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.     

Micropore Filling of Supercritical Xe in Micropores of Activated Carbon Fibers

The adsorption isotherms of Xe vapor at 196 K and supercritical Xe at 300 K on activated carbon fibers of different pore widths were gravimetrically measured. The adsorption isotherms of Xe vapor were compared with the N(2) adsorption isotherms. A Dubinin-Radushkevich (DR) plot of the adsorption isotherms of Xe vapor showed a good linearity, indicating that Xe vapor is adsorbed by the representative micropore filling mechanism. The adsorption isotherms of supercritical Xe were approximated by the Langmuir equation. The saturated adsorption amounts of supercritical Xe, W(L), were in the range of 0.14 to 0.22 ml g(-1). The adsorption isotherms of supercritical Xe were described by the supercritical DR equation, which provides the quasisaturated vapor pressure P(0q). Both P(0q) and W(L) lead to the reduced isotherm, which can describe three isotherms. The obtained reduced isotherm derived from the isotherms of supercritical Xe could describe even those of Xe vapor. Hence, both Xe vapor and supercritical Xe should be adsorbed by the same mechanism. The isosteric heat of Xe adsorption was greater than the enthalpy of vaporization of Xe by more than 12 kJ mol(-1). These results suggest that Xe molecules are stabilized in the form of a cluster in micropores even at 300 K. Copyright 2000 Academic Press.     

几种植物基活性炭材料的孔结构与吸附性能比较——(I)孔结构表征

测定了3种植物基活性炭材料:椰壳活性炭 (CAC4)、剑麻茎基活性炭 (SSAC) 和剑麻基活性碳纤维 (SACF) 的氮吸附等温线,并用不同的理论方法对其孔结构进行了分析和表征。结果表明:CAC4为微孔型,孔径分布集中且大部分是0.7nm以下的极微孔;在相同条件下制备的SSAC和SACF孔分布较为相似,都呈多分散性,结构中除微孔外,还含有丰富的中孔,中孔率均超过50%以上。两者相比,SACF的中孔量和平均孔径更大。3个样品的形态特征和孔结构虽然不同,但其吸附过程都可以用微孔多段填充机理来解析。     

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

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

Isotherm analysis of phenol adsorption on polymeric adsorbents from nonaqueous solution

Macroporous poly(methyl methacrylate-co-divinylbenzene) (PMMA), interpenetrating polymer adsorbent based on poly(styrene-co-divinylbenzene) (PS) and poly(methyl methacrylate-co-divinylbenzene) (PMMA/PS), and macroporous cross-linked poly(N-p-vinylbenzyl acetylamide) (PVBA) were prepared for the adsorption of phenol from cyclohexane. The sorption isotherms of phenol on the three polymeric adsorbents were measured and fitted to Langmuir and Freundlich isotherms. It is shown that the Langmuir isotherm, which is based on a homogeneous surface model, is unsuitable to describe the sorption of phenol on the adsorbents from nonaqueous solution and the Freundlich equation fits the tested three adsorption systems well. The isosteric enthalpy was quantitatively correlated with the fractional loading for the sorption of phenol onto the three polymeric adsorbents. The surface energetic heterogeneity patterns of the adsorbents were described with functions of isosteric enthalpy. The results showed that the tested three polymeric adsorbents exhibited different surface energetic heterogeneity patterns. The initial isosteric enthalpy of phenol sorption on polymeric adsorbent has to do with the surface chemical composition and is free from the pore structure of the polymeric adsorbent matrix. Forming hydrogen bonds between phenol molecules and adsorbent is the main driving force of phenol sorption onto PVBA and PMMA adsorbent from nonaqueous solution. When phenol is adsorbed on PMMA/PS, pi-pi interaction resulting from the stacking of the benzene rings of the adsorbed phenol molecules and the pendant benzene ring of adsorbent is involved.     

ADSORPTION OF BENZOIC ACID AND P-NITROBENZOIC ACID ON A NEW HYPERCROSSLINKED PHENOL GROUP PST ADSORBENT

A comparison of the adsorption of benzoic acid and p-nitrobenzoic acid on the new hypercrosslinked polymeric adsorbent AM-I, with that by macroporous Amberlite XAD-4, including the equilibrium adsorption isotherms, the dynamic adsorption behaviors through column and the adsorption thermodynamics were studied. Results show that Freundlich equation gives a fitting adsorption isotherm. The specific surface of AM-l is only 67% of that of Amberlite XAD-4, but the adsorption capacities on AM-1 are much higher about 125%～166% than that on Amberlite XAD-4,which is contributed to the micropore mechanism and polarity. The negative values of the adsorption enthalpy are indicative of an exothermic process. Enthalpy and free energy changes of adsorption both manifest a physic-sorption process. The negative values of the adsorption entropy indicate that the adsorption is well consistent with the restricted mobilities and the configurations of the adsorbed benzoic acid molecules on the surface of studied adsorbents with superficial heterogeneity. Both adsorbents were used in mini-column experiments for adsorbing benzoic acid expecting to elucidate the higher breakthrough adsorption capacity of the new hypercrosslinked polymeric adsorbent AM-1 as compared with that of Amberlite XAD-4.     

