Nonlocal Density Functional Theory Model Research Articles

Selection Effect of Liquid Nitrogen Freeze-Thaw Cycles on Full Pore Size Distribution of Different Rank Coals.

In China, the capacity to produce coalbed methane and extract underground gas is restricted by the prevalence of low-permeability coal seams. Liquid nitrogen fracturing is a new low temperature-high-pressure anhydrous fracturing technology that uses low temperature and high frost heave forces to increase coal permeability. To better understand the liquid nitrogen fracturing effect on coal, we conduct the liquid nitrogen freeze-thaw cycle (LNCFT) experiments on different rank coals from Qinghai, Shanxi, and Shaanxi provinces. We combined the low-pressure nitrogen and carbon dioxide adsorption experiment with the non-local density functional theory model and mercury injection porosimetry with compressibility corrections to examine the full pore size distributions of untreated and water-saturated samples before and after LNCFT. The results found that LNCFT can effectively increase the pore volume (PV) and specific surface area of the water-saturated coal sample. Compared with the raw coal, the increased ratio of the full pore size PV is 70.41-100.17%. However, the scale-selective transformation effect on pores during liquid nitrogen fracturing is noticeable. Under the same conditions, LNCFT can significantly increase the pore volume of micropores (>2 nm) and macropores (>50 nm), and the increase ratios are 24.40-44.16 and 103.55-327.93%, respectively. The PV of mesopores (2-50 nm) shows a slightly increasing trend with the increase in metamorphic degree, and the increase ratio is between 8.7 and 56%. Comparing the full pore size distribution curves before and after LNCFT, it is found that the alteration of high-volatile bituminous coal (BLT coal) and anthracite (SH coal) has more significance in the range of less than 2 and 50-20,000 nm, while middle-volatile bituminous coal (YJL coal) varies between 50 and 2000 nm. Meanwhile, the ratio of micropore and mesopore PV to the total decreased gradually before and after LNCFT, while the proportion of macropores increased, indicating that small-scale pores would intersect and connect to form larger-scale pores during the fracturing. The combined effects of temperature gradient, water-ice phase transition, and heat transmission rate are the key factors that determine the impact of LNCFT on pore size distribution. Our results provide new information for enhancing the permeability of low-permeability coal seams of different ranks.

Applicability Analysis of Determination Models for Nanopores in Coal Using Low-Pressure CO₂ and N₂ Adsorption Methods.

The development characteristics of nanopores (with pore sizes <200 nm) in coal are a key factor affecting the accumulation and migration of coalbed methane (CBM). Thus, an appropriate determination method and calculation model are essential for accurate nanopore representation. Based on the experiments of low-pressure CO₂ adsorption (LP-CO₂GA) at 273 K and low-pressure N₂ adsorption (LP-N₂GA) at 77 K on four coals with different ranks, the abilities of different models (e.g., Langmuir, Dubinin-Radushkevich (D-R), Dubinin-Astakhov (D-A), Brunauer-Emmett-Teller (BET) and nonlocal density functional theory (NLDFT)) to accurately predict the pore parameters were analyzed. The results showed that (1) for LP-N₂GA, the Langmuir model is only suitable for gas adsorptions at low relative pressure conditions (P/P0 < 0.01), and its error value increased with the relative adsorption pressure. The fitting results of the D-R model showed good agreement with the D-A model under low relative pressure of LP-CO₂GA (P/P0 < 0.01), and the D-A model had more accurate fitting results. The BET model is more accurate than the other models (φ = -1.2733%) only in the interval of LP-N₂GA with 0.05 < P/P0 < 0.35. The data also showed that the NLDFT model can maintain a higher fitting accuracy for LPCO₂/N₂GA processes at relative adsorption pressures from 0.001-0.9996. (2) Using LP-CO₂GA with the Langmuir, D-R, D-A, and NLDFT models, the micropore specific surface area (SSA; 66.9570-248.6736 m²/g) and pore volume (0.0201- 0.0997 cm³/g) were obtained, while the values of meso-/macropore SSA (0.0007-2.3398 m²/g) and pore volume (0.0036-0.04 cm³/g) were calculated by LP-N₂GA with the BET and NLDFT models. The results showed that the fitting accuracy in descending order was the D-R, D-A, Langmuir and NLDFT models. (3) In combination with the applicable model range, LP-CO₂GA with the NLDFT model was recommended for micropore analysis of the coal pore sizes from 0.36-1.1 nm, while LP-N₂GA combined with the NLDFT model was recommended for nanopore analysis of pore sizes from 1.1-200 nm. (4) The characteristics of pore development in the Beiloutian coal were analyzed using LP-CO₂/N₂GA combined with the NLDFT model. It was found that a pore volume and SSA less than 1.0 nm accounted for 88.82% of the total pore volume and 98.05% of the total SSA, indicating that micropores in coal are the main space for CBM storage and are key physical factors for the occurrence and migration of coalbed methane. The conclusions of this article will provide a basis for the accurate calculation of nanopores in coal.

