A grand canonical Monte Carlo study of capillary condensation in mesoporous media: effect of the pore morphology and topology

We study by means of Grand Canonical Monte Carlo simulations the condensation and evaporation of argon at 77 K in nanoporous silica media of different morphology or topology. For each porous material, our results are compared with data obtained for regular cylindrical pores. We show that both the filling and emptying mechanisms are significantly affected by the presence of a constriction. The simulation data for a constricted pore closed at one end reproduces the asymmetrical shape of the hysteresis loop that is observed for many real disordered porous materials. The adsorption process is a quasicontinuous mechanism that corresponds to the filling of the different parts of the porous material, cavity, and constriction. In contrast, the desorption branch for this pore closed at one end is brutal because the evaporation of Ar atoms confined in the largest cavity is triggered by the evaporation of the fluid confined in the constriction (which isolates the cavity from the gas reservoir). This evaporation process conforms to the classical picture of "pore blocking effect" proposed by Everett many years ago. We also simulate Ar adsorption in a disordered porous medium, which mimics a Vycor mesoporous silica glass. The adsorption isotherm for this disordered porous material having both topological and morphological defects presents the same features as that for the constricted pore (quasicontinuous adsorption and steep desorption process). However, the larger degree of disorder of the Vycor surface enhances these main characteristics. Finally, we show that the effect of the disorder, topological and/or morphological, leads to a significant lowering of the capillary condensation pressure compared to that for regular cylindrical nanopores. Also, our results suggest that confined fluids isolated from the bulk reservoir evaporate at a pressure driven by the smallest size of the pore.     

Adsorption of simple fluid on silica surface and nanopore: effect of surface chemistry and pore shape

This paper reports a molecular simulation study on the adsorption of simple fluids (argon at 77 K) on hydroxylated silica surfaces and nanopores. The effect of surface chemistry is addressed by considering substrates with either partially or fully hydroxylated surfaces. We also investigate the effect of pore shape on adsorption and capillary condensation by comparing the results for cylindrical and hexagonal nanopores having equivalent sections (i.e., equal section areas). Due to the increase in the polarity of the surface with the density of OH groups, the adsorbed amounts for fully hydroxylated surfaces are found to be larger than those for partially hydroxylated surfaces. Both the adsorption isotherms for the cylindrical and hexagonal pores conform to the typical behavior observed in the experiments for adsorption/condensation in cylindrical nanopores MCM-41. Capillary condensation occurs through an irreversible discontinuous transition between the partially filled and the completely filled configurations, while evaporation occurs through the displacement at equilibrium of a hemispherical meniscus along the pore axis. Our data are also used to discuss the effect of surface chemistry and pore shape on the BET method. The BET surface for fully hydroxylated surfaces is much larger (by 10-20%) than the true geometrical surface. In contrast, the BET surface significantly underestimates the true surface when partially hydroxylated surfaces are considered. These results suggest that the surface chemistry and the choice of the system adsorbate/adsorbent is crucial in determining the surface area of solids using the BET method.     

Evaluation of pore size distribution in boundary region of micropore and mesopore using gas adsorption method

This paper discusses an accurate method of pore size distribution evaluation in boundary regions of micropores and mesopores using the gas adsorption process on the basis of the capillary condensation theory, which is liable to be underestimated with the existing BJH and DH methods. A typical nitrogen adsorption isotherm for highly ordered mesoporous silica, which has cylindrical pores with diameter smaller than 4 nm, is considered to be type IV and it is well known for the steep increase of the amount adsorbed through capillary condensation in the region of the relative pressure P/P0 smaller than 0.4. In calculating the distribution of the pore size from the change of the amount adsorbed due to capillary condensation, it is important to accurately predict both the multilayer thickness t of the adsorbed nitrogen molecules and the critical radius rc where capillary condensation occurs. It is necessary to consider the curvature of the adsorption layer-gas phase interface when predicting the multilayer thickness t of nitrogen adsorbed within the pore of highly ordered mesoporous silica. Revision of the Kelvin equation is also required when rc is to be predicted. While the predicted value of t based on the Broekhoff and de Boer theory is matched well with the value of t which is actually measured using highly ordered mesoporous silica, and the predicted value of rc based on the GTKB-Kelvin-cylindrical equation that has been revised considering the effect of the interfacial curvature on the interfacial tension of the adsorption layer-gas phase interface is matched with the value of rc which is actually measured using highly ordered mesoporous silica. A combination method of the Broekhoff and de Boer equation and the GTKB-Kelvin-cylindrical equation is proposed as a means of accurately evaluating, from the nitrogen adsorption isotherm, the pore size distribution in the highly ordered mesoporous silica in boundary region of micropore and mesopore. The proposed new method of pore size evaluation features high accuracy and offers the convenience of obtaining the pore size distribution without repeated calculations by employing the same algorithm as DH method. The pore size predicted by the Halsey equation and the Kelvin equation of the conventional DH method is about 20% smaller than the pore size predicted by the newly proposed evaluation method.     

