Measurement of the Thermodynamic Properties of Multiple Phases (eBook)

Measurement of the Thermodynamic Properties of Multiple Phases 4
Contents 6
List of Contributors 12
Foreword 14
1 Introduction 17
References 18
2 Phase Changes in Pure Component Systems: Liquids and Gases 20
2.1 Static Measurements 21
2.2 Ebulliometry 22
2.3 Knudsen Effusion Methods for Vapour Pressure Measurement 24
2.3.1 Conventional Mass-Loss Technique 24
2.3.2 Torsion–Effusion Method 24
2.3.3 Simultaneous Torsion and Mass-Loss Effusion Techniques 26
2.3.4 Isothermal Knudsen Effusion Method in Thermogravimetric-Type Apparatus 27
2.3.5 Non-Isothermal Knudsen Effusion Method in TG-Type Apparatus 28
2.3.6 Mass-Loss Knudsen Technique with a Quartz Crystal Microbalance 28
2.3.7 Mass-Loss Knudsen Technique by Heat-Conducting Calorimetry 29
2.3.8 Mass-Loss Knudsen Technique with a Mass Spectrometry Method 30
2.3.9 Knudsen Cell with Differential Scanning Calorimetry 31
DSC as a Boiling Point Method 31
DSC as a Mass-Loss Method 32
2.4 Langmuir Effusion Methods for Vapour Pressure Measurement 32
2.5 The Transpiration Method 34
2.6 Chromatographic Methods 35
2.6.1 Headspace Analysis 36
2.6.2 GC-Correlations with Retention Times and Vapour Pressures of Reference Compounds 36
2.6.3 GC-Correlations with Net Retention Times 37
2.7 Calorimetric Measurements of the Enthalpy of Vaporization 39
2.7.1 Adiabatic Calorimeters 39
2.7.2 Drop Calorimetry Method 41
2.7.3 Differential Calorimetry 41
2.8 Conclusions 41
References 42
3 Phase Changes in Pure Component Systems: Liquids and Solids 46
3.1 Thermal Methods and Calorimetry 49
3.1.1 Measurements at Normal Pressure 49
Adiabatic Calorimetry 49
Ice Calorimeter 50
Dynamic Methods 50
Levitation Techniques 51
Time–Temperature Methods 51
3.1.2 Measurements at High Pressure 51
Calorimetry 51
DTA and DSC 52
Thermobarometry 52
Piezothermal Method 53
Thermal Conductivity Measurements 53
3.2 Density and Volume Changes 53
3.2.1 Measurements at Normal Pressure 53
3.2.2 Measurements at High Pressure 54
3.3 Melting Curves at High Temperatures and Pressures 56
3.4 Miscellaneous Methods 57
3.4.1 Dielectric Measurements 57
3.4.2 Ultrasonic Measurements 57
3.4.3 Other Methods 58
Acknowledgement 58
References 58
4 Pure Component Phase Changes: Solid and Solid 64
4.1 Classification of Solid–Solid Phase Transitions 65
4.2 Thermodynamics of Solid–Solid Phase Transitions 67
4.3 Introduction into Soft Modes and the Central Peak 68
4.4 Phase Transitions in Plastic Crystals and Fullerenes 69
4.5 Experimental Techniques 71
4.5.1 Thermal Methods 71
4.5.2 Optical Methods 72
4.5.3 X-Ray and Neutron Scattering 73
Elastic Scattering (Diffraction) 73
Inelastic Scattering 73
4.5.4 Ultrasonic Methods 74
4.5.5 Magnetic Resonance 74
4.6 Review of Recent Developments 75
4.6.1 Inorganic Compounds 75
Ammonium Hexahalometallates (NH4)2MX6 75
Inorganic Azides 75
BaB2O4 75
CCI4, CF4 and H2S at High Pressure 75
GaP and GaAs 76
KNO2 76
Li2SO4 (Powders) 76
NH3 (Solid) at High Pressures 77
NOCl 77
4.6.2 Organic Compounds 77
