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Ultrasonic Technique for Determination of the Shear Elastic Modulus of Polycrystalline Soft Materials Fatemeh Maleky and Alejandro Marangoni* Department of Food Science, University of Guelph, Guelph, Ontario, Canada ABSTRACT: The effects of laminar shear on crystalline orientation and the mechanical properties of triacylglycerol crystal networks were quantified using ultrasonic spectrometry. In this communication, we demonstrate the feasibility of determining the shear elastic modulus of irregularly shaped, small pieces of polycrystalline materials. Results obtained were comparable to those obtained by conventional small deformation oscillatory rheometry. Moreover, in-line, in situ measurements, as well as specific directional probing, are possible using this technique. Here we also show that cocoa butter crystallized under an external shear field displays a higher shear storage modulus than cocoa butter crystallized statically. This opens up the possibility of structuring edible fats with less structuring material, that is, saturated and trans fats, resulting in a food material with improved health characteristics.
he determination of the storage modulus (G0 ) of soft viscoelastic materials, such as edible fats, is nowadays a common analytical procedure.1-6 The storage modulus (G0 ) of a polycrystalline material is sensitive not only to the ratio of solid crystalline material to liquid but also the structure of the solid at different length scales.7,8 Moreover, the mechanical strength of such plastic materials, in the form of the yield stress, Young’s modulus, or storage modulus, is widely considered a good indicator of material functionality.9-11 It is thus of great interest, from both academic and industrial perspectives, to be able to quantify these mechanical properties rapidly and accurately. Most conventional mechanical testing methods may suffer from some limitations. They are not rapid, cannot be used in-line, and are sometimes difficult to implement if samples have an irregular shape and dimension. All these limitations ultimately limit these techniques to be used on samples that have been crystallized, or set, in off-line mold of specific shape and dimensions. It would be therefore advantageous to have an alternative analytical technique that could overcome these limitations. Previously, the authors developed a rapid, precise, and nondestructive method for the determination of the storage modulus of fats using ultrasonic velocity measurements.12 In this study, we validate the accuracy of the proposed method for another fat system, namely, cocoa butter, the structuring material in chocolate and confections. We also demonstrate here the feasibility of using the developed ultrasonic method for irregularly shaped pieces of material obtained by crystallizing cocoa butter under an external laminar shear field such as a Couette-type device. Cocoa butter was sheared at a shear rate of approximately 320 s-1 using a continuous Couette-type laminar shear crystallizer (two concentric cylinders, with the outermost cylinder rotating).13
Samples were crystallized from the melt to 20 °C at 2 °C/min for 15 min. Reduction of temperature was achieved by three water jackets connected to cooling water, and a sheet of crystallized sample was obtained. Details of the crystallization process were explained elsewhere.13 This sample is curved with a 2.5 mm thickness and will be called “oriented sample” for the rest of this study. Powder X-ray diffraction and cryo-scanning electron microcopy (cryo-SEM) analysis confirmed the crystalline orientation of the crystalline network in the oriented sample.13-15 To crystallize cocoa butter under shear without crystalline alignment, cocoa butter was sheared in a beaker. Cocoa butter was heated to 60 °C in an oven to erase all crystal memory. The molten sample was transferred to a glass beaker placed inside a temperature-controlled Neslab water bath (Neslab RTE-111, Fisher Scientific, St. Louis, MO) for cooling from 60 to 20 °C for 30 min. During cooling, a Lightnin mixer (Lightnin Labmaster LIU10F, Wytheville, VA, USA) was used to perform a constant agitation rate of approximately 340 s-1. The partially crystallized cocoa butter was then transferred to a cylindrical shear cell (with the same geometry of the laminar shear crystallizer) set at 20 °C to complete crystallization statically. We named this sample the “sheared sample”. The static sample was made by transferring the molten cocoa butter into the shear cell placed inside a cooling jacket connected to the temperature-controlled Neslab water bath. Cocoa butter was cooled to 20 °C at 2 °C/min and then the shear cell was transferred to an incubator set at 20 °C to complete crystallization. The samples obtained are curved. All the samples were stored for 7 days in an incubator set at 20 °C before further
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r 2011 American Chemical Society
Received: January 7, 2011 Revised: February 18, 2011 Published: March 04, 2011 941
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Figure 1. (A) Wide and small (inset) angle powder X-ray diffraction patterns of shear-oriented (OR), sheared (SH), and statically crystallized (ST) samples sample after 7 days of storage at 20 °C. (B) Differential scanning calorimetric thermograms of shear-oriented (OR), sheared (SH), and statically crystallized (ST) samples after 7 days of storage at 20 °C. The table reports the solid fat contents (SFC) and corresponding standard deviations of the samples under the same conditions.
