Effects of the juxtaposition of carbonaceous slit pores on the overall transport behavior of adsorbed fluids

It is a common approximation in the modeling of adsorption in microporous carbons to treat the pores as slit pores, whose walls are considered to consist of an infinite number of graphitic layers. In practice, such an approximation is appropriate as long as the number of graphitic layers in the wall is greater than three. However, it is understood that pore walls in microporous carbons commonly consist of three or fewer layers. As well as affecting the solid--fluid interaction within a pore, such narrow walls permit the interaction of fluid molecules through the wall, with consequences for the adsorption characteristics. We consider the effect that a distributed pore-wall thickness model can have on transport properties. At low density we find that the only significant deviation in the transport properties from the infinite pore-wall thickness model occurs in pores with single-layer walls. For a model of activated carbons with a distribution of pore widths and pore-wall thicknesses, the transport properties are generally insensitive to the effects of finite walls, in terms of both the solid-fluid interaction within a pore and fluid-fluid interaction through the pore walls.     

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.     

Contact angles, pore condensation, and hysteresis: insights from a simple molecular model

We discuss the thermodynamics of adsorption of fluids in pores when the solid-fluid interactions lead to partial wetting of the pore walls, a situation encountered, for example, in water adsorption in porous carbons. Our discussion is based on calculations for a lattice gas model of a fluid in a slit pore treated via mean field density functional theory (MFDFT). We calculate contact angles for pore walls as a function of solid-fluid interaction parameter, alpha, in the model, using Young's equation and the interfacial tensions calculated in MFDFT. We consider adsorption and desorption in both infinite pores and in finite length pores in contact with the bulk. In the latter case, contact with the bulk can promote evaporation or condensation, thereby dramatically reducing the width of hysteresis loops. We show how the observed behavior changes with alpha. By using a value of alpha that yields a contact angle of about 85 degrees and maintaining the bulk fluid in a supersaturated vapor state on adsorption, we find an adsorption/desorption isotherm qualitatively similar to those for graphitized carbon black where pore condensation occurs at supersaturated bulk vapor states in the spaces between the primary particles of the adsorbent.     

Adsorption, structure and dynamics of benzene in ordered and disordered porous carbons

Molecular simulations are used to study the adsorption, structure, and dynamics of benzene at 298 K in atomistic models of ordered and disordered nanoporous carbons. The ordered porous carbon is a regular slit pore made up of graphene sheets. The disordered porous carbon is a structural model that reproduces the morphological (pore shape) and topological (pore connectivity) disorder of saccharose-based porous carbons. As expected for pores of a regular geometry, the filling occurs at well-defined pressures which are an increasing function of the pore width H. In contrast, in qualitative agreement with experimental data for activated carbon fibers, the filling of the disordered carbon is continuous and spans over a large pressure range. The structure and dynamics of benzene in the disordered carbon also strongly depart from that for the slit pore geometry. While benzene in the slit graphite nanopores exhibits significant layering, benzene in the disordered porous carbon exhibits a liquid-like structure very close to its bulk counterpart. Both the ordering and self-diffusivity of benzene in the graphite nanopores depend in a complex manner on the pore width. The dynamics is either slower or faster than its bulk counterpart; our data show that the self-diffusivity decreases as the number of confined layers n divided by the pore width H increases (except for very small pore sizes for which benzene crystallizes and is necessarily slower than the liquid phase). The dynamics of benzene in the disordered porous carbon is isotropic and is much slower than that for the graphite slit nanopores (even with the smallest slit nanopore considered in this work). The results above show that the adsorption, structure, and dynamics of benzene confined in disordered porous carbons cannot be described in simple terms using an ideal model such as the slit pore geometry.     

Adsorptive behavior of CO2, CH4 and their mixtures in carbon nanospace: a molecular simulation study

Using molecular simulation, four types of nanoporous carbons are examined as adsorbents for the separation of CO(2)/CH(4) mixtures at ambient temperature and pressures up to 10 MPa. First, the adsorption selectivity of CO(2) is investigated in carbon slit pores and single-walled carbon nanotube bundles in order to find the optimal pore dimensions for CO(2) separation. Then, the adsorptive properties of the optimized slit pore and nanotube bundle are compared with two realistic nanoporous carbon models: a carbon replica of zeolite Y and an amorphous carbon. For the four carbon models, adsorption isotherms and isosteric heats of adsorption are presented for both pure components and mixtures. Special attention is given to the calculation of excess isotherms and isosteric heats, which are necessary to assess the performance of model nanoporous materials in the context of experimental measurements. From these results, we discuss the impact that variables such as pore size, pore morphology, pressure and mixture composition have on the performance of nanoporous carbons for CO(2) separation.     

