A Conceptual Model for Shear-Induced Phase Behavior in

CRYSTAL GROWTH & DESIGN 2007 VOL. 7, NO. 7 1230-1241

Articles A Conceptual Model for Shear-Induced Phase Behavior in Crystallizing Cocoa Butter Gianfranco Mazzanti,†,§ Sarah E. Guthrie,† Alejandro G. Marangoni,†,‡ and Stefan H. J. Idziak*,† Department of Physics and Guelph-Waterloo Physics Institute, UniVersity of Waterloo, Waterloo, and Department of Food Science, UniVersity of Guelph, Guelph, Ontario, Canada ReceiVed September 12, 2005; ReVised Manuscript ReceiVed January 10, 2007

ABSTRACT: We propose a conceptual model to explain the quantitative data from synchrotron X-ray diffraction experiments on the shear-induced phase behavior of cocoa butter, the main structural component of chocolate. We captured two-dimensional diffraction patterns from cocoa butter at crystallization temperatures of 17.5, 20.0, and 22.5 °C under shear rates from 45 to 1440 s-1 and under static conditions. From the simultaneous analysis of the integrated intensity, correlation length, lamellar thickness, and crystalline orientation, we postulate a conceptual model to provide an explanation for the distribution of phases II, IV, V, and X and the kinetics of the process. As previously proposed in the literature, we assume that the crystallites grow layer upon layer of slightly different composition. The shear rate and temperature applied define these compositions. Simultaneously, the shear and temperature define the crystalline interface area available for secondary nucleation by promoting segregation and affecting the size distribution of the crystallites. The combination of these factors (composition, area, and size distribution) favors dramatically the early onset of phase V under shear and determines the proportions of phases II, IV, V, and X after the transition. The experimental observations, the methodology used, and the proposed explanation are of fundamental and industrial interest, since the structural properties of crystalline networks are determined by their microstructure and polymorphic crystalline state. Different proportions of the phases will thus result in different characteristics of the final material. I. Introduction During crystallization of any multicomponent system, the compositional changes in the liquid and solid phases and in the particle size distribution follow paths defined by the cooling rate, shear rate, and final crystallization temperature. Natural fats are multicomponent lipid systems, and in the case of cocoa butter, the main structural component of chocolate, those paths lead to specific proportions between different solid phases (also called polymorphic forms) in the polycrystalline solid, as well as different microstructures and mechanical properties.1-6 The composition of cocoa butter is unique among other fats because over 90% of the triacyl- and diacylglycerols (TAGs and DGs) are composed of only four fatty acids, rather than a broad distribution of them. Two of these fatty acids are saturated (s), stearic (S, 18 carbons), and palmitic (P, 16 carbons), and two are unsaturated (u), oleic (O, 18 carbons, 1 double bond), and linoleic (L, 18 carbons, 2 double bonds). The vast majority of cocoa butter’s TAGs have a “sus” or “suu” structure, and * To whom correspondence should be addressed. E-mail: [email protected]. † University of Waterloo. ‡ University of Guelph. § Present address: Department of Process Engineering and Applied Science, Room D-405, 1360 Barrington Street, P.O. Box 1000, Dalhousie University, Halifax NS B3J 2X4 Canada.

SOS, POS, and POP constitute over 80% of this fat.7 The cocoa butter components can be loosely classified into three groups of molecules, which we will refer to as high-, medium-, and low-melting-point fractions, HMF (especially rich in SOS), MMF (rich in POS), and LMF (rich in POP). Since they are readily intermiscible, they provide a continuous spectrum of melting points along the solidus-liquidus lines of the multicomponent system. Fat crystals have been found to have different compositions at different times and under different conditions.5,8-14 This happens because a typical crystallization process of a multicomponent fat starts with nucleation of small crystallites rich in HMF.8,14 Newer nuclei have a composition slightly poorer in HMF. At any given time, the crystals that were nucleated earlier grow by adding layers of lamellae made of the same HMF-depleted material as the nuclei currently appearing.8,9,15,16 As the nucleation-growth process goes on, the average size of the molecules being incorporated into the crystals keeps changing and the average size of the crystallite population grows larger. This “layered” growth produces what is called a kinetic distortion of the phase diagrams17,18 and also leaves behind a liquid of varying composition, i.e., the complement of the material crystallized up to that point. Eventually a situation of “equilibrium” may be reached when the concentration at the surface of the crystals (not the average composition) is in

10.1021/cg050467r CCC: $37.00 © 2007 American Chemical Society Published on Web 05/25/2007

Shear-Induced Phase Behavior in Cocoa Butter

equilibrium with the remaining liquid.17,18 As explained in the literature, this results from the complex combination of competing mechanisms, e.g., liquid diffusion across the boundary layer surrounding the crystals vs speed of crystal growth, rate of nucleation vs crystalline growth rate, and rate of local heat transfer vs diffusion.19,20 Time-resolved synchrotron X-ray studies are necessary to follow the evolution of the crystalline phases and understand the genesis of their structures.7,9,15,21,22 The application of shear makes measurements difficult, so it is not surprising that very few in situ X-ray studies under shear have ever been published.2-4,23-25 Some studies have been done using rheometers or other means, though a direct observation of the phases present at a given time was not possible in those cases.26-29 Six traditionally recognized crystalline phases of cocoa butter30 are identified by roman numerals I-VI in order of increasing melting temperature and enthalpy1,9,11,14-16,30-42 although some debate still lingers on how many do really exist.11,39 Phase II has an R-type lateral packing (hexagonal), with a 2L longitudinal stacking. Phase IV crystallizes in a β′ arrangement (orthorhombic) and a 2L longitudinal stacking of the TAGs. The existence of phase III is highly questioned, since it is likely a mixture of phases II and IV.11,39 Phases V and VI have a β-type lateral packing (triclinic) with a 3L longitudinal stacking. A detailed structure of phase V has been proposed only recently,43 because of the difficulties associated with the powder diffraction pattern from polycrystalline cocoa butter resulting from crystallites of mixed composition. To further complicate matters, the formation under shear of another phase, called phase X, has been recently reported.3 The characteristics of phase X were compared with data reported in the literature for cocoa butter fractions and its crystallized components1,9,15,16,44-49 and found consistent with phase X being a 3L β′-type crystalline mixture rich in SOS and POS, which are two of the three main components of cocoa butter. It was also noted that the partial permanence of phases II and IV after the fast transition to phase V depended on the shear applied.3 It has been known for a long time that shear reduces dramatically the time required to form the desirable phase V41,50,51 that gives chocolate its ideal characteristics, and recent studies using rheology25,27-29,52,53 support the generality of this observation. Recent X-ray diffraction data showed that this formation of phase V under shear bypassed phase IV.2,3,24,25 The qualitative and quantitative phase behavior turned out to be more complex when phase IV was found to appear under high-shear-temperature conditions3 and phase X appeared mixed with phase V. Shear has also been shown to induce significant orientation of the crystalline population2 and segregation of the crystals.25 It is of enormous technical and scientific interest to understand how shear induces the phase changes, so that processes can be designed accordingly. Two main questions remain to be fully answered: How does shear reduce the onset times and accelerate the kinetics of phase transition, and how does shear determine different pathways for these transformations? There has been considerable effort in the literature to propose explanatory mechanisms, yet some do not seem satisfactory because either they are highly improbable or they lack supporting evidence. In the very useful industrial papers by Ziegleder51,54 and by Windhab and Niediek,55 there are two sketches of a shear field squeezing TAG molecules from their crystalline arrangement in phase IV into the desired stable triclinic β structure of phase V, as if they were a bunch of pencils in your hand or hair being combed by a brush. This picture perhaps makes sense if referred

