Structure and Mechanical

Properties of Fat Crystal

Networks

Alejandro G. Marangoni

University of Guelph

Guelph, Ontario, Canada

What is this? How is it different from this?

margarine olive oil

3

So, what is a fat after all?

To the chemist and chemical engineer:

• a complex mixture of high melting point

triacylglycerols in low melting point

triacylglyceorls with complex phase

behavior – all can be explained from

knowledge of molecular composition and

phase behavior (SFC and phase diagrams

are king…)

To the crystallographer:

• a metastable polycrystalline material prone

to recrystallization and fractionation – all

can be explained from knowledge of

polymorphism (XRD is king and DSC is

queen…)

To the colloidal scientist:

• a colloidal gel (or colloidal crystal)

composed of a network of polycrystalline

fat particles which trap liquid oil within –

all can be explained from knowledge of the

mesoscale structure, i.e., colloidal sizes,

interactions, distribution (rheometer is king

and microscope is queen…)

To the consumer:

• something that makes you fat, but tastes

good (cookies and chocolate rule…)

Factors affecting the texture

of fats and fat-structured foods

1. Solid fat content

2. Primary crystal habit (polymorphism)

3. Nano and Microstructure

a. crystallite morphology and size

b. spatial distribution of network mass

4. Interparticle interaction forces

Temperature

(ºC)

G´ (Pa) SFC (%) Fy (N) K

(N/mm)

5 2.19E+07a 90.5a 602a 231a

15 2.64E+07b 90.5a 593a 223a

20 1.63E+07c 80.5b 312b 90b

24 4.08E+07d 60.0c 344b 96b

Means with a common superscript within a column are not significantly different (P>0.05).

What controls hardness?

Triacylglycerol Molecules

Crystals

Crystal Clusters

Crystal Network

Fat

Nanostructure

0.4–100nm

Microstructure

0.1-200m

Macroscopic World

>0.2mm

Polymorphism

Rheology

Mechanical Strength

Sensory Impressions

Heat, mass, momentum transfer

Heat, mass, momentum transfer

Heat, mass, momentum transfer

Molecular Structure

Solid Fat Content

Triacylglycerols– Molecular Structure

H2C-O-C-CH2-(CH2)n-CH3

H2C-O-C-CH2-(CH2)n-CH3

|

CH3-(CH2)n-CH2-C-O-C-H

|

O

O

O

Triacylglycerol = glycerol + 3 fatty acids

Glycerol

Backbone

Fatty Acyl Chain

Fatty Acids and Triacylglycerol Types

Fatty Acids Long-Chain Saturated 14:0, 16:0, 18:0

Medium-Chain Saturated 8:0, 10:0, 12:0

Short-Chain Saturated 4:0, 6:0

Mono-Unsaturated 18:1

Poly-Unsaturated 18:2, 18:3, 22:6

Geometric Isomers (cis vs. trans)

Positional Isomers (-3,6,9)

Triacylglycerols Simple Homogeneous

Mixed

Complex and varied positional distribution of

fatty acids on TAG molecule.

Triacylglycerol Crystallization

Process

Isotropic Melt

Crystalline Solid

Decrease temperature below melting

point of solid into metastable region

(where the material is undercooled or

supersaturated)

T<Tm

T>Tm

0 5 10 15 20286

290

294

298

302

306

310

T

ti

ATm

Te

mp

era

ture

(K

)

So

lids (--- )

Tset

0 5 10 15 20286

290

294

298

302

306

310

T

ti

BTm

TsetTe

mp

era

ture

(K

)

So

lids (--- )

0 5 10 15 20286

290

294

298

302

306

310

tc

Tc

CTm=1/2(Tc*tc)

Time

Te

mp

era

ture

(K

)

So

lids (--- )

Tc

Tset

Isothermal

Quasi-isothermal

Non-isothermal

Driving force for nucleation and

crystallization is the degree of undercooling

ΔT=Tm-Tset

Defines which polymorph will be formed

and determines rates of nucleation and

crystallization

Temperature/supersaturation effect

-polymorph, 5oC, ΔT=29oC β’-polymorph, 25oC, ΔT=9oC

A difference in chemical

potential: the driving force

for crystallization

ln

f

l s

f

HT

T

RT

*[ ]

ln

i

i

i

c

c

RT

, ,i j i

i

GT P n

n

A “proper” crystallization table

for FHCO crystallized at 30oC

FHCO

(%) 20 30 40 50 60 70 80 90 100

Hm

(kJ.mol-1) 32.5 61.4 73.4 95.4 106.8 120.3 129.6 148.4 164.9

Tm (K) 333.3 336.5 337.4 338.8 340.7 342.0 344.2 344.4 344.9

(kJ.

mol-1) 10.06 11.52 11.93 12.55 13.41 13.98 14.94 15.05 15.25

lnβ 3.9 4.4 4.6 4.8 5.1 5.4 5.7 5.8 5.9

Energetics of Nucleation

Rousset, 2002

*

*[ ][ ] [ ]

G

S RTL Lk k e

t

Gibbs-Thompson Equation

Gn=An-Vn(/Vm)

1.0×10 -08 1.0×10 -07 1.0×10 -06 0.00001-1.0×10 -13

-5.0×10 -14

0.0×10 -00

5.0×10 -14

rc

=30 mJ m-2

Gm=150 J mol-1

Vms=8.510-4 m3 mol-1

Gn=1.4610-14

J/n

rc=3.410-7

m

r (m)

G

n(J

/nucle

us)

Quantification of

crystallization behavior

nkte1)(SFC

)t(SFC

1. Growth mode (Avrami model)

k - rate constant of crystallization

n - dimensionality of growth and

the type of nucleation

2. Nucleation (, Gc- Fisher-Turnbull model)

1G Gc d

kTNkTh

J e

Gc - activation free energy

of nucleation

Gd - activation free

energy of diffusion

Phase Technology Cloud Point

Analyzer

0 100 200 300 4000

25

50

75

nucleation-A nucleation-B

Time (min)

Sig

nal (

a.u

.)

0.00000 0.00001 0.00002 0.000037.5

10.0

12.5

15.0

Slope = 221100

R2=0.99

A

1/T(T)2

ln(

T)

0 10 20 300.0

2.5

5.0

7.5

B

Crystallization Temperature ( C)

G

c (kJ/m

ol)

Fisher-Turnbull approach

3 2 2

2 2

16 ( ) 1ln( ) ~ ln

3 ( )

s

m fB

B f

V TNkT

h k H T T

2

223

3

)(16

fB

f

s

m

Hk

TVm

#

2( )

Bn

mkG

T

Interfacial Tension

3

1

22

2

)(16

3

f

s

m

fB

TV

Hmk

)/101()/(

)/()/( 363 mlm

mlgdensity

molgMWmolmvolumemolar

Induction Times as Determined from

Crystallization Curves at Various

Temperatures…cocoa butter

-30 -20 -10 0 10 20 30-5.0

-2.5

0.0

2.5

5.0

7.5

10.0 ' +'

Crystallization Temperature (oC)

log

Quantification of

crystallization behavior

nkte1)(SFC

)t(SFC

1. Growth mode (Avrami model)

k - rate constant of crystallization

n - dimensionality of growth and

the type of nucleation

2. Nucleation (, Gc- Fisher-Turnbull model)

1G Gc d

kTNkTh

J e

Gc - activation free energy

of nucleation

Gd - activation free

energy of diffusion

Table 6: Avrami exponent values for the different types of growth and nucleation (Sharples, 1966)

Avrami Exponent Various types of growth and nucleation

3 + 1 = 4 Spherulitic growth from sporadic nuclei 3 + 0 = 3 Spherulitic growth from instantaneous nuclei

2 + 1 = 3 Disc-like growth from sporadic nuclei

2 + 0 = 2 Disc-like growth from instantaneous nuclei

1 + 1 = 2 Rod-like growth from sporadic nuclei

1 + 0 = 1 Rod-like growth from sporadic nuclei

n=4 n=1

0 50 100 150 200 250 300 3500

25

50

75

k=0.00103min-1.5

SFC=67.7%n=1.50

Time (min)

SF

C (

%)

tnkSFC

SFCA lnln1lnln

max

Linearization of the Avrami

Model

Multiple crystallization steps

)1(1

max,

n

i

tk

io

inieSFCSFCSFC

Avrami Exponent vs. Crystallization

Temperature….cocoa butter

-30 -20 -10 0 10 20 300

1

2

3

4

5

Crystallization Temperature (oC)

