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Factors affecting the texture of plastic fats

Lipids form plastic crystal net-works, which demonstrate ayield value and viscoelastic

behavior. This network is essential inproviding the macroscopic sensoryattributes of food products such asmargarine, butter, spreads, chocolate,and peanut butter, It is fairly obviousthat predicting the rheological charac-teristics of fat crystal networks fromprocessing, compositional, and struc-tural perspectives is of immenseimportance to the food industry.Therefore, it is not surprising that thisarea has been the focus of intense aca-demic endeavor over the past 50years.

Methods to determine triglycerideand fatty acid composition as well as10 determine stereospecific structuralfeatures are well established. Theclassification of lipid crystals via X-ray diffraction (XRD) has been estab-lished since the ea.rly 19605, andother methods such as differentialscanning calorimetry (OSC) andFourier transform infrared spec-troscopy (Ff-fR) are also now avail-able for this purpose. Furthermore,with the advent of relatively newsynchrotron radiation facilities, thekinetics of rapid crystallizationevents can be monitored in terms ofchanges in crystalline nature (seeAllen Blaurock's article in the March1993 issue of INFORM). In addition,the quantification of solidlliquidratios in fat crystal networks is rou-tinely performed with pulsed nuclearmagnetic resonance (NMR). Howev-er, until now there has been no con-clusive theory to relate triglyceridecomposition, crystal orientation,crystal sizes. crystal shape,microstructural characteristics, andsolid fat content to the rheologicalindicators of the fat network. It haslong been the authors' contentionthat such a comprehensive model wasnot forthcoming because of the lackof quantification and consideration ofthe microstructural level of structurein fat crystal networks. Much of theprevious work concentrated on therelationship of lipid composition,pclyrncrphism/polytypisrn. and solid

This article is by SIlTf!shS. Narine and Alejandro G. MarOJlgon; of 1MDepartment of Food Science at the University of G~Jph. G~lph. Ontario.NIG 2WI. Conada.

fat content to the macroscopic prop-erties of the network.

In 1996 a student, DerickRousseau, working in our laboratorynoticed that the polymorphic natureand the solid fat content of interesteri-fied and noninteresterifiedmllkfar-cenola oil blends were essen-tially the same, while the rheologicalproperties were very different. Thisprovided motivation to search for anew "structural indicator" of themechanical strength of fat crystal net-works. Help was available in the guiseof an excellent publication by Vreekeret al. from Unilever. Essentially, thispublication presented an interpretationof rheological data for aggregated fatnetworks in the framework of fractaltheories. They showed thai the elasticmodulus (G') varied with particle con-centration of solid fat (Ill) according toa power law, which was similar tomodels proposed for colloidal gels.The treatment of Vreeker et al. wasapplied to aggregated systems with alow solid fat content (low Ill), andequations developed for colloidal sys-tems similar to low IP fat systemswere utilized to procure a fractaldimension from the rheological analy-sis.

At this point, it is important to pro-vide a brief introduction to the fractalconcept to aid those readers who areunfamiliar with the area. The follow-ing is not intended to be a comprehen-sive review, but simply to provide anintroduction that is adequate forunderstanding the concepts dealt within this article.

Fractal geometry was proposed byBenoit Mandelbrot as a way of quanti-fying natural objects with a complexgeometrical structure that defied quan-tification by regular Euclidean geo-metrical methods. In classicalEuclidean geometry, objects haveinteger dimensions: the reader wouldbe familiar with the reasoning that a

line is a one-dimensional object, aplane a two-dimensional object, and avolume a three-dimensional object. lnthis way, Euclidean geometry is suitedfor quantifying objects that are ideal,man-made, or regular.

One may imagine that if enoughkinks are placed in a line or a plane,the result is to have an object that maybe classified as being an intermediatebetween a line and a plane or a planeand a cube. The dimension of such anobject is fractional (i.e., between Iand 2 or between 2 and 3) and theobject may be classified as a fractalobject, from the fact that instead ofhaving an Euclidean dimension (inte-ger) it has a fractional dimension.

One of the most important featuresof fractal objects is that they are self-similar; i.e .. there is a repetition ofpatterns in the object at many differentscales. For natural objects such astrees, clouds, coastlines, etc.,Euclidean geometry fails to providean adequate quantification, but manyof these natural objects are self-simi-lar at different scales. For example, atree has branches, these branches havesmaller branches and so on, and if onechanges the scale of observation of thetree, the same pattern is observed, atleast in a statistical sense if not in adeterministic sense. Therefore, fractalgeometry provides a good measure ofsuch objects with nonintegral dimen-sions.

