- Email: [email protected]
Viscoelastic properties of edible lipids
PII:
SO260-8774(97)00030-7
Joumul of Food Engineering 33 (1997) 305-320 0 1997 Elsevier Science Limited All rights reserved. Printed in Great 13ritain 0260-8774197 $17.00 +O.(H)
ELSEVIER
Viscoelastic Properties of Edible Lipids T. H. Shellhammer,“‘f
T. R. Rumsey” & J. M. Krochta”Th*
“Department
of Biological and Agricultural Engineering, University of California, Davis. CA 95616, USA “Department of Food Science and Technology, University of California, Davis,
CA 95616, USA (Received 22 April 1996; revised 12 March 1997; accepted 17 March 1997)
ABSTRACT The viscoelastic natures of beeswax, candelilla wax, camauba wax and a highmelting milkfat fraction were compared by estimating their relaxation parameters from stress relaxation data. A generalized Maxwell model consisting of one spring element and two Maxwell elements best descn’bed the stress relaxation of all lipids tested. The stress responses over both the compressive and relaxation portions of a stress relaxation test were considered. Cone penetration tests were used as a comparison to the stress relaxation tests. Candelilla wax and camauba wax behaved similarly as hard and elastic materials which resisted deformation, Beeswax and the milkfat fraction, on the other hand, were significantly more viscous, less elastic, and more easily deformed. 0 1997 Elsevier Science Limited. All rights reserved
NOTATION E
~3, Ei fI t t’
[I
Elastic modulus (Pa) Elastic modulus for a first spring element of the generalized model (Pa) Elastic modulus for an ith spring element (Pa) Number of elements in the generalized Maxwell model Time (s) Dummy variable for time Elapsed time to reach E()(s)
Maxwell
*To whom correspondence should be addressed. Tel.: (916) 752-2164, Email: jmkrochta@ ucdavisedu tcurrently with Departments of Food Science and Technology and Food; Agricultural and Biological Engineering; The Ohio State University, Columbia, OH 43210. 305
T H. Shellhammer et al.
306 E
Eo 4(t) Vi
0 z
Strain (unitless) Strain at the end of the compression phase of the stress relaxation procedure (unitless) Relaxation modulus (Pa) Viscosity of the fluid in the ith dashpot of the generalized Maxwell model (Pa s) Stress (Pa) Relaxation time (s)
INTRODUCTION Beeswax, candelilla wax, carnauba wax, and high-melting milkfat fractions are natural lipid materials which have been examined for use alone, or in conjunction with other materials, for use as edible barriers (Greener, 1992; McHugh & Krochta, 1994; Shellhammer et al., 1993). The chemical composition of these materials is quite diverse (Table 1). Anhydrous milkfat is composed chiefly of triglycerides of various fatty acid length and degree of saturation. Over 60% (w/w) of the fatty acids in milkfat are saturated, approximately 30% are monounsaturated, and 4% are polyunsaturated (Baer, 1991). It is this range of triglyceride size and degree of saturation that gives milkfat a broad melting range, from -20 to 37°C (Banks, 1991). At room temperature, it is a mixture of oil, semi-hard fat, and hard fat. The ratio of liquid to solid fat determines milkfat’s rheological properties. The melting point, and in turn the mechanical properties of milkfat, can be altered by separation into high and low temperature-melting fractions. This can be accomplished by a number of methods, but the most popular industrial technique is selective crystallization (Mortensen, 1983). Fractionation by selective crystallization from melted milkfat concentrates the higher-melting, long-chained saturated triglycerides in the higher-melting fraction while concentrating the short-chained TABLE 1
The Chemical Composition and Melting Point of Selected Lipids
Wax acid esters (%) Wax acids (free) (%) Fatty alcohols (%) Lactides (%) Fatty acid esters (%) Hydrocarbons (%) Resins (%) Triacylglycerides (%) Mono- and diglycerides (%) Moisture (%) Melting point (“C) aBanks (1991). ‘Bennett (1975). ‘Kaylegian (1993).
Milkfat fraction”
Beeswaxh
98 2 0 _ 45’
Candelilla
Camauba
WfLVh
WUXh
71 14 1
28.5 8 13
84.5 3.0
T 12 -
50
;:: ::tl
T 62-64
0.5
66-71
OS 83-86
Viscoelasticproperties of edible lipids
307
triglycerides in the lower-melting fractions. This results in the higher-melting fractions having significantly higher solid-fat : liquid-fat ratios than the original milkfat (deMan & Finoro, 1980). These fractions are therefore harder in terms of mechanical properties than the non-fractionated milkfat. Waxes are naturally occurring esters of long-chained carboxylic acids (C,, or greater) with long-chained alcohols (C,, or greater) (Streitwieser & Heathcock, 1985). Beeswax is considered an animal wax and is produced by honey bees for building honeycomb cells. It is a mixture of wax esters, wax acids and hydrocarbons. Hydrolysis of these esters yields mainly CZ6 and Cl8 carboxylic acids and C30 and C& straight-chained primary alcohols (Streitwieser & Heathcock, 1985). Candelilla wax is a vegetable wax that is produced by a reed-like plant (Euphorbia antisiphilitica, Euphorbia cerifera, and Pedilanthus pavonis) which grows wild in northwestern Mexico and southern Texas (Bennett, 1975). It is composed in large part of hydrocarbons with some wax acid esters and alcohols. Carnauba wax is a plant exudate from the Brazilian ‘tree of life’ (Copemica cerifera). It is the hardest, highest-melting, natural commercial wax (Bennett, 1975) and is composed almost entirely of esters of CZ4 and CZ8 carboxylic acids and C32 and C34 straight-chained primary alcohols (Streitwieser & Heathcock, 1985). Instrumental measurement of solid and semi-solid lipid rheological properties has been accomplished with a wide variety of methods. Penetrometers are most commonly used, while extrusion instruments, parallel plastometers and wire cutting devices are used less frequently (deMan, 1976). Penetrometers are classified as constant-weight or constant-speed. In the former test, the weight of the penetrometer drives the plunger into the sample until it comes to rest due to the lipid’s resistive force. Constant-speed tests involve driving a penetrometer into a lipid sample at a constant speed and measuring either the distance of penetration to reach a specified resistive force or the magnitude of resistance at a specified penetration distance. A standard, constant-weight, cone penetration method (AOCS, 1960) has been used for determining consistency of fats (Davey, 1989; Hayakawa & deMan, 1982). Comparisons of cone angles and test speeds were performed by Tanaka et al. (1971) on solid and semi-solid foods including several fats. The viscoelastic nature of lipids, in a few instances, have been studied by examining their creep compliance (deMan et al., 1985; Shama & Sherman, 1970). Although the experimental procedure and data analysis are more complex with viscoelastic measurements than with the cone penetrometer, the results obtained give more information about the structure of the lipid materials (Shama & Sherman, 1970). The objectives of this study were to determine the viscoelastic properties of edible lipid film-forming materials using stress relaxation testing, and to compare these results with constant-speed, cone penetrometer measurements to determine whether these two tests provided unique or redundant measures of lipid hardness.
THEORETICAL
BACKGROUND
The stress-strain relationship for linear viscoelastic behavior is often given in hereditary integral form. Hereditary integrals describe the stress response given a strain input plus any strain history (Fltigge, 1975). For uniaxial stress relaxation, this integral is written as
308
T H. Shellhammer et al.
