Development of equations for differential and integral enthalpy change of adsorption for simulation studies

Computational investigation of hysteresis and phase equilibria of n-alkanes in a metal-organic framework with both micropores and mesopores

Adsorption hysteresis is a phenomenon related to phase transitions that can impact applications such as gas storage and separations in porous materials. Computational approaches can greatly facilitate the understanding of phase transitions and phase equilibria in porous materials. In this work, adsorption isotherms for methane, ethane, propane, and n-hexane were calculated from atomistic grand canonical Monte Carlo (GCMC) simulations in a metal-organic framework having both micropores and mesopores to better understand hysteresis and phase equilibria between connected pores of different size and the external bulk fluid. At low temperatures, the calculated isotherms exhibit sharp steps accompanied by hysteresis. As a complementary simulation method, canonical (NVT) ensemble simulations with Widom test particle insertions are demonstrated to provide additional information about these systems. The NVT+Widom simulations provide the full van der Waals loop associated with the sharp steps and hysteresis, including the locations of the spinodal points and points within the metastable and unstable regions that are inaccessible to GCMC simulations. The simulations provide molecular-level insight into pore filling and equilibria between high- and low-density states within individual pores. The effect of framework flexibility on adsorption hysteresis is also investigated for methane in IRMOF-1.

Enthalpic and Liquid-Phase Adsorption Study of Toluene-Cyclohexane and Toluene-Hexane Binary Systems on Modified Activated Carbons

The liquid-phase adsorption of toluene in cyclohexane and hexane solutions on modified activated carbons was evaluated; the energy involved in the interaction between these solutions and the solids was determined by immersion enthalpies of pure solvents and their mixtures, and the contribution of the system constituents was calculated by differential enthalpies. The thermal treatment generated modifications that favored adsorption and interaction with the evaluated solutions, since it increased the textural parameters and the basic character of the samples. Cyclohexane could create greater competition with the adsorption sites compared to hexane, but it favored the increase in adsorption capacities (0.416 to 1.026 mmol g⁻¹) and the interactions with the solid evaluated through the immersion enthalpies. The immersion enthalpies of pure solvents (−16.36 to −112.7 J g⁻¹) and mixtures (−25.65 to −104.34 J g⁻¹) had exothermic behaviors that were decreasing due to the possible displacement of solvent molecules when increasing the solute concentration in the mixtures. The differential enthalpies for toluene were negative (−18.63 to −2.14 J), mainly due to the π–π interaction with the solid, while those of the solvent–solid component tended to be positive values (−4.25 to 55.97 J) due to the displacement of the solvent molecules by those of toluene.

Behavior of the Enthalpy of Adsorption in Nanoporous Materials Close to Saturation Conditions

Many important industrial separation processes based on adsorption operate close to saturation. In this regime, the underlying adsorption processes are mostly driven by entropic forces. At equilibrium, the entropy of adsorption is closely related to the enthalpy of adsorption. Thus, studying the behavior of the enthalpy of adsorption as a function of loading is fundamental to understanding separation processes. Unfortunately, close to saturation, the enthalpy of adsorption is hard to measure experimentally and hard to compute in simulations. In simulations, the enthalpy of adsorption is usually obtained from energy/particle fluctuations in the grand-canonical ensemble, but this methodology is hampered by vanishing insertions/deletions at high loading. To investigate the fundamental behavior of the enthalpy and entropy of adsorption at high loading, we develop a simplistic model of adsorption in a channel and show that at saturation the enthalpy of adsorption diverges to large positive values due to repulsive intermolecular interactions. However, there are many systems that can avoid repulsive intermolecular interactions and hence do not show this drastic increase in enthalpy of adsorption close to saturation. We find that the conventional grand-canonical Monte Carlo method is incapable of determining the enthalpy of adsorption from energy/particle fluctuations at high loading. Here, we show that by using the continuous fractional component Monte Carlo, the enthalpy of adsorption close to saturation conditions can be reliably obtained from the energy/particle fluctuations in the grand-canonical ensemble. The best method to study properties at saturation is the NVT energy (local-) slope methodology.

Determination of Isosteric Heat of Adsorption by Quenched Solid Density Functional Theory

The heat of adsorption is one of the most important parameters characterizing energetic heterogeneity of the adsorbent surface. Heats of adsorption are either determined directly by calorimetry or calculated from adsorption isotherms measured at different temperatures using the thermodynamic Clausius-Clapeyron equation. Here, we present a method for calculating the isosteric heat of adsorption that requires as input only a single adsorption isotherm measured at one temperature. The proposed method is implemented with either nonlocal (NLDFT) or quenched solid (QSDFT) density functional theory models of adsorption that are currently widely used for calculating pore size distributions in various micro- and mesoporous solids. The pore size distribution determined from the same experimental isotherm is used for predicting the isosteric heat. The QSDFT method has advantages of taking into account two factors contributing to the structural heterogeneity of adsorbents: the molecular level roughness of the surface and the pore size distribution. The method is illustrated with examples of low temperature nitrogen and argon adsorption on selected samples of carbons of different degree of graphitization and MCM-41 mesoporous silicas of different pore size. The isosteric heat predictions from the NLDFT and QSDFT methods are compared against relevant experiments and the results of Monte Carlo (MC) simulations, with good agreement found in the cases where the surface model adequately reflects the pore surface roughness. Analyses with the QSDFT method show that the isosteric heat of adsorption significantly depends of the molecular level roughness of the adsorbent surface, which is ignored in NLDFT and MC models. The proposed QSDFT method with further verification can be used for calculating the isosteric heat as an additional parameter characterizing the adsorbent surface in parallel with routine calculations of the pore size distribution from a single adsorption isotherm.

Microscopic configurations of methanol molecules in graphitic slit micropores: a computer simulation study

We report a detailed computer simulation study of methanol adsorption in graphitic slit-like micropores to investigate the effects of temperature and pore size on the adsorptive capacity and the configurations of methanol molecules in a confined space. Simulation results show that in the temperature range studied (273-422 K) the amount adsorbed increases gradually with pressure in 0.65 and 0.8 nm pores (where only one molecular layer can be accommodated), while for pores having widths greater than 1.0 nm the adsorption isotherms exhibit a sharp jump at low temperatures which becomes gradual as temperature is increased above the critical pore temperature, which increases with pore width. For a given pore size, the pressure at which a large uptake of adsorption occurs, increases and the excess amount adsorbed, decreases with temperature. The interaction between adsorbate molecules and a pore was studied via the solvation pressure, which exhibits oscillations with pore size. The peaks of this oscillation correspond to pores that have an integer number of layers of methanol molecules. At low loadings snapshots showed methanol molecules in isolated clusters of four or five molecules which maximise the hydrogen bonding within each cluster, in the same way as they do on an open surface. At high loadings, the isolated cluster configuration changes to molecular chains in small pores (0.65 and 0.8 nm), which become more distorted by inter-layer interactions in larger pores. The positions of the first peaks of the O-O and O-H radial distributions for the confined methanol are the same as those for bulk liquid for all pore sizes. However, for confined methanol in pores with an integer number of molecular layers, the amplitude of the first peaks of the O-O and O-H radial distributions are higher than for the bulk liquid, and the positions of the second peaks are slightly shifted to the left. In the incommensurate pores the amplitude of the first peaks and the positions of the second peaks of the O-O and O-H radial distributions are similar to those of liquid methanol. Our simulation results agree well with the experimental results of Ohkubo et al.