DOI: 10.1021/cg900218f
Effects of Crystal Growth and Polymorphism of Triacylglycerols on NMR Relaxation Parameters. 1. Evidence of a Relationship between Crystal Size and Spin-Lattice Relaxation Time
2009, Vol. 9 4273–4280
Matthieu Adam-Berret,†,‡,§ Alain Riaublanc,‡ Corinne Rondeau-Mouro,‡ 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: Fat crystal networks confer their physical properties on fat-containing products. They are characterized by the solid fat content (SFC) and the design of the crystals, that is, their polymorphism and their size. Different techniques such as NMR, differential scanning calorimetry, and X-ray diffraction (XRD) are used to determine these parameters. Low-field NMR, the reference method for evaluation of SFC, has been proven to allow the determination of polymorphism through spin-lattice relaxation time (T1) and second moment (M2) measurements. However, this technique could provide more information on the system. On the basis of the effects of supercooling on the NMR parameters, the first evidence of a possible relationship between the size of the crystals and T1 was demonstrated. The effects of a liquid phase on the fat crystal network were investigated with liquid tricaprin and solid tristearin. It was demonstrated that the two triacylglycerols can cocrystallize, and that the liquid phase modified the polymorphic behavior of tristearin. The evolution of T1 over time could be related to the Ostwald ripening phenomenon. In view of this evidence, it was concluded that there was a relationship between T1 and the size of the crystals in the fat crystal network.
*To whom correspondence should be addressed. E-mail: francois.
[email protected].
Supercooling, which is at the basis of the nucleation and crystal growth processes, has a direct impact on crystal size and thus on the rheological properties of the fat crystal networks.1,9,13,15-17 Growth rates have already been measured by microscopy in different conditions and indicate that an increase in cooling rate leads to a decrease in crystal size.18 Marangoni et al.19 also proved that crystals of different sizes but with the same polymorphism showed similar X-ray diffraction patterns and had the same melting temperature. The liquid phase has been proven to modify the polymorphic behavior of triacylglycerols, and also to promote crystallization of more stable crystals, allow the recrystallization of imperfect crystals into well packed crystals, and finally to favor the growth of microstructural elements.6,18,20 SFC, which measures the solid/liquid ratio, monitors some of the rheological properties of fats. However, it has been shown that two samples with a same SFC can have different functional properties.10 The effects of storage time, a primary concern for consumers, were proven to increase the hardness of the fat crystal network.1 This effect has been attributed to the Ostwald Ripening effect. This phenomenon assumes the recrystallization of smaller crystals into larger ones and thus is related to evolution of cluster sizes in the fat crystal network. Ripening is supported by an increase in the average crystal volume21 and the fractal dimension of the fat crystal network.22 Few methods have been developed to quantify the different network structures because of the complexity of the system. After some attempts at modeling the system by Van den Temple,23 Vreeker et al.22 introduced the fat fractal dimension. This parameter was used to establish a relationship between the mass of a cluster and its size, and thus to obtain information about the microstructure and the physical properties of fats.24-26 There are currently various techniques to
r 2009 American Chemical Society
Published on Web 08/20/2009
Introduction Triacylglycerols are the main constituents of fat-containing products such as chocolate and butter.1 The physical characteristics of the fat crystal network created by triacylglycerols monitor changes in the functional properties of these products such as their texture, plasticity, and morphology, and they are of paramount importance for industrial manufacture.2,3 The macroscopic properties of the fat crystal network are influenced by the quantity of crystals, determined by the solid fat content (SFC), and the crystal design.4 The latter is characterized by the polymorphism of the crystals, crystallite size and shape, and the spatial distribution of mass.5 All these parameters are sensitive to the crystallization process,6,7 which can be divided into two phases, namely, nucleation and crystal growth.8 During these two phenomena, the formation of submicrometer crystallites starts first, then larger particles and aggregates grow, and finally large crystallized structures appear to form a three-dimensional network.2 In the presence of liquid oil, aggregation continues and results in the formation of microstructures.9 The network is then characterized at different levels by crystals and aggregates, and all these levels of organization have to be considered to explain the rheological properties of the fat.2,10-12 However, fats and lipids present in natural resources are mixtures of different types of triacylglycerols, which complicate the crystallization process and the phase behaviors.13,14 Nevertheless, most fats can be described as a combination of a solid and a liquid phase, and study of well-designed triacylglycerols could thus improve the understanding of the relationships between crystallization conditions and the characteristics of the fat crystal network.
