Introduction. Chapter 1 Crystallography and 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 Energetics of Crystallization as 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 Quantification of the Driving Force for Crystallization 29 Better Understanding the Chemical Potential 31 2.2 Crystallization Kinetics 35 2.2.1 Nucleation 35 Isothermal Steady-State Nucleation Theory 35 2.2.1.2 Theory of Reaction Rates 38 Determination of the Free Energy of Nucleation for an Isothermal Process 40 2.2.1.4 Estimates and 42 Metastability and Free Energy of Nucleation 43 2.2.2 Isothermal Crystal Model 43 2.2.2.1 Derivation Model 45 2.2.2.2 Use Model 54 Marangoni, Alejandro G. Structure and properties of fat crystal networks 2013 digitalisiert durch: IDS Basel Bern
vi Contents 2.3 Isothermal Crystallization Kinetics and Microstructure 57 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 Nucleation of Fats 79 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 ß Is Very Small 84 2.4.6 Nonisothermal Nucleation of Five Commercial 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 101 David A. Pink 3.1 Introduction 101 3.2 Van der Interactions 102 3.3 Field 104 3.3.1 Lifshitz Theory and the Coupled Dipole 104 3.3.2 The Lennard Jones 6-12 Potential 108 3.3.3 Fractal Model and Model 110 3.3.4 Coarse-Grained 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 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
vii 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 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 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 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 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 Real Viscoelastic Generalization Model 166 6.1.2 Complex Modulus 167 6.1.3 Complex Viscosity 168 Some Basic Considerations for Rheological Studies of Fats under Dynamic Conditions 169
viii Contents 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 186 7.2.3 Elastic Properties of Colloidal Exploiting the Fractal Nature Aggregates 189 7.2.4 Application of Scaling Theory Developed for Colloidal to Fat Crystal Networks 197 7.2.5 Network 201 7.3 Where Lies the Fractality in Fat Crystal Networks? 203 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 Permeability Measurements 221 7.3.8.2 Fractal Dimensions by Light 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 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 dessen, P. Overbosch, P.A.M. Grootscholten, Struik, E. Royers, A. Don, Th. de Loos, C. Peters, and I.
IX 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 Forms of TAGs 244 9.1.3.2 246 9.1.3.3 Stability 248 Methods for Predicting Solid Phase 248 Linear Regression 249 9.1.4.2 Excess Contribution Method 249 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 Solid-Liquid Equilibrium 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 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 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 Curves 270 9.3.6 Conclusion 271 9.4 Pure Component Properties 272 9.4.1 Literature Correlations 272 Correlating Enthalpy of Fusion and Melting Points of Lipids 272 9.4.1.2 Data and Correlations for TAGs 274
9.4.2 Experimental Work 276 9.4.3 Development 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 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 298 Evidence for Partial Retained Chain Mobility in the 298 9.6.1.1 Supercooling 300 Excess Gibbs Energy in the a-modification 301 9.6.2 Comparison of Experimental and Calculated 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 ß'- and ß-Modifications 307 9.7.1 Excess Gibbs Energy 308 9.7.1.1 Excess Gibbs Energy 308 9.7.1.2 Athermal? 310 9.7.1.3 Phase Diagram 310 9.7.2 Experimental Phase 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 How to Proceed? 333 9.7.3.2 of an Alternative Method 336
xi 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 MPM withrä-unsaturatedtags 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 Are Interaction Parameters Related to Structural Differences? 361 9.8.1.1 361 TAGs and the Degree of Isomorphism 363 9.8.2 Calculation of Lattice Distortion 366 Equivalent Distortions in the ß-2 Modification 367 9.8.2.2 ß-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 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 Solid-Liquid Phase Behavior of...383 9.9.4.2 Petroleum Waxes 384 9.9.4.3 ß-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 of Several Probes in Stationary Phases of Liquid TAGs 405 Appendix 9.C: Purity 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 Measurement of Inductions Times by Light Scattering 422 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 Profiles by Solid Fat Content 433 10.3.1.1 Procedure 433 10.3.2 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 Particle Counting Method to Fractal Dimension 477
xiii 10.7.2 Box Counting Method to Determine Fractal Dimension 478 10.7.3 Rheological Method to Determine Fractal Dimension 479 10.7.3.1 Procedure 480 10.8 Migration 481 10.8.1 Oil Loss Assay 482 10.8.1.1 Procedure 482 10.8.2 Flatbed Scanner Technique 484 10.8.2.1 Procedure 484 Acknowledgments 487 References 487 Index 491