The Beer-Lambert law is indispensable for both quantitative and qualitative analysis of spectral data and is undeniably the most significant law in optical spectroscopy. It offers a thorough account of the implications resulting from the interaction of light with matter. Any discrepancy from this standard can usually be explained as an alteration in the chemical reactions happening in the specimen or a shift in the molecular framework at the atomic level. This article focuses on the importance of Beer-Lambert law and its applications in spectroscopy.
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The Basics of Beer-Lambert Law
The Beer-Lambert-Bouguer law is widely utilized for spectroscopy in the field of optics which entails that there is a linear relationship between the concentration of a particular substance and the absorption of light by that substance. Beer–Lambert law (BLL) defines the relationship between light attenuation and the attributes of the material that it passes through.
As per the expression of Beer-Lambert law A = ε*c*l; the optical absorbance is represented by A, ε is the molar absorptivity or molar extinction coefficient representing the inherent absorption capability of a substance at a particular wavelength, c represents the concentration of the substance, and l is depicting the path length of light through the solution.
This law is extensively used in biomedical optics, for instance for determining O2 saturation for human connective tissue, estimating the mole fractional absorption of bilirubin in blood plasma samples, and estimating the number of hemoglobin elements or optical path length (OPL) through a tissue.
History and Modifications of the Beer-Lambert Law
The article published in the Journal of Biomedical Optics discusses the modifications as well as the origin of the Beer-Lambert law. Pierre Bouguer, also known as the father of photometry, conducted studies that measured and compared the perceived luminance of various materials. In 1729, he described Bouger's law, which states that in a medium of homogeneous transparency, the light persisting in a collimated beam is an exponential measure of the substance's path length.
A paper published by Johann Heinrich Lambert in 1760 claimed a direct proportional relationship between absorbance and optical path length whereas the thickness/breadth of the medium led to an attenuation in the intensity of radiations. In 1852, Beer modified this exponentially varying absorption law after extensive studies by including the number of mixtures (mass of absorbing substance) in the absorption parameter.
The law is corrected by the scientists as per the experimental and application requirements to cater for any particular scattering effects etc. in the medium.
Limitation of the Beer-Lambert Law
Several assumptions are considered during the application of the Beer-Lambert law. However, these conditions are not met during real-life analysis leading to some prominent limitations in the application of Beer-Lambert law.
Scattering is a major obstacle to the efficient utilization of the Beer-Lambert law. The law presumed a homogeneous substrate; however, the presence of imperfections causes optical waves to disperse. By using time-resolved spectroscopic measurements or intensity-modulated spectroscopy, the effects of absorption and scattering can be measured independently; consequently, it can still be employed.
The equilibrium between the absorbing substance and any other chemicals (if present) does not influence the BLL calculations. However, the effectiveness of BLL at high chromophore quantities is due to absorber–absorber interaction; if variations in the absorption quantities are insignificant, BLL functions properly.
Non-linearity is another limitation hindering the vast applicability of the BLL. The nonlinear nature may take place when the absorbing species encounters association, disintegration, or contact with the solvent, producing compounds with distinct absorbance attributes. Typically, this impact arises with multi-complex monomer-dimer, acid-base, and metal association equilibria or solvent-analyte associations’ equilibria.
Microscopic Beer-Lambert Law (MBL) for Frequency-domain Near Infrared Spectroscopy
Researchers have developed a fast and efficient technique for determining the absorption coefficient variations of an element. The article is published in Optics Communications and deals with data extracted from frequency-domain diffuse optical spectroscopy (FD-DOS) or frequency-domain near-infrared spectroscopy (FD-NIRS) measurements. A precise method for measuring the absorption (μa) and reduced scattering (μ's) factors is required.
Photon dispersion in turbid media is described thoroughly by the microscopic Beer–Lambert law (MBL) as the product of exponential degradation by absorbance and a probability function derived from other properties such as scattering or geometry.
A 16 dB power output radio frequency (RF) signal generator was employed for producing modified light signals. An analog-to-digital converter concurrently digitized both recorded impulses from the APD and reference signals from the RF generator.
Multi-distance observations were used for calibrating the phase and amplitude outputs of the measurement system. By adjusting the proportions of water, milk, and black India ink, fifteen liquid phantoms with distinct adsorption and dispersion coefficients were produced.
The MBL technique performed calculations 21.3 times quicker than the conventional Non-linear square fitting (NLSF) approach. The square root of the mean error was 1.5 times less than the NLSF analysis. In conclusion, these measurements demonstrate that the MBL method's rapid and stable analysis is advantageous.
Beer-Lambert Law in Absorption Spectroscopy
The latest article published in Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy linked proportional deviations with the Beer-Lambert law to spectral resolution, concentration, and light intensity, and confirmed this justification by analyzing sulfur dioxide at different overall column levels using spectrometers with varying spectral resolutions in the waveband range of 216–230 nm.
Equipped with a broad emission spectrum, a high-pressure deuterium lamp was employed during the experiment. Consistent with theory, the linear variation with absorption boosted as the total columnar quantity increased.
At the identical total column level, the linear divergence between absorption and overall column concentration was reduced when the spectrometer's spectrum resolution was increased. Furthermore, the results of the experiment showed that the intensity of the incoming light lowered with the increase in absorption.
This study can provide an empirical foundation for minimizing continuous deviation with the Beer-Lambert law when utilizing an absorption spectroscopic analysis.
Deviations between BLL and Electromagnetic Theory for Spectroscopic Analysis
As per the article published in Chemistry Europe, in the field of spectroscopy, optics also made significant strides forward. Maxwell's theory, which led to the interpretation of light as an electromagnetic wave and the introduction of electromagnetic theory, was undoubtedly the most significant step concurrent with the BLL.
An empirical comparison between the two indicates that the BBL law is approximatively accurate under specific circumstances but utterly incorrect under others. Under one of these conditions, the BBL typically fails; the absorbance determined by the reflection bands of layers on exceptionally reflective materials plays a role.
Absorption is not at all linearly dependent on layer thickness, which is wholly unanticipated. Not only does absorption not varies linearly with its thickness, but it can also even decline with increasing thickness.
A second unanticipated behavior involves the apex positions, which can be both blue- and red-shifted as the thickness increases. Both effects can interact to produce asymmetries in the form of peaks. All of these variables affect spectroscopic measurements.
To summarize, the Beer-Lambert law, which provides an empirical connection between absorption and length of the path, plays an essential function in spectroscopy. This is essential for the industrialization of innovative methods involving nanoparticle integration for spectroscopic measurements.
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References and Further Reading
Kim, J. et. al. (2022). Fast noniterative data analysis method for frequency-domain near-infrared spectroscopy with the microscopic Beer–Lambert law. Optics Communications, 520, 128417. Available at: https://doi.org/10.1016/j.optcom.2022.128417
Oshina, I., & Spigulis, J. (2021). Beer–Lambert law for optical tissue diagnostics: current state of the art and the main limitations. Journal of biomedical optics, 26(10), 100901-100901. Available at: https://doi.org/10.1117/1.JBO.26.10.100901
Mayerhöfer, T. et. al. (2020). The bouguer‐beer‐Lambert law: Shining light on the obscure. ChemPhysChem, 21(18), 2029-2046. Available at: https://doi.org/10.1002/cphc.202000464
Li, L. et al. (2022). Study on the origin of linear deviation with the Beer-Lambert law in absorption spectroscopy by measuring sulfur dioxide. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 275, 121192. Available at: https://doi.org/10.1016/j.saa.2022.121192