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.     

Investigation of activated carbon surface heterogeneity by argon and nitrogen low-pressure quasi-equilibrium volumetry

Surface heterogeneity can be assessed by adsorption of different gaseous probes on solid materials. In the present study, four types of activated carbons were analyzed by classical N2 Brunauer-Emmett-Teller (BET) measurements and by low-pressure quasi-equilibrium volumetry (LPQEV) (Villieras, F.; Michot, L. J.; Bardot, F.; Cases, J. M.; Francois, M.; Rudzinski, W. Langmuir 1997, 13, 1104). Three methods of data evaluation were applied: (a) the Frenkel-Halsey-Hill method for estimation of fractal dimensions from BET data, (b) the Horwath-Kawazoe method to calculate the pore size distribution from LPQEV Ar and N2 adsorption isotherms, and (c) the derivative isotherm summation (DIS) method to describe the solid's surface heterogeneity by a concept of local derivative isotherms. Similar Ar and N2 adsorption energy distributions were obtained on all carbons, which indicates the presence of mainly nonpolar surfaces. When adsorption was described by the van der Waals equation, the ratio between the interaction energy of different energetic sites with argon and nitrogen was 0.88. This value corresponded very well with a slope obtained when Ar and N2 positions of local isotherms by the DIS method were compared. This relationship has an important impact because it enables one to constrain the modeling of local isotherms. This study, besides the surface information, showed large possibilities of the DIS method for the surface analysis not only in terms of solid heterogeneity characterization but also in terms of polarity assessment.     

What is the correct form of BET isotherm for modeling liquid phase adsorption?

In this work subtleties of application of BET isotherm for liquid phase adsorption is presented. It has been shown that direct use of the classical BET equation (which was developed for gas phase adsorption) to liquid phase adsorption leads to ambiguous and erroneous results. Some cases of misuse of BET equation for liquid phase adsorption have been revisited. By close examination of the development of the classical equation, the causes of misunderstandings were elucidated and the suitable form of the BET equation for liquid phase adsorption was developed. As case studies, the classical form of the BET equation along with the correct form of the equation for liquid phase have been applied for modeling liquid phase adsorption of methyl tert-butyl ether (MTBE) on perfluorooctyl alumina, phenol on activated carbon and pentachlorophenol on carbonized bark. It has been shown that direct application of the classical BET isotherm to liquid phase adsorption results in poor and erroneous estimation of the equation parameters. For example, in aqueous phase adsorption of MTBE on perfluorooctyl alumina, the monolayer adsorption capacity of the adsorbent was calculated as 9.7 mg/g instead of 3.3 mg/g or the saturation concentration of MTBE in water was calculated as 1212 mg/L instead of 42000 mg/L.     

A new integrated method for characterizing surface energy heterogeneity from a single adsorption isotherm

To characterize surface energy heterogeneity of fine particles, this paper presents an integrated strategy from a single adsorption isotherm. By coupling the well-known integral equation method and derivative isotherm summation (DIS) procedure based on a patchwise model, the newly proposed strategy could calculate adsorption energy distributions (AEDs) for different surface patches. Correspondingly, the surface heterogeneity of materials can be described by weighted summation of patch AEDs, that is, the total AED. The validity of this new method is confirmed by both tests of rutile nanoparticles and multiwalled carbon nanotubes (MWNTs). The total AED obtained by the new method agrees well with the result from solving the integral equation directly, and it shows that AED peaks can be assigned to specific energy patches of real surface exactly. Furthermore, a detailed comparison showed that some artificial oscillation in the results can be identified with the new strategy, and the patches with low area and high surface energy could be characterized as well. In conclusion, this strategy constructs a correspondence between derived AEDs and different patches of real surface, so it will be more effective to understand surface heterogeneity by using the adsorption probe method.     

