Kinetics of photon upconversion by triplet–triplet annihilation: a comprehensive tutorial

This perspective article provides a comprehensive but organized tutorial introduction of the kinetics related to photon upconversion (UC) by triplet–triplet annihilation (TTA) (TTA-UC). The field of TTA-UC is multi-disciplinary and rapidly growing with the involvement of researchers from diverse backgrounds. TTA-UC consists of a series of tangled photophysical processes, so a solid understanding of the kinetic features and consequences is important to develop and evaluate materials for TTA-UC. This tutorial starts with an introduction of the standard model of TTA-UC along with the assumptions used in the model. The essential concept of the spin statistics for TTA and how this concept is related to the singlet branching ratio, which directly affects the efficiency of UC, are then explained through step-by-step analyses. Using these foundations, solutions for the steady-state behaviors are derived, featuring the universal curve that describes the excitation intensity dependence of the UC quantum yield for any sample type. Various useful functions for analyzing experimental data are also introduced and summarized. The transient behaviors of TTA-UC are then discussed along with their equations, and the usefulness for analyzing transient experimental data is explained using examples. In this article, self-consistent derivations and relevant references are provided for an easy understanding of the advanced discussion and analyses.