Interdroplet heterogeneous nucleation of supercooled liquid droplets by solid droplets in oil-in-water emulsions

The crystallization of oil droplets inn-hexadecane oil-inwater emulsions was monitored by pulsed nuclear magnetic resonance (NMR). The emulsions initially contained an equal mixture of solid droplets and supercooled liquid droplets at either 6 or 8°C. The degree of crystallization in the droplets was determined by measuring the NMR signal 30 μs after a 90^o radio frequency pulse was applied to the sample. The signal from the solid droplets decayed rapidly after the radio frequency pulse, allowing the measured signal to be related to the fraction of liquid droplets. No crystallization was observed in a sample that contained only supercooled liquid droplets, but crystallization was observed when solid droplets of the same material were present. This indicated that crystallization was induced in the liquid droplets by the solid droplets and was most likely caused by interactions between solid and liquid droplets-that is, by interdroplet heterogeneous nucleation. The rate of induced crystallization decreased as the viscosity of the continuous phase was increased and the size of the droplets was increased, but was independent of droplet concentration (20–40%).     

Bloom Formation on Poorly-Tempered Chocolate and Effects of Seed Addition

Bloom on chocolate with different levels of cocoa butter seed addition was investigated. When insufficient cocoa butter seed crystals were added to give proper temper, the chocolate developed bloom as dark brown spheres in lighter color areas, similar to that seen in bloom on untempered chocolate. These dark colored spheres overlapped and the lighter color areas disappeared with increasing seed amount added. The relationship between seed amount and lighter color area (bloom), as quantified by image analysis, showed that over 270 ppm seeds (fat basis) were needed to accomplish good tempering. The cocoa butter crystallization behavior with various amounts of seed was observed by light microscopy. Too few seeds caused sparse β crystallization and massive β′ crystallization, which explains the appearance of poorly tempered chocolate bloom. As seed amount increased, β crystallization of cocoa butter took less time to reach the upper level of solid fat content and the size became smaller. In addition, DSC analysis was carried out to study crystallization and melting behavior of cocoa butter with different seed amounts. Higher levels of added seeds resulted in greater amounts of β crystal formation and the crystallization temperature increased, which meant crystallization occurred earlier. These results showed that the mechanism of bloom formation on poorly tempered chocolate (insufficient seeds) is due to sufficient time and space for phase (particles and fat) separation as the stable polymorphs grow.     

Dynamic crystallization of cocoa butter. II. Morphological,thermal, and chemical characteristics during crystal growth

After an induction period, crystallization of cocoa butter under dynamic conditions at 26.5°C occurs in two stages, primary and secondary. The primary stage involves nucleation, crystal growth, aggregation, and sintering. Crystals formed during the primary stage were slightly or non-birefringent, and had long, irregular-shaped filaments. The secondary stage was initiated by the formation of spherulites. Total crystallization time may depend upon the crystal growth rate in the primary stage and the time that coca butters take to form the spherulitic crystals in the secondary stage. After the spherulitic crystals formed, the crystal growth rates were rapid. Cocoa butters crystallized into two fractions during the primary and secondary stages. The low-melting fractions had onset melting temperatures similar to those of polymorphs IV and V of cocoa butter. The high-melting fractions, which were observed at the latter stages of crystallization, had differential scanning calorimetry endotherms with peak maxima at approximately 34–36°C (Form VI). The concentrations of 1,3-stearoyl-2-oleoylglycerol (SOS) in the crystals during growth were higher than those in the original cocoa butter. As crystallization progressed, crystals increased in their proportions of SOS in the triacylglycerol fraction. Concentrations of the C₁₈ free fatty acids were lower during early crystallization as compared to the original cocoa butter.     

Seeding effects on solidification behavior of cocoa butter and dark chocolate. I. Kinetics of solidification

Effects of seeding of fat crystals on the crystallization kinetics of cocoa butter and dark chocolate were examined with a rotational viscometer. The seed crystals employed were cocoa butter, 1,3-distearoyl-2-oleoylglycerol (SOS), 1,3-dibehenoyl-2-oleoylglycerol (BOB) and 1,2,3-tristearoylglycerol (SSS). The seed powders were prepared by pulverization below —50°C, the dimensions being in a range from 20–70 μm. Particular attention was paid to the influence of polymorphism of the seed crystal. We found that all of the above seed materials accelerated the crystallization, the degree of acceleration being in a following order; SOS (β ₁) > cocoa butter (Form V) > SOS (a mixture ofβ’ andβ ₂) > BOB (β ₂) > BOB (pseudo-β’) > SSS (β). Precise measurements of the crystallization kinetics showed that the most influential factors in the seeding effects are the physical properties of the seed materials—above all, thermodynamic stability, and similarity in the crystal structure to cocoa butter are the most determinative.     

