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 Pyx-G(N), where x (= 2N) 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 Pyx-G(N) dendrons. The slope of each straight line changed with the nature of the solvent and represented kdiff, the bimolecular rate constant for PEF. kdiff 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, kdiff for the Pyx-G(N) dendrons was about 360 ± 30 times smaller than kdiff 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 kdiff observed for the Pyx-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 kdiff values obtained for the Pyx-G(N) dendrons and the PyBE model compound followed similar trends as a function of solvent, indicating that the difference in behavior between the kdiff 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 Pyx-G(N) dendrons by the kdiff values obtained for PyBE in the same solvents accounted for changes in η and p, resulting in a master curve upon plotting <k>/(fdiff × kdiff) as a function of [Py]loc, where fdiff 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.

Figure 1. Schematic representation of the pyrene species Py* diff , Py* free , and Py* agg for a pyrene-labeled dendron.Note

A common issue with hydrogel formulations is batch-to-batch irreproducibility originating from poorly defined polymer precursors. Here, we report the use of dendritic polymer end-groups to address this issue and maintain reproducibility between batches of poly(ethylene glycol) (PEG) hydrogels. Specifically, we synthesized two end-functionalized PEG chains: one with azide-terminated first- and second-generation dendrons and the other with strained cyclooctynes. The two complementary azide and alkyne polymers react via strain-promoted alkyne-azide cycloaddition (SPAAC) to produce hydrogels quickly in the absence of additional reagents or catalyst at low polymer concentrations. Hydrogels made with first-generation dendrons gelled in minutes and exhibited a small degree of swelling when incubated in PBS buffer at 37 °C, whereas hydrogels made from second-generation dendrons gelled in seconds with almost no swelling upon incubation at 37 °C. In both cases, the hydrogels proved reproducible, resulting in identical Young's modulus values from different batches. The hydrogels prepared with second-generation dendrons were seeded with human mesenchymal stem cells and showed high cell viability as well as cell spreading over a two-week time frame. These studies show that the SPAAC hydrogels are noncytotoxic and are capable of supporting cell growth.