a(t)=
b&t-t’) Eat
The time-dependent relaxation modulus, 4(t), describes the relationship between the strain input and stress response. Models for the relaxation modulus are often determined from mechanical models, that is combinations of springs and dashpots in series or parallel. A spring and dashpot in series is called a Maxwell model (Mohsenin & Mittal, 1977) or Maxwell material (Fhigge, 1975), and a number of Maxwell bodies in parallel with each other and with a spring is called a generalized Maxwell model (Mohsenin, 1986). The relaxation modulus for the generalized Maxwell model can be shown to be $(t) = Eo+ jg, Eje-
$’
(2)
In the present study, a static, constant-strain test was used to observe stress relaxation. Viscoelastic materials behave in a linear manner generally under very small strains. Findely et al. (1976) suggest that strain be no greater than one to two percent; Mohsenin and Mittal (1977) found that fresh fruit exhibit linear viscoelastic behavior if they are strained less than 1.5 to 3.0%; and Skinner and Rao (1986) reported that frankfurters should be strained no more than 3.8%. Ideally, a stress relaxation test involves an instantaneous strain to a fixed value (co) followed by observation of the material stress decaying over time. In reality, instantaneous loading to a fixed strain is impossible to achieve because of the mechanical limitations of the testing equipment. Depending upon the viscous nature of the material, the material will begin to relax as it is deformed to reach co. Rather than ignore the initial loading portion of the experiment and assume that the material was instantaneously strained, the relaxation which occurs during the loading of the sample can be included in the mathematical analysis using eqn 1. Mathematically, these conditions are Compression:
a& = Z!L mo
t, i3E
Relaxation:
-
=O@ t>t,
(4)
at
Substituting eqn 2 in place of 4 in eqn 1 and using the strain rate stated in eqn 3, the stress response during compression (0
(5) Using the same substitution of 4 but evaluating the test (t > t,), the stress response is
a(t) over the relaxation
portion
of
Viscoelasticproperties of edible lipids
309
(6) A similar development was performed by Chen & Fridley (1972) yielding nearly identical equations. Their development differed in that they used a generalized Maxwell model which did not have a spring element in parallel with the series of Maxwell bodies. A relaxation time (r) is frequently used rather than the quantity vi/E, so that eqn 2 would read
In the case of a Maxwell body, when t = z the stress will have decayed to 37% of the total stress relaxation. This describes why z is called the ‘relaxation time’; it is a measure of how fast the stress decays. A material that has a short relaxation time infers that the stress imposed by a strain input dissipates quickly and is therefore more viscous than elastic in nature. The converse is true for long relaxation times. One means of determining z is to measure it as the time when 63% of the stress dissipation has occurred; however, it can be calculated by fitting the relaxation modulus to stress relaxation data using non-linear regression. Equally, the coefficients ye and E can be calculated using non-linear regression and then 7 is simply IIIE. The objective of stress relaxation testing is to identify the elastic (spring) and viscous (dashpot) constants, E, and vi. This is achieved by testing the materials under a set of given conditions and then fitting eqn 5 and 6 to the loading and relaxation data by adjusting the viscoelastic constants. However, difficulties can occur in gathering and interpreting force-deformation data because of interactions at the sample-platen interface. Bonding between the sample surface and the crosshead platen can result in the cylindrical sample assuming a barrel shape, whose surface is a paraboloid of revolution (Prentice, 1992). If the material can be bonded to the platen using an adhesive, results may be more consistent than without adhesion (Bagley & Christianson, 1987). Alternatively, the friction between the sample and the platen can be eliminated by using a thin coating of paraffin or silicone oil on a platen surface which is made of Teflon (Bagley et al., 1985). The latter method was used in this study. For lubricated compression, stress on the sample is calculated as recommended by Casiraghi et al. (1985).
MATERIALS
AND METHODS
Stress relaxation sample preparation Carnauba wax (Aldrich Chemical Company, Milwaukee, WI), candelilla wax (Strahl & Pitsch Inc., West Babylon, NY), beeswax (Fisher Scientific Inc., Fair Lawn, NJ), and a high-melting industrial milkfat fraction (VH-66, Center for Dairy Research, University of Wisconsin, Madison) were melted in glass beakers immersed in a hot
310
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water bath at 100°C. The molten lipids were poured into 10.0 mm i.d. by 10.2 mm height cylindrical copper molds and allowed to cool until solidified. The beeswax and the milkfat fraction were cooled to room temperature on a level granite slab under ambient conditions. The carnauba and candelilla waxes had high melting points: 82-85°C and 68-72°C respectively. Because of their volume change during cooling and the large temperature difference between their melting points and the room temperature, these materials would solidify too rapidly, producing irregularly shaped cylinders under ambient conditions. To alleviate this problem, the molten cylinders of wax were cooled slowly (approximately 0.5”C per minute) on a proSeries 720, PMC grammable hot plate (Dataplate@ Digital Hot Plate/Stirrer, Industries, Inc., San Diego, CA). The slow cooling allowed the waxes to shrink uniformly as they cooled. Once the lipids had solidified but not completely cooled, the excess material was shaved from the top of the mold to produce uniform, right cylinders which had smooth and parallel ends. The wax material slipped from the copper mold once they had cooled to room temperature because of thermal shrinkage. The milkfat fraction, which exhibited the least amount of shrinkage, was removed by gently heating the copper sleeve between one’s fingers until the cylinder slipped out into an ice bath. The lipid cylinders were stored at room temperature for 2 days prior to testing. The dimensions of the cylinders were measured with a caliper micrometer after storage but prior to testing. Stress relaxation data collection At least 15 min prior to testing, individual lipid cylinders were placed in a water bath held constant at 25fO.l”C. Tempered cylinders were removed from the water bath and brushed dry with’ tissue paper. Each sample was placed between two parallel polymethylmethacrylate plates mounted on a TA-XT2 Texture Analyzer (Texture Technologies Corp., Scarsdale, New York). The surfaces of the plates were lubricated with a thin film of silicone oil to prevent friction or bonding between the lipid sample and the plate faces. The lipid cylinders were strained to 2% at a crosshead speed of 1.0 mm per second, and the stress decay data (force, distance, and time) were gathered for 140 s at a rate of 200 points per second. The plate faces were cleaned and relubricated with silicone oil between each run. The room temperature was monitored during testing to ensure that the environmental conditions did not deviate significantly from the 25°C setpoint. During testing, the room varied in temperature from a low of 23.5”C to a high of 26.2”C. Four individual samples of each material were tested in a completely randomized fashion; however, in certain cases samples failed during testing either due to cracking or incomplete straining (~0.5%) and these data were eliminated. Incomplete straining was the result of background vibrations in the TA-XT2 which triggered the commencement of data collection prior to the crosshead actually contacting the sample surface. Additional replicates of the failed sample were tested so that four replicates were tested for each material. Stress relaxation data reduction and analyses The high data collection rate over the 140 s relaxation time produced nearly 30000 data points. To facilitate further analyses, a C-based data-reduction program was written to reduce each data set to 106 points. Since much of the change in resistive
Viscoelasticproperties of edible lipids
311
force during relaxation can occur shortly after compression, more data was retrieved from the beginning of the relaxation than from the end. From each data set, the first 60 points were gathered over the first 0.3 s of the test without reduction and included the compression (0.2 s) and initial relaxation (0.1 s) of the sample. The next 17 points were gathered one point every 0.1 s and lasted from t = 0.3 to t = 2.0 s. Another 17 points were gathered one point every 1.0 s from t = 2.0 to t = 20 s. Finally, the last 13 points were gathered one point every 10 s from t = 20 s until the completion of the test. This method of reduction provided a more manageable data set while minimizing the loss of information from the relaxation history. The objective of the data analysis stage was to fit the relaxation modulus to the stress relaxation data by adjusting the modulus coefficients. This was accomplished by using a derivative-free, non-linear regression statistical package, BMDP AR (BMDP, 1985). Initial estimates of the coefficients were required to use BMDP AR, and these came as approximations derived using the method of successive residuals. The method of successive residuals is a graphical technique used to approximate the coefficient terms of an exponential equation (Mohsenin, 1986). A spreadsheet was prepared (Microsoft Excel 4.0 for the Macintosh@) to calculate the exponential terms’ coefficients using this technique. In addition to the estimates of the relaxation modulus coefficients, a compressive elastic modulus was recorded from the loading portion of the stress relaxation curves. A linear regression was fitted to stress versus strain data and the slope of this regression was used as an estimate of the elastic modulus. In nearly all cases, the compression of the lipid cylinders did not immediately produce a steady increase of force with time. In these instances, the force-time data exhibited an initial toe prior to the linear increase in force from the compression of the lipid cylinder (Fig. 1). The toe was likely due to compression of non-uniformities on the lipid cylinder ends as the plunger face came into contact with the entire lipid cylinder face. Once the two surfaces mated, the entire cylinder was strained. The
/
0 Immediate deformation o Delayed deformhon
I
5
5
tstrain
t2
Time (set)
Fig. 1. Delayed deformation resulting from surface non-uniformities on the lipid cylinders.
312
7: H. Shellhammer et al.
