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.     

Characteristic features of phase diagrams describing condensation of adsorbate in narrow pores

The phase diagrams describing condensation of adsorbate in micro- and mesoporous adsorbents having slit-shaped and cylindrical pores whose size varied from 1 to 20 monolayers were constructed. The study was performed using the lattice-gas model in the quasichemical approximation to take into account the intermolecular interactions. The phase diagrams for various values of the potential arising from different types of adsorbate--adsorbent interaction were analyzed for adsorption of helium, neon, methane, and carbon tetrachloride in graphite pores. Other adsorption systems are considered and the relationship between the pressure and temperature of adsorbate condensation is discussed. A nonmonotonic variation of the critical densities for pore widths from 3 to 10 molecular diameters was found. The pattern of this variation depends on the ratio of the energy of lateral interactions of the adsorbate molecules to the energy of interaction of the adsorbate molecules with pore walls. The critical temperature decreases monotonically with a decrease in the pore width. The stronger the adsorbate interaction with the pore walls, the greater the decrease in the critical temperature.     

Calculation of the adsorption-desorption hysteresis curves in narrow-pore systems

The gas and liquid spinodal branches for an adsorbate located in narrow slit-shaped, cylindrical, and spherocylindrical pores were calculated. The adsorbate is modeled by Lennard-Jones spherical particles. The calculation was based on the lattice gas model taking into account the intermolecular interactions of nearest neighbors in the quasichemical approximation. The density-temperature diagrams for the gas and liquid spinodal branches in the pores are similar to the equilibrium vapor-liquid phase diagrams: they have a common critical point; the dense-phase branches are shifted to lower pore fillings, while the rarefied-phase branches are shifted toward higher pore fillings. The width of adsorption-desorption hysteresis loop in the adsorption isotherms for Lennard-Jones particles was analyzed as a function of the pore size and the interaction potential of the adsorbate with the pore walls. The effect of pore wall roughness and the accuracy of isotherm calculation on the width of the adsorption-desorption hysteresis loop in cylindrical pores is discussed Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 813–823, May, 2007.     

Relation between characteristic adsorption energy and internal pressure in the theory of volume filling of micropores

An equation for the internal pressure acting on an adsorbate in micropores was obtained on the basis of the assumption that the chemical potential of an adsorbate in micropores is equal to that in an equilibrium gas phase and using the Dubinin-Radushkevich equation. The empirical relation between the characteristic adsorption energy and the half width of pores was expressed in terms of internal pressure and diameter of adsorbate molecules. The two-dimensional pressure was calculated for micropores with plane-parallel walls, where the width of a micropore coincides with the diameter of an adsorbate molecule. The results obtained were compared with the two-dimensional pressure of a monolayer on a free planar surface for an adsorbate and adsorbent of the same nature.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1928–1930, October, 1995.     

Analysis of van der Waals loops in the adsorption isotherms of porous systems

The properties of the van der Waals loops for isotherms of the adsorbate located in the slit-shaped and cylindrical pores of different width were analyzed. The adsorbate molecules are modeled by spherical Lennard-Jones type particles. The calculation was based on the latticegas model in the quasichemical approximation for intermolecular interactions. The accuracy of calculations of the adsorption hysteresis loops increases due to the use of distributed models, which reflect the spatial inhomogeneity of the distribution of molecules along the normal to the pore wall. The effect of the adsorbate-adsorbent interaction potential and pore width on the pattern of adsorption isotherms is considered. Taking into account the inhomogeneity of the spatial distribution of molecules changes the course of the spinodal sections of the adsorption isotherms.     

Adsorption on nonporous and supermicroporous adsorbents

The mean values of the characteristic energy of C₆H₆ adsorption in large micropores were calculated from the adsorption isotherms of benzene vapor on carbon blacks. The supermicropores are characterized by the significant dispersion of the adsorption potential resulted from the pore-size distribution, which imparts the polymolecular character to adsorption. The effect of enhancement of the characteristic energy of adsorption was analyzed, which was caused by the overlap of the force fields of the opposite pore walls and the reduction of the adsorption film surface with micropore volume filling. The both factors are comparable by magnitude and depend on the micropore sizes.     

