Solving the adsorption integral equation with Langmuir-kernel and the influence of temperature on the stability of the solution
Solving the adsorption integral equation with Langmuir-kernel and the influence of temperature on the stability of the solution
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DOI：
10.1007/s10910-015-0531-5
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发表时间：
2015-07
影响因子：
1.7
通讯作者：
S. Arnrich;P. Bräuer;G. Kalies
中科院分区：
文献类型：
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作者：
S. Arnrich;P. Bräuer;G. Kalies
通过求解吸附积分方程，可从测量的吸附等温线计算出吸附能分布函数。在这种情况下，通常的做法是使用一般的正则化方法，它与吸附积分方程的核无关，但不允许误差估计。为了克服这一缺点，本文提出了一种专门针对吸附积分方程Langmuir核的解理论。通过微分和傅立叶级数提出的理论是误差放大显式正则化方法的基础。通过简单的吸附能分布函数和复杂的吸附能分布函数，证明了无测量误差的理想气体吸附等温线可以得到可靠的吸附能分布函数。此外，我们还说明了溶液的稳定性如何取决于温度。
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.