freezin g ra te a n d th awin g rate o n rheo lo g ical parameters.(. F. Max im u m co mp ressio n fo rce,. E app aren t m o d u lu s o f elasticity. ,º energy required fo.
Z Lebensm Unters Forsch A (1997) 204: 356—364
( Springer-Verlag 1997
OR I G I N A L P AP E R
M.D. Alvarez · W. Canet · M.E. Tortosa
Effect of freezing rate and programmed freezing on rheological parameters and tissue structure of potato (Cv. Monalisa)
Received: 29 July 1996
Abstract Compression, shear and tension tests were carried out to determine the effect on potato tissues of different freezing rates (0.5, 1.25 and 2 °C/min down to !18 °C), thawing up to #20 °C at the same rates, and one, two, three or four successive freeze/thaw cycles. The effect of freezing rate on the zone of maximum crystallization was also examined, along with different combinations of programmed freezing, and the effect of prior cooling was assessed. Minimum alteration of the rheological behaviour of slowly thawed tissues was achieved by pre-freezing (3 °C for 30 min), slow cooling phases (0.5 °C/min) before and after the phase of maximum ice crystallization and quick freezing (2 °C/min) in the same phase. The shear test was found to be well suited to the study of these effects. Examination of the tissues by SEM revealed differing degrees of mechanical damage to tissue structure, which accounted for the rheological behaviour of the samples. Coefficients of softening per freeze/thaw cycle were determined for the various rheological parameters, the highest value being given by the modulus of rigidity (17.75%). Key words Potato · Freezing · Thawing · Rheological parameters · Structure
Introduction Incorrect processing and storage conditions cause loss of the textural quality of frozen fruit and vegetables,
M.D. Alvarez · W. Canet ( ) Departamento de Ciencia y Tecnologı´ a de Productos Vegetales, Instituto del Frı´ o (CSIC), Ciudad Universitaria s/n, E-28040 Madrid, Spain M.E. Tortosa Departamento de Fisiologı´ a y Biologı´ a Vegetal, Escuela Te´cnica Superior de Ingenieros Agro´nomos, Ciudad Universitaria s/n, E-28040 Madrid, Spain
resulting in excessive softening. It is therefore necessary to determine the processing specifications that will ensure the optimum final texture of the products [1]. A review of the literature shows that the freezing rate is crucial to the quality of frozen products, and the majority finding is that quick freezing has a positive effect on the texture of potatoes [2], carrots [3—5], cranberries and blackberries [6]. The aspect of freezing that really produces irreversible negative effects on textural quality is crystallization [7]; therefore, the freezing rate is particularly important in the phase of maximum ice crystal formation. Freezing rates can now be modified in the various processing stages using programmed freezing. This is a possibility that the food industry ought to consider seriously in order to optimize quality while achieving lower costs than those incurred by conventional freezing. Fuchigami et al. [4] have studied the effects of different combinations of freezing rates on frozen carrots using programmed freezing, modifying freezing rates in the different stages of the process and using the fastest rate in the phase of maximum crystal formation. The authors found that samples which were quick-frozen throughout the process exhibited better firmness upon thawing. Although the rheological behaviour of vegetable tissues before and after freezing and thawing has been studied, the nature of texture is too complex and multidimensional for the texture of a product to be characterized by the measurement of one single parameter. Canet [2] has used shear, compression and relaxation tests to examine the effects of various blanching processes and freezing/thawing rates on the texture and structure of potato. Jackman et al. [8] concluded that the texture of a product can only be characterized by applying objective methods based on a variety of principles (compression or tension and shear) and measurements on different scales (large-scale as opposed to small-scale measurements of deformation).
357
The texture of vegetable tissue is determined by its morphological structure and its chemical composition [9]. Monzini et al. [10] have used histological methods to evaluate the positive effect of high freezing rates. According to Raeuber and Nikolaus [11], microscopy can describe visible structure, but mechanical linkage can only be determined intrinsically by means of parameters that require the application of stress-strain using rheological methods of texture measurement. The various objective means of evaluating texture (histological, fundamental rheological, imitative and indirect methods), particularly rheological methods, have been successfully used to detect the effect of high freezing rates, even after cooking, on green beans and carrots [12], potatoes [13, 14], carrots [3] and peas [15]. Although, in theory, the temperature fluctuations to which vegetables are subjected rarely go as far as total thawing and subsequent re-freezing, the effect of this at different rates can usefully be examined in order to assess the mechanical damage inflicted on tissue structure and its cumulative effect. The aim of the present work was to assess the effects of freezing and thawing rates and of programmed freezing procedures on the rheological behaviour of potato tissues and to determine what parameters will best account for the mechanical behaviour of the tissue in response to structural damage caused by a variety of freezing conditions. The changes in rheological parameters resulting from successive freeze/thaw cycles were also quantified and expressed mathematically. These changes were interpreted and related to the structural damage revealed by scanning electron microscopy (SEM).