Avra

mi E

xp

on

en

t

Chemical Potential and Viscosity

36

1

1

( )

( , )

( )

nucleation

growth

J f

J f

D f

Thoughts: - nucleation and growth rates are strongly influenced by chemical potential - molecular, particle and cluster diffusion strongly influenced by viscosity (building mesoscale) - shear will not affect liquid oil viscosity (Newtonian) - shear will affect momentum transfer but only when diffusing objects are large enough* *May have to include in future as another state variable

37

20% FHSO (SFC=99.2%) in HOSO @ 40oC

Chemical Potential Changes in Time

38

lni iRT ( )

max,

*

max,[ ]

final

final final

T T t

sol soli

i T T

i neat sol

SFC SFCc

c x SFC SFC

Phase Trajectory

39

Let’s consider the actual solubility at Each temperature on the way to equilibrium

?

cr

cr

Factors affecting the texture

of fats and fat-structured foods

1. Primary crystal habit (polymorphism)

2. Solid fat content

3. Nano and Microstructure

a. crystallite morphology and size

b. spatial distribution of network mass

4. Interparticle interaction forces

40

41

Hardness Index

HI = mass of cone (g) / depth of penetration (mm)

SFC is one of the most

influential factors in

determining fat mechanical

properties, but

Not the only one!

Milkfat crystallized

Statically at 5oC

Phase Behavior

Fats are mixtures of lipids, predominantly triacylglycerols,

but also contain minor polar components such as diacyl-

glycerols, monacylglycerols, free fatty acids, phospho-

lipids, sterols, etc.

Continuous solid solution (mixed crystals), eutectic,

monotectic (partial solid solution), compound formation

phase behaviors are commonly observed

Continuous solid solution: SSS/ESS, POS/SOS

Eutectic behavior: PPP/SSS, EEE/SOS, POS/PSO,

PPP/LLL, PPP/SOS

Compound formation: SSO/SOS, POP/OPO

Monotectic behavior: SSS/OOO, SSS/LLL, PPP/POP,

SSS/SOS

Conditions for fat compatibility

1. Equivalent thermal properties

Melting points

Melting and solidification ranges

SFC

2. Similar molecular size, shape and packing

To allow isomorphous replacement or

formation of a single lattice unit in mixtures

3. Similar polymorphism

Transformation from stable to unstable forms

should occur as readily for binary mixtures as with

individual components

Continuous solid solution – compatible

Eutectic – incompatible (minima)

Monotectic – significant amounts of lower

melting component solubilized by higher melting

component. Eutectic point close to m.p. of

lower melting component; partial solid solution

Compound formation (maxima)

Lever Rule – Phase composition

o lsolid

l s

s oliquid

l s

w wX

w w

w wX

w w

Tie line

47

‘‘Eutectic,’’ in Greek, means ‘‘easily melted’’ and indicates a melting point

lower for the solution than that of the individual pure products in solution

Eutectic

Hildebrand equation: ln(xi)=Hi/R (1/Tm-1/T)

Liquidus Line

POP-OPO Molecular Compounds

Ideal Solubility – TAGs are ideally

soluble in liquid state

ln(xi)=Hi/R (1/Tm-1/T)

Bruker Minispec pNMR

Magn

etization S

ignal In

tensity

Pulse

Time (s)

Solid – liquid

components (total

hydrogen content)

Liquid

component

only

tB=10 tA=70

Magn

etization S

ignal In

tensity

Pulse

Time (s)

Solid – liquid

components (total

hydrogen content)

Liquid

component

only

tB=10 tA=70

52

How to construct Lipid phase diagrams

1- Prepare dilutions of the two fats

2-Measure SFC as a function of temperature for

each dilution, create a spline and obtain

temperatures corresponding to a series of SFCs

(every 5%) SFC vs. temperature profile forAMF/Cocoa Butter

0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70

80

90

1000% AMF

10% AMF

20% AMF

30% AMF

40% AMF

50% AMF

60% AMF

70% AMF

80% AMF

90% AMF

100% AMF

Temperature (oC)

So

lid F

at C

on

ten

t (%

)

3- Plot Temperature vs. Composition

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

35

40

Composition (%w/w MMF)

Tem

pe

ratu

re (

oC

)

0 10 20 30 40 50 60 70 80 90 10010

20

30

40

50

60

Composition (% HMF)

Tem

pera

ture

(oC

)

55

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

Iso-solid GraphicTemperature vs % of SMS

Top line is 0% SFC:liquidus

Bottom line is 95 % SFC:solidus

Composition (%w/w SMS)

Te

mp

era

ture

(oC

)

partial solid solution behavior

Iso-Solid graphic

)

56

HMF + CB:

partial compatibility

MMF + HMF :

Monotectic, compatibility

MMF + CB:

EUTECTIC, incompatibility

57

Dropping point machine

58

Holder to slide inside

“Cup” for the sample

Holder to “catch” the

first drop of melted

sample

Sample Temperature for the

first drop

10 % A 34 ° C

60 % A 32 ° C

0 10 20 30 40 50 60 70 80 90 10020

25

30

35

40

45

50

55

60

AMF

MMF

HMF

Composition (%w/w milkfat fraction)

Dro

pp

ing

Po

int (o

C)

Dropping point machine use for solubility

SFC influences hardness…

24 hr Tempering 48 hr Tempering0

15

30

45

60

75

90

105

120

135

150Cocoa Butter

MMF

AMF

40% HMF

40% AMF

40% MMF

10% MMF

10% HMF

10% AMF

* * *

*<150

Tempering Time (hours)

Pe

ne

tratio

n D

ep

th(1

/10

mm

)

Microstructure

Brightfield microscopy

62

Bright field microscopy is the simplest of all the light microscopy

techniques. Sample illumination is via transmitted white light

(typically from a halogen microscope bulb), illuminated from below

and observed from above .

.

Polarized light Microscope

63

64

http://www.microscopyu.com/tutorials/java/

polarized/crystal/index.html

The polarized light microscope is designed to observe and photograph specimens that are

visible primarily due to their optically anisotropic character. In order to accomplish this task,

the microscope must be equipped with both a polarizer, positioned in the light path

somewhere before the specimen, and an analyzer (a second polarizer), placed in the

optical pathway between the objective rear aperture and the observation tubes or camera

port. Image contrast arises from the interaction of plane-polarized light with a birefringent

(or doubly-refracting) specimen to produce two individual wave components that are each

polarized in mutually perpendicular planes. The velocities of these components are different

and vary with the propagation direction through the specimen. After exiting the specimen,

the light components become out of phase, but are recombined with constructive and

destructive interference when they pass through the analyzer. Polarized light is a contrast-

enhancing technique that improves the quality of the image obtained with birefringent

materials when compared to other techniques such as darkfield and brightfield illumination,

differential interference contrast, phase contrast, Hoffman modulation contrast, and

fluorescence.

Why can we see fat crystals?

65

70

Characteristic α form β’ form β form

Size 5 µm 1-5 µm <50 µm

Shape platelets Tiny needles Long needles

G

Time –Temperature State Diagram for the

Polymorphism of Statically Crystallized Cocoa

Butter

’ SOS

1 10 100 1000 10000 100000-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

Time (min)

Tem

pe

ratu

re (

oC

)

+

’

+’

’+

The form

A

B

C

D

The ’ form

A

B

C

D

The form A

B

C

D

E

F

Growth of a Polycrystalline

Fat Crystal Network

Growth of a fat crystal network

Effect of cooling rate

0.4oC/min

1.2oC/min

6.0oC/min

Effect of Surfactant Addition

0.1% vs. 0.5% Tween 60

Temperature Effect

5oC 25oC

Effect of film size on slide

170um 20um

83

Atomic Force microscope

Cocoa Butter Fat Crystal Network

Visualized using AFM

Rheology of Fats

Small Deformation

Dynamic Controlled

Stress Rheometer

TA AR2000

Viscoelasticity of Fats

G”/G’ ~ 0.1

Shear strains of ~ 0.1% or less

G’ frequency-independent

0 2000 4000 6000 8000 100000

5000000

10000000

15000000

20000000

25000000

30000000

0.00

0.01

0.02

0.03

0.04

0.05

Stress (Pa)

Sto

rag

e M

od

ulu

s (

Pa)

Stra

in (%

)

0 2 4 6 8 100

4000000

8000000

12000000

16000000

20000000

A

Frequency (Hz)

Sh

ear

Mo

du

lus (

Pa)

