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 of graphitized 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.

Capillary phenomena in the framework of the two-dimensional density functional theory

We present results of application of the density functional theory (DFT) to adsorption and desorption in finite and infinite cylindrical pores accounting for the density distribution in radial and axial directions. Capillary condensation via formation of bridges is considered using canonical and grand canonical versions of the 2D DFT. The potential barrier of nucleation is determined as a function of the bulk pressure and the pore diameter. In the framework of the conventional assumptions on intermolecular interactions both 1D and 2D DFT versions lead to the same results and confirm the classical scenario of condensation and evaporation: the condensation occurs at the vapor-like spinodal point, and the evaporation corresponds to the equilibrium transition pressure. The analysis of experimental data on argon and nitrogen adsorption on MCM-41 samples seems to not completely corroborate this scenario, with adsorption branch being better described by the equilibrium pressure - diameter dependence. This points to the necessity of the further development of basic representations on the hysteresis phenomena.

Van der Waals-corrected density functional theory: benchmarking for hydrogen-nanotube and nanotube-nanotube interactions

Density functional theory (DFT) is a powerful approach to electronic structure calculations in extended systems, but suffers currently from inadequate incorporation of long-range dispersion, or Van der Waals (VdW) interactions. VdW-corrected DFT is tested for interactions involving molecular hydrogen, graphite, single-walled carbon nanotubes (SWCNTs), and SWCNT bundles. The energy correction, based on an empirical London dispersion term with a damping function at short range, allows a reasonable physisorption energy and equilibrium distance to be obtained for H-2 on a model graphite surface. The VdW-corrected DFT calculation for an (8, 8) nanotube bundle reproduces accurately the experimental lattice constant. For H-2 inside or outside an (8, 8) SWCNT, we find the binding energies are respectively higher and lower than that on a graphite surface, correctly predicting the well known curvature effect. We conclude that the VdW correction is a very effective method for implementing DFT calculations, allowing a reliable description of both short-range chemical bonding and long-range dispersive interactions. The method will find powerful applications in areas of SWCNT research where empirical potential functions either have not been developed, or do not capture the necessary range of both dispersion and bonding interactions.

Modeling of adsorption and nucleation in infinite cylindrical pores by two-dimensional density functional theory

In this paper, we present an analysis of argon adsorption in cylindrical pores having amorphous silica structure by means of a nonlocal density functional theory (NLDFT). In the modeling, we account for the radial and longitudinal density distributions, which allow us to consider the interface between the liquidlike and vaporlike fluids separated by a hemispherical meniscus in the canonical ensemble. The Helmholtz free energy of the meniscus was determined as a function of pore diameter. The canonical NLDFT simulations show the details of density rearrangement at the vaporlike and liquidlike spinodal points. The limits of stability of the smallest bridge and the smallest bubble were also determined with the canonical NLDFT. The energy of nucleation as a function of the bulk pressure and the pore diameter was determined with the grand canonical NLDFT using an additional external potential field. It was shown that the experimentally observed reversibility of argon adsorption isotherms at its boiling point up to the pore diameter of 4 nm is possible if the potential barrier of 22kT is overcome due to density fluctuations.

Adsorption of binary hydrocarbon mixtures in carbon slit pores: A density functional theory study

Adsorption of binary hydrocarbon mixtures involving methane in carbon slit pores is theoretically studied here from the viewpoints of separation and of the effect of impurities on methane storage. It is seen that even small amounts of ethane, propane, or butane can significantly reduce the methane capacity of carbons. Optimal pore sizes and pressures, depending on impurity concentration, are noted in the present work, suggesting that careful adsorbent and process design can lead to enhanced separation. These results are consistent with earlier literature studies for the infinite dilution limit. For methane storage applications a carbon micropore width of 11.4 Angstrom (based on distance between centers of carbon atoms on opposing walls) is found to be the most suitable from the point of view of lower impurity uptake during high-pressure adsorption and greater impurity retention during low-pressure delivery. The results also theoretically confirm unusual recently reported observations of enhanced methane adsorption in the presence of a small amount of heavier hydrocarbon impurity.

Close packed transitions in slit-shaped pores: Density functional theory study of methane adsorption capacity in carbon

An important feature of improving lattice gas models and classical isotherms is the incorporation of a pore size dependent capacity, which has hitherto been overlooked. In this paper, we develop a model for predicting the temperature dependent variation in capacity with pore size. The model is based on the analysis of a lattice gas model using a density functional theory approach at the close packed limit. Fluid-fluid and solid-fluid interactions are modeled by the Lennard-Jones 12-6 potential and Steele's 10-4-3, potential respectively. The capacity of methane in a slit-shaped carbon pore is calculated from the characteristic parameters of the unit cell, which are extracted by minimizing the grand potential of the unit cell. The capacities predicted by the proposed model are in good agreement with those obtained from grand canonical Monte Carlo simulation, for pores that can accommodate up to three adsorbed layers. Single particle and pair distributions exhibit characteristic features that correspond to the sequence of buckling and rhombic transitions that occur as the slit pore width is increased. The model provides a useful tool to model continuous variation in the microstructure of an adsorbed phase, namely buckling and rhombic transitions, with increasing pore width. (C) 2002 American Institute of Physics.

