The cooling rate effect on the microstructure and rheological properties of blends of cocoa butter with vegetable oils

Food Research International 40 (2007) 47–62 www.elsevier.com/locate/foodres

The cooling rate effect on the microstructure and rheological properties of blends of cocoa butter with vegetable oils David Pe´rez-Martı´nez b, C. Alvarez-Salas b, M. Charo´-Alonso a, E. Dibildox-Alvarado a, J.F. Toro-Vazquez a,* a

b

Facultad de Ciencias Quı´micas-CIEP, Universidad Auto´noma de San Luis Potosı´, Av. Dr. Manuel Nava 6, Zona Universitaria, San Luis Potosı´ 78210, Mexico Facultad de Quı´mica-DIPA (PROPAC), Universidad Auto´noma de Quere´taro, Circuito Universitario S/N, Quere´taro, Mexico Received 16 March 2006; accepted 30 July 2006

Abstract The elasticity (G 0 ) and yield stress (r*) of blends of cocoa butter (CB) in vegetable oils (i.e., 30% CB/canola and 30% CB/soybean oil) crystallized at temperatures (TCr) between 9.5 C and 13.5 C and two cooling rates (1 C/min and 5 C/min) were determined, evaluating their relationship with parameters associated with the formation and structural organization of the crystal network [i.e., solid fat content (SFC), Avrami index, crystallization rate, fractal dimension (D)]. The results showed that TCr and cooling rate had a different effect for each blend on the three-dimensional organization of the crystal network, and on the proportion and size of b 0 and b crystals. Thus, under low supercooling conditions at both cooling rates, the crystallized CB/canola oil blend was formed by a mixture of small b 0 and large b crystals that provided high G 0 and r* at low SFC (i.e., 20.5–20.9%) and D (i.e., 1.66–1.72) values. The CB/soybean oil blend achieved similar G 0 and r* independent of cooling rate only at high supercooling. In this case, the crystal network was formed mainly by small b 0 crystals with SFC (i.e., 25.4–26.3%) and D (i.e., 2.86–2.79) values higher (P < 0.05) than in the CB/canola oil blend at low supercooling.  2006 Elsevier Ltd. All rights reserved. Keywords: Cooling rate; Cocoa Butter; Rheometry; Fractals; Microstructure

1. Introduction Vegetable oils and vegetable oil blends are multicomponent systems containing different families of triacylglycerides (TAGS). In these systems the molecular relationships occurring among TAGS families determine the thermodynamic conditions (i.e., supercooling and supersaturation) that drive the formation of a solid in a liquid phase and the phase behavior of the solid phase. The resulting threedimensional TAGS crystal network and the phase behavior of TAGS are major factors determining the physical and functional properties (i.e., rheology, liquid phase entrapment, mouthfeel, appearance, and spreadability) in prod-

*

Corresponding author. Tel.: +52 444 8262450; fax: +52 444 8342548. E-mail address: [email protected] (J.F. Toro-Vazquez).

0963-9969/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodres.2006.07.016

ucts such as margarine, butter, confectionary coatings, and fillings (Campos, Narine, & Marangoni, 2002; Pe´rezMartı´nez et al., 2005; Takeuchi, Ueno, Flo¨eter, & Sato, 2002). Additionally, crystallization conditions such as cooling rate, and thermal history (i.e., crystallization temperature and tempering process) have significative effects on the kinetics and physical properties of the crystallized systems. Cocoa butter (CB) is also a mixture of different TAGS. Nevertheless, CB observes a great extent of homogeneity in both TAGS conformation and composition with more than 75% of TAGS with oleic acid in the sn-2 position and saturated fatty acids in the sn-1 and sn-3 positions. Consequently, its polymorphism is complex observing at least six polymorphic forms (van Malssen, van Langevelde, Peschar, & Schenk, 1999; Wille & Lutton, 1966). CB is used as the main lipid phase in chocolate, and

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in confectionary products blended with hydrogenated soybean oil, palm oil fractions, palm kernel, and coconut oil. Crystallization of CB provides to these products unique characteristics of texture and flavor release. Nevertheless, these vegetable oils have trans fatty acids and/ or high proportion of saturated fatty acids, both with recognized negative health implications because their impact on the ratio of high density to low density lipoproteins. Limited research has been done to study the crystallization process of CB in blends with native unsaturated vegetable oils. Several authors have investigated the effect of cooling rate on crystallization of multicomponent TAGS systems (Campos et al., 2002; deMan, 1964; Herrera & Hartel, 2000a, 2000b, 2000c). In the present investigation we studied the cooling rate effect on the rheology and microstructure in binary model systems, where different extent of molecular compatibility existed between the major TAGS of the crystallizing phase (i.e., CB) and major TAGS of the solvent phase (i.e., canola or soybean oil). Major TAGS in soybean oil have a higher degree of unsaturation (i.e., LLL, LLO and LLP) than the major TAGS present in canola oil (i.e., OOO and LOO). This ought to result in different extent of molecular compatibility between TAGS of vegetable oils and the symmetrical saturated–unsaturated–saturated (SUS) TAGS and saturated TAGS from CB. Blending between vegetable oils provides flexibility to achieve particular functional properties in crystallized systems. However, the complex interactions that occur among TAGS as a function of the crystallization conditions must be first understood to achieve particular physical and functional properties through blending. Within this framework our objective was to study the relationships between the rheological properties of CB crystallized in blends with canola or soybean oil at two cooling rates (1 C/min and 5 C/min) with parameters associated with the development and structural organization of the crystal network such as the Avrami index, the crystallization rate constant, the fractal dimension, and the solid fat content. 2. Materials and methods 2.1. Preparation of cocoa butter/vegetable oil blends The 30% (wt/vol) blend of CB in canola or soybean oil was prepared with CB previously vacuum filtered through Whatman paper No. 5. The CB was melted (80 C for 20 min) and the corresponding proportion weighted in a 100 mL volumetric flask. The volume was completed with the vegetable oil (25 C) and the blend stored (4 C) under nitrogen in the dark. For some dynamic calorimetric analysis blends of CB in the vegetable oil were prepared at ratios between 0% and 100% CB (% wt/vol). The TAGS profiles for CB and the vegetable oils were determined by HPLC as reported by Pe´rez-Martı´nez et al. (2005).

2.2. Calorimetry analysis Dynamic calorimetric analyses were done in a Perkin Elmer DSC-7 (Norwalk, CT, USA) equipment calibrated as previously indicated (Toro-Vazquez, Dibildox-Alvarado, Charo´-Alonso, Herrera-Coronado, & Go´mez-Aldapa, 2002). Briefly, 0.12 mg samples of the blends (i.e., 0–100% CB/vegetable oil) were sealed in aluminum pans held at 80 C for 20 min and then cooled down (10 C/min) from 80 C to 50 C. After 1 min at 50 C the melting thermogram was obtained at a heating rate of 5.0 C/min. For differential scanning calorimetry (DSC) analysis under isothermal conditions the blends of 30% CB in the vegetable oils were first held for 20 min at 80 C. The sample pans were then cooled at 1 C/min or 5 C/min until attaining a particular crystallization temperature (TCr). After completion of the crystallization exotherm (i.e., heat capacity returned to the baseline) the system was left for additional 30 min and then the melting thermogram was determined by heating (5 C/min). Two independent determinations were done at each TCr and cooling rate. The corresponding TCr’s used in the isothermal crystallization studies were 9.5 C, 10.5 C, 11.5 C, and 13.0 C for the 30% CB/canola oil and 10 C, 11 C, 12 C, and 13.5 C for the 30% CB/soybean oil. The TCr’s investigated were between the onset of crystallization in the corresponding dynamic crystallization thermogram and 3.5 C above this temperature. The use of isothermal TCr’s above this temperature interval produced a significative increase in the induction time of crystallization and broadened the exotherm making difficult to determine the beginning and end of crystallization. 2.3. Solid fat content and determination of the Avrami index and crystallization rate constant Samples (4 mL) of the blends were heated (80 C for 20 min) in NMR tubes (10 mm · 20 cm) and then cooled in a programable temperature bath (Julabo Labortechnik GMBH, Selbach, Germany) set to provide linear cooling rates of 1 C/min (±0.1 C/min) (Model F25) or 5 C/ min (Model F25 connected to a Presto system). The SFC (%) of the CB blends was determined as a function of time at a particular TCr and cooling rate by pulsed NMR with a Minispec Bruker model mq20 equipped with a jacketed measuring probe connected to a circulating water bath set to the corresponding TCr. The SFC readings as a function of isothermal crystallization time (SFCt) were recorded by the equipment software until 30 min after achieving a sustained plateau in the measurements. These values were considered the maximum or equilibrium SFC (SFCeq). Using as crystallization model the Avrami equation (1), the SFC values were used to calculate the fractional crystallization, F, as a function of isothermal crystallization time, t, as F = SFCt/SFCeq. The Avrami index (n) and the crystallization rate constant (z) were

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determined by fitting Eq. (1) through the nonlinear estimation procedure available in STATISTICA (v. 7.0, StatSoft, Inc. Tulsa, OK, USA). In all cases at least two independent determinations were done at each TCr and cooling rate. 1  F ¼ expðztn Þ

ð1Þ

2.4. Rheometry and fractal analysis The elasticity (G 0 ) and the yield stress (r*) of the crystallized blends were determined with a mechanical spectrometer equipped with a 50 mm diameter parallel plates geometry (Paar Physica UDS 200, Stuttgart, Germany). Temperature was controlled by a Peltier system located in the base of the measurement geometry. The melted blend (80 C) was applied on the base of the plate avoiding bubble formation and the superior plate was positioned on the sample surface using the auto-gap function of the rheometer software (1 mm). After erasing the crystallization memory (80 C for 20 min) the system was cooled at 1 C/min or 5 C/min until achieving the corresponding TCr. The G 0 and the r* for each blend at the different TCr’s and cooling rates were determined by applying a strain sweep (0.025% up to 5%) to the crystallized systems after times equivalent to the ones used for the SFCeq measurements. G0eq was determined from the log–log plots of G 0 , G00 vs. strain (%) within the linear viscoelastic region (LVR). The r* was determined from the log–log plot of shear stress vs. strain (%) at the corresponding upper limit of strain within the LVR. The determination of the mass fractal dimension (D) and the pre-exponential term [Log(c)] was based on the weak-link regime for colloidal dispersions following the technique described by Pe´rez-Martı´nez et al. (2005). D is a measurement of the fractional dimension that describes the structure whose geometrical and topographical features are repeated at different levels of magnification in the crystal network structure. D has fractional values between 1 and 3, and the higher its value the denser the crystal network structure. On the other hand c is a constant independent of the volume fraction of solid fat that forms the crystal network structure but dependent on the size of the primary particles (i.e., crystals) and on the interactions between them (i.e., polymorphic nature of the fat) (Narine & Marangoni, 1999). Duplicate determinations of D and Log(c) were done at each TCr and cooling rate. 2.5. Microstructure Polarized light microscopy (PLM) was used to examine the microstructure of the crystallized blends using a polarized light microscope (Olympus BX51; Olympus Optical Co., Ltd., Tokyo, Japan) equipped with a color video camera (KP-D50; Hitachi Digital, Tokyo, Japan) and a platina (TP94; Linkam Scientific Instruments, Ltd., Surrey, England) connected to a temperature control station (LTS 350; Linkam Scientific Instruments, Ltd.) and a liquid