For a disordered distribution ofmass, such as in a clustering of starsin the Milky Way or the clustering ofparticles in a colloid, fractal geometryis also useful. A short example mightbe useful. For a solid two-dimensionaldisk, the relationship of mass to theradius of the disk is given by:

M(r) ocr' [IJ

such that in this case, the dimension isan integer and the object is an

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relate the elastic constant of the net-work, G', to <1>:

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Euclidean object. However, for a dis-ordered distribution of mass, if at dif-ferent scales of observation the pat-terns are statistically self-similar. thenthe relationship of mass to radius maybe given by:

M(r) ocrD [2]

where D is a fractional or fractaldimension.

It was unclear what the fractaldimension measured by vreeker etat. was an indicator of in terms of

the physical structure of the fat net-work. However, this analysis provid-ed the impetus for a rheologicalinvestigation of nonintcresterifiedand intere sterified milkfat byMarangoni and Rousseau in 1996.Since this analysis was performed onhigh particle concentrations of solidfat (high Cb) systems, an equationproposed for colloidal systems (seethe references contained in the arti-cle by Narine and Marangoni cited inthe bibliography at end of this paper)similar to high 4> fats was used to

FIgure1. Images of microstructures

IG' = r<f>d-D [3]

where d is the Euclidean dimension ofthe system (usually 3), D is the fractaldimension of the system, and r is aconstant independent of the panicleconcentration of solid fat (4)) butdependent on the interactions of theparticles in the network as well as thesize of the particles. In brief. the anal-ysis consisted of measuring the elasticconstant. G'. of samples of a particularfat system at various values of particleconcentration of solid fat, 4> (achievedby diluting the fat with appropriateamounts of canola oil). Then a plot of10g(G) vs. log($) yields as its slopel/(d-D). AI this point it was stillunclear as to what D was a measureof, as well as what structures in a fatcrystal constituted particles. There-fore, imagine the surprise whenMarangoni and Rousseau found thaiD was the only "indicator" thatchanged with associated changes inG' due to interestenficarion, whensuch traditional physical indicators aspolymorphism/polytypism and solidfat content failed to demonstrate theexpected changes. It was obvious atthis point that the as-yet-undefinedfractal dimension, D. was an impor-tant fundamental indicator of the net-work that also could be used toexplain changes in G' nOI attributableto other measurable properties of thenetwork. In a gargantuan effort.Rousseau and Marangoni analyzedsome nine different fat systems duringRousseau's doctoral and postdoctoralwork and in all cases found Equation3 to be valid. This made a resoundingcase for the definition of the fractaldimension in tenns of structure of thenetwork and urged the creation of amechanical model to relate the elasticconstant, G', to the particle concentra-tion of solid fat. 4>, via the fractaldimension, D. and other structuralcharacteristics of the network.

The work presented below is asummary of the doctoral work of oneof the authors. Suresh Narine, underthe supervision of the other author,Alejandro Marangcnl. The informa-

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567

MACROSCOPICPROP£RTU:S

l'oIlCROSTRUCll.IRE -,•POLnIOIU'H1S.W PROC1:SSING

POLY'J'YP1S.\f CONDITIONS

/LlJ>lDCOMPOSmON

size of one microstructure. Themicrostructures themselves pack in aregular. homogenous, space-fillingmanner to provide the largest struc-tural building block of the fat crystalnetwork. Interspersed between themicrostructures and microstructuralelements is the liquid phase (oil) ofthe network. Figures ta and b showmicrostructures of cocoa butter andmilkfar: the fats were diluted in canolaoil (50% w/w) 10 facilitate the imag-ing of the microstructures via a polar-ized light microscope (PLM). Figures1c and Id show microstructural ele-ments of cocoa butter and milkfat,taken with a PLM in situ, Figure Ieshows an atomic force microscope(AFM) image of a microstructure ofthe high-melting fraction of milkfat(HM F) and Figure I f shows amicrostructural element of HMF takenwith an AFM.

The structural arrangement of fatcrystal networks led us to believe thatthe macroscopic properties of the net-work must depend in a significantmanner on the nature of themicrostructures, since these form thelevel of structure closest to the macro-scopic world. Figure 2 shows aschematic depicting our view of theinfluence of the various levels ofstructure on the macroscopic rheologi-cal properties of the network.

In a recent Physical Review E pub-lication, the authors outlined thedevelopment of a scaling theory torelate the elastic modulus, C', to thefractal arrangement within themicrostructures and the particle con-centration of solid fat. ¢I, of the net-work. This theory was based upon theassumption that when the network isstressed, the links between themicrostructures are more likely to bestressed than the microstructures andstructures within them. This is in factreminiscent of the adage "a chain isonly as strong as its weakestlink"-here the weakest pans are thelinks between the microstructures.

