Toward accurate measurement of the intrinsic quantum yield of lanthanide complexes with back energy transfer

Trivalent lanthanide complexes are an important class of luminescent material characterized by their strong absorption of light by the organic ligands and subsequent energy transfer to the lanthanide ion, realizing intense luminescence from the ion. With this mechanism of luminescence, the total quantum yield of a lanthanide complex is the product of the energy transfer efficiency from the ligand to the lanthanide ion and the "intrinsic" quantum yield of the lanthanide ion itself. The "absolute" method in measuring the quantum yield uses an integrating sphere, and this method can be used for measuring both the total and the intrinsic quantum yields. The presence of back energy transfer (the reverse process of energy transfer) adds complication to this by affecting both the dynamics of the excited state of the ligands and the lanthanide ion. Herein, we theoretically derive an equation that shows that in the presence of back energy transfer the intrinsic quantum yield may differ depending on whether it is determined from the measurement through excitation of the ligands or the lanthanide directly. The value measured by direct lanthanide excitation could decrease to 20% or less of the actual value when back energy transfer is prominent. Several previously reported Tb(iii) complexes are within the range to be cautious. This report shows that the "absolute" method for measuring the lanthanide ion-centered quantum yield may not be suitable in the presence of back energy transfer by principle. We also provide a possible workaround in the case that several approximations and assumptions can be made.