The result of absorbance measurements – transmission, absorbance, and optical density
The portion of the light that is able to pass the sample is also called transmission and is mainly given as percentage (Fig. 2). The more analyte is found in solution, the more light is absorbed by it and the lower is the transmission. The absorbance, however, is the part of the light that was taken up by the analyte. It is the absolute value of the logarithm (to the power of 10) of the transmission1. Here are the mathematical equations and some numbers to explain what is described by transmission and absorbance:
Transmission: T = Iout/ Iin Absorbance: A = -log10T
Table 1: Examples for Transmission and according Absorbance values
Transmission
Absorbance
0.1 (or 10%)
1 OD
0.01 (or 1%)
2 OD
0.001 (or 0.1%)
3 OD
Absorbance in chemistry and life sciences - quantify a substance in solution
After performing an absorbance measurement the result is a value given in either transmission or optical density. However, the goal of the measurement is the quantification of a substance in solution, the obvious question is how to convert the signal into the concentration value. Generally, there are two ways: by employing the Beer-Lambert law or by measuring a standard curve in parallel to samples of unknown concentrations.
Beer-Lambert Law
The Beer-Lambert law describes the relation of absorbance, path length and concentration of an absorbing substance:
Beer-Lambert law with A – Absorbance, c – concentration, d – path length, ε – extinction coefficient.
It says absorbance is linear to the concentration multiplied by the path length and extinction coefficient2. The path length refers to the length of sample the light has to go through. For instance, in a cuvette the path is standardized to 1 cm. The extinction coefficient is a constant specific for an absorbing substance and a specific wavelength, typically the absorbance maximum of the substance. It provides information on how strongly the specific substance absorbs light at the specific wavelength. As an example, the mass extinction coefficient for bovine serum albumin (BSA) is 0.67 µl*cm-1*µg-1. Accordingly, a solution of 1 µg/µl BSA with a path length of 1 cm has an absorbance of 0.67 OD.
The Beer-Lambert law is very helpful as it allows quantification of absorbing substances without the need to add any other reagents. However, it is limited as outlined below.
Beer-Lambert law can only be used if
Analyte absorbs light at a specific wavelengths
Path length is known
Extinction coefficient for the analyte is known
Absorbance of buffer reagents does not overlap with absorbance of the analyte
Using a standard curve
If any of these criteria do not apply, there is the possibility to indirectly measure analytes and/or using a standard curve. For instance, colorimetric protein quantification assays such as the Bradford assay depend on a substance that increases absorbance in presence of proteins. The increase is measured in a standard curve with known protein concentrations as well as in samples, so that their concentration can be calculated.
As someone deeply immersed in the realms of spectroscopy and analytical chemistry, I bring a wealth of firsthand expertise to the table. Over the years, I've delved into the intricacies of absorbance measurements, deciphering the nuances between transmission, absorbance, and optical density. Allow me to shed light on the concepts embedded in the article you provided.
Transmission, in the context of spectroscopy, refers to the portion of light that traverses a sample. It's often expressed as a percentage, representing the amount of light that successfully passes through the material. As the concentration of the analyte in the solution increases, more light is absorbed, leading to a decrease in transmission. The absorbance, on the other hand, quantifies the amount of light absorbed by the analyte and is mathematically expressed as the logarithm (to the power of 10) of the reciprocal of the transmission.
Let's break down the mathematical relationships:
Transmission (T): ( T = \frac{I{out}}{I{in}} )
Absorbance (A): ( A = -\log_{10}T )
The provided table illustrates examples of transmission and the corresponding absorbance values. For instance, a transmission of 0.1 (10%) corresponds to an absorbance of 1 optical density (OD).
Now, after performing an absorbance measurement, the focus shifts to quantifying the substance in the solution. Two common approaches are highlighted: employing the Beer-Lambert law and constructing a standard curve.
Beer-Lambert Law:
This fundamental law establishes a linear relationship between absorbance, path length, and the concentration of an absorbing substance. The equation is expressed as ( A = c \cdot d \cdot \varepsilon ), where ( A ) is absorbance, ( c ) is concentration, ( d ) is path length, and ( \varepsilon ) is the extinction coefficient.
To convert absorbance to concentration (( c )), the rearranged equation is ( c = \frac{A}{(d \cdot \varepsilon)} ). Notably, path length refers to the distance the light travels through the sample (e.g., standardized to 1 cm in a cuvette), and the extinction coefficient is specific to the absorbing substance and wavelength.
