Efficient simulation of binary adsorption isotherms using transition matrix Monte Carlo

Molecular simulations of binary adsorption in porous materials are a useful complement to experimental studies of mixture adsorption. Most molecular simulations of binary adsorption are performed using grand canonical Monte Carlo (GCMC) to independently examine a range of state points of interest. A disadvantage of this approach is that it only yields information at a discrete set of state points; therefore, if a complete isotherm is required for arbitrary conditions, some type of data fitting or interpolation must be used in combination with the GCMC data. We show that the transition matrix Monte Carlo (TMMC) method of Shen and Errington (Shen, V. K.; Errington, J. R. J. Chem.Phys. 2005, 122, 064508) is well-suited to simulation of binary adsorption in porous materials. At the completion of a TMMC simulation, the adsorption isotherm for all possible bulk phase compositions and pressures is available without data fitting or interpolation. It is also straightforward to use results from TMMC to compute derivatives of the isotherm such as the mixture thermodynamic correction factors, partial differential ln f(i)/partial differential ln c(j), again without data fitting or interpolation. This approach should be useful in contexts where information on the full adsorption isotherm is needed, such as the design of adsorption- or membrane-based separations.     

用实验吸附等温线和计算机分子模拟表征中孔分子筛MCM-41

首先比较了表征MCM-41的两个势模型对吸附等温线的影响。发现在一维势模型 中,低压部分的吸附应与选用的势模型的势阱深度有关,而毛细凝聚发生的位置与 孔壁在离壁面较远处与流体分子的相互作用的强弱有关。然后作者使用了一个“混 合”的势模型,即采用作者提出的势函数表征孔壁中氧原子对MCM-41中流体分子的 作用,而采用Tjatjopoulos等提出的势函数近似地表征MCM-41表面硅醇基团以及一 些未知因子对流体分子的作用。虽然这种势模型仍然是一维的,但这种势模型将孔 壁内氧原子的作用和表面上非均匀性分开考虑,具有较明确的物理意义。通过计算 机模拟与实验数据的比较发现,这种势模型可以较好地拟合氮气在MCM-41中的吸附 等温线。     

Chemistry of Soft Porous Crystals: Structural Dynamics and Gas Adsorption Properties

In this Minireview, we discuss the fundamental chemistry of soft porous crystals (SPCs) by characterizing their common structural features and the resulting structural softness and transitions. In particular, we focus on the recently emerging properties based on metastable transitions and those arising from local dynamics. By comparing the resulting adsorption properties to those of commonly applied rigid adsorbents, we highlight the potential of SPCs to revolutionize adsorption‐based technologies, considering our current understanding of the thermodynamic and kinetic aspects. We provide brief outlines for the experimental and computational characterization of such phenomena and offer an outlook toward next‐generation SPCs likely to be discovered in the next decade.     

Water adsorption and desorption on microporous solids at elevated temperature

Summary An accurate gravimetric method was used to explore water adsorption/desorption isotherms between 105 and to 250°C for a number of synthetic and natural porous solids including controlled pore glass, activated carbon fiber monoliths, natural zeolites, pillared clay, and geothermal reservoir rocks. The main goal of this work was to evaluate water adsorption results, in particular temperature dependence of hysteresis, for relatively uniform, nano-structured solids, in the context of other state-of-the-art experimental and modeling methods including nitrogen adsorption, spectroscopy, neutron scattering, and molecular simulation. Since no single method is able to provide a complete characterization of porous materials, a combination of approaches is needed to achieve progress in understanding the fluid-solid interactions on the way to developing a predictive capability.     

氮气在MCM－41分子筛中的吸附：实验和分子模拟

用美国Micromeritics公司生产的ASAP2010物理吸附仪测定了低温（77 K） N_2在MCM-41分子筛中的吸附等温线，获得了表征MCM-41特征的BET比表面、BJH孔 容和平均孔径。同时用巨正则Monte Carlo（GCMC）模拟方法考究了N_2在MCM-41中 的吸附，得到了N_2在MCM-41中的模拟吸附等温线，分析了流体在MCM-41分子筛中 的微观结构。GCMC模拟中MCM-41介孔材料模型化为圆柱孔，N_2模型化为Lennard- Jones（LJ）球。N_2和MCM-41介孔墙壁间的相互作用采用Tjatjopoulos-Feke- Mann（TFM）势能模型进行表征。通过使模拟和实验结果有一个好的吻合，确定了 一组有效的MCM-41分子筛的势能参数（σ_(ww) = 0.265 nm，∈_(ww)/k = 190 K ）。这为以后其他吸附质在MCM-41中吸附的预测奠定了基础、提供了依据。     

