Adsorbed chain-stretched coil: An unusual phase transition

An exact expression is obtained for the partition function of a Gaussian chain of arbitrary length adsorbed on a plane with stretching force acting on the chain’s free end. It is found that the increase in the stretching force makes the macromolecule undergo an unusual phase transition from the adsorbed state into a stretched chain state. In the thermodynamic limit, the free energy has a discontinuity in the slope at the transition point, the average number of chain segments contacting with the plane changes abruptly, and finite latent heat is absorbed. However, metastable states are completely absent and the dependence of the thermodynamic potential on the order parameter always has only one minimum. In the vicinity of the transition point, the anomalous slowing down of large scale relaxation takes place. Thus the transition under consideration has simultaneously some features of both first- and second-order phase transitions. Behavior of the finite systems under the transition is discussed.