Density functional theory adsorption models

Figure 7.5 (a) A comparison of experimental data for nitrogen adsorbed at 77 K on Vulcan 3-G(2700) (points) with the fit given by the modified nonlocal density functional theory (MNLDFT) models (line), (b) The adsorptive potential distribution for the Vulcan 3 graphite. 

Fig. 4.14 a N2 sorption isotherms (solid circles adsorption open circles desorption) and b pore size distributions of PAF-1 and PAF-1-350, PAF-1-380, PAF-1-400, PAF-1-450 derived from N2 adsorption calculated by density functional theory (DFT) model, respectively... 

We suggest a model of adsorption in pores with amorphous and microporous solid walls, named the quenched solid non-local density functional theory (QSNLDFT) model. We consider a multicomponent non-local density functional theory (NLDFT), in which the solid is treated as a quenched component with a fixed spatially distributed density. Drawing on several prominent examples, we show that QSNLDFT model produces smooth Isotherms of mono- and polymolecular adsorption, which resemble experimental isotherms on amorphous surfaces. The model reproduces typical behaviors of N2 isotherms on micro- mesoporous materials, such as SBA-15. QSNLDFT model offers a systematic approach to the account for the surface roughness/heterogeneity in pore structure characterization methods. 

If the elements Cn and FI (element 114) have a noble-gas like character [54], then, in a fictitious solid state, they would form non-conducting colorless crystals. A physisorptive type of adsorption may occur and their adsorption properties, for example on quartz, can be calculated with this method, see Table 3. For physi-sorbed noble gas atoms a roughly uniform distance to different surfaces of about 2.47 0.2 A was deduced from experimental results [47]. A predicted value of the adsorption properties of HSO4 was based on this model in [37]. In conjunction with molecular and elemental data, which were calculated using density functional theory, this model yields valuable predictive results see chapter Theoretical Chemistry of the Heaviest Elements . 

Figure 6.36. Calculated variation in the heats of adsorption of molecular CO and NO compared with the heats of adsorption of the dissociation products. Open symbols follow from the Newns— Anderson model, closed symbols from density functional theory. [Adapted from B. Hammer and J.K. N0rskov, Adv. Catal. 45 (2000) 71.]...

Using perturbation theory. Hammer and Nprskov developed a model for predicting molecular adsorption trends on the surfaces of transition metals (HN model). They used density functional theory (DFT) to show that molecular chemisorption energies could be predicted solely by considering interactions of a molecule s HOMO and LUMO with the center of the total d-band density of states (DOS) of the metal.In particular. 

The measured electronic structure, occupied or unoccupied, provides the fullest information when also combined with theory. Electronic structure calculations in surface chemistry have advanced immensely in the past decades and have now reached a level of accuracy and predictive power so as to provide a very strong complement to experiment. Indeed, the type of theoretical modeling that will be employed and presented here can be likened to computer experiments, where it can be assumed that spectra can be computed reliably and thus computed spectra for different models of the surface adsorption used to determine which structural model is the most likely. In the present chapter, we will thus consistently use the interplay between experiment and theory in our analysis of the interaction between adsorbate and substrate. Before discussing what quantities are of interest to compute in the analysis of the surface chemical bond, we will briefly discuss and justify our choice of Density Functional Theory (DFT) as approach to spectrum and chemisorption calculations. 

A database of molecularly adsorbed species on various surfaces is also included (see Table 4.3). In all cases, the chemisorption energies have been calculated on stepped surfaces using density functional theory (see [56] for details). The metals have been modeled by slabs with at least three close-packed layers. The bcc metals are modeled by the bcc(210) surface and the fee and hep metals have been modeled by the fcc(211) surface. A small discrepancy between the adsorption on the hep metals in the fcc(211) structure is thus expected when the results are compared to the adsorption energies on the correct stepped hep structure instead. When mixing... 

Olivier JP. Modeling physical adsorption on porous and nonporous solids using density functional theory. J. Porous Mat., 1995 2(1) 9-17. 

As expected, the total interaction energies depend strongly on the van der Waals radii (of both sorbate and sorbent atoms) and the surface densities. This is true for both HK type models (Saito and Foley, 1991 Cheng and Yang, 1994) and more detailed statistical thermodynamics (or molecular simulation) approaches (such as Monte Carlo and density functional theory). Knowing the interaction potential, molecular simulation techniques enable the calculation of adsorption isotherms (see, for example, Razmus and Hall, (1991) and Cracknell etal. (1995)). 

The density functional theory and the cluster model approach enable the quantitative computational analysis of the adsorption of small chemical species on metal surfaces. Two studies are presented, one concerning the adsorption of acetylene on copper (100) surfaces, the other concerning the adsorption of ethylene on the (1(X)) surfaces of nickel, palladium and platinum. These studies support the usefulness of the cluster model approach in studies of heterogeneous catalysis involving transition metal catalysts. 

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

The Horvath-Kawazoe (HK) method is capable of generating model isotherms more efficiently than either molecular simulation (MS) or density functional theory (DFT) to characterize the pore size distribution (PSD) of microporous solids. A two-stage HK method is introduced that accounts for monolayer adsorption in mesopores prior to capillary condensation. PSD analysis results from the original and two-stage HK models are evaluated. 

The methods depend on the theoretical treatment which is used. A majority of them are based on the Generalised Adsorption Isotherm (GAI) also called the Integral Adsorption Equation (LAE). The more recent approaches use the Monte Carlo simulations or the density functional theory to calculate the local adsorption isotherm. The analytical form of the pore size distribution function (PSD) is not a priori assumed. It is determined using the regularization method [1,2,3]. Older methods use the Dubinin-Radushkevich or the Dubinin-Astakhov models as kernel with a gaussian or a gamma-type function for the pore size distribution. In some cases, the generalised adsorption equation can be solved analytically and the parameters of the PSD appear directly in the isotherm equation [4,5,6]. Other methods which do not rely on the GAI concept are sometimes used the MP and the Horvath-Kawazoe (H-K) methods are the most well known [7,8]. 

Textural Parameters. Adsorption-desorption isotherms of N2 at 77K were determined in a Micromeritics ASAP 2010 with a micropore system. Prior to measurement, the samples were outgassed at 140 C for at least 16 h. The specific surface area was determined by the BET method, assuming that the area of a nitrogen molecule is 0.162 nm [12]. Micropore volume was calculated by the t-plot method using the Harkins and Jura [13] thickness. We used model isotherms calculated from density functional theory (DFT) to determine the pore size distributions and cumulative pore volume of the pillared samples by taking the adsorption branch of the experimental nitrogen isotherm, assuming slit-like pores [14]. 

The Ne adsorption isotherms on model AIPO4-5 micropores were calculated from the Tarazona s version of the nonlocal density functional theory [34,35] which has beer actually applied to the study on micropore filling [36,37]. The necessary parameters were obtained fram the adsorption isotherms of Ne on AIPO4-S at 27K and 30K in a lov pressure range. 

Lastoskie, C.M., Gubbins, K.E. and Quiike, N.J., Pore size distribution analysis of microporous carbons a density functional theory approach. J. Phys. Chem. 97 (1993) 4786. Olivier, J.P., Modeling physical adsorption on porous and nonporous solids using density functional theoiy. J. Porous Materials 2 (1995) 9. 

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