Linear regression (LR) is used to predict thermochemical properties of alkanes at temperatures (0–1000) K to study chemical reaction equilibria inside zeolites. The thermochemical properties of C1 until C10 isomers reported by Scott are used as training data sets in the LR model which is used to predict these properties for alkanes longer than C10 isomers. Second-order groups are used as independent variables which account for the interactions between the neighboring groups of atoms. This model accurately predicts Gibbs free energies, enthalpies, Gibbs free energies of formation, and enthalpies of formation for alkanes which exceeds the chemical accuracy of 1 kcal/mol and outperforms the group contribution methods developed by Benson et al., Joback and Reid, and Constantinou and Gani. Predictions from our model are used to compute the reaction equilibrium distribution of hydroisomerization of C10 and C14 isomers in MTW-type zeolite. Calculation of reaction equilibrium distribution inside zeolites also requires Henry coefficients of the isomers which can be computed using classical force field-based molecular simulations using the RASPA2 software for which we created an automated workflow. The reaction equilibrium distribution for C10 isomers obtained using the LR model and the training data set for this model are in very good agreement. The tools developed in this study will enable the computational study of hydroisomerization of long-chain alkanes (>C10).@en

We study important aspects of shape selectivity effects of zeolites for hydroisomerization of linear alkanes, which produces a myriad of isomers, particularly for long chain hydrocarbons. To investigate the conditions for achieving an optimal yield of branched hydrocarbons, it is important to understand the role of chemical equilibrium in these reversible reactions. We conduct an extensive analysis of shape selectivity effects of different zeolites for the hydroisomerization of C₇ and C₈ isomers at chemical reaction equilibrium conditions. The reaction ensemble Monte Carlo method, coupled with grand-canonical Monte Carlo simulations, is commonly used for computing reaction equilibrium of heterogeneous reactions. The computational demands become prohibitive for a large number of reactions. We used a faster alternative in which reaction equilibrium is obtained by imposing chemical equilibrium in the gas phase and phase equilibrium between the gas phase components and the adsorbed phase counterparts. This effectively mimics the chemical equilibrium distribution in the adsorbed phase. Using Henry’s law at infinite dilution and mixture adsorption isotherm models at elevated pressures, we calculate the adsorbed loadings in the zeolites. This study shows that zeolites with cage or channel-like structures exhibit significant differences in selectivity for alkane isomers. We also observe a minimal impact of pressure on the gas-phase equilibrium of these reactions at typical experimental reaction temperatures 400 − 700 K . This study marks initial strides in understanding the reaction product distribution for long-chain alkanes.

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We present the RUPTURA code (https://github.com/iraspa/ruptura) as a free and open-source software package (MIT license) for (1) the simulation of gas adsorption breakthrough curves, (2) mixture prediction using methods like the Ideal Adsorption Solution Theory (IAST), segregated-IAST and explicit isotherm models, and (3) fitting of isotherm models on computed or measured adsorption isotherm data. The combination with the RASPA software enables computation of breakthrough curves directly from adsorption simulations in the grand-canonical ensemble. RUPTURA and RASPA have similar input styles. IAST is implemented near machine precision but we also provide several explicit mixture prediction methods that are non-iterative and potentially faster than IAST. The code supports a wide variety of isotherm models like Langmuir, Anti-Langmuir, BET, Henry, Freundlich, Sips, Langmuir-Freundlich, Redlich-Peterson, Toth, Unilan, O'Brian & Myers, Asymptotic Temkin, and Bingel & Walton. The isotherm model parameters can easily be obtained by the fitting module. Breakthrough plots and animations of the column properties are automatically generated. In addition to highlighting the code, we also review all the developed techniques from literature for mixture prediction, breakthrough simulations, and isotherm model fitting, and provide a tutorial discussing the workflows.

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Ideal Adsorbed Solution Theory (IAST) is a common method for modelling mixture adsorption isotherms based on pure component isotherms. When the adsorbent has distinct adsorption sites, the segregated version of IAST (SIAST) provides improved adsorbed loadings compared to IAST. We have adopted the concept of SIAST and applied it to an explicit isotherm model which takes into account the different sizes of the adsorbates: the so called Segregated Explicit Isotherm (SEI). The purpose of SEI is to have an explicit adsorption model that can consider both size-effects of the co-adsorbed molecules and surface heterogeneities. In sharp contrast to IAST and SIAST, no iterative scheme is required in case of SEI, which leads to much faster simulations. A comparative study has been performed to analyse the adsorption isotherms calculated using these three methods. The adsorbed loadings predicted by SEI and SIAST are in excellent agreement with the Grand-Canonical Monte Carlo (GCMC) simulation data. The loadings estimated by IAST show considerable deviations from the GCMC data at high pressures. Breakthrough curve modelling is used to compare the effects of these three models at dynamic conditions. The explicit model (SEI) leads to the fastest simulation run time, followed by SIAST.