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nitrogen tank. To guarantee a uniform sample thickness, two cover slips were glued on a glass microscope slide leaving 2.2 cm between them. The sample (80 C) was placed within the gap of the preheated (80 C) glass slide and a glass cover slip was placed over the sample such that is rested on the glued cover slips. This provided a uniform sample thickness of 0.16 mm. After 30 min at 80 C the system was cooled at 1 C/min or 5 C/min until attaining the TCr. Once TCr was attained microphotographs and video of the blends were obtained as a function of crystallization time. A 10· lens was used in all cases. 2.6. Statistical analysis The levels of TCr and cooling rate evaluated were set up in a full factorial experiment design, and the resulting treatments distributed in a completely randomized experiment design with two replicates. The effect of TCr and cooling rate on the parameter measured (i.e., SFCeq, n, z, G0eq and r*) was established for each CB/vegetable oil blend by analysis of variance and multiple contrasts among the least squared means using the corresponding procedure in STATISTICA (v. 7.0, StatSoft, Inc. Tulsa, OK). 3. Results and discussion TAGS composition for CB, canola oil, soybean oil are shown in Table 1. The corresponding crystallization and melting thermograms and for different proportions of CB in the vegetable oils are shown in Figs. 1 and 2, respectively. The melting thermograms (Fig. 2) were obtained after dynamic crystallization (Fig. 1) of the systems according to the conditions described in the materials and methods section. The arrows in the melting thermograms show major differences in the behavior between the CB/ canola oil blends (Fig. 2(A)) and the CB/soybean oil blends (Fig. 2(B)). Thus, the characteristic melting profile of soybean oil that started at 50 C and ended at 0 C was present in the thermograms at all CB/soybean oil proportions. This was particularly evident with the sharp endotherm indicated by the arrow in Fig. 2(B). In contrast, the melting profile of pure canola oil (i.e., starting at 36 C and ending at 7 C; Fig. 2(A)) was modified by the presence of CB. These results pointed out differences in the molecular interactions between the major TAGS present in canola and soybean oil with TAGS of CB. According to Pe´rez-Martı´nez et al. (2005), the higher degree of unsaturation in TAGS from soybean oil in contrast with TAGS from canola oil, limits the molecular interaction with the TAGS from CB. Thus, in the liquid phase major TAGS of soybean oil (e.g., 21.4% of LLL, 21.2% of LLO, and 14.5% LLP, Table 1) had limited molecular compatibility with the symmetrical SUS type and the saturated TAGS present in CB. As a result melting of soybean oil was independent of CB melting at all CB/ soybean oil proportions (Fig. 2(B)). In the same way, the melting temperature of CB in the blends decreased as a

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Table 1 Triacylglycerides concentration (TAGS) in the vegetable oils used in the study TAGSa

Cocoa butterb

Canolab

Soybeanb

LLnL LLL LLnP LLPo LLO LLnEo LLP LOO LLSt PLO POL PLP OOO StLO POO PLSt PPO POP StOO StLSt POSt PPSt StOSt PStSt StOA StStSt Unidentified

n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. 0.16 ± 0.03 n.d. 0.55 ± 0.38 0.48 ± 0.59 0.26 ± 0.21 1.86 ± 0.05 1.99 ± 0.02 n.d. 14.80 ± 0.04 3.76 ± 0.31 1.20 ± 0.05 43.81± 0.64 0.32 ± 0.04 29.33 ± 0.05 0.21± 0.08 1.00 ± 0.03 0.20 ± 0.02 n.d.

n.d. 0.78 ± 0.10 n.d. 4.48 ± 0.68 7.35 ± 0.47 8.90 ± 0.44 n.d. 26.14 ± 0.01 n.d. n.d. 3.34 ± 0.12 n.d. 39.41 ± 1.38 n.d. 4.28 ± 0.18 n.d. 0.97 ± 0.20 n.d. 1.86 ± 0.10 n.d. n.d. n.d. n.d. n.d. n.d. n.d. 2.46 ± 0.60

3.18 ± 0.17 21.39 ± 0.45 1.16 ± 0.16 n.d. 21.18 ± 0.87 n.d. 14.49 ± 0.64 9.88 ± 0.12 3.84 ± 0.23 10.42 ± 0.03 n.d. 1.70 ± 0.39 3.67 ± 0.03 2.93 ± 0.04 2.72 ± 0.26 1.36 ± 0.35 n.d. 0.39 ± 0.18 0.84 ± 0.43 0.32 ± 0.19 0.50 ± 0.02 n.d. n.d. n.d. n.d. n.d. n.d.

n.d.: Not detected. a P, palmitic; Po, palmitoleic; St, stearic; O, oleic; L, linoleic; Ln, linolenic; A, arachidic; Eo, gadoleic. b % w/w, mean and standard deviation of two independent determinations (n = 2).

function of the soybean oil proportion in the blends (Fig. 2(B)), i.e., solubility effect. On the other hand, major TAGS of canola oil (e.g., 39.4% of OOO, and 26.1% of LOO, Table 1) seemed to have a higher extent of molecular compatibility with TAGS of CB (Pe´rez-Martı´nez et al., 2005). This resulted in a modification of both, the melting profile of canola oil and CB (Fig. 2(A)). In particular, the melting profile of CB in the CB/canola oil blends showed the presence of an endotherm that became larger as CB concentration increased from 15% up to 45%, and then decreased as CB concentration increased from 60% up to 100% (see the arrow in Fig. 2(A)). At the 30% and 45% CB/canola oil concentrations an exotherm preceded this endotherm pointing out the presence of a polymorphic transformation. This endotherm might be associated with the development of the b polymorph via an a ! b 0 ! b polymorphic transition since, as shown through DSC and X-ray analysis by Marangoni and McGauley (2002), TAGS from CB do not nucleate directly from the melt into the b phase. However, the direct b 0 ! b polymorphic transition cannot be excluded from this process. b 0 polymorphs of symmetrical TAGS, like the ones present in CB, are less prone to b 0 ! b polymorphic transition when b 0 crystallizes directly from the melt that when occurring via the

a ! b 0 ! b process (Gibon, Durant, & Deroanne, 1986). Nevertheless, the molecular interactions between TAGS of CB and canola oil ought to decrease the interfacial viscosity of the crystallizing phase in the 30% and 45% CB/canola oil blends with respect to the one present in pure CB melt. This might resulted in an increased molecular mobility in the crystallizing phase of 30% and 45% CB/canola oil blends, promoting both the b 0 ! b and the a ! b 0 ! b transitions from the ones occurring in pure CB melt. Similar results for the b 0 ! b polymorphic transformation has been reported in blends of anhydrous milk fat and canola by (Wright, Batte, & Marangoni, 2005). The overall result was a larger b polymorph production during the heating process of 30% and 45% CB/canola oil blends in comparison with the one achieved in pure CB melt. This as evaluated by the magnitude of the corresponding endotherm (see the arrow in Fig. 2(A)). However, as CB became the major phase in the CB/canola blends (i.e., 60–100% CB) the increase in interfacial viscosity of the crystallizing phase limited the molecular mobility. This limited the occurrence of the b 0 ! b transition, making the formation of the b polymorph in the 60-85% CB/canola oil blends and in CB just dependent of an slow a ! b 0 ! b transition (van Malssen et al., 1999). The endotherm associated with the b polymorph was also present in the CB/soybean oil blends at all proportions but its magnitude was just comparable to the one present in CB (Fig. 2(A)). The limited molecular interactions between TAGS of soybean oil and TAGS of CB might result in no effect on the molecular mobility at the crystallizing interface. Therefore, in the CB/soybean oil blends the production of b polymorph during the heating process was just associated with the slow a ! b 0 ! b transition. Regarding the behavior of the CB/vegetable oil blends during dynamic crystallization we did not find any significant difference between the crystallization profiles of CB/ canola oil (Fig. 1(A)) and CB/soybean oil blends (Fig. 1(B)). As can be observed in the crystallization thermograms in both types of blends, the onset (TO) and the peak temperature (TP) of the crystallization exotherm decreased linearly as CB concentration in the blends decreased from 100% down to the 30%. Then, between 30% and 100% of CB in the blends no mixed crystals were developed between TAGS of CB and TAGS of canola or soybean oil. However, below the 30% CB concentration there was a drastic decrease in the onset and the peak temperature of the crystallization exotherm (Fig. 1). It seemed that below 30% CB concentration some TAGS from canola or soybean oil and TAGS from CB produced mixed crystals resulting in crystals with lower crystallization temperatures. Norton, Lee-Tuffnell, Ablett, and Bociek (1985) and Toro-Vazquez and Gallegos-Infante (1996) have reported similar behavior in different TAGS systems, and Pe´rezMartı´nez et al. (2005) in similar CB blends. From now on just the results of the 30% CB/canola and 30% CB/soybean oil blends will be discussed. This blend corresponded to the lowest concentration of CB in

