External factors affecting polymorphic crystallization of lipids

Many physical properties (e.g., hardness, texture, rheology, and spreadability) of lipid-based products largely depend on the extent of crystallization and transformation of lipids, and their network formation. Therefore, many studies have focused on controlling the crystallization of lipids in order to determine the functionality of lipid crystals. Both internal and external factors greatly affect the processes of lipid crystallization. The most important internal factors are polymorphism, which depends on variation in fatty acid moieties, and the composition or blending of different lipid materials. Important external factors are thermal treatment, additives, application of shear, sonication, and pressure. This paper briefly reviews recent advances in research on these external factors. We discuss the results by considering the relationships between external factors and thermodynamics, as well as kinetic properties of the crystallization and transformation of polymorphic forms of lipid crystals.

ccep t e d A Arti cle directly influenced by nucleation behavior.
A major problem in controlling the polymorphic crystallization of lipids is clarification of how a specific polymorphic form starts to nucleate in comparison with other polymorphic forms. The Ostwald step rule is useful in clarifying the behavior of multiple polymorphic forms when they are crystallized from vapor, solution, and melt phases. This rule dictates that less stable polymorphic forms crystallize much faster than more stable forms when the driving force for crystallization is supplied by decreasing the temperature, and that less stable forms stepwise transform to more stable forms during the storage processes after crystallization.
Actually, the kinetic behavior of polymorphic nucleation of various systems (e.g., biominerals [7,8] and drug materials [9,10]) often follows this rule. For example, a metastable vaterite form crystallizes faster than the more stable calcite in CaCO 3. However, more detailed studies are needed to examine the effects of external factors, and it is necessary to establish some rules regarding the influences of kinetics on polymorphic crystallization and to study situations where the Ostwald step rule may be complemented.
Recent studies on the polymorphic crystallization of lipids under various external factors have indicated that the Ostwald step rule is insufficient, and more detailed studies are needed to examine the effects of external factors on polymorphic crystallization. One example is the effects of cooling rate on the competitive nucleation rates of three polymorphs of a TAG (Fig. 2) [1].
A general tendency in melting temperature (T m ) is that the T m s of less stable forms are lower than those of more stable forms. For the three typical polymorphs of TAGs, T m is lowest for α, intermediate for β', and highest for β. When crystallization occurs from the neat liquid, the relative rates and extent of crystallization of these three polymorphs are determined by the rate of nucleation, which is governed by the magnitude of activation free energy for nucleation, ΔG # .
We may reasonably assume that the values of ΔG # are smallest for α, intermediate for β′, and largest for β (Fig. 2a). The nucleation rate thus increases with increasing ΔT most rapidly for α and most slowly for β (Fig. 2b). The rate of nucleation J is most simply expressed as J = A exp(-ΔG # /RT), (1) ccep t e d

A Arti cle
where ΔG # is the activation free energy for nucleation, A is a kinetic factor including transfer rates of mass and heat and attachment/detachment rates of lipid molecules among clusters and liquid, R is the gas constant, and T is temperature [6]. ΔG # can be expressed by where K is a constant, γ is interfacial energy between the crystal nucleus and liquid, and Δμ is the chemical potential difference between the supercooled liquid and crystal expressed in where ΔH m is enthalpy of melting.
Having determined the polymorph-dependent nucleation rates, we may now determine the nucleation rates for the three typical polymorphs of TAG (α, β', and β) at different crystallization temperatures. Since T m is highest for β, nucleation starts in the range of T c far above those of α and β'. Then β' and α start to nucleate with decreasing T c , and competitive nucleation occurs in a range of T c below T m of β' and α (Fig. 2b).
From graphical consideration, we assume that the most preferred nucleation of β may occur in the range of T c between T m of β and the crossing temperature of the two nucleation rates of β and β'. On further cooling, the nucleation of α starts quite rapidly below T m of α. Therefore, it can be assumed that the preferred nucleation for β' may occur in the range of T c between the crossing temperatures of the nucleation rates of β and β' and those of α and β'.
