“…To solve for k 0 and β, we numerically fit the Stern-Volmer curve based on the methods described in the literature. 26,37–41 Briefly, the fluorescence decay signal, I ( t ), is described as:
where τ 0 is the intrinsic fluorescence lifetime of the fluorophore, is the bulk concentration of the quencher, and time-dependent quenching rate, k ( t ), is calculated based on the following equation:
where C Q ( r , t ) is the quencher concentration at a distance r and time t , which is governed by the rate of diffusion and the rate of quenching, given by:
A normalized concentration of quencher, y( r,t ) was defined to simplify the calculation:
Using appropriate initial conditions and boundary conditions,
…”