Chapter 1 Statistical Mechanics ................................ 1
1.1 Introduction ............................................... 1
1.1.1 Thermodynamic Functions and Relationships ........... 1
1.2 Definition of Microstate and Macrostate .................... 2
1.3 Definition of Ensemble ..................................... 4
1.4 The Canonical Ensemble ..................................... 5
1.5 Evaluation of α and β for the Canonical Ensemble ........... 8
1.6 The Grand Canonical Ensemble ............................... 9
1.7 Evaluation of α, β and γ for the Grand Canonical
Ensemble .................................................. 11
1.8 Canonical Partition Function for a System of
Noninteracting Particles .................................. 13
1.9 Factorization of the Molecular Partition Function ......... 15
1.10 Density Functional Theory (DFT) ........................... 16
1.11 Thermodynamics of Irreversible Processes .................. 20
1.12 Statistical Mechanics of Irreversible Processes ........... 23
1.12.1 Correlation Functions and Generalized
Susceptibilities ................................... 24
1.12.2 Calculation of the Mean Square Displacement and
the Self-Diffusion Coefficient ..................... 26
1.12.2.1 Calculation of the Mean Square
Displacement with the Help of the
Velocity Autocorrelation Function ......... 26
1.12.2.2 Langevin's Brownian Motion Model .......... 27
1.12.2.3 The Diffusion Equation .................... 29
References ..................................................... 31
Appendix 1.1 Legendre Transformations ......................... 33
Appendix 1.2 The Lagrange Multipliers ......................... 33
Appendix 1.3 Methods of Counting .............................. 35
Appendix 1.4 Calculus of Variations ........................... 36
Chapter 2 General Introduction to Adsorption in Solids ........ 39
2.1 Definitions and Terminology ............................... 39
2.1.1 What Is the Meaning of the Term Adsorption ......... 39
2.1.2 Phases and Components Involved in the Adsorption
Process ............................................ 39
2.1.3 Porous Materials ................................... 40
2.2 Interfacial Layer, Gibbs Dividing Surface, and Gibbs
Adsorption ................................................ 41
2.3 Thermodynamics of Gas-Solid Adsorption .................... 43
2.3.1 Adsorption Interaction Fields ...................... 43
2.3.2 Isosteric and Differential Heats of Adsorption ..... 44
2.3.3 Some Relations between Adsorption Macroscopic and
Microscopic Parameters ............................. 46
2.4 Gases and Vapors Adsorption in Porous Materials ........... 47
2.4.1 Measurement of Adsorption Isotherms by the
Volumetric Method .................................. 47
2.4.2 Porous Materials Characterization by Vapor
Adsorption Methods ................................. 49
2.5 Some Examples of the Application of the Volumetric
Method .................................................... 50
2.5.1 Volumetric Automatic Surface Area and Porosity
Measurement Systems ................................ 50
2.5.2 Adsorption Isotherms of Nitrogen at 77 К in
Zeolites ........................................... 52
2.5.3 Calorimetry of Adsorption of NH3 in AlPO4-5 and
FAPO-5 Molecular Sieves ............................ 53
References ..................................................... 54
Chapter 3 Microporosity and Surface Area Evaluation Methods ... 57
3.1 Introduction .............................................. 57
3.2 The Dubinin and Osmotic Adsorption Isotherms .............. 57
3.2.1 Dubinin Adsorption Isotherm ........................ 57
3.2.2 Osmotic Adsorption Isotherm ........................ 61
3.3 Langmuir and Fowler-Guggenheim Type Adsorption Isotherm
Equations ................................................. 63
3.3.1 Introduction ....................................... 63
3.3.2 Application of the Grand Canonical Ensemble
Methodology to Describe Adsorption in Zeolites ..... 64
3.3.2.1 Immobile Adsorption ....................... 65
3.3.2.2 Mobile Adsorption ......................... 68
3.3.3 Some Remarks in Relation with the Langmuir Type
and Fowler-Guggenheim Type Adsorption Isotherm
