Fat Crystal Networks (Food Science and Technology)

dk1243fm......Page 2
Fat Crystal Networks......Page 11
Preface......Page 13
Contents......Page 15
Contributors......Page 17
1.1. Crystal Lattices......Page 19
Table of Contents......Page 0
1.2. Lattices and Unit Cells......Page 21
1.3. The Miller Indices......Page 23
1.4. Powder X-Ray Diffraction and Bragg’s Law......Page 24
1.5. A Typical Powder XRD Setup......Page 27
1.6. Indexing Reflections......Page 30
2.1 Single Crystal Structures......Page 31
2.2 Polymorphism......Page 33
2.2.1 Subcells and Subcell Packing......Page 34
2.2.2. Energetics of Crystallization as it Relates to Polymorphism......Page 36
REFERENCES......Page 37
1.1 Nucleation......Page 39
1.2 Growth......Page 41
1.3 The Effects of Impurities on Crystallization......Page 44
2.1.1. Steady-State Nucleation Theory......Page 45
2.1.2. Theory of Reaction Rates......Page 49
2.1.3. The Fisher-Turnbull Equation......Page 52
2.1.4. Estimates of DeltaHf and Vms......Page 56
2.2 Crystal Growth: The Avrami model......Page 57
2.2.1 Derivation of the Model......Page 60
2.2.1.1 Spherical Growth with Instantaneous Nucleation......Page 64
2.2.1.2 Spherical Growth with Sporadic Nucleation......Page 65
2.2.1.3 Plate-Like Growth with Instantaneous Nucleation......Page 66
2.2.1.4 Plate-Like Growth with Sporadic Nucleation......Page 67
2.2.1.6 Rod-Like Growth with Sporadic Nucleation......Page 68
2.2.2 Use of the Model......Page 69
3. RELATIONSHIP BETWEEN CRYSTALLIZATION KINETICS AND MICROSTRUCTURE......Page 74
Introduction......Page 78
Experimental......Page 81
Results and Discussion......Page 85
CASE STUDY: ON THE USE AND MISUSE OF THE AVRAMI EQUATION IN CHARACTERIZATION OF THE KINETICS OF FAT CRYSTALLIZATION......Page 90
Empirical Fits of Crystallization Data to Polynomial Functions and Their Relationship to the Avrami Equation......Page 94
The Misuse of Turbidity Measurements to Monitor Fat Crystallization......Page 95
REFERENCES......Page 97
1. INTRODUCTION......Page 101
2. TYPES OF PHASE BEHAVIOR......Page 103
3. IDEAL SOLUBILITY BEHAVIOR......Page 107
4. LIPID PHASE BEHAVIOR DETERMINATION......Page 108
4.1. Solid Content......Page 109
4.2. Melting Point......Page 110
4.3. Polymorphic Type......Page 111
4.4. Volume Expansion......Page 112
4.5. Constructing Lipid Phase Diagrams......Page 113
6. INTERPRETATION OF PHASE DIAGRAMS......Page 115
7 THE USE OF PHASE BEHAVIOR IN CONJUNCTION WITH OTHER TECHNIQUES: A CASE STUDY......Page 121
8. SUMMARY......Page 128
REFERENCES......Page 129
1.1 Hooke’s Law......Page 133
1.2 Stress-Strain Relationships and Elastic, Shear, and Bulk Moduli......Page 135
1.3 Types of Stresses and Corresponding Definitions of Moduli......Page 136
1.4 Elastic behavior......Page 138
1.4.1. Structural Theory of Elasticity......Page 139
1.5 Yield Value from Constant Force Cone Penetrometry Measurements......Page 150
2.1 Viscosity......Page 153
2.2.2 Nonideal, Non-Newtonian Behavior......Page 155
2.2.2.1 Time-independent fluids......Page 156
2.3 Modeling Flow Behavior......Page 157
REFERENCES......Page 158
1. INTRODUCTION......Page 160
1.1 Creep and Recovery/Stress Relaxation......Page 162
1.1.1 Kelvin-Voigt Solid......Page 164
1.1.2 The Maxwell Fluid......Page 165
2.1.3 The Burger Model......Page 167
2.1.4. Real Viscoelastic Materials......Page 169
2.1.5 Creep-Recovery Studies of Fats......Page 171
REFERENCES......Page 176
1. INTRODUCTION......Page 177
