The effect of heterogeneity in the randomly etched graphite model for carbon pore size characterization

Using perfect slit pores for the determination of the pore size distribution of activated carbons presents some drawbacks such as the observed absence of pores around 12-13 Å and usually poor correlation between simulated and experimental isotherms. In this study, we propose a model to introduce geometric heterogeneity using the randomly etched graphite approach. We calculated kernels of N₂ isotherms mixing the etched pores isotherms with the perfect ones. The isotherms were calculated using biased grand canonical Monte Carlo and Lennard-Jones potentials in graphene sheets with explicit carbon atoms and solid-fluid parameters carefully adjusted. We found that the observed absence of pores around 12-13 Å was eliminated with the introduction of a few etched pores. Also, a surprising improvement of the fitting between the theoretical and the experimental isotherms was obtained. The study also showed that this approach can be used to establish a parameter (etched pore volume) that would characterize heterogeneity. Tests using real carbons showed consistently that the volume of etched pores is larger for those samples that present more heterogeneity. The obtained improvements are a strong indication that kernels with randomly etched pore models can effectively improve the pore size distribution of activated carbon.     

Increased H2 gravimetric storage capacity in truncated carbon slit pores modeled by Grand Canonical Monte Carlo

Hydrogen adsorption in slit shaped pores built up from truncated graphene fragments has been simulated using Grand Canonical Monte Carlo technique and the influence of pore wall edges on hydrogen storage by physisorption has been analyzed. We show that due to the additional gas adsorption at the pore edges the adsorbed gravimetric amount significantly increases (by a factor of two) with respect to models of pores with infinite graphene walls. The contribution of the edges’ adsorption to the total hydrogen uptake is independent of the pore wall shape but it depends on its surface. We also show that the maximum of the excess adsorption shifts towards higher pressures when the edge contribution increases. This information can be used to characterize experimentally structures of porous adsorbents and complement pore size distribution analysis usually performed with gases others than hydrogen. We suggest that porous carbons built from polycyclic hydrocarbons can achieve storage performances required for practical applications.     

The theoretical maximum isosteric heat of adsorption in the Henry’s law region for slit-shaped carbon nanopores

The isosteric heat of adsorption in the Henry’s law region is calculated as a function of the width of slit-shaped pores. We determine the pore width where the isosteric heat is a maximum, which is shown to be a strong function of the solid-fluid collision diameter σ_sf and a weak function of the solid-fluid well depth potential ?_sf. Thus, general results are reported for the pore size where the isosteric heat of adsorption is a maximum that apply to a wide variety of gases. We compare our values of isosteric heat with those in the Henry’s law region determined from adsorption data for nitrogen, argon, carbon dioxide, and methane on various activated carbons. The isosteric heats of adsorption for helium and hydrogen in carbon slit pores are also calculated, but are not compared with experimental data. Reasons for differences between the theoretical maximum and the experimental values are discussed.     

Effect of pore geometry on the sintering of Ca-based sorbents during calcination at high temperatures

In this article, we present a mathematical model that describes the calcination and sintering of calcium-based sorbents in furnace sorbent injection (FSI) conditions. We assumed that the sorbent decomposition follows a shrinking core model with a changing pore size distribution in every layer and we used a comprehensive mathematical model for sintering. Cylindrical and plate-like or slit pore geometries, usually associated with carbonate- and hydroxide-derived sorbents, respectively, were adopted and compared. It was concluded that sorbents with cylindrical pores sinter to a greater extent than those with slit pores. The decomposition and sintering kinetics were determined for three calcium sorbents with different pore geometries in FSI conditions. The study revealed that the presence of CO₂ and H₂O in the reaction atmosphere affects the sintering parameters whereas the calcination parameters remain constant. The model effectively correlated the experimental data and adequately predicted not only the evolution of the specific surface area but also the evolution of the pore size distribution of the sorbent over time. The most striking aspect of the research was that although our model calculated the total area by adding together the pore sizes in all the layers of the sorbent, the results were very similar to those of other sintering models.     

