## 2 Materials and Methods
### Fluorescence Decay Analysis  
The monomer and excimer fluorescence decays were fitted with, respectively, Equations (2) and (3) according to the model free analysis (MFA). The standard MFA of fluorescence decays acquired with polymers randomly labeled with pyrene assumes the existence of four pyrene species in solution. These pyrene species are those that form excimer by diffusive encounter with a ground-state pyrene (\(Py_{\text{diff}}\)*), that do not form excimer because they are located in sections of the polymer with low pyrene concentrations (i.e., they emit as if they were free in solution and with the natural lifetime \(\tau_{\text{M}}\) of the pyrenyl label (\(Py_{\text{free}}\)*)), and that are pre-associated with a ground-state pyrene to form a well-stacked (\(E\)0*) or poorly stacked (\(EL\)*) pyrene dimer that emits with a shorter (\(\tau_{E0}\)) or longer (\(\tau_{\text{EL}}\)) excimer lifetime, respectively. Equation (2) describes the diffusive encounters of the pyrene labels as a sum of exponentials and leads to the expression of the excimer given in Equation (3). The pre-exponential factors \(a_{\text{i}}\) are normalized to unity in Equation (2). More detailed explanations about the derivation of the MFA can be found in earlier reviews [6; 7]. \[\left[Py^{*}\right]_{(t)}=\left(\left[Py^{*}_{\text{diffEO}}\right]_{(t=0)}+ \left[Py^{*}_{\text{diffEO}}\right]_{(t=0)}\right)\times\sum\limits_{i=1}^{n} a_{i}\times\exp(-t/\tau_{\text{i}})+\left[Py^{*}_{\text{free}}\right]_{(t=0)} \times\exp(-t/\tau_{\text{M}}) \tag{2}\]  
\[\left[E*\right]_{(t)}=-\left[Py^{*}_{\text{diffEO}}\right]_{(t=0)}\times\sum \limits_{i=1}^{n}a_{i}\frac{\frac{1}{\tau_{\text{i}}}-\frac{1}{\tau_{\text{M }}}}{\frac{1}{\tau_{\text{i}}}-\frac{1}{\tau_{\text{M}}}}\,\exp(-t/\tau_{ \text{i}})\]  
\[+\left(\left[E0*\right]_{(t=0)}+\left[Py^{*}_{\text{diffEO}}\right]_{(t=0)} \times\sum\limits_{i=1}^{n}a_{i}\frac{\frac{1}{\tau_{\text{i}}}-\frac{1}{\tau_ {\text{M}}}}{\frac{1}{\tau_{\text{i}}}-\frac{1}{\tau_{\text{E0}}}}\right) \times\exp(-t/\tau_{\text{EL}}) \tag{3}\]  
The monomer and excimer decays were fitted globally with Equations (2) and (3). The parameters were optimized with the Marquardt-Levenberg algorithm [16]. The fits were considered acceptable when \(\chi^{2}\) values were <1.3 and residuals and autocorrelation of the residuals were randomly distributed around zero. The parameters retrieved from the MFA of the decays are listed in Tables S1-S3 of the Supplementary Materials file. The parameters retrieved from the MFA of the fluorescence decays with Equations (2) and (3) could be used to find the molar fractions of all pyrene species in solution. This derivation, which was complicated by the presence of pyrene-labeled ODMS and free 1-pyreneacetic acid in the solution, has been described in Supplementary Materials file. Also, the pre-exponential factors \(a_{\text{i}}\) and decay times \(\tau_{\text{i}}\) in Equation (2) could be employed to calculate the average rate constant <\(k\)> for pyrene excimer formation as shown in Equation (4). Within the MFA framework, <\(k\)> is a pseudo-unimolecular rate constant that depends on the local pyrene concentration. As such, it increases with the pyrene content of a PyLLP. The normalization of <\(k\)>, as shown in Equation (5), yields <\(k\)MF>blob, which has been shown to be independent of pyrene content and to reflect accurately the LRPCD for a broad range of polymer backbones. \[<k>=\frac{1}{\tau_{\text{M}}}-\frac{\sum\limits_{i=1}^{n}a_{\text{i}}}{\sum \limits_{i=1}^{n}a_{\text{i}}\tau_{\text{i}}} \tag{4}\]  
\[<k^{MF}>^{blob}=\frac{1-f_{\text{Mfree}}}{x}\times<k> \tag{5}\]  
The parameters retrieved from the MFA of the fluorescence decays could also be combined to yield an absolute measure of the ratio of the fluorescence intensity of the excimer to that of the monomer, \((I_{\text{E}}/I_{\text{M}})^{\text{TRF}}\) (Equation (6)).