Effects of Crystal Growth and Polymorphism of Triacylglycerols on

†Cemagref, UR TERE, 17 avenue de Cucill´e, CS 64427, F-35044 Rennes, France, ‡INRA-BIA, Rue de la. G´eraudi`ere, BP 71627, 44316 Nantes cedex 3,...
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DOI: 10.1021/cg900219b

Effects of Crystal Growth and Polymorphism of Triacylglycerols on NMR Relaxation Parameters. 2. Study of a Tricaprin-Tristearin Mixture

2009, Vol. 9 4281–4288

Matthieu Adam-Berret,†,‡,§ Alain Riaublanc,‡ and Franc- ois Mariette*,†,§ †

Cemagref, UR TERE, 17 avenue de Cucill e, CS 64427, F-35044 Rennes, France, ‡INRA-BIA, Rue de la e europ eenne de Bretagne, France G eraudi ere, BP 71627, 44316 Nantes cedex 3, France, and §Universit

Received February 20, 2009; Revised Manuscript Received July 6, 2009

ABSTRACT: Being able to determine the physical properties of fats such as polymorphism and crystal size is very important for the food industry. After a relationship was observed between spin-lattice relaxation time and crystal size in a solid-liquid mixture of triacylglycerols, the effects of polymorphism and crystal size were investigated by low-field NMR relaxation and powder X-ray diffraction on three binary mixtures of tricaprin and tristearin in the solid state. Second moment (M2) was proven to be only sensitive to polymorphism. Its measurements permitted the quantification of polymorphic forms in a binary mixture, with a model based on M2 of the pure components. As for the spin-lattice relaxation time (T1), it was proven to be only sensitive to crystal size and not to polymorphism. Quantification was not possible with T1 measurements, but information on the pattern of the crystal thickness distribution was obtained using the maximization entropy method algorithm. The determination of polymorphism was thus possible because of the difference in size between the R and β triacylglycerol crystals. Finally, a phase diagram mainly based on NMR data was constructed for the tricaprin/tristearin system.

*To whom correspondence should be addressed. Address: Cemagref, Food Process Engineering Research Unit, CS 64426, 17 av de Cucille, 35044 Rennes, France. Phone: (33) 2-23482178. Fax: (33) 2-23482115. E-mail: [email protected].

consequently modifies taste, graininess, and texture. Marangoni et al.18 demonstrated that crystals with different sizes but the same polymorphism showed similar XRD patterns and had the same melting temperature. Low-field NMR relaxation is currently the reference method to evaluate solid fat content (SFC) in food with a measurement based on the intensity of the signals.19,20 However, the latter technique has shown more potential with the measurement of relaxation parameters, especially in the case of determination of polymorphism. A recent study based on pure triacylglycerols showed that it was possible to assess polymorphism independently of temperature and chain length.21 The distinction was proven to be possible via second moment (M2) measurements, and greater sensitivity was found with spin-lattice relaxation time (T1) measurements. Trezza et al.22 developed a model based on T2 measurements and semiempirical mathematical functions to quantify the R and β polymorphic forms as well as SFC through a single measurement. However, they were not able to distinguish between β and β0 polymorphs. A recent study showed that spin-lattice relaxation time measurements could provide more information on the fat system. Indeed, evidence of a correlation between T1 and crystal size, as well as the existence of cocrystals of tricaprin and tristearin after fast supercooling, was highlighted in this study.23 T1 measurements can thus provide interesting information on fat systems. After demonstrating the relationships between NMR relaxation parameters and the design (i.e., their crystal size and polymorphism) for pure triacylglycerols, the aim of this study was to establish the ability of low-field NMR relaxation to obtain information on triacylglycerol mixtures. Second moment and spin-lattice relaxation time measurements were combined for model mixtures of tricaprin and tristearin in the solid state at three different ratios. These two parameters were used to determine the behavior of the triacylglycerols in a solid mixture and to establish new methods for the quantification of blended triacylglycerol polymorphs.

