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BET theory
About: BET theory is a research topic. Over the lifetime, 9046 publications have been published within this topic receiving 286142 citations.
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19 Jul 1984
TL;DR: In this article, the authors compare the single-point and multi-point methods for surface area analysis with the single point and multipoint methods for measuring porosimetry and gas adsorption.
Abstract: I Theoretical.- 1 Introduction.- 1.1 Real surfaces.- 1.2 Factors affecting surface area.- 1.3 Surface area from size distributions.- 2 Gas adsorption.- 2.1 Introduction.- 2.2 Physical and chemical adsorption.- 2.3 Physical adsorption forces.- 3 Adsorption isotherms.- 4 Langmuir and BET theories.- 4.1 The Langmuir isotherm, type I.- 4.2 The Brunauer, Emmett and Teller (BET) theory.- 4.3 Surface areas from the BET equation.- 4.4 The meaning of monolayer coverage.- 4.5 The BET constant and site occupancy.- 4.6 Applicability of the BET theory.- 4.7 Some criticism of the BET theory.- 5 The single point BET method.- 5.1 Derivation of the single-point method.- 5.2 Comparison of the single-point and multipoint methods.- 5.3 Further comparisons of the multi- and single-point methods.- 6 Adsorbate cross-sectional areas.- 6.1 Cross-sectional areas from the liquid molar volume.- 6.2 Nitrogen as the standard adsorbate.- 6.3 Some adsorbate cross-sectional areas.- 7 Other surface area methods.- 7.1 Harkins and Jura relative method.- 7.2 Harkins and Jura absolute method.- 7.3 Permeametry.- 8 Pore analysis by adsorption.- 8.1 The Kelvin equation.- 8.2 Adsorption hysteresis.- 8.3 Types of hysteresis.- 8.4 Total pore volume.- 8.5 Pore-size distributions.- 8.6 Modelless pore-size analysis.- 8.7 V?t curves.- 9 Microporosity.- 9.1 Introduction.- 9.2 Langmuir plots for microporous surface area.- 9.3 Extensions of Polanyi's theory for micropore volume and area.- 9.4 The t-method.- 9.5 The MP method.- 9.6 Total micropore volume and surface area.- 10 Theory of wetting and capillarity for mercury porosimetry.- 10.1 Introduction.- 10.2 Young and Laplace equation.- 10.3 Wetting or contact angles.- 10.4 Capillarity.- 10.5 Washburn equation.- 11 Interpretation of mercury porosimetry data.- 11.1 Application of the Washburn equation.- 11.2 Intrusion-extrusion curves.- 11.3 Common features of porosimetry curves.- 11.4 Solid compressibility.- 11.5 Surface area from intrusion curves.- 11.6 Pore-size distribution.- 11.7 Volume In radius distribution function.- 11.8 Pore surface area distribution.- 11.9 Pore length distribution.- 11.10 Pore population.- 11.11 Plots of porosimetry functions.- 11.12 Comparisons of porosimetry and gas adsorption.- 12 Hysteresis, entrapment, and contact angle.- 12.1 Introduction.- 12.2 Contact angle changes.- 12.3 Porosimetric work.- 12.4 Theory of porosimetry hysteresis.- 12.5 Pore potential.- 12.6 Other hysteresis theories.- 12.7 Equivalency of mercury porosimetry and gas adsorption.- II Experimental.- 13 Adsorption measurements-Preliminaries.- 13.1 Reference standards.- 13.2 Other preliminary precautions.- 13.3 Representative samples.- 13.4 Sample conditioning.- 14 Vacuum volumetric measurements.- 14.1 Nitrogen adsorption.- 14.2 Deviation from ideality.- 14.3 Sample cells.- 14.4 Evacuation and outgassing.- 14.5 Temperature control.- 14.6 Isotherms.- 14.7 Low surface areas.- 14.8 Saturated vapor pressure, P0 of nitrogen.- 15 Dynamic methods.- 15.1 Influence of helium.- 15.2 Nelson and Eggertsen continuous flow method.- 15.3 Carrier gas and detector sensitivity.- 15.4 Design parameters for continuous flow apparatus.- 15.5 Signals and signal calibration.- 15.6 Adsorption and desorption isotherms by continuous flow.- 15.7 Low surface area measurements.- 15.8 Data reduction-continuous flow.- 15.9 Single-point method.- 16 Other flow methods.- 16.1 Pressure jump method.- 16.2 Continuous isotherms.- 16.3 Frontal analysis.- 17 Gravimetric method.- 17.1 Electronic microbalances.- 17.2 Buoyancy corrections.- 17.3 Thermal transpiration.- 17.4 Other gravimetric methods.- 18 Comparison of experimental adsorption methods.- 19 Chemisorption.- 19.1 Introduction.- 19.2 Chemisorption equilibrium and kinetics.- 19.3 Chemisorption isotherms.- 19.4 Surface titrations.- 20 Mercury porosimetry.- 20.1 Introduction.- 20.2 Pressure generators.- 20.3 Dilatometer.- 20.4 Continuous-scan porosimetry.- 20.5 Logarithmic signals from continuous-scan porosimetry.- 20.6 Low pressure intrusion-extrusion scans.- 20.7 Scanning porosimetry data reduction.- 20.8 Contact angle for mercury porosimetry.- 21 Density measurement.- 21.1 True density.- 21.2 Apparent density.- 21.3 Bulk density.- 21.4 Tap density.- 21.5 Effective density.- 21.6 Density by mercury porosimetry.- References.
1,066 citations
TL;DR: The prepared MMWCNT adsorbent displayed the main advantage of separation convenience compared to the present adsorption treatment and was well fitted by a pseudo second-order model.
942 citations
TL;DR: Grand canonical Monte Carlo simulations were used to predict adsorption isotherms for nitrogen in a series of MOFs to test the applicability of the BET theory for obtaining surface areas of microporous MOFs, and the results provide a strong validation that the bet theory can be used to obtain surface areasof MOFs.
Abstract: The surface area is one of the most important quantities for characterizing novel porous materials. The BET analysis is the standard method for determining surface areas from nitrogen adsorption isotherms and was originally derived for multilayer gas adsorption onto flat surfaces. Metal-organic frameworks (MOFs) are a relatively new class of crystalline, porous materials that have been shown to exhibit very large BET surface areas. These materials are microporous and possess surfaces that are far from flat. In some MOFs, adsorption occurs through a pore-filling mechanism rather than by layer formation. Thus, it is unclear whether BET surface area numbers reported for these materials are truly meaningful. Given the standard practice of reporting BET surface areas for novel porous materials, a critical test of the BET method is much needed. In this work, grand canonical Monte Carlo simulations were used to predict adsorption isotherms for nitrogen in a series of MOFs. The predicted isotherms were used as pseudoexperimental data to test the applicability of the BET theory for obtaining surface areas of microporous MOFs. BET surface areas calculated from the simulated isotherms agree very well with the accessible surface areas calculated directly from the crystal structures in a geometric fashion. In addition, the surface areas agree well with experimental reports in the literature. These results provide a strong validation that the BET theory can be used to obtain surface areas of MOFs.
856 citations
TL;DR: In this paper, a series of activated carbons (ACs) with progressively changing nanotextural characteristics was obtained by heat-treatment of a bituminous coal at temperatures ranging from 520 to 1000°C, and subsequent activation by KOH at 700 or 800°C.
855 citations
TL;DR: The most active catalysts were formed when Fe was added to the support before the pyrolysis; however, samples in which Ni or no metal was added still showed increased activity for oxygen reduction compared with untreated carbon as mentioned in this paper.
849 citations