From the polymorph-dependent nucleation rate and the effects of the cooling rate on preferred nucleation, we can assume that the preferred nucleation may change from α to β' to β with a decreasing cooling rate. This behavior was recently observed for many TAGs, as discussed below.
Crystal growth proceeds through the incorporation of lipid molecules at the interface of growing crystals after nucleation, which takes place at molecular-level step-kink positions ( Fig. 1). We may predict that the additives may retard the incorporation of the lipid molecules at the step-kink positions when they are adsorbed at the kink position and reject the incorporation of lipid molecules. The metastable and more stable polymorphic forms of lipids are greatly influenced by dynamic temperature variations, such as cooling rate, heating rate, and thermal thawing (tempering). These effects are highly significant for applications in the pharmaceutical, biomedical, and food areas, since specific polymorphic forms should be crystallized by tailoring the most efficient thermal treatment.

Solid
(1) Effects of cooling and heating rates The role of thermal treatment in the crystallization and transformation of lipids has been studied for model fats [13][14][15][16][17], natural lipids [18][19][20][21][22][23][24], emulsion [25], and end products [26,27]. observed that higher oil content increased the stability of emulsions when the cooling rate was high, whereas emulsion stability increased with decreasing cooling rate for emulsions formulated with lower amounts of oil [25]. The key to understanding this opposing effect may be the nucleation and further growth of crystals fats, which affect emulsion stability.
Cooling rates may act through the effects of ΔT, which increases with increasing cooling rates, causing increased crystallization rates. Transmission electron microscope (TEM) observation of nanometer-scale fat crystals grown from organic solution indicated that fast cooling rates and application of shear significantly decreased the dimensions of fat crystals [28,29]. Figure 4 depicts changes in the length, width, and thickness of the crystals of fully hydrogenated canola oil (FHCO) [29]. FHCO was mixed with high oleic sunflower oil (HOSO) at different concentration ratios (solid mass fraction (SMF)), which was defined by SFC/100 (SFC: solid fat content), and crystallization was conducted at fast (10 ºC/min) and slow (1 ºC/min) cooling rates.
Nanocrystal dimensions clearly became smaller as the cooling rate increased, and the extent of decrease was more pronounced at lower SMFs. The effects of heating rates after crystallization appear either in solid-state or meltmediated transformations, whose kinetics are determined by activation energies for the transformation and the heating rates.
For example, POP possesses seven polymorphic forms (T m ): α (15.2ºC), γ (27.0ºC), δ (29.2ºC), β' 2 (30.3ºC), β' 1 (33.5ºC), β 2 (35.1ºC), and β 1 (36.7ºC) [41]. The crystallization and transformation pathways of the polymorphs of POP indicate that more stable forms developed in higher quantities when POP was slowly cooled and heated, whereas less stable forms developed at higher cooling and heating rates. Figure   5 presents DSC cooling and heating patterns and wide-angle SR-XRD patterns during cooling at 2ºC/min, and heating at 2ºC/min and 1ºC/min. The SR-XRD patterns indicate that α was crystallized by cooling and transformed to γ and β (here, the two β forms were not separated), and finally β melted during the heating. However, the transformation mechanisms from α to γ differ between the heating rates of 2ºC/min and 1ºC/min, since the melting of α and successive crystallization of γ occurred at a heating rate of 2ºC/min (melt-mediated transformation). This can be shown as an endothermic peak of melting of α, which was associated with an exothermic of re-crystallization of γ shown in Fig. 5 Table 1 indicates the crystallization and transformation behavior of POP polymorphs at different cooling and heating rates observed using DSC and SR-XRD [39].