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characterize fat crystals. Differential scanning calorimetry (DSC) is based on melting temperature and enthalpy, but in the case of analysis of a mixture, peak overlapping is observed that complicates the interpretation of the thermograms. X-ray diffraction (XRD), sometimes using synchrotron radiation or combined with DSC, can be used to determine polymorphism and obtain information on the thickness of the crystallites.15,27-32 Microscopy and rheology can be employed to quantify microstructure,25 while low-field NMR is currently used to evaluate SFC with measurements based on the intensity of the solid/liquid signals.33 The latter technique has recently opened up new prospects in the measurement of relaxation parameters. An initial study proved that SFC and polymorphism could be determined through a single measurement.34 In a further study based on pure triacylglycerols, it was found that NMR relaxation parameters could be used to assess polymorphism, independently of temperature and chain length.35 The distinction was proved to be possible via second magnetic moment (M2) measurements, and greater sensitivity was found with spin-lattice relaxation time (T1) measurements, with a 10 times greater T1 for the β polymorph. As T1 is linked to molecular mobility, it appeared that the molecules in the β polymorphic form were less mobile than the molecules in the R polymorphic form. It would now be interesting to evaluate the possibilities of this technique for the characterization of fat crystal networks. Colquhoun and Grant36 showed that the NMR parameters measured, and more precisely the spin-lattice relaxation times, evolved over time. They observed an increase in T1 which could be attributed to an increase in crystallite size. Ostwald Ripening has already been studied by NMR in frozen sugar solutions, and a correlation was found between the recrystallization rate and the spin-spin relaxation time.37 The NMR relaxation parameters therefore appeared to be usable for the characterization of crystal networks. The interest of the present study is the correlation of NMR relaxation mechanisms with the structural results currently obtained by other techniques. Indeed, low field NMR is available in many food laboratories and is mainly used to determine solid fat content. However, with a single apparatus, low-field NMR could provide additional information on the fat crystal network which is currently provided by different techniques such as XRD, DSC, microscopy, and rheology. In order to correlate the properties of the fat crystal networks with the NMR relaxation parameters, different effects were investigated such as supercooling and the effects of solid fat content and storage time. Triacylglycerol polymorphism remained constant for all these experiments, but the size of the crystals was the changing parameter. Materials and Methods Materials and Tempering Procedures. Triacylglycerols were purchased commercially (Sigma, St Louis, MO, USA; >98% purity) and samples were used without any further purification. Trilaurin and tristearin were melted at 80 C for 20 min to erase thermal history. For the study related to the supercooling, the two triacylglycerols were rapidly cooled at different temperatures included between 40 C and -60 C for 20 min by direct immersion inside the probe of the NMR spectrometer, previously cooled to the desired temperature, which corresponded to a supercooling of -15 C to -105 C. The temperature was then increased to the measurement temperature (0 C for trilaurin and 25 C for tristearin). The sample was stabilized for 10 min before measurement. To study the SFC effects, tricaprin and tristearin were blended in the melted state at ratios of 25/75, 50/50, and 75/25 (w/w). The
Adam-Berret et al. mixtures were melted at 80 C for 20 min, then quenched to -50 C for 10 min directly inside the probe of the NMR spectrometer, where the two triacylglycerols crystallized in the R form, and the temperature was increased by 30 C stages until 40 C and after 1 h to 60 C. At these latter temperatures, tricaprin was in the liquid state and tristearin was in the solid state. For the effects of storage time, the 50/50 and 25/75 (w/w) tricaprin/tristearin blends were melted at 80 C for 20 min, then cooled to 5 C by direct immersion in a water bath for 10 min, and the sample was inserted inside the NMR spectrometer heated to 40 C. The sample was kept at this temperature for 12 days. 