Relation between cyclization of polymers with different initial conditions

¹ School of Science, The Pennsylvania State University at Erie, The Behrend College Erie, PA 16563-0203, USA
² Department of Physics, Sam Houston State University - Huntsville, TX 77341, USA

Received: 30 September 2005
Accepted: 26 December 2005

Abstract

We study cyclization of polymer chains in which the reactive ends of the chains are initially in close proximity (ring initial conditions). We find a surprising general relation between cyclization with ring and equilibrium initial conditions, namely that , where is the survival fraction. We show that this proportionality is exact for a special type of non-generic ring initial conditions and use an approximate argument to motivate the proportionality for more general ring initial condition. Our analytic results are confirmed by Langevin simulations of Gaussian chains. Earlier work for very long Rouse chains with equilibrium initial conditions shows that for times less than the longest polymer relaxation time. Therefore our relation shows that for a ring initial distribution under the same conditions.