Contents. Introduction.

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1 Introduction. Chapter 1 Crystallography and 1.1 Crystal Lattices Lattices and Unit Cells Miller Indices Powder X-Ray Diffraction and Bragg's Law Typical Powder XRD Setup Indexing Reflections Crystallographic Structure of Fats Single Crystal Structures Polymorphism 13 Energetics of Crystallization as Relates to Polymorphism Subcells and Subcell Packing 20 References 24 Chapter 2 Nucleation and Crystalline Growth Kinetics Introduction to Crystallization Nucleation Overview 27 Quantification of the Driving Force for Crystallization 29 Better Understanding the Chemical Potential Crystallization Kinetics Nucleation 35 Isothermal Steady-State Nucleation Theory Theory of Reaction Rates 38 Determination of the Free Energy of Nucleation for an Isothermal Process Estimates and 42 Metastability and Free Energy of Nucleation Isothermal Crystal Model Derivation Model Use Model 54 Marangoni, Alejandro G. Structure and properties of fat crystal networks 2013 digitalisiert durch: IDS Basel Bern

2 vi Contents 2.3 Isothermal Crystallization Kinetics and Microstructure 57 Relationship between Isothermal Nucleation Kinetics and the Fractal Dimension of a Fractal Cluster Relationship between Fractal Cluster Size and the Isothermal Free Energy of Nucleation Fractal Growth of Milk Fat Crystals Is Unaffected by Microstructural Confinement Comparison of Experimental Techniques Used in Lipid Crystallization Studies Nucleation of Fats 79 Isothermal, and Nonisothermal Processes Formulation of the Time-Dependent Supercooling Parameter Probabilistic Approach to Modeling Nonisothermal Nucleation Kinetics Clustering Energy for Nonisothermal Nucleation Special Case When ß Is Very Small Nonisothermal Nucleation of Five Commercial Practical Example of This Approach Materials and Methods Used Results 87 References 96 Chapter 3 Intermolecular Forces in Triacylglycerol Particles and 101 David A. Pink 3.1 Introduction Van der Interactions Field Lifshitz Theory and the Coupled Dipole The Lennard Jones 6-12 Potential Fractal Model and Model Coarse-Grained Example: Aggregation of Triacylglycerol CNPs Application: Oils in Confined Nanospaces Coarse-Grained Van der Waals Interactions and Rheological Characteristics X-Ray Scattering and Fractal Dimensions Conclusion 119 Acknowledgments 119 References 119

3 vii Chapter 4 Rheology of Fats 125 Alejandro G. Marangoni and Suresh S. Narine 4.1 Hooke's Law Stress-Strain Relationships and Elastic Shear and Moduli Types of Stresses and Corresponding Definitions of Moduli Elastic Behavior Structural Theory of Elasticity Value from Constant Force Cone Penetrometry Measurements Rheology of Liquids Viscosity Types of Fluid Flow Ideal, Newtonian Behavior Nonideal, Non-Newtonian Behavior Fluids Time-Dependent Fluids Modeling Flow Behavior 144 References 145 Chapter 5 Viscoelastic Properties of Fats Creep and Recovery/Stress Relaxation Kelvin-Voigt Solid Maxwell Fluid Model Real Viscoelastic Materials Creep-Recovery Studies of Fats 155 References 158 Chapter 6 Dynamic Rheological Studies of Fats Introduction Theoretical Considerations Hookean Solids (Springs) Newtonian Fluids (Dashpots) Kelvin-Voigt Viscoelastic Solid Maxwell Viscoelastic Fluid 164 Real Viscoelastic Generalization Model Complex Modulus Complex Viscosity 168 Some Basic Considerations for Rheological Studies of Fats under Dynamic Conditions 169

4 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 Mesoscale and Nanoscale in Fat Crystal Networks Fractals Scaling Theory as Applied to Colloidal Elastic Properties of Colloidal Exploiting the Fractal Nature Aggregates Application of Scaling Theory Developed for Colloidal to Fat Crystal Networks Network Where Lies the Fractality in Fat Crystal Networks? 203 Structural Model of the Fat Crystal Network Characterizing Microstructure Fractality Weak Link Revisited Relating the Particle Volume Fraction to the Solid Fat Content Rheology Physical Significance of Fractal Dimension Other Methods for the Determination of the Fractal Dimension Fractal Dimension from Permeability Measurements Fractal Dimensions by Light Thermomechanical Method for Determining Fractal Dimensions Fractal Dimension from the Stress at the Limit of Linearity: Fats Are in the Weak-Link Rheological Regime Modified Fractal Model Conclusions 226 References 227 Chapter 8 Stress and Elastic Modulus of a Fat Crystal Network 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.