Table 1a Rate of freezing (°C/min) uses at any stage of normal freezing processes and progammed freezing. (SF slow freezing, IF intermediate freezing, QF quick freezing, PF programmed freezing)
Temperature (°C)
20P3 3P!3.5 !3.5P!18 !18P#20
Table 1b Rate of freezing (°C/min) uses at any stage of programmed freezing with precooling. Cte: constant
Materials and methods Raw material. The potato samples (Solanum tuberosum, L., Cv. Monalisa) came from Segovia (Spain). The mass of the potatoes ranged from 153.83 g to 186.56 g and specific weights (g/cm3) were within the interval 1.06354l41.0796 (P40.01). The material was kept at 4 °C and 85% relative humidity throughout the experiment. Sample preparation. Uniaxial compression (n"10) and shear (n"10) mechanical tests were carried out using cylindrical specimens (diameter"25.4 mm, height 10 mm). Tension tests (n"10) were conducted on dog-bone-shaped specimens that were 5 mm thick (dimensions: 75 mm long and 20 mm wide at the retaining ends and 8 mm wide at the neck). Percentage exudate was determined using ten cylindrical specimens. Each experimental unit consisted of 40 specimens subjected simultaneously to the same heat treatment. Freezing and thawing procedures. The experimental units were frozen under the various sets of conditions by forced convection with liquid nitrogen vapour in an Instron (Canton, Mass., USA) programmable chamber (Mod. 3119-05, !70 °C/#250 °C), at !60 °C (!2 °C/min), !40 °C (!1.25 °C/min), and !20 °C (!0.5 °C/min), until their thermal centres reached !18 °C. They were thawed by forced convection air at #20 °C (0.5 °C/min), #40 °C (1.25 °C/min) and #60 °C (2 °C/min) until their thermal centres reached 20 °C. In pre-cooling for programmed freezing (PF4—PF5—PF6—PF7—PF8—PF9), the thermal centres of the specimens were kept at 3 °C for 30 min. Variation of the freezing rate in the zone of maximum ice crystal formation was carried out with the combinations PF1—PF2—PF3—PF4—PF5—PF6, with a slow rate (!0.5 °C/min) for cooling prior to the crystallization phase and for freezing to !18 °C after that phase. The freeze/thaw cycles (SF1—IF2—QF3) were performed a total of four times at the experimental rates. In the case of programmed freezing and freeze/thaw cycles, thawing was fixed at the slowest rate (#0.5 °C/min). Air and product temperatures were monitored by K-type thermocouples using a hardware and software system that permitted real-time data gathering, storage and calculation of freezing and thawing rates. Tables 1a and 1b show the processes used in conjunction with the different experimental units and the rates at each phase. Figure 1 shows an example of the time course of the specimen centre and air
Rate of freezing (°C/min) Slow
Intermediate
Quick
Programmed freezing
(SF1)
(IF2)
(QF3)
(PF1)
(PF2)
(PF3)
!0.5 !0.5 !0.5 #0.5
!1.25 !1.25 !1.25 #0.5
!2 !2 !2 #0.5
!0.5 !2 !0.5 #0.5
!0.5 !1.25 !0.5 #0.5
!0.5 !0.25 !0.5 #0.5
Temperature (°C) 20P3 3 (30 min) 3P!3.5 !3.5P!18 !18P#20
Rate of freezing during programmed freezing (°C/min) (PF4)
(PF5)
(PF6)
(PF7)
(PF8)
(PF9)
!0.5 cte !2 !0.5 #0.5
!0.5 cte !1.25 !0.5 #0.5
!0.5 cte !0.25 !0.5 #0.5
!0.5 cte !0.5 !0.5 #0.5
!1.25 cte !1.25 !1.25 #0.5
!2 cte !2 !2 #0.5
358 Fig. 1 Example of the evolution of the thermal centre and air temperature in pre-cooled specimens subjected to a high freezing rate during the phase of maximum crystallization and a low thawing rate (PF4)
