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- ItemThe Global Polarity of Alcoholic Solvents and Water – Importance of the Collectively Acting Factors Density, Refractive Index and Hydrogen Bonding Forces(Weinheim : Wiley-VCH-Verl., 2022) Spange, Stefan; Weiß, Nadine; Mayerhöfer, Thomas G.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.
- ItemBeyond Beer's Law: Revisiting the Lorentz-Lorenz Equation(Weinheim : Wiley-VCH Verl., 2020) Mayerhöfer, Thomas G.; Popp, JürgenIn 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.
- ItemPeriodic array-based substrates for surface-enhanced infrared spectroscopy(Berlin : de Gruyter, 2017-7-29) Mayerhöfer, Thomas G.; Popp, JürgenAt the beginning of the 1980s, the first reports of surface-enhanced infrared spectroscopy (SEIRS) surfaced. Probably due to signal-enhancement factors of only 101 to 103, which are modest compared to those of surface-enhanced Raman spectroscopy (SERS), SEIRS did not reach the same significance up to date. However, taking the compared to Raman scattering much larger cross-sections of infrared absorptions and the enhancement factors together, SEIRS reaches about the same sensitivity for molecular species on a surface in terms of the cross-sections as SERS and, due to the complementary nature of both techniques, can valuably augment information gained by SERS. For the first 20 years since its discovery, SEIRS relied completely on metal island films, fabricated by either vapor or electrochemical deposition. The resulting films showed a strong variance concerning their structure, which was essentially random. Therefore, the increase in the corresponding signal-enhancement factors of these structures stagnated in the last years. In the very same years, however, the development of periodic array-based substrates helped SEIRS to gather momentum. This development was supported by technological progress concerning electromagnetic field solvers, which help to understand plasmonic properties and allow targeted design. In addition, the strong progress concerning modern fabrication methods allowed to implement these designs into practice. The aim of this contribution is to critically review the development of these engineered surfaces for SEIRS, to compare the different approaches with regard to their performance where possible, and report further gain of knowledge around and in relation to these structures.
- ItemBeyond Beer's Law: Why the Index of Refraction Depends (Almost) Linearly on Concentration(Weinheim : Wiley-VCH Verl., 2020) Mayerhöfer, Thomas G.; Dabrowska, Alicja; Schwaighofer, Andreas; Lendl, Bernhard; Popp, JürgenBeer's empiric law states that absorbance is linearly proportional to the concentration. Based on electromagnetic theory, an approximately linear dependence can only be confirmed for comparably weak oscillators. For stronger oscillators the proportionality constant, the molar attenuation coefficient, is modulated by the inverse index of refraction, which is itself a function of concentration. For comparably weak oscillators, the index of refraction function depends, like absorbance, linearly on concentration. For stronger oscillators, this linearity is lost, except at wavenumbers considerably lower than the oscillator position. In these transparency regions, linearity between the change of the index of refraction and concentration is preserved to a high degree. This can be shown with help of the Kramers–Kronig relations which connect the integrated absorbance to the index of refraction change at lower wavenumbers than the corresponding band. This finding builds the foundation not only for refractive index sensing, but also for new interferometric approaches in IR spectroscopy, which allow measuring the complex index of refraction function. © 2020 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.
- ItemBeer's Law-Why Integrated Absorbance Depends Linearly on Concentration(Weinheim : Wiley-VCH Verl., 2019) Mayerhöfer, Thomas G.; Pipa, Andrei V.; Popp, JürgenAs 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.
- ItemThe Bouguer-Beer-Lambert Law: Shining Light on the Obscure(Weinheim : Wiley-VCH Verl., 2020) Mayerhöfer, Thomas G.; Pahlow, Susanne; Popp, JürgenThe 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.
- ItemCorrecting systematic errors by hybrid 2D correlation loss functions in nonlinear inverse modelling(San Francisco, California, US : PLOS, 2023) Mayerhöfer, Thomas G.; Noda, Isao; Pahlow, Susanne; Heintzmann, Rainer; Popp, JürgenRecently a new family of loss functions called smart error sums has been suggested. These loss functions account for correlations within experimental data and force modeled data to obey these correlations. As a result, multiplicative systematic errors of experimental data can be revealed and corrected. The smart error sums are based on 2D correlation analysis which is a comparably recent methodology for analyzing spectroscopic data that has found broad application. In this contribution we mathematically generalize and break down this methodology and the smart error sums to uncover the mathematic roots and simplify it to craft a general tool beyond spectroscopic modelling. This reduction also allows a simplified discussion about limits and prospects of this new method including one of its potential future uses as a sophisticated loss function in deep learning. To support its deployment, the work includes computer code to allow reproduction of the basic results.