Adsorption‐stretching analogy for a polymer chain on a plane. Symmetry property of the phase diagram

We consider a Gaussian chain of finite length adsorbing 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→∞ 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...

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