ADSORPTION-STRETCHING ANALOGY FOR A POLYMER-CHAIN ON A PLANE - SYMMETRY PROPERTY OF THE PHASE-DIAGRAM

We consider a Gaussian chain of finite length absorbing on a planar surface with the stretching force applied to its free end. The model is exactly solvable and appears to have an unexpectedly rich behavior, exhibiting in the thermodynamic limit N --> infinity phase transitions of both the first and the second order. A closed analytical form for the partition function at arbitrary N is obtained. The phase diagram is completely symmetrical with respect to stretching force and adsorption strength parameters. Thus, a rigorous analogy is established between the adsorption of a chain onto a plane in the absence of external force and-the stretching of a nonadsorbed chain attached to a plane by one end, both being the second-order transitions. Competition of simultaneous stretching and adsorption leads to a first-order transition. Adsorption of ring polymers is discussed as a natural by-product of this scheme. Nonequilibrium free energy is obtained as a function of the order parameter and compared with the Landau theory of phase transitions. Finite-size effects are discussed.