TA-XT2 calculated the distance to strain each sample by measuring the sample’s height at the moment the plunger came into contact and determined the correct displacement based on a preset strain value (2% in this study). In the case of the delayed deformation, the instrument thought it was straining the sample to 2%, when in fact it was straining the sample to something less than 2%. The true strain was calculated based on the time over which the linear increase in force occurred. In Fig. 1, this time is the difference between tstrain and to for the data in which the deformation begins the moment the plunger meets the lipid cylinder. In the case where the data exhibited a toe (as does the delayed deformation data in Fig. l), actual deformation of the entire cylinder was calculated as the distance the plunger traveled during the time t1 to tz (i.e., tstrain, multiplied by the crosshead speed). The time axis of the force-time graph was adjusted in these instances such that the beginning of the stress relaxation test occurred at t, and not to. Once the initial estimates of the relaxation modulus coefficients had been determined via the method of successive residuals, they were used as initial values for the non-linear regression to fit eqn 5 and 6 to the stress relaxation data. These two equations represent the stress response over different periods of the test. Eqn 5, representing the compression phase, was fitted to the compression data, while eqn 6 was fitted to the subsequent relaxation portion of the same data. The coefficients of the relaxation modulus are the same for both of these equations since they are material specific, The non-linear regression package returned the ‘fitted’ coefficients along with residual statistics such as mean squared error and a pseudo-?. The experimental design for stress relaxation tests on individual lipid samples was a single factor completely randomized experiment. Using these coefficients returned from the non-linear regression, statistical differences among the four lipids were determined using a single factor analysis of variance via Statistical Analysis Software (SAS, 1989). Means comparisons were performed in the cases which were significantly different using a Duncan’s multiple range test and a Tukey’s studentized range test. Cone penetration of lipih materials Empirical measurements of fat ‘hardness’ have been standardized in a number of cases (AOCS, 1960; ASTM, 1986, 1987, 1988, 1991). In the absence of the specific cone penetrometer required by the ASTM methods, the TA-XT2 Texture Analyzer was employed to measure resistive force to a 3 mm penetration by a 60” cone. Samples were prepared by heating the lipid materials in a boiling water bath for at least 15 min beyond melting. The molten lipid was poured into 5.0 cm i.d. by 1.0 cm cylindrical cups and allowed to temper at room temperature for 24 h. Once the lipid had crystallized during the cooling process, the exposed lipid surface was shaved level with the edge of the cup so that a smooth, uniform surface was produced. An hour prior to testing, the cups containing the lipids were placed in a water bath held constant at 25°C. Testing consisted of first removing the cup from the water bath and gently brushing the surface dry with tissue paper. A 60” cone (2.6 cm height and 3 cm maximum diameter), lubricated with a light coating of silicone oil, penetrated the lipid sample at a rate of 0.2 mm/s to a distance of 3 mm. Force readings were sampled at a rate of 400 points per second, and the maximum force at, or near, 3 mm penetration was recorded. The sample was placed back in the water bath prior
Viscoelastic properties of edible lipids
31.3
to repetitive testing. Five replicate penetrations on the exposed surface of the lipid in each cup were performed in a completed randomized fashion. The experimental design for the penetration tests was similar to that of the stress relaxation study, a completely randomized design. Data were analyzed using a single factor analysis of variance and a multiple correlation via Statistical Analysis Software (SAS, 1989). The high-melting waxes were brittle enough that a 3 mm penetration caused cracking in some instances. A second test was performed in which the cone penetrated to a depth of only 2 mm. Force readings were recorded at 1 mm and at 2 mm. As with the first test, five replicates of each material were tested in a completely randomized fashion.
RESULTS
AND DISCUSSION
Model selection for the relaxation modulus The mathematical description of a viscoelastic material’s stress response to strain input, eqn 5 and 6, was derived using a generalized Maxwell model as the relaxation modulus. Before eqn 5 and 6 could be fitted to stress relaxation data, a specific model (rather than the generalized Maxwell model) had to be chosen for the relaxation modulus. The question was how many Maxwell bodies to include and whether to include the spring element. Peleg (1976) lists several requirements for constructing a rheological model of a food material. The model must be able to predict real material behavior, it should be able to respond to both positive and negative forces, and changes in the material’s behavior must be explainable in terms of the model parameters. These requirements suggested reaching a balance between choosing a model with as few terms as possible with one that has many. For the sake of simplicity, as well as being able to explain changes in the material’s behavior, a model should have few terms. On the other hand, a model with many terms will yield predictable results with high accuracy. Initial tests of the viscoelastic properties of the lipid materials using small strains pointed towards a five element model (Fig. 2) because none of the lipid materials relaxed completely such that the stress went to zero. The elastic spring element in parallel with the Maxwell bodies accounts for this residual stress in the lipid, thus it was kept as part of the relaxation modulus. Determining how many Maxwell bodies to be included was based on a degree-of-fit of predicted stress response to the actual stress response. A model with one spring element and one Maxwell element in parallel yielded r’ values from the non-linear regression which ranged from 0.926 to 0.974 depending on the lipid type. Adding another Maxwell body, as shown in Fig. 2, yielded significantly improved 2 values which ranged from 0.991 to 0.998. Models with more elements yielded slightly higher ? values, as would be expected since the number of parameters in the model increased. Yet, the authors felt that a five parameter model would be optimal by achieving the previously mentioned balance of model size. A similar model was used by Sato and Nakayama (1970) to describe the mechanical behavior of white chicken meat. The five-parameter relaxation modulus is written as 6, F.(b(t) = Eo+EIe
T’+E2e
‘I,
I
(8)
T H. Shellhammer
314
et al.
Fig. 2. Model used for the relaxation modulus for the lipid materials. Stress, 0 (kPa); strain,
F.(unitless); spring constants, Ej (kPa); and dashpot viscosities, vi (kPa s).
Adjustments to strain Achieving a 2% strain in all samples was difficult because of the inability to achieve a true right cylinder in each of the samples and because of irregularities in the samples’ surfaces. The actual distance each sample was strained was calculated as described in the methodology section. These values ranged from 1.52% to 1.93%. Averaged among the four replicates of each material, the true strain ranged from a low of 1.6% for carnauba and candelilla waxes to a high of 1.8% for the milkfat fraction. Stress relaxation of the lipid materials The parameters in eqn 8, EiS and qis, for each replicate tested were averaged to produce Table 2 and Fig. 3. The individual parameters were compared using a single-factor analysis of variance and means testing, the results of which are included in Table 2. Large differences in the relaxation modulus coefficients were observed among the four lipid types. Carnauba and candelilla wax behaved relatively similarly as hard, non-deformable materials following the 2% strain input (Fig. 3 and Table 2). In comparison to the candelilla wax, the carnauba wax displayed a TABLE 2
Averaged Actual Strain and Relaxation Modulus Coefficients of Selected Lipids Material
Milkfat fraction Beeswax Candelilla wax Carmaiba wax
Corrected strain
EI Pa)
‘II (Pas)
vr
$
(Pa s)
2
0.018
13517”
3722”
4831”
2092”
201420”
0.565”
0.017
21347b
7589’
5507”
1206h
78 987’
0.161’
14.31h
0.016 0.016
34830’ 34 270’
2094’ 3880”
1917h 1647’
706’ 282d
3961 lb 10459h
0.352’ 0.072h
20.81h
Means (n = 4) with different superscripts are significantly different at a = 0.05.
40.69” 6.71h
Viscoelastic properties of edible lipids
315
rapid relaxation immediately upon loading (Fig. 4). Analysis of variance indicated that these two materials were not significantly different in terms of residual stress (E,,) and f2 (Table 2) while they were significantly different with respect to z,. It is also clear from Fig. 4 that the peak stress upon loading was very different among the four lipids. The large differences in the degree to which these waxes resisted deformation made comparisons of their relaxation behavior difficult. To improve the contrast in relaxation behavior, the stress data were normalized by dividing each stress data point by the maximum stress during the test. In this manner, the normalized stress values ranged from zero to one for all of the materials (Fig. 5). The four materials appear as two similar groups in Fig. 5. Carnauba and candelilla wax were hard materials resisting deformation. They had very high peak stresses (Figs 3 and 4) and dissipated less than 9% of this stress. The beeswax and milkfat fraction, on the other hand, had much lower peak stress, and they yielded much more of this stress during relaxation. It is clear from Figs 4 and 5 that carnauba wax exhibited the fastest relaxation times along with a very small degree of relaxation, thus it was the most elastic material of the four. The candelilla wax relaxed over a much longer period of time than the carnauba wax, as indicated by a significantly
I
1 l
T
I
i T
a
Beeswax
I
Milkfat Fraction
lb0 Time (set)
Fig. 3. Average stress relaxation response following a 2% compressive strain of the bulk lipid materials (n = 4). Solid lines represent fitted values based on eqn 5 and 6 using average coefficients from Table 2. Due to the time scale, the loading portion of the stress history has been removed.
T. H. Shellhammer et al.
316
larger z1 and a considerably larger r2. These results indicate that candelilla wax had more viscous behavior than the carnauba wax, yet both behaved more as elastic materials as compared to the beeswax and the milkfat fraction. The other group in Fig. 5 included beeswax and the milkfat fraction. One would expect the milkfat fraction to be less elastic and more viscous than the high-melting waxes. The milkfat fraction is comprised of triglycerides which are made in large part by saturated fatty acids, principally palmitic and stearic fatty acids. The milkfat fraction also contains unsaturated fatty acids, principally oleic acid (Jenness & Patton, 1959); thus a portion of the milkfat fraction is liquid at room temperature. Beeswax, on the other hand, is comprised of esters of rather long fatty acid and fatty alcohol, hence its elevated melting point. It resisted deformation but also exhibited a large degree of stress relaxation. The presence of a significant amount of free fatty acids contributed to its viscous qualities. Penetrometer results Lipid type had a significant effect (p
I
,
I
0.25
0.5
0.75
Time (set)
Fig. 4. Compression and initial stress relaxation following a 2% compressive strain of the bulk lipid materials (n = 4). Solid lines represent fitted values based on eqn 5 and 6 using average coefficients from Table 2.
Viscoelasticproperties of edible lipids
317
resistive forces which were not significantly different, while carnauba wax and candelilla wax were significantly different from each other and from the beeswax and milkfat fraction group (p < 0.05). Differences that might have stemmed from cracking of the lipid material during penetration did not appear outstanding, since the trend in hardness was similar at all three depths. The reason that cracking may not have been as large a problem as initially expected lies with the experimental procedure. The lipid materials were tested in the aluminum cups in which they were cast. When the high-melting waxes cracked during deep penetration, the various segments of the cracked lipid disk were contained by the mold and continued to offer resistance as the cone penetrated further into the newly formed crack. One concern with gathering viscoelastic property data is whether the information is of more value than data from simpler tests such as cone penetration. Usually, a cone test gives a composite parameter and not a true property of the material being tested. With regard to viscoelastic data, a stress relaxation test yields more information than a penetrometer (Shama & Sherman, 1970). As for discriminating differences among lipids, this may not always be the case. For example, hardness as measured by the cone penetrometer might correlate well with degree of elastic behavior. To examine whether this was the case in this experiment, a multiple
100
Time (set)
Fig. 5. Normalized stress relaxation response following a 2% compressive strain of the bulk lipid materials (n = 4). The loading portion of the stress history has been removed from this figure.
7: H. Shellhammer et al.
318
correlation was performed on the hardness and viscoelastic data. The force readings from the penetrometer did not correlate well with most of the relaxation modulus coefficients. The best correlations with the penetrometer readings and the relaxation coefficients were with E0 (r = 0.9372) and E2 (r = -0.9547). The magnitude of E2 values was inversely related to measures of hardness from the penetrometer; but the results for E2 fell into two groups (Table 2), while the results from the penetrometer fell into three separate groups. Based on the correlation analysis, it is safe to state that the results from penetrometer testing were different from the stress relaxation analyses, and that these two tests were not redundant measures of the rheological properties of the four materials tested in this study. SUMMARY
AND CONCLUSIONS
A five-element model, one spring and two Maxwell bodies in parallel, was chosen for the relaxation modulus of viscoelastic lipid film materials. Parameters for this relaxation modulus were identified by fitting equations which described the stress response to a strain input over the loading and relaxation portions of the data. Results of the stress relaxation analyses indicate that carnauba wax and candelilla wax were very elastic, non-deformable materials. Penetrometer results indicated that carnauba wax was the hardest wax of the four tested. Beeswax and the milkfat
250 -
q
Imm
penetration
q
Zmm
penetration
n
3mmpenetration
200-
iz 1500 2 IE loo-
50-
oMilkfat Fractiona
Beeswax a
Candelilla wax’ Camauba waxE
Fig. 6. Resistive force of lipid materials to cone penetration (n = 5). Lipids with different superscripts are significantly different at tl = 0.05 at all three depths of penetration.
Viscoelasticproperties of edible lipids
319
fraction were of similar hardness and exhibited similar relaxation behavior to each other, but were significantly softer and more deformable than either the carnauba or candelilla waxes. The milkfat fraction was the most viscoelastic material of the four lipids tested as characterized by its long relaxation times, and the smallest amount of residual stress remaining in the sample following relaxation. These later two materials could be characterized as soft, viscous lipids which offer much less resistance to deformation than the high-melting waxes. The performance of these materials as edible lipid coatings would be dramatically affected by their mechanical properties. The greater viscoelasticity of the beeswax and milkfat fraction means these materials would be more flexible and less likely to crack than the more elastic materials. Whether beeswax or milkfat would be better films from this standpoint remains unknown. Comparative studies of the barrier and mechanical properties of multicomponent films containing these lipids are needed to verify that these latter two materials are more suitable as film forming materials than carnauba wax or candelilla wax.
ACKNOWLEDGEMENTS This work was supported by the California Milk Advisory Board and Dairy Management, Inc., through the California Dairy Research Foundation and the California Dairy Foods Research Center.
REFERENCES AOCS (1960). Oficial and Tentative Methods: Additions and Revision, Method Cc. 16-60. American Oil Chemist’s Society (reapproved 1973). ASTM (1986). Designation 1321: standard test methods for needle penetration of petroleum waxes. In Annual Book of ASTM Standards. American Society for Testing and Materials, Philadelphia, PA. ASTM (1987). Designation 937: standard test methods for cone penetration of petrolatum. In Annual Book of ASTM Standards. American Society for Testing and Materials, Philadelphia, PA. ASTM (1988). Designation 217: standard test methods for cone penetration of lubricating grease. In Annual Book of ASTM Standards. American Society for Testing and Materials, Philadelphia, PA. ASTM (1991). Designation 1403: standard test methods for cone penetration of lubricating grease using one-quarter and one-half scale cone equipment. In Annual Book of ASTM Standards. American Society for Testing and Materials, Philadelphia, PA. Baer, R. J. (1991). Alteration of the fatty acid content of milk fat. J. Food Protect., 54, 5 383-386.
Bagley, E. B. & Christianson, D. D. (1987). Stress relaxation of chemically leavened dough: data reduction using the BKZ elastic fluid theory. J. Rheol., 31, 404-413. Bagley, E. B., Wolf, W. J. & Christianson, D. D. (1985). Effect of sample dimensions, lubrication and deformation rate on uniaxial compression of gelation gels. Rheol. Acta, 24, 265-271.
Banks, W. (1991). Milk fat. J. Sot. Dairy Technol., 44, 2 31-32. Bennett, H. (1975). Industrial Waxes. Chemical Publishing Company, New York. BMDP StatisticalSoftware (1985). University of California Press, Berkeley, CA.