Dynamic crystallization of cocoa butter. I. characterization of simple lipids in rapid- and slow-nucleating cocoa butters and their seed crystals

Six cocoa butters with different crystallization induction times and their seed crystals were analyzed for simple lipid composition. The rapid-nucleating cocoa butter samples had higher concentrations of 1-palmitoyl-2-oleoyl-3-stearoylglycerol and 1,3-stearoyl-2-oleoylglycerol (SOS), and lower concentrations of the diunsaturated triacylglycerols, 1-palmitoyl-2,3-oleoylglycerol and 1-stearoyl-2,3-oleoylglycerol, as well as higher stearic acid concentrations within their diacylglycerol fractions when compared to the slow-nucleating samples. At the early stages of crystallization, under agitation conditions at 26.5°C, cocoa butters solidified into two fractions, high-melting and low-melting. The low-melting fractions were composed of polymorphs IV and V of cocoa butter, as indicated by the onset melting temperatures of the endotherms from differential scanning calorimetry. The high-melting fractions, which had wide melting ranges, had peak maxima of 38.5–52.2°C. Seed crystals isolated at the early stage of crystallization were characterized by high concentrations of complex lipids, saturated triacylglycerols, saturated fatty acid-rich diacylglycerols, and monoacylglycerols. The rapid-nucleating seed crystals had higher concentrations of SOS when compared to their respective cocoa butters. The slow-nucleating seed crystals did not exhibit this characteristic.     

Crystallization Kinetics of Cocoa Fat Systems: Experiments and Modeling

Isothermal crystallization kinetics of unseeded and seeded cocoa butter and milk chocolate is experimentally investigated under quiescent conditions at different temperatures in terms of the temporal increase in the solid fat content. The theoretical equations of Avrami based on one-, two- and three-dimensional crystal growth are tested with the experimental data. The equation for one-dimensional crystal growth represents well the kinetics of unseeded cocoa butter crystallization of form α and β′. This is also true for cocoa butter crystal seeded milk chocolate. The sterical hindrance due to high solids content in chocolate restricts crystallization to lineal growth. In contrast, the equation for two-dimensional crystal growth fits best the seeded cocoa butter crystallization kinetics. However, a transition from three- to one-dimensional growth kinetics seems to occur. Published data on crystallization of a single component involving spherulite crystals are represented well by Avrami’s three-dimensional theoretical equation. The theoretical equations enable the determination of the fundamental crystallization parameters such as the probability of nucleation and the number density of nuclei based on the measured crystal growth rate. This is not possible with Avrami’s approximate equation although it fits the experimental data well. The crystallization can be reasonably well defined for single component systems. However, there is no model which fits the multicomponent crystallization processes as observed in fat systems.     

Microstructures formed by spray freezing of food fats

The spray-freezing of two food fats, tripalmitin (PPP) and cocoa butter (CB) and mixtures thereof, has been modeled experimentally using a novel single droplet freezing apparatus configured so that temperature profiles or samples for microstructure analysis can be obtained. For 2 mm diameter droplets suspended in a cold air flow at temperatures around 2–15°C, initial cooling rates were on the order of 10 K s⁻¹ and the temperature profiles could be correlated directly to DSC data collected at 20 K min⁻¹, indicating that minimal supercooling of the materials occurred in the droplet form. Microstructure analysis confirmed that PPP crystallized preferentially in mixtures, and that the surface structure was very sensitive to storage conditions. The bulk structure was much less sensitive, and the internal microstructure of the PPP droplets revealed distinct nucleation sites, which were absent from the CB: These persisted in the mixtures up to 50 wt%. X-ray analysis indicated that the fats crystallized in their more stable forms, namely, β for PPP and Form V/V1 in CB.     

