Relationship Between Fluorescence Intensity and Concentration

The intensity of fluorescence F is proportional to the amount of light absorbed by the analyte molecule. We know from Beer s law that 

A - A = amount of light absorbed, the fluorescence intensity, F, may be defined as 

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. 

The fluorescence intensity is directly proportional to the intensity of the source radiation, Iq. In theory, the fluorescence intensity will increase as the light source intensity increases, so very intense light sources such as lasers, mercury arc lamps, or xenon arc lamps are frequently used. There is a practical limit to the intensity of the source because some organic molecules are susceptible to photodecomposition. 

When the term abc is 0.05, which can be achieved at low concentrations of analyte, the fluorescence intensity can be expressed as 

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For analytical applications, when a linear relationship between fluorescence intensity and concentration is desirable, a correction curve must be built up under the same conditions as those that will be used for the actual experiment. 

Figure 1 Typical relationship between fluorescence intensity and concentration for a single fluorophore in solution.

The linear model predicts the relationship between fluorescence intensity, /, and analyte concentration, x, to be of the form. 

LIF is a well-established method for concentration measurement. In fact, STED is also a LIF-based method. Therefore, it is straightforward to utilize STED to measure concentration profile in nanochannels. As aforementioned, LIFPA itself measures the real concentration of fluorescent dye. The principle of measuring proton concentration in a nanochannel is that the fluorescence intensity increases with the increase of pH, which is related to H [46]. Through measurement of the calibration relationship between fluorescence intensity and pH, one can measure H by simply measuring fluorescence intensity, similar to LIFPA. 

When nsing flnorescent protein recombinants (e.g., green flnorescent protein—GFP), the relationship between fluorescence intensity and antigen concentration is likely to be linear. 

The concentration of the indicator is kept low enough that the linear relationship between aborbance or fluorescence intensity and concentration is fulfilled. 

The fluorescence properties of two fulvic acids, one derived from the soil and the other from river water, were studied. The maximum emission intensity occurred at 445-450 nm upon excitation at 350 nm, and the intensity varied with pH, reaching a maximum at pH 5.0 and decreasing rapidly as the pH dropped below 4. Neither oxygen nor electrolyte concentration affected the fluorescence of the fulvic acid derived from the soil. Complexes of fulvic acid with copper, lead, cobalt, nickel and manganese were examined and it was found that bound copper II ions quench fulvic acid fluorescence. Ion-selective electrode potentiometry was used to demonstrate the close relationship between fluorescence quenching and fulvic acid complexation of cupric ions. It is suggested that fluorescence and ion-selective electrode analysis may not be measuring the same complexation phenomenon in the cases of nickel and cobalt complexes with fulvic acid. 

The system is standardized in the absence of cells with known amounts of peroxide either generated as H202 or from glucose in the medium and glucose oxidase or added directly as ethyl peroxide. The relationship between fluorescence intensity of 2 pM scopoletin and peroxide concentration is shown in Fig. 3.13. 

Luminescence spectroscopy is used more often in quantitative analysis than in any other application. The quantitative relationship between fluorescence intensity F and analyte concentration C is derived from the Beer-Lambert law ... 

In the following considerations, it will be assumed that the linear relationship between absorbance or fluorescence intensity and concentration is always fulfilled. Moreover, we will consider only the case where M does not absorb or emit light. In a titration experiment, the concentration of L is kept constant and M is gradually added. The absorption spectrum and/or the fluorescence spectrum are recorded as a function of the concentration of M. Changes in these spectra upon complexation allow one to determine the stability constant and the stoichiometry of the complexes. 

Here, t] is the fluorescence quantum yield, E .) the absorbance, and F a geometric factor. In practice (cuboid-shaped cell), this factor corrects for non-isotropic intensity distribution. The factor (1 - I0" V (2) describes the finite absorption and becomes E if linear relationship exists between observed fluorescence intensity and concentration [3], [28],... 

It is often experimentally convenient to use an analytical method that provides an instrumental signal that is proportional to concentration, rather than providing an absolute concentration, and such methods readily yield the ratio clc°. Solution absorbance, fluorescence intensity, and conductance are examples of this type of instrument response. The requirements are that the reactants and products both give a signal that is directly proportional to their concentrations and that there be an experimentally usable change in the observed property as the reactants are transformed into the products. We take absorption spectroscopy as an example, so that Beer s law is the functional relationship between absorbance and concentration. Let A be the reactant and Z the product. We then require that Ea ez, where e signifies a molar absorptivity. As initial conditions (t = 0) we set Ca = ca and cz = 0. The mass balance relationship Eq. (2-47) relates Ca and cz, where c is the product concentration at infinity time, that is, when the reaction is essentially complete. 

In a later work, Stokes established the relationship between the intensity of fluorescence and the concentration, pointing out that the emission intensity depended on the concentration of the sample (analyte), but that attenuation of the signal occurred at higher concentrations as well as in the presence of foreign substances. He actually was the first to propose, in 1864, the application of fluorescence as an analytical tool, based on its sensitivity, on the occasion of a conference given previously in the Chemical Society and the Royal Institution, and entitled On the Application of the Optical Properties to the Detection and Discrimination of Organic Substances [5],... 

The importance of comparing time-dependent and steady-state fluorescence measurements is well illustrated by the difficulty of resolving purely static from purely dynamic quenching. In either case, the basic relationship between the steady-state fluorescence intensity and quencher concentration is the same. The Stem-Volmer relationship for static quenching due to formation of an intermolecular complex is i... 

Experiments using the technique of laser-induced fluorescence (LIF) in flames have provided ample demonstration of its selectivity and sensitivity, and hence of its applicability as a probe for the reactive intermediates present in combustion systems. The relationship between the measured fluorescence intensity and the concentration of the molecule probed, however, must take into account the collisional quenching of the electronically excited state pumped by the laser. Because the flame contains a mixture of species, each with different quenching cross sections, it may be difficult to estimate the total quenching rate even if many of these cross sections are known. 

Thanks to the linear relationship between the intensity of the characteristic X-ray radiation generated in the sample by electrons and the concentration of the given element, quantitative elemental analysis is also possible. X-ray microanalysis performed using SEM-EDX is, in principle, point analysis and is suitable for studying very small samples of solid materials that are stable in an electron beam. The X-ray fluorescence method, on the other hand, can be applied to the study of both solids and liquids. The signal reaching the detector always originates from a certain sample volume, and thus it is not point analysis. It is more sensitive than the SEM-EDX method. 

In the absence of secondary fluorescence, the relationship between the intensity measured and the concentration level for the element / is of the following type ... 

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