The effect of heat treatment on the adsorption properties of solids. II. The effect of heat treatment on the character of the adsorption isotherm

In this study the nitrogen adsorption isotherms of heat-treated zinc oxalate, sintered magnesium oxide, and some oxidised pitch resins are considered. It is shown that characterisation of the adsorption isotherm can be via the monolayer capacity, the BET constant C, or plots of the degree of coverage of the surface at various relative vapour pressures. These parameters are critically assessed and shown to be dependent upon the closeness to the manner in which the complete adsorption isotherm is described by the BET equation. In considering the complete adsorption isotherm it is considered best to characterise the adsorption data by quoting the statistical monolayer capacity and the value of C at this point on the adsorption isotherm. The adsorption isotherms are then best compared by plotting as the number of statistical layers against the relative pressure. The further characterisation by plotting the apparent variation in C or the degree of coverage of the surface against the relative pressure has a usefulness if the limitations of the method are noted.     

Modeling of the hysteresis phenomena in finite-sized slitlike nanopores. Revision of the recent results by rigorous numerical analysis

The systematic investigation of the hysteresis phenomena in finite-sized slitlike nanopores via the Aranovich-Donohue (AD) lattice density functional theory (LDFT) is presented. The new reliable quantitative modeling of the adsorption and desorption branch of the hysteresis loop, through the formation and movement of the curved meniscus, is formulated. As a result, we find that our proposal, which closely mimics the experimental findings, can reproduce a rounded shape of the desorption branch of the hysteresis loop. On the basis of the exhausted commutations, we proved that the hysteresis loop obtained in the considered finite-sized slitlike geometry is of the H1 type of the IUPAC classification. This fundamental result and the other most important results do not confirm the results of the recent studies of Sangwichien et al., whereas they fully agree with the recent lattice studies due to Monson et al. We recognize that the nature of the hysteresis loops (i.e. position, width, shape, and the multiple steps) mainly depends on the value of the energy of both the adsorbate-adsorbate and adsorbate-adsorbent interactions; however, the first one is critical for the appearance of hysteresis. Thus, for relatively small adsorbate-adsorbate interactions, the adsorption-desorption process is fully reversible in the whole region of the bulk density. We show that the strong adsorbate-adsorbent interactions produce (also observed experimentally) multiple steps within hysteresis loops. Contrary to the other studies of the hysteresis phenomena in confined geometry via the LDFT formalism, we constructed both ascending and descending scanning curves, which are known from the experimental observations. Additionally, we consider the problem of the stability of both the obtained adsorption and desorption branches of the computed hysteresis loop in finite-sized slitlike nanopores.     

A density functional theory for Lennard-Jones fluids in cylindrical pores and its applications to adsorption of nitrogen on MCM-41 materials

A density functional theory (DFT) constructed from the modified fundamental-measure theory and the modified Benedict-Webb-Rubin equation of state is presented. The Helmholtz free energy functional due to attractive interaction is expressed as a functional of attractive weighted-density in which the weight function is a mean-field-like type. An obvious advantage of the present theory is that it reproduces accurate bulk properties such as chemical potential, bulk pressure, vapor-liquid interfacial tension, and so forth when compared with molecular simulations and experiments with the same set of molecular parameters. Capabilities of the present DFT are demonstrated by its applicability to adsorption of argon and nitrogen on, respectively, a model cylindrical pore and mesoporous MCM-41 materials. Comparison of the theoretical results of argon in the model cylindrical pore with those from the newly published molecular simulations indicates that the present DFT predicts accurate average densities in the pore, slightly overestimates the pore pressure, and correctly describes the effect of the fluid-pore wall interaction on average densities and pressures in the pore. Application to adsorption of nitrogen on MCM-41 at 77.4 K shows that the present DFT predicts density profiles and adsorption isotherms in good agreement with those from molecular simulations and experiments. In contrast, the hysteresis loop of adsorption calculated from the mean-field theory shifts toward the low pressure region because a low bulk saturated pressure is produced from the mean-field equation of state. The present DFT offers a good way to describe the adsorption isotherms of porous materials as a function of temperature and pressure.     

