Physical adsorption of gases: the case for absolute adsorption as the basis for thermodynamic analysis

We discuss the thermodynamics of physical adsorption of gases in porous solids. The measurement of the amount of gas adsorbed in a solid requires specialized volumetric and gravimetric techniques based upon the concept of the surface excess. Excess adsorption isotherms provide thermodynamic information about the gas-solid system but are difficult to interpret at high pressure because of peculiarities such as intersecting isotherms. Quantities such as pore density and heats of adsorption are undefined for excess isotherms at high pressure. These difficulties vanish when excess isotherms are converted to absolute adsorption. Using the proper definitions, the special features of adsorption can be incorporated into a rigorous framework of solution thermodynamics. Practical applications including mixed-gas equilibria, equations for adsorption isotherms, and methods for calculating thermodynamic properties are covered. The primary limitations of the absolute adsorption formalism arise from the need to estimate pore volumes and in the application to systems with larger mesopores or macropores at high bulk pressures and temperatures where the thermodynamic properties may be dominated by contributions from the bulk fluid. Under these circumstances a rigorous treatment of the thermodynamics requires consideration of the adsorption cell and its contents (bulk gas, porous solid and confined fluid).     

Adsorption of supercritical CO2 in aerogels as studied by small-angle neutron scattering and neutron transmission techniques

Small-angle neutron scattering (SANS) has been used to study the adsorption behavior of supercritical carbon dioxide (CO2) in porous Vycor glass and silica aerogels. Measurements were performed along two isotherms (T=35 and 80 degrees C) as a function of pressure (P) ranging from atmospheric up to 25 MPa, which corresponds to the bulk fluid densities ranging from rho(CO2) approximately 0 to 0.9 gcm3. The intensity of scattering from CO2-saturated Vycor porous glass can be described by a two-phase model which suggests that CO2 does not adsorb on the pore walls and fills the pore space uniformly. In CO2-saturated aerogels an adsorbed phase is formed with a density substantially higher that of the bulk fluid, and neutron transmission data were used to monitor the excess adsorption at different pressures. The results indicate that adsorption of CO2 is significantly stronger in aerogels than in activated carbons, zeolites, and xerogels due to the extremely high porosity and optimum pore size of these materials. SANS data revealed the existence of a compressed adsorbed phase with the average density approximately 1.07 gcm3, close to the density corresponding to closely packed van der Waals volume of CO2. A three-phase model [W. L. Wu, Polymer 23, 1907 (1982)] was used to estimate the volume fraction phi3 of the adsorbed phase as a function of the fluid density, and gave phi3 approximately 0.78 in the maximum adsorption regime around rho(CO2) approximately 0.374 gcm3. The results presented in this work demonstrate the utility of SANS combined with the transmission measurements to study the adsorption of supercritical fluids in porous materials.     

Adsorption of argon from sub- to supercritical conditions on graphitized thermal carbon black and in graphitic slit pores: a grand canonical Monte Carlo simulation study

In this paper we consider the adsorption of argon on the surface of graphitized thermal carbon black and in slit pores at temperatures ranging from subcritical to supercritical conditions by the method of grand canonical Monte Carlo simulation. Attention is paid to the variation of the adsorbed density when the temperature crosses the critical point. The behavior of the adsorbed density versus pressure (bulk density) shows interesting behavior at temperatures in the vicinity of and those above the critical point and also at extremely high pressures. Isotherms at temperatures greater than the critical temperature exhibit a clear maximum, and near the critical temperature this maximum is a very sharp spike. Under the supercritical conditions and very high pressure the excess of adsorbed density decreases towards zero value for a graphite surface, while for slit pores negative excess density is possible at extremely high pressures. For imperfect pores (defined as pores that cannot accommodate an integral number of parallel layers under moderate conditions) the pressure at which the excess pore density becomes negative is less than that for perfect pores, and this is due to the packing effect in those imperfect pores. However, at extremely high pressure molecules can be packed in parallel layers once chemical potential is great enough to overcome the repulsions among adsorbed molecules.     

