## 3 Results and Discussion
While the maxima of the PL spectra of both samples are located near 600 nm, the PL intensity of the MWS sample is about five-six times higher in the red-NIR spectral regions. The stronger PL of the MWS Gd-CNPs correlates with the stronger absorption in the visible spectral region (see Figure 2B). This fact can be explained by the higher density of the optically active states in the MWS Gd-CNPs. As for the PL QY of the latter under the used green laser excitation, it is estimated to be about 10 \(\pm\) 5%. Note, the observed red-NIR PL spectra of the prepared samples lie in the first optical-transparency window of biotissue [31] that is favorable for fluorescent bioimaging application of Gd-CNPs. It is interesting to note that the PL spectra of both types of Gd-CDs under green light excitation consist of the emission with photon energy above the excitation one. Because the PL excitation was carried out with the continuous wave (CW) light of relatively low intensity, one can rule out the two-photon absorption and other non-linear optical up-conversion processes. The anti-Stokes PL under low intensive CW excitation is well known for semiconductor nanocrystals, and it is explained by phonon-assisted absorption of exciting light [32]. The up-conversion PL excitation in Gd-CDs can be related to the absorption of vibrations of the carbon mesh, carbon-oxygen, and other functional groups that required further detailed studies. Figure 4 shows dependencies of the reciprocal values of the longitudinal (T\({}_{1}\)) and transverse (T\({}_{2}\)) proton relaxation times on Gd-concentration in aqueous suspensions of Gd-CNPs. The relaxation efficiencies, i.e., the longitudinal (r\({}_{1}\)) and transverse (r\({}_{2}\)) relaxivities, can be obtained from linear fits of the corresponding dependences on Cd concentration [19; 20; 21; 22; 23]. Considering the different initial Cd content in the samples prepared by MWS and HTS methods, the relaxivity dependences were obtained in the different titration degrees. It was found that the HTS-prepared sample exhibited larger values r\({}_{1}\) and r\({}_{2}\), which account for 42 and 70 mM\({}^{-1}\)s\({}^{-1}\), whereas the corresponding relativities for the MWS samples were about 8 and 13 mM\({}^{-1}\)s\({}^{-1}\), respectively. These differences may be attributed to the synthesis conditions, which are more temperature-controllable for the HTS process and promote desired coordination of Gd-ions on the surfaces of mostly amorphous CNPs to ensure more efficient  
Figure 3: (**A**) PL spectra of the MWS (red curve) and HTS (blue curve) Gd-CNPs under UV excitation (365 nm); the excitation line is indicated by black arrow. (**B**) PL spectra of the MWS (red curve) and HTS (blue curve) Gd-CNPs under excitation at 532 nm (indicated by black arrow). Insets show photographic images of quvetes with the MWS (right hand) and HTS (left hand) Gd-CNPs excited by the UV light and laser radiation at 532 nm, which are indicated by blue and green arrows, respectively. involvement of the formers in the shortening of the proton relaxation times. It means that the Gd-ions in the HTS samples with mostly amorphous CNPs are about five-times more efficient in the proton relaxation shortening than the same number of GD-ions in the MWS samples. It should be noticed that the longitudinal relaxivity of the HTS-prepared Gd-CNPs is several times higher than other results on similar Gd-doped CNPs [18; 19; 20; 21]. However, the observed relaxivity of our Gd-CNPs is four times smaller than that for 3 nm sized amorphous Cd-CDs prepared by HTS at 180 \({}^{\circ}\)C for 8 h, when the commercial CA, i.e., Gadovist\({}^{\circledR}\), was used as a precursor [22]. However, the corresponding Gd-CDs exhibited an exciting wavelength-independent green-yellow PL band centered at 500 nm [22], which did not correspond to the biotissue transparency window.