SESAMI APP: An Accessible Interface for Surface Area Calculation of Materials from Adsorption Isotherms

1 Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States of America 2 School of Chemical Engineering, Pusan National University, Busan, South Korea 3 William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH, United States of America 4 Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 5 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, United States of America ¶ Corresponding author DOI: 10.21105/joss.05429


BET theory background
The surface area of a material, , can be calculated as where is the molar amount of adsorbate forming a monolayer per unit mass of material, is the Avogadro constant, and is the area taken up by a single adsorbate molecule in the monolayer.
In order to attain , the monolayer loading region from the isotherm can be identified using the BET equation, where is the vapor pressure, 0 is the saturation vapor pressure, is the adsorbate loading, and is the BET constant.
The monolayer loading region is assigned to a section of the isotherm where / 0 1− / 0 ⋅ 1 is linear as a function of 0 . The linear region for BET analysis is usually chosen based on the consistency criteria proposed by Rouquerol et al. (F. Rouquerol et al., 2013;J. Rouquerol et al., 2007). The consistency criteria are as follows: 1. The linear region should only span a range of / 0 values in which (1 − / 0 ) monotonically increases with / 0 .
2. The value of should be positive.
3. The value of the monolayer loading capacity, , should correspond to a value of / 0 which falls within the selected linear region.
5. The linear region should end at the knee of the isotherm.
Once a linear region is selected, the identified uptake value is multiplied by the molecular cross-sectional area of the adsorbate, typically derived from the bulk liquid density (16.2 Å 2 /molecule for N 2 ; 14.2 Å 2 /molecule for Ar), to obtain the material's surface area, under the assumption that the adsorbate molecules only form a monolayer (Equation 1). The surface area obtained this way is referred to as the BET area.

Summary
The SESAMI web interface allows a user to make surface area calculations on their web browser simply by uploading isotherm data. The website facilitates access to the previously developed SESAMI models (SESAMI 1 and 2) for the evaluation of material's surface area (Datar et al., 2020;Sinha et al., 2019). The motivation for this interface is to lower the barrier of entry for research groups seeking to use SESAMI code, which was previously packaged in Python and Jupyter Notebook scripts.
SESAMI 1 applies computational routines to identify suitable linear regions of adsorption isotherms for BET area calculations (Fagerlund, 1973). The automated workflow includes consideration of the Rouquerol criteria and the use of coefficients of determination as a measure of linearity. Furthermore, SESAMI 1 supports a combined BET+ESW (excess sorption work) approach for linear region selection; this combined approach has been shown to outperform the BET method in some cases (Sinha et al., 2019). A user can specify a cutoff R 2 and a minimum R 2 , such that a candidate linear region is favored to be selected if it has an R 2 above the cutoff, and a candidate linear region is only considered if it has an R 2 above the minimum. SESAMI 2 applies a machine learning (specifically, regularized linear regression with LASSO) model for the accurate surface area prediction of high surface area materials, improving on BET performance for these materials (Datar et al., 2020). The LASSO model uses as input the average loading in seven isotherm pressure regions as well as pairwise products of these loadings. The SESAMI 1 and 2 routines support isotherms with N 2 and argon adsorbate at 77 K and 87 K, respectively. We note that a recent study shows that surface areas determined from N 2 and Ar isotherms are similar, despite the 2015 IUPAC report's suggested use of Ar (Datar et al., 2022;Thommes et al., 2015). In addition, the SESAMI 1 code supports isotherms with arbitrary user-specified adsorbates if temperature and adsorbate cross-section and saturation vapor pressure are specified.
The SESAMI web interface has extensive error handling and clearly alerts users of issues with their adsorption isotherm data. For example, it alerts the user if no ESW minima are found by SESAMI 1 or if the data is incompatible with SESAMI 2 code due to data sparsity in certain pressure regions. As shown in Figure 1, the interface displays SESAMI 1 calculation results including information on the chosen linear region, namely the satisfied Rouquerol criteria, the pressure range and number of data points in the region, and the coefficient of determination. The interface also displays intermediate SESAMI 1 values for surface area calculation, namely and . Furthermore, the SESAMI web interface allows the user to download figures generated by SESAMI 1 that indicate, among other things, the linear monolayer loading regions chosen by the BET and BET+ESW approaches, as well as the ESW plot ( Figure 1). The user can convert output from commercial equipment to AIF format and upload the converted data to the interface for analysis. The SESAMI web interface is publicly available at https://sesami-web.org/, and source code is available at https://github.com/hjkgrp/SESAMI_web.

Benchmarking
To assess the performance of the SESAMI code in calculating surface areas from isotherms, we benchmark the SESAMI routines against other similar programs for 13 simulated and 9 experimental N 2 isotherms obtained at 77 K for 14 metal-organic frameworks (MOFs), some of which are shown in Figure 2. Simulated isotherms are obtained from grand canonical Monte Carlo (GCMC) simulations using the open-source RASPA 2.0.47 software (Dubbeldam et al., 2016), and experimental adsorption isotherms are obtained from the experimental data reported by Islamoglu and coworkers (Islamoglu et al., 2022). The isotherms are used to calculate surface areas with the SESAMI website, BETSI (Osterrieth et al., 2022;Rampersad et al., 2020), pyGAPS (Iacomi, 2019;Iacomi & Llewellyn, 2019), and BEaTmap (Sadeghi et al., 2020). We find that over the set of 13 GCMC isotherms, the SESAMI machine learning model (run from the web interface) and BEaTmap have the best correlation with Zeo++ version 0.3 surface areas (Willems et al., 2012) calculated with a 1.67 Å radius probe N 2 molecule (Table 1  and Table 2). Differences in performance across software on this benchmark set can be attributed to the differing implementations of linear region identification, or in the case of the SESAMI machine learning model, fundamental differences in how the software calculate surface areas. Nevertheless, all software are in generally good agreement, underscoring the benefit of a computational approach to surface area calculation. The agreement between software is also not surprising due to the similar approach taken by most of the codes of considering multiple subsets of consecutive data points and applying checks like the Rouquerol criteria to select a linear region for BET analysis (SESAMI 1, BETSI, BEaTmap). The agreement between software is also observed over the 9 experimental isotherms ( Table 3).
The CIF files used to generate GCMC isotherms, benchmark isotherms, XLSX files of calculated surface areas across different software tools for both GCMC and experimental isotherms, detailed settings used for each software, and analysis scripts employed are available at https: //github.com/hjkgrp/SESAMI_web. Software settings are also reported in Table 4. When a software for isotherm to surface area calculation does not find a surface area, the reason can vary from no ESW minimum being found or no suitable linear region containing an ESW minimum being found in the case of SESAMI 1 (BET+ESW), to an insufficient number of data points in the chosen BET region in the case of pyGAPS.