Grand canonical monte carlo simulation study of methane adsorption at an open graphite surface and in slit-like carbon pores at 273 K

Grand canonical Monte Carlo (GCMC) simulation was used for the systematic investigation of the supercritical methane adsorption at 273 K on an open graphite surface and in slit-like micropores of different sizes. For both considered adsorption systems the calculated excess adsorption isotherms exhibit a maximum. The effect of the pore size on the maximum surface excess and isosteric enthalpy of adsorption for methane storage at 273 K is discussed. The microscopic detailed picture of methane densification near the homogeneous graphite wall and in slit-like pores at 273 K is presented with selected local density profiles and snapshots. Finally, the reliable pore size distributions, obtained in the range of the microporosity, for two pitch-based microporous activated carbon fibers are calculated from the local excess adsorption isotherms obtained via the GCMC simulation. The current systematic study of supercritical methane adsorption both on an open graphite surface and in slit-like micropores performed by the GCMC summarizes recent investigations performed at slightly different temperatures and usually a lower pressure range by advanced methods based on the statistical thermodynamics.     

Modeling of gas adsorption equilibrium over a wide range of pressure: a thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV. The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R1 in the temperature range from 25 to 70 degrees C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems.     

Modeling of monolayer adsorption of hydrogen on ZSM‐5 zeolite by lattice density functional theory

The adsorption isotherms of hydrogen on microporous zeolite ZSM‐5, at supercritical conditions, have been modeled using the monolayer lattice density functional theory (LDFT) models, where the simple cubic lattice, face‐centered cubic lattice, body‐centered cubic lattice and tetragonal lattice structures are assumed for the arrangements of the adsorption sites inside pores based on the size and shape of the zeolite. The results indicate that the monolayer LDFT models appear to be effective in describing hydrogen adsorption on zeolite ZSM‐5 at supercritical conditions, and the calculated adsorption isotherms agree well with the experimental isotherms measured previously. The layer density of adsorbed phase is presented versus the bulk density and temperature. It is found that the densities of adsorbed phase on adsorbent surface are much higher than the bulk density for temperature range under study. However, in the core region, the layer densities are close to the bulk density. The monolayer adsorption is suitable for hydrogen on ZSM‐5 zeolite. Copyright © 2013 John Wiley & Sons, Ltd.     

Near-critical CO2 in mesoporous silica studied by in situ FTIR spectroscopy

Attenuated total reflection Fourier transform infrared spectroscopy was used to correlate the band shift of the nu2 vibrational band of carbon dioxide with the density of the fluid. Upon adsorption of CO2 on mesoporous silica and a nonporous SiO2 film, additional bands were detected due to interactions of CO2 with SiO2. Near the saturation pressure for the porous samples, the absorbance of the nu2 band increased strongly, which was concluded to be caused by liquidlike CO2 inside the pores. Integration of single-beam-sample-reference spectra between bulk CO2 and CO2 adsorbing on the mesoporous silica coated on one part of the internal reflection element revealed excess adsorption type isotherms with sharp maxima at 21 degrees C. A flatter curve shape could be observed at 25 degrees C, which allowed estimating the pore critical temperature. Moreover, the density of the fluid inside and outside the pores could be compared. Over the investigated ranges of pressure, temperature, and pore size, the results evidenced that the CO2 density was always higher in the silica pores than in the bulk, even under supercritical conditions. This has important consequences on the pressure dependence of dissolution power and diffusivity of fluids in mesoporous solids. An overview is given on the influences of fluid phase behavior in the bulk and in the pores at various conditions on solubility and diffusivity.     

氮气和氧气在膜表面和狭缝孔内平衡吸附的分子模拟

采用巨正则系综的MonteCarlo方法(GCMC)模拟常温(T=303K)下,氮气和氧气在具有狭缝状膜孔的碳膜内的吸附.气体分子之间、气体分子与膜原子之间的相互作用均采用Shifted-Lennard-Jones势能模型.研究了303K和10MPa下,不同膜厚度和膜孔宽度时氧气在膜面和膜孔内的密度分布以及303K和压力从1MPa到10MPa变化时,氮气和氧气在狭缝膜孔内超额吸附等温线.实验结果表明,膜孔端口效应显著,膜厚和膜孔宽度对孔内吸附影响较大,而膜构型对膜面吸附影响显著.     