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). For the study of supercooling effects, FID signals were recorded for 300 μs with 32 scans and a recycling delay (Rd) of 2 s, and the FSR were recorded between 25 and 2000 ms with 100 points. To study the SFC and storage time effects, FID signals were recorded for 300 μs with 16 scans and a Rd between 30 and 40 s, and FSR signals were recorded between 30 and 40000 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 (λ=1.54059 A˚) and sample alignment by microscopic video and laser. Glass capillaries (1.5 80 mm) were filled with mixtures in the melted state. The kinetics applied to the capillary were exactly the same as the kinetics applied to the NMR tubes, but measurements were performed only at 10, 40, and 60 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. For the study on the effects of storage time, the powder diffraction profiles were plotted in the reciprocal lattice spacing q where q= 2π/d=4π sin θ/λ with d the interplanar spacing and 2θ the Bragg scattering angle. After a linear baseline correction, the powder diffraction profiles from the small-angle experiments were fitted by a pseudo-Voigt function, which is a weighed combination of Gaussian and Lorentzian peak functions, using the Levenberg-Marquardt algorithm. In this situation, the full width halfmaximum (fwhm) of the peak (Δq) is related to the correlation length (ξ) by the Scherrer equation according to ξ=2π/Δq. For a small single-domain crystallite, this correlation length is an approximate measure of the thickness of that crystallite.31 Differential Scanning Calorimetry. Melted blends of TAG at 80 C were poured into an aluminum T0 pan (Perkin-Elmer, Courtaboeuf, France) and analyzed using a Q100 calorimeter (Perkin-Elmer, Courtaboeuf, France). Pans were introduced into the oven at 20 C, heated for 10 min at 80 C, and cooled at 20 C/min until -40 C. The fusion enthalpy was then recorded by applying the same thermal treatment as for NMR measurements. Light Polarization Microscopy. Blends of TAG were melted at 80 C for 20 min, and then a drop was deposited on a preheated glass microscope slide and then rapidly cooled to 0 C by ice contact. The crystallized drop was then observed at 40 C under 90 polarized light using an Eclipse E400 microscope (Nikon, Champigny, France) equipped with a thermostatted sample holder (Linkam, Tadworth, UK). Slides were stored in an oven at 40 C between observations. Data Analysis. The data from spin-lattice relaxation time measurements were fitted using the Levenberg-Marquardt algorithm according to the monoexponential function presented in eq 1. sðtÞ ¼ A ð1 - R e -t=T1 Þ
ð1Þ
The R parameter is necessary for low-field spectrometers in order to correct errors from the 90 pulse. Polymorph decays were fitted in
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Table 1. Ratios of Protons in the Three Mixtures triacyglycerol 1
H TG 10 1 H TG18
25/75 (w/w) (%)
50/50 (w/w) (%)
75/25 (w/w) (%)
23.2 76.8
47.5 52.5
73.1 26.9
Figure 2. Variations in M2 as a function of supercooling temperature (T - Tm) measured at 0 C for trilaurin (() and 25 C for tristearin (*).
Figure 1. Variations in T1 as a function of supercooling (T - Tm) measured at 0 C for trilaurin (() and 25 C for tristearin (*). order to determine the second moment M2. The model used was based on the Abragam model as already presented by Adam-Berret et al.:35 sðtÞ ¼ A e -ða
2
t2 =2Þ
sin cðb tÞ þ B e -t=c
ð2Þ
a, b, and c being parameters determined from the fit. The second moment was determined by 1 M2 ¼ a2 þ b2 ð3Þ 3 SFC was estimated using the adjusted parameters from eq 2: A corresponds to the total intensity of the solid signal, and B corresponds to the intensity of the liquid signal. SFC is thus determined by A 100 ð4Þ SFC ¼ AþB The low-field NMR signal intensity is directly proportional to the quantity of protons present in the sample analyzed. Thus, for the three mixtures prepared, we determined the ratios in terms of quantity of protons present in the samples, because the quantity of protons is different for tricaprin and tristearin. The ratios based on the quantity of protons which are expected in NMR are given in Table 1. Ostwald Ripening. This well-known phenomenon characterizes the coarsening process occurring with time in a crystallized system. This theory predicts that the smaller crystals in the system recrystallize into larger crystals with time according to the growth law:38-41 Ælæ tn, where l is the average grain size.
Results (a) Effects of Supercooling. The evolution of the spinlattice relaxation times as a function of supercooling for trilaurin and tristearin are presented in Figure 1. Trilaurin was chosen for this study instead of tricaprin because of its wider temperature range available for investigation. Two different behaviors were observed. Tristearin T1 remained almost constant with supercooling around 160 ms, showing just an increase to 175 ms at low supercooling, whereas trilaurin T1 increased continuously from 210 to 310 ms. It has been previously shown that spin-lattice relaxation times remain equal at the same temperature for the same triacylglycerol studied.35 The only parameter that changed in this study was the supercooling, which was directly linked to the cooling rate and thus modified the size of the crystals.
