Nitrogen adsorption on silica surfaces of nonporous and mesoporous materials

We present an accurate comparative analysis of N 2 adsorption at 77 K on nonporous silica and the pore wall surface of MCM-41 materials. The analysis shows that in the low-pressure region of N 2 adsorption obeys a peculiar mechanism governed by short-ranged forces, which makes the surface curvature effect on the N 2 adsorption in mesopores nearly negligible. We used this observation to define more exactly compared to the BET technique the specific surface area of the reference adsorption isotherm on nonporous silica basing on XRD data and linear sections of t-plots. Calculation of the capillary evaporation and condensation pressures seems to confirm our previous finding that the capillary condensation pressure corresponds to the equilibrium transition rather than spinodal condensation at least for pore sizes less than 7 nm. It allowed us to provide more reliable pore size distribution (PSD) analysis of mesoporous silica materials. For example, the PSDs of MCM-41 samples do not show artificial peaks in the micropore range that we obtained in our earlier publications.     

Gas adsorption in mesoporous micelle-templated silicas: MCM-41, MCM-48, and SBA-15

This paper reports a molecular simulation and experimental study on the adsorption and condensation of simple fluids in mesoporous micelle-templated silicas MCM-41, MCM-48, and SBA-15. MCM-41 is described as a regular cylindrical silica nanopore, while SBA-15 is assumed to be made up of cylindrical nanopores that are connected through lateral channels. The 3D-connected topology of MCM-48 is described using a gyroid periodic minimal surface. Argon adsorption at 77 K is calculated for the three materials using Grand Canonical Monte Carlo simulations. Qualitative comparison with experiments for nitrogen adsorption in mesoporous micelle-templated silicas is made. The adsorption isotherm for SBA-15 resembles that for MCM-41. In particular, capillary condensation and evaporation are not affected by the presence of the connecting lateral channels. In contrast, the argon adsorption isotherm for MCM-48 departs from that for MCM-41 having the same pore size. While condensation in MCM-41 is a one-step process, filling of MCM-48 involves two successive jumps in the adsorbed amounts which correspond to condensation in different domains of the porosity. The condensation pressure for MCM-48 is larger than that for MCM-41. We attribute this result to the morphology of the MCM-48 surface (made up of both concave and convex regions) that differs from that for MCM-41 (concave only). Our results suggest that the pore connectivity affects pore filling when the size of the connections is comparable to that of the nanopores.     

Monte Carlo Simulation and Experimental Studies of CO2, CH4 and Their Mixture Capture in Porous Carbons

Adsorption of carbon dioxide and methane in porous activated carbon and carbon nanotube was studied experimentally and by Grand Canonical Monte Carlo (GCMC) simulation. A gravimetric analyzer was used to obtain the experimental data, while in the simulation we used graphitic slit pores of various pore size to model activated carbon and a bundle of graphitic cylinders arranged hexagonally to model carbon nanotube. Carbon dioxide was modeled as a 3-center-Lennard-Jones (LJ) molecule with three fixed partial charges, while methane was modeled as a single LJ molecule. We have shown that the behavior of adsorption for both activated carbon and carbon nanotube is sensitive to pore width and the crossing of isotherms is observed because of the molecular packing, which favors commensurate packing for some pore sizes. Using the adsorption data of pure methane or carbon dioxide on activated carbon, we derived its pore size distribution (PSD), which was found to be in good agreement with the PSD obtained from the analysis of nitrogen adsorption data at 77 K. This derived PSD was used to describe isotherms at other temperatures as well as isotherms of mixture of carbon dioxide and methane in activated carbon and carbon nanotube at 273 and 300 K. Good agreement between the computed and experimental isotherm data was observed, thus justifying the use of a simple adsorption model.     

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.     

