Foreword ....................................................... xi
Acknowledgments ................................................ xv
Symbol List .................................................. xvii
CHAPTER 1 : AN OVERVIEW OF PHYSISORPTION
Introduction Scope and Terminology .............................. 1
General Description of Physisorption ............................ 1
Measuring the Surface Area by Physisorption ..................... 4
Preliminary Analysis ............................................ 6
The Adsorption Isotherm Types ................................ 6
Characterization of Hysteresis Loops ........................ 11
Measuring the Surface Area from the Isotherm ................... 14
Determining Porosity by Physical Adsorption .................... 16
Micropores .................................................. 16
Mesopores ................................................... 18
Obtaining Pore Radius from the Two Slopes ................ 19
The Use of the Kelvin Equation Value of rp for
Mesopores ................................................ 21
Macropores ............................................... 21
Statistical Treatment of Isotherms ............................. 21
Adsorption Types in Standard Isotherm Transformations .......... 23
References ..................................................... 26
CHAPTER 2 : MEASURING THE PHYSISORPTION ISOTHERM
Introduction: Equipment Requirements ........................... 29
The Volumetric Method .......................................... 30
Equipment Description ....................................... 30
Determination Method ........................................ 32
Error Analysis for the Volumetric Method .................... 34
Design Errors ............................................ 34
Poor Calibration of V1 ................................... 35
Molecular Flow Versus Viscous Flow ....................... 35
Equation of State Errors ................................. 37
Temperature Control of the Sample ........................ 37
Limit of Detection ....................................... 37
Advantages and Disadvantages of the Volumetric Technique .... 38
The Gravimetric Method ......................................... 38
Equipment Description ....................................... 38
Determination Method ........................................ 41
Error Analysis for the Gravimetric Technique ................ 42
Advantages and Disadvantages of the Gravimetric Technique ... 43
General Error Analysis - Common to both Volumetric and
Gravimetric .................................................... 44
Pressure and Temperature Measurements ....................... 44
Kinetic Problems ............................................ 46
Sample Density Problems ..................................... 46
Calorimetric Techniques ........................................ 47
Adiabatic Calorimetry ....................................... 47
Measuring the Isosteric Heat of Adsorption .................. 48
The Thermal "Absolute" Method ............................... 49
Differential Scanning Calorimetry ........................... 50
Flow Method or Carrier Gas Method .............................. 51
References ..................................................... 52
CHAPTER 3 : INTERPRETING THE PHYSISORPTION ISOTHERM
Objectives in Interpreting Isotherms ........................... 55
Determination of Surface Area from Isotherms ................... 59
The BET Analysis ............................................ 60
χPlot Analysis .............................................. 62
The Method of Determining Surface Area by Dubinin et al ..... 63
Toth T-Equation Isotherm .................................... 63
The Harkins-Jura Absolute/Relative Method ................... 64
Porosity Determinations from the Isotherm ...................... 65
Micropore Analysis .......................................... 66
Mesoporosity Analysis ....................................... 68
Isotherm Fits which Yield Relative Numbers for the Surface
Area ........................................................... 72
Langmuir Isotherm ........................................... 72
Freundlich Isotherm ......................................... 74
Polanyi Formulations ........................................ 75
deBoer-Zwikker Formulation .................................. 76
The Frenkel, Halsey, Hill (FHH) Isotherm .................... 76
Analysis Using Standard Isotherms ........................... 77
Standard Isotherms .......................................... 78
The arCurve Standard (see Sing, Everett and Ottewill
[6]) ..................................................... 78
The α5-Curve ............................................. 78
IUPAC Standards on Silica and Carbon ..................... 80
RMBM Carbon Standard ..................................... 82
KFG Segmented Standard Carbon Curve ...................... 84
Cranston and Inkley Standard for Pore Analysis ........... 84
Thoria Standard Curves ................................... 85
Standard Curves for Lunar Soil ........................... 86
References ..................................................... 89
CHAPTER 4: THEORIES BEHIND THE CHI PLOT
Introduction: Historical Background ............................ 91
Theory Behind χ Plots .......................................... 91
The Disjoining Pressure Derivation .......................... 91
The Meaning of Гm in the Hard Sphere Model .................. 93
The Quantum Mechanical Derivation of the "Simple" χ
Equation .................................................... 95
The Meaning of αex - the Perfect Adsorption Equation for
Hard Spheres ............................................. 98
The Energy Correction ....................................... 99
Simultaneous Physisorption and Chemisorption .................. 102
Heterogeneous Surfaces ........................................ 104