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to Loisel et al.’s9 hypothetical partially liquid bound molecules at the surface of a crystal, but certainly does not seem feasible if the molecules are already part of a solid crystalline structure. The cohesive forces in the crystal would be far too strong for the shear forces on the surface to induce the transition: the idealized picture of shear simply wringing the crystals directly from phase IV to phase V is not plausible. In the second case, when in the liquid, the TAG molecules are much too small not to undergo random Brownian motion. The shear rates required to orient them would be many orders of magnitude larger than even the highest ones applied in this study. It has been suggested that shear may modify the liquid crystalline domains that supposedly precede the formation of the actual crystals.56-59 These liquid crystalline structures have been documented in systems that have been crash cooled and/ or subsequently melted.9,60 However, so far there is no direct unquestionable evidence of their existence under our crystallization conditions or as general precursors of crystallizing bulk fats.59 Recently, the phase transition to phase V has been convincingly presented as the result of a secondary nucleation event.25 In this paper we report detailed quantitative data from synchrotron X-ray diffraction on the effects which the shear rate and temperature have on the pathways and kinetics of phase transitions and growth of cocoa butter. Our discussion of both static and shear experiments is structured around the characteristics of the system derived from the diffraction patterns, namely, the crystalline fraction (SFC (solid fat content) is proportional to the integrated intensity Iq), correlation length (related to the crystal thickness), lamellar thickness (related to the molecular composition of the crystallites), and crystalline orientation (related to the segregation of crystallites and the solid-liquid interfacial area). Combining this experimental evidence with a wide body of literature, we propose a conceptual model of the complex mechanisms involved in the multiple phase transitions of this natural material. This conceptual model constitutes an important advance in the fundamental understanding of the so-called polymorphic transformations of cocoa butter. It also has significant industrial application, since the structural properties of the solid fat networks are determined by their microstructure and polymorphic crystalline state,1,61 and the mechanisms by which shear modifies the phase transitions that lead to those structures are just beginning to be understood. II. Experiments and Methods Melted cocoa butter was placed in the gap (δ ) 1 mm) between the cylinders of a Couette shear cell as described by Mazzanti et al.2,4 We used two different pairs of concentric cylinders, one with an inner diameter of 39 mm and an outer diameter of 41 mm and one with an inner diameter of 15 mm and an outer diameter of 17 mm. The shear rate, γ˘ , can be approximated by dividing the relative velocity u between the shearing cylinders by the gap (γ˘ ≈ u/δ). The values of the applied shear rates were in the range from 45 to 1440 s-1, as well as static, i.e., γ˘ ) 0 s-1. Two different samples of commercially available cocoa butter were used, one from Cacao de Zaan (The Netherlands) and the other from Barry-Callebaut (Belgium), referred to as CZ and BC, respectively. The melted sample was kept at 50 °C at the selected shear rate for 30 min. Then the system was cooled at a controlled rate (3 °C/min in most cases, but a few were cooled at 0.5 °C/min) to the final crystallization temperature, maintaining the shear in the cell. The system was then sheared at this final temperature until the experiment was ended, typically after 30-45 min at 17.5 °C, 45-60 min at 20.0 °C, and 60-90 min at 22.5 °C. The static experiments had longer durations, up to 180 min. The temperature of the Couette cell was controlled using two small thermistors (reproducible to 0.1 °C) placed in the small circulation chamber inside the cell, next to the inner Lexan wall. It is possible that a small difference in temperature existed between

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Figure 1. (a) Two-dimensional small-angle diffraction pattern from BC cocoa butter crystallized under shear (180 s-1) 6 min after 17.5 °C was reached at a cooling rate of 3 °C/min. The phase II diffraction ring (q ≈ 0.127 Å-1) is visible. (b) Diffraction pattern from the same experiment 20 min after 17.5 °C was reached. The phase transition has occurred, and phase V (q(002) ) 0.194 Å-1) is clearly present, coexisting with a small remnant of phase II. (c) Radial plots obtained from (a) (solid line) and (b) (dashed line) of the intensity (normalized units (nu) on the log scale) vs the reciprocal lattice spacing q. The peak position q0 and the full width at half-maximum ∆q of the diffraction peak for phase II are indicated. (d) Azimuthal plot from the diffraction pattern in (a) showing the oriented fraction of material above the dotted line. The squares are the data points, the Gaussian fit is the solid line, and ∆χ is the azimuthal width of the oriented portion. the actual material being crystallized and the thermistors. We did a simulation in Mathcad to estimate this difference, and it is macroscopically negligible before the onset of phase V at all shear rates used, except at 1440 s-1, where we calculated it could be as high as 1 °C. The experiments were conducted at the ExxonMobil beamline X10A at the National Synchrotron Light Source in Brookhaven National Laboratory, Upton, NY. A Bruker 1500 two-dimensional CCD detector was used to capture diffraction patterns with exposure times of 50 s, as shown in Figure 1a,b. The X-rays had a wavelength λ ) 1.097 Å, and the detector was located at a distance L ) 1132 mm from the cell axis for the small-angle X-ray diffraction experiments. A beam size of 0.5 × 0.5 mm gave an instrumental resolution of 0.003 Å-1. Preliminary wide-angle X-ray diffraction experiments were performed with the detector located at a distance L ) 150 mm from the cell. The X-ray diffraction intensity from each 2D diffraction image was radially averaged and plotted as a function of the reciprocal lattice spacing q (Figure 1a,c), q ) 2π/d ) (4π/λ) sin(θ), where d is the interplanar spacing and 2θ is the Bragg angle. The radial averaging was done by circular integration of the X-ray intensity at a fixed radius rd and repeated for all radial distances. These radial averages were obtained with a custom plug-in for the ImageJ software62 which normalized the intensities with respect to the incident beam and corrected the absorption distortion introduced by the Couette cell. The resulting one-dimensional powder diffraction profiles were fit to a Gaussian-Lorentzian peak profile using a modified Levenberg-Marquardt algorithm. Fitting the radial plots was challenging because both the intense small-angle diffuse scattering and the liquid background changed in time as the phases grew or transformed. To evaluate the crystalline orientation in the sample,2 the ImageJ plug-in provided azimuthal plots, by recording the intensity along the circumference (χ angle) of the 2D diffraction rings, as illustrated in Figure 1d, which was obtained from the diffraction pattern in Figure 1a. The plots were fit to a Gaussian function with full width at halfmaximum ∆χ. The orientation ratio χr is defined as the ratio of the area above the dotted line over the total area. Small ∆χ and large χr are the hallmarks of better oriented crystallites. For an unoriented, polycrystalline material, the area under the X-ray diffraction peak seen in the radial plots in Figure 1c, referred to as the integrated X-ray intensity Iq, is proportional to the total crystalline mass (also called SFC) of a given phase present in the volume illuminated by the X-rays.63 However, in our measurements taken at higher shear rates, orientation of the crystallites is observed for wide-angle and for

