Effect of time on the rate of long range polymer segmental intramolecular encounters

The kinetics of encounters between the pyrene pendants randomly attached along a polystyrene chain (Py-PS) were monitored with a fluorescence blob model (FBM) as an external quencher was added to the solution to decrease the lifetime of the excited pyrene. The fluorescence decays acquired with the Py-PS samples yielded a measure of the volume Vblob probed by an excited pyrene during its lifetime in the form of N0blob, the number of monomers found within Vblob, and K0blob, which is inversely proportional to Vblob. Both N0blob and K0blob(-1) were found to increase with increasing probing time as the excited pyrene was allowed to probe a larger Vblob volume. The rate constant for pyrene-pyrene encounters was obtained from the product (KblobNblob). (KblobNblob) was found to decrease with increasing probing time, in agreement with scaling arguments suggesting that, as the probing time increases, the exited pyrene probes a larger Vblob where the local concentration of ground-state pyrenes in the polymer coil, [Py]loc, is smaller. K0blob, which is inversely proportional to Vblob, was found to scale as N0blob(alpha), where alpha equaled -1.5 and -1.2 in DMF and THF, respectively. The alpha exponents found for the Py-PS samples are in the same range as those found for other polymers exhibiting a random polymer coil conformation in solution and where much smaller than those obtained with more compact structured alpha-helical polypeptides randomly labeled with pyrene. Master curves were also constructed that describe how K0blob and the product (KblobNblob) scale as a function of solvent viscosity, probing time, and N0blob. These scaling laws illustrate the opposite effects that probing time and viscosity have on N0blob, V0blob, and the product (KblobNblob).