SMALL AMPLITUDE OSCILLATORY SHEAR STUDIES ON MOZZARELLA CHEESE PART 11. RELAXATION SPECTRUM

Transcription

1 Trurnbull, SMALL AMPLITUDE OSCILLATORY SHEAR STUDIES ON MOZZARELLA CHEESE PART 11. RELAXATION SPECTRUM R. SUBRAMANIAN and S. GUNASEKARAN' Food di Bioprocess Engineering Laboratoty Department of Biological Systems Engineering University of Wisconsin-Madison ~ Wisconsin (Manuscript received September 4, 1996; accepted August 6, 1997) ABSTRACT The frequency dispersion of dynamic mechanical spectru of a low-moisture, part-skim and a low-fat, part-skim Mozzarella cheese are presented. Small amplitude oscillatory shear measurements within the linear viscoelustic range (0.05% strain) were made over 12 weeks of storage. Proteolysis during storage led to softening of the cheeses and thus decreases in storage (G') and loss (G") moduli. Master curves (at a reference temperature of 4OC) were obtained by shifting the temperature-dependent frequency dispersion of storage modulus. mere was no significant change in G' afer 4 weeks of aging. The variation of relaxation time and viscosity spectrum of both cheeses with age were obtained from the muster curves using the generalized Maxwell model and nonlinear regression analysis. With maturation the viscosity distribution of corresponding Maxwell elements shifed towards smaller values, indicating that cheeses become softer and melt more easily. INTRODUCTION Cheese is increasingly used as an ingredient in prepared foods to add texture, flavor and color. Therefore, texture and melting characteristics of cheese are the most important factors in determining quality of cheese for a particular product application (Park et al. 1984, Kindstedt 1993). Several recent studies have examined the effect of aging on rheological properties of Mozzarella cheese. Diefes 'Author for correspondence Journal of Texture Studies 28 (1997) Alf Rights Reserved. 0 Copyright 1997 by Food & Nutrition Press, Inc. ~ Connecticut 643

2 644 R. SUBRAMANIAN and S. GUNASEKARAN et al. (1993) performed dynamic tests to compare rheological properties of lowmoisture, part-skim Mozzarella cheese subjected to freezing storage and refrigerated storage. Hsieh et al. (1993) used dynamic tests to evaluate temperature effects (10-60C) on the functional properties of Mozzarella cheese containing various protein fillers. When dynamic viscoelastic data are available for a wide range of strain (or strain rate) and temperature, it is convenient to display the data as master curves. This is possible only if there are significant regions of overlap in the data (Vinogradov and Malkin 1980; Bird et al. 1985). The dynamic data are shifted along the frequency axis and superimposed on to a single master curve at a reference temperature. This is called the temperature-frequency superposition principle. This principle is especially important as it allows one to significantly extend the range of variation of the argument (frequency) and to cover such wide regions of reduced frequencies which are difficult, if not impossible, to cover by direct methods of measuring the storage modulus at a single temperature, because one would have to carry out measurements with the frequency varying by a factor of up to decimal orders. Although this technique has been widely used for polymer melts and solutions (Bird et al. 1985), only a few researchers have used it to study the dynamic rheology of foodstuffs. Taneya et al. (1979) examined the rheological properties of natural (Gouda and Cheddar) and processed (hard and soft) cheese types by measuring the dynamic viscoelasticity in the temperature range of -5 to 9OC. Using the superposition principle they generated master curves to study the effect of maturation on the dynamic storage modulus of each cheese. Yoon et al. (1996) studied the thermorheological properties of surimi-based seafood products and they generated master curves for each dynamic property using a shift factor. The objective for this part of the study was to examine the effects of temperature and refrigerated storage on the dynamic mechanical properties of a low-moisture, part-skim and a low fat, part-skim Mozzarella cheese using the small amplitude oscillatory shear (SAOS) technique, and generate master curves (using the temperature-frequency superposition principle) to study the effect of maturation on the dynamic storage modulus. In addition, we have described a nonlinear regression procedure to obtain the relaxation spectrum (time and viscosity) of cheese from master curves using the generalized Maxwell model. Dynamic Rheological Measurements MATERIALS AND METHOD Small amplitude shear measurements in the frequency sweep mode were performed using a Bohlin VOR rheometer at frequencies from to rads