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A reactor model that deconvolutes thermodynamics of adsorption of hydrocarbon in the pores of zeolite Beta, obtained by Configurational-bias Monte Carlo simulations, from intrinsic, intraporous kinetics of hydroisomerization and hydrocracking reactions, provides a good quantitative description of all significant reactions in the kinetic network for interconversion and cracking of different heptane isomers. Activation enthalpies obtained for intraporous reactions follow the expected order according to the carbenium ion formalism: methyl shift< ethyl shift < isom(B) ∼ crack(B2) < crack(B1) < crack(C) ∼ crack(D) < crack(E) and apparently within each isomerization class, in terms of carbenium ions formally involved: sec → tert < sec → sec ∼ tert → tert < tert → sec. except for the ethyl shift reaction forming 3-ethylpentane. Cracking happens primarily through 2,4-dimethylpentane (type B2), regardless of the initial reactant. The model can be subsequently used to separate the effect of pore structure on selective adsorption and on intraporous reaction kinetics. Zeolite Beta will serve as a base case for a comparison of different zeolite structures.

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The separation of xylenes is one of the most important processes in the petrochemical industry. In this article, the competitive adsorption from a fluid-phase mixture of xylenes in zeolites is studied. Adsorption from both vapor and liquid phases is considered. Computations of adsorption of pure xylenes and a mixture of xylenes at chemical equilibrium in several zeolite types at 250 °C are performed by Monte Carlo simulations. It is observed that shape and size selectivity entropic effects are predominant for small one-dimensional systems. Entropic effects due to the efficient arrangement of xylenes become relevant for large one-dimensional systems. For zeolites with two intersecting channels, the selectivity is determined by a competition between enthalpic and entropic effects. Such effects are related to the orientation of the methyl groups of the xylenes. m-Xylene is preferentially adsorbed if xylenes fit tightly in the intersection of the channels. If the intersection is much larger than the adsorbed molecules, p-xylene is preferentially adsorbed. This study provides insight into how the zeolite topology can influence the competitive adsorption and selectivity of xylenes at reaction conditions. Different selectivities are observed when a vapor phase is adsorbed compared to the adsorption from a liquid phase. These insight have a direct impact on the design criteria for future applications of zeolites in the industry. MRE-type and AFI-type zeolites exclusively adsorb p-xylene and o-xylene from the mixture of xylenes in the liquid phase, respectively. These zeolite types show potential to be used as high-performing molecular sieves for xylene separation and catalysis.@en

We systematically study how the degree of framework flexibility affects the adsorption and diffusion of aromatics in MFI-type zeolites as computed by Monte Carlo simulations. It is observed that as the framework is more flexible, the zeolite structure is inherently changed. We have found that framework flexibility has a significant effect on the adsorption of aromatics in MFI-type zeolites, especially at high pressure. Framework flexibility allows the zeolite framework to accommodate to the presence of guest aromatic molecules. For very flexible zeolite frameworks, loadings up to two times larger than that in a rigid zeolite framework are obtained at a given pressure. We assessed the "flexible snapshot"method, which captures framework flexibility using independent snapshots of the framework. We have found that this method only works well when the loadings are low. This suggests that the effect of the guest molecules on the zeolite framework is important. Framework flexibility lowers the free-energy barriers between low energy states, increasing the rate of diffusion of aromatics in the straight channel of MFI-type zeolites for many orders of magnitude compared to a rigid zeolite framework. The simulations show that framework flexibility should not be neglected and that it significantly affects the diffusion and adsorption properties of aromatics in an MFI-type zeolite.

