Xia Xinyu, Litvinov Sergey, Muhler Martin
Laboratory of Industrial Chemistry, Ruhr-University Bochum, D-44780 Bochum, Germany.
Langmuir. 2006 Sep 12;22(19):8063-70. doi: 10.1021/la061233s.
Adsorption on heterogeneous surfaces with three basic energy distribution models (uniform model, exponential model, and normal-like model) is studied. Exact analytical solutions of the adsorption isotherms and the heats of adsorption are derived for the uniform and exponential models, and, with these solutions including a numerical solution for the normal-like model, the behavior of the differential heat of adsorption and the "apparent" standard adsorption entropy concerning the overall surface is described as a function of coverage and temperature. The approximations underlying the isotherms and heats of adsorption in the Temkin, Freundlich, and Langmuir-Freundlich types of adsorption are rationalized. By comparing these empirical formulas to the exact solutions, the level of these approximations is found to be identical, which is similar to the "condensation approximation". Their preconditions are that either the temperature is low enough, or the surface is strongly heterogeneous. Generally, they are suitable for the middle coverage range. The exact solutions provide a method to obtain more information on the heats, entropy, and heterogeneity of the catalyst surface from the calorimetric measurement of the heat of adsorption.
研究了在具有三种基本能量分布模型（均匀模型、指数模型和类正态模型）的非均匀表面上的吸附。推导了均匀模型和指数模型的吸附等温线和吸附热的精确解析解，并利用这些解（包括类正态模型的数值解），描述了关于整个表面的吸附微分热和“表观”标准吸附熵随覆盖度和温度的变化行为。对Temkin、Freundlich和Langmuir-Freundlich类型吸附中的吸附等温线和吸附热所基于的近似进行了合理化分析。通过将这些经验公式与精确解进行比较，发现这些近似的程度是相同的，这类似于“凝聚近似”。它们的前提条件是温度足够低，或者表面具有很强的非均匀性。一般来说，它们适用于中等覆盖度范围。精确解提供了一种从吸附热的量热测量中获取关于催化剂表面的热、熵和非均匀性更多信息的方法。
