2.1 Potato samples

Potatoes (Solanum tuberosum, Red Shef) were purchased from a local market and stored in a refrigerated room (4°C) in a plastic bag with few perforations for about 4 days during which all cooking trials were completed. Test samples of potatoes were prepared using a cork borer and a sharp knife as cubes (15 mm × 15 mm × 15 mm) that are often used in commercial canning. Copper–Constantan thermocouple wires (diameter = 0.0762 mm, Omega Engineering Corp, Stamford, CT, USA) were inserted at the cube center with the aid of tooth pick and epoxy glue to measure the internal product temperature. Intricate details on thermocouple attachment can be found in Sablani and Ramaswamy [29]. A data logger model (HP34970A, Hewlett Packard, Loveland, CO) was used to record the temperature signals at regular interval of 10 s.

2.2 Thermal treatment

Test samples (8 pieces of 15 mm potato cubes) weighing approximately 40 g were placed in a small perforated basket and cooked in a water bath at selected temperatures (70–100°C) for different times (1–50 min). Each treatment was given separately in order to prevent a large temperature change in the bath. Water bath temperature was monitored while heating and showed a maximum variation of ±1°C from the set point. After the heat treatment, the cooked product was cooled immediately to 3°C, using iced water and drained.

2.3 Texture measurement

Cooked samples were subjected to a single cycle compression test using a texture-testing machine (Lloyd model LRX-2500 N; Lloyd Instruments Ltd., Fareham, Hants, UK). A cross-head speed of 10 mm/min and chart speed of 100 mm/min were used. A cylindrical plate (diameter ~5 cm) cross head plunger was used to compress cubes of test samples simulating parallel plate compression between the moving plunger and the stationary base plate. Similar procedures have been used in some previous studies [5, 8] from our group. Each test was repeated individually on eight cubes and their mean values were used as indicators of the textural properties of cooked potatoes. The typical deformation curve during the compression test is shown in Figure 1. The texture parameters, including firmness (F), stiffness (S) and hardness (H), were evaluated using following equations:

where P_max is the maximum force for the compression cycle, ΔL is the maximum deformation, A₀ is the initial cross-sectional area of the potato sample, L is the initial length of the potato sample, ΔP is the force difference at the linear portion and ΔL_l is the deformation at the linear portion. Tests were repeated several time and the average variation around the mean of eight values were small (coefficients of variation<5%).

Figure 1:

A typical force–deformation curve of potato sample.

2.4 Color measurement

The color characteristics were assessed using a tristimulus Minolta Chroma Meter (Minolta Corp, Ramsey, NJ, USA) to determine L, a and b values of cooked samples. The colorimeter was calibrated with a white standard. L, a and b measurements were evaluated from 10 samples and the values were averaged. The total color difference (ΔE) was given by

where L₀, a₀ and b₀ represent the readings at heating time zero (i.e. raw samples), and L, a and b represent the instantaneous individual readings after cooking.

2.5 Ascorbic acid estimation

About 50 g potato sample was blended with an equal weight of 6% metaphosphoric acid (HPO₃) for 1 min. An aliquot (5 mL) was made up to 100 mL by adding 6% HPO₃. The solution was then centrifuged at 4,000 rpm for 15 min. About 5 mL of the supernatant was topped with 10 mL of 2,6-dichlorophenol–indophenol dye at appropriate concentration and shaken. A volume of 3 mL of the mixture was piped to a cuvette and placed in a spectrophotometer. The absorbance at a wavelength of 518 nm was measured within 15–20 s and related to the concentration using a standard curve.

2.6 Kinetic models

Change kinetics of quality factors during storage and processing have been investigated by a great number of researchers. Generally, first-order models as below can describe the time dependence of a quality factor “X”:

where k is the rate constant, X is the concentration of a quality factor at time t. X_e is the equilibrium quality value. By integrating above equations, following equations can be developed:

where X₀ represents the initial value of a quality factor. In this study, eq. (7) was used for time dependence of kinetics of texture properties and the ascorbic concentration, while eq. (8) was applied for the color change kinetics. It should be noted that the two simultaneous first-order kinetic mechanisms were used for the kinetics of texture properties. The whole process was divided into two stages with different softening rates (k₁ and k₂). During the first stage, the thermal softening rate consisted of k₁ and k₂, while during the second stage, it was determined only by k₂.

The Arrhenius equation is usually applied to evaluate the temperature dependence of the rate constant k:

where T is the absolute temperature, s is the frequency factor, E_a the activation energy and R the universal gas constant (8.314 J/mol K).