temperatures during the course of one of the freeze/thaw processes involving pre-cooling (PF4). Percentage exudate was determined according to Marti and Aguilera [6]. Rheological parameters. Compression, shear and tension tests were performed using an Instron Food Testing Instrument Mod. 4501 using a 5-kN load cell and Instron series IX software. Samples were compressed at a deformation rate of 200 mm/min to determine the maximum compression force, i.e. F (in N), the apparent modulus of # elasticity, i.e. E (in MPa) and the energy required for breaking per # unit of volume, i.e. º (lJ/mm3). Shear test was performed using # a shear cell [2] at a deformation rate of 400 mm/min to give the maximum shear force, i.e. F (in N), the modulus of rigidity, i.e. G (in 4 4 KPa) and the shear energy required per unit of volume, i.e. º 4 (lJ/mm3). The tension test was performed at a deformation rate of 100 mm/min, using a cell consisting of two compressed-air clamps (1.5]105 Pa) fitted to the specimen necks over filter paper to prevent slipping and breakage, to give the maximum tensile force, i.e. F (in N), the apparent modulus of elasticity, i.e. E (in MPa) and the 5 5 energy required for breaking per unit of volume, i.e. º (in lJ/mm3). 5 Uniform stress was applied over a length of 30 mm. Structural examination. Structure was examined by SEM using a Hitachi Mod. S-2500 microscope. Tissue samples were fixed in FAA [ethanol 70% (90 ml), acetic glacil acid (5 ml), formol (5 ml)] for 2 h and dehydrated in a series of ethanol solutions of increasing strength, from 70% to 100%: 15 min of immersion each in concentrations of 70, 80 and 90% and 1 h in each of the final concentrations of 100% ethanol. Finally, they were preserved in acetone until processing. Samples were critical-point dried then mounted and platinum coated (400-A) in P-S1 Diode Sputtering System metallizer. Photomicrographs were taken with a Mamiya camera using Ilford 6]9 cm FF-4 film. Films were processed following the standard method. The magnifications ranged from 60 to 78 (1 cm"160 and 128 lm). Statistical analysis. Multifactorial and unifactorial analysis of variance were performed and means compared by least significant differ-
ence (LSD, 95%). The relationship between rheological parameters was determined by analysis of correlation and mathematical expression of changes in parameters with respect to the number of successive freeze/thaw cycles, using inverse regression models with a significance level of 0.05%.
Results and discussion Tables 2a, b and 3 show the mean values of the various rheological parameters and the exudate under the different processing conditions. They also show that there were significant differences between these conditions. The effect of the freezing rate (Table 2a) was significant for all rheological parameters (P40.01); likewise, the thawing rate significantly affected all the parameters relating to the compression test (P40.05) and also the maximum shear force and modulus of rigidity (P40.01). Parameter values for the frozen and thawed samples all differed significantly from those of the fresh control. These values were highest for the fastest freezing rate (!2 °C/min) and the slowest thawing rate (#0.5 °C/min). The histological section in Fig. 2 (photomicrograph 1) shows the hexagonal polyhedron characteristic of fresh tissue, with the starch granules inside the cell cytoplasm. Quick freezing and slow thawing did little damage to the structure photomicrograph 2), with hardly any rupturing of cell walls or loss of internal cell pressure. The positive effect of high freezing rates was apparent for all the thawing rates used.
