Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation

In our recent paper (Jagiello and Olivier, Carbon 55:70–80, 2013) we considered introducing energetical heterogeneity (EH) and geometrical corrugation (GC) to the pore walls of the standard carbon slit pore model. We treated these two effects independently and we found that each of them provides significant improvement to the carbon model. The present work is a continuation of the previous one, as we include both effects in one comprehensive model. The existing standard slit pore model widely used for the characterization of activated carbons assumes graphite-like energetically uniform pore walls. As a result of this assumption adsorption isotherms calculated by the non-local density functional theory (NLDFT) do not fit accurately the experimental N₂ data measured for real activated carbons. Assuming a graphene-based structure for activated carbons and using a two-dimensional-NLDFT treatment of the fluid density in the pores we present energetically heterogeneous and geometrically corrugated (EH–GC) surface model for carbon pores. Some parameters of the model were obtained by fitting the model to the reference adsorption data for non-graphitized carbon black. For testing, we applied the new model to the pore size analysis of porous carbons that had given poor results when analyzed using the standard slit pore model. We obtained an excellent fit of the new model to the experimental data and we found that the typical artifacts of the standard model were eliminated.     

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.     

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.     

Simple fabrication of a phosphorus-doped hierarchical porous carbon via soft-template method for efficient CO2capture

Hierarchical porous carbons are widely used as adsorbents, catalyst supports, electrode materials, and other applications because of their high specific surface area (SSA), varied pore structure, adjustable porosity, and excellent physicochemical stability. Introducing heteroatoms such as N, P, or S, with electronegativities different from that of carbon, into the carbon skeleton can change the chemical properties of the surface and the density of the electron cloud around the carbon matrix, thus altering interactions of CO₂molecules with the surface and improving CO₂adsorption capacity. Therefore, doping heteroatoms in carbon materials has attracted a great amount of attention. In this paper, the template method was used with F108 (polyethylene glycol–polypropylene glycolpolyethylene glycol) as the template, resorcinol and formaldehyde solutions as the carbon sources, phosphoric acid as the phosphorus source, and KOH as the activator to prepare phosphorus-doped hierarchical porous carbons. Through a series of characterization and CO₂adsorption experiments, the influence of the amount of KOH and template agent on the pore structure of carbon materials was studied. We conclude that these phosphorus-doped hierarchical porous carbon materials are promising CO₂adsorbents.     

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.     

Influence of MgO template on carbon dioxide adsorption of cation exchange resin-based nanoporous carbon

In this work, porous carbons with well-developed pore structures were directly prepared from a weak acid cation exchange resin (CER) by the carbonization of a mixture with Mg acetate in different ratios. The effect of the Mg acetate-to-CER ratio on the pore structure and CO(2) adsorption capacities of the obtained porous carbons was studied. The textural properties and morphologies of the porous carbons were analyzed via N(2)/77K adsorption/desorption isotherms, SEM, and TEM, respectively. The CO(2) adsorption capacities of the prepared porous carbons were measured at 298 K and 1 bar and 30 bar. By dissolving the MgO template, the porous carbons exhibited high specific surface areas (326-1276 m(2)/g) and high pore volumes (0.258-0.687 cm(3)/g). The CO(2) adsorption capacities of the porous carbons were enhanced to 164.4 mg/g at 1 bar and 1045 mg/g at 30 bar by increasing the Mg acetate-to-CER ratio. This result indicates that CER was one of the carbon precursors to producing the porous structure, as well as for improving the CO(2) adsorption capacities of the carbon species.     

Adsorption of carbon dioxide-methane mixtures in porous carbons: effect of surface chemistry

A combined experimental and molecular simulation study of the coadsorption of CO₂ and CH₄ in porous carbons is reported. We address the effect of surface chemistry by considering a numerical model of disordered porous carbons which has been modified to include heterochemistry (with a chemical composition consistent with that of the experimental sample). We discuss how realistic the numerical sample is by comparing its pore size distribution (PSD), specific surface area, porous volume, and porosity with those for the experimental sample. We also discuss the different criteria used to estimate the latter properties from a geometrical analysis. We demonstrate the ability of the MP method to estimate PSD of porous carbons from nitrogen adsorption isotherms. Both the experimental and simulated coadsorption isotherms resemble those obtained for pure gases (type I in the IUPAC classification). On the other hand, only the porous carbon including the heterogroups allows simulating quantitatively the selectivity of the experimental adsorbent for different carbon dioxide/methane mixtures. This result shows that taking into account the heterochemistry present in porous carbons is crucial to represent correctly adsorption selectivities in such hydrophobic samples. We also show that the adsorbed solution theory describes quantitatively the simulated and experimental coadsorption isotherms without any parameter adjustment.     

多孔炭物理化学结构及其表征

以碳为基本骨架的多孔炭因具有丰富的孔隙结构和表面化学宫能团,在吸附分离、催化、电子等领域应用广泛.在阐述多孔炭孔结构（物理结构）和表面化学宫能团（化学结构）基础上,重点介绍了透射电镜等可直接观察多孔炭孔结构的表征方法及Dubinin微孔充填理论、平均场密度泛函理论、吸附法、压汞法等表征多孔炭孔结构的主要理论及方法,以及...     

