Characterization of porous solids and powders: surface area, pore size, and density (2005)

1 Theoretical.- 1 Introduction.- 1.1 Real Surfaces.- 1.2 Factors Affecting Surface area.- 1.3 Surface Area from Particle Size Distributions.- 1.4 References.- 2 Gas Adsorption.- 2.1 Introduction.- 2.2 Physical and Chemical Adsorption.- 2.3 Physical Adsorption Forces.- 2.4 Physical Adsorption on a Planar Surface.- 2.5 References.- 3 Adsorption Isotherms.- 3.1 Pore Size and Adsorption Potential.- 3.2 Classification of Adsorption Isotherms.- 3.3 References.- 4 Adsorption Mechanism.- 4.1 Langmuir and BET Theories (Kinetic Isotherms).- 4.1.1 The Langmuir Isotherm.- 4.1.2 The Brunauer, Emmett, and Teller (BET) Theory.- 4.2 The Frenkel-Halsey-Hill (FHH) Theory of Multilayer Adsorption.- 4.3 Adsorption in Microporous Materials.- 4.3.1 Introduction.- 4.3.2 Aspects of Classical, Thermodynamic Theories for Adsorption in Micropores: Extension of Polanyi's Theory.- 4.3.3 Aspects of Modern, Microscopic Theories for Adsorption in Micropores: Density Functional Theory and Molecular Simulation.- 4.3.3.1 Density Functional Theory (DFT).- 4.3.3.2 Computer Simulation Studies: Monte Carlo Simulation and Molecular Dynamics.- 4.3.3.3 NLDFT and Monte Carlo Simulation for Pore Size Analysis.- 4.4 Adsorption in Mesopores.- 4.4.1 Introduction.- 4.4.2 Multilayer Adsorption, Pore Condensation and Hysteresis.- 4.4.3 Pore Condensation: Macroscopic, Thermodynamic Approaches.- 4.4.3.1 Classical Kelvin Equation.- 4.4.3.2 Modified Kelvin Equation.- 4.4.4 Adsorption Hysteresis.- 4.4.4.1 Classification of Hysteresis Loops.- 4.4.4.2 Origin of Hysteresis.- 4.4.5 Effects of Temperature and Pore Size: Experiments and Predictions of Modern, Microscopic Theories.- 4.5 References.- 5 Surface Area from the Langmuir and BET Theories.- 5.1 Specific Surface Area from the Langmuir Equation.- 5.2 Specific Surface Area from the BET Equation.- 5.2.1. BET-Plot and Calculation of the Specific Surface Area.- 5.2.2 The Meaning of Monolayer Coverage.- 5.2.3 The BET Constant and Site Occupancy.- 5.2.4 The Single Point BET Method.- 5.2.5 Comparison of the Single Point and Multipoint Methods.- 5.2.6 Applicability of the BET Theory.- 5.2.7 Importance of the Cross-Sectional Area.- 5.2.8 Nitrogen as the Standard Adsorptive for Surface Area Measurements.- 5.2.9 Low Surface Area Analysis.- 5.3 References.- 6 Other Surface Area Methods.- 6.1 Introduction.- 6.2 Gas Adsorption: Harkins and Jura Relative Method.- 6.3 Immersion Calorimetry: Harkins and Jura Absolute Method.- 6.4 Permeametry.- 6.5 References.- 7 Evaluation of the Fractal Dimension by Gas Adsorption.- 7.1 Introduction.- 7.2 Method of Molecular Tiling.- 7.3 The Frenkel-Halsey-Hill Method.- 7.4 The Thermodynamic Method.- 7.5 Comments About Fractal Dimensions Obtained from Gas Adsorption.- 7.6 References.- 8 Mesopore Analysis.- 8.1 Introduction.- 8.2 Methods based on the Kelvin equation.- 8.3 Modelless Pore Size Analysis.- 8.4 Total Pore Volume and Average Pore Size.- 8.5 Classical, Macroscopic Thermodynamic Methods versus Modern, Microscopic Models for Pore Size Analysis.- 8.6 Mesopore Analysis and Hysteresis.- 8.6.1 Use of Adsorption or Desorption Branch for Pore Size Calculation?.