密度泛函与分子模拟计算介孔孔径分布比较

用巨正则系综Monte Carlo模拟(GCMC)方法和密度泛函理论（ DFT）结合统计积分方程（SIE）计算了介孔材料的孔径分布.为比较这两种方法,以77 K氮气在介孔活性碳微球中的吸附数据为依据,求出其孔径分布.在GCMC模拟和DFT计算中,流体分子模型化为单点的Lerrnard-Jones球;流体分子与吸附剂材料之间的作用采用平均场理论中的10-4-3模型.在DFT方法中,自由能采用Tarazona 提出的加权近似密度泛函方法(weighted density approximation,WDA)求解.结果表明,对于孔径大于1.125 nm的介孔材料,GCMC和DFT两种方法都可以用来研究介孔材料的孔径分布;对于小于1.125 nm的介孔材料,不能用DFT方法计算孔径分布（DFT方法本身的近似产生了误差）,只能用分子模拟方法.     

Sorption thermodynamics of CO2, CH4, and their mixtures in the ITQ-1 zeolite as revealed by molecular simulations

The thermodynamic properties and siting of carbon dioxide and methane sorbed in the siliceous form of zeolite MCM-22, ITQ-1, were studied by means of grand canonical Monte Carlo simulation. ITQ-1 comprises two independent pore systems of different geometry. It was found to be CO(2)-selective toward CO(2)/CH(4) gas mixtures, its equilibrium selectivity being distinctly higher in its sinusoidal channel pore system than in the large cavity system over a wide range of pressures starting from the Henry law regime, at the three temperatures considered. A maximum in selectivity is observed at low temperature, high pressure, and methane-rich gas-phase composition.     

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.     

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.     

Thermodynamics of hydrogen adsorption in slit-like carbon nanopores at 77 K. Classical versus path-integral Monte Carlo simulations

Hydrogen in slit-like carbon nanopores at 77 K represents a quantum fluid in strong confinement. We have used path-integral grand canonical Monte Carlo and classical grand canonical Monte Carlo simulations for the investigation of the "quantumness" of hydrogen at 77 K adsorbed in slit-like carbon nanopores up to 1 MPa. We find that classical simulations overpredict the hydrogen uptake in carbon nanopores due to neglect of the quantum delocalization. Such disagreement of both simulation methods depends on the slit-like carbon pore size. However, the differences between the final uptakes of hydrogen computed from both classical and quantum simulations are not large due to a similar effective size of quantum/classical hydrogen molecules in carbon nanospaces. For both types of molecular simulations, the volumetric density of stored energy in optimal carbon nanopores exceeds 6.4 MJ dm(-3) (i.e., 45 kg m(-3); Department of Energy target for 2010). In contrast to the hydrogen adsorption isotherms, we found a large reduction of isosteric enthalpy of adsorption computed from the quantum Feynman's path-integral simulations in comparison to the classical values at 77 K and pressures up to 1 MPa. Depression of the quantum isosteric enthalpy of adsorption depends on the slit-like carbon pore size. For the narrow pores (pore width H in [0.59-0.7] nm), the reduction of the quantum isosteric enthalpy of adsorption at zero coverage is around 50% in comparison to the classical one. We observed new phenomena called, by us, the quantum confinement-inducing polymer shrinking. In carbon nanospaces, the quantum cyclic polymers shrink, in comparison to its bulk-phase counterpart, due to a strong confinement effect. At considered storage conditions, this complex phenomenon depends on the size of the slit-like carbon nanopore and the density of hydrogen volumetric energy. For the smallest nanopores and a low density of hydrogen volumetric energy, the reduction of the polymer effective size is the highest, whereas an increase of the pore size and the density of hydrogen volumetric energy causes the polymer swelling up to a value slightly below the one computed from the bulk phase. Quantum confinement-inducing polymer shrinking is of great importance for realizing the potential of quantum molecular sieves.     

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.     

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.     

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.     