Density functional theory analysis of the influence of pore wall heterogeneity on adsorption in carbons

Density functional theory for adsorption in carbons is adapted here to incorporate a random distribution of pore wall thickness in the solid, and it is shown that the mean pore wall thickness is intimately related to the pore size distribution characteristics. For typical carbons the pore walls are estimated to comprise only about two graphene layers, and application of the modified density functional theory approach shows that the commonly used assumption of infinitely thick walls can severely affect the results for adsorption in small pores under both supercritical and subcritical conditions. Under supercritical conditions the Henry's law coefficient is overpredicted by as much as a factor of 2, while under subcritical conditions pore wall heterogeneity appears to modify transitions in small pores into a sequence of smaller ones corresponding to pores with different wall thicknesses. The results suggest the need to improve current pore size distrubution analysis methods to allow for pore wall heterogeneity. The density functional theory is further extended here to allow for interpore adsorbate interactions, and it appears that these interaction are negligible for small molecules such as nitrogen but significant for more strongly interacting heavier molecules such as butane, for which the traditional independent pore model may not be adequate.

A comparative study of carbon gasification with O-2 and CO2 by density functional theory calculations

A comparative study of carbon gasification with O-2 and CO2 was conducted by using density functional theory calculations. It was found that the activation energy and the number of active sites in carbon gasification reactions are significantly affected by both the capacity and manner of gas chemisorption. O-2 has a strong adsorption capacity and the dissociative chemisorption of O-2 is thermodynamically favorable on either bare carbon surface or even isolated edge sites. As a result, a large number of semiquinone and o-quinone oxygen can be formed indicating a significant increase in the number of active sites. Moreover, the weaker o-quinone C-C bonds can also drive the reaction forward at (ca. 30%) lower activation energy. Epoxy oxygen forms under relatively high O-2 pressure, and it can only increase the number of active sites, not further reduce the activation energy. CO2 has a lower adsorption capacity. Dissociative chemisorption of CO2 can only occur on two consecutive edge sites and o-quinone oxygen formed from CO2 chemisorption is negligible, let alone epoxy oxygen. Therefore, CO2-carbon reaction needs (ca 30%) higher activation energy. Furthermore, the effective active sites are also reduced by the manner Of CO2 chemisorption. A combination of the higher activation energy and the fewer active sites leads to the much lower reaction rate Of CO2-carbon.

High-pressure adsorption of supercritical gases on activated carbons: An improved approach based on the density functional theory and the bender equation of state

Adsorption of nitrogen, argon, methane, and carbon dioxide on activated carbon Norit R1 over a wide range of pressure (up to 50 MPa) at temperatures from 298 to 343 K (supercritical conditions) is analyzed by means of the density functional theory modified by incorporating the Bender equation of state, which describes the bulk phase properties with very high accuracy. It has allowed us to precisely describe the experimental data of carbon dioxide adsorption slightly above and below its critical temperatures. The pore size distribution (PSD) obtained with supercritical gases at ambient temperatures compares reasonably well with the PSD obtained with subcritical nitrogen at 77 K. Our approach does not require the skeletal density of activated carbon from helium adsorption measurements to calculate excess adsorption. Instead, this density is treated as a fitting parameter, and in all cases its values are found to fall into a very narrow range close to 2000 kg/m(3). It was shown that in the case of high-pressure adsorption of supercritical gases the PSD could be reliably obtained for the range of pore width between 0.6 and 3 run. All wider pores can be reliably characterized only in terms of surface area as their corresponding excess local isotherms are the same over a practical range of pressure.