n-Alkane (C27H56) Crystals of High Purity (Uniaxially Oriented) 77
Benzodiazepine Chlordiazepoxide 78
5-Bromo-9-Hydroxyphenalenone (BHP) 78
t-Butylammonium Tetrafluoroborate 78
Methane CH4 78
Chloranil 79
(CH3)2NH2H2PO4 79
Chlorodifluoromethane 79
Cholesterol 80
Choline Tetrafluoroborate and Iodide 80
Cycloheptane 80
Cyclohexane 80
Cyclohexanol 80
DL-a-Amino-n-Butyric Acid 81
4,4'-Di-n-Butyloxyazozybenzene 81
Fluoro- and Aminocyclohexane 81
Trans-4-n-Hexyl-(4'-Cyanophenyl)-Cyclohexane 81
Hexatriacontane (n-C36H74) 81
n-Undecylammonium Chloride 81
4.6.3 Fullerenes 82
4.6.4 Advances in Experimental Techniques and Interpretation of Results 83
Adiabatic Calorimetry – Design Improvements 83
Fluoroprobe 83
X-Ray Powder Diffraction 83
References 83
5 Vapour–Liquid Equilibrium at Low Pressure 86
5.1 Equipment and Procedures 87
5.1.1 Static Methods 88
5.1.2 Computations from Static Cell Data 89
5.1.3 Semi-Micro Cells 90
5.1.4 Data Reduction from P–x Measurements 91
5.1.5 Sensitivity of Temperature and Pressure 93
5.2 Dynamic Methods 95
5.2.1 Attainment of Equilibrium 96
5.2.2 Partial Condensation of Equilibrium Vapour 97
5.2.3 Smooth Boiling 98
5.2.4 Measurement and Control of Temperature and Pressure 99
5.2.5 Measurement of Composition 99
5.3 Conclusions 101
References 101
6 Vapour–Liquid Equilibrium at High Pressure 104
6.1 Closed-Circuit Methods 105
6.1.1 Static–Analytic Methods 105
Sampling 106
In Situ Analyses 112
6.1.2 Quasi-Static Method (Circulated Phases) 114
Mechanical Circulation 114
Thermal Circulation 117
Sampling 117
In Situ Analyses 118
6.1.3 Static–Synthetic Methods 118
Direct Determination of Bubble or Dew Point Properties 120
Semi-Transparent Cells 120
Blind Cells 123
Simultaneous Determination of Bubble and Dew Point Properties 125
Isothermal Method 125
Isochoric Method 129
Measurement of Total Pressure 130
6.2 Open-Circuit Methods 132
6.2.1 Forced Circulation of the Mixture 132
Sampling 132
In Situ Analyses: Measurements and Related Methods 135
6.2.2 Open Flow of the Gas Phase 136
Circulation of the Gaseous Component in a Cell Containing a Quasi-Saturated Liquid 137
Inert Gas Stripping Method 140
Saturation of a Gas by Passing it through a Weak Volatile Liquid or a Solid Powder 143
Retention Time Methods 145
6.3 Conclusions 148
References 149
7 Low-Pressure Solubility of Gases in Liquids 152
7.1 Thermodynamics 154
7.1.1 Fundamentals 154
7.1.2 Practical Implementation 164
The Vapour Phase 165
The Liquid Phase 168
7.2 Instruments, Experimental Techniques, Data Correlation and Selected Results 171
7.3 Concluding Remarks 183
Acknowledgements 184
Notation 184
Greek Letters 186
Superscripts 186
Subscripts 187
References 187
8 Liquid–Liquid Equilibrium 192
8.1 Liquid–Liquid Equilibrium in Binary Systems 193
8.1.1 Direct Analytical Methods 193
8.1.2 Synthetic or Turbidimetry Method 195
Cloud-Point Method 195
Titration Method 196
8.1.3 Volumetric Method 199
8.1.4 Indirect Methods 201
8.1.5 Measurement of very Low Mutual Solubility 201
Dynamic Flow Method 202
Circulation Apparatus for Solute Vapour Saturation 203
8.1.6 Measurements in the Vicinity of the Critical Point 203