- 8.6.2 Lower Limit of the Hysteresis Loop- Tensile Strength Hypothesis.- 8.7 Adsorptives other than Nitrogen for Mesopore Analysis.- 8.8 References.- 9 Micropore Analysis.- 9.1 Introduction.- 9.2 Micropore Analysis by Isotherm Comparison.- 9.2.1 Concept of V-t curves.- 9.2.2 The t- Method.- 9.2.3 The ?s method.- 9.3 The Micropore Analysis (MP) Method).- 9.4 Total Micropore Volume and Surface Area.- 9.5 The Dubinin-Radushkevich (DR) Method.- 9.6 The Horvath-Kawazoe (HK) Approach and Related Methods.- 9.7 Application of NLDFT: Combined Micro/Mesopore Analysis With a Single Method.- 9.8 Adsorptives other than Nitrogen for Super- and Ultramicroporosimetry.- 9.9 References.- 10 Mercury Porosimetry: Non-Wetting Liquid Penetration.- 10.1 Introduction.- 10.2 Young-Laplace Equation.- 10.3 Contact Angles and Wetting.- 10.4 Capillarity.- 10.5 The Washburn Equation.- 10.6 Intrusion - Extrusion Curves.- 10.7 Common Features of Porosimetry Curves.- 10.8 Hysteresis, Entrapment and Contact Angle.- 10.9 Contact Angle Changes.- 10.10 Porosimetric Work.- 10.12 Theory of Porosimetry Hysteresis.- 10.13 Pore Potential.- 10.14 Other Hysteresis Theories (Throat-Pore Ratio Network Model).- 10.15 Equivalency of Mercury Porosimetry and Gas Sorption.- 10.16 References.- 11 Pore Size and Surface Characteristics of Porous Solids by Mercury Porosimetry.- 11.1 Application of The Washburn Equation.- 11.2 Pore Size and Pore Size Distribution from Mercury Porosimetry.- 11.2.1 Linear Pore Volume Distribution.- 11.2.2 Logarithmic Pore Volume Distribution.- 11.2.3 Pore Number Distributions.- 11.2.4 Pore Length Distribution.- 11.2.5 Pore Population (Number Distribution).- 11.2.6 Surface Area and Surface Area Distribution from Intrusion Curves.- 11.2.7 Pore Area Distributions.- 11.3 Pore Shape from Hysteresis.- 11.4 Fractal Dimension.- 11.5 Permeability.- 11.6 Tortuosity.- 11.7 Particle Size Distribution.- 11.7.1 Mayer & Stowe Approach.- 11.7.2 Smith & Stermer Approach.- 11.8 Comparison of Porosimetry and Gas Sorption.- 11.9 Solid Compressibility.- 11.10 References.- 12 Chemisorption: Site Specific Gas Adsorption.- 12.1 Chemical Adsorption.- 12.2 Quantitative Measurements.- 12.3 Stoichiometry.- 12.4 Monolayer Coverage.- 12.4.1 Extrapolation.- 12.4.2 Irreversible Isotherm and Bracketing.- 12.4.3 Langmuir Theory.- 12.4.4 Temperature Dependent Models.- 12.4.5 Temkin Method.- 12.4.6 Freundlich Method.- 12.4.7 Isotherm Subtraction - Accessing Spillover.- 12.4.8 Surface Titration.- 12.5 Active Metal Area.- 12.6 Dispersion.- 12.7 Crystallite (Nanoparticle) Size.- 12.8 Heats of Adsorption and Activation Energy.- 12.8.1 Differential Heats of Adsorption.- 12.8.2 Integral Heat of Adsorption.- 12.8.3 Activation Energy.- 12.9 References.- 2 Experimental.- 13 Physical Adsorption Measurements - Preliminaries.- 13.1 Experimental Techniques for Physical Adsorption Measurements.- 13.2 Reference Standards.- 13.3 Representative Samples.- 13.4 Sample Conditioning: Outgassing of the Adsorbent.- 13.5 Elutriation and Its Prevention.- 13.6 References.- 14 Vacuum Volumetric Measurements (Manometry).- 14.1 Basics of Volumetric Adsorption Measurement.- 14.2 Deviations from Ideality.- 14.3 Void Volume Determination.