First-order coil-to-flower transition of a polymer chain pinned near a stepwise external potential: Numerical, analytical, and scaling analysis

Abstract

A polymer chain near a penetrable interface is studied in the Gaussian model, in the lattice random walk model and by a scaling analysis. The interface is modeled as an external potential u of a Heaviside step-function form. One end of the chain is fixed at a distance z0 away from this interface. When the end point is fixed in the high potential region, a first-order coil-to-flower transition takes place upon variation of the distance z0. Here, the flower has a strongly stretched stem from the grafting point towards the interface and, on top of it, a crown composed of the remaining segments in a (perturbed) coil conformation. The coil-to-flower transition is analyzed in terms of the Landau free energy. The order parameter is taken to be related to the fraction of segments residing in the energetically favorable region. Exact analytical expressions for the Landau function are obtained in the Gaussian model for any distances z0 and potential strength u. A phase diagram in the z0 versus u coordinates is constructed. It contains a line of the first-order phase transitions (binodal line) ending at a critical point z0=u=0, and two spinodal lines. Numerical results are obtained for several chain lengths in the lattice random walk model demonstrating the effects of finite extensibility on the position of the transition point. Excluded volume effects are analyzed within the scaling approach.