Effects of ultrasonic irradiation on crystallization behavior of tripalmitoylglycerol and cocoa butter

Effects of application of ultrasonic power (20 kHz, 100 W) on the crystallization behavior of tripalmitoylglycerol (PPP) and cocoa butter have been examined in terms of rate of nucleation and polymorphic control. High-purity PPP (>99%) and low-purity PPP (>80%) samples were employed to mimic real fat systems, which usually have higher concentrations of minor components in addition to the main component. For both the high-purity and low-purity PPP, the application of ultrasonic power accelerated the rate of nucleation as measured by induction time for the occurrence of crystals and by the number of crystals nucleated. As for the polymorphic influences, the nucleation of both the β′ and β forms was accelerated by the ultrasound, yet the β′ form nucleation was more accelerated when the low-purity PPP samples were employed. As for cocoa butter, sonication for a short period accelerated the crystallization of Form V. The present results indicate that ultrasound irradiation is an efficient tool for controlling polymorphic crystallization of fats.     

Seeding effects on solidification behavior of cocoa butter and dark chocolate. II. Physical properties of dark chocolate

Demolding property just after solidification, we examined the polymorphism of cocoa butter in seed-solidified dark chocolate and fat-bloom stability through two thermocycle tests between 38 and 20°C (38/20) and between 32 and 20°C (32/20). The seed crystals employed are Form VI of cocoa butter,β ₁ of SOS (1,3-distearoyl-2-oleoyl-glycerol), pseudo-β’ andβ ₂ of BOB (1,3-dibehenoyl-2-oleoylglycerol) and β of SSS (1,2,3-tristearoylglycerol). The influence of the seed concentration was also examined. The seeding of cocoa butter (Form VI) and SOSβ ₁ caused the crystallization of Form V of cocoa butter and exhibited better demolding. As to the fat-bloom stability, the two, seed crystals were effective through the 32/20 cycle test, but the fat-bloom occurred through the 38/20 test. The seeding ofβ ₂ of BOB caused better demolding, crystallization of Form V of cocoa butter, and the most preferable fat-bloom stability; particularly, the seeding of 5 wt% concentration ofβ ₂ of BOB completely prevented the fat-bloom after the 38/20 test, although the seeding of all of the other materials and conditions caused the fat-bloom by this thermo-cycle test. The seeding of pseudo-β’ of BOB did not prevent the fat-bloom, although the demolding property was improved. In the case of the seed of β of SSS, both the demolding and fat-bloom stability were not improved. We concluded that the seeding ofβ ₂ of BOB revealed the most desirable, influences on the demolding and the fat-bloom stability of dark chocolate. This conclusion suggests the usage ofβ ₂ of BOB as the most preferable seed material in the solidification of dark chocolate, since the crystallization rate was also enhanced by this material as described in Paper I.     

Kinetics of nucleation and growth of L-sorbose crystals in a continuous MSMPR crystallizer with draft tube: Size-independent growth model approach

The experimental data concerning kinetics of a continuous mass crystallization in L-sorbose - water system are presented and discussed. Influences of L-sorbose concentration in a feeding solution and mean residence time of suspension in a working volume of laboratory DT MSMPR crystallizer on the resulting crystal size distributions, thus on the nucleation and growth kinetics, were determined. The kinetic parameter values were evaluated on the basis of size-independent growth (SIG) kinetic model (McCabe’s ΔL law). It was observed that within the investigated range of crystallizer productivity (220–2,200 kg of L-sorbose crystals m⁻³ h⁻¹), a crystal product of mean size Lm from 0.22 to 0.28 mm and CV from 68.8 to 44.0% was withdrawn. The values of linear growth rate show increasing trend (from 6.6·10⁻⁸ to 7.6·10⁻⁸ m s⁻¹) with the productivity enlargement (assuming constant residence time τ=900 s). Occurrence of secondary nucleation phenomena within the circulated suspension, resulting from the crystals attrition and breakage was observed. The parameter values in a design equation, matching linear growth rate and suspension density with nucleation rate were determined.     

