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.     

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.     

Modeling of adsorption and nucleation in infinite cylindrical pores by two-dimensional density functional theory

In this paper, we present an analysis of argon adsorption in cylindrical pores having amorphous silica structure by means of a nonlocal density functional theory (NLDFT). In the modeling, we account for the radial and longitudinal density distributions, which allow us to consider the interface between the liquidlike and vaporlike fluids separated by a hemispherical meniscus in the canonical ensemble. The Helmholtz free energy of the meniscus was determined as a function of pore diameter. The canonical NLDFT simulations show the details of density rearrangement at the vaporlike and liquidlike spinodal points. The limits of stability of the smallest bridge and the smallest bubble were also determined with the canonical NLDFT. The energy of nucleation as a function of the bulk pressure and the pore diameter was determined with the grand canonical NLDFT using an additional external potential field. It was shown that the experimentally observed reversibility of argon adsorption isotherms at its boiling point up to the pore diameter of 4 nm is possible if the potential barrier of 22kT is overcome due to density fluctuations.     

Principles of hierarchical meso- and macropore architectures by liquid crystalline and polymer colloid templating

The generation of porous silica with hierarchically organized bimodal mesoporosity of adjustable size and well-defined shape was investigated by using surfactant mixtures and the nanocasting procedure (liquid crystalline templating). A systematic study of combinations of various block copolymers (Pluronics F127, KLE (poly(omega-hydroxypoly(ethylene-co-butylene)-co-poly(ethylene oxide))) and SE (PS-co-PEO)) with smaller surfactants (Pluronics P123, C16mimCl, and CTAB) revealed that hierarchical bimodal mesopore architectures could only be obtained by the usage of block copolymers with a strong hydrophilic-hydrophobic contrast, such as KLE and SE, giving rise to pores between 6 and 22 nm. Furthermore, the ionic liquid (IL) C16mimCl appeared to have advantageous templating properties, resulting in 2-3-nm pores being located between the block copolymer mesopores, whereas phase separation was observed for Pluronics and CTAB as small templates. Thereby, the study provided also general insights into the mixing and co-self-assembly behavior of block copolymers and ionic surfactants in water and confirmed the special templating properties of ILs, as recently proposed. In addition to the bimodal mesoporosity, additional tunable macroporosity was created by the presence of poly(styrene) or poly(methyl methacrylate) spheres, leading to well-defined trimodal hierarchical pore architectures with the small pores being located in the walls of the respective larger pores. As a major improvement, due to the pore hierarchy, these large-pore materials showed relatively large surface areas and pore volumes, and the size of densely packed macropores could even be decreased down to 90 nm. The materials were characterized by electron microscopy, small-angle X-ray scattering, and nitrogen sorption using a proper NLDFT (nonlocal density functional theory) approach for calculations of the pore size distribution in the entire range of micro- and mesopores.     

Characterization of the pore structure of three-dimensionally ordered mesoporous carbons using high resolution gas sorption

The use of colloidal crystals with various primary particle sizes as templates leads to the formation of three-dimensionally ordered mesoporous (3DOm) carbons containing spherical pores with tailorable pore size and extremely high pore volumes. We present a comprehensive structural characterization of these novel carbons by using nitrogen (77.4 K) and argon (87.3 K) adsorption coupled with the application of novel, dedicated quenched solid density functional theory (QSDFT) methods which assume correctly the underlying spherical pore geometry and also the underlying adsorption mechanism. The observed adsorption isotherms are of Type IV with Type H1-like hysteresis, despite the fact that pore blocking affects the position of the desorption branch. This follows also from detailed, advanced scanning hysteresis experiments which not only allow one to identify the underlying mechanisms of hysteresis, but also provide complementary information about the texture of these unique porous materials. This work addresses the problem of pore size analysis of novel, ordered porous carbons and highlights the importance of hysteresis scanning experiments for textural analysis of the pore network.     

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.     

