Storage time effect on the rheology of refrigerated potato tissue. (cv. Monalisa). Received: 28 December 1999. Abstract Potato tubers were held in refrigerated ...
Eur Food Res Technol (2000) 212 : 48–56
Q Springer-Verlag 2000
ORIGINAL PAPER
María Dolores Alvarez 7 Wenceslao Canet
Storage time effect on the rheology of refrigerated potato tissue (cv. Monalisa)
Received: 28 December 1999
Abstract Potato tubers were held in refrigerated storage and their firmness periodically sampled over a period of 140 days. At each sampling, the rheological properties uniaxial compression, shear, uniaxial tension, successive cycles of stress relaxation, creep compliance and texture profile analysis were determined, as was moisture content. Compression energy, maximum shear force, longitudinal tension stiffness and maximum tension deformation, stress relaxation parameters and moisture content were all significantly affected by storage time. Relaxed forces decreased consistently and linearly with time over a 140-day storage period, reflecting the decrease in cell turgor pressure resulting from the predominance of water loss through evaporation over water production. Longitudinal tension stiffness and maximum shear force increased linearly in the early stages, reflecting the increase in cell wall stiffness and elastic tissue behavior. Maximum tension deformation increased linearly with time reflecting the plastic deformation of the cell wall caused by growth in cell turgor pressure at early stages. Changes in the trends of rheological parameters over 140, 64 and 28 days evidenced the importance of extending the time period considered for rheological parameters of potato tissue. Keywords Potato tuber 7 Storage time 7 Rheological parameters 7 Turgor pressure 7 Cell wall stiffness
Introduction Changes in the mechanical properties of stored potato tubers seem to be primarily caused by physiological changes affecting structural components (cell wall, middle lamella) and by changes in turgor pressure within M.D. Alvarez (Y) 7 W. Canet Department of Plant Foods Science and Technology, Instituto del Frío-CSIC, Ciudad Universitaria s/n, 28040 Madrid, Spain e-mail: ifrat446if.csic.es
the cells (which are affected by either water loss or water production, and membrane integrity) [1–4]. The physiological changes are probably brought about by enzymatic reactions involving substrates (mainly pectic substances) in the afore above mentioned cell wall and middle lamella [5]. Several mechanical properties of potatoes have been shown to be affected by storage time: tensile strength [6], torsional strength [7], longitudinal and shear stiffness [2–4], compressive failure stress and strain [3], and cutting energy [8]. Compression testing has been widely applied to assess the mechanical behavior of stored potato tissue, and the term longitudinal stiffness is used to describe tissue stiffness as a whole, which has been shown to increase with both cell wall stiffness and cell turgor pressure [2, 3]. Gao et al. [9] demonstrated that the stiffness of potato cell wall increases after the cell wall is plastically deformed. In stored potato tissue, increasing internal cell turgor induces plastic or viscoplastic deformations over long periods of time; of these, the plastic component parenchyma tissue distension by turgor pressure is irreversible, resulting in increasing cell wall stiffness so that only elastic tissue behavior can be expected [3, 10]. Stiffness values as determined by compression tests are clearly dependent on turgor pressure in osmotically manipulated potato tissue, and there is a well-documented fall in longitudinal stiffness with increasing concentration of mannitol [2–4]. However, changes in longitudinal stiffness with storage time in unsoaked potato tissue, i.e., under common cell turgor pressure, are less well documented, depending as they do on the conditions and the duration of storage. For potato tissue stored over 7 weeks at 10 7C, Brusewitz et al. [3] found that the increase in cell wall stiffness and the decrease in turgor at early stages resulted in a nonmonotonic trend in whole tissue stiffness, as determined by compression test. At later stages, both cell wall stiffness and turgor pressure increased, producing a rise in tissue stiffness. Others authors have found that under exactly the same storage conditions as used in this study, cell
49
turgor pressure of potato tissue decreased during the first 2 weeks, increased between 2 weeks and 4 weeks and finally decreased monotonically up to 12 weeks [8]. Scanlon et al. [4] reported a larger fall in longitudinal stiffness of unmanipulated potato tissue calculated from both compression and shear tests, but over a prolonged storage period (10 months) at 6 7C prior to testing. In compression tests, the non-linear force/deflection behavior of the tissue makes unequivocal determination of longitudinal stiffness difficult. Alternative mechanical tests have been used to assess the fracture behavior of potato parenchyma in different turgor states [11]. Potato cutting energy fell with increasing concentrations of mannitol in soaking solutions due to a strong decrease in cell turgor pressure [8, 11]. Moreover, in unsoaked tissue, the inverse trend shown by cutting energy and turgor pressure between 2 weeks and 8 weeks of storage suggested that this mechanical parameter could detect the postulated increase in cell wall stiffness with storage time. Hiller et al. [10] developed a micropenetration technique which enables the direct measurement of cell wall mechanical properties in situ in samples of potato tissue, pointing out that accurate determination of cell wall stiffness requires an accurate knowledge of the size and thickness of the cell wall element being tested. Davies et al. [12] proposed values for the elastic constants of potato cell wall, guided by statistical data for cell size and stiffness obtained from micropenetration tests. There is often disagreement between rheological properties obtained from different mechanical tests or even between properties derived from the same test, evidencing the complexity and multidimensionality of the texture. Different methods can furnish different information on the structural components of the tissue that are deformed [13–15]. The objectives of this research were to determine the changes in the mechanical properties of potato tissue stored over 140 days by application of a number of mechanical tests based on different principles and measurement properties of differing scales. The purpose was to separate the rheological parameters that seem suitable for measuring changes related to cell turgor pressure from those measuring cell wall mechanical properties. From the mechanical parameter trends identified, linear regression models were established to describe the effect of storage time on the rheology of potato tissue.
Materials and methods Test material. The potato samples (Solanum tuberosum, L., cv. Monalisa) came from Segovia (Spain) and consisted of potatoes having weights (in grams) within the confidence interval (153.83^m^186.56) and specific weights (g/cm 3) within the interval (1.0635^m^1.0796); P^0.01. The material was stored in a chamber (4 7C and 85% relative humidity) [16]. Twelve experiments were conducted at 1, 2 and 4 week intervals over a 140 day storage period.
Mechanical tests. Compression, shear and tension tests were carried out using an Instron Food Testing Instrument Model 4501 [14, 15]. Ten replicates were performed for each of the mechanical tests. Stress relaxation and texture profile analysis (TPA) tests were carried out using a Stable Micro Systems TA-HD250. Five replicates were performed for stress relaxation and TPA tests. Cylindrical specimens (diameter, 25.40 mm, height, 10 mm) were compressed between parallel plates at a deformation rate of 200 mm min –1. This test was used to measure the maximum compression force [Fc (N)], the end apparent modulus of elasticity or longitudinal stiffness [Ec (MPa)] and the energy required for breaking per unit of volume [Uc (mJ mm –3)]. Shear tests were performed on cylindrical specimens (diameter, 25.40 mm, height, 10 mm) using a shear cell [17] at a deformation rate of 400 mm min –1 to give the maximum shear force [Fs (N)], the end modulus of rigidity or shear stiffness [Gs (kPa)] and the shear energy required for breaking per unit of volume [Us (mJ mm –3)]. The tension test was performed on 5-mm-thick bone shaped specimens (dimensions: 75 mm long, 20 mm wide at the retaining ends and 8 mm wide at the neck) at a deformation rate of 100 mm min –1, using a cell consisting of two compressed-air clamps (0.15 MPa) fitted to the specimen ends by filter paper to prevent slippage and failure. This gave the maximum tension force [Ft (N)], the end apparent modulus of elasticity or longitudinal stiffness [Et (MPa)], the energy required for breaking per unit of volume [Ut (mJ mm –3)], the maximum tension deformation [Dt (mm)] and the maximum tension stress [st (MPa)]. In the stress relaxation test, cylindrical specimens (diameter, 25.40 mm, height, 10 mm) were compressed to a distance of 2 mm (20% strain based on original size) between parallel plates, at a deformation rate of 400 mm min –1. The deformation was then held constant and the specimens were allowed to relax for 1 min following deformation. Following previous studies [18, 19], the relaxed force [Fr (%)] was calculated as F(1 min)p(F0–Fi)/F0 where F0 is the maximum compression force for deformation of 2 mm and Fi is the force recorded after 1 min of relaxation. The relaxation gradient [Sr (N s –1)], is the slope of the straight line joining the maximum compression force and relaxed force points after 1 min. The residual relaxation area [Ar (N s)] is the area below the force-time curve. Each specimen was compressed and allowed to relax three times. In the TPA test, cylindrical specimens (diameter, 25.40 mm, height, 10 mm) were doubly compressed to a deformation of 7 mm (70%) between parallel plates, at a deformation rate of 100 mm min –1. Textural properties were derived from the forcetime curves according to Szczesniak [20] and Bourne [21] to give fracturability [F (N)] (the force at the first significant break in the curve) and hardness 1 [H1(N)] (the peak force necessary to attain the given deformation during the first compression cycle). Creep behavior of cylindrical specimens (diameter 19.06 mm, height 10 mm) was measured using a parallel plate viscoelastometer [15, 22] based on the one described by Sherman [23]. The results from only three samples were considered at each time interval due to the high variability found. Creep compliance behavior of samples was measured at a constant applied shear stress of 516.27 Pa over 2 min (for stress calculation a dead weight of 30.031 g was selected so that it would be within the range of up to about 70% of the breaking strength, and this was considered the imposed force). Two software systems simplified the acquisition and analysis of creep behavior. The software used to collect displacement-time data was developed by Rico [24] with the LabWindows for DOS package in C language. Analysis of creep data was performed by a program developed in Quick-Basic 4.5 on the basis of the software described by Sherman [25] using the graphic method of Inokuchi [26]. Full details of both software systems are reported elsewhere [15, 22]. Creep compliance [J] is defined as J (t, s0) p
g (t) s0
50 where, g(t) is the shear strain at time t and s0 is the constant applied shear stress F0/2A, A being the cross-sectional area of the cylindrical specimen. The behavior defined by this equation was delineated into one instantaneous elastic component [J0 (Pa –1)], one or two retarded elastic compliances [J1 (Pa –1)] and [J2 (Pa –1)] with their associated retardation times [t1 (s)] and [t2 (s)] and coefficients of viscosity [h1 (Pa s)] and [h2(Pa s)] respectively; and one steady state viscous flow component where [hN (Pa s)] is the coefficient of viscosity associated with Newtonian flow. Moisture content. Determinations were made by drying samples in a Philips microwave oven (model M-718, 700 W) with output power at 70% [27]. Weighing was performed on a Mettler AT 100 analytical balance with metering precision of 0.00001 g. The initial weight of each sample was approximately 5 g. Samples were weighed every 5 min until a constant weight was attained. Ten determinations were performed for each treatment. Statistical analysis. Storage time effect on mechanical properties of the stored tubers was statistically tested using one-way analysis and the means were compared by least significant difference (99%). Linear regression analysis was used to express the effect of storage time on the mechanical parameters. Statgraphics software version 5.0 (STSC, Rockville, Md., USA) was used in the statistical analysis [28].
