Configurations of polymers attached to probes

Abstract

We study polymers attached to spherical (circular) or paraboloidal (parabolic) probes in three (two) dimensions. Both self-avoiding and random walks are examined numerically. The behavior of a polymer of size R[subscript 0] attached to the tip of a probe with radius of curvature R, differs qualitatively for large and small values of the ratio s=R[subscript 0]/R. We demonstrate that the scaled compliance (inverse force constant) S/R[2 over 0], and scaled mean position of the polymer end-point (x[subscript ⊥])/R can be expressed as a function of s. Scaled compliance is anisotropic, and quite large in the direction parallel to the surface when R[subscript 0]~R. The exponent γ, characterizing the number of polymer configurations, crosses over from a value of γ[subscript 1] – characteristic of a planar boundary – at small s to one reflecting the overall shape of the probe at large s. For a spherical probe the crossover is to an unencumbered polymer, while for a parabolic probe we cannot rule out a new exponent.