Relationship between Crystallization Behavior and Structure in

CRYSTAL GROWTH & DESIGN

Relationship between Crystallization Behavior and Structure in Cocoa Butter

2003 VOL. 3, NO. 1 95-108

Alejandro G. Marangoni* and Sara E. McGauley Department of Food Science, University of Guelph, Guelph, Ontario N1G2W1, Canada Received September 9, 2002;

Revised Manuscript Received November 5, 2002

ABSTRACT: Cocoa butter was crystallized statically from the melt to various temperatures in the range of -20 to 26 °C and annealed for up to 45 days. During this period, the polymorphism of the solid state was monitored using differential scanning calorimetry and powder X-ray diffraction. Moreover, the microstructure of the materials was imaged using polarized light microscopy. Below -15 °C, a mixture of the transient metastable γ and R phases was observed. Between -15 and 20 °C, the material nucleated initially into an R form and then gradually transformed into more stable phases. The lifetime of the R phase was at least 7 days at and below 0 °C and decreased gradually above 0 °C to 30 min at 15 and 20 °C. The R phase transformed into the β′ phase, which was stable for 28 days between 0 and 15 °C. Above 15 °C, the lifetime of the β′ phase decreased gradually to 10 h at 24 °C. The β′ form could be formed directly from the melt above 20 °C. Above 15 °C, the β′ phase could transform into the β phase. Interestingly, cocoa butter crystals did not nucleate directly from the melt into the β phase and did not form under any conditions below 20 °C. The β polymorph could only be formed via the β′ form. Microstructural studies indicated that cocoa butter initially nucleated as metastable γ or R phases below 15 °C remained granular in appearance, irrespective of further phase transformations into other more stable forms. The microstructures of the β′ form could thus appear granular, clustered, and needlelike, depending on whether they were formed through the R form or directly from the melt. The microstructure of the β form was complex and varied, from granular to needlelike to featherlike. Crystallization kinetics was quantified from solid fat content-time curves at the different crystallization temperatures using the Avrami model. Changes in the Avrami exponent and the induction time of crystallization were correlated with certain polymorphic transformations, particularly the β′ to β transition. Microstructure was quantified using a box-counting fractal dimension. Changes in microstructure as a function of time at 20, 22, and 26 °C correlated with changes in the fractal dimension. A particularly interesting finding in this work was the fact that the fractal dimension was directly related to the rate of nucleation as well as inversely related to the Avrami exponent. Introduction Triglycerides are known to crystallize in a number of different polymorphic forms depending on processing conditions (heat, mass, and momentum transfer) and chemical composition.1,2 Cocoa butter, the main structuring material in chocolate and confections, displays complex crystallization behavior in that six different polymorphs have been identified. These solid phases have characteristic melting ranges (Table 1) and wide angle X-ray reflections (Table 2). In a few cases, distinct microstructures have been associated with particular polymorphic forms. Essential to the manufacturing of good quality chocolate is the ability to induce the formation and stabilization of certain polymorphic forms in cocoa butter. This in turn will lead to the formation of a fat crystal network with desirable mechanical and thermal properties.3 Modern studies on cocoa butter polymorphism have included real-time powder X-ray diffraction (XRD).4-10 Results from these studies suggest that the metastable γ (orthorhombic subcell) and R (hexagonal subcell) phases, as well as the more stable β′ (orthorhombic subcell) phase, can crystallize directly from the melt, whereas the stable β (triclinic) polymorph can only be obtained via phase transformation from the β′ form. Moreover, the different solid phases display wide melting ranges rather than unique melting points. Of particular importance is the static isothermal phase transition scheme constructed by van Malssen et al.8

Table 1. Melting Ranges of the Different Polymorphic Forms Found in Cocoa Butter (as Reported by van Malssen et al.8) polymorphic form (I-IV) γ (sub-R) R β2 ′ β1′

polymorphic form (V-VI)

M.R. (°C) -5 to +5 17-22 20-27

β2 β1

M.R. (°C) 29-34

Table 2. Characteristic Powder XRD Wide Angle Reflections (Short Spacings) for the Various Polymorphic Forms of Cocoa Butter27 a polymorphic form γ (sub-R) R β2′ β1′ β2 β1

short spacings (Å) 3.87(m), 4.17(s) 4.20(vs) 3.87(vw), 4.20(vs) 3.75(m), 3.88(w), 4.13(s), 4.32(s) 3.65(s), 3.73(s), 3.87(w), 3.98(s), 4.22(w), 4.58(vs), 5.13(w), 5.38(m) 3.67(s), 3.84(m), 4.01(w), 4.21(vw), 4.53(vs), 5.09(vw), 5.37(m)

a The relative intesity is noted as very strong (vs), strong (s), medium (m), weak (w), or very weak (vw).

using real-time powder XRD. This state diagram catalogues the polymorphism of the solid state in cocoa butter at different time-temperature combinations. The study of microstructure in fats has become increasingly important since many macroscopic properties of fats and fat-containing products depend on their fat

10.1021/cg025580l CCC: $25.00 © 2003 American Chemical Society Published on Web 11/23/2002

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Crystal Growth & Design, Vol. 3, No. 1, 2003

Marangoni and McGauley

Figure 1. Charactaristic melting profiles obtained by DSC of the different polymorphic forms of cocoa butter (A), statically crystallized at 0 °C for 3 days (B), 20 °C for 6 days (C), and -20 °C for 2 days (D).