r 2009 American Chemical Society

Published on Web 08/20/2009

Introduction The physical properties of fats depend on the polymorphic behavior and intersolubility of their major triacylglycerol components. The phase behavior of these mixtures is of paramount importance for the manufacture of fat-containing products such as chocolate and butter.1 Indeed, fat structures formed by triacylglycerols determine the functional properties of these products such as their texture, plasticity, and morphology.2,3 Various studies have been carried out on pure triacylglycerols,4,5 but fats and lipids present in natural resources are mixtures of different types of triacylglycerols and the blends show a far more complicated polymorphic behavior.6 Moreover, the complexity is increased by the intersolubility of the different triacylglycerols which can cocrystallize.7 As an understanding of the physical properties of the triacylglycerol mixture system is essential, binary triacylglycerol mixtures have been extensively studied.8,9 It has been demonstrated that the phase behavior of the binary systems can be classified into three situations, which are solid-solution, eutectic, and molecular compound. Differential scanning calorimetry (DSC) and X-ray diffraction (XRD) are the two techniques generally used to characterize triacylglycerol mixtures.10 Time-resolved synchrotron radiation XRD has provided the most interesting results on the polymorphic behavior of pure triacylglycerols and in mixtures.11-17 It was shown that the solid-solution phase was enhanced when the triacylglycerols were in the R and the β0 form, and when the difference in chain length between the triacylglycerols was shorter than four carbons. However, crystal size is another important parameter for determination of the physical properties of fats because it affects the rheological properties and

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Figure 1. Powder XRD spectra at 10 °C for the three mixtures. SAXS pattern on the left and WAXS pattern on the right.

Materials and Methods Materials and Tempering Procedures. triacylglycerols (TA) were purchased commercially (Sigma, St. Louis, MO, USA; >98% purity) and samples were used without any further purification. Tricaprin and tristearin were blended in the melted state at ratios of 25:75, 50:50, and 75:25 (w/w). The mixtures were melted at 80 °C for 20 min, and then quenched to -50 °C for 10 min directly in the NMR spectrometer (crystallization in the R form for the two triacylglycerols). The temperature was increased to -20 °C for 10 min and to 10 °C for 30 min. Low-Field NMR Measurements. Measurements were carried out with a 0.47 T NMR spectrometer (Minispec MQ20, Bruker SA, Wissembourg, France) operating at 20 MHz for protons. The NMR probe temperature was controlled with a dedicated device (BVT 3000, Bruker SA, Wissembourg, France) with temperature measurement accuracy of (0.15 °C. Low temperatures were obtained using a dedicated device operating with liquid nitrogen. The instrument was equipped with a 10 mm probehead. Magnetic field tuning, homogeneity of the magnet, detection angles, receiver gain, and pulse lengths were checked before each measurement. Two kinds of NMR sequence were used, that is, free induction decay (FID) and fast saturation recovery (FSR). At -50 °C and -20 °C, signal decays were recorded for 300 μs with 32 scans and a recycling delay (Rd) up to 2 s, and the FSR signals were recorded between 25 and 5000 ms with 100 points. At 10 °C, signal decays were recorded for 300 μs with 16 scans and a recycling delay (Rd) of 10 s, and the FSR signals were recorded between 30 and 10 000 ms with 100 points. Powder X-ray Diffraction. Measurements were performed using a D8 Discover spectrometer with GADDS and cross-coupled mirrors from Bruker-AXS, working at 40 kV and 40 mA, with a copper monochromator (λ = 1.54059 A˚). Sample alignment was performed by microscopic video and laser. Glass capillaries (1.5  80 mm) were filled with mixtures in the melted state. The kinetics applied to the capillaries were exactly the same as the kinetics applied to the NMR tubes, but measurements were performed only at 10 °C. The temperature of the capillary during acquisition was controlled by a Eurotherm unit equipped with a Pt100 probe with an accuracy of (0.1 °C. Data Analysis. The data from spin-lattice relaxation time measurements were fitted using the Marquardt method according to the multiexponential function presented in eq 1. sðtÞ ¼

n X

Ai  ð1 -R  e -t=T1i Þ

ð1Þ

i ¼1

The R parameter is necessary for low-field spectrometers in order to correct errors from the 90° pulse. The n parameter depends on the measurement temperature. A monoexponential function was used for fitting at -50 °C, whereas a biexponential fitting was performed at the other temperatures. The data were also fitted according to the maximisation entropy method (MEM) algorithm which provided the distribution of spin-lattice relaxation times. FID signals were fitted in order to determine the second moment M2. The model used was based on the Abragam model as already presented by Adam-Berret et al.21

Quantification of polymorphs was performed by T1 and M2 measurements. For T1 measurements, the proportions estimated from eq 1 were used directly. For M2 measurements, the model used for quantification was based on M2 of pure triacylglycerols. FID signals of the mixtures were fitted with the model presented below: 2 2 sinðbR  tÞ 2 2 sðtÞ ¼ A  e -ðaR t Þ=2  þB  e -ðaβ t Þ=2 bR  t 

sinðbβ  tÞ 2 2 þC  e -t =T2c þD bβ  t

ð2Þ

A and B were the unknown parameters which were used for determination of the proportions, aR, bR, aβ, and bβ were the parameters previously determined by the fitting of the pure triacylglycerol signals in the right polymorphic form at the same temperature measurement.21 The third Gaussian function was used for a better fit and its parameters will not be discussed further.

Results Quantification of the Polymorphic Forms. According to the melting temperatures, tricaprin should be in the β0 form and tristearin in the R form at 10 °C.5 However, because of the kinetics applied to the sample, the polymorphic behavior may be different. Indeed, the two triacylglycerols were crystallized in the R form, which involved a polymorphic transformation for tricaprin. X-ray measurements were performed to determine the polymorphic forms present at 10 °C. The small angle X-ray scattering (SAXS) and wide angle X-ray scattering (WAXS) XRD patterns at 10 °C are shown in Figure 1. Only two different polymorphic forms were detected in the samples. They were characterized by the two peaks on the SAXS diffractogram. The peak at 0.12 A˚-1 corresponds to the R 2 L form of tristearin, whereas the peak at 0.22 A˚-1 corresponds to the β 2 L form of tricaprin. The WAXS diffraction pattern confirmed these results. Indeed, the singlet at 1.52 A˚-1 is characteristic of the R form, whereas the peak at 1.38 A˚-1 with the doublet at 1.63 A˚-1 and 1.67 A˚-1 are characteristic of the β form.5 Tristearin was thus always in the R form, and tricaprin was always in the β form at 10 °C in our systems. According to the powder XRD results, there was no β0 form for tricaprin at 10 °C after the kinetics was applied. The system appeared more compact in the case of the 25/75 mixture, which was characterized by a shift of the peaks to the shorter distances. However, XRD measurements did not permit the quantification of the two polymorphic forms because of the overlapping peak. In order to find a quantitative method, second moments were measured at different temperatures. The

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Figure 2. Evolution of FID signals and M2 as a function of tricaprin content (% w) at 10 °C.

different FID signals and M2 obtained for the mixtures at 10 °C are presented in Figure 2. FID signals of the mixtures fell between the signals of the pure triacylglycerols, and mixtures tended toward the behavior of the pure triacylglycerols. FID signals thus effectively demonstrated different polymorphic forms in a mixture. Second moment measurements confirmed this result. M2 increased with tricaprin concentration, which meant that the system became less mobile. This result was expected because of the presence of more β polymorphs in the system whose side chain mobility is lower than the side chain mobility of the R polymorph. However, M2 remained between the M2 values of the pure compounds. Quantification of the polymorphic forms was thus evaluated from M2 measurements according to eq 2, and T1 proportions were evaluated according to eq 1. The proportions of the polymorphic forms determined by FSR fitting and M2 measurements are presented in Figure 3. Cocrystals were assumed to be in the β form. The proportions determined by M2 measurements were close to the proportions expected when cocrystals were assumed to be in the β form. M2 seemed to be an accurate method for the quantification of polymorphic forms in a binary mixture. Second moments were therefore measured for the three mixtures at -50 °C and -20 °C (Figure 4). According to their melting temperatures, tricaprin and tristearin should be in the R form at these temperatures. Two different behaviors could be observed. A single value of M2 (10.7  109 s-2) was found for all three mixtures at -50 °C, corresponding to an average between the M2 of the two pure compounds. As M2 measurements were proven to be effective for the determination of polymorphism, it was possible to conclude that tricaprin and tristearin were in the R form when they were in the mixtures at -50 °C. The single value obtained at this temperature proved that M2 was only sensitive to polymorphism and not to triacylglycerol type. However, quantification of polymorphism was not possible at this temperature because the second moment of the R form of tristearin is in an area of nonlinearity and the M2 of the two polymorphic forms are close (11.5  109 s-2 for the R form and 12  109 s-2 for the β form). The situation at -20 °C was more complicated. It was first possible to see that tricaprin was not always in the R form. Indeed, the M2 of the mixtures did not fall between the M2 of the pure compounds in the R form. We needed to introduce the second moment of pure β tricaprin in order to determine the correct polymorphic forms. β Tricaprin was thus present

Figure 3. Deviation between expected proportions of β form and measured proportions with M2. Solid line represents theoretical proportions.

Figure 4. Second moments of pure tricaprin and tristearin and their three blends (25/75 (0), 50/50 (O), and 75/25 ()) (w/w)) in relation to temperature. Table 1. Proportions of the Polymorphic Forms Determined by M2 Measurements at -20 °C % of TAG in weight

% of protons expected

M2 measurements

TG10

TG18

TG10

TG18

β form

R form

25 50 75

75 50 25

23.2 47.5 73.1

76.8 52.5 26.9

0 37.2 50.1

100 62.8 49.9

at -20 °C. The proportions of the polymorphic forms determined at -20 °C by M2 measurements are given in Table 1.

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Figure 5. Evolution of T1 as a function of tricaprin content (% w).

At -20 °C, tricaprin is close to the melting temperature of its R form, and therefore the behavior of the mixture depended on the polymorphic modification of tricaprin from 0 the R to the β(0 ) form (β( ) corresponds to a β or a β0 form, 25,26 For the their M2 being too close to permit distinction). (0 ) 25/75 (w/w) mixture, no trace of β form was detected. Tricaprin was thus in the R form, as was tristearin. The proportions determined for the other mixtures can be explained by the partial transformation of the R tricaprin into 0 the β( ) form. Indeed, it was shown that all the tricaprin was in the R form at -50 °C, and in the β form at 10 °C. There was therefore a polymorphic modification between these two temperatures. At -20 °C, the temperature was close to the melting temperature of R tricaprin (-15 °C), and thus the transformation occurred at this temperature. It proved that 79% and 68% of tricaprin was modified for the 50/50 (w/w) and 75/25 (w/w) mixtures, respectively. The transformation was not complete because the mixtures were probably not at equilibrium at the time of measurement. Tristearin was therefore in the R form in the sample at -20 °C and tricaprin 0 in the R form and in the β( ) form. It was therefore interesting to measure the spin-lattice relaxation times of these mixtures in order to determine whether the proportions of the two polymorphic forms were measurable via T1 measurements. The evolution of spin-lattice relaxation times of the mixtures was followed according to the amount of tricaprin introduced into the sample at 10 °C. The T1 distributions and values are presented in Figure 5. It was checked that the systems were in equilibrium before measurements. The distributions evolved differently according to the amount of tricaprin. There was only one peak for 25% tricaprin and there were three peaks for 75% tricaprin. These peaks were attributed to the two triacylglycerols. The first peak around 200 ms was attributed to R tristearin. Indeed, this value corresponded to the T1 of pure R tristearin and the intensity of the peak decreased when the tricaprin concentration increased. The second and third peaks over 500 ms were attributed to β tricaprin as the T1 distribution of pure tricaprin had two peaks and the T1 values corresponded to β polymorphs. Moreover, when the tricaprin concentration increased, the mixtures tended toward the behavior of pure tricaprin. Discrete T1 values were determined by biexponential fitting of the signals. As the peaks were broad and the first two values were close, it was not possible to estimate three discrete values correctly, and consequently the first exponential corresponded to the first two peaks of the MEM distribution. The evolution of discrete values was different

for the two triacylglycerols. Tricaprin T1 increased continuously with tricaprin concentration, whereas tristearin T1 remained almost constant around 200 ms, with a small decrease when there was less tricaprin. It should be noted that the tricaprin behavior was different when it was in the presence of tristearin: the tricaprin T1 decreased considerably when the amount of tristearin increased, passing from 2300 ms in the pure state to 600 ms when there was a maximum of tristearin. The presence of another triacylglycerol thus modified the tricaprin behavior. Moreover, there was a wide difference between the spin-lattice relaxation times of the two compounds, and the difference became greater when there was more tricaprin. The wide difference between the T1 of tricaprin and tristearin was due to a different polymorphism, as previously observed with the X-ray measurements. However, the problem of quantification remained, and the use of a biexponential instead of a triexponential model generated an error in the estimated proportions. Quantification was thus not possible with T1 measurements. Information about Crystal Size. As shown in a previous study, T1 is correlated to the spin diffusion and the crystal size, and it is not appropriate for the quantification of the polymorphic form. However, it can provide information on the distribution of the crystal size in the sample. Spin-lattice relaxation times were then measured in order to determine the pattern of the crystal size distribution. The distributions of T1 at -50 °C according to the quantity of tristearin are shown in Figure 6. Spin-lattice relaxation times were different according to the quantity of tricaprin introduced into the sample. A single peak was observed for the 25/75 (w/w) mixture, whereas a shoulder appeared in the distribution for the 50/50 (w/w) mixture and there were two separate peaks for the most concentrated sample. The T1 value of 220 ms for the first peak was always the same, whereas its intensity decreased when the tricaprin concentration increased. This peak therefore corresponded to the small crystals of tristearin. When there was little tricaprin, only one peak was distinguishable. The tricaprin crystal network was embedded in the tristearin crystal network, and because of the spin diffusion, an average value of T1 is observed. However, when there was the same quantity of triacylglycerols, some of tricaprin crystals could grow a little more freely and the two triacylglycerols were not intimately mixed anymore. As the size of tricaprin crystals remained close to the size of the tristearin crystals, there was only one peak plus a shoulder. When there was an excess of tricaprin, most of its crystals could grow