#0.5 #1.25 #2 #0.5 #1.25 #2 #0.5 #1.25 #2
Raw !2 !2 !2 !1.25 !1.25 !1.25 !0.5 !0.5 !0.5 30.73
559.61a 352.90b 342.42b 282.57c 309.74c 283.28c 243.62d 230.02d, e 193.99e, f 205.77f
F # (N)
0.24
3.35a 2.05b, c 2.23b 1.78d, e 1.98c, d 1.77d, e 1.39f, g 1.57e, f 1.26f 1.39f, g
E # (MPa)
22.91
248.92a 207.36b 202.82b 129.48c 165.08d 163.68d 134.30c 95.55e 82.41e 105.32e
º # (lJ /mm3)
4.31
89.00a 52.55b 55.14b 46.13c 47.60c 39.67d, e 39.57d, e 41.62d 35.21f 36.74e, f
F 4 (N)
Shear
1.06
15.29a 9.05b, c 9.43b 7.06d 8.17c 6.21d, e 6.03d, e 6.93d 5.44e 5.54e
G 4 (kPa)
23.51
215.50a 151.98b 164.24b 142.29b, c 154.97b 110.78d 127.60c, d 106.78d 107.50d 113.49d
º 4 (lJ /mm3)
2.19
26.55a 12.81b 13.38b 10.18c, d 11.51b—d 11.39b—d 11.62b, c 6.23e 9.42d 9.72c, d
F 5 (N)
Tension
0.26
3.06a 0.96b 0.075b, c 0.72b, c 0.78b, c 0.78b, c 0.73b, c 0.53c 0.68c 0.60c
E 5 (MPa)
27.46
147.04a 62.79b—d 80.45b 81.29b 69.70b, c 59.50b—d 70.25b, c 40.83d 51.45c, d 49.50c, d
º 5 (lJ /mm3)
0.91
00.00a 14.28c 19.05f 17.47e 13.33b 17.59e 20.06g 16.27d 18.92f 20.62g
Drip (%)
per unit of volume, F maximum tensile force, E apparent modulus of elasticity, º energy 5 5 5 required for breaking per unit of volume, » rate of freezing, » rate of thawing). Means # $ (n"10). Different letters in the same column indicate significant differences (P40.05)
LSD, 95%
Raw (PF4) (PF9) (PF1) (QF3) (PF5) (PF8) (PF2) (IF2) (PF6) (PF7) (PF3) (SF1)
29.60
559.61a 421.94b 363.87c 355.09c 352.90c 313.45d 293.73d 300.16d 309.74d 226.93e 207.45e 201.69e 230.02e 0.27
3.35a 2.78b 2.45c 2.27c, d 2.05d, e 2.10d, e 1.89e 1.95e 1.98e 1.45f 1.50f 1.40f 1.57f 20.43
248.92a 176.33c, d 169.15d 212.37b 207.36b 194.69b, c 144.81e, f 136.92f 165.08d, e 126.99f 99.44g 102.44g 95.55g 5.17
89.00a 62.13b 54.75c 52.29c, d 52.22c, d 45.04e, f 45.92e, f 37.51f, g 47.60d, e 37.46g, h 36.00h 36.81g, h 41.62f, g
F 4 (N)
º # (lJ /mm3)
F # (N)
E # (MPa)
Shear
Compression
1.18
15.29a 10.00b 9.35b, c 8.41c, d 9.05b, c 7.58d, e 7.23d—f 5.75g 8.17c, d 6.39f, g 5.82g 6.12f, g 6.93e—g
G 4 (kPa)
26.98
215.50a 184.04b 174.08b, c 155.83c, d 151.98c, d 115.05d, f 134.87d, e 100.37f 154.97c, d 99.37f 97.80f 104.65f 106.78f
º 4 (lJ /mm3)
1.89
26.55a 18.25b 15.56c 14.99c 12.81d, e 14.26c, d 12.20e 12.65d, e 12.31e 11.08e 11.89e 12.62d, e 6.23f
F 5 (N)
Tension
0.23
3.06a 0.95b 0.96b 0.88b, c 0.96b 0.83b, c 0.82b, c 0.71c, d 0.79b, c 0.66c, d 0.73b—d 0.73b—d 0.53d
E 5 (MPa)
23.12
147.04a 106.70b 80.62c 78.16c, d 62.79c—e 77.83c, d 60.83c—e 69.12c, d 70.00c, d 55.12d, e 57.91c—e 68.04c, d 40.83e
º 5 (lJ /mm3)
2.29
00.00a 15.01b—d 15.83c—e 16.27c—e 14.28b, c 15.67b—e 16.80d, e 16.49c—e 13.33b 17.51e 17.37e 16.44c—e 16.27c—e
Drip (%)
Table 2b Effect of freezing rate, phase of freezing rate application and pre-cooling on rheological parameters. Means (n"10). Different letters in the same column indicate significant differences (P40.05)
LSD, 95%
» $ (°C/min)
» # (°C/min)
Compression
Table 2a Effect of freezing rate and thawing rate on rheological parameters. (F Maximum # compression force, E apparent modulus of elasticity, º energy required for breaking per # # unit of volume, F maximum shear force, G modulus of rigidity, º shear energy required 4 4 4
359