3 PART 11. RELAXATION SPECTRUM 645 and at a shear strain of 0.05 % were performed on cheese samples after I, 4 and 12 weeks of refrigerated storage. The dynamic viscosities and viscoelasltic moduli were measured from 10 to 70C in all cases. Additional details of experimental methods are presented in Part 1 of this paper (Subramanian and Gunasekaran 1997). Dynamic Viscuelastic Properties RESULTS AND DISCUSSION The dynamic viscoelastic properties of both Mozzarella cheeses were measured within the linear range (shear strain = 0.05%) after 1, 4 and 12 weeks of ripening. Figures 1 and 2 show the frequency dispersion of storage and loss modulus, respectively, of low-fat, part-skim Mozzarella that had been ripened for I week. At any given point, G ' was greater than G " which indicated a dominant contribution of the elastic component to the viscoelasticity. This behavior is typical for c c 0 0 c 0 I -1 1oc 20 C A 30 C T 40 C + 50 c 60C 0 70 c 1031 I1lbl,,i I l l l l l l L 1 I 8 t 8 r J lo-' ' Frequency [a], rad/s FIG. 1. FREQUENCY DISPERSION OF STORAGE MODULUS AT DIF- FERENT TEMPERATURES FOR I-WEEK OLD LOW-FAT, PART-SKIM MOZZARELLA CHEESE (SHEAR STRAIN = 0.05%)

4 646 R. SUBRAMANIAN and S. GUNASEKARAN t: 0 c 0 0 1oc zoc A 30C V 40C + 50C b eoc 0 70 C lo-' ' Frequency [a], radls FIG. 2. FREQUENCY DISPERSION OF LOSS MODULUS AT DIFFERENT TEMPERATURES FOR 1-WEEK OLD LOW-FAT, PART-SKIM MOZ- ZARELLA CHEESE (SHEAR STRAIN = 0.05%) a viscoelastic solid (Rao and Steffe 1992). This kind of response has also been reported by other researchers, even for melted cheese (Nolan et al. 1989; Hsieh et al. 1993; Diefes et al. 1993; Ak and Gunasekaran 1996). Changes in G" of the cheeses up to 70C followed the same trend as that of G'. Both G' and G" decreased with age and this effect was more noticeable in the first 4 weeks of maturation. It is known that proteolysis during ripening accounts for decreases in viscosity and elasticity of cheese (Creamer and Olson 1982; Lawrence and Gilles 1987), and the degree of proteolysis contributes to softening of cheese because degradation products of casein are water-soluble and cannot contribute to the framework provided by the protein matrix (Visser 1992). Hydrolysis of casein in Mozzarella during refrigerated storage have been reported before (Farkye et al. 1991; Ak et al. 1993). Master Curves from Frequency Dispersion of Storage Modulus Figure 1 shows the frequency dispersion of storage modulus at different temperatures for the low-fat, part-skim Mozzarella cheese after 1 week of matura-

5 PART 11. RELAXATION SPECTRUM 647 tion. The storage moduli corresponding to various temperatures are similar, i.e., there are significant regions of overlap, and they can be superimposed to obtain a master curve using the temperature-frequency superposition principle on the basis of a standard or reference temperature. For this study a reference temperature of 40C was chosen and the storage modulus shifted along the frequency axis to obtain a master curve (Fig. 3). This figure shows that higher temperature data (50,60 and 70C) moved towards lower frequencies on the master curve and lower temperature data (10,20 and 30C) moved towards higher frequencies on the master curve. Applying the temperature-frequency superposition method to both Mozzarella cheeses, master curves were obtained after 1,4 and 12 weeks of maturation (Fig. 4 and 5). Figures 6 and 7 show the plot of shift factor (as a function of temperature) used to obtain the master curves for both types of Mozzarella cheese. At any age, the shift factor decreases with increasing temperature. The master curves span a frequency range of 8-9 orders of magnitude compared to the experimental range of about 3 orders of magnitude. The low and high end of the master b Shifted Frequency [a], radls FIG. 3. STORAGE MODULUS MASTER CURVE AT A REFERENCE TEMPERATURE OF 40C FOR 1-WEEK OLD LOW-FAT, PART-SKIM MOZZARELLA CHEESE (SHEAR STRAIN = 0.05%)

6 648 R. SUBRAMANIAN and S. GUNASEKARAN E.* c.- lo lo-' Shifted Frequency [o], radls FIG. 4. STORAGE MODULUS MASTER CURVES AT A REFERENCE TEMPERATURE OF 4OC FOR LOW-FAT, PART-SKIM MOZZARELLA CHEESE AFTER I, 4, AND 12 WEEKS OF MATURATION (SHEAR STRAIN = 0.05%) curve are not experimentally measurable because of sample slippage, noise at extremely low frequencies, and physical stability of the apparatus at extremely high frequencies. It is clear that both cheeses become softer with age and G' decreases significantly within the first 4 weeks of maturation. Note that the 12 week old low-fat, part-skim Mozzarella cheese exhibits a higher frequency dispersion of storage modulus in the low frequency region (crossover at a shifted frequency of about 0.3 rads) than 1 and 4 week old cheese (Fig. 4). This was because the measured high temperature frequency dispersion of storage modulus (unshified data) of the 12 week old low-fat, part-skim Mozzarella cheese was slightly higher than 1 and 4 week old cheese. Relaxation Spectrum from Dynamic Storage Modulus Master Curves The response of a viscoelastic material to small deformation is related to the dynamic mechanical spectra. The storage modulus G' of a generalized Maxwell model is given by the following expression:

7 PART 11. RELAXATION SPECTRUM 649 t lo-* lo* Shifted Frequency [a], radls FIG. 5. STORAGE MODULUS MASTER CURVES AT A REFERENCE TEMPERATURE OF 40C FOR LOW-MOISTURE, PART-SKIM MOZ- ZARELLA CHEESE AFTER 1, 4, AND 12 WEEKS OF MATURATION (SHEAR STRAIN = 0.05%) where N = number of Maxwell elements: a, = frequency of measurement; hk = relaxation time ofthe k"' Maxwell element; yk = viscosity of the k"' Maxwell element. Although this technique has been used to obtain relaxation spectrum parameters for polymer melts and solutions (Bird et al. 1985; Papanastasiou et al. 1983), it has not been applied to study the rheological characteristics of cheeses. In this study, nonlinear regression analyses, using PC-STATGRAPHICS PLUSTM package, were conducted on dynamic storage moduli master curves to obtain agedependent relaxation spectrum parameters for the generalized Maxwell model. The procedure was as follows: (1) Select a set of relaxation times hk for the spectrum. The spacing of the

8 650 R. SUBRAMANIAN and S. GUNASEKARAN piq 12 wk 10 B L s 0 z 100 t A Temperature, C FIG. 6. STORAGE MODULUS MASTER CURVE SHIFT FACTORS AS A FUNCTION OF TEMPERATURE FOR LOW-FAT, PART-SKIM MOZ- ZARELLA CHEESE AFTER 1,4, AND 12 WEEKS OF MATURATION (REFERENCE TEMPERATURE = 40C) relaxation times was conveniently chosen to be decade intervals in order to reduce the amount of computation and have greater accuracy of fitting. The following constraints were imposed: where hmax = longest relaxation time; Xmin = shortest relaxation time; umax = highest frequency for which data was available; amin = lowest frequency for which data was available. (2) Once the relaxation time spectrum was chosen, best fit viscosities Tk were obtained for each relaxation time. This was done by minimizing the difference between measured moduli (master curve) and predicted moduli (using Eq. 1) at N frequencies aj. Care was taken to ensure that the fitted values of 7)k were always positive in order to make physical sense.

