Kinetics of Energy Transfer from the Triplet State in Rigid Solutions

Assuming the energy transfer is dependent on the inverse nth power of the donor—acceptor distance (1/Rⁿ), Inokuti and Hirayama derived an expression for the observed decay of donor emission, using flash excitation of a random solid solution, ${\mathrm{I=I}}_0\exp {\text{[−t/τ−(2/π}}^{\text{1/2}}{\text{)Γ(1−3/n)γ(t/τ)}}^{\text{3/n}}]$ , where τ is the measured lifetime in the absence of an acceptor, γ is linear in acceptor concentration, and n is the distance dependence parameter. This reduces to the Förster result for a dipole—dipole interaction where n=6. The extent to which we can determine n experimentally will allow us to measure the ``purity'' of the dipole—dipole interaction presumed to induce the transfer. To this effect, a detailed kinetic analysis of triplet—singlet energy transfer in rigid solution has been carried out using triphenylene‐d₁₂ as the donor and rhodamine B as the acceptor. A computer fit of the decay data to the above expression was carried out with a nonlinear regression routine that determined I₀, γ, and n simultaneously using the least‐squares criterion. Over the concentration range of γ=0.26 to 2.1, a value n=6.05±0.17 was determined, indicating no measurable derivation from the behavior predicted by Förster. In principle, this procedure could be used to identify a quadrupole transition in the acceptor, where a value of n=8 would signify a dipole—quadrupole interaction.