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.     

Why the pore geometry model could affect the uniqueness of the PSD in AC characterization

In this paper we discuss why the pore geometry can affect the unicity of the pore size distribution (PSD) of a given activated carbon (AC) sample, when different probe gases are used in adsorption measures. In order to characterize the solid sample we used grand canonical Monte Carlo simulation and the independent pore model with slit or triangular pore geometry, focusing our analysis on the possibility of representing the adsorptive processes of a triangular pore of defined size by means of a combination of slit pores of different sizes. This representation is tested on experimental adsorption data of N₂ (77 K) on AC samples and acceptable results were obtained. Finally, we have performed a theoretical test, which consisted of analyzing a virtual porous solid with this approach and different probe gases (N₂ at 77 K and CO₂ at 273 K), showing that the differences between the pore representations can cause differences between the solid representations for the adsorptive properties, for these different gases. The analysis presented here can be extended to other pore geometries and other adsorbates, and provide arguments to further explain results presented in our previous paper, which refers to cases when different adsorbates yield different PSDs for a given sample and the same pore geometry model.     

The role of accessibility in the characterization of porous solids and their adsorption properties

This paper addresses the role of accessibility for adsorption in porous solids on the adsorption properties including Henry constant, adsorption isotherms and isosteric heat of adsorption. The relevant parameters are the accessible volume, the accessible geometrical surface area and the accessible pore size and its associated volume. This concept will be demonstrated to be important and calls for the need to consider adsorption characteristics in the most coherent and consistent manner. It is particularly reinforced by the limitations inherent in the conventional ways in determining the void volume, surface area and pore size. We provide a number of examples to support this; the challenge that faces us is the development of consistent experimental procedures to determine these accessible quantities. We define the accessible pore size as the size of the largest sphere that rests on three closest solid atoms in such a manner that any probe particle residing in that sphere would have a non-positive solid-fluid potential energy. For each accessible pore size there is an associated accessible pore volume, giving rise to a new accessible pore size distribution (APSD). This is distinct from the classical pore size distribution commonly used in the literature, and in our definition of accessible pore size, a zero pore size is possible. It is also emphasized that the accessible quantities that we introduce here are dependent on the choice of molecular probe, which is entirely consistent with the concept of molecular sieving.     

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.     

Importance of molecular shape in the adsorption of nitrogen,carbon dioxide and methane on surfaces and in confined spaces

The importance of shape in the adsorption of nitrogen, carbon dioxide and methane (common molecular probes for solid characterization) on surfaces and in confined spaces is investigated for its effects on the adsorption capacity and isosteric heat. We study the possibility of using an equivalent pseudo-sphere model to describe the potential energy of interaction of these molecular probes. On a flat open surface, we find that the equivalent pseudo-sphere model describes adsorption of these species sufficiently well. However, in the confined space of pores, especially pores that accommodate three layers or less, the pseudo-sphere model describes the adsorption badly because of the geometrical constraint on the molecular packing. It is recommended that to study adsorption properly in small pores, potential models that correctly describe molecular shape should be used. In characterization, pseudo-sphere models are commonly used to generate the kernels (local isotherms) for the determination of pore size distribution which can lead to misleading results. We illustrate this with an example to show that the wrong pore size distribution results if pseudo-sphere kernels are used.     

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

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

Probing the pore wall structure of nanoporous carbons using adsorption

Hitherto, adsorption has been traditionally used to study only the porous structure in disordered materials, while the structure of the solid phase skeleton has been probed by crystallographic methods such as X-ray diffraction. Here we show that for carbons density functional theory, suitably adapted to consider heterogeneity of the pore walls, can be reliably used to probe features of the solid structure hitherto accessibly only approximately even by crystallographic methods. We investigate a range of carbons and determine pore wall thickness distributions using argon adsorption, with results corroborated by X-ray diffraction.     

