BET theory

Abstract: 1 Theoretical- 1 Introduction- 11 Real Surfaces- 12 Factors Affecting Surface area- 13 Surface Area from Particle Size Distributions- 14 References- 2 Gas Adsorption- 21 Introduction- 22 Physical and Chemical Adsorption- 23 Physical Adsorption Forces- 24 Physical Adsorption on a Planar Surface- 25 References- 3 Adsorption Isotherms- 31 Pore Size and Adsorption Potential- 32 Classification of Adsorption Isotherms- 33 References- 4 Adsorption Mechanism- 41 Langmuir and BET Theories (Kinetic Isotherms)- 411 The Langmuir Isotherm- 412 The Brunauer, Emmett, and Teller (BET) Theory- 42 The Frenkel-Halsey-Hill (FHH) Theory of Multilayer Adsorption- 43 Adsorption in Microporous Materials- 431 Introduction- 432 Aspects of Classical, Thermodynamic Theories for Adsorption in Micropores: Extension of Polanyi's Theory- 433 Aspects of Modern, Microscopic Theories for Adsorption in Micropores: Density Functional Theory and Molecular Simulation- 4331 Density Functional Theory (DFT)- 4332 Computer Simulation Studies: Monte Carlo Simulation and Molecular Dynamics- 4333 NLDFT and Monte Carlo Simulation for Pore Size Analysis- 44 Adsorption in Mesopores- 441 Introduction- 442 Multilayer Adsorption, Pore Condensation and Hysteresis- 443 Pore Condensation: Macroscopic, Thermodynamic Approaches- 4431 Classical Kelvin Equation- 4432 Modified Kelvin Equation- 444 Adsorption Hysteresis- 4441 Classification of Hysteresis Loops- 4442 Origin of Hysteresis- 445 Effects of Temperature and Pore Size: Experiments and Predictions of Modern, Microscopic Theories- 45 References- 5 Surface Area from the Langmuir and BET Theories- 51 Specific Surface Area from the Langmuir Equation- 52 Specific Surface Area from the BET Equation- 521 BET-Plot and Calculation of the Specific Surface Area- 522 The Meaning of Monolayer Coverage- 523 The BET Constant and Site Occupancy- 524 The Single Point BET Method- 525 Comparison of the Single Point and Multipoint Methods- 526 Applicability of the BET Theory- 527 Importance of the Cross-Sectional Area- 528 Nitrogen as the Standard Adsorptive for Surface Area Measurements- 529 Low Surface Area Analysis- 53 References- 6 Other Surface Area Methods- 61 Introduction- 62 Gas Adsorption: Harkins and Jura Relative Method- 63 Immersion Calorimetry: Harkins and Jura Absolute Method- 64 Permeametry- 65 References- 7 Evaluation of the Fractal Dimension by Gas Adsorption- 71 Introduction- 72 Method of Molecular Tiling- 73 The Frenkel-Halsey-Hill Method- 74 The Thermodynamic Method- 75 Comments About Fractal Dimensions Obtained from Gas Adsorption- 76 References- 8 Mesopore Analysis- 81 Introduction- 82 Methods based on the Kelvin equation- 83 Modelless Pore Size Analysis- 84 Total Pore Volume and Average Pore Size- 85 Classical, Macroscopic Thermodynamic Methods versus Modern, Microscopic Models for Pore Size Analysis- 86 Mesopore Analysis and Hysteresis- 861 Use of Adsorption or Desorption Branch for Pore Size Calculation?- 862 Lower Limit of the Hysteresis Loop- Tensile Strength Hypothesis- 87 Adsorptives other than Nitrogen for Mesopore Analysis- 88 References- 9 Micropore Analysis- 91 Introduction- 92 Micropore Analysis by Isotherm Comparison- 921 Concept of V-t curves- 922 The t- Method- 923 The ?s method- 93 The Micropore Analysis (MP) Method)- 94 Total Micropore Volume and Surface Area- 95 The Dubinin-Radushkevich (DR) Method- 96 The Horvath-Kawazoe (HK) Approach and Related Methods- 97 Application of NLDFT: Combined Micro/Mesopore Analysis With a Single Method- 98 Adsorptives other than Nitrogen for Super- and Ultramicroporosimetry- 99 References- 10 Mercury Porosimetry: Non-Wetting Liquid Penetration- 101 Introduction- 102 Young-Laplace Equation- 103 Contact Angles and Wetting- 104 Capillarity- 105 The Washburn Equation- 106 Intrusion - Extrusion Curves- 107 Common Features of Porosimetry Curves- 108 Hysteresis, Entrapment and Contact Angle- 109 Contact Angle Changes- 1010 Porosimetric Work- 1012 Theory of Porosimetry Hysteresis- 1013 Pore Potential- 1014 Other Hysteresis Theories (Throat-Pore Ratio Network Model)- 1015 Equivalency of Mercury Porosimetry and Gas Sorption- 1016 References- 11 Pore Size and Surface Characteristics of Porous Solids by Mercury Porosimetry- 111 Application of The Washburn Equation- 112 Pore Size and Pore Size Distribution from Mercury Porosimetry- 1121 Linear Pore Volume Distribution- 1122 Logarithmic Pore Volume Distribution- 1123 Pore Number Distributions- 1124 Pore