Figure 2. Characteristic XRD patterns of the various polymorphic forms of cocoa butter crystallized at -20 °C for 2 min (A), 5 °C for 2 min (B), 5 °C for 5 days (C), and 22 °C for 28 days (D).

crystal network structure.11-17 Despite its obvious importance, very few studies have been carried out on the microstructure of cocoa butter. The only studies to date include those of Hicklin et al.,18 Manning and Dimick,19 and Narine and Marangoni.20 It is thus the purpose of this study to characterize the microstructure of cocoa butter crystallized at different temperatures up to 45 days. Moreover, we establish relationships between crystallization behavior, in terms of kinetics and polymorphism, and the resulting microstructure of the material.

Materials and Methods Cocoa Butter. The cocoa butter used in this study was commercially available refined cocoa butter from Cacao de Zaan (Koog aan de Zaan, The Netherlands). Free fatty acid content (AOCS Ca 5a-40) was determined to be 1.2% (w/w), and the phosphorus content, determined by atomic absorption after wet digestion in sulfuric acid, was less than 0.006% (w/w). Differential Scanning Calorimetry (DSC). The peak melting temperature of cocoa butter crystallized under different conditions was determined using DSC. Approximately 6-10 mg of melted cocoa butter was introduced into standard

Crystallization Behavior and Structure in Cocoa Butter

Crystal Growth & Design, Vol. 3, No. 1, 2003 97

Figure 3. Time-temperature state diagram for the polymorphism of statically crystallized cocoa butter. Symbol (f) represents the polymorphic forms that have been determined by XRD.

Figure 5. Changes in the Avrami exponent as a function of crystallization temperature. Symbols represent the average ( standard error of the mean of three replicates.

Figure 4. Crystallization curves of cocoa butter crystallized at -20 (9), 10 (1), and 15 °C (2) (A) and 17.5 (9), 20 (1), and 22.5 °C (2) (B). Symbols represent average ( standard error of three replicates. DSC aluminum pans and hermetically sealed and heated for 30 min at 80 °C. Four replicates of each sample were then placed in an incubator at a predetermined crystallization temperature. After the desired crystallization time, the pans were transferred to a Dupont model 2910 DSC (Wilmington, DE). The DSC was set to the same temperature as the pan being introduced, and analyses were performed from the crystallization temperature to 50 °C at a heating rate of 5 °C per minute relative to an empty pan. Empty pans were used for the baseline calibration, indium was used for the cell

Figure 6. Induction times for statically crystallized cocoa butter as a function of crystallization temperature. The polymorphic designation indicates the dominant polymorphic form present at a particular crystallization temperature as determined from melting points and XRD patterns. Symbols represent the average ( standard error of three replicates. constant calibration, and a two point temperature calibration was performed using indium and gallium. The DSC monitored the changes in heat flow of the samples during melting and

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Figure 7. (A) Two step growth curve for cocoa butter crystallized at 17.5 °C. (B) Changes in peak melting temperature as a function of time, indicating the growth of the R and β′ polymorphs and the transition between the two forms. expressed these results as heat flow (W/g) vs temperature (°C). Thermograms were analyzed for temperature maxima. Powder XRD. The polymorphic modifications of cocoa butter were determined by powder XRD. Approximately 50 µL of melted cocoa butter was introduced into thin-walled glass capillary tubes and placed into a prechilled glass vial in an incubator set to the appropriate crystallization temperature. At a predetermined time, the polymorphic form of the crystallized cocoa butter sample was determined using an EnrafNonius Kappa CCD diffractometer (Nonius, Delft, The Netherlands). The samples were mounted horizontally in modeling clay and placed in the X-ray beam at the temperature at which the sample was stored (maintained by circulating liquid nitrogen). The X-ray beam was generated by a molybdenum anode set at 50 kV and 36 mA. The beam stop was all the way out, and the camera distance was set at 165 mm. There was a 1° rotation on φ, and data were collected over 1 iteration for 5 min. The system was calibrated using calcium sulfate, which has strong reflections at 13.6, 4.27, 3.80, and 2.80 Å. Crystallization Kinetics. The crystallization behavior of cocoa butter was followed by measuring the change in solid fat content (SFC) as a function of time. Glass NMR tubes (10 mm diameter) were filled with approximately 3 g of melted cocoa butter and heated for 30 min at 80 °C to destroy any crystal history. The samples were then placed directly in a water bath at a predetermined crystallization temperature. SFC was determined by pulsed NMR with a Bruker PC/20 series NMR Analyzer (Bruker, Milton, ON, Canada). SFC measurements were taken at suitable time intervals at each crystallization temperature. Two determinations on two replicates were performed. The data were fitted to the Avrami model by nonlinear regression:21,22