Porous structure of natural and modified clinoptilolites

The evaluation of the pore-size distribution (PSD) of natural and modified mesoporous zeolites, i.e., clinoptilolites is presented. We demonstrate the SEM results showing that the pores of fracture-type from 25-50 nm to 100 nm in size between clinoptilolite grains, as well as pores between crystal aggregates up to 500 nm in size are present in the studied material. The detailed distribution of pore sizes and tortuosity factor of the above-mentioned materials are determined from the adsorption-desorption isotherms of nitrogen measured volumetrically at 77 K. To obtain the reliable pore size distribution (PSD) of the above-mentioned materials both adsorption and desorption branches of the experimental hysteresis loop are described simultaneously by recently developed corrugated pore structure model (CPSM) of Androutsopoulos and Salmas. Evaluated pore size distributions are characterized by well-defined smooth peaks placed in the region of the mesoporosity. Moreover, the mean pore diameter calculated from the classical static measurement of nitrogen adsorption at 77 K correspond very well to the pore diameters from SEM, showing the applicability of the CPSM for characterization of the porosity of natural zeolites. We conclude that classical static adsorption measurements combined with the proper modeling of the capillary condensation/evaporation phenomena are a powerful method which can be applied for pore structure characterization of natural and modified clinoptilolites.     

Grand canonical Monte Carlo simulation of argon adsorption at the surface of silica nanopores: effect of pore size, pore morphology, and surface roughness

Argon adsorption (77 K) in atomistic silica nanopores of various sizes and shapes has been studied by means of grand canonical Monte Carlo simulations (GCMC). We discuss the effects of confinement (pore size), pore morphology (ellipsoidal, hexagonal, constricted pore), and surface texture (rough/smooth) on the thickness variation of the adsorbed film with pressure onto the disordered inner surface of porous materials (usually called t-plot or t-curve). We show that no confinement effect occurs when the diameter of the regular cylindrical pore is larger than 10 nm. For pores smaller than 6 nm, we find that the film thickness increases as the pore size decreases. We show that the adsorption isotherm in the rough pore can be described as the sum of an adsorbed amount similar to that found for a smooth pore (of the same radius) and a constant contribution due to atoms "trapped" in the infractuosities of the rough surface which act as a microporous texture. Simulation snapshots for Ar adsorption in hexagonal and ellipsoidal smooth pores indicate that at low pressures the gas/adsorbate interface retains memory of the pore shape and becomes cylindrical prior to the capillary condensation of the fluid in the pore. The film thickness in the hexagonal pore is close to that obtained for a cylindrical pore having a similar dimension. By contrast, we find that the film thickness for an ellipsoidal pore is always larger than that for an equivalent cylindrical pore (having the same length and volume but a circular section). We show that this effect strengthens as the pore size decreases and/or the pore asymmetry increases. Ar adsorption in a cylindrical constricted pore shows that the presence of the narrower part considerably modifies the adsorption mechanism. Finally, we report GCMC simulations of Ar adsorption (77 K) on a plane silica reference substrate for different intermolecular potentials. We discuss the effect of the interaction on the shape of the adsorption isotherm and compare our results with experiments.     

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.     

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.     

Equilibrium adsorption in cylindrical mesopores: a modified Broekhoff and de Boer theory versus density functional theory

This paper presents a thermodynamic analysis of capillary condensation phenomena in cylindrical pores. Here, we modified the Broekhoff and de Boer (BdB) model for cylindrical pores accounting for the effect of the pore radius on the potential exerted by the pore walls. The new approach incorporates the recently published standard nitrogen and argon adsorption isotherm on nonporous silica LiChrospher Si-1000. The developed model is tested against the nonlocal density functional theory (NLDFT), and the criterion for this comparison is the condensation/evaporation pressure versus the pore diameter. The quantitative agreement between the NLDFT and the refined version of the BdB theory is ascertained for pores larger than 2 nm. The modified BdB theory was applied to the experimental adsorption branch of adsorption isotherms of a number of MCM-41 samples to determine their pore size distributions (PSDs). It was found that the PSDs determined with the new BdB approach coincide with those determined with the NLDFT (also using the experimental adsorption branch). As opposed to the NLDFT, the modified BdB theory is very simple in its utilization and therefore can be used as a convenient tool to obtain PSDs of all mesoporous solids from the analysis of the adsorption branch of adsorption isotherms of any subcritical fluids.     