Quenched solid density functional theory and pore size analysis of micro-mesoporous carbons

We present a new model of adsorption on micro-mesoporous carbons based on the quenched solid density functional theory (QSDFT). QSDFT quantitatively accounts for the surface geometrical inhomogeneity in terms of the roughness parameter. We developed the QSDFT models for pore size distribution calculations in the range of pore widths from 0.4 to 35 nm from nitrogen at 77.4 K and argon at 87.3 K adsorption isotherms. The QSDFT model improves significantly the method of adsorption porosimetry: the pore size distribution (PSD) functions do not possess gaps in the regions of ∼1 nm and ∼2 nm, which are typical artifacts of the standard non-local density functional theory (NLDFT) model that treats the pore walls as homogeneous graphite-like plane surfaces. The advantages of the QSDFT method are demonstrated on various carbons, including activated carbons fibers, coal based granular carbon, water purification adsorbents, and mirco-mesoporous carbon CMK-1 templated on MCM-48 silica. The results of PSD calculations from nitrogen and argon are consistent, however, argon adsorption provides a better resolution of micropore sizes at low vapor pressures than nitrogen adsorption.     

Determination of pore size distribution and adsorption of methane and CCl4 on activated carbon by molecular simulation

A combined method of grand canonical Monte Carlo (GCMC) simulation and statistics integral equation (SIE) for the determination of pore size distribution (PSD) is developed based on the experimental adsorption data of methane on activated carbon at ambient temperature, T=299 K. In the GCMC simulation, methane is modeled as a Lennord-Jones spherical molecule, and the activated carbon pore is described as slit-shaped with the PSD. The well-known Steele’s 10-4-3 potential is used to represent the interaction between the fluid molecule and the solid wall. Covering the range of pore sizes of the activated carbon, a series of adsorption isotherms of methane in several uniform pores were obtained from GCMC. In order to improve the agreement between the experimental data and simulation results, the PSD is calculated by means of an adaptable procedure of deconvolution of the SIE method. Based on the simulated results, we use the activated carbon with the PSD as the prototype of adsorbent to investigate adsorption. The adsorption isotherms of methane and CCl₄ at 299 K in the activated carbon with the PSD are obtained. The adsorption amount of CCl₄ reaches 20 mmol/g at ambient temperature and pressure. The results indicate that the combined method of GCMC and SIE proposed here is a powerful technique for calculating the PSD of activated carbons and predicting adsorption on activated carbons.     

Using DFT analysis of adsorption data of multiple gases including H2 for the comprehensive characterization of microporous carbons

Hydrogen and nitrogen adsorption isotherms at cryogenic temperatures (77 and 87 K) were used to characterize the microporosity of a series of activated carbons, representing various pore size distributions (PSD). The PSD for each carbon was calculated by simultaneous fitting of the DFT model isotherms to their experimental counterparts. The resulting PSD represents robust characteristics of the carbon structure that is consistent with all the data used in the analysis. The range of pore size analysis in this method is extended to smaller pore sizes compared to the standard nitrogen adsorption analysis. In addition, it is shown that this approach allows to detect and exclude experimental points that are not fully equilibrated due to diffusion problems in narrow micropores. The results of the analysis of a series of carbons activated with systematically increasing burn-off show that the presented approach is a useful tool for a comprehensive characterization of microporous carbons, and for obtaining detailed and reliable carbon PSDs.     

Studies on the preparation of C/SiC composite as a catalyst support by CVI in a fluidized bed reactor

In this research, in order to improve the mechanical strength and oxidation resistance of a catalyst support, we studied the formation of SiC layer on the pore surfaces of activated carbons by permeating and depositing SiC from a reaction between hydrogen and dichlorodimethylsilane (DDS). The porous structure should be kept during deposition. A fluidized bed reactor and activated carbons of size of 20-40 mesh were used. By studying characteristics of deposits under various deposition conditions, we confirmed that the best conditions of manufacturing catalyst support are a lower pressure and a lower concentration. In this work, at the conditions of 5 torr of total pressure and 3% of DDS concentration, during the 10 hr processing time, deposition occurred on the pore walls before plugging pores. The results from the mathematical modeling were compared with the experimental results.     

Small-angle neutron scattering characterization of the structure of nanoporous carbons for energy-related applications