Figure 2. Factor. inlluencing the macro.copic properties 01 a lat cry.tal network.

lion presented describes a quantitativemodel, which correctly agrees withexperimental observations. that relatesnetwork characteristics and particleconcentration of solid fat to themacroscopic elastic modulus of fatcrystal networks. Furthermore, thisstructural and mechanical model of fatcrystal networks has implications forthe relationship of processing condi-lions, triglyceride composition, andpolymorphism to the shear elasticmodulus of the network. We also pre-sent recent advances in quantifyingthe microstructural level of structurein fat crystal networks Ilia rheologicaland microscopic fractal analysis. Aswill become obvious. this model wasnot possible without taking into con-sideration the fractal nature of themicrostructurallevel of fat crystal net-works.

Any attempt to model the mechani-cal properties of a network in terms ofits structure must essentially have asits starting point the definition of the

structural levels that exist within thenetwork. The hierarchical organiza-tion of structural levels in fat crystalnetworks is best elucidated through anexamination of the structural levelsthat are defined as the network isformed when the fat crystallizes fromthe melt. In describing the growth of asolid-fat crystal network, we are alsodefining nomenclature of the struc-tural hierarchy, some of which is theauthors' own coinage. Growth of thesolid network begins with initialnucleation sites, which grow into larg-er crystals as triglyceride moleculescrystallize (there may be furthernucleation during growth). Theselarger crystals grow into microstruc-tural elements (collection of crystals)of approximately the same size(-4-8 ",m), which then aggregate intolarger microstructures (-80-120 '"Ill).The microstructural elements arearranged in a fractal manner in thelength range bounded by the size ofone microstructural element and the

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INFORM. \obi. 10. no. 6 (June 1999)

568

FOOD TECHNOLOGY

Force •

microstructural element

L

ForceI

K = force constant between twomicrostructures

Figure 3. Ideallt-ad fat cryat'l network under shear, ~ is the diameter of onemicrostructure. L I, the 81zeof the nmpte under shear.

This theory is simply and appropriate-ly called the weak-link theory (see ref-erences in the paper by Narine andMarangoni, 1999). Figure 3 shows aschematic of a fat network under shearwhen the weak-link theory is applica-ble.

Now that we had utilized scalingtheory and a structural hierarchy toexplain the rheological behaviorobserved by Rousseau, it was impor-tant 10 infuse the fractal dimension ofthe network with some fundamentalstructural meaning. Toward this goal,the authors imaged the ;/1 situ fat crys-tal network using a PLM at themicrostructural element level (exam-pIes are shown in Figures Ib and Ic).The images of fat networks that wereacquired from our PLM were not suit-able for analysis by the traditionalmethods of fractal dimension calcula-tion. Therefore. a new method to cal-culate fractal dimensions was created.Utilizing the theory of mass fractals(see references contained in the paperby Nerine and Marangoni. 1999), andthe following equation:

[4]

where N is the number of microstruc-tural elements present in a cube ofside Rand c is a proportionality con-

Table 1Fractal dimension calculated via image analysis compared to fractal dimensioncalculated via rheology using the weak-link theory. Errors in D are standarderrors of 3 repllcatas. (NE = noninteresterlfled)

Fractal dimension Fractal dimensionrrom image from rhwlogy Percent

Fat system analysis (weak-regime) deviationCocoa buller 2.31::t1.7% 2.37::t4.0% 2.5NIE milkfat(Analyzed using DMA) 2.01::t1.2% 2.01±15.7% 1.5Palm oil 2.8hO.6% 2.82tO.6% 0.0Lard 2.86±0.6% 2.88:t<1.5% 1.0Tallow 2.4~1.2% 2.41~.4% 0.4

stant. R is bounded by the diameter ofone microstructural element «(1) andthe diameter of one microstructure (;).In brief, the method to calculate thefractal dimension of the fat crystalnetwork (described in detail by Narineand Marangoni, 1999) involves count-ing the number of microstructural ele-ments, N. in a cube of length R forvarious values of R, not exceeding thesize of one microstructure. Then,10g(N} vs. 10g(R) is plotted, yieldinglog(e) as the intercept and 0 as theslope. We were pleasantly surprisedby the results-there was excellentagreement between rbeologically cal-

culated values of fractal dimensionusing the weak-link theory and fractaldimensions calculated microscopical-ly. Table I shows a set of five differentsystems with fractal dimensions calcu-lated by both rheological and micro-scopic methods. Figure 4a shows anexample of a plot of 10g(G') vs .10g(cJ» and Fig. 4b shows a plot oflog(N} vs. log(R), demonstrating therheological and microscopic methods,respectively. Even more interestingwas the finding that the same fat sys-tern at different solid fat contents hadidentical fractal dimensions. Thisseemed to indicate that the fractaldimension was indeed a fundamentalconstant of the solid network, akin toa bonding parameter or lattice con-stant.

