OKK Unsal Thermodynamic and Kinetic Aspects of Fat Crystallization

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Thermodynamic and kinetic aspects of fat crystallization

C. Himawan, V.M. Starov, A.G.F. Stapley

Department of Chemical Engineering, Loughborough University, Ashby Road, Loughborough, Leicestershire, LE11 3TU, United Kingdom

Available online 14 August 2006

Abstract

Naturally occurring fats are multi-component mixtures of triacylglycerols (TAGs), which are triesters of fatty acids with glycerol, and of which

there are many chemically distinct compounds. Due to the importance of fats to the food and consumer products industries, fat crystallization hasbeen studied for many years and many intricate features of TAG interactions, complicated by polymorphism, have been identified. The melting

and crystallization properties of triacylglycerols are very sensitive to even small differences in fatty acid composition and position within the TAG

molecule which cause steric hindrance. Differences of fatty acid chain length within a TAG lead to packing imperfections, and differences in chain

lengths between different TAG molecules lead to a loss of intersolubility in the solid phase. The degree of saturation is hugely important as the

presence of a double bond in a fatty acid chain causes rigid kinks in the fatty acid chains that produce huge disruption to packing structures with

the result that TAGs containing double bonds have much lower melting points than completely saturated TAGs. All of these effects are more

pronounced in the most stable polymorphic forms, which require the most efficient molecular packing. The crystallization of fats is complicated

not just by polymorphism, but also because it usually occurs from a multi-component melt rather than from a solvent which is more common in

other industrial crystallizations. This renders the conventional treatment of crystallization as a result of supersaturation somewhat meaningless.

Most studies in the literature consequently quantify crystallization driving forces using the concept of supercooling below a distinct melting point.

However whilst this is theoretically valid for a single component system, it can only at best represent a rough approximation for natural fat

systems, which display a range of melting points. This paper reviews the latest attempts to describe the sometimes complex phase equilibria of fats

using fundamental relationships for chemical potential that have so far been applied to individual species in melts of unary, binary and ternary

systems. These can then be used to provide a framework for quantifying the true crystallization driving forces of individual components within a

multi-component melt. These are directly related to nucleation and growth rates, and are also important in the prediction of polymorphic

occurrence, crystal morphology and surface roughness. The methods currently used to evaluate induction time, nucleation rate and overall

crystallization rate data are also briefly described. However, mechanistic explanations for much of the observed crystallization behaviour of TAG

mixtures remain unresolved.

2006 Elsevier B.V. All rights reserved.

Keywords: Nucleation; Crystal growth; Triacylglycerol; Melts; Polymorphism; Crystal morphology

Contents

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1. Molecular structure and composition of fats. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2. Basic polymorphism of TAGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3. Scope of this review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2. Thermodynamic aspects of the melt crystallization of fats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1. Free energy diagrams and polymorph stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2. Correlating and predicting the melting temperature and enthalpy of pure TAGs . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3. The polymorphic behaviour of pure TAGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.1. Monoacid saturated TAGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Advances in Colloid and Interface Science 122 (2006) 3 33

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Corresponding author. Tel.: +44 1509 222525; fax: +44 1509 223923.

E-mail address: [email protected] (A.G.F. Stapley).

0001-8686/$ - see front matter 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.cis.2006.06.016
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2.3.2. Mixed-acid saturated TAGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.3. Mixed-acid saturated/unsaturated TAGs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4. Phase behaviour of binary mixtures of TAGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.1. Phase diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.2. Modelling the solidliquid equilibria of TAGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3. Kinetic aspects of the melt crystallization of fats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1. Nucleation and crystal growth rates

theoretical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.1.1. Thermodynamic driving force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.2. Nucleation thermodynamics, kinetics and mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.3. Polymorphic-dependent nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1.4. Induction time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1.5. Growth rate and mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1.6. Morphology of TAG crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.7. Spherulitic growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.8. Polymorphic transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2. Measurement of fat crystallization kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.1. Induction time and nucleation rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.2. Overall crystallization rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1. Introduction

Fats are highly abundant compounds in nature and are

widely used in food and other consumer products [1]. Their

behaviour heavily influences the microstructure and physical

properties of these products. The development of solid fat

microstructure from a liquid melt to create commercial fat

products such as margarine or chocolate is schematically

presented in Fig. 1 [2], which illustrates how both the

initial processing (within the factory) and subsequent

storage conditions (in the warehouse, shop or home)

ultimately affect final product structure, texture and quality.

Fig. 1. Schematic presentation of processes involved in crystallization and storage of fats (adapted from [2]).

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A number of factors, including crystallization conditions,

are important.

Crystallization occurs in the initial processing stage, and

the relative rates of nucleation and growth determine the initial

crystal size distribution. This is a key parameter for texture as

crystals greater than a few tens of microns in size are

detectable on the tongue, and are thus undesirable in productswhich require a smooth texture. As the solid fraction

increases, individual crystals begin to touch each other

which slows crystal growth (growth impingement). Interac-

tions between crystals then start to dominate the process.

Depending on the nature of the fat substances, gel formation

may also occur [3].

During storage, a number of post crystallization processes

occur, which can affect properties such as hardness, which often

noticeably increases [4]. This is due to sintering, i.e. the

formation of solid bridges between crystals to form a network

[2,4,5]. Polymorphic transformation (see Section 1.2) towards

more stable phases and changes in size distribution via Ostwaldripening may occur [6].

The above events are not necessarily chronological once

nucleation occurs. It is possible, even usual, in processing fats,

that after primary nucleation and subsequent growth that

secondary nucleation, defined as nucleation occurring due to

the presence of the growing crystals [7], can take place

simultaneously along with crystal growth and ripening.

Furthermore, polymorphic transformations may occur in the

processing stage. Transformation into the desirable poly-

morphic forms that deliver favourable properties is often forced

via manipulating conditions. For example, shearing and

tempering have been applied in cocoa butter crystallization

for controlling its polymorphism [812].The characterization of microstructure and the relation to the

mechanical properties of the final product is a difficult (and still

largely unresolved) field of study in its own right, and readers

are suggested to consult the reviews by Walstra et al. [2],

Narine and Marangoni [13,14], and Marangoni [15]. It can be

seen, however, that control of the initial crystallization of the fat

is crucially important to the final quality of any fat based

product.

The crystallization of fats also determines the behaviour of

fractionation processes in which fat fractions with different

melting ranges are separated by crystallizing the highermelting fats and filtering the slurry that is formed. The

resulting fractions are used as ingredients in food formula-

tions and the main reason for fractionation is to tailor these

fats to improve their functionality. The crystallization

conditions in fractionation are different to those in other

food processes as growth impingement generally does not

occur and larger crystals are required to promote easy filtering

[16,17].

The study of fat crystallization is thus a valuable activity

as a greater understanding of fat crystallization enables

fractionation and food processes to operate more efficiently

and the functional effectiveness of fats in food products to be optimised. However, before reviewing fat crystallization

in detail, it is necessary to first cover two complicating

aspects of fats their multi-component nature and

polymorphism.

1.1. Molecular structure and composition of fats

Edible oils and fats mainly consist of a multi-component mix

of triacylglycerols (TAGs) with a small amount of other minor

components. An edible oil or fat can typically contain more than

a hundred different TAGs. A TAG is a triester of glycerol with

three fatty acid molecules, and the general chemical structure is

depicted in Fig. 2. Fatty acids consist of a hydrocarbon chainterminated by a carboxylic acid group. The hydrocarbon chain

length ranges from 4 to 30 carbons (between 12 and 24 are the

most common). The chain usually has an even number of

carbons and is linear unless double bonds are present in which

Fig. 2. (a) A general molecular structure of triacylglycerol (R1, R2, and R3 are individual fatty acid moieties). (b) The chemical structures of a saturated and a non-saturated fatty acid [5].

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case the chain becomes kinked. The carbon atoms of these

linear chains are arranged in a zigzag fashion, which has

implications for crystal packing (see next section). The physical

properties of TAGs heavily depend upon the fatty acid

composition [18].

For convenience, TAGs are usually identified by a 3-letter

code. Each of the characters in the code represents a fatty acidwith the middle character always indicating the fatty acid that is

on the 2-position of the glycerol. For example, PSP represents

glycerol-1,3-dipalmitate-2-stearate. If the three fatty acids are

the same, the TAG is monoacid; otherwise it is called mixed-

acid. ATAG is unsaturated if a CfC double bond is present in at

least one of the fatty acid moieties, otherwise it is referred to as

saturated. The characters used to represent fatty acids are given

in Table 1 and will be used throughout this paper.

1.2. Basic polymorphism of TAGs

TAG molecules are inherently able to pack in different

crystalline arrangements or polymorphs, which exhibit sig-nificantly different melting temperatures [19,20]. The poly-

morphism of most fats is based around three main forms: , ,

and ; the nomenclature scheme following Larsson [21] as

reviewed in Hagemann [20], Hernqvist [22], Wesdorp [23],

Sato [24], and Gothra [5]. However, some fats display more

polymorphs than this.

TAG molecules are three legged molecules that can pack

with the acyl chains (legs) in one of two configurations,

neither of which involves all three chains packing alongside

each other. They can pack in a chair configuration where the

acyl chain in the 2 position is alongside the chain on either the 1

or 3 positions. Alternatively, a tuning fork configuration can

be adopted where the acyl chain in the 2 position is alone and

the chains in the 1 and 3 positions pack alongside each other.

Either configuration naturally packs in a chair-like manner. The

stacking of these chairs can be in either a double of triple chain

length structure (see Fig. 3a), and these stack side by side in

crystal planes, sometimes at an angle. The differences between

polymorphs are most apparent from a top view of these planeswhich shows the subcell structure (Fig. 3b). These structures

can be identified by powder X-ray diffraction patterns [22,24],

where long spacings give information on the repeat distance

between crystal planes (chain length packing) and short

spacings give information on subcell structure (interchain

distances). These interchain distances depend on how the

chains pack together and this is complicated by the zigzag

arrangement of successive carbon atoms in aliphatic chains.

Closer packing is achieved when the zigzags of adjacent chains

are in step with each other (parallel) as opposed to out of step

(perpendicular).

The -form is characterized by one strong short spacing linein the XRD pattern near 0.42 nm. The chains are arranged in

a hexagonal structure (H), with no angle of tilt and are far

enough apart for the zigzag nature of the chains to not

influence packing.

The -form is characterized by two strong short spacing

lines at 0.370.40 nm and at 0.420.43 nm. The chain

packing is orthorhombic and perpendicular (O), that is

adjacent chains are out of step with each other so they cannot

pack closely. The chains have an angle of tilt between 50

and 70.

The -form is characterized by a strong lattice spacing line at

near 0.46 nm and a number of other strong lines around

Table 1

Nomenclature of commonly occurring fatty acids

Code Fatty acid Chain length Double bonds Code Fatty acid Chain length Double bonds

2 acetic acid (ethanoic acid) 2 none P palmitic acid (hexadecanoic acid) 16 none

4 butyric acid (butanoic acid) 4 none S stearic acid (octadecanoic acid) 18 none

6 caproic acid (hexanoic acid) 6 none O oleic acid (cis-9-octadecanoic acid) 18 1

8 caprilic acid (octanoic acid) 8 none E elaidic acid (trans-9-octadecanoic acid) 18 1C capric acid (decanoic acid) 10 none l linoleic acid (cis-cis-9,12-octadecadienoic acid) 18 2

L lauric acid (dodecanoic acid) 12 none R ricinoleic acid (12-hydroxy-9-octadecenoic acid) 18 1

M myristic acid (tetradecanoic acid) 14 none A arachidic acid (eicosanoic acid) 20 none

B behenic acid (docosanoic acid) 22 none

Fig. 3. (a) Chain-length packing structures in TAGs, and (b) the subcell structures of the three most common polymorphs in TAGs (viewed from above the crystalplanes) [24]. Reprinted with permission.



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0.360.39 nm. This is the densest polymorphic form having

a triclinic chain packing, in which adjacent chains are in step

(parallel), and thus pack snugly together. The chains also

have an angle of tilt between 50 and 70.

The and polymorphs can exist as either double chain-

length or triple chain length structures. A double chain lengthstructure normally occurs when the chemical nature of the three

fatty acid moieties are the same or very similar. Conversely, if

the moieties are quite different to each other (for instance in a

mixed saturated-unsaturated TAG), a triple chain-length

structure is formed. The form is normally only found to

exist in a double chain length structure.

1.3. Scope of this review

Many efforts have been performed to unravel the complex

behaviour of fat systems. Crystallization studies are regularly

carried out for natural fats and these are classified by theirorigins, e.g. palm oil and related oils [11,12,2533], milk fats

[11,3443] and cocoa butter [11,12,4449]; just to mention a

few of the most recent contributions. Further reviews can be

found in Smith [50] for palm oil, in Hartel and Kaylegian [51]

for milk fat, and in Sato and Koyano [52] for cocoa butter. Many

other studies have investigated the blending of natural fats as

means of tailoring the physical and thermal properties of fats

[5358].

The disadvantage of the above approach is the empirical and

case by case nature of the information obtained. This can causedifficulties when coping with the compositional variations in

natural fats that originate from geographical, climatic, or

seasonal factors. A more fundamental approach is to study the

crystallization of fats by considering them as multi-component

systems. This is a huge challenge but has already given

extended insights on the behaviour observed in natural fats as

excellently reviewed by Sato [24,59]. This is necessarily a

bottom-up exercise, whereby an understanding of pure TAG

and binary systems must first be obtained.

This review seeks to provide an overview of the current

fundamental understanding of fat crystallization approached

from the thermodynamic and kinetic behaviour of pure TAGsand binary mixtures of pure TAGs. Fat crystallization differs

from most industrial crystallization processes in that crystal-

lization is seldom from a solvent, and thus traditional

Table 2

Literature on polymorphic and phase behaviour of pure and binary mixtures of TAGs

Author Systems Measurement techniques Remarks

(A) Polymorphic occurrence and transformation of pure TAGs

Miura et al. [168] PPP, SSS, POP, SOS, POS, POS/SOS mixtures DSC, XRD Effect of ultrasound

Ueno et al. [167] PPP, LLL DSC, SR XRD Effect of ultrasound

Higaki et al. [48] Pure and impure PPP DSC, XRD Effect of magnetic fields

Smith et al. [213] Different TAGs Light microscopy, DSC, XRD Effect of phospholipids additives

Sprunt et al. [214] SOS FT Raman spectroscopy, DSCBoubekri et al. [111] SRS FTIR, SR XRD

Ueno et al. [110] SOS SR XRD

Dibildox-Alvarado et al. [215] PPP in sesame oil DSC, light microscopy, XRD

Toro-Vazquez et al. [216] PPP in sesame oil DSC, light microscopy, XRD

Ueno et al. [66] SOS DSC, SR XRD Intermediate structured liquids

Rousset et al. [197] POP, POS, SOS Light microscopy, DSC

Yano et al. [109] SOS, POP, POS FTIR Molecular structure and interactions

Kellens et al. [95] PPP Light microscopy, DSC Variability of morphology

Arishima et al. [107] POS DSC, XRD

Kellens et al. [94] PPP, SSS SR XRD

Kellens et al. [93] PPP SRXRD

Arishima et al. [97] POP, SOS DSC, XRD

Koyano et al. [105] POP, SOS DSC, light microscopy, XRD

(B) Phase behaviour and polymorphic transformation of binary TAG mixturesMiura et al. [168] POS/SOS DSC, XRD Effect of ultrasound

Takeuchi et al. [125] LLL/MMM, LLL/PPP, LLL/SSS SR XRD Effect of the difference of molecule length

Takeuchi et al. [124] SOS/SLS DSC, SR XRD

Takeuchi et al. [123] SOS/SSO DSC, SR XRD Existence of molecular compounds

Rousset et al. [146] SOS/POS DSC, SR XRD Phase diagram of metastable phases

Minato et al. [121] POP/PPO DSC, SR XRD Existence of molecular compounds

Minato et al. [122] POP/OPO DSC, SR XRD Existence of molecular compounds

Minato et al. [120] PPP/POP DSC, SR XRD Immiscibility of the least unstable polymorph

Engstrom et al. [128] SOS/SSO DSC, XRD Existence of molecular compounds

Kellens et al. [181] PPP/SSS DSC, XRD

Koyano et al. [119] SOS/OSO DSC, XRD Existence of molecular compounds

Kellens et al. [192] PPP/SSS DSC, SR XRD

Wesdorp [23] Binary TAGs DSC Mixing properties

Cebula and Smith [194] PPP/SSS SR XRD Confirmation of the intermediate phase ()

DSC= Differential scanning calorimetry. SR XRD = synchrotron radiation X-ray diffraction.



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concepts of supersaturation are not helpful. A more detailed

examination of thermodynamic driving forces based upon

chemical potential relationships is needed. The thermody-

namics of fats systems are thus first discussed in Section 2,

and subsequently extended in Section 3 to quantify crystal-

lization driving forces and to examine the kinetic aspects of

fat crystallization. Tables 2 and 3 list the current literature on

the polymorphic and kinetic behaviour of pure and binary

mixtures of TAGs, on which much of this review is based.

2. Thermodynamic aspects of the melt crystallization of fats

Traditionally, a solid fat mixture is characterized by its solid

fraction content (SFC), i.e. the mass fraction of solid present at a

certain temperature. The SFC is then normally used as a basis to

predict and determine the many physical properties of the

material [60].

The typical melting temperature (i.e. normally defined as the

temperature at which the SFC is zero) and SFC characteristics

of some natural fats are shown in Table 4 [6163]. These are

determined most importantly by the composition of the fat. For

instance, the main TAGs in palm oil are POP (22%), POO(22%), PPO (5%), PPP (5%), POS (5%), PlP (7%), PlO (7%),

OOO (5%), and POl (3%) [50]; meanwhile those in coconut

butter are POS (46%), SOS (29%), POP (13%), PlS (3%), SOO

(2%), and SlS (2%) [52].

In this section the thermodynamic aspects of fat systems are

addressed. This begins with a general outline of polymorphism,

before focussing on individual systems. The inherently complex

nature of fats dictates that the discussion of phase equilibria is

best tackled starting with the simplest systems first, namely pure

TAGs of a single saturated fatty acid moiety (e.g. PPP, see Table

1 for the nomenclature). Increasing complexity can then beadded by the presence of double bonds and mixing different

fatty acid moieties within a TAG molecule whilst still

maintaining a single component system. Finally, the phase

behaviour of binary mixtures of different TAG molecules is

introduced.

2.1. Free energy diagrams and polymorph stability

Two types of polymorphism generally exist in lipids and

organic compounds [20,23,64]. Enantiotropic polymorphism

occurs when each polymorphic form is thermodynamically the

most stable in a particular range of temperature and pressure.Changing the temperature or pressure to outside this range will

Table 3

Literature on crystallization kinetics of pure and binary mixtures of TAGs

Reference Systems Measurement techniques Kinetic aspects

(A) Crystallization kinetics of pure TAGs

Hollander et al. [178] Different TAGs Light microscopy Crystal growth rate and morphology

Meekes et al. [217] Different TAGs Simulation of morphology

Hollander et al. [149] Different TAGs Light microscopy Crystal growth rate and morphologyHigaki et al. [48] Pure PPP, impure PPP DSC, XRD Induction time, effect of ultrasound

Smith et al. [213] Different TAGs Light microscopy, SEM and DSC Crystal growth rate and morphology (effect of additives)

Dibildox-Alvarado et al. [215] PPP in sesame oil DSC, XRD Using Avrami model for kinetic analysis

Toro-Vazquez et al. [216] PPP in sesame oil DSC, XRD Using Avrami model for kinetic analysis

Rousset et al. [146] POP, POS, SOS DSC, light microscopy Nucleation and growth rates. Mapping of crystal morphology

Kellens et al. [95] PPP DSC, light microscopy, XRD Induction t ime, nucleation, and growth rate

Kellens et al. [218] SSS DSC, light microscopy, XRD Induction time and nucleation

Koyano et al. [199] POS Light microscopy Induction time. Direct melt and melt mediated crystallization

Koyano et al. [106] POP, SOS Light microscopy Induction t ime. Direct melt and melt mediated crystal lization

Sato and Kuroda [92] PPP DSC, light microscopy Induction time

Zhao et al. [219] PPP, LLL, SSS DSC Bulk and emulsified samples

(B) Crystallization kinetics of binary TAG mixtures

Rousset et al. [146] SOS/POS DSC, light microscopy Nucleation and growth rates. Mapping of crystal morphology

MacNaughtan et al. [127] PPP/SSS DSC Induction time and half time of crystallizationHimawan et al. [150,182,193] PPP/SSS DSC, light microscopy Nucleation and growth rates. Spherulite morphology

Table 4

Melting temperatures and SFC values of natural fats in their most stable polymorph

Fat Melting

temperature (C)

SFC (%) at temperature Data sources

10 C 15 C 20 C 25 C 30 C 35 C

Butter 36 55 37 19 11 5 1 Bockisch [61]

Cocoa butter 34 76 70 45 1 Gunstone [62]

Lard 42 27 20 3 Bockisch [61]

Palm oil 40 54 40 26 16 11 8 Gunstone [63]

Palm kernel oil 28 68 56 40 17 Gunstone [63]

Tallow 50 58 45 25 15 Bockisch [61]



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favour the transformation into a different polymorph (that which

is most stable under the new conditions) [6,65]. Long chain odd

carbon number alkanes exhibit such behaviour [23]. In

monotropic polymorphism, on the other hand, one polymorphic

form is always the most thermodynamically stable. Transforma-

tions occur from the less stable polymorphs to the more stable

ones given sufficient time [6,65].The relative stability of two polymorphs and the driving

force for transformations between them at constant temperature

and pressure are determined by their respective Gibbs free

energies (G) the polymorph which has the lowest Gibbs free

energy is the most stable. Gibbs free energytemperature

diagrams are utilised to map the thermodynamic stability of the

polymorphs. Fig. 4a shows the GTdiagram for the three basic

polymorphs in TAGs from which G values between phases

can be deduced. The form of the plots follows the defining

equation for Gibbs free energy as a function of enthalpy (H),

entropy (S) and temperature (T) which is:

G HTS 1

Due to its monotropic nature, the Gibbs free energy values

are largest for the -form (least dense crystal packing),

intermediate for the -form, and smallest for the -form

(most dense crystal packing). This is mainly a consequence of

the higher heats of fusion of polymorphs with higher melting

temperature. Each polymorphic form has its own melting

temperature, Tm, shown as the intersection points of the GT

curves of the polymorphs and the liquid phase (Fig. 4a).

The transformation pathways among the three main poly-

morphs are shown in Fig. 4b and can be summarised as follows:

The three polymorphic forms can all be directly crystallized

from the melt.

Although any polymorph can be returned to the liquid phase

by raising the temperature above the melting point,

interpolymorphic transformations are always irreversible

(i.e. cannot transform to and cannot transform to ).

Two different modes of transformation are possible: (i)

transformations within the solid state, and (ii) a recrystalliza-

tion of the more stable forms after the less stable forms have

melted. The latter is normally called melt-mediated

transformation.

It has been found in some fat systems that a thermotropic

liquid crystalline phase exists (not shown in the GT

diagram) as a mesophase or intermediate phase which occurs

before the crystallization of the polymorphic crystals or

during melt-mediated transformation [6668]. In such cases,the transformation pathway diagram becomes more compli-

cated (Fig. 4b).

The transformations between liquid and crystalline states and

between crystalline states are all first order transitions where

there is a discontinuity in the first derivative of the free energy

[69].

2.2. Correlating and predicting the melting temperature and

enthalpy of pure TAGs

The melting temperature and the melting enthalpy of pureTAGs are central to a thermodynamic description of solid liquid

phase equilibria in multi-component fat systems as they can be

accurately measured and can be used to construct basic free

energy diagrams assuming constant H and S. Here

correlations between these thermal properties and the chemical

structure of the compounds are described.

Fig. 4a shows that each polymorph in a pure TAG has its

own distinct melting temperature. As at equilibrium G= 0, the

melting temperature can be written as the ratio of the enthalpy to

the entropy of melting (Hm and Sm) given by:

Tm DHm

DSm2

Thus one strategy for correlating melting points is to

combine separate correlations for melting enthalpy and entropy.

However, enthalpy and entropy are also difficult to correlate.

The values ofHm and Sm are governed by several factors

such as hydrogen bonding, the molecular packing in crystals

(influenced by molecular shape, size and symmetry), and other

intermolecular interactions such as charge transfer and dipole-

dipole interactions in the solid phase [70]. These interactions are

Fig. 4. (a) The relation between Gibbs free energy and temperature for the three main polymorphic forms of TAGs (monotropic polymorphism). (b) The polymorphictransformation pathways in fats involving liquid crystals. Adapted from [59].



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complex and it is difficult to predict them (and thus HandS)

with confidence. Due to such complex interactions, only limited

guidelines exist for describing the relationship between the

melting temperature of an organic compound and its chemical

structure despite the enormous amount of available melting

temperature data.

Several recent studies on the estimation of the meltingtemperature and melting enthalpy of organic compounds have

been reported covering a wide variety of classes of organic

compounds. A review on this subject was given by Katritzky

[70] who classified existing correlations into three categories:

Models utilising physicochemical and structural parameters,

such as bulkiness, cohesiveness, hydrogen-bonding para-

meters, and geometric factors [7173].

Group contribution methods in which a molecular break-

down scheme is generally employed and multiple regression

analysis is performed to determine the contribution of a large

number of molecular groups to the melting temperature [74

78]. Usually, melting enthalpy is calculated from group

contribution methods while melting entropy consists of a

group contribution value as well as non-additive molecular

parameters. The latter represents rotational and conforma-

tional entropies [77,78].

Estimations from Monte Carlo or molecular dynamics

computer simulations for the phase transitions and related

properties of compounds including the melting temperature

[7982].

In the case of TAGs, saturated fatty acids are relatively linear

molecules (Fig. 2b) and thus TAGs containing only saturated

fatty acids can easily align themselves to form a compact mass.On the other hand, unsaturated fatty acids in TAGs have kinks

in their aliphatic chains (Fig. 2b). The disrupted packing of the

unsaturated TAGs hinders the formation of crystals and causes

unsaturated TAGs to have a lower melting temperature than

saturated TAGs with the same chain length.

Molecular symmetry [83,84] and crystal packing [70,74] are

considered to be the most influential factors governing the

thermal properties of TAGs. The many different combinations

of arranging fatty acid moieties in TAGs, along with

polymorphism, means that the estimation of melting tempera-

ture of TAGs is more difficult compared to that of most organic

compounds.The methods used for general organic compounds can,

nevertheless, be applied to TAGs. Normally, the melting

enthalpy and entropy are expressed as the sum of a contribution

of the hydrocarbon chains (depending linearly on the chain

length) and a contribution of the end and head groups

(independent of chain length) [23].

DHm hn h0 3

DSm sn s0 4

Here, n is the length of hydrocarbon chains, h and s are

constants that do not depend on the nature of the compound but

only on the way hydrocarbon chains are packed, thus they are

universal constants that only depend on the polymorphic form.

The other constants h0 and s0 that account for the end-group

contributions (the structure of fatty acid moieties) are specific to

each class of lipid.

Combining Eqs. (2)(4), gives:

Tm DHm

DSm

hn h0sn s0

Tl 1 A

n B

5a

with:

Tl h

s; A

h0

h

s0

s; B

s0

s5b

This implies that if the melting temperatures of a class of

lipids have been correlated, only one data point for the enthalpy

of fusion is in principle sufficient to obtain a correlation for the

enthalpy of fusion of the complete class of lipids. However, this

is an oversimplification, as differences in chain lengths of

individual moieties need to be accounted for.

Timms [85] compiled Tm and Hm data of- and -forms

of selected TAGs and gave regressed correlations for each

polymorphic form. Zacharis [86] used Eq. (3) to represent the

thermal data of monoacid TAGs. Perron [87,88] updated the

work of Timms [85] and published correlations for the three

polymorphic forms for saturated TAGs. Furthermore, Perron

modelled the lower melting enthalpy of unsaturated TAGs

(Hm,unsat) by comparing them with the corresponding

saturated TAG (Hm,sat) and then making an adjustment

according to the following equation:

DHm;unsat DHm;sat

1151

e

0:706d

6where dis the number of double bonds in the unsaturated TAG.

Won [89] followed the approach of Zacharis [86] but applied the

equations to saturated TAGs with mono and mixed acyl groups.

However, data were only correlated with the total number of

carbon atoms and the effects of position were not considered.

Thus the fitted values were identical for different TAGs with the

same total number of carbon atoms.

Zeberg-Mikkelsen and Stenby [90] developed empirical

correlations based upon a group-contribution method which

took into account the position of the acyl groups. The

correlations were only valid for saturated TAGs which had an

even number of carbon atoms (between 10 and 22) in each acylgroup. Chickos and Nichols [74] developed simple relation-

ships for homologous series and showed that they were

applicable to the three polymorphic forms of symmetrically

substituted TAGs. Anomalous behaviour, which was revealed in

some cases, was argued to be caused by different packing

between members of a series. Molecular modelling has also

recently been applied to estimate the thermal and transport

properties of TAGs with reasonable predictive capability [91].

Wesdorp [23] developed a model to estimate Tm and Hmfor different polymorphic forms of saturated and unsaturated

TAGs from a large database. He improved the method of Eqs.

(5a) and (5b) to account for the effect of position and chain

length of the three acyl groups in TAGs (symbolised by pqr).



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Two parameters were introduced x = qp and y = rp, where q

is the chain length of the acyl group in position 2 of the TAG

and p is the shortest chain length of the acyl group in positions 1

or 3. From many regression trials, Wesdorp [23] identified

several factors to be important in order to successfully estimate

Tm and Hm values of TAGs. These were (1) the length of each

chain, (2) whether the chain has an even or odd number ofcarbon atoms, (3) whether the chain is saturated or unsaturated,

and (4) the molecular symmetry. It was also found that the

melting enthalpy of the -form depended on whether it was

double chain length or triple chain length packed. Correlations

obtained for unsaturated TAGs in the study were found to be

less reliable due to the limited data available compared to those

for saturated TAGs. Although aimed at the development of an

empirical model, the work of Wesdorp [23] indicated that the

thermal behaviour of TAGs directly follows from their

molecular structure.

2.3. The polymorphic behaviour of pure TAGs

The polymorphic nature of TAGs is well established. It is

also well known that mixing different fatty acid moieties in a

TAG produces more complex polymorphic behaviour (princi-

pally the number of observable polymorphs). Thus saturated

monoacid TAGs are simplest, followed by mixed acid saturated,

with mixed acid saturated/unsaturated being the most complex

[18,59].

2.3.1. Monoacid saturated TAGs

This group of TAGs has been examined by thermal

techniques (such as DTA and DSC) more than any other

group and shows the basic , , and polymorphic forms [20].Melting temperature and enthalpy data for the three poly-

morphic forms with fatty acid chain lengths ranging from 8 to

30 have been compiled by Hagemann [20], Wesdorp [23], and

by Zelberg-Mikkelsen and Stenby [90].

Generally, the polymorphic behaviour of TAGs with an even

carbon number are well represented by the behaviour of PPP

[67,9295] and SSS [20,94,96] and summarised as follows (see

Fig. 5 for the SSS thermal behaviour and the structural model of

the molecular packing of each polymorph):

The -form is crystallized upon cooling from the melt at

moderate to high cooling rates. Remelting the -form

induces an endotherm at a slightly higher temperature than

the cooling exotherm, but this is soon followed by an

exotherm associated with the formation of the stable -form

[20,94].

The -form crystallizes if the temperature is maintained

slightly above the melting temperature of the -form (about

30 min induction time for SSS). Several endotherms may be

observed upon remelting caused by submodifications of the

-form [20,94].

The -form can be crystallized directly using a solvent

[20,97] or by tempering/holding (about 60 min induction

time for SSS) slightly above the melting temperature of-

form [94]. Only CCC (tricaprin) was reported to reveal

multiple -forms [98].

The chain length of fatty acid moieties has a significant

influence on the polymorphic behaviour. Of particular note is

that the crystal packing of and forms also depends on

whether the number of carbons in the chain is even or odd

[22].

For TAGs of C22 and longer, rapid cooling exhibits a singleexotherm associated with the formation of the -form.

However, Hagemann [20] showed that tempering can lead to

Fig. 5. (a) Typical thermograms of monoacid saturated TAGs represented by tristearin. Adapted from [20]: cooling from the melt at 20 C/min (dashed line), followed

by heating at 2.5 C/min (solid line). Intermediate forms (1 and 2) are observed after holding 30 min slightly above the melting point of the -form. (b) Side-view

structural model of molecular packing of the ,

and; the different between the structure of the

- and the -form is in their subcell structure (see Fig. 2). Adaptedfrom [22].



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two submodifications of the -form with greater separation

between the two peaks as the chain length increases.

Three different submodifications of the -form were

reported in even carbon numbers shorter than C16. The

third modification melted close to the -form, the difference

in melting points decreasing wth increasing chain length

[20].

The -form of odd carbon number monoacid TAGs is more

stable compared to even number TAGs [20]. X-ray

diffraction analysis indicates this is due to a closer similarity

of the crystal structure of the - and -forms with odd TAGs

than is the case with even TAGs [98].

The melting points of the -form increase monotonicallywith fatty acid chain length but those of the - and -forms

show fluctuations due to the oddeven chain length effect

(see Fig. 6) as reported in hydrocarbon type materials

[20,23,99]. The trend of melting temperature versus chain

length for odd numbered TAGs is generally lower than that

for even numbered TAGs. The effect is most pronounced at

lower chain lengths and is maintained for the polymorph at

higher chain lengths. This reflects the less packed crystal

structure due to steric hindrance of the molecular structure of

odd number TAGs and the more precise packing of the

polymorph.

2.3.2. Mixed-acid saturated TAGs

Mixed-acid saturated TAGs, mainly those with acids with

even carbon number chain lengths in the range 1220, arewidely prevalent in natural fats. Modifications of polymorphic

behaviour from that of monoacid saturated TAGs result from

differences in chain length between the fatty acid moieties, and

this is also influenced by their relative positions [20,59]. This

was best described by Sato [59] when analysing the

polymorphic and thermal behaviour of the asymmetric PPn

TAGs [24,100102] the symmetric CnCn + 2Cn TAGs [103,104].

Here n represents even chain lengths varying from 0 to 16 in

PPn and from 10 to 16 in CnCn+2Cn.

Sato and Ueno [59] observed that heterogeneity in the chain

lengths of the three acyl groups tends to reduce the gap in

stability of the -form and -form such that the -form is not

observed. This is illustrated by the behaviour of asymmetric

PPn TAGs, where was the most stable form of PP6, PP8, and

PPM, while was most stable in PP2, PP4, and PPC. The

chain-length structure of the most stable forms also varied with

increasing n from double (PP2, PP4) to triple (PP6, PP8, PPC)

and back to double again (PPL, PPM). The irregular trend of the

melting temperatures of the PPn, shown in Fig. 7a, reflects the

variation in the chain length structures.

In CnCn+2Cn TAGs, was always found to be the most

stable form as no form was observed [103]. The melting

temperatures and long spacings of the CnCn+2Cn series

increased monotonically with increasing n (Fig. 7b) as would

be expected.The complexity of polymorphs of mixed acid TAGs is

illustrated by Fig. 8 which shows the polymorph structures of

PPC [101]. The most notable aspect is that there are various

submodifications of the -form of this molecule. The -form

occurs by rapid cooling from the melt which further transforms

to 3 (O subcell). Upon remelting, the 3-form transforms to

the 2-form with the same subcell type. All -, 2- and 3-

forms are double chain length structures. A transformation from

Fig. 6. Melting temperatures plotted against fatty acid chain lengths of-, -,

and -forms of monoacid saturated TAGs [99]. Reprinted with permission from

the American Oil Chemists' Society.

Fig. 7. Long spacing values (open squares) and melting temperatures (closed circles) of (a) PP n TAGs [100] and (b) CnCn+2Cn TAGs [103]. Adapted from Sato andUeno [59].



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the 2-form to the triple chain length -form proceeds at higher

temperatures. Additionally, rapid melting of the -form induces

another-form showing a hexa-layered structure (1-6).

Many issues regarding the polymorphic behaviour in

asymmetric mixed-acid saturated TAGs remain unresolved

[59], due to the various interchain interactions of the methyl end

groups, aliphatic chains and glycerol groups [24].

2.3.3. Mixed-acid saturated/unsaturated TAGs

TAGs with unsaturated fatty acids at the sn-2 position and

saturated acids at the other positions (Sat-U-Sat) are the main

components of a number of widely used vegetable fats such as

palm oil and cocoa butter. These will be considered here to

illustrate the complexities of unsaturated systems. Particularlycommonplace are those containing oleic acid at the sn-2

position. The presence of the double bond (with the inflexible

kink) gives greater steric hindrance than found in completely

saturated TAGs, which forces specific structures to be formed to

enable the saturated and unsaturated fatty acid moieties to be

packed together in the same lamella leaflet. Consequently, this

TAG group exhibits still more complicated polymorphic

behaviour as observed in the systems of SOS, POP, POS,

SRS, and SlS [66,105112].

Kaneko et al. [113] and Sato [24] expressed this complexity

by highlighting the importance of olefinic conformations (see

Fig. 9) in addition to the molecular chain packing (subcellpacking) and the chain-length structure. These relate to how the

aliphatic chains on either side of the double bond are twisted

with respect to the plane of the double bond. Information on

these structures can be obtained from XRD, Fourier Transform

Infra Red (FTIR) [109,114,115] and Nuclear Magnetic

Resonance (NMR) [116,117].

The polymorphic structures of all Sat-O-Sat TAGs (with Sat

being saturated fatty acid and O being oleic acid) are similar,

with the exception of POP [24,59]. Fig. 10 shows the structures

of both POP and SOS (which can be taken to be representative

of the other Sat-O-Sat TAGs) [109]. Particularly noteworthy for

this TAG group are:

Another intermediate phase, can occur which has a triple

chain-length structure. The saturated and oleic acid chains of

this form are disordered with oleic acid chains packing in a

hexagonal subcell (as in the -form) whilst the saturated

chain leaflet shows a parallel packing.

The -form is a triple chain-length structure, whereby the

saturated chain leaflets form an ordered O subcell whilst the

oleic acid chain leaflets remain in a disordered hexagonal

subcell.

In the case of the two -forms the saturated and oleic acid

leaflets both pack in an ordered manner. There is a slight

difference in the length of the triple chain-length structure ofthese two forms, and a small difference in melting

temperature of 1.52.0 C.

The presence of a double bond in Sat-O-Sat TAGs generally

forces the - and -forms to adopt a triple chain-length

Fig. 9. Representation of the olefinic conformations of fatty acids in TAGs containing oleic acid moieties; S

C

S

when - and-chains are placed in the same planeand SCS when the two chains are normal to each other [113].

Fig. 8. Polymorphic transformations in PP10 [59,101,220].



12/31

structure so that the oleic acid chains are packed together and

separately from the saturated chains. The exception is the -

form of POP which forms a double chain-length structure

(Fig. 10)). This is probably because the palmitic and oleic acid

chains pack to a similar length once the kink in the longer

oleic acid chain is taken into account. This would result in a

weaker steric hindrance to the formation of a double chain

length structure than would be the case with the other Sat-O-

Sat TAGs.The long spacings (representing the chain-length structure)

and melting temperatures of Sat-O-Sat TAGs are presented in

Fig. 11. In general, a smooth increase of the long spacing and

melting temperature with increasing length of the saturated acid

chains is observed except for the more stable polymorphs which

show rather jagged profiles. The long spacing of the -form of

POP is much shorter than for the other TAGs as it forms a

double rather than triple chain-length structure (Fig. 10). An

exception to the general pattern is POS, which does not show a

-form and only shows a single -form. Sato and Ueno [59]

have suggested that this might be due to the racemic nature of

POS (although the similarly racemic SOA does not show the

same behaviour).

Boubekri et al. [111] and Takeuchi et al. [112] in turn

reported that SRS and SlS exhibit similar polymorphism to the

other Sat-U-Sat TAGs, except that their polymorph stability andthermal properties are modified significantly. In SRS, hydrogen

bonding in the ricinoleoyl chains of the -form is much tighter

than that in the case of SOS so that the -form is much more

stable. Evidence for the greater hydrogen bonding comes from

the much higher melting enthalpy and entropy of the -form of

SRS than in SOS and SSS [59]. In SlS, the -form is stabilised

due to interactions among the linoleoyl chains at the sn-2

position. Accordingly, the enthalpy and the entropy values for

the melting of of SlS are much larger than those of SOS and

SRS.