How realistic is the pore size distribution calculated from adsorption isotherms if activated carbon is composed of fullerene-like fragments?

A plausible model for the structure of non-graphitizing carbon is one which consists of curved, fullerene-like fragments grouped together in a random arrangement. Although this model was proposed several years ago, there have been no attempts to calculate the properties of such a structure. Here, we determine the density, pore size distribution and adsorption properties of a model porous carbon constructed from fullerene-like elements. Using the method proposed recently by Bhattacharya and Gubbins (BG), which was tested in this study for ideal and defective carbon slits, the pore size distributions (PSDs) of the initial model and two related carbon models are calculated. The obtained PSD curves show that two structures are micro-mesoporous (with different ratio of micro/mesopores) and the third is strictly microporous. Using the grand canonical Monte Carlo (GCMC) method, adsorption isotherms of Ar (87 K) are simulated for all the structures. Finally PSD curves are calculated using the Horvath-Kawazoe, non-local density functional theory (NLDFT), Nguyen and Do, and Barrett-Joyner-Halenda (BJH) approaches, and compared with those predicted by the BG method. This is the first study in which different methods of calculation of PSDs for carbons from adsorption data can be really verified, since absolute (i.e. true) PSDs are obtained using the BG method. This is also the first study reporting the results of computer simulations of adsorption on fullerene-like carbon models.     

Prediction of high-pressure adsorption equilibrium of supercritical gases using density functional theory

In this paper, we present the results of the prediction of the high-pressure adsorption equilibrium of supercritical gases (Ar, N2, CH4, and CO2) on various activated carbons (BPL, PCB, and Norit R1 extra) at various temperatures using a density-functional-theory-based finite wall thickness (FWT) model. Pore size distribution results of the carbons are taken from our recent previous work,(1,2) using this approach for characterization. To validate the model, isotherms calculated from the density functional theory (DFT) approach are comprehensively verified against those determined by grand canonical Monte Carlo (GCMC) simulation, before the theoretical adsorption isotherms of these investigated carbons calculated by the model are compared with the experimental adsorption measurements of the carbons. We illustrate the accuracy and consistency of the FWT model for the prediction of adsorption isotherms of the all investigated gases. The pore network connectivity problem occurring in the examined carbons is also discussed, and on the basis of the success of the predictions assuming a similar pore size distribution for accessible and inaccessible regions, it is suggested that this is largely related to the disordered nature of the carbon.     

Construction by molecular dynamics modeling and simulations of the porous structures formed by dextran polymer chains attached on the surface of the pores of a base matrix: characterization of porous structures

Significant increases in the separation of bioactive molecules by using ion-exchange chromatography are realized by utilizing porous adsorbent particles in which the affinity group/ligand is linked to the base matrix of the porous particle via a polymeric extender. To study and understand the behavior of such systems, the M3B model is modified and used in molecular dynamics (MD) simulation studies to construct porous dextran layers on the surface of a base matrix, where the dextran polymer chains and the surface are covered by water. Two different porous polymer layers having 25 and 40 monomers per main polymer chain of dextran, respectively, are constructed, and their three-dimensional (3D) porous structures are characterized with respect to porosity, pore size distribution, and number of conducting pathways along the direction of net transport. It is found that the more desirable practical implications with respect to structural properties exhibited by the porous polymer layer having 40 monomers per main polymer chain, are mainly due to the higher flexibility of the polymer chains of this system, especially in the upper region of the porous structure. The characterization and analysis of the porous structures have suggested a useful definition for the physical meaning and implications of the pore connectivity of a real porous medium that is significantly different than the artificial physical meaning associated with the pore connectivity parameter employed in pore network models and whose physical limitations are discussed; furthermore, the methodology developed for the characterization of the three-dimensional structures of real porous media could be used to analyze the experimental data obtained from high-resolution noninvasive three-dimensional methods like high-resolution optical microscopy. The MD modeling and simulations methodology presented here could be used, considering that the type and size of affinity group/ligand as well as the size of the biomolecule to be adsorbed onto the affinity group/ligand are known, to construct different porous dextran layers by varying the length of the polymeric chain of dextran, the number of attachment points to the base matrix, the degree of side branching, and the number of main polymeric chains immobilized per unit surface area of base matrix. After the characterization of the porous structures of the different porous dextran layers is performed, then only a few promising structures would be selected for studying the immobilization of adsorption sites on the pore surfaces and the subsequent adsorption of the bioactive molecules onto the immobilized affinity groups/ligands.     