0 2 4 6 8 100

400000

800000

1200000

1600000

B

Frequency (Hz)

Sh

ear

Mo

du

lus (

Pa)

0 2 4 6 8 100

2000000

4000000

6000000

8000000

10000000

C

Frequency (Hz)

Sh

ear

Mo

du

lus (

Pa)

0 2 4 6 8 100

15000000

30000000

45000000

60000000

D

Frequency (Hz)

Sh

ear

Mo

du

lus (

Pa)

0 5000 10000 15000 20000 25000 30000 350001000000

10000000

100000000

0.0

0.1

0.2

0.3

0.4

0.5A

Stress (Pa)

She

ar

Mo

dulu

s (

Pa)

Stra

in (%

)

Large Deformation Mechanical Tests

0.5 1.0 1.5 2.00.0

5.0

2.5

7.5

12.5

10.0

15.0

17.5

20.0

22.5

25.0

27.5

0.0

Displacement (mm)

Forc

e (N

)

Yield Force (N)

Yield deformation (mm)

Yield Work (N mm)

0.5 1.0 1.5 2.00.0

5.0

2.5

7.5

12.5

10.0

15.0

17.5

20.0

22.5

25.0

27.5

0.0

Displacement (mm)

Forc

e (N

)

Yield Force (N)

Yield deformation (mm)

Yield Work (N mm)

94

Cone penetrometer

95

Drop the cone for 5 s into the sample.

Measure the penetration depth.

96

Hardness Index

HI = mass of cone (g) / depth of penetration (1/10mm)

Repetitions

At least 3

Ideal measurement: one “poke” in a container with walls

2.5 cm away from the indentation.

Yield Value

Y = Yield value g/cm2

K = constant depending on the geometry of the cone used

W = weight of cone and all parts belonging to the shaft

p= penetration depth in 0.1 mm

J.Haighton

Depth of penetration (1/10 mm)

97

Cone penetrometer – results for a mix

Modeling the microstructure of a fat

5.3

5.0

24

5

oH

ADG

G~

30 35 40 45 50 55 600.0

2.5

5.0

7.5

10.0

A

(%)

G' (

MP

a)

40 50 60 70 805

10

15

20

25

B

(%)

G' (

MP

a)

20 30 40 50 60 700

5

10

15

C

(%)

G' (

MP

a)

20 25 30 35 40 450.0

0.5

1.0

1.5

D

(%)

G' (

MP

a)

milkfat

palm

oil lard

tallow

Network model needs to take

into account the presence of

particle (crystal) aggregates

G~ for single particle network does

not provide satisfactory description of

system’s behavior

Rather: G~

Several parameters that determine

the state of aggregation are lumped

together into one dimensionless

‘scaling factor’

He also suggests that ~N

Good agreement with experiments

About 106 particles per

aggregate

More agitation leads to

less aggregation

~'G

D

Dd

xd

3

3.4

Heertje, I. (1993)

Microstructural Studies in

Fat Research

Food Structure 12, 77-94

Support for the view of fats as

crystallite fractal gels grows

Johansson also shows that:

~1/(D-d)

Weak-link vs. Strong Link

High SFC vs. Low SFC

Fractal analysis explains the

softening observed

in milkfat upon chemical

interesterification

Narine, S.S. and Marangoni, A.G. (1999)

Fractal nature of fat crystal networks

Physical Review E 59: 1908

Structural view – a colloidal gel?

Fractal Floc

Particle

Link

Fat crystal networks display

statistical self-similarity

and scaling behavior

characteristic of stochastic

fractal systems

Statistical Self similarity – you guess!

Db=1.60

4x

10x

40x

100x

Self-similarity?