SFCt ) SFC∞(1 - exp-kt ) n

(1)

SFCt describes the SFC as a function of time, SFC∞ is the limiting SFC as time approaches infinity, k is the Avrami rate constant, and n is the Avrami exponent. The Avrami exponent (n) is sensitive to the mechanism of crystallization. This

parameter is sensitive to both the time dependence of nucleation and the dimensionality of growth.23,24 Induction times of crystallization (τ) were also determined from curves of SFC as a function of time by extrapolating back to the onset time of the linear SFC increase.25,26 Polarized Light Microscopy (PLM). The microstructures of the various polymorphic forms of cocoa butter were observed using PLM. One drop (∼15 µL) of cocoa butter heated for 30 min at 80 °C was placed on a glass microscope slide preheated to 80 °C. A preheated cover slip was then placed on top of the sample. The cover slip was placed parallel to the plane of the slide and centered on the drop of sample to ensure that the sample thickness was uniform. The samples were then placed on prechilled metal pans at the desired crystallization temperature. After a predetermined time, the slides were observed under polarized light using an Olympus BH polarized light microscope (Olympus, Tokyo, Japan) using 10× and 40× objective lenses. Slides were kept at the desired temperature during the imaging using an LTS 350 large heating and freezing stage operated by a TP93 temperature programmer (Linkam Scientific Instruments Ltd., Surrey, England). An electric element was used to heat the stage while liquid nitrogen (BOC gases) was used as the coolant. Images were recorded using a Sony XC-75 CCD video camera (Sony Corporation, Japan) with the gain switch in the auto position. The images were digitized using Scion Image software (Scion Corporation, Fredrick, MD). Image quality was enhanced by taking the average of 16 frames and by applying a background correction, using the Scion Image software. At least three images were captured from each of four slides at the desired time and temperature combination. Image Processing and Fractal Dimension Determination. Images were processed using Adobe Photoshop 5.5 (Adobe Systems Inc., San Jose, CA). Original grayscale images were thresholded using the bilevel auto threshold command. In most cases, the auto threshold provided a good representation of the reflections present in the images. In a few of the images, where two different microstructures were present, a manual threshold was used since the auto threshold was not found to provide an adequate representation of the image. The fractal dimensions of images obtained using the 40× objective lens were determined using the box-counting algorithm of BenoitTM 1.3 (TruSoft Int’l Inc., St. Petersburg, FL).

Results and Discussion Polymorphic Occurrence. The polymorphic forms of cocoa butter were determined from peak melting temperatures obtained by DSC (Figure 1A) and powder XRD (Figure 2) and confirmed using published melting ranges (Table 1). The DSC thermograms of cocoa butter sometimes displayed a split endothermic peak (Figure 1B). The first peak at 19.7 °C is characteristic of the R form while the second peak at 24.4 °C indicates that the more stable β′ form is also present. This split could be due to the presence of both solid phases or due to an artifactual heating-induced transformation of the R to the β′ phase during the DSC run. For some timetemperature combinations, on the other hand, two distinct melting profiles were evident within a sample batch. Figure 1C shows thermograms with peak melting temperatures of 27.3 and 31.8 °C. This behavior was interpreted as a sample batch undergoing polymorphic transformation from the β′ form to the more stable β polymorph at different rates. The metastable γ polymorph has been shown to form directly from the melt at low crystallization temperatures.8 In our DSC experiments, however, the γ phase did not exist in isolation. At low temperatures, a species with a peak melting temperature of 1.6 °C, which is within the reported melting range for the γ polymorph (-5 and 5 °C), was



Figure 8. Images obtained by PLM of the R form of cocoa butter crystallized at -20 °C for 1 day (A), -20 °C for 7 days (B), -15 °C for 7 days (C), and 0 °C for 1 day (D).

