New method for calculating the adsorption of noble gases on amorphous surfaces

A new approach to calculating the equilibrium characteristics of the adsorption of noble gases on the amorphous surfaces of adsorbents was developed and applied to the Ar−TiO₂(rutile) system. Intermolecular adsorbate-adsorbate interactions are taken into account for the nearest neighbors in the quasi-chemical approximation. The lattice energy parameters of all interactions of the model are determined from the Lennard-Jones potential (12-6). The formation of amorphous TiO₂(rutile) surface includes completion of the surface layers and partial removal of the surface oxygen ions. The quality of the amorphization procedure was confirmed by the experimentally measured heats and isotherms of adsorption of the system under study. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1109–1118, June, 1997.     

Monte Carlo modeling of chiral adsorption on nanostructured chiral surfaces and slit pores

Adsorptive separation of chiral molecules is a powerful technique that has long been used in the chemical and pharmaceutical industries. An important challenge in this field is to design and optimize new adsorbents to provide selective discrimination of enantiomers. In this article, we introduce an off-lattice model of chiral adsorption on nanostructured surfaces and slit pores with the aim of predicting their enantioslective properties. The concept presented here involves finding the optimal chiral pattern of active sites on the pore walls that maximizes the difference between the binding energies of the enantiomers. Our initial effort focuses on chiral molecules that do not have specific interactions with the pore surface. One candidate meeting this requirement is 1,2-dimethylcyclopropane (DMCP), a chiral hydrocarbon whose interaction with a model pore surface was described using the Lennard-Jones potential. To model the adsorption of DMCP, we used the Monte Carlo simulation method. It was demonstrated that the separation of the enantiomers of DMCP is hardly obtainable because of the smoothness of the potential energy surface for molecules physisorbed in the pore. However, the simulated results allowed the identification of key factors that influence the binding of the enantiomers of DMCP to the pore walls with a special distribution of active sites. This information will be useful in future considerations of the adsorption of more complex chiral molecules.     

Modeling of adsorption of gases on graphite surfaces accounting for the solid-fluid nonadditivity correction

A series of graphitized carbon blacks have been studied using argon and nitrogen adsorption at their boiling points. Analysis of adsorption isotherms was performed with nonlocal density functional theory (NLDFT) accounting for the Axilrod-Teller equation to describe the effect of nonadditivity of the gas-solid interaction. In our previous study [Ustinov, E. A. J. Chem. Phys. 2010, 132, 194703] we have shown that the nonadditivity effect decreases the attractive component of Ar-Ar interaction in the first molecular layer adjacent to the graphite surface by about 23%. This is a source of a large error (up to 40%) when a standard NLDFT is applied to fitting the low-temperature Ar adsorption isotherm on a graphitized carbon black. A new approach that incorporates the Axilrod-Teller equation into the standard NLDFT diminishes the relative error from 40 to 4%, which suggests that the nonadditivity correction should not be ignored in most adsorption systems including crystalline and amorphous solids. The present study is an extension of our approach to N(2) adsorption isotherms at 77.3 K on graphitized carbon blacks. We show that the approach allows to reliably determine the gas-solid molecular parameters, the gas-solid nonadditivity coefficient, the Henry coefficient, and the specific surface area. The surface areas of different carbon blacks determined with the N(2) at 77.35 K and Ar at 87.29 K are very close to each other, though in the former case the values proved to be slightly smaller presumably due to nonspherical shape of the nitrogen molecule. A comparison with the Brunauer, Emmett, and Teller method is provided.     

A site energy distribution function from Toth isotherm for adsorption of gases on heterogeneous surfaces

A site energy distribution function based on a condensation approximation method is proposed for gas-phase adsorption systems following the Toth isotherm. The proposed model is successfully applied to estimate the site energy distribution of three pitch-based activated carbons (PA, PFeA and PBA) developed in our laboratory and also for other common adsorbent materials for different gas molecules. According to the proposed model the site energy distribution curves of the activated carbons are found to be exponential for hydrogen at 77 K. The site energy distribution of some of the activated carbon fibers, ambersorb, Dowex optipore, 13X Zeolite for different adsorbate molecules represents a quasi-Gaussian curve with a widened left hand side, indicating that most sites have adsorption energies lower than a statistical mean value.     