多孔碳材料的化学气相后处理及其超级电容性能

以廉价的椰壳为原料制备了高比表面积的多孔碳材料,然后在密闭的反应釜中以硝酸蒸汽对多孔碳材料进行了后处理,制备了亲水性更好的多孔碳材料。采用扫描透射电子显微镜(TEM)、物理吸附、X射线粉末衍射(XRD)、拉曼光谱(Raman)和接触角测试对材料的微观形貌、孔道结构、组成和亲水性进行了表征,探究了不同温度下硝酸蒸汽对多孔碳材料的形貌、结构的影响,并采用循环伏安法、恒电流充放电法和交流阻抗法考察了多孔碳材料的超级电容性能。结果表明,经过硝酸蒸汽处理后的多孔碳材料的比表面积和孔体积均有所降低,且随着处理温度的升高,降低得更加明显,而亲水性却越来越好。电化学测试结果表明,经过100℃硝酸蒸汽处理的多孔碳材料(CSC-100)具有最佳的超级电容性能。在以6 mol·L^-1 KOH为电解液的三电极体系中,当电流密度为0.5 A·g^-1时CSC-100的比电容可达452.9 F·g^-1,而未经硝酸蒸汽处理的多孔碳材料(CSC)的比电容仅为350.4 F·g^-1。电容贡献分析表明CSC-100良好的亲水性和表面官能团不仅提高了双电层电容,也提高了赝电容。     

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.     

Estimating the pore size distribution of activated carbons from adsorption data of different adsorbates by various methods

Experimental adsorption isotherms of four adsorbates (N2, Ar, C6H6, and CCl4) as well as adsorption enthalpy (C6H6 and CCl4) measured on two strictly microporous carbons are used to evaluate the porosity of adsorbents (i.e., pore size distributions (PSDs) and average pore diameter ( Lav )). The influence of the diameter of adsorbates ( dA) as well as of the temperature ( T ) is analyzed in order to explain the differences or similarities between the above-mentioned quantities for all systems. Proposed previously, the general relationships between the parameters of the Dubinin-Astakhov (DA) isotherm equation (the characteristic energy of adsorption ( E0 ) and the exponent of this equation ( n )) and the average slit-width of carbon micropores are investigated. Moreover, the thermodynamic verification of the Horvath-Kawazoe (HK) theory and the ND model is presented based on data of the adsorption and enthalpy of adsorption of benzene and carbon tetrachloride on two carbons. Finally, the pore diameters calculated from calorimetry data using the Everett and Powl method and those calculated applying the recently developed equations are compared. In our opinion the change of apparent PSD should be monitored by performing a series of isotherm measurements from high (equal and higher than room temperature) to low temperatures (ca. 77.5 K) as was presented in the current study. Moreover, the analysis of the experimental data leads to the conclusion that the entropy of C6H6 and CCl4 can approach to the values characteristic of quasi-solid (a partially ordered structure). Therefore, this behavior of the adsorbate should be taken into consideration in the theoretical assumptions of model and its thermodynamic verification.     

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.     

New method for atomistic modeling of the microstructure of activated carbons using hybrid reverse Monte Carlo simulation

We propose a new hybrid reverse Monte Carlo (HRMC) procedure for atomistic modeling of the microstructure of activated carbons whereby the guessed configuration for the HRMC construction simulation is generated using the characterization results (pore size and pore wall thickness distributions) obtained by the interpretation of argon adsorption at 87 K using our improved version of the slit-pore model, termed the finite wall thickness (FWT) model (Nguyen, T. X.; Bhatia, S. K. Langmuir 2004, 20, 3532) . This procedure overcomes limitations arising from the use of short-range potentials in the conventional HRMC method, which make the latter unsuitable for carbons such as activated carbon fibers that are anisotropic with medium-range ordering induced by their complex pore structure. The newly proposed approach is applied specifically for the atomistic construction of an activated carbon fiber ACF15, provided by Kynol Corporation (Nguyen, T. X.; Bhatia, S. K. Carbon 2005, 43, 775) . It is found that the PSD of the ACF15's constructed microstructure is in good agreement with that determined using argon adsorption at 87 K. Furthermore, we have also found that the use of the Lennard-Jones (LJ) carbon-fluid interaction well depth obtained from scaling the flat graphite surface-fluid interaction well depth taken from Steele (Steele, W. A. Surf. Sci. 1973, 36, 317) provides an excellent prediction of experimental adsorption data including the differential heat of adsorption of simple gases (Ar, N(2), CH(4), CO(2)) over a wide range of temperatures and pressures. This finding is in agreement with the enhancement of the LJ carbon-fluid well depth due to the curvature of the carbon surface, found by the use of ab initio calculations (Klauda, J. B.; Jiang, J.; Sandler, S. I. J. Phys. Chem. B 2004, 108, 9842) .     

<Superscript>129</Superscript>Xe NMR spectroscopy of adsorbed xenon: Possibilites for exploration of microporous carbon materials

Despite the extensive use of ¹²⁹Xe NMR for characterization of high surface-to-volume porous solids, particularly zeolites, this method has not been widely used to explore the properties of microporous carbon materials. In this study, commercial amorphous carbons of different origin (produced from different precursors) and a series of activated carbons obtained by successive cyclic air oxidation/pyrolysis treatments of a single precursor were examined. Models of ¹²⁹Xe chemical shift as a function of local Xe density, mean pore size, and temperature are discussed. The virial coefficient arising from binary xenon collisions, σ_Xe-Xe, varied linearly with the mean pore size given by N₂ adsorption analysis; σ_Xe-Xe appeared to be a better probe of the mean pore size than the chemical shift extrapolated to zero pressure, σ_S.     

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.