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Fig. 1. Crystallization thermograms for pure CB, canola oil (A), soybean oil (B) and blends at different proportion of CB to vegetable oil (% wt/vol). TO and TP represent the onset and the peak temperature of the crystallization exotherm.

the vegetable oils that still provided crystallization and melting properties mainly associated to TAGS from CB. Characteristic thermograms for isothermal crystallization of 30% CB/soybean oil blends at different TCr’s at cooling rates of 1 C/min and 5 C/min are shown in Fig. 3. The corresponding melting thermograms are shown in Fig. 4. Similar crystallization behavior was observed for the 30% CB/canola oil blend (data not show). The crystallization and melting thermograms of the CB/vegetable oil blends

at both cooling rates showed the same behavior as the one observed by pure CB (Toro-Vazquez, Pe´rez-Martı´nez, Dibildox-Alvarado, Charo´-Alonso, & Reyes-Herna´ndez, 2004). This confirmed our previous observation that in the 30% CB/vegetable oil blends TAGS from CB were the only ones crystallizing. Nevertheless, giving the lower concentration of CB in the blends lower TCr’s were needed to achieve TAGS crystallization in the CB/vegetable oil blends (i.e., TCr’s between 9.5 C and 13.5 C) in

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Fig. 2. Melting thermograms for pure CB, canola oil (A), soybean oil (B) and blends at different proportion of CB to vegetable oil (% wt/vol). The arrows indicate differences in the thermal behavior between the CB/soybean oil and the CB/canola oil blends.

comparison to the ones required with pure CB (i.e. TCr’s between 18 C and 22 C; Toro-Vazquez et al., 2004). Thus, as with pure CB we assigned the first exotherm to the a polymorph and the second exotherm to the b 0 polymorph (Fig. 3 for CB/soybean oil; for CB/canola oil data not shown). The corresponding melting thermograms of the CB/vegetable oil blends showed the presence of two endotherms that as with pure CB melting were assigned, the first one to b 0 melting and the second one to b poly-

morph melting (Fig. 4 for 30% CB/soybean; for 30% CB/ canola data not shown). The b polymorph was developed in the CB/soybean oil blend probably just through the a ! b 0 ! b polymorphic transition, and in the CB/canola oil blend also via the b 0 ! b polymorphic transition as discussed previously. Here we observed no difference between the melting behavior of the CB/soybean oil blend and the CB/canola oil blend like after dynamic crystallization (Fig. 2). During isothermal crystallization and further

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Fig. 3. Isothermal crystallization thermograms for the 30% CB/soybean oil blend at different crystallization temperatures using a cooling rate of 1 C/min (A) and 5 C/min (B).

melting there was enough time to develop similar levels of b 0 and b polymorphs in both types of blends. However, during dynamic crystallization and posterior melting the constant change in temperature allowed the development of the b polymorph just under conditions of higher molecular mobility (i.e., 30% CB/canola oil). Although the assignment of particular polymorphs to specific crystallization exotherms and melting endotherm is in line with the discussion and the thermal behavior of pure CB (Toro-

Vazquez et al., 2004) and the CB/vegetable oil blends, no X-ray analysis was done to confirm this. On the other hand, the SFCeq, the parameters that describe the crystallization kinetics (i.e., n and z), and the three-dimensional organization of the crystal network [i.e., D and Log(c)] at the cooling rates investigated are shown for both blends in Tables 2 and 3. For both CB/vegetable oil blends investigated there was no significative difference (P < 0.05) between the SFCeq obtained at 1 C/min

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Fig. 4. Melting thermograms for the 30% CB/soybean oil blend previously crystallized at different crystallization temperatures using a cooling rate of 1 C/min (A) and 5 C/min (B).

and 5 C/min (Tables 2 and 3). Thus, independent of cooling rate the SFCeq’s for the 30% CB/soybean oil blend were 25.85%, 24.85%, 23.38%, and 21.95% with a standard error of 0.45% for the TCr’s of 10 C, 11 C, 12 C, and 13.5 C, respectively. For the 30% CB/canola oil blend the corresponding SFCeq’s independent of cooling rate for the TCr’s of 9.5 C, 10.5 C, 11.5 C, and 13 C were, respectively, 24.29%, 23.48%, 22.50%, and 20.66% with a standard

error of 0.26%. In general, although higher TCr’s were used with the CB/soybean oil blend higher SFCeq’s values were obtained in this system than with the CB/canola oil blend (P < 0.05). This agrees with previous results that showed that under similar TCr’s higher supercooling conditions exist in the CB/soybean oil blend than in the CB/canola oil blend (Pe´rez-Martı´nez et al., 2005). On the other hand, our results contrast with the ones reported

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Table 2 Solid fat content at equilibrium (SFCeq), Avrami index (n), crystallization rate constant (z), fractal measurement (D), and pre-exponential term of the fractal measurement [Log(c)] for the 30% CB/soybean oil blend as a function of crystallization temperatures (TCr) achieved at the cooling rates of 1 C/min and 5 C/min TCr

