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

Abstract

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.-