Specifically, less stable α and γ forms were directly obtained at cooling rates of 15 to 0.5ºC/min. More stable forms of β' (β' 1 and β' 2 ) or β (β 1 and β 2 ) did not develop even at a cooling rate of 0.5ºC/min. Polymorphic transformations occurred either in solidstate or melt-mediated transformation, which was influenced mainly by heating rate. Figure 6 illustrates the relationships between the nucleation rates of α, γ, and β' of POP and the cooling rates and suggests that α can preferentially be nucleated in a low T c region (α-dominating region), γ in an intermediate T c region (γ-dominating region), and β' in the highest T c region (β'-dominating region). Therefore, we may expect that the cooling rates of 15ºC/min and 2ºC/min may reach the α-dominating region, and that those of 1ºC/min and 0.5ºC/min may reach the γ−dominating region. More stable polymorphs of the β' and β forms could be obtained only by cooling POP at rates much lower than 0.5ºC/min.
The complex transformation pathways observed during heating (summarized in Table   1) can be understood by comparing the induction time for the transformation pathways with the time allocated to the samples for transformation (transformation time) at a defined heating rate [39].
τ ss = A 1 exp (ΔG ss # /RT) Here, A 1 to A 3 are coefficients, R is the gas constant, T is temperature, ΔG ss # is the activation Gibbs free energy for solid-state transformation, ΔG mm # = ΔG m # +ΔG c # is that for melt-mediated transformation including melting of less stable forms and crystallization of more stable forms, and ΔG m # is that for melting.
Obviously, the induction time for the transformation increases as ΔG # increases. It is reasonable that ΔG m # is much smaller than the others, and that ΔG ss # and ΔG c # increase when the polymorphic form becomes more stable, as the crystal packing of the more ccep t e d A Arti cle stable form is more stabilized than that of less stable forms. This may apply to α, γ, β', and δ of POP in such a manner that ΔG ss # for γ→β', γ→δ, and δ→β may be greater than that of α→γ. Similarly, ΔG c # is clearly greater for β' and γ than for α. Therefore, the following relationships can be obtained.
As the heating rate is increased, the time for the polymorphic form to transform into more stable forms is decreased, as expressed in r -1 , where r is the heating rate. This is applied to very low heating rates of α→γ (1ºC/min and 0.1ºC/min) and γ→δ (0.1ºC/min).
Finally, the transformation pathways clearly tend to change from solid-state to meltmediated and simple melting when the starting polymorph changes from α to γ and the heating rate is increased (Table 1).
(2) Thermal thawing (tempering) Thermal thawing (cooling-heating-cooling cycle) can produce optimal polymorphic forms through melt-mediated or solid-state transformation. Such a process is often called tempering, as applied to confectionary fats [42] and creams [43]. Tempering was also applied to form organogels using high-melting fats [46,47].
During this tempering process, the least stable α crystals of high-melting fats were formed by very rapid cooling, and subsequent reheating caused melt-mediated transformation into β form. The β crystals were so tiny compared with those formed by simple cooling, that organogel (β-fat gel) was formed. Figure 7 illustrates the formation process of β-fat gel composed of high-melting fat (fully-hydrogenated rapeseed oil rich in behenic acid (FHR-B)) and liquid oil (sal fat olein) [46]. The T m of α form FHR-B crystals is 29°C and that of β form is 47°C at a concentration of 5wt.% of FHR-B in liquid oil. When crystallization was performed through process A, the molten mixture was slowly cooled to a temperature below T m (β), large β crystals of FHR-B were formed, and no gel phase was formed. In contrast, the gel phase was formed after crystallization process B, in which the molten mixture was rapidly cooled to below T m (α) and heated to a temperature between T m (βα) and T m (β).
After this tempering process, many small β crystals were formed and randomly distributed in liquid oil, which was entrapped by the β crystal network of FHR-B. Such a network was formed due to melt-mediated transformation from α to β forms, because the nucleation rate of α crystals was high enough to cause the transformed β crystals to be randomly distributed, rather than aggregated as with slow cooling process A.
The above fundamental studies on the polymorphic crystallization of fats using pure  [49]. The minor components and additives they considered were free fatty acids; mono-, di-and triacylglycerols; phospholipids; and such emulsifiers as sorbitan fatty acid esters and sucrose fatty acid esters. Their effects on crystallization included microscopic aspects (e.g., nucleation, crystal growth, morphology, heat capacity, and polymorphic stability), as well as macroscopic aspects (e.g., visual aspects, melting profiles, post-hardening, and rheology of lipid crystals). Since this review, further studies have been reported [50][51][52][53].
