Lambert deviations

Allen, H. C. Brauers, T. Finlayson-Pitts, B. J. Illustrating Deviations in the Beer-Lambert Law in an Instrumental Analysis Laboratory Measuring Atmospheric Pollutants by Differential Optical Absorption Spectrometry, /. Chem. 

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. 

Fig. 4.13. Evidence for the presence of 5 2 per cent 6Li in the warm halo subdwarf HD 84937 with [Fe/H] = -2.4, 7 = 6090 K. The left panel shows synthesized profiles for 0, 5 and 10 per cent 6Li with the observational points on an absolute wavelength scale in the rest frame of the stellar photosphere. The right panel shows the central wavelengths of the doublets of each isotope and a deviation plot for the three hypotheses on 6Li/7Li. Adapted from Smith, Lambert and Nissen (1993).

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

There are no known exceptions to the Lambert law for homogeneous samples. Beer s law is a limiting case applicable only to dilute solutions and monochromatic radiation. Deviations may be observed in practice, but these are all apparent in the sense that the limiting conditions have been contravened either chemically or instrumentally. Such deviations show as a curvature of the calibration graph, but this does not necessarily preclude the use of a particular method unless the deviation is non-reproducible. Apparent deviations may be summarized as follows ... 

The results indicate that the formation of long-lived trimethyl substituted silyl cations, in the presence of aromatic solvents, as claimed by Lambert et al.95 is not feasible under these conditions. Persistent silicenium ions require sterically more shielding substituents at silicon or hypercoordinative stabilization.96 98 13C and 29Si NMR chemical shifts were calculated for a series of disilylated arenium ions 85 using density functional theory (DFT). The calculations predict consistently the unsaturated carbon atoms to be too deshielded by 8-15 ppm. Applying an empirical correction, the deviation between experiment and theory was reduced to -0.4 to 9 ppm, and the 13C NMR chemical shift of the highly diagnostic cipso is reproduced by the calculations (Ad = -3.8 to 2.7 ppm).99... 

Alterations that may occur in the molecular nature of the sample due to changes in concentration may also result in deviation from the Beer-Lambert relationship. Molecules may tend to associate with one another when the concentration is high or, conversely, complexes may tend to dissociate in low concentrations. Both types of change may possibly affect the absorption characteristics of the compound and result in non-linear graphs. 

Imperfections in monochromators result in the presence of a small proportion of unwanted wavelengths in the incident radiation. Such stray light results in a deviation from a Beer-Lambert relationship (Figure 2.14) and the effect is that absorbance measurements are lower than they should be. 

Stray light may cause deviations from the Beer-Lambert relationship BECAUSE... 

When one or more of the component elements of sorption is governed by a nonlinear relationship between the solution and the sorbed phase, the composite isotherm deviates from linearity. In these cases, modifications to the Freundhch isotherm have been developed (e.g., Lambert 1967 Weber et al. 1992) to express these conditions. 

ENZYME STABILITY STANDARD CURVE BEER-LAMBERT LAW ABSORPTION SPECTROSCOPY STANDARD DEVIATION STATISTICS (A Primer)... 

The main limitation of this model [6,14] is that it assumes that the measured response at a given sensor is due entirely to the constituents considered in the calibration step, whose spectra are included in the matrix of sensitivities, S. Hence, in the prediction step, the response of the unknown sample is decomposed only in the contributions that are found in S. If the response of the unknown contains some contributions from constituents that have not been included in S (in addition to background problems and baseline effects), biased predicted concentrations may be obtained, since the system will try to assign this signal to the components in S. For this reason, this model can only be used for systems of known qualitative composition (e.g. gas-phase spectroscopy, some process monitoring or pharmaceutical samples), in which the signal of all the pure constituents giving rise to a response can be known. For the same reason, CLS is not useful for mixtures where interaction between constituents or deviations from the Lambert-Beer law (nonlinear calibration curves) occur. 

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. 

Equations (4) through (7) produce more reliable estimates of Kow and S for hydrophobic dyes than other methods. Isnard and Lambert (1989) calculated root mean square deviations for a dataset of 20 disperse and solvent dyes, using a number of available equations They showed that equations in the form of Equation (4) had root mean square deviations (a) values of 1.6 to 3.3 log Kow units, regressions in the form of equations (6) and (7) gave c values ranging from 1.3 to 3.3, and equations similar to Equation (5) had root mean square deviations ranging from 0.57 to 1.4. 

These considerations are confirmed, in particular, by Oedberg et al. who concluded from their IR investigations with Li- and CsDNNS micelles in heptane that all the water molecules in the reversed micelles are hydrogen bonded. It appears worth mentioning that the first water molecules added to the system induced deviations from the Lambert-Beer law for LiDNNS and large intensity changes of the vibrations of the sulfonic acid group in CsDNNS. 

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... 

Methods for calculating molar extinction coefficients of minerals are outlined in chapter 4 ( 4.3). The importance of the Beer-Lambert law, eq. (3.7), is that the molar extinction coefficient of an absorption band should be independent of the concentration of the absorbing species. Deviations from this law originating from cation ordering are discussed in chapter 4. 

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