Particle size measurement. Vol. 2, Surface area and pore size determination: 5th ed

Acknowledgments xi Preface to fifth edition xiii Preface to first edition xv Editor's foreword xvii 1. Permeametry and gas diffusion 1 1.1 Flow of a viscous fluid through a packed bed of powder 1 1.2 The aspect factor k 4 1.3 Other flow equations . 6 1.4 Experimental applications 11 1.5 Bed preparation 12 1.6 Constant flow rate permeameters 12 1.6.1 The Lea and Nurse permeameter 12 1.6.2 The Fisher sub-sieve sizer 13 1.7 Constant volume permeameters 16 1.7.1 The Blaine apparatus 16 1.7.2 The Griffin Surface Area of Powder Apparatus 18 1.7.3 Reynolds and Branson autopermeameter 18 1.7.4 Pechukas and Gage permeameter 18 1.8 Types of flow 19 1.9 Transitional region between viscous and molecular flow 20 1.10 Calculation of permeability surface 21 1.11 An experimental approach to the two-term permeametry equation 23 12 Diffusional flow for surface area measurement 24 13 The relationship between diffusion constant and specific surface 26 14 Non-steady state diffusional flow 27 15 Steady state diffusional flow 29 16 The liquid phase permeameter 32 17 Application to hindered settling 32 1.18 Turbo Powdersizer Model TPO-400 In-Line Grain Analyzer 33 1.19 Permoporometry 33 1.19.1 Theory 33 vi Contents 2 Surface area determination by gas adsorption 39 2.1 Introduction 39 2.2 Shapes of isotherms 40 2.3 Langmuir's equation for monolayer adsorption 43 2.3.1 Henry's law 45 2.3.2 Halsey equation 46 2.3.3 Freundlich equation 46 2.3.4 Sips equation 46 2.4 BET equation for multilayer adsorption 47 2.4.1 Single point BET method 51 2.4.2 Discussion of the BET equation 52 2.4.3 Mathematical nature of the BET equation 53 2.4.4 n-layer BET equation 56 2.4.5 Pickett's equation 57 2.4.6 Anderson's equation 57 2.5 Polanyi's theory for micropore adsorption 58 2.6 Dubinen-Radushkevich equation 58 2.6.1 Dubinen-Askakhov equation 60 2.6.2 Dubinen-Kaganer equation 60 2.7 Jovanovic equations 61 2.8 Hiittig equation 62 2.9 Harkins and Jura relative method 62 2.10 Comparison between BET and HJr methods 64 2.11 Frenkel-Halsey-Hill equation 64 2.12 V-t curve 65 2.13 Kiselev's equation 6 6 2.14 Experimental techniques 68 2.14.1 Introduction 68 2.15 Volumetric methods 68 2.15.1 Volumetric methods for high surface areas 68 2.15.2 Volumetric methods for low surface areas 70 2.16 Gravimetric methods 71 2.16.1 Single spring balances 72 2.16.2 Multiple spring balances 72 2.16.3 Beam balances 73 2.17 Flow, thermoconductivity methods 74 2.18. Sample preparation 78 2.18.1 Degassing 78 2.18.2 Pressure 78 2.18.3 Temperature and time 79 2.18.4 Adsorbate. 79 2.14.5 Interlaboratory tests 81 2.19 Standard volumetric gas adsorption apparatus 81 2.19.1 Worked example using BS 4359 standard apparatus 83 2.20 Haynes apparatus 86 2.21 Commercial equipment 86 Contents vii 2.21.1 Static volumetric apparatus 86 2.21.2 Continuous flow gas chromatographic methods 92 2.21.3 Gravimetric methods 96 3 Determination of pore size distribution by gas adsorption 104 3.1 Introduction 104 3.2 The Kelvin equation 105 3.3 The hysteresis loop 108 3.4 Theoretical evaluation of hysteresis loops 111 3.4.1 Cylindrical pore model 111 3.4.2 Ink-bottle pore model 112 3.4.3 Parallel plate model 113 3.5 Classification of pores 113 3.6 Relationship between the thickness of the adsorbed layer and the