Introduction ................................................... xv
Chapter 1 Crystallography and Polymorphism ..................... 1
1.1 Crystal Lattices ........................................... 1
1.2 Lattices and Unit Cells .................................... 1
1.3 Miller Indices ............................................. 4
1.4 Powder X-Ray Diffraction and Bragg's Law ................... 5
1.5 Typical Powder XRD Setup ................................... 7
1.6 Indexing Reflections ....................................... 9
1.7 Crystallographic Structure of Fats ........................ 10
1.7.1 Single Crystal Structures .......................... 10
1.7.2 Polymorphism ....................................... 13
1.7.2.1 Energetics of Crystallization as It
Relates to Polymorphism ................... 19
1.7.2.2 Subcells and Subcell Packing .............. 20
References ..................................................... 24
Chapter 2 Nucleation and Crystalline Growth Kinetics ......... 27
2.1 Introduction to Crystallization ........................... 27
2.1.1 Nucleation Overview ................................ 27
2.1.2 Quantification of the Driving Force for
Crystallization .................................... 29
2.1.3 Better Understanding the Chemical Potential ........ 31
2.2 Crystallization Kinetics .................................. 35
2.2.1 Nucleation ......................................... 35
2.2.1.1 Isothermal Steady-State Nucleation
Theory .................................... 35
2.2.1.2 Theory of Reaction Rates .................. 38
2.2.1.3 Determination of the Free Energy
of Nucleation for an Isothermal Process ... 40
2.2.1.4 Estimates of ДЯГ and ...................... 42
2.2.1.5 Metastability and Free Energy
of Nucleation ............................. 43
2.2.2 Isothermal Crystal Growth - The Avrami Model ....... 43
2.2.2.1 Derivation of the Model ................... 45
2.2.2.2 Use of the Model .......................... 54
2.3 Isothermal Crystallization Kinetics and Microstructure .... 57
2.3.1 Relationship between Isothermal Nucleation
Kinetics and the Fractal Dimension of a Fractal
Cluster ............................................ 57
2.3.2 Relationship between Fractal Cluster Size
and the Isothermal Free Energy of Nucleation ....... 61
2.3.3 Fractal Growth of Milk Fat Crystals Is
Unaffected by Microstructural Confinement .......... 65
2.3.4 Comparison of Experimental Techniques Used
in Lipid Crystallization Studies ................... 70
2.4 Nonisothermal Nucleation of Fats .......................... 79
2.4.1 Isothermal, Near-Isothermal, and Nonisothermal
Processes .......................................... 79
2.4.2 Formulation of the Time-Dependent Supercooling
Parameter .......................................... 80
2.4.3 Probabilistic Approach to Modeling Nonisothermal
Nucleation Kinetics ................................ 82
2.4.4 Clustering Energy for Nonisothermal Nucleation ..... 83
2.4.5 Special Case When β Is Very Small .................. 84
2.4.6 Nonisothermal Nucleation of Five Commercial
Fats - A Practical Example of This Approach ........ 85
2.4.6.1 Materials and Methods Used ................ 85
2.4.6.2 Results ................................... 87
References ..................................................... 96
Chapter 3 Intermolecular Forces in Triacylglycerol Particles
and Oils ...................................................... 101
David A. Pink
3.1 Introduction ............................................. 101
3.2 Van der Waals Interactions ............................... 102
3.3 Mean Field Models ........................................ 104
3.3.1 Lifshitz Theory and the Coupled Dipole Method ..... 104
3.3.2 The Lennard Jones 6-12 Potential .................. 108
3.3.3 Fractal Model and Semi-Classical Model ............ 110
3.3.4 Coarse-Grained Approaches-1 ....................... 112
3.3.4.1 Example: Aggregation of Triacylglycerol
CNPs ..................................... 112
3.3.4.2 Application: Oils in Confined
Nanospaces ............................... 114
3.3.5 Coarse-Grained Approaches-2 ....................... 116
3.4 Van der Waals Interactions and Rheological
Characteristics .......................................... 117
3.5 X-Ray Scattering and Fractal Dimensions .................. 118
3.6 Conclusion ............................................... 119
Acknowledgments ............................................... 119
References .................................................... 119
Chapter 4 Rheology of Fats ................................... 125
Alejandro G. Marangoni and Suresh S. Narine
4.1 Hooke's Law .............................................. 125
4.2 Stress-Strain Relationships and Elastic .................. 125
4.2.1 Shear and Bulk Moduli ............................. 125
4.3 Types of Stresses and Corresponding ...................... 127
4.3.1 Definitions of Moduli ............................. 127
4.4 Elastic Behavior ......................................... 129