5 IX 9.1 Introduction and Problem Definition Solid-Liquid Phase Equilibria and Fats Triacylglycerols: Nomenclature Triacylglycerols: Polymorphism Basic Forms of TAGs Stability 248 Methods for Predicting Solid Phase 248 Linear Regression Excess Contribution Method 249 TAGs Inductors de Crystallization Method Classification of TAGs Method Other TAG-Based Methods Conclusion Approach to the Problem 251 Solid-Liquid Equilibrium Kinetics of Crystallization Polymorphism and Kinetics of Crystallization Shell Formation Crystallinity Conclusion and Approach to the Problem Flash Calculations Introduction Initial Estimates and Stability Tests Splitting Component Method Michelsen's Tangent Plane Criterion Method Iterating Procedures Direct Substitution Gibbs Free Energy Minimization of Phases Comparing Methods Criteria Test Results Calculation of Differential Scanning Curves Conclusion Pure Component Properties Literature Correlations 272 Correlating Enthalpy of Fusion and Melting Points of Lipids Data and Correlations for TAGs 274

6 9.4.2 Experimental Work Development Correlation Saturated TAGs Unsaturated TAGs Conclusion Mixing Behavior in Liquid State Literature Model Calculations Experiments 289 Method for Determination of Activity Coefficients of Mixtures of Nonvolatile Liquids Experimental Work Results and Discussion Conclusion Mixing Behavior in the 298 Evidence for Partial Retained Chain Mobility in the Supercooling 300 Excess Gibbs Energy in the a-modification Comparison of Experimental and Calculated Ranges Experimental Procedure Calculations Results Conclusion Mixing Behavior in the ß'- and ß-Modifications Excess Gibbs Energy Excess Gibbs Energy Athermal? Phase Diagram Experimental Phase of TAGs Measuring Phase Diagrams Literature Overview Fitting Experimental Phase Diagrams Saturated TAGs Saturated TAGs + Trans-TAGs Saturated TAGs + Mono- and Di-Unsaturated TAGs Unsaturated TAGs Summarizing Alternative to Phase Diagram Determination 333 How to Proceed? of an Alternative Method 336

7 xi DSC Curves of Binary Systems Dissolved in a Liquid TAG What Experiments? Experimental Principles of DSC Thermal Lag Experimental Procedure Results PSP and MPM with SEE and ESE PSP and MPM with EPE and PEE PSP and MPM with EEE MPM withrä-unsaturatedtags Discussion Use of DSC Melting Curves Binary Interaction Parameters Kinetics Ternary Solids Conclusion Predicting Interaction Parameters 361 Are Interaction Parameters Related to Structural Differences? TAGs and the Degree of Isomorphism Calculation of Lattice Distortion 366 Equivalent Distortions in the ß-2 Modification ß-2A Lattice Distortion Calculations Empirical Method Method Discussion Conclusion Practical Applications Prediction of Melting Ranges Fractional Crystallization Recrystallization Phenomena 379 Influence of Precrystallization and Temperature Cycling Sandiness Conclusion Applications outside Edible Oils and Fats 383 Solid-Liquid Phase Behavior of Petroleum Waxes ß-Substituted Naphthalenes Conclusions of This Chapter 386

8 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 Appendix 9.D: Binary Phase Diagrams of TAGs: Data 409 References 415 Chapter 10 Experimental Methodology 419 Rodrigo Campos 10.1 Introduction Crystallization Nucleation Events 422 Measurement of Inductions Times by Light Scattering 422 Monitoring Early Crystal Growth by Polarized Light Microscopy Crystallization Kinetics by Nuclear Magnetic Resonance Procedure Thermal Properties Profiles by Solid Fat Content Procedure Phase Diagram Construction Procedure Thermal Behavior By Differential Scanning Calorimetry Procedure Polymorphism X-Ray Diffraction X-Ray Diffractometer Procedure Microstructure Polarized Light Microscopy Procedure Mechanical Properties Small Deformation Rheology Procedure Large Deformation Testing Procedure Fractal Dimension 476 Particle Counting Method to Fractal Dimension 477

9 xiii Box Counting Method to Determine Fractal Dimension Rheological Method to Determine Fractal Dimension Procedure Migration Oil Loss Assay Procedure Flatbed Scanner Technique Procedure 484 Acknowledgments 487 References 487 Index 491

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