Characterization of micro-mesoporous materials from nitrogen and toluene adsorption: experiment and modeling

Universal mechanisms of adsorption and capillary condensation of toluene and nitrogen on ordered MCM-41 and PHTS materials are studied by means of high-resolution experiments and Monte Carlo molecular simulations. A molecular simulation model of toluene adsorption in silica nanopores, which accounts for surface heterogeneity, and a hybrid molecular-macsroscopic method for pore size distribution (PSD) calculations have been developed. For a range of reference materials, the PSD results obtained from toluene isotherms are consistent with the results of nitrogen adsorption using the nonlocal density functional theory method.     

超临界甲烷在纳米材料中最适吸附压力的确定

用巨正则Monte Carlo (GCMC)方法模拟了超临界甲烷在层柱纳米材料中的吸附.模拟中,层柱纳米材料采用了柱子均匀分布在层板间的模型, 非极性分子甲烷采用Lennard Jones分子模型, 层板墙采用Steele的10 4 3模型, 流体分子与柱子的相互作用采用点 点 (site to site) 的方法计算.得到了甲烷的随着压力先增大后减小的超额吸附等温线.在T=207.3 K时,1.02、1.70和2.38 nm孔宽对应的最适操作压力 (即对应于最大吸附量时的操作压力) 分别为2.4、3.1和3.7 MPa.然而,在T=237.0 K时,1.02、1.70和2.38 nm孔宽对应的最适操作压力分别为2.9、3.6和4.9 MPa,分别比T=207.3 K时相同孔宽下对应的最适操作压力至少高0.5 MPa. 模拟结果表明, GCMC方法是研究材料吸附性能的一种强有力的工具.     

Effect of open metal sites on adsorption of polar and nonpolar molecules in metal-organic framework Cu-BTC

Atomistic grand canonical Monte Carlo simulations were performed in this work to investigate the role of open copper sites of Cu-BTC in affecting the separation of carbon monoxide from binary mixtures containing methane, nitrogen, or hydrogen. Mixtures containing 5%, 50%, or 95% CO were examined. The simulations show that electrostatic interactions between the CO dipole and the partial charges on the metal-organic framework (MOF) atoms dominate the adsorption mechanism. The binary simulations show that Cu-BTC is quite selective for CO over hydrogen and nitrogen for all three mixture compositions at 298 K. The removal of CO from a 5% mixture with methane is slightly enhanced by the electrostatic interactions of CO with the copper sites. However, the pore space of Cu-BTC is large enough to accommodate both molecules at their pure-component loadings, and in general, Cu-BTC exhibits no significant selectivity for CO over methane for the equimolar and 95% mixtures. On the basis of the pure-component and low-concentration behavior of CO, the results indicate that MOFs with open metal sites have the potential for enhancing adsorption separations of molecules of differing polarities, but the pore size relative to the sorbate size will also play a significant role.     

空气中微量1,1,1,2-四氟乙烷吸附分离的分子模拟

利用实验和巨正则系综蒙特卡罗(GCMC)方法研究了N2/HFC-134a(1,1,1,2-四氟乙烷)二元混合物在活性碳纤维(ACF)内的吸附分离.重点讨论了孔径、压强及温度对HFC-134a吸附选择性的影响,为不同条件下吸附空气中的微量HFC-134a提供了理论参考.结果表明:较小孔径、低压以及低温条件有利于HFC-134a的吸附分离.在常温下,HFC-134a在带有孔径分布的活性碳纤维材料内的吸附选择性可以达到62,表明我们所制备的活性碳纤维材料可以较好地分离空气中微量的HFC-134a.特别地,在常温和0.41×105Pa下,0.75nm的碳孔对HFC-134a的吸附选择性达到了230.因此,为了有效地吸附空气中的HFC-134a,推荐使用小孔径的碳材料.     

