Recent progress in single molecule manipulation methods allows us to measure forces in the pN range. In these methods, a polymer is usually attached by one end to the tip of a microscopic probe, approaching a surface. The force is then measured with respect to the displacement of the probe. In this work, we investigate these polymermediated forces. In our model, the force is purely entropic, with amplitude A which is determined by the difference between the universal exponent η of two different scale-invariant geometries. We investigate these forces through the conformations of ideal polymers in such geometries. By finding the conformation of a polymer, we can find the end-to-end distance of the polymer, which is related to the exponent η. We use simulation of a diffusing particle on a lattice to derive η for several scale-invariant geometries, such as cones with various cross-sections, two circular cones and cone touching a plane. We only look at the limit of long polymers, while the surfaces are all considered infinite. The results of our simulations match analytical predictions perfectly. We also investigate many geometries that cannot be studied analytically. We find that the more confined the polymer is, the larger the end-to-end distance is. We show that if the polymer is more confined at one area in space, it ‘escapes’ to the more open area in space and its properties change accordingly. We also investigate the winding angle of a polymer connected to a cone near a plane. We find that short polymers do not surround the cone, but ‘escape’ to one side and propagate there. We also study the winding angle of a monomer inside the polymeric chain, and find no conclusive evidence that it changes when the polymer is elongated.

@inproceedings{KantorConformationsOP,
title={Conformations of Polymers in Confined Spaces},
author={Yacov Kantor}
}