Modified Beer-Lambert law

A. Sassaroli and S. Fantini. Comment on the modified beer-lambert law for scattering media. Physics in Medicine and Biology, 49 N255-N257, 2004. 

Keywords— skin chromophores, melanin, pheomelanin, eumelanin, modified Beer-Lambert law. 

Shimada proposed a simple analytical model based on modified Beer-Lambert Law for an inhomogeneous seatter-ing medium [Shimada, 2001]. The absorbance. A, is defined from the reflectance, R, of the skin which is considered to be a semi-infinite medium. 

In this paper, we have developed a skin pigmentation model for melanin pigment (eumelanin /pheomelanin) analysis. The proposed model is based on modified Beer-Lambert law of skin reflectance model. Clinical study involving 118 participants with three different skin phototypes (SPTs) is conducted. In the study, it was found that the pheomelanin concentration is -4.6E5 5.4E-6 moles/1 for SPT III, -5.9E-5 6.4E-6 moles/1 for SPT IV, and -8.2E-5 9.8E-6 moles/1 for SPT V) and the eumelanin concentration is 9.7E-5 7.3E-6... 

The survival of these arcane units is a consequence of the wealth of informational data already in the literature. The disclosure that CD is no more than a modified absorbance technique should ultimately motivate investigators to adopt the term molar ellipticity, M, in the CD analog of the Beer-Lambert law, that is, y = = Med. 

IMECs of the IR bands of propene adsorbed by the different cationic forms of zeolites were calculated by modifying the Lambert-Beer law in the following way to describe the adsorption on solid wafers ... 

The last case study deserves a special comment as it deals with the attenuation provoked by spatial constraints and not by a conduction process as was the case for all previous case studies in this chapter (and as usually done for this case). The Maxwell equations need to be modified to take into account this peculiarity, thus allowing demonstration of the Lambert-Beer-Bouguer law of light absorption in materials that can be electrically nonconducting and noncharged (which is the most frequently encountered situation). 

According to the Lambert—Beer s law the absorbance is linear with the absorption coefficient, concentration c and volume of the probed sample. Assuming that the absorption coefficient, concentration and cross-section do not change, it can be supposed that the absorbance of a sample is linear with thickness. This is actually true for most data recorded using transmission or similar sampling techniques. In the case of ATR spectra the exponential decay of the evanescent wave has to be taken into account if the band area and film thickness are to be correlated. For use in ATR spectroscopy, the Lambert—Beer s law can be empirically modified to ... 

In weak acid solution, pH 3.5-5.8, iron(//) forms a violet complex with 2,4,6-tris(2-pyri-dyl)-l,3,5-triazine (TPTZ). The reagent was introduced by Collins et al. (1959) and modified by Koroleff (1974). In the procedure given here ascorbic acid is used to reduce Fe(//1) to Fe(/7). The molar absorptivity of the method (at 594-595 nm) is ca. 22300 and the smallest amount of iron that can be determined directly is 20nmol/L, which equals an absorbance of 0.004 with a 10 cm cell. Beer-Lambert s Law is valid to about 21 pmol/L. Interferences occur only from large amounts of Cu, Co or Ni (in mg/L range) in industrial waste waters. 

In the pump-probe experiments, we can describe the transmitted x-ray intensity as a function of the amount of excited species, thus modifying the stationary Lambert-Beer law with respect to the time dependent photoexcitation yield flf). As a result, we can define the signal as the natural logarithm of the ratio of transmitted intensities between the laser-pumped (// "") and unpumped (Ii np) sample, which yields [12]... 

Assuming that reflectance and/or scattering do not contribute significantly to the differences in the attenuation and is only due to absorbance, the Lambert-Beer law (Eq. 7.12) can be modified in order to obtain the absorbance for the two IR polarized directions ... 

---