Comparative features of ar adsorption on smooth and amorphous surfaces examined by density functional theory

We analyze argon adsorption isotherms and isosteric heat of adsorption on graphitized and nongraphitized carbon black and silica surfaces by means of nonlocal density functional theory (NLDFT). It is shown that in the case of graphitized carbon black the behavior of the adsorbed phase is nearly identical to that in the bulk phase at a distance larger than about 3-4 molecular diameters from the surface. At a smaller distance argon forms solid-like molecular layers at a temperature at least 3.5 K above the triple point, with the interlayer distance being markedly smaller than the argon collision diameter. In the case of defected or amorphous surfaces adsorbed argon is liquid-like below its triple point. Our extension of the Tarazona NLDFT to amorphous solids (NLDFT-AS) and the Kierlik and Rosinberg version of NLDFT excellently fit argon adsorption isotherms and properly predict the isosteric heat of adsorption. We showed that the surface roughness affects the calculated heat of adsorption, which allowed us to adjust the width of the diffuse zone of the nongraphitized carbon black and the silica surface.     

Cavitation and pore blocking in nanoporous glasses

In gas adsorption studies, porous glasses are frequently referred to as model materials for highly disordered mesopore systems. Numerous works suggest that an accurate interpretation of physisorption isotherms requires a complete understanding of network effects upon adsorption and desorption, respectively. The present article deals with nitrogen and argon adsorption at different temperatures (77 and 87 K) performed on a series of novel nanoporous glasses (NPG) with different mean pore widths. NPG samples contain smaller mesopores and significantly higher microporosity than porous Vycor glass or controlled pore glass. Since the mean pore width of NPG can be tuned sensitively, the evolution of adsorption characteristics with respect to a broadening pore network can be investigated starting from the narrowest nanopore width. With an increasing mean pore width, a H2-type hysteresis develops gradually which finally transforms into a H1-type. In this connection, a transition from a cavitation-induced desorption toward desorption controlled by pore blocking can be observed. Furthermore, we find concrete hints for a pore size dependence of the relative pressure of cavitation in highly disordered pore systems. By comparing nitrogen and argon adsorption, a comprehensive insight into adsorption mechanisms in novel disordered materials is provided.     

Application of density functional theory to capillary phenomena in cylindrical mesopores with radial and longitudinal density distributions

In this paper, we applied a version of the nonlocal density functional theory (NLDFT) accounting radial and longitudinal density distributions to study the adsorption and desorption of argon in finite as well as infinite cylindrical nanopores at 87.3 K. Features that have not been observed before with one-dimensional NLDFT are observed in the analysis of an inhomogeneous fluid along the axis of a finite cylindrical pore using the two-dimensional version of the NLDFT. The phase transition in pore is not strictly vapor-liquid transition as assumed and observed in the conventional version, but rather it exhibits a much elaborated feature with phase transition being complicated by the formation of solid phase. Depending on the pore size, there are more than one phase transition in the adsorption-desorption isotherm. The solid formation in finite pore has been found to be initiated by the presence of the meniscus. Details of the analysis of the extended version of NLDFT will be discussed in the paper.     

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.     

氩吸附法研究多级孔分子筛的孔结构

采用不同方法分别制备了双介孔分子筛、介微孔分子筛及介孔沸石材料,利用氩吸附法并结合XRD技术表征了多级孔分子筛的孔结构。探讨了适用于多级孔分子筛的孔径分布计算方法,揭示了不同类型吸附等温线与孔径分布、孔型及孔容等之间的关系。研究表明,对于多级孔分子筛、微孔和介孔的孔径分布分别用SF法和BJH法计算较适宜,全孔分析可用NLDFT法计算。通过对TS-1介孔沸石的孔结构分析发现, TPAOH 在改性制备介孔TS-1的过程中起到了生成介孔及促进二次晶化的双重作用。     

交联聚苯乙烯型多孔吸附剂的中孔性质研究

采用77K温度下的氮气吸附方法,测定了经悬浮聚合制备的不同交联度的交联聚苯乙烯多孔吸附剂的吸附/脱附等温线.根据BET吸附模型计算了比表面,由吸附量计算了总的孔体积,由孔体积和比表面计算出平均孔径,并依据脱附等温线采用BJH方法计算孔径分布.结果表明,交联度对交联聚苯乙烯多孔吸附剂的孔结构均具有显著影响.随着交联聚苯乙烯多孔吸附剂的交联度升高,其孔径变小,比表面增大,而且低交联度吸附剂的中孔接近圆柱形,高交联吸附剂的中孔形状接近“墨水瓶”形.显然,交联度对孔性质的影响与孔结构在交联聚苯乙烯多孔吸附剂制备和后处理过程中的稳定性密切相关.交联度低时,初期形成的小孔不能保持稳定,在后续聚合及后处理过程中合并为大孔,结果造成低交联吸附剂大孔径、低比表面的现象.通过对孔径分布的研究,揭示了不同吸附剂在中孔范围内的孔特征,并对其形成机制进行了分析.     