In basic agreement with the main findings presented in the review by Smith et al., here we elaborate on the effects of additives on the polymorphic crystallization of lipids.
It has often been observed that some additives promote the process, whereas others retard it, even when the adding conditions are similar [54].
Conditions related to the effects of additives on the nucleation of lipid crystals (Fig. 8) may be understood by considering the following four factors.
(1) Similarity in molecular shape and polymorphism It is reasonable to assume that similarity in molecular shape between the additive and the lipid, especially the fatty acid moiety, is required, as Smith et al. indicated [49]. For example, when the lipid contains long-chain saturated fatty acid moiety, an additive having the same or similar acyl chain structure may affect crystallization more than those containing short-chain or unsaturated fatty acid moieties. Such effects were observed for polyglycerine fatty acid esters having different fatty acid moieties [55].
(2) Concentration of additive There may be a critical concentration of the additive, as determined by the solubility of the additive in supercooled liquid of the lipids at T c . When the solubility of the additive is high or the concentration of the additive is lower than the solubility limit, it may not crystallize prior to the lipid during cooling, but prevent the formation of crystal nuclei of the lipid through attractive molecular interactions between the additive and the lipid molecules, due to the similarity in molecular shape (de-clustering) (Fig. 8a). Many food emulsifiers exhibit such retardation effects when added to the lipid at low concentrations [56,57].
In contrast, an additive having low solubility may crystallize prior to the lipid when the concentration of the additive exceeds its solubility limit. Additive may then act as a "template" promoting crystallization (templating) (Fig. 8b), as observed in bulk [53] and emulsion [50]. The same effect may alter the preferred nucleation of polymorphic crystallization from that without the additive, if the crystal structure of the additive can act as a template for the nucleation of a specific polymorphic form of lipid (Fig. 9), as already reported for bulk [58] and emulsion [59,60].
(3) Cooling rate The cooling rate also influences the additive effects, as noted by Smith et al. [49], and such effects may occur through the following two mechanisms.
First, additive effects are minimized when ΔT is high enough to induce spontaneous nucleation because undesired polymorphic crystals are formed without the effects of additives. Therefore, the cooling rate and the range of ΔT may not exceed optimal values, over which spontaneous nucleation can occur and diminish the effects of the additives.
Second, the cooling rate is related to the preferred nucleation of the polymorphic forms. For example, the nucleation rate of α is higher than that of β'; the relative occurrence of α exceeds that of β' as T c is lowered and the cooling rate is increased, as explained earlier (Fig. 2). However, this effect may be altered when the additive acts as a template and thus increases the nucleation rate of the more stable form more effectively than that of the less stable form. In this case, the nucleation rate of specific polymorphic form may increase with an increasing concentration of the additive and decreasing rate of cooling ( Fig. 9).

(4) Polymorphic matching
When the additive acts as a template to promote the nucleation of lipid crystals, it may selectively promote the nucleation of specific polymorphic forms. A prerequisite for this to occur may be polymorphic matching between the template crystals and the lipid crystals. The results of previous studies [60,61] may be interpreted by this mechanism.

Application of Shear
The study of fat crystallization under shear was initiated half a century ago, as we described earlier [62]. Since this review, detailed work on natural fats has been reported by many researchers [52,. These studies clearly demonstrate that applying shear increases the rates of polymorphic crystallization and transformation of lipids, and modifies the aggregation of nanocrystals of the crystal network. However, conversion from Form III to Form V was observed to be much more rapid than transformation without shear.
The mechanisms of the effects of shear on the increase in rates of crystallization and polymorphic transformation of lipids are still unclear. The promotion may be due to increased rates of heat and mass transfer, which reduce ΔG # for nucleation (Fig. 2a), thus promoting nucleation. Tiny nanocrystals then formed, causing transformation from less stable to more stable forms through recrystallization of more stable forms onto the surfaces of the less stable forms. This transformation may be facilitated by the enormous increase in surface area compared to the volume of nanocrystals. Promotion of polymorphic transformation may also be due to melt-mediated transformation, as shear may increase the local temperature within the crystallizing medium above T m of Form III.
