Beer's Law – Why Absorbance Depends (Almost) Linearly on Concentration

Mayerhöfer, Thomas G.; Popp, Jürgen

doi:10.1002/cphc.201801073

Cited by 74 publications

(68 citation statements)

References 16 publications

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“…[3] Planck's results were included, e. g., in Kayser's Handbook of Spectroscopy (vol. [7] However, due to the use of the simplification introduced by Lorentz in 1906 [8] known as the Lorentz-profile, [9] instead of a damped harmonic oscillator ("Lorentz-oscillator"), a linear dependence of absorbance from concentration was found, which indicated that Planck's original findings had been lost. [4] Planck's finding is also implicitly contained in Max Born's book "Optik".…”

Section: Beer's Law-why Integrated Absorbance Depends Linearly On Conmentioning

confidence: 99%

“…[24] We also derived this dependence from simple electromagnetic theory, [25] without referring to a particular oscillator model or the corresponding shape functions. [24] We also derived this dependence from simple electromagnetic theory, [25] without referring to a particular oscillator model or the corresponding shape functions.…”

Section: Beer's Law-why Integrated Absorbance Depends Linearly On Conmentioning

confidence: 99%

“…The corresponding relative dielectric function is given by Equation (9): [24,25] ð9Þ where S*2 is the molar oscillator strength,ṽ 0 is the oscillator position and γ is the damping constant. The corresponding relative dielectric function is given by Equation (9): [24,25] ð9Þ where S*2 is the molar oscillator strength,ṽ 0 is the oscillator position and γ is the damping constant.…”

Section: Beer's Law-why Integrated Absorbance Depends Linearly On Conmentioning

confidence: 99%

“…[24,25] We did not investigate how the area under the curves changes as the band shape changes. Correspondingly, the values for the absorbance at certain wavenumbers vary nonlinearly with concentration.…”

Section: Beer's Law-why Integrated Absorbance Depends Linearly On Conmentioning

confidence: 99%

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Beer's Law‐Why Integrated Absorbance Depends Linearly on Concentration

2019

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As derived by Max Planck in 1903 from dispersion theory, Beer's law has a fundamental limitation. The concentration dependence of absorbance can deviate from linearity, even in the absence of any interactions or instrumental nonlinearities. Integrated absorbance, not peak absorbance, depends linearly on concentration. The numerical integration of the absorbance leads to maximum deviations from linearity of less than 0.1 %. This deviation is a consequence of a sum rule that was derived from the Kramers‐Kronig relations at a time when the fundamental limitation of Beer's law was no longer mentioned in the literature. This sum rule also links concentration to (classical) oscillator strengths and thereby enables the use of dispersion analysis to determine the concentration directly from transmittance and reflectance measurements. Thus, concentration analysis of complex samples, such as layered and/or anisotropic materials, in which Beer's law cannot be applied, can be achieved using dispersion analysis.

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Section: Beer's Law-why Integrated Absorbance Depends Linearly On Conmentioning

confidence: 99%

Section: Beer's Law-why Integrated Absorbance Depends Linearly On Conmentioning

confidence: 99%

Section: Beer's Law-why Integrated Absorbance Depends Linearly On Conmentioning

confidence: 99%

Section: Beer's Law-why Integrated Absorbance Depends Linearly On Conmentioning

confidence: 99%

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Beer's Law‐Why Integrated Absorbance Depends Linearly on Concentration

2019

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“…[37] These results clearly show that an infrared spectrum obtained from a single droplet provides a basis for chemical identification and quantification of an extracted analyte. [40] At a droplet height of 5 µm, the signal intensity saturates the detector. For all the IR measurements, the aperture size is fixed at ≈8 µm.…”

Section: Ir Detection Of Organic Compoundsmentioning

confidence: 99%

One‐Step Nanoextraction and Ultrafast Microanalysis Based on Nanodroplet Formation in an Evaporating Ternary Liquid Microfilm

Qian

Yamada

Wei

et al. 2019

Adv Materials Technologies

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in chemical analysis workflow is sample pretreatment to extract the analytes before detection. The recent development of dispersive liquid-liquid microextraction (DLLME) has stimulated progress for extracting and preconcentrating trace hydrophobic analytes from aqueous solutions both rapidly and efficiently. [4][5][6] DLLME is based on spontaneous emulsification upon mixing of a water-insoluble extractant, a dispersive solvent, and an analyte aqueous solution. [7,8] The hydrophobic analyte could be rapidly extracted into extractant nanodroplets because of the higher solubility of the analyte in the extractant than in water. The large surface area of nanodroplets enhances the transfer of the analyte from the surrounding solution to the droplets. Relying on the combination of DLLME and various detection techniques, such as inductively coupled plasma optical emission spectrometry or fluorescence spectrometry, trace chemical analysis has been achieved for diverse applications. [9][10][11] However, these existing approaches require significant improvement due to their time-consuming nature, their requirement for specialized equipment in droplet separation and for large volumes of the analyte solution. [12,13] Many studies have focused on concentrating compounds from a single sessile drop evaporation. [14][15][16][17] A common issue comes from the coffee stain effect that leads to uncontrolled deposition of the analyte on the substrate rather than into a focused spot. Although an evaporating drop can shrink isotropically on superhydrophobic surfaces, micro/nanoscale structures on these surfaces can influence solute deposition, in particular at the final stage of evaporation when the drop size becomes comparable with the structures. [18] Supersensitive detection can be achieved for the materials deposited on highly ordered nanostructures on the substrate by using the plasmonic effect. [19] However, these nanostructures are difficult to fabricate for fast and high throughput analysis. Recent work on drop evaporation of ternary liquid mixtures shows advantageous features that may lead to unpinned drop for solute concentrating. [20,21] Selective evaporation of the volatile co-solvent (ethanol) in the mixture leads to oversaturation of oil and consequently spontaneously formation of tiny droplets. This phenomenon of Preconcentration is key for detection from an extremely low concentration solution, but requires separation steps from a large volume of samples using extracting solvents. Here, a simple approach is presented for ultrafast and sensitive microanalysis from a tiny volume of aqueous solutions. In this approach, liquid-liquid nanoextraction in an evaporating thin liquid film on a spinning substrate is coupled with quantitative analysis in one step. The approach is exemplified using a liquid mixture comprising a target compound to be analyzed in water, mixed with extractant oil and co-solvent ethanol. With rapid evaporation of ethanol, nanodroplets of oil form spontaneously in the film. The compounds are highly conce...

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