We study the behavior of a polymer chain near a stepwise external potential u. The exact partition function of the chain tethered at a distance z0 away from this interface is analyzed in a Landau framework. In this model, there exists a conformational coil-to-flower transition. Here the flower has a strongly stretched stem from the grafting point toward the interface and, on top of it, a crown composed of the remaining segments in a (perturbed) coil conformation. The classical behavior of binodal and spinodal states of the system is identified. A phase diagram in the z0 vs u coordinates is presented with a line of first-order phase transitions ending at a critical point at z0 = 0. In this last point, the transition is referred to as the rolling transition. Particular attention is payed to small systems, i.e., to systems near the critical point. This region is relevant for relatively short polymer chains and small values of the external field.
Leermakers, F. A. M., van Male, J., & Skvortsov, A. M. (2001). Coil-to-flower transition of a polymer chain pinned near a stepwise external potential : finite size effects. Macromolecules, 34, 8294-8302. https://doi.org/10.1021/ma010074a