Accurate relations between pore size and the pressure of capillary condensation and the evaporation of nitrogen in cylindrical pores

To examine the theoretical and semiempirical relations between pore size and the pressure of capillary condensation or evaporation proposed so far, we constructed an accurate relation between the pore radius and the capillary condensation and evaporation pressure of nitrogen at 77 K for the cylindrical pores of the ordered mesoporous MCM-41 and SBA-15 silicas. Here, the pore size was determined from a comparison between the experimental and calculated X-ray diffraction patterns due to X-ray structural modeling recently developed. Among the many theoretical relations that differ from each other in the degree of theoretical improvements, a macroscopic thermodynamic approach based on Broekhoff-de Boer equations was found to be in fair agreement with the experimental relation obtained in the present study.     

碳纳米管内N2吸附行为及等量吸附热的GCMC分子模拟研究

碳纳米管及石墨烯具有高比表面积、高化学稳定性以及高耐蚀性等优点,被认为是一种理想的吸附材料。分子模拟技术的发展和应用丰富了人们对吸附机理研究的方式,而简单气体吸附体系的吸附机理研究对吸附理论的发展有着重要的推动作用。本文以单壁碳纳米管（SWCNT）-N₂吸附体系为研究对象,首先通过透射扫描电镜和氮气吸/脱附测试对所选用碳纳米管的微观孔形貌及吸/脱附等温线进行了表征,然后根据对应孔径参数采用巨正则蒙特卡罗方法对该体系的吸附过程进行了分子模拟,并详细研究了碳纳米管孔径和温度对该体系吸附行为的影响。结果显示,SWCNT孔径越小,吸附能力则越强;孔半径为0.746nm的SWCNT的吸附体系发生凝聚相变的临界温度为66K。通过对等量吸附热进行计算发现,孔半径0.746、1.15、1.56和1.83 nm的SWCNT-N₂吸附体系对应的初始固-液等量吸附热分别为10.9、9.2、8.6和8.4 kJ/mol。67.5K时,孔半径1.56和1.83 nm的吸附体系的等量吸附热有热峰出现。     

Permporometry characterization of microporous ceramic membranes

An evaluation of nano-order pore size of membranes was carried out using permporometry, the basic principle of which is based on capillary condensation of vapor and the blocking effect of permeation of a non-condensable gas. A computer-controlled apparatus was constructed, where liquid was injected by a syringe pump and nitrogen was used as a carrier, and was applied to the evaluation of the pore size of ceramic membranes prepared from a silica–zirconia composite. The pore size distribution, based on the Kelvin equation (Kelvin diameter), was evaluated over a range of 0.5–30 nm, using water as a condensable vapor. Vapors used in the present study were water, methanol, ethanol, isopropanol, carbon tetrachloride, and hexane. For the case of relatively large pore sizes (larger than 1 nm, based on water vapor), pore size distribution obtained by water vapor agreed very well with those by carbon tetrachloride and hexane. However, pore sizes measured using alcohols were found to be smaller than those determined by water vapor. For the case of pore sizes smaller than 1 nm, the adsorption layer before capillary condensation appears to play an important role.     

Lower closure point of adsorption hysteresis in ordered mesoporous silicas

To examine the nature of the lower closure point of adsorption hysteresis in ordered mesoporous silicas, we measured the temperature dependence of the adsorption-desorption isotherm of nitrogen for three kinds of ordered silicas with cagelike pores and three kinds of ordered silicas with cylindrical pores. The lower closure point pressure of nitrogen in the cagelike pores with sufficiently small necks, that is, the cavitation pressure of a confined liquid, did not depend appreciably on the cage size in the temperature region far away from a hysteresis critical temperature (Tch) but its cage-size dependence was noticeable in the vicinity of Tch. The lower closure point in the cylindrical pores depended on the pore size, and its thermal behavior was totally different from that in the cagelike pores. Nevertheless, the hysteresis critical points of nitrogen in the ordered mesoporous silicas, which are defined as a threshold of temperatures (Tch) and pressure above which reversible capillary condensation takes place in a given size and shape of pores, fell on a common line in a temperature-pressure diagram regardless of the pore geometries. We consider this finding as evidence that capillary evaporation in the cylindrical pores follows a cavitation process in the vicinity of Tch in the same way as that in the cagelike pores and also that the low limit of the hysteresis loop that has been long recognized since 1965 is due to the occurrence of a vapor bubble in a stretched metastable liquid confined to the pores with decreasing pressure (cavitation).     

