Energy Transfer Networks within Upconverting Nanoparticles Are Complex Systems with Collective, Robust, and History-Dependent Dynamics
Applications of photon upconverting nanoparticles (UCNPs) in biological imaging and solar energy conversion demand that their anti-Stokes luminescence be both tunable and efficient. Rational design of more efficient UCNPs requires an understanding of energy transfer (ET) between their lanthanide dopants, dynamics that are typically characterized by measuring luminescence lifetimes. Existing knowledge, however, cannot explain basic observations in lifetime experiments, such as their dependence on excitation power, significantly limiting the generality and reliability of lifetime measurements. Here in this paper, we elucidate the origins of the ET dynamics and luminescence lifetimes of Yb 3+ -, Er 3+ -co-doped NaYF 4 UCNPs using time-resolved luminescence and novel applications of rate equations and stochastic simulations. Experiments and calculations consistently show that at high concentrations of Er 3+ , the luminescence lifetimes of UCNPs decrease as much as six-fold when excitation power densities are increased over 6 orders of magnitude. Since power-dependent lifetimes cannot be explained by intrinsic relaxation rates of individual transitions, we analyze lifetime data by treating each UCNP as a complex ET network. We find that UCNP ET networks exhibit four distinguishing characteristics of complex systems: collectivity, nonlinear feedback, robustness, and history dependence. We conclude that power-dependent lifetimes are the consequence of thousands of minor relaxation pathways that act collectively to depopulate and repopulate Er 3+ emitting levels. These ET pathways are dependent on past excitation power because they originate from excited donors and excited acceptors; however, each transition has an unexpectedly small impact on lifetimes due to negative feedback in the network. This robustness is determined by systematically “knocking out”, or disabling, ET transitions in kinetic models. Our classification of UCNP ET networks as complex systems explains why UCNP luminescence lifetimes do not match the intrinsic lifetimes of emitting states. In the future, UCNP networks may be engineered to rival the complexity of biological networks that pattern features with unmatched precision.