A Grand Canonical Monte Carlo Study of Adsorption and Capillary Phenomena in Nanopores of Various Morphologies and Topologies: Testing the BET and BJH Characterization Methods

We report a Grand Canonical Monte Carlo simulation study of Ar adsorption at 77 K in silica nanopores having various morphologies/topologies. Both the morphological and topological disorders are shown to significantly affect the capillary condensation phenomenon. In the case of an ellipsoidal pore, we observe that the filling mechanism is similar to that of a cylindrical pore having the same section area but with a lower condensation pressure. We show that the adsorption/desorption hysteresis loop is asymmetrical for the pore with constrictions while it is symmetrical for the regular cylindrical pore. Moreover, the Ar adsorption isotherm for the constricted pore reproduces the main features of that for the fully disordered Vycor‐like porous matrix. The results for the different pore geometries (having no direct interface with the gas reservoir) indicate that the desorption occurs through cavitation at a pressure driven by the smallest void size. We also consider the validity of the BET and BJH methods for the different porous matrices. Except for the Vycor‐like matrix, the BET surface assessed from Ar adsorption isotherm at 77 K always significantly overestimates the intrinsic surface of the pore (even for a planar surface). The disagreement between the BET surface and the geometrical surface is found to increase as the confinement increases (cylindrical pore) and/or the shape of the pore becomes asymmetrical (ellipsoidal pore). Interestingly, the best agreement between the BET and the geometrical surface is found in the case of the pore with a constriction, i.e. a system that exhibits a surface with both negative and positive curvature regions. This idea is supported by the results for the Vycor‐like matrix, which has a distorted surface (many negative curvature regions combined with positive curvature regions): for this disordered porous matrix, the BET surface is found to underestimate the intrinsic surface. Finally, we show that the pore size determined using the BJH method always underestimates the pore size, in agreement with previous experimental and simulation studies.     

The adsorption of water in finite carbon pores

Grand canonical Monte Carlo simulations were applied to the adsorption of SPCE model water in finite graphitic pores with different configurations of carbonyl functional groups on only one surface and several pore sizes. It was found that almost all finite pores studied exhibit capillary condensation behaviour preceded by adsorption around the functional groups. Desorption showed the reverse transitions from a filled to a near empty pore resulting in a clear hysteresis loop in all pores except for some of the configurations of the 1.0?nm pore. Carbonyl configurations had a strong effect on the filling pressure of all pores except, in some cases, in 1.0?nm pores. A decrease in carbonyl neighbour density would result in a higher filling pressure. The emptying pressure was negligibly affected by the configuration of functional groups. Both the filling and emptying pressures increased with increasing pore size but the effect on the emptying pressure was much less. At pressures lower than the pore filling pressure, the adsorption of water was shown to have an extremely strong dependence on the neighbour density with adsorption changing from Type IV to Type III to linear as the neighbour density decreased. The isosteric heat was also calculated for these configurations to reveal its strong dependence on the neighbour density. These results were compared with literature experimental results for water and carbon black and found to qualitatively agree.     

Characterization of PSD of activated carbons by using slit and triangular pore geometries

A mixed geometry model for activated carbons, representing the porous space as a collection of an undetermined proportion of slit and triangular pores, is developed, evaluated theoretically and applied to the characterization of a controlled series of samples of activated carbon obtained from the same precursor material. A method is proposed for the determination of the Pore Size Distribution (PSD) for such a mixed geometry model, leading to the unique determination of the proportion of pores of the two geometries fitting adsorption data. By using the Grand Canonical Monte Carlo (GCMC) simulation method in the continuum space, families of N2 adsorption isotherms are generated both for slit and triangular geometry corresponding to different pore sizes. The problem of the uniqueness in the determination of the PSD by fitting an adsorption isotherm using the mixed geometry model is then discussed and the effects of the addition of triangular pores on the PSD are analyzed by performing a test where the adsorption isotherm corresponding to the known PSD is generated and used as the “experimental” isotherm. It is found that a pure slit geometry model would widen the PSD and shift it to smaller sizes, whereas a pure triangular geometry model would produce the opposite effect. The slit and triangular geometry families of isotherms are finally used to the fit experimental N₂ adsorption data corresponding to a family of activated carbons obtained from coconut shells through a one-step chemical activation process with phosphoric acid in air, allowing for the determination of the micropore volume, the proportion of slit and triangular pores and the PSD corresponding to the mixed geometry. The same experimental data were fit using both the conventional slit pore model and the mixed geometry model. From the analysis of the effect of different preparation procedures on the resulting PSDs, it is concluded that the proposed mixed geometry model may probably better capture the morphology and energetics of activated carbons prepared by chemical activation under mild temperatures.     