Exciting findings related to shear include preferred orientation of fat crystal particles, which was discovered by in-situ observation of SR-XRD patterns acquired during the crystallization of various fats with two-dimensional (2D) detectors [64,68]. Such effects resulted in oriented crystal network formation; therefore, porosity and oil migration were affected when fat crystallized in a laminar flow. Figure 11 indicates the effects of shear on the orientation of tiny fat crystals present in the shear flow, as determined by SR-XRD analysis. The fat was crystallized in a Couett cell with shear applied at different temperatures (Fig. 11a). The polymorphic structure and the orientation of the crystals growing in a Couett cell were obtained simultaneously using a 2-dimensional X-ray beam detector. The former was determined by observing the diffraction angle of 2θ (2θ-extension), and the orientation of crystals was determined with respect to shear direction by observing diffraction intensity at varying azimuthal angle positions (χ-extension) at the fixed θ angle. The degree of orientation can be assessed by defining Δχ (Fig. 11b).
For example, AMF crystals grown with shear applied (1440sec -1 ) at 17ºC are β' narrow Δχ values are observed [73]. These results are in contrast to crystallization without shear, since α and β' forms crystallized at the same time and no crystal orientation was observed.
The effects of shear have practical significance for crystallization in edible fats because various macroscopic physical properties of fat crystals are changed [75][76][77][78]81].
The effects of laminar shear on crystalline orientation and the nanostructure of fat crystal networks of CB were quantified using cryogenic scanning electron microscopy (Cryo-SEM), which indicated oriented sheets of crystalline CB in the sample obtained in the laminar shear crystallizer, while spherulitic structures were observed in the statically crystallized sample. These effects increased breaking force, Young's modulus, and elastic storage modulus (G') of the solid CB materials [76,77].
Furthermore, the effect of laminar shear on the migration kinetics of liquid oil through a polycrystalline colloidal fat crystal network was characterized and quantified. A shear rate of 340sec -1 was applied, and the CB was crystallized from melt (60 ºC) to 20ºC.
The resulting solid sheet of CB was stored for seven days at 20ºC, and the crystal dimensions of CB were observed using TEM [76,77]. Statistical analysis demonstrated that shear processing significantly reduced the dimensions of the nanoparticles of CB so that a length of 2085 ±128nm and a width of 164 ±6.4nm without shear were reduced to a length of 310 ±7.3nm and a width of 138 ±5.3nm under laminar shear. The aspect ratio (length/width) was thus greatly reduced, meaning that the crystal morphology changed from needle shape to plate shape. We can reasonably assume that the combined effect of the orientation and the morphological changes of CB crystals caused reduced rates of oil migration due to the formation of a more tightly packed crystal network.
This study suggested that the migration rate of liquid oil through a polycrystalline fat crystal network can be modified using laminar shear flow. A lower migration rate was observed in shear-crystallized samples having smaller and better-oriented nanocrystals, which retard oil migration (Fig. 12) [4,78].
The kinetic processes of sonocrystallization of tripalmitin (PPP) and CB were examined with SR-XRD and optical microscopy [94]. The main observations of these preliminary experiments indicate that the nucleation rate of PPP was enhanced and induction time was shortened by ultrasound application when it was irradiated properly, and that the polymorphic Form V of CB was directly crystallized when ultrasound was applied under optimal conditions of temperature and a short period of sonication.
Martini et al. recently applied high-intensity ultrasound (HIU) to the crystallization of palm kernel oil (PKO), AMF, and shortening [96,97]. The following results were observed.
(a) HIU induced primary and secondary nucleation of fat crystals, generating smaller crystals.
(b) Consequently, harder materials were formed when HIU was applied at higher T c , as observed for AMF, and when HIU was applied after the first crystals were formed, as observed for PKO and shortening.
