Dynamics of chain molecules. Intramolecular diffusion controlled reactions for a pair of terminal reactive groups

Abstract

AbstractThe first order intramolecular rate constant for the reaction between the terminal groups of flexible macromolecules is calculated in the partial draining case, following the theory formulated by Wilemski and Fixman for diffusion controlled reactions. Substantial differences with respect to the nondraining and free‐draining limits are evidenced, and it is shown that the rate constant in the partial‐draining case has relevant contributions from all the modes of the bead‐spring chain. The effects of chain flexibility and hydrodynamic interaction in macromolecules of increasing molecular weight are examined. The effective diffusion constant of the end groups increases with both the flexibility and the length of the chain. Numerical results for polystyrene (PS) and polydimethylsiloxane (PDMS) are presented and employed to calculate the relative quantum yield for fluorescence quenching. For highly flexible chains, like PDMS, quenching effects are expected in a range of molecular weight well above the limit of validity of the bead‐spring model. On the contrary, for more rigid polymers, like PS, the quenching can be observed only at molecular weights lower than this limit. The calculated behavior is compared with some experimental results recently obtained by the authors.