360 Fig. 2 Photomicrographs of potato tissues at the different freezing/thawing specifications and mechanical assays. M1"Fresh product. M2"(QF3): freezing at !2 °C/min throughout the process and thawing at #0.5 °C/min. M3"(PF4): precooling (3 °C, 30 min) and freezing at !2°C/min duirng the phase of maximum crystallization. M4"(PF3): freezing at !0.25 °C/min during the phase of maximum crystallization. M5"Four cycles of freezing at !2 °C/min and thawing at #0.5 °C/min. M6, M7 and M8"Samples of tissues subjected to compression, shear and tension mechanical tests after 4 freeze/thaw cycles
The exudate increased at lower freezing rates, but not significantly. The freezing rate and the amount of juice exuded were inversely proportional to each other, as has been found to be the case for cranberries and wild blackberries [6], unblanched carrots [16], green beans and peas [17] and carrots [4]. Then again the amount of exudate proved to be directly proportional to thawing rate, highlighting the advantage of thawing slowly. Table 2b shows that the effect of the freezing rate was significant during the phase of maximum crystalliza-
tion and pre-cooling. The values of the rheological parameters were highest when samples were cooled for 30 min at 3 °C before freezing then frozen at the highest rate (!2 °C/min) during the phase of maximum crystal formation. No significant difference was observed between sample frozen at the highest rate throughout and the sample frozen at the highest rate only during the period of maximum ice crystal formation. Similarly, Fuchigami et al. [4] reported that there was no difference in the firmness of thawed carrots when they were frozen at !2 °C/min throughout the process and when
4
2
No.
LSD, 95%
!1.25 !1.25 !1.25 !0.5 !0.5 !0.5
#0.5 #1.25 #2 #0.5 #1.25 #2 21.76
160.59c 168.67b, c 173.90b, c 120.91d 122.37d 118.37d
352.90a 180.27b, c 183.93b 176.16b, c
(QF3) !2 !2 !2
#0.5 #1.25 #2
24.53
197.82c 216.35b, c 229.07b 136.43d 144.21d 141.23d
352.90a 235.83b 222.05b, c 240.03b
F # (N)
LSD, 95%
#0.5 #1.25 #2 #0.5 #1.25 #2
#0.5 #1.25 #2
(QF3) !2 !2 !2
!1.25 !1.25 !1.25 !0.5 !0.5 !0.5
» $ (°C/min)
» # (°C/mim)
Compression
0.19
1.23b 1.15b 1.18b 0.83c 0.92c 0.85e
2.05a 1.18b 1.18b 1.17b
0.19
1.31c, d 1.50b 1.38b, c 1.01e, f 0.90f 1.14d, e
2.05a 1.39b, c 1.32b—d 1.40b, c
E # (MPa)
13.49
65.32c, d 75.72b, c 79.21b 48.58e 52.02d, e 47.85e
207.36a 80.00b 83.08b 71.71b, c
17.15
91.17d 90.86d 103.76c, d 51.39f 73.27e 53.62f
207.36a 120.28b, c 102.76d 121.74b
º # (lJ /mm3)
3.00
21.88c—e 24.75b, c 24.02b—d 21.43d, e 19.56e 19.29e
52.22a 24.68b, c 26.33b 24.86b, c
2.98
31.68c, d 29.57d 29.82d 22.59e 24.47e 22.59e
52.22a 30.88d 35.37b 34.39b, c
F 4 (N)
Shear
0.63
3.11b—d 3.62b 3.52b, c 3.19b—d 2.89c, d 2.68d
9.05a 3.50b, c 3.72b 3.62b
0.68
4.76c d 4.56c, d 4.26d, e 3.47f 3.66e, f 3.44f
9.05a 4.86b—d 5.11b, c 5.50b
G 4 (kPa)
15.26
80.98b—d 92.81b 85.83b—d 77.27c, d 73.99c, d 70.57d
151.98a 77.84b—d 85.97b, c 84.97b—d
17.51
113.63b 86.82c, d 99.94b, c 69.14e 74.99d, e 72.28d, e
151.98a 110.78b 111.77b 109.78b
º 4 (lJ /mm3)
1.22
6.88b—d 7.50b—c 7.84b 5.10f 5.75d—f 5.41e, f
12.81a 7.57b, c 7.16b, c 6.43c—e
1.38
8.98b, c 9.22b, c 6.80d, e 6.51e 6.05e 6.55e
12.81a 8.06c, d 6.08e 9.80b
F 5 (N)
Tension
0.14
0.50c, d 0.53c, d 0.74b 0.42d 0.47d 0.49c, d
0.96a 0.52c, d 0.62b, c 0.51c, d
0.12
0.58b—d 0.61b, c 0.54c, d 0.46d 0.50c, d 0.54c, d
0.96a 0.56b 0.55c, d 0.69b
E 5 (MPa)
9.78
46.70d, c 57.08b, c 71.33a 39.62e 51.25c, d 45.95d, e
62.79a, b 42.75d, e 71.75a 51.54c, d
11.63
62.95a 59.91a 51.12a, b 47.33c, d 34.58e 46.62c, d