Equations .......................................... 69
3.4 The t-Plot Method ......................................... 72
3.5 Additional Comments about the Application of the Dubinin
and Osmotic Isotherms, the LT and the FGT Isotherm
Equation Types, and the t-Plot Method in the Measurement
of the Micropore Volume ................................... 76
3.6 The BET Method ............................................ 79
3.7 Horvath-Kawazoe Method .................................... 85
References ..................................................... 89
Chapter 4 Nanoporous Materials Mesoporosity Evaluation ........ 93
4.1 Introduction .............................................. 93
4.2 Capillary Condensation .................................... 93
4.3 Macroscopic Theories to Describe Pore Condensation ........ 96
4.3.1 The Kelvin-Cohan Equation .......................... 96
4.3.2 The Derjaguin-Broeckhoff-de Boer Theory ........... 102
4.3.3 Some Concluding Remarks about the Macroscopic
Theories to Describe Multilayer Adsorption and
Pore Condensation ................................. 105
4.4 Density Functional Theory ................................ 106
4.4.1 The Density Functional Theory Methodology in
General ........................................... 106
4.4.2 Calculation of the Pore Size Distribution ......... 108
4.4.3 The Nonlocal Density Functional Theory for the
Description of Adsorption in Slit Pores,
Cylindrical Pores, and Spherical Cavities ......... 109
4.4.4 Some Concluding Remarks about the Molecular
Models to Describe Adsorption ..................... 117
References .................................................... 119
Chapter 5 Diffusion in Porous Materials ...................... 121
5.1 Introduction ............................................. 121
5.2 Fick's Laws .............................................. 121
5.3 Transport, Self-Diffusion, and Corrected Coefficients .... 123
5.3.1 Transport Diffusion and Self-Diffusion ............ 123
5.3.2 Interdiffusion and the Frame of Reference for
Porous Materials .................................. 124
5.3.3 Relation between the Transport, D,
the Corrected, D0, and the Diffusion
Coefficients ...................................... 125
5.3.4 Relation between the Transport, D, the
Corrected, D0, and the Self-Diffusion
Coefficients in Zeolites .......................... 126
5.4 Mean Square Displacement, the Random Walker, and
Gaseous Diffusion ........................................ 127
5.4.1 The Mean Square Displacement (MSD) ................ 127
5.4.2 Gaseous Diffusion and the Random Walker ........... 128
5.5 Transport Mechanisms in Porous Media ..................... 130
5.6 Viscous, Knudsen, and Transition Flows ................... 132
5.7 Viscous and Knudsen Flows in Model Porous Systems ........ 134
5.7.1 Viscous Flow in a Straight Cylindrical Pore ....... 134
5.7.2 Knudsen Flow in a Straight Cylindrical Pore ....... 135
5.8 Transport in Real Porous Systems: Membranes .............. 136
5.8.1 Membranes ......................................... 136
5.8.2 Permeation Mechanisms in Porous Membranes ......... 137
5.8.3 Viscous Flow in Membranes ......................... 139
5.8.4 Knudsen Flow in Membranes ......................... 140
5.8.5 Transition Flow ................................... 141
5.8.6 Surface Flow in the Adsorbed Phase ................ 142
5.8.7 Experimental Permeation Study of Zeolite-Based
Porous Ceramic Membranes .......................... 143
5.9 Diffusion in Microporous Materials: Zeolites and
Related Materials ........................................ 146
5.9.1 Model Description of Molecular Diffusion in
Zeolites and Related Materials .................... 147
5.9.2 Anomalous Diffusion ............................... 152
5.9.3 Experimental Methods for the Study of Diffusion
in Zeolites ....................................... 155
References .................................................... 163
Chapter 6 The Plug-Flow Adsorption Reactor ................... 167
6.1 Dynamic Adsorption ....................................... 167
6.2 The Plug-Flow Adsorption Reactor Model ................... 169
References .................................................... 175