Micropore Filling of Supercritical Xe in Micropores of Activated Carbon Fibers

The adsorption isotherms of Xe vapor at 196 K and supercritical Xe at 300 K on activated carbon fibers of different pore widths were gravimetrically measured. The adsorption isotherms of Xe vapor were compared with the N(2) adsorption isotherms. A Dubinin-Radushkevich (DR) plot of the adsorption isotherms of Xe vapor showed a good linearity, indicating that Xe vapor is adsorbed by the representative micropore filling mechanism. The adsorption isotherms of supercritical Xe were approximated by the Langmuir equation. The saturated adsorption amounts of supercritical Xe, W(L), were in the range of 0.14 to 0.22 ml g(-1). The adsorption isotherms of supercritical Xe were described by the supercritical DR equation, which provides the quasisaturated vapor pressure P(0q). Both P(0q) and W(L) lead to the reduced isotherm, which can describe three isotherms. The obtained reduced isotherm derived from the isotherms of supercritical Xe could describe even those of Xe vapor. Hence, both Xe vapor and supercritical Xe should be adsorbed by the same mechanism. The isosteric heat of Xe adsorption was greater than the enthalpy of vaporization of Xe by more than 12 kJ mol(-1). These results suggest that Xe molecules are stabilized in the form of a cluster in micropores even at 300 K. Copyright 2000 Academic Press.     

Effects of confinement on the molar enthalpy of argon adsorption in graphitic cylindrical pores: a grand canonical Monte Carlo (GCMC) simulation study

Using a grand canonical Monte Carlo simulation, we study argon adsorption in graphitic cylindrical pores to investigate the differences between the isosteric heat and the integral molar enthalpy under subcritical and supercritical conditions and compare these results against those for a flat graphite surface to investigate the role of confinement on the enthalpy change of adsorption. The isosteric heat curve is finite under subcritical conditions, but for supercritical adsorption, it becomes infinite at the pressure where the excess concentration versus pressure is maximum. This can be circumvented using the integral molar enthalpy, which is a better variable to describe the energy change for supercritical adsorption. Finally, the effects of pore geometry (radius and length) on argon adsorption under subcritical and supercritical conditions are discussed.     

Volumetric Properties of the Binary System Trihexyltetradecylphosphonium Bromide (CYPHOS IL 102) + N,N-Dimethylformamide (DMF) at Temperatures from T=293.15 to 313.15 K at Atmospheric Pressure

Volumetric properties for the trihexyltetradecylphosphonium bromide (CYPHOS IL 102) + N,N-dimethylformamide (DMF) binary system were determined at temperatures from T=293.15 to 313.15?K and ambient pressure (p=0.7 atm). Densities were measured by means of a vibrating tube densimeter (VTD). These measurements covered the full range of compositions along with the pure compounds; expansion coefficients, excess molar volumes, and partial molar volumes were calculated from the experimental densities. Excess molar volumes were fitted to a Redlich?CKister type equation. The excess molar volumes exhibit negative deviations from ideal behavior.     

Study of structural and thermodynamic parameters of adsorption layers using density functional theory. Local density and adsorption isotherms on spherical surfaces

Local density profiles in adsorption layers of Lennard-Jones fluids on two-dimensional adsorbents with spherical geometry and isotherms of excess (Gibbs) adsorption have been calculated using the classical density functional theory (approximations with weighting coefficients). The local density profiles have been found in hydrogen adsorption layers on C₆₀, C₂₄₀, and C₅₄₀ fullerene molecules. The calculations have been performed for both subcritical and supercritical temperature ranges. It has been shown that, at a pressure of 10 MPa and a temperature of 77 K, the gravimetric (mass) hydrogen density on C₆₀ fullerene is 7.6 wt %, which is in good agreement with the results of molecular dynamics simulation and experimental data. It has also been established that the gravimetric hydrogen density on C₆₀ fullerene is higher than that on C₂₄₀ and C₅₄₀ fullerenes, being comparable with its value in a slitlike pore of a carbon adsorbent.     

Surface excess free energy of simple fluids confined in cylindrical pores by isothermal-isobaric Monte Carlo: influence of pore size

Confined fluid properties are mainly determined by interfacial phenomena characterized by surface quantities. Based on a simple model of Lennard-Jones particles confined in a cylindrical pore, this study introduces a grand potential surface quantity to quantify the difference in the thermodynamic pressure between the bulk and the confined fluids. The usual surface tension gamma defined as this grand potential difference for the same chemical potential in both confined and bulk states is generally strongly dependent on both the chemical potential and temperature. It is proposed here to introduce another surface quantity zeta which measures the thermodynamic pressure difference between confined and bulk states for identical densities. It is shown that this quantity is much less dependent on confined fluid density or chemical potential. It is actually constant along the gas-like and liquid-like adsorption/desorption branches for an irreversible isotherm (hysteresis), with a different value for each branch. For reversible supercritical isotherms, zeta is shown to remain constant in the low and high density parts of the isotherm. This independence on chemical potential (or equivalently fluid density) is believed to be of great interest for practical applications when one desires to calculate thermodynamic quantities such as the usual surface tension gamma or the thermodynamic pressure of a confined fluid for any given chemical potential and temperature. Such calculations are required to determine fundamental properties such as metastability or coexistence. The effects of temperature, fluid/substrate interaction strength, and pore size are studied.     