We have discussed here only the Sat-U-Sat TAGs to give an

impression of the complex polymorphism that can occur in fats.Other mixed acid saturatedunsaturated TAGs also exist such as

Sat-Sat-U and Sat-U-U. For information on these systems the

reader is recommended to consult the review by Sato and Ueno

[59].

2.4. Phase behaviour of binary mixtures of TAGs

The next step up in complexity of systems is to consider

binary mixtures of TAGs. The equilibrium behaviour of a binary

mixture is best illustrated using phase diagrams.

2.4.1. Phase diagrams

Timms [118] identified four main types of phase diagramthat are commonly observed in binary mixtures of TAGs

(Fig. 12):

Monotectic continuous solid solutions, which are formed

when the TAGs, are very similar in melting temperature,

molecular volume and polymorphism (e.g. SSS/SSE, POS/

SOS).

Eutectic systems, which are the most commonly found, tend

to occur when the components differ in molecular volume,

Fig. 11. Long spacing values (left) and melting temperatures (right) of polymorphs of Sat-O-Sat TAGs [108]. Adapted from [59].

Fig. 10. A structural model of the polymorphic behaviour in Sat-O-Sat TAGs

represented by the behaviour of POP and SOS [109]. Reprinted with permission

from The Journal of Physical Chemistry. Copyright (1993) American Chemical

Society.



13/31

shape, and polymorph but not greatly in melting temperature

(e.g. PPP/SSS, POS/POP, SOS/SSO).

Monotectic partial solid solutions form in preference to a

eutectic system if the difference in melting temperature of the

TAG components is increased (e.g. PPP/POP).

Peritectic systems (2 solid solutions and 1 liquid) have only

been found to occur in mixed saturated/unsaturated systems

where at least one TAG has two unsaturated acids (e.g. SOS/

SOO, POP/POO).

An extensive compilation of phase diagrams of binary TAG

mixtures from the literature has been made by Wesdorp [23]

who identified three critical issues when considering such

diagrams: (i) the purity of materials used in experiments, (ii) the

stabilisation procedure for producing the most stable phase

(which must be standardised to reduce error), and (iii)

difficulties in the determination of the solidus resulting from

kinetic effects (discussed in Section 3).

Recently, binary phase diagrams have been constructed via

the use of synchrotron radiation (SR) XRD [119125]. The

high intensity of this X-ray technique provides richer

information about the polymorphic phases and it is also

gained in real time which allows metastable polymorphs to be

characterized distinctly, in contrast to traditional methods

[125].

For binary TAG mixtures, the primary factors determining

phase behaviour are differences between the TAGs in chain

length, the degree of saturation and position of the fatty acid

moieties, and which polymorphs are involved. Different phase

behaviour is frequently observed for different polymorphs,

e.g. PPP/SSS shows complete miscibility of the less stable

forms ( and ) but a eutectic system for the -form

[126,127].The effect of the differences in chain length is illustrated by

the behaviour of mixtures of two monosaturated TAGs.

Takeuchi et al. [125] studied the phase diagrams of LLL/

MMM, LLL/PPP, and LLL/SSS and after also considering that

of PPP/SSS, came to the following conclusions for binary

monosaturated TAG mixtures:

The metastable - and -forms are miscible when the

carbon numbers for the fatty acid chains of the three TAGs

differ by 2 or less. This is the case, for example, with PPP/

SSS and LLL/MMM (see Fig. 13a).

Immiscibility of the metastable phases appears when

differences in carbon chain lengths of 4 or 6 are present

Fig. 12. The four main types of phase diagram in binary mixtures of TAGs (a) monotectic, continuous solid solution, (b) eutectic, (c) monotectic, partial solid solution,

(d) peritectic [118].



14/31

such as with LLL/PPP and LLL/SSS (see Fig. 13b). Eutectic

and monotectic behaviour are observed in the -form for the

LLL/PPP and LLL/SSS systems, respectively, with the

form of SSS co-existing with the form of LLL under

certain conditions.

As already mentioned, increasing the difference between the

melting temperatures of the pure TAG's shifts the phase

behaviour from eutectic to monotectic. The reasons for this are

largely unexplored [125].

In mixtures where monosaturated and mixed-acid saturated-unsaturated TAGs are combined, such as the PPP/POP system

(see Fig. 14), there is a pronounced steric effect. It is difficult for

the oleic acid chain to pack directly with PPP and this results in

limited miscibility and is reflected by eutectic behaviour for all

three polymorphic forms , and [120].

Combining two TAGs which both contain an unsaturated

fatty acid is less problematic as like chains from either TAG can

arrange themselves together. Indeed it is sometimes the case that

two TAGs can display a synergistic compatibility and pack

more easily together than on their own. These form so-called

molecular compounds with a 50:50 ratio of the two

components. This is observed in systems such as SOS/OSO

[119], SOS/SSO [123,128], POP/PPO [121], and POP/OPO

[122]. As an example, the phase behaviour of the POP/PPOsystem is presented in Fig. 15. The three polymorphs , and

form eutectic phases at the 50:50 molar composition.

The properties of molecular compounds have been investi-

gated using FT-IR and XRD, and show significant deviations

from those of the component molecules [113]. Molecular

compounds also consistently form double chain length

structures in the metastable and stable phases in contrast to

the triple chain length structures that are found in the stable

polymorphs of the pure TAG components. These molecular

compounds also crystallize faster than the pure components of

the same polymorph [59,123].

The formation of molecular compounds impacts upon the performance of fractionation processes, as only limited

separation is thus experienced. On the other hand this can be

useful for blending purposes [59,119].

2.4.2. Modelling the solidliquid equilibria of TAGs

With the plethora of binary phase diagrams in existence for

TAGs, it is useful to be able to condense this information into a

(relatively) small number of parameters by the use of modelling.

This also potentially enables extensions to be made to describe

ternary and higher systems.

The equilibrium condition for a multi-component system

with a liquid phase and at least one solid phase can be described

as the point where the chemical potential of each component (i)

Fig. 14. The effect of steric hindrance in the PPP/POP system, an example of a

mixture of a monosaturated and a mixed-acid saturatedunsaturated TAG. All

three polymorphs show eutectic behaviour [120]. Reprinted with permissionfrom the American Oil Chemists' Society.

Fig. 13. The effect of the difference of carbon numbers in binary saturated TAG mixtures on phase behaviour: (a) miscible metastable phases in LLL/MMM, (b)

immiscible metastable phases in LLL/SSS [125]. The melting temperatures reported are slightly higher than the onset temperatures of melting. Reprinted with

permission from Crystal Growth and Design. Copyright (2003) American Chemical Society.



15/31

in each phase is equal to that in any other phases present[129],i.e.:

lLi lSji 7

where iL and i

Sj are the chemical potentials of each component

i in the liquid and the jth solid phase, respectively. The chemical

potential of componenti in a mixed phase p (solid or liquid) is

given by:

lpi l

pi;0 RTlng

pi x

pi 8

where i,0p is the chemical potential of the pure component i in

the respective phase, xip is the mole fraction of componenti and

ip is the activity coefficient for component i.Substitution of Eq. (8) into Eq. (7) results in the equilibrium

condition for component i:

lng

Sji x

Sji

gLi xLi

!lLi;0l

Sji;0

RT9

To evaluate the right hand side of Eq. (9), let di,0p =Si,0

p dT

+ Vi,0p dP (where Si,0

p and Vi,0p are the pure component molar

entropy and molar volume of the p phase for component i,

respectively, P is pressure) and Si,0 =Hi,0/T (where Hi,0 is

the change of molar enthalpy upon melting of pure component

i). Using these definitions we obtain:d Dli;0

DSi;0dT DVi;0dP

DHi;0

TdT DVi;0dP 10a

or

dDli;0

RT

DHi;0

RT2dT

DVi;0

RTdP 10b

A simplification of Eq. (10b) can be made by assuming the

following:

The reference temperature is the melting temperature of the

pure componenti at the system pressure, Tm,i(P). Thus the

effect of pressure does not need to be considered further(dP=0).

The change in molar enthalpy can be represented by

Hi,0Hm,i,0 +Cpi,0(TTm,i), where Hm,i,0 is the

molar enthalpy of melting of pure component i at the

reference temperature Tm,i and Cpi,0 is the molar heat

capacity difference between the liquid and solid for the pure

component i (assumed to be independent of temperature).

