Modeling the Effect of Core-Shell Structure on Upconverting Nanoparticle Emission Intensity

The phenomenon of upconversion is useful in many applications, such as biological imaging, due to its ability to produce light with greater energy than that of the incident photons. In order to design nanoparticles with maximum emission intensity, it would be useful to create accurate models of the upconversion phenomenon in a nanoparticle and run simulations while varying important reaction parameters. Prior models have been used to describe upconversion, but these models have focused on quenching of excited states at the surface. These models do not consider the migration of energy from the center of the nanoparticle to the surface, which significantly reduces the emission intensity from the nanoparticle. In this project, a reaction-diffusion mathematical model was used to model and simulate the photophysical processes that give rise to upconversion. The process of upconversion was represented by a “reaction”, while the process of energy migration in the nanoparticle was modeled as “diffusion”. MATLAB was used to simulate the model under varying parameters, using finite-element analysis to solve the partial differential equations. First, the accuracy of the model was tested using a simpler two-state ytterbium model with instantaneous surface reactions. The results obtained from the model were verified analytically. Next, these simple cases were simulated to determine the effect of surface reactions (which represent surface quenching of upconversion emission) on the concentration of excited states in the nanoparticle. Finally, a more complicated scenario (involving series reactions, which is more closely related to upconversion) was simulated with this model, using both a core model and active core-inactive shell model to determine whether the latter provided an enhancement in upconversion emission intensity. The simulation results demonstrate that the core-shell model provides a greater average concentration of the doubly excited state of Er³⁺ within the nanoparticle, which would result in a significant enhancement in the upconversion emission intensity from the nanoparticle.