small-angle X-ray diffraction rings. The degree of orientation in azimuthal plots such as Figure 1d was not very high (∆χ > 50°), even when the fraction of oriented crystals χr coexisting with the unoriented crystallites was high (0.8). We will thus assume that this weak orientation does not strongly impact the relationship between SFC and total integrated intensity. The determination of an exact proportionality coefficient between the SFC and integrated intensity would require their simultaneous determination, but this is not technically feasible at the present time for our system under shear. The position of the diffraction peak, q0 ) 2π/d in Figure 1c, is inversely related to the thickness of the TAG lamellae (d spacing). The d spacing is thus proportional to the longitudinal size of the crystallized molecules, and it is therefore associated with the composition of the crystalline population. Just how well does a change in peak position reflect a change in composition? The ternary diagram for the system SOS-POS-POP developed by Koyano et al.64 shows precisely this correlation, for a phase of type β. In their diagram, large d spacing values are reported for crystals rich in SOS (the main component of HMF) whereas shorter spacings are seen when the mixture is richer in POS or POP. Thus, d is indeed a sensitive indicator of the composition for this system. Although it is not trivial to uniquely map the average d value to a specific composition, it is possible to use it to follow the progress of a particular process and to compare between variations of the same process.4,65 Temperature variations can also produce diffraction peak position displacements. However, the experiments were performed at constant crystallization temperature, and the behavior of the peak positions is consistent with previous experiments with other lipid materials.4,65 The full width at half-maximum (fwhm) of the peak, ∆q in Figure 1c, is related to the correlation length of the crystallites ξ by the relationship ξ ) 2π/(∆q). For a small single-domain plateletlike crystallite this correlation length is an approximate measure of the thickness of that crystallite and thus provides information on the average crystal size. To have an approximate idea of the microstructures and crystal sizes present under shear, some microscopy observations were performed by quickly transferring a sample from a temperature-controlled Couette cell to a glass slide, placing a coverslip on the slide, and capturing images with a 40× objective under cross polarizers using an inverted Zeiss Axiovert microscope. For more detailed microscopy observations under shear, we will rely on the literature.25


III. Results from Static Experiments These experiments were performed in the Couette cell without shear, as a reference, and only phases II and IV were observed at a cooling rate of 3 °C/min at final temperatures of 17.5, 20.0, and 22.5 °C. We decided not to explore temperatures below 17.5 °C because at 15 °C and below we observed that phase I (also known as γ) appeared for a short time, and thus, the study would have been far more complicated. Under static conditions at 17.5 °C, comparison of our X-ray diffraction peak integrated intensities, in normalized units (nu), for the BC cocoa butter with the SFC curve of Marangoni and McGauley,1 obtained by pulsed magnetic resonance (pNMR), results in a proportionality coefficient of 1.7% SFC/nu for phase II and 3.2% SFC/nu for phase IV. Comparison with the pNMR-SFC data from Ziegleder54 at 20.0 °C yields values of 1.7% SFC/nu for phase II and 4.0 % SFC/nu for phase IV. The value for phase IV is also consistent with pNMR data reported by Dewettinck,66 but not the value for phase II. In these experiments the cooling rates and types of cocoa butter are not exactly the same as ours, and thus, some variability is to be expected, yet from these approximate values, it is important to point out that, as expected, the X-ray diffraction structure factors of the phases are different, and thus, the ratios between the integrated intensity and SFC are quite different between phases. Phase II appeared almost at the same time in all experiments at 3 °C/min, manifested as a diffraction ring at q0 ) 0.125 Å-1, and the peak position moved up to q0 ) 0.128 Å-1. The corresponding variation of the lamellar thickness from 5.03 to 4.91 nm reflects a considerable change in the average composition during the crystallization. The width of the phase II X-ray peak resulted in a correlation length ξ of the crystals between 110 and 126 nm. Phase II grew up to maximum values equivalent to SFC of 10.1%, 3.2%, and 1% at 17.5, 20.0, and 22.5 °C. Extrapolation to 0% SFC coincides with the end of the DSC melting range recorded for phase II,1 around 25 °C. In a previous study66 it was assumed that the sum of the three integrated intensities (phase II, phase IV, and liquid) is proportional to the total mass, and the amount of each phase is estimated simply by the ratio of its integrated intensity over the sum of all integrated intensities. Unfortunately, this procedure turns out to be inaccurate, because the proportionality factor between the integrated intensity and mass of phase II is considerably different from the factor for phase IV, and even more dissimilar to the proportionality factor for the liquid. This difference is a consequence of the structure factors of each phase. It is not surprising then that the SFC values estimated from their X-ray data are so different from those obtained from pNMR. Although our proportionality factors were not obtained simultaneously, and thus suffer from imprecision, we cannot assume that they are the same for all phases. In the present work we will use our estimated factors whenever the need arises to convert integrated intensity data to SFC. It is interesting that in all static cases the integrated intensity of phase II continued to grow for a considerable time after we observed the first indications of the presence of phase IV. At 20.0 °C there was a definite reduction in the growth regime of phase II long before the onset of form IV. At 22.5 °C phase II reached a long-lasting plateau that was sustained for a long time after the onset of phase IV. These observations are consistent with the report on the crystallization of cocoa butter under static conditions by Dewettinck et al.66 and by Sonwai et al.,25 where the authors observed that phase IV appeared before phase II stopped growing. This suggests the possibility that phase IV