SFCeq (%)

z · 107 (minn)

n

D

Log(c) (Pa)

a

1 C/min 10.0 11.0 12.0 13.5

26.3 25.2 24.2 22.1

(1.0)b (0.9)b (0.9)b (0.4)b

102.1 (12.4)b 19.41 (1.07)b 31.20 (4.39)b 0.024 (0.001)b

3.34 3.25 3.42 4.16

(0.26)b,d (0.20)b,d (0.81)b,e (0.25)b,e

2.79 2.77 2.78 2.76

(0.02)b (0.02)b (0.01)b (0.01)b

0.231 0.012 0.552 1.139

(0.470)b (0.202)b (0.078)b (0.001)b

5 C/mina 10.0 11.0 12.0 13.5

25.4 24.5 22.6 21.8

(1.1)b (1.4)b (0.8)b (1.2)b

645.9 (75.4)c 8.91 (2.84)c 0.01 (0.00)c 0.01 (0.00)b

3.07 3.66 4.33 4.02

(0.45)b,d (0.11)b,d (0.01)b,e (0.07)b,e

2.86 2.82 2.80 2.78

(0.01)c (0.00)c (0.01)b (0.01)b

0.785 0.305 0.271 0.563

(0.289)c (0.346)b (0.152)b (0.332)c

a

For all measurements we show the mean and standard deviation of at least two independent determinations. Within each column and same TCr values with the same letter are statistically the same at the two cooling rates. A different letter indicates statistical difference (P < 0.05). d Instantaneous nucleation as shown by the video recordings. e Sporadic nucleation as shown by the video recordings. b,c

Table 3 Solid fat content at equilibrium (SFCeq), Avrami index (n), crystallization rate constant (z), fractal measurement (D), and pre-exponential term of the fractal measurement [Log(c)] for the 30% CB/canola oil blend as a function of crystallization temperatures (TCr) achieved at the cooling rates of 1 C/min and 5 C/min TCr

SFCeq (%)

z · 107 (minn)

n

D

Log(c) (Pa)

a

1 C/min 9.5 10.5 11.5 13.0

24.1 23.5 22.4 20.5

(0.2)b (0.0)b (0.0)b (0.0)b

5 C/mina 9.5 10.5 11.5 13.0

24.5 23.5 22.6 20.9

(0.6)b (0.9)b (0.5)b (1.2)b

352.7 (15.5)b 4.76 (0.273)b 1.42 (0.195)b 0.030 (0.002)b

5375.8 (17.4)c 1.67 (0.22)c 0.01 (0.001)c 0.01 (0.007)b

2.82 3.44 3.59 3.60

(0.39)b,d (0.11)b,d (0.44)b,e (0.04)b,e

2.84 2.80 2.45 1.66

(0.00)b (0.05)b (0.04)b (0.37)b

0.990 0.297 4.016 5.514

(0.080)b (0.663)b (0.001)b (0.232)b

2.44 4.23 4.40 3.50

(0.05)b,d (0.32)c,d (0.10)c,e (0.13)b,e

2.85 2.83 2.62 1.72

(0.02)b (0.01)b (0.04)b (0.24)b

1.278 1.109 3.244 5.283

(0.01)b (0.408)c (0.331)c (0.154)b

a

For all measurements we show the mean and standard deviation of at least two independent determinations. Within each column and same TCr values with the same letter are statistically the same at the two cooling rates. A different letter indicates statistical difference (P < 0.05). d Instantaneous nucleation as shown by the video recordings. e Sporadic nucleation as shown by the video recordings. b,c

by Campos et al. (2002) and Herrera and Hartel (2000a) that observed higher SFC at the higher cooling rate in lard and milk fat systems. However, Campos et al. (2002) cooled lard and anhydrous milk fat using, for the slow cooling rate, a stepwise procedure with an average cooling rate of 0.1 C/min, and for fast cooling a Newtonian temperature decrease. In contrast, Herrera and Hartel (2000a) investigated the effect of slow (0.2 C/min) and fast (5.3–5.5 C/min) cooling rates in blends of milk fat fractions at different stirring (50–300 rpm) and TCr’s conditions, determining the SFC before achieving equilibrium (i.e., SFC at 20 and 80 min of crystallization). In the present investigation we compared the SFC at equilibrium achieved at different TCr’s under static conditions using two different linear cooling rates (1 C/min and 5 C/min).

Regarding the behavior of n we did not observe a significant effect of cooling rate (P < 0.05) in the CB/soybean oil system at any of the TCr’s investigated (Table 2). With the CB/canola oil blend higher n values were obtained just at the TCr’s of 10.5 C and 11.5 C when the higher cooling rate was used. However, after the visual analysis of the video recordings of the crystallization process it was established that instantaneous nucleation occurred at the lower TCr’s used in each blend (i.e., 11.0 C for the CB/soybean oil blend and 10.5 C for the CB/canola oil blend; Tables 2 and 3, respectively). Above these TCr’s sporadic nucleation occurred (Tables 2 and 3). With this observation and considering that n is function of the time dependence of nucleation (i.e., sporadic or instantaneous) and the dimensionality of the crystal growth process (Sharples, 1966), the n values showed that, independent of the TCr

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Fig. 5. Polarized light microphotographs for the 30% CB/soybean oil blend crystallized using a cooling rate of 1 C/min (A, C, E) and 5 C/min (B, D, F) at 10 C [after 140 min(A) or 120 min (B)], 12 C [after 220 min (C) or 240 min (D)], and 13.5 C [after 420 min (E and F)]. The minutes indicate the crystallization time under isothermal conditions.

used, TAGS of CB followed a spherulitic crystal growth mechanism in both blends. The fractional values of n (Tables 2 and 3) might indicate the simultaneous development of at least two types of crystals, as observed in the microphotographs of some crystallized blends (see Figs. 5(C)–(F) and 6(C)–(F)). Regarding the behavior of z, the overall crystallization process, including nucleation and crystal growth, occurred at the fastest rate at the lower TCr, particularly at the cooling rate of 5 C/min and with the CB/canola oil blend (Tables 2 and 3). However, as TCr increased and cooling rate decreased higher values of z were obtained with the CB/soybean oil blend (Table 2). Then, although higher TCr’s were used in the CB/soybean oil blend as TCr

increased the crystallization process (i.e., nucleation and crystal growth) occurred at a faster rate in the 30% CB/soybean blend (Table 2) than in the 30% CB/canola oil blend, particularly at the lower cooling rate (Table 3). As with SFCeq, these results show the existence of higher supercooling conditions in the CB/soybean oil blend than in the CB/ canola oil blend as pointed out by Pe´rez-Martı´nez et al. (2005). On the other hand, for the same CB/vegetable oil blend and at both cooling rates the parameters associated with the organization of the crystal network, D and Log(c), followed the same trend as a function of TCr (Tables 2 and 3). Thus, D in the CB/soybean oil blend at both cooling rates investigated observed a linear tendency to decrease as TCr