Time distribution of adsorption entropy of gases on heterogeneous surfaces by reversed-flow gas chromatography

The reversed-flow gas chromatography (RF-GC) technique has been applied to measure the adsorption entropy over time, when gaseous pentane is adsorbed on the surface of two solids (gamma-alumina and a silica supported rhodium catalyst) at 393.15 and 413.15K, respectively. Utilizing experimental chromatographic data, this novel methodology also permits the simultaneous measurement of the local adsorption energy, epsilon, local equilibrium adsorbed concentration, c(s)(*), and local adsorption isotherm, theta(p, T, epsilon) in a time resolved way. In contrast with other inverse gas chromatographic methods, which determine the standard entropy at zero surface coverage, the present method operates over a wide range of surface coverage taking into account not only the adsorbate-adsorbent interaction, but also the adsorbate-adsorbate interaction. One of the most interesting observations of the present work is the fact that the interaction of n-pentane is spontaneous on the Rh/SiO(2) catalyst for a very short time interval compared to that on gamma-Al(2)O(3). This can explain the different kinetic behavior of each particular gas-solid system, and it can be attributed to the fact that large amounts of n-C(5)H(12) are present on the active sites of the Rh/SiO(2) catalyst compared to those on gamma-Al(2)O(3), as the local equilibrium adsorbed concentration values, c(s)(*), indicate.     

The fundamentals of adsorption theory for a mixture of bulky molecules in slit-shaped pores with heterogeneous wall surfaces

The fundamentals of the adsorption theory for a mixture of bulky molecules blocking more than one adsorption site on the surface in slit-shaped pores with heterogeneous wall surfaces are outlined. The adsorbate—adsorbate lateral interactions are taken into account in the quasi-chemical approximation and in the mean-field approximation. The expressions for the partial adsorption isotherms and for the binary coefficients of mixture separation and the way of isolation of the partial contributions of molecules on heterogeneous adsorption sites on pore walls are discussed. A simplified variant of adsorption theory for a binary mixture of molecules of different sizes in two-layer pores with the assumption of complete coverage of the pores is considered. The influence of the energy of binding of molecules to pore walls, lateral interactions, and the ratio of the component sizes on the shape of adsorption isotherms is analyzed. The results of calculations are compared with the experimental data for the benzene—CCl₄—microporous AC carbon adsorbent system.     

Two-dimensional mobile films of gases on solids: Adaptation of three-dimensional equations of state to physical adsorption of single gases on homogeneous surfaces

The generalized van der Waals theory for dense fluids, presented in terms of statistical thermodynamics by Vera and Prausnitz, is adapted to physical adsorption of single gases on homogeneous solid surfaces. Using the procedure of Vera and Prausnitz, new three-dimensional equations of state and their two-dimensional analogues are derived. Furthermore, the adsorption isotherms are obtained from the two-dimensional equations of state by using well-known thermodynamic relations.     

Influence of surface chemical heterogeneities on adsorption/desorption hysteresis and coexistence diagram of metastable states within cylindrical pores

Grand canonical Monte Carlo simulations are performed to determine the adsorption/desorption isotherms at different temperatures of a Lennard-Jones fluid confined within a simple model of cylindrical pores presenting chemical heterogeneities. A complex hysteresis loop is observed, showing hysteresis subloops (scanning curves). This is shown to be consistent with the existence of several metastable states (local minima in the system free energy). A recent extension to the Gibbs ensemble technique is then used to calculate the complete coexistence diagram of these local minima.     

Synthesis and adsorption properties of gold nanoparticles within pores of surface‐functional porous polymer microspheres

Mesoporous polymer microspheres with gold (Au) nanoparticles inside their pores were prepared considering their surface functionality and porosity. The Au/polymer composite microspheres prepared were characterized by transmission electron microscope (TEM), X‐ray diffraction (XRD), and Brunauer–Emmett–Teller (BET) techniques. The results showed that the adsorption of Au nanoparticles could be increased by imparting the pore structure and surface‐functional groups into the supporting polymer microspheres (in this study, poly (ethylene glycol dimethacrylate‐co‐acrylonitrile) and poly (EGDMA‐co‐AN) system). Above all, from this study, it was established that the porosity of the polymer microspheres is the most important factor that determines the distribution and adsorption amount of face‐centered cubic (fcc) Au nanoparticles in the final products. Our study showed that the continuous adsorption of Au nanoparticles with the aid of the large surface area and surface interaction sites formed more favorably the Au/polymer composite microspheres. The BET measurements of Au/poly(EGDMA‐co‐AN) composite microspheres reveals that the adsorption of Au nanoparticles into the pores kept the pore structure intact and made it more porous. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5627–5635, 2004     

On Ritchie's equation for adsorption kinetics of gases on solids

Ritchie's equation for the kinetic adsorption isotherm has been derived on the basis of the theory describing the kinetics of adsorption of gases on energetically heterogeneous solid surfaces. This eqation has also been generalized to the kinetics of adsorption of multicomponent gas mixtures.

