| 摘要: | 金屬有機骨架（MOFs）是一類多孔材料，因其在氣體儲存、分離與催化等應用中具有極大潛力而備受關注。其中，比表面積是一個關鍵參數，直接影響其吸附能力。傳統上，比表面積多以 Brunauer-Emmett-Teller（BET）方法進行估算。然而，此方法需從吸附等溫線中選擇一個符合 Rouquerol 四項一致性準則的線性區段，過程中需依賴主觀判斷，因此不同研究者之間常會導致結果不一致。
為解決此問題，本研究對 263 個 MOFs 的比表面積進行系統性分析，吸附等溫線透過大正則蒙地卡羅（GCMC）模擬，在 87 K 下以氬氣為探針分子獲得。我們不再僅選擇單一線性區段，而是整合 SESAMI 程式碼中所有符合準則的可能線性區段，進一步提出加權平均 BET 方法（WA BET），根據各區段特性分配權重。結果顯示，WA BET 有效提升預測準確度，使與真實單層覆蓋量的偏差降低超過 4\%。
此外，本研究也比較了兩種無需選擇線性區段的方法：ESW法與轉折點（I-point）法。儘管這兩種方法能避免主觀選擇所帶來的誤差，然而結果顯示 WA BET 在整體準確性與穩健性方面仍表現最佳，尤其適用於具有高比表面積或複雜吸附行為的 MOF。
進一步地，本研究也嘗試以機器學習方法取代傳統物理模型。我們分別訓練了卷積神經網路（CNN）、深度神經網路（DNN）與線性回歸模型，使用吸附等溫線作為輸入以預測單層比表面積。結果顯示，CNN 與 DNN 模型在多數情況下均優於傳統方法，尤其在 BET 方法常出現偏差的區段表現更為穩定；而線性回歸雖準確度略低，卻具備高度可解釋性，其輸出權重有助於了解不同壓力點對預測結果的影響。
綜上所述，本研究揭示傳統 BET 方法因主觀選擇單一線性區段所造成的侷限，並提出數種改進策略，結合物理原理與資料驅動模型，為多孔材料比表面積的準確預測與一致性提供了新的解方。;Metal-organic frameworks (MOFs) are a class of porous materials with exceptional potential in applications such as gas storage, separation, and catalysis. Surface area is a key parameter governing adsorption capacity, traditionally estimated using the Brunauer-Emmett-Teller (BET) method. Although widely adopted, the BET method requires selecting a linear region from the isotherm that satisfies Rouquerol′s four consistency criteria—a process prone to subjectivity and inconsistency across researchers. To address this, we systematically analyzed 263 MOFs using argon adsorption isotherms at 87 K obtained via grand canonical Monte Carlo (GCMC) simulations. Rather than relying on a single linear region, we implemented a comprehensive evaluation of all valid linear regions identified by the SESAMI code and proposed a novel weighted-average BET (WA BET) approach that assigns weights based on region-specific characteristics. This method significantly improves accuracy, reducing the overall deviation from the true monolayer area by over 4\%.
In parallel, we benchmarked WA BET against two methods: the Excess Sorption Work (ESW) method and the inversion point (I-point) method. While both provide alternatives without requiring linear region selection, our results show that WA BET consistently outperforms them in terms of accuracy and robustness—particularly for MOFs with high surface areas or complex adsorption behavior.
Furthermore, machine learning models including convolutional neural networks (CNN), deep neural networks (DNN), and linear regression were trained on isotherm data to explore data-driven alternatives for surface area prediction. These models achieve even lower deviations than conventional methods, with CNN and DNN models demonstrating strong predictive power, especially in regions where BET-based methods tend to fail. The linear regression model, although slightly less accurate, provides interpretability through feature weights, offering insights into the influence of specific pressure regions.
Altogether, this study highlights the limitations of single-region BET selection and offers a suite of improved approaches—both physics-based and data-driven—for more accurate and consistent surface area estimation in porous materials. |