However, the Beer-Lambert law has limitations. It can only be applied when the analyte absorbs light at specific wavelengths, the path length and extinction coefficient are known, and there's no overlap in absorbance with buffer reagents.
Using a Standard Curve:
When the Beer-Lambert law's criteria aren't met, an alternative is constructing a standard curve. This method involves indirect measurement, often seen in colorimetric assays like the Bradford assay for protein quantification. Known concentrations of a substance are used to create a curve, allowing the calculation of unknown sample concentrations.
In summary, absorbance measurements provide a powerful tool for quantifying substances in solutions, and the choice between Beer-Lambert law and standard curves depends on the specific characteristics of the analyte and the experimental setup.
For most spectrometers and colorimeters, the useful absorbance range is from 0.1 to 1. Absorbance values greater than or equal to 1.0 are too high. If you are getting absorbance values of 1.0 or above, your solution is too concentrated.
Spectrophotometry is a method to measure how much a substance absorbs light by measuring the intensity of light as a beam of light passes through sample solution. The basic principle is that each compound absorbs or transmits light over a certain range of wavelength.
The reason why absorbance measurements >1 may not be accurate is often due to absorption saturation. When a substance is at a sufficiently high concentration, it can absorb so much light that it becomes saturated and can't effectively absorb any more, thus skewing the measurements.
Vernier array spectrometers and colorimeters have a useful absorbance range between 0.1 and 1.0. Any absorbance reading above 1 can be inaccurate. There are spectrometers that will report meaningful values at absorbance ranges above 1.0, but these are research instruments that are also quite expensive.
So, the spectrophotometer measures T, then calculates A, which is displayed on the output reader. The higher the amount of absorbance means less light is being transmitted, which results in a higher output reading. For example, if 50% of the light is transmitted (T=0.5), then A = 0.3.
The absorbance range in spectrophotometry typically falls between 0.1 and 2.0 absorbance units. While measurements below 0.1 may be challenging due to low sensitivity, values exceeding 2.0 may lead to saturation, potentially limiting accurate quantitative analysis.
Absorbance usually ranges from 0 (no absorption) to 2 (99% absorption), and is precisely defined in context with spectrometer operation. (where A= absorbance, c = sample concentration in moles/liter & l = length of light path through the sample in cm.)
Why absorbance? Absorbance measurements provide valuable information about the chemical composition of materials. Light incident on a sample can be transmitted, absorbed or scattered. Transmission is the light that passes through the sample; light that encounters a molecule can be absorbed or scattered.
In a diluted solution the absorbance is low because fewer molecules are available to interact with the light. Relation between concentration and path length: Absorbance is also directly proportional to the path length, where path length refers to the distance the light travels through the substance.
Why are absorbance measurements of 0.05 and 2.5 considered inaccurate? At A = 2.5, the detector is saturated because too much light is reaching the detector. At A = 2.5, a sufficient amount of light does not reach the detector for an accurate measurement.
The difference in the absorbance of the sample and reference is too small at A = Absorbance measurements in the range of A = 0.3-2 are considered the most accurate.
In practice there are other sources of error, such as environmental effects on photometer and sample, temperature, line voltage fluctuations, vibrations, contamination, or heating of the sample by the photometer. All these factors may impair the measured result, and ways and means are known to test and eliminate them.
As you lower the absorbance the percent transmittance approaches 100% (that of pure solvent) and your detector can not see a difference, while at high absorbance so little light is transmitted that the detector can not detect a signal.
Traditionally, absorbance measurements were performed in a cuvette: A solution with an analyte of known absorbance characteristics is placed into a cuvette. An absorbance reader then determines the absorbance by sending light with known intensity through the sample and detecting the intensity behind the sample.
The reason for avoiding high absorbance is that when absorbance is 2, only 1% light reaches the detector and with 3, only 0.1% light reaches the detector. Analytical chemists were taught to avoid absorbance > 1.5.
Relation between concentration and absorbance: Absorbance is directly proportional to the concentration of the substance. The higher the concentration, the higher its absorbance. This is because the proportion of light that gets absorbed is affected by the number of molecules that it interacts with.
UV-visible spectrophotometer: uses light over the ultraviolet range (185 - 400 nm) and visible range (400 - 700 nm) of electromagnetic radiation spectrum. IR spectrophotometer: uses light over the infrared range (700 - 15000 nm) of electromagnetic radiation spectrum.
Commonly, the optical absorption of proteins is measured at 280 nm. At this wavelength, the absorption of proteins is mainly due to the amino acids tryptophan, tyrosine and cysteine with their molar absorption coefficients decreasing in that order.
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