Estimating adsorption isotherm parameters in chromatography via a virtual injection promoting double feed-forward neural network

The means to obtain the adsorption isotherms is a fundamental open problem in competitive chromatography. A modern technique of estimating adsorption isotherms is to solve a nonlinear inverse problem in a partial differential equation so that the simulated batch separation coincides with actual experimental results. However, this identification process is usually ill-posed in the sense that the uniqueness of adsorption isotherms cannot be guaranteed, and moreover, the small noise in the measured response can lead to a large fluctuation in the traditional estimation of adsorption isotherms. The conventional mathematical method of solving this problem is the variational regularization, which is formulated as a non-convex minimization problem with a regularized objective functional. However, in this method, the choice of regularization parameter and the design of a convergent solution algorithm are quite difficult in practice. Moreover, due to the restricted number of injection profiles in experiments, the types of measured data are extremely limited, which may lead to a biased estimation. In order to overcome these difficulties, in this paper, we develop a new inversion method – the virtual injection promoting double feed-forward neural network (VIP-DFNN). In this approach, the training data contain various types of artificial injections and synthetic noisy measurement at outlet, generated by a conventional physics model – a time-dependent convection-diffusion system. Numerical experiments with both artificial and real data from laboratory experiments show that the proposed VIP-DFNN is an efficient and robust algorithm.

Data-driven matching of experimental crystal structures and gas adsorption isotherms of metal-organic frameworks

Porous metal-organic frameworks are a class of materials with great promise in gas separation and gas storage applications. Due to the large material space, computational screening techniques have long been an important part of the scientific toolbox. However, a broad validation of molecular simulations in these materials is hampered by the lack of a connection between databases of gas adsorption experiments and databases of the atomic crystal structure of corresponding materials. This work aims to connect the gas adsorption isotherms of metal-organic frameworks collected in the NIST/ARPA-E Database of Novel and Emerging Adsorbent Materials to a corresponding crystal structure in the Cambridge Structural Database. With tens of thousands of isotherms and crystal structures reported to date, an automatic approach is needed to establish this link, which we describe in this paper. As a first application and consistency check, we compare the pore volume deduced from low-temperature argon or nitrogen isotherms to the geometrical pore volume computed from the crystal structure. Overall, 545 argon or nitrogen isotherms could be matched to a corresponding crystal structure. We find that the pore volume computed via the two complementary methods shows acceptable agreement only in about 35% of these cases. We provide the subset of isotherms measured on these materials as a seed for a future, more complete reference data set for computational studies.

Data-driven matching of experimental crystal structures and gas adsorption isotherms of metal-organic frameworks

Porous metal-organic frameworks are a class of materials with great promise in gas separation and gas storage applications. Due to the large material space, computational screening techniques have long been an important part of the scientific toolbox. However, a broad validation of molecular simulations in these materials is hampered by the lack of a connection between databases of gas adsorption experiments and databases of the atomic crystal structure of corresponding materials. This work aims to connect the gas adsorption isotherms of metal-organic frameworks collected in the NIST/ARPA-E Database of Novel and Emerging Adsorbent Materials to a corresponding crystal structure in the Cambridge Structural Database. With tens of thousands of isotherms and crystal structures reported to date, an automatic approach is needed to establish this link, which we describe in this paper. As a first application and consistency check, we compare the pore volume deduced from low-temperature argon or nitrogen isotherms to the geometrical pore volume computed from the crystal structure. Overall, 545 argon or nitrogen isotherms could be matched to a corresponding crystal structure. We find that the pore volume computed via the two complementary methods shows acceptable agreement only in about 35% of these cases. We provide the subset of isotherms measured on these materials as a seed for a future, more complete reference data set for computational studies.

Use of Microfluidic Capillary Electrophoresis for the Determination of Multi-Component Protein Adsorption Isotherms: Application to High-Throughput Analysis for Hydrophobic Interaction Chromatography

Chromatography is a widely used separation process for purification of biopharmaceuticals that is able to obtain high purities and concentrations. The phenomena that occur during separation, mass transfer and adsorption are quite complex. To better understand these phenomena and their mechanisms, multi-component adsorption isotherms must be investigated. High-throughput methodologies are a very powerful tool to determine adsorption isotherms and they waste very small amounts of sample and chemicals, but the quantification of component concentrations is a real bottleneck in multi-component isotherm determination. The behavior of bovine serum albumin, Corynebacterium diphtheriae CRM197 protein and lysozyme, selected as model proteins in binary mixtures with hydrophobic resin, is investigated here. In this work we propose a new method for determining multi-component adsorption isotherms using high-throughput experiments with filter plates, by exploiting microfluidic capillary electrophoresis. The precision and accuracy of the microfluidic capillary electrophoresis platform were evaluated in order to assess the procedure; they were both found to be high and the procedure is thus reliable in determining adsorption isotherms for binary mixtures. Multi-component adsorption isotherms were determined with a totally high-throughput procedure that turned out to be a very fast and powerful tool. The same procedure can be applied to every kind of high-throughput screening.