Adsorption of simple gases in MCM-41 materials: the role of surface roughness

This paper reports the development and testing of atomistic models of silica MCM-41 pores. Model A is a regular cylindrical pore having a constant section. Model B has a surface disorder that reproduces the morphological features of a pore obtained from an on-lattice simulation that mimics the synthesis process of MCM-41 materials. Both models are generated using a similar procedure, which consists of carving the pore out of an atomistic silica block. The differences between the two models are analyzed in terms of small angle neutron scattering spectra as well as adsorption isotherms and isosteric heat curves for Ar at 87 K and Xe at 195 K. As expected for capillary condensation in regular nanopores, the Ar and Xe adsorption/desorption cycles for model A exhibit a large hysteresis loop having a symmetrical shape, i.e., with parallel adsorption and desorption branches. The features of the adsorption isotherms for model B strongly depart from those observed for model A. Both the Ar and Xe adsorption branches for model B correspond to a quasicontinuous pore filling that involves coexistence within the pore of liquid bridges and gas nanobubbles. As in the case of model A, the Ar adsorption isotherm for model B exhibits a significant hysteresis loop; however, the shape of the loop is asymmetrical with a desorption branch much steeper than the adsorption branch. In contrast, the adsorption/desorption cycle for Xe in model B is quasicontinuous and quasireversible. Comparison with adsorption and neutron scattering experiments suggests that model B is too rough at the molecular scale but reproduces reasonably the surface disorder of real MCM-41 at larger length scales. In contrast, model A is smooth at small length scales in agreement with experiments but seems to be too ordered at larger length scales.     

Adsorption potential distributions for carbons having defined pore structure—GCMC simulations of the effect of heterogeneity

Adsorption Potential Distribution (APD) is one of the most important and widely propagated by Jaroniec and co-workers method since it is modeless. Using the GCMC simulation of Ar adsorption in pores with well defined geometry (slit-like, cylindrical, hexagonal and quadratic) we study the effect of heterogeneity on the APDs. The heterogeneity is introduced by controlled removal of carbon atoms from the first internal layer of an adsorbent. Since defects are introduced for pores having different initial geometries it is possible to study the systematic changes in the APD curves. Electronic Supplementary Material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The effects of energy sites on adsorption of Lennard-Jones fluids and phase transition in carbon slit pore of finite length a computer simulation study

A Monte Carlo simulation method is used to study the effects of adsorption strength and topology of sites on adsorption of simple Lennard-Jones fluids in a carbon slit pore of finite length. Argon is used as a model adsorbate, while the adsorbent is modeled as a finite carbon slit pore whose two walls composed of three graphene layers with carbon atoms arranged in a hexagonal pattern. Impurities having well depth of interaction greater than that of carbon atom are assumed to be grafted onto the surface. Different topologies of the impurities; corner, centre, shell and random topologies are studied. Adsorption isotherms of argon at 87.3 K are obtained for pore having widths of 1, 1.5 and 3 nm using a Grand Canonical Monte Carlo simulation (GCMC). These results are compared with isotherms obtained for infinite pores. It is shown that the surface heterogeneity affects significantly the overall adsorption isotherm, particularly the phase transition. Basically it shifts the onset of adsorption to lower pressure and the adsorption isotherms for these four impurity models are generally greater than that for finite pore. The positions of impurities on solid surface also affect the shape of the adsorption isotherm and the phase transition. We have found that the impurities allocated at the centre of pore walls provide the greatest isotherm at low pressures. However when the pressure increases the impurities allocated along the edges of the graphene layers show the most significant effect on the adsorption isotherm. We have investigated the effect of surface heterogeneity on adsorption hysteresis loops of three models of impurity topology, it shows that the adsorption branches of these isotherms are different, while the desorption branches are quite close to each other. This suggests that the desorption branch is either the thermodynamic equilibrium branch or closer to it than the adsorption branch.     

