The Bouguer-Beer-Lambert Law: Shining Light on the Obscure

The Beer-Lambert law is unquestionably the most important law in optical spectroscopy and indispensable for the qualitative and quantitative interpretation of spectroscopic data. As such, every spectroscopist should know its limits and potential pitfalls, arising from its application, by heart. It is the goal of this work to review these limits and pitfalls, as well as to provide solutions and explanations to guide the reader. This guidance will allow a deeper understanding of spectral features, which cannot be explained by the Beer-Lambert law, because they arise from electromagnetic effects/the wave nature of light. Those features include band shifts and intensity changes based exclusively upon optical conditions, i. e. the method chosen to record the spectra, the substrate and the form of the sample. As such, the review will be an essential tool towards a full understanding of optical spectra and their quantitative interpretation based not only on oscillator positions, but also on their strengths and damping constants

The Global Polarity of Alcoholic Solvents and Water – Importance of the Collectively Acting Factors Density, Refractive Index and Hydrogen Bonding Forces

The DHBD quantity represents the hydroxyl group density of alcoholic solvents or water. DHBD is purely physically defined by the product of molar concentration of the solvent (N) and the factor Σn=n×f which reflects the number n and position (f-factor) of the alcoholic OH groups per molecule. Whether the hydroxyl group is either primary, secondary or tertiary is taken into account by f. Σn is clearly linearly correlated with the physical density or the refractive index of the alcohol derivative. Relationships of solvent-dependent UV/Vis absorption energies as ET(30) values, 129Xe NMR shifts and kinetic data of 2-chloro-2-methylpropane solvolysis with DHBD are demonstrated. It can be shown that the ET(30) solvent parameter reflects the global polarity of the hydrogen bond network rather than specific H-bond acidity. Significant correlations of the log k1 rate constants of the solvolysis reaction of 2-chloro-2-methylpropane with DHBD show the physical reasoning of the approach

Present and Future of Surface-Enhanced Raman Scattering.

The discovery of the enhancement of Raman scattering by molecules adsorbed on nanostructured metal surfaces is a landmark in the history of spectroscopic and analytical techniques. Significant experimental and theoretical effort has been directed toward understanding the surface-enhanced Raman scattering (SERS) effect and demonstrating its potential in various types of ultrasensitive sensing applications in a wide variety of fields. In the 45 years since its discovery, SERS has blossomed into a rich area of research and technology, but additional efforts are still needed before it can be routinely used analytically and in commercial products. In this Review, prominent authors from around the world joined together to summarize the state of the art in understanding and using SERS and to predict what can be expected in the near future in terms of research, applications, and technological development. This Review is dedicated to SERS pioneer and our coauthor, the late Prof. Richard Van Duyne, whom we lost during the preparation of this article

Beyond Beer's Law: Revisiting the Lorentz-Lorenz Equation

In this contribution we show how the Lorentz-Lorenz and the Clausius-Mosotti equations are related to Beer's law. Accordingly, the linear concentration dependence of absorbance is a consequence of neglecting the difference between the local and the applied electric field. Additionally, it is necessary to assume that the absorption index and the related refractive index change is small. By connecting the Lorentz-Lorenz equations with dispersion theory, it becomes obvious that the oscillators are coupled via the local field. We investigate this coupling with numerical examples and show that, as a consequence, the integrated absorbance of a single band is in general no longer linearly depending on the concentration. In practice, the deviations from Beer's law usually do not set in before the density reaches about one tenth of that of condensed matter. For solutions, the Lorentz-Lorenz equations predict a strong coupling also between the oscillators of solute and solvent. In particular, in the infrared spectral region, the absorption coefficients are prognosticated to be much higher due to this coupling compared to those in the gas phase. © 2020 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA

Structures for surface-enhanced nonplasmonic or hybrid spectroscopy

Absorption, scattering, and fluorescence are processes that increase with electric field intensity. The most prominent way to enhance electric field intensity is to use localized or propagating surface plasmon polaritons (SPPs) based on metallic particles and nanostructures. In addition, several other, much less well-known, photonic structures that increase electric field intensity exist. Interference enhancement provided by thin dielectric coatings on reflective substrates is able to provide electric field intensity enhancement over the whole substrate and not only at certain hotspots, thereby being in particular suitable for the spectroscopy of thin surface layers. The same coatings on high refractive index substrates may be used for interference-enhanced total internal reflection-based spectroscopy in much the same way as Kretschmann or Otto configuration for exciting propagating SPPs. The latter configurations can also be used to launch Bloch surface waves on 1D photonic crystal structures for the enhancement of electric field intensity and thereby absorption, scattering, and fluorescence-based spectroscopies. High refractive index substrates alone can also, when nanostructured, enhance infrared absorption or Raman scattering via Mie-type resonances. As a further method, this review will cover recent developments to employ phonon polaritons in the reststrahlen region

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

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. ©2019 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA