Analytical Methods | Microscopy (Microstructure of Milk Constituents and Products)

508 Pages·32.139 MB·English

by  M Auty Affiliation: Teagasc Food Research Centre, Moorepark, Fermoy, County Cork, Ireland

Structure
and ProPertieS
of fat cryStal
networkS
S e c o n d e d i t i o n

STRUCTURE
AND PROPERTIES
OF FAT CRYSTAL
NETWORKS
S E C O N D E D I T I O N
Alejandro G. Marangoni
Leendert H. Wesdorp
Boca Raton London New York
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Version Date: 20120803
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Contents
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.ΔHf.and.Vms..............................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
v
vi Contents
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
Contents 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.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
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.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
Contents 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.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
x Contents
9.4.2. .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-Modifications....................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