Boltzmann luminescent nanothermometry: mechanistic criteria and predictive design of thermally coupled levels

Boltzmann-type luminescent nanothermometry using thermally coupled levels (TCLs) of lanthanide ions is promising for applications in nanotechnology, biomedicine, and aerospace. However, the fundamental rules governing TCLs formation and the reliable prediction of relative sensitivity (S_r) in specific hosts remain unclear. Here, we develop a population-dynamics framework that quantitatively defines the onset temperature and the thermal coupling window for Boltzmann behavior, dictated by nonradiative rates and the thermalization energy gap (ΔE). Mechanistic analysis reveals how adjacent levels disturb the balance between thermal population and multi-phonon relaxation, and establishes a practical stability criterion: robust coupling occurs when the nearest lower level lies beyond 2ΔE. To enable predictive thermometric design, we introduce a splitting factor that correlates macroscopic S_r with microscopic chemical bond parameters. Leveraging two TCLs pairs, we further demonstrate ultrathin, flexible thermosensing patches with high brightness and S_r up to 6.17% K^-1, enabling real-time in situ temperature mapping during reactions. This work provides physics-based guidelines for the rational design of high-precision luminescent nanothermometers.