62.79a 47.95c, d 38.08d, e 66.08a
º 5 (lJ /mm3)
1.41
20.26b, c 23.87d 23.25d 19.97b, c 21.02c 25.66e
14.28a 23.42d 21.28c 19.53b
1.51
20.46c, d 17.72b 20.46c, d 21.40d, e 22.16e 17.92b
14.28a 17.97b 19.81c 22.04e
Drip (%)
Table 3 Effect of number of successive freeze/thaw cycles on rheological parameters. Means (n"10). Different letters in the same column indicate significant differences (P40.05)
361
362
this rate was only applied between 0 °C and !5 °C. This illustrates the importance of applying the quick rate in the phase of maximum crystallization; the rate is less important during the cooling phases immediately preceding and following freezing proper. Application of a very slow freezing rate (!0.25 °C/min) in the phase of maximum crystal formation (photomicrograph 4) caused a total loss of structural integrity, with rupturing of cell walls and contraction from loss of internal pressure, resulting in loss of tissue rigidity. When tissue was cooled at a low temperature (3 °C) for a long period (30 min) prior to freezing, the mechanical strength of the tissue increased for all the freezing rates assayed. This is thought to occur because precooling cuts down the time lapse between freezing at the surface and freezing at the product’s thermal centre, so that freezing-induced expansion takes place before too rigid a crust forms on the surface. The structure is thus better able to withstand the internal stresses and the result is a product with a higher mechanical strength. These findings are borne out by photomicrograph 3, where there is virtually no appreciable rupture of walls or dispersal of cell contents: the starch granules remain inside the cells and turgidity is retained. The loss of exudate in thawing decreased significantly (P40.05) with higher freezing rates. Exudate values were not affected by whether high freezing rates were applied throughout the process or only in the phase of maximum crystallization, or by pre-cooling. The number of successive periods of freezing and thawing likewise significantly affected all the rheological parameters considered (P40.01). When more than one freeze thaw cycle was applied, all values of the variables differed significantly from those of the frozen control. Exudate was found to be directly proportional to the number of freeze/thaw cycles. For each rheological parameter, a softening coefficient was calculated. This is defined as the percentage decrease in the value of the parameter per freeze/thaw cycle. These coefficients are shown in Table 4. The highest coefficient was for the modulus of rigidity (17.75%). This means that the structural rigidity of samples subjected to four freeze/thaw cycles was less than half that of samples subjected to only one cycle. Photomicrograph 5 shows a histological section of tissue after four freeze/thaw cycles (!2 °C/min and #0.5 °C/min). The image shows how, even under the best conditions, successive freeze/thaw cycles cause rupture of cell walls, loss of intercellular adhesion and pronounced cell separation (as compared to photomicrograph 2). The softening undergone by the tissue in successive freeze/thaw cycles is expressed by means of regression models estimated for each mechanical parameter (Table 5). It was found that, after two or three cycles, softness ceased to be much affected by subsequent cycles (Fig. 3).