Nucleation kinetics of emulsified triglyceride mixtures

The purpose of this study is to determine character istic nucleation parameters such as the surface free energy for nucleus formation in mixtures of fully hydrogenated palm oil (HP) in sunflower oil (SF). These parameters will be used to model the bulk crystallization kinetics of the same mixtures. This was achieved by determining the crystallization kinetics in emulsified triglyceride mixtures using differential scanning calorimetry, proton nuclear magnetic resonance, and ultrasound velocity measurements. The latter technique appeared to be very sensitive for monitoring the crystallization kinetics of fat dispersions containing triglycerides with a simple phase behavior. Isothermal crystallization of emulsified HP stabilized by sodium caseinate started at 7 K below the α clear point, and the kinetics were best fitted assuming heterogeneous nucleation. Isothermal crystallization of emulsified 10% HP in SF stabilized by caseinate started at 14 K below the α melting point, and the kinetics were best fitted assuming homogeneous nucleation. If the same dispersion was stabilized by Tween 20, crystallization started at 11 K below the α melting point, and the kinetics were fitted best using heterogeneous nucleation. Analysis of the temperature dependency of the fit parameters yielded a surface free energy of a nucleus of about 4 mJ.m⁻² in the case of homogeneous nucleation. Pre-exponential nucleation frequencies indicated that a large proportion of the triglyceride molecule should be in the right conformation to be incorporated in a nucleus.     

Interfacial Crystallization of Diacylglycerols Rich in Medium‐ and Long‐Chain Fatty Acids in Water‐in‐Oil Emulsions

The effects of diacylglycerols rich in medium‐ and long‐chain fatty acids (MLCD) on the crystallization of hydrogenated palm oil (HPO) and formation of 10% water‐in‐oil (W/O) emulsion are studied, and compared with the common surfactants monostearoylglycerol (MSG) and polyglycerol polyricinoleate (PGPR). Polarized light microscopy reveals that emulsions made with MLCD form crystals around dispersed water droplets and promotes HPO crystallization at the oil‐water interface. Similar behavior is also observed in MSG‐stabilized emulsions, but is absent from emulsions made with PGPR. The large deformation yield value of the test W/O emulsion is increased four‐fold versus those stabilized via PGPR due to interfacial crystallization of HPO. However, there are no large differences in droplet size, solid fat content (SFC), thermal behavior or polymorphism to account for these substantial changes, implying that the spatial distribution of the HPO crystals within the crystal network is the driving factor responsible for the observed textural differences. MLCD‐covered water droplets act as active fillers and interact with surrounding fat crystals to enhance the rigidity of emulsion. This study provides new insights regarding the use of MLCD in W/O emulsions as template for interfacial crystallization and the possibility of tailoring their large deformation behavior. Practical Applications: MLCD is applied in preparing W/O emulsion. It is found that MLCD forms unique interfacial Pickering crystals around water droplets, which promote the surface‐inactive HPO nucleation at the oil‐water interface. Thus MLCD‐covered water droplets act as active fillers and interact with surrounding fat crystals, which can greatly enhance the rigidity of emulsion. This observation would provide a theoretical reference and practical basis for the application of the MLCD with appreciable nutritional properties in lipid‐rich products such as whipped cream, shortenings margarine, butter and ice cream, so as to substitute hydrogenated oil. MLCD‐stabilized emulsions can also be explored for the development of novel confectionery products, lipsticks, or controlled release matrices.     

Phospholipid composition of lipid seed crystal isolates from ivory coast cocoa butter

Seed crystals isolated from Ivory Coast cocoa butter were shown to differ in chemical and thermal characteristics from solidified Ivory Coast butter. Higher concentrations of complex lipids in the seed crystals have led to speculation on the role these polar molecules play in lipid crystallization events. Phospholipids separated from lipid seed crystal isolates were twelve-fold more concentrated than the original cocoa butter. Seed crystals contained 3.99% phospholipids while cocoa butter samples contained 0.34%. Phosphatidylglycerol, phosphatidylcholine, phosphatidylethanolamine, phosphatidylinositol, lysophosphatidylcholine, phosphatidylserine, and phosphatidic acid were identified in cocoa butter with phosphatidylcholine (37.7%), phosphatidylglycerol (27.3%) and phosphatidyl-ethanolamine (15.6%) being the major phospholipid constituents. Two phospholipids not previously reported in cocoa butter were identified as phosphatidylglycerol and diphosphatidylglycerol based on co-migration of standards. Cocoa butter and its seed crystals contained the same phospholipid entities; however, individual phospholipids differed significantly in concentration. Phosphatidylethanolamine (30.4%) and phosphatidylcholine (30.2%) were the major phospholipids in seed crystal samples. Fatty acid composition of cocoa butter and seed crystal phospholipids were found to be similar, with the exception of myristic, stearic and oleic acids. Myristic acid was three-fold higher in phosphatidylglycerol and phosphatidylethanolamine in the seed crystals, whereas stearic acid was significantly lower in the seed crystals when compared to the cocoa butter. Concentrations of oleic acid were twice as high in seed crystal phosphatidylethanol-amine and almost four times as high in seed crystal phosphatidylcholine than in corresponding cocoa butter samples. The possible role phospholipids play in seed crystal development and in crystallization events is discussed.     

