Dependence of the Fluorescent Lifetime τ on the Concentration at High Dilution

Abstract

Long-range interactions between electronically excited molecules and molecules at the ground state were found for distances of much more than 100 nm, as indicated by the dependence of the fluorescence lifetime on the concentration of dyes in diluted solutions. In contrast to this experimental result, the fluorescence lifetimes of distant isolated molecules should be independent from the concentration according to basic theory for light emission, such as that reported by Forster and Strickler−Berg. As a consequence, the theory of such emission should be modified for real systems to include electromagnetic interactions with distant resonating structures. Consequences of these findings concern many subjects, such as imaging methods (FLIM) in biochemistry.

Comment on “Dependence of the Fluorescent Lifetime τ on the Concentration at High Dilution”

“…Langhals and Schlücker recently reported a surprising dependence of the fluorescence lifetime on solute concentration at low concentrations where there was no evidence of chromophore aggregation . The lifetime of a perylene dye ( 1 ) with near-unity quantum yield in chloroform was found to decrease by about 25% on reducing the concentration from 22.6 to 0.108 μM, while the lifetime of Nile Blue in ethanol, which has a lower fluorescence quantum yield, was found to decrease by about 5% on reducing the concentration from 140 to 0.058 μM.…”

“…Figure compares the reported (Table 1 of ref ) and calculated 1/e decay times for three different excitation beam diameters, assuming a 90° detection geometry. All three plots show the expected lengthening of emission lifetime with increasing concentration, and the agreement between experiment and calculation is essentially quantitative for the 5 mm beam diameter.…”

“…The original paper provides no specific information about the excitation and detection geometry used in the experiments. However, it does mention that the samples were contained in 1 cm path length cuvettes.…”

“…The probability of an emitted photon being absorbed at the center of the cell (i.e., the center of the detection volume) is given by where σ T is the effective absorption cross section given by σ T = Θ 2303 ε max /N A , ε max is the maximum extinction, Θ is the overlap between the absorption and emission spectra, s = ( r 2 + Δ z 2 ) 1/2 , Δ z in a 1 cm cell is given by (0.5 – z). The product ε max Θ is the effective extinction coefficient for the emitted light; ref gives ε max = 88,000 M –1 cm –1 and Θ = 0.35 for structure 1 . As indicated in eq , the calculated decay depends on the relative fractions of molecules initially excited and those excited by emitted light, I 1 ( t ) and I 2 ( t ).…”

“…Concentration-dependent plots of total emission intensity of structure 1 of ref (black curves) and the fits to single-exponential decays (red curves) for assumed concentrations of 12 μM (left panel) and 24 μM (right panel) and an excitation beam diameter of 5 mm. The gray curves are the difference between the calculated intensities and the exponential fits.…”