3.2.9.5. Beer’s Law Applies to Turbidimetry and to Spectrophotometry
The experiments presented above confirm that absorbancy (A) measured on suspensions of Formazin and other heterogenous solutions by spectrophotometry is reproducible and fits into a strictly linear calibration response correlated with NTU units. This is because loss of light in the Long Light Path flow cell follows the Beer's Law that describes a linear relationship between concentration and logarithmic loss of light intensity along the light path length (l) and concentration (c) of target analyte:
It is well known that when loss of light is due to absorption pf light by target molecules, but it is generally NOT recognized that loss of light by scattering has exactly the same result (Table 2). However, as our experiments show, Beer’s Law applies equally for spectrophotometry of heterogenous and homogeneous solutions.
In spectrophotometry of homogenous solutions, the coefficient (ε) is molar absorptivity, which is dependent on wavelength. In comparison, when the light loss is due to scattering, the scattering coefficient (σ) is dependent on wavelength, particle sizes, shape, and color. In analogy, in spectrophotometry of heterogeneous solution, loss of light intensity by scattering is also logarithmic vs. concentration of particles (P, T, AB), which fits the mathematical structure of Beer’s law. Therefore the scattering coefficient (σ), is dependent on wavelength, particle sizes, shape, density and color. For Formazin σ A = 0.002 = 1.0 NTU at 550 nm for 1cm light path (P).
Correlation of molar absorptivity of target analyte with scattering coefficient at the same sample and wavelength (or AAb with ASc) allows us to calculate the influence of Suspended Matter on concentration of target analyte, in order to decide if samples should be filtered prior to analysis (Appendix 3).
This is possible because absorbancies measured on a mixture of heterogeneous and a homogenous solution are additive:
ATot = AAbs + ASc
This is also why the spectra and calibrations of SiMo Green (zz) formed by reaction of silicate with ammonium molybdate in the presence of ascorbic acid are linearly dependent on the concentration of silica, although it contains a mixture of heterogeneous particles (Table 1). This is because SiMo Green is not well soluble and therefore present as a mixture of dissolved and colloidal SiMo Blue, and therefore the absorbance spectrum (Amax at 810 nm) is modified by the scatter spectrum of the colloidal forms. The ratio of forms is dependent on the acidity of the reaction mixture, and optimization of reaction conditions is a topic of many studies, since this reaction is the basis for spectrophotometric determination of soluble silica and optimized conditions must yield a linear calibration of A versus concentration of silica. Thus, at 810 nm (zz right), the slope of the calibration line, which is strictly linear, is maximized. Note that at any other wavelength (zz left), the calibration response will also be linear (albeit with a lower slope), which confirms that AAbs and ASc are additive while their ratio varies along the recorded wavelengths. Considering the variety of geometrical forms made by polymerization of the same compound (Table 1), it is difficult to perceive how such heterogeneous materials can filter light intensity so that it will decrease linearly with increasing concentration of suspended matter.
And how is it possible that the same light loss mode takes place when the difference in properties of SM HK yield similar response? One may only speculate that the linearity and reproducibility of experiments with Formazin, SiMoG, PMoB, and SM HK are explained by the Law of Large Numbers. When the light beam passes through a sample containing a sufficiently large number of randomly formed particles, the random variations will cancel each other, and the light beam will experience a stable average scattering effect of the entire population. It is the unique geometry and construction of the Long Light Path flow cell, which functions as a neutral optical density filter designed to reduce the intensity of light along the entire spectrum range of the light source by scatter, thus allowing only light measured as ASc to reach the detector (Lambert). And does the LLP flow cell function as a selective optical density filter designed to reduce the intensity of light along a narrow set of wavelengths by absorption by a selected molecule (Beer). However, at low particle concentration, the reproducibility of monitored absorbance (R.S.D.) will decrease as differences in optical properties of particles will not be smoothed out (Q right), while the slope of the calibration line will be the same (Q left), as for higher concentrations of particles. Obviously, more research is needed to establish upper boundaries of linearity as well as properties of Suspended Matter from other sources.
Surprisingly, calibration obtained by SS dilution of Suspended Matter has the same slope of 0.02A NTU in a 10 cm light path. This is because the scattering spectra of Formazin (R, Z) are the same as the spectra of the Suspended Matter (X, Z), and the loss of light is monitored at the same wavelength and length of the light path (10 cm) (AC). Considering the physical differences between Formazin and SM particles this finding is unexpected and unprecedented. But it is supported by the Law of Large Numbers. When the light beam passes through a sample containing a sufficiently large number of randomly formed particles, the random variations will cancel each other, and the light beam will experience a stable average scattering effect of the entire population. It is the unique geometry and construction of the Long Light Path flow cell which fulfills this condition and prevents scattered and stray light from reaching the detector. However, at low particle concentration reproducibility of monitored absorbance (R.S.D.) will decrease as differences in the size of particles will not be smoothed out. Obviously, more research is needed to establish the upper boundaries of linearity as well as the properties of Suspended Matter from other sources.