Scaling Behavior and Fractional

Dimensionality

3.50 3.75 4.00 4.25 4.5014

15

16

17

18

19

20

D=2.45

r2=0.88

ln

ln G

'

Scaling behavior G~

3.5 4.0 4.5 5.0 5.5 6.02

3

4

5

6

D=2.01 (0.06)

r2=0.994

log (length)

log

(N

)

Scaling behavior N~LD

~

Marangoni and Ollivon, 2007, Chemical Physics Letters 442: 360-364

2.00 2.25 2.50 2.75 3.00 3.251.25

1.50

1.75

2.00

2.25

slope = 0.67 ± 0.009

A

D = 1.49 0.019

SFC linear with time

Log10 Time (seconds)

Lo

g1

0 D

iam

ete

r (

m)

2.00 2.25 2.50 2.75 3.00 3.25

slope = 0.72 ± 0.055

B

SFC linear with time

D = 1.40 0.106

Log10 Time (seconds)

~t1/D

Milkfat Spherulites at 20oC

for M~t

Batte and Marangoni, 2005, Crystal Growth and Design 5: 1703-1705

Fractal Structural-mechanical model

The view

Weak-link Theory - Fat Crystal Networks

Developed for colloidal gels and adapted to

fat crystal networks:

G’ = dynamic shear elastic modulus (storage modulus)

= constant which depends on particle properties and

particle-particle interactions

= solids’ volume fraction of fat sample

G’ ~ ~ 1/(d-D)

Narine and Marangoni, 1999, PRE 59:1908

Fractal dimension - rheology

100'

SFCG

100lnln'ln

SFCG

15 20 25 30 35 40

0

2

4

6

8A

Solid Fat Content (%)

Sto

rag

e M

odulu

s(M

Pa)

20 25 30 35 40 45 50 55 600

2

4

6

8

10

12B

Solid Fat Content (%)

Sto

rag

e M

odulu

s(M

Pa)

3.00 3.25 3.50 3.75 4.00 4.25-6

-4

-2

0

2

4

6A

ln

ln G

'

3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.42.0

2.5

3.0

3.5

4.0

4.5

5.0B

ln

ln G

'

1.8 2.0 2.2 2.4 2.6 2.8 3.00.0

0.2

0.4

0.6

Df

G'/

(

=0

.5)

Effect of D on the Elastic Modulus

Relationship to Large Deformation

Rheological Behavior?

4 6 8 10 120

1000

2000

3000

4000

r2=0.80

E' (MPa)

Yie

ld F

orc

e (

g fo

rce

)

0 100 200 300 4002.0

2.2

2.4

2.6

2.8

3.0

21oC

26.5oC

Shear Rate (RPM)

Dr

Effects of shear on Dr (AMF)

VANHOUTTE, 2002 (Ph.D. thesis, Gent University)

0 100 200 300 400-10

-5

0

5

10

21oC

26.5oC

ln=:5.5-0.018SR

Shear Rate (RPM)

ln

ln=:8.1-0.045SR

SRDD

max

)(ln SRo

0.000 0.005 0.010 0.015 0.020 0.0252.0

2.2

2.4

2.6

2.8

3.0

21oC

26.5oC

D=3.0-50SR-1

D=2.8-29SR-1

1/Shear Rate (RPM-1)

Dr

-10 -8 -6 -4 -2 0 2 4 6 81.5

1.6

1.7

1.8

1.9

2.0

D=0.023ln(-1

) -1.81

r2=0.91

A

ln (-1)

D

0 1 2 3 41.5

1.6

1.7

1.8

1.9

2.0

D=1.92-0.08n

r2=0.93

B

n

D

Crystallization behavior and structure

JDD ln*

Marangoni and McGauley, 2003,

Crystal Growth and Design 3, 95

11

' * lnd D Jd DG

Thermomechanical Method for the

Determination of the Rheology

Fractal Dimension

AMF SFC vs Temperature

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35 40

Temperature (deg Celcius)

SF

C (

%)

AMF G' vs Temperature

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

1.20E+07

1.40E+07

1.60E+07

1.80E+07

2.00E+07

4 7 10 13 16 19 22 25

Temperature (deg Celcius)

G' (P

a)

AMF G' vs SFC

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

0 10 20 30 40 50 60

SFC (%)

G' (P

a)

-1.4 -1.2 -1.0 -0.8 -0.613

14

15

16

17

18

Thermo

r2=0.996D=2.68

Dilution

r2=0.938D=2.70

(SFC/100)

ln G

'

CB SFC vs. Temperature vs.