1.1.1. Hookean Solids (Springs)......Page 180
1.1.2. Newtonian Fluids (Dashpots)......Page 181
1.1.3. Kelvin-Voigt Viscoelastic Solid......Page 183
1.1.4. Maxwell Viscoelastic Fluid......Page 184
1.2. The Complex Modulus......Page 186
1.3 Complex Viscosity......Page 188
1.4. Some Basic Considerations for Rheologic Studies of Fats Under Dynamic Conditions......Page 189
1. INTRODUCTION......Page 194
2. THE MESOSCALE IN A FAT CRYSTAL NETWORK......Page 196
2.1 Fractals......Page 198
2.2 Scaling Theory as Applied to Colloidal Gels......Page 202
2.3. Elastic Properties of Colloidal Gels: Exploiting the Fractal Nature of the Aggregates......Page 207
2.4 Application of Scaling Theory Developed for Colloidal Gels to Fat Crystal Networks......Page 215
2.5 Network Models......Page 220
3.1 Characterizing Microstructure......Page 223
3.2 Structural Model of the Fat Crystal Network......Page 245
3.3 Fractality......Page 248
3.4 The Weak Link Revisited......Page 249
3.5 Relating the Particle Volume fraction to the Solid Fat Content......Page 253
3.6 Rheology......Page 254
3.7 Physical Significance of Fractal Dimension......Page 255
3.8 Conclusions......Page 262
REFERENCES......Page 263
1. INTRODUCTION......Page 270
MODEL......Page 271
REFERENCES......Page 279
1. INTRODUCTION......Page 281
2.1. Crystallization Kinetics by Pulsed Nuclear Magnetic Resonance......Page 282
2.1.1.3. Data Analysis......Page 284
2.2 Nucleation Events......Page 286
2.2.1.1. Procedure......Page 287
2.2.2.1. Procedure......Page 289
2.3. Estimations of Inductions Times and Nucleation Rates by Polarized Light Microscopy......Page 294
2.3.1.3. Data Analysis......Page 295
3.1. Melting Profiles by Solid Fat Content......Page 296
3.1.1.2. Experimental Procedure......Page 299
3.2. Iso-Solid Phase Diagram Determination......Page 301
3.2.1.1. Sample Preparation......Page 302
3.2.1.3. Data Analysis......Page 303
3.3.1.1. Sample Preparation......Page 305
3.3.1.2. Calibration of the Differential Scanning Calorimetry......Page 306
3.3.1.3. Experimental Procedure......Page 313
3.3.1.4. Data Analysis......Page 316
3.4. Polymorphism......Page 319
4.1. Polarized Light Microscopy......Page 321
4.1.1.1. Microscope Alignment......Page 323
4.1.1.2. Sample Preparation......Page 326
4.1.1.3. Experimental Procedure......Page 328
4.1.1.4. Data Analysis......Page 329
5. MECHANICAL PROPERTIES......Page 340
5.1.1. Small Deformation Rheology......Page 342
5.1.2. Fractal Dimension......Page 344
5.1.3.1. Sample Preparation......Page 345
5.1.3.2. Preparation of the Instrument......Page 348
5.1.4.1. Storage Modulus Determination......Page 351
5.1.5. Data Analysis......Page 352
5.2.1. Sample Preparation......Page 354
5.2.2. Instrument Calibration......Page 355
5.2.4. Data Analysis......Page 357
REFERENCES......Page 360
INTRODUCTION......Page 363
Strong-Link Regime......Page 365
Strain at the Limit of Linearity (gammao)......Page 366
Solid Fat Content......Page 367
Crystallization and Melting......Page 368
Image Processing and Fractal Dimension Determination......Page 369
Thick Sample Preparation......Page 370
RESULTS AND DISCUSSION......Page 371
Fat Crystal Network as a Particle Gel?......Page 372
Rheology......Page 373
Scaling Behavior of sigmao with Solid Fat Content......Page 376
Crystallization and Melting Behavior......Page 377
Polarized Light Microscopy......Page 383
Image Analysis......Page 388
REFERENCES......Page 392
INTRODUCTION......Page 395
Fourier Analysis and Fractality......Page 397