The suitability of infinite slit-shaped pore model to describe the pores in highly porous carbon materials

The slit-shaped pore model is often assumed to be the most suitable to describe the pores in micro-/mesoporous carbon materials. This article analyses the suitability of this assumption when pore size distribution of carbon materials is calculated applying non-local density functional theory (NLDFT) to nitrogen adsorption isotherms. For further insight, three micro-/mesoporous carbide derived carbons (CDC-s) synthesised from SiC, TiC and Mo2C, respectively, and denoted as SiC-CDC, TiC-CDC and Mo2C-CDC, were characterized with nitrogen sorption, small angle neutron scattering (SANS) and Raman spectroscopy methods. Although the SANS and NLDFT with slit-shaped pore model produced coinciding results for pore widths, it was found that the pores in all three carbon materials have different shapes and width-to-length ratios. Pores in SiC-CDC can be approximated to sphere-like, in TiC-CDC to cylinder-like and in Mo2C-CDC to slit-like shape. It was also suggested that the pore length may contribute significantly to the pore size distribution calculated using NLDFT model. Thus, the shape of pores in the carbon material investigated should be verified before the performance of carbon materials is explained in detail by the size and porous structure of micro-/mesoporous carbon materials.

Density Functional Theory Model of Adsorption Deformation

Molecules adsorbed in pores cause elastic deformations of the solid matrix leading to either contraction or swelling of the material. Although experimental manifestation of adsorption-induced deformation in clays, coals, carbons, silicas, and other materials has been known for a long time, a rigorous theoretical description of this phenomenon is lacking. We report the nonlocal density functional theory (NLDFT) calculations that reproduce almost quantitatively the adsorption and strain isotherms of Kr and Xe on zeolite X. This system exhibits characteristic contraction at low vapor pressures and swelling at high vapor pressures. We show that the experimentally observed changes in the adsorbent volume are proportional to the solvation (disjoining) pressure caused by the adsorption stress exerted on the pore walls. The proposed NLDFT model can be used for the interpretation of adsorption measurements in micro- and mesoporous materials and for the characterization of their mechanical properties.

DFT-Based Prediction of High-Pressure H2 Adsorption on Porous Carbons at Ambient Temperatures from Low-Pressure Adsorption Data Measured at 77 K

Hydrogen adsorption isotherms were measured both at cryogenic temperatures below 1 atm and at ambient temperature at high pressures, up to 90 atm, on selected porous carbons with various pore structures. The nonlocal density functional theory (NLDFT) model was used to calculate the pore size distributions (PSDs) of the carbons, from H2 adsorption isotherms measured at 77 K, and then to predict H2 adsorption on these carbons at 87 and 298 K. An excellent agreement between the predicted and measured data was obtained. Prior to analyzing the porous carbons, the solid-fluid interaction parameters used in the NLDFT model were derived from H2 adsorption data measured at 77 K on nonporous carbon black. The results show that the NLDFT model with appropriate parameters may be a useful tool for optimizing carbon pore structures and designing adsorption systems for hydrogen storage applications.

Determination of Pore Size Distribution, Surface Area, and Acidity in Fluid Cracking Catalysts (FCCs) from Nonlocal Density Functional Theoretical Models of Adsorption and from Microcalorimetry Methods

A method based on nonlocal density functional theory (NLDFT) has been used to interpret the data for the adsorption of nitrogen at 77 K within the pores of three different commercial fluid cracking catalysts (FCCs) before and after their use in a refinery catalytic cracking unit. The integral equation of adsorption was inverted by a regularization method to yield the micropore and mesopore size distribution over a wide range of pore widths. The results obtained are compared with the results of more traditional data treatments and indicate that the NLDFT model can provide a realistic pore volume and surface area estimation in commercial FCCs irrespective of their chemical composition and pore width distribution. Both BET and Langmuir methods grossly underestimate the FCCs surface area, and only the NLDFT method yields reliable surface area and pore volume measurements over the entire micro−meso porosity range present in the cataysts under study. Adsorption microcalorimetry results using ammonia as a probe ...

Density functional theories and molecular simulations of adsorption and phase transitions in nanopores.