nucleates from the melt rather than by direct solid-state transformation from phase II. Recall that the SFC of phase II was 10% at most, the rest of the material being liquid. Probably phase II starts to disappear when the growth of phase IV is fast enough to release heat and to modify the composition of the melt, by incorporating the least soluble components from it. This process may be seen also as an Ostwald ripening, where the least stable material melts to recrystallize on previously formed more stable crystals. However, there is no direct proof at this point to rule out the possibility of a solid-solid transformation from II to IV occurring simultaneously with the growth of phases II and IV, though the presence of liquid has proven to facilitate the transition from phase R to phase β′ in other systems.67 The onset times for phase IV were 20, 38, and 94 min after crystallization temperatures of 17.5, 20.0, and 22.5 °C were reached. After 120 min at 17.5 °C the integrated intensity reached a value equivalent to an SFC of 70%, at 20.0 °C it reached 56% after 180 min, and at 22.5 °C it reached 4% after 180 min. Therefore, the formation of phase IV used a larger fraction of the liquid than the fraction that had been crystallized for phase II. The correlation length grew from 30 to 50 nm, corresponding to crystal sizes considerably smaller than those of phase II. The average lamellar thickness was reduced from 4.69 to 4.35 nm likely as a consequence of the changing average composition of the cocoa butter as the crystallization progressed. In an experiment cooling at 0.5 °C/min to 17.5 °C, the first diffraction ring, from phase II, was observed during the cooling ramp, when the sample was at 21 °C. Phase IV appeared after 26 min of reaching the crystallization temperature, i.e., 35 min after the onset of phase II. Simultaneously with the formation of phase IV, another phase was observed, with a distinct (002) diffraction peak at q ) 0.179 Å-1 and a very weak (001) peak at q ) 0.0895 Å-1, corresponding to a lamellar thickness of 7.02 nm. These coincide with the peak positions reported for phase X previously found under shear conditions.3 This is the first time X-ray diffraction confirms the formation of phase X under static conditions. It was postulated3 that phase X was probably formed via a fractionation or molecular segregation process. Its presence under a slow cooling rate and its absence at the fast cooling rate reinforce that hypothesis. It is interesting that in both cases phase X does not appear on its own, but simultaneously with another phase, i.e., with phase IV under static conditions and with phase V under shear. This is reminiscent of the formation of mixtures of β′ and β phases in milkfat through an R precursor.65 IV. Results from Experiments under Shear The two typical diffraction patterns presented in Figure 1 were captured by the 2D X-ray detector from cocoa butter crystallized at 17.5 °C under a 180 s-1 shear rate, after a cooling rate of 3 °C/min. Taken 5 min after 17.5 °C was reached, Figure 1a shows the characteristic small-angle (001) diffraction ring from phase II at q ) 0.127 Å-1. The wide-angle diffraction pattern was also consistent with phase II, as was confirmed by other researchers.25 In Figure 1b, taken after 20 min at 17.5 °C, the two characteristic diffraction rings of phase V, (001) and (002) at q ) 0.0974 Å-1 and q ) 0.195 Å-1, are visible, along with a weak remnant of the (001) ring from phase II. In both diffraction patterns the orientation around the beamstop in the diffuse small-angle scattering from the particles is evident. The radial plots obtained from these 2D patterns are plotted in Figure 1c, showing obvious differences before and after the phase transition. Most of the 2D diffraction patterns from cocoa butter


displayed crystalline orientation,2,3 but we will focus in this section on the phase behavior. The importance of the orientation will be discussed later in the paper. We will discuss first the observations related to phases II, V, and X and subsequently comment on the cases where phase IV was present. The presentation of results will focus initially on the behavior of the X-ray integrated intensity, followed by the behaviors of the width and position of the diffraction peaks. The last section of the results will present our findings on orientational ordering. A. Integrated Intensities of the X-ray Diffraction Peaks. For any quantitative estimates, we will assume that the factors that relate integrated intensity with SFC for phases II and IV are similar to those under static conditions. However, an estimate of the proportionality factors for phases V and X under static conditions was not possible at present, due to time constraints at the synchrotron. The SFCs that cocoa butter reaches under static conditions at 17.5, 20.0, and 22.5 °C after 48 h1 are 78%, 74%, and 48%, whereas after 28 days37 they are 85%, 80%, and 68%. Our preliminary experiments in capillaries showed a mixture of phases IV and V after 48 h at room temperature, whereas after 28 days the cocoa butter was mostly phase V or a mixture of phases V and VI. The shear experiments induced the early formation of phase V, but the paste was still “flowing” in the Couette cell. It is therefore unlikely that we reached such high SFC values. The general trends of behavior were similar for both cocoa butters. However, the CZ cocoa butter, tested in the small cell, showed somewhat slower kinetics, more tendency to form phase IV, and less tendency to go into phase V than the BC cocoa butter, tested in the large cell. This is not surprising, since differences in composition affect the kinetics of crystallization of cocoa butter.68 The effects related to phases II, V, and X were clearer at 17.5 °C; thus, we will present mostly examples derived from experiments at that temperature. The integrated intensities of phases II, V, and X are presented in Figure 2 for different shear rates at a crystallization temperature of 17.5 °C. The growth of phase II under shear (open symbols) can be compared to the growth under static conditions (dashed line). The phase transition results in a sudden sharp decrease in the integrated intensity of phase II, although at low shear rates there is a remaining amount, which declines slowly. The sudden phase transition to phase V observed at 17.5 °C was also observed at 20.0 °C, and at 22.5 °C at the lower shear rates. The integrated intensity of phase V in Figure 2b increased rapidly and soon reached a slow-growing regime. Please note the change in scale with respect to the plot of phase II. Due to the high viscosity and high SFC of the experiments, the cell had to be stopped after 30 min in the experiments at 17.5 °C. Phase V was observed to appear in all the experiments at 17.5 and 20 °C. In the experiments at 22.5 °C it only appeared at the three lower shear rates, within the time frame of our experiments. BC cocoa butter had a stronger tendency to produce phase V and showed shorter onset times at the lower temperatures. Phase X appeared simultaneously with phase V. Note that the scale of integrated intensity in Figure 2c is half the size of the scale for phase V (and 2/3 of the scale for phase II). Phase X was clearly present at 17.5 °C and lower shear rates in larger amounts than in the static conditions at slow cooling rates. To gain a better understanding of the phenomena that lead to the phase transition that forms phase V, we need to look at what is happening just before and after the transition.

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Figure 2. Integrated intensity Iq of the three phases present at 17.5 °C as a function of time under different shear rates. (a) Phase II, showing its onset at time t ) 0. The growth under static conditions follows the dashed line. The sharp decrease after the phase transition is common to all shear rates. (b) Phase V showed a rapid increase, and its maximum value grew with shear, except at 1440 s-1. (c) Phase X appeared simultaneously with phase V, and its amount seemed to be maximum at 90 s-1, decreasing and almost disappearing at the higher shear rates.

Two points in time, before and after the phase transition, have been selected to observe the effect of the different shear rates. The comparison times are indicated in Figure 3a, which shows a composite of integrated intensity for the three phases of BC cocoa butter crystallized at 17.5 °C and 180 s-1. The first time point was chosen where phase II reached its maximum integrated intensity, i.e., just before the phase transition, and will be identified by an open triangle. The second point in time has been chosen as 20 min into the experiment, measured from the moment the cell reached 17.5 °C. The integrated intensity of each phase is identified by a filled symbol, a triangle for phase II, a square for phase V, and a star for phase X. The arrow indicates how the onset time for the phase transition toV was estimated. The onset times, measured from the moment when the cell reached the crystallization temperature, are plotted in Figure 3b, as a function of the shear rate. The presence of shear accelerates dramatically the onset of phase V in the presence of phase II when compared to static conditions. The onset time is reduced as the shear is increased, in this case up to 360 s-1. The onset times observed at 20.0 °C were longer than those reported by MacMillan24 (X-ray diffraction at shear rates between 3 and 12 s-1) and Ziegleder54 (rheology, shear rates between 30 and 140 s-1); they are consistent with the data from Sonwai et al.25 up to 360 s-1. The onset times up to 360 s-1 can be fit to a power law with exponents of -0.20 for 17.5 °C and -0.27 for 20.0 °C. The exponent from the plot in Ziegleder54 was ca. -1.1 at 20.0 °C at shear rates below 140 s-1. The exponent magnitude decreases as the temperature increases, to -0.23 at 29 °C. Provided shear is present, the trend