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。     

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。     

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.     

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.     

Opening mechanism of internal nanoporosity of single-wall carbon nanohorn

Single-wall carbon nanohorn (SWNH), which is a tubular particle with a cone cap, was oxidized in an oxygen flow at various temperatures. N(2) adsorption at 77 K, thermogravimetry (TG), differential thermal analysis (DTA), transmission electron microscopy, and Raman spectroscopy measurements were carried out on the oxidized SWNHs. The specific surface area of the oxidized SWNHs can be controlled by oxidation temperature, giving the maximum value of 1420 m(2)/g. The pore size distribution by the BJH method and the comparison plot of the N(2) adsorption isotherms of SWNH oxidized at different temperatures against that of as-grown SWNH revealed the minimum oxidation temperature for opening internal nanopores. TG-DTA analyses determined the components of as-grown SWNH: amorphous carbon 2.5 wt %, defective carbon at the cone part 15 wt %, tubular carbon 70 wt %, and graphitic carbon 12 wt %. These systematic analyses provided the exact internal nanopore volume of 0.49 mL/g for pure SWNH particles.     

Modeling of Adsorption in Finite Cylindrical Pores by Means of Density Functional Theory

Adsorption of argon at its boiling point in finite cylindrical pores is considered by means of the non-local density functional theory (NLDFT) with a reference to MCM-41 silica. The NLDFT was adjusted to amorphous solids, which allowed us to quantitatively describe argon adsorption isotherm on nonporous reference silica in the entire bulk pressure range. In contrast to the conventional NLDFT technique, application of the model to cylindrical pores does not show any layering before the phase transition in conformity with experimental data. The finite pore is modeled as a cylindrical cavity bounded from its mouth by an infinite flat surface perpendicular to the pore axis. The adsorption of argon in pores of 4 and 5 nm diameters is analyzed in canonical and grand canonical ensembles using a two-dimensional version of NLDFT, which accounts for the radial and longitudinal fluid density distributions. The simulation results did not show any unusual features associated with accounting for the outer surface and support the conclusions obtained from the classical analysis of capillary condensation and evaporation. That is, the spontaneous condensation occurs at the vapor-like spinodal point, which is the upper limit of mechanical stability of the liquid-like film wetting the pore wall, while the evaporation occurs via a mechanism of receding of the semispherical meniscus from the pore mouth and the complete evaporation of the core occurs at the equilibrium transition pressure. Visualization of the pore filling and empting in the form of contour lines is presented.     

Capillary condensation hysteresis in overlapping spherical pores: a monte carlo simulation study

The mechanisms of hysteretic phase transformations in fluids confined to porous bodies depend on the size and shape of pores, as well as their connectivity. We present a Monte Carlo simulation study of capillary condensation and evaporation cycles in the course of Lennard-Jones fluid adsorption in the system of overlapping spherical pores. This model system mimics pore shape and connectivity in some mesoporous materials obtained by templating cubic surfactant mesophases or colloidal crystals. We show different mechanisms of capillary hysteresis depending on the size of the window between the pores. For the system with a small window, the hysteresis cycle is similar to that in a single spherical pore: capillary condensation takes place upon achieving the limit of stability of adsorption film and evaporation is triggered by cavitation. When the window is large enough, the capillary condensation shifts to a pressure higher than that of the isolated pore, and the possibility for the equilibrium mechanism of desorption is revealed. These finding may have important implications for practical problems of assessment of the pore size distributions in mesoporous materials with cagelike pore networks.