4.4.1 Structural Theory of Elasticity ................... 129
4.5 Yield Value from Constant Force Cone ..................... 139
4.5.1 Penetrometry Measurements ......................... 139
4.6 Rheology of Liquids ...................................... 141
4.6.1 Viscosity ......................................... 141
4.7 Types of Fluid Flow ...................................... 142
4.7.1 Ideal, Newtonian Behavior ......................... 142
4.7.2 Nonideal, Non-Newtonian Behavior .................. 142
4.7.2.1 Time-Independent Fluids .................. 143
4.7.2.2 Time-Dependent Fluids .................... 144
4.8 Modeling Flow Behavior ................................... 144
References .................................................... 145
Chapter 5 Viscoelastic Properties of Fats .................... 147
5.1 Creep and Recovery/Stress Relaxation ..................... 148
5.1.1 Kelvin-Voigt Solid ................................ 149
5.1.2 Maxwell Fluid ..................................... 150
5.1.3 Burger Model ...................................... 152
5.1.4 Real Viscoelastic Materials ....................... 154
5.1.5 Creep-Recovery Studies of Fats .................... 155
References .................................................... 158
Chapter 6 Dynamic Rheological Studies of Fats ................ 159
6.1 Introduction ............................................. 159
6.1.1 Theoretical Considerations ........................ 160
6.1.1.1 Hookean Solids (Springs) ................. 161
6.1.1.2 Newtonian Fluids (Dashpots) .............. 162
6.1.1.3 Kelvin-Voigt Viscoelastic Solid .......... 163
6.1.1.4 Maxwell Viscoelastic Fluid ............... 164
6.1.1.5 Real Viscoelastic Materials-
Generalization of the Model .............. 166
6.1.2 Complex Modulus ................................... 167
6.1.3 Complex Viscosity ................................. 168
6.1.4 Some Basic Considerations for Rheological
Studies of Fats under Dynamic Conditions .......... 169
Chapter 7 Nanostructure and Microstructure of Fats ........... 173
Alejandro G. Marangoni, Suresh S. Narine, Nuria C. Acevedo,
and Dongming Tang
7.1 Introduction ............................................. 173
7.2 Mesoscale and Nanoscale in Fat Crystal Networks .......... 174
7.2.1 Fractals .......................................... 180
7.2.2 Scaling Theory as Applied to Colloidal Gels ....... 186
7.2.3 Elastic Properties of Colloidal Gels: Exploiting
the Fractal Nature of the Aggregates .............. 189
7.2.4 Application of Scaling Theory Developed
for Colloidal Gels to Fat Crystal Networks ........ 197
7.2.5 Network Models .................................... 201
7.3 Where Lies the Fractality in Fat Crystal Networks? ....... 203
7.3.1 Structural Model of the Fat Crystal Network ....... 204
7.3.2 Characterizing Microstructure ..................... 205
7.3.3 Fractality ........................................ 209
7.3.4 Weak Link Revisited ............................... 211
7.3.5 Relating the Particle Volume Fraction to the
Solid Fat Content ................................. 213
7.3.6 Rheology .......................................... 214
7.3.7 Physical Significance of Fractal Dimension ........ 215
7.3.8 Other Methods for the Determination of the
Fractal Dimension ................................. 221
7.3.8.1 Fractal Dimension from Oil
Permeability Measurements ................ 221
7.3.8.2 Fractal Dimensions by Light Scattering ... 223
7.3.8.3 Thermomechanical Method for
Determining Fractal Dimensions ........... 224
7.3.8.4 Fractal Dimension from the Stress at
the Limit of Linearity: Fats Are in the
Weak-Link Rheological Regime ............ 225
7.3.9 Modified Fractal Model ........................... 225
7.4 Conclusions ............................................. 226
References ................................................... 227
Chapter 8 Yield Stress and Elastic Modulus of a Fat Crystal
Network ...................................................... 233
8.1 Model ................................................... 233
References ................................................... 240
Chapter 9 Liquid-Multiple Solid Phase Equilibria in Fats .... 241
Leendert H. Wesdorp, J.A. van Meeteren, S. de Jong, R. van
der Giessen, P. Overbosch, P.A.M. Grootscholten, M. Struik,
E. Royers, A. Don, Th. de Loos, C. Peters, and
I. Gandasasmita
9.1 Introduction and Problem Definition ..................... 241
9.1.1 Solid-Liquid Phase Equilibria and Fats ........... 241
9.1.2 Triacylglycerols: Nomenclature ................... 243
9.1.3 Triacylglycerols: Polymorphism ................... 244
9.1.3.1 Basic Polymorphic Forms of TAGs ......... 244
9.1.3.2 Submodifications ........................ 246
9.1.3.3 Stability ............................... 248
9.1.4 Methods for Predicting Solid Phase Composition
and Quantity ..................................... 248
9.1.4.1 Linear Programming/Multiple
Regression .............................. 249
