Knowledge Bank

Triplet-triplet annihilation in dilute mixed crystals of benzene containing $C6H6$ or $1,3,5-C6H3D3(\sim 0.2$ dissolved in $C6D6$ has been studied in detail as a function of temperature from $2\circ$ to $15\circ K$. Measurements have been made of the build up and decay kinetics as well as the steady-state intensities of phosphorescence and delayed fluorescence as a function of time, temperature, excitation intensity and wavelength, and guest concentration and trap depth. All observations on the two-component systems can be adequately explained on the basis of the following rate law: $d[T]dt=Roc-(k1+Ro)[T]-k2[T]2.$ Here [T] is the triplet state population, $k1$ and $k2$ are respectively the first- and second-order decay constants, $Ro$ is a factor proportional to the excitation intensity, and c is the guest concentration. Computer analysis of the phosphorescence decay as the sum of first- and second-order processes and measurements of the steady-state phosphorescence intensity as a function of temperature yield independent measurements of the first- and second-order rate constants. The second-order annihilation rates calculated by both methods agree very well and imply both a temperature activated and a large (20%) temperature independent annihilation process. It is both predicted and observed that with increasing the temperature from $8\circ$ to $12\circ K$ in these ultrapure crystals, the first-order decay constant increases by less than a factor of two while the second-order annihilation constant increases by five or more orders of magnitude!