Surface Area and Porosity Determinations by Physisorption (eBook)

Cover 1
Table of Contents 6
Foreword 12
Acknowledgments 16
Symbol List 18
Chapter 1 : An Overview of Physisorption 24
Introduction Scope and Terminology 24
General Description of Physisorption 24
Measuring the Surface Area by Physisorption 27
Preliminary Analysis 29
The Adsorption Isotherm Types 29
Characterization of Hysteresis Loops 34
Measuring the Surface Area from the Isotherm 37
Determining Porosity by Physical Adsorption 39
Micropores 39
Mesopores 41
Obtaining Pore Radius from the Two Slopes 42
The Use of the Kelvin Equation Value of rp for Mesopores 44
Macropores 44
Statistical Treatment of Isotherms 44
Adsorption Types in Standard Isotherm Transformations 46
References 49
Chapter 2 : Measuring the Physisorption Isotherm 52
Introduction: Equipment Requirements 52
The Volumetric Method 53
Equipment Description 53
Determination Method 55
Error Analysis for the Volumetric Method 57
Design Errors 57
Poor Calibration of V1 58
Molecular Flow Versus Viscous Flow 58
Equation of State Errors 60
Temperature Control of the Sample 60
Limit of Detection 60
Advantages and Disadvantages of the Volumetric Technique 61
The Gravimetric Method 61
Equipment Description 61
Determination Method 64
Error Analysis for the Gravimetric Technique 65
Advantages and Disadvantages of the Gravimetric Technique 66
General Error Analysis – Common to both Volumetric and Gravimetric 67
Pressure and Temperature Measurements 67
Kinetic Problems 69
Sample Density Problems 69
Calorimetric Techniques 70
Adiabatic Calorimetry 70
Measuring the Isosteric Heat of Adsorption 71
The Thermal AbsoluteŽ Method 72
Differential Scanning Calorimetry 73
Flow Method or Carrier Gas Method 74
References 75
Chapter 3 : Interpreting the Physisorption Isotherm 78
Objectives in Interpreting Isotherms 78
Determination of Surface Area from Isotherms 82
The BET Analysis 83
. Plot Analysis 85
The Method of Determining Surface Area by Dubinin et al. 86
Tóth T-Equation Isotherm 86
The Harkins–Jura Absolute/Relative Method 87
Porosity Determinations from the Isotherm 88
Micropore Analysis 89
Mesoporosity Analysis 91
Isotherm Fits which Yield Relative Numbers for the Surface Area 95
Langmuir Isotherm 95
Freundlich Isotherm 97
Polanyi Formulations 98
deBoer–Zwikker Formulation 99
The Frenkel, Halsey, Hill (FHH) Isotherm 99
Analysis Using Standard Isotherms 100
Standard Isotherms 101
The as-Curve Standard (see Sing, Everett and Ottewill [6]) 101
The t-Curve 101
IUPAC Standards on Silica and Carbon 103
RMBM Carbon Standard 105
KFG Segmented Standard Carbon Curve 107
Cranston and Inkley Standard for Pore Analysis 107
Thoria Standard Curves 108
Standard Curves for Lunar Soil 109
References 112
Chapter 4 : Theories Behind the Chi Plot 114
Introduction: Historical Background 114
Theory Behind . Plots 114
The Disjoining Pressure Derivation 114
The Meaning of Gm in the Hard Sphere Model 116
The Quantum Mechanical Derivation of the “Simple” . Equation 118
The Meaning of aex – the Perfect Adsorption Equation for Hard Spheres 121
The Energy Correction 122
Simultaneous Physisorption and Chemisorption 125
Heterogeneous Surfaces 127
Additivity of . Plots 127
Insensitivity for .= max .c 130
Reformulation for a Distribution of Ea Values 130
Heats of Adsorption 131
Isosteric Heat of Adsorption, qst 131
The Integral Heats of Adsorption 132
Adsorption of more than one Adsorbate3 134
Binary Adsorption on a Flat Surface 135
Depth Profiles and . Theory 139
The Thermodynamics of the Spreading Pressure 142
Gibbs’ Phase Rule in Systems with Surfaces 142
Derivation of the Spreading Pressure 143
Is the . Plot Compatible with the Freundlich and Dubinin Isotherms? 146
References 148
Chapter 5 : Comparison of the Chi Equation to Measurements 150
Comparsion to Standard Isotherms 150
The a–s Standard Plots 150
Cranston and Inkley Standard t Curve 151
deBoer’s Standard t-Plots 152
Standard Thoria Plots 153
Standard Curves for Lunar Soils 157
Isotherms by Nicolan and Teichner 159
Isotherms Quoted by Bradley 159
Conclusion and some Comments about Carbon 161
The Observation of .c 163
Observations of the Energy Implications of .c 164
Direct Observation of .c 166
Conclusion Concerning .c 171
Multiplane Adsorption 172
Examples of Two Plane Adsorption 172
The Freundlich, Dubinin-Polanyi and Tóth Isotherms 173
Conclusion Concerning Multiple Energies 177
Heat of Adsorption 177
Adsorption of more than One Adsorbate 179
Adsorption on Non-Porous Surface 179
Binary Adsorption in Micropores 181
Lewis Rule Assumption 181
Binary Adsorption at a Constant Pressure 183
Comparison to Experiments 184
Conclusions Regarding Binary Adsorption 188
Statistical Comparisons of other Isotherms to the . Plot 188
General Conclusions 190
References 191
Chapter 6 : Porosity Calculations 194
Introduction 194
Micropore Analysis 195
The BDDT Equation 195
The DR and DA Equations 197
Standard Curve Analysis using Distributions – Uninterpreted 198
Chi Theory Interpretation of the Distribution Fit 203
Surface Areas and Pore Volume Calculations 203
Calculation of Pore Size Assuming a Geometry 204
Calculating rp from ..p 204
Examples of Results 205
Analysis of Mesoporosity 209
Some Comments about the Standard Plot of Determining Mesoporosity 210
The Broekhoff„deBoer Theory 212
Is it Microporous or Mesoporous and Does it Matter? 219
Combined Mesopore/Micropore Equation 219
The Interpretation of Mesopore Equation using Standard Curve 220
The Boundary between Mesopores and Micropores 221
Does it Matter Whether to Use a Micropore or a Mesopore Analysis? 222
Real Data Examples 224
What Does Chi Theory Say about Hysteresis? 225
Conclusions 226
References 228
Chapter 7 : Density Functional Theory 230
Introduction 230
What is a Functional? 230
The Functional Derivative 232
Correlation Functions 234
A Quick Trip through Some Partition Functions 235
Direct Correlation Functions 239
The Hard-Rod Approximations 240
Hard Rods between Two Walls 244
Percus–Yevick Solution Expansion for Hard Spheres 246
Thiele Analytical Approximation 247
The Carnahan–Starling Approximation 248
Helmholtz Free Energy from the CS Approximation 249
Non-Local Density Functional Theory 250
Modeling with the Presence of a Surface 253
References 256
Appendix : Equipment Specifications 258
Author Index 292
Subject Index 296