多孔活性炭孔径分布的表征

总结了利用气体吸附法表征多孔活性炭中孔和微孔孔径分布的各种方法。BJH方法和MP模型忽略了微孔内势能叠加效应,仅适合描述中孔孔径分布;HK模型和以Dubinin填充理论为基础的各种方法,考虑了微观下势能叠加的效果,在一定程度上能很好地描述微孔孔径分布;最近围绕GAI(GeneralizedAdsorptionIsotherm)而展开的利用密度范函理论(DFT,densityfunctiontheory)和巨正则系综蒙特卡罗(GCMC,grandcanonicalensemblemontecarlo)模拟确定微孔孔径分布的方法较好地克服了Dubinin理论中存在的缺点,是较好的两种方法,但其有效性还需要更多的实验结果来证明。     

Analysis of Adsorbate–Adsorbate and Adsorbate–Adsorbent Interactions to Decode Isosteric Heats of Gas Adsorption

A qualitative interpretation is proposed to interpret isosteric heats of adsorption by considering contributions from three general classes of interaction energy: fluid–fluid heat, fluid–solid heat, and fluid—high‐energy site (HES) heat. Multiple temperature adsorption isotherms are defined for nitrogen, T=(75, 77, 79) K, argon at T=(85, 87, 89) K, and for water and methanol at T=(278, 288, 298) K on a well‐characterized polymer‐based, activated carbon. Nitrogen and argon are subjected to isosteric heat analyses; their zero filling isosteric heats of adsorption are consistent with slit‐pore, adsorption energy enhancement modelling. Water adsorbs entirely via specific interactions, offering decreasing isosteric heat at low pore filling followed by a constant heat slightly in excess of water condensation enthalpy, demonstrating the effects of micropores. Methanol offers both specific adsorption via the alcohol group and non‐specific interactions via its methyl group; the isosteric heat increases at low pore filling, indicating the predominance of non‐specific interactions.     

Modification of the theory of a three-dimensional filling of micropores

Compressibility of the adsorbate has been taken into account in calculating the maximum adsorption in micropores. On this basis, an equation has been derived for improvement of the theory of three-dimensional filling of micropores in application to the calculation of micropore volume by the Dubinin-Radushkevich equation. Evaluations for the case of benzene adsorption on activated carbons at 20°C have shown that the accounting for adsorbate compressibility leads to corrections of the Dubinin-Radushkevich theory amounting to approximately 10%.Institute of Physical Chemistry, Russian Academy of Sciences, Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 13–18, January, 1992.     

Sorption Equilibria and Kinetics of Hydrocarbons onto Activated Carbon Samples Having Different Micropore Size Distributions

This paper deals with the prediction of adsorption equilibrium and kinetics of hydrocarbons onto activated carbon samples having different micropore size distribution (MPSD). The microporous structure of activated carbon is characterised by the distribution of slit-shaped micropores, which is assumed to be the sole source of surface heterogeneity. The interaction between adsorbate molecule and pore walls is described by the Lennard-Jones potential theory. Different adsorbates have access to different pore size range of activated carbon due to the size exclusion, a phenomenon could have a significant influence on both multicomponent equilibria and kinetics. Activated carbons with three different MPSDs are studied with ethane and propane as the two model adsorbates. The Heterogeneous Macropore Surface Diffusion model (HMSD) is employed to simulate adsorption kinetics. The simulation results show that the MPSD is an important factor affecting both the multicomponent equilibria and kinetics.     

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.     

Concentration relationships of coefficients of self-diffusion and viscosity of the adsorbate in narrow slit-like pores

Concentration relationships of dynamic characteristics of the adsorbate (coefficients of self-diffusion and shear viscosity) in narrow slit-like pores with different widths were considered. These coefficients were calculated using the simplest molecular model (lattice-gas model), which takes into account the intrinsic volume of molecules and their interactions in the quasi-chemical approximation. The values of coefficients of self-diffusion and shear viscosity of the adsorbate depend strongly on the distance to the pore wall.     

The influence of the nonuniformity of cylindrical pore walls on estimates of the specific surface area of MSM-41 adsorbents

The influence of the nonuniformity of pore walls in narrow cylindrical channels of MSM-41-type mesoporous materials on specific surface area values is analyzed. It was shown on the assumption that pore walls were characterized by a chaotic distribution of centers with different energies and in conformity with the concept of their amorphous character that the inflection point of isotherms considered in the Brunauer-Emmett-Teller theory characterized the capacity of the monolayer to within ～20%. The initial portions of the experimental adsorption isotherms for pores 3 to 5 nm in diameter were described.     

