Direct Measure of the Local Concentration of Pyrenyl Groups in Pyrene-Labeled Dendrons Derived from the Rate of Fluorescence Collisional Quenching

The model-free analysis (MFA) was applied to measure the average rate constant (<k>) for pyrene excimer formation (PEF) in a series of pyrene-labeled dendrons referred to as Py(x)-G(N), where x (= 2(N)) is the number of pyrenyl labels born by a dendron of generation N ranging from 1 to 6. <k> was measured in four different solvents, namely tetrahydrofuran (THF), toluene, N,N-dimethylformamide (DMF), and dimethylsulfoxide (DMSO). <k> was found to increase linearly with increasing local pyrene concentration ([Py](loc)), where [Py](loc) had been determined mathematically for the Py(x)-G(N) dendrons. The slope of each straight line changed with the nature of the solvent and represented k(diff), the bimolecular rate constant for PEF. k(diff) depended on the solvent viscosity (η) and the probability (p) for PEF upon encounter between an excited and a ground-state pyrene. In a same solvent, k(diff) for the Py(x)-G(N) dendrons was about 360 ± 30 times smaller than k(diff) obtained for ethyl 4-(1-pyrene)butyrate (PyBE), a pyrene model compound similar to the pyrene derivative used to label the dendrons. The massive decrease in k(diff) observed for the Py(x)-G(N) samples reflected the massive loss in mobility experienced by the pyrenyl labels after being covalently attached onto a macromolecule compared to freely diffusing PyBE. Interestingly, the k(diff) values obtained for the Py(x)-G(N) dendrons and the PyBE model compound followed similar trends as a function of solvent, indicating that the difference in behavior between the k(diff) values obtained in different solvents were merely due to the changes in the η and p values between the solvents. Normalizing the <k> values obtained with the Py(x)-G(N) dendrons by the k(diff) values obtained for PyBE in the same solvents accounted for changes in η and p, resulting in a master curve upon plotting <k>/(f(diff) × k(diff)) as a function of [Py](loc), where f(diff) was introduced to account for some pyrene aggregation in the higher generation dendron (Py(64)-G(6)). This result demonstrates that <k> represents a direct measure of [Py](loc) in pyrene-labeled macromolecules.