Integration of Eq. (10b) and substitution into Eq. (9) results

in [60,130]:

lng

Sji x

Sji

gLi xLi ! Dli;0

RTDHm;i;0DT

RTm;i;0T

DCpi;0DT

RT

DCpi;0

Rln

Tm;i;0

T

11

where T= Tm,iT.

Eq. (11) relates the equilibrium compositions in the two

phases (left hand side) to the system temperature (right hand

side). These equilibrium compositions are heavily dependent on

the activity coefficients, and to describe the equilibrium

conditions, the effect of composition and temperature on the

activity coefficients (in Eq. (11)) must be appropriately

modelled. This is usually only required for the solid phase

activity coefficients as the liquid phase can generally be

assumed to be ideal. Prausnitz [129] elaborately describes theexisting thermodynamic models for such a purpose.

The simplest case is where there is a large difference in

melting points. The high melting component essentially forms a

pure crystal (xiS = 1). Both liquid and solid activity coefficients

are unity and Eq. (11) is rearranged and reduced to the so-called

Hildebrand equation (where xi in Eq. (12) is the mole fraction

of the high melting component in the liquid phase):

lnxi DHmDT

RTmTDHm

R

1

Tm

1

T

12

Of course, the activity coefficients also dictate the mixing

behaviour of the system in both the liquid and solid phases. If it

is possible for the overall system Gibbs free energy to be

Fig. 15. Formation of molecular compounds in the mixture of unsaturated TAGs (PPO/POP): (a) the most stable phase and (b) metastable phases; C represents

molecular compounds [121]. Reprinted with permission from The Journal of Physical Chemistry B. Copyright (1997) American Chemical Society.



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reduced by splitting the solid into two different solid fractions of

different compositions then immiscibility will occur. Thisgenerally requires activity coefficients to be greater than unity.

The thermodynamic modelling of binary solid liquid

equilibria involving solid solutions has been applied to many

different areas of application. An example is the long chain

hydrocarbons (waxes), which exhibit non-ideal mixing (activity

coefficients deviate from unity) in both liquid and solid phases.

Investigations have thus focused on finding the appropriate

model to describe activity coefficients for liquid and solid

phases and then assessing the capability of binary parameters to

describe the multicomponent mixtures [131137]. Equations of

state have also been applied in this particular case [138]. The

use of thermodynamic models in the food area has also recently

been reported [139142], and Tao [143] has reviewed theirapplication in material science.

Despite the usefulness of thermodynamic modelling in many

other areas of application, there has been relatively little work

on modelling the solidliquid equilibria of TAG mixtures [60].

Wesdorp [23] studied the mixing behaviour of TAG mixtures in

the liquid phase and three different polymorphic forms. He

found that melts of TAG mixtures and solid solutions of -

polymorphs behave as ideal mixtures (as long as the difference

of chain length does not exceed 15 carbon atoms) while - and

-forms exhibit significantly non-ideal behaviour. Based on

those findings, a thermodynamic model to describe the phase

behaviour of multi-component fats was proposed.The excess Gibbs energy for all solid phases, GE

S, was

successfully fitted using a 3-suffix Margules equation (see Eqs.

(13) and (14) for binary systems). A drawback of this equation

is the lack of a rational base for its extension to multi-

component systems. It is generally assumed that the contribu-

tions of the binary parameters (A12 and A21 in Eqs. (13) and

(14)) to the excess Gibbs energy in the multi-component

mixture are the same as in the binary mixture at the same

relative concentrations.

DGE A21x1 A12x2x1x2 13

RTlng1 x22A12 2A21A12x1

RTlng2 x21A21 2A12A21x2 14

All 4 types of binary TAG phase diagram [118] have been well

simulated by the 3-suffix Margules equation. Examples are shown

in Fig. 16 for eutectic and non-eutectic binary TAG mixtures [60].

Binaryinteractions parameters of various TAG combinations have

been documented [23] and have been used to simulate the SFC of

fats containing many TAG components; showing reasonably good

agreement with experimental data [23,60,144,145]. A similar

approach was employed by Rousset et al. [146] to characterise the

equilibrium states of binary mixtures of the POS/SOS system

which was then used to define the crystallization driving forces for

a kinetic study (see Section 3.1.1).

Having demonstrated the ability of the 3-suffix Margules

equation to simulate phase diagrams of TAG mixtures, Wesdorp[23] attempted to theoretically estimate the binary interaction

coefficients needed in the Margules equation by evaluating the

degree of isomorphism [147] and lattice distortion and thus

produce a predictive model. However, reliable correlations were

not achieved.

Ideally, thermodynamics should give a firm foundation for

predictive models of SFC provided the compositions of the fat

mixture are known. By extracting binary interaction coefficients

between the triacylglycerol components in the mixture, it is

possible to extrapolate to ternary and more complex mixtures

[23,60,146]. In practice, however, kinetics cannot be neglected

due to the often slow process of fat crystallization [144,145] and

the presence of metastable regions. Yet thermodynamic aspects

are critical since equilibrium information of a fat mixture will

enable the driving force of crystallization to be quantified and

establish a benchmark for the kinetic behaviour. The kinetic

aspects will now be addressed.

3. Kinetic aspects of the melt crystallization of fats

Although a solid becomes the thermodynamically stable

phase when a melt is cooled down below its melting

temperature, this liquidsolid transition does not occur sponta-

neously. The occurrence of a solid phase in its early stages

requires two distinct events: (1) the formation of nuclei in the

Fig. 16. Modelling of the phase diagram of the stable phases in binary TAG mixtures [23]. Examples are shown for PSP/SPS which forms a eutectic (left) and for PPP/

POP without a eutectic point (right) [60].



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mother phase followed by (2) the advancement of the faces of the

nuclei resulting in crystal growth. In fat systems, it has been

proposed that an ordering process of molecules into lamellae

acts as a precursor to the formation of a crystalline solid phase

[24,51] (see Fig. 17a). This process follows a path through

transitory states that requires energy barriers to be overcome as

shown in Fig. 17b for different polymorphic forms [148].The finite diffusion rates of molecules in the liquid and solid

phases and the arrangement and subsequent attachment of

molecules onto the surface of growing crystals all contribute to

the kinetics of the overall process [149]. Consequently, kinetic

factors are as important as thermodynamic ones in determining

which polymorph will form from the melt and the amount,

composition and properties of the crystalline phase. Examples

of these kinetic effects are described below.

(a) Polymorphic occurrence

Usually fats crystallize first in the least stable polymorph

with the lowest energy barrier () and later transform or

recrystallize to more stable polymorphs (

or ). Directcrystallization of- or-forms from melts tends to occur only

when no supercooling, or sometimes little, of the less stable

forms is present. Fig. 18 shows the kinetic phase diagram of

PPP/SSS [150] upon linear cooling at different cooling rates.

Depending on the cooling rates applied, either- or-forms

crystallize. This illustrates the strong influence of kinetics on

polymorphic occurrence in fats.

(b) Composition gradients within crystals

Differences in composition between the outer and inner

regions of a crystal are thought to occur during a slow cooling

crystallization as described in Wesdorp [23] and Los et al.

[144,145]. This would be due to the higher melting components

preferentially solidifying during the early stages of crystalgrowth which are then depleted from the liquid melt. The low

diffusion rate in the solid phase hampers the inner part of the

growing crystals to reach equilibrium with the liquid phase as

the composition of the liquid phase changes, whereas the

surface composition is much closer to equilibrium. The crystals

are ultimately inhomogeneous in composition having a

concentration gradient between the centre and the surface of

the crystal. However, although the concept of a composition

gradient within crystals is plausible, as far as we know no

experimental proof has been published.(c) Crystal perfection

Fig. 17. (a) Simplified schematic representation of ordering in the liquid state of TAGs preceding the formation of a crystalline solid phase [24,51] (reprinted withpermission). (b) Energy barrier diagrams for the three main polymorphic forms of a TAG at a given conditions below their melting temperatures. Adapted from [148].

Fig. 18. Effect of kinetics on the polymorphic occurrence in the binary PPP/SSSsystem at a number of cooling rates [150]. Tm, is the equilibrium temperature of

the -form. The -form crystallised at 0.5 and 1 K min1 in PPP-rich mixtures

(shown as open symbols).



