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