Phosphorescence Kinetics of Singlet Oxygen Produced by Photosensitization in Spherical Nanoparticles. Part I. Theory.

The singlet oxygen produced by energy transfer between an excited photosensitizer (pts) and ground-state oxygen molecules plays a key role in photodynamic therapy. Different nanocarrier systems are extensively studied to promote targeted pts delivery in a host body. The phosphorescence kinetics of the singlet oxygen produced by the short laser pulse photosensitization of pts inside nanoparticles is influenced by singlet oxygen diffusion from the particles to the surrounding medium. Two theoretical models are presented in this work: a more complex numerical one and a simple analytical one. Both the models predict the time course of singlet oxygen concentration inside and outside of the spherical particles following short-pulse excitation of pts. On the basis of the comparison of the numerical and analytical results, a semiempirical analytical formula is derived to calculate the characteristic diffusion time of singlet oxygen from the nanoparticles to the surrounding solvent. The phosphorescence intensity of singlet oxygen produced in pts-loaded nanocarrier systems can be calculated as a linear combination of the two concentrations (inside and outside the particles), taking the different phosphorescence emission rate constants into account.