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We present a theoretical model for understanding the kinetics of a longpolymer in solution. A Smoluchowski-like equation has been used to model theproblem of polymer looping with a Dirac delta function sink of finite strength.The results for rate constants have been obtained by using Green's function. Inthis model, the rate constants for end-to-end looping of polymer exhibitssimple Arrhenius behavior. The rate constants are sensitive to relaxation time,bond length and chain length dependence of the looping probability. Inparticular, for short term rate constant, relaxation time makes loop formationbetween two ends of a polymer chain slower but has a direct dependence withlong term rate constant. We also show that for shorter polymer strands loopingis slower as compared to polymer having longer chain length. The long term rateconstant shows inverse square root dependence on the length of the chain. Thebond length strongly affects the probability of loop formation as for longconstructs of polymer, the end-to-end distance is found to exhibit inversepower law relationship to bond length. We also observe that the short term rateconstant for flexible polymer shows stronger affinity for loop formation.

Exploring the relaxation time, bond length and length of the polymer chain in the kinetics of end-to-end looping of a long polymer chain