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Vapor-liquid equilibria of xylenes were computed using Monte Carlo simulations in the Gibbs ensemble. For binary mixtures, the predicted composition of the liquid phase is in agreement with experiments. The computed vapor phase densities of each isomer showed an effect on the predicted composition of the vapor phase of the mixture. Unfortunately, the Monte Carlo code used to calculate the vapor-liquid equilibrium contained an error in the acceptance rule for molecule transfer in multi-component mixtures. The Continuous Fractional Component (CFCMC) [1–3] algorithm in the Gibbs ensemble adds an extra molecule -the fractional molecule-per molecule type. In the CFCMC algorithm, trial moves are attempted to transform a fractional molecule of type a in box i to a whole molecule and, simultaneously, transform a molecule of type a in box j [Formula presented] i to a fractional molecule. These trial moves should be accepted according to Ref. [1]: [Formula presented] where [Formula presented] is the number of molecules of type a in box j, [Formula presented] is the number of molecules of type a in box i, and [Formula presented] is the energy difference between the old and the new configuration. Unfortunately, what was implemented (incorrectly) in the computer code is: [Formula presented] where [Formula presented] and [Formula presented] are the total number of molecules of all types in box i and j, respectively, and not only of type a. For the simulation of a single component, [Formula presented] and [Formula presented]. Therefore, the mistake in the acceptance rule only affects the simulations that include more than one component. As such, Figs. 1, Fig. 2, Fig. 3, Fig. 4, and Table 1 of the article are not affected by this error. This error was hard to detect for xylene isomers, as the boiling point of these isomers are close, and therefore [Formula presented] is close to [Formula presented]. The corrected code has been tested to yield the same results as the RASPA software [4,5] for various multi-component systems. The phase composition diagram using the correct code is shown in Fig. 5. The observations based on the incorrect results remain. The composition of the liquid phase is not affected by the choice of force field or method for electrostatic interactions. For all the force fields, the correct vapor phase composition calculated with the Ewald and the Wolf methods are closer than in the incorrect simulations. In the incorrect results, the largest difference between vapor phase composition calculated with the Wolf and the Ewald method was 0.089 [mol/mol]. In the correct results, this difference is reduced to 0.067 [mol/mol]. [Figure presented] The predicted composition of the liquid phase is in excellent agreement with the experimental data. The correct simulations of the vapor phase compositions are closer to the experimental data than the incorrect simulations. The simulations with the incorrect acceptance rules showed an azeotrope behaviour that is not present in the correct simulations of the phase compositions. [Figure presented] The phase composition of the binary mixture and the excess chemical potential are not related. This is consistent with the observations from the incorrect simulations. [Formula presented] The predicted composition of the liquid phase is in excellent agreement with the experimental data. The correct simulations of the vapor phase compositions are closer to the experimental data than the incorrect simulations. The simulations with the incorrect acceptance rules showed an azeotrope behaviour that is not present in the correct simulations. [Figure presented]@en

Computer simulations of adsorption of aromatics in zeolites are typically performed using rigid zeolite frameworks. However, adsorption isotherms for aromatics are very sensitive to small differences in the atomic positions of the zeolite (Chem. Phys. Lett., 1999, 308, 155-159). This article studies the effect of framework flexibility on the adsorption of aromatics in MFI-type zeolites computed by grand-canonical Monte Carlo simulations. New experimental data of adsorption of ethylbenzene in a MFI-type zeolite at 353 K is presented. The adsorption of n-heptane, ethylbenzene, and xylene isomers is computed in three MFI-type zeolite structures. It is observed that the intraframework interactions in flexible framework models induce small but important changes in the atom positions of the zeolite and hence in the adsorption isotherms. Framework flexibility is differently "rigid": flexible force fields produce a zeolite structure that vibrates around a new equilibrium configuration with limited capacity to accommodate to a bulky guest molecule. The vibration of the zeolite atoms only plays a role at high loadings, and the adsorption is mainly dependent on the average positions of the atoms. The simulations show that models for framework flexibility should not be blindly applied to zeolites and a general reconsideration of the parametrization schemes for such models is needed.

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This article explores how well vapor-liquid equilibria of pure components and binary mixtures of xylenes can be predicted using different force fields in molecular simulations. The accuracy of the Wolf method and the Ewald summation is evaluated. Monte Carlo simulations in the Gibbs ensemble are performed at conditions comparable to experimental data, using four different force fields. Similar results using the Wolf and the Ewald methods can be obtained for the prediction of densities and the phase compositions of binary mixtures. With the Wolf method, up to 50% less CPU time is used compared to the Ewald method, at the cost of accuracy and additional parameter calibration. The densities of p-xylene and m-xylene can be well estimated using the TraPPE-UA and AUA force fields. The largest differences of VLE with experiments are observed for o-xylene. The p-xylene/o-xylene binary mixtures at 6.66 and 81.3 kPa are simulated, leading to an excellent agreement in the predictions of the composition of the liquid phase compared to experiments. The composition of the vapor phase is dominated by the properties of the component with the largest mole fraction in the liquid phase. The accuracy of the predictions of the phase composition are related to the quality of the density predictions of the pure component systems. The phase composition of the binary system of xylenes is very sensitive to slight differences in vapor phase density of each xylene isomer, and how well the differences are captured by the force fields.

