## 4 Discussion  
In this study, PASA-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles were synthesized via the one-pot polyol method and characterized with various techniques. Their relaxometric and MRI imaging properties were studied. Surface-coating ligands can affect r\({}_{1}\) and r\({}_{2}\) values of Gd\({}_{2}\)O\({}_{3}\) nanoparticles [16; 17]. The PASA has not been used as a surface-coating ligand and thus, was investigated here. The r\({}_{1}\) and r\({}_{2}\) values of PASA-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles were 19.1 and 53.7 s\({}^{-1}\)mM\({}^{-1}\), respectively, which are much higher than those [5; 6; 7] of commercial Gd-chelates. Interestingly, PASA-coated ultrasmall Gd\({}_{2}\)O\({}_{3}\) nanoparticles exhibited an appreciable r\({}_{2}\)/r\({}_{1}\) ratio of 2.80 and provided both T\({}_{1}\) and T\({}_{2}\) MR images. To explain this, we used the relationship between hydrophilicity of polymers and r\({}_{2}\)/r\({}_{1}\) ratio of polymer-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles using various polymer-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles studied here and previously [34; 35; 36]. As provided in Table 3, the r\({}_{2}\)/r\({}_{1}\) ratio of PASA-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles was higher than those [34; 35; 36] of the other hydrophilic polymer-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles. To understand this, the r\({}_{2}\)/r\({}_{1}\) ratio of various polymer-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles [34; 35; 36] was plotted as a function of COO\({}^{-}\) group weight percentage of polymers in Figure 10, showing that the r\({}_{2}\)/r\({}_{1}\) ratio generally decreased with increasing COO\({}^{-}\) group weight percentage of the polymers. In this plot, it was assumed that among hydrophilic groups of the polymers, the COO\({}^{-}\) group could most strongly attract water molecules around the Gd\({}_{2}\)O\({}_{3}\) nanoparticles through its negative charge and electronegative oxygens. Thus, other hydrophilic groups such as C\(-\)O, C\(=\)O, and NH were excluded from the hydrophilic group weight percentage of the polymers. This plot indicates that a more water-attracting (or more hydrophilic) polymer can provide the r\({}_{2}\)/r\({}_{1}\) ratio which is closer to one. This is because T\({}_{1}\) water-proton spin relaxation can be more strongly induced if more water molecules are attracted closer to the Gd\({}_{2}\)O\({}_{3}\) nanoparticles according to the inner-sphere model [5]. Under such conditions, the r\({}_{2}\)/r\({}_{1}\) ratio will be close to one; thus, contrast agents can efficiently act as T\({}_{1}\) MRI contrast agents. However, PASA has the lowest  
Figure 9: (**a**) T\({}_{1}\) and T\({}_{2}\) MR images of mice liver before (labeled as \"0\") and 5 and 15 min after intravenous injection of an aqueous solution of PASA-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles into mice tails, respectively (N\({}_{\text{mice}}\) = 2 for each modal imaging). (**b**) Plots of SNR-ROIs (labeled as dotted circles) as a function of time.  
COO\({}^{-}\) group weight percentage among the polymers (Table 3 and Figure 10) and thus, the lowest water-attracting power around the Gd\({}_{2}\)O\({}_{3}\) nanoparticles. Therefore, PASA-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles will most weakly induce T\({}_{1}\) water-proton spin relaxation among polymer-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles in Table 3. This explains the observed appreciable r\({}_{2}\)/r\({}_{1}\) ratio of 2.80 in this study, which is higher than those of the other hydrophilic polymer-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles in Table 3. Due to this, PASA-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles showed T\({}_{2}\) MR images as well as T\({}_{1}\) MR images, thus acting as a dual-modal T\({}_{1}\) and T\({}_{2}\) MRI contrast agent. This result indicates that dual-modal T\({}_{1}\) and T\({}_{2}\) MRI is possible through a proper choice of hydrophilic polymers as surface-coating ligands of Gd\({}_{2}\)O\({}_{3}\) nanoparticles with which the r\({}_{2}\)/r\({}_{1}\) ratio is appreciable.