Phosphorescence

Figure 5: Phosphorescence

First, let's distinguish phosphorescence from fluorescence. A fluorescent paint glows under a UV lamp, but stops glowing as soon as the lamp is turned off. A phosphorescent paint keeps glowing for a while.

Phosphorescent substances have the ability to store up light and release it gradually. The notion of a metastable state explains this. If the molecules of the substance can get from the ground state to a metastable state, and if the metastable state can slowly decay back to the ground state via photon emission, then we have phosphorescence.

Typically, the metastable state is a triplet state, and the ground state is a singlet state. Ground state molecules absorb photons and go to excited singlet states (see figure 0). Most of them immediately hop right back to the ground state, emitting a photon, but non-radiative processes take a few to a less energetic triplet state. Once these molecules get to the lowest triplet state, they are stuck there, at least for a while. Some low probability process accomplishes the triplet-singlet conversion, and the molecules slowly leak out light.

What are the singlet-triplet and triplet-singlet processes? I mention one possibility of several. If the molecule contains two unpaired electrons, and each is subject to spin-orbit coupling-- but with different strengths-- then ${\bf s}_1$ and ${\bf s}_2$ will precess at different rates, and the magnitude of the combined vector ${\bf s}_1+{\bf s}_2$ will flip-flop between $S=0$ and $S=1$.

Complicating matters a little, the energy of a molecule consists of many parts. For example, the vibration and rotation of the ``nuclear framework'' stores energy. Suppose the excited singlet state is close in energy to a triplet state. After the molecule makes the singlet-triplet transition, it may shed energy into the environment through the vibrational modes (vibrational relaxation). Finally it arrives at the bottom triplet state. Eventually it decays back to the ground state via a triplet-singlet transition.

Both the singlet-triplet and triplet-singlet transitions violate the $\Delta S = 0$ selection rule. This rule applies absolutely only for pure electric dipole transitions, so the glow-in-the-dark T-shirts don't violate the laws of universe. Still, transitions that violate it are apt to be slow.

One last fact completes the explanation. A result of perturbation theory says that the probability of a transition between state $u_i$ and state $u_j$ is determined by two factors: the matrix element connecting the two states (the ``strength'' of the coupling), and the difference in energy levels. It is, in general, easier to make a transition when the energies are close together. Thus the singlet-triplet transition goes faster than the triplet-singlet transition.

© 2001 Michael Weiss

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