Indeed, nucleation is favored at a high degree of supercooling, whereas crystal growth is favored at a low degree of supercooling. Himawan et al.18 proved that crystal growth rates decreased as the chain length increased, and that the growth rate for tristearin was very low. Since the two triacylglycerols followed the same cooling kinetics, trilaurin crystals were assumed to be larger than the tristearin crystals at a low degree of supercooling. At a low degree of supercooling, where crystal growth was favored, the difference in crystal sizes between the two triacylglycerols became greater. Moreover, at a high degree of supercooling, the crystal growth is limited and the density inside the crystal becomes the changing parameter. All these phenomena explained our results described in Figure 1 if we assume that there is a relationship between T1 and crystal size. Indeed, for trilaurin T1 increased when supercooling decreased, that is, when the size of trilaurin structures increased. The tristearin T1 remained constant, which agrees with a slow crystal growth rate. Moreover, the trilaurin T1 was always higher than that of tristearin, which is compatible with larger crystals for trilaurin. The difference in T1 between the two triacylglycerols increased when supercooling decreased, that is, when crystal growth was favored. In the solid state, an increase in T1 can be correlated with a more compact crystal. The density was therefore enhanced for trilaurin. The second moment (M2) was measured as a function of supercooling temperature for the previous systems and the results are given in Figure 2. The results were the same as in the case of spin-lattice relaxation time measurements. Indeed, when M2 increases, the mobility decreases in the system. Thus, as shown in Figure 2, the mobility of trilaurin decreased with the degree of supercooling, whereas the mobility of tristearin remained almost constant. The M2 was always greater for tristearin than for trilaurin and the difference in M2 increased when the degree of supercooling decreased. These results were similar to those found on T1 measurements, with the same shape and behavior, and therefore confirmed the possibility of the existence of a relationship between the NMR relaxation parameters and the size and the density of the crystals. (b) Effects of the Liquid Phase. The next step consisted of studying the effects of the presence of a fat liquid phase on the behavior of tristearin crystals. The liquid phase was obtained using tricaprin, which was liquid at 40 and 60 C. Three different ratios were used for the mixtures of tricaprin
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Figure 3. Variations in T1 of tristearin at 40 C (9) and 60 C (() as a function of solid fat content.
and tristearin, that is, 25/75, 50/50, and 75/25 (w/w). The evolution of T1 as a function of the SFC is given in Figure 3. First, it was possible to demonstrate that T1 decreased when SFC increased at both temperatures, and that a plateau was reached when SFC was under 50%. The behavior was very similar at 40 and 60 C. The difference in spin-lattice relaxation times between the two temperatures was due to the evolution of T1 with temperature, as reported by AdamBerret et al.35 It is worth noting that the polymorphic behavior of tristearin at 40 C was different when it was a pure solid or in the presence of a liquid phase. Indeed, tristearin was in the R form when it was pure with a T1 of 300 ms, whereas it was in the β form when there was a liquid phase in the sample, with a T1 of 3000 ms for a SFC of 80%. This phenomenon was explained by the presence of the liquid phase which allowed more rapid reorganization of the system by mass transfer. A similar T1 between 20% and 60% of SFC suggested that the characteristics of the two crystal networks were similar at these two SFC. Thus, it seemed that the degree of organization of the system increased with the amount of liquid whatever the temperature, and when SFC was lower than 50% the evolution of the organization remained constant and the crystals were similar. This behavior explained why the T1 were equal at low SFC. Powder XRD was also performed in order to determine the influence of the liquid phase on the compactness of the system and to compare it with the NMR results. To perform these experiments, the capillaries were submitted to the same temperatures as the NMR tubes. The results for the three mixtures and pure tristearin at 40 C are presented in Figure 4. X-ray measurements confirmed the previous NMR results. Indeed, it was possible to observe the different polymorphic behavior of tristearin when it was pure and with a liquid phase. The singlet at 1.51 A˚-1 is characteristic of an R form, whereas the singlet at 1.38 A˚-1 with the doublet at 1.62 A˚-1 and 1.70 A˚-1 characterize the β form.42 Tristearin was therefore in the R form when the system was completely solid, but it was in the β form as soon as a liquid phase was present and allowed rapid reorganization of the crystals. Another interesting point shown in Figure 3 was the possibility of observing a deviation of the SFC compared to the expected value presented in Table 1. Indeed, as tricaprin in the β form melts at 33 C, it should be totally liquid at 40 C and the SFC would be equal to the amount of
Adam-Berret et al.