Modeling of adsorption in pores with strongly heterogeneous walls: parametric lattice-site wall model

We present results of grand canonical Monte Carlo simulations of adsorption in cylindrical pores with rough surface modeled by a parametric lattice-site approach. The sites are randomly distributed over the pore walls. They could be attractive, neutral or repulsive with respect to the smooth pore model. Each site is characterized by two amplitudes (structural and energetic) which modify locally the structure and energetic properties of the surface. The results presented here show how different parameters of the model affect the mechanism of adsorption and, consequently, the form of the isotherm.     

用实验吸附等温线和计算机分子模拟表征中孔分子筛MCM-41

首先比较了表征MCM-41的两个势模型对吸附等温线的影响。发现在一维势模型 中,低压部分的吸附应与选用的势模型的势阱深度有关,而毛细凝聚发生的位置与 孔壁在离壁面较远处与流体分子的相互作用的强弱有关。然后作者使用了一个“混 合”的势模型,即采用作者提出的势函数表征孔壁中氧原子对MCM-41中流体分子的 作用,而采用Tjatjopoulos等提出的势函数近似地表征MCM-41表面硅醇基团以及一 些未知因子对流体分子的作用。虽然这种势模型仍然是一维的,但这种势模型将孔 壁内氧原子的作用和表面上非均匀性分开考虑,具有较明确的物理意义。通过计算 机模拟与实验数据的比较发现,这种势模型可以较好地拟合氮气在MCM-41中的吸附 等温线。     

Packing effects on argon and methanol adsorption inside graphitic cylindrical and slit pores: a GCMC simulation study

Using Grand Canonical Monte Carlo simulation, we have studied the effects of confinement on argon and methanol adsorption in graphitic cylindrical and slit pores. Linear chain, zigzag and incomplete helical packing are observed for argon adsorption in cylindrical pores. However, for methanol adsorption different features appear because the electrostatic interactions favour configurations that maximize the hydrogen bonding among methanol molecules. We have found zigzag chains with hydrogen-bonded structures for methanol adsorption in cylindrical and slit pores. To investigate how dense the adsorbed phase is and how many molecules could be packed per unit physical volume of the solid, we consider two different definitions of pore density; one based on the physical volume and the other on the accessible volume. That based on accessible volume gives a measure of the fluid density, while that based on the physical volume gives a measure of how much adsorbate can be stored per unit volume of the adsorbent. It is found that the adsorbate is denser in cylindrical pores, but that slit pores can pack more molecules per unit solid volume. We also discuss the effects on the isosteric heat of argon and methanol of pore size, pore geometry and loading.     

Quasi one-dimensional nanopores in single-wall carbon nanohorn colloids using grand canonical Monte Carlo simulation aided adsorption technique

The average interstitial nanopore structure of single-wall carbon nanohorn (SWNH) assemblies was determined using X-ray diffraction and grand canonical Monte Carlo (GCMC) simulation aided N(2) adsorption at 77 K. The interstitial nanopores of SWNH assemblies can be regarded as quasi one-dimensional pores due to the partial orientation of the SWNH particles; the average pore width of the interstitial pores is 0.6 nm. Good agreement between the GCMC simulation of a structural model with one-dimensional interstitial nanopores and an experimental adsorption isotherm below P/P(0) = 10(-4) is evidence of the quasi one-dimensionality of the interstitial nanopores. A snapshot from the GCMC simulation showed one-dimensional growth of adsorbed N(2) molecules.     

Adsorption hysteresis of nitrogen and argon in pore networks and characterization of novel micro- and mesoporous silicas

We report results of nitrogen and argon adsorption experiments performed at 77.4 and 87.3 K on novel micro/mesoporous silica materials with morphologically different networks of mesopores embedded into microporous matrixes: SE3030 silica with worm-like cylindrical channels of mode diameter of approximately 95 angstroms, KLE silica with cage-like spheroidal pores of ca. 140 angstroms, KLE/IL silica with spheroidal pores of approximately 140 angstroms connected by cylindrical channels of approximately 26 angstroms, and, also for a comparison, on Vycor glass with a disordered network of pores of mode diameter of approximately 70 angstroms. We show that the type of hysteresis loop formed by adsorption/desorption isotherms is determined by different mechanisms of condensation and evaporation and depends upon the shape and size of pores. We demonstrate that adsorption experiments performed with different adsorptives allow for detecting and separating the effects of pore blocking/percolation and cavitation in the course of evaporation. The results confirm that cavitation-controlled evaporation occurs in ink-bottle pores with the neck size smaller than a certain critical value. In this case, the pressure of evaporation does not depend upon the neck size. In pores with larger necks, percolation-controlled evaporation occurs, as observed for nitrogen (at 77.4 K) and argon (at 87.3 K) on porous Vycor glass. We elaborate a novel hybrid nonlocal density functional theory (NLDFT) method for calculations of pore size distributions from adsorption isotherms in the entire range of micro- and mesopores. The NLDFT method, applied to the adsorption branch of the isotherm, takes into account the effect of delayed capillary condensation in pores of different geometries. The pore size data obtained by the NLDFT method for SE3030, KLE, and KLE/IL silicas agree with the data of SANS/SAXS techniques.     

