Exploring the role of relaxation time, bond length and the length of the polymer chain in the end-to-end looping kinetics of a long polymer chain in solution. An exact analytical model

Abstract A Smoluchowski-like equation is accounted for modeling the end-to-end looping kinetics. The phenomenon of looping is represented by a Dirac delta function sink of finite strength, placed at a point where the end-to-end distance between the monomers is zero. The sink is a physical quantity determining the possibility of looping at that point. We formulate two different rate constants, showing arrhenius type behaviour, which are obtained using the Green’s function method. The long term rate constant depends directly on relaxation time and inversely on the bond length and for shorter polymer constructs, the end-to-end looping is faster than the longer one.