Utilização de equações de taxa no estudo das emissões de nanopartículas de niobato de sódio codopadas com Yb3+/Tm3+ para aplicações em nanotermometria

Abstract

Nanothermometry has emerged as a promising tool for disease detection, monitoring, and, in some cases, even treatment—particularly in the context of cancer. This technique enables high spatial resolution thermal mapping of biological tissues, including deep regions, thereby overcoming the limitations of conventional methods such as thermal cameras. Among the materials employed as thermal sensors, nanoparticles doped with rare-earth ions are particularly suitable due to their optical temperature sensitivity, biocompatibility, and stability. To understand and predict the behavior of these luminescent systems in nanothermometry applications, theoretical modeling based on rate equations provides an effective approach. Such modeling allows for the simulation of population dynamics across different energy levels, estimation of optical parameters, and assessment of thermal responses without the need for direct experimentation, thus reducing both costs and laboratory efforts. This work aimed to employ rate equations and computational simulations, conducted using the GNU Octave software, to study the optical emissions of sodium niobate nanoparticles doped with rare-earth ions, with a focus on nanothermometry applications. Three configurations were analyzed: samples doped only with trivalent thulium; codoped with ytterbium and thulium at low thulium concentration; and codoped with ytterbium and thulium at high thulium concentration. The simulation results were compared with experimental data available in the literature and obtained by members of the GNFI research group. Overall, good agreement between theory and experiment was observed, particularly for intermediate values of the thermal coupling parameter. In one case, however, a noticeable discrepancy indicated the need to incorporate additional terms into the rate equations. The findings of this study reinforce the validity of computational modeling as a complementary tool to experimentation, contributing to the advancement of luminescent nanothermometers for biomedical diagnostics.