Figure 3. (a) Composite showing the evolution of the three phases at 17.5 °C and 180 s-1. The symbols indicate the time points used for the comparative analysis in Figures 4 and 8. The open triangle indicates the maximum attained by phase II just before the transition, the filled triangle indicates the amount of phase II left after the transition, 20 min into the experiment, the filled square corresponds to the amount of phase V at that same time, and the filled star is used for phase X. (b) Onset times toV of the phase transition to phase V as a function of the shear rate γ˘ applied, measured after the crystallization temperature was reached. Up to 360 s-1 the times decrease, but at higher shear rates they increase again, perhaps due to viscous heating.

of onset time reduction is valid from very small values of the shear rate24,25 (3 s-1) up to a certain limit of the shear rate that depends on the specific setup. Above this limit value, the increase in shear starts delaying the onset, perhaps due to generation of viscous heat, as suggested by Ziegleder.54 The onset data provided by Windhab et al.55 cannot be compared, because the rheology experiments were done under constant shear stress rather than under constant shear rate. Different experimental systems may control the temperature somewhat differently, use different cooling rates, and crystallize cocoa butters of different origins. Thus, the observations provide useful general trends and are not necessarily happening for a given system at exactly the same nominal combination of shear rate and temperature. At 17.5 °C, before the phase transition, all the radial plots look very similar to the solid line of Figure 1c. The sudden decrease of intensity for phase II coincides with the formation of phase V, which appears suddenly and massively, producing a large amount of heat and a swift intense change in the background, as seen in the radial plot (dashed line) in Figure 1c. A similar sudden effect is seen at the lower shear rates at 20 °C. The transitions are more smooth and moderate at 22.5 °C. The radial plots from diffraction patterns taken 10 min after the phase transition of BC cocoa butter at 17.5 °C are shown in Figure 4a to illustrate the gradual variation in the response of the system to the application of different shear rates. The curves are plotted on a log scale with their baselines shifted


Figure 4. (a) Radial plots of the log of the intensity as a function of q after the phase transition to phase V at 17.5 °C under different shear rates. The relative variation of the three phases (II, V, and X) can be appreciated. The baselines are shifted arbitrarily for clarity. (b) Integrated intensity Iq as a function of the shear rate γ˘ at 17.5 °C. The integrated intensity from the (001) diffraction peak for phase II is represented by open triangles (4) before the phase transition to phase V and by filled triangles (2) 20 min after the crystallization temperature was reached. The integrated intensity from the (002) diffraction peak from phase V is represented by filled squares (9) and that from phase X by filled stars (f), 20 min after the crystallization temperature was reached.

for clarity. The characteristic peaks for the three phases are identified near the top curve (45 s-1), and it is quite clear that the increase in shear causes a gradual reduction of the remnant amounts of phase II and increases the proportion of phase V with respect to phase X. A quantitative view of the integrated intensity values before and after the transition is presented in Figure 4b by plotting them against the logarithm of the applied shear rates. As the shear rate is increased, the maximum value of the intensity attained by phase II before the transition decreases steadily, as seen in Figure 2a. The amount of phase V increases with the applied shear rate, except at 1440 s-1. Conversely, the integrated intensity of both phases II and X present after the transition is decreased with the increasing shear. Thus, the amount of phase II left and the amount of phase X formed after the transition are proportional to the amount of phase II present just before the transition. The amount of phase V is inversely proportional to all three (phase II before and after the transition and phase X). The amount of phase X was reduced with shear, except from 45 to 90 s-1. Phase X had not been reported before by other researchers to form under static conditions, although we did find it under the slow cooling rate. Therefore, it seems that there is a maximum formation of this phase at around 90 s-1 for these temperatures, observed in both CZ and BC cocoa butters. At


Figure 5. (a) Time dependency of the correlation length ξ of phase II. The zero shear case is shown for comparison as a dashed line. The solid line follows the experiment at 180 s-1. The correlation length at different shear rates follows a similar growing trend up to approximately 95 nm. When the transition to phase V happened, the correlation length increased suddenly simultaneously with the partial melt of phase II. (b) Time dependency of the lamellar thickness d of phase II. The d values decrease very rapidly at the beginning from values above 5.03 nm (off scale in the graph) and at the transition to phase V jump back to ca. 4.945 nm.

20.0 °C and the lower shear rates phase X was clearly present, but at the higher shear rates or at 22.5 °C its amount was too small to be accurately quantified. In the next three sections the crystalline size, composition, and orientation characteristics of phase II are closely examined before and after the transitions, yielding essential clues as to the nature of the events leading to the transition and happening during the transition. B. Correlation Lengths of the X-ray Diffraction Peaks. The time dependence of the correlation lengths for phase II from BC cocoa butter at 17.5 °C can be seen in Figure 5a and provides an indication of the thickness of the platelet crystallites, if they are assumed to be monodomains. The open symbols represent the different shear rates. The dashed line is used for the static case. The solid line follows the symbols for the experiment at 180 s-1 as a typical case. The growth of the correlation length is initially similar at all shear rates, up to a point where a sudden and abrupt increase in the correlation length is observed, coinciding in time with the onset of phase V. This increase in the correlation lengths is indicative of a considerable increase in the average size of the crystalline population of phase II, coincident with the rapid decrease in the amount of phase II, which is rather surprising. At 720 and 1440 s-1 no detectable amount of phase II was left after the onset of phase V. The transition happens more or less when the average size of the crystallites of phase II reaches the same value of the correlation length. The correlation length went from ca. 30 nm at the onset of crystallization of phase II to 95 nm at the phase transition to phase V at 17.5 °C (105 nm at 20.0 °C). After the transition, the coherence length jumped to 115-130 nm. The correlation length of phase V increased with time usually up to values between 40 and 70 nm, considerably smaller than those of phase II, consistent with much smaller crystallites being formed, as documented by the microscopy work in the literature.25 This is also consistent with the strong increase of diffuse scattering at small angles. The values of the correlation

