A novel model extended from the Bouguer-Lambert-Beer law can describe the non-linear absorbance of potassium dichromate solutions and microalgae suspensions

Abstract

Introduction: The Bouguer-Lambert-Beer law is widely used as the fundamental equation for quantification in absorption spectroscopy. However, deviations from the Bouguer-Lambert-Beer law have also been observed, such as chemical deviation and light scattering effect. While it has been proven and shown that the Bouguer-Lambert-Beer law is valid only under very restricted limitations, there are only a few alternatives of analytical models to this law. Based on the observation in the experiments, we propose a novel model to solve the problem of chemical deviation and light scattering effect.Methods: To test the proposed model, a systematic verification was conducted using potassium dichromate solutions and two types of microalgae suspensions with varying concentrations and path lengths.Results: Our proposed model demonstrated excellent performance, with a correlation coefficient (R2) exceeding 0.995 for all tested materials, significantly surpassing the Bouguer-Lambert-Beer law, which had an R2 as low as 0.94. Our results confirm that the absorbance of pure pigment solutions follows the Bouguer-Lambert-Beer law, while the microalgae suspensions do not due to the light scattering effect. We also show that this scattering effect leads to huge deviations for the commonly used linear scaling of the spectra, and we provide a better solution based on the proposed model.Discussion: This work provides a powerful tool for chemical analysis and especially for the quantification of microorganisms, such as the concentration of biomass or intracellular biomolecules. Not only the high accuracy but also the simplicity of the model makes it a practical alternative to the existing Bouguer-Lambert-Beer law.

Improving Determination of Pigment Contents in Microalgae Suspension with Absorption Spectroscopy: Light Scattering Effect and Bouguer–Lambert–Beer Law

“…The mBLB model, augmented with an additional intercept term, also exhibits improved descriptive capabilities compared to the BLB model. The current study affirms the suitability of the nonlinear model proposed in [25] for characterizing the nonlinear absorbance patterns observed in light-scattering suspensions. Furthermore, we observe that absorbances characterized by higher pigment absorption tend to yield better accuracies when using both the BLB and mBLB models.…”

“…The absorbance measurement procedure of P. tricornutum in the current work follows the same steps, setups, and measurement devices/equipment as described in [25]. The procedure can be summarized in the following four steps.…”

“…The BLB law serves as the cornerstone of quantification in absorption spectroscopy. However, it has been demonstrated that this law is not applicable to microalgae suspensions due to the light scattering effect [25].…”

“…Different models have been proposed as alternatives to the BLB law, such as the modified BLB model (mBLB) [26]. In previous research, a nonlinear model for absorbance was also proposed [25], where different levels of nonlinearity were observed at different wavelengths through the absorbance spectrum of P. tricornutum. Extended from the observation, we hypothesized that (1) the level of nonlinearity will also influence the accuracy of the determination of pigment contents when using the BLB model, and (2) the use of the mBLB model is more accurate than the BLB model for pigment content determination.…”

Utilization of ultraviolet‐visible spectrophotometry in conjunction with wrapper method and correlated component regression for nitrite prediction outside the Beer–Lambert domain

“…The Beer–Lambert law is widely used for the quantification of concentrations in absorption spectroscopy. However, at high concentrations a chemical deviation and light scattering has been observed, which shows that the Beer–Lambert law has restricted limits 15 …”