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 (Py₆₄-G(6)). This result demonstrates that <k> represents a direct measure of [Py]_loc in pyrene-labeled macromolecules.