## 3 Electron Spin-Dependent Processes in Si Nanocrystals
### Si NPs with Electron Spin Centers as Potential Contrast Agents for \({}^{1}h\) Mri
The both spectra have the effective \(g\)-factor of about 2.005, which can be explained by superposition of several types of Si DBs [96], for example, \(P_{\mathrm{b}}\)-centers with differently coordinated Si and O atoms [97, 98]. The number of Si DBs after TA increases due to thermally induced desorption of hydrogen from the internal surface of \(\mu\)Psi. Despite the concentration of DBs after TA increased by a factor of 10, the \(T_{2}\) relaxation time decreases only by 3 times (Figure 38b). This discrepancy can be explained by a partial passivation of Si DBs by water molecules [96]. While TA in vacuum can induce a lot of new DBs in por-Si [77], the DB concentration decreases strongly in MPSi after thermal oxidation (TO) in air at 900 \({}^{\circ}\)C. This effect is explained by passivation of Si DBs due to formation of a thin layer of the thermal oxide [96]. The transverse proton relaxation rate induced by Si NPs can be defined as follows [96]:  
\[R_{2}\equiv\left(T_{2}^{NP}\right)^{-1}\ =\ \left(T_{2}\right)^{-1}-\left(T_{2}^{W }\right)^{-1}, \tag{22}\]  
where \(T_{2}^{NP}\) is the time of transverse relaxation due to the presence of NPs, \(T_{2}\) is the measured transverse relaxation time and \(T_{2}^{W}\) is the transverse relaxation time in pure water. Figure 39 shows that \(R_{2}\) depends almost linearly on concentration of as-prepared MPSi NPs and those after TO. The latter NPs are characterized by nearly 3 times lower concentration of paramagnetic centers in comparison to the as-prepared ones (see Table 1), what causes 3 times lower \(R_{2}\) in the whole range of the NP concentration (see Figure 39). This fact indicates that both types of NPs do not aggregate in highly concentrated suspensions and the pores are still open to ensure access of water molecules. Si NP based CAs can be characterized by their specific relaxation efficiency, that is, relaxivity, which is defined as the change in relaxation rate after addition of CAs, divided to the concentration of NPs [95, 96]. The transverse proton relaxivity can be given by the following expression:  
\[r_{2}\ \ =\ R_{2}/C_{NP}, \tag{23}\]  
where \(R_{2}\) is the proton relaxation rate governed by Si NPs, \(C_{NP}\) is the concentration of NPs in suspensions. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Number of Electron** & \multicolumn{2}{c}{**\({}^{\mathbf{1}}\)H relaxation Times**} \\ \cline{2-4}  & **Spin Centers (1/g)** & \(T_{1}\) **(s)** & \(T_{2}\) **(s)** \\ \hline
**Crystalline Si (c-Si) NPs** & 2\(\cdot 10^{16}\) & 3.6 \(\pm\) 0.2 & 2.7 \(\pm\) 0.2 \\ \hline Thermally oxidized & & & \\ meso porous Si & 3\(\cdot 10^{14}\) & 3.5 \(\pm\) 0.2 & 2.5\(\pm\) 0.2 \\ (TO MPSi) NPs & & & \\ Mesoporous Si & \(10^{15}\) & 3.6 \(\pm\) 0.2 & 2.3 \(\pm\) 0.2 \\ (MPSi) NPs & \(10^{16}\) & 3.1 \(\pm\) 0.2 & 1.7 \(\pm\) 0.2 \\ Microporous Si NPs after & & & \\ thermal annealing in & \(10^{17}\) & 2.7 \(\pm\) 0.2 & 1.2\(\pm\) 0.2 \\ vacuum & & & \\ (TA \(\mu\)PSi) & & & \\ Water & 0 & 4.0 \(\pm\) 0.1 & 2.7 \(\pm\) 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Electron spin concentration for several types of Si NPs and proton relaxation times \(T_{1}\) and \(T_{2}\) in aqueous suspensions with NP concentration of 1 g/L and for pure water, for comparison. (Reprinted from Reference [96] by permission from John Wiley and Sons © 2018). The transverse relaxativity \(r_{2}\approx 0.5\) L/(gs) was determined for \(\mu\)Psi NPs after TA that resulted in the large number of electron spin centers -10\({}^{17}\) g\({}^{-1}\)[96]. The corresponding maximal relaxivity normalized on the number of Si atoms in NPs is about 0.01 L/(mMs) that is smaller than for the standard CAs based on Gd\({}^{3+}\) ions, which is about 4-6 L/(mMs) [99]. Note, the relaxivity of superparamagnetic iron oxide NPs is reported to be up to 10\({}^{2}\)-10\({}^{3}\) L/(mMs) [100]. However, specially designed porous Si NPs with required number of electron spin centers seem to be considered as potential CAs for biomedical application in MRI [96].