氮气在MCM－41分子筛中的吸附：实验和分子模拟

用美国Micromeritics公司生产的ASAP2010物理吸附仪测定了低温（77 K） N_2在MCM-41分子筛中的吸附等温线，获得了表征MCM-41特征的BET比表面、BJH孔 容和平均孔径。同时用巨正则Monte Carlo（GCMC）模拟方法考究了N_2在MCM-41中 的吸附，得到了N_2在MCM-41中的模拟吸附等温线，分析了流体在MCM-41分子筛中 的微观结构。GCMC模拟中MCM-41介孔材料模型化为圆柱孔，N_2模型化为Lennard- Jones（LJ）球。N_2和MCM-41介孔墙壁间的相互作用采用Tjatjopoulos-Feke- Mann（TFM）势能模型进行表征。通过使模拟和实验结果有一个好的吻合，确定了 一组有效的MCM-41分子筛的势能参数（σ_(ww) = 0.265 nm，∈_(ww)/k = 190 K ）。这为以后其他吸附质在MCM-41中吸附的预测奠定了基础、提供了依据。     

Effect of pore size on adsorption of a polyelectrolyte to porous glass

The adsorption of quaternized poly(vinylpyridine) (QPVP) on controlled pore glass (CPG) size, over the ionic strength range 0.001-0.5 M was found to display nonmonotonic behavior as a function of pore size. Both adsorption kinetics and ionic strength effects deviated dramatically from behavior typical of adsorption on flat surfaces when the ratio of the pore radius Rp to the polymer hydrodynamic radius Rh became smaller than ca. 2. Ionic strength enhancement of adsorption for small pore sizes was observed at much higher salt concentrations than is typical for polycation adsorption on flat surfaces. The amount of polymer adsorbed per unit surface area of glass GammaA, in 0.5 M NaCl, exhibited a shallow maximum at Rp/Rh approximately 5. Since the value of GammaA for small pore size CPG is strongly depressed by the large surface area, an alternative and more interesting observation is that the amount of polymer adsorbed per gram of CPG, Gammaw, displays a strong maximum when Rp is equal to or slightly smaller than Rh. The efficiency with which QPVP binds anionic micelles to (negatively charged) CPG (grams of surfactant/grams of QPVP) increases strongly with diminishing pore size, indicating that the configuration of polycation bound to small pores favors micelle binding. Since the micelles are larger than small pores, the results indicate that when Rp < Rh, adsorbed polycation molecules reside only partially within the pore. The results of this study are supported by simulations of polyelectrolytes within cylindrical cavities.     

Melting mechanism of monolayers adsorbed in cylindrical pores: the influence of the pore wall roughness

We have analyzed the mechanism of melting of molecular layers adsorbed in porous materials with cylindrical pores and rough pore walls. The working example studied here is a monolayer of methane molecules adsorbed in MCM-41 pore of diameter 2R=4 nm. Both experimental (neutron scattering) and simulation (Monte Carlo) results demonstrate the strong influence of the wall roughness on the melting mechanism. In particular, the transformation between solidlike and liquidlike monolayer phases adsorbed on a rough surface is observed over a broad temperature range, and solidlike properties persist even above the bulk methane melting temperature.     

On the cavitation and pore blocking in slit-shaped ink-bottle pores

We present GCMC simulations of argon adsorption in slit pores of different channel geometry. We show that the isotherm for an ink-bottle pore can be reconstructed as a linear combination of the local isotherms of appropriately chosen independent unit cells. Second, depending on the system parameters and operating conditions, the phenomena of cavitation and pore blocking can occur for a given configuration of the ink-bottle pore by varying the geometrical aspect ratio. Although it has been argued in the literature that the geometrical aspects of the system govern the evaporation mechanism (either cavitation or pore blocking), we here put forward an argument that the local compressibility in different parts of the ink-bottle pore is the deciding factor for evaporation. When the fluid in the small neck is strongly bound, cavitation is the governing process, and molecules in the cavity evaporate to the surrounding bulk gas via a mass transfer mechanism through the pore neck. When the pore neck is sufficiently large, the system of neck and cavity evaporates at the same pressure, which is a consequence of the comparable compressibility between the fluid in the neck and that in the cavity. This suggests that local compressibility is the measure of cohesiveness of the fluid prior to evaporation. One consequence that we derive from the analysis of isotherms of a number of connected pores is that by analyzing the adsorption branch or the desorption branch of an experimental isotherm may not lead to the correct pore sizes and the correct pore volume distribution.     