Adsorption kinetics of deamidated antibody variants on macroporous and dextran-grafted cation exchangers. III. Microscopic studies

The kinetics of single and multicomponent adsorption of deamidated monoclonal antibody (mAb) charge variants is investigated using confocal laser scanning microscopy for two commercial cation exchangers, one with an open macroporous structure--UNOsphere S--and the other with charged dextran grafts--Capto S. Markedly different intraparticle concentration profiles are obtained, being very sharp for UNOsphere S, indicating pore diffusion control, but much more diffuse for Capto S, consistent with a solid or surface diffusion mechanism. For single-component adsorption, the mAb effective pore diffusivities for UNOsphere S are approximately D(e)=4.5×10(-8) and 8.3×10(-8) cm(2)/s at pH 5 and 7.5, respectively, while effective solid diffusivities for Capto S are D(s)=0.98×10(-9) and 5.0×10(-9) cm(2)/s at pH 5 and 7.5, respectively. Two-component adsorption at pH 7.5, where the deamidated variants are bound selectively also showed markedly different profiles for the two matrices. UNOsphere S showed distinct adsorption zones within the particles indicating that multicomponent transport occurs with continuous displacement of the more deamidated variant by the less deamidated one. Capto S, however, showed no spatial resolution of the variants within the particle during co-adsorption and very slow mass transfer during sequential adsorption suggesting that protein counter-diffusion is severely hindered in this material.     

Mechanism and kinetics of protein transport in chromatographic media studied by confocal laser scanning microscopy. Part I. The interplay of sorbent structure and fluid phase conditions

An experimental study on the interplay of sorbent structure and fluid phase conditions (pH) has been carried out examining adsorption and transport of bovine serum albumin (BSA) and a monoclonal antibody (IgG 2a) on SP Sepharose Fast Flow and SP Sepharose XL. SP Sepharose Fast Flow is characterised by a relatively open pore network, while SP Sepharose XL is a composite structure with ligand-carrying dextran chains filling the pore space. Both adsorbents have similar ionic capacity. Protein transport and adsorption profiles were evaluated using confocal laser scanning microscopy. Under all investigated conditions, BSA uptake could be adequately explained by a pore diffusion mechanism. The adsorption profiles obtained for IgG 2a, however, indicated that changes in fluid phase conditions as well as a change in the solid phase structure could result in a more complex uptake mechanism as compared to pore diffusion alone. This mechanism results in a fast transport of proteins into the adsorbent, followed by an overshoot of protein in the center of the sorbent and a setback towards a homogeneous adsorption profile.     

Characterization of the hydrophobicity of mesoporous silicas and clays with silica pillars by water adsorption and DRIFT

The hydrophobic-hydrophilic properties of a solid are related to the material chemistry and, often, these properties are relevant to the applications of a particular material. Contrarily to what happens with other properties, such as specific surface areas or pore volumes, the methodologies to ascertain on the hydrophilicity of a porous material are not well defined. In this work, we discuss and relate the information on the hydrophobicity degree obtained from water adsorption isotherms and from diffuse reflectance infrared Fourier transform (DRIFT), in a set of porous materials. The studied materials were mainly mesoporous solids, namely of MCM-41 and SBA-15 types, two xerogels and also different porous clays heterostructures. Both techniques were informative on the hydrophobic-hydrophilic properties of the studied samples, but the correlation between the information obtained by each technique was not straightforward. Water adsorption isotherms are much more sensitive to the differences of the studied materials than the DRIFT spectra. For silica-based mesoporous materials with similar surface chemistry, the water adsorption process and hence, the hydrophobic-hydrophilic properties, is mainly dependent on the pore diameters. However, water adsorption is much more sensitive to changes in the nature of the adsorbent surface than to changes in the pore diameter.     

Density functional theory model of adsorption on amorphous and microporous silica materials

We present a novel quenched solid density functional theory (QSDFT) model of adsorption on heterogeneous surfaces and porous solids, which accounts for the effects of surface roughness and microporosity. Within QSDFT, solid atoms are considered as quenched component(s) of the solid-fluid system with given density distribution(s). Solid-fluid intermolecular interactions are split into hard-sphere repulsive and mean-field attractive parts. The former are treated with the multicomponent fundamental measure density functional. Capabilities of QSDFT are demonstrated by drawing on the example of adsorption on amorphous silica materials. We show that, using established intermolecular potentials and a realistic model for silica surfaces, QSDFT quantitatively describes adsorption/desorption isotherms of Ar and Kr on reference MCM-41, SBA-15, and LiChrosphere materials in a wide range of relative pressures. QSDFT offers a systematic approach to the practical problems of characterization of microporous, mesoporous, and amorphous silica materials, including an assessment of microporosity, surface roughness, and adsorption deformation. Predictions for the pore diameter and the extent of pore surface roughness in MCM-41 and SBA-15 materials are in very good agreement with recent X-ray diffraction studies.     