the compression test. Figure 1a–c shows average values of compression parameters and trends at 140, 64 and 28 day storage periods respectively. Fcand Ec increased with time (Fig. 1a). However, Uc was significantly affected by time (P^0.01), with significant differences between values at 0 days (the highest value) and values at 7, 14 and 110 days (the lowest value). Specimens failed under a higher strain (48.12%) at 140 days than at 0 days (45.68%), i.e. with time, the specimen had to be deformed to a greater extent before a crack was initiated. During compression of potato tissue, starch grains are rearranged into a flatter configuration and dissipate energy [29], requiring greater deformation to store sufficient strain energy for cracking after prolonged tuber storage. Since Fcincreased with time, Uc, defined as the area under the curve force-deformation, would be expected to increase following the same trend. One possible explanation is that energy was expressed by unit volume, and although specimen height was taken within narrow confidence intervals (10.00 mm to 10.38 mm, P^0.05), the height effect could have accounted at least partially for the inverse trend shown by compression energy.
Results and discussion Unifactorial analysis of variance showed that storage time did not significantly affect Fc and Ec(P 1 0.01) from
Fig. 1a–f Changes and trends in compression and shear parameters with storage time
51 Table 1 Regression coefficients and analysis of variance of linear models fitted for the rheological parameters and moisture content as functions of storage time. a Estimated intercept, b estimated
Fc a Ec a Uc a Fs a Gs a Us a Ft a Et a Ut a Dt a tt a Fr1 a Fr2 a Fr3 a Sr1 a Sr2 a Sr3 a Ar1 a Ar2 a Ar3 a J0 a hN a Fa Ha Mo b
slope, Ta, Tb computed statistics (Student’s t), P-value probability level, r-value:correlation coefficient, ns not significant
a
b
Ta
Tb
F-ratio
P-value
r-value
685.754 4.235 369.331 99.266 19.769 253.627 26.573 4.022 150.582 11.786 0.491 54.365 49.264 48.535 P2.388 P2.705 P2.836 8410.900 11479.900 12557.900 1.893E-7 4.580Ec8 770.726 613.710 81.651
0.220 2.590E-3 P0.194 P0.065 P0.013 P0.116 5.829E-3 P0.012 0.157 0.016 P1.271E-5 P0.060 P0.051 P0.058 5.341E-3 4.504E-3 4.660E-3 P8.575 P5.040 P2.137 1.275E-10 P1.035Ec6 P0.166 P0.530 P5.906E-5
111.033 63.404 28.988 54.658 51.939 78.612 159.999 16.235 49.949 29.843 57.519 36.101 33.088 30.661 P22.436 P25.021 P25.446 34.962 26.028 26.351 56.318 14.976 175.529 46.774 534.502
2.274 2.475 P0.970 P2.291 P2.233 P2.288 2.240 P3.119 3.318 2.569 P0.095 P2.533 P2.235 P2.359 3.204 2.659 2.669 P2.275 P0.729 P0.286 2.420 P2.161 P2.413 P2.577 P2.468
5.171 6.128 0.941 5.250 4.988 5.237 5.019 9.731 11.011 6.599 0.009 6.416 4.998 5.566 10.264 7.071 7.127 5.000 0.500 0.080 5.858 4.670 5.823 6.640 6.090
0.046* 0.033* 0.355 ns 0.045* 0.049* 0.045* 0.049* 0.011* 0.008** 0.028* 0.926 ns 0.030* 0.049* 0.040* 0.009** 0.024* 0.023* 0.046* 0.482 ns 0.780 ns 0.036* 0.050* 0.036* 0.027* 0.033*
0.584 0.616 P0.293 P0.587 P0.577 P0.586 0.578 P0.702 0.724 0.630 P0.030 P0.625 P0.577 P0.598 0.712 0.643 0.645 P0.584 P0.225 P0.090 0.608 P0.564 P0.607 P0.632 P0.615
* significant at 5%; ** significant at 1% a For definitions, please go to Mechanical tests in Materials and Methods
b
In spite of the lack of significance of storage time in maximum force Fc and longitudinal stiffness Ec, these were dependent on time and increased linearly over 140 days as evidenced by the significance of the models fitted (P^0.05, Table 1). The similarity of the behavior of both parameters was corroborated by a significant correlation (rp0.791). A significant decrease in Uc did not fit a linear model (P 1 0.05), and this parameter showed no significant correlations with any other mechanical property. The importance of the length of storage period for the rheology of potato parenchyma is evidenced by the change observed in trends of rheological properties when only data corresponding to shorter periods are taken account. Linear models did not fit compression