Grand canonical Monte Carlo simulation for determination of optimum parameters for adsorption of supercritical methane in pillared layered pores

A grand canonical Monte Carlo (GCMC) method is carried out to determine optimum adsorptive storage pressures of supercritical methane in pillared layered pores. In the simulation, the pillared layered pore is modeled by a uniform distribution of pillars between two solid walls. Methane is described as a spherical Lennard-Jones molecule, and Steele's 10-4-3 potential is used for representing the interaction between the fluid and a layered wall. The site-site interaction is also used for calculating the interaction energy between methane molecules and pillars. An effective potential model that reflects the characteristics of a real pillared layered material is proposed here. In the model, a binary interaction parameter, k(fw), is introduced into the combining rule for the cross-energy parameter for the interaction between the fluid and a layered wall. Based on the experimental results for the Zr-pillared material synthesized and characterized by Boksh, Kikkinides, and Yang, the binary interaction parameter, k(fw), is determined by fitting the simulation results to the experimental adsorption data of nitrogen at 77 K. Then, by taking it as a model of pillared layered material, a series of GCMC simulations have been carried out. The excess adsorption isotherms of methane in a pillared layered pore with three different pore widths and porosities are obtained at three supercritical temperatures T=207.3, 237.0, and 266.6 K. Based on the simulation results at different porosities, various pore widths and different supercritical temperatures, the pillared layered pore with porosity psi=0.94 and pore width hsigma(p)=1.02 nm is recommended as adsorption storage material of supercritical methane. Moreover, the optimum adsorption pressure is determined at a given temperature and a fixed width of the pillared layered pore. For example, at temperature T=207.3 K, the optimum adsorption pressures are 3.1, 3.7, and 4.5 M Pa at H=1.02, 1.70, and 2.38 nm, respectively. In summary, the GCMC method is a useful tool for optimizing adsorption storage of supercritical methane in pillared layered material.     

Temperature dependence of local density augmentation for acetophenone N,N,N',N'-tetramethylbenzidine exciplex in supercritical water

Local density augmentation around exciplex between acetophenone and N,N,N',N'-tetramethylbenzidine in supercritical water was measured by observing the peak shift of transient absorption spectrum at temperatures from 380 to 410 degrees C and at pressures from 6 to 37 MPa. Large local density augmentation was observed at lower solvent densities. Local density augmentation was evaluated by the excess density, which was defined as the difference between local density and bulk density, and the density enhancement factor, which was defined by the ratio of the local density to the bulk density. The number of solvating molecules was estimated with a Langmuir adsorption model. The excess density was found to exhibit a maximum at approximately 0.15 g cm(-3), which decreased with increasing temperature. The density enhancement factor was found to decrease with increasing temperature; however, its value was much greater than unity at 410 degrees C, which provides evidence that exciplex-water interactions still exist at these conditions. The temperature dependence of local density augmentation around the exciplex in supercritical water was comparable with that in supercritical carbon dioxide, which suggests that the ratios of the solute-solvent and solvent-solvent interactions are comparable between these two systems.     

Molecular simulation evidence for solidlike adsorbate in complex carbonaceous micropore structures