observed to exist concurrently with a species with a peak temperature of 20.6 °C, characteristic of the R form (Figure 1D). Moreover, using DSC, the γ form was not observed prior to 2 days of crystallization, whereas melting profiles indicated that the R polymorph was formed after 4 min. The γ polymorph was detected only after 2 days of crystallization at -15 or -20 °C. Because polymorphic transformations are monotropic, it is not possible for the γ form to appear after the more stable R form. We thus speculate that fractionation could have taken place; therefore, some of the lower melting triglycerides could have crystallized directly into the γ form and coexisted with the R phase. DSC did not allow for measurements prior to 3-4 min of crystallization. It is therefore also possible that a polymorphic transformation from the γ to the R form took place before the peak melting temperatures could be determined. On the other hand, an artifactual heating-induced conversion of the γ to the R form during the DSC run could be partially responsible for this effect. Some of the polymorphic forms determined from peak melting temperatures obtained by DSC were confirmed using powder XRD. The short spacings obtained were identified as R, β′, or β by comparison with published work27 (Table 2). As discussed above, using DSC, an isolated γ form was not observed, even at low temperatures. However, powder XRD allowed for the observation of a polymorphic form after 2 min of crystllization. Static crystallization for 2 min at -20 °C yielded an XRD pattern with short spacings at 3.79 and 4.19 Å (Figure 2A) characteristic of the γ polymorphic form. After crystallization for 2 min at 5 °C, a short spacing was observed from the XRD patterns at 4.21 Å (Figure 2B). This value is characteristic of the R form and confirms the polymorphic form determined by DSC. After 5 days of incubation at 5 °C, the β′ form was

determined by DSC and confirmed using XRD with short spacings at 3.81 and 4.18 Å (Figure 2C). Crystallization at 22 °C for 28 days lead to the characteristic β form with the diffraction pattern displaying short spacings at 3.70, 3.94, 4.58, and 5.42 Å (Figure 2D). Cocoa butter crystallized statically at 22 °C for 28 days had a peak melting temperature of 32.7 °C, also indicative of the β polymorph. Only the β2′ form, with short spacings at 3.87 and 4.20 Å, was observed. Using the peak melting temperatures to determine polymorphism, two different β′ polymorphs were observed. In many instances where DSC detected the β1′, the β polymorph was also present. It appears that in regions where both of these polymorphic forms are present, the short spacings have values that more closely resemble those of the β form. Results from these DSC and powder XRD experiments were used to construct a time-temperature state diagram for the polymorphism of statically crystallized cocoa butter (Figure 3). At the low temperatures (-20 and -15 °C), both the γ and the R forms were present for a period of 7 days. After 2 min at -20 °C, the γ form was observed by XRD but not by DSC. This most likely was due to the limitations of the DSC equipment, as previously discussed. The melting profiles obtained by DSC indicated that only the R polymorph was present at -15 and -20 °C after 4 min of crystallization. Subsequently, DSC detected the existence of the γ form concurrently with the dominant R polymorph and both remained stable for 7 days. The R polymorph was initially observed by DSC at crystallization temperatures ranging from -10 to 20 °C. Van Malssen et al.8 reported that the γ polymorph was present for 3 min between -10 and 3 °C. Because of limitations of the DSC, we did not observe this. The initial formation of the R polymorph at 5 and 20 °C was confirmed by XRD.

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Figure 9. Micrographs of the β′ form obtained by static crystallization at 0 °C for 14 days (A), 10 °C for 5 days (B), 15 °C for 14 days (C), 20 °C for 1 day (D), 22 °C for 1 day (E), and 24 °C for 3 days (F).

The R polymorph remained stable for 7 days at -10 and -5 °C. At crystallization temperatures higher than -5 °C, the R polymorph was found to remain stable for periods ranging from 30 min (17.5 and 20 °C) to 25 h (0 °C). Moreover, at crystallization temperatures ranging from 0 to 20 °C, a polymorphic transition region from the R polymorph to the β′ form was observed (Figure 3). The state diagram (Figure 3) clearly shows that the β′ polymorph can be formed directly from the melt or via the R polymorph. At temperatures from 20 to 26 °C, formation of the β′ polymorph can take from 30 min to 3 days. The stability of the β′ polymorph is dependent on the crystallization temperature. At 15 °C, the β′ form remained stable for 28 days, whereas at the higher temperatures, a transformation to the more stable β form took place after a few hours. The second polymorphic transition region, from the β′ polymorph to the β form, took place at crystallization temperatures in the range of 20-26 °C (Figure 3). At 20 °C, this transition occurred over a 3 week period; on the other hand, at 25 and 26 °C, the transition was

complete within hours. Finally, the β form did not form directly from the melt, in contrast to a previous report6 on the crystallization of the β form from the melt due to a putative “memory effect” in the melt. In our experiments, the β phase was always formed via the β′ phase. This stable polymorphic form was only observed at higher crystallization temperatures (20-26 °C) and in some cases only after incubation times of 35 days. The β polymorph was found to remain stable for several weeks of storage at crystallization temperatures ranging from 22 to 26 °C. An anomalous region, termed γ 1,3-di-steroyl-2-oleoyl glycerol (SOS), was detected at 25 and 26 °C (Figure 3). The first crystal structure formed melted in the range of 35.2-37.3 °C after crystallization at 25 °C for 20 h or 26 °C for 1 day. Initially, we believed that this particular crystal form could be a β1 polymorph; however, after crystallization at 25 °C for 1 day and at 26 °C for 3 days, the β′ form was detected. It is unlikely that the stable β1 form would transform to the unstable β′ form suggesting that the initial polymorph was not β1. The XRD pattern displayed a broad short spacing



