Deviation from the Beer-Lambert Law

Factors such as dissociation, association, or solvation, which result in deviation from the Beer-Lambert law, can be expected to have a similar effect in fluorescence. Any material that causes the intensity of fluorescence to be less than the expected value given by equation (2) is known as a quencher, and the effect is termed quenching it is normally caused by the presence of foreign ions or molecules. Fluorescence is affected by the pH of the solution, by the nature of the solvent, the concentration of the reagent which is added in the determination of inorganic ions, and, in some cases, by temperature. The time taken to reach the maximum intensity of fluorescence varies considerably with the reaction. 

The values of 6 2, etc., are calculated from calibration graphs for the separate components. Deviations from the Beer-Lambert Law... 

A difficulty encountered in measuring the concentration of an unknown absorbing species in solution is deviation from the Beer-Lambert law. For reasons stated earlier in this chapter, some absorbing species do not demonstrate an increase in absorbance that is proportional to an increase in concentration. (In reality, most compounds follow the Beer-Lambert relationship over a relatively small concentration range.) When measuring solution concentration, adherence to the Beer-Lambert law must always be tested in the concentration range under study. 

I 8.1 The Becr-Lambcrt Law in the Molecular System, 41 1 8.2 Deviation from the Beer-Lambert Law, 42 I 8.3 Measurement of the Integrated Absorption Coefficient, 44... 

A number of chemical factors may also contribute to errors in measurement. These factors generally lead to deviations from the Beer-Lambert law, and can largely be controlled once they are recognized as potential sources of error. Solute-solute interaction, for example, whether it leads to aggregation or precipitation of the aggregate, diminishes the apparent concentration of the analyte of interest. Aggregation of hydrophobic polycyclic aromatics at high concentrations in aqueous media is one such example where deviation from the Beer-Lambert law would be seen. Similarly, dimerization of molecules, for example, carboxylic acids, or even polymerization of analyte in solution may also lead to apparent deviation from the Beer-Lambert law. Both can be controlled to some extent by use of appropriately diluted solutions. 

Ionization or even complexation of the analyte in solution can also lead to apparent deviation from the Beer-Lambert law. Again, by appropriate control of pH or complexation conditions it is possible to ensure that only one form predominates in solution, permitting quantitation of the absorbing species. Measurement of absorbance at the isosbestic point has been used to counter this problem. However, this approach is limited by the fact that the absorbance of the analyte at this point is frequently not high enough. 

Stray-light is not responsible for negative deviations from the Beer-Lambert law at high absorbance, particularly if the solvent absorbs significantly. 

Stray-light causes deviations from the Beer-Lambert law and limits the upper limit of the absorbance scale. Figure 13 illustrates the effect. 

Usually, the absorbance measurements are taken in the maximum of the spectrum (peak for example) due to several reasons. On one hand, the maximum sensitivity (greater slope in the calibration curve) is obtained at this wavelength. On the other hand, the centre of the maximum is where the absorbance gradient is minimum vs. the wavelength, which means lower probability of deviations from the Beer-Lambert law due to the polychromatism of the selected radiation. Finally, it will be a lesser variation of the method sensitivity due to the imprecision in positioning the wavelength. Measurements are sometimes performed not at the maximum, but in other places (shoulder, for... 

Deviations from the Beer-Lambert law (both positive and negative) can also occur because of concentration-depasdent properties of the sample, such as a monomer-dimer equilibrium, that can alter spectral properties... 

Thus, errors incurred in quantitative analysis by the infrared method include error in measurement of the 100% line, deviations from the Beer-Lambert law, error in the zero line and error in the measurement of %T. The effect of deviations from the Beer-Lambert law is such that one should try to work at values of %T greater than 407o for the most accurate results. 

ABSORPTION OF LIGHT AND DEVIATION FROM THE BEER-LAMBERT LAW... 

Apparent deviations from the Beer-Lambert law arise when concentration variation causes changes in the distribution of several chromophore species in the solution. In these cases, if the absorption contribution from each species is considered, the Beer-Lambert law is obeyed by each species, but it is the variation in species concentrations which produces the apparent deviation. For example, dimerization of the chromophore molecules at higher concentrations may take place, providing a dimer with an e value other than that of the monomeric form, causing a non-linear dependence of absorbance upon the solute concentration. 

Apparent deviations from the Beer-Lambert law arise mainly because of instrumental factors such as stray light, sample fluorescence, and use of a wide radiation bandwidth. Real deviations arise because of high concentrations which introduce solute-solute interactions and changes in s with solution refractive index, and concentration dependent chemical equilibria. 

There are, however, some complications that have not been taken into account in this interpretation, arising from spectroscopy. One of these is that absorption by the excited I2 molecules (formed on geminate recombination) is mostly into the lower energy levels, so the molar absorptivity is not the same for all the molecules and there will be deviations from the Beer-Lambert law. Another concerns the use of a neodymium laser to provide the excitation flash (Section 4.2.3.1). The wavelength (532 nm) is such as to produce two excited states, with consequences which may complicate calculation of the quantum yield. The difficulty may be overcome by using a lower-energy pulse from a dye laser the excited... 

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