Adsorption of a model nitrogen vapor on a range of complex nanoporous carbon structures is simulated by grand canonical Monte Carlo simulation for a single subcritical temperature above the bulk freezing point. Adsorption and desorption isotherms, heats of adsorption, and three-dimensional singlet distribution functions (SDFs) were generated. Inspection of the SDFs reveals significant levels of solidlike adsorbate at saturation even in the most complex of the microporous solids considered. This strongly suggests that solidlike adsorbate will also occur for simple subcritical vapors adsorbed on real noncrystalline solids such as microporous carbons at temperatures above the bulk freezing point, supporting indirect experimental observations. The presence of significant levels of solidlike adsorbate has implications for characterization of microporous solids where adsorbate density is used (e.g., determination of pore volume from loading). Detailed consideration of the SDF at different loadings for a model microporous solid indicates solidlike adsorbate forms at distributed points throughout the pore space at pressures dependent on the nature of the local porosity. The nature of the local porosity also dictates the freezing mechanism. A local freezing/ melting/refreezing process is also observed. Introduction of mesoporosity into the model causes hysteresis between the adsorption and desorption isotherms. Adsorption in the hysteresis loop occurs by a series of local condensation events. It appears as if the presence of adjacent microporosity and/or adsorbate within it affects the pressure at which these events occur. Reversal of the condensation during desorption occurs throughout the mesoporosity at a single pressure; this pressure is unaffected by the presence of adjacent microporosity or the adsorbate within it. It is also shown that the empirical concept of "pore size" is not consistent for describing adsorption in the complex solids considered here. A new concept is, therefore, proposed that seeks to account for the factors that affect local adsorption energy: local geometry, microtexture, surface atom density, and surface chemistry.     

Stockmayer流体在活性炭孔中的吸附的分子模拟

应用巨正则系综monteCarlo方法模拟Stockmayer流体[以一氯二氟甲烷(R22)为代表]在活性炭孔中的吸附。模拟中R22分子采用等效Stockmayer势能模型,狭缝碳孔墙采用10-4-3模型。通过模拟得到了最佳孔径,并在最佳孔径下,针对不同的主体压力及活性基团密度,得到了吸附等温线、孔中流体的局部密度分布图和较为直观的孔内流体分子的瞬时构象,分析了吸附等温线的特征及孔内流体的吸附结构,认为在0.0,1.0sites/nm^2的活性基团密度下的碳孔内分别发生物理及化学吸附,并确定了最佳操作压力,为工业设计合适的催化剂提供依据。     

超临界甲烷在纳米材料中最适吸附压力的确定

用巨正则Monte Carlo (GCMC)方法模拟了超临界甲烷在层柱纳米材料中的吸附.模拟中,层柱纳米材料采用了柱子均匀分布在层板间的模型, 非极性分子甲烷采用Lennard Jones分子模型, 层板墙采用Steele的10 4 3模型, 流体分子与柱子的相互作用采用点 点 (site to site) 的方法计算.得到了甲烷的随着压力先增大后减小的超额吸附等温线.在T=207.3 K时,1.02、1.70和2.38 nm孔宽对应的最适操作压力 (即对应于最大吸附量时的操作压力) 分别为2.4、3.1和3.7 MPa.然而,在T=237.0 K时,1.02、1.70和2.38 nm孔宽对应的最适操作压力分别为2.9、3.6和4.9 MPa,分别比T=207.3 K时相同孔宽下对应的最适操作压力至少高0.5 MPa. 模拟结果表明, GCMC方法是研究材料吸附性能的一种强有力的工具.     

A density functional theory for Lennard-Jones fluids in cylindrical pores and its applications to adsorption of nitrogen on MCM-41 materials

A density functional theory (DFT) constructed from the modified fundamental-measure theory and the modified Benedict-Webb-Rubin equation of state is presented. The Helmholtz free energy functional due to attractive interaction is expressed as a functional of attractive weighted-density in which the weight function is a mean-field-like type. An obvious advantage of the present theory is that it reproduces accurate bulk properties such as chemical potential, bulk pressure, vapor-liquid interfacial tension, and so forth when compared with molecular simulations and experiments with the same set of molecular parameters. Capabilities of the present DFT are demonstrated by its applicability to adsorption of argon and nitrogen on, respectively, a model cylindrical pore and mesoporous MCM-41 materials. Comparison of the theoretical results of argon in the model cylindrical pore with those from the newly published molecular simulations indicates that the present DFT predicts accurate average densities in the pore, slightly overestimates the pore pressure, and correctly describes the effect of the fluid-pore wall interaction on average densities and pressures in the pore. Application to adsorption of nitrogen on MCM-41 at 77.4 K shows that the present DFT predicts density profiles and adsorption isotherms in good agreement with those from molecular simulations and experiments. In contrast, the hysteresis loop of adsorption calculated from the mean-field theory shifts toward the low pressure region because a low bulk saturated pressure is produced from the mean-field equation of state. The present DFT offers a good way to describe the adsorption isotherms of porous materials as a function of temperature and pressure.