The nonlocal density functional theory (NLDFT) of confined fluids is tested against Monte Carlo simulations by using the example of Lennard-Jones (LJ) fluid sorption in slit-shaped and cylindrical nanopores ranging from 0.3 to 10 nm in width. The fluid-fluid and solid-fluid parameters of the LJ potentials were chosen to represent several experimentally important adsorption systems: nitrogen and carbon dioxide in activated carbons, zeolites, and mesoporous molecular sieves of the MCM-41 type. Freezing in nanopores is discussed using the example of methane sorption in carbon at 111 K. Comparison with reference experiments is given when available. Two versions of NLDFT, the smoothed density approximation and the fundamental measure theory, are considered. It is shown that NLDFT approaches with properly chosen parameters provide quantitative agreement with the results of Monte Carlo simulations and reference experiments. Appreciable deviations are found in extremely narrow pores of less than two molecular diameters in width. In wider pores, NLDFT models can be used for quantitative predictions of reversible and hysteretic adsorption isotherms and analyses of the specifics of phase transformations, including the equilibrium and spinodal phase transitions.

Molecular Level Models for CO2 Sorption in Nanopores

Adsorption of carbon dioxide in slit-shaped carbon micropores at 273 K has been studied by means of the grand canonical Monte Carlo (GCMC) simulations and the nonlocal density functional theory (NLDFT). Three molecular models of CO2 have been used. Long-run GCMC simulations were performed with the three-center model of Harris and Yung (J. Phys. Chem. 1995, 99, 12021). For NLDFT calculations, we developed an effective Lennard-Jones (LJ) model. GCMC simulations of the effective LJ model of CO2 have been performed for comparison. For each model used, parameters of intermolecular potentials have been determined and validated against two-phase bulk equilibrium data and experimental adsorption isotherms on graphite at 273 and 195 K. In the range of pore widths from 3 to 15 Å, the NLDFT isotherms of CO2 adsorption are overall in a satisfactory agreement with the GCMC isotherms generated using the three-center model. Some deviations have been observed between 6.5 and 8.5 Å, where the adsorbate undergoes a transition from a single-layer to a two-layer structure. The models developed are recommended for studying carbon dioxide adsorption in microporous adsorbents and also for calculating pore size distributions in carbonaceous materials and soil particles. The NLDFT model has the advantage of being much less computationally demanding, whereas the three-center GCMC model serves as a benchmark for quantitative estimates and can be used for studying CO2 sorption at ambient conditions close to the critical temperature.

Pore Size Analysis of MCM-41 Type Adsorbents by Means of Nitrogen and Argon Adsorption

Methods of nonlocal density functional theory (NLDFT), proposed recently for predictions of adsorption equilibrium and calculations of pore size distributions in micro- and mesoporous materials, were tested on reference MCM-41 materials. Five newly synthesized MCM-41 adsorbents with presumably uniform pore channels varying from 32 to 45 Å were characterized by X-ray diffraction (XRD), nitrogen adsorption at 77 K, and argon adsorption at 77 and 87 K. New sets of intermolecular interaction parameters of the NLDFT model for N2and Ar adsorption on MCM-41 were determined. The parameters were specified to reproduce the bulk liquid–gas equilibrium densities and pressures, liquid–gas interfacial tensions, and standard adsorption isotherms on nonporous surfaces in the multilayer adsorption region. The pore size distributions calculated from the desorption branches of the experimental isotherms measured at three different temperatures were consistent with each other. Comparison of the NLDFT-calculated pore sizes with XRD data showed that the thickness of pore walls in the MCM-41 samples under consideration varied from ca. 6 to 12 Å. We found no correlation between the pore size and the pore wall thickness. The results obtained support the NLDFT model as a suitable tool for characterizing nanoporous materials and predicting adsorption equilibrium. The MCM-41 samples studied can be used as references for adsorption measurements.

Density functional theory model for calculating pore size distributions: pore structure of nanoporous catalysts

Using the example of nanoporous catalysts, we discuss the non-local density functional theory (NLDFT) model applied to physical adsorption of nitrogen and argon. The model has been used for predicting adsorption/desorption isotherms in nanopores of different geometries over a wide range of pore sizes (0.5–100 nm), and for calculating pore size distributions from adsorption isotherms based on given intermolecular fluid–fluid and fluid–solid potentials. The development of new nanoporous catalysts requires reliable characterization methods. We critically analyze different methods which are currently used for pore structure characterization in the range of nanometers. Calculations of the pore size distributions from nitrogen and argon adsorption isotherms are presented. Our primary method is based on the NLDFT model of adsorption on MCM-41, developed earlier. The results obtained with the NLDFT model are compared with other methods. It is shown, that the pore structure of nanoprous catalysts can be quite complex, and that Ar and N 2 isotherms contain complimentary information. The NLDFT model is recommended for evaluation of pore size distributions in nanoporous catalysts and other MCM-41 based materials.