Configurations of polymers attached to probesRoy Bubis1, Yacov Kantor1 and Mehran Kardar2
1 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University - Tel Aviv 69978, Israel
2 Department of Physics, Massachusetts Institute of Technology - Cambridge, MA 02139, USA
received 2 October 2009; accepted in final form 29 October 2009; published November 2009
published online 12 November 2009
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 R0 attached to the tip of a probe with radius of curvature R, differs qualitatively for large and small values of the ratio s = R0/R. We demonstrate that the scaled compliance (inverse force constant) S/R02, and scaled mean position of the polymer end-point /R can be expressed as a function of s. Scaled compliance is anisotropic, and quite large in the direction parallel to the surface when R0 ~ R. The exponent , characterizing the number of polymer configurations, crosses over from a value of – 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.
82.35.Lr - Physical properties of polymers.
64.60.F- - Equilibrium properties near critical points, critical exponents.
36.20.Ey - Conformation (statistics and dynamics).
© EPLA 2009