Upgrading the Hydrogen Storage of MOF-5 by Post-Synthetic Exchange with Divalent Metal Ions

In metal-organic frameworks (MOFs), mixed-metal clusters have the opportunity to adsorb hydrogen molecules due to a greater charge density of the metal. Such interactions may subsequently enhance the gravimetric uptake of hydrogen. However, only a few papers have explored the ability of mixed-metal MOFs to increase hydrogen uptake. The present work reveals the preparation of mixed metal metal-organic frameworks M-MOF-5 (where M = Ni2+, Co2+, and Fe2+) (where MOF-5 designates MOFs such as Zn2+ and 1,4-benzenedicarboxylic acid ligand) using the post-synthetic exchange (PSE) technique. Powder X-ray diffraction patterns and scanning electron microscopy images indicate the presence of crystalline phases after metal exchange, and the inductively coupled plasma–mass spectroscopy analysis confirmed the exchange of metals by means of the PSE technique. The nitrogen adsorption isotherms established the production of microporous M-MOF-5. Although the additional metal ions decreased the surface area, the exchanged materials displayed unique features in the gravimetric uptake of hydrogen. The parent MOF-5 and the metal exchanged materials (Ni-MOF-5, Co-MOF-5, and Fe-MOF-5) demonstrated hydrogen capacities of 1.46, 1.53, 1.53, and 0.99 wt.%, respectively. The metal-exchanged Ni-MOF-5 and Co-MOF-5 revealed slightly higher H2 uptake in comparison with MOF-5; however, the Fe-MOF-5 showed a decrease in uptake due to partial discrete complex formation (discrete complexes with one or more metal ions) with less crystalline nature. The Sips model was found to be excellent in describing the H2 adsorption isotherms with a correlation coefficient ≅ 1. The unique hydrogen uptakes of Ni− and Co-MOF-5 shown in this study pave the way for further improvement in hydrogen uptake.

Computation-informed optimization of Ni(PyC)₂ functionalization for noble gas separations

Metal-organic frameworks (MOFs) are promising nanoporous materials for the adsorptive capture and separation of noble gases at room temperature. Among the numerous MOFs synthesized and tested for noble gas separations, Ni(PyC)₂ (PyC = pyridine-4-carboxylate) exhibits one of the highest xenon/krypton selectivities at room temperature. Like lead-optimization in drug discovery, here we aim to tune the chemistry of Ni(PyC)₂, by appending a functional group to its PyC ligands, to maximize its Xe/Kr selectivity. To guide experiments in the laboratory, we virtually screen Ni(PyC-X)₂ (X=functional group) structures for noble gas separations by (i) constructing a library of Ni(PyC-X)₂ crystal structure models then (ii) using molecular simulations to predict noble gas (Xe, Kr, Ar) adsorption and selectivity at room temperature in each structure. The virtual screening predicts several Ni(PyC-X)₂ structures to exhibit a higher Xe/Kr, Xe/Ar, and Kr/Ar selectivity than the parent Ni(PyC)₂ MOF, with Ni(PyC-m-NH₂)₂ among them. In the laboratory, we synthesize Ni(PyC-m-NH₂)₂, determine its crystal structure by X-ray powder diffraction, and measure its Xe, Kr, and Ar adsorption isotherms (298 K). In agreement with our molecular simulations, the Xe/Kr, Xe/Ar, and Kr/Ar selectivities of Ni(PyC-m-NH₂)₂ exceed those of the parent Ni(PyC)₂. Particularly, Ni(PyC-m-NH₂)₂ exhibits a [derived from experimental, equilibrium adsorption isotherms] Xe/Kr selectivity of 20 at dilute conditions and 298 K, compared to 17 for Ni(PyC)₂. According to in situ X-ray diffraction, corroborated by molecular models, Ni(PyC-m-NH₂)₂ presents well-defined binding pockets tailored for Xe and organized along its one-dimensional channels. In addition to discovering the new, performant Ni(PyC-m-NH₂)₂ MOF for noble gas separations, our study illustrates the computation-informed optimization of the chemistry of a "lead" MOF to target adsorption of a specific gas.