Dynamical Effects in Triplet ESR Spectra of Solid Solutions. II. Correlation of the Rate of Intermolecular Triplet Excitation Transfer with the Line Shape of the ESR Spectrum of a Solution of Aromatic Phosphorescent Hydrocarbons in a Rigid Matrix

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Abstract
The stochastic theory of resonance absorption, as formulated by Anderson, is used to simulate the effect of excitation transfer observed by de Groot and van der Waals in the ESR spectra of a number of aromatic hydrocarbons excited to the lowest triplet state in a glassy solution. The single‐transition correlation function φ(t) of Anderson is modified to include the important nonsecular contribution of the dipolar interaction. In a ``three‐site'' case, the latter approximation reduces a 9×9 matrix to a 3×3 matrix problem and allows actual calculations. ``Δm=1'' and ``Δm=2'' line shapes of an assembly of randomly oriented molecules of tribenzotriptycene are calculated for a set of transfer rates from 0 to 1011 sec−1. These simulations are in good agreement with the experimental ESR spectra recorded at 77° and at 20°K and allow a fair derivation of the transfer rate vs temperature. The absorption formular in a ``three‐site'' case has been fitted into a computer program, the input data being the zero‐field splitting constants, the angles characterizing the mutual orientation of the sites and the triplet‐excitation transfer rate k.

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