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Figure 6. T1 distribution of three mixtures of tricaprin and tristearin and of pure tricaprin at -50 °C according to tricaprin concentration (in % w).

Crystal Growth & Design, Vol. 9, No. 10, 2009

Figure 8. T1 distribution of the 50/50 (w/w) mixture of tricaprin and tristearin at -50 °C obtained by the MEM algorithm. Table 2. T1 and Proportions Determined by T1 Measurements in the 50/ 50 (w/w) Mixture of Tricaprin and Tristearin at -50 °C R form β form

Figure 7. T1 distribution of the three mixtures of tricaprin and tristearin and of pure tricaprin at -20 °C according to tricaprin concentration (in % w).

freely and thus there were two peaks because of the differences in size. Moreover, the T1 of tricaprin was higher than in a pure system, and its crystals were therefore larger. This was due to the presence of tristearin which acted as a catalyst for crystal growth and then led to larger tricaprin crystals.1,6 As the T1 of tristearin was not modified by the presence of tricaprin, it meant that it behaved independently of tricaprin. The temperature of the mixtures was then increased to -20 °C. The distribution of the spin-lattice relaxation times according to the tricaprin concentration at this temperature is given in Figure 7. The behavior was similar to the behavior of the mixtures at -50 °C. There still was one peak for the 25/75 (w/w) mixture, because of the inclusion of the tricaprin crystal network into the tristearin crystal network. For the other mixtures, it was possible to distinguish two peaks which corresponded to the tricaprin crystals and to the tristearin crystals. Differentiation between the two triacylglycerols was easier than at -50 °C. The explanation for this was that the T1 of tristearin decreased between -50 °C and -20 °C, whereas that of tricaprin increased at the same time, as shown by AdamBerret et al.21 However, there were some differences between the distributions at the two temperatures. The tricaprin peak was broader for the 75/25 (w/w) mixture, which meant that there was greater diversity of crystal sizes. For the 25/75 (w/w) blend, a small peak appeared at around 600 ms, possibly related to a polymorphic transformation

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T1 (ms)

proportion (%)

570 ( 4 2510 ( 111

41.5 ( 1.1 58.5 ( 1.1

of tricaprin from the R to the β form. This type of transformation could be detected with the M2 measurements. Another experiment was performed to confirm that spin-lattice relaxation times were related to the proportions of crystal sizes. The 50/50 (w/w) mixture was melted at 80 °C and then crystallized at -50 °C. Tricaprin and tristearin were thus in the R form. The temperature was then increased to 60 °C. It has previously been shown that tricaprin is liquid and tristearin in the β form at this temperature.23 This mixture was recrystallized at -50 °C. The stable crystals of tristearin thus remained in the β form, and liquid tricaprin crystallized in the R form. Before recrystallization, the SFC was 59% with this tempering; thus, theoretically large crystals represented 59% of the sample. The distribution of spin-lattice relaxation times for this system is shown in Figure 8. Two broad peaks were observed, the first, with a maximum at 500 ms, corresponded to the population of small R crystals, and the second, with a maximum at 2600 ms, corresponded to the population of larger β crystals. The width of the peaks was related to the wide diversity of T1, and thus of crystal sizes, because of the differences in size between the R and β crystals. This result has already been reported by Fitzgerald et al.24 in relation to the particle size distribution of tripalmitin crystallized at 30 °C. It therefore appeared that the pattern of distribution of the different crystal sizes could be obtained through T1 measurements, and it was thus interesting to quantify the proportions of small and large crystals. If T1 was only sensitive to crystal size, it could be expected that the 59% of large crystals would be found in proportions determined with eq 1. The results for the T1 measurements using eq 1 are presented in Table 2. As can be seen from the distribution, there was a considerable difference between the two spin-lattice relaxation times. The T1 of the β form was 4 times higher than the T1 of the R form and the proportions measured matched the expected proportions. Consequently, spin-lattice relaxation times were only related to crystal size and provided information on proportions of crystals. This parameter may thus be useful for the determination of polymorphism, but only with crystals of very different sizes, which rarely occurs. However, it could be possible to determine crystal populations with T1