Length Distribution- 1125 Pore Population (Number Distribution)- 1126 Surface Area and Surface Area Distribution from Intrusion Curves- 1127 Pore Area Distributions- 113 Pore Shape from Hysteresis- 114 Fractal Dimension- 115 Permeability- 116 Tortuosity- 117 Particle Size Distribution- 1171 Mayer & Stowe Approach- 1172 Smith & Stermer Approach- 118 Comparison of Porosimetry and Gas Sorption- 119 Solid Compressibility- 1110 References- 12 Chemisorption: Site Specific Gas Adsorption- 121 Chemical Adsorption- 122 Quantitative Measurements- 123 Stoichiometry- 124 Monolayer Coverage- 1241 Extrapolation- 1242 Irreversible Isotherm and Bracketing- 1243 Langmuir Theory- 1244 Temperature Dependent Models- 1245 Temkin Method- 1246 Freundlich Method- 1247 Isotherm Subtraction - Accessing Spillover- 1248 Surface Titration- 125 Active Metal Area- 126 Dispersion- 127 Crystallite (Nanoparticle) Size- 128 Heats of Adsorption and Activation Energy- 1281 Differential Heats of Adsorption- 1282 Integral Heat of Adsorption- 1283 Activation Energy- 129 References- 2 Experimental- 13 Physical Adsorption Measurements - Preliminaries- 131 Experimental Techniques for Physical Adsorption Measurements- 132 Reference Standards- 133 Representative Samples- 134 Sample Conditioning: Outgassing of the Adsorbent- 135 Elutriation and Its Prevention- 136 References- 14 Vacuum Volumetric Measurements (Manometry)- 141 Basics of Volumetric Adsorption Measurement- 142 Deviations from Ideality- 143 Void Volume Determination- 144 Coolant Level and Temperature Control- 145 Saturation Vapor Pressure, P0 and Temperature of the Sample Cell- 146 Sample Cells- 147 Low Surface Area- 148 Micro- and Mesopore Analysis- 1481 Experimental Requirements- 1482 Micropore Analysis and Void Volume Determination- 1483 Thermal Transpiration Correction- 1484 Adsorptives other than Nitrogen for Micro- and Mesopore Analysis - Experimental Aspects- 149 Automated Instrumentation- 1491 Multistation Sorption Analyzer- 1492 The NOVA Concept- 1410 References- 15 Dynamic Flow Method- 151 Nelson and Eggertsen Continuous Flow Method- 152 Carrier Gas (Helium) and Detector Sensitivity- 153 Design Parameters for Continuous Flow Apparatus- 154 Signals and Signal Calibration- 155 Adsorption and Desorption Isotherms by Continuous Flow- 156 Low Surface Areas Measurement- 157 Data Reduction - Continuous Flow Method- 158 Single Point Method- 159 References- 16 Volumetric Chemisorption: Catalyst Characterization by Static Methods- 161 Applications- 162 Sample Requirements- 163 General Description of Equipment- 164 Measuring System- 1641 Pressure Measurement- 1642 Valves- 1643 Vacuum- 1644 Sample Cell- 1645 Heating System- 1646 Gases and Chemical Compatibilities- 165 Pretreatment- 1651 Heating- 1652 Atmosphere- 166 Isotherms- 1661 Reactive Gas- 1662 The Combined Isotherm- 1663 The Weak Isotherm- 1664 The Strong Isotherm- 1665 Multiple Isotherms- 167 References- 17 Dynamic Chemisorption: Catalyst Characterization By Flow Techniques- 171 Applications- 172 Sample Requirements- 173 General Description of Equipment- 1731 Flow Path- 1732 Sample Cell- 1733 Gases- 1734 Heating- 1735 Pulse Injection- 1736 Detector- 174 Pretreatment- 175 Pulse Titration- 176 Additional Requirements for Temperature Programmed Methods- 1761 Programmed Heating- 1762 Sample Temperature- 177 Temperature Programmed Reduction- 178 Temperature Programmed Oxidation- 179 Temperature Programmed Desorption- 1791 Some Specific Applications- 17811 Acid/Base- 17812 Oxidizers- 17813 Reducers- 1710 Mass Spectrometry- 1711 Metal Parameters- 1711 References- 18 Mercury Porosimetry: Intra and Inter- Particle Characterization- 181 Applications- 182 Working with Mercury- 183 Experimental Requirements- 184 Sample Cell- 185 Volume Measurement- 186 Contact Angle- 1861 Dynamic Contact Angle- 1862 Static Contact Angle- 187 A Modern Porosimeter- 188 Low Pressure Measurements- 1881 Sample Cell Evacuation- 1882 Filling with Mercury- 1883 Low Pressure Intrusion-Extrusion- 189 High Pressure Measurements- 1810 Scanning Method- 1811 Stepwise Method- 1812 Mercury Entrapment- 1813 Working with Powders- 1814 Inter/Intra Particle Porosity- 1815 Isostatic Crush Strength- 1816 References- 19 Density Measurement- 191 Introduction- 192 True Density- 193 Apparent Density- 194 Open-Closed Porosity- 195 Bulk Density- 196 Tap Density- 197 Envelope or Geometric Density- 198 Effective Density- 199 Density by Mercury Porosimetry- 1910 Standard Methods- 1911 References

