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.     

气体临界温度以上吸附平衡的预测研究

Experimental adsorption isotherms of CH4 and N2 higher than critical temperatures on K02 activated carbon were measured with the volumetric method The pressure and temperature ranges were 0～12 MPa and 273～333 K respectively. A model, which took into account the adsorbate properties above critical temperatures and the adsorbent surface heterogeneity by pore size distribution, was proposed in this paper to predict the equilibrium data only using one adsorption isotherm. The gamma distribution was adopted to express the pore size distribution of the activated carbon, and the adsorption potential was calculated bythe 10-4-3 equation for slit shape micro pores. The relationships between the adsorbate density, the saturated adsorption amount and the equilibrium temperature have been discussed in detail. Through this method, the experimental adsorption data of CH4 and N2 were compared with the prediction equilibria. The study illustrates that the predicting method could present the adsorption equilibria accurately in the whole research range. And the mean relative deviations of the prediction of CH4 and N2 are only about 1.9% and 2.9%. This proves that the analyses of the adsorbate properties are reasonable. Inaddition, the model was applied to calculating the equilibrium data of various supercritical adsorption systems published in literatures. Despite different adsorbents and equilibriaconditions, the investigation results demonstrate that the suggested model performs well in predicting the gases adsorption equilibrium data with all mean relatived eviations less than 6.8%. Therefore, the model could be utilized to calculate the gases adsorption equilibrium data above critical temperatures in a wide range.     

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.     

Comparisons of porous and adsorption properties of carbons activated by steam and KOH

In this work, fir woods and pistachio shells were used as source materials to prepare porous carbons, which were activated by physical (steam) and chemical (KOH) methods. Pore properties of these activated carbons including the BET surface area, pore volume, pore size distribution, and pore diameter were first characterized by a t-plot method based on N(2) adsorption isotherms. Highly porous activated carbons with BET surface area up to 1009-1096 m(2)/g were obtained. The steam and KOH activation methods produced carbons with mesopore content in the range 9-15 and 33-49%, respectively. The adsorption equilibria and kinetics of tannic acid, methylene blue, 4-chlorophenol, and phenol from water on such carbons at 30 degrees C were then investigated to check their chemical characteristics. The Freundlich equation gave a better fit to all adsorption isotherms than the Langmuir equation. On the other hand, the intraparticle diffusion model could best follow all adsorption processes. In comparison with KOH-activated carbons, it was shown that the rate of external surface adsorption with steam-activated carbons was significantly higher but the rate of intraparticle diffusion was much lower.     

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) .     

Water vapor adsorption and microporous structure of carbon adsorbents. 17. Analysis of experimental isotherms for water vapor adsorption

Water vapor adsorption for various activated carbons with narrow and wide micropore volume distributions and mesopore surface areas between 40 and 300 m²/g have been investigated. For all the isotherms the point of inflection was determined, which can be taken as the point characterizing the formation of a water adsorption layer on the pore wall surface of carbon adsorbents. To do this the adsorption and desorption branches of the isotherms were approximated according to Weibull's distribution. A good correlation was obtained between values for the water monolayer capacity, calculated from the porous structure parameters of the carbons, and the adsorption values corresponding to the isotherm inflection pointsa _inf. For the group of carbons studied the values of relative pressure at the inflection point of the isotherms fell within the range 0.5–0.72.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 31–34, January, 1991.     

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.     

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.     

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.     

A priori calculation of adsorption equilibria on microporous active carbons

A method is proposed for a priori calculating adsorption isotherms based on the combination of the molecular dynamics method and Dubinin-Radushkevich and Tolmachev-Aranovich equations. The isotherms of adsorption of individual gases and vapors, as well as components of gaseous and vaporous mixtures and liquid solutions on microporous active carbons, are calculated using this method.     

Pseudocritical or hysteresis temperature versus pore size for simple fluids confined in cylindrical nanopores

The adsorption/desorption isotherms measured in nanoporous materials generally present a hysteresis. The hysteresis shrinks upon increasing the temperature (for a given pore size) or decreasing the pore size (for a given temperature), until it finally disappears at the so-called hysteresis (or pseudocritical) temperature T(h) or hysteresis (or pseudocritical) pore size R(h), not to be confused with a true critical point. In this paper, a Monte Carlo approach allowed calculating the surface free energy of confined fluid along the adsorption/desorption isotherms for various cylindrical pore sizes and temperatures. A simple phenomenological model then allowed exploiting these results to determine the relation between T(h) and R(h). The prediction is compared to various literature models and experimental data, showing agreement within uncertainties. On the other hand, the simulations cannot be used directly to predict T(h) and R(h) since they significantly overestimate the hysteresis width. The model predicts a nonlinear relation between the reduced hysteresis temperature and the inverse pore radius.     

