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

## TL;DR

This paper introduces a new framework for designing luminescent nanothermometers using lanthanide ions, enabling precise temperature measurements in various applications.

## Contribution

The study provides a population-dynamics framework and a splitting factor to predict and design thermally coupled levels in luminescent nanothermometers.

## Key findings

- A stability criterion for robust thermal coupling is established when the nearest lower level lies beyond 2ΔE.
- A splitting factor correlates macroscopic sensitivity with microscopic chemical bond parameters for predictive design.
- Ultrathin thermosensing patches achieved Sr up to 6.17% K−1 with high brightness for real-time temperature mapping.

## Abstract

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 (Sr) 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 Sr with microscopic chemical bond parameters. Leveraging two TCLs pairs, we further demonstrate ultrathin, flexible thermosensing patches with high brightness and Sr 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.