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Journal ArticleDOI

Unified Approach to Pore Size Characterization of Microporous Carbonaceous Materials from N2, Ar, and CO2 Adsorption Isotherms†

04 Jan 2000-Langmuir (American Chemical Society)-Vol. 16, Iss: 5, pp 2311-2320
TL;DR: In this paper, a unified approach to pore size characterization of microporous carbonaceous materials such as activated carbon and carbon fibers by nitrogen, argon, and carbon dioxide adsorption at standard temperatures, 77 K for N2 and Ar and 273 K for CO2, was presented.
Abstract: We present a unified approach to pore size characterization of microporous carbonaceous materials such as activated carbon and carbon fibers by nitrogen, argon, and carbon dioxide adsorption at standard temperatures, 77 K for N2 and Ar and 273 K for CO2. Reference isotherms of N2, Ar, and CO2 in a series of model slit-shaped carbon pores in the range from 0.3 to 36 nm have been calculated from the nonlocal density functional theory (NLDFT) using validated parameters of intermolecular interactions. Carbon dioxide isotherms have also been generated by the grand canonical Monte Carlo (GCMC) method based on the 3-center model of Harris and Yung. The validation of model parameters includes three steps: (1) prediction of vapor−liquid equilibrium data in the bulk system, (2) prediction of adsorption isotherm on graphite surface, (3) comparison of the NLDFT adsorption isotherms in pores to those of GCMC simulations, performed with the parameters of fluid-fluid interactions, which accurately reproduce vapor−liqui...
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Journal ArticleDOI
24 Jun 2011-Science
TL;DR: This work synthesized a porous carbon with a Brunauer-Emmett-Teller surface area, a high electrical conductivity, and a low oxygen and hydrogen content that has high values of gravimetric capacitance and energy density with organic and ionic liquid electrolytes.
Abstract: Supercapacitors, also called ultracapacitors or electrochemical capacitors, store electrical charge on high-surface-area conducting materials. Their widespread use is limited by their low energy storage density and relatively high effective series resistance. Using chemical activation of exfoliated graphite oxide, we synthesized a porous carbon with a Brunauer-Emmett-Teller surface area of up to 3100 square meters per gram, a high electrical conductivity, and a low oxygen and hydrogen content. This sp 2 -bonded carbon has a continuous three-dimensional network of highly curved, atom-thick walls that form primarily 0.6- to 5-nanometer-width pores. Two-electrode supercapacitor cells constructed with this carbon yielded high values of gravimetric capacitance and energy density with organic and ionic liquid electrolytes. The processes used to make this carbon are readily scalable to industrial levels.

5,486 citations

Journal ArticleDOI
18 Nov 2005-Science
TL;DR: Covalent organic frameworks (COFs) have been designed and successfully synthesized by condensation reactions of phenyl diboronic acid and hexahydroxytriphenylene to form rigid porous architectures with pore sizes ranging from 7 to 27 angstroms.
Abstract: Covalent organic frameworks (COFs) have been designed and successfully synthesized by condensation reactions of phenyl diboronic acid {C6H4[B(OH)2]2} and hexahydroxytriphenylene [C18H6(OH)6]. Powder x-ray diffraction studies of the highly crystalline products (C3H2BO)6.(C9H12)1 (COF-1) and C9H4BO2 (COF-5) revealed expanded porous graphitic layers that are either staggered (COF-1, P6(3)/mmc) or eclipsed (COF-5, P6/mmm). Their crystal structures are entirely held by strong bonds between B, C, and O atoms to form rigid porous architectures with pore sizes ranging from 7 to 27 angstroms. COF-1 and COF-5 exhibit high thermal stability (to temperatures up to 500 degrees to 600 degrees C), permanent porosity, and high surface areas (711 and 1590 square meters per gram, respectively).

4,843 citations

Journal ArticleDOI
TL;DR: A critical review of adsorption methods that are currently used in the characterization of ordered organic−inorganic nanocomposite materials is presented in this paper, where the authors compare and evaluate the available methods for mesopore size analysis.
Abstract: A critical review of adsorption methods that are currently used in the characterization of ordered organic−inorganic nanocomposite materials is presented, and the adsorption methodology that is potentially useful for this characterization, but has not yet been applied, is discussed. The ordered organic−inorganic nanocomposites include surface-functionalized ordered mesoporous materials (OMMs) with siliceous frameworks (synthesized either via postsynthesis surface modification or via direct co-condensation method), periodic mesoporous organosilicas, and surfactant-containing OMMs. This review covers the methods for determination of the specific surface area and pore volume. The available methods for mesopore size analysis are critically compared and evaluated, with special emphasis on the recent developments related to the application of advanced computational methods for studying adsorption in porous media and to the direct modeling of adsorption using highly ordered surface-functionalized OMMs as model a...

