Time-Resolved Rate Equation Analysis Disclose Kinetics Controlling Luminescence of Nanometer Tm-Upconverting Nanoparticles

Upconversion luminescence of lanthanide-based upconversion nanoparticles (UCNPs) is a nonlinear step-wise process in which the consecutive absorption of multiple, low-energy photons results in the subsequent emission of a high-energy photon. The primary upconversion mechanism is energy transfer upconversion (ETU) from a sensitizer (Yb³⁺) to an activator (Tm³⁺). It requires the absorption of several excitation low-energy photons by Yb³⁺, followed by the sequential energy transfer to Tm³⁺ions. Excited states relax to their ground states either radiatively by emitting a high-energy photon or non-radiatively by multiphonon relaxation through the crystalline host matrix. The time-resolved rise and decay luminescence curves of a set of five ultrasmall have been recorded under varying power near-infrared μs pulses. Six wavelengths have been used to monitor the evolution of the main Yb and Tm excited states. We use an average rate equations model to decipher the relationships between the compositional constraints and size of these ultrasmall UCNPs and the luminescence kinetic parameters. Several rate constants of ETU and other depopulation processes involving the multiple states of the Tm³⁺ energy scaffold have been retrieved from the simultaneous fit of the recorded curves. Their values have been interpreted by considering bulk and surface quenching, radiative and multi-phonon relaxations, and ion-to-ion hopping. Energy transfer between Yb³⁺ and Tm³⁺ is mainly occurring within neighbor atoms. The importance of mismatches on multiphonon relaxations, ETUs, and back-transfers has also been highlighted. For these numerical modeling, it appears that changing the composition and synthesis conditions with the aim to improve a single-specific parameter could remain a major challenge as this modification would automatically impact other properties with immediate consequences on UCNP dynamics.