Concentration-dependent fluorescence quenching and electron scavenging in liquids

We present a theory for the dependence of the fluorescence quenching lifetime τ on quencher concentration and the dependence of the electron-scavenger rate constant kf on scavenger concentration. At low quencher (scavenger) concentration these quantities are obtained by solution of the Smoluchowski–Debye diffusion equation. For nondilute quenchers we find positive deviations from the linear Stern–Volmer equation for 1/τ and for nondilute scavengers we find positive deviations from linear behavior in kf. With reactants that interact by a long range potential, such as charged fluorophores and quenchers, and electrons with charged scavengers, a length ã∼100–300 Å vs the collisional encounter length a ∼1–10 Å is the significant length. Corrections to dilute behavior are found to depend on the effective volume fraction of quenchers (or scavengers) φ̃=4π3ã3c/3 which can be much larger than the material volume fraction φ=4π3a3c/3 [c is the quencher (or scavenger) number density]. We consider both the initial value and steady state situations and find that, for our exact results, no transient behavior of the rate coefficient enters the initial value expression.