Elsevier, First edition 2006, 297c.
1. Physisorption.
2. Porosity.
3. Surfaces, Isothermic.
4. Density functionals.
5. Adsorption. I. Title.
Notice
No responsibility is assumed by the publisher for any injury and/or damage to persons
or property as a matter of products liability, negligence or otherwise, or from any use
or operation of any methods, products, instructions or ideas contained in the material
herein. Because of rapid advances in the medical sciences, in particular, independent
verification of diagnoses and drug dosages should be made.
Table of Contents
Foreword.xi
Acknowledgments .xv
Symbol List .xvii
CHAPTER 1 : AN OVERVIEW OF PHYSISORPTION
Introduction Scope and Terminology
General Description of Physisorption
Measuring the Surface Area by Physisorption
Preliminary Analysis
The Adsorption Isotherm Types
Characterization of Hysteresis Loops
Measuring the Surface Area from the Isotherm
Determining Porosity by Physical Adsorption
Micropores
Mesopores
Obtaining Pore Radius from the Two Slopes
The Use of the Kelvin Equation Value of rp for Mesopores
Macropores
Statistical Treatment of Isotherms
Adsorption Types in Standard Isotherm Transformations
References
Introduction: Equipment Requirements
The Volumetric Method
Equipment Description
Determination Method
Error Analysis for the Volumetric Method
Design Errors
Poor Calibration of V
Molecular Flow Versus Viscous Flow
Equation of State Errors
Temperature Control of the Sample
Limit of Detection
Advantages and Disadvantages of the Volumetric Technique
The Gravimetric Method
Equipment Description
Determination Method
Error Analysis for the Gravimetric Technique
Advantages and Disadvantages of the Gravimetric Technique
General Error Analysis – Common to both Volumetric and Gravimetric
Pressure and Temperature Measurements
Kinetic Problems
Sample Density Problems
Calorimetric Techniques
Adiabatic Calorimetry
Measuring the Isosteric Heat of Adsorption
The Thermal Absolute Method
Differential Scanning Calorimetry
Flow Method or Carrier Gas Method
References
CHAPTER 3 : INTERPRETING THE PHYSISORPTION ISOTHERM
Objectives in Interpreting Isotherms
Determination of Surface Area from Isotherms
The BET Analysis
Plot Analysis
The Method of Determining Surface Area by Dubinin et al
T?th T-Equation Isotherm
The Harkins–Jura Absolute/Relative Method
Porosity Determinations from the Isotherm
Micropore Analysis
Mesoporosity Analysis
Isotherm Fits which Yield Relative Numbers for the Surface Area
Langmuir Isotherm
Freundlich Isotherm
Polanyi Formulations
deBoer–Zwikker Formulation
The Frenkel, Halsey, Hill (FHH) Isotherm
Analysis Using Standard Isotherms
Standard Isotherms
The s-Curve Standard (see Sing, Everett and Ottewill [6])
The t-Curve
IUPAC Standards on Silica and Carbon
RMBM Carbon Standard
KFG Segmented Standard Carbon Curve
Cranston and Inkley Standard for Pore Analysis
Thoria Standard Curves
Standard Curves for Lunar Soil
References
CHAPTER 4 : THEORIES BEHIND THE CHI PLOT
Introduction: Historical Background
Theory Behind Plots
The Disjoining Pressure Derivation
The Meaning of ?m in the Hard Sphere Model
The Quantum Mechanical Derivation of the Simple Equation
The Meaning of aex – the Perfect Adsorption Equation for
Hard Spheres
The Energy Correction
Simultaneous Physisorption and Chemisorption
Heterogeneous Surfaces
Additivity of Plots
Insensitivity for max c
Reformulation for a Distribution of Ea Values
Heats of Adsorption
Isosteric Heat of Adsorption, qst
The Integral Heats of Adsorption
Adsorption of more than One Adsorbate
Binary Adsorption on a Flat Surface
Depth Profiles and Theory
The Thermodynamics of the Spreading Pressure
Gibbs’ Phase Rule in Systems with Surfaces
Derivation of the Spreading Pressure
Is the Plot Compatible with the Freundlich and Dubinin
Isotherms?