Box-Counting Method......Page 398
Sample Preparation......Page 400
Optimization of Image Acquisition and Processing......Page 401
Including and Excluding Issue......Page 402
Small Boxes Issue......Page 403
Ranges Issue (Small, Large, and Whole Range)......Page 408
Df vs. Db......Page 409
Network Structure and Fractal Dimension......Page 418
REFERENCES......Page 422
INTRODUCTION......Page 426
MECHANICAL PROPERTIES AND STRUCTURE......Page 428
WHAT IS FRACTALITY?......Page 435
DETERMINATION OF THE FRACTAL DIMENSION OF FAT CRYSTAL NETWORKS BY MICROSCOPY—THE PARTICLE COUNTING METHOD......Page 441
RELATIONSHIP BETWEEN FRACTAL DIMENSIONS DETERMINED BY RHEOLOGY AND MICROSCOPY......Page 448
REFERENCES......Page 449
INTRODUCTION......Page 453
Binary Phase Diagrams......Page 454
Differential Scanning Calorimetry......Page 455
Polarized Light Microscopy and Image Analysis......Page 456
RESULTS AND DISCUSSION......Page 457
REFERENCES......Page 472
1. INTRODUCTION......Page 474
Multiple-Step Solvent Fractionation......Page 477
Phase Equilibrium Studies......Page 478
RESULTS AND DISCUSSION......Page 479
REFERENCES......Page 489
1. INTRODUCTION AND PROBLEM DEFINITION......Page 492
1.1 SOLID-LIQUID PHASE EQUILIBRIA AND FATS......Page 493
1.2 TRIACYLGLYCEROLS: NOMENCLATURE......Page 495
1.3 TRIACYLGLYCEROLS: POLYMORPHISM......Page 496
1.3.1 Basic polymorphic forms of TAGs......Page 497
Saturated TAGs......Page 499
Unsaturated TAGs......Page 501
Conclusion......Page 502
1.4 METHODS FOR PREDICTING SOLID PHASE COMPOSITION AND QUANTITY......Page 503
1.4.1 Linear programming/multiple regression......Page 504
1.4.3 TAGs Inductors de Crystallization Method......Page 505
1.4.4 The Classification of TAGs method......Page 506
2. APPROACH TO THE PROBLEM......Page 507
2.1 SOLID-LIQUID EQUILIBRIUM THERMODYNAMICS......Page 508
2.2.1 Polymorphism and kinetics of crystallization......Page 510
2.2.2 Shell formation......Page 511
2.3 CONCLUSION AND APPROACH TO THE PROBLEM......Page 513
3. FLASH CALCULATIONS......Page 514
3.1 INTRODUCTION......Page 515
3.2.1 Splitting component method......Page 516
3.2.2 Michelsen’s tangent plane criterion method......Page 518
3.3.1 Direct substitution......Page 522
3.3.2 Gibbs free energy minimisation......Page 523
3.4.1 Criteria......Page 528
3.4.2. Test Results......Page 529
3.5 CALCULATION OF DIFFERENTIAL SCANNING CALORIMETRY CURVES......Page 531
4. PURE COMPONENT PROPERTIES......Page 533
4.1.1 Correlating enthalpy of fusion and melting points of lipids......Page 534
4.1.2 Data and correlations for TAGs......Page 536
Literature......Page 537
4.2 EXPERIMENTAL WORK......Page 539
4.3 DEVELOPMENT OF THE CORRELATION......Page 540
Melting enthalpy......Page 541
Melting points......Page 542
Simultaneous fit of melting points and melting enthalpies......Page 543
Melting enthalpy......Page 547
Melting point......Page 550
5.1 LITERATURE......Page 552
5.2 MODEL CALCULATIONS......Page 553
5.3.1. Method for determination of activity coefficients of mixtures of non-volatile liquids......Page 556
Experimental procedure......Page 559
5.3.3 Results and discussion......Page 560
Interpretation with the Flory-Huggins theory......Page 562
Implications for natural edible oils......Page 564
6.1 EVIDENCE FOR PARTIAL RETAINED CHAIN MOBILITY IN THE alpha-MODIFICATION......Page 566
6.1.1 Supercooling of the alpha-modification......Page 568
6.2.1 Experimental procedure......Page 570
6.2.3 Results......Page 573
