“molar absorption” coefficient in L/mol/cm, c is the concentration in mol/L, and l is the pathlength in cm, an expression commonly used for light absorption in liquid solutions. When applied to light absorption by gases, the absorption coefficient is often expressed as A = σ(λ)Nl, where σ(λ) is the “absorption cross section” in cm2 and N is the number density of the gas being measured (no./cm3). In the field of continuous emission monitoring, the absorbance has traditionally been expressed as α(λ)cl, where α(λ) is termed the absorption coefficient [used instead of the IUPAC symbol ɛ(λ)], c is the concentration of the gas being measured, and l is the pathlength. [This convention has been used in this book.]
The absorption coefficient α(λ) is dependent upon the light wavelength and the properties of the pollutant molecules. The coefficient is a quantitative expression of the degree to which a molecule will absorb light energy at a given wavelength. If no absorption occurs, α(λ) will be zero, and the transmittance would equal 100%. If an electronic or vibrational–rotational transition occurs at some wavelength, the absorption coefficient will have some value, and the reduction of light energy across the path will also depend upon the pollutant concentration, c, and the pathlength, l.
Based on this principle, an instrument can be designed to measure pollutant gas concentrations. All that is needed is light having a wavelength that will cause some transition in the molecule of interest, a light path through the gas (either through a sample cell or through the stack or duct), and a light detector. Io is determined by taking a reading from the detector when no pollutant is in the light path of the duct or sample cell. The concentration can be obtained from the Beer–Lambert expression if α(λ) and l are known, but typically a calibration curve is generated with known gas concentrations, rather than using theoretical values for α(λ). Figure 4‐9 shows a calibration plot typical of an instrument designed to measure light absorption by pollutant molecules.
Here, ln(1/Tr) is plotted against concentration instead of plotting transmittance against concentration. This logarithmic plot gives a straight line, from which it is much easier to develop the calibration plot. In the example of Figure 4‐9, a calibration line is generated using three calibration standards of known concentration. Calibration gases are then injected one at a time into a sample cell to obtain values at the detector of I1, I2, and I3. The ratios of I/Io are calculated, the logarithm is taken, and values of ln(1/Tr) are plotted against the concentration to obtain the line. Injecting an unknown gas into the sample cell gives a value, Iu, at the detector. The unknown concentration can then be determined by drawing a line from the calculated value of ln(1/Tru) on the y axis to intersect the calibration line. At the point of intersection, a line is drawn down to the x axis to obtain the concentration of the unknown gas.
Note that it is not necessary to know the value of the absorption coefficient to obtain the unknown concentration value. The use of gas calibration standards avoids that necessity in this type of instrumentation.
Note also that the instrument response can be given as the logarithm to the base ten instead of in Naperian logarithms. The conversion between the two is simply log10(1/Tr) = (1/2.303)ln(1/Tr). Spectroscopists commonly use the base 10 logarithm, A, where absorbance is expressed as A = log10(1/Tr).
LIGHT SCATTERING BY PARTICLES
There is another way that light energy is removed from a beam of light, other than by absorption from individual molecules. If particulate matter, aerosols, or droplets are present in the flue gas, light incident on these materials can be scattered in various directions. As a result, not all of the light will continue in its initial direction and its transmittance through the gas will be reduced. The mechanisms of light scattering are dependent upon the particle refractive index, the particle size (as defined by its radius, r) and the wavelength (λ) of light that impinges on it – different phenomena come into play, depending on how r compares to λ. Three basic types of scattering processes occur (see Figure 4‐10).
1 Rayleigh scattering. If the particle is smaller than the light wavelength, then the particle–light interaction can be characterized as “Rayleigh” scattering (Figure 4‐10a: r/λ ≤ 1), where the light is scattered isotropically equally in all directions.
2 Mie scattering. If the particle size and light wavelength are comparable, r/λ ≈ 1, Mie scattering occurs. In this scattering, electrons in the particle see varying electric fields from the impinging electromagnetic field. Electrons accelerated in an electromagnetic field will emit light, which combines constructively or destructively as it comes from different locations within the particle. The scattering pattern is somewhat complex as shown in Figure 4‐10b where r/λ ≈ 1.
3 Macroscopic scattering. When particles are very much larger than the light wavelength, r/λ ≥ 1, the concepts of geometric optics (such as reflection and refraction) can be used to explain how light scatters (Figure 4‐10c).
Figure 4‐9 Calibration plot for the Beer–Lambert relation.
Figure 4‐10 Three regimes of light scattering. (a) Rayleigh scattering r/λ ≤ 1. (b) Mie scattering r/λ ≈ 1. (c) Geometric optics r/λ ≥ 1.
In a typical flue gas, particle sizes may range from 0.1 to 10 μm or greater. When visible light ranging from 400 to 700 nm (0.4–0.7 μm) is directed through a gas, all of the aforementioned scattering processes can take place, with respect to the particle size distribution. These three scattering processes are described in the following sections.
Rayleigh Scattering: r/λ ≤ 1
Particles smaller than about 0.1 μm will scatter visible light by Rayleigh scattering. In this case, the electric field of light interacts with electrons within the particle molecules.
The electrons are correspondingly accelerated in their motion in the molecule. It is a phenomenon of nature that an accelerated electron will emit electromagnetic radiation in all directions. The net effect is that the oscillating electron scatters light out of the light beam. Due to this phenomenon, small particles (<0.1 μm) are very effective in scattering visible light.
Mie Scattering: r/λ = 1
As the particle size increases relative to the wavelength, the molecular electrons throughout the particle no longer see a uniform field. The intensity and field direction vary at different points within the particle and the electrons will accelerate in different directions, generating a complex scattering pattern. In fact, the scattered light waves can add together constructively or can subtract destructively