E. A. Ustinov

High-Pressure Adsorption of Supercritical Gases on Activated Carbons: An Improved Approach Based on the Density Functional Theory and the Bender Equation of State

Adsorption of nitrogen, argon, methane, and carbon dioxide on activated carbon Norit R1 over a wide range of pressure (up to 50 MPa) at temperatures from 298 to 343 K (supercritical conditions) is analyzed by means of the density functional theory modified by incorporating the Bender equation of state, which describes the bulk phase properties with very high accuracy. It has allowed us to precisely describe the experimental data of carbon dioxide adsorption slightly above and below its critical temperatures. The pore size distribution (PSD) obtained with supercritical gases at ambient temperatures compares reasonably well with the PSD obtained with subcritical nitrogen at 77 K. Our approach does not require the skeletal density of activated carbon from helium adsorption measurements to calculate excess adsorption. Instead, this density is treated as a fitting parameter, and in all cases its values are found to fall into a very narrow range close to 2000 kg/m(3). It was shown that in the case of high-pressure adsorption of supercritical gases the PSD could be reliably obtained for the range of pore width between 0.6 and 3 run. All wider pores can be reliably characterized only in terms of surface area as their corresponding excess local isotherms are the same over a practical range of pressure.

Two-dimensional order-disorder transition of argon monolayer adsorbed on graphitized carbon black: Kinetic Monte Carlo method

We present results of application of the kinetic Monte Carlo technique to simulate argon adsorption on a graphite surface at temperatures below and above the triple point. We show that below the triple point the densification of the adsorbed layer with loading results in the rearrangement of molecules to form a hexagonal structure, which is accompanied by the release of an additional heat, associated with this disorder-order transition. This appears as a spike in the plot of the heat of adsorption versus loading at the completion of a monolayer on the surface. To describe the details of the adsorbed phase, we analyzed thermodynamic properties and the effects of temperature on the order-disorder transition of the first layer.

Application of density functional theory to capillary phenomena in cylindrical mesopores with radial and longitudinal density distributions.

In this paper, we applied a version of the nonlocal density functional theory (NLDFT) accounting radial and longitudinal density distributions to study the adsorption and desorption of argon in finite as well as infinite cylindrical nanopores at 87.3 K. Features that have not been observed before with one-dimensional NLDFT are observed in the analysis of an inhomogeneous fluid along the axis of a finite cylindrical pore using the two-dimensional version of the NLDFT. The phase transition in pore is not strictly vapor-liquid transition as assumed and observed in the conventional version, but rather it exhibits a much elaborated feature with phase transition being complicated by the formation of solid phase. Depending on the pore size, there are more than one phase transition in the adsorption-desorption isotherm. The solid formation in finite pore has been found to be initiated by the presence of the meniscus. Details of the analysis of the extended version of NLDFT will be discussed in the paper.

Simulation of gas adsorption on a surface and in slit pores with grand canonical and canonical kinetic Monte Carlo methods

We present for the first time in the literature a new scheme of kinetic Monte Carlo method applied on a grand canonical ensemble, which we call hereafter GC-kMC. It was shown recently that the kinetic Monte Carlo (kMC) scheme is a very effective tool for the analysis of equilibrium systems. It had been applied in a canonical ensemble to describe vapor-liquid equilibrium of argon over a wide range of temperatures, gas adsorption on a graphite open surface and in graphitic slit pores. However, in spite of the conformity of canonical and grand canonical ensembles, the latter is more relevant in the correct description of open systems; for example, the hysteresis loop observed in adsorption of gases in pores under sub-critical conditions can only be described with a grand canonical ensemble. Therefore, the present paper is aimed at an extension of the kMC to open systems. The developed GC-kMC was proved to be consistent with the results obtained with the canonical kMC (C-kMC) for argon adsorption on a graphite surface at 77 K and in graphitic slit pores at 87.3 K. We showed that in slit micropores the hexagonal packing in the layers adjacent to the pore walls is observed at high loadings even at temperatures above the triple point of the bulk phase. The potential and applicability of the GC-kMC are further shown with the correct description of the heat of adsorption and the pressure tensor of the adsorbed phase.