7. MIXING BEHAVIOUR IN THE BETA′ AND BETA MODIFICATIONS......Page 575
7.1.1 Excess Gibbs energy models......Page 578
7.1.2 Regular or athermal?......Page 580
7.1.3 Phase diagrams......Page 581
Use of phase diagrams to determine interaction parameters......Page 584
Stabilization......Page 585
Other experimental problems......Page 586
An illustration......Page 587
7.2.2 Literature overview......Page 589
7.2.3 Fitting experimental phase diagrams......Page 591
SSS, SSP, PSP, SPS, PPS and PPP......Page 592
Saturated mono acid TAGs......Page 600
7.2.5 Saturated TAGS + trans TAGs......Page 602
7.2.6 Saturated TAGs + mono- and di-unsaturated TAGs......Page 605
Mono unsaturated TAGs......Page 607
Other unsaturated TAGs......Page 609
Triolein......Page 611
7.2.8 Summarizing......Page 613
7.3.1 How to proceed?......Page 614
7.3.2 Formulation of an alternative method......Page 615
7.3.3 DSC curves of binary systems dissolved in a liquid TAG......Page 616
7.3.4 What experiments?......Page 619
7.4.1 Principles of DSC......Page 620
7.4.2 Thermal lag......Page 621
7.4.3 Experimental procedure......Page 622
7.5.1 PSP and MPM with ESE and SEE......Page 625
7.5.2 PSP and MPM with EPE and PEE......Page 629
7.5.3 PSP and MPM with EEE......Page 633
7.5.4 PSP and MPM with cis-unsaturated TAGs......Page 635
7.6.1 The use of DSC-melting curves......Page 638
The beta´-modification......Page 643
7.6.3 Kinetics......Page 644
7.7 TERNARY SOLIDS......Page 645
7.8 CONCLUSION......Page 648
8.1 ARE INTERACTION PARAMETERS RELATED TO STRUCTURAL DIFFERENCES?......Page 649
8.1.1 Degree of isomorphism......Page 650
The beta´-modification......Page 652
The beta-modification......Page 654
8.2.1 Equivalent distortions in the beta-2 modification......Page 657
8.2.2 beta-2A lattice distortion calculations......Page 662
8.3 AN EMPIRICAL METHOD......Page 663
8.3.1 The method......Page 664
8.3.2 Discussion......Page 666
8.4 CONCLUSION......Page 667
9.1. PREDICTION OF MELTING RANGES......Page 668
9.2 FRACTIONAL CRYSTALLIZATION......Page 672
9.3.1 The influence of precrystallization and temperature cycling......Page 673
9.3.2. Sandiness......Page 677
9.3.3. Conclusion......Page 678
9.4.1. Solid liquid phase behaviour of n-alkanes......Page 679
9.4.3. beta-substituted naphtalenes......Page 682
9.5. CONCLUSION OF THIS CHAPTER......Page 684
SUMMARY......Page 685
LIST OF SYMBOLS......Page 687
Saturated TAGs......Page 689
UNSATURATED TAGs......Page 698
APPENDIX 2. SPECIFIC RETENTION VOLUMES OF SEVERAL PROBES IN STATIONARY PHASES OF LIQUID TAGS......Page 703
APPENDIX 3. PURITY OF THE TAGS USED IN SECTION 15.7......Page 706
APPENDIX 4. BINARY PHASE DIAGRAMS OF TAGS - DATA......Page 707
REFERENCES......Page 715
1.1. Introduction......Page 721
1.2. Objectives......Page 723
1.3.1.1. The Concept of Fractality......Page 724
1.3.1.2. Fractality as It Pertains to Colloidal Gels......Page 729
1.3.1.3. The Adaptation of Fractal Scaling to Fat Crystal Network......Page 730
1.3.1.4. Fractal Dimensions by Microscopy and Image Analysis......Page 732
1.3.2.1. Polarized Light Microscopy......Page 735
1.3.2.2. What is a ‘‘Particle’’?......Page 736
1.3.2.3. Thin Film Crystallization Studies......Page 737
1.3.3.1. Scanning Electron Microscopy......Page 740
1.3.3.2. Fluorescence Confocal Scanning Laser Microscopy......Page 741
1.3.3.3. Atomic-Force Microscopy......Page 742
1.3.4.1. The Deconvolution Principle......Page 743
