In chemistry, absorbance or decadic absorbance is the common logarithm
of the ratio of incident to transmitted radiant power through a
material, and spectral absorbance or spectral decadic absorbance is
the common logarithm of the ratio of incident to transmitted spectral
radiant power through a material.[2]
Contents 1 Mathematical definitions 1.1 Absorbance 1.2 Spectral absorbance 2 Relationship with attenuation 2.1 Attenuance
2.2
3 Measurements 3.1 Logarithmic vs. directly proportional measurements 3.2 Instrument measurement range 3.3 Method of measurement 4 Shade number 5 See also 6 References Mathematical definitions[edit]
Absorbance[edit]
A = log 10 ( Φ e i Φ e t ) = − log 10 T , displaystyle A=log _ 10 !left( frac Phi _ mathrm e ^ mathrm i Phi _ mathrm e ^ mathrm t right)=-log _ 10 T, where Φet is the radiant flux transmitted by that material; Φei is the radiant flux received by that material; T is the transmittance of that material.
A = τ ln 10 , displaystyle A= frac tau ln 10 , where τ is the optical depth. Spectral absorbance[edit] Spectral absorbance in frequency and spectral absorbance in wavelength of a material, denoted Aν and Aλ respectively, are given by[2] A ν = log 10 ( Φ e , ν i Φ e , ν t ) = − log 10 T ν , displaystyle A_ nu =log _ 10 !left( frac Phi _ mathrm e ,nu ^ mathrm i Phi _ mathrm e ,nu ^ mathrm t right)=-log _ 10 T_ nu , A λ = log 10 ( Φ e , λ i Φ e , λ t ) = − log 10 T λ , displaystyle A_ lambda =log _ 10 !left( frac Phi _ mathrm e ,lambda ^ mathrm i Phi _ mathrm e ,lambda ^ mathrm t right)=-log _ 10 T_ lambda , where Φe,νt is the spectral radiant flux in frequency transmitted by that material; Φe,νi is the spectral radiant flux in frequency received by that material; Tν is the spectral transmittance in frequency of that material; Φe,λt is the spectral radiant flux in wavelength transmitted by that material; Φe,λi is the spectral radiant flux in wavelength received by that material; Tλ is the spectral transmittance in wavelength of that material. Spectral absorbance is related to spectral optical depth by A ν = τ ν ln 10 , displaystyle A_ nu = frac tau _ nu ln 10 , A λ = τ λ ln 10 , displaystyle A_ lambda = frac tau _ lambda ln 10 , where τν is the spectral optical depth in frequency; τλ is the spectral optical depth in wavelength. Although absorbance is properly unitless, it is sometimes reported in
"arbitrary units", or AU. Many people, including scientific
researchers, wrongly state the results from absorbance measurement
experiments in terms of these made-up units.[3]
Relationship with attenuation[edit]
Attenuance[edit]
Φ e t + Φ e a t t = Φ e i + Φ e e , displaystyle Phi _ mathrm e ^ mathrm t +Phi _ mathrm e ^ mathrm att =Phi _ mathrm e ^ mathrm i +Phi _ mathrm e ^ mathrm e , where Φet is the radiant power transmitted by that material; Φeatt is the radiant power attenuated by that material; Φei is the radiant power received by that material; Φee is the radiant power emitted by that material, that is equivalent to T + A T T = 1 + E , displaystyle T+ATT=1+E, where T = Φet/Φei is the transmittance of that material; ATT = Φeatt/Φei is the attenuance of that material; E = Φee/Φei is the emittance of that material, and according to Beer–Lambert law, T = 10−A, so A T T = 1 − 10 − A + E ≈ A + E if A ≪ 1 , displaystyle ATT=1-10^ -A +Eapprox A+Equad text if All 1, and finally A T T ≈ A if E ≪ A . displaystyle ATTapprox Aquad text if Ell A.
A = ∫ 0 l a ( z ) d z , displaystyle A=int _ 0 ^ l a(z),mathrm d z, where l is the thickness of that material through which the light travels; a(z) is the decadic attenuation coefficient of that material at z, and if a(z) is uniform along the path, the attenuation is said to be a linear attenuation and the relation becomes: A = a l . displaystyle A=al. Sometimes the relation is given using the molar attenuation coefficient of the material, that is its attenuation coefficient divided by its molar concentration: A = ∫ 0 l ε c ( z ) d z , displaystyle A=int _ 0 ^ l varepsilon c(z),mathrm d z, where ε is the molar attenuation coefficient of that material; c(z) is the molar concentration of that material at z, and if c(z) is uniform along the path, the relation becomes: A = ε c l . displaystyle A=varepsilon cl. The use of the term "molar absorptivity" for molar attenuation
coefficient is discouraged.[2]
Measurements[edit]
Logarithmic vs. directly proportional measurements[edit]
The amount of light transmitted through a material diminishes
exponentially as it travels through the material, according to the
Absorbance: −log10(Φet/Φei) Transmittance: Φet/Φei 0 1 0.1 0.79 0.25 0.56 0.5 0.32 0.75 0.18 0.9 0.13 1 0.1 2 0.01 3 0.001 Instrument measurement range[edit] Any real measuring instrument has a limited range over which it can accurately measure absorbance. An instrument must be calibrated and checked against known standards if the readings are to be trusted. Many instruments will become non-linear (fail to follow the Beer–Lambert law) starting at approximately 2 AU (~1% transmission). It is also difficult to accurately measure very small absorbance values (below 10−4) with commercially available instruments for chemical analysis. In such cases, laser-based absorption techniques can be used, since they have demonstrated detection limits that supersede those obtained by conventional non-laser-based instruments by many orders of magnitude (detections have been demonstrated all the way down to 5 × 10−13). The theoretical best accuracy for most commercially available non-laser-based instruments is in the range near 1 AU. The path length or concentration should then, when possible, be adjusted to achieve readings near this range. Method of measurement[edit] Typically, absorbance of a dissolved substance is measured using absorption spectroscopy. This involves shining a light through a solution and recording how much light and what wavelengths were transmitted onto a detector. Using this information, the wavelengths that were absorbed can be determined.[4] First, measurements on a "blank" are taken using just the solvent for reference purposes. This is so that the absorbance of the solvent is known, and then any change in absorbance when measuring the whole solution is made by just the solute of interest. Then measurements of the solution are taken. The transmitted spectral radiant flux that makes it through the solution sample is measured and compared to the incident spectral radiant flux. As stated above, the spectral absorbance at a given wavelength is A λ = log 10 ( Φ e , λ i Φ e , λ t ) . displaystyle A_ lambda =log _ 10 !left( frac Phi _ mathrm e ,lambda ^ mathrm i Phi _ mathrm e ,lambda ^ mathrm t right)!. The absorbance spectrum is plotted on a graph of absorbance vs.
wavelength.[5]
A UV-Vis spectrophotometer will do all this automatically. To use this
machine, solutions are placed in a small cuvette and inserted into the
holder. The machine is controlled through a computer and, once you
"blank" it, will automatically display the absorbance plotted against
wavelength. Getting the absorbance spectrum of a solution is useful
for determining the concentration of that solution using the
S N = 7 3 A + 1 , displaystyle SN= frac 7 3 A+1, or S N = 7 3 ( − log 10 T ) + 1 , displaystyle SN= frac 7 3 (-log _ 10 T)+1, where SN is the shade number. So, if the filter has 0.1% transmittance (0.001 transmittance, which is 3 absorbance units) the shade number would be 8. See also[edit] Absorptance
References[edit] ^ Zitzewitz, Paul W. (1999). Glencoe Physics. New York, N.Y.: Glencoe/McGraw-Hill. p. 395. ISBN 0-02-825473-2. ^ a b c d e IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Absorbance". ^ "How to Make Your Next Paper Scientifically Effective". J. Phys. Chem. Lett. 4 (9): 1578–1581. 2013. doi:10.1021/jz4006916. ^ Reusch, William. "Visible and Ultraviolet Spectroscopy". Retrieved 2014-10-29. ^ Reusch, William. "Empirical Rules for Absorption Wavelengths of Conjugated Systems". Retrieved 2014-10-29. ^ Russ Rowlett (2004-09-01). "How Many? A Dictionary of Units of Measurement". Unc.edu. Retrieved 2010-09-20. v t e Protein structural analysis High resolution Cryo-electron microscopy X-ray crystallography NMR Electron crystallography EPR Medium resolution Fiber diffraction Mass spectrometry SAXS Spectroscopic NMR
Circular dichroism
Dual-polarization interferometry
Absorbance
Fluorescence
Translational Diffusion Analytical ultracentrifugation Size exclusion chromatography Light scattering NMR Rotational Diffusion
Chemical Hydrogen-deuterium exchange Site-directed mutagenesis Chemical modification Thermodynamic Equilibrium unfolding Computational
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