a single polymer chain of N monomers either a Bred pair of forc es +/- f acting at the chain ends (stress ensemble) or a fixed end-to-end v ector R (strain ensemble) does correspond to the use of different statistic al mechanical ensembles. In particular, the two elasticity laws, R-f=g(f) a nd f(R)=h(R), where R-f is the length of the average end-to-end vector [R]( f) in the stress ensemble and f(R), is the intensity of the average interna l force [f](R) in the strain ensemble, are not equivalent. For these conjug ated ensembles, the quantity Delta(f)=f-h(g(f)) and more generally Delta(O) =[O](f)-[O](R) where O is an arbitrary observable, is studied systematicall y in this paper for a wide class of polymer models corresponding to chains at temperatures equal or above the theta point. The leading term Delta(O)(( 2)) of an expansion of Delta(O) in terms of the successive moments of the e nd-to-end vector fluctuations in the stress ensemble can be used to analyze the scaling properties of Delta(f). For the Gaussian and the freely jointe d chain models, Delta(O)proportional to 1/N for large N with the particular ity that, for the elasticity law, Delta(f) strictly vanishes for the Gaussi an chain at any finite N. For chains in good solvent, the usual result Delt a(f)proportional to 1/N at fixed f is only valid in the highly stretched ch ain regime (Pincus regime). N independent large ensemble differences of the order of 20% on Delta(f) are noticed when the chain is stretched over a di stance of the order of the unstretched chain average end-to-end distance R- 0. These effects decrease to the 1% level for R-f>3R(0). Monte Carlo calcul ations for a chain model containing both excluded volume and finite extensi bility features illustrate the distinction between the elasticity laws in t he two ensembles over all stretching regimes. Our study suggests that the n ature of the constraints used in single chain micromanipulations could be r elevant to the interpretation of experimental elasticity law data. [S1063-6 51X(99)15411-4].