parameters over 64 days (Fig. 1b). Moreover, for a shorter period (28 days), there was a change in the trend of the compression parameters (Fig. 1c), with significant linear models fitting the decrease in Fc and Ec. Changes in parameter trends according to the length of the storage period considered illustrate the difficulty of interpreting results and highlight the discrepancies between authors in the literature. De Baerdemaeker et al. [30] found that the maximum compression force of potato specimens decreased over a 6 month storage period in response to increasing cell turgor pressure, whereas Diehl et al. [31] reported an increase in potato tissue compression parameters with time in response to decreasing turgor pressure. In
both cases, changes in compression parameters were inversely related to turgor pressure. Potato cell turgor pressure estimations during cold storage are few and unclear. Brusewitz et al. [3] found that the turgor of potato tissue decreased over the first 14 days and increased monotonically over the following 49 days. Alvarez et al. [8] found that the cell turgor pressure of stored potato increased between 14 days and 28 days and decreased monotonically after 28 days in storage. It seems evident that when cell turgor pressure is high, the cell wall is subjected to stress, and a low force would result in its failure [32]. From our results, a linear increase in Fc and Ec over 140 days appears more likely to reflect the decrease in cell turgor pressure by water loss and stress relaxation in the cell wall. Large-scale deformation methods are rarely useful for the assessment of small-scale changes at the cell level due to their relative insensitivity [13, 15]. It is therefore unlikely that the compression-induced increase in longitudinal stiffness accurately reflects the increase in the elastic response of the cell wall with time. Moreover, the linear decreases in Fc and Ec over 28 days could reflect the increase in potato cell turgor in the early stages due to the predominance of water production by respiratory processes over water loss by evaporation, resulting in a decrease in whole tissue stiffness. The nonmonotonic trend identified for compression parameters in an intermediate period (between 1 month and 2 months) may be due to the fact that the increase in cell wall stiffness
Mo: Moisture content
52
is compensated for by a nonmonotonic cell turgor pressure trend, with water loss by evaporation and production of water by respiration, resulting in nonmonotonic total tissue stiffness. Maximum shear force was significantly affected by storage time (P^0.01). Fs decreased over 140 days (Fig. 1d), with the highest value at 14 days and the lowest at 110 days. Gs and Us were not affected by storage time (P 1 0.01). All shear parameters decreased linearly during 140 days (P^0.05) with similar and significant mutual correlations (P^0.01). Linear models also did not fit shear parameter trends over 64 days (Fig. 1e) or 28 days (Fig. 1f). A change in the behavior of maximum force and modulus of rigidity was observed, with a significant linear model fitting the increase in Gs. Comparison of the trends of Ec and Gs revealed inverse behavior of both stiffnesses at 140 days and 28 days. The modulus of rigidity reflects the elastic response capacity of the cell wall [15, 17], so that Gs and Fs trends could reflect the increase in cell wall elastic response and stiffness over 28 days. Shear parameters fell over 140 days, probably because cell wall stiffness was weakened by distension due to turgor pressure under longer storage [4]. Storage time significantly affected Et and Dt (P^0.01). Figure 2a–c shows average values of tension