References
CHAPTER 5 : COMPARISON OF THE CHI EQUATION TO
MEASUREMENTS
Comparsion to Standard Isotherms
The –s Standard Plots
Cranston and Inkley Standard t Curve
deBoer’s Standard t-Plots
Standard Thoria Plots
Standard Curves for Lunar Soils
Isotherms by Nicolan and Teichner
Isotherms Quoted by Bradley
Conclusion and some Comments about Carbon
The Observation of c
Observations of the Energy Implications of c
Direct Observation of c
Conclusion Conceing c
Multiplane Adsorption
Examples of Two Plane Adsorption
The Freundlich, Dubinin-Polanyi and T?th Isotherms
Conclusion Conceing Multiple Energies
Heat of Adsorption
Adsorption of more than One Adsorbate
Adsorption on Non-Porous Surface
Binary Adsorption in Micropores
Lewis Rule Assumption
Binary Adsorption at a Constant Pressure
Comparison to Experiments
Conclusions Regarding Binary Adsorption
Statistical Comparisons of other Isotherms to the Plot
General Conclusions
References
CHAPTER 6 : POROSITY CALCULATIONS
Introduction
Micropore Analysis
The BDDT Equation
The DR and DA Equations
Standard Curve Analysis using Distributions – Uninterpreted
Chi Theory Interpretation of the Distribution Fit
Surface Areas and Pore Volume Calculations
Calculation of Pore Size Assuming a Geometry
Calculating rp from
Examples of Results
Analysis of Mesoporosity
Some Comments about the Standard Plot of Determining Mesoporosity
The Broekhoff—deBoer Theory
Is it Microporous or Mesoporous and Does it Matter?
Combined Mesopore/Micropore Equation
The Interpretation of Mesopore Equation using Standard Curve
The Boundary between Mesopores and Micropores
Does it Matter Whether to Use a Micropore or a Mesopore Analysis?
Real Data Examples
What Does Chi Theory Say about Hysteresis?
Conclusions
References
CHAPTER 7 : DENSITY FUNCTIONAL THEORY
Introduction
What is a Functional?
The Functional Derivative
Correlation Functions
A Quick Trip through Some Partition Functions
Direct Correlation Functions
The Hard-Rod Approximations
Hard Rods between Two Walls
Percus–Yevick Solution Expansion for Hard Spheres
Thiele Analytical Approximation
The Caahan–Starling Approximation
Helmholtz Free Energy from the CS Approximation
Non-Local Density Functional Theory
Modeling with the Presence of a Surface
References
APPENDIX : EQUIPMENT SPECIFICATIONS
Author Index
Subject Index
1. Physisorption.
2. Porosity.
3. Surfaces, Isothermic.
4. Density functionals.
5. Adsorption. I. Title.
Notice
No responsibility is assumed by the publisher for any injury and/or damage to persons
or property as a matter of products liability, negligence or otherwise, or from any use
or operation of any methods, products, instructions or ideas contained in the material
herein. Because of rapid advances in the medical sciences, in particular, independent
verification of diagnoses and drug dosages should be made.
Table of Contents
Foreword.xi
Acknowledgments .xv
Symbol List .xvii
CHAPTER 1 : AN OVERVIEW OF PHYSISORPTION
Introduction Scope and Terminology
General Description of Physisorption
Measuring the Surface Area by Physisorption
Preliminary Analysis
The Adsorption Isotherm Types
Characterization of Hysteresis Loops
Measuring the Surface Area from the Isotherm
Determining Porosity by Physical Adsorption
Micropores
Mesopores
Obtaining Pore Radius from the Two Slopes
The Use of the Kelvin Equation Value of rp for Mesopores
Macropores
Statistical Treatment of Isotherms
Adsorption Types in Standard Isotherm Transformations
References
Introduction: Equipment Requirements
The Volumetric Method
Equipment Description
Determination Method
Error Analysis for the Volumetric Method
Design Errors
Poor Calibration of V
Molecular Flow Versus Viscous Flow
Equation of State Errors
Temperature Control of the Sample
Limit of Detection
Advantages and Disadvantages of the Volumetric Technique
The Gravimetric Method
Equipment Description
Determination Method
Error Analysis for the Gravimetric Technique
Advantages and Disadvantages of the Gravimetric Technique
General Error Analysis – Common to both Volumetric and Gravimetric
Pressure and Temperature Measurements
Kinetic Problems
Sample Density Problems
Calorimetric Techniques
Adiabatic Calorimetry