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Casiraghi, E. M., Bagley, E. B. & Christianson, D. D. (1985). Behavior of mozzarella, cheddar and processed cheese spread in lubricated and bonded uniaxial compression. J. Texture Studies, 16, 281-301. Chen, P. & Fridley, R. B. (1972). Analytical method for determining viscoelastic constants of agricultural materials. Trans. ASAE, 15,6 1103-l 106. Davey, K. R. (1989). Temperature dependence of flow for plastic fats from penetration data. J. Texture Studies, 19, 4 397-405. deMan, J. M. (1976). Texture of fats and fat products. In Rheology and Tenture in Food Quality, eds J. M. deMan, P. W. Voisey, V. F. Rasper and D. W. Stanley. AVI Publishing Company, Westport, CT. deMan, J. M. & Finoro, M. (1980). Characteristics of milk fat fractionated by crystallization from the melt. Can. Inst. Food Technol. J., 13, 4 167-173. deMan, J. M., Gupta, S., Kloek, M. & Timbers, G. E. (1985). Viscoelastic properties of plastic fat products, J. Am. Oil Chemists Sot., 62, 12 1672-1675. Findely, W. N., Lai, J. S. & Onaran, K. (1976). Creep and Relaxation of Nonlinear Viscoelastic Materials. North-Holland, Amsterdam. Fltigge, W. (1975). Viscoelasticity,2nd rev. ed. Springer-Verlag, Berlin. Greener, I. K. (1992). Physical properties of edible films and their components. Ph.D. thesis, University of Wisconsin, Madison. Hayakawa, M. & deMan, J. M. (1982). Interpretation of cone penetrometer consistency measurement of fats. J. Tature Studies, 13, 2 201-210. Jenness, R. & Patton, S. (1959). Principles of Dairy Chemistry. Wiley, New York. Kaylegian, K. E. (1993). Experimental Milqat Fraction Technical Data Sheet: Milkfat Fraction W-66,42,45. Center for Dairy Research, University of Wisconsin, Madison. McHugh, T. H. & Krochta, J. M. (1994). Water vapor permeability properties of edible whey protein-lipid emulsion films. J. Am. Oil Chemists Sot., 71, 3 307-312. Mohsenin, N. N. (1986). Physical Properties of Plant and Animal Materials. Gordon & Breach, New York. Mohsenin, N. N. & Mittal, J. P. (1977). Use of rheological terms and correlation of compatible measurements in food texture research. J. Texture Studies, 8, 395-408. Mortensen, B. K. (1983). Physical properties and modification of milk fat. In Developments in Dairy Chemist9 2: Lipids, ed. P. F. Fox. Applied Science Publishers, London, pp. 159-194. Peleg, M. (1976). Considerations of a general rheological model for the mechanical behavior of viscoelastic solid food materials. J. Texture Studies, 7, 243-255. Prentice, J. H. (1992). Dairy Rheology: A Concise Guide. VCH Publishers, New York. SAS Institute Inc. (1989) SASISTAP Users Guide, Version 6, 4th ed. SAS Institute, Cary, NC. Sato, Y. & Nakayama, T. (1970). Discussion of the binding quality of minced meats based on their rheological properties before and after heating. J. Texture Studies, 1, 309-326. Shama, F. & Sherman, P. (1970). The influence of work softening on the viscoelastic properties of butter and margarine. J. Texture Studies, 1, 1 196-205. Shellhammer, T. S., Fairley, P., German, J. B. & Krochta, J. M. (1993). Water vapor barrier properties of simulated milkfat fractions. Annual Meeting of the Institute of Food Technologists, Chicago, IL, lo-14 July. Skinner, G. E. & Rao, V. N. M. (1986). Linear viscoelastic behavior of frankfurters. J. Tatwe Studies, 17, 421-432. Streitwieser, A. & Heathcock, C. H. (1985). Zntroduction to Organic Chemistry, 3rd ed. Macmillan, New York. Tanaka, M., DeMan, J. M. & Voisey, P. W. (1971). Measurement of textural properties of foods with a constant speed cone penetrometer. J. Texture Studies, 2, 1 306-315.
SO260-8774(97)00030-7
Joumul of Food Engineering 33 (1997) 305-320 0 1997 Elsevier Science Limited All rights reserved. Printed in Great 13ritain 0260-8774197 $17.00 +O.(H)
ELSEVIER
Viscoelastic Properties of Edible Lipids T. H. Shellhammer,“‘f
T. R. Rumsey” & J. M. Krochta”Th*
“Department
of Biological and Agricultural Engineering, University of California, Davis. CA 95616, USA “Department of Food Science and Technology, University of California, Davis,
CA 95616, USA (Received 22 April 1996; revised 12 March 1997; accepted 17 March 1997)
ABSTRACT The viscoelastic natures of beeswax, candelilla wax, camauba wax and a highmelting milkfat fraction were compared by estimating their relaxation parameters from stress relaxation data. A generalized Maxwell model consisting of one spring element and two Maxwell elements best descn’bed the stress relaxation of all lipids tested. The stress responses over both the compressive and relaxation portions of a stress relaxation test were considered. Cone penetration tests were used as a comparison to the stress relaxation tests. Candelilla wax and camauba wax behaved similarly as hard and elastic materials which resisted deformation, Beeswax and the milkfat fraction, on the other hand, were significantly more viscous, less elastic, and more easily deformed. 0 1997 Elsevier Science Limited. All rights reserved
NOTATION E
~3, Ei fI t t’
[I
Elastic modulus (Pa) Elastic modulus for a first spring element of the generalized model (Pa) Elastic modulus for an ith spring element (Pa) Number of elements in the generalized Maxwell model Time (s) Dummy variable for time Elapsed time to reach E()(s)
Maxwell
*To whom correspondence should be addressed. Tel.: (916) 752-2164, Email: jmkrochta@ ucdavisedu tcurrently with Departments of Food Science and Technology and Food; Agricultural and Biological Engineering; The Ohio State University, Columbia, OH 43210. 305
T H. Shellhammer et al.
306 E
Eo 4(t) Vi
0 z
Strain (unitless) Strain at the end of the compression phase of the stress relaxation procedure (unitless) Relaxation modulus (Pa) Viscosity of the fluid in the ith dashpot of the generalized Maxwell model (Pa s) Stress (Pa) Relaxation time (s)
INTRODUCTION Beeswax, candelilla wax, carnauba wax, and high-melting milkfat fractions are natural lipid materials which have been examined for use alone, or in conjunction with other materials, for use as edible barriers (Greener, 1992; McHugh & Krochta, 1994; Shellhammer et al., 1993). The chemical composition of these materials is quite diverse (Table 1). Anhydrous milkfat is composed chiefly of triglycerides of various fatty acid length and degree of saturation. Over 60% (w/w) of the fatty acids in milkfat are saturated, approximately 30% are monounsaturated, and 4% are polyunsaturated (Baer, 1991). It is this range of triglyceride size and degree of saturation that gives milkfat a broad melting range, from -20 to 37°C (Banks, 1991). At room temperature, it is a mixture of oil, semi-hard fat, and hard fat. The ratio of liquid to solid fat determines milkfat’s rheological properties. The melting point, and in turn the mechanical properties of milkfat, can be altered by separation into high and low temperature-melting fractions. This can be accomplished by a number of methods, but the most popular industrial technique is selective crystallization (Mortensen, 1983). Fractionation by selective crystallization from melted milkfat concentrates the higher-melting, long-chained saturated triglycerides in the higher-melting fraction while concentrating the short-chained TABLE 1
The Chemical Composition and Melting Point of Selected Lipids
Wax acid esters (%) Wax acids (free) (%) Fatty alcohols (%) Lactides (%) Fatty acid esters (%) Hydrocarbons (%) Resins (%) Triacylglycerides (%) Mono- and diglycerides (%) Moisture (%) Melting point (“C) aBanks (1991). ‘Bennett (1975). ‘Kaylegian (1993).
Milkfat fraction”
Beeswaxh
98 2 0 _ 45’
Candelilla
Camauba
WfLVh
WUXh
71 14 1
28.5 8 13
84.5 3.0
T 12 -
50
;:: ::tl
T 62-64
0.5
66-71
OS 83-86
Viscoelasticproperties of edible lipids
307
triglycerides in the lower-melting fractions. This results in the higher-melting fractions having significantly higher solid-fat : liquid-fat ratios than the original milkfat (deMan & Finoro, 1980). These fractions are therefore harder in terms of mechanical properties than the non-fractionated milkfat. Waxes are naturally occurring esters of long-chained carboxylic acids (C,, or greater) with long-chained alcohols (C,, or greater) (Streitwieser & Heathcock, 1985). Beeswax is considered an animal wax and is produced by honey bees for building honeycomb cells. It is a mixture of wax esters, wax acids and hydrocarbons. Hydrolysis of these esters yields mainly CZ6 and Cl8 carboxylic acids and C30 and C& straight-chained primary alcohols (Streitwieser & Heathcock, 1985). Candelilla wax is a vegetable wax that is produced by a reed-like plant (Euphorbia antisiphilitica, Euphorbia cerifera, and Pedilanthus pavonis) which grows wild in northwestern Mexico and southern Texas (Bennett, 1975). It is composed in large part of hydrocarbons with some wax acid esters and alcohols. Carnauba wax is a plant exudate from the Brazilian ‘tree of life’ (Copemica cerifera). It is the hardest, highest-melting, natural commercial wax (Bennett, 1975) and is composed almost entirely of esters of CZ4 and CZ8 carboxylic acids and C32 and C34 straight-chained primary alcohols (Streitwieser & Heathcock, 1985). Instrumental measurement of solid and semi-solid lipid rheological properties has been accomplished with a wide variety of methods. Penetrometers are most commonly used, while extrusion instruments, parallel plastometers and wire cutting devices are used less frequently (deMan, 1976). Penetrometers are classified as constant-weight or constant-speed. In the former test, the weight of the penetrometer drives the plunger into the sample until it comes to rest due to the lipid’s resistive force. Constant-speed tests involve driving a penetrometer into a lipid sample at a constant speed and measuring either the distance of penetration to reach a specified resistive force or the magnitude of resistance at a specified penetration distance. A standard, constant-weight, cone penetration method (AOCS, 1960) has been used for determining consistency of fats (Davey, 1989; Hayakawa & deMan, 1982). Comparisons of cone angles and test speeds were performed by Tanaka et al. (1971) on solid and semi-solid foods including several fats. The viscoelastic nature of lipids, in a few instances, have been studied by examining their creep compliance (deMan et al., 1985; Shama & Sherman, 1970). Although the experimental procedure and data analysis are more complex with viscoelastic measurements than with the cone penetrometer, the results obtained give more information about the structure of the lipid materials (Shama & Sherman, 1970). The objectives of this study were to determine the viscoelastic properties of edible lipid film-forming materials using stress relaxation testing, and to compare these results with constant-speed, cone penetrometer measurements to determine whether these two tests provided unique or redundant measures of lipid hardness.
THEORETICAL
BACKGROUND
The stress-strain relationship for linear viscoelastic behavior is often given in hereditary integral form. Hereditary integrals describe the stress response given a strain input plus any strain history (Fltigge, 1975). For uniaxial stress relaxation, this integral is written as
308
T H. Shellhammer et al.
a(t)=
b&t-t’) Eat
The time-dependent relaxation modulus, 4(t), describes the relationship between the strain input and stress response. Models for the relaxation modulus are often determined from mechanical models, that is combinations of springs and dashpots in series or parallel. A spring and dashpot in series is called a Maxwell model (Mohsenin & Mittal, 1977) or Maxwell material (Fhigge, 1975), and a number of Maxwell bodies in parallel with each other and with a spring is called a generalized Maxwell model (Mohsenin, 1986). The relaxation modulus for the generalized Maxwell model can be shown to be $(t) = Eo+ jg, Eje-
$’
(2)
In the present study, a static, constant-strain test was used to observe stress relaxation. Viscoelastic materials behave in a linear manner generally under very small strains. Findely et al. (1976) suggest that strain be no greater than one to two percent; Mohsenin and Mittal (1977) found that fresh fruit exhibit linear viscoelastic behavior if they are strained less than 1.5 to 3.0%; and Skinner and Rao (1986) reported that frankfurters should be strained no more than 3.8%. Ideally, a stress relaxation test involves an instantaneous strain to a fixed value (co) followed by observation of the material stress decaying over time. In reality, instantaneous loading to a fixed strain is impossible to achieve because of the mechanical limitations of the testing equipment. Depending upon the viscous nature of the material, the material will begin to relax as it is deformed to reach co. Rather than ignore the initial loading portion of the experiment and assume that the material was instantaneously strained, the relaxation which occurs during the loading of the sample can be included in the mathematical analysis using eqn 1. Mathematically, these conditions are Compression:
a& = Z!L mo
t, i3E
Relaxation:
-
=O@ t>t,
(4)
at
Substituting eqn 2 in place of 4 in eqn 1 and using the strain rate stated in eqn 3, the stress response during compression (0
(5) Using the same substitution of 4 but evaluating the test (t > t,), the stress response is
a(t) over the relaxation
portion
of
Viscoelasticproperties of edible lipids
309
(6) A similar development was performed by Chen & Fridley (1972) yielding nearly identical equations. Their development differed in that they used a generalized Maxwell model which did not have a spring element in parallel with the series of Maxwell bodies. A relaxation time (r) is frequently used rather than the quantity vi/E, so that eqn 2 would read
In the case of a Maxwell body, when t = z the stress will have decayed to 37% of the total stress relaxation. This describes why z is called the ‘relaxation time’; it is a measure of how fast the stress decays. A material that has a short relaxation time infers that the stress imposed by a strain input dissipates quickly and is therefore more viscous than elastic in nature. The converse is true for long relaxation times. One means of determining z is to measure it as the time when 63% of the stress dissipation has occurred; however, it can be calculated by fitting the relaxation modulus to stress relaxation data using non-linear regression. Equally, the coefficients ye and E can be calculated using non-linear regression and then 7 is simply IIIE. The objective of stress relaxation testing is to identify the elastic (spring) and viscous (dashpot) constants, E, and vi. This is achieved by testing the materials under a set of given conditions and then fitting eqn 5 and 6 to the loading and relaxation data by adjusting the viscoelastic constants. However, difficulties can occur in gathering and interpreting force-deformation data because of interactions at the sample-platen interface. Bonding between the sample surface and the crosshead platen can result in the cylindrical sample assuming a barrel shape, whose surface is a paraboloid of revolution (Prentice, 1992). If the material can be bonded to the platen using an adhesive, results may be more consistent than without adhesion (Bagley & Christianson, 1987). Alternatively, the friction between the sample and the platen can be eliminated by using a thin coating of paraffin or silicone oil on a platen surface which is made of Teflon (Bagley et al., 1985). The latter method was used in this study. For lubricated compression, stress on the sample is calculated as recommended by Casiraghi et al. (1985).
MATERIALS
AND METHODS
Stress relaxation sample preparation Carnauba wax (Aldrich Chemical Company, Milwaukee, WI), candelilla wax (Strahl & Pitsch Inc., West Babylon, NY), beeswax (Fisher Scientific Inc., Fair Lawn, NJ), and a high-melting industrial milkfat fraction (VH-66, Center for Dairy Research, University of Wisconsin, Madison) were melted in glass beakers immersed in a hot
310
lTH. Shellhammer et al.
