# Absorbance

"Optical density" redirects here. "Optical density" can also refer to index of refraction.[1] For use of the term "optical density" in molecular biology, see Nucleic acid quantitation. See also Neutral-density filter

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] Absorbance is dimensionless, and in particular is not a length, though it is a monotonically increasing function of path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for absorbance is discouraged.[2] In physics, a closely related quantity called "optical depth" is used instead of absorbance: the natural logarithm of the ratio of incident to transmitted radiant power through a material. The optical depth equals the absorbance times ln(10).

The term absorption refers to the physical process of absorbing light, while absorbance does not always measure absorption: it measures attenuation (of transmitted radiant power). Attenuation can be caused by absorption, but also reflection, scattering, and other physical processes.

## Mathematical definitions

### Absorbance

Absorbance of a material, denoted A, is given by[2]

${\displaystyle A=\log _{10}\!\left({\frac {\Phi _{\mathrm {e} }^{\mathrm {i} }}{\Phi _{\mathrm {e} }^{\mathrm {t} }}}\right)=-\log _{10}T,}$

where

• Φet is the radiant flux transmitted by that material;
• T is the transmittance of that material.

Absorbance is related to optical depth by

${\displaystyle A={\frac {\tau }{\ln 10}},}$

where τ is the optical depth.

### Spectral absorbance

Spectral absorbance in frequency and spectral absorbance in wavelength of a material, denoted Aν and Aλ respectively, are given by[2]

${\displaystyle A_{\nu }=\log _{10}\!\left({\frac {\Phi _{\mathrm {e} ,\nu }^{\mathrm {i} }}{\Phi _{\mathrm {e} ,\nu }^{\mathrm {t} }}}\right)=-\log _{10}T_{\nu },}$
${\displaystyle A_{\lambda }=\log _{10}\!\left({\frac {\Phi _{\mathrm {e} ,\lambda }^{\mathrm {i} }}{\Phi _{\mathrm {e} ,\lambda }^{\mathrm {t} }}}\right)=-\log _{10}T_{\lambda },}$

where

Spectral absorbance is related to spectral optical depth by

${\displaystyle A_{\nu }={\frac {\tau _{\nu }}{\ln 10}},}$
${\displaystyle A_{\lambda }={\frac {\tau _{\lambda }}{\ln 10}},}$

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

### Attenuance

Absorbance is a number that measures the attenuation of the transmitted radiant power in a material. Attenuation can be caused by the physical process of "absorption", but also reflection, scattering, and other physical processes. Absorbance of a material is approximately equal to its attenuance when both the absorbance is much less than 1 and the emittance of that material (not to be confused with radiant exitance or emissivity) is much less than the absorbance. Indeed,

${\displaystyle \Phi _{\mathrm {e} }^{\mathrm {t} }+\Phi _{\mathrm {e} }^{\mathrm {att} }=\Phi _{\mathrm {e} }^{\mathrm {i} }+\Phi _{\mathrm {e} }^{\mathrm {e} },}$

where

• Φet is the radiant power transmitted by that material;
• Φeatt is the radiant power attenuated by that material;
• Φee is the radiant power emitted by that material,

that is equivalent to

${\displaystyle T+ATT=1+E,}$

where

• T = Φetei is the transmittance of that material;
• ATT = Φeattei is the attenuance of that material;
• E = Φeeei is the emittance of that material,

and according to Beer–Lambert law, T = 10−A, so

${\displaystyle ATT=1-10^{-A}+E\approx ln(10)A+E\quad {\text{if}}\ A\ll 1,}$

and finally

${\displaystyle ATT\approx ln(10)A\quad {\text{if}}\ E\ll A.}$

### Attenuation coefficient

Absorbance of a material is also related to its decadic attenuation coefficient by

${\displaystyle A=\int _{0}^{l}a(z)\,\mathrm {d} z,}$

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:

${\displaystyle A=al.}$

Sometimes the relation is given using the molar attenuation coefficient of the material, that is its attenuation coefficient divided by its molar concentration:

${\displaystyle A=\int _{0}^{l}\varepsilon c(z)\,\mathrm {d} z,}$

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:

${\displaystyle A=\varepsilon cl.}$

The use of the term "molar absorptivity" for molar attenuation coefficient is discouraged.[2]

## Measurements

### Logarithmic vs. directly proportional measurements

The amount of light transmitted through a material diminishes exponentially as it travels through the material, according to the Beer–Lambert law (A=(ε)(l)). Since the absorbance of a sample is measured as a logarithm, it is directly proportional to the thickness of the sample and to the concentration of the absorbing material in the sample. Some other measures related to absorption, such as transmittance, are measured as a simple ratio so they vary exponentially with the thickness and concentration of the material.

Absorbance: −log10etei) Transmittance: Φetei
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

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 attained 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

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

${\displaystyle A_{\lambda }=\log _{10}\!\left({\frac {\Phi _{\mathrm {e} ,\lambda }^{\mathrm {i} }}{\Phi _{\mathrm {e} ,\lambda }^{\mathrm {t} }}}\right)\!.}$

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 Beer–Lambert law and is used in HPLC.

Some filters, notably welding glass, are rated by shade number, which is 7/3 times the absorbance plus one:[6]

${\displaystyle SN={\frac {7}{3}}A+1,}$

or

${\displaystyle SN={\frac {7}{3}}(-\log _{10}T)+1,}$

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.

## References

1. ^ Zitzewitz, Paul W. (1999). Glencoe Physics. New York, N.Y.: Glencoe/McGraw-Hill. p. 395. ISBN 0-02-825473-2.
2. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Absorbance". doi:10.1351/goldbook.A00028
3. ^ "How to Make Your Next Paper Scientifically Effective". J. Phys. Chem. Lett. 4 (9): 1578–1581. 2013. doi:10.1021/jz4006916.
4. ^ Reusch, William. "Visible and Ultraviolet Spectroscopy". Retrieved 2014-10-29.
5. ^ Reusch, William. "Empirical Rules for Absorption Wavelengths of Conjugated Systems". Retrieved 2014-10-29.
6. ^ Russ Rowlett (2004-09-01). "How Many? A Dictionary of Units of Measurement". Unc.edu. Retrieved 2010-09-20.

The Bradford protein assay was developed by Marion M. Bradford in 1976. It is a quick and accurate spectroscopic analytical procedure used to measure the concentration of protein in a solution. The reaction is dependent on the amino acid composition of the measured proteins.

Chlorophyll

Chlorophyll (also chlorophyl) is any of several related green pigments found in cyanobacteria and the chloroplasts of algae and plants. Its name is derived from the Greek words χλωρός, chloros ("green") and φύλλον, phyllon ("leaf"). Chlorophyll is essential in photosynthesis, allowing plants to absorb energy from light.

Chlorophylls absorb light most strongly in the blue portion of the electromagnetic spectrum as well as the red portion. Conversely, it is a poor absorber of green and near-green portions of the spectrum, which it reflects, producing the green color of chlorophyll-containing tissues. Two types of chlorophyll exist in the photosystems of green plants: chlorophyll a and b.

Colorimeter (chemistry)

A colorimeter is a device used in colorimetry. In scientific fields the word generally refers to the device that measures the absorbance of particular wavelengths of light by a specific solution. This device is commonly used to determine the concentration of a known solute in a given solution by the application of the Beer-Lambert law, which states that the concentration of a solute is proportional to the absorbance.

Cuvette

A cuvette (French: cuvette = "little vessel") is a small tube-like container with straight sides and a circular or square cross section. It is sealed at one end, and made of a clear, transparent material such as plastic, glass, or fused quartz. Cuvettes are designed to hold samples for spectroscopic measurement, where a beam of light is passed through the sample within the cuvette to measure the absorbance, transmittance, fluorescence intensity, fluorescence polarization, or fluorescence lifetime of the sample. This measurement is done with a spectrophotometer.