9.1.4.2 Excess Contribution Method .............. 249
9.1.4.3 TAGs Inductors de Crystallization
Method .................................. 250
9.1.4.4 Classification of TAGs Method ........... 250
9.1.4.5 Other TAG-Based Methods ................. 251
9.1.5 Conclusion ....................................... 251
9.2 Approach to the Problem ................................. 251
9.2.1 Solid-Liquid Equilibrium Thermodynamics .......... 251
9.2.2 Kinetics of Crystallization ...................... 253
9.2.2.1 Polymorphism and Kinetics of
Crystallization ......................... 253
9.2.2.2 Shell Formation ......................... 254
9.2.2.3 Poor Crystallinity ...................... 254
9.2.3 Conclusion and Approach to the Problem ........... 255
9.3 Flash Calculations ...................................... 256
9.3.1 Introduction ..................................... 256
9.3.2 Initial Estimates and Stability Tests ............ 257
9.3.2.1 Splitting Component Method .............. 258
9.3.2.2 Michelsen's Tangent Plane Criterion
Method .................................. 259
9.3.3 Iterating Procedures ............................. 262
9.3.3.1 Direct Substitution ..................... 262
9.3.3.2 Gibbs Free Energy Minimization .......... 263
9.3.3.3 Removal of Phases ....................... 267
9.3.4 Comparing Methods ................................ 268
9.3.4.1 Criteria ................................ 268
9.3.4.2 Test Results ............................ 269
9.3.5 Calculation of Differential Scanning
Calorimetry Curves ............................... 270
9.3.6 Conclusion ....................................... 271
9.4 Pure Component Properties ............................... 272
9.4.1 Literature Data and Correlations ................. 272
9.4.1.1 Correlating Enthalpy of Fusion
and Melting Points of Lipids ............ 272
9.4.1.2 Data and Correlations for TAGs .......... 274
9.4.1.2 Experimental Work ....................... 276
9.4.3 Development of the Correlation ................... 277
9.4.3.1 Saturated TAGs .......................... 277
9.4.3.2 Unsaturated TAGs ........................ 283
9.4.4 Conclusion ....................................... 286
9.5 Mixing Behavior in Liquid State ......................... 287
9.5.1 Literature ....................................... 287
9.5.2 Model Calculations ............................... 288
9.5.3 Experiments ...................................... 289
9.5.3.1 Method for Determination of Activity
Coefficients of Mixtures of
Nonvolatile Liquids ..................... 289
9.5.3.2 Experimental Work ....................... 292
9.5.3.3 Results and Discussion .................. 293
9.5.4 Conclusion ....................................... 298
9.6 Mixing Behavior in the α-Modification ................... 298
9.6.1 Evidence for Partial Retained Chain Mobility
in the α-Modification ............................ 298
9.6.1.1 Supercooling of the α-Modification ...... 300
9.6.1.2 Excess Gibbs Energy in the
α-Modification .......................... 301
9.6.2 Comparison of Experimental and Calculated
α-Melting Ranges ................................. 301
9.6.2.1 Experimental Procedure .................. 301
9.6.2.2 Calculations ............................ 305
9.6.2.3 Results ................................. 305
9.6.3 Conclusion ....................................... 306
9.7 Mixing Behavior in the β'- and β-Modirications .......... 307
9.7.1 Excess Gibbs Energy .............................. 308
9.7.1.1 Excess Gibbs Energy Models .............. 308
9.7.1.2 Regular or Athermal? .................... 310
9.7.1.3 Phase Diagram ........................... 310
9.7.2 Experimental Phase Diagrams of TAGs .............. 313
9.7.2.1 Measuring Phase Diagrams ................ 313
9.7.2.2 Literature Overview ..................... 316
9.7.2.3 Fitting Experimental Phase Diagrams ..... 318
9.7.2.4 Saturated TAGs .......................... 318
9.7.2.5 Saturated TAGs + Trans-TAGs ............. 324
9.7.2.6 Saturated TAGs + Mono- and
Di-Unsaturated TAGs ..................... 325
9.7.2.7 Unsaturated TAGs ........................ 327
9.7.2.8 Summarizing ............................. 331
9.7.3 Alternative to Phase Diagram Determination ....... 333
9.7.3.1 How to Proceed? ......................... 333
9.7.3.2 Formulation of an Alternative Method .... 336
9.7.3.3 DSC Curves of Binary Systems Dissolved
in a Liquid TAG ......................... 337
9.7.3.4 What Experiments? ....................... 339
9.7.4 Experimental ..................................... 339
9.7.4.1 Principles of DSC ....................... 339
9.7.4.2 Thermal Lag ............................. 340
9.7.4.3 Experimental Procedure .................. 340
9.7.5 Results .......................................... 343
9.7.5.1 PSP and MPM with SEE and ESE ............ 343
9.7.5.2 PSP and MPM with EPE and PEE ............ 346
9.7.5.3 PSP and MPM with EEE .................... 349
9.7.5.4 PSP and MPM with cis-Unsaturated TAGs ... 350
9.7.6 Discussion ....................................... 354