Molecular simulation of binary mixture adsorption in buckytubes and MCM-41

MCM-41 and buckytubes are novel porous materials with controllable pore sizes and narrow pore size distributions. Buckytubes are carbon tubes with internal diameters in the range 1–5 urn. The structure of each tube is thought to be similar to one or more graphite sheets rolled up in a helical manner. MCM-41 is one member of a new family of highly uniform mesoporous silicate materials produced by Mobil, whose pore size can be accurately controlled in the range 1.5–10 nm. We present grand canonical Monte Carlo (GCMC) simulations of single fluid and binary mixture adsorption in a model buckytube, and nonlocal density functional theory (DFT) calculations of trace pollutant separation in a range of buckytubes and MCM-41 pores. Three adsorbed fluids are considered; methane, nitrogen and propane. The GCMC studies show that the more strongly adsorbed pure fluid is adsorbed preferentially from an equimolar binary mixture. Ideal adsorbed solution theory (IAST) is shown to give good qualitative agreement with GCMC when predicting binary mixture separations. The DFT results demonstrate the very large increases in trace pollutant separation that can be achieved by tuning the pore size, structure, temperature and pressure of the MCM-41 and buckytube adsorbent systems to their optimal values.     

Monte Carlo Calculations of Polymer Adsorption at the Entrance of Cylindrical Pores in Flat Adsorbing Surfaces

The influence of surface interactions on the conformation of flexible polymers partially confined inside narrow cylindrical pores in a flat surface is studied above the critical adsorption energy in a good solvent. We use a static configurational bias computational sampling method to calculate the adsorption free energy and the radius of gyration components parallel and perpendicular to the pore axis as a function of the polymer center of mass position at different degrees of confinement. We find strong free‐energy minima just in front of the pore entry for all degrees of confinement studied. At the location of the free‐energy minimum, polymers are partially adsorbed inside the pore and on the outer solid surface and adopt “drawing pin”‐like conformations. A distinct maximum in the average loop length at the pore entry indicates that the polymer bridges the pore entry of small pores.     

Effect of surface functionalities on gas adsorption in microporous carbons: a grand canonical Monte Carlo study

In an attempt to offer a more realistic picture of adsorption in highly heterogeneous porous systems, such as oxygen functionalized porous carbons, we consider a series of carbon surfaces baring different amounts of oxygen functionalities (hydroxyl and epoxy). These surfaces are used to construct “oxidized” slit pores of varying width and functionality. With the aid of such inhomogeneous structures we study the interaction of Ar (87 K) inside “functionalized” pores and report grand canonical Monte Carlo adsorption simulations results. Based on our simulation data, we discuss the role of chemical heterogeneity on adsorbed/gas phase equilibrium properties such as density, heat of adsorption, and molecular packing within the pores. Comparisons are made with the case of the oxygen–free (completely homogeneous) slit pore models and conclusions on the suitability of Ar based pore size distributions for functionalized porous carbons are drawn.     

煤中可溶有机质对煤的孔隙结构及甲烷吸附特性影响

采用四氢呋喃对临涣7煤和祁南3煤进行微波辅助抽提,进行了原煤和残煤等温吸附实验和低温氮气吸附测试,对比分析了抽提前后原煤和残煤的甲烷吸附量和比表面积、孔分布情况,并理论测算煤中可溶有机质吸附溶解甲烷量.结果表明,残煤的甲烷吸附能力低于原煤;抽提后,煤的比表面积和总孔体积增大,平均孔径减少,影响煤吸附气体能力的主要孔径为1.7~5.0 nm,且该范围内的孔数有不同程度的增加;压力为0.1~5.0 MPa时,两煤样中可溶有机质吸附溶解的甲烷量分别为0.45~4.22 mL/g、0.69~4.99 mL/g,最大吸附量分别占到原煤最大吸附量的30%和38%.分析认为,煤中可溶有机质占据部分煤中孔隙,影响煤孔隙结构,同时,在压力的作用下,甲烷可以溶解和吸附煤中可溶有机质.