Adsorption energy distribution from the Aranovich-Donohue lattice density functional theory

We propose a new methodology projected for the estimation of the adsorption energy distribution from the monolayer part of a single nitrogen adsorption isotherm determined at 77 K based on the lattice density functional theory (DFT) via the Aranovich-Donohue formalism. At first sight, the presented approach is computationally more difficult than a classical one. However, it is more flexible and comprehensible. Next, we developed a numerical program and used it for the estimation of the adsorption energy distribution from the experimental data on carbon black samples. The main nitrogen molecule-carbon black surface interaction energy can be estimated as approximately 7-8 kJ/mol, but the heterogeneity of the investigated materials differs significantly. Furthermore, we compare the results obtained from the lattice DFT via the Aranovich-Donohue formalism with the solution of the integral equation with the kernel represented by the classical monolayer localized Fowler-Guggenheim isotherm equation. The similarity between these two independent approaches is observed. The proposed methodology can be used for the investigation of the energetic heterogeneity of not only the carbonaceous materials but also the other "flat-surfaced" solids.     

Characterization of aluminium surface treatments by means of gas adsorption measurements

Adsorption measurements were used to determine the specific surface area of a.c. electrolytically grained aluminium and the porosity distribution diagram of porous anodized aluminium. Alternating current electrolytic graining of aluminium is used to increase the specific surface area for the preparation of litho sheets or capacitor foil. The specific surface area S (calculated by the BET procedure from the nitrogen adsorption isotherm) was studied as a function of the graining frequency between 0.1 and 1000 Hz. The results were related to the graining morphology by comparing them with scanning electron microscopy micrographs. It is concluded that in contrast to the more common surface investigation techniques the method can be used to measure quantitatively the gain in surface area after such a treatment as a.c. electrolytic graining. In the second part of the paper the pore size distribution diagrams are calculated from the adsorption isotherm for porous sulphuric acid films. It is shown that the dominant pore diameter corresponds rather well to the pore diameter observed in transmission electron microscopy sectional views. This means that the adsorption method can be applied to study the porosity of the aluminum oxide films. The method was then used to study the influence of the pretreatment on the porous oxide film morphology.     

Applicability of the BET method for determining surface areas of microporous metal-organic frameworks

The surface area is one of the most important quantities for characterizing novel porous materials. The BET analysis is the standard method for determining surface areas from nitrogen adsorption isotherms and was originally derived for multilayer gas adsorption onto flat surfaces. Metal-organic frameworks (MOFs) are a relatively new class of crystalline, porous materials that have been shown to exhibit very large BET surface areas. These materials are microporous and possess surfaces that are far from flat. In some MOFs, adsorption occurs through a pore-filling mechanism rather than by layer formation. Thus, it is unclear whether BET surface area numbers reported for these materials are truly meaningful. Given the standard practice of reporting BET surface areas for novel porous materials, a critical test of the BET method is much needed. In this work, grand canonical Monte Carlo simulations were used to predict adsorption isotherms for nitrogen in a series of MOFs. The predicted isotherms were used as pseudoexperimental data to test the applicability of the BET theory for obtaining surface areas of microporous MOFs. BET surface areas calculated from the simulated isotherms agree very well with the accessible surface areas calculated directly from the crystal structures in a geometric fashion. In addition, the surface areas agree well with experimental reports in the literature. These results provide a strong validation that the BET theory can be used to obtain surface areas of MOFs.     

Theoretical and experimental investigation of morphology and temperature effects on adsorption of organic vapors in single-walled carbon nanotubes

Hexane adsorption on single-walled carbon nanotube (SWNT) bundles is studied by both simulation and experimentally using a previously developed computer-aided methodology, which employed a smaller physisorbed probe molecule, nitrogen, to explore the porosity of nanotube samples. Configurational-bias grand canonical Monte Carlo simulation of hexane adsorption on localized sites of the bundles is carried out to predict adsorption on their external surface and in their internal sites. These localized isotherms are then combined into a global isotherm for a given sample by using knowledge of its tube-diameter distribution and structural parameters, such as the fraction of open-ended nanotubes and the external surface area of bundles in samples, which have been independently determined from the standard nitrogen adsorption isotherm. The near-perfect replication of experimental isotherms demonstrates the validity of our method for structural characterization of SWNT samples. The effect of temperature on adsorption is also studied and the simulation results are extrapolated to predict the limiting hexane adsorption capacity of the samples. The similarity between the hexane adsorption isotherms and those of other organic molecules demonstrates that the adsorption mechanisms explored here are not specific to hexane, and that the proposed methodology can be potentially applicable to other sorbates with equal success.     

