General Considerations of Phosphorescence Yield

The long lifetime has important consequences on the decay rates. First, we consider what affects the nonradiative rates (knr) which change the yields of fluorescence and phosphorescence. The nonradiative decay rate is often enhanced in molecules which have flexible constituents (the so-called loose-bolt effect). Therefore, both fluorescence and phosphorescence yields are generally larger for rigid molecules than flexible molecules. For the same reason, a rigid environment will increase the emission yields hence both fluorescence and phosphorescence yields often increase with increasing viscosity. 

The long lifetime also has important consequences for the effect of specific quenching between the chromophore and surrounding quenching species. The probability of bimolecular collisions is related to the duration of the excited state. The triplet excited state molecule is more susceptible than the singlet excited molecule to quenching simply because it has more time to interact with the surroundings. 

The intersystem crossing process has opposite effects on the yields of fluorescence and phosphorescence since it depletes the singlet state and populates the triplet state. It is commonly known that heavy ions, such as iodide and bromide, increase intersystem crossing by spin-orbit coupling.(1617) For proteins, fluorescence can be quenched as phosphorescence yield is enhanced. 8,19) However, although the phosphorescence yield is increased, the lifetime is decreased. This effect arises because spin-orbit coupling, which increases the intersystem crossing rate from 5, to Tt, also increases the conversion rate from T, to S0. 

Tryptophan at 77 K in rigid solution has a phosphorescence quantum yield of 0.17(20) and a lifetime of 6 s. These values at 77 K are relatively invariant from protein to protein and do not vary significantly between buried and exposed tryptophans.(21,22) If one assumes that the intersystem crossing yield is a constant, a calculation of the quantum yield of indole phosphorescence can be roughly estimated from the lifetimes. The phosphorescence yield is related to lifetime by 

A tryptophan with a lifetime of 1 s has a quantum yield of 3 x 10-2, and when the lifetime is 1 ms, then the quantum yield is 3x 10 s. 

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