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Fig. 6. Polarized light microphotographs for the 30% CB/canola oil blend crystallized using a cooling rate of 1 C/min (A, C, E) and 5 C/min (B, D, F) at 9.5 C [after 90 min(A) or 120 min (B)], 11.5 C [after 190 min (C) or 240 min (D)], and 13 C [after 450 min (E) or 680 min (F)]. The minutes indicate the crystallization time under isothermal conditions.

increased (P < 0.10). In this blend, as TCr decreased higher D values were obtained at 5 C/min than at 1 C/min (P < 0.05) (Table 2). In contrast, in the CB/canola oil blend (Table 3) D decreased quadratically as TCr increased (P < 0.05) and cooling rate did not affect the magnitude of D (P < 0.05). Regarding Log(c) in the CB/soybean oil blend, this parameter showed a linear increase as a direct function of TCr (P < 0.05) at both cooling rates. In the CB/canola oil blend at 5 C/min, Log(c) increased quadratically as TCr increased (P < 0.05), while at 1 C/min followed a linear increase as a direct function of TCr (P < 0.05). These results showed that, although similar TCr’s were used, their effect on the three-dimensional organization of the crystal network was different in each blend.

In the same way, cooling rate had a differential effect on D and Log(c) in each CB/vegetable oil blend. Figs. 5 and 6 show PLM microphotographs of crystallized CB/soybean oil and CB/canola oil blends corresponding to crystallization times where SFCeq was achieved at 1 C/min and 5 C/min. The behavior profile of G0eq and r* for the CB/vegetable oil blends investigated as a function of SFCeq and cooling rate are shown in Figs. 7 and 8. These figures show the corresponding mean SFCeq value for both cooling rates, since for each CB/vegetable oil blend there was not statistical difference between the SFCeq obtained at 1 C/min and 5 C/min. Positive linear relationships between Log(G 0 ) and Log(SFC) have been observed in blends of high and low melting fractions from

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Fig. 7. Rheograms for the storage modulus ðG0eq Þ for the 30% CB/canola oil (A) and 30% CB/soybean oil blends (B) as a function of SFCeq and cooling rates investigated. The solid and dotted lines are the least squared fitting for data for 1 C/min and 5 C/min, respectively.

milk fat (Herrera & Hartel, 2000b), and between Log(Hardness) and Log(SFC) in anhydrous milk fat and lard (Campos et al., 2002). However, in the present investigation positive linear relationships between LogðG0eq Þ and Log(SFCeq) were found just with the 30% CB/soybean oil blend (Fig. 7(B)) at both 1 C/min (r = 0.8244, P < 0.02) and 5 C/min (r = 0.6624, P < 0.08). PLM microphotographs associated with these relationships in increasing order of SFCeq are shown in Fig. 5(E), (C), and (A) for

1 C/min, and for 5 C/min in Fig. 5(F), (D), and (B). Evidently, at both cooling rates as TCr decreased (i.e., SFCeq increased) the overall crystal size decreased. However, at some TCr’s (i.e., 12 C and 13.5 C) crystals with two different sizes were present (e.g., Fig. 5(E) and (C) at 1 C/min; Fig. 5(F) and (D) at 5 C/min). In a previous investigation with similar CB/vegetable oil blends crystallized at a cooling rate of 1 C/min, the small crystals were associated with the b 0 polymorph and large crystals with the b polymorph

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Fig. 8. Rheograms for the yield stress (r*) for the 30% CB/canola oil (A) and 30% CB/soybean oil blends (B) as a function of SFCeq and cooling rates investigated. The solid and dotted lines are the least squared fitting for data for 1 C/min and 5 C/min, respectively.

(Pe´rez-Martı´nez et al., 2005). This assignation was confirmed analysing the video recordings obtained by PLM observing the order of appearance of the crystals during isothermal crystallization (e.g., the small b 0 crystals appeared first) and their apparent melting temperature during subsequent melting (e.g., the large b crystals melt at higher temperature). Then, using the same kind of assignation to the crystals present in the 30% CB/soybean oil blend, it was evident that b 0 crystals became smaller and

were the predominant polymorph as TCr decreased (Fig. 5). In contrast, as TCr increased (i.e., SFCeq decreased) b 0 crystals increased in size and the development of large b crystals became more evident (Fig. 5). On the other hand, from PLM microphotographs it was clear that for the same TCr different proportions of b 0 to b crystals were present at each cooling rate. This as determined by the qualitative visual evaluation of the corresponding PLM microphotographs. Thus, at the higher TCr used in