DFT-based prediction of high-pressure H2 adsorption on porous carbons at ambient temperatures from low-pressure adsorption data measured at 77 K

Hydrogen adsorption isotherms were measured both at cryogenic temperatures below 1 atm and at ambient temperature at high pressures, up to 90 atm, on selected porous carbons with various pore structures. The nonlocal density functional theory (NLDFT) model was used to calculate the pore size distributions (PSDs) of the carbons, from H2 adsorption isotherms measured at 77 K, and then to predict H2 adsorption on these carbons at 87 and 298 K. An excellent agreement between the predicted and measured data was obtained. Prior to analyzing the porous carbons, the solid-fluid interaction parameters used in the NLDFT model were derived from H2 adsorption data measured at 77 K on nonporous carbon black. The results show that the NLDFT model with appropriate parameters may be a useful tool for optimizing carbon pore structures and designing adsorption systems for hydrogen storage applications.     

Adsorption of bulky molecules of nonylphenol ethoxylate on ordered mesoporous carbons

Ordered mesoporous carbons (OMCs) with varying pore sizes were prepared using ordered mesoporous silica SBA-15 as hard templates. The OMCs possess abundant mesopores with narrow pore size distribution, on which the adsorption behavior of bulky molecules of nonylphenol ethoxylate (NPE) were investigated. The isotherms of NPE on OMCs can be fitted by Langmuir adsorption model, evidenced by the adsorption data. The surface area of the pores larger than 1.5 nm is a crucial factor to the adsorption capacity of NPE, whereas the most probable pore diameter of OMCs is crucial to the adsorption rate of NPE. The adsorption temperature has more significant effects on adsorption rate than the adsorption capacity. Theoretical studies show that the adsorption kinetics of NPE on OMCs can be depicted with the pseudo-second-order kinetic model. In addition, thermodynamic parameters of adsorption were evaluated based on the equilibrium constants related to the equilibrium of adsorption at different temperatures.     

Improvement of the Derjaguin-Broekhoff-de Boer theory for the capillary condensation/evaporation of nitrogen in spherical cavities and its application for the pore size analysis of silicas with ordered cagelike mesopores

In a previous work, we proposed an improvement of the Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in open-ended cylindrical mesopores. In this paper, we report a further extension of this approach to the capillary condensation/evaporation of nitrogen in siliceous spherical cavities. The main idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the variation of the surface tension in spherical mesopores. In addition, the statistical film thickness (the so-called t-curve), which is evaluated accurately on the basis of adsorption isotherms measured for MCM-41 materials, is used instead of the originally proposed t-curve to take into account the excess chemical potential due to the surface forces. It is shown that the aforementioned modifications of the original DBdB theory that was refined by Ravikovitch and Neimark have significant implications for the pore size analysis of cagelike mesoporous silicas. To verify the proposed improvement of the DBdB pore size analysis (IDBdB), two series of FDU-1 samples, which are well-defined cagelike mesoporous materials (composed of siliceous spherical cavities interconnected by short necks), were used for the evaluation of the pore size distributions (PSDs). The correlation between the spinodal condensation point in the spherical pores predicted by the nonlocal density functional theory (NDFT) developed by Ravikovitch and Neimark and that predicted by the IDBdB theory is very good in the whole range of mesopores. This feature is mirrored to the realistic PSD characterized by the bimodal structure of pores computed from the IDBdB theory. As in the case of open-ended cylindrical pores, the improvement of the classical DBdB theory preserves its simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the average pore size by the NDFT and the powder X-ray diffraction method.     

Water adsorption-desorption isotherms of two-dimensional hexagonal mesoporous silica around freezing point

Zr-doped mesoporous silica with a diameter of approximately 3.8 nm was synthesized via an evaporation-induced self-assembly process, and the adsorption-desorption isotherms of water vapor were measured in the temperature range of 263-298 K. The measured adsorption-desorption isotherms below 273 K indicated that water confined in the mesopores did not freeze at any relative pressure. All isotherms had a steep curve, resulting from capillary condensation/evaporation, and a pronounced hysteresis. The hysteresis loop, which is associated with a delayed adsorption process, increased with a decrease in temperature. Furthermore, the curvature radius where capillary evaporation/condensation occurs was evaluated by the combined Kelvin and Gibbs-Tolman-Koening-Buff (GTKB) equations for the modification of the interfacial tension due to the interfacial curvature. The thickness of the water adsorption layer for capillary condensation was slightly larger, whereas that for capillary evaporation was slightly smaller than 0.7 nm.     