Influence of PVP buffer layer on the formation of NaA zeolite membrane

The support substrates were modified with the aqueous solutions of 1 and 3 wt% of polyvinyl pyrrolidine (PVP) as intermediate buffer layer followed by NaA zeolite seed (prepared hydrothermally at 85 °C for 2 h) coating with 2.5 wt% aqueous dispersion in each case. A better surface coverage with the oriented layer of NaA seed crystals was found with 1 wt% PVP buffer layer. The secondary crystallization of NaA membranes in the PVP-seed-coated supports was carried out hydrothermally at 65 °C for 2, 4, 6 h (single-stage each) and (2 + 2), (4 + 2)h (double-stage each) crystal growth processes. The crystallization behaviours of NaA membranes were studied by X-ray diffraction (XRD) while the microstructures of the same films were observed by scanning electron microscope (SEM). The single-stage secondary crystallization at 65 °C for 4 h showed highly interlocked and oriented NaA grains in the membranes and it rendered the permeance value of 2.2 × 10⁻⁸ mol m⁻²s⁻¹Pa⁻¹ for single gas, nitrogen (N₂) at ambient temperature (30 °C).     

Permeability of some fat products to moisture

Summary Films of cocoa butter, highly hydrogenated cottonseed oil, mixtures of highly hydrogenated cottonseed oil and cottonseed oil, chocolate liquor, and sweet milk chocolate were prepared; and their permeability to water vapor was determined by the cup method. The permeability constant was calculated in terms of grams of water diffusing through a centimeter cube in one second under a vapor pressure gradient of one millimeter of mercury across the cube. Under the test conditions employed, the permeability constant for cocoa butter at room temperature was found to vary from 5.8×10⁻¹² to 81.6×10⁻¹². The permeability constants for the highly hydrogenated cottonseed oil and the cocoa butter, under comparable conditions at room temperature, was found to be approximately 1.3×10⁻¹² and 33×10⁻¹², respectively. From data obtained with cocoa butter it was concluded that the permeability constant increased with moderate increases in film thickness. Polymorphism was found to have a large effect on permeability, an approximately 15-fold difference was found between quickly chilled and tempered films of cocoa butter at 3°C. (37.4°F.). The percentage of liquid component in the fat was found to have a large effect on permeability. The increasing of the percentage of liquid cottonseed oil in highly hydrogenated cottonseed oil from 0 to 40% increased the permeability constant from 1.3×10⁻¹² to about 420×10⁻¹². The permeability of chocolate liquor and sweet milk chocolate at room temperature was increased greatly when the relative humidity on the wet side of the films was increased to 100%. The nonfat components absorbed enough moisture to impair the structure of the film. Presented at the 32nd Fall Meeting of the American Oil Chemists' Society, Chicago, Ill., October 20–22, 1958. Fellow, National Confectioners' Association. One of the laboratories of the Southern Utilization Research and Development Division, Agricultural Research Service, U. S. Department of Agriculture.     

Lipid composition of high-melting seed crystals formed during cocoa butter solidification

High-melting seed crystals which form during the early stages of cocoa butter solidification possess a lipid composition different than the cocoa butter from which the seed crystals were grown. Significantly large quantities of glycolipids, 11.1%, and phospholipids, 6.6–8.1%, were found in the high-melting seed crystals along with a dramatic decrease in the simple lipid class. The fatty acids comprising the simple lipid fraction of the seed crystals were considerably more saturated than the fatty acids present in the same fraction of the original cocoa butter. The increase in the degree of saturation was reflected in the triacylglycerol composition. Cocoa butter samples were predominantly monounsaturated triacylglycerols while the seed crystal samples were mainly trisaturated triacylglycerols. The elevated melting point (60–70°C) of the seed crystals was due to the presence of higher melting complex lipids as well as to the increase in saturated triacylglycerol species. As a result of the evidence provided, the high-melting seed crystal is indeed a distinct crystalline entity and not an additional polymorphic form of cocoa butter.     