properties and trends at 140, 64 and 28 days. Significant linear models were fitted to the decrease in apparent modulus of elasticity or longitudinal stiffness in tension and the increase in maximum tension deformation (P^0.05). Et displayed the same trend as the shear parameters, whereas Dt showed the same trend as the compression parameters over 140 days. Average Ft, Ut and st values were not significantly affected by storage time (P 1 0.05), although like Fc, Ec, and Dt, Ft and Ut they also increased with storage time, and significant linear models were fitted to these increases, in particular Ut (P^0.01). st did not decrease linearly over 140 days (P 1 0.05). The highest correlations between tension parameters were established between Ft and st (rp0.786), and Ut and Dt (rp0.832) respectively. Over a 64-day period neither an increasing nor a decreasing behavior trend was identified for Ft, st and Ut; however, it was possible to express the decrease in Et and the increase in Dt (Fig. 2b) through linear models. These properties maintained the same trend found at 140 days. Over 28 days storage (Fig. 2c), Ft, and Dt exhi-
Fig. 2a–f Changes and trends in tension and stress relaxation parameters with storage time
53
bited the same behavior as was observed over 140 days, and the respective data fitted significant linear models. However, the trends of Ut, and Et changed, decreasing and increasing respectively with a significant model fitting the increase in Et (P^0.01). The constant increase in Dt for all three periods considered could reflect plastic deformation of the cell wall following an increase in turgor pressure. Stiffnesses Et and Ec presented an inverse trend at both 140 days and 28 days, with Et exhibiting the same trend as Gs. Also, De Baerdemaeker et al. [30] reported an inverse behavior trend for forces derived from compression and tension tests in stored potato tissue. The term ’cell wall stiffness’ has been used to describe the stiffness of the cell wall as would be obtained from uniaxial tension test, i.e., a material property independent of geometry [12]. Longitudinal stiffness from tension seems more likely to reflect the increase in the elastic response of the cell wall in the early stages and therefore the increasing cell wall stiffness occurred during potato storage. Properties derived from successive stress relaxation cycles were statistically analyzed to determine the effects of relaxation cycle number, storage time and interaction. Both cycle number and storage time had a significant effect (P^0.01) on stress relaxation parameters Fr, Sr and Ar, although the interaction between effects was not significant. Fr was lower when the number of cycles was increased. Fr1 and Fr2 were significantly different, as were Fr1 and Fr3; the differences between Fr2 and Fr3 were not significant. In contrast, Sr and Ar were higher when the number of cycles was increased, which was to be expected for the residual area, defined as the area below the force-time curve. All three residual areas differed significantly from one another. Sr1 was also significantly different from Sr2and Sr3. When the cells are compressed, fluid in the cells exerts additional pressure on the cell wall causing them to stiffen [33]. The decrease in relaxed forces and the increase in relaxation gradients with cycle number seem to confirm this fact. Relaxed forces and relaxation gradients decreased linearly (P^0.05) over 140 days (Fig. 2d) (Table 1). However, only Ar1 decreased linearly (P^0.05) over the whole period. Correlation coefficients between stress relaxation parameters were high, but residual areas presented the lowest correlations with forces and gradients. Over a 64 day period (Fig. 2e), significant models were fitted to the decrease in the three relaxation forces, whereas the slopes did not show any clear trend; residual areas increased with time, and the trend was different from that found over 140 days. Over a 28 day period (Fig. 2f), the models fitting the decreases in the forces and the increases in the areas were more significant. Relaxation forces presented the same significant downward trend for the three time periods studied, and could be considered suitable to reflect the mechanical response of cell turgor pressure [14, 15, 17], which decreased during prolonged storage through water loss and stress relaxation of the cell wall.
