Department of Materials Science and Engineering and ‡Department of Chemistry, University of Florida , Gainesville, Florida 32611, United States.
Langmuir. 2017 Oct 24;33(42):11138-11145. doi: 10.1021/acs.langmuir.7b01961. Epub 2017 Aug 22.
The pore size distribution (PSD) is one of the most important properties when characterizing and designing materials for gas storage and separation applications. Experimentally, one of the current standards for determining microscopic PSD is using indirect molecular adsorption methods such as nonlocal density functional theory (NLDFT) and N isotherms at 77 K. Because determining the PSD from NLDFT is an indirect method, the validation can be a nontrivial task for amorphous microporous materials. This is especially crucial since this method is known to produce artifacts. In this work, the accuracy of NLDFT PSD was compared against the exact geometric PSD for 11 different simulated amorphous microporous materials. The geometric surface area and micropore volumes of these materials were between 5 and 1698 m/g and 0.039 and 0.55 cm/g, respectively. N isotherms at 77 K were constructed using Gibbs ensemble Monte Carlo (GEMC) simulations. Our results show that the discrepancies between NLDFT and geometric PSD are significant. NLDFT PSD produced several artificial gaps and peaks that were further confirmed by the coordinates of inserted particles of a specific size. We found that dominant peaks from NLDFT typically reported in the literature do not necessarily represent the truly dominant pore size within the system. The confirmation provides concrete evidence for artifacts that arise from the NLDFT method. Furthermore, a sensitivity analysis was performed to show the high dependency of PSD as a function of the regularization parameter, λ. A higher value of λ produced a broader and smoother PSD that closely resembles geometric PSD. As an alternative, a new criterion for choosing λ, called here the smooth-shift method (SSNLDFT), is proposed that tuned the NLDFT PSD to better match the true geometric PSD. Using the geometric pore size distribution as our reference, the smooth-shift method reduced the root-mean-square deviation by ∼70% when the geometric surface area of the material is greater than 100 m/g.
孔径分布（PSD）是描述和设计用于气体储存和分离应用的材料的最重要性质之一。在实验中，确定微观 PSD 的当前标准之一是使用间接分子吸附方法，例如非局部密度泛函理论（NLDFT）和 77 K 下的 N 等温线。由于从 NLDFT 确定 PSD 是一种间接方法，因此对于非晶微孔材料来说，验证可能是一项艰巨的任务。由于该方法已知会产生伪影，因此这一点尤其重要。在这项工作中，将 NLDFT PSD 的准确性与 11 种不同模拟的非晶微孔材料的精确几何 PSD 进行了比较。这些材料的几何表面积和微孔体积分别在 5 到 1698 m/g 之间和 0.039 到 0.55 cm/g 之间。77 K 下的 N 等温线是使用吉布斯系综蒙特卡罗（GEMC）模拟构建的。我们的结果表明，NLDFT 和几何 PSD 之间的差异非常显著。NLDFT PSD 产生了几个人为的间隙和峰值，这些间隙和峰值通过特定尺寸插入粒子的坐标进一步得到了证实。我们发现，NLDFT 通常在文献中报告的主导峰不一定代表系统内真正的主导孔径。这种确认为 NLDFT 方法产生的伪影提供了具体的证据。此外，还进行了敏感性分析以显示 PSD 作为正则化参数 λ 的函数的高度依赖性。更高的 λ 值会产生更宽且更平滑的 PSD，该 PSD 与几何 PSD 非常相似。作为替代方案，提出了一种选择 λ 的新准则，称为平滑移位方法（SSNLDFT），它可以调整 NLDFT PSD 以更好地匹配真实的几何 PSD。使用几何孔径分布作为参考，当材料的几何表面积大于 100 m/g 时，平滑移位方法将均方根偏差降低了约 70%。
