## 2 Results  
**Optical and structural characterization of Fe\({}_{3}\)O\({}_{4}\) NPs. ** Structural characterization of the Fe\({}_{3}\)O\({}_{4}\) NPs--purchased commercially--were done to verify the specification provided by the manufacturer and also predict the optical absorption coefficient. X-ray diffraction spectra of the Fe\({}_{3}\)O\({}_{4}\) NPsrevealed the presence of peaks at 2\(\theta\) = 31.5\({}^{\circ}\), 35.8\({}^{\circ}\), 38.35\({}^{\circ}\), 42.75\({}^{\circ}\), 47.2\({}^{\circ}\), 54.04\({}^{\circ}\), 57.24\({}^{\circ}\), and 62.75\({}^{\circ}\) (Figure 1a). The observed peaks correspond to diffraction planes: (220), (311), (222), (400), (110), (422), (511), and (440), which have been attributable to cubic spinel phase of Fe\({}_{3}\)O\({}_{4}\) (space group, _Fd-3m_, JCPDS-#19-0629). Since no other prominent phase was detected, the result implied that the NPs are essentially crystalline Fe\({}_{3}\)O\({}_{4}\). Transmission electron method (TEM) confirmed the morphology of the NPs to be spherical (with agglomerations) and size distribution to be between 15 and 20 nm in diameter as indicated by the manufacturer (Figure 1b). The agglomeration revealed in the TEM image have been attributed to dipolar coupling between the NPs [22; 23]. For any NP, its NIR photothermal effects are controlled by their NIR optical absorbance. UV-vis-NIR spectra of the NPs showed an extended optical absorption that slowly increased in the NIR region relative to the visible light region (Figure 1c). The absorbance intensity at 810 nm increased linearly with concentration, from 0.35 ([Fe\({}_{3}\)O\({}_{4}\)] = 6 mM) to 1.51 ([Fe\({}_{3}\)O\({}_{4}\)] = 24 mM) (Figure 1d). The absorbance band in the NIR region of UV-vis-NIR optical spectra is consistent with the results in the literature and has been attributed to multiple charge (electron) transfer [24]. Furthermore, the linear increase of absorbance for the range of concentration tested in this work has been previously reported elsewhere [19; 25]. [PERSON] and co-workers [25] showed that saturation starts occurring at high concentration (100 mM, absorbance values \(>\) 3 at 808 nm). In an effort to translate the experimentally measured photothermal heat generation capabilities of the Fe\({}_{3}\)O\({}_{4}\) NPs tested in this study, we followed the flow-chart shown in Figure 1e to obtain the extinction cross sections of the MNPs, which was then used in Equation (2) to predict absorbance, \(A_{\text{pred}}\). The validity of \(A_{\text{pred}}\) was tested by evaluating its agreement with the experimentally measured absorbance, \(A_{\text{exp}}\), for the different concentrations of Fe\({}_{3}\)O\({}_{4}\) (6, 12, 24 mM). We observed that the predictions agreed reasonably well with experiments to within 2% for all concentrations when the sample size, \(n\), in Equation (5) was equal to 5 (see Figure 1f). **Photothermal effects of Fe\({}_{3}\)O\({}_{4}\) NPs. ** The influence of laser power (\(P_{0}=0.5\) and 1.0 W) and NP concentration ([Fe\({}_{3}\)O\({}_{4}\)] = 0-24 mM) on photothermal effects was accessed in aqueous solution (deionized water) to quantify their heat generation capabilities under an irradiation duration of 5 min. Pure  
Figure 1: Structural and optical characterization results. (**a**) X-ray diffraction spectra at a power of 45 kV \(\times\) 40 mA. (**b**) Transmission electron microscopy at magnification of 0.5 mm, Scale bar: 50 nm. Absorbance as a function of (**c**) wavelength (\(\lambda\)) and (**d**) concentration ([Fe\({}_{3}\)O\({}_{4}\)]) at \(\lambda=810\) nm. (**e**) Flow-chart for the comparison of theoretical predictions and experiment measurements. (**f**) Comparison of the \(A_{\text{pred}}\) and \(A_{\text{exp}}\) for different [Fe\({}_{3}\)O\({}_{4}\)] (6, 12, 24 mM). deionized water--containing no Fe\({}_{3}\)O\({}_{4}\) nanoparticles--was used as a control. The rate of change of the temporal curves increased with concentration at 5 min independent of the laser power that was used (Figure 2a,b).