Persistence Length and Encounter Frequency Determination from Fluorescence Studies of Pyrene-Labeled Poly(oligo(ethylene glycol) methyl ether methacrylate)s

A series of nine pyrene-labeled poly(oligo(ethylene glycol) methyl ether methacrylate)s (Py-PEG_nMAs) with n equal to 0–5, 9, 16, and 19 were prepared by random radical copolymerization of 1-pyrenebutyl methacrylate and nine different EG_nMA monomers. The process of pyrene excimer formation (PEF) in the Py-PEG_nMA samples was characterized in acetone, THF, toluene, N,N-dimethylformamide (DMF), dioxane, and dimethyl sulfoxide (DMSO). The fluorescence decays of all Py-PEG_nMA samples were acquired in the six solvents and analyzed with the fluorescence blob model (FBM) to yield the number N_blob of structural units (SU) in the subvolume of the polymer coil probed by an excited pyrene and referred to as a blob, and the rate constant k_blob describing the encounters between two SU bearing an excited and a ground-state pyrenyl label located inside a same blob. N_blob and k_blob remained constant with pyrene content for a same series of Py-PEG_nMA samples. After averaging N_blob and k_blob over all pyrene contents for a same Py-PEG_nMA series, ⟨N_blob⟩ and the product ⟨k_blob × N_blob⟩ were found to decrease with increasing side chain length reflecting a progressive stiffening and decrease in the internal dynamics of the polymethacrylate backbone, respectively. ⟨N_blob⟩ and ⟨k_blob × N_blob⟩ could be parametrized as a function of the molecular weight of an SU and the solvent viscosity. The parametrized form of ⟨N_blob⟩ was applied to determine the persistence length (l_p) of the PEG_nMA samples using the Kratky–Porod equation. l_p was found to increase linearly with the square of the side chain length of the PEG_nMA samples, as expected theoretically. The parametrized form of ⟨k_blob × N_blob⟩ was used as a calibration curve against which the internal dynamics of several polypeptides and poly(methyl acrylate) could be compared in DMSO. This study illustrates the ability of PEF measurements to determine the persistence length and quantify the internal dynamics of polymers in solution, two important parameters in the characterization of macromolecules.