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40

Temperature (deg Celcius)

SF

C (

%)

CB G' vs. Temperature

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

3.00E+07

3.50E+07

4.00E+07

4.50E+07

15 17 19 21 23 25 27 29

Temperature (deg Celcius)

G' (P

a)

CB G' vs. SFC

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

3.00E+07

3.50E+07

4.00E+07

4.50E+07

0 10 20 30 40 50 60 70 80 90

SFC (%)

G' (P

a)

-2.0 -1.5 -1.0 -0.5 0.013

14

15

16

17

18

19Dilution

r2=0.92D=2.43

Thermo

r2=0.98D=2.40

(SFC/100)

ln G

'

Structure-mechanical model

Thermodynamic arguments

Dd

o

D

da

A

aE

1

2*3

1

* 2

6

EG31

Marangoni, 2000, Phys. Rev. B 62, 13951

Marangoni and Rogers, 2003, Appl. Phys. Lett. 82, 3239

The Yield Stress (Compression)

D

a

E

3

1

*

**

6

Marangoni and Rogers, 2003, Appl. Phys. Lett. 82, 3239

Global indicator of functionality!

• Yield Stress is a function of SFC, structure

and intercrystalline interactions

• Easy to determine precisely

• Possible to deconvolve into SFC, structure

and interaction effects

Model simulations

0.15 0.20 0.25 0.30 0.350

1000

2000

3000a=200 nmD=2.8

(J m-2)var

(a)

0.005

0.03

0.01

*

(Pa

)

0.15 0.20 0.25 0.30 0.350

1000

2000

3000(b)=0.01J m-2

D=2.8

a (nm)var

100

500

*

(Pa

)

200

0.15 0.20 0.25 0.30 0.350

1000

2000

3000

(c)=0.01J m-2

a=200 nm

Dvar

2.75

2.7

2.8

*(

Pa

)

0.1 0.2 0.3 0.4 0.5 0.60

5000

10000

15000

*(

Pa)

=0.01J m-2

a=740 nmD=2.69

(c)

0.15 0.20 0.25 0.30 0.350

1000

2000

3000=0.01J m-2

a=130 nmD=2.79

(a)

*(

Pa

)

0.1 0.2 0.3 0.4 0.50

2000

4000

6000

8000

(b)

=0.01J m-2

a=810 nmD=2.67

*(

Pa

)

What about intermolecular

interactions?

Van der Waal Interactions

• Origen: permanent and induced dipoles

• Contribution to the van der Waals

Interactions

• Keesom: P-D P-D

• Debye : P-D I-D

• London : I-D I-D also called

“Dispersion”

+

-

145

Hamaker coefficient = property of the material

Strength of the material via van der Waals interactions

Hamaker Coefficient

EvdW (r) = c rm

A

Configuration m

Molecule: point to point 6

Two-plane parallel bodies 2

Two spherical particles 1

A = A (ν=0) + A MIC (rot.) +A IR (vib.) + A UV (elec.)

Lifshitz theory

K Boltzmann’s constant

T Temperature (absolute )

ε dielectric permittivity

146

1 1 3 B 1 3

r

2 Measured dielectric response of the

material for the whole

electromagnetic spectrum

Effective medium theory

147

Intermolecular and Surface

Forces, Israelachvili

Intermolecular and Surface

Forces, Israelachvili

K Boltzmann’s constant

h Planck’s constant

T Temperature (absolute )

ε dielectric permittivity

n index of refraction

ν electronic absorption frequency in the UV region = 3 x 1015 s-1

Index 1 and 3 are for “particle” and “medium” respectively

Approximation to Lifshitz Theory Ignoring the Retarded Potential

A (J) ε FHCO ε

HOSO Lab.

nFHCO

(λ=589nm)

nHOSO

(λ=589nm)

5.35 10-22 3.55 2.38 U o C 1.506737 1.466133

5.70 10-22 1.68Est. 2.65 U o W 1.506737 1.466133

4.43 10-22 3.55 2.92 U o Win 1.506737 1.466133

148

“A” obtained from the approximation to LT

149

Dielectric Constant Index of refraction

ε and n Measurements

Parallel Plate capacitor device

OSCAR: Open Source Capacitance Analyzer

150

Structural-mechanical fractal model

Fractal Floc

Particle

Link

Marangoni, 2000, Phys. Rev. B 62, 13951

Marangoni and Rogers, 2003, Appl. Phys. Lett. 82, 3239

Narine and Marangoni, 1999, Phys. Rev. E 60, 6991

Narine and Marangoni, 1999, Physical Review E 59: 1908

D31

D-31

da 6

Aλ G'