8.1.7 Test System 205
8.2 Liquid–Liquid Equilibrium in Ternary and Multi-Component Systems 205
8.2.1 Determination of the Equilibrium Curves in a Ternary or Pseudo-Ternary System 205
8.2.2 Direct Analytical Method 207
8.2.3 Determination of the Tie Lines in a Ternary System using the Binodal Curve 208
8.2.4 Determining of the Distribution (Partition) Coefficient 209
Shake-Flask Method 210
Slow-Stirring Method 211
Generator-Column Method 211
Counter-Current Chromatography 212
Reversed-Phase High-Pressure-Liquid Chromatography (RP-HPLC) 212
Distribution Coefficient through the Experimental Limiting Activity Coefficients 213
8.3 Basic Monographs 214
References 214
9 Condensed Phases of Organic Materials: Solid–Liquid and Solid–Solid Equilibrium 216
9.1 Thermodynamic Treatment 219
9.1.1 The Gibbs Energy Function 219
9.1.2 The Lowest Possible Gibbs Energy 220
9.1.3 Limiting Cases of Experimentation 222
9.1.4 Analysis of the Phase Diagram 223
9.1.5 Polymorphism 227
9.2 Experimental 228
9.2.1 Sample Preparation 228
9.2.2 Microcalorimetry 234
The Thermogram 235
Heat Effect 237
Presence of Three Phases in Equilibrium 240
9.2.3 X-Ray Diffraction 242
Isothermal Measurements 244
CH3CCl3 + CCl4 [59] 244
1,4-Dichlorobenzene + 1-Bromo-4-Iodobenzene [8] 244
2-Amino-2-Methyl-1,3-Propanediol + 1,1,1-Tris(hydroxymethyl)propane [14] 246
Nonadecane + Heneicosane [58] 247
Isoplethic Experiments as a Function of Temperature 249
2,2-Dimethyl-1,3-Propanediol + Tris(hydroxymethyl) Aminomethane [70] 249
9.2.4 High-Order Phase Transitions 251
9.3 Key Systems 257
9.3.1 Naphthalene + 2-Naphthol 257
9.3.2 Tricosane (C23H48) + Pentacosane (C25H52) 263
9.3.3 2,2-Dimethylpropane + Carbon Tetrachloride 271
9.4 Empirical Relationships 276
9.4.1 Enthalpy–Entropy Compensation 276
9.4.2 Mismatch Parameters 280
9.5 Concluding Remarks 285
References 285
10 Condensed Phases of Inorganic Materials: Metallic Systems* 290
10.1 Solution Thermodynamics and Phase Diagram Development 292
10.2 Experimental Methods 299
10.2.1 Microscopic Phase Examination 300
10.2.2 X-Ray Diffraction 302
10.2.3 Emf Cells 303
10.2.4 Vapour Pressure Techniques 308
10.2.5 Thermal Methods 310
10.2.6 Scanning Calorimetry 311
Calorimetric Methods 314
10.3 Multi-Component Systems 314
10.4 Conclusions 318
References 319
11 Condensed Phases of Inorganic Materials: Ceramic Systems 322
11.1 Techniques Yielding Formation Enthalpies 324
11.1.1 Combustion Calorimetry 324
11.1.2 Solution Calorimetry 325
11.2 Techniques Yielding Heat Capacities and Entropies 328
11.2.1 Drop Calorimetry 328
11.2.2 Differential Thermal Methods 329
11.2.3 Adiabatic Calorimetry 329
11.3 Techniques Yielding Partial Molar Quantities 330
11.3.1 Gas Equilibration Techniques 330
11.3.2 Knudsen Cell Methods 332
11.3.3 Electrochemical Techniques 335
11.4 Conclusions 338
References 338
12 Condensed Phases of Inorganic Materials: Molten Salts 342
12.1 Structure of Molten Salts 343
12.2 Experimental Determination of Thermodynamic Properties 344
12.2.1 Calorimetric Measurements 345