1.3.4.2. Applications of Deconvolution in Two-Dimensional Imaging......Page 745
1.3.4.3. Applications of Deconvolution to Three-Dimensional Imaging......Page 748
1.3.4.4. Adaptation of Deconvolution Techniques to Three-Dimensional Transmitted Brightfield (TLB) Microscopy......Page 753
2.1.1. Conventional Two Dimensional (Thin Film) Slide Preparation......Page 754
2.1.2. Conventional 2D (Thin Film) Imaging......Page 756
2.1.3.1. Thresholding......Page 757
2.1.3.2. Image Calibration......Page 759
2.1.3.3. Fractal Dimensions......Page 760
2.1.3.5. Number of Particles and Microstructural Element Size......Page 763
2.1.3.6. Mean Nearest-Neighbor Distance (NND)......Page 764
2.2.1. Three-Dimensional Slide Preparation......Page 765
2.2.2 Three-Dimensional Imaging......Page 767
2.2.3.1. Image Deconvolution—Nearest-Neighbors Algorithm......Page 768
2.2.3.2. Image Deconvolution—Blind Algorithm......Page 770
2.2.3.4. Three-Dimensional Renderings and Animations......Page 773
2.2.4.1. Two-Dimensional Slices from Three-Dimensional Data Sets......Page 775
2.2.4.2. Two-Dimensional Projections......Page 776
3.1.1. Crystallization in a Thin Film (Two-Dimensional, Confined Space)......Page 777
3.1.2.1. Raw Polarized Light Microscopy (PLM) at Multiple Imaging Planes......Page 781
3.1.2.3. Blind Deconvolved Images of Multiple Planes......Page 784
3.1.3.1. Raw PLM Two-Dimensional Projection......Page 789
3.1.3.2. Deconvolved Two-Dimensional Projections......Page 790
3.1.4. Three-Dimensional Volume Renderings......Page 791
3.2.1. Area Fraction (% black)......Page 792
3.2.1.1. Two-Dimensional Slices of the Three-Dimensional Volume......Page 793
3.2.1.2. Two-Dimensional Projections of Three-Dimensional Volumes......Page 795
3.2.2. Fractal Dimension (Df)—Degree of Order and Fill......Page 796
3.2.2.1. Two-Dimensional slices of the Three-Dimensional Volume......Page 797
3.2.2.2. Two-Dimensional Projections of Three-Dimensional Volumes......Page 798
3.2.3. Fractal Dimension (Db)—Degree of Fill and Order......Page 800
3.2.3.1. Two-Dimensional Slices of the Three-Dimension Volume......Page 801
3.2.3.3. Thin Film Conditions......Page 802
3.2.4. The Relationships between Fractal Dimensions and Area Fraction......Page 803
3.2.5.1. Two-Dimensional Slices of the Three-Dimension Volume......Page 804
3.2.5.2. Two-Dimensional Projections of Three-Dimension Volumes......Page 805
3.2.7. The Relationships between Number of Particles (N) and Fractal Dimensions (Df and Db)......Page 806
3.2.8. Microstructural Element Size......Page 807
3.2.8.1. Microstructural Element Size and Depth......Page 809
3.2.8.3. Microstructural Element Size and Degree of Fill (Db)......Page 810
3.2.9. Standard Deviation of Mean Nearest-Neighbor Analysis as an Indicator of Order......Page 811
3.2.11.1. Edge Effects on Fractal Dimension Determination......Page 814
3.2.11.2. Effects of Optics, Magnification, and Image Resolution on Fractal Dimension Determination......Page 816
4.1. Z-Stage Calibration......Page 817
4.1.1. Standardization Attempt: Bright-field Vs. Polarized Light Microscopy......Page 819
4.3. Limitations Related to Properties of Fat Crystal Networks......Page 820
5. CONCLUSIONS......Page 822
6. RECOMMENDATIONS FOR FUTURE RESEARCH......Page 823
6.2. Various Systems, Crystallization Conditions, and Degrees of Confinement......Page 824
6.5. Development of a Three-Dimensional Imaging-based Fractal Dimension Method......Page 825
ABBREVIATIONS......Page 826
REFERENCES......Page 827