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length were of the same order of magnitude at the three temperatures, and no clear trend was observed with respect to temperature. The correlation length of phase X was quite small, ∼16 nm, compared to those obtained from diffraction peaks of the other phases, or the 112 nm obtained for phase X under static conditions. This, together with the small values of integrated intensity, suggests as well that only a small amount of material is found in this phase, likely composed of very small crystals. It is therefore not surprising that other researchers have not detected its presence,24,25 especially if the intensity plots are not studied on a logarithmic scale (Figure 4a). C. Lamellar Thickness from the X-ray Diffraction Patterns. The precise position of the diffraction peaks was used to compute the average lamellar thickness of the crystalline population, and thus, it served as an indicator of the compositional changes. The values of the lamellar thickness for phase II of BC cocoa butter at 17.5 °C are plotted as a function of time in Figure 5b. The dashed line represents the static case, whereas the solid line follows the points for 180 s-1 as an example. Initially, the lamellar thickness moves from values as large as 5.03 nm (off scale in the plot) down to 4.92 nm as the crystallization progresses in time. This variation is a consequence of the larger proportions of longer molecules (such as SOS or SLS) crystallizing initially, followed by an increase in the proportion of shorter molecules (such as POP or PLP) as time goes by. At the time of the transition to phase V, the lamellar thickness jumps back to a higher value, around 4.95 nm for all shear rates. The position of the peaks for phase V in the radial plots (e.g., Figure 4a) was consistent with a lamellar thickness between 6.46 and 6.53 nm, similar to the values reported in the literature for this phase, with a 3L longitudinal stacking.7,9,30 The trend of the lamellar thickness with time was generally downward, consistent with the accretion of molecules forming thinner lamellae as time went by. The reduction in thickness was between 0.035 and 0.06 nm during each experiment. The values of the lamellar thickness for phase X increased with applied shear rate and time, up to values between 6.8 and 7.6 nm. The precise determination of the peak position at high shear rates is difficult due to the small amount of phase X present, manifested only as a weak shoulder on the X-ray diffraction peak of phase V on a logarithmic scale. D. Experiments at a Slow Cooling Rate of 0.5 °C/min. The results for four experiments cooling BC cocoa butter at 0.5 °C/min in the large cell at 90 and 1440 s-1 and 17.5 and 20 °C are very similar to those obtained for the same conditions at fast cooling rates, in terms of phases II, V, and X. Phase II appeared during the cooling ramp 5 min prior to 17.5 °C being reached, i.e., at 20 °C, and almost exactly at the end of the ramp for the experiments at 20 °C. However, phase IV was not detected in the experiment at a shear rate of 1440 s-1 and 20.0 °C. The trajectories and the jumps in correlation length and lamellar thickness are very similar to those of the experiments at a fast cooling rate. The lamellar thickness of phase II after the transition to phase V was 0.005 nm higher than observed at the fast cooling rates, suggesting that a slightly larger proportion of long molecules had been incorporated into phase II during its initial crystallization period above 17.5 °C. E. Orientation Effects. Of the materials we have studied so far, cocoa butter has displayed the strongest orientation,2,4 i.e., a large orientation ratio χr and a small azimuthal width ∆χ. After the onset of the transition to phase V, the crystalline material, often in a mixture of phases, maintained its orientation in the



Figure 6. (a) Orientation ratio χr from the azimuthal plots of phase II before the transition to phase V. As the shear rate was increased, the proportion of oriented crystallites was larger, following a power law, above a critical shear rate that depended on the temperature. (b) The azimuthal width of the oriented portion ∆χ also followed a power law above a critical value dependent on the temperature.

cell even after the shear had been reduced to zero by stopping the motor. The orientation was observed in all phases, but for the purpose of understanding the phenomena that lead to the early phase transition, we focus here on the orientation displayed by phase II before the phase transition to phase V. Figure 6a shows the values for the orientation ratio obtained for BC cocoa butter at different shear rates. The dashed line follows a power law with an exponent of 0.647. Even in the cases where the values of the orientation ratio were low, there was an oriented portion in the azimuthal scans that allowed for a large but meaningful value of the azimuthal width to be computed, as seen in Figure 6b. At 17.5 °C we observed the highest orientation of all our experiments, i.e., the largest orientation ratio combined with the smallest azimuthal width. The strong tendency of phase II to display orientation is indicative of how easy it is for the shear field to keep the crystallites apart, as documented by the micrographs in the literature,25 a fact that will serve to explain the events happening during the phase transition to phase V. V. Discussion of the Events Happening during the Phase Transitions A. Orientation Effects. Although the particles move with the overall flow of the fluid, a velocity gradient, as seen from the frame of reference of the particle, induces a rotation in the particle. For a free small particle in the fluid this rotation can be described by a Jeffery orbit69 that results in slow motion when the longer axis of the particle is parallel to the flow lines and fast motion when it is at an angle. The resulting timeaveraged position of the particle is a preferred orientation along the flow line. Disorder introduced by Brownian movement affects small isolated particles,2 whereas larger groups of particles are affected by other types of movements such as tumbling and collisions and by the aggregation tendencies of

Figure 7. Polarized light micrographs of cocoa butter crystallized (a) statically (24 h, 20 °C) and (b) under shear (20 °C, 90 s-1). The aggregation under static conditions is in clear contrast with the segregation observed under shear.

the fat crystallites. The orientation observed at a given shear rate results from the competition of the orienting effect of the shear field against the other disordering forces. The aspect ratio (e.g., the ratio of the diameter and thickness for a disklike platelet) and the size of the particles determine how sensitive they are to be oriented by the shear field and therefore define the observed orientation ratio and azimuthal width. The azimuthal width followed a remarkably similar trend for the experiments at higher shear rates at 17.5 and 20.0 °C and at 1440 s-1 even for 22.5 °C as shown in Figure 6b. At each of the temperatures there is a shear rate value (90, 180, and 1440 s-1) above which the azimuthal width follows the power law shown by the dashed line. This power law has an exponent of -0.215. A possible explanation for this behavior is that, once a fraction of the crystalline population falls above a certain aspect ratio, characteristic for each shear rate, it can be oriented by the shear field.69 At each combination of temperature and shear rate, the system has a specific SFC and a specific crystal size distribution. The orientable fraction is larger as the shear rate is increased, but decreases with temperature. The ability to orient requires the particles to be segregated, rather than aggregated in spherical clusters.2,25 The different aggregation behavior under shear compared to static conditions is clearly seen in the polarized light micrographs presented in Figure 7. Panel a was taken after the cocoa butter was kept under static conditions at 20 °C for 1 day. The large round clusters formed are not spherulites, since they do not produce a Maltese cross under polarized light.2,25 These clusters are


packed with randomly oriented smaller crystallites, consistent with microscopy observations.25 The micrograph in panel b was taken by sampling cocoa butter 2 min after the onset of crystallization from a Couette cell rheometer at a shear rate of 90 s-1 and 20 °C and placing the suspension in a microscope glass slide. It is quite evident that the material is uniformly distributed, even at that low shear rate. It is clear that shear has a very large effect in the segregation of the otherwise selfagglomerating crystallites, as has been described in detail in the literature.25 This segregation effect is reflected in the capacity of the particles to orient in the shear field, which in turn is observed in the X-ray diffraction pattern, since the crystallites have similar shapes that correlate with their internal crystalline structure. This distribution of the crystallites across the system results in a much larger interface area between the liquid and the crystallites, which offers a much larger number of potential nucleation sites for the secondary crystallization of other polymorphs.4 We believe that this effect of shear provides a very important contribution to the reduction of onset times of phase V. Our estimates of the particle sizes from the micrographs suggest that most of our crystals had a thickness smaller than a few micrometers. This is consistent with crystal sizes reported in the literature.70 Hence, the observed “crystals” appear as collections of many distinct crystallites stacked on top of each other.25 B. Phase Transitions from II to V + X. The information from the integrated intensity, correlation length, and lamellar thickness, together with the orientation parameters for phases II, V, and X, can be combined to create an explanation of the processes occurring during this complicated phase transition, supported as well by the microscopy observations from the literature.25 It can be seen in Figure 4b that the amounts of phase X and phase II that were present after the transition were in direct proportion to the amount of phase II present before the transition. Conversely, the amount of phase V obtained after the transition bears an inverse relationship to the maximum amount of phase II present before the transition. The changes in correlation length reflect changes in the averaged size of the crystallites, while the changes in lamellar thickness reflect changes in their average composition. The summary of the values for both parameters before and after the phase transition at 17.5 °C can be seen in Figure 8, with the symbol convention indicated in Figure 3a. At the phase transition to phase V, there is a sudden increase in the correlation length for phase II, as seen by comparing the open triangles (before transition) to the filled triangles (after transition) in Figure 8a. This increase is rather puzzling since the total amount of phase II was reduced, while the average size of the crystallites became suddenly larger. A possible explanation is to assume a broad crystal size distribution in the crystalline population at low shear rates.25 This would cause the smaller crystallites to melt, and only the larger ones would survive, thus producing a larger average size for phase II. This selective melting of the smaller crystallites of the population, and likely a partial melting of the external layers of larger crystallites, is consistent with the compositional change reflected by the lamellar thickness, since the smaller younger crystallites are made of material poor in HMF as are the late layers of the larger crystallites.