20

Fat Crystal Network Model

Variables Explanation

λ Experimental value, obtained

from a ln G’ vs. ln plot

a diameter of particles

γ Strain at the limit of linearity

d0 separation between the “flocs”,

d=0.165nm (Israelachvili)

Hamaker Constant

SFC

Experimental values :

Temperature : 30°C

ε = 1.9 10-4

λ = 1.7 107 Pa

A (J) do (nm) a (nm)

1.46 10-22 0.2 110

2.44 10-22 0.2 200

5.82 10-22 0.2 240

153

Hamaker constant obtained from Fractal Model

Comparison to previous work

154

1Fully Hydrogenated Canola oil

2Tristearin

3High Oleic Sunflower Oil

4Soybean oil

5* infer from reference

Reference Temp.

(°C)

Refractive index

Media Medium

Permittivity

Media Medium

Hamaker

Coefficient (J)

Peyronel and Marangoni 30 1.50671 1.46613 3.551 2.383 0.55 10-21

Johansson and

Bergenstahl 60* 1.452 1.47354 22 2.54 0.17 10-21

Kloek 60* 1.562 1.47354 22 2.54 1.8 10-21

155

Summary

Afractal model 1.46 10-22 J – 5.82 10-22 J

A Lifshitz

4.43 10-22 J - 5.35 10-22 J

A=2 10-22 J Tristearin in soybean oil . Johannson et al.

(JAOCS, Vol.69,8,1992)

Afractal model ≈ ALifshitz

Interesterified fully hydrogenated

stocks (high stearic acid) with

high-oleic oils

Type of raw material used for the experiment

Major fatty

acids

Carbon

No.

Fully

hydrogenated

canola oil

High oleic

sunflower oil

% of total fat or oil

Palmitic acid 16:0 8.8 5.1

Stearic acid 18:0 88.0 5.9

Oleic acid 18:1 0.08 76.8

Linoleic acid 18:2 0.03 8.0

Linolenic acid 18:3 0.0 0.9

Eicosanoic

acid

20:0 1.9 0.0

Interesterification of a binary mixture (50/50)

of OOO and SSS

Equilibrium

composition

25%

12.5%

25%

25%

12.5%

OSO

OOS / SOO

OOO + SSS

SSO / OSS

SOS

OOO + SSS

Sodium methoxide,

Lipases

Dramatic change in

SFC-temperature profile

0 10 20 30 40 50 60 700

10

20

30

40

30%S:70%O-CI

30%S:70%O-NI

30%S:70%O-EI

Temperature (oC)

Solid F

at

Conte

nt

(%)

NI CI EI

0 10 20 30 400

50

100

150

200

250

300

10

90

4.6Å

3.9Å 3.7Å

2 []

Inte

nsit

y

0 10 20 30

4.6 4.23.8

4.11

10

100

15.2A

2 []

0 10 20 30

100

10

3.8

4.14.2

4.5B

2 []

β ’>

1/32

2 2

3

16 ( )

B f

s

m f

mk H

V T

0 20 40 60 80 1000

1.0×10 -3

2.0×10 -3

3.0×10 -3

4.0×10 -3

5.0×10 -3

CI

EI

NI

SFC (%)

(

J/m

2)

m= Slope of the Fisher-Turnbull plot, ΔHf= (J/mol) enthalpy of fusion, kB= Boltzman’s

constant (1.38×10-23 J/K), Vm (m3/mol) = MW/density, Tf (K) = melting temperature

Dr. Latifeh

Ahmadi

D

a 3

16

80%S

30oC

80sni, eq diam

40 120

200

280

360

0

5

10

15

20

25

Crystal length, nm

Fre

qu

en

cy,

%

80sci, eq diam

50 150

250

350

0

10

20

30

40

50

Crystal length, nm

Fre

qu

en

cy,

%~140nm

/a = 0.0286

Fy=206 N

~100nm

/a = 0.020

Fy=114 N

-30%

-45% D

a 3

16

100sni, sheared eq diam

20 60 100

140

180

220

260

300

340

380

420

0

10

20

30

Size, nm

Fre

cu

en

cy,

%

100sni, eq diam

40 120

200

280

360

0

5

10

15

20

25

Crystal length, nm

Fre

qu

en

cy,

%

Effects of shear

~100nm

~80nm

Thank You!