Figure 3a–c shows average values and trends of textural properties F and H for 140, 64 and 28 day storage periods. Storage time did not significantly (P 1 0.01) affect either of the properties, which decreased linearly with time (P^0.05) over 140 days. Both properties maintained the same decreasing trend during both shorter periods. There was significant correlation between fracturability and hardness (rp0.499). Moisture content values are shown together with textural properties in Fig. 3a–c. Storage time significantly affected the moisture content (P^0.01). The lowest value was registered at 28 days and the highest value a week later. Moisture content decreased linearly with time (P^0.05), evidencing the consequent water loss of the cells over 140 days. Moisture content presented a significant negative correlation with apparent modulus of elasticity in tension (rp–0.257) and significant positive correlations with relaxation forces at first and second cycles (rp0.305 and rp0.309 respectively). Over 64 days, moisture content tended to increase (Fig. 3b); over 28 days it decreased linearly (P^0.05) (Fig. 3c). Because changes in turgor pressure are the result of water loss from evaporation, stress relaxation in the cell wall and production of water by respiratory processes [3], the first two processes predominated between 64 days and 140 days and during the 1st month in storage; water production increased moisture content and hence cell turgor pressure between 28 days and 64 days, justifying the undefined trends of the mechanical properties found between 28 days and 64 days storage. Burger models containing one or two discrete Voigt units satisfactorily defined potato creep behavior [22]; this was defined in terms of three or four separated compliances, with one or two viscoelastic compliances J1 and J2, characterized by the retarded elastic components E1 and E2, the corresponding viscous components h1 and h2, and retardation times t1 and t2. Average values for viscoelastic constants could not be estimated since retarded elastic compliance JR was associated equally with one or two viscoelastic elements. However, it was observed that when storage time increased, a simple model containing one Voigt unit (ip1) better defined tissue viscoelastic behavior (Table 2). The microstructural changes associated with the second unit either ceased or were not detected after 35 days in storage. The elastic components of the two units decreased with storage time. E2 was greater than E1, reflecting the greater elasticity associated with the second viscoelastic element in the models. Viscous component h1 also decreased with the time, although there was a considerable increase in the h2 component at 140 days, reflecting less fluidity of the structural components associated with this unit. In an earlier study, Alvarez et al. [22] showed that viscoelastic elements 1 and 2 could reflect viscoelastic properties of pectic substances and hemicelluloses of the cell wall and middle lamella respectively. The increase in retarded compliance associated with element 1, in particular over 28 days, could reflect
54
Fig. 3a–f Changes and trends in textural properties, moisture content and creep compliance properties with storage time
plastic deformation of the cell wall, accounting for the increase in cell wall stiffness with storage time. Instantaneous elastic component J0, and steady-state viscous flow component JN, are both independent of the number of Voigt units, and it was therefore possible to obtain average values of both properties at each time interval studied. Storage time had no significant effect on either parameter (P 1 0.05), although J0 increased linearly and hN decreased linearly (P^0.05) over 140 days (Fig. 3d). For shorter periods, linear models did not fit the trends of the creep compliance properties (Fig. 3e, f). The increase in instantaneous elastic compliance J0 and the increase in the state of flow appear to be consistent with the irreversible plastic component of potato tissue distension when this is subjected to maximum turgor pressure. Only elastic tissue persisted, resulting in increasing cell wall stiffness in cold storage. Statistical analysis showed that storage time significantly affected values of stress relaxation parameters of stored potato tissue, with relaxed forces decreasing linearly during a prolonged period of 140 days. The trend