Comparison of nitrogen adsorption at 77 K on non-porous silica and pore wall of MCM-41 materials by means of density functional theory

Nitrogen adsorption on a surface of a non-porous reference material is widely used in the characterization. Traditionally, the enhancement of solid-fluid potential in a porous solid is accounted for by incorporating the surface curvature into the solid-fluid potential of the flat reference surface. However, this calculation procedure has not been justified experimentally. In this paper, we derive the solid-fluid potential of mesoporous MCM-41 solid by using solely the adsorption isotherm of that solid. This solid-fluid potential is then compared with that of the non-porous reference surface. In derivation of the solid-fluid potential for both reference surface and mesoporous MCM-41 silica (diameter ranging from 3 to 6.5 nm) we employ the nonlocal density functional theory developed for amorphous solids. It is found that, to our surprise, the solid-fluid potential of a porous solid is practically the same as that for the reference surface, indicating that there is no enhancement due to surface curvature. This requires further investigations to explain this unusual departure from our conventional wisdom of curvature-induced enhancement. Accepting the curvature-independent solid-fluid potential derived from the non-porous reference surface, we analyze the hysteresis features of a series of MCM-41 samples.     

Comparative Studies of the Micropore Size Distributions of an Alumina Pillared Montmorillonite and a Molecular Sieve Carbon

The aim of this work is to applicate and to compare various analysis methods for the characterization of the microporous structure from nitrogen adsorption at 77 K of an alumina pillared montmorillonite and a molecular sieve carbon. The adsorption potential distribution (X(A)), the Horvath-Kawazoe (HK) method, the Jaroniec-Gadkare-Choma (JGC) one and a numerical algorithm for the reconstruction of the micropore size distribution (MPSD) from the adsorption equilibrium isotherm have been applied. Comparison of all distributions revealed that the molecular sieve carbon shows smaller micropores and smaller structural hetereogeneity than the alumina pillared montmorillonite.     

Engineering micromechanics of soft porous crystals for negative gas adsorption

Framework materials at the molecular level, such as metal–organic frameworks (MOF), were recently found to exhibit exotic and counterintuitive micromechanical properties. Stimulated by host–guest interactions, these so-called soft porous crystals can display counterintuitive adsorption phenomena such as negative gas adsorption (NGA). NGA materials are bistable frameworks where the occurrence of a metastable overloaded state leads to pressure amplification upon a sudden framework contraction. How can we control activation barriers and energetics via functionalization of the molecular building blocks that dictate the frameworks'' mechanical response? In this work we tune the elastic and inelastic properties of building blocks at the molecular level and analyze the mechanical response of the resulting frameworks. From a set of 11 frameworks, we demonstrate that widening of the backbone increases stiffness, while elongation of the building blocks results in a decrease in critical yield stress of buckling. We further functionalize the backbone by incorporation of sp³ hybridized carbon atoms to soften the molecular building blocks, or stiffen them with sp² and sp carbons. Computational modeling shows how these modifications of the building blocks tune the activation barriers within the energy landscape of the guest-free bistable frameworks. Only frameworks with free energy barriers in the range of 800 to 1100 kJ mol⁻¹ per unit cell, and moderate yield stress of 0.6 to 1.2 nN for single ligand buckling, exhibit adsorption-induced contraction and negative gas adsorption. Advanced experimental in situ methodologies give detailed insights into the structural transitions and the adsorption behavior. The new framework DUT-160 shows the highest magnitude of NGA ever observed for nitrogen adsorption at 77 K. Our computational and experimental analysis of the energetics and mechanical response functions of porous frameworks is an important step towards tuning activation barriers in dynamic framework materials and provides critical design principles for molecular building blocks leading to pressure amplifying materials.

We characterise the elastic properties of molecular building blocks and how they impact the mechanical properties of soft porous crystals.     

Calculations of the energy distribution from perturbation peak data--a new tool for characterization of chromatographic phases

The calculation of the adsorption energy distribution (AED) was recently introduced as an important tool for the chromatographic community for characterization of modern phases. The AED-calculations, provides model-independent information about the numbers of different adsorption sites and their respective energy-levels, prior to the selection of an adsorption isotherm model which narrows the number of possible rival models. The selection of a proper model for the fitting of the determined raw data is crucial; if the wrong model is selected misleading information about the retention mechanism may be drawn. The AED-calculations require raw adsorption isotherm data (i.e. data points) which is unfortunately not obtained by the newly validated perturbation peak method. In this study, we developed mathematical expression allowing the use of the raw tangential slope provided by the perturbation peak method for AED calculations. The approach worked excellently and was verified against both computer-generated adsorption isotherm data as well as experimentally determined data, using three different experimental systems. It was found that the calculations of the AED, as based on perturbation peak data, converts faster and are not more sensitive to experimental noise as compared to the classical AED calculations using raw adsorption isotherm data.     

