Kowalczyk Piotr, Jaroniec Mietek, Terzyk Artur P, Kaneko Katsumi, Do Duong D
Department of Chemistry, Faculty of Science, Chiba University, 1-3 Yayoi, Chiba, 263, Japan.
Langmuir. 2005 Mar 1;21(5):1827-33. doi: 10.1021/la047645n.
In this work, we propose an improvement of the classical Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in mesoporous systems. The primary idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the surface tension changes in mesopores. In addition, the statistical film thickness (so-called t-curve) evaluated accurately on the basis of the adsorption isotherms measured for the MCM-41 materials is used instead of the originally proposed t-curve (to take into account the excess of the chemical potential due to the surface forces). It is shown that the aforementioned modifications of the original DBdB theory have significant implications for the pore size analysis of mesoporous solids. To verify our improvement of the DBdB pore size analysis method (IDBdB), a series of the calcined MCM-41 samples, which are well-defined materials with hexagonally ordered cylindrical mesopores, were used for the evaluation of the pore size distributions. The correlation of the IDBdB method with the empirically calibrated Kruk-Jaroniec-Sayari (KJS) relationship is very good in the range of small mesopores. So, a major advantage of the IDBdB method is its applicability for small mesopores as well as for the mesopore range beyond that established by the KJS calibration, i.e., for mesopore radii greater than approximately 4.5 nm. The comparison of the IDBdB results with experimental data reported by Kruk and Jaroniec for capillary condensation/evaporation as well as with the results from nonlocal density functional theory developed by Neimark et al. clearly justifies our approach. Note that the proposed improvement of the classical DBdB method preserves its original simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the mean pore size by the powder X-ray diffraction method.
在这项工作中，我们提出了对介孔体系中毛细凝聚/蒸发的经典德亚金-布罗克霍夫-德布尔（DBdB）理论的改进。这种改进的主要思路是采用吉布斯-托尔曼-柯尼希-布夫方程来预测介孔中的表面张力变化。此外，基于对MCM-41材料测量的吸附等温线准确评估的统计膜厚度（即所谓的t曲线），取代了最初提出的t曲线（以考虑表面力导致的化学势过剩）。结果表明，对原始DBdB理论的上述修正对介孔固体的孔径分析具有重要意义。为了验证我们对DBdB孔径分析方法（IDBdB）的改进，使用了一系列煅烧后的MCM-41样品，这些样品是具有六方有序圆柱形介孔的明确材料，用于评估孔径分布。在小介孔范围内，IDBdB方法与经验校准的克鲁克-亚罗涅茨-萨亚里（KJS）关系的相关性非常好。因此，IDBdB方法的一个主要优点是它适用于小介孔以及超出KJS校准所确定范围的介孔范围，即介孔半径大于约4.5 nm。将IDBdB结果与克鲁克和亚罗涅茨报道的毛细凝聚/蒸发实验数据以及内马克等人开发的非局部密度泛函理论结果进行比较，清楚地证明了我们的方法是合理的。请注意，对经典DBdB方法的改进保留了其原有的简单性，同时确保了孔径分析的显著改进，这通过粉末X射线衍射法对平均孔径的独立估计得到了证实。