of these properties appears to be a more consistent and significant indicator of the evolution of internal cell pressure. The significant linear decrease in the moisture content of cells can be seen as the response to the predominance of water loss by evaporation over water production by respiration over 140 days. This factor and the tension relaxation of the cell wall would seem to indicate that the cell turgor pressure of the potato tissue decreased over 140 days, although this would need to be confirmed by estimation of moisture content and its evolution over time. Storage time also significantly affected values of longitudinal stiffness, maximum deformation in tension and maximum shear force. The linear increase in maximum tension deformation appears to reflect plastic deformation of the cell wall, possibly caused by internal cell turgor pressure, while the increase in both longitudinal stiffness in tension and maximum shear force in the early stages reflects the increase in cell wall stiffness and the persistence of elastic tissue behavior. The decrease in these properties by the end of the experimental period would appear to indicate that cell wall stiffness is weakened by distension over long storage periods. The results demonstrate the importance of prolonging the target storage period for determination of the behavior trends of mechanical
55 Table 2 Models fitted for the viscoelastic compliances. J1 Retarded compliance associated with viscoelastic element 1, J2 retarded compliance associated with viscoelastic element 2, E1, E2
retarded elastic modulus corresponding to J1and J2, h1, h2 coefficients of viscosity corresponding to J1and J2, t1, t2 retardation times corresponding to J1 and J2
Days
N
i
J1 (!10 P7 Pa P1)
J2 (!10 P8 Pa P1)
t1 (s)
t2 (s)
E1 (!10 6 Pa)
E2 h1 (!10 7 Pa) (!10 9 Pa s)
h2 (!10 8 Pa s)
Error (%)
0
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
ip2 ip2 ip2 ip2 ip2 ip2 ip1 ip2 ip1 ip1 ip2 ip1 ip2 ip2 ip1 ip1 ip1 ip1 ip2 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip1 ip2
0.672 1.481 1.737 0.948 0.535 1.783 2.482 1.224 1.896 2.058 1.815 1.350 0.926 1.807 1.224 1.463 0.776 1.622 1.572 1.441 1.836 1.655 1.754 1.441 1.952 1.830 1.525 1.781 0.907 1.632 1.643 1.920 1.364 1.463 1.735 2.071
3.324 3.155 9.475 1.170 3.475 1.653 – 3.668 – – 1.413 – 2.664 9.067 – – – – 8.880 – – – – – – – – – – – – – – – – 2.453
657.113 175.021 632.459 175.928 134.732 621.789 82.210 118.191 122.853 200.752 208.385 783.441 119.239 366.690 124.973 121.349 226.833 134.865 168.339 706.444 152.276 119.171 512.186 119.835 187.387 84.310 77.554 230.430 228.727 165.834 129.853 189.634 88.562 77.436 165.688 208.310
14.686 17.096 24.350 32.148 19.456 26.798 – 61.775 – – 20.013 – 19.522 47.301 – – – – 18.517 – – – – – – – – – – – – – – – – 70.681
14.885 6.750 5.757 10.550 18.696 5.607 4.029 8.173 5.273 4.795 5.510 7.406 10.799 5.532 8.171 6.835 12.888 6.166 6.361 6.939 5.445 6.042 5.700 6.937 5.124 5.463 6.556 5.616 11.027 6.127 6.086 5.208 7.330 6.834 5.764 4.828
3.009 3.169 1.055 8.554 2.877 6.049 – 2.726 – – 7.076 – 3.753 1.103 – – – – 1.126 – – – – – – – – – – – – – – – – 4.077
4.419 5.418 2.570 27.500 5.598 16.209 – 16.841 – – 14.161 – 7.326 – – – – – 5.217 – – – – – 2.085 – – – – – – – – – – 28.814
2.466 3.940 4.790 1.326 3.476 2.897 4.941 3.529 4.532 4.981 3.441 4.369 3.369 2.975 3.780 3.245 2.636 2.123 3.241 4.872 1.270 2.168 2.125 3.489 2.600 1.715 3.185 1.933 1.670 2.314 2.104 1.879 4.256 3.567 4.231 1.983
7 14 21 28 35 42 49 64 79 110 140
9.781 1.181 3.641 1.856 2.519 3.477 0.331 0.966 0.648 0.963 1.148 5.802 0.129 2.029 1.022 0.829 2.923 0.831 1.071 4.902 0.829 0.720 2.920 0.831 0.960 0.460 0.508 1.294 2.522 1.016 0.0790 0.0988 0.0649 0.0529 0.0955 1.006
a
For definitions, please go to Mechanical tests in Materials and Methods N: sample number
properties. Over a period of less than 2 months, the tissue stiffness trend was unclear because both cell wall stiffness and cell turgor pressure trends were unclear and inverse. More precise techniques and estimation methods for these cell parameters will be required before we can determine what phenomena really measure rheological properties as determined by different tests in relation to storage time. Acknowledgements We are indebted to the CICyT for financial support (project ALI98–1055).
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