9 PART 11. RELAXATION SPECTRUM E: E L Q 10' m U g 100 rn lo-' 1 E A A 8 I A A! " " ~ ' ~ ~ " ~ ~ " ~ ' " " ~ ~ ' ~ ' " ~ ' ~ ~ ' ~ Temperature, O C FIG. 7. STORAGE MODULUS MASTER CURVE SHlFT FACTORS AS A FUNCTION OF TEMPERATURE FOR LOW-MOISTURE, PART-SKIM MOZZARELLA CHEESE AFTER I, 4, AND 12 WEEKS OF MATURA- TION (REFERENCE TEMPERATURE = 40C) Figures 8 and 9 show the fit of generalized Maxwell model to the master curves for both types of Mozzarella with maturation, and the values of the relaxation spectrum parameters are listed in Tables 1 and 2. Such a behavior is also shown by polymer melts like low-density polyethylene (Laun 1978). In these figures the low-frequency region (high temperature unshifted data) is dominated by the long relaxation times and the high-frequency region (corresponds to low temperature unshifted data) is controlled by the short relaxation times. The lowmoisture, part-skim Mozzarella had lower values of relaxation time than lowfat, part-skim Mozzarella because of lower storage moduli at each temperature. Tables 1 and 2 show the values of viscosities increased with age for Maxwell elements corresponding to higher relaxation times (low-frequency region on the master curve). Although this method is quite accurate in describing the dynamic linear viscoelastic properties (using the generalized Maxwell model) of cheese in the mid- and high-frequency range, care should be taken while using the master curve data in the low frequency region. Once the Maxwell model parameters are obtained, other linear viscosities properties such as complex viscosity and loss

10 652 m I I Q I 8 fi I@ z R. SUBRAMANIAN and S. GUNASEKARAN 0 Measured El Maxwell model (a), 103 ; log 2 P ' 4 g) ' m l(r T B z (b) a - a P Maxwell model E i z : 16 I '. amnnn' ' oc3- ' i,llj '. * n d '"l*ll.l ' zalul " 10' loo 10' l(r Shifted Frequency [w], radh FIG. 8. STORAGE MODULUS (MASTER CURVE AND USING GENERALIZED MAXWELL MODEL) AS A FUNCTION OF FREQUEN- CY AT A REFERENCE TEMPERATURE OF 40C FOR LOW-FAT, PART- SKIM MOZZARELLA CHEESE. (a) AFTER 1 WEEK (b) AFTER4 WEEKS (c) AFTER 12 WEEKS

11 PART 11. RELAXATION SPECTRUM & 108 T 2. v) m g LLLYY m 107 v1 103 lllllj t8iiul I 8 ~~~~d - ctlu4 a I,ltd 8 8 (c) FIG. 9. STORAGE MODULUS (MASTER CURVE AND USING GENERALIZED MAXWELL MODEL) AS A FUNCTION OF FREQUEN- CY AT A REFERENCE TEMPERATURE OF 40C FOR LOW-MOISTURE, PART-SKIM MOZZARELLA CHEESE. (a) AFTER 1 WEEK (b) AFTER 4 WEEKS (cl AFTER 12 WEEKS

12 654 R. SUBRAMANIAN and S. GUNASEKARAN TABLE 1. GENERALIZED MAXWELL MODEL PARAMETERS OF LOW-FAT, PART-SKIM (LFPS) MOZZARELLA CHEESE After I wk After 4 wk After 12 wk Relaxation Time, h, viscosrty,,,, Viswsity,qi ViSCOSrty.q, (9) (Pas) (Pas) (Pas) modulus can be evaluated (Bird ef al. 1985). This method can be used to study the effect of compositional parameters like age, ph, etc. on the linear viscoelastic properties of cheese. In general it was found that, with maturation, viscosity distribution of corresponding Maxwell elements shifted towards smaller values, indicating that cheese became softer and melted more easily. Also, a comparison between corresponding Maxwell elements of the low-fat, part-skim Mozzarella cheese and lowmoisture, part-skim Mozzarella cheese at the same maturation time indicated that the low-fat, part-skim Mozzarella had higher dynamic viscosity than the lowmoisture, part-skim Mozzarella. Thus, low-fat, part-skim Mozzarella cheese could be described as more solid-like than low-moisture, part-skim Mozzarella cheese. CONCLUSIONS Within the linear range of 0.05% strain, the viscoelastic properties of Mozzarella cheese obtained from frequency sweep tests decreased with increasing temperature. Master curves of frequency dispersion of the storage modulus indicated that significant decrease in storage modulus took place within the first 4 weeks of ripening. Generalized Maxwell model parameters like Newtonian viscosity (Vk) and relaxation time (Ak) can be obtained from master curves of dynamic viscoelastic properties and they could be used to explain structural