(c) In addition, fat crystal networks in AMF and shortening obtained after HIU application exhibited steeper and sharper melting profiles than did nonsonicated samples. Figure 13 presents the effects of applying HIU at different temperatures on induction time and viscosity of the crystallized sample of AMF [96]. Induction time was clearly shortened when HIU was applied at 26°C and 28°C, and viscosity increased as sonication time and HIU were decreased.
In-situ observation of the sonocrystallization of PPP and LLL using SR-XRD indicated that polymorphic crystallization was remarkably modified by the irradiation of ultrasound [95]. Without ultrasound application, β' and β forms were crystallized in the melt of each TAG. With ultrasound treatment of the melt, the following effects were observed: (i) marked decrease of induction times for crystallization of both PPP and LLL, (ii) increased nucleation rate, and (iii) crystallization of only β forms for both PPP with an initial crystallization temperature of 50°C and LLL with that of 30°C, and with ultrasound applied for 2sec.
Based on the dynamic nucleation of PPP and LLL crystals induced by collapsing cavitation bubbles, we proposed that a pronounced decline in induction times and an ccep t e d A Arti cle increase in nucleation rate result from the melting point shift due to high pressure pulses associated with collapsing bubbles [95].
The studies reviewed above clearly indicate that ultrasound does affect the crystallization of fats in many ways. However, we still do not know what mechanisms are responsible for these effects. To improve our knowledge and predictability in terms of desired polymorphism, induction times, and nucleation rates that are influenced by sonocrystallization, a better understanding of the following issues is crucial: (i) the establishment of a P-T phase diagram for polymorphic forms, since a primary effect of sonocrystallization may be due to high pressure when a sonication-induced cavity is collapsed, (ii) stability (lifetime) of different polymorphic forms as a function of ΔT and temperature, (iii) mechanism and lifetime of collapsing cavities, and (iv) the basic mechanism of dynamic nucleation near a collapsing bubble.

Pressure
The application of pressure has been useful in food engineering, particularly because of the viability of sterilization and protein denaturation [100]. However, quite limited trials have been conducted to analyze lipid crystallization, due to difficulty in applying high pressure on a factory scale. Most machines that apply high pressure work only in batch processing, which is unsuitable for large-scale production of food lipids.
However, in 2002 innovative technology was presented to produce food emulsion under ambient high pressure of 10 to 150MPa [101]. This high pressure was applied to promote fat crystallization in the emulsion, while the entire process was performed in continuous production lines, not by batch processing. This technology increased the rate of fat crystallization and decreased undesirable problems of grain growth of fat crystals that occur after crystallization. The result was improved efficiency of the production process in terms of time and energy.
Quite recently, Wierschem et al. conducted fundamental studies of pressure effects on fat crystallization [102,103]. They observed induction times for crystallization (induction time for nucleation) and rates of increase in crystal size (crystal growth rate) of various fats, while applying pressure and observing the crystals using an optical microscope. The results suggested that the induction time was shortened and the growth rate was increased with increasing pressures.
The above two studies clearly indicate that the application of hydrostatic pressure promotes nucleation and crystal growth of lipids. It is reasonable to assume that the ccep t e d A Arti cle underlying principle of these pressure effects is the increase in T m by pressure, as defined by the Clausius-Clapeyron equation: dp/dT = ΔH m /TΔV, (4) where dp/dT gives the slope in a p-T phase transition diagram, ΔH m is the molar enthalpy of melting, T is the temperature, and ΔV is the difference in molar volume between crystal and liquid states. When pressure is applied rapidly without any change in T c , it reaches the entire volume of supercooled liquid at the sonic speed and increases (PPP) and 37K (LLL), which is large enough to increase the rates of nucleation and crystal growth One specific advantage of applying pressure is that, as mentioned above, the pressure is applied to the whole body of liquid of lipids quite quickly (1μsec per centimeter).
This may be in contrast with thermal treatment, whose kinetics is governed by thermal conductivity of the liquid of lipids (4min per centimeter). However, the machines used to apply high pressure in the continuous production line must tolerate an inner pressure as high as several hundred bars, which may be the effective pressure range to promote fat crystallization.