多孔活性炭孔径分布的表征

总结了利用气体吸附法表征多孔活性炭中孔和微孔孔径分布的各种方法。BJH方法和MP模型忽略了微孔内势能叠加效应,仅适合描述中孔孔径分布;HK模型和以Dubinin填充理论为基础的各种方法,考虑了微观下势能叠加的效果,在一定程度上能很好地描述微孔孔径分布;最近围绕GAI(GeneralizedAdsorptionIsotherm)而展开的利用密度范函理论(DFT,densityfunctiontheory)和巨正则系综蒙特卡罗(GCMC,grandcanonicalensemblemontecarlo)模拟确定微孔孔径分布的方法较好地克服了Dubinin理论中存在的缺点,是较好的两种方法,但其有效性还需要更多的实验结果来证明。     

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.     

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.     

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.     

Effects of Cetylpyridinium Chloride on Phase and Rheological Behavior of the Diluted C(12)E(4)/Benzyl Alcohol/Water System

The influence of the pore size distribution of activated carbon on the adsorption of phenol from aqueous solutions was explored. Activated carbons with different porous structures were prepared by gasifying a bituminous coal char to different extents of burn-off. The results of adsorption experiments show that the phenol capacity of these carbons does not proportionally increase with their BET surface area. This reflects the heterogeneity of the carbon surface for adsorption. The pore size distributions of these carbons, determined according to the Dubinin-Stoeckli equation, were found to vary with the burn-off level. By incorporating the distribution with the Dubinin-Radushkevich equation using an inverse proportionality between the micropore size and the adsorption energy, the isotherms for the adsorption of phenol onto these carbons can be well predicted. The present study has demonstrated that the heterogeneity of carbon surface for the phenol adsorption can be attributed to the different energies required for adsorption in different-size micropores. Copyright 2000 Academic Press.     

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.     

Comparison of heterogeneous pore models QSDFT and 2D-NLDFT and computer programs ASiQwin and SAIEUS for calculation of pore size distribution

The pore size distributions (PSD) of selected carbons were calculated from their nitrogen adsorption isotherms using both the QSDFT model implemented in ASiQwin version 3.0 software (Quantachrome Instruments) and 2D-NLDFT model implemented in SAIEUS software (Micromeritics). The results showed that both the QSDFT and the 2D-NLDFT methods give similar PSDs despite the different methods for accounting for the heterogeneity of the carbon adsorbent. The characteristic features of the methods and software were discussed and possible improvements were proposed.     

Kinetic restriction of simple gases in porous carbons: transition-state theory study

The separation of simple gases such as N2, Ar, CO2, and CH4 is an industrially important problem, particularly for the mitigation of greenhouse emissions. Furthermore, these gases are widely accepted as standard probing gases for the characterization of the microstructure of porous solids. However, a consistent set of microstructural parameters of a microporous solid determined from the use of adsorption measurements of these different gases is not always achieved because of differences in their pore accessibility. This is a long-standing and poorly understood problem. Here, we present the calculated results of the crossing time of N2, Ar, CO2, and CH4 between two neighboring cages through a constricted window in a realistic structural model of saccharose char, generated from hybrid reverse Monte Carlo (HRMC) simulation (Nguyen, T. X.; Bhatia, S. K.; Jain, S. K.; Gubbins, K. E. Mol. Simul. 2006, 32, 567-577) using transition state theory (TST), as described in our recent work (Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. 2007, 111, 2212-2222). The striking feature in these results is that whereas very fast diffusion of carbon dioxide within the temperature range of 273-343 K, with crossing time on the molecular dynamics scale (10-4-10-6 s), leads to instantaneous equilibrium and no hysteresis on the experimental time scale, slower diffusion of Ar and N2 at the low temperature of analysis indicates an accessibility problem. These results rationalize the experimental results of hysteresis for N2 at 77 K and Ar at 87 K but not for CO2 at 273 K in Takeda 3 A carbon molecular sieves. Furthermore, it is shown that CH4 diffusion through narrow pore mouths can be hindered even at ambient temperature. Finally, we show that the use of pore size and wall thickness distributions extracted from the adsorption of Ar at 87 K using the finite wall thickness (FWT) model (Nguyen, T. X.; Bhatia, S. K. Langmuir 2004, 20, 3532-3535 and Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. B 2004, 108, 14032-14042) provides the correct prediction of experimental CO2 adsorption in BPL and PCB carbons whereas that from N2 at 77 K gives a significant underprediction for both CO2 and CH4 in the BPL carbon. These trends are in excellent agreement with those predicted using the calculated crossing times.     

Simulating the changes in carbon structure during the burn-off process

Using a simple energetic criterion, we modelled the process of activation of 'soft' activated carbons. Eighteen carbon samples, differing in degree of graphitisation, and obtained using Molecular Dynamics annealing of an amorphous carbon precursor were studied. For all samples, the geometric pore size distribution was calculated using the method proposed by Bhattacharya and Gubbins. Adsorption isotherms for Ar at 87 K were simulated and analysed using different approaches widely applied in adsorption science (α(s), DA, APD, ND, BET). It is shown that our approach leads to similar changes in microporosity (with the rise in carbon burn-off) to those observed in real experiments. Moreover, the conclusions about the reality of popular methods of carbon porosity characterisation are given.