water bath at 100°C. The molten lipids were poured into 10.0 mm i.d. by 10.2 mm height cylindrical copper molds and allowed to cool until solidified. The beeswax and the milkfat fraction were cooled to room temperature on a level granite slab under ambient conditions. The carnauba and candelilla waxes had high melting points: 82-85°C and 68-72°C respectively. Because of their volume change during cooling and the large temperature difference between their melting points and the room temperature, these materials would solidify too rapidly, producing irregularly shaped cylinders under ambient conditions. To alleviate this problem, the molten cylinders of wax were cooled slowly (approximately 0.5”C per minute) on a proSeries 720, PMC grammable hot plate (Dataplate@ Digital Hot Plate/Stirrer, Industries, Inc., San Diego, CA). The slow cooling allowed the waxes to shrink uniformly as they cooled. Once the lipids had solidified but not completely cooled, the excess material was shaved from the top of the mold to produce uniform, right cylinders which had smooth and parallel ends. The wax material slipped from the copper mold once they had cooled to room temperature because of thermal shrinkage. The milkfat fraction, which exhibited the least amount of shrinkage, was removed by gently heating the copper sleeve between one’s fingers until the cylinder slipped out into an ice bath. The lipid cylinders were stored at room temperature for 2 days prior to testing. The dimensions of the cylinders were measured with a caliper micrometer after storage but prior to testing. Stress relaxation data collection At least 15 min prior to testing, individual lipid cylinders were placed in a water bath held constant at 25fO.l”C. Tempered cylinders were removed from the water bath and brushed dry with’ tissue paper. Each sample was placed between two parallel polymethylmethacrylate plates mounted on a TA-XT2 Texture Analyzer (Texture Technologies Corp., Scarsdale, New York). The surfaces of the plates were lubricated with a thin film of silicone oil to prevent friction or bonding between the lipid sample and the plate faces. The lipid cylinders were strained to 2% at a crosshead speed of 1.0 mm per second, and the stress decay data (force, distance, and time) were gathered for 140 s at a rate of 200 points per second. The plate faces were cleaned and relubricated with silicone oil between each run. The room temperature was monitored during testing to ensure that the environmental conditions did not deviate significantly from the 25°C setpoint. During testing, the room varied in temperature from a low of 23.5”C to a high of 26.2”C. Four individual samples of each material were tested in a completely randomized fashion; however, in certain cases samples failed during testing either due to cracking or incomplete straining (~0.5%) and these data were eliminated. Incomplete straining was the result of background vibrations in the TA-XT2 which triggered the commencement of data collection prior to the crosshead actually contacting the sample surface. Additional replicates of the failed sample were tested so that four replicates were tested for each material. Stress relaxation data reduction and analyses The high data collection rate over the 140 s relaxation time produced nearly 30000 data points. To facilitate further analyses, a C-based data-reduction program was written to reduce each data set to 106 points. Since much of the change in resistive
Viscoelasticproperties of edible lipids
311
force during relaxation can occur shortly after compression, more data was retrieved from the beginning of the relaxation than from the end. From each data set, the first 60 points were gathered over the first 0.3 s of the test without reduction and included the compression (0.2 s) and initial relaxation (0.1 s) of the sample. The next 17 points were gathered one point every 0.1 s and lasted from t = 0.3 to t = 2.0 s. Another 17 points were gathered one point every 1.0 s from t = 2.0 to t = 20 s. Finally, the last 13 points were gathered one point every 10 s from t = 20 s until the completion of the test. This method of reduction provided a more manageable data set while minimizing the loss of information from the relaxation history. The objective of the data analysis stage was to fit the relaxation modulus to the stress relaxation data by adjusting the modulus coefficients. This was accomplished by using a derivative-free, non-linear regression statistical package, BMDP AR (BMDP, 1985). Initial estimates of the coefficients were required to use BMDP AR, and these came as approximations derived using the method of successive residuals. The method of successive residuals is a graphical technique used to approximate the coefficient terms of an exponential equation (Mohsenin, 1986). A spreadsheet was prepared (Microsoft Excel 4.0 for the Macintosh@) to calculate the exponential terms’ coefficients using this technique. In addition to the estimates of the relaxation modulus coefficients, a compressive elastic modulus was recorded from the loading portion of the stress relaxation curves. A linear regression was fitted to stress versus strain data and the slope of this regression was used as an estimate of the elastic modulus. In nearly all cases, the compression of the lipid cylinders did not immediately produce a steady increase of force with time. In these instances, the force-time data exhibited an initial toe prior to the linear increase in force from the compression of the lipid cylinder (Fig. 1). The toe was likely due to compression of non-uniformities on the lipid cylinder ends as the plunger face came into contact with the entire lipid cylinder face. Once the two surfaces mated, the entire cylinder was strained. The
/
0 Immediate deformation o Delayed deformhon
I
5
5
tstrain
t2
Time (set)
Fig. 1. Delayed deformation resulting from surface non-uniformities on the lipid cylinders.
312
7: H. Shellhammer et al.
TA-XT2 calculated the distance to strain each sample by measuring the sample’s height at the moment the plunger came into contact and determined the correct displacement based on a preset strain value (2% in this study). In the case of the delayed deformation, the instrument thought it was straining the sample to 2%, when in fact it was straining the sample to something less than 2%. The true strain was calculated based on the time over which the linear increase in force occurred. In Fig. 1, this time is the difference between tstrain and to for the data in which the deformation begins the moment the plunger meets the lipid cylinder. In the case where the data exhibited a toe (as does the delayed deformation data in Fig. l), actual deformation of the entire cylinder was calculated as the distance the plunger traveled during the time t1 to tz (i.e., tstrain, multiplied by the crosshead speed). The time axis of the force-time graph was adjusted in these instances such that the beginning of the stress relaxation test occurred at t, and not to. Once the initial estimates of the relaxation modulus coefficients had been determined via the method of successive residuals, they were used as initial values for the non-linear regression to fit eqn 5 and 6 to the stress relaxation data. These two equations represent the stress response over different periods of the test. Eqn 5, representing the compression phase, was fitted to the compression data, while eqn 6 was fitted to the subsequent relaxation portion of the same data. The coefficients of the relaxation modulus are the same for both of these equations since they are material specific, The non-linear regression package returned the ‘fitted’ coefficients along with residual statistics such as mean squared error and a pseudo-?. The experimental design for stress relaxation tests on individual lipid samples was a single factor completely randomized experiment. Using these coefficients returned from the non-linear regression, statistical differences among the four lipids were determined using a single factor analysis of variance via Statistical Analysis Software (SAS, 1989). Means comparisons were performed in the cases which were significantly different using a Duncan’s multiple range test and a Tukey’s studentized range test. Cone penetration of lipih materials Empirical measurements of fat ‘hardness’ have been standardized in a number of cases (AOCS, 1960; ASTM, 1986, 1987, 1988, 1991). In the absence of the specific cone penetrometer required by the ASTM methods, the TA-XT2 Texture Analyzer was employed to measure resistive force to a 3 mm penetration by a 60” cone. Samples were prepared by heating the lipid materials in a boiling water bath for at least 15 min beyond melting. The molten lipid was poured into 5.0 cm i.d. by 1.0 cm cylindrical cups and allowed to temper at room temperature for 24 h. Once the lipid had crystallized during the cooling process, the exposed lipid surface was shaved level with the edge of the cup so that a smooth, uniform surface was produced. An hour prior to testing, the cups containing the lipids were placed in a water bath held constant at 25°C. Testing consisted of first removing the cup from the water bath and gently brushing the surface dry with tissue paper. A 60” cone (2.6 cm height and 3 cm maximum diameter), lubricated with a light coating of silicone oil, penetrated the lipid sample at a rate of 0.2 mm/s to a distance of 3 mm. Force readings were sampled at a rate of 400 points per second, and the maximum force at, or near, 3 mm penetration was recorded. The sample was placed back in the water bath prior
Viscoelastic properties of edible lipids
31.3
to repetitive testing. Five replicate penetrations on the exposed surface of the lipid in each cup were performed in a completed randomized fashion. The experimental design for the penetration tests was similar to that of the stress relaxation study, a completely randomized design. Data were analyzed using a single factor analysis of variance and a multiple correlation via Statistical Analysis Software (SAS, 1989). The high-melting waxes were brittle enough that a 3 mm penetration caused cracking in some instances. A second test was performed in which the cone penetrated to a depth of only 2 mm. Force readings were recorded at 1 mm and at 2 mm. As with the first test, five replicates of each material were tested in a completely randomized fashion.
RESULTS
AND DISCUSSION
Model selection for the relaxation modulus The mathematical description of a viscoelastic material’s stress response to strain input, eqn 5 and 6, was derived using a generalized Maxwell model as the relaxation modulus. Before eqn 5 and 6 could be fitted to stress relaxation data, a specific model (rather than the generalized Maxwell model) had to be chosen for the relaxation modulus. The question was how many Maxwell bodies to include and whether to include the spring element. Peleg (1976) lists several requirements for constructing a rheological model of a food material. The model must be able to predict real material behavior, it should be able to respond to both positive and negative forces, and changes in the material’s behavior must be explainable in terms of the model parameters. These requirements suggested reaching a balance between choosing a model with as few terms as possible with one that has many. For the sake of simplicity, as well as being able to explain changes in the material’s behavior, a model should have few terms. On the other hand, a model with many terms will yield predictable results with high accuracy. Initial tests of the viscoelastic properties of the lipid materials using small strains pointed towards a five element model (Fig. 2) because none of the lipid materials relaxed completely such that the stress went to zero. The elastic spring element in parallel with the Maxwell bodies accounts for this residual stress in the lipid, thus it was kept as part of the relaxation modulus. Determining how many Maxwell bodies to be included was based on a degree-of-fit of predicted stress response to the actual stress response. A model with one spring element and one Maxwell element in parallel yielded r’ values from the non-linear regression which ranged from 0.926 to 0.974 depending on the lipid type. Adding another Maxwell body, as shown in Fig. 2, yielded significantly improved 2 values which ranged from 0.991 to 0.998. Models with more elements yielded slightly higher ? values, as would be expected since the number of parameters in the model increased. Yet, the authors felt that a five parameter model would be optimal by achieving the previously mentioned balance of model size. A similar model was used by Sato and Nakayama (1970) to describe the mechanical behavior of white chicken meat. The five-parameter relaxation modulus is written as 6, F.(b(t) = Eo+EIe
T’+E2e
‘I,
I
(8)
T H. Shellhammer
314
et al.