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the CB/soybean oil blend (i.e., 13.5 C), where the smaller SFCeq was obtained and the larger difference in G0eq between the cooling rates was observed (Fig. 5(B)), a mixture of small b 0 and large b crystals were present at both cooling rates (Fig. 5(E) and (F)). However, a higher proportion of b 0 crystals of smaller size were obtained at 1 C/min (Fig. 5(E)) than at 5 C/min (Fig. 5(F)). At intermedia TCr’s (i.e., 11 C and 12 C) a greater proportion of b 0 crystals of larger size and higher extent of agglomeration were observed in the PLM microphotographs obtained at 5 C/min (Fig. 5(D)) than at 1 C/min (Fig. 5(C)). Decreasing TCr at both cooling rates produced a decrease in b 0 crystal size and the large b crystals became less evident until, at the lowest TCr (i.e., 10 C) just aggregates of very small b 0 crystals were present (Fig. 5(A) and (B)). Additionally, the fractal dimension (D) of the 30% CB/ soybean oil blend showed a positive linear relationships with the LogðG0eq Þ at both 1 C/min [r = 0.94, P < 0.001; LogðG0eq Þ ¼ 34:46 þ 17:56ðDÞ] and 5 C/min [r = 0.72, P < 0.05; LogðG0eq Þ ¼ 7:77 þ 2:36ðDÞ] with a tendency to achieve higher D values with corresponding higher LogðG0eq Þ at 5 C/min than at 1 C/min. These results showed that with the CB/soybean oil blend the denser the crystal network organization (i.e., the greater the D value) the higher the elastic properties of the crystallized blend. In general, with the CB/soybean oil blend sharper crystallization exotherms, particularly at TCr’s of 10 C, 11 C and 12 C, were obtained at 5 C/min (Fig. 3(B)) than at 1 C/min (Fig. 3(A)). This, as pointed out by Narine and Marangoni (1999), indicates a higher level of order in the nucleation template. As a result greater D values were developed at 5 C/min than at 1 C/min, leading to higher elastic properties (i.e., G0eq ) in the crystallized systems. Then, although the crystallization kinetics of the CB/soybean oil blend was affected by cooling rate (i.e., z values in Table 2), the solid phase developed (i.e., SFCeq) at the TCr’s investigated were the same (P < 0.05). Nevertheless, the nucleation template established by TCr and the cooling rate determined both, the proportion of b 0 to b polymorphs and the size of the crystals developed (i.e., Fig. 5(C) vs. (D) for TCr of 12 C and Fig. 5(E) vs. (F) for TCr of 13.5 C at 1 C/min and 5 C/min). This, in turn, determined the microstructural organization of the crystal network (i.e., D) and therefore the elastic properties (i.e., G0eq ) of the crystallized system. In the case of r* there was not a marked effect of cooling rate as with G0eq (Fig. 7(B)). The Log(r*) behavior in the CB/soybean oil as a function of Log(SFCeq) (Fig. 8(B)) showed a curvilinear behavior with the lower r* value at SFCeq corresponding, for 1 C/min to TCr’s of 11 C and 12 C, and for 5 C/ min to a TCr of 12 C. The greatest r* values were obtained, for both cooling rates, at the TCr where the highest SFCeq was achieved and just aggregates of small b 0 crystals were present (TCr = 10 C, Fig. 5(A) and (B) for 1 C/ min and 5 C/min, respectively). Minimum r* values were associated with the TCr above which large b crystals were developed (i.e., TCr of 13.5 C, Fig. 5(E) and (F) for

1 C/min and 5 C/min, respectively) with a subsequent increase in r*. Then, the polymorphic transitions occurring in the CB/soybean oil blend as a function of TCr were associated with modifications in the spatial distribution of the crystal network. This as evaluated by PLM (Fig. 6) and D, and by the changes associated with G0eq and r*. However, in contrast with LogðG0eq ) we did not find a particular relationship that described the behavior of r* (i.e., the resistance to flow) as a function of D or Log(c). In this blend, the crystallizing conditions that developed the crystal network with the highest elasticity also provided the greatest yield stress. Such crystallizing conditions were independent of cooling rate, at the highest supercooling investigated (i.e., TCr of 10 C). Regarding the G0eq and r* behavior in the 30% CB/ canola oil blend both values decreased as SFCeq increased (Figs. 7(A) and 8(A)). This behavior was observed independent of the cooling rate investigated. The corresponding PLM microphotographs in increasing order of SFCeq are shown in Fig. 6(E), (C), and (A) for 1 C/min, and for 5 C/min in Fig. 6(F), (D), and (B). This behavior is quite peculiar since as SFCeq decreased and more loosely packed crystal networks were developed (i.e., lower D values), the crystallized blends have higher G0eq and r* values than the ones with more dense crystal network structures (i.e., greater D and SFCeq values; Table 3). These results were observed at both cooling rates. However, as with the CB/ soybean oil blend, higher G0eq values were obtained at 5 C/min than at 1 C/min (P < 0.025; Fig. 7(A)). This, except at the TCr of 9.5 C where the highest SFCeq was obtained and the main polymorph present was small b 0 crystals (Fig. 6(A) and (B) for 1 C/min and 5 C/min, respectively). At this TCr, G0eq values were statistically the same at both cooling rates (P = 0.34; Fig. 7(A)). In the same way, as with the CB/soybean oil blend, cooling rate had no effect on r* at any of the TCr’s investigated (Fig. 8(A)). However, in contrast with the CB/soybean oil blend, the exotherms from the isothermal crystallization of CB/canola oil had the same sharpness at all TCr’s and cooling rates investigated (data not shown), i.e.,the same level of order in the nucleation template was obtained at both cooling rates. As a result, at the same TCr similar D values were obtained at 1 C/min than at 5 C/min (Table 3). Since D is associated with the crystal network structure and therefore with the mechanical properties of the crystallized system (Narine & Marangoni, 1999), at the same TCr and independent of cooling rate similar G0eq values were expected for the CB/canola oil blend. Nevertheless, as pointed out previously, with the exception of TCr of 9.5 C, higher G0eq values were obtained at 5 C/min than at 1 C/min (Fig. 7(A)). From the PLM microphotographs it was observed that as TCr increased (i.e., SFCeq decreased) a mixture of small b 0 crystal and large b crystals became more evident at both cooling rates (Fig. 6). Additionally, b crystals grew larger as TCr increased with this effect more pronounced at 5 C/min (Fig. 6(D) and (F)) than at 1 C/min (Fig. 6(C) and (E)). It seems that the pres-

