Probing end-to-end cyclization beyond Willemski and Fixman.

A series of poly(ethylene oxide)s labeled at both ends with pyrene, (PEO(X)-Py(2), where X represents the number average molecular weight (M(n)) of the PEO chains and equals 2, 5, 10, and 16.5 K) was prepared together with one-pyrene-monolabeled PEO (PEO(2K)-Py). The process of end-to-end cyclization (EEC) was investigated by monitoring intramolecular excimer formation in seven organic solvents with viscosities (η) ranging from 0.32 to 1.92 mPa·s. The steady-state fluorescence spectra showed that excimer formation of PEO(X)-Py(2) decreased strongly with increasing η and M(n). The monomer and excimer time-resolved fluorescence decays were analyzed according to the traditional Birks' scheme. Birks' scheme analysis indicated that the decrease in excimer formation with increasing M(n) and η was due partly to a decrease in the rate constant of EEC, but most importantly, to a large increase in the fraction of pyrenes that did not form excimer (f(Mfree)). This result is in itself incompatible with Birks' scheme analysis which requires that f(Mfree) be the molar fraction of chains bearing a single pyrene at one chain end; in short, f(Mfree) does not depend on M(n) and η within the framework of Birks' scheme analysis. In turn, this unexpected result agrees with the framework of the fluorescence blob model (FBM) which predicts that quenching takes place inside a blob, which is the finite volume probed by an excited chromophore during its lifetime. Increasing M(n) and η results in a larger fraction of chains having a conformation where the quencher is located outside the blob resulting in an increase in f(Mfree). Equations were derived to apply the FBM analysis, originally designed to study randomly labeled polymers, to the end-labeled PEO(X)-Py(2) series. FBM analysis was found to describe satisfyingly the data obtained with the longer PEO(X)-Py(2) samples.