Nonlocal density functional theory NLDFT

Thus, either type I or type IV isotherms are obtained in sorption experiments on microporous or mesoporous materials. Of course, a material may contain both types of pores. In this case, a convolution of a type I and type IV isotherm is observed. From the amount of gas that is adsorbed in the micropores of a material, the micropore volume is directly accessible (e.g., from t plot of as plot [1]). The low-pressure part of the isotherm also contains information on the pore size distribution of a given material. Several methods have been proposed for this purpose (e.g., Horvath-Kawazoe method) but most of them give only rough estimates of the real pore sizes. Recently, nonlocal density functional theory (NLDFT) was employed to calculate model isotherms for specific materials with defined pore geometries. From such model isotherms, the calculation of more realistic pore size distributions seems to be feasible provided that appropriate model isotherms are available. The mesopore volume of a mesoporous material is also rather easy accessible. Barrett, Joyner, and Halenda (BJH) developed a method based on the Kelvin equation which allows the calculation of the mesopore size distribution and respective pore volume. Unfortunately, the BJH algorithm underestimates pore diameters, especially at... 

The nonlocal density functional theory (NLDFT) has been used to characterize mesocaged structures.[164] NLDFT analysis gives accurate information about the cage size, the total meso- and micropore volumes and surface area, and the pore-wall thickness in combination with XRD measurements. Argon- and nitrogen-desorption data on FDU-1 provided evidence that there are two major populations of pore entrances. Argon desorption was superior in providing information about pore connectivity in FDU-1 samples. 

G activated carbon (points) with the fit given by the nonlocal density functional theory (NLDFT) models (line), (b) The pore width distribution for the carbon. 

Figure 7.10 The average pore fluid density in pores of various widths as calculated hy nonlocal density functional theory (NLDFT). Note the periodic nature of the density, with density maxima near the positions of the minima in the distrihutions shown in Figs 7.8(h) and 7.9(h).

The solid line is calculated by the nonlocal density functional theory (NLDFT), which will be described to some detail in Section 11.4. As seen in the figure, the curve obtained with the HK method (dashed fine) correlates with NLDFT much better than that calculated with the Kelvin equation (dash-dotted line). 

This would allow performing accurate PSD calculations using these simple algorithms. Theoretical considerations [13], nonlocal density functional theory (NLDFT) calculations [62, 146], computer simulations [147], and studies of the model adsorbents [63, 88] strongly suggested that the Kelvin equation commonly used to provide a relation between the capillary condensation or evaporation pressure and the pore size underestimates the pore size. 

Beside classical methods of pore size analysis, there are many advanced methods. Seaton et al. [161] proposed a method based on the mean field theory. Initially this method was less accurate in the range of small pore sizes, but even so it g ve a more realistic -way for evaluation of the pore size distribution than the classical methods based on the Kelvin equation [162]. More rigorous methods based on molecular approaches such as grand canonical Monte Carlo (GCMC) simulations [147, 163-165] and nonlocal density functional theory (NLDFT) [86, 146, 147, 161, 163-169] have been developed and their use for pore size analysis of active carbons is continuously growing. 

Finn and Monson [139] first tested the predictability of IAS theory for binary systems using the isothermal isobaric Monte Carlo simulation on a single surface. However, this system does not represent real adsorption systems. Tan and Gubbins [140,141] conducted detailed studies on the binary equilibria of the methane-ethane system in slit-shaped micropores using the nonlocal density function theory (NLDFT). The selectivity of ethane to methane was studied in terms of pore width, temperature, pressure, and molar fractions. 

HCP-l,4-benzenedimethanol (HCP-BDM) and HCP-ben l alcohol (HCP-BA) networks synthesized by the Friedel-Crafts self-condensation method have shown high selectivity for CO2 over N2, measured by nitrogen adsorption isotherm at two different temperatures, 273 and 298 Nonlocal density functional theory (NLDFT) calculations confirmed the pore sizes to be below 2 nm for both of the networks. Such small pore sizes, as well as the high ojq gen content in both the polymers, is most probably tbe reason for the strong interactions with polar CO2 rather than N2, making these good candidates for the selective separation of CO2 from N2. 

Note that several variants of the above functional (i.e., Eq. 41) exist. Instead of using WDA for treating as shown in Eq. (43), the EDA can also be appHed which provides comparable accuracy as discussed by Fu et al. (2015a). In addition, if we simply ignore this correlation term F ot and apply WCA scheme for the decomposition of repulsion and attraction in the LJ potential, the above combined functional recovers to the so-called nonlocal density functional theory (NLDFT) initiated by Balbuena and Gubbins (1993) and extensively appfred by Neimark et al. (Landers et al., 2013 Olivier et al., 1994). 

The use of nonlocal density functional theory (NLDFT) for modeling adsorption isotherms of Lennard-Jones (LJ) fluids in porous materials is now well-established [1-5], and is central to modem characterization of nanoporous carbons as well as a variety of other adsorbent materials [1-3]. The principal concept here is that in confined spaces the potential energy is related to the size of the pore [6], thereby permitting a pore size distribution (PSD) to be extracted by fitting adsorption isotherm data. For carbons the slit pore model is now well established, and known to be applicable to a variety of nanoporous carbon forms, where the underlying micro structure comprises a disordered aggregate of crystallites. Such slit width distributions are then useful in predicting the equilibrium [1-5] and transport behavior [7,8] of other fluids in the same carbon. 

Because of the present availability of commercial software, the nonlocal version of density functional theory (i.e., NLDFT) is now widely used for pore... 

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