Hysteresis and scanning curves in linear arrays of mesopores with two cavities and three necks. classification of the scanning curves

Adsorption of argon at 87K in a linear array of slit mesopores composed of two cavities and three necks has been investigated using Grand Canonical Monte Carlo simulation. Hysteresis and scanning was found to depend on the relative size of the necks and cavities and on whether the necks are wider or narrower than the critical width that demarcates cavitation from pore blocking. There are 26 possible combinations for the linear array. By considering the behaviour of hysteresis scanning curves, we are able to identify four distinct groups: (I) Group 1: The descending scanning spans the boundary curve of the hysteresis loop due to stretching of the condensate in the small cavity. (ii) Group 2: The descending curve partially spans the loop and returns to the adsorption boundary. This occurs either because the condensate stretches in the small cavity, followed by evaporation via a pore blocking mechanism; or because the condensate evaporates as the meniscus recedes in the large neck that joins the two cavities. (iii) Group 3: The descending curve spans the loop as in Group 1 but there is a small sub-loop associated with emptying and filling of the large neck connecting the large cavity to the surrounding gas. (iv) Group 4: The descending scanning curve is similar to that in Group 2; but when the large cavity of the array is filled with adsorbate, and the small cavity is empty (except for an adsorbed film) the ascending curve partially spans the loop. This happens when molecular layers build-up in the small cavity (c.f. stretching of condensate in a descending scan) is followed by condensation, which results in the scanning curve returning to the desorption boundary (c.f. evaporation of the condensate and return to the adsorption boundary). There is also a sub-loop which has similar characteristics to those in Group 3

A re-assessment of the isosteric heat for CCl4 adsorption on graphite

We have carried out molecular simulations of carbon tetrachloride adsorption on graphite, in order to investigate the role of the octopole in potential models for the CCl/graphite system, and the temperature dependence of the first-order gas-liquid transition in the first adsorbate layer. Two classes of potential model for carbon tetrachloride were considered: the first has 5 LJ sites and the second includes five partial charges to model the leading octopole. Both models are adequate to represent the vapour-liquid equilibrium, suggesting that the octopole makes an insignificant contribution to the properties of the bulk phase. Both models show that adsorbed CCl molecules are delocalized on a graphite surface because of the strong intermolecular interactions. It is found that the LJ sites on the chlorine atoms, not the octopole, play the most important role in matching the experimental isotherm and isosteric heat data with simulation. The heat is constant, across the first-order transition of the first adsorbate layer. The simulation results show that both the magnitude of the density jump, and the isosteric heat across the first-order transition, decrease as the temperature increases. This is in qualitative agreement with the 1972 experimental data of Avgul and Kiselev, but these experimental data exhibit an unusually strong decrease in the isosteric heat, and the coexistence region between the two phases displays an unusual asymmetrical shape. Detailed analysis of our simulation results, together with the calculated isosteric heat from the experimental isotherms of Machin and Ross, show that there may be errors associated with the heat data of Avgul and Kiselev at high temperatures

An improved model for N2 adsorption on graphitic adsorbents and graphitized thermal carbon black - the importance of the anisotropy of graphene

