Time-Resolved Rate\nEquation Analysis Disclose Kinetics\nControlling Luminescence of Nanometer Tm-Upconverting Nanoparticles

Upconversion luminescence of lanthanide-based upconversion\nnanoparticles\n(UCNPs) is a nonlinear step-wise process in which the consecutive\nabsorption of multiple, low-energy photons results in the subsequent\nemission of a high-energy photon. The primary upconversion mechanism\nis energy transfer upconversion (ETU) from a sensitizer (Yb<sup>3+</sup>) to an activator (Tm<sup>3+</sup>). It requires the absorption of\nseveral excitation low-energy photons by Yb<sup>3+</sup>, followed\nby the sequential energy transfer to Tm<sup>3+</sup>ions. Excited\nstates relax to their ground states either radiatively by emitting\na high-energy photon or non-radiatively by multiphonon relaxation\nthrough the crystalline host matrix. The time-resolved rise and decay\nluminescence curves of a set of five ultrasmall have been recorded\nunder varying power near-infrared μs pulses. Six wavelengths\nhave been used to monitor the evolution of the main Yb and Tm excited\nstates. We use an average rate equations model to decipher the relationships\nbetween the compositional constraints and size of these ultrasmall\nUCNPs and the luminescence kinetic parameters. Several rate constants\nof ETU and other depopulation processes involving the multiple states\nof the Tm<sup>3+</sup> energy scaffold have been retrieved from the\nsimultaneous fit of the recorded curves. Their values have been interpreted\nby considering bulk and surface quenching, radiative and multi-phonon\nrelaxations, and ion-to-ion hopping. Energy transfer between Yb<sup>3+</sup> and Tm<sup>3+</sup> is mainly occurring within neighbor\natoms. The importance of mismatches on multiphonon relaxations, ETUs,\nand back-transfers has also been highlighted. For these numerical\nmodeling, it appears that changing the composition and synthesis conditions\nwith the aim to improve a single-specific parameter could remain a\nmajor challenge as this modification would automatically impact other\nproperties with immediate consequences on UCNP dynamics.