Phase behavior and fluid-solid surface tension of argon in slit pores and carbon nanotubes

Phase behaviors of argon in several types of cylindrical and slit pores are examined by grand-canonical Monte Carlo simulations. Condensation processes in single- and multi-walled carbon nanotubes along with those in hard-wall tubes are compared. Effects of the pore size on pressure-tensor components, the fluid-wall surface tension, and the adsorption are also compared for the different fluid-pore interactions. The chemical potential at which the fluid begins to condense in the single-walled nanotube is greater than that in the multi-walled nanotube by an amount nearly equal to the difference in the potential-well depth of the fluid-pore interaction, and the adsorption isotherms overlap each other almost completely for narrow pores and partially for wider pores. Similar analyses are performed for slit pores of two different hydrocarbon models.     

Hydrogen adsorption in slit-shaped pores of carbon adsorbents

The hydrogen adsorption in slit-shaped pores of carbon adsorbents is investigated using the density functional theory. Hydrogen adsorption in the gap between two monocarbon (graphene) walls is calculated for 20.33, 77, and 200 K. At T = 20.38 and 77 K, our data on the hydrogen storage capacities in slit pores are in good agreement with the results of A.A. Fomkin and V.A. Sinitsyn [23], obtained using Dubinin’s volume pore filling theory and the standard data on benzene adsorption. Under supercritical conditions, the adsorption capacity in the modeling adsorbents is underestimated by half.     

Adsorption of argon and nitrogen in cylindrical pores of MCM-41 materials: application of density functional theory

Adsorption of argon and nitrogen at their respective boiling points in cylindrical pores of MCM-41 type silica-like adsorbents is studied by means of a non-local density functional theory (NLDFT), which is modified to deal with amorphous solids. By matching the theoretical results of the pore filling pressure versus pore diameter against the experimental data, we arrive at a conclusion that the adsorption branch (rather than desorption) corresponds to the true thermodynamic equilibrium. If this is accepted, we derive the optimal values for the solid-fluid molecular parameters for the system amorphous silica-Ar and amorphous silica-N₂, and at the same time we could derive reliably the specific surface area of non-porous and mesoporous silica-like adsorbents, without a recourse to the BET method. This method is then logically extended to describe the local adsorption isotherms of argon and nitrogen in silica-like pores, which are then used as the bases (kernel) to determine the pore size distribution. We test this with a number of adsorption isotherms on the MCM-41 samples, and the results are quite realistic and in excellent agreement with the XRD results, justifying the approach adopted in this paper.     

D2/H2 quantum sieving in microporous carbons: a theoretical study on the effects of pore size and pressure

The adsorption of hydrogen and deuterium in slit-shaped carbon pores is studied by grand canonical Monte Carlo simulations. All interactions are assumed to be of Lennard–Jones type, while the Feynman–Hibbs expression is used to account for quantum effects. The interaction energy of both isotopes inside the slit pore space is discussed thoroughly. Furthermore, pure component adsorption isotherms of both isotopes were simulated at 77?K for pressures up to 20?bar in slit pores having widths of up to 2.0?nm. According to our simulations, in equilibrium, slit pores reveal slight deuterium selectivity over hydrogen, and this quantum-based selectivity depends both on pressure and pore size.     

Adsorption in cylindrical pores: Mixed lattice-site/off-site Monte Carlo simulations in pores with heterogeneous wall structure

We present results of grand canonical Monte Carlo simulations of adsorption in cylindrical pores with rough surface modeled by lattice-site approach. Each site is characterized by two parameters: structural and energetic, which locally modify the structure and energy properties of the surface. There are three types of sites, randomly distributed over the wall: attractive, neutral and repulsive with respect to the smooth pore model. The results presented here show how this model affects the mechanism of adsorption and how it changes the forms of adsorption isotherm. We compare our numerical results with the experimental data of adsorption of a simple fluid (CH₄, T = 77 K) in cylindrical silica pore of diameter d = 4 nm (MCM-41 material).     

Further observations on the polarized absorption spectrum of benzene crystals at 2000 Å

The structure of a hard sphere fluid confined by model slit and cylindrical pores is investigated. Results from grand canonical Monte Carlo (GCMC) simulations and from the hypernetted chain/mean spherical approximation (HNC/MSA) equation are reported. GCMC results are compared with those from the HNC/MSA equation, and agreement is good. The effect of confinement on liquids at the same chemical potentials is that the absorption of the hard sphere fluid into the pores decreases with increasing confinement, i.e., when going from planar to cylindrical geometry or by narrowing the pores. The adsorption on the pore walls has, in general, the opposite behaviour. For high bulk concentrations and certain values of cylindrical pore diameter the concentration profile is higher at the centre of the pore than next to the pore wall. A very strong, but continuous, transition occurs in the concentration profile, as a function of the cylinder's diameter. These results could be of some interest in catalysis studies.     