We used small-angle neutron scattering (SANS) and neutron contrast variation to study the structure of four nanoporous carbons prepared by thermo-chemical etching of titanium carbide TiC in chlorine at 300, 400, 600, and 800 °C with pore diameters ranging between ∼4 and ∼11 Å. SANS patterns were obtained from dry samples and samples saturated with deuterium oxide (D₂O) in order to delineate origin of the power law scattering in the low Q domain as well as to evaluate pore accessibility for D₂O molecules. SANS cross section of all samples was fitted to Debye-Anderson-Brumberger (DAB), DAB-Kirste-Porod models as well as to the Guinier and modified Guinier formulae for cylindrical objects, which allowed for evaluating the radii of gyration as well as the radii and lengths of the pores under cylindrical shape approximation. SANS data from D₂O-saturated samples indicate that strong upturn in the low Q limit usually observed in the scattering patterns from microporous carbon powders is due to the scattering from outer surface of the powder particles. Micropores are only partially filled with D₂O molecules due to geometrical constraints and or partial hydrophobicity of the carbon matrix. Structural parameters of the dry carbons obtained using SANS are compared with the results of the gas sorption measurements and the values agree for carbide-derived carbons (CDCs) obtained at high chlorination temperatures (>600 °C). For lower chlorination temperatures, pore radii obtained from gas sorption overestimate the actual pore size as calculated from SANS for two reasons: inaccessible small pores are present and the model-dependent fitting based on density functional theory models assumes non-spherical pores, whereas SANS clearly indicates that the pore shape in microporous CDC obtained at low chlorination temperatures is nearly spherical.     

Simulation study on the relationship between a high resolution αs-plot and the pore size distribution for activated carbon

The effects of the micropore structure of activated carbons on the high resolution α_s-plot for nitrogen adsorption isotherms were examined with the grand canonical Monte Carlo simulation. Adsorption isotherms of nitrogen were simulated in graphitic slit pores at 77 K as a function of the slit width (w). As no pore effect was observed below P/P₀=0.6 for w=3.5 nm, α_s-plots for the simulated adsorption isotherms were constructed using the standard isotherm simulated for w=3.5 nm. The simulated α_s-plots had filling and cooperative swings which were experimentally shown in the previous works, and the shape of the simulated α_s-plot varied with the micropore structure. As the subtracting pore effect (SPE) method for the specific surface area (SSA) determination using the α_s-plot was proposed in the previous experimental works, the theoretical ground for the SPE method was discussed. The best evaluation method of SSA using the α_s-plot was shown, almost agreeing with the SPE method. This simulation study showed clearly that the SPE method is available for pore systems of w≥0.7 nm, whereas even the SPE method underestimates the SSA of the pores of w≤0.6 nm. The observed swings of the α_s-plot were simulated using the different micropore size distribution. The bimodal micropore size distribution lead to both of filling and cooperative swings, while a single pore size distribution <0.9 nm gave only the filling swing. Thus, four representative types of the α_s-plot for activated carbons were proposed and it was shown how to understand the micropore size distribution through the α_s-plot.     

An Experimentally Fitted and Simple Model for the Pores in Nuclepore Membranes

Abstract

The porosities (percentage of empty volume over the total volume) of several Nuclepore membranes are measured by means of a pycnometric method which is shown. If cylindrical pores are assumed, the porosities can be calculated from the surface pore densities and mean pore radii, both measured by microscopy. The disagreement between these two methods implies that the pores are not cylindrical in shape. A model is proposed that assumes an internal pore radius, r_r different from the external one, r_e (mean pore radius). When it is assumed that there is a mean angle, φ, between the pores and the membrane surface, this angle can be calculated if we assume that the experimental surface pore density is the maximum one compatible with the model. From a comparison of calculated and experimental φ, the maximization of the surface pore density can be tested.     

New adsorption-condensation theory for adsorption of vapors on porous activated carbons

A new analytical model to describe equilibrium adsorption of condensable vapors on porous adsorbents is developed. It accounts for the heterogeneous pore structure of the adsorbent, adsorption in the micropores by a pore filling mechanism and adsorption and condensation in the macropores. A gamma-type pore size distribution function is used. Langmuir-type adsorption equations are used to describe both micropore filling and adsorption on the macropore walls. The vapor condensation in the pores is described by the Kelvin equation. The model is successfully tested using isotherm data for adsorption of various condensable vapors on different porous activated carbons and charcoals. All three types (I, IV and V) of adsorption isotherms by the Brunauer classification which are depicted by the porous adsorbents can be described by the model.     

Surface wettability effect on fluid transport in nanoscale slit pores

The surface wettability effect on fluid transport in nanoscale slit pores is quantitatively accessed by using non‐equilibrium molecular dynamics (NEMD) simulation incorporating with density functional theory (DFT). In particular, the slip lengths of benzene steady flows under various wetting conditions are computed with NEMD simulations and a quasi‐general expression is given, while the structural properties are investigated with DFT. By taking into account the inhomogeneity of fluid density inside pore, we find that the conventional flux enhancement rate is associated with both the molecule slipping and geometrical confinement, and it becomes drastically high in solvophobic pores especially when the pore size is of several fluid diameters. In good agreement with experimental results, we further show that the wettability effect competes with pore size effect in determining the flux after pore inner surface modification, and a high flux can be achieved when the deposited layer is solvophobic yet thin. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1704–1714, 2017     