Figure 10. Images of the stable β form of cocoa butter statically crystallized at 20 °C for 28 days (A), 22 °C for 28 days (C and D), and 26 °C for 28 days (E and F).

at 4.45 Å, confirming that the β1 polymorph was not present in cocoa butter. The determination of the various polymorphic forms of 1,3-di-palmitoyl-2-oleoyl glycerol (POP), 2-oleoyl-palmitoyl-stearoylglycerol (POS), and SOS, the main triglycerides in cocoa butter, has been carried out.28,29 In particular, the γ polymorph of SOS forms directly from the melt at temperatures between 24 and 28 °C.28 The γ polymorph of this triglyceride has a melting temperature of 35.4 °C and a XRD pattern including two sharp short spacings at 3.88 and 4.72 Å as well as a broad short spacing at 4.5 Å8. A polymorphic form was observed with a similar melting point and a broad short spacing at 4.45 Å. We speculate that the SOS fraction of cocoa butter may have crystallized initially, with the remainder of the triglycerides remaining in the melt. Thereafter, the SOS rearranged and cocrystallized with POP, POS, and other minor triglycerides into the β′ crystal form. Crystallization Kinetics. The crystallization kinetics of cocoa butter was examined using pNMR, monitoring increases in SFC as a function of time. The effect of temperature on crystallization kinetics is shown in

Figure 4. The characteristic curves have an initial lag period followed by a rapid increase in crystal mass. Both the induction time and the level at which curves level off are a function of the crystallization temperature. Crystallization kinetic data were fitted to the Avrami model in order to obtain estimates of the Avrami exponent (Figure 5). Statistically, two different regions were determined from this graph (P < 0.001), from -20 to 15 °C and from 20 to 26 °C. The values of n for the first and second regions were, respectively, less than 1.0 and approximately 3.0. The R polymorph is predominant at crystallization temperatures ranging from -20 to 0 °C, while the β′ form is the dominant polymorph between 5 and 22.5 °C. The β form is the final predominant phase at 25 and 26 °C (Figure 5). The Avrami exponent changed dramatically in the vicinity of 20 °C, the temperature at which the β′ polymorph nucleates directly from the melt. It would appear that the Avrami exponent was very sensitive to differences in crystallization behavior between metastable and stable polymorphic forms (γ and R vs β′ and β). Induction times were plotted as a function of crystallization temperature (Figure 6) and found to be sensitive

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Figure 11. PLM images of cocoa butter statically crystallized at 0 °C for 1 (A), 5 (B), 7 (C), 14 (D), 21 (E), and 28 days (F).

to the type of polymorph being nucleated. Discontinuities in induction time-crystallization temperature plots are indicative of a change in nucleation rate due to the crystallization of different polymorphs30 or different fractions.31 Interestingly, growth curves sometimes displayed two steps (Figure 7A). Peak temperatures determined by DSC (Figure 7B) suggested that the different regions were associated with the growth of the R and β′ polymorphs. Thus, SFC-time profiles are sensitive to both formation and transformation of the various polymorphic forms. Crystal Morphology. The microstructures of the various polymorphic forms determined in the state diagram were imaged and analyzed. The γ and R polymorphs of cocoa butter had a granular appearance at all time-temperature combinations (Figure 8). The microstructure of the β′ polymorph, on the other hand, varied substantially depending on the position in the time-temperature coordinate (Figure 9). The microstructure at low crystallization temperatures (0-10 °C), where the β′ phase was formed via the R phase, was similar to that of the R crystal form (Figure 9A,B). The β′ polymorph crystallized at 15 °C and formed via the R form also had a granular texture; however, there was

some evidence of crystal clustering (Figure 9C). Aggregation of crystallites was observed at 20 °C (Figure 9D). Cocoa butter incubated for 1 day at 22 °C resulted in a similar microstructure (Figure 9E). At 24 °C, the β′ polymorph was also formed directly from the melt, but ∼25 µm crystallites with a needlelike appearance were evident (Figure 9F). Thus, both temperature and temperature history will affect the microstructure of the β′ form. The β polymorph can also display different microstructures (Figure 10). The β polymorph was obtained after 4-5 weeks at crystallization temperatures of 20 and 22 °C. After these extended incubation times, the morphology within the same sample was no longer uniform. A continuous phase was observed with a similar morphology to that observed in the early stages of crystallization; however, large microstructures (600 µm to 2 mm) were also observed. After 4 weeks at 20 °C (Figure 10A), a granular morphology was the predominant structure of the continuous phase. The larger microstructures also present, visible by the naked eye, had a featherlike appearance (Figure 10B). A similar structure was observed for cocoa butter crystallized at 22 °C for 28 days (Figure 10C,D). At crystallization