9.7.6.1 Use of DSC Melting Curves ............... 354
9.7.6.2 Binary Interaction Parameters ........... 356
9.7.6.3 Kinetics ................................ 357
9.7.7 Ternary Solids ................................... 358
9.7.8 Conclusion ....................................... 359
9.8 Predicting Interaction Parameters ....................... 361
9.8.1 Are Interaction Parameters Related to
Structural Differences? .......................... 361
9.8.1.1 Degree of Isomorphism ................... 361
9.8.1.2 TAGs and the Degree of Isomorphism  .... 363
9.8.2 Calculation of Lattice Distortion ................ 366
9.8.2.1 Equivalent Distortions in the β-2
Modification ............................ 367
9.8.2.2 β-2A Lattice Distortion Calculations .... 370
9.8.3 Empirical Method ................................. 372
9.8.3.1 Method .................................. 372
9.8.3.2 Discussion .............................. 374
9.8.4 Conclusion ....................................... 375
9.9 Practical Applications .................................. 375
9.9.1 Prediction of Melting Ranges ..................... 375
9.9.2 Fractional Crystallization ....................... 378
9.9.3 Recrystallization Phenomena ...................... 379
9.9.3.1 Influence of Precrystallization and
Temperature Cycling ..................... 379
9.9.3.2 Sandiness ............................... 381
9.9.3.3 Conclusion .............................. 382
9.9.4 Applications outside Edible Oils and Fats ........ 383
9.9.4.1 Solid-Liquid Phase Behavior of
n-Alkanes ............................... 383
9.9.4.2 Petroleum Waxes ......................... 384
9.9.4.3 β-Substituted Naphthalenes .............. 385
9.9.5 Conclusions of This Chapter ...................... 386
9.10 Summary ................................................. 387
List of Symbols .............................................. 388
Appendix 9.A: Pure Component Data ............................ 390
Appendix 9.B: Specific Retention Volumes of Several Probes
in Stationary Phases of Liquid TAGs ............ 405
Appendix 9.C: Purity of the TAGs Used in Section 15.7 ........ 408
Appendix 9.D: Binary Phase Diagrams of TAGs: Data ............ 409
References ................................................... 415
Chapter 10 Experimental Methodology .......................... 419
Rodrigo Campos
10.1 Introduction ............................................ 419
10.2 Crystallization ......................................... 419
10.2.1 Nucleation Events ................................ 422
10.2.1.1 Measurement of Inductions Times
by Light Scattering ..................... 422
10.2.1.2 Monitoring Early Crystal Growth
by Polarized Light Microscopy ........... 425
10.2.2 Crystallization Kinetics by Nuclear Magnetic
Resonance ........................................ 428
10.2.2.1 Procedure ............................... 430
10.3 Thermal Properties ...................................... 433
10.3.1 Melt Profiles by Solid Fat Content ............... 433
10.3.1.1 Procedure ............................... 433
10.3.2 Iso-Solid Phase Diagram Construction ............. 435
10.3.2.1 Procedure ............................... 436
10.3.3 Thermal Behavior By Differential Scanning
Calorimetry ...................................... 437
10.3.3.1 Procedure ............................... 437
10.4 Polymorphism ............................................ 446
10.4.1 X-Ray Diffraction ................................ 447
10.4.1.1 X-Ray Diffractometer .................... 449
10.4.1.2 Procedure ............................... 450
10.5 Microstructure .......................................... 453
10.5.1 Polarized Light Microscopy ....................... 453
10.5.1.1 Procedure ............................... 454
10.6 Mechanical Properties ................................... 463
10.6.1 Small Deformation Rheology ....................... 463
10.6.1.1 Procedure ............................... 467
10.6.2 Large Deformation Testing ........................ 472
10.6.2.1 Procedure ............................... 474
10.7 Fractal Dimension ....................................... 476
10.7.1 Particle Counting Method to Determine Fractal
Dimension ........................................ 477
10.7.2 Box Counting Method to Determine Fractal
Dimension ........................................ 4^8
10.7.3 Rheological Method to Determine Fractal
Dimension ........................................ 479
10.7.3.1 Procedure ............................... 480
10.8 Oil Migration ........................................... 481
10.8.1 Oil Loss Assay ...................................
10.8.1.1 Procedure ............................... 482
10.8.2 Flatbed Scanner Imaging Technique ................ 484
10.8.2.1 Procedure ............................... 484
Acknowledgments .............................................. 487
References ................................................... 491
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