Fluids in nanospaces: molecular simulation studies to find out key mechanisms for engineering

We have analyzed various phenomena that occur in nanopores, focusing on elucidating their key mechanisms, to advance the effective engineering use of nanoporous materials. As ideal experimental systems, molecular simulations can effectively provide information at the molecular level that leads to mechanistic insight. In this short review, several of our recent results are presented. The first topic is the critical point depression of Lennard-Jones fluid in silica slit pores due to finite size effects, studied by our original Monte Carlo (MC) technique. We demonstrate that the first layers of adsorbed molecules in contact with the pore walls act as a “fluid wall” and impose extra finite size effects on the fluid confined in the central portion of the pore. We next present a new kernel for pore size distribution (PSD) analysis, based entirely on molecular simulation, which consists of local isotherms for nitrogen adsorption in carbon slit pores at 77 K. The kernel is obtained by combining grand canonical Monte Carlo (GCMC) method and open pore cell MC method that was developed in the previous study. We show that overall trends of the PSDs of activated carbons calculated with our new kernel and with conventional kernel from non-local density functional theory are nearly the same; however, apparent difference can be seen between them. As the third topic, we apply a free energy analysis method with the aid of GCMC simulations to investigate the gating behavior observed in a porous coordination polymer, and propose a mechanism for the adsorption-induced structural transition based on both the theory of equilibrium and kinetics. Finally, we construct an atomistic silica pore model that mimics MCM-41, which has atomic-level surface roughness, and perform molecular simulations to understand the mechanism of capillary condensation with hysteresis. We calculate the work required for the gas–liquid transition from the simulation data, and show that the adsorption branch with hysteresis for MCM-41 arise from spontaneous capillary condensation from a metastable state.     

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.     

Stockmayer流体在活性炭孔中的吸附的分子模拟

应用巨正则系综monteCarlo方法模拟Stockmayer流体[以一氯二氟甲烷(R22)为代表]在活性炭孔中的吸附。模拟中R22分子采用等效Stockmayer势能模型,狭缝碳孔墙采用10-4-3模型。通过模拟得到了最佳孔径,并在最佳孔径下,针对不同的主体压力及活性基团密度,得到了吸附等温线、孔中流体的局部密度分布图和较为直观的孔内流体分子的瞬时构象,分析了吸附等温线的特征及孔内流体的吸附结构,认为在0.0,1.0sites/nm^2的活性基团密度下的碳孔内分别发生物理及化学吸附,并确定了最佳操作压力,为工业设计合适的催化剂提供依据。     

巨正则系综Monte Carlo模拟方法确定活性炭的微孔尺寸

根据299K下甲烷在活性炭中的吸附实验数据,通过调节狭缝微孔的孔宽参数,利用巨正则系综MonteCarlo(GCEMC)方法得到不同孔宽下流体的微观结构以及吸附等温线.比较并拟合模拟结果和实验数据,确定了活性炭微孔的平均孔宽,为下一步求解微孔尺寸分布以及为预测吸附剂在不同温度下吸附不同吸附质分子时的吸附性能提供了基础与指导.模拟中,甲烷分子采用单点Lennard-Jones球型分子模型,活性炭用狭缝孔来近似表征,流体分子与单个狭缝墙的相互作用采用著名的Steele的10－4-3势能模型.模拟表明,此方法为考察介孔材料的微孔分布以及微孔平均孔宽提供了新的思路.     

Does water condense in carbon pores?