Molecular grounds of the calculation of equilibrium and transport characteristics of inert gases and liquids in complex narrow-pore systems

A self-consistent approach to the calculation of equilibrium and transport characteristics of inert gases and liquids in complex narrow-pore systems based on the lattice-gas model is proposed. A supramolecular structure for fine-grained solids was constructed and the adsorbate distribution within the pore volume is described. The supramolecular structure is simulated using slit-shaped, cylindrical, spherical, and globular segments. Additionally, junctions of pore systems with different structures are included, and the heterogeneity of their walls and the presence of structural defects in the pore segments are taken into account. The distributions of molecules are described in the quasi-chemical approximation to take into account intermolecular interactions using calibration functions to correct this approximation in the near-critical area. Expressions for local and integrated flow transfer coefficients are constructed, in particular, self-diffusion, shear viscosity and heat conductivity. The contributions of the near-wall areas and the core parts of pores to the general form of phase diagrams, the effect of the pore size on the conditions of capillary condensation, and the role of surface mobility of molecules are discussed.     

The adsorption of chlorobenzene on a carbon adsorbent obtained by the pyrolysis of hypercrosslinked polystyrene

The adsorption of chlorobenzene vapor on an experimental D4609 (Purolite Int.) adsorbent prepared by the pyrolysis of hypercrosslinked polystyrene was studied. The adsorbent was characterized by a large specific surface area, a narrow pore size distribution with the predominant fraction of pore diameters 0.9–3.4 nm, and a high absorption ability with respect to chlorobenzene. The adsorption isotherms were measured over the temperature range 100–140°C, and the thermodynamic characteristics of adsorption were determined. In spite of the correspondence to the formal requirements of the theory of volume filling of micropores, the mechanism of adsorption in narrow micropores (<1.2—1.5 nm) was different from filling with a condensed phase.     

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.     

Estimation of micropore size distribution in active carbons from adsorption isotherms of water vapor

A possibility of estimation of the micropore size distribution in the carbon adsorbents with the developed micro-and mesoporous structure by analysis of the adsorption isotherms of water vapors was considered. At saturation water condenses in micropores in a form of a weakly compressed liquid. However, water molecules in micropores are packed not so closely as in the liquid because of steric hindrance. Therefore, the real density of water adsorbed in the micropores is lower than that of water adsorbed on an open surface and lower than the density of the normal liquid. An analysis of the adsorption isotherms of water vapors with account for the both opposite effects on the water density gives reliable data on the micropore sizes of the carbon adsorbents. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 40–43, January, 2007.     

Multicomponent Adsorption of Pesticides onto Activated Carbon Fibers

The adsorption equilibria of pesticides and metabolites (atrazine, deethylatrazine, deisopropylatrazine and simazine) are studied onto activated carbon fibers –ACF– with a broad pore size distribution (32% mesopore volume, 68% micropore volume). Mono-and multi-component isotherms have been determined for low concentrations, from 0.23×10⁻⁶ to 9.52×10⁻⁶ mol L⁻¹. Single solute isotherms, modeled by Freundlich and Langmuir models, tend to prove the influence of the adsorbate's solubility in the adsorption capacity of activated carbon fibers. Binary solute isotherms confirm the strong influence of pesticide solubility on the competitive adsorption mechanism: the competition is higher in the case of adsorbates of different solubilities (atrazine and DEA or DIA for example). Multicomponent experimental data were modeled by extended Langmuir-based equations and the Ideal Adsorbed Solution theory. Whereas the first ones failed to model accurately binary adsorption due to restrictive hypothesis, the IAS model showed a good agreement between experimental and predicted data. It emphasised also the difficulty in satisfying the hypothesis of the model in the case of highly adsorbed compounds. Finally, the simultaneous adsorption of atrazine and NOM (in a natural water, DOC = 18.2 mg L⁻¹) shows no adsorption competition effects between natural organic matter and atrazine. This is due to the presence of secondary micropores (0.8–2 nm) and mesopores in the ACF, which limit a pore blockage phenomenon by NOM.