Figure 4. X-ray diffraction spectra at 40 C of pure tristearin as a function of solid fat content.
Figure 5. Deviation between theoretical SFC (solid line) and SFC measured at 40 C (*) and 60 C (þ).
tristearin, but this was not the case. The deviation of the SFC value from the theoretical SFC is shown in Figure 5. There was a linear relationship between the predicted and the measured SFC according to the quantity of tricaprin introduced into the sample. SFC was always greater at 40 C than predicted, meaning that part of the tricaprin was still in the solid state. This phenomenon was probably due to the presence in the system of cocrystals which melt above 40 C. This hypothesis was reinforced by the SFC measurements at 60 C. Tristearin in the β form melts at 73 C, so at 60 C it should be totally solid. However, the SFC was lower than expected for the 75/25 and 50/50 mixtures, and the deviation at 60 C became greater when the amount of tricaprin in the mixture increased. Part of the tristearin had therefore already melted, probably because it was comprised into cocrystals. This can be explained by the presence of more tricaprin in the cocrystals which decreased the melting temperatures of the cocrystals to below 60 C. Thus, they had already melted at 60 C. The SFC for the 25/75 mixture was higher than predicted and thus part of the tricaprin was still in the solid state at 60 C. These results were confirmed by the DSC measurements, presented in Figure 6. These DSC thermograms display the melting of the three mixtures crystallized at -20 C. It was possible to observe the melting of a compound between 40 and 73 C. This peak was attributed to cocrystals formed during the fast supercooling. The peak was broadened by the different compositions of cocrystals, which contained greater or lesser amounts of
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tricaprin: the greater the amount of tricaprin present in the sample, the lower the melting temperature of cocrystals, as we assumed from our SFC measurements. It should be noted that for high tristearin content, tristearin was present in the tricaprin crystal network. These thermograms were in agreement with SFC measurements. (c) Effects of Storage Time. Spin-lattice relaxation times were measured over time. Two mixtures with different SFC (80% and 60%) were studied for 12 days at 40 C. The results in logarithmic coordinates are shown in Figure 7. There was a linear relationship for the two mixtures, which meant that the evolution of T1 with storage time followed
Figure 6. DSC heating thermopeaks of tricaprin and tristearin blends for three different SFC.
Figure 7. Evolution of T1 as a function of storage time for the 25-75 (w/w) mixture () and the 50-50 (w/w) mixture (Δ) at 40 C.
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a power law model. T1 was always higher for the 50-50 mixture than for the 25-75 mixture. This difference in T1 can be explained by a difference in crystal size, since if the crystals are larger it can be assumed that their density increases. Moreover, the known phenomenon occurring with time is Ostwald ripening, which corresponds to the melting of the smaller crystals to form larger ones. The crystal growth related to this phenomenon has been proven to follow a power law model. The power law exponents determined here were almost the same for the two mixtures, which corresponded to a similar organization for their fat crystal networks. However, a difference was observed for the ordinates at the origin, with a higher value when more liquid was present in the sample, which corresponded to larger crystals. The liquid phase thus provided larger crystals more quickly, but maintained the organization of the system. From the Lyfshitz and Slyozov model,38,43 the power law exponent is usually between 0.20 and 0.33. The power law in our case was close to 0.1. The actual deviation was because we measured spin-lattice relaxation times and not crystal size directly. However, the fact that we still retained the power law model confirmed that there is a relationship between crystal size and spin-lattice relaxation time. It is worth noting that second moment dipolar (M2) and SFC remained constant with time, as can be shown in Figure 8. If M2 remained constant over the storage time, this meant that there was no modification of the polymorphic behavior during this period. The increase in T1 was thus not related to the polymorphism but was only related to crystal growth due to the Ostwald ripening effect. On the other hand, M2 was not sensitive to crystal size. We saw earlier in the study that SFC could modify T1, but as SFC remained constant over time, the evolution of T1 was not due to this parameter. In order to follow the evolution of the thickness of the crystals over time, XRD measurements were performed on the 50-50 (w/w) mixture at 40 C for 7 days, and the SAXS diffraction peaks were monitored for fwhm determinations The results obtained from this experiment are shown in Figure 9 and are plotted with the T1 of the system determined previously. It was possible to observe that the thickness of the crystals followed exactly the same evolution as the spin-lattice relaxation time. Indeed, only one power law function was used to fit the evolutions of the two parameters. This result showed that the increase in T1 is related to the growth of the thickness of the crystals. A size around 40-45 nm for the
Figure 8. Evolution of M2 and SFC as a function of storage time for the 25-75 (w/w) mixture (80% SFC) and the 50-50 (w/w) mixture (60% SFC).
