Opening of a weak link of a closed looped polymer immersed in solution. Analytical modelling using a delta function sink

We present an analytical approach in order to investigate the theory for opening of a weak link of a long chain closed polymer molecule when present in dilute solution. In general the process of formation of end loops in long chain polymer molecule has received appreciable interest in many research areas. The opposite processes of breaking open of a loop is equally important but has been less explored. Thus researchers are trying to formulate analytical model for the phenomenon. We give analytical model for calculation of rate constants of the process. The physical problem of opening of a weak link can be analytically traced by a Smoluchowski-like equation. It has a reactive Dirac delta function sink of finite strength which takes care of the possible window of reaction. The two rate constants, the long term rate constant (k(L)) and the average rate constant (k(I)) are derived from the survival probability. We find that k(L) is independent of initial distribution, so for both loop closing and loop opening reaction the expression for k(L) is same, but that is not the case for k(I).