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Figure 9. Phase diagram of the CCC/SSS mixture constructed using NMR, X-ray, and DSC data from our experiments. Lines do not represent exact data and are given as indications, and the points ()) correspond to NMR data.

using an analysis based on their size. In order to obtain the distribution of spin-lattice relaxation times instead of the discrete values, and thus to obtain the pattern of the crystal size distribution in the sample, the MEM algorithm was used for subsequent experiments. Phase Diagram. A phase diagram based mainly on NMR results was constructed from the results obtained in the two studies on the effects of crystal growth and polymorphism of triacylglycerols on NMR relaxation parameters (Figure 9). Information from Takeuchi et al.15 was used to complete the different parts of the diagram, such as the shape of the lines. This diagram is similar to that constructed by Takeuchi et al.15 for the LLL/SSS mixture. The main difference is that we observed two polymorphs for the 25/75 (w/w) mixture at 10 °C whereas Takeuchi et al. observed only R tristearin for this proportion. The cause of this difference may be the different thermal diagram applied to the sample. It is worth noting that we were able to observe cocrystals of tricaprin and tristearin whose melting temperatures increased with the quantity of tristearin. Discussion Having demonstrated the existence of a correlation between the spin-lattice relaxation time and crystal size,23 it was then interesting to continue evaluating the potential of low-field NMR relaxation for the study of triacylglycerols. The next step was the study of a solid mixture of tricaprin and tristearin. On the basis of the results obtained for the different experiments in the solid state, it was possible to conclude that T1 could be used to obtain information on crystal sizes. Indeed, as for the solid-liquid study, T1 was sensitive to crystal size. First, it was possible to highlight two spin-lattice relaxation times at 10 °C corresponding to two different polymorphic forms: tristearin in the R form, with its small crystals, and tricaprin in the β form, with larger crystals. The distinction between the two triacylglycerols was easier when there was more tricaprin. This result was logical, because the growth of tricaprin crystals was limited when there was more tristearin and because of the spin diffusion, an average T1 was obtained. It should be noted that tristearin behavior was little modified by the presence of tricaprin, probably because of the slow growth rate of tristearin crystals. X-ray powder diffraction measurements could also be used to confirm that there were two different polymorphic forms in the solid mixtures at 10 °C. It has been already proven that T1 is sensitive to crystal

Adam-Berret et al.

