Breakdown of the Lambert-Beer Law

Rose, H. E.

doi:10.1038/169287a0

Cited by 27 publications

(14 citation statements)

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“…The technically simplest method for the reduction of the multiple scattering is to minimize the optical path length . Another optical approach is to reduce the beam cross section and the aperture of the detector …”

Section: Basics Of the Statistical Extinction Methodsmentioning

confidence: 99%

Investigations on the Capability of the Statistical Extinction Method for the Determination of Mean Particle Sizes in Concentrated Particle Systems

Schwarz

Ripperger

Antonyuk

2018

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Due to the fast growing number of processes involving particulate systems, simple and robust measurement techniques which enable an inline monitoring of the particle size and their concentration are urgently required, since this ensures control but also process optimization. In this work, an inline measurement technique based on the statistical extinction method is developed that provides a process monitoring for a wide range of particulate processes, such as dispersion processes and spray processes. The method allows the determination of the mean size and concentration for particle systems with the size larger than 1 µm. For this purpose, a light beam illuminates the particle system, whereby the fluctuating light intensity due to the particle movement through the light beam is detected. The statistical fluctuation of the signal can be related to a mean particle size and a particle concentration. Since concentrated particle systems cause effects that additionally influence the signal, such as multiple scattering, approaches are needed to reduce or eliminate these effects. In this work, an approach using a spatial frequency filter is applied. The experimental investigations reveal that the effects can be significantly reduced with the spatial frequency filter.

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Section: Basics Of the Statistical Extinction Methodsmentioning

confidence: 99%

Investigations on the Capability of the Statistical Extinction Method for the Determination of Mean Particle Sizes in Concentrated Particle Systems

Schwarz

Ripperger

Antonyuk

2018

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“…Hence the effective impact of multiple scattering on extinction measurements is a question of receiver type and design. Examples of this can be found in a large number of publications, only few of which are cited here [2,7,9,221. In a plot of particle concentration versus path length Az (Figure 7), the domain of disturbances from multiple scattering is delimited by a hyperbola.…”

Section: Steric Interactions Versus Multiple Scatteringmentioning

confidence: 99%

“…k ----x 4 a 4 Assuming a regular cubic lattice of spherical particles, the a/A 5 0.3 criterion may be used to estimate the particle volume concentration which is critical for the onset of dependent scattering: (7) As Eq. (7) shows, the critical concentration depends on the particle size parameter nx/L Going more into detail, two limiting cases of dependent scattering may be distinguished: i) If the criterion a / l 5 0.3 is used with particles smaller than the wavelength, x 4 A, this implies that the average distances between particle centres are small compared with the wavelength even for low concentrations.…”

Section: Steric Interactions Versus Dependent Scatteringmentioning

confidence: 99%

Extinction of Radiations in Sterically Interacting Systems of Monodisperse Spheres. Part 1: Theory

Riebel¹,

Kräte²

1994

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So far, the evaluation of extinction measurements has mostly relied on Bouguer‐Lambert‐Beer's law (BLBL), even though BLBL is known to be valid in the limit of low concentrations only. With higher particle concentrations, particle‐particle interactions such as multiple scattering, dependent scattering and steric interactions can lead to important deviations from BLBL. In a discussion of the various interaction mechanisms, steric interactions are shown to be dominating in a wide and practically important range of parameters. For the theoretical description of steric interactions, different complementary models are introduced, including a statistical model, a layer model and a numerical simulation model. The various approaches coincide to yield a simple extinction equation in two versions, applying to the regimes of Fraunhofer diffraction and straight ray propagation, respectively. In any case, BLBL is found as the low concentration limit of the extinction equation. All considerations are restricted, so far, to the case of monodisperse spherical particles.

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“…However, many studies have found that Beer's law only works for analytes with low concentrations and that a nonlinear relationship may exist between the absorbance and the concentration when the analytes are at high‐concentration levels . These deviations may be ascribed to the occurrence of fluorescence, scattering, physical interactions or chemical equilibrium, the refractive index of the solvent, and many other effects . The errors introduced by using Beer's law without correction can easily exceed one order of magnitude, so the limits should be clearly understood before applying Beer's law for any absorbance‐related analysis .…”

Section: Introductionmentioning

confidence: 99%

“…14,15 These deviations may be ascribed to the occurrence of fluorescence, scattering, physical interactions or chemical equilibrium, the refractive index of the solvent, and many other effects. [14][15][16][17][18] The errors introduced by using Beer's law without correction can easily exceed one order of magnitude, so the limits should be clearly understood before applying Beer's law for any absorbance-related analysis. 19 Because of the low sensitivity of CD detectors for CD detection, a high concentration is often necessary to acquire sufficient CD signals for ee analysis.…”

Section: Introductionmentioning

confidence: 99%

Deviations from Beer's law in electronic absorption and circular dichroism: Detection for enantiomeric excess analysis

et al. 2019

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The electronic absorption (UV) to circular dichroism (CD) signal ratio can be used for enantiomeric excess (ee) analysis within linear range. However, CD detection often requires a high sample concentration where deviations from Beer's law may occur. Individual enantiomers of four chiral compounds were separated from commercial racemates by semipreparative high‐performance liquid chromatography (HPLC) with chiral columns. They were used to trace possible deviations in both UV and CD detection on achiral HPLC with a photodiode array detector and a CD detector. The CD/UV ratios for samples with the same ee value decreased by up to 7.8 to 52% when the injection volume increased, indicating that the linear standard curve of ee versus CD/UV is only valid within a narrow range. To extend the sample amount to a wider range, a data‐processing method was developed based on two second‐order polynomial functions, which were constructed to fit the relationship between the intensities of the UV and CD signals for two enantiomers. Moreover, a more simplified method based on a third‐order polynomial function was established to calculate the ee values. The variations between the predicted and experimental ee values were within ±0.08 for both methods. To our knowledge, this is the first study that the deviations from Beer's law are considered in both UV and CD detection for ee analysis.

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Breakdown of the Lambert-Beer Law

Cited by 27 publications

References 0 publications

Investigations on the Capability of the Statistical Extinction Method for the Determination of Mean Particle Sizes in Concentrated Particle Systems

Investigations on the Capability of the Statistical Extinction Method for the Determination of Mean Particle Sizes in Concentrated Particle Systems

Extinction of Radiations in Sterically Interacting Systems of Monodisperse Spheres. Part 1: Theory

Deviations from Beer's law in electronic absorption and circular dichroism: Detection for enantiomeric excess analysis

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