Appendix 6.1 Laplace Transforms .............................. 176
Chapter 7 Amorphous Porous Adsorbents: Silica and Active
Carbon ............................................. 181
7.1 Basic Features of Amorphous Silica ....................... 181
7.2 Amorphous Silica Morphology and Surface Chemistry ........ 182
7.3 Precipitated Amorphous Silica Synthesis .................. 185
7.4 Silica Modification ...................................... 188
7.5 Fundamental Characteristics of Active Carbon ............. 190
7.6 Active Carbon Morphology, Surface Chemistry, and
Surface Modification ..................................... 191
7.7 Active Carbon Production Methods ......................... 193
7.8 Some Applications of Precipitated Silica in Gas Phase
Adsorption Processes ..................................... 195
7.8.1 Adsorption of NH3, H2O, CO, N2O, CO2, and SH2 in
Precipitated Silica ............................... 195
7.8.2 Application of Precipitated Silica in Hydrogen
Storage ........................................... 197
7.8.3 Adsorption of Volatile Organic Compounds (VOCs)
in Precipitated Silica ............................ 198
7.9 Some Applications of Activated Carbons and Other
Carbonaceous Materials in Gas-Phase Adsorption
Processes ................................................ 199
7.9.1 Adsorption of H2O and CO2 and Removal of SH2 and
SO2 with Active Carbon ............................ 199
7.9.2 Hydrogen Storage with Active Carbon and Other
Carbonaceous Materials ............................ 202
7.9.3 Methane Storage in Activated Carbon and Other
Carbonaceous Materials ............................ 202
7.9.4 Adsorption of Volatile Organic Compounds (VOCs)
in Activated Carbon ............................... 203
7.9.5 Air-Conditioning with Activated Carbon ............ 204
References .................................................... 204
Chapter 8 Crystalline and Ordered Nanoporous Materials ....... 211
8.1 Introduction ............................................. 211
8.2 Fundamental Characteristics of Zeolites and Mesoporous
Molecular Sieves ......................................... 212
8.3 Structure ................................................ 213
8.3.1 Crystalline Microporous Materials ................. 213
8.3.2 Ordered Mesoporous Materials ...................... 216
8.4 Synthesis and Modification ............................... 219
8.4.1 Zeolite Synthesis ................................. 219
8.4.2 Zeolite Modification .............................. 222
8.4.3 Synthesis of Ordered Silica Mesoporous
Materials ......................................... 223
8.4.4 Modification of Ordered Silica Mesoporous
Materials ......................................... 225
8.5 Some Applications of Crystalline and Ordered Nanoporous
Materials in Gas Separation and Adsorption Processes ..... 227
8.5.1 Gas Cleaning ...................................... 227
8.5.1.1 Zeolites ................................. 227
8.5.1.2 Mesoporous Molecular Sieves .............. 230
8.5.2 Pressure Swing Adsorption ......................... 232
8.5.3 Other Separation Applications ..................... 233
8.5.4 Air-Conditioning .................................. 234
References .................................................... 235
Chapter 9 Adsorption from Liquid Solution .................... 243
9.1 Introduction ............................................. 243
9.2 Surface Excess Amount and Amount of Adsorption for
Liquid-Solid Adsorption Systems .......................... 244
9.3 Empirical Adsorption Isotherms Applied for the
Correlation of Liquid-Solid Adsorption Equilibria in
Systems Containing One Dissolved Component ............... 247
9.4 Model Description of Adsorption from the Liquid Phase
on Solids ................................................ 250
9.5 Some Applications of Liquid-Solid Adsorption ............. 252
9.5.1 Activated Carbons ................................. 252
9.5.2 Precipitated Silica ............................... 253
9.5.3 Zeolites .......................................... 255
References .................................................... 255
Index ......................................................... 259
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