Measuring the Isosteric Heat of Adsorption
The Thermal Absolute Method
Differential Scanning Calorimetry
Flow Method or Carrier Gas Method
References
CHAPTER 3 : INTERPRETING THE PHYSISORPTION ISOTHERM
Objectives in Interpreting Isotherms
Determination of Surface Area from Isotherms
The BET Analysis
Plot Analysis
The Method of Determining Surface Area by Dubinin et al
T?th T-Equation Isotherm
The Harkins–Jura Absolute/Relative Method
Porosity Determinations from the Isotherm
Micropore Analysis
Mesoporosity Analysis
Isotherm Fits which Yield Relative Numbers for the Surface Area
Langmuir Isotherm
Freundlich Isotherm
Polanyi Formulations
deBoer–Zwikker Formulation
The Frenkel, Halsey, Hill (FHH) Isotherm
Analysis Using Standard Isotherms
Standard Isotherms
The s-Curve Standard (see Sing, Everett and Ottewill [6])
The t-Curve
IUPAC Standards on Silica and Carbon
RMBM Carbon Standard
KFG Segmented Standard Carbon Curve
Cranston and Inkley Standard for Pore Analysis
Thoria Standard Curves
Standard Curves for Lunar Soil
References
CHAPTER 4 : THEORIES BEHIND THE CHI PLOT
Introduction: Historical Background
Theory Behind Plots
The Disjoining Pressure Derivation
The Meaning of ?m in the Hard Sphere Model
The Quantum Mechanical Derivation of the Simple Equation
The Meaning of aex – the Perfect Adsorption Equation for
Hard Spheres
The Energy Correction
Simultaneous Physisorption and Chemisorption
Heterogeneous Surfaces
Additivity of Plots
Insensitivity for max c
Reformulation for a Distribution of Ea Values
Heats of Adsorption
Isosteric Heat of Adsorption, qst
The Integral Heats of Adsorption
Adsorption of more than One Adsorbate
Binary Adsorption on a Flat Surface
Depth Profiles and Theory
The Thermodynamics of the Spreading Pressure
Gibbs’ Phase Rule in Systems with Surfaces
Derivation of the Spreading Pressure
Is the Plot Compatible with the Freundlich and Dubinin
Isotherms?
References
CHAPTER 5 : COMPARISON OF THE CHI EQUATION TO
MEASUREMENTS
Comparsion to Standard Isotherms
The –s Standard Plots
Cranston and Inkley Standard t Curve
deBoer’s Standard t-Plots
Standard Thoria Plots
Standard Curves for Lunar Soils
Isotherms by Nicolan and Teichner
Isotherms Quoted by Bradley
Conclusion and some Comments about Carbon
The Observation of c
Observations of the Energy Implications of c
Direct Observation of c
Conclusion Conceing c
Multiplane Adsorption
Examples of Two Plane Adsorption
The Freundlich, Dubinin-Polanyi and T?th Isotherms
Conclusion Conceing Multiple Energies
Heat of Adsorption
Adsorption of more than One Adsorbate
Adsorption on Non-Porous Surface
Binary Adsorption in Micropores
Lewis Rule Assumption
Binary Adsorption at a Constant Pressure
Comparison to Experiments
Conclusions Regarding Binary Adsorption
Statistical Comparisons of other Isotherms to the Plot
General Conclusions
References
CHAPTER 6 : POROSITY CALCULATIONS
Introduction
Micropore Analysis
The BDDT Equation
The DR and DA Equations
Standard Curve Analysis using Distributions – Uninterpreted
Chi Theory Interpretation of the Distribution Fit
Surface Areas and Pore Volume Calculations
Calculation of Pore Size Assuming a Geometry
Calculating rp from
Examples of Results
Analysis of Mesoporosity
Some Comments about the Standard Plot of Determining Mesoporosity
The Broekhoff—deBoer Theory
Is it Microporous or Mesoporous and Does it Matter?
Combined Mesopore/Micropore Equation
The Interpretation of Mesopore Equation using Standard Curve
The Boundary between Mesopores and Micropores
Does it Matter Whether to Use a Micropore or a Mesopore Analysis?
Real Data Examples
What Does Chi Theory Say about Hysteresis?
Conclusions
References
CHAPTER 7 : DENSITY FUNCTIONAL THEORY
Introduction
What is a Functional?
The Functional Derivative
Correlation Functions
A Quick Trip through Some Partition Functions
Direct Correlation Functions
The Hard-Rod Approximations
Hard Rods between Two Walls
Percus–Yevick Solution Expansion for Hard Spheres
Thiele Analytical Approximation
The Caahan–Starling Approximation
Helmholtz Free Energy from the CS Approximation
Non-Local Density Functional Theory
Modeling with the Presence of a Surface
References
APPENDIX : EQUIPMENT SPECIFICATIONS
Author Index
Subject Index