## 3 Results and Discussion
### In Vitro Drug Release Kinetics  
An in vitro drug release study was conducted using a dialysis method at 37 \({}^{\circ}\)C, in phosphate-buffered saline (PBS), and at two different pH values (7.4 and 5.5). The slightly acidic environment (pH 5.5) was used to simulate the pH of endosomal or lysosomal microenvironments. As shown in Figure 7, the results demonstrate that the pH affected the DOX release rate from all four DOX-loaded unimolecular micelles investigated. The release rate was slower at pH 7.4, with total release after 50 h reaching 12, 14.4, and 19.7% for G2 PBG\({}_{15}\)-\(g\)-PEO/DOX (Figure 7a), G2 PBG\({}_{29}\)-\(g\)-PEO/DOX (Figure 7b) and G2 PBG\({}_{65}\)-\(g\)-PEO/DOX (Figure 7c), respectively, as compared with 17.7, 21.6 and 25.6% at pH 5.5. The relatively slower release at pH 7.4 is attributed to stronger hydrophobic interactions between the core of the nanocarriers and DOX. These results demonstrate that the DOX-loaded unimolecular micelles exhibit pH-dependent in vitro release behavior, whereby faster release of DOX takes place in an acidic environment (e.g., in endosomes/lysosomes) than at physiological pH (e.g., the bloodstream). The protonation of DOX in the acidic environment would also lead to higher aqueous solubility for DOX since this would weaken the hydrophobic interactions between the DOX and the core of the micelles, and thus enhance DOX release [(37; 38)]. This pH-dependent drug release behavior is highly desirable for drug delivery applications, as it should increase the efficacy of cancer therapy while minimizing undesirable side effects [(39; 40)]. For comparison, the release profile for free DOX is also presented (Figure 7e). The sustained release was observed for all the DOX-loaded micelles, in contrast to the burst release seen for free DOX in the absence of the copolymers. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**G2 PBG-\(g\)-PEO**} & \multicolumn{3}{c}{**G2 PBG-\(g\)-PEO/DOX**} \\ \cline{2-7}
**Copolymer** & **Size** & **PDI** & **Size** & **PDI** & **DLC (wt\%)** & **DLE** \\  & **(nm)** & **PDI** & **(nm)** & **PDI** & **DLC (wt\%)** & **(\%)** \\ \hline G1 PBG\({}_{15}\)-\(g\)-PEO/DOX & 16 & 0.41 & 17 & 0.38 & 8.3 \(\pm\) 0.3 & 50 \(\pm\) 2 \\ G1 PBG\({}_{29}\)-\(g\)-PEO/DOX & 17 & 0.51 & 17 & 0.54 & 7.1 \(\pm\) 0.2 & 42 \(\pm\) 3 \\ G1 PBG\({}_{65}\)-\(g\)-PEO/DOX & 19 & 0.43 & 20 & 0.44 & 7.4 \(\pm\) 0.2 & 44 \(\pm\) 4 \\ G2 PBG\({}_{15}\)-\(g\)-PEO/DOX & 35 & 0.28 & 37 & 0.49 & 10.8 \(\pm\) 0.2 & 65 \(\pm\) 3 \\ G2 PBG\({}_{29}\)-\(g\)-PEO/DOX & 34 & 0.26 & 35 & 0.51 & 10.1 \(\pm\) 0.2 & 60 \(\pm\) 3 \\ G2 PBG\({}_{65}\)-\(g\)-PEO/DOX & 39 & 0.17 & 41 & 0.47 & 10.3 \(\pm\) 0.3 & 62 \(\pm\) 3 \\ \hline \hline \end{tabular}  
* The data represent the mean \(\pm\) standard deviation (n = 3).  
\end{table} 
Table 3: Characterization of DOX-loaded unimolecular micelles. The drug release mechanism from unimolecular arborescent micelles is expected to be passive diffusion. It is generally recognized that the smaller the mean particle diameter, the shorter the diffusion path for drug release, and thereby the higher the release rate. The release rate of DOX at each pH was indeed slower for all the G2 PBG-\(g\)-PEO/DOX systems as compared with G1 PBG\({}_{29}\)-\(g\)-PEO/DOX. For example, the total amount of drug released from G2 PBG\({}_{29}\)-\(g\)-PEO/DOX (Figure 7b) after 50 h reached 14.4 and 21.6% at pH 7.4 and at pH 5.5, respectively, as compared with 30.5 and 34.9% from G1 PBG\({}_{29}\)-\(g\)-PEO/DOX (Figure 7d). This is a consequence of the larger hydrodynamic diameter of G2 PBG-\(g\)-PEO/DOX relative to G1 PBG-\(g\)-PEO/DOX, which increases the diffusion path for drug release, thus reducing the release rate. However, since the G2 PBG micelles used in the current investigation, all had comparable diameters, no correlation between the micelle diameter and the release rate was attempted.