Visual observation of the five dif-ferent fat systems shown in Table Imakes it obvious that fat systems withhigh fractal dimensions demonstrate ahigher order of packing than thosewith lower fractal dimensions (seeNarine and Marangoni, 1999. forexamples). Therefore, it began toemerge that the fractal dimension ofthe network was a measure of the dis-tribution of the solid portion of thenetwork, with higher fractal dimen-sions leading to a more ordered distri-bution. It becomes obvious, therefore,that the elastic properties of the net-work are more dependent on the modeof distribution of the solid portion ofthe network than the amount of solidin the network. This realization leadsto the question: can fractal dimensionsof fat systems be altered in order to

INFORM, Vol. 10, no. 6 (June 1999)

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transfer-limited pro-cess also will influ-ence the fractaldimension. If thenucleation sites serveas templates for thegrowth of micro-structural elements,there seems to bemore order, whereasif the growth of thenet work is notrestricted to thenucleation centers,the structure be-comes more amor-phous.The various frac-

tions within a partic-ular fat network andthe temperatures atwhich and the size ofthe temperaturerange over whichthey crystallize willtherefore fundamen-tally affect the fractaldimension. Byincreasing the rate ofcooling through anucleation event ofthe purticular fatbeing crystallizedfrom the melt, onc

can render the peaks of any particularfraction sharper, thereby introducingmore order and raising the [racialdimension. The converse is also true.Therefore, one can alter fractal dimen-sions of fat crystal networks by alter-ing the processing conditions underwhich the fat is crystallized. How thistranslates to the elastic properties ofthe network is depicted in Figure 5,which shows the shear elastic modu-lus, C', normalized by the pre-expo-nential constant y. plotted against thefractal dimension of 13 different fatsystems whose fractal dimensionswere determined rheologically. Thesolid line represents the theoreticalexpectation of the behavior of the nor-malized modulus. From Figure 5, anincrease in fractal dimension implies adecrease in the elastic modulus of thesystem. Therefore, by altering the pre-cessing conditions for the crystalliza-tion of a particular fat system, the rhe-ological properties of the network

may be altered, using the fractaldimension as an indicator.

The fact that the authors havedeveloped a method to calculate frac-tal dimensions easily from PLMimages of the fat systems provides thefood engineer with an easily deter-mined indicator of changes In

mechanical strength of the networkduring processing. Additionally. thefractal dimension so calculated alsomay serve as a quality control methodfor consistent mechanical strength of aparticular fat network. The authors arein the process of trouble-shooting acomputer program developed to calcu-late fractal dimensions of fat crystalnetworks-it is the intention to makethis software commercially availablein the near future.

Although the value of the fractaldimension of the fat network as anindicator of the mechanical strength ofthe network cannot be denied, it mustbe understood that the value of thepre-exponential term y is also equallyimportant. The next challenge wastherefore to define y in tenus of net-work characteristics. Inspiration camein the form of another publicationoriginating from Unilever, this timeby van den Tempel. This publicationsuggested modeling the network as acollection of particles held together byvan der Waals-London forces. Thework by van den Tempel failed to pre-dict correctly the experimentallyobserved power law relationship of G'to <l> because it did not take into con-sideration the structural hierarchy ofthe network described earlier and thefractal arrangement of the microstruc-tural elements.

As described in a recent publica-tion submitted to Physical Review Eby the authors, we constructed amechanical and structural model of fatcrystal networks whose elastic modu-lus is measured at low deformations.In this model, the microstructural ele-ments were assumed to be spherical,and the forces between themicrostructures were attributed to theforces of interactions between neigh-boring microstructural elements at theinterface between two microsuuc-tures.

These forces were formulated byfirst solving the integral describing the

<a) 3.5,------------,

-s-!!; 3.0

e~ 2.5

D=2.31? =0.99

2.0+-~-~~~-~~-_...j3.50 '.503.75 '.00

Log ¢I (%)

'.25

.,------------,

2+--~--_r--._-~1.5() 1.75 2.00 2.25 2.5()

log Ill)Figure 4. (a) Jog (G) as a function of tog('P) for a sample ofcocoa butter, (b) log(N) as a function of log(R) for mllkfat. G' isthe elastic constant of the network, measured theologically, 'lIIs the particle concentrallon of saUd fat, measured usingnuclear magnetic resonance, N is the number of mIcrostruc-tural elements In a cube of sIde R, and MPa refers 10 the unitsmega Pascals.