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Figure 8. (a) Correlation lengths ξ and (b) lamellar thickness d as a function of the shear rate γ˘ . The points for phase II (4, ×) were taken just before the transition to phase V and those for phases II (2), V (9), and X (f) 20 min after the crystallization temperature was reached. Please note each phase has its own scale, all in nanometers, indicated by the corresponding symbol at the bottom. The correlation length values for phase V are about half those for phase II, indicative of a smaller size. The size seems to increase with the shear rate for phases II and V and decrease for phase X. The lamellar thickness d of phase II and phase X increased with the shear rate, suggesting that their compositions are closely correlated. The d values for phase V followed the opposite trend, likely correlated with the composition of the remaining liquid, with the exception of 1440 s-1.

The lamellar thicknesses for phase II before (open triangles) and after (filled triangles) the transition to phase V are summarized in Figure 8b. It can be seen that the lamellar thickness of phase II increased after the transition; i.e., the crystallite population of phase II after the transition had a larger average lamellar thickness than the population just before the transition, as if the population had returned to a value of the lamellar thickness consistent with that of an earlier stage of its formation. Since the lamellar thickness is related to the composition of the phase, it is likely that the material of the surviving crystallites of phase II belongs to the older part of the crystallites, i.e., those formed early in the crystallization, and, according to the information from the correlation length, to the larger ones as well. The strong linear relationship between the lamellar thickness of phase II before the transition (open triangles) and phase X (filled stars) after the transition is clear in Figure 8b. This dependency suggests that the materials composing phase X came mostly from the part of phase II that melted in the transition due to the sudden highly exothermic formation of phase V. Thus, it would make sense that the amount of phase X formed has a direct relationship to the amount of phase II present before the transition, as seen in Figure 4b. The average values of the lamellar thickness for the melted portion of phase II were estimated using a weighted integrated intensity average. The subindex “b” is used to indicate the data before the phase transition, the subindex “a” to indicate data after the transition to phase V, whereas the subindex “m” is used for the melted portion. I represents the integrated intensity of phase II and d the lamellar thickness.

Ibdb ) Iada + (Ib - Ia)dm dm )

Ibdb - Iada (Ib - Ia)

(1)


Figure 9. Sketch describing the phase transition behavior at 17.5 °C. The left-hand side shows three snapshots before the phase transition, at different shear rates, with only phase II crystals present, indicated as rectangles. (a) At low shear rates, γ˘ the crystal size distribution is broad, and the older larger crystals have a multilayer structure with the material crystallized early (large d values) in the core and that crystallized recently (smaller d value) at the surface. The younger smaller crystals are composed of smaller d value molecules. (c) At high shear rates, the crystal size distribution of phase II is rather narrow and the crystallites are likely to have similar average compositions, even if they have a gradient between the core and the surface. The right-hand side of the sketch shows the material after the phase transition. Phase V is represented by small polygons and phase X by white ellipses. At the high shear rate, all the crystallites of phase II melt and only the newly formed phase V crystallites remain. At lower shear rates, the smaller crystals disappear during the phase transition and only the cores of the larger crystallites remain, thus explaining the increase in the average size and the reduction in the d value of the surviving phase II. Phase X is formed from part of the melted phase II.

The resulting values of dm are plotted with the symbol × in Figure 8b up to 360 s-1. Above this value, all phase II was melted and Ia f 0, making dm ) db. The linearity with the d values of phase X is striking, thus reinforcing the hypothesis that phase X probably is formed from material melted directly from phase II. It can also be seen in Figure 8a that the thickness of the phase V crystallites increased with shear, even though the values are about half those for phase II. The lamellar thickness values of phase V in Figure 8b decrease with increasing shear. The composition of phase V, accordingly, is defined by its primary source material, which is the liquid phase coexisting with phase II before the transition, as has been shown clearly in the microscopy work of Sonwai et al.25 where phase V is seen engulfing the preexisting crystallites of phase II. D. Crystalline Compositions before and after the Phase Transition to Phase V. Putting together the several pieces of this puzzle, Figure 9 emerges as a summary picture of what may be happening during the transition to phase V. Each horizontal band represents a snapshot in time of the situation before and after the phase transition to phase V. The top band represents the scenario at lower shear rates, the bottom band at high shear rates, and the middle band at an intermediate shear rate. The left-hand side is the situation before the phase transition, where only phase II is present, and the right-hand side depicts the situation that results after the phase transition, where phase V may or may not coexist with phases II and X, depending on the shear rate applied. Let us first take a look at how the crystals are formed as time goes by to reach the snapshot that we see just before the phase transition to phase V on the left-hand side of the figure. From our X-ray diffraction patterns, we observed that, under both static and sheared conditions, the phases that had a clearly