Table 4 Softening coefficients of rheological parameters per freeze/ thaw cycle
F (N) E/G (MPa)/(kPa) º (lJ/mm3)
Compression
Shear
Tension
14.17 12.38 17.68
15.83 17.75 12.69
12.68 8.89 5.00
Fig. 3 Models fitted for the effect of the number of freeze/thaw cycles on the apparent moduli of elasticity in the compression (E ) # and tensile tests (E ) and on the modulus of rigidity (G ) in the shear 5 4 test
Tables 6 and 7 show the coefficients of correlation between rheological parameters in the different mechanical tests. The high level of correlation between maximum compression force and apparent modulus of elasticity suggests that there could be redundancy between the two parameters; in other words they may be reflecting the same effect on frozen tissue, that is, the mechanical response in terms of adhesion and internal cell pressure. The highest correlation in both tables was found to occur between maximum shear force and the modulus of rigidity; therefore, these again may reflect one and the same effect, in this case the mechanical response in terms of resistance to strain and rupture of cell walls [2]. Maximum shear force and the modulus of rigidity detect the effects of freezing rate, thawing rate and successive freeze/thaw cycles to a high degree of significance and show up the strongest correlations with percentage exudate. The shear test may therefore be considered the most suitable for studying these three effects all together, and likewise for the separate study of the effects of freezing rate and successive freeze/thaw cycles. The tension test gave the lowest correlations among rheological parameters. Tension energy was the parameter that correlated least well with the others, expressed as it was in units which reflect the alterations in specimen geometry, with values that embraced changes
363 Table 5 Regression coefficients and analysis of variance for rheological parameters 1/½"a#bX
F #
F 4
F 5
E #
G 4
E 5
º #
º 4
º 5
a b R2 (%) F Probability of F
2.28E-3 1.11E-3 93.28 27.75 0.03*
0.01406 7.96E-3 94.20 32.49 0.02*
0.0562 0.0270 85.17 11.49 0.07
0.3843 0.1510 89.13 16.40 0.05*
0.0807 0.0588 95.96 47.51 0.02*
0.7243 0.3478 70.93 4.88 0.15
4.45E-3 2.74E-3 97.21 69.56 0.01*
5.49E-3 1.88E-3 91.04 20.32 0.04*
0.0106 2.65E-3 59.01 2.87 0.23
* Significant at a level of 0.05
Table 6 Matrix of correlations derived from analysis of the effects of freezing, thawing and successive freeze/thaw cycles (n"280)
F # E # º # F 5 E 5 º 5 F 4 G 4 º 4 % Ex
F #
E #
º #
F 5
E 5
º 5
F 4
G 4
º 4
1 0.9458 0.9256 0.8192 0.7392 0.5791 0.9111 0.9009 0.8027 !0.7782
1 0.8559 0.7974 0.7051 0.5870 0.8624 0.8617 0.7443 !0.7563
1 0.7655 0.6289 0.5153 0.8571 0.8538 0.7947 !0.6597
1 0.8751 0.7723 0.8293 0.8224 0.7219 !0.7417
1 0.6265 0.7631 0.7455 0.6319 !0.7662
1 0.5729 0.5607 0.5313 !0.5169
1 0.9763 0.8782 !0.8034
1 0.8499 !0.7999
1 !0.6651
% Ex
1
Table 7 Matrix of correlations derived from analysis of the effects of freezing rate, phase of applicatiion and pre-cooling (n"130)
F # E # º # F 5 E 5 º 5 F 4 G 4 º 4 % Ex
F #
E #
º #
F 5
E 5
º 5
F 4
G 4
º 4
1 0.9045 0.8134 0.7580 0.7109 0.5971 0.8568 0.8143 0.6852 !0.7412
1 0.7451 0.6946 0.6111 0.5666 0.7724 0.7445 0.6406 !0.6518
1 0.6456 0.5844 0.4624 0.7056 0.6987 0.5926 !0.5780
1 0.8314 0.7349 0.7580 0.7280 0.5882 !0.7165
1 0.5278 0.7822 0.7516 0.5604 !0.8726
1 0.5588 0.5302 0.4583 !0.5328
1 0.9509 0.8250 !0.8046
1 0.7367 !0.7900
1 !0.5438
in both force and strain. The apparent modulus of elasticity, in contrast, was the parameter that correlated best with the exudate (Table 7). Photomicrographs 6—8 show the effect of the three mechanical tests on tissue which had previously been put through four freeze/thaw cycles. Cell slipping was detected caused by the mechanical compression test [6], tissue tearing caused by the shear test [7] and narrow, stretched cells caused by the tension test [8]. The results of the rheological and histological assays demonstrated the following: (1) that pre-cooling and a high freezing rate during the phase of maximum ice crystal formation has a positive effect on potato texture and tissue structure, (2) that slow thawing has a positive effect, and (3) that it is best not to subject potatoes to more than one freeze/thaw cycle.
% Ex
1
Acknowledgements Thanks are due to the Spanish Comisio´n Interministerial de Ciencia y Tecnologı´ a (CICyT) for financing this research (ALI94-943). The authors are also grateful to Ma Carmen Rodrı´ guez for her assistance.
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