Dashpot

A dashpot is a mechanical device, a damper which resists motion via viscous friction. The resulting force is proportional to the velocity, but acts in the opposite direction, slowing the motion and absorbing energy. It is commonly used in conjunction with a spring (which acts to resist displacement). The process and instrumentation diagram (P&ID) symbol for a dashpot is .

Deoxyribonuclease

A deoxyribonuclease (DNase, for short) is an enzyme that catalyzes the hydrolytic cleavage of phosphodiester linkages in the DNA backbone, thus degrading DNA. Deoxyribonucleases are one type of nuclease, a generic term for enzymes capable of hydrolyzing phosphodiester bonds that link nucleotides. A wide variety of deoxyribonucleases are known, which differ in their substrate specificities, chemical mechanisms, and biological functions.

Hydrolysable tannin

A hydrolyzable tannin or pyrogallol-type tannin is a type of tannin that, on heating with hydrochloric or sulfuric acids, yields gallic or ellagic acids.At the center of a hydrolyzable tannin molecule, there is a carbohydrate (usually D-glucose but also cyclitols like quinic or shikimic acids). The hydroxyl groups of the carbohydrate are partially or totally esterified with phenolic groups such as gallic acid in gallotannins or ellagic acid in ellagitannins. Hydrolysable tannins are mixtures of polygalloyl glucoses and/or poly-galloyl quinic acid derivatives containing in between 3 up to 12 gallic acid residues per molecule.Hydrolyzable tannins are hydrolyzed by weak acids or weak bases to produce carbohydrate and phenolic acids.

Examples of gallotannins are the gallic acid esters of glucose in tannic acid (C76H52O46), found in the leaves and bark of many plant species.

Hydrolysable tannins can be extracted from different vegetable plants, such as chestnut wood (Castanea sativa), oak wood (Quercus robur, Quercus petraea and Quercus alba), tara pods (Caesalpinia spinosa), gallnuts (Quercus infectoria and Rhus semialata), myrobalan (Terminalia chebula), sumac (Rhus coriaria) and Aleppo gallnuts (Andricus kollari).

Hyperchromicity

Hyperchromicity is the increase of absorbance (optical density) of a material. The most famous example is the hyperchromicity of DNA that occurs when the DNA duplex is denatured. The UV absorption is increased when the two single DNA strands are being separated, either by heat or by addition of denaturant or by increasing the pH level. The opposite, a decrease of absorbance is called hypochromicity.

Molar attenuation coefficient

The molar attenuation coefficient is a measurement of how strongly a chemical species attenuates light at a given wavelength. It is an intrinsic property of the species. The SI unit of molar attenuation coefficient is the square metre per mole (m2/mol), but in practice, it is usually taken as the M−1⋅cm−1 or the L⋅mol−1⋅cm−1. In older literature, the cm2/mol is sometimes used with corresponding values 1,000 times larger. In practice these units are the same, with the difference being expression of volume in either cm3 or in L. The molar attenuation coefficient is also known as the molar extinction coefficient and molar absorptivity, but the use of these alternative terms has been discouraged by the IUPAC.

Optical depth

In physics, optical depth or optical thickness, is the natural logarithm of the ratio of incident to transmitted radiant power through a material, and spectral optical depth or spectral optical thickness is the natural logarithm of the ratio of incident to transmitted spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged.In chemistry, a closely related quantity called "absorbance" or "decadic absorbance" is used instead of optical depth: the common logarithm of the ratio of incident to transmitted radiant power through a material, that is the optical depth divided by ln 10.

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Peroxynitrite

Peroxynitrite (sometimes called peroxonitrite) is an ion with the formula ONOO−. It is an unstable structural isomer of nitrate, NO−3. Although its conjugate acid is highly reactive, peroxynitrite is stable in basic solutions. It is prepared by the reaction of hydrogen peroxide with nitrite:

H2O2 + NO−2 → ONOO− + H2OPeroxynitrite is an oxidant and nitrating agent. Because of its oxidizing properties, peroxynitrite can damage a wide array of molecules in cells, including DNA and proteins. Formation of peroxynitrite in vivo has been ascribed to the reaction of the free radical superoxide with the free radical nitric oxide:

O•−2 + NO• → ONO−2The resultant pairing of these two free radicals results in peroxynitrite, a molecule that is itself not a free radical, but that is a powerful oxidant.

