## 5 Conclusions  
In summary, surface-coating ligand plays an important role in relaxometric and MRI properties of Gd\({}_{2}\)O\({}_{3}\) nanoparticles. The PASA has not been used as a surface-coating ligand of Gd\({}_{2}\)O\({}_{3}\) nanoparticles and thus, was investigated here. PASA-coated ultrasmall Gd\({}_{2}\)O\({}_{3}\) nanoparticles were synthesized using the one-pot polyol method and their relaxometric and imaging properties in MRI were investigated. The PASA-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles were ultrasmall with a d\({}_{\rm avg}\) of 2.0 \(\pm\) 0.1 nm and exhibited good biocompatibility up to 500 uM Gd as determined from cellular cytotoxicity tests. The PASA-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles were paramagnetic and exhibited r\({}_{1}\) = 19.1 \(\pm\) 0.1 s\({}^{-1}\)mM\({}^{-1}\) and r\({}_{2}\) = 53.7 \(\pm\) 0.1 s\({}^{-1}\)mM\({}^{-1}\), which are higher than those of commercial Gd-chelates. Due to an appreciable r\({}_{2}\)/r\({}_{1}\) ratio of 2.80, the PASA-coated ultrasmall Gd\({}_{2}\)O\({}_{3}\) nanoparticles exhibited both in vivo T\({}_{1}\) and T\({}_{2}\) MR  
Figure 10: Plot of r\({}_{2}\)/r\({}_{1}\) ratio of polymer-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles dispersed in aqueous media as a function of COO\({}^{-}\) group weight percentage of polymers (polymer = PASA, PMVEMA, PAA, and PAAMA).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{d}_{\rm avg}\) (nm)} & \multirow{2}{*}{**Polymer**} & \multicolumn{2}{c}{**CO\({}_{2}\)\({}^{-}\) Group Weight**} & \multicolumn{2}{c}{**Temperature**} & \multicolumn{1}{c}{**Applied Field**} & \multicolumn{1}{c}{**r\({}_{1}\) (s\({}^{-1}\)mM\({}^{-1}\))**} & \multicolumn{1}{c}{**r\({}_{2}\)/r\({}_{1}\)**} & \multicolumn{1}{c}{**Ref.**} \\  & & **Percent** & **(20 °C)** & **(T)** & **(T)** & **(T)** \\ \hline
2.0 & PASA (9900 Amu) & 38.6 & 22 & 3.0 & 19.1 & 2.80 & This Study \\
2.0 & PAA (5100 Amu) & 62.0 & 22 & 1.5 & 31.0 & 1.2 & [34] \\
1.8 & PAAMA (3000 Amu) & 71.4 & 22 & 3.0 & 40.6 & 1.56 & [35] \\
1.9 & PMVEMA (80,000 Amu) & 51.2 & 22 & 3.0 & 36.2 & 2.0 & [36] \\ \hline \hline \end{tabular} PAA = polyacrylic acid; PAAMA = polyacrylic acid-co-maleić acid; PMVEMA = polymethyl vinyl ether-alt-maleić acid.  
\end{table}
Table 3: r\({}_{1}\) and r\({}_{2}\) values of various polymer-coated Gd\({}_{2}\)O\({}_{3}\) nanoparticles.  
images in mice. 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 which provide appreciable r\({}_{2}\)/r\({}_{1}\) ratios.  
Methodology, S.M. and H.Y.; conceptualization, S.M.; formal analysis, S.M., H.Y., A.G., S.L.H., S.L., T.T., M.Y.A., A.K.A.A.S., D.Z. and Y.L.; investigation, S.M., H.Y., J.A.P., S.K., H.C. and K.-S.C.; data curation, S.M., H.Y., J.A.P., S.K., H.C. and K.-S.C.; writing--original draft preparation, S.M.; writing--review and editing, G.H.L.; supervision, G.H.L. and Y.C.; funding acquisition, G.H.L., Y.C. and J.A.P. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Basic Science Research Program of the National Research Foundation (NRF) funded by the Ministry of Education, Science, and Technology (No. 2016 RID1A3B01007622 to GHL and 2020R1A2C2008060 to YC), the Korea government (Ministry of Science, and Information and Communications Technology: MSIT) (No. 2021R1A4A1029433), and by a grant of the KIRAMS funded by MSIT (No. 50461-2021).  
The in vivo animal imaging experiments were conducted according to the rules and regulation of the animal research committee of the Korea Institute of Radiological and Medical Sciences (approval number: Kirams2018-0072 and approval date: 9 January 2019).  
Not applicable.  
The data presented in this study are available on request from the corresponding authors.  
The XRD machine belongs to the Korea Basic Science Institute.  
The authors declare no conflict of interest.