## 1 Introduction  
During the past forty years, monitoring pyrene excimer fluorescence and formation (PEF) has become an important tool to characterize long-range polymer chain dynamics (LRPCD) for polymers dissolved in various media [1; 2; 3; 4; 5]. PEF experiments take advantage of the ability of pyrene to form an excimer when an excited pyrene encounters a ground-state pyrene. When the two pyrene labels are covalently attached to a polymer, PEF indicates that the two structural units of the polymer are sufficiently close to enable an encounter. Since PEF experiments are conducted at extremely low polymer concentrations (\(<\)10 mg\(\cdot\)L\({}^{-1}\)), where inter-chain interactions can be neglected, the rate constant for PEF reflects the ability of one polymer chain to bring two structural units of a same polymer chain, separated by a long contour length, into contact, and thus provides a quantitative measure of LRPCD. Several applications of PEF to characterize LRPCD have been reviewed recently [6; 7]. The establishment of reliable techniques capable of probing the magnitude of LRPCD of polymers in solution is important in several aspects of polymer science, including the field of protein folding. The folding of a polypeptide that is initially in a random coil conformation is believed to involve multiple encounters between amino acids that can be located at large separations along a polypeptide sequence. These encounters lead to strong interactions between specific amino acids, resulting in the generation of secondary and then tertiary structural motifs that eventually converge into a structured protein [8]. The entire folding process revolves around the ability of some segments of the polypeptide to diffuse within the spatial frame of the macromolecule and encounter each other. The initial stages of protein folding are thus controlled by LRPCD, and methods capable of characterizing LRPCD quantitatively, such as those based on PEF, are implicitly relevant to the field [7]. To date, benchmarking the ability of PEF to report quantitatively on the LRPCD of pyrene-labeled polymers in solution has been achieved mostly with synthetic polymers due to their wide availability and ease of preparation and handling [7] The PEF experiments conducted on pyrene-labeled linear polymers (PyLLPs) fall into two main categories depending on whether the labels are covalently attached at the ends of a polymer chain having a narrow molecular weight distribution [4; 5], or randomly attached along a polymer that can be polydisperse in length [7]. Due to the inherent constraints associated with end-labeled monodisperse polymers, such as extremely low rates of end-to-end encounter for long and rigid chains, the bulk of experiments aiming to characterize LRPCD by PEF have been conducted with linear polymers randomly labeled with pyrene [7]. In one type of PEF experiment, the fluorescence decays of the pyrene monomer and excimer of a series of randomly labeled polymers with different pyrene contents are analysed globally with the Model Free Analysis (MFA), and the LRPCD of the polymer backbone is described by the average rate constant \(<\)k\({}^{\text{Mrf}}\)\(>\)blob that is normalized to account for the different pyrene contents of the PyLLPs [7; 9]. So far, the trends obtained with \(<\)k\({}^{\text{Mrf}}\)\(>\)blob on LRPCDs have been found to match closely those expected from the glass transition temperatures (\(T_{\text{g}}\)) of polymers in the bulk [7; 9]. For instance, polystyrene (PS) and poly(methyl methacrylate) (PMMA), which share similar \(T_{\text{g}}\) values of about 100 \({}^{\circ}\)C, also have similar \(<\)k\({}^{\text{Mrf}}\)\(>\)blob values, namely 0.43 and 0.41 ns\({}^{-1}\) for PS and PMMA, respectively, in tetrahydrofuran (THF) at 22 \({}^{\circ}\)C. Poly(methyl acrylate) (PMA), being much less sterically hindered than PMMA, has a much lower \(T_{\text{g}}\) (10 \({}^{\circ}\)C) and a \(<\)k\({}^{\text{Mrf}}\)\(>\)blob value (0.88 ns\({}^{-1}\)) that is twice that of PMMA.