defined peak showed a displacement of the peak position, consistent usually with going from a larger to a smaller lamellar thickness. These changes are small but significant. They are due to the progressive change in composition of the crystallizing material.9,11,14,31 This change is not a sharp transition from one species to another, i.e., not simply that SOS crystallizes first and then POS crystallizes. The change is a progressive variation in the ratio of TAGs that are cocrystallizing at a given time on the external surface of the crystallites. Since the crystallization process takes place by nucleation and growth, the younger crystals have a composition different from that of the older ones, and it is likely that the older crystals have layers of slightly different composition, as illustrated schematically in Figure 9a. At higher shear rates, as depicted in (c), the particle size distribution of the population is more uniform than at low shear rates (a), resulting in a population of smaller crystallites, as shown by the microscopy study of Sonwai et al.25 They are also more uniform in size and probably in composition. Conversely, low shear rates result in a population with a broader particle size distribution25 and likely a corresponding broader compositional distribution of crystals. Below a certain value of shear, the population size distribution includes crystals that are large enough to survive the melting at least partially, as shown in (a), consistent with the micrographs published recently.25 After the transition a small amount of phase II is left. However, not all the material melted from phase II recrystallizes as phase V. Part of it crystallizes as phase X, represented by the white ovals in the figure, following the proportions observed in Figure 4b, and explaining the correlation between the values of the lamellar thickness of phase II before the transition and the values of the lamellar thickness of the resulting phase X, as seen in Figure 8b. The amount of melted phase II, estimated from the proportionality factors, was more or less constant in each case, about 6.5% SFC for the experiments at 17.5 °C. Part of the melted material would have recrystallized as phase X, although inclusion of material from the liquid cannot be excluded. At lower shear rates, the proportion of phase II that survives the transition grows larger, and so does the amount of phase X formed, since it depends on the amount of preexisting phase II. The amount of phase V formed is reduced at lower shear rates, since the total SFC is made up of a mixture of three phases. At higher shear rates (c) the distribution of crystal sizes and compositions is more uniform, and at the moment of the formation of phase V, all the crystallites of phase II are melted, so that after the transition only a large quantity of crystals of phase V is left. This is consistent with microscopy observations recently provided in the literature.25 This mechanism developed to explain the main trends observed in the 17.5 °C experiments is applicable as well for the 20 °C experiments and for the low shear rate experiments at 22.5 °C, as far as the transition from phase II to phases V and X is concerned. However, above certain shear rates phase IV appears at 20.0 °C, and it always appeared at 22.5 °C. The discussion of the mechanisms relevant to these conditions is presented in the next section. C. Phase Transitions Including Phase IV. As the temperature is increased the phase scenario is further complicated by the introduction of phase IV. At 20.0 °C it was observed at 1440 s-1 for BC cocoa butter and above 360 s-1 for the CZ cocoa butter.3 Other authors did not observe its presence at 20 °C perhaps due to the use of a different cocoa butter3,25 or the use of very low shear rates.24 At 22.5 °C its presence was observed in all our experiments. In the shear experiments phase


IV appeared initially only as a weak shoulder on the strong X-ray diffraction peak from phase II and survived the phase transition to phase V much better than phase II, which disappeared rapidly.3 There was no clear effect of the shear on the onset time of phase IV, although its determination is difficult given that it is a very slowly growing shoulder. The maximum integrated intensity of phase IV under shear at 20 °C was much smaller than the values obtained under static conditions. The comparison at 22.5 °C would require longer experiments. The correlation lengths of phase IV at 20 °C were in a range similar to the 52.3 nm observed under the static conditions. A progressive increase in correlation length with time was observed under shear in the cases where the peak was better resolved, mostly at high shear rates and 22.5 °C, from 41.9 to 57.1 nm. As mentioned earlier, a very large variation in the peak position of phase IV was observed in the static experiments. The average lamellar thickness corresponding to the position of the peak in the static crystallization went from 4.69 to 4.46 nm. In the shear experiments the determination of the peak position was often difficult before the peak became well resolved from the phase II peak. In the experiments at 22.5 °C with CZ cocoa butter, the peak position shift resulted in an increase of the lamellar thickness as the shear was increased. This indicates that the species preferentially crystallized are of smaller size than the average, as was the case with palm oil,4 because phase II had already incorporated a large portion of the crystallizable HMF and the liquid was enriched with LMF, where POP predominates. The formation of phase IV under shear coincided with an onset of decreasing intensity in phase II, so the independent initial growth mechanism observed under static conditions is not obvious under shear. However, the rate of formation of the phase was still more gradual compared to the “catastrophic” events that happened when phase V was formed. When phase V was formed in the presence of phases II and IV (e.g., CZ cocoa butter, 22.5 °C, 45, 90, and 180 s-1), the growth of phase IV stopped and its integrated intensity started to decrease slowly, while phase II was reduced considerably faster. The crystallization enthalpy for the β polymorph (phase V) of many TAGs is 2 times larger than that of the R polymorph (phase II), while the corresponding β′ polymorph (phase IV) is only about 30% higher. The difference in latent heat and melting temperature can partially explain the difference between the kinetics of formation of phases IV (a β′ type) and V (a β type). The crystalline orientation in phase IV, although weak, was observed to increase with shear rate, in a fashion similar to that observed for phase II. If we imagine bringing the picture in Figure 9 to a higher temperature, the first thing we would notice is a general reduction in the amount of crystalline material. As the temperature is increased, the relative supersaturation for each potential phase is reduced. The composition of the liquid in contact with phase II is different at each temperature as well. At some temperature-shear combination, this liquid will preferentially form phase IV rather than jump into phase V; i.e., there is a crossover of the relative energies of activation of nucleation and growth of the two phases, depending on the temperature and shear rate applied. Eventually, at the lower shear rates, phase V is formed simultaneously with very small amounts of phase X. Longer time experiments will be necessary to better characterize this temperature-shear space.

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VI. Conclusion The use of synchrotron X-ray diffraction has allowed us to probe directly into the evolving crystalline structure of cocoa butter, following its crystallization growth and phase transitions under controlled conditions of cooling rate, crystallization temperature, and applied shear rate with unprecedented detail. On the basis of a careful analysis of the integrated intensity, precise lamellar thickness, correlation length, and crystalline orientation, we have drawn a possible picture of the phase change process. The picture includes the generally accepted idea that the crystallites grow layer after layer, each having slightly different compositions, and the shear rate and temperature define these compositions. The shear rate, cooling rate, and temperature define as well the crystalline surface area available for nucleating new phases by affecting the crystal size distribution and the segregation of the crystallites. The segregation of crystallites is a specific shear effect. It plays a very important role in the modification of the kinetics of the phase transitions. If the crystallites are tightly clustered, it is more difficult to produce large structural changes, and in a static system the concentration gradients induced in the liquid span longer distances, making the transport processes more difficult than for a collection of segregated particles in contact with a well-mixed liquid. In the presence of crystallites in a suspension, a small amount of shear is enough to enhance mixing, even if the flow regime is still laminar. The segregation also results in a much larger active interface area between the liquid and the solid phases than under static conditions where agglomeration is present. This larger area increases the number of nucleation sites available for new phases to appear and thus boosts the probability of nucleation onset. Shear is also likely to produce a significant enhancement of heat transfer and to foster crystallite collisions. The precise temperatures at which phenomena appear to happen may depend on the different compositions of the material used and on the method for measuring the temperature and the cooling rates of the sample, which may vary from system to system. However, the general trends and mechanisms have proven to be consistent for different types of cocoa butters in different devices. We are aware that our proposed model has not solved all the questions and that experiments that can directly test at a molecular level the hypothesis of secondary nucleation are needed. However, the microscopy work and the shear step experiments of Sonwai et al.25 support our hypothesis, which was drawn independently from X-ray observations. Our contribution, in line with the efforts of many previous investigators, stresses the need to incorporate the multicomponent nature of fats into multicausal models; there does not seem to be a simple explanation. Acknowledgment. We thank Steve Bennett for technical assistance at the ExxonMobil synchrotron beamline. Funding was provided by the National Sciences and Engineering Research Council of Canada and the Canadian Advanced Food and Materials Network. Research was carried out in part at the NSLS, Brookhaven National Laboratory, New York, which is supported by the U.S. DOE, Division of Materials Sciences and Division of Chemical Sciences. References (1) Marangoni, A. G.; McGauley, S. E. Cryst. Growth Des. 2003, 3, 95-108.

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A Conceptual Model for Shear-Induced Phase Behavior in

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