12.2.2 Incorporation of Calorimetric Data into a Thermodynamic Model for Molten Salts 345
12.2.3 Vapour Pressure Methods 347
12.2.4 Electrochemical Methods 347
12.2.5 Solubility Measurements 350
12.2.6 Cryoscopy 350
12.3 Thermodynamic Properties from Phase Diagrams 350
12.4 Solid and Gas Phases 351
12.4.1 Differential Thermal Analysis (DTA) 351
12.4.2 Mass Spectroscopy 351
12.5 Conclusions 352
References 352
13 Measurement of Limiting Activity Coefficients: Non-Analytical Tools 354
13.1 Experimental Methods 355
13.2 Differential Ebulliometry and Equipment 357
13.3 Characterization of an Ebulliometer 359
13.3.1 Principal Ebulliometer Equation 360
13.3.2 Evaluation of E Parameter 361
13.3.3 Evaluation of Holdups (R'/S') and (V'/S') 362
13.3.4 Determination of the Vaporization Ratio f 363
Iterative Procedure 363
Procedure Based on Macroscopic Energy Balance 364
13.4 Static Differential Methods 366
13.4.1 Calculation of Equilibrium Liquid Composition, x1 367
13.4.2 Calculation of Activity Coefficient at Infinite Dilution .[sup(& #8734
13.5 Inert Gas Stripping 370
13.5.1 Attainment of Equilibrium 370
13.5.2 Calculation of Activity Coefficient at Infinite Dilution .[sup(& #8734
13.6 Conclusions 371
References 371
14 Measurement of Limiting Activity Coefficients Using Analytical Tools 374
14.1 Retention Measurements in GLC 377
14.1.1 Conventional GLC 377
14.1.2 Relative GLC 378
14.1.3 Non-Steady-State GLC 379
14.2 Headspace Method of Analysis 381
14.3 Static Mass Balance Methods 383
14.3.1 Equilibrium Partitioning in Closed Systems 383
14.3.2 Phase Ratio Variation (PRV) Method 384
14.3.3 Headspace Stepwise Extraction Methods 385
14.4 Rate Measurements on Continuous Gas–Liquid Separation Processes 385
14.4.1 Inert Gas Stripping 385
14.4.2 Exponential Saturator Method 388
14.5 Distillation Methods 390
14.5.1 Rayleigh Distillation Method (RDIST) 390
14.5.2 Differential Distillation 391
14.5.3 Measurements by Circulation Stills 391
14.6 Concluding Remarks 392
References 393
15 Measurement of Surface and Interfacial Tension 398
15.1 Terminology 401
15.2 Static Methods 402
15.2.1 Capillary Rise and Related Methods 402
15.2.2 Drop and Bubble Shape Methods 404
15.2.3 Spinning Drop Method 407
15.2.4 Oscillating Drop Method 408
15.3 Quasi-Static ("Detachment") Methods 408
15.3.1 Drop Volume–Weight 409
15.3.2 du Noüy Ring 411
15.3.3 Wilhelmy Plate 413
15.3.4 Maximum Bubble Pressure 414
15.4 Dynamic Surface and Interfacial Tension 415
15.4.1 Oscillating Jet Method 416
15.4.2 Capillary Wave Methods 417
15.4.3 Oscillating Drop and Bubble Methods 418
15.4.4 Maximum Bubble Pressure Method 419
15.4.5 Capillary Pressure and Related Methods 419
References 420
16 Critical Parameters 424
16.1 Experimental Techniques 425
16.1.1 Sealed Ampoule Method 425
16.1.2 Flow Method 429
16.1.3 Spontaneous Boiling Methods 431
16.1.4 Open Tube Methods 433
16.1.5 Methods Based on the PvT Behaviour of a Substance 434
16.1.6 Other Methods 435
16.2 Note on Experimental Errors 437
16.3 Extrapolation Techniques 437
References 438
Subject Index 442
Chemical Substance Index 448