13 PART 11. RELAXATION SPECTRUM 655 TABLE 2. GENERALIZED MAXWELL MODEL PARAMETERS OF LOW-MOISTURE, PART-SKIM (LMPS) MOZZARELLA CHEESE After 1 wk After 4 wk After 12 wk Relaxation Time, hi wscosity, qi Viscosity.q, Viscosity,q, (s) (Pas) (Pas) (Pas) characteristics and changes in cheese due to reduction of fat, moisture, etc. By comparing the corresponding Maxwell elements we found that, at the same maturation time, the low-fat, part-skim Mozzarella cheese had higher values of dynamic viscosity than the low-moisture, part-skim Mozzarella cheese. REFERENCES AK, M.M., BOGENRIEF, D., G UNASEKARAN, S. and OLSON, N.F Rheological evaluation of Mozzarella cheese by uniaxial horizontal extension. J. Texture Studies 24, AK, M.M. and GUNASEKARAN, S Dynamic rheological properties of Mozzarella cheese during refrigerated storage. J. Food Sci. 61, BIRD, R.B., ARMSTRONG, R.C. and HASSAGER, Dynamics of Polymeric Liquids. Vol. 1, Wiley-Interscience Publication, New York. CREAMER, L.K. and OLSON, N.F Rheological evaluation of maturing Cheddar cheese. J. Food Sci. 47, , 646. DIEFES, H.A., RIZVI, S.S.H. and BARTSCH, J.A Rheological behavior of frozen and thawed low-moisture, part-skim Mozzarella cheese. J. Food Sci. 58,

14 656 R. SUBRAMANIAN and S. GUNASEKARAN FARKYE, N.Y., KIELY, L.J., ALLSHOUSE, R.D. and KINDSTEDT, P.S Proteolysis in Mozzarella cheese during refrigerated storage. J. Dairy Sci. 74, HSIEH, Y.L., YUN, J.J. and RAO, M.A Rheological properties of Mozzarella cheese filled with dairy, egg, soy protein and gelatin. J. Food Sci. 58, KINDSTEDT, P.S Effect of manufacturing factors, composition and proteolysis on the functional characteristics of Mozzarella cheese. Crit. Rev. Food Sci. Nut. 33(2), LAUN, H.M Description of the non-linear shear behaviour of a low-density polyethylene melt by means of an experimentally determined strain dependent memory function. Rheol. Acta 17, LAWRENCE, R.C. and GILLES, J Cheddar cheese and related dry-salted cheese varieties. In Cheese Chemistry, Physics and Microbiology, Vol. 2, (P.F. Fox, ed), Elsevier Applied Science, London. NOLAN, E.J., SHIEH, J.J. and HOLSINGER, V.H A comparison of some rheological properties of Cheddar and pasteurized process American cheese. Proc. 5th Int. Congress Food Eng., Cologne, Germany. PAPANASTASIOU, A.C., SCRIVEN, L.E. and MACOSKO, C.W An integral constitutive equation for mixed flows: viscoelastic consideration. J. Rheol. 27, PARK, J., ROSENAU, J.R. and PELEG, M Comparison of four procedures of cheese meltability evaluation. J. Food Sci. 49, , RAO, M.A. and STEFFE, J.F Viscoelusticity of Foods. Elsevier Applied Science, New York. SUBRAMANIAN, R. and GUNASEKARAN, S Small amplitude oscillatory shear studies on Mozzarella cheese. Part 1. Region of linear viscoelasticity. J. Texture Studies 28, TANEYA, S., IZUTSU, T. and SONE, T Dynamic viscoelasticity of natural and processed cheese. In Food Texture and Rheology. (P. Sherman, ed.) Academic Press, London. VINOGRADOV, G.V. and MALKIN, A.Y Rheology of Polymers. Mir Publishers, Moscow. VISSER, J Factors affecting the rheological and fracture properties of hard and semi-hard cheese. Bull. Int. Dairy Federation 268, YOON, W.B., PARK, J.W. and KIM, B.Y Use of WLF equation for optimum storage conditions of Surimi-based seafood products. Paper 14A-11, Institute of Food Technologist Annual Meeting, New Orleans.