Abstract: The theoretical external specific surface area of single- and multi-walled carbon nanotubes and of carbon nanotube bundles is calculated as a function of their characteristics (diameter, number of walls, number of nanotubes in a bundle). The results are reported in diagrams and tables useful to correlate the microscopic characteristics and the specific surface area of samples. The calculated values are in good agreement with the microscopic characteristics and the specific surface area measurements which have been previously reported in the literature. The specific surface area is a macroscopic parameter which can be helpful to adjust the synthesis conditions of carbon nanotubes.

Abstract: The prototypical metal-organic framework Zn4O(BDC)3 (MOF-5, BDC2- = 1,4-benzenedicarboxylate) decomposes gradually in humid air to form a nonporous solid. Recognizing this, improved procedures for its synthesis and handling were developed, leading to significant increases in N2 and H2 gas adsorption capacities. Nitrogen adsorption isotherms measured at 77 K reveal an enhanced maximum N2 uptake of 44.5 mmol/g and a BET surface area of 3800 m2/g, compared to the 35.8 mmol/g and 3100 m2/g obtained for a sample prepared using previous methods. High-pressure H2 adsorption isotherms show improvements from 5.0 to 7.1 excess wt % at 77 K and 40 bar. The total H2 uptake was further observed to climb to 11.5 wt % at 170 bar, corresponding to a volumetric storage density of 77 g/L. Thus, the air-free compound exhibits the highest gravimetric and volumetric H2 uptake capacities yet demonstrated for a cryogenic hydrogen storage material. Moreover, no loss of capacity was apparent during 24 complete adsorption−desorpti...

Abstract: Analysis of adsorption on a uniform surface using the quasi‐chemical theory of interaction shows that the hypotheses of the BET theory lead to substantially no adsorption beyond the first layer if E2 = EL, and stepwise isotherms if E1>E2>E3>···>EL. For the monolayer adsorption of gases on silver, platinum, and steel, the heterogeneous nature of the adsorbing surface is clearly indicated. Cooperative adsorption on the non‐uniform surface is treated, and the cooperative analog of the Freundlich equation derived. The typical multi‐layer isotherm is shown to be composed of three regions: non‐cooperative adsorption on a strongly heterogeneous surface; cooperative adsorption on a still heterogeneous surface; and cooperative multi‐layer adsorption induced by small van der Waals perturbations some distance from the surface.The isotherm p/p0=exp{—a/θr} is derived and shown to be a good representation of adsorption data that conform to the BET Type I, II, or III shapes.

Abstract: The sections in this article are Introduction General Definitions and Terminology Methodology Methods for the Determination of Adsorption Isotherms Operational Definitions of Adsorption Experimental Procedures Outgassing the Adsorbent Determination of the Adsorption Isotherm Evaluation of Adsorption Data Presentation of Primary Data Classification of Adsorption Isotherms Adsorption Hysteresis Determination of Surface Area Application of the BET Method Empirical Procedures for Isotherm Analysis Assessment of Mesoporosity Properties of Porous Materials Application of the Kelvin Equation Computation of Mesopore Size Distribution Assessment of Microporosity Terminology Concept of Surface Area Assessment of Micropore Volume General Conclusions and Recommendations Keywords: physisorption data; IUPAC; adsorption isotherms; surface area; BET isotherm