Abstract
We consider the properties of a self-avoiding polymer chain with nearestneighbor contact energyɛ on ad-dimensional hypercubic lattice. General theoretical arguments enable us to prescribe the exact analytic form of then-segment chain partition functionC n ,and unknown coefficients for chains of up to 11 segments are determined using exact enumeration data ind=2–6. This exact form provides the main ingredient to produce a large-n expansion ind −1of the chain free energy through fifth order with the full dependence on the contact energy retained. The ɛ-dependent chain connectivity constant and free energy amplitude are evaluated within thed −1expansion toO(d −5). Our general formulation includes for the first time self-avoiding walks, neighboravoiding walks, theta, and collapsed chains as particular limiting cases.
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