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

Abstract

A series of nine pyrene-labeled poly(oligo(ethylene glycol) methyl ether methacrylate)s (Py-PEG n MAs) with n equal to 0–5, 9, 16, and 19 were prepared by random radical copolymerization of 1-pyrenebutyl methacrylate and nine different EGnMA monomers. The process of pyrene excimer formation (PEF) in the Py-PEG n MA samples was characterized in acetone, THF, toluene, N,N-dimethylformamide (DMF), dioxane, and dimethyl sulfoxide (DMSO). The fluorescence decays of all Py-PEG n MA 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 n MA samples. After averaging N blob and k blob over all pyrene contents for a same Py-PEG n MA 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 n MA samples using the Kratky–Porod equation. l p was found to increase linearly with the square of the side chain length of the PEG n MA 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.

Probing the inner local density of complex macromolecules by pyrene excimer formation

“…Numerous reports have indicated that within experimental error, k blob and N blob do not depend on the pyrene content of the PyLM and their product k blob × N blob represents the encounter frequency between structural units inside a blob and is thus a measure of the internal dynamics of the polymer. 21,37,39–41 The slower internal dynamics expected for a polymer constituted of heavier structural units rationalizes why k blob × N blob decreases with increasing molar mass of a structural unit ( MW SU ) as shown in Fig. 1B.…”

“…Consequently, n Py equals 〈 n 〉 and L Py in eqn (3) is given by eqn (5).Representing 〈 k 〉 as a function of s × 〈 n 〉/( N bb × N blob ) 3/2 in the log–log plots shown in Fig. 3 yields straight lines for the series of poly(methyl acrylate) (Py-PC 1 A), 41 poly(methyl methacrylate) (Py-PC 1 MA), 40,41 polystyrene (Py-PS), 21,37 poly(butyl methacrylate) (Py-PC4MA), 40,41 poly(methoxyethyl methacrylate) (Py-PEG 1 MA), 41 and poly( N -isopropylacrylamide) (Py-PNIPAM) 39 randomly labeled with pyrene in THF, toluene, DMF, and DMSO. Since the trends overlapped each other, they were translated laterally to spread them apart using the shift factor s , whose value is indicated in the caption of Fig.…”

“…Since PEF occurs over a few nanometers, a length scale small enough to avoid excluded volume effects, the polymeric segments probed by the excited pyrenyl label are expected to obey Gaussian statistics. Most of the 〈 n 〉 and N blob parameters obtained from the FBM 39–41 as well as the pre-exponential factors ( a i ) and decay times ( τ i ) used in the MFA to determine 〈 k 〉 were reported in earlier publications. 51,52 The missing parameters for some specific polymer and solvent pairs were obtained by acquiring their fluorescence decays and fitting them with the appropriate model.…”

“…In view of the importance of the k q - vs. -[ Q ] loc relationship to firmly establish the applicability of FCQ experiments as a robust analytical methodology to characterize the local density, and thus the conformation, of complex macromolecules, this report re-visit the parameters obtained from the FCQ studies conducted on 3 series of pyrene end-labeled oligomers, 37–39 6 series of polymers randomly labeled with pyrene, 37,39–41 and 2 series of dendrimers end-labeled with pyrene, 42–44 to demonstrate that the underlying physical principle connecting these apparently unrelated parameters is the k q - vs. -[ Q ] loc relationship. This report focuses on pyrene-labeled macromolecules (PyLM) because pyrene excimer formation (PEF) upon diffusive encounters between an excited and a ground-state pyrene is a well-known example of FCQ, which has been employed to characterize the internal dynamics of numerous PyLM.…”

“…This report focuses on pyrene-labeled macromolecules (PyLM) because pyrene excimer formation (PEF) upon diffusive encounters between an excited and a ground-state pyrene is a well-known example of FCQ, which has been employed to characterize the internal dynamics of numerous PyLM. 19–21,37–46 After reviewing the different parameters retrieved through the models developed over the years to analyse the fluorescence decays acquired with PyLM, the direct relationship existing between the average rate constant 〈 k 〉 for PEF and the local concentration [ Py ] loc of ground-state pyrenes in a PyLM will be demonstrated for the 11 series of PyLM. The demonstration that 〈 k 〉 is directly related to [ Py ] loc will establish PEF experiments in particular and FCQ experiments in general as a robust methodology to probe the internal density of complex macromolecules in solution that nicely complements scattering techniques.…”