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thickness of the crystals corresponds to 9-10 lamellae of triacylglycerols in the crystal. This evolution was also due to the Ostwald ripening phenomenon. Polarized light microscopy observations were performed on the 75/25 (w/w) blend. This mixture was preferred to the 50/50 mixture because of the clearer images which can be obtained due to better differentiation of the solid and liquid phases. Moreover, it has already been demonstrated in this study that when SFC was below 50%, the mixtures had the same behavior. The images were taken during the first 4 days, when the increase in T1 was maximal (Figure 10). Note that polarized microscopy is only sensitive to changes in two dimensions, whereas T1 is sensitive to the changes in the sample volume. The system evolved over time. It was possible to observe an increase in the average crystal size. At the beginning, the tristearin crystals in the β form were small, and they grew for 4 days. The most significant evolution occurred during the first 24 h when the nonorganized small crystals formed larger crystallites. All these findings confirmed the NMR measurements and the hypothesis of a relationship between spinlattice relaxation time and crystal size.
Figure 9. Evolution of T1 (4) and crystal thickness (() over time for the 50-50 (w/w) mixture at 40 C. The line corresponds to the power law fit of T1.
Adam-Berret et al.
Discussion The aim of this study was to establish whether there was a relationship between fat spin-lattice relaxation times and the size of its crystals. Different factors known to influence the size of fat crystals were investigated by measuring NMR relaxation parameters and by comparing NMR to other techniques. Two different levels were highlighted by our experiments. The first was the molecular level, related to the density inside the crystal and characterized by spin-lattice relaxation time and second dipolar moment. This level was directly related to supercooling as proven in this study. The second was at the level of crystal thickness and aggregates. This level was only characterized by spin-lattice relaxation. The latter parameter provided interesting information regarding the fat crystal network. Different phenomena were demonstrated by the study of the influence of the liquid phase on the fat crystal network. The first was a modification of the polymorphic behavior of triacylglycerols. It was shown by NMR and XRD that pure solid tristearin was in the R form at 40 C and that it was in the β form as soon as there was a liquid phase in the sample. The liquid phase permitted rapid reorganization of the side chains from a metastable state into a well-packed system. The second phenomenon induced by the presence of a liquid phase in the sample was an effect on the crystal network and crystal size. Indeed, measurements over time showed that T1 and XRD data could be fitted by the same power law model. Moreover, this power law model was already known as a consequence of the Ostwald Ripening phenomenon, which relates crystal size and the effects of time. The decrease of the fwhm of the diffraction peak of tristearin over time was related to the increase of the thickness of the crystals. It meant that the small crystals melted in the liquid phase and recrystallized at the surface of the bigger crystals by adding a new lamella. However, the microscopic observations showed that the evolution of the thickness of the crystals was not the prevailing phenomenon which was the increase of the length of the crystals. The same power law model used to fit T1 and X-rays showed that T1 was mainly sensitive to the thickness of the crystals.
Figure 10. Polarized light micrographs of tricaprin/tristearin 75/25 (w/w) mixture at 40 C after (a) 5 min, (b) 24 h, (c) 64 h, and (d) 88 h. Scale is common for the four images.