Prediction of the conditions for breathing of metal organic framework materials using a combination of X-ray powder diffraction, microcalorimetry, and molecular simulation

The adsorption of C1 to C4 linear hydrocarbons in the flexible metal organic framework MIL-53(Cr) has been followed by adsorption manometry coupled with microcalorimetry and Synchrotron X-ray powder diffraction. This experimental investigation was completed by molecular modeling. In the case of methane, the solid remains rigid whatever the adsorbate amount. However for the C2-C4 series, an increasing flexibility of the structure is observed, which is ascribed first to a breathing of the material from a large pore to a narrow pore form followed by a further expansion at high pressure. The collected thermodynamic and structural information suggests that a minimum adsorption enthalpy of ca. 20 kJ mol (-1) in the initial large pore structure of MIL-53(Cr) is required to induce the structural transition "large to narrow pore". Further, the enthalpy of adsorption can be used to predict the pressure at which the structure reopens. Finally, the magnitude of the breathing can be related to the size of the probe molecule via the van der Waals volume. The above trends have been successfully verified in the case of water and carbon dioxide. This combined experimental and theoretical approach gives the first elements for the prediction of whether or not the MIL53 and similar flexible structures will respond to gas loading and what would be the pressure required and further the amplitude of the induced breathing.     

各种孔结构活性炭吸附苯、环己烷、正戊烷和正己烷的~1H和~(13)C NMR研究

~1H和~(13)C NMR研究证明被吸附在不同孔结构活性炭中的烃类以毛细管凝聚和吸附在固体表面两种状态存在。链状烷烃平铺地吸附在固体表面。被吸附烃与活性炭表面酸性基团的质子交换在弛豫过程中起着重要作用。     

Quantitative information on pore size distribution from the tangents of comparison plots

The comparison plot obtained from the nitrogen adsorption data has a similar shape to that of the curve of accumulating pore volume of a solid. The intrinsic nature of this relation is discussed. It is known that the derivatives of the accumulating pore volume with respect to the pore size are the pore size distribution (PSD) of the solid. Thus, the tangent curve of the comparison plot can display, at least qualitatively, the PSD of a solid, over a wide range of pore sizes (from approximately 1 to 50 nm) because the comparison plot is applicable to both micropores and mesopores. Quantitative pore structure information can be derived from the comparison plots by establishing a relationship between the t value and the pore size from the samples with uniform pore structure and known pore sizes, such as MCM-41 and alumina pillared clay samples. A calculation procedure to derive quantitative PSD from the comparison plots is suggested, giving reasonable results. This study proposes concise and reliable methods based on the comparison plots to derive information on pore structure in porous solids.     

Effect of the pore geometry in the characterization of the pore size distribution of activated carbons

In this work, the characterization of Activated Carbons (AC) by using the independent pore models is discussed, with special emphasis on the issue of how the assumed pore geometry can affect the resulting Pore Size Distribution (rPSD) and on the problem of the unicity of the PSD when different probe molecules are used in adsorption experiments. A theoretical test was performed using virtual solids based in the so-called Mixed Geometry Model (MGM) (Azevedo et al. 2010). The MGM uses a kernel of adsorption isotherms generated by GCMC for different pore sizes and two pore geometries: slit and triangular. The adsorption isotherms of a virtual MGM solid were fitted with both the traditional Slit Geometry Model (SGM) and the Mixed Geometry Model (MGM). It is demonstrated that, by assuming a different pore geometry model from that of the real sample, different PSDs may be obtained by fitting adsorption isotherms of different probe gases. Finally, experimental results are shown which both point toward the MGM as an acceptable extension of the SGM and confirm that the MGM is a closer representation of the actual porous structure of most activated carbons.     

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.     

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.     

Temperature Influence of Benzene Adsorption by a Microporous Silica

The theory for volume filling of micropores is used to describe benzene adsorption isotherms measured over a 25 K temperature range. The adsorption potential or molar work of adsorption for the isotherm at 298 K is derived and compared with Weibull, Gaussian, and gamma potential distribution functions. The Weibull function is fitted via a two-term Dubinin-Radushkevich (D-R) equation. The closest data fit occurs for the gamma distribution. The two-term D-R potentials are interpreted as indicating adsorption by primary micropores followed sequentially by secondary micropores. Analysis of the distribution of adsorption enthalpy for the porous solid compared with a nonporous standard suggests that the predominant pore width is 1.2 nm. The interpretation of the differential molar adsorption entropy at 298 K suggests that strongly localized adsorption occurs in the primary micropores and two-dimensional translational motion with rotation in the plane of the ring occurs in the secondary micropores. Copyright 2000 Academic Press.     

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.