Isolation and thermal characterization of high-melting seed crystals formed during cocoa butter solidification

Seed crystals which formed during early stages of cocoa butter solidification have been isolated and determined to have extremely high melting points. The melting points of the seed crystals generally exceeded 60°C, in contrast to cocoa butter, which melts between 30–35°C. In addition, the melting point of the seed crystals decreased as a function of crystal growth time. Evidence suggests that the high-melting seed crystal is not an additional polymorphic form of cocoa butter, but rather a distinct crystalline entity. Consequently, a unique compositional make-up is suspected as being responsible for the elevated melting point. A technique to separate seed crystals from the molten cocoa butter mass has been developed. The procedure has been shown not to alter the thermal and compositional properties of the isolated seed crystals.     

Effect of temperature on recrystallization behavior of cocoa butter

Crystallization of cocoa butter in the β phase directly from the melt is only possible by employing the memory effect of cocoa butter. Cocoa butter crystallized in the β phase, heated to the so-called maximal temperature (just above its melting end point), recrystallizes in the β phase after cooling to a crystallization temperature. The influence of the maximal and crystallization temperatures on the recrystallization behavior has been investigated for two cocoa butters. Rapid-starting recrystallization into the β(VI) phase and slow-starting recrystallization into the β(V) have been observed. It is concluded that rapid-starting recrystallization is induced by high-melting 1,3-distearoyl-2-oleoyl-glycerol (SOS)-rich crystals. The two β phases were identified by X-ray powder diffraction and melting ranges. However, the X-ray powder diffraction patterns for the β phases depended on the composition of the cocoa butter and on the crystallization method used. Therefore, it was not possible to take any particular β(VI) X-ray powder diffraction pattern as a standard for the β(VI) phase of all cocoa butters.     

Confined crystallization phenomena in immiscible polymer blends with dispersed micro- and nanometer sized PA6 droplets, part 3: crystallization kinetics and crystallinity of micro- and nanometer sized PA6 droplets crystallizing at high supercoolings

Crystallization kinetics and crystallinity development of PA6 droplets having sizes from 0.1 to 20 μm dispersed in immiscible uncompatibilized PS/PA6 and reactively compatibilized (PS/Styrene-maleic anhydride copolymer=SMA2)/PA6 blends are reported. These blend systems show fractionated crystallization, leading to several separate crystallization events at different lowered temperatures. Isothermal DSC experiments show that micrometer-sized PA6 droplets crystallizing in an intermediate temperature range (T_c∼175 °C) below the bulk crystallization show a different dependency on cooling rate compared to bulk crystallization, and an athermal crystallization mechanism is suggested for PA6 in this crystallization temperature region. The crystallinity in these blends decreases with PA6 droplet size. Random nucleation, characteristic for a homogeneous nucleation process, is found for sub-micrometer sized PA6 droplets crystallizing between T_c 85 and 110 °C using isothermal DSC experiments. However, crystallization in the PA6 droplets is most likely initiated at the PA6-PS interface due to vitrification of the PS matrix during crystallization. Very imperfect PA6 crystals are formed in this low temperature crystallization region, leading to a strongly reduced crystallinity. These crystals show strong reorganization effects upon heating.     

Crystallization kinetics of fully hydrogenated palm oil in sunflower oil mixtures

The crystallization kinetics of mixtures of fully hydrogenated palm oil (HP) in sunflower oil (SF) was studied. The thermal properties and phase behavior of this model system were characterized by means of differential scanning calorimetry and X-ray diffraction. From the melting enthalpy and clear point of HP, it was possible to calculate the supersaturation at a given temperature for every composition of the model system. Supersaturation of the model system for the β′ but not for the α polymorph yielded the β′ polymorph, while supersaturation for the α polymorph yielded a mixture of mainly β and some β′ polymorphs. The crystallization kinetics of HP/SF mixtures were determined by pulsed wide-line proton nuclear magnetic resonance for various initial supersaturations in the β′ polymorph. The determined curves were modeled by a modified classical nucleation model and an empirical crystal growth function, which are both functions of supersaturation. Heterogeneous nucleation rates in the β′ polymorph yielded a surface Gibbs energy for heterogeneous nucleus formation of 3.8 mJ·m⁻². About 80% of the triglyceride was assumed to be in a suitable conformation for incorporation in a nucleus. Induction times for isothermal crystallization in the β′ polymorph yielded a surface free energy for heterogeneous nucleus formation of 3.4 to 3.9 mJ·⁻².