Table 1. Comparison of the Shear Storage Modulus (G0 ) of Crystallized Disk Samples Obtained Using Rheometry and Ultrasonic Velocimetry a G0 (MPa) sample
rheology
ultrasonic velocimetry
static
170.3 ( 19.2A
sheared
226.2 ( 7.9
B
180 ( 3.3A 228.7 ( 3.9B
a
Values with the same letters within a row are not statistically different (P < 0.05).
diameter and 3.2 mm height) and allowed to crystallize for 7 days at 20 °C. Oscillatory tests (small deformation) were performed by means of a strain sweep experiment at a frequency of 1 Hz, within the range of 6 10-3 to 1.0% strain, and a maximum applied normal force of 5 N. The reported data are the average of eight individual replications. An SIA-7 ultrasonic spectrometer (VN Instruments Ltd., Elizabethtown, ON, Canada) was used for ultrasonic measurements. Transducers of 1 MHz center frequency (GE Panametrics, MA, USA) were used to generate a chirp wave over a range of frequencies and amplitudes. Curved crystallized samples were cut into narrow equal size pieces (20-25 mm length and 10-12 mm wide) and placed between the ultrasound transducers. The use of such dimensions allows for good contact between the sample and the transducers, and conceivably gives a more accurate velocity value. Canola oil was used as a coupling media. This experimental set up is illustrated in Figure 2a. Pieces with a similar width (10-12 mm) were cut from the samples in PVC molds and placed between the transducers. The data reported corresponds to the average of 12-15 individual measurements. Using the sample width as the wave distance traveled (D) and time-of-flight, the time taken for the wave to travel from one transducer to another (TF), the ultrasound velocity was calculated from V = D/TF. The bulk modulus (Ki) of a medium i through which an ultrasonic wave travels at a velocity vi is given by19,20
Figure 2. (a) Crystallized samples cut into narrow pieces and placed between the two transducers. (b) An illustration of a piece of oriented sample, showing the direction of crystalline alignment through the sample thickness.
analyses. Since ultrasonic velocity and the mechanical properties of edible fats are influenced by the amount of solids (SFC) and the polymorphism of the solid-state,10,16-18 all the measurements in this study were done after aging the samples for 7 days and confirming their similarity in SFC and phase behavior. Pulsed NMR and powder X-ray diffraction measurements confirmed a solid fat content of 78% and the presence of the βV polymorphic phase (triclinic) in all specimens as shown in Figure 1. This figure also displays a typical graph of differential scanning calorimetry (DSC) melting profile of the samples, stored at 20 °C for 7 days, corresponding to βV polymorphic form. To perform the rheological measurements in static and sheared samples, a TA Instruments AR2000 controlled-stress dynamic rheometer (TA Instruments, Mississauga, ON, Canada) was used. Partially crystallized (not set) sheared and static samples were poured into pretempered PVC molds (20 mm
4 Ki ¼ v2i Fi - Gi 3
ð1Þ
where Gi is the shear modulus and Fi is the density of the medium. In this procedure, we determined the ultrasonic velocity and density of the liquid oil phase and solid crystalline phase, as well as the shear modulus of the solid phase. In previous work, we 942
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Figure 3. Cryo-SEM and TEM micrographs of the static (a), sheared (b), oriented (c), samples displaying different crystalline arrangements, nanoplatelet morphologies, and sizes.