2,987 citations

Journal ArticleDOI
TL;DR: In this article, the pore size distributions derived from adsorption isotherms of micro- and mesoporous materials are identified and discussed based on new results and examples reported in the recent literature.

1,775 citations

Reference EntryDOI
15 Mar 2008
TL;DR: The sections in this article are==================PRECI and the standard isotherm concept as mentioned in this paper, the BET method, the standard isotope concept, and an assessment of porosity.
Abstract: The sections in this article are Introduction Physisorption of Gases Determination of Surface Area The BET Method The Standard Isotherm Concept Assessment of Porosity Capillary Condensation and the Kelvin Equation Adsorption Hysteresis Microporosity Micropore Analysis: Dubinin's Theory of Micropore Filling Micropore Analysis: Empirical Methods Other Methods for Micropore Pore Size Analysis Application of Density Functional Theory Adsorption at the Liquid–Solid Interface Adsorption from Solution Heat of Immersion Mercury Porosimetry General Conclusions Keywords: physisorption; pore size; mercury porosimetry; heat of immersion

1,170 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a new equation of state for rigid spheres has been developed from an analysis of the reduced virial series, which possesses superior ability to describe rigid-sphere behavior compared with existing equations.
Abstract: A new equation of state for rigid spheres has been developed from an analysis of the reduced virial series. Comparisons with existing equations show that the new formula possesses superior ability to describe rigid‐sphere behavior.

4,659 citations

Journal ArticleDOI
TL;DR: In this paper, the Fourier transform of the pair correlation function is used to calculate the structure factor of a reference system in which the intermolecular forces are entirely repulsive and identical to the repulsive forces in a Lennard-Jones fluid.
Abstract: The different roles the attractive and repulsive forces play in forming the equilibrium structure of a Lennard‐Jones liquid are discussed. It is found that the effects of these forces are most easily separated by considering the structure factor (or equivalently, the Fourier transform of the pair‐correlation function) rather than the pair‐correlation function itself. At intermediate and large wave vectors, the repulsive forces dominate the quantitative behavior of the liquid structure factor. The attractions are manifested primarily in the small wave vector part of the structure factor; but this effect decreases as the density increases and is almost negligible at reduced densities higher than 0.65. These conclusions are established by considering the structure factor of a hypothetical reference system in which the intermolecular forces are entirely repulsive and identical to the repulsive forces in a Lennard‐Jones fluid. This reference system structure factor is calculated with the aid of a simple but accurate approximation described herein. The conclusions lead to a very simple prescription for calculating the radial distribution function of dense liquids which is more accurate than that obtained by any previously reported theory. The thermodynamic ramifications of the conclusions are presented in the form of calculations of the free energy, the internal energy (from the energy equation), and the pressure (from the virial equation). The implications of our conclusions to perturbation theories for liquids and to the interpretation of x‐ray scattering experiments are discussed.

4,462 citations

Journal ArticleDOI
TL;DR: The main purpose of this paper is to advocate the use of the graph associated with Tikhonov regularization in the numerical treatment of discrete ill-posed problems, and to demonstrate several important relations between regularized solutions and the graph.
Abstract: When discrete ill-posed problems are analyzed and solved by various numerical regularization techniques, a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector. In particular, the graph associated with Tikhonov regularization plays a central role. The main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill-posed problems. The graph is characterized quantitatively, and several important relations between regularized solutions and the graph are derived. It is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic L-shaped “corner” of the graph.

3,585 citations

Journal ArticleDOI
TL;DR: In this paper, a method for the calculation of effective pore size distribution from adsorption isotherms in molecular-sieve carbon is described, which is more exact theoretically as well as practically than previously described methods.
Abstract: A method for the calculation of effective pore size distribution from adsorption isotherms in molecular-sieve carbon is described. This method is more exact theoretically as well as practically than previously described methods. An average potential function has been determined inside the slit-like pores. With the help of this function the doubtful use of the Kelvin equation can be avoided at the scale of molecular dimensions. The method gives poor values for the larger pores but can be combined with the well-known Dollimore-Heal method at a pore size of 1.34 nm. Calculation is possible over a wide range of pore sizes. The calculation is shown through two examples from N2 isotherms at 77.4K. The model can be extended to other pore shapes as well as to other adsorbent-adsorbate pairs.

1,784 citations