Complex Pore Structure of Mesoporous Zeolites: Unambiguous TEM Imaging Using Platinum Tracking

The article proposes a new way for visualization of mesopores and quantitative evaluation of the pore structure in zeolite crystals. The approach is based on platinum tracking inside the zeolite material after its incorporation from a gaseous precursor using an electron beam prior to preparing a TEM specimen by the focused ion beam technique. The pores in mesoporous silica and purely microporous zeolite Y were visualized in TEM images in a demonstration of the capabilities of the approach. Finally, platinum tracking was used for studying the pore structure of zeolite Y (CBV 720) containing mesopores both inside the crystal and those emerging at its surface, which were unambiguously distinguished from each other. The obtained sizes of the mesopores and the calculated material porosity are in good agreement with the results obtained by the low-temperature argon sorption isotherms method.     

Textural characterization of native and n-alky-bonded silica monoliths by mercury intrusion/extrusion, inverse size exclusion chromatography and nitrogen adsorption

Native and n-alkyl-bonded (n-octadecyl) monolithic silica rods with mesopores in the range between 10 and 25 nm and macropores in the range between 1.8 and 6.0 microm were examined by mercury intrusion/extrusion, inverse size exclusion chromatography (ISEC) and nitrogen sorption. Our results reveal very good agreement for the mesopore size distribution obtained from nitrogen adsorption (in combination with an advanced NLDFT analysis) and ISEC. Our studies highlight the importance of mercury porosimetry for the assessment of the macropore size distribution and show that mercury porosimetry is the only method which allows obtaining a combined and comprehensive structural characterization of macroporous/mesoporous silica monoliths. Our data clearly confirm that mercury porosimetry hysteresis and entrapment have different origin, and indicate the intrinsic nature of mercury porosimetry hysteresis in these silica monoliths. Within this context some silica monoliths show the remarkable result of no entrapment of mercury after extrusion from the mesopore system (i.e. for the first intrusion/extrusion cycle). The results of a systematic study of the mercury intrusion/extrusion behavior into native silica monoliths and monoliths with bonded n-alkyl groups reveals that the macro (through) pore structure, which controls the mass transfer to and from the mesopores, here mainly controls the entrapment behavior. Our data suggest that mercury intrusion/extrusion porosimetry does not only allow to obtain a comprehensive pore structure analysis, but can also serve as a tool to estimate the mass transport properties of silica monoliths to be employed in liquid-phase separation processes.     

Surface morphology of nanostructured polymer-based activated carbons

Complementary techniques, including nitrogen adsorption, small-angle X-ray scattering (SAXS), and atomic force microscopy (AFM), have been utilized to characterize the surface features of highly microporous carbon materials prepared from highly aromatic polymers. Nitrogen adsorption measurement interpreted by BET, DR, HK, and NLDFT methods reveals these nanostructured activated carbons exhibit a high surface area of up to 4000 m2/g, a micropore volume up to approximately 1.75 mL/g, and an average pore size of approximately 10-20 angstroms. A modified equation, based on Porod's law, the Debye-Bueche equation, and fractal dimension theories, has been proposed and successfully applied to analyze the SAXS spectra and to extract the porous texture of these unique activated carbons. AFM 3D imaging combined with the Fourier transform technique has been applied to statistically quantify pore sizes on the carbon surface.     

GCMC simulation of argon adsorption in wedge shaped mesopores of finite length

We have used Grand Canonical Monte Carlo simulation to study argon adsorption at 87 K in wedge shaped mesopores. The structural parameters, including mean pore size, wall length and wedge angle, were varied to investigate their effects on the size, shape and the position of the hysteresis loop. Although the effects of pore size have been studied previously, the wall length and wedge angle have received little attention. We find that the wedge angle can have a significant effect on the existence, position, size and shape of the hysteresis loop, while the wall length affects the adsorptive capacity associated with the loop and the behaviour of the isotherm beyond the loop. The results of this work have far-reaching consequences for the characterization of pore size distribution where it is commonly assumed, when constructing a kernel of local isotherms, that pore size is uniform, since even a small deviation from a constant pore width can shift the condensation and evaporation pressures significantly and thus lead to an incorrect estimation of pore size.