Using grand canonical Monte Carlo (GCMC) simulations of molecular models, we investigate the nature of water adsorption and desorption in slit pores with graphitelike surfaces. Special emphasis is placed on the question of whether water exhibits capillary condensation (i.e., condensation when the external pressure is below the bulk vapor pressure). Three models of water have been considered. These are the SPC and SPC/E models and a model where the hydrogen bonding is described by tetrahedrally coordinated square-well association sites. The water-carbon interaction was described by the Steele 10-4-3 potential. In addition to determining adsorption/desorption isotherms, we also locate the states where vapor-liquid equilibrium occurs for both the bulk and confined states of the models. We find that for wider pores (widths >1 nm), condensation does not occur in the GCMC simulations until the pressure is higher than the bulk vapor pressure, P0. This is consistent with a physical picture where a lack of hydrogen bonding with the graphite surface destabilizes dense water phases relative to the bulk. For narrow pores where the slit width is comparable to the molecular diameter, strong dispersion interactions with both carbon surfaces can stabilize dense water phases relative to the bulk so that pore condensation can occur for P < P0 in some cases. For the narrowest pores studied--a pore width of 0.6 nm--pore condensation is again shifted to P > P0. The phase-equilibrium calculations indicate vapor-liquid coexistence in the slit pores for P < P0 for all but the narrowest pores. We discuss the implications of our results for interpreting water adsorption/desorption isotherms in porous carbons.     

Structural characteristics of activated carbons and ibuprofen adsorption affected by bovine serum albumin

Structural characteristics of a series of MAST carbons were studied using scanning electron microscopy images and the nitrogen adsorption isotherms analyzed with several models of pores and different adsorption equations. A developed model of pores as a mixture of gaps between spherical nanoparticles and slitlike pores was found appropriate for MAST carbons. Adsorption of ibuprofen [2-(4-isobutylphenyl)propionic acid] on activated carbons possessing different pore size distributions in protein-free and bovine serum albumin (BSA)-containing aqueous solutions reveals the importance of the contribution of mesopores to the total porosity of adsorbents. The influence of the mesoporosity increases when considering the removal of the drug from the protein-containing solution. Cellulose-coated microporous carbon Norit RBX adsorbs significantly smaller amounts of ibuprofen than uncoated micro/mesoporous MAST carbons whose adsorption capability increases with increasing mesoporosity and specific surface area, burnoff dependent variable. A similar effect of broad pores is observed on adsorption of fibrinogen on the same carbons. Analysis of the ibuprofen adsorption data using Langmuir and D'Arcy-Watt equations as the kernel of the Fredholm integral equation shows that the nonuniformity of ibuprofen adsorption complexes diminishes with the presence of BSA. This effect may be explained by a partial adsorption of ibuprofen onto protein molecules immobilized on carbon particles and blocking of a portion of narrow pores.     

Characteristics of Nonafluorobutyl Methyl Ether (NFE) Adsorption onto Activated Carbon Fibers and Different-Size-Activated Carbon Particles

The characteristics of adsorption of 1,1,1,2,2,3,3,4,4-nonafluorobutyl methyl ether (NFE), a chlorofluorocarbon (CFC) replacement, onto six different activated carbon; preparations (three activated carbon fibers and three different-sized activated carbon particles) were investigated to evaluate the interaction between activated carbon surfaces and NFE. The amount of NFE adsorbed onto the three activated carbon fibers increased with increasing specific surface area and pore volume. The amount of NFE adsorbed onto the three different-sized-activated carbon particles increased with an increase in the particle diameter of the granular activated carbon. The differential heat of the NFE adsorption onto three activated carbon fibers depended on the porosity structure of the activated carbon fibers. The adsorption rate of NFE was also investigated in order to evaluate the efficiency of NFE recovery by the activated carbon surface. The Sameshima equation was used to obtain the isotherms of NFE adsorption onto the activated carbon fibers and different-sized-activated carbon particles. The rate constant k for NFE adsorption onto activated carbon fibers was larger for increased specific surface area and pore volume. The rate of NFE adsorption on activated carbons of three different particle sizes decreased with increasing particle diameter at a low initial pressure. The adsorption isotherms of NFE for the six activated carbons conformed to the Dubinin-Radushkevich equation; the constants BE(0) (the affinity between adsorbate and adsorbent) and W(0) (the adsorption capacity) were calculated. These results indicated that the interaction between the activated carbon and NFE was larger with the smaller specific surface area of the activated carbon fibers and with the smaller particle diameter of the different-sized-activated carbon particles. The degree of packing of NFE in the pores of the activated carbon fibers was greater than that in the pores of the granular activated carbons. Copyright 2000 Academic Press.     