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Poorly packed crystals can result from rapid crystallization

[67,151,152]. The thermal properties of such imperfect crystals

deviate significantly from those of well-ordered ones. Imperfect

crystals may persist for years in the absence of a liquid phase

[20] but can easily recrystallize into well packed crystals via the

liquid phase if a liquid phase is present [22].

Los et al. [130,144,145] extended the work of Wesdorp [23]by implementing a simple kinetic expression into the flash

calculation of multi-component TAG mixtures. They showed,

via simulation using thermodynamic parameters from Wesdorp

[23], that the effect of kinetics on the prediction of the SFC of

fat mixtures is substantial. However, comparisons with experi-

mental data were not presented.

It is clear that kinetic factors should be considered in order to

describe properly the crystallization behaviour of fats. In the

following sections aspects characterising the dynamics of fats

crystallization are examined.

3.1. Nucleation and crystal growth rates

theoretical aspects

3.1.1. Thermodynamic driving force

The fundamental thermodynamic driving force for the crys-

tallization of a component i is the difference in chemical po-

tential ofi (i) between the liquid (iL) and solid (i

S) phases.

The chemical potentials are formulated as in Eq. (8), and thus:

Dli lLi l

Si Dli;0 RTln

gLi xLi

gSi xSi

14a

Substituting in the expression for (i,0) from Eq. (11)

yields:

DliRT

DHm;iTm;iT

RTm;iTDCpiTm;iT

RT

DCpi

Rln

Tm;i

T

ln

gLi xLi

gSi xSi

14b

However, in almost all cases in the literature, one of two

simplified approaches is used [148,153].

(a) Liquid-solution approach

The first approach represents the fat blend as a mixture of

two pseudo-components that are immiscible in the solid state.

The pseudo-component with the higher melting temperature is

considered to be the solute, while the one with lower melting

temperature is the solvent. This is normally applied when fatscontain two families of distinctly different TAGs [2,31,154].

The approach is similar to most studies of industrial

crystallization, where the crystallization driving force is

modelled as the result of supersaturation. Thus for a liquid

phase of a defined concentration of solute, the difference

between the saturation concentration is evaluated (at the same

temperature). The saturation composition (xiL,eq) is that which is

in equilibrium with the forming solid phase (xiS), which can

related by Eq. (9) thus:

lngSi x

Si

gL;eqi xL;eqi ! Dli;0

RT15

Combining Eqs. (14a) and (15) and eliminating (i,0)

results in:

Dli RTlngSi x

Si

gL;eqi x

L;eqi

! RTln

gLi xLi

gSi xSi

RTlngLi x

Li

gL;eqi x

L;eqi

!

16

In many cases, the liquid phase of multi-component fats is

nearly ideal due to the relatively similar size and structure of the

component molecules [23], i.e. iL,eq

iL1. Eq. (16) is thus

further simplified to:

DliiRTlnxLi

xL;eqi

17

For small supersaturations (xiL/xi,eq

L 1.1), Eq. (16) should be used.

A limitation of this method is that it is reliant on the

availability of an equilibrium liquid concentration for the solid

phase. This cannot be evaluated if the sample temperature is

below the solidus, in which case a different approach is called

for.

(b) Liquid-melt approach

When fats are composed of relatively similar component

TAGs, it is often assumed that crystallization can be described

as occurring from a pure melt. Thus the last term in Eq. (14b) is

neglected. A further simplication can also be made byneglecting the second and third terms on the right-hand side

of Eq. (14b), which for fats are at least two orders of magnitude

smaller than the first term, where T= Tm,iTis not larger than

10 K [130]. This gives:

DliiDHm;iTm;iT

Tm;i

18

According to the latter equation, the driving force is thus

proportional to the difference between the actual temperature

and the melting temperature.

Note, however, that for very complex systems such as naturalfats which have many different TAG components, the definition

of the above crystallization driving force becomes ambiguous as

melting typically occurs over a broad range [51] and a single

representative melting point is difficult to establish in a way that

can be consistently reliable under different conditions. Different

polymorphic forms can also crystallize concomitantly to

hamper accurate melting temperature identification. A reason-

able strategy in some circumstances is to apply a global

supercooling approximation [5]. The global melting tempera-

ture of the complex melt mixture is defined to be the highest

temperature at which solid phases can exist and are about to

disappear. The difference between the crystallization tempera-

ture and this global melting temperature is regarded as the



19/31

driving force of crystallization [28]. If this does not appear to

work satisfactorily then recourse should be made to Eq. (14b).

3.1.2. Nucleation thermodynamics, kinetics and mechanisms

The formation of nuclei is an early stage of solid phase

formation. Theoretical models are well known for nucleation

from a solution [157,158], and from a melt[159,160]. Classicalnucleation theory visualises the event as bimolecular reactions

of growth units. The Gibbs free energy of the system, Ghom,

changes due to the decrease of free energy per unit volume

arising from the enthalpy of fusion, GV, and the increase of

the surface energy due to the surface tension, GS. For

spherical nuclei of isotropic pure substances undergoing

homogeneous nucleation this yields the familiar equation:

DGhom DGVV DGSS 4

3pr3DGV 4pr

2r 19

where V, S and r are the volume, surface and radius of the

cluster respectively; is the surface energy. Ghom increaseswith r until a critical (maximum) value Ghom is reached at a

critical size r, i.e. when dGhom/dr=0. Any clusters larger

than r =2/GV decrease the free energy when they grow

and hence become more stable. Eq. (17) gives forGVH

(T/TmVm), where Vm is the molar volume of the clusters, and

T= TmT is the supercooling. The critical free energy, the

activation energy barrier, of nucleation can thus be written as:

DGhom 16

3

pr3V2mT2m

DHmDT2

20

Thermodynamic considerations yield the energy barrier for

nucleation and the critical nucleus size, but not the nucleationrate (the number of nuclei formed per unit volume per unit

time). It is normally postulated that for a particular value of

(=Ghom) a cluster size distribution arises which follows

the Boltzmann distribution and thus the density of the critical

size clusters (Chom) can be expressed as Chom =Noexp

(Ghom/kT), where No is the number of molecules per

unit volume, and k is the Boltzmann constant [6,153]. As

only clusters greater than the critical size are able to grow

into a stable crystal, the frequency of nuclei formation (Jhom)

turns out to be proportional to Chom, as well as the maximum

molecular frequency of collision, given by kT/h where h is

Planck's constant:

Jhom NAkT

hexp

DGhom

kT

21

and where NA is the Avogadro number.

Note, however, that there are other barriers to nucleation as

molecules must diffuse to the nucleus site and adopt the

appropriate configuration to the surface of the growing nuclei.

These barriers lead to additional diffusive and entropy terms

[159]. The diffusive term reflects the fact that as the

temperature is lowered the diffusion rate falls caused by an

increase in the viscosity of the melt or solution. The entropy

term can be significant for long and flexible TAG molecules.

The loss of entropy due to the incorporation of molecules into

a nucleus is given by Sm =Hm/Tm. The probability of the

fraction, S, of molecules in the melt with suitable conformation

to incorporate to the surface of nuclei is exp(SS/R).

However, one often assumes this conformation barrier is

included in the expression for the diffusion barrier (Gdiff ),

hence Eq. (21) becomes:

Jhom NkT

hexp

DGdiff

kT

exp

DGhom

kT

22

In real solutions, nucleation is substantially accelerated due

to the presence of impurities which act as catalytic nucleation

sites [6,148,153]. In fat processes these can be the vessel wall,

impellers, mono- or diglycerides and other minor lipids, as well

as dust particles.

TAGs thus almost always undergo heterogeneous nucleation

since they are normally impure [5]. The activation energy is

lower than that of homogeneous type (a result of the catalyticaction of foreign substances). Consequently, the supercooling

required is also reduced. The activation energy for hetero-

geneous nucleation can be related to that for homogeneous

nucleation as Ghet =Ghomf(), with represents the wetting

characteristics of foreign solid impurities by the supercooled

melts [6]; thus a similar expression to Eq. (22) applies.

Another nucleation mechanism is secondary nucleation

which is caused from (1) fragments of growing crystals

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OKK Unsal Thermodynamic and Kinetic Aspects of Fat Crystallization