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A mathematical model is used to predict adsorption isotherms from experimentally measured breakthrough curves. Using this approach, by performing only breakthrough experiments for a mixture of two (or more) components, one can obtain pure component adsorption isotherms up to the pressure of the experiment. As a case study, the adsorption of an equimolar mixture of CO₂ and CH₄ in zeolite ITQ-29 is investigated. Pure component linear adsorption isotherms for CO₂ and CH₄ are predicted by fitting the theoretical breakthrough curves to the experimental ones. Henry coefficients obtained from our approach are in excellent agreement with those measured experimentally. A similar procedure is applied to predict the complete Langmuir adsorption isotherm from breakthrough curves at high pressures. The resulting adsorption isotherms are in very good agreement with those measured experimentally. In our model for transient adsorption, mass transfer from the gas phase to the adsorbed phase is considered using the Linear Driving Force model and dispersion of the gas phase in the packed bed is taken into account. IAST is used to compute the equilibrium loadings for a mixture of gases. The influence of the dispersion coefficient and the effective mass transfer coefficient on the shape of breakthrough curves is investigated and discussed. Rough estimations of these values are sufficient to predict adsorption isotherms from breakthrough curves.

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The influence of product shape selectivity on the bifunctional conversion of n-C₇ by zeolite catalysts is investigated. Three different zeolite catalysts with different pore sizes (MFI-type, MEL-type, and BEA-type zeolites) have been investigated experimentally. For all three catalysts, n-C₇ is isomerized to monobranched isomers which are further isomerized into dibranched isomers, and these dibranched molecules are converted into cracking products. More dibranched isomers and less cracking products are produced by BEA-type zeolite compared to MFI-type and MEL-type zeolites and clear differences are observed in the distribution of dibranched isomers produced by different catalysts. Molecular simulation is used to compute the adsorption isotherms and free energy barriers for diffusion of dibranched isomers in MFI-type, MEL-type, and BEA-type zeolites. Combining simulation results and experimental observations, it is shown that product shape selectivity can explain the distribution of dibranched molecules while transition state shape selectivity fails to do so. For the medium-pore zeolites (MFI-type and MEL-type zeolites), free energy barriers for diffusion of dibranched molecules are significant. For MFI-type and MEL-type zeolites, the dibranched molecule that has to overcome lower diffusion barrier is produced with a higher yield and the distribution of dimethylpentane molecules is determined by their diffusion rate. It is shown that there is almost no free energy barrier for the diffusion of any of these molecules in BEA-type zeolite. As BEA-type zeolite imposes no free energy barrier for diffusion of any of dibranched isomers, the distribution of dibranched isomers is very close to the equilibrium distribution in the gas phase. Due to the limited mobility of dimethylpentanes within the pores of MFI-type and MEL-type zeolites, most of the dimethylpentane molecules are trapped inside the zeolite and undergo consecutive cracking. Dimethylpentane molecules diffuse sufficiently fast in the large pores of BEA-type zeolite and transfer to the gas phase, before consecutive reaction converts these molecules into cracking products. Moreover, the effect of the MFI-type crystal size on the production of dibranched isomers is investigated. The yield of dibranched isomers reduces by increasing the size of the crystal and larger part of dibranched isomers are cracked as the crystal size of MFI-type is increased.

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A series of faujasite zeolites was modified by extraframework Al (Al_EF) with the goal to investigate the influence of such species on the intrinsic Brønsted acidity and catalytic activity towards paraffin cracking. The chemical state of Al_EF and zeolite acidity were investigated by ²⁷Al MAS NMR and CO_ads IR spectroscopy, H/D exchange reaction, and propane cracking. Strongly acidic defect-free Y zeolites were obtained by substitution of framework Al by Si with (NH₄)₂SiF₆. In accordance with the next-nearest-neighbor model, the intrinsic acidity of the protons increased with decreasing framework Al density. This increased acidity was evidenced by an increased shift of the OH stretching vibration upon CO adsorption in CO_ads IR spectroscopy and by an increased H/D exchange rate in H/D exchange reactions with perdeuterobenzene. All of the acid sites in these zeolites were of equal strength beyond a certain Si/Al ratio. The increased acidity resulted in an enhanced propane cracking activity. Modification of a model dealuminated Y zeolite by Al_EF only resulted in a small fraction of cationic Al_EF species, because it was difficult to control the ion exchange process. In comparison, commercial ultrastabilized Y zeolites contained less Al_EF and these species were predominantly present in cationic form. The rate of propane cracking strongly correlated to the concentration of Brønsted acid sites perturbed by cationic Al_EF species. The results of MQMAS ²⁷Al NMR spectroscopy confirmed the presence of sites perturbed by Al_EF and unaffected framework Al sites. Zeolites with higher intrinsic cracking activities contained a higher proportion of perturbed sites. Although CO_ads IR and H/D exchange methods proved to be suitable methods to probe the acidity of Y zeolites free from Al_EF, they were less suitable to predict the reactivity if the Brønsted acid sites were affected by cationic Al_EF species.

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