Figure 12. PLM images of cocoa butter crystallized at 15 °C for 1 (A), 7 (B and C), 14 (D), 21 (E and F), and 28 days (G and H).

temperatures of 24 and 26 °C, the β polymorph displayed a needlelike appearance (Figure 10E) and after 7 days a second microstructure was observedslarge microstructures (200-500 µm) with a granular center were surrounded by featherlike crystallites (Figure 10F). The β polymorph was not obtained directly from the melt at any of the crystallization temperatures used in this study. The phase transition from the β′ form to the β polymorph usually lead to the formation of the large microstructures. So far, this discussion has addressed the appearance of the various polymorphic forms of cocoa butter obtained by crystallization at different temperatures but not times. At low temperatures (10 °C and below), the morphology of cocoa butter crystals was similar after

28 days of storage, irrespective of changes in polymorphic form (Figure 11). Microstructural rearrangement was probably impeded by the high solids’ content and viscosity. At a crystallization temperature of 15 °C, the R polymorph is only stable for the first 20 min, so images were not obtained since only 8% of the cocoa butter was solid. All images shown in Figure 12 correspond to the β′ polymorph obtained via the R form at 15 °C. From 1 to 28 days, the microstructure was found to have a granular texture but some clustering of the crystallites was evident (Figure 12A,B,D,E,G). At all times after 7 days of storage, two different microstructures were observed, the continuous granular morphology and large spherulitic microstructures (Figure 12C,F,H). The large microstructures (∼100-600 µm) were only observed in

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Figure 13. Polarized light microscope images of cocoa butter statically crystallized at 20 °C for 1 (A), 5 (B), 7 (C), 21 (D and E), 28 (F and G), and 35 days (H-J).

a few of the samples incubated at 15 °C for 7 days. After 28 days, these large microstructures were present in all

of the samples along with the granular microstructure (Figure 12G,H). Because the β′ polymorph was found



Figure 14. Images obtained by PLM of cocoa butter crystallized at 26 °C for 1 (A), 3 (B), 7 (C and D), 14 (E and F), and 28 days (G and H).

to remain stable for 28 days at 15 °C, we speculate that the presence of two different microstructures within the sample is a result of cocoa butter fractionation. At 20 °C, however, cocoa butter microstructure changed throughout the 35 day storage period (Figure 13). Clusters of β′ crystals were evident after 1 day of crystallization at 20 °C (Figure 13A). These clusters grew and changed in morphology during the annealing period (Figure 13B,C). This coincided with the β′ to β polymorphic transition. Once the polymorphic transformation was complete, individual clusters were difficult to distinguish (Figure 13D,F). Extremely large microstructures were also observed in the sample (Figure 13E,G). After 35 days of incubation, the polymorphic

transformation was complete and the crystals were in the β form. The two different microstructures observed at 21 and 28 days were still present. Clusters were no longer discernible, resulting in a granular morphology because they had grown into each other (Figure 13H). The large microstructures had a granular center similar in appearance to the R polymorph; however, individual crystallites were much larger (Figure 13I). On the periphery of this granular center was a distinct featherlike crystal growth (Figure 13J). Small crystallites and larger needlelike crystals (∼25 µm) were observed after 1 day of incubation at 26 °C (Figure 14A). This time-temperature combination corresponded to the putative γ polymorph of an SOS rich

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Figure 15. Changes in the fractal dimension of cocoa butter microstructure as a function of time at four different temperatures. Values represent means and standard errors of at least five replicates.