Superior electric double layer capacitors using ordered mesoporous carbons

This paper reports for the first time superior electric double layer capacitive properties of ordered mesoporous carbon (OMCs) with varying ordered pore symmetries and mesopore structure. Compared to commercially used activated carbon electrode, Maxsorb, these OMC carbons have superior capacitive behavior, power output and high-frequency performance in EDLCs due to the unique structure of their mesopore network, which is more favorable for fast ionic transport than the pore networks in disordered microporous carbons. As evidenced by N₂ sorption, cyclic voltammetry and frequency response measurements, OMC carbons with large mesopores, and especially with 2-D pore symmetry, show superior capacitive behaviors (exhibiting a high capacitance of over 180 F/g even at very high sweep rate of 50 mV/s, as compared to much reduced capacitance of 73 F/g for Maxsorb at the same sweep rate). OMC carbons can provide much higher power density while still maintaining good energy density. OMC carbons demonstrate excellent high-frequency performances due to its higher surface area in pores larger than 3 nm. Such ordered mesoporous carbons (OMCs) offer a great potential in EDLC capacitors, particularly for applications where high power output and good high-frequency capacitive performances are required.     

In silico designed microporous carbons

This work presents a computational study on the packing of three-dimensional carbon nanostructures and their effect on gas adsorption properties. We show that it is possible to obtain intrinsically microporous materials without specifying structural properties such as surface area or pore size distribution by packing individual graphene platelets connected at a contortion site. The resulting structures can potentially represent disordered carbons and provide understanding of the relationship between pore structure and adsorption performance. The calculated CO₂/CH₄ selectivity of these materials at the zero coverage selectivity can be as high as 25, whilst at low finite pressures (0.05 bar) is between 6 and 10, which is comparable with what is expected for most carbons. We compare the results to the ones obtained from a simple slit pore model and highlight the importance of pore morphological complexity to adsorption of industrially important gases.     

Using the high pressure methane isotherm for determination of pore size distribution of carbon adsorbents

A method of determining pore size distribution, PSD, of carbon adsorbents based on the high pressure methane isotherm is presented. A generic software package, and an IBM compatible PC, have been used to search for a PSD in the form of a histogram. The method relies on a known local isotherm, in this case, assuming a simplified model of infinite slit shaped carbon pores.Three carbons, having very different pore structures: BPL, PX-21, and PVDC, were analyzed using the new method and the results compared with those obtained from subcritical Ar, and N₂ isotherms. The analysis from the high pressure methane isotherm gave results which are different than those from the low pressure low temperature isotherms but not significantly enough to be unrealistic.     

A nanoscale model for characterizing the complex pore structure of biochars

The development of a novel nanoscale model that can accurately describe the reactivity of solids consisting of multiple components and having ordered and random pores is presented. Domains of multiple solid phases are distributed on a computational grid to simulate reactants with different specific reactivities and dispersions. Sub‐nanometer slit pores and larger cylindrical pores with given size distributions are also distributed on the grid in regular and random arrangements respectively. The generated solids are then eroded using rules that simulate a gas‐solid, non‐catalytic reaction occurring in the kinetic control regime. A parametric study is first carried out to demonstrate how key pore structural parameters affect the reactivity patterns. Model predictions are found to be in excellent agreement with experimental thermogravimetric data for the combustion of biochars, both when the slit and random cylindrical pores are fully accessible to the reactant and when diffusional limitations appear in the smaller slit pores. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3412–3420, 2013     

On the Charges on the Pore Walls off Microporous Membranes

Abstract

A method of calculation of the distribution of charges on the pore surfaces of microporous membranes is shown. The membranes are Nuclepore filters separating two diluted NaCl water solutions (concentrations c_o and c_i > c_o). The method is based on the integration in the steady state of the Nernst-Planck-Poisson equations by using Goldman's hypothesis of a linear gradient of electric potential. This integration permits us to obtain the volume charge density inside the pores as a function of the distance. In order to obtain the surface density of charges on the pore walls, the pore shape has to be known. It has been proved by us that the pores of our Nuclepore membranes can be described as bent revolution parabolas whose parameters can be determined by adjusting them in order to fit the experimental porosity data. These membranes have very tow permselectivities and they are unaffected by the diffusion layers, but the ionic permeabilities are smaller if these diffusion layers exist This effect on the ionic