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Three-dimensional equilibrium shapes of drops on hysteretic surfaces

In this paper, we study equilibrium three-dimensional shapes of drops on hysteretic surfaces. We develop a function coupled with the publicly available surface energy minimization code Surface Evolver to handle contact angle hysteresis. The function incorporates a model for the mobility of the triple line into Surface Evolver. The only inputs to the model are the advancing and receding contact angles of the surface. We demonstrate this model’s versatility by studying three problems in which parts of the triple line advance while other parts either recede or remain stationary. The first problem focuses on the three-dimensional shape of a static pendant drop on a vertical surface. We predict the finite drop volume when impending sliding motion is observed. In the second problem, we examine the equilibrium shapes of coalescing sessile drops on hysteretic surfaces. Finally, we study coalescing puddles in which gravity plays a leading role in determining the equilibrium puddle shape along with hysteresis.     

Hamiltonian theory for vibrational line shapes of atoms adsorbed on surfaces

The vibrational motions of atomic adsorbates on surfaces can be probed by helium atom scattering. The experimental observable is the dynamic structure factor, which shows an inelastic peak around the vibrational frequency of the isolated adsorbates known as the frustrated translational or T-mode peak. In this paper we develop a theory for the line shape of this peak, as well as for its temperature-dependent shift and broadening, based on a Hamiltonian equivalent of the generalized Langevin equation. The theory can be used to infer physical parameters of the adatom-surface interaction, such as the friction coefficient, the barrier height to diffusion, and the anharmonicity parameter. Numerical simulations are used to ascertain the range of validity of the theory, which is also generalized to describe multidimensional systems and to include quantum corrections. We compare the theoretical predictions for the shift and broadening with experimental results for the Na/Cu(001) system, showing quantitative agreement within experimental resolution.     

Kinetics and isotherms of asphaltene adsorption in narrow pores

New data relating to the kinetics and adsorption isotherms of asphaltene in consolidated sandstone core samples are reported. The data were obtained from the measurements of electrokinetics of consolidated sandstone core samples in asphaltene/toluene solutions and petroleum oils. The numerical reduction in the (negative) zeta potential of the sandstone samples were attributed to the adsorption of positively charged molecules of asphaltenes. The hydrodynamics thickness δ of adsorption of asphaltene were followed by monitoring the pressure increase that occurred as the adsorbed layer restricted the rock pores and applying Poiseuille's equation. The flow rates indicated a plateau of asphaltene adsorption at a pore blocking thickness of about δ/r = 0.3, which was also the point at which the streaming current reached a plateau. After increasing to about 30% of the pore radius, the adsorbed layer thickness δ stopped growing either with time or with concentration of asphaltene in the flowing liquid. Alternative hypotheses involving asphaltene adsorption isotherms have been investigated. A theoretical treatment advanced describing particle adsorption in the same terms as molecular adsorption and the Langmuir isotherm, with the free energy of asphaltene adsorption on the rock surface (modeled on silica) calculated on the basis of van der Waals attraction. Acceptable agreement was obtained with the electrokinetic measurements.     

Nature of adsorption and desorption branches in cylindrical pores

To examine the nature of the adsorption and desorption branches in hysteretic adsorption isotherms of gases on mesoporous materials, we measured the temperature dependence of the adsorption and desorption isotherms of argon, oxygen, and carbon dioxide onto MCM-41 with a pore diameter of 4.4 nm. The results clearly show that in the open-ended cylindrical pores of MCM-41, capillary condensation rather than evaporation takes place near a thermodynamical equilibrium transition, as opposed to the general statement that capillary evaporation can occur via a meniscus formed at the pore mouth, and, thus, takes place at equilibrium.     

Effect of adsorbate vibrations on adsorption isotherms in slit-like pores

A molecular model of adsorbate melting in slit-like pores [1] is used to calculate adsorption isotherms with regard to the contribution from vibrational motions of the adsorbate. The equations are based on discrete distribution functions (the lattice gas model). Molecular distributions are calculated in a quasi-chemical approximation reflecting the effects of direct correlations of interacting particles using the Lennard-Jones potential. The vibrational motion of molecules is taken into account using a modified quasi-dimer Mie model. It is shown that considering vibrations shifts the adsorption isotherms in the chemical potential-density coordinates to higher vapor pressures in the region of high filling. This is due to the need for additional compression of the vapor to transfer it into the adsorbed state with increased kinetic energy.