Radiative decay rate fluorescence

Herein, F is the radiative decay rate and km is the nonradiative decay rate, which comes from quenching. It has been demonstrated that silica nanomatrixes can change the fluorescence quantum yield and lifetime of fluorophores. Several groups have reported that both quantum yield and lifetime of fluorophores increased in DDSNs [27, 28, 52, 65-67]. However, the mechanisms regarding this enhancement were reported differently. 

The geometry of the nanoscaled metals has an effect on the fluorescence enhancement. Theoretically, when the metal is introduced to the nanostructure, the total radiative decay rate will be written as T + rm, where Tm corresponds to the radiative decay rate close to the metal surface. So, (1) and (2) should be modified and the quantum yield and lifetime are represented as ... 

From the practical point of view, the radiative decay rate kr may be assumed to be independent of the external parameters surrounding the excited sensor molecule. Its value is determined by the intrinsic inability of the molecule to remain in the excited state. The radiative decay rate kr is a function of the unperturbed electronic configuration of the molecule. In summary, for a given luminescent molecule, its unperturbed fluorescent or phosphorescent decay rate (or lifetime) may be regarded to be only a function of the nature of the molecule. 

It is of interest to correlate the above results with experimental quantities such as the integrated quantum yield of fluorescence. The observed radiative decay rate of the excited molecule is given by... 

Here Wn is the average energy of the two fine structure levels. The real numerical coefficients a and b, where a2+b2=1, depend on the polarizations used in the excitation scheme, but are constant in time. Thus the relative amounts of d5/2 and d3/2 states do not change with time but simply decay together at the radiative decay rate T. However, the relative amounts of m character oscillate at the fine structure frequency, and this oscillation is manifested in any property which depends upon m, such as the fluorescence polarized in a particular direction, or the field ionization signal due to a particular value of m. This fact becomes more apparent... 

Level crossing spectroscopy has been used by Fredriksson and Svanberg44 to measure the fine structure intervals of several alkali atoms. Level crossing spectroscopy, the Hanle effect, and quantum beat spectroscopy are intimately related. In the above description of quantum beat spectroscopy we implicitly assumed the beat frequency to be high compared to the radiative decay rate T. We show schematically in Fig. 16.11(a) the fluorescent beat signals obtained by... 

When decay curves were analyzed using a biexponential function, the nonradiative decay rate tsnr 1 of the slow component was evaluated by subtracting the radiative decay rate from the slow fluorescence decay rate. Figure 10 shows... 

The fluorescence lifetimes (t determined at 580 nm) and quantum yields () of SRB were determined in water-dioxane mixtures and a series of alcohols at 25°C. The km value varied with the medium in the range of (4.1-0.7) x 10 s whereas the radiative decay rate constant (kr) was rather insensitive to the medium properties (2.8-1.7) X 10 s" . The relationship between In km and t(30) fall on a straight line and the slope value of the plot was 0.074 0.01. Therefore, the photophysical properties of SRB and Equation (20) are applicable to probing the polarity at a water/oil interface. 

In about 2000, my laboratory started to study the interactions of fluorophores with metallic nanoparticles, both solution-based and surface-immobilized. Our findings agreed with other workers whom had observed increases in fluorescence emission coupled with a decrease in the fluorophores radiative lifetime. Subsequently, we applied classical far-field fluorescence descriptions to these experimental observations, which ultimately suggested a modification in the fluorophores s intrinsic radiative decay rate, a rate thought to be mostly unchanged and only weakly dependent on external environmental factors. This simple description, coupled with what seemed like a limitless amount of applications led to a paper published by our laboratory in 2001 entitled Metal-Enhanced Fluorescence , or MEF, a term now widely used today almost a decade later. 

The non-radiative decay rate is as before (its spectral density is irrelevant here) and the total decay rate is therefore as before. The spectral density of the radiated (fluorescence) signal... 

To understand the importance of spectral overlap to metal-enhanced fluorescence, it is useful to review the basics of metal-enhanced fluorescence. Metal nanostructures can alter the apparent fluorescence from nearby fluorophores in two ways. First, metal nanoparticles can enhance the excitation rate of the nearby fluorophore, as the excitation rate is proportional to the electric field intensity that is increased by the local-field enhancement. Fluorophores in such "hot spots" absorb more light than in the absence of the metal nanoparticle. Second, metal nanoparticles can alter the radiative decay rate and nonradiative decay rate of the nearby fluorophore, thus changing both quantum yield and the lifetime of the emitting species. We can summarize the various effects of a nanoparticle on the apparent fluorescence intensity, Y p, of a nearby fluorophore as ... 

Gryczynski, L, et al. (2002) The CFS Engineers the Intrinsic Radiative Decay Rate of Low Quantum Yield Fluorophores. J Fluoresc 12 11-13. 

Several other studies (150-153) reported that metal surfaces were able to either enhance or suppress the radiative decay rates of fluorophores. Furthermore, an increase in the extent of resonance energy transfer was also observed. These effects might be due to the interactions of excited-state fluorophores with SPs, which in turn produce constructive effects on the fluorophore. The effects of metallic surfaces include fluorophore quenching at short distances ( 0-5 nm), spatial variation of the incident light field (-0-15 nm), and changes in the radiative decay rates (-0-20 nm) (64). The term of metal-enhanced fluorescence could be referred to the appplication of fluorophore and metal interactions in biomedical diagnosis (64). 

In addition to the field enhancement, the increases of the radiative decay rate of the molecule also lead to the fluorescence enhancement. This happens when molecules are S -20nm away from metal nanoparticies aggregated on surfaces [19-21]. Lakowicz and coworkers have characterized this phenomena by using silver island films deposited on the internal surface of two quartz plates which sandwich a bulk fluorophore solution [20]. The fluorophores are physically placed close to silver islands so that there are a range of distances between the fluorophore and metal. The fluorescence enhancement is accompanied by decreased lifetimes and increased photostability. This phenomenon shows that the silver island increases the radiative decay rate of the fluorophore and therefore induces the fluorescence enhancement. 

Experimentally, the total decay rate is obtained by following the time evolution of the fluorescence, that is counting the total number of photons emitted per unit time. Let be the total radiative decay rate out of the state 5),... 

When the predissociation rate is so much larger than the radiative decay rate that the fluorescence quantum yield is too low to measure a radiative decay rate directly, it is possible to infer the decay rate of the parent molecule from the effect of a static magnetic field on the polarization of a photofragment (Buijsse and van der Zande, 1997). 

---