Non-additivity of attractive potentials in modeling of N-2 and Ar adsorption isotherms on graphitized carbon black and porous carbon by means of density functional theory

We present a new approach accounting for the nonadditivity of attractive parts of solid-fluid and fluidfluid potentials to improve the quality of the description of nitrogen and argon adsorption isotherms on graphitized carbon black in the framework of non-local density functional theory. We show that the strong solid-fluid interaction in the first monolayer decreases the fluid-fluid interaction, which prevents the twodimensional phase transition to occur. This results in smoother isotherm, which agrees much better with experimental data. In the region of multi-layer coverage the conventional non-local density functional theory and grand canonical Monte Carlo simulations are known to over-predict the amount adsorbed against experimental isotherms. Accounting for the non-additivity factor decreases the solid-fluid interaction with the increase of intermolecular interactions in the dense adsorbed fluid, preventing the over-prediction of loading in the region of multi-layer adsorption. Such an improvement of the non-local density functional theory allows us to describe experimental nitrogen and argon isotherms on carbon black quite accurately with mean error of 2.5 to 5.8% instead of 17 to 26% in the conventional technique. With this approach, the local isotherms of model pores can be derived, and consequently a more reliab * le pore size distribution can be obtained. We illustrate this by applying our theory against nitrogen and argon isotherms on a number of activated carbons. The fitting between our model and the data is much better than the conventional NLDFT, suggesting the more reliable PSD obtained with our approach.

Application of density functional theory to capillary phenomena in cylindrical mesopores with radial and longitudinal density distributions

In this paper, we applied a version of the nonlocal density functional theory (NLDFT) accounting radial and longitudinal density distributions to study the adsorption and desorption of argon in finite as well as infinite cylindrical nanopores at 87.3 K. Features that have not been observed before with one-dimensional NLDFT are observed in the analysis of an inhomogeneous fluid along the axis of a finite cylindrical pore using the two-dimensional version of the NLDFT. The phase transition in pore is not strictly vapor-liquid transition as assumed and observed in the conventional version, but rather it exhibits a much elaborated feature with phase transition being complicated by the formation of solid phase. Depending on the pore size, there are more than one phase transition in the adsorption-desorption isotherm. The solid formation in finite pore has been found to be initiated by the presence of the meniscus. Details of the analysis of the extended version of NLDFT will be discussed in the paper. (C) 2004 American Institute of Physics.

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, N-2, 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.

Application of density functional theory to equilibrium adsorption of argon and nitrogen on amorphous silica surface

We present a new version of non-local density functional theory (NL-DFT) adapted to description of vapor adsorption isotherms on amorphous materials like non-porous silica. The novel feature of this approach is that it accounts for the roughness of adsorbent surface. The solid–fluid interaction is described in the same framework as in the case of fluid–fluid interactions, using the Weeks–Chandler–Andersen (WCA) scheme and the Carnahan–Starling (CS) equation for attractive and repulsive parts of the Helmholtz free energy, respectively. Application to nitrogen and argon adsorption isotherms on non-porous silica LiChrospher Si-1000 at their boiling points, recently published by Jaroniec and co-workers, has shown an excellent correlative ability of our approach over the complete range of pressures, which suggests that the surface roughness is mostly the reason for the observed behavior of adsorption isotherms. From the analysis of these data, we found that in the case of nitrogen adsorption short-range interactions between oxygen atoms on the silica surface and quadrupole of nitrogen molecules play an important role. The approach presented in this paper may be further used in quantitative analysis of adsorption and desorption isotherms in cylindrical pores such as MCM-41 and carbon nanotubes.

Adsorption of argon and nitrogen in cylindrical pores of MCM-41 materials: application of density functional theory

Adsorption of argon and nitrogen at their respective boiling points in cylindrical pores of MCM-41 type silica-like adsorbents is studied by means of a non-local density functional theory (NLDFT), which is modified to deal with amorphous solids. By matching the theoretical results of the pore filling pressure versus pore diameter against the experimental data, we arrive at a conclusion that the adsorption branch (rather than desorption) corresponds to the true thermodynamic equilibrium. If this is accepted, we derive the optimal values for the solid–fluid molecular parameters for the system amorphous silica–Ar and amorphous silica–N2, and at the same time we could derive reliably the specific surface area of non-porous and mesoporous silica-like adsorbents, without a recourse to the BET method. This method is then logically extended to describe the local adsorption isotherms of argon and nitrogen in silica-like pores, which are then used as the bases (kernel) to determine the pore size distribution. We test this with a number of adsorption isotherms on the MCM-41 samples, and the results are quite realistic and in excellent agreement with the XRD results, justifying the approach adopted in this paper.

Modeling nitrogen adsorption in spherical pores of siliceous materials by density functional theory

Adsorption of nitrogen in spherical pores of FDU-1 silica at 77 K is considered by means of a nonlocal density functional theory (NLDFT) accounting for a disordered structure of pore walls. Pore size distribution analysis of various FDU-1 samples subject to different temperatures of calcination revealed three distinct groups of pores. The principal group of pores is identified as ordered spherical mesopores connected with each other by smaller interconnecting pores and irregular micropores present in the mesopore walls. To account for the entrances (connecting pores) into spherical mesopores, a concept of solid mass distribution with respect to the apparent density was introduced. It is shown that the introduction of the aforementioned distribution was sufficient to quantitatively describe experimental adsorption isotherms over the entire range of relative pressures spanning six decades.