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.     

Adsorption-induced deformation of microporous carbons: pore size distribution effect

We present a thermodynamic model of adsorption-induced deformation of microporous carbons. The model represents the carbon structure as a macroscopically isotropic disordered three-dimensional medium composed of stacks of slit-shaped pores of different sizes embedded in an incompressible amorphous matrix. Adsorption stress in pores is calculated by means of Monte Carlo simulations. The proposed model reproduces qualitatively the experimental nonmonotonic dilatometric deformation curve for argon adsorption on carbide-derived activated carbon at 243 K and pressure up to 1.2 MPa. The elastic deformation (contraction at low pressures and swelling at higher pressures) results from the adsorption stress that depends strongly on the pore size. The pore size distribution determines the shape of the deformation curve, whereas the bulk modulus controls the extent of the sample deformation.     

Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that ofgraphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.     

Pore wall thickness and interpore influence on adsorption of alkanes in carbons using explicit pore models

In modeling of activated carbons, the pores are often assumed to be slit-shaped formed of a constant number of graphene layers. X-ray diffraction studies show that micropores are formed between stacks of different numbers of graphene layers. In this study, we investigate, through the grand canonical Monte Carlo method, the influence on the adsorbed alkanes densities of pore walls with different graphene layers thickness and the related interpore adsorbate interaction when the pore wall has only one graphene layer. All studies of thickness and interpore interaction to date were performed using the Steele 10-4-3 potential model. Instead of Steele model, we propose explicit models made up of graphene layers of discrete carbon atoms. We also investigated the sensitivity of the system to the cut-off and solid-fluid parameter. With our explicit model we found that the influence of the number of carbon layers is not significant for n>2 as previously observed by Steele model??DFT studies. The system was also insensitive to cut-off and well deep parameter variations. A new pore model with an extra dummy graphene wall was proposed to investigate the interpore interaction. The interpore interaction study with the alkanes series C1 to C4 shows that the retention capacity of heavier alkanes is the same whether for activated carbons with few layers (stronger interpore interaction) as for carbons with two or more layers (stronger solid-fluid interaction) assuming negligible surface mediation. The explicit models proposed can be successfully used in the elaboration of virtual porous carbon models to reproduce wall thickness and interpore adsorbate interactions phenomena.     

Methane adsorption and diffusion in a model nanoporous carbon: an atomistic simulation study

A constricted slit model was introduced to improve, one step further, the performance of the simple slit model in prediction of the adsorption and diffusion behavior of simple molecules in the nanoporous carbons (NPCs). The grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations are performed to study the adsorption and diffusion behavior of methane within the constricted slit models. The models are called slit-1, 2, and 3 with constriction heights 5, 7, and 9 Å respectively. For comparison, we used the slit-0 name for the simple slit without constriction. Adsorption results show that at low pressures, the constriction increases the adsorbed amount irrespective of its height. Slit-2 with a constriction height as a molecular diameter has the greatest heat of adsorption and has highest loading at pressures up to 3,000 kPa. At high pressures, when all pores are filled, the adsorption trend is in line with the pore volumes of slits where slit-0 with higher pore volume is dominant. The density profiles in the models were calculated and examined. The spatial distribution of adsorbed methane molecules was examined by various radial distribution functions calculated by MD. Also, MD simulation results show that the diffusion coefficient of methane decreases in constricted slits. The calculated diffusion coefficients in slit-2 in the direction of the constriction are one order of magnitude smaller than the calculated one in the simple slit model but it is far from the experimental values in the NPCs.     

Density functional theory of adsorption in pillared slit-like pores

We propose a density functional theory to describe adsorption of Lennard-Jones fluid in pillared slit like pores. Specifically, the pillars are built of chains that are bonded by their ends to the opposite pore walls. The approach we propose combines theory of quenched-annealed systems and theory of nonuniform fluids involving chain molecules. We compare the results of theoretical predictions with grand canonical ensemble Monte Carlo simulations and compute theoretical capillary condensation phase diagrams for several model systems.