The ins and outs of capillary condensation in cylindrical pores

A series of simulations has been performed of adsorption and desorption of a simple model of xenon in cylindrical pores of a silica-like material. Closed-ended, open-ended, and single-ended pores of either 3 nm or 4 nm diameter were considered, and the pore length was varied between 8nm and 108 nm. This study exposes some of the possible mechanisms of pore filling and emptying, and demonstrates that hysteresis can be almost entirely suppressed in certain pore geometries. The effects of pore length are considered, and the thermodynamics of 1-dimensional systems and the nature of ‘capillary critical points’ are discussed.     

Melting and freezing of argon in a granular packing of linear mesopore arrays

Freezing and melting of Ar condensed in a granular packing of template-grown arrays of linear mesopores (SBA-15, mean pore diameter 8 nm) has been studied by specific heat measurements C as a function of fractional filling of the pores. While interfacial melting leads to a single melting peak in C, homogeneous and heterogeneous freezing along with a delayering transition for partial fillings of the pores result in a complex freezing mechanism explainable only by a consideration of regular adsorption sites (in the cylindrical mesopores) and irregular adsorption sites (in niches of the rough external surfaces of the grains and at points of mutual contact of the powder grains). The tensile pressure release upon reaching bulk-liquid-vapor coexistence quantitatively accounts for an upward shift of the melting and freezing temperature observed while overfilling the mesopores.     

水蒸气对二氧化硅膜的影响：吸附性能与渗流效应

研究了在50和90 oC时水蒸气对孔径约为4 ?的二氧化硅膜的吸附性能和渗流效应影响,采用椭圆偏振光谱分析水蒸气的吸附性能,以及测定氦气-H₂O二元混合气体的透过性能. 研究表明水蒸气在二氧化硅膜上的吸附行为符合一阶Langmuir等温线,同时,在H₂O分子存在的条件下,氦气的透过率会急剧下降. 通常,在极小孔内气体分子的传输被认为是不连续的,而是在势能下从一个占有位置跳跃到另外一个空位上. 当在二氧化硅表面的H₂O分子覆盖率上升时,氦气的透过率急剧下降可能与渗流效应有关,其中吸附在二氧化硅表面的H₂O分子阻碍了氦气分子的跳跃.     

Demixing of a binary mixture in slit-like pores at high temperatures

We investigate the fluid—fluid demixing transitions in the case of adsorption of so-called symmetric binary mixtures in slit-like pores at temperatures higher than the bulk gas—liquid critical temperature. The aim of the study is to determine how the demixing of such mixtures in the pores depends on the bulk phase composition and on the parameters characterizing the pore. The calculations have been carried out by means of a density functional theory. In the case of an equimolar bulk mixture, the demixing transition inside the pore occurs only when the adsorption potentials of both species are identical. The occurrence of this transition is manifested by a cusp in the adsorption isotherm. For nonequimolar bulk phase compositions, the transition can also take place if the adsorption energies of both components are different. However, the difference in the adsorption energies should be small enough, otherwise a continuous demixing takes place. For non-equimolar compositions two branches of the grand canonical potential intersect, whereas for equimolar bulk composition they meet tangentially. We have determined phase behaviour for several model systems.     

Influence of structural heterogeneity of nanoporous sorbent walls on hydrogen storage

Heterogeneity is an ubiquitous aspect of adsorption, often modifying substantially the observed behaviour of the adsorbate-adsorbent system. In this paper, the influence of heterogeneity is explicitly analyzed for the case of the adsorption of molecular hydrogen onto nanoporous carbon. Grand Canonical Monte Carlo simulations were used to study the mechanism of adsorption in the models of the adsorbate that include both energetic and structural modifications of graphene-based slit pores. In particular, a partial substitution of carbons by boron modifies both the symmetry of the energy landscape and the strength of hydrogen physisorption; which results in considerable increases of the amount of adsorbed gas without major modification of the mechanism of adsorption. Additional heterogeneity arises from structural modifications of the adsorbent by neutron irradiation of boron-doped samples, where the boron fission products generate additional surface area for adsorption. Simulations of adsorption in such pores show that hydrogen uptake is strongly dependent on the chemical nature of the modified pore walls.     

Structural and thermodynamic properties of inhomogeneous fluids in rectangular corrugated nano-pores

Based on the free-energy average method, an area-weighted effective potential is derived for rectangular corrugated nano-pore. With the obtained potential, classical density functional theory is employed to investigate the structural and thermodynamic properties of confined Lennard-Jones fluid in rectangular corrugated slit pores. Firstly, influence of pore geometry on the adsorptive potential is calculated and analyzed. Further, thermodynamic properties including excess adsorption, solvation force, surface free energy and thermodynamic response functions are systematically investigated. It is found that pore geometry can largely modulate the structure of the confined fluids, which in turn influences other thermodynamic properties. In addition, the results show that different geometric elements have different influences on the confined fluids. The work provides an effective route to investigate the effect of roughness on confined fluids. It is expected to shed light on further understanding about interfacial phenomena near rough walls, and then provide useful clues for the design and characterization of novel materials.     

