Q7(a). Stokes shift; why phosphorescence is slow

Introduction. After a molecule absorbs light it loses part of the energy before (or instead of) emitting. Emitted light therefore has lower energy, longer wavelength than the exciting light (Stokes shift). The routes are best followed on a Jablonski diagram.

(i) Phenomena causing the shift

1. Vibrational relaxation: absorption reaches upper vibrational levels of S₁ (Franck–Condon); collisions remove this energy in about 10⁻¹² s.
2. Internal conversion S₂→ S₁ (Kasha's rule): emission comes only from the lowest level of S₁, whatever was excited.
3. Emission ends in upper vibrational levels of S₀: the band is the mirror image of absorption, at lower energy.

Figure: Jablonski diagram: A absorption, IC/VR non-radiative loss, F fluorescence, ISC intersystem crossing, P phosphorescence.

1. Solvent relaxation: polar solvent molecules reorient round the more polar excited state and lower its energy before emission.
2. Intersystem crossing to T₁, which lies below S₁ (Hund's rule): phosphorescence is at even longer wavelength.
3. Excited-state reactions that give a new emitter of lower energy: excimers and exciplexes (pyrene excimer emits at about 480 nm against 380 nm for the monomer) and excited-state proton transfer.

(ii) Why phosphorescence is slower

Fluorescence is S₁→ S₀: the spins do not change, the transition is spin-allowed, and the radiative rate constant is about 10⁶–10⁹ s⁻¹ (lifetime nanoseconds). Phosphorescence is T₁→ S₀: an electron must reverse its spin, so the transition is spin-forbidden (Δ S≠0). It becomes weakly allowed only through spin–orbit coupling, which mixes a little singlet character into T₁. The radiative rate is therefore about 10⁻²–10⁴ s⁻¹, and lifetimes are from about 10⁻⁴ s to many seconds. Heavy atoms (Br, I) increase spin–orbit coupling and shorten phosphorescence lifetimes. Because the triplet lives so long, it is easily quenched by O₂ and by collisions, so phosphorescence is usually seen in rigid glasses at 77 K.

Conclusion. (i) Vibrational relaxation, internal conversion, emission to excited vibrational levels of S₀, solvent relaxation, intersystem crossing to the lower triplet and excimer/exciplex formation all make emission longer in wavelength than absorption. (ii) Phosphorescence is slow because T₁→ S₀ is spin-forbidden and is allowed only weakly through spin–orbit coupling.

Application. The Stokes shift lets fluorescence be measured against the scattered exciting light (fluorescence microscopy, fluorescent brighteners in detergents); long phosphorescence lifetimes are used in OLED emitters containing iridium and in oxygen sensors.