relative pressure 114 3.7 Non-linear V-t curves 119 3.8 The as method 120 3.9 The ns-nR method 121 3.10 Relationship between gas volume and condensed liquid volume for nitrogen 121 3.11 Pore size determination 122 3.11.1 ModeUess method 122 3.11.2 Cylindrical core model 127 3.11.3 Cylindrical pore model 127 3.11.4 Parallel plate model 131 3.12 Network theory 136 3.13 Analysis of micropores; the MP method 138 3.14 Density functional theory 143 3.15 Benzene desorption 143 3.16 Other adsorbates 144 4 4 Pore size determination by mercury porosimetry 149 4.1 Introduction 149 4.2 Relationship between pore radii and intrusion pressure 150 4.3 Equipment fundamentals 151 4.4 Incremental mode 153 4.5 Continuous mode 154 4.6 Discussion 155 4.7 Limitations of mercury porosimetry 157 4.8 Effect of interconnecting pores 159 4.9 Hysteresis 159 4.10 Contact angle for mercury 161 4.10.1 Effect of contact angle 162 4.11 Surface tension of mercury 162 4.12 Corrections for compressibility 163 4.13 Structural damage 165 vm Contents 4.14 Delayed intrusion 165 4.15 Theory for volume distribution determination 166 4.16 Theory for surface distribution determination 167 4.16.1 Cylindrical pore model 167 4.16.2 Modelless method 167 4.17 Theory for length distribution determination 168 4.18 Illustrative examples 169 4.18.1 Narrow size range 169 4.18.2 Wide size range 169 4.19 Commercial equipment 175 4.19.1 Incremental mode 175 4.19.2 Incremental and continuous mode 175 4.19.3 Continuous mode 176 4.20 Anglometers 177 4.21 Assessment of mercury porosimetry 179 4.21.1 Effect of experimental errors 179 4.22 Mercury porosimetry report 180 4.22.1 Data 181 4.23 Liquid porosimetry 182 4.24 Applications 187 5 Other methods for determining surface area 191 5.1 Introduction 191 5.2 Determination of specific surface from size distribution data 192 5.2.1 Number distribution 192 5.2.2 Surface distribution 193 5.2.3 Volume (mass) distribution 193 5.3 Turbidity methods of surface area determination 195 5.4 Adsorption from solution 196 5.4.1 Molecular orientation at the solid-liquid interface 197 5.4.2 Polarity of organic liquids and adsorbents 198 5.4.3 Drying of organic liquids and adsorbents 200 5.5 Theory for adsorption from solution 200 5.6 Methods for determining the amount of solute adsorbed 201 5.6.1 Langmuir trough 202 5.6.2 Gravimetric methods 202 5.6.3 Volumetric method 202 5.6.4 Rayleigh interferometer 203 5.6.5 Precolumn method 203 5.7 Experimental procedures for adsorption from solution 203 5.7.1 Non-electrolytes 203 5.7.2 Fatty acids 203 5.7.3 Polymers 204 5.8 Adsorption of dyes 204 5.9 Adsorption of electrolytes 206 Contents ix 5.10 Deposition of silver 206 5.11 Adsorption of p-nitrophenol 206 5.12 Chemisorption 207 5.12.1 Hydrogen 207 5.12.2 Oxygen 207 5.12.3 Carbon monoxide 208 5.13 Other systems 208 5.14 Theory for heat of adsorption from a liquid phase 209 5.14.1 Surface free energy of a fluid 209 5.14.2 Surface entropy and energy 210 5.14.3 Heat of immersion 210 5.15 Static calorimetry 211 5.16 Flow microcalorimetry 213 5.16.1 Experimental procedures - liquids 213 5.16.2 Calibration 215 5.16.3 Precolumn method 215 5.16.4 Experimental procedure - gases 216 5.16.5 Applications to surface area determination 217 5.17 Density methods 217 Appendix: Names and addresses of manufacturers and suppliers 224 Author index 239 Subject index 248