fraction. The microstructure of the β′ polymorph at 26 °C was characterized by ∼50 µm needlelike crystals (Figure 14B). The needlelike morphology was observed throughout the 28 days of incubation at 26 °C (Figure 14C,E,G). Three days after the β′ to β polymorphic transition had taken place, large spherical microstructures (∼100-600 µm) were observed (Figure 14D,F,H). These were similar to the large microstructures observed at 20 °C, with a granular center and a needlelike periphery. Similar microstructures were observed at 24 °C, except after 1 day, where the crystallites had a needlelike appearance. The microstructure of the various polymorphic forms is a function of both temperature and time. Cocoa butter, crystallized at different temperatures, may be in the same polymorphic modification, but the microstructure may vary. At low crystallization temperatures, little change in the microstructure occurs during storage due to mass transfer limitations. At higher incubation temperatures, only one microstructure remains stable over time, but different microstructures form most likely as a result of phase separation, fractionation, or a combination of both. From these studies, we are able to assign a set of possible microstructures to particular polymorphic forms. Fractal Properties. Image analysis of the polarized light micrographs indicated that the fractal dimension remained constant in time at crystallization temperatures below 20 °C (not shown). Statistically significant changes in the fractal dimension were observed though at 20, 22, 24, and 26 °C (Figure 15). Even though the changes were subtle, they were statistically significant (P e 0.05). This implies that changes in cocoa butter microstructure were reflected in changes in the boxcounting fractal dimension determined by PLM. To determine the effects of temperature on the fractal dimension, the limiting value (in time) of the fractal dimension was plotted as a function of crystallization temperature (Figure 16). The fractal dimension below ∼10 °C was about 1.88. This fractal dimension charac-

Figure 16. Fractal dimension vs temperature. The value corresponds to the limiting fractal dimension at each crystallization temperature. Symbols represent the average ( standard error of at least 40 replicates.

terized the granular morphology of the R and γ forms. This granular morphology fills space in a homogeneous fashion, thus resulting in a high fractal dimension. Above 10 °C, the fractal dimension gradually decreased to ∼1.47 at 26 °C. This latter fractal dimension characterized the morphology of the β form. A more clustered, or heterogeneous, distribution of mass results in lower values of the fractal dimension. Thus, it was possible to relate a particular polymorphic form, albeit in a qualitative fashion, to the resulting microstructure of the fat crystal network. We were interested, however, in establishing quantitative relationships between microstructure and crystallization behavior. Relationship between Microstructure and Crystallization Kinetics. We plotted the values of the fractal dimension as a function of the inverse of the induction time, in logarithmic coordinates (Figure 17A), and as a function of the Avrami exponent (Figure 17B). Some very interesting relationships became apparent. The inverse of the induction time of a process is proportional to the rate of that process. For nucleation, the inverse of the induction time (τ) is proportional to the nucleation rate (J). Moreover, the Fisher-Turnbull model predicts that the natural logarithm of the nucle-



This equation could also be expressed as a function of the free energy of nucleation

∆Gn kT

D - D* ) κ - β

Figure 17. Relationship between the fractal dimension, Dbox, of the fat crystal network microstructure and natural logarithm of the inverse of the induction time (A). Relationship between the fractal dimension and the Avrami exponent (B). Relationship between the Avrami exponent and the natural logarithm of the inverse of the induction time (C).

ation rate is proportional to the free energy of nucleation (∆Gn)23, namely

lnJ ) R -

∆Gn kT

∆Gd

(NkT h ) kT

(3)

where h is Planck’s constant, N is the number of molecules participating in the crystallization process, and ∆Gd is the free energy of diffusion, assumed to remain constant during the crystallization process. Thus, our results suggest that there is a direct relationship between the nucleation rate and the resulting microstructure of the fat crystal network of the form

D - D* ) β ln J

where κ ) Rβ. These results suggest that the microstructure is partly a consequence of the energetics of nucleation. These results agree in principle with the work of Rousset32 on the modeling of microstructural growth in POP, one of the main triacylglyerols in cocoa butter. In Figure 8 of his work, Rousset demonstrates how different nucleation regimes and rates lead to the development of different microstructures. The microstructures shown would have different fractal dimensions. A statistically significant relationship (P < 0.001) also existed between the fractal dimension and the Avrami exponent (Figure 17B). The fractal dimension was inversely related to the Avrami exponent. The Avrami exponent is a function of the type of nucleation (instantaneous or sporadic) and the dimensionality of growth;23 thus, it is not surprising that it is strongly correlated to the final microstructure of the system. We also found a correlation between the nucleation rate and the Avrami exponent (Figure 17C). This is also not surprising since the Avrami exponent contains information about the type of nucleation process. Interestingly, it is therefore possible to define an Avrami exponent at a nucleation rate of unity (n* ) 1.34 for this system). This work is the first systematic investigation of the microstructure of cocoa butter in light of its crystallization kinetics and polymorphism. Here we establish qualitative and quantitative relationships between crystallization behavior and microstructure in cocoa butter and demonstrate that the microstructure is a direct consequence of the crystallization kinetics (nucleation and growth) of the system. It would be worthwhile to investigate if the relationship described in eqs 4 and 5 holds true for other systems. This would generalize the model for all such materials. Moreover, a theoretical derivation of eq 5 would shed light into the nature of the parameter β.

(2)

where k is Boltzman’ constant and T is the absolute temperature. The parameter R corresponds to

R ) ln

(5)

(4)

where β is a constant characteristic of a particular system and D* is the fractal dimension of a microstructure arising from a crystallization process with a nucleation rate of unity (J ) 1).