Water in carbon nanotubes: adsorption isotherms and thermodynamic properties from molecular simulation

Grand canonical Monte Carlo simulations are performed to study the adsorption of water in single-walled (6:6), (8:8), (10:10), (12:12), and (20:20) carbon nanotubes in the 248-548 K temperature range. At room temperature the resulting adsorption isotherms in (10:10) and wider single-walled carbon nanotubes (SWCNs) are characterized by negligible water uptake at low pressures, sudden and complete pore filling once a threshold pressure is reached, and wide adsorption/desorption hysteresis loops. The width of the hysteresis loops decreases as pore diameter narrows and it becomes negligible for water adsorption in (8:8) and (6:6) SWCNs. Results for the isosteric heat of adsorption, density profiles along the pore axis and across the pore radii, order parameter across the pore radii, and x-ray diffraction patterns are presented. Layered structures are observed when the internal diameter of the nanotubes is commensurate to the establishment of a hydrogen-bonded network. The structure of water in (8:8) and (10:10) SWCNs is ordered when the temperature is 298 and 248 K, respectively. By simulating adsorption isotherms at various temperatures, the hysteresis critical temperature, e.g., the lowest temperature at which no hysteresis can be detected, is determined for water adsorbed in (20:20), (12:12), and (10:10) SWCNs. The hysteresis critical temperature is lower than the vapor-liquid critical temperature for bulk Simple Point Charge-Extended (SPCE) water model.     

Adsorption of argon from sub- to supercritical conditions on graphitized thermal carbon black and in graphitic slit pores: a grand canonical Monte Carlo simulation study

In this paper we consider the adsorption of argon on the surface of graphitized thermal carbon black and in slit pores at temperatures ranging from subcritical to supercritical conditions by the method of grand canonical Monte Carlo simulation. Attention is paid to the variation of the adsorbed density when the temperature crosses the critical point. The behavior of the adsorbed density versus pressure (bulk density) shows interesting behavior at temperatures in the vicinity of and those above the critical point and also at extremely high pressures. Isotherms at temperatures greater than the critical temperature exhibit a clear maximum, and near the critical temperature this maximum is a very sharp spike. Under the supercritical conditions and very high pressure the excess of adsorbed density decreases towards zero value for a graphite surface, while for slit pores negative excess density is possible at extremely high pressures. For imperfect pores (defined as pores that cannot accommodate an integral number of parallel layers under moderate conditions) the pressure at which the excess pore density becomes negative is less than that for perfect pores, and this is due to the packing effect in those imperfect pores. However, at extremely high pressure molecules can be packed in parallel layers once chemical potential is great enough to overcome the repulsions among adsorbed molecules.     

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。     

Structures and adsorption of binary hard-core Yukawa mixtures in a slitlike pore: grand canonical Monte Carlo simulation and density-functional study

The grand canonical ensemble Monte Carlo simulation and density-functional theory are applied to calculate the structures, local mole fractions, and adsorption isotherms of binary hard-core Yukawa mixtures in a slitlike pore as well as the radial distribution functions of bulk mixtures. The excess Helmholtz energy functional is a combination of the modified fundamental measure theory of Yu and Wu [J. Chem. Phys. 117, 10156 (2002)] for the hard-core contribution and a corrected mean-field theory for the attractive contribution. A comparison of the theoretical results with the results from the Monte Carlo simulations shows that the corrected theory improves the density profiles of binary hard-core Yukawa mixtures in the vicinity of contact over the original mean-field theory. Both the present corrected theory and the simulations suggest that depletion and desorption occur at low temperature, and the local segregation can be observed in most cases. For binary mixtures in the hard slitlike pore, the present corrected theory predicts more accurate surface excesses than the original one does, while in the case of the attractive pore, no improvement is found in the prediction of a surface excess of the smaller molecule.     

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.     

Molecular beam measurements and Monte Carlo simulations of the kinetics of N2O decomposition on Rh(111) single-crystal surfaces

The kinetics of N2O decomposition on Rh(111) single-crystal surfaces were investigated both experimentally by isothermal molecular beam measurements and theoretically using a Monte Carlo algorithm. The present work was directed to the understanding of two unusual observations derived from our previous work on this system, namely, (1) the lower rates for N2O decomposition seen at higher reaction temperatures, and (2) the lower total nitrogen yields and final oxygen surface coverages that accompany that behavior. Experimentally, it was determined here that after the rhodium surface is rendered inactive by N2O decomposition at high (520 K) temperatures, significant activity is still possible at lower (350 K) temperatures. The Monte Carlo simulations explain these observations by assuming that the surface sites required for the activation of adsorbed N2O increase in size with increasing reaction temperature.