Adsorption integral equation via complex approximation with constraints: kernel of general form

For the monolayer adsorption on a homogeneous surface, including arbitrary range lateral interactions, the isotherm can be written as a power series of the Langmuir isotherm. If this isotherm is used as the kernel in the adsorption integral equation, this integral equation can be solved in an analytical form. Because the global isotherm is usually known as a set of experimental values, the use of a numerical method is inevitable. A new numerical method for solving the adsorption integral equation with a kernel of general form is developed. It is based on recent results concerning the structure of the local isotherm and on the ideas of complex approximation with constraints, and allows reduction of the problem under consideration to a linear‐quadratic programming problem. Results of numerical experiments are presented. The method can be useful for the evaluation of the adsorption energy distribution from experimental data. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1058–1066, 2001     

Interpretation of negative values of the interaction parameter in the adsorption equation through the effects of surface layer heterogeneity

The problem of the negative values of the interaction parameter in the equation of Frumkin has been analyzed with respect to the adsorption of nonionic molecules on energetically homogeneous surface. For this purpose, the adsorption states of a homologue series of ethoxylated nonionic surfactants on air/water interface have been determined using four different models and literature data (surface tension isotherms). The results obtained with the Frumkin adsorption isotherm imply repulsion between the adsorbed species (corresponding to negative values of the interaction parameter), while the classical lattice theory for energetically homogeneous surface (e.g., water/air) admits attraction alone. It appears that this serious contradiction can be overcome by assuming heterogeneity in the adsorption layer, that is, effects of partial condensation (formation of aggregates) on the surface. Such a phenomenon is suggested in the Fainerman-Lucassen-Reynders-Miller (FLM) "Aggregation model". Despite the limitations of the latter model (e.g., monodispersity of the aggregates), we have been able to estimate the sign and the order of magnitude of Frumkin's interaction parameter and the range of the aggregation numbers of the surface species.     

生物质碳材料的孔道分析

生物质碳材料的孔道类型和孔径大小制约着材料有效的活性位点数量,影响材料的性能。孔道分类又是孔径分析的前提条件。因此,建立孔道分类的方法非常有意义。随着生物质碳材料的深入研究,研究者对其孔道分析的要求逐渐提高。他们用实际的吸脱附等温线与IUPAC规范中的吸脱附等温线进行匹配,来分类生物质碳材料的孔道。然而实际的吸脱附等温线具有不规则性,难以匹配IUPAC规范中的吸脱附等温线。所以,本文提出了孔隙率和比表面积占有率的孔道分类新方法。自制生物质碳材料,运用物理吸附仪和TEM (Transmission electron microscope)对其进行表征,采用BET方程（Brunauer-Emmett-Teller）、t-plot方法(Thickness-plot)、DFT方法（Non-local Density Functional Theory）、BJH（Barrett Joyner and Halenda）方法对其孔道进行分析。研究表明,采用孔隙率和比表面积占有率对其进孔道分类,可以准确的定义出微孔生物质碳材料、介孔生物质碳材料和微介孔生物质碳材料。本文用标准样品对孔隙率和比表面积占有率的孔道分类新方法进行论证,结果一致。因此,本文提出的孔隙率和比表面积占有率的孔道分类新方法准确可靠,实用性高。     

Variation in surface energy heterogeneity of graphite due to adsorption of polyoxyethylene sorbitan monooleate

The heterogeneity of surface energy of graphite before and after adsorption of polyoxyethylene sorbitan monooleate (Tween80) was investigated by the nitrogen adsorption technique. The nitrogen adsorption energy distributions (AEDs) were calculated from the low-pressure isotherm data (i.e., the data of submonolayer adsorption) according to the regularization method. Based on the AED of pristine graphite, two types of dominant energetic surface are identified and assigned respectively to the basal surface and the irregular surface, including the stepped edges and defect sites. When the adsorption amount of Tween80 is raised, both the surface energy and the energy heterogeneity of graphite gradually decline. It is thus demonstrated that Tween80 prefers interacting with and screening higher energetic surfaces to lower ones.     

