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

A polymer chain near a penetrable interface is studied in the Gaussian mode l, in the lattice random walk model and by a scaling analysis. The interfac e is modeled as an external potential u of a Heaviside step-function form. One end of the chain is fixed at a distance z(0) away from this interface. When the end point is fixed in the high potential region, a first-order coi l-to-flower transition takes place upon variation of the distance z(0). Her e, 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 segment s in a (perturbed) coil conformation. The coil-to-flower transition is anal yzed in terms of the Landau free energy. The order parameter is taken to be related to the fraction of segments residing in the energetically favorabl e region. Exact analytical expressions for the Landau function are obtained in the Gaussian model for any distances z(0) and potential strength u. A p hase diagram in the z(0) versus u coordinates is constructed. It contains a line of the first-order phase transitions (binodal line) ending at a criti cal point z(0)=u=0, and two spinodal lines. Numerical results are obtained for several chain lengths in the lattice random walk model demonstrating th e effects of finite extensibility on the position of the transition point. Excluded volume effects are analyzed within the scaling approach. (C) 2001 American Institute of Physics.