Stretching of a Fractal Polymer around a Disc Reveals Kardar-Parisi-Zhang Scaling.

ABSTRACT

While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting open question. We use scaling analysis and computer simulations to examine stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius R. We reveal that the typical excursions of the polymer away from the surface and curvature-induced correlation length scale as Δ∼R^{ß} and S^{*}∼R^{1/z}, respectively, with the Kardar-Parisi-Zhang (KPZ) growth ß=1/3 and dynamic exponents z=3/2. Although probability distribution of excursions does not belong to KPZ universality class, the KPZ scaling is independent of the fractal dimension of the polymer and, thus, is universal across classical polymer models, e.g., SAW, randomly branching polymers, crumpled unknotted rings. Additionally, our Letter establishes a mapping between stretched polymers in curved geometry and the Balagurov-Vaks model of random walks among traps.