Computer simulations of N adsorption on graphite frequently use the 10-4-3 equation with Steele’s molecular parameters to describe the dispersive-repulsive interaction between a molecule and graphite. This model assumes that graphite is a uniformly homogeneous continuum solid, and its derivation implies the following assumptions: (1) the solid is built from stacked, equally spaced graphene layers, (2) there is an infinite number of layers, and (3) the carbon atom molecular parameters are invariant for all layers (collision diameter of 0.34 nm and reduced well depth of interaction energy of 28 K). Despite the fact that this model can give an acceptable description of experimental data for this system, there are experimental observations that simulation results fail to account for. First, the isotherm does not exhibit a step in the sub-monolayer coverage region at 77 K, which is attributed to a transition from the supercritical state of the adsorbate to the commensurate state, and therefore fails to reproduce the cusp and heat spike in the experimental isosteric heat curve versus loading at close to monolayer coverage. Second, the simulation results overpredict the experimental data in the multilayer region. These discrepancies suggest that (1) the absence of lateral corrugation in the 10-4-3 potential misses the commensurate to incommensurate transition and (2) the long-range solid-fluid potential, experienced by the second and higher layers onwards, is too strong. Here we examine a revised graphite potential model that incorporates three features absent from the 10-4-3 model: (1) an energetic corrugation of the potential arising from the discrete atom structure of the adsorbent, (2) the unequal spacing of the graphene layers due to the anisotropic force field acting on graphene layers at the surface, and (3) the different polarizabilities of carbon atoms in graphite, parallel and normal to the graphene surface. These features are corroborated by a number of experimental measurements and quantum-mechanical calculations: (1) the Low-Energy Electron Diffraction (LEED) and Surface-Extended X-ray Absorption Fine Structure (SEXAFS) experiments show that the first adsorbate layer is smaller than predicted by the 10-4-3 model with the traditional molecular parameters suggested by Steele, and (2) the potential well depth for atoms in graphene is stronger than for C-atoms in graphite. The simulation results using this revised graphite model give an improved description of the fine features of adsorption of N on graphite: the sub-step in the first layer of the isotherm, the spike in the isosteric heat curve versus loading, and the coverage at higher loadings

On the consistency of NVT, NPT, μVT and Gibbs ensembles in the framework of kinetic Monte Carlo – fluid phase equilibria and adsorption of pure component systems

This paper aims to show the consistency between simulations of fluid phase properties, obtained with various ensembles, developed within the framework of kinetic Monte Carlo (kMC) simulation: NVT (canonical), NPT (isothermal-isobaric systems), μVT (grand canonical) and Gibbs ensembles, to ensure the reliability of the kMC methodology. The advantages of the kMC scheme, as compared to the conventional Metropolis Monte Carlo, are: (1) accurate determination of the chemical potentials compared to the Widom insertion method, and (2) a rejection-free algorithm, making the implementation of the kMC scheme simpler. For internal consistency in a grand canonical ensemble simulation, we have developed a means to calculate the intrinsic chemical potential of the system accurately, which must be the same (within statistical error of the simulation) as the specified chemical potential to ensure convergence to equilibrium. We test the consistency of canonical (NVT-kMC) and grand canonical (GC-kMC) ensembles for argon adsorption at 87\ua0K and 120\ua0K in a uniform open-ended slit pore, and hence derive governing factors affecting hysteresis in the isotherm and the microscopic mechanisms of condensation and evaporation

The role of adsorbate size on adsorption of Ne and Xe on graphite

We have carried out an extensive grand canonical Monte Carlo simulation to investigate the adsorption of neon and xenon on graphite. The adsorbate collision diameters of neon and xenon are smaller and greater respectively, than the commensurate graphite lattice spacing λ=3×3R30 of 0.426 nm. Simulated isotherms and isosteric heats were obtained using a graphite model that has been shown to describe successfully the adsorbate transitions for krypton, methane and nitrogen by Prasetyo et al. (2017), which have collision diameters close to λ. Neon does not exhibit commensurate (C) packing because the gain in the intermolecular potential interactions in the incommensurate (IC) packing when molecules move away from carbon hexagon centres, does not compensate for the increase in the solid-fluid potential energy. Xenon, on the other hand, exhibits IC packing because its molecular size is greater than λ. Nevertheless, at a sufficiently high chemical potential, the first layer of xenon changes from the IC to C packing (in contrast to what is observed for krypton, nitrogen and methane). This transition occurs because the decrease in the xenon intermolecular interactions is sufficiently compensated by the increase in the solid-fluid interaction, and the increase in the fluid-fluid interactions between molecules in the first layer and those in the second layer. This finding is supported by the X-ray diffraction study by Mowforth et al. (1986) and Morishige et al. (1990)