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Furthermore, polarized light microscopy confirmed the relationship between crystal size and T1 by observation of crystal growth over time. The parameters derived from the power law model of Ostwald ripening provided interesting information on the system. Indeed, the exponent is linked to the organization of the system. The present measurements proved that the organization of the two systems having different SFC was similar. However, the changing parameter between the two power law fits was the ordinate at the origin, which is related to crystal size and recrystallization rate. The recrystallization rate increased with the amount of liquid, and thus the more liquid present in the sample, the quicker the reorganization of the crystals. This finding explained the evolution of T1 as a function of SFC. The spin-lattice relaxation time was in fact higher at low SFC because of the recrystallization rate, which was higher when SFC decreased. Thus, the crystals were larger and thicker at low SFC and then T1 was higher. Moreover, the recrystallization rate was the same for SFC of 60% and 40%, and it seems therefore that there is an amount of liquid for which the recrystallization rate becomes maximal and the reorganization is the most rapid. SFC measurements demonstrated the formation of triacylglycerol cocrystals. SFC measurements at 40 C were higher than expected, unlike the measurements at 60 C for which the SFC was lower. DSC measurements confirmed the hypothesis of cocrystallization by proving the presence of cocrystals in the system on thermograms. Indeed, tricaprin and tristearin are miscible in the melted state. During fast supercooling (70 C/min), the two compounds crystallized in the R form. This metastable and disorganized state favored cocrystallization despite the significant difference between the fatty acid chain lengths.28 The sample thus contained pure tristearin, pure tricaprin, and cocrystals. According to the amount of tricaprin in the sample, cocrystals contained greater or smaller amounts of tricaprin: the greater the amount of tricaprin present in the cocrystals, the lower their melting temperatures, which were between 33 and 73 C, as proved by DSC. These melting temperatures explained the deviation of SFC from the theoretical value. Few cocrystals melted at 40 C. Cocrystals melted at 60 C for high concentrations of tricaprin, and SFC was then lower than the amount of tristearin. On the other hand, for the mixture with a majority of tristearin, most of the cocrystals had a melting temperature above 60 C, and SFC was then higher than expected. The linear relationship between the SFC measured and the concentration in tricaprin proved that the higher the amount of tricaprin in the sample, the more cocrystals were formed. This relationship was also useful when preparing samples with a desired SFC. Cocrystals were not responsible for the increase in T1 because if they had melted, leading to an improvement in purity of the tristearin crystal network, the SFC would not have remained constant. Thus, the evolution of T1 over time was not due to polymorphism, SFC, and melting of cocrystals. It followed a power law model, as for Ostwald ripening, and XRD data and microscopy observations proved that crystals grew with time. Therefore, we can conclude that T1 is related to crystal size and thickness, contrary to the second moment which was only sensitive to polymorphism and crystal density. The sensitivity of T1 to the crystal size may be explained by the spin diffusion process. Indeed, the relaxation time T1 is affected by the spin diffusion which depends on the presence of relaxation sinks. These relaxation sinks can be natural such as mobile group in the molecule or can be generated by the
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presence of defects. The more relaxation sinks, the more the spin diffusion is efficient and T1 is reduced. Pure crystals with few relaxation sinks have long relaxation times because they lack the mobility necessary to transfer energy to the lattice. Mobile regions of a sample relax quickly, and magnetization from slow-relaxing domains is transferred to them via proton spin diffusion. The regions with greater mobility thus act as sinks for the relaxation of the entire sample. In the crystal lattice system, the most mobile domains are on the crystallite surfaces and at crystal defect sites. A sample containing small and imperfect crystals will relax quickly due to the large volume of the fast-relaxing area compared to the slow relaxing domain. When crystals grow in time via recrystallization, there are less imperfections and the slow-relaxing domain becomes predominant on the fast relaxing area, leading to an increase of the relaxation time T1. A nice description of this phenomenon was provided by Lubach et al.44 Consequently, the increase of T1 over time for tristearin can be related to the modification of the crystals (recrystallization, growth) which modified the spin diffusion process and thus T1. Finally, all these measurements demonstrated that lowfield NMR could be useful for the study of fat crystal networks. First, we investigated the effects of supercooling, since it has already been established that larger crystals are formed when supercooling decreased. This phenomenon was directly linked to crystal nucleation and growth rate mechanisms. The presence of the liquid fat had two different effects on the fat crystal network, which were the modification of the polymorphic behavior of the triacylglycerols and the formation of larger and thicker crystals. Spin-lattice relaxation time measurements could be used to determine the evolution of the physical properties of fat crystal networks over time. Indeed, this NMR method could be used to evaluate whether the system is close to equilibrium or not and whether the physical properties of food products will remain constant with time. It appeared that the Ostwald Ripening effect stopped when the system was totally solid, and continued until there was a liquid phase in the system. As fractal dimension D is the parameter currently used to characterize fat crystal networks, it would be interesting to determine to what extent T1 and D are related, bearing in mind that D evolves like T1 during aging.22 Acknowledgment. The authors thank Mr. Bruno PONTOIRE, INRA-BIA for his help with powder X-ray diffraction measurements and Mrs. Corinne RONDEAU-MOURO and Mr. Gianfranco MAZZANTI for valuable discussions.
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