Measurement of curved surface by stereo vision and error analysis

Using the advantage of reconstructing the surface of a body, the stereo vision is used to study the measurement of a curved surface, and the error of the measurement is analyzed. Under the world coordinate X–Y–Z erected by the stereo vision, the surface of the cylinder is measured, and the position coordinate of each point on the cylindrical surface is determined. By the use of the nonlinear optimization technique, the equation of cylindrical surface is solved to obtain a set of parameters: the direction cosine of the centerline of the cylinder, the point of intersection of the centerline of the cylinder with the XZ-plane, and the radius of the cylinder. The computed radius of the cylinder is compared to the measured value to evaluate the measurement error. Through coordinate transformation, the measured position coordinate of each point on the cylindrical surface, which is in the rectangular coordinate, is transformed into the cylindrical coordinate. The radial coordinate of each point is compared to the computed radius and the mean error and standard deviation are estimated. Results indicate that the stereo vision may accurately measure the curved surface in various curvatures, and a cylindrical coordinate system may be erected for the measured cylinder. Hence, the analysis method proposed in the paper may be further applied to study the deformation problems such as piping under pressure, and fracture problems such as piping with cracks.     

Effect of confinement in nano-porous materials on the solubility of a supercritical gas

By combining Gibbs Ensemble Monte Carlo simulations and density functional theory, we investigate the influence of confinement in a slit-shaped carbon pore on the solubility of a supercritical solute gas in a liquid solvent. In the cases studied here, competing adsorption of the solvent and solute determines whether the solubility is enhanced or suppressed for larger pores. We find that the solubility in the confined system is strongly dependent on pore width, and that molecular packing effects are important for small pore widths. In addition, the solubility decreases on increase in the temperature, as for the bulk mixture, but the rate of decrease is greater in the pore due to a decrease in the partial molar enthalpy of the solute in the pore; this effect becomes greater as pore width is decreased. The solubility is increased on increasing the bulk pressure of the gas in equilibrium with the pore, and obeys Henry's law at lower pressures. However, the Henry constant differs significantly from that for the bulk mixture, and the range of pressure over which Henry's law applies is reduced relative to that for the bulk mixture. The latter observation indicates that solute–solute interactions become more important in the pore than for the bulk at a given bulk pressure. Finally, we note that different authors use different definitions of the solubility in pores, leading to some confusion over the reported phenomenon of ‘oversolubility’. We recommend that solubility be defined as the overall mole fraction of solute in the pores, since it takes into account the increase in density of the solvent in the pores, and avoids ambiguity in the definition of the pore volume.     

方解石纳米孔隙内二氧化碳毛细凝聚的分子模拟

在二氧化碳地质封存、增产非常规油气以及孔隙材料表征测量方面,纳米孔隙中二氧化碳相态的准确预测具有重要意义。然而,由于纳米尺度下毛细力、分离压等作用力占据主导因素,流体在孔隙中的相行为与体相流体存在根本不同。已有实验和模拟表明,Kelvin毛细凝聚理论无法预测特征尺度10nm下的,孔隙内流体凝聚压力与体相饱和蒸气压的偏离程度。本文利用分子模拟方法,研究了孔径范围为0.83-8.0nm的方解石纳米孔隙中二氧化碳毛细凝聚。结果表明,微孔(小于2nm)中二氧化碳受吸附层影响,凝聚压力远低于体相饱和蒸气压,介孔(2?50nm)中二氧化碳受壁面影响,凝聚压力仍低于体相饱和蒸气压,且受孔径影响显著,并获得了纳米孔隙中二氧化碳相态随压力的变化规律。     

CARS diagnostics of fluid adsorption and condensation in small mesopores

Coherent anti‐Stokes Raman scattering (CARS) spectroscopy is applied to diagnostics of phase behavior of a fluid in pores of nanoporous glasses. Samples with mean pore radii of 2 and 3.5 nm were filled with compressed carbon dioxide at near‐room temperatures. CARS spectra of the 1388 cm⁻¹ Q‐branch were measured at isothermal compressing in a wide pressure range including the transition from gaseous to condensed state. The spectra show specific transformations caused by fluid adsorption and condensation in nanopores. We have carried out calculations of the spectral profiles based on the phase behavior of carbon dioxide in cylindrical glass nanopores. Phase behavior modeling was performed using thermodynamic concepts of surface adsorption and capillary condensation. A good agreement between experimental spectra and calculations was obtained. The potential of CARS technique for the diagnostics of fluid phase behavior in pores and for the characterization of nanoporous host structure is discussed. Copyright © 2011 John Wiley & Sons, Ltd.