Analytical treatment of EPR spectra of weakly coupled spin-correlated radical pairs in disordered solids: Application to the charge-separated state in TiO₂ nanoparticles

An analytical treatment of spin-correlated radical pair EPR spectra for the general case of weakly coupled spins is presented. In contrast to the multiparametric computer simulation of these spin-polarized EPR spectra, the analytical treatment reveals the relationship and rules that clarify the physical interpretation of the spectra. The analytical treatment developed here is applied to an analysis of the spin-polarization pattern of time-resolved EPR spectra of TiO₂ nanoparticles, recorded with the light-modulation technique. It is shown that the experimental spectra are satisfactorily fitted within the model of spin-correlated radical pairs for which the S_o and T_o or T₊ and T_- levels are initially populated. Only a weak dipole-dipole interaction is required for spectral fitting. Computer simulation of the spectra allows for a determination of the range of distances between the trapped electron within the TiO₂ particle and the trapped hole on the surface of the particle.