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Solving the adsorption integral equation with Langmuir-kernel and the influence of temperature on the stability of the solution

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Abstract

Adsorption energy distribution functions can be calculated from measured adsorption isotherms by solving the adsorption integral equation. In this context, it is common practice to use general regularization methods, which are independent of the kernel of the adsorption integral equation, but do not permit error estimation. In order to overcome this disadvantage, we present in this paper a solution theory which is tailor-made for the Langmuir kernel of the adsorption integral equation. The presented theory by means of differentiation and Fourier series is the basis for a regularization method with explicit terms for error amplification. By means of simple and complicated adsorption energy distribution functions we show for ideal gas adsorption isotherms without measurement error that reliable distribution functions can be obtained from the isotherms. Furthermore we show how the stability of the solution depends on temperature.

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Notes

  1. In the following whenever it is necessary, F is continued by 0 outside of \([u_{\min } ,u_{\max } ]\).

  2. This is actually done for the Stieltjes transform but the proof can be done analogously for our case by using a simple change of variables that transforms (7) into a Stieltjes integral.

  3. In order to distinguish this approximation by the approximation \(F_n\) given in (43), we choose the symbol \({\mathcal {F}}_n\).

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Acknowledgments

The financial support for this project by Deutsche Forschungsgemeinschaft (DFG, KA 1560/6-1) is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering/Process Engineering, University of Applied Sciences Dresden (HTW), Friedrich-List-Platz 1, 01069, Dresden, Germany

    Steffen Arnrich, Peter Bräuer & Grit Kalies

Authors
  1. Steffen Arnrich
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  2. Peter Bräuer
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  3. Grit Kalies
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Correspondence to Steffen Arnrich.

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Arnrich, S., Bräuer, P. & Kalies, G. Solving the adsorption integral equation with Langmuir-kernel and the influence of temperature on the stability of the solution. J Math Chem 53, 1997–2017 (2015). https://doi.org/10.1007/s10910-015-0531-5

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  • DOI: https://doi.org/10.1007/s10910-015-0531-5

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