In the laboratory, a solution of peroxynitrite can be prepared by treating acidified hydrogen peroxide with a solution of sodium nitrite, followed by rapid addition of NaOH. Its concentration is indicated by the absorbance at 302 nm (pH 12, ε302 = 1670 M−1 cm−1).

Plate readers, also known as microplate readers or microplate photometers, are instruments which are used to detect biological, chemical or physical events of samples in microtiter plates. They are widely used in research, drug discovery, bioassay validation, quality control and manufacturing processes in the pharmaceutical and biotechnological industry and academic organizations. Sample reactions can be assayed in 6-1536 well format microtiter plates. The most common microplate format used in academic research laboratories or clinical diagnostic laboratories is 96-well (8 by 12 matrix) with a typical reaction volume between 100 and 200 µL per well. Higher density microplates (384- or 1536-well microplates) are typically used for screening applications, when throughput (number of samples per day processed) and assay cost per sample become critical parameters, with a typical assay volume between 5 and 50 µL per well. Common detection modes for microplate assays are absorbance, fluorescence intensity, luminescence, time-resolved fluorescence, and fluorescence polarization.

Specific ultraviolet absorbance

Specific ultraviolet absorbance (SUVA) is the absorbance of ultraviolet light in a water sample at a specified wavelength that is normalized for dissolved organic carbon (DOC) concentration. Specific UV absorbance (SUVA) wavelengths have analytical uses to measure the aromatic character of dissolved organic matter by detecting density of electron conjugation which is associated with aromatic bonds.

Spectral power distribution

In radiometry, photometry and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination (radiant exitance). More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity (e.g. radiant energy, radiant flux, radiant intensity, radiance, irradiance, radiant exitance, radiosity, luminance, luminous flux, luminous intensity, illuminance, luminous emittance).Knowledge of the SPD is crucial for optical-sensor system applications. Optical properties such as transmittance, reflectivity, and absorbance as well as the sensor response are typically dependent on the incident wavelength.

Spectrophotometry

In chemistry, spectrophotometry is the quantitative measurement of the reflection or transmission properties of a material as a function of wavelength. It is more specific than the general term electromagnetic spectroscopy in that spectrophotometry deals with visible light, near-ultraviolet, and near-infrared, but does not cover time-resolved spectroscopic techniques.

Time-resolved spectroscopy

In physics and physical chemistry, time-resolved spectroscopy is the study of dynamic processes in materials or chemical compounds by means of spectroscopic techniques. Most often, processes are studied after the illumination of a material occurs, but in principle, the technique can be applied to any process that leads to a change in properties of a material. With the help of pulsed lasers, it is possible to study processes that occur on time scales as short as 10−16 seconds.

Trolox equivalent antioxidant capacity

The Trolox equivalent antioxidant capacity (TEAC) assay measures the antioxidant capacity of a given substance, as compared to the standard, Trolox. Most commonly, antioxidant capacity is measured using the ABTS Decolorization Assay. Other antioxidant capacity assays which use Trolox as a standard include the diphenylpicrylhydrazyl (DPPH), oxygen radical absorbance capacity (ORAC) and ferric reducing ability of plasma (FRAP) assays. The TEAC assay is often used to measure the antioxidant capacity of foods, beverages and nutritional supplements.

Ultraviolet–visible spectroscopy

Ultraviolet–visible spectroscopy or ultraviolet–visible spectrophotometry (UV–Vis or UV/Vis) refers to absorption spectroscopy or reflectance spectroscopy in the ultraviolet-visible spectral region. This means it uses light in the visible and adjacent ranges. The absorption or reflectance in the visible range directly affects the perceived color of the chemicals involved. In this region of the electromagnetic spectrum, atoms and molecules undergo electronic transitions. Absorption spectroscopy is complementary to fluorescence spectroscopy, in that fluorescence deals with transitions from the excited state to the ground state, while absorption measures transitions from the ground state to the excited state.

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