(b)

D""2.02? =099

alter the elastic properties? Theanswer lay in the relationship of thecrystallization behavior of the fat sys-tems (as measured by DSC) to thefractal dimension.

Fat systems with a sharp nucleationstep, i.e .• those systems that undergomost of their nucleation in a narrowtemperature mnge as the sample crys-tallizes from the melt, have higherfractal dimensions (evident from anexamination of the crystallizationcurves of the five systems in Table 1,shown in Narine and Marangoni,1999). Samples with instantaneousnucleation characteristics will havenucleation sites that are more ordereddue to heat transfer considerations.This is true because the heat releasedfrom the nucleation events wouldhave to be dissipated throughout thenetwork, and the most effective wayof heat transfer would be an orderedarray of sites. The subsequent growthof the network via a mass- and heat-

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570

FOOD TECHNOLOGY

o.•"c;c------------------------,

c.o-t-.__ -_-_-_-_-_-_-_-_-?-...-j1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3,0

Fractal Dimension, DFigure 5. G'tyee 8 function of O. Symbols with error bars represent average values ofrheological measurement. and their standard errors.

.. "mllidat OMA.3

... = mUlde! OMA,4t:J. = CIEmilkfall2X "cocoa butter '1

Lennard-Jones potential energybetween two microstructural elementsconsidered spherical, and then differ-entiating the resulting expression withrespect 10 the intermicrostructural ele-ment distance. In a nontrivial treat-ment difficult to reproduce in the lim-ited space available. the fractal natureof the network was also taken intoconsideration. Other assumptionsinclude considering as negligible thehydrodynamic forces when the net-work is stressed as well as inertialforces. The final expression for theshear elastic modulus provided by themodel is:

where til is the number of neighboringmicrostructural elements at an inter-face between two microstructures, A is

• '" cocoa butter DMA t2o '"NIE mllkfat 12• "EIE mllkfat.1V '" NIE palm oil

o ,. CIE lard() "NtE tard• '" Salatrim

the development of pbenomenologl-cal investigations of relationshipsbetween triglyceride compositionand polymorphism and values of theconstant A and sizes of rnicrcstruc-rural elements as well as the effectsof processing conditions on thesenetwork characteristics. From thediscussion above. values of do. a.and D can be manipulated bychanges in processing conditions. Bydefining the network characteristicsresponsible for the mechanicalstrength of the network, the modelprovides an array of indicators.which can be monitored duringdevelopmental stages of tailored fatcrystal networks, as well as keyparameters to be monitored as indi-cators of quality control. Work in ourlaboratory is continuing in definingthe relationships between trtgtyc-eride composition and polymorphismto parameters outlined by the model.

[6]

BibliographyD. Chapman, The polymorphism of

glycerides, Chem, Rev. 62:433-456 (1962).

A.G. Marangoni and D. Rousseau, Isplastic fat rheology governed bythe fractal nature of the fat crystalnetwork? J. Am. Oil Chem. Soc.73,991-993 (1996).

5.S. Narine and A.G. Marangoni,Fractal nature of fat crystal net-works, Phys. Rev. E.59,1908-1920 (1999).

W.H. Shih, W.Y. Shih, 5.1. Kim. J.Lin. and I.A. Aksay, Scalingbehavior of the elastic propertiesof colloidal gels. Phys. Rev. A42:4772-4779 (1990).

M. van den Tempel, Mechanical prop-erties of plastic-disperse systemsat very small deformations, J.Colloid Interface Sci. /6:284-296(1961).

R. Vreeker. L. L. Hoekstra, D.C. denBoer. and W.O.M. Agteroff, Thefractal nature of fat crystal net-works, Col/oids Surf. 65:185-189(1992). •

a constant depending on the polariz-abilities of the atoms present, c is theconstant of proportionality in Equa-tion 4, a is the diameter of amicrostructural element, ~ is the diam-eter of one microstructure, and do isthe average equilibrium distancebetween microstructural elements.From a consideration of Equation 5and Equation 3, j-is given by:

INFORM. Val. 10. no. 6 (June 1999)

This model therefore identifies keynetwork parameters important indetermining the value of y. Further-more. the model agrees well withexperimental observations and withEquation 3, which has been shown tobe valid for fat crystal networks. Thefinal equation provides impetus for