## 3 Results
### Dls  
Intensity of scattered light vs. the hydrodynamic diameter curves measured for aqueous dispersions of the three kinds of sample are shown in Figure 3 and the results of the measurements are summarized in Table 3. \begin{table}
\begin{tabular}{l c c c c} \hline  & **\textless{}D\textgreater{} (nm)** & \(\sigma\) (nm) & \(\sigma\)/**\textless{}D\textgreater{}** & \(\mathbf{a_{0}}\) (nm) \\ \hline Bare NPs (sample A) & 8.8 \(\pm\) 0.7 & 3.1 \(\pm\) 0.4 & 0.35 \(\pm\) 0.07 & 0.837 \(\pm\) 0.001 \\ Sample B (Fe\({}_{3}\)O\({}_{4}\) NPs cit. ex situ) & 9.5 \(\pm\) 0.9 & 3.3 \(\pm\) 0.4 & 0.35 \(\pm\) 0.07 & 0.837 \(\pm\) 0.001 \\ Sample C (Fe\({}_{3}\)O\({}_{4}\) NPs cit. in situ) & 3.9 \(\pm\) 0.5 & 1.2 \(\pm\) 0.4 & 0.31 \(\pm\) 0.14 & 0.837 \(\pm\) 0.001 \\ \hline \end{tabular}
\end{table} 
Table 2: For samples A, B and C, the averages of <D> determined by the Scherrer, Williamson-Hall, Pielaszek and Rietveld methods, the averages of \(\sigma\) obtained by the Pielaszek and Rietveld procedures and the relative standard deviations, \(\sigma\)/<D>, are also shown. The averages of the \(\mathbf{a_{0}}\) values derived by using the Scherrer and Rietveld methods are reported. Figure 2: Solid line: domain size distributions of sample A, B and C obtained by the Pielaszek method. Dashed lines: fitting of the Gamma distribution functions with lognormal distributions. The sizes of the particles in these dispersions are much larger than that of the single NPs as determined by XRD analysis. This is an indication that bare NPs and those with adsorbed citrate form aggregates in diluted aqueous dispersions at neutral pH. The aggregates are larger for bare NPs than for the other samples. The effect of citrate adsorption can be seen on the longterm stability of the dispersions. For bare NPs, one week after preparation the intensity of the light scattered by the residual particles in the dispersions was so week that reliable DLS measurements could not be performed. This is the result of the formation of aggregates which grow in size and eventually sediment. For the samples B and C, the aggregation process of the particles present in the dispersions immediately after sonication is prevented by the citrate coating. As a result, one week after preparation, the majority of particles remains in the dispersions. The larger aggregates initially present sedimented and a decrease in the \(Z\)-average is observed (Figure 3, dashed lines and Table 3). These results can be explained taking into account the \(\zeta\)-potential values measured for the samples (Table 3). Due to adsorption of citrate anions, B and C NPs have a \(\zeta\)-potential which, in absolute value, is significantly larger than that of bare NPs and higher than 30 mV, the limiting value for particle dispersions to be stable against aggregation. Hence, for the citrate covered particles, the electrostatic repulsion between the negatively charged aggregates prevents their adhesion and growth. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Hydrodynamic Diameter (nm)** & **PDI** &
\begin{tabular}{c} \(\zeta\)**-Potential** \\ **(mV)** \\ \end{tabular} \\ \hline Sample A & 398 \(\pm\) 22 & 0.39 \(\pm\) 0.1 & 16 \(\pm\) 1 \\ (1 week after preparation) & - & - & - \\ Sample B & 194 \(\pm\) 6 & 0.29 \(\pm\) 0.06 & \(-58\pm\) 3 \\ (1 week after preparation) & 155 \(\pm\) 2 & 0.41 \(\pm\) 0.02 & \(-55\pm\) 2 \\ Sample C & 163 \(\pm\) 3 & 0.30 \(\pm\) 0.02 & \(-65\pm\) 5 \\ (1 week after preparation) & 136 \(\pm\) 3 & 0.12 \(\pm\) 0.02 & \(-71\pm\) 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the DLS and \(\zeta\)-potential measurements for the three kinds of samples. The hydrodynamic diameter (nm), the PDI and the \(\zeta\)-potential (mV) are reported. For the bare NPs one week after preparation DLS measurements could not be performed. For the other samples. The concentration of the dispersions was ca. 0.02 mg/mL for all samples and the pH 6.5.