- 14.4 Coolant Level and Temperature Control.- 14.5 Saturation Vapor Pressure, P0 and Temperature of the Sample Cell.- 14.6 Sample Cells.- 14.7 Low Surface Area.- 14.8 Micro- and Mesopore Analysis.- 14.8.1 Experimental Requirements.- 14.8.2 Micropore Analysis and Void Volume Determination.- 14.8.3 Thermal Transpiration Correction.- 14.8.4 Adsorptives other than Nitrogen for Micro- and Mesopore Analysis - Experimental Aspects.- 14.9 Automated Instrumentation.- 14.9.1 Multistation Sorption Analyzer.- 14.9.2 The NOVA Concept.- 14.10 References.- 15 Dynamic Flow Method.- 15.1 Nelson and Eggertsen Continuous Flow Method.- 15.2 Carrier Gas (Helium) and Detector Sensitivity.- 15.3. Design Parameters for Continuous Flow Apparatus.- 15.4 Signals and Signal Calibration.- 15.5 Adsorption and Desorption Isotherms by Continuous Flow.- 15.6 Low Surface Areas Measurement.- 15.7 Data Reduction - Continuous Flow Method.- 15.8 Single Point Method.- 15.9 References.- 16 Volumetric Chemisorption: Catalyst Characterization by Static Methods.- 16.1 Applications.- 16.2 Sample Requirements.- 16.3 General Description of Equipment.- 16.4 Measuring System.- 16.4.1 Pressure Measurement.- 16.4.2 Valves.- 16.4.3 Vacuum.- 16.4.4 Sample Cell.- 16.4.5 Heating System.- 16.4.6 Gases and Chemical Compatibilities.- 16.5 Pretreatment.- 16.5.1 Heating.- 16.5.2 Atmosphere.- 16.6 Isotherms.- 16.6.1 Reactive Gas.- 16.6.2 The Combined Isotherm.- 16.6.3 The Weak Isotherm.- 16.6.4 The Strong Isotherm.- 16.6.5 Multiple Isotherms.- 16.7 References.- 17 Dynamic Chemisorption: Catalyst Characterization By Flow Techniques.- 17.1 Applications.- 17.2 Sample Requirements.- 17.3 General Description of Equipment.- 17.3.1 Flow Path.- 17.3.2 Sample Cell.- 17.3.3 Gases.- 17.3.4 Heating.- 17.3.5 Pulse Injection.- 17.3.6 Detector.- 17.4 Pretreatment.- 17.5 Pulse Titration.- 17.6 Additional Requirements for Temperature Programmed Methods.- 17.6.1 Programmed Heating.- 17.6.2 Sample Temperature.- 17.7 Temperature Programmed Reduction.- 17.8 Temperature Programmed Oxidation.- 17.9 Temperature Programmed Desorption.- 17.9.1 Some Specific Applications.- 17.8.1.1 Acid/Base.- 17.8.1.2 Oxidizers.- 17.8.1.3 Reducers.- 17.10 Mass Spectrometry.- 17.11 Metal Parameters.- 17.11 References.- 18 Mercury Porosimetry: Intra and Inter- Particle Characterization.- 18.1 Applications.- 18.2 Working with Mercury.- 18.3 Experimental Requirements.- 18.4 Sample Cell.- 18.5 Volume Measurement.- 18.6 Contact Angle.- 18.6.1 Dynamic Contact Angle.- 18.6.2 Static Contact Angle.- 18.7 A Modern Porosimeter.- 18.8 Low Pressure Measurements.- 18.8.1 Sample Cell Evacuation.- 18.8.2 Filling with Mercury.- 18.8.3 Low Pressure Intrusion-Extrusion.- 18.9 High Pressure Measurements.- 18.10 Scanning Method.- 18.11 Stepwise Method.- 18.12 Mercury Entrapment.- 18.13 Working with Powders.- 18.14 Inter/Intra Particle Porosity.- 18.15 Isostatic Crush Strength.- 18.16 References.- 19 Density Measurement.- 19.1 Introduction.- 19.2 True Density.- 19.3 Apparent Density.- 19.4 Open-Closed Porosity.- 19.5 Bulk Density.- 19.6 Tap Density.- 19.7 Envelope or Geometric Density.- 19.8 Effective Density.- 19.9 Density by Mercury Porosimetry.- 19.10 Standard Methods.- 19.11 References.