Fig. 2. Model used for the relaxation modulus for the lipid materials. Stress, 0 (kPa); strain,
F.(unitless); spring constants, Ej (kPa); and dashpot viscosities, vi (kPa s).
Adjustments to strain Achieving a 2% strain in all samples was difficult because of the inability to achieve a true right cylinder in each of the samples and because of irregularities in the samples’ surfaces. The actual distance each sample was strained was calculated as described in the methodology section. These values ranged from 1.52% to 1.93%. Averaged among the four replicates of each material, the true strain ranged from a low of 1.6% for carnauba and candelilla waxes to a high of 1.8% for the milkfat fraction. Stress relaxation of the lipid materials The parameters in eqn 8, EiS and qis, for each replicate tested were averaged to produce Table 2 and Fig. 3. The individual parameters were compared using a single-factor analysis of variance and means testing, the results of which are included in Table 2. Large differences in the relaxation modulus coefficients were observed among the four lipid types. Carnauba and candelilla wax behaved relatively similarly as hard, non-deformable materials following the 2% strain input (Fig. 3 and Table 2). In comparison to the candelilla wax, the carnauba wax displayed a TABLE 2
Averaged Actual Strain and Relaxation Modulus Coefficients of Selected Lipids Material
Milkfat fraction Beeswax Candelilla wax Carmaiba wax
Corrected strain
EI Pa)
‘II (Pas)
vr
$
(Pa s)
2
0.018
13517”
3722”
4831”
2092”
201420”
0.565”
0.017
21347b
7589’
5507”
1206h
78 987’
0.161’
14.31h
0.016 0.016
34830’ 34 270’
2094’ 3880”
1917h 1647’
706’ 282d
3961 lb 10459h
0.352’ 0.072h
20.81h
Means (n = 4) with different superscripts are significantly different at a = 0.05.
40.69” 6.71h
Viscoelastic properties of edible lipids
315
rapid relaxation immediately upon loading (Fig. 4). Analysis of variance indicated that these two materials were not significantly different in terms of residual stress (E,,) and f2 (Table 2) while they were significantly different with respect to z,. It is also clear from Fig. 4 that the peak stress upon loading was very different among the four lipids. The large differences in the degree to which these waxes resisted deformation made comparisons of their relaxation behavior difficult. To improve the contrast in relaxation behavior, the stress data were normalized by dividing each stress data point by the maximum stress during the test. In this manner, the normalized stress values ranged from zero to one for all of the materials (Fig. 5). The four materials appear as two similar groups in Fig. 5. Carnauba and candelilla wax were hard materials resisting deformation. They had very high peak stresses (Figs 3 and 4) and dissipated less than 9% of this stress. The beeswax and milkfat fraction, on the other hand, had much lower peak stress, and they yielded much more of this stress during relaxation. It is clear from Figs 4 and 5 that carnauba wax exhibited the fastest relaxation times along with a very small degree of relaxation, thus it was the most elastic material of the four. The candelilla wax relaxed over a much longer period of time than the carnauba wax, as indicated by a significantly
I
1 l
T
I
i T
a
Beeswax
I
Milkfat Fraction
lb0 Time (set)
Fig. 3. Average stress relaxation response following a 2% compressive strain of the bulk lipid materials (n = 4). Solid lines represent fitted values based on eqn 5 and 6 using average coefficients from Table 2. Due to the time scale, the loading portion of the stress history has been removed.
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larger z1 and a considerably larger r2. These results indicate that candelilla wax had more viscous behavior than the carnauba wax, yet both behaved more as elastic materials as compared to the beeswax and the milkfat fraction. The other group in Fig. 5 included beeswax and the milkfat fraction. One would expect the milkfat fraction to be less elastic and more viscous than the high-melting waxes. The milkfat fraction is comprised of triglycerides which are made in large part by saturated fatty acids, principally palmitic and stearic fatty acids. The milkfat fraction also contains unsaturated fatty acids, principally oleic acid (Jenness & Patton, 1959); thus a portion of the milkfat fraction is liquid at room temperature. Beeswax, on the other hand, is comprised of esters of rather long fatty acid and fatty alcohol, hence its elevated melting point. It resisted deformation but also exhibited a large degree of stress relaxation. The presence of a significant amount of free fatty acids contributed to its viscous qualities. Penetrometer results Lipid type had a significant effect (p
I
,
I
0.25
0.5
0.75
Time (set)
Fig. 4. Compression and initial stress relaxation following a 2% compressive strain of the bulk lipid materials (n = 4). Solid lines represent fitted values based on eqn 5 and 6 using average coefficients from Table 2.
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resistive forces which were not significantly different, while carnauba wax and candelilla wax were significantly different from each other and from the beeswax and milkfat fraction group (p < 0.05). Differences that might have stemmed from cracking of the lipid material during penetration did not appear outstanding, since the trend in hardness was similar at all three depths. The reason that cracking may not have been as large a problem as initially expected lies with the experimental procedure. The lipid materials were tested in the aluminum cups in which they were cast. When the high-melting waxes cracked during deep penetration, the various segments of the cracked lipid disk were contained by the mold and continued to offer resistance as the cone penetrated further into the newly formed crack. One concern with gathering viscoelastic property data is whether the information is of more value than data from simpler tests such as cone penetration. Usually, a cone test gives a composite parameter and not a true property of the material being tested. With regard to viscoelastic data, a stress relaxation test yields more information than a penetrometer (Shama & Sherman, 1970). As for discriminating differences among lipids, this may not always be the case. For example, hardness as measured by the cone penetrometer might correlate well with degree of elastic behavior. To examine whether this was the case in this experiment, a multiple
100
Time (set)
Fig. 5. Normalized stress relaxation response following a 2% compressive strain of the bulk lipid materials (n = 4). The loading portion of the stress history has been removed from this figure.
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correlation was performed on the hardness and viscoelastic data. The force readings from the penetrometer did not correlate well with most of the relaxation modulus coefficients. The best correlations with the penetrometer readings and the relaxation coefficients were with E0 (r = 0.9372) and E2 (r = -0.9547). The magnitude of E2 values was inversely related to measures of hardness from the penetrometer; but the results for E2 fell into two groups (Table 2), while the results from the penetrometer fell into three separate groups. Based on the correlation analysis, it is safe to state that the results from penetrometer testing were different from the stress relaxation analyses, and that these two tests were not redundant measures of the rheological properties of the four materials tested in this study. SUMMARY
AND CONCLUSIONS
A five-element model, one spring and two Maxwell bodies in parallel, was chosen for the relaxation modulus of viscoelastic lipid film materials. Parameters for this relaxation modulus were identified by fitting equations which described the stress response to a strain input over the loading and relaxation portions of the data. Results of the stress relaxation analyses indicate that carnauba wax and candelilla wax were very elastic, non-deformable materials. Penetrometer results indicated that carnauba wax was the hardest wax of the four tested. Beeswax and the milkfat
250 -
q
Imm
penetration
q
Zmm
penetration
n
3mmpenetration
200-
iz 1500 2 IE loo-
50-
oMilkfat Fractiona
Beeswax a
Candelilla wax’ Camauba waxE
Fig. 6. Resistive force of lipid materials to cone penetration (n = 5). Lipids with different superscripts are significantly different at tl = 0.05 at all three depths of penetration.
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fraction were of similar hardness and exhibited similar relaxation behavior to each other, but were significantly softer and more deformable than either the carnauba or candelilla waxes. The milkfat fraction was the most viscoelastic material of the four lipids tested as characterized by its long relaxation times, and the smallest amount of residual stress remaining in the sample following relaxation. These later two materials could be characterized as soft, viscous lipids which offer much less resistance to deformation than the high-melting waxes. The performance of these materials as edible lipid coatings would be dramatically affected by their mechanical properties. The greater viscoelasticity of the beeswax and milkfat fraction means these materials would be more flexible and less likely to crack than the more elastic materials. Whether beeswax or milkfat would be better films from this standpoint remains unknown. Comparative studies of the barrier and mechanical properties of multicomponent films containing these lipids are needed to verify that these latter two materials are more suitable as film forming materials than carnauba wax or candelilla wax.
ACKNOWLEDGEMENTS This work was supported by the California Milk Advisory Board and Dairy Management, Inc., through the California Dairy Research Foundation and the California Dairy Foods Research Center.
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