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.     

Thermodynamics of vapour adsorption on heterogeneous microporous adsorbents

Fundamental thermodynamic functions have been derived for equations of adsorption isotherms including structural heterogeneity connected with micropore dimensions. Good agreement has been achieved between values of the differential molar enthalpy of adsorption and values of the isosteric adsorption heats obtained experimentally.     

Optimization of structural and energy characteristics of adsorbents for methane storage

Using numerical and analytical methods, a model for microporous carbon adsorbents with slit-shaped pores of different widths was developed. Such pores are formed during activation procedure by the removal of the hexagonal carbon layers burnt out in a graphite-like crystallites. Dubinin’s theory of volume filling of micropores was used to calculate methane adsorption equilibria on these model adsorbents. Isobaric dependences of methane adsorption on pore width, specific micropore volumes, and the specific surface were plotted in the range of pressures from 1 to 10 MPa. It was found that the isobaric adsorption curves had a maximum the position of which depends on both the structural-energy characteristics of the adsorbent and thermodynamic conditions chosen to operate the adsorption system. As pressure increased, the maximum of adsorption shifts to the porous systems with wider pores and larger micropore volume.     

活性炭吸附CO2与其微孔体积的关系

对五种活性炭样品进行液氮温度下的N2吸附、碘吸附测定和冰点下的CO2吸附表征。结果表明,碘吸附值测定法和基于N2吸附等温线的BET方程、D-R方程,孔结构参数都不能正确反映活性炭对CO2的吸附特性;由CO2吸附等温线得到的D A模型参数也不适合分析活性炭吸附CO2特性;CO2吸附等温线的密度泛函理论（DFT）分析结果表明,CO2在活性炭上的吸附发生在极微孔内,DFT分析的微孔孔容与吸附等温线反映的吸附性能完全一致。因此,根据CO2吸附等温线的DFT模型是准确反映活性炭吸附CO2特性的表征分析方法。     

Cluster-Mediated Water Adsorption on Carbon Nanopores

The adsorption isotherms of water at 303 K and N2 at 77 K on various kinds of porous carbons were compared with each other. The saturated amounts of water adsorbed on carbons almost coincided with amounts of N2 adsorption in micropores. Although carbon aerogel samples have mesopores of the great pore volume, the saturated amount of adsorbed water was close to the micropore volume which is much small than the mesopore volume. These adsorption data on carbon aerogels indicated that the water molecules are not adsorbed in mesopores, but in micropores only. The adsorption isotherms of water on activated carbon having micropores of smaller than 0.7 nm in width had no clear adsorption hysteresis, while the water adsorption isotherms on micropores of greater than 0.7 nm had a remarkable adsorption hysteresis above P/P0 = 0.5. The disappearance of the clear hysteresis for smaller micropores suggested that the cluster of water molecules of about 0.7 nm in size gives rise to the water adsorption on the hydrophobic micropores; the formation and the structure of clusters of water molecules were associated with the adsorption mechanism. The cluster-mediated pore filling mechanism was proposed with a special relevance to the evidence on the formation of the ordered water molecular assembly in the carbon micropores by in situ X-ray diffraction.     

Hydrogen adsorption in transition metal carbon nano-structures

Templated microporous carbons were synthesized from metal impregnated zeolite Y templates. Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) were employed to characterize morphology and structure of the generated carbon materials. The surface area, micro- and meso-pore volumes, as well as the pore size distribution of all the carbon materials were determined by N₂ adsorption at 77 K and correlated to their hydrogen storage capacity. All the hydrogen adsorption isotherms were Type 1 and reversible, indicating physisorption at 77 K. Most templated carbons show good hydrogen storage with the best sample Rh-C having surface area 1817 m²/g and micropore volume 1.04 cm³/g, achieving the highest as 8.8 mmol/g hydrogen storage capacity at 77 K, 1 bar. Comparison between activated carbons and synthesized templated carbons revealed that the hydrogen adsorption in the latter carbon samples occurs mainly by pore filling and smaller pores of sizes around 6 Å to 8 Å are filled initially, followed by larger micropores. Overall, hydrogen adsorption was found to be dependent on the micropore volume as well as the pore-size, larger micropore volumes showing higher hydrogen adsorption capacity.     

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。     

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.     