Kinetic derivation of common isotherm equations for surface and micropore adsorption

The Langmuir equation is one of the most successful adsorption isotherm equations, being widely used to fit Type I adsorption isotherms. In this article we show that the kinetic approach originally used by Langmuir for 2D monolayer surface adsorption can also be used to derive a 1D analogue of the equation, applicable in ultramicropores with single-file diffusion. It is hoped that such a demonstration helps dispel the idea that the Langmuir isotherm equation cannot apply to some micropores as more than a mathematical correlation. We furthermore seek to extend the insight provided by the simple kinetic derivation of the Langmuir equation to other isotherm equations capable of modelling Type I isotherms. The same kinetic approach is thus also used to derive the Volmer, Fowler–Guggenheim and Hill–de Boer equations, both for surface (2D adsorbed phase) and micropore adsorption (1D and 3D adsorbed phases). It is hoped that this will help make more intuitively clear that these equations can be used as phenomenological models in some instances of adsorption in micropores.     

A density functional theory approach to noncovalent interactions via interacting monomer densities

A recently proposed "DFT + dispersion" treatment (Rajchel et al., Phys. Rev. Lett., 2010, 104, 163001) is described in detail and illustrated by more examples. The formalism derives the dispersion-free density functional theory (DFT) interaction energy and combines it with the dispersion energy from separate DFT calculations. It consists of the self-consistent polarization of DFT monomers restrained by the exclusion principle via the Pauli blockade technique. Within the monomers a complete exchange-correlation potential should be used, but between them only the exact exchange operates. The application to a wide range of molecular complexes from rare-gas dimers to hydrogen-bonds to π-electron interactions shows good agreement with benchmark values.     

Equilibrium and Kinetic Modelling of Adsorption of Phosphorus on Calcined Alunite

The adsorption of phosphorus onto calcined alunite has been studied. Its equilibrium isotherm has been measured. The isotherm was determined by shaking 1.0 g calcined alunite, particle size range 90–150 m, with 100 mL phosphorus solution of initial concentrations from 0.5 to 2.5 mmol/L. The water bath shaking a constant rate of 200-rpm was used and the temperature maintained at 298 ± 2 K. A contact time of 120 min was required to achieve equilibrium. The experimental isotherm data were analyzed using the Langmuir, Freundlich, Temkin and Dubinin-Radushkevich equations. The monolayer adsorption capacity is 1.355 mmol P per g calcined alunite. Three simplified kinetic models including a pseudo first-order equation, pseudo second-order equation and intraparticle diffusion equation were selected to follow the adsorption process. Kinetic parameters, rate constants, equilibrium sorption capacities and related correlation coefficients, for each kinetic model were calculated and discussed. It was shown that the adsorption of phosphorus could be described by the pseudo second-order equation.     

Examination of the surface heterogeneity of reversed-phase packing materials with solvent adsorption

The adsorption isotherms of acetonitrile, ethanol, 2-propanol, and THF were measured using frontal analysis on six columns packed with octadecyl RP stationary phase. The effect of the bonding density of the end-capped octadecyl bonded phase on the adsorption properties was measured. Adsorption isotherm data were collected from aqueous solutions of the four organic modifiers. The isotherm model for solvent adsorption was selected using two independent parameter estimation methods, the regression analysis and adsorption energy distribution. The fitted isotherm parameters were tested by modeling of overloaded elution bands with the aid of the equilibrium-dispersive model of chromatography. The surface heterogeneity estimations and the effect of the silanol groups on the adsorption of solvents were based on those data.     

吸附与润湿II.Triton X-100和Triton x-305在炭黑/水和炭黑/环己烷界面上的吸附层结构

测定了15℃和30℃时炭黑自水和环己烷中吸附非离子型表面活性剂TritonX-100和Triton X-305的等温线;计算了吸附过程的标准热力学函数;测定了石墨/水/环己烷和石墨/水/空气的接触角与表面活性剂浓度的关系, 分析所得结果,可得结论:在炭黑/水或石墨/水界面上,Triton型表面活性分子形成单分子吸附层,分子以憎水的iso-C8H17C6H4基团附着在表面,而以亲水的聚氧乙烯链伸入水相的方式取向;在炭黑/环已烷或石墨/环己烷界面上,分子是通过聚氧乙烯链吸附到表面上的,当浓度增加时分子在表面可能通过聚氧乙烯链间的相互作用而发生聚集,即可能形成表面反式胶团。