Additivity of χ Plots ...................................... 104
Insensitivity for χ ≥ max χc ............................... 107
Reformulation for a Distribution of Eα Values .............. 107
Heats of Adsorption ........................................... 108
Isosteric Heat of Adsorption, qst .......................... 108
The Integral Heats of Adsorption ........................... 109
Adsorption of more than One Adsorbate ......................... 111
Binary Adsorption on a Flat Surface ........................ 112
Depth Profiles and χ Theory ................................... 116
The Thermodynamics of the Spreading Pressure .................. 119
Gibbs' Phase Rule in Systems with Surfaces ................. 119
Derivation of the Spreading Pressure ....................... 120
Is the χ Plot Compatible with the Freundlich and Dubinin
Isotherms? .............................................. 123
References .................................................... 125
CHAPTER 5: COMPARISON OF THE CHI EQUATION TO MEASUREMENTS
Comparsion to Standard Isotherms .............................. 127
The α-s Standard Plots ..................................... 127
Cranston and Inkley Standard t Curve ....................... 128
deBoer's Standard t-Plots .................................. 129
Standard Thoria Plots ...................................... 130
Standard Curves for Lunar Soils ............................ 134
Isotherms by Nicolan and Teichner .......................... 136
Isotherms Quoted by Bradley ................................ 136
Conclusion and some Comments about Carbon .................. 138
The Observation of χc ......................................... 140
Observations of the Energy Implications of χc .............. 141
Direct Observation of χc ................................... 143
Conclusion Concerning χc ................................... 148
Multiplane Adsorption ......................................... 149
Examples of Two Plane Adsorption ........................... 149
The Freundlich, Dubinin-Polanyi and Toth Isotherms ......... 150
Conclusion Concerning Multiple Energies .................... 154
Heat of Adsorption ............................................ 154
Adsorption of more than One Adsorbate ......................... 156
Adsorption on Non-Porous Surface ........................... 156
Binary Adsorption in Micropores ............................ 158
Lewis Rule Assumption ................................... 158
Binary Adsorption at a Constant Pressure ................ 160
Comparison to Experiments ............................... 161
Conclusions Regarding Binary Adsorption .................... 165
Statistical Comparisons of other Isotherms to the χ Plot ...... 165
General Conclusions ........................................... 167
References .................................................... 168
CHAPTER 6 : POROSITY CALCULATIONS
Introduction .................................................. 171
Micropore Analysis ............................................ 172
The BDDT Equation .......................................... 172
The DR and DA Equations .................................... 174
Standard Curve Analysis using Distributions -
Uninterpreted .............................................. 175
Chi Theory Interpretation of the Distribution Fit .......... 180
Surface Areas and Pore Volume Calculations .............. 180
Calculation of Pore Size Assuming a Geometry ............ 181
Calculating rp from Δχp ................................. 181
Examples of Results ..................................... 182
Analysis of Mesoporosity ...................................... 186
Some Comments about the Standard Plot of Determining
Mesoporosity ............................................... 187
The Broekhoff-deBoer Theory ................................ 189
Is it Microporous or Mesoporous and Does it Matter? ........... 196
Combined Mesopore/Micropore Equation ....................... 196
The Interpretation of Mesopore Equation using Standard
Curve ...................................................... 197
The Boundary between Mesopores and Micropores .............. 198
Does it Matter Whether to Use a Micropore or a Mesopore
Analysis? .................................................. 199
Real Data Examples ......................................... 201
What Does Chi Theory Say about Hysteresis? ................. 202
Conclusions ................................................... 203
References .................................................... 205
CHAPTER 7: DENSITY FUNCTIONAL THEORY
Introduction .................................................. 207
What is a Functional? ......................................... 207
The Functional Derivative ..................................... 209
Correlation Functions ......................................... 211
A Quick Trip through Some Partition Functions ................. 212
Direct Correlation Functions .................................. 216
The Hard-Rod Approximations ................................... 217
Hard Rods between Two Walls ................................... 221
Percus-Yevick Solution Expansion for Hard Spheres ............. 223
Thiele Analytical Approximation ............................... 224
The Carnahan-Starling Approximation ........................... 225
Helmholtz Free Energy from the CS Approximation ............... 226
Non-Local Density Functional Theory ........................... 227
Modeling with the Presence of a Surface ....................... 230
References .................................................... 233
APPENDIX : EQUIPMENT SPECIFICATIONS ........................... 235
Author Index .................................................. 269
Subject Index ................................................. 273
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