A GCMC simulation and experimental study of krypton adsorption/desorption hysteresis on a graphite surface

Adsorption isotherms and isosteric heats of krypton on a highly graphitized carbon black, Carbopack F, have been studied with a combination of Monte Carlo simulation and high-resolution experiments at 77 K and 87 K. Our investigation sheds light on the microscopic origin of the experimentally observed, horizontal hysteresis loop in the first layer, and the vertical hysteresis-loop in the second layer, and is found to be in agreement with our recent Monte Carlo simulation study (Diao et al., 2015). From detailed analysis of the adsorption isotherm, the latter is attributed to the compression of an imperfect solid-like state in the first layer, to form a hexagonally packed, solid-like state, immediately following the first order condensation of the second layer. To ensure that capillary condensation in the confined spaces between microcrystallites of Carbopack F does not interfere with these hysteresis loops, we carried out simulations of krypton adsorption in the confined space of a wedge-shaped pore that mimics the interstices between particles. These simulations show that, up to the third layer, any such interference is negligible

Understanding the effect of pore size on the separation efficiency of methane-ethane mixtures using kinetic Monte Carlo simulation

Although it is well acknowledged that pores are beneficial for enhancing adsorption, the effect of pore size on the selective adsorption of gas mixtures under subcritical condition is not known due to experimental challenges. To bridge this gap, the kinetic Monte Carlo method, which provides an accurate determination of chemical potential, was employed to understand the preferential adsorption of mixtures of methane and ethane on a graphitic plane, as well as graphitic pores sized between 1 and 4 nm. For a graphitic plane, results indicate high ethane selectivity of at least 80 mol % in the first adsorbed layer even at a low ethane mole fraction of 1 mol % in the gas phase, and the ethane proportion decreases further away to approach that of the bulk liquid. Regarding pore size, smaller ones provide higher ethane selectivity due to strong ethane-graphite affinity, but an extremely low pressure is required for desorption, which can be remedied with larger pores at the expense of a poorer ethane selectivity. The selectivity of ethane in the pore decreases as pressure increases, except at the onset of condensation. Therefore, in view of the trade-off between selectivity and amount adsorbed, adsorption can be performed at the pressure required for pore condensation rather than at the saturated vapor pressure.Agency for Science, Technology and Research (A*STAR)Ministry of Education (MOE)The authors acknowledge funding from A*STAR (Singapore) Advanced Manufacturing and Engineering (AME) under its Pharma Innovation Programme Singapore (PIPS) program (A20B3a0070) and A*STAR (Singapore) Advanced Manufacturing and Engineering (AME) under its Individual Research Grant (IRG) program (A2083c0049), the Singapore Ministry of Education Academic Research Fund Tier 1 Grant (2019-T1- 002-065; RG100/19), and the Singapore Ministry of Education Academic Research Fund Tier 2 Grant (MOE-MOET2EP10120-0001)

An efficientmethod to determine chemical potential of mixtures in the isothermal and isobaric bulk phase with kineticMonte Carlo simulation

A kinetic Monte Carlo (kMC) scheme in the NPT ensemble (constant number of molecules, pressure and temperature) has been developed to determine accurate chemical potentials for all components in a homogeneous mixture. The simulation requires two moves: (1) a displacement move and (2) a volume change move. In the former, the mobility rate of a selected molecule is determined by its interaction with all the other molecules in the system and is moved to a random position within the simulation box, according to the Rosenbluth algorithm, without any rejections (entropic sampling). The volume change move is decided by a comparison between either the instant pressure or the partial average pressure (with long-range correction) and the specified pressure and is carried out much less frequently than the displacement move. We applied this NPT scheme to a number of mixtures in both the gaseous and liquid phases, and show that the derived chemical potentials are accurate and reproducible. The method is recommended for obtaining chemical potentials in mixtures that are required as input in a grand canonical ensemble simulation