Features of nitrogen adsorption on nonporous carbon and silica surfaces in the framework of classical density functional theory

Equilibrium adsorption data of nitrogen on a series of nongraphitized carbon blacks and nonporous silica at 77 K were analyzed by means of classical density functional theory to determine the solid-fluid potential. The behavior of this potential profile at large distance is particularly considered. The analysis of nitrogen adsorption isotherms seems to indicate that the adsorption in the first molecular layer is localized and controlled mainly by short-range forces due to the surface roughness, crystalline defects, and functional groups. At distances larger than approximately 1.3-1.5 molecular diameters, the adsorption is nonlocalized and appears as a thickening of the adsorbed film with increasing bulk pressure in a relatively weak adsorption potential field. It has been found that the asymptotic decay of the potential obeys the power law with the exponent being -3 for carbon blacks and -4 for silica surface, which signifies that in the latter case the adsorption potential is mainly exerted by surface oxygen atoms. In all cases, the absolute value of the solid-fluid potential is much smaller than that predicted by the Lennard-Jones pair potential with commonly used solid-fluid molecular parameters. The effect of surface heterogeneity on the heat of adsorption is also discussed.     

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.     

ADSORPTION OF BENZOIC ACID AND P-NITROBENZOIC ACID ON A NEW HYPERCROSSLINKED PHENOL GROUP PST ADSORBENT

1.INTRODUCTIONThepolymericadsorbentAmberliteXAD-4isconsideredoneofthemostsuitablepolymericadsorbentsforremovingphenoliccompoundsfromwaterstreams[1,2]becauseitischemicallystable,notsolubleinsolventsandmoreselectiveforaromaticringsduetoitshydrophobicproperties.However,methanol,acetoneoracetonitrile,hastobeusedtoenhancethesurfacecontactbetweenadsorbentandthesolute.DavankovandTsyurupadescribedanewseriesofadsorbents[3,4].Thistechniqueyieldedpolystyrenesorbentsofunusualhypercrosslinkedstructu…     

Adsorption of Carbon Dioxide on Activated Carbon

The adsorption of CO2 on a raw activated carbon A and three modified activated carbon samples B, C, and D at temperatures ranging from 303 to 333 K and the thermodynamics of adsorption have been investigated using a vacuum adsorption apparatus in order to obtain more information about the effect of CO2 on removal of organic sulfur-containing compounds in industrial gases. The active ingredients impregnated in the carbon samples show significant influence on the adsorption for CO2 and its volumes adsorbed on modified carbon samples B, C, and D are all larger than that on the raw carbon sample A. On the other hand, the physical parameters such as surface area, pore volume, and micropore volume of carbon samples show no influence on the adsorbed amount of CO2. The Dubinin-Radushkevich (D-R) equation was the best model for fitting the adsorption data on carbon samples A and B, while the Preundlich equation was the best fit for the adsorption on carbon samples C and D. The isosteric heats of adsorption on carbon samples A, B, C, and D derived from the adsorption isotherms using the Clapeyron equation decreased slightly increasing surface loading. The heat of adsorption lay between 10.5 and 28.4 kJ/mol, with the carbon sample D having the highest value at all surface coverages that were studied. The observed entropy change associated with the adsorption for the carbon samples A, B, and C (above the surface coverage of 7 ml/g) was lower than the theoretical value for mobile adsorption. However, it was higher than the theoretical value for mobile adsorption but lower than the theoretical value for localized adsorption for carbon sample D.     

Hydrogen adsorption on model adsorbents from the viewpoint of the theory of volumetric filling of micropores

Hydrogen adsorption on model microporous adsorbents with slit-shaped pores was calculated on the basis of Dubinin’s theory of volumetric filling of micropores using the property of linearity of adsorption isosters. Model adsorbents with micropore widths of 0.5, 0.9, and 1.2 nm obtained by the successive exclusion of one, two, and three layers of hexagonal carbon in the crystalline lattice of graphite were used. Hydrogen adsorption was calculated in the structures with single-layer and two-layer carbon walls at temperatures 20, 33, 77, 200, 300, and 400 K and pressures up to 20 MPa. The maximal hydrogen desorption for the AU structure (1:3) with the pressure drop from 20 to 0.1 MPa was 8 wt.% at 200K. The parameters of the porous adsorbent structure were calculated.     

Correct procedures for the calculation of heats of adsorption for heterogeneous adsorbents from molecular simulation

Several procedures for calculating the heat of adsorption from Monte Carlo simulations for a heterogeneous adsorbent are presented. Simulations have been performed to generate isotherms for nitrogen at 77 K and methane at 273.15 K in graphitic slit pores of various widths. The procedures were then applied to calculate the heat of adsorption of an activated carbon with an arbitrary pore size distribution. The consistency of the different procedures shows them to be correct in calculating interaction energy contributions to the heat of adsorption. The currently favored procedure for this type of calculation, from the literature, is shown to be incorrect and in serious error when calculating the heat of adsorption of activated carbon.