Acknowledgment. We acknowledge the financial assistance of the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Ontario Ministry of Agriculture and Food (OMAF). References (1) Sato, K.; Ueno, S.; Yano, J. Prog. Lipid Res. 1999, 38, 91116. (2) Sato, K. Chem. Eng. Sci. 2001, 56, 2255-2265. (3) Fryer, P.; Pinschower, K. MRS Bull. 2000, 25 (12), 25-29. (4) Van Malssen, K.; Peschar, R.; Schenk, H. J. Am. Oil Chem. Soc. 1996, 73, 1209-1215. (5) Van Malssen, K.; Peschar, R.; Schenk, H. J. Am. Oil Chem. Soc. 1996, 73, 1217-1223. (6) Van Malssen, K.; Peschar, R.; Brito, C.; Schenk, H. J. Am. Oil Chem. Soc. 1996, 73, 1225-1230. (7) Loisel, C.; Keller, G.; Lecq, G.; Bourgaux, C.; Ollivon, M. J. Am. Oil Chem. Soc. 1998, 75, 425-439. (8) Van Malssen, K.; van Langevelde, A.; Peschar, R.; Schenk, H. J. Am. Oil Chem. Soc. 1999, 76, 669-676. (9) Van Langevelde, A.; Driessen, R.; Molleman, W.; Peschar, R.; Schenk, H. J. Am. Oil Chem. Soc. 2001, 78, 911-918. (10) Van Langevelde, A.; van Malssen, K.; Peschar, R.; Schenk, H. J. Am. Oil Chem. Soc. 2001, 78, 919-925.

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(11) Marangoni, A. G. Trends Food Sci. Technol. 2002, 13, 3747. (12) Narine, S. S.; Marangoni, A. G. Adv. Food Nutr. Res. 2002, 44, 33-145. (13) Marangoni, A. G. Phys. Rev. B 2000, 62, 13951-13955. (14) Marangoni, A. G.; Narine, S. S. J. Cryst. Growth 1999, 198/ 199, 1315-1319. (15) Narine, S. S.; Marangoni, A. G. Phys. Rev. E 1999, 59, 69917000. (16) Narine, S. S.; Marangoni, A. G. Phys. Rev. E 1999, 60, 19081920. (17) Narine, S. S.; Marangoni, A. G. Food Res. Int. 1999, 32, 227248. (18) Hicklin, J. D.; Jewell, G. G.; Heathcock, J. F. Food Microstruct. 1985, 4, 241-248. (19) Manning, D. M.; Dimick, P. S. Food Microstruct. 1985, 4, 249-265. (20) Narine, S. S.; Marangoni, A. G. J. Am. Oil Chem. Soc. 1999, 76, 7-13. (21) Marangoni, A. G. J. Am. Oil Chem. Soc. 1998, 75, 14651467. (22) Wright, A. J.; Hartel, R. W.; Narine, S. S.; Marangoni, A. G. J. Am. Oil Chem. Soc. 2000, 77, 463-475. (23) Sharples, A. Introduction to Polymer Crystallization; Edward Arnold Ltd.: London, 1966; pp 44-59.

Marangoni and McGauley (24) Strickland-Constable, R. F. Kinetics and Mechanism of Crystallization; Academic Press: London, 1968; pp 74129. (25) Wright, A. J.; Narine, S. S.; Marangoni, A. G. J. Am. Oil Chem. Soc. 2000, 77, 1239-1242. (26) Wright, A. J.; Narine, S. S.; Marangoni, A. G. In Crystallization and Solidification Properties of Lipids; Widlak, N., Hartel, R. W., Narine, S. S., Eds.; AOCS Press: Champaign, IL, 2002; pp 123-543. (27) Larsson, K. Lipids-Molecular Organization, Physical Functions and Technical Applications; The Oily Press: Dundee, 1994; pp 7-47. (28) Sato, K.; Arishima, T.; Wang, Z. H.; Ojima, K.; Sagi, N.; Mori, H. J. Am. Oil Chem. Soc. 1989, 66, 664-674. (29) Arishima, T.; Sagi, N.; Mori, H.; Sato, K. J. J. Am. Oil Chem. Soc. 1991, 68, 710-715. (30) Kellens, M.; Meeussen, W.; Reynaers, H. J. Am. Oil Chem. Soc. 1992, 69, 906-911. (31) Litwinenko, J. W.; Rojas, A. M.; Gerschenson, L. N.; Marangoni, A. G. J. Am. Oil Chem. Soc. 2002, 79, 647-654. (32) Rousset, P. In Physical Properties of Lipids; Marangoni, A. G., Narine, S. S., Eds.; Marcel Dekker: New York, NY, 2002; pp 1-36.

CG025580L

Relationship between Crystallization Behavior and Structure in

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