estimated both the density of crystallized samples (Fs= 0.92 g cm-3) and storage modulus of 100% solid tristearin (G0 = 250.67 MPa).12 Since it is not possible to determine the storage modulus of 100% solid cocoa butter, the value of 100% solid tristearin in the beta polymorphic form should be a good estimate of the storage modulus of any 100% solid triglyceride in the beta polymorphic form. The shear modulus of the liquid phase is zero. With this data, we could determine the bulk modulus of the liquid and solid phases (Kl and Ks) using eq 1. However, our material is a mixture of solid and liquid phases, and the bulk modulus of such mixture is given by12,19 Kmix ¼
Ks Kl ΦKl þ ð1 - ΦÞKs
Table 2. Ultrasonic Velocity and Derived Shear Storage Modulus (G0 ) Determined on Curved Samples of Crystallized Cocoa Buttera sample
ultrasonic velocity, ν, (m/s) 1950.9 ( 23 0
shear modulus, G , (MPa)
sheared
oriented
1606.9 ( 55
A
B
124.2 ( 3.74
A
180.6 ( 8.8
B
1487.6 ( 66C 197.1 ( 8.6C
a
Values with the same letters within a row are not statistically different (P < 0.05).
was confirmed by cryo-SEM,14 as shown in Figure 3. Alignment of crystals parallel to the direction of the external shear field is clearly observed in the oriented sample, whereas both sheared and static samples revealed a random arrangement of crystal clusters. At the nanoscale, smaller platelets were observed in the sheared and oriented samples compared to the static samples, as determined by cryo-transmission electron microscopy (cryo-TEM). Crystallization under laminar shear (360 s-1) caused a reduction in nanoplatelet length from 2 μm to 300 nm and width from 165 to 130 nm.14 This anisotropic distribution of platelets within the material suggests therefore different mechanical properties depending on the orientation. In order to quantify these effects, measurements need to be carried out in the appropriate direction shown in Figure 2b. Surprisingly, we could not find any conventional rheological method suitable for these measurements. Here, the storage modulus of these curved samples was obtained using the proposed ultrasonic technique. The ultrasonic velocity and the corresponding storage moduli of the samples are presented in Table 2. The results in Table 2 suggest that the ultrasonic wave travels more slowly through samples crystallized under laminar shear than through samples crystallized under static conditions. This implies that the wave velocity not only depends on the solid fat content16,17,21 but also on particle size and size distribution. Moreover, sheared and oriented samples display a much stronger network structure compared to the one crystallized under static conditions. Here we show that crystallizing cocoa butter under laminar shear increases the mechanical strength of the material by ∼50% relative to the statically crystallized sample and ∼10% relative to the sample crystallized under a conventional turbulent shear field. These results suggest that ultrasonic velocimetry is a reliable indicator of the effects of crystal size and crystalline
ð2Þ
where Φ corresponds to the mass fraction of solids. The shear modulus of this mixture could be then easily estimated from a simple measurement of the ultrasonic velocity of a wave traveling though this mixture, and from knowledge of the bulk modulus and solid mass fraction of the mixture:19,20 3 Gmix ¼ v2mix F - Kmix 4
static
ð3Þ
The reproducibility and accuracy of values obtained were assessed on crystallized samples of well-defined geometries. To do so, the provided flat disks of the crystallized samples were used for rheology analysis. Using small deformation rheology, a strain sweep test was carried out on sample disks and the G0 was determined. At the same time, the storage moduli of the samples were determined using our ultrasonic method. Table 1 shows the G0 values of static and sheared samples determined by rheology and ultrasonic velocimetry. As can be appreciated in this table, there are no significant differences between the storage moduli determined using the two different techniques (P < 0.05). This result confirms our initial finding and validates that ultrasound velocimetry can be successfully used to measure the mechanical properties of fats. As explained, samples used in this study have a distinct shape which makes them difficult to analyze using conventional rheological methods; they are curved and only 2.5 mm thick. Moreover, previous work13,15 has shown that samples are anisotropic in terms of their microstructure, as determined by powder X-ray diffraction. This anisotropy in mesoscale structure 943
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orientation on the mechanical properties of fats at equivalent amounts of solid crystalline material and similar polymorphism. This technique potentially constitutes a new way to determine the small deformation mechanical properties of soft polycrystalline materials in situ.
’ AUTHOR INFORMATION Corresponding Author
*Address: Department of Food Science, University of Guelph, 50 Stone Road West, Guelph, Ontario, Canada, N1G 2W1. Telephone: (þ1) 519-824-4120 Ext. 54340. Fax: (þ1) 519-824-6631. E-mail:
[email protected].
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