## 3 Results and Discussion
Table S1 summarizes the results of our BI analyses. Figure 4: \({}^{1}\)H NMR (600 MHz, CDCl\({}_{3}\)) spectra of the polymerization products formed in a single solvent at various temperatures (St/VBC/EBiB/CuBr/Bpy = 160/80/5/1/2; [St]\({}_{0}=3.5\) M). (**a**) In T (less-polar solvent); (**b**) In A (higher-polar solvent). Figure 7 presents the kinetic plot for the manipulations of the polymer topology as a result of increasing the solvent polarity. Again, we monitored the consumptions of St and VBC through GC analysis. After a 5-h reaction in T at 70 \({}^{\circ}\)C, we added an equal volume of A and continued the reaction for another 19 h. Figure 7a reveals ramped increases in the conversions of St and VBC upon increasing the solvent polarity, to approximately 35% and 66%, respectively. Figure 7b displays the progress in the molecular evolution and broad molecular weight distributions (\(D=1.43\)-\(1.60\)) of samples (1)-(3) in Figure 7a. Figure S3 displays the conversions in two sets of one-pot reactions for the manipulation of the polymer topology. Figure S3a (from T/1 h to 50T50A/+23 h) reveals conversions of St and VBC of approximately 43% and 66%, respectively, after the additional reaction time; in contrast, Figure S3b (from T/24 h to 50T50A/+24 h) reveals almost no changes in the conversions of St (_ca._ 35%) and VBC (_ca._ 62%). These results also suggest that the first stage of the reaction should proceed for a  
Figure 5: **(a)** Kinetic plot of conversion _vs._ time and **(b)** gel permeation chromatography (GPC) traces (eluent: THF) of one-pot reaction performed at various temperatures (St/VBC/EBiB/CuBr/Bpy = 160/80/5/1/2; [St]\({}_{0}\) = 3.5 M). Figure 6: \({}^{1}\)H NMR spectra (600 MHz, CDCl\({}_{3}\)) of branched polymers obtained at various reaction temperatures in one-pot (St/VBC/EBiB/CuBr/Bpy = 160/80/5/1/2; [St]\({}_{0}\) = 3.5 M). suitable period of time such that propagating radicals remain in the reaction medium to perform the catalyst phase transfer AT-SCVP procedure through the polarity change. We used \({}^{1}\)H NMR spectroscopy to analyze the microstructures of the resulting branched polymers in Figures 8 and S3. As revealed in Figure 8A-C, the FBs and BIs followed the order 8C \(>\) 8B \(>\) 8A, the same as that in the case of varying the temperature; nevertheless, here we obtained a higher FBs. Concerning the composition of the branched polymer, herein we classify poly(St-_co_-VBC) as an analogue of the hyperbranched polystyrene macroinitiator (hbPSt MI) ended with initiating sites. Thus, we employed the resulting hbPSt MI (\(M_{\mathrm{n}}=1700\); \(D=1.31\)) to synthesize hyperbranched core star polymers through typical chain extension procedures using ATRP. Figure 9a displays a pseudo-first-order kinetic plot for the chain extension of hbPSt MI using St in A at 100 \({}^{\circ}\)C (St/hbPSt/CuCl/CuCl\({}_{2}\)/PMDETA = 1.31\(\pm\)0.01). 200/1/0.9/0.1/1; [St]\({}_{0}\) = 4.3 M). The apparent rate constant had a moderate value (\(k_{\rm app}=1.17\times 10^{-5}\) s\({}^{-1}\)). In Figure 9b, we observe an evolution of the molecular weight (MW) in the GPC traces during chain extension. However, the initiation efficiency was 0.71 based on the molecular weight at 20 h. The GPC traces reveal tailing toward low-MW presumably because of the occurrence of side reactions (e.g., radical termination or Mayo thermal reaction) that result in losing the integrity of the chain end. The products with low-MW were readily removed through further precipitation in MeOH/H\({}_{2}\)O. Using the approach, we obtained an hbPSt-\(g\)-PSt hyperbranched core star polymer (\(M_{\rm n}\) = 25,000; \(D\) = 1.77). We also examined chain extension of hbPSt MI using \(t\)BA. Again, we observed a pseudo-first-order kinetic plot (Figure 10a) for the chain extension of hbPSt MI with \(t\)BA in A at 100 \({}^{\circ}\)C (\(t\)BA/hbPSt/CuCl/CuCl\({}_{2}\)/PMDETA = 200/1/1/0.1/1.1; [\(t\)BA]\({}_{0}\) = 3.5 M).