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ence of mixtures of b 0 and b crystals were the responsible for the increase in G0eq and r* as SFCeq decreased. This behavior has been explained previously as follows (Pe´rezMartı´nez et al., 2005). As TCr increased and SFCeq decreased, b crystals became larger with the small b 0 crystals filling the spaces among the large b crystals, acting as binder particles and increasing the surface area for van der Waals’ forces among large b crystals. This process might, eventually, results in a sintering phenomenon among nearby b 0 and b crystals. Both two events would provide structural properties (i.e., elasticity and yield stress) to crystal networks with low SFCeq and D values (Fig. 6(E) and (F); Table 3). In contrast with the CB/soybean oil blend, the crystallizing conditions that developed the crystal network with the highest elasticity and yield stress were conditions of low supercooling (i.e., TCr of 13 C), independent of cooling rate used. At this point, it is important to point out differences in the crystallization process followed by the CB/vegetable oil blends that affected the microstructural organization of the crystal network and therefore the rheological properties of the crystallized system. Thus, although similar TCr’s were used in both types of blends, b crystals grew larger in the CB/canola oil blend (Fig. 6(E) and (F)) than in the CB/soybean oil blend (Fig. 5(E) and (F)). Additionally, at the TCr’s where crystallization produced a mixture of b 0 and b crystals in both blends, the relative proportion of small b 0 to large b crystals was greater in the CB/soybean oil blend (Fig. 5(C)–(F)) than in the CB/canola oil blend (Fig. 6(C)–(F)). This effect seemed to be more pronounced at 1 C/min (Fig. 5(C) and (E) vs. Fig. 6(C) and (E), respectively) than at 5 C/min (Fig. 5(D) and (F) vs. Fig. 6(D) and (F), respectively). Under these conditions and independent of the vegetable oil present in the blend, higher G0eq values were obtained at 5 C/min than at 1 C/min (Fig. 7(A) and (B)). However, the larger G0eq values were not always achieved by crystallized blends formed by mixtures of small b 0 crystals and large b crystals (i.e., 13.5 C and 12 C in CB/soybean oil, Fig. 5(C)–(F); and 10.5 C and 11.5 C in CB/canola oil blend, Fig. 6(C) and (D)), mainly when a cooling rate of 1 C/min was used for crystallization. It seems that the occurrence of the cooperative structural effect that provided high G0eq and r* even with low SFCeq and D values, requires of the appropriate proportion of b 0 and b crystals and the right b 0 to b crystal size ratio. In the present investigation these conditions were achieved with the CB/canola oil blend at a TCr of 13 C. At this temperature the cooling rate of 5 C/min [D = 1.66 (±0.37); SFCeq = 20.5% (±0.0)] developed a crystal network of higher elastic properties than the one developed at 1 C/min [D = 1.72 (±0.24); SFCeq = 20.9% (±1.2)] (Fig. 7(A)). However, both crystal networks had the same yield stress (Fig. 8(A)). Similar elastic and yield stress properties might be achieved with the CB/canola oil blend crystallized at high supercooling where the crystal network was formed mainly by aggregates of small b 0 crystals. However, in this case high SFCeq and D values were

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required to provide the appropriate structural properties to the crystal network. It is important to point out that under high supercooling conditions (i.e., TCr of 10 C for the CB/soybean oil blend and 9.5 C for the CB/canola oil blend), quite similar D values were obtained with both CB/vegetable oil blends (Tables 2 and 3). However, the crystallized CB/soybean oil blend had higher G0eq and r* (Figs. 7(B) and 8(B), respectively) than the crystallized CB/canola oil blend (Figs. 7(A) and 8(A), respectively). This, independently of the cooling rate used. The main difference is that, independent of the cooling rate, higher SFCeq values were achieved with the CB/soybean oil blend (Table 2) than with the CB/canola oil blend (Table 3) (P < 0.05). Then, both types of blends under high supercooling conditions developed a crystal network formed mainly by small b 0 crystals with a rather constant value of D. The higher G0eq and r* values observed in the CB/soybean oil blend in comparison with the ones showed by the crystallized CB/canola oil blend both crystallized at high supercooling conditions, were associated more with its higher SFCeq than with a different fractal organization of the crystal network. The three-dimensional crystal network organization and the polymorphic state of the TAGS crystals as affected by the crystallization conditions are major factors determining physical (i.e., rheology) and functional (i.e., texture) properties of crystallized TAGS systems (Herrera & Hartel, 2000a, 2000b, 2000c; Narine & Marangoni, 1999; ToroVazquez et al., 2002). The results obtained in the present research are in line with this concept. However, in industrial crystallizers (i.e., scraped surface crystallizers) additional factors, such as sinusoidal temperature fluctuations during crystallization, secondary nucleation and crystal attrition promoted by shearing, establish a different thermodynamic scenario under which crystallization takes place. Then, the actual processing conditions where particular G0eq and r* values are achieved with CB/vegetable oil blends must be different from the ones established under static conditions. In the same way the crystal network organization associated with these G0eq and r* values must be different from the ones obtained under static crystallization. Current research in this direction is now underway crystallizing the same CB/vegetable oil blends with a scraped surface crystallizer and evaluating different input and output temperature settings and shearing rates. References Campos, R., Narine, S. S., & Marangoni, A. G. (2002). Effect of cooling rate on the structure and mechanical properties of milk fat and lard. Food Research International, 35, 971–981. deMan, J. M. (1964). Effect of cooling procedure on consistency, crystal structure and solid fat content of milk fat. Dairy Industries, 29, 244–246. Gibon, V., Durant, F., & Deroanne, C. L. (1986). Polymorphism and intersolubility of some palmitic, stearic, and oleic triglycerides: PPP, PSP, POP. Journal of the American Oil Chemists Society, 63, 1047–1055.

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Takeuchi, M., Ueno, S., Flo¨eter, E., & Sato, K. (2002). Binary phase behavior of 1,3-distearoyl-2-oleoyl-sn-glycerol (SOS) and 1,3-distearoyl-2-linoleoyl-sn-glycerol (SLS). Journal of the American Oil Chemists Society, 79, 627–632. Toro-Vazquez, J. F., Dibildox-Alvarado, E., Charo´-Alonso, M. A., Herrera-Coronado, V., & Go´mez-Aldapa, C. A. (2002). The Avrami index and the fractal dimension in vegetable oil crystallization. Journal of the American Oil Chemists Society, 79, 855–866. Toro-Vazquez, J. F., & Gallegos-Infante, A. (1996). Visocosity and its relationship to crystallization in a binary system of saturated triacylglycerides and sesame seed oil. Journal of the American Oil Chemists Society, 73, 1237–1246. Toro-Vazquez, J. F., Pe´rez-Martı´nez, D., Dibildox-Alvarado, E., Charo´Alonso, M., & Reyes-Herna´ndez, J. (2004). Rheometry and polymorphism of cocoa butter during crystallization under static and stirring conditions. Journal of the American Oil Chemists Society, 81, 195–203. van Malssen, K., van Langevelde, A., Peschar, R., & Schenk, H. (1999). Phase behavior and extended phase scheme of static cocoa butter investigated with real-time X-ray powder diffraction. Journal of the American Oil Chemists Society, 76, 669–676. Wille, R. L., & Lutton, E. S. (1966). Polymorphism of cocoa butter. Journal of the American Oil Chemists Society, 43, 491–496. Wright, A. J., Batte, H. D., & Marangoni, A. G. (2005). Effects of canola oil dilution on anhydrous milk fat crystallization and fractional behavior. Journal of Dairy Science Association, 88, 1955–1965.