Fluorescence efficiency equation

Equation (2) also shows how the intensity of fluorescence varies when the frequency of the exciting light varies. For a given solution the fluorescence intensity is proportional to 7oe0 and for many substances in solution the fluorescence efficiency () is approximately independent of the excitation frequency. Thus, if the intensity of exciting light is kept constant as the frequency is varied, the fluorescence intensity will be proportional to e, the molecular extinction coefficient of the solute. Hence the true excitation spectrum frequently corresponds closely to the absorption spectrum of the compound (see Fig. 2). Spectrofluorimetry can thus be used to measure the absorption spectra of fluorescent solutes, but at concentrations far lower than could be measured directly with an absorption spectrophotometer. It has the further advantage that the... 

Equation (4r>) for the ratio of the delayed fluorescence efficiencies of dimer and monomer at low concentrations of ground state (c) can be written in the following form ... 

In the presence of a quencher, Q, there is an additional rate process for relaxation. The ratio of the fluorescence efficiency in the absence of (( )f0) and the presence of a quencher is given by the Stem-Volmer equation.7 140... 

Other steps could be added. I is a molecule of isomer and it may revert to a normal molecule either by a first or second order homogeneous reaction or at the walls. The fluorescence efficiency would be given by the equation... 

The experimental conditions for the excitation and detection of all the species are listed in Table I along with the radiative lifetimes of the excited states. Under the narrow detection bandwidth conditions for these measurements the quench term is much greater than T 1 for the species studied and the fluorescence efficiency varies as x T1/2. Thus with fixed geometry, laser excitation wavelength, and detection parameters, the fluorescence intensity in Equation (1) simplifies to... 

From Equation 5.8, it can be seen that fluorescence intensity is related to the concentration of the analyte, the quantum efficiency, the intensity of the incident (source) radiation, and the absorptivity of the analyte. O is a property of the molecule, as is the absorptivity, a. A table of typical values of O for fluorescent molecules is given in Table 5.13. The absorptivity of the compound is related to the fluorescence intensity (Equation 5.8). Molecules like saturated hydrocarbons that do not absorb in the UV/VIS region do not fluoresce. 

Standardizing the Method Equations 10.32 and 10.33 show that the intensity of fluorescent or phosphorescent emission is proportional to the concentration of the photoluminescent species, provided that the absorbance of radiation from the excitation source (A = ebC) is less than approximately 0.01. Quantitative methods are usually standardized using a set of external standards. Calibration curves are linear over as much as four to six orders of magnitude for fluorescence and two to four orders of magnitude for phosphorescence. Calibration curves become nonlinear for high concentrations of the photoluminescent species at which the intensity of emission is given by equation 10.31. Nonlinearity also may be observed at low concentrations due to the presence of fluorescent or phosphorescent contaminants. As discussed earlier, the quantum efficiency for emission is sensitive to temperature and sample matrix, both of which must be controlled if external standards are to be used. In addition, emission intensity depends on the molar absorptivity of the photoluminescent species, which is sensitive to the sample matrix. 

A particular strength of Equation (7) is that the intensity ratio is formed between mea-surements of the same X-ray energy in both the unknown and standard. This procedure has significant advant es First, there is no need to know the spectrometer s efficiency, a value that is very difficult to calibrate absolutely, since it appears as a multiplicative factor in both terms and therefore cancels. Second, an exact knowledge of the inner shell ionization cross section or fluorescence yields is not needed, since they also cancel in the ratio. 

NAA is a quantitative method. Quantification can be performed by comparison to standards or by computation from basic principles (parametric analysis). A certified reference material specifically for trace impurities in silicon is not currently available. Since neutron and y rays are penetrating radiations (free from absorption problems, such as those found in X-ray fluorescence), matrix matching between the sample and the comparator standard is not critical. Biological trace impurities standards (e.g., the National Institute of Standards and Technology Standard Rference Material, SRM 1572 Citrus Leaves) can be used as reference materials. For the parametric analysis many instrumental fiictors, such as the neutron flux density and the efficiency of the detector, must be well known. The activation equation can be used to determine concentrations ... 

Quantitative aspects. The total fluorescence intensity, F, is given by the equation F = Ia(f> where Ia is the intensity of light absorption and 4>f the quantum efficiency of fluorescence. Since 70 = 7a + 7t where 70 = intensity of incident light and 7t = intensity of transmitted light, then... 

In order to clear up the mechanism of inactivation of excited states, we examined the processes of quenching of fluorescence and phosphorescence in PCSs by the additives of the donor and acceptor type253,2S5,2S6 Within the concentration range of 1 x 1CT4 — 1 x 10"3 mol/1, a linear relationship between the efficiency of fluorescence quenching [(/0//) — 1] and the quencher concentration was found. For the determination of quenching constants, the Stem-Volmer equation was used, viz. 

Let us now return to the question of how E-type and P-type delayed fluorescence may be used to determine the triplet energy level. The efficiency of E-type delayed fluorescence is given by the following equation ... 

In dynamic quenching (or diffusional quenching) the quenching species and the potentially fluorescent molecule react during the lifetime of the excited state of the latter. The efficiency of dynamic quenching depends upon the viscosity of the solution, the lifetime of the excited state (x ) of the luminescent species, and the concentration of the quencher [Q], This is summarized in the Stern-Volmer equation ... 

Combining the above equations, we can write a useful expression for the collected fluorescence from a distribution of dipoles in terms of the collection efficiency Q for a single dipole ... 

The intensity of delayed fluorescence was proportional to the square of the rate of absorption of exciting light and the general equation (67) for P-type delayed fluorescence can therefore be applied. If we consider only the 3 X 10-aM solution at temperatures of — 77 °C. and higher, where the proportion of dimer emission is low, and assume that the conversion of triplets to excited- and ground-state singlet is 100% efficient, i.e., kd/(k j + k 0 + kd) = 1, then... 

In our discussion above, it was pointed out that a molecule in the excited state can return to lower energy levels by collisional transfer or by light emission. Since these two processes are competitive, the fluorescence intensity of a fluorescing system depends on the relative importance of each process. The fluorescence intensity is often defined in terms of quantum yield, represented by (X This describes the efficiency or probability of the fluorescence process. By definition, XL is the ratio of the number of photons emitted to the number of photons absorbed (Equation 5.6). 

If the light emitted during the decay of F"j is still of a wavelength too short for efficient measurement by a PMT, a secondary fluor, F2, that accepts energy from F j may be added to the scintillation system. Equations 6.13 and 6.14 outline the continued energy transfer process and fluorescence of F2. 

In this equation, F is the observed fluorescence, quantum efficiency (see above), / is the intensity of the incident radiation, e is the molar absorptivity, b is the cell s path length, and c is the compound s molar concentration. 

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