Experiment and theory of low-pressure nitrogen adsorption in organic layers supported or grafted on inorganic adsorbents: toward a tool to characterize surfaces of hybrid organic/inorganic systems

We report experimental nitrogen adsorption isotherms of organics-coated silicas, which exhibit a low-pressure desorption branch that does not meet the adsorption branch upon emptying of the pores. To address the physical origin of such a hysteresis loop, we propose an equilibrium thermodynamic model that enables one to explain this phenomenon. The present model assumes that, upon adsorption, a small amount of nitrogen molecules penetrate within the organic layer and reach adsorption sites that are located on the inorganic surface, between the grafted or adsorbed organic molecules. The number of accessible adsorption sites thus varies with the increasing gas pressure, and then we assume that it stays constant upon desorption. Comparison with experimental data shows that our model captures the features of nitrogen adsorption on such hybrid organic/inorganic materials. In particular, in addition to predicting the shape of the adsorption isotherm, the model is able to estimate, with a reasonable number of adjustable parameters, the height of the low-pressure hysteresis loop and to assess in a qualitative fashion the local density of the organic chains at the surface of the material.     

Determination of chromatographic separation parameters of tryptophan enantiomers on a Chirosil-SCA chiral stationary phase by using the inverse method based on the initial guesses estimated from elution by characteristic point method

An effective chiral stationary phase (CSP) for enantioseparation of amino acids was established previously by bonding (18-crown-6)-2, 3, 11, 12-tetracarboxylic acid to silica gel. This CSP has recently been commercialized under the name of Chirosil-SCA. As a first step for developing a Chirosil-SCA simulated moving bed chromatographic process for separation of tryptophan enantiomers, the adsorption isotherm and mass-transfer parameters of each tryptophan enantiomer on the Chirosil-SCA CSP were determined in this study while using only water as a mobile phase. For this task, inverse method (IM) was applied on the basis of the initial guesses estimated from elution by characteristic point (ECP) method, which was found to be more advantageous in the aspects of both accuracy and computational efficiency than the case of utilizing individually only IM or ECP method. The results revealed that the adsorption behavior of each tryptophan enantiomer on the Chirosil-SCA could be well described by the Langmuir-Freundlich isotherm. The model predictions based on the determined parameter values were in close agreement with the experimental chromatograms from a series of single-component or mixture pulse tests that were performed under various feed concentrations and flow rates. It was also found that the Langmuir-Freundlich isotherm parameters of each enantiomer were largely affected by temperature. Such a marked dependence of the parameters on temperature was investigated quantitatively. The results of such an investigation indicated that as the temperature decreases, the adsorption affinities of both enantiomers become higher and the heterogeneity of the Chirosil-SCA becomes more pronounced.     

Extension of the Dubinin-Astakhov equation for evaluating the micropore size distribution of a modified carbon molecular sieve

A new method for the characterization of the pore size distribution of microporous solids is applied on data obtained for activated carbon molecular sieve samples. In this method, based on the Dubinin-Astakhov equation, a simple numerical algorithm is used for the reconstruction of the micropore size distribution from the integral equation that represents the experimental nitrogen adsorption isotherm. The results are compared with the ones obtained on the basis of the well-known Horvath-Kawazoe method. The samples used in this study come from a carbon molecular sieve that has been treated with solutions of concentrated HNO3 at various temperatures and with solutions of H2O2 of various concentrations.     

A fully consistent experimental and molecular simulation study of methane adsorption on activated carbon

The adsorption of pure methane in activated carbon Ecosorb was studied by combining grand canonical ensemble Monte Carlo molecular simulations and an experimental approach based on a gravimetric device. Experimental and calculated adsorption isotherms of methane were determined in supercritical conditions at 303.15 and 353.15 K and pressures up to 10 MPa. The comparison between both experimental and estimated data proves the consistency of the methodology used in this work, starting from the characterization of the porous media in terms of pore size distribution, the determination of the experimental adsorption isotherms, and the final estimation of computational results through estimated isotherms determination. Moreover, additional differential enthalpy of adsorption calculations were compared with experimental values obtained by means of a manometric/calorimetric technique. The good agreement shows the strength and the originality of this paper by combining experimental and computational homemade results allowing a complete characterization of the activated carbon substrate and its methane storage capacity.