Simulation study of two-dimensional phase transitions of argon on graphite surface and in slit micropores

Molecular simulation has been increasingly used in the analysis and modeling of gas adsorption on open surfaces and in porous materials because greater insight could be gained from such a study. In case of homogeneous surfaces or pore walls the adsorption behavior is often complicated by the order–disorder transition. It is shown in our previous publications (Ustinov and Do, Langmuir 28:9543–9553, 2012a; Ustinov and Do, Adsorption 19:291–304, 2013) that once an ordered molecular layer has been formed on the surface, the lattice constant depends on the simulation box size, which requires adjusting the box dimensions parallel to the surface for each value of loading. It was shown that this can be accomplished with the Gibbs–Duhem equation, which results in decreasing lattice constant with an increase of the amount adsorbed. The same feature is expected to be valid for gas adsorption in narrow pores, but this has not been analyzed in the literature. This study aims at an extension of our approach to adsorption in slit graphitic pores using kinetic Monte Carlo method (Ustinov and Do, J Colloid Interface Sci 366:216–223, 2012b). The emphasis rests on the thermodynamic analysis of the two-dimensional (2D) ordering transition and state of the ordered phase; if the ordered phase exists in narrow slit pores, simulation with constant volume box always leads to erroneous results, for example, seemingly incompressible adsorbed phase. We proposed a new approach that allows for modeling thermodynamically consistent adsorption isotherms, which can be used as a basis for further refinement of the pore size distribution analysis of nanoporous materials.

Porous texture characterization from gas-solid adsorption

Characterization of porous activated carbon and its derivatives has been a subject of great interest for many decades. Various tools for equilibria characterization are available in the literature, and they can be broadly classified into two groups: One is based on classical approaches while the other has firm foundation on molecular interaction calculations. Scientists constantly develop new tools or refine existing methods to better characterize porous carbons as the structure has significant effects on equilibria as well as kinetics.

Phase equilibria and surface tension of pure fluids using a molecular layer structure theory (MLST) model

This paper presents a new model based on thermodynamic and molecular interaction between molecules to describe the vapour-liquid phase equilibria and surface tension of pure component. The model assumes that the bulk fluid can be characterised as set of parallel layers. Because of this molecular structure, we coin the model as the molecular layer structure theory (MLST). Each layer has two energetic components. One is the interaction energy of one molecule of that layer with all surrounding layers. The other component is the intra-layer Helmholtz free energy, which accounts for the internal energy and the entropy of that layer. The equilibrium between two separating phases is derived from the minimum of the grand potential, and the surface tension is calculated as the excess of the Helmholtz energy of the system. We test this model with a number of components, argon, krypton, ethane, n-butane, iso-butane, ethylene and sulphur hexafluoride, and the results are very satisfactory

Adsorption Equilibrium of Binary Mixtures in Zeolites and State of Adsorbed Phase

The criterion of ideal behavior of a mixture of a few molecules within a separate zeolite cavity is formulated on the basis of the statistical thermodynamics. The criterion determines the dependence of the Helmholtz free energy, internal energy, and entropy of a molecular aggregate on the ratio of the number of molecules of components 1 and 2. The similarity between this criterion and the criterion of ideal behavior for bulk solutions is shown. Expressions of excess thermodynamic functions of the molecular mixture in a cavity are obtained. The negative magnitude of these excess functions is proposed to be due to rearrangement of molecules under influence of energetic heterogeneity. The calculation procedure of the excess functions has been demonstrated for the system CO2-C2 H6-zeolite NaX, the information of both isotherms and isosteric adsorption heats being used simultaneously. The approach offered allows the state of adsorbed mixture in a separate cavity to be analyzed from pure-component and multicomponent experimental data.

Modeling Nitrogen Adsorption in Spherical Pores of Siliceous Materials by Density Functional Theory.

Adsorption of nitrogen in spherical pores of FDU-1 silica at 77 K is considered by means of a nonlocal density functional theory (NLDFT) accounting for a disordered structure of pore walls. Pore size distribution analysis of various FDU-1 samples subject to different temperatures of calcination revealed three distinct groups of pores. The principal group of pores is identified as ordered spherical mesopores connected with each other by smaller interconnecting pores and irregular micropores present in the mesopore walls. To account for the entrances (connecting pores) into spherical mesopores, a concept of solid mass distribution with respect to the apparent density was introduced. It is shown that the introduction of the aforementioned distribution was sufficient to quantitatively describe experimental adsorption isotherms over the entire range of relative pressures spanning six decades.

Multicomponent Equilibrium Adsorption on Heterogeneous Adsorbents

A generalized method for prediction of multicomponent adsorption is suggested based on representing that adsorbent volume as energetically inhomogeneous. The method depends on extending the Polanyi potential theory to mixture adsorption. The main feature of the method is that, at constant partial pressure and temperature the composition of an adsorbed phase is not uniform over its volume. Results of applying this theory to non-porous adsorbents have been considered. The prediction ability of the theory is confirmed for the strongly non-ideal system acetone–chloroform–graphitized carbon black. It was shown that the departure from ideal behavior of adsorbed phase is quite close to that for the liquid mixture. Another system considered was oxygen–nitrogen–anatase at 78 K. Although this mixture is ideal, it has been found that there is significant variation in composition over the adsorbed layer due to the difference in the interactions of the quadrupolar N2 molecule and nonpolar O2 molecule with the anatase surface.