size and to polymorphism.23 The wide difference between the T1 of tricaprin and that of tristearin at 10 °C was attributed to a different polymorphism, as suggested by X-ray results. However, as crystal size is related to polymorphism, and because R crystals are smaller than β crystals,27 T1 measurements were proven to be effective in the distinction of polymorphism using analysis based on crystal size. Another application was derived from the relationship between T1 and crystal size. It involved the possibility of obtaining the distribution of spin-lattice relaxation times and thus the pattern of the distribution of the crystal sizes. The experiment with the 50/50 (w/w) solid-liquid mixture crystallized at -50 °C showed the efficacy of the method. We prepared small and large crystals, and this was exactly what could be observed on the MEM distribution of the spin-lattice relaxation times. As a result, this method was applied to the study of the mixtures at low temperatures. At -50 °C, tricaprin and tristearin had the same polymorphic form; it was not possible to observe two relaxation times and second moments were equal. However, from the T1 distribution, there was the possibility of seeing different behaviors according to the quantity of tricaprin introduced into the sample. The appearance of a second peak when there was more tricaprin may be related to the presence of large tricaprin crystals which grow faster than tristearin crystals.28 Moreover, growth was easier when there was less tristearin because of the restriction of tricaprin crystal growth. It is worth noting that tristearin acted as an impurity for tricaprin and then promoted its crystal growth.29 As the crystal growth rate of tricaprin was more rapid than the tristearin crystal growth rate, the T1 was higher when there was more tricaprin. Thus, although the two triacylglycerols were in the same polymorphic form, some differences occurred because of the differences between the sizes of their crystals. The differences were the same at -20 °C, that is, a single peak for the 25/75 (w/w) mixture and two peaks for the other blends. The single peak proved that tricaprin was embedded in the tristearin crystal network, and it thus behaved like tristearin. However, it was always possible to observe independent behavior for tristearin, even when there was an excess of tricaprin. Distinction between the two peaks became easier when there was more tricaprin. Differentiation was due to the evolution of the T1 of the two compounds. The T1 of the tricaprin increased between -50 °C and -20 °C whereas that of tristearin decreased. Tricaprin showed considerable diversity of crystal size for the 50/50 and 75/25 (w/w) blends. At -20 °C, M 2 measurements proved that tricaprin was partially 0 in the β( ) form. This could explain the presence of small crystals of the R form, and larger crystals originating from the growth of β(0 ) crystals. Consequently, T1 distribution did not allow the distinction of polymorphism at this temperature. The reason is that different polymorphic forms can have similar crystal sizes. This is exactly what happened here; the system was crystallized in the R form with many small crystals, and when the temperature increased R tricaprin evolved to the β form, but the crystals did not grow. There is therefore a limit to the distinction of polymorphism through T1 measurements. After demonstrating the efficacy of spin-lattice relaxation time measurements to provide information on crystal size in the solid state, the problem of quantification of the polymorphic forms remained. Indeed, as for XRD measurements, quantification of the polymorphs was not possible with T1 measurements, because this parameter is sensitive to crystal size and, according to the kinetics applied to the sample,

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different polymorphs can have similar crystal sizes. It has been shown that M2 measurements can be used for the determination of polymorphism of pure triacylglycerols, in spite of lower sensitivity than T1 measurements. M2 was introduced here in order to evaluate its potential for the quantification of polymorphism. A method has already been developed by Trezza et al.22 based on the fit of FID-CPMG data. The method developed here appeared to be effective for the characterization and quantification of binary mixtures of triacylglycerols. This model was based on second moments of the pure compounds which can be found in Adam-Berret et al.21 M2 measurements provided proportions which matched the expected proportions taking into account cocrystals. This therefore meant that M2 is only sensitive to polymorphism. Indeed, if proportions had matched the real proportions introduced into the sample without taking into account the cocrystals, M2 would have been sensitive to the triacylglycerol under consideration. The deviation from the expected proportions (less than 2%), showed that second moment was accurate for the quantification of polymorphism within a system containing two polymorphic forms. However, no information was obtained for crystal size, and quantification was not possible when the two triacylglycerols had the same polymorphic form, such as at -50 °C. In the case of a mixture of polymorphic forms of the same triacylglycerol, as at -20 °C for tricaprin, the proportions converted from one form to another could be estimated. There were two problems with this technique. The first was differentiation between the β and the β0 polymorphs. Second moments for these two polymorphic forms are very close,22 and no information on the β0 polymorph could be obtained with our measurements. The second problem was that in order to apply the model, it was necessary to know the M2 of the pure compounds in the correct polymorphic form. Nevertheless, the accuracy of the method proved that this model should be valuable for the determination of SFC and polymorphism in a binary mixture of triacylglycerols with a single measurement. To summarize the results obtained for the two studies on the effects of polymorphism and crystal growth on NMR relaxation parameters, the first study,23 mainly dealing with high temperatures, highlighted a correlation between crystal size and spin-lattice relaxation time. Moreover, it was proved that T1 was especially sensitive to crystal size and not to the polymorphism. However, as crystals of the β polymorph are larger than crystals of the R polymorph, it was possible to differentiate polymorphs by their crystal size. Different applications using this relationship between crystal size and T1 were highlighted. The first was the possibility of following the evolution of the fat crystal network over time. The second was the possibility of obtaining the pattern of the distribution of crystal sizes. These results are potentially valuable because the physical properties of food are affected by crystal size. M2 measurements were proved to be sensitive to the polymorphism and could be used for the quantification of polymorphic forms in the case of a binary mixture. Acknowledgment. The authors thank Mr. Bruno PONTOIRE, INRA-BIA, for his help with powder X-ray diffraction measurements and Mrs. Corinne RONDEAU-MOURO for valuable discussions.

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