In food thermal processing, kinetics of microorganisms and quality factors are often described by other two parameters: decimal destruction time, D and decimal change temperature, z, respectively. The relation between k and D is given by following equation:

where D_ref is the D value at the reference temperature (T_ref). The conversion relationship between E_a and z was determined by Ramaswamy et al. [30]. They found that by defining the temperature limits over which kinetic data were obtained plus for an E_a or z value, a consistent and reasonable estimate of the unknown can be obtained by the following equation:

where T_min is the lower limit of the temperature range and T_max is the upper limit of the temperature range.

2.7 Correction of thermal lag

Heat transfer from cooking medium to the center of the particle is a gradual process due to the thermal lag caused by the heat transfer resistance; hence, there exists a come-up time during which the sample temperature increases from the initial temperature to the cooking medium temperature. Correction of the resulting thermal lag is essential to avoid overestimation of the cooking time for both texture and ascorbic acid concentration changes during cooking process. In this experiment, the temperature profile at the center of the particle was monitored by copper constantan thermocouples in order to calculate the effective portion of the come-up time. The procedure reported by Awuah et al. (1993) was used for the correction of the come-up time as simplified in the following equation:

where t_e is the corrected time. T is the temperature recorded by the thermocouple at the center of the potato particulate. Since z value is unknown before D values are obtained, an estimate of z₀ was initially made from the D values with real heating times. Using this estimate, the heating times were corrected using eq. (13) and then the D values were computed. These D values were then used to get a z₁ value. By comparison of z₁ and z₀, a new z value was determined to replace z₀. This calculation procedure was repeated until the difference in two z values is less than 0.5°C. This procedure of correcting thermal lag is also known as iterative method for thermal lag correction.

It should be noted that t_e was used for both texture and ascorbic acid kinetic calculation but not for the color because the color change was affected by the surface temperature.

3.1 Kinetics of texture softening

Figure 2 shows the firmness curves of potato samples as a function of heating time at different temperatures. As expected, the firmness of potato samples decreased with time and the rate of softening increased with temperature. In addition, it can be also found that there existed a switching point that can divide the whole heating process into two stages. The first stage had much higher softening rate than the second stage. This meant that the texture of potato samples was more sensitive to thermal softening during the beginning stage. This behavior of thermal softening was in consistence with what Huang and Bourne [9] first reported and it was later confirmed by other group of researchers as well [5, 8, 11, 26, 32].

Figure 2:

Thermal softening of potato sample at different temperatures.

Kinetic parameters of thermal softening of potatoes estimated by using non-linear regression method are summarized in Table 1. Statistical test results (R²) of the regression fitness for time-dependent kinetics were larger than 0.91 except for individual cases of stiffness at 70°C, indicating that the two simultaneous first-order kinetic mechanisms were suitable for description of the time-dependent kinetics of the potato firmness change during cooking process. It was also noticed that the second stage had higher R² value than the first stage for all different temperatures, meaning that there existed better agreements between model predicted and experimental results for the second stage. This is important because practical cooking process is usually carried out for long time. For the temperature dependence kinetics, both Arrhenius model and the first-order model had very high R² value (>0.97). This demonstrated that both models were reliable to be used for the temperature-dependent kinetics of potato firmness change during cooking.

As shown in Table 1, the D values at a reference temperature of 85°C were calculated for both mechanisms, which can be used for comparison of softening rates for them. For example, D₈₅ values of the firmness change were 31 and 95 min for both mechanisms, respectively. This meant that mechanism 1 had much faster change rate than mechanism 2.

The relative error of conversion from z to E_a or E_a to z using eq. (12) was less than 1% for most of cases, confirming that it was reliable to obtain z or E_a by using the conversion eq. (12) with the minimum and maximum temperatures. This method can be also used to check the accuracy of regression calculations for z or E_a.

The z values of the firmness found from this study were 27°C and 21°C for both mechanisms 1 and 2, respectively. These z values are higher than those (20.4°C and 17.2°C) reported by Harada et al. [33]. The D values of thermal firmness obtained in the temperature range of 70–100°C were relatively lower than what Nourian and Ramaswamy [8] reported. They found that D values associated with the slower mechanism (mechanism 2) were 138 and 578 min in the temperature range 80–100°C, nearly 5–10 times larger than the range of values for the rapid mechanism (mechanism 1). These differences could be caused by the difference of potato varieties.

Other two texture properties, stiffness (S) and hardness (H), demonstrated similar trends during cooking process as firmness. Their kinetics of time and temperature dependences was similarly determined by above methods. Kinetic parameters of S and H and regression statistical results are also listed in Table 1.

3.2 Kinetics of color change

The color parameters L and ΔE for surface color changes of potato samples during cooking at different temperatures are illustrated in Figure 3(a) and 3(b), respectively. Since the “a” and “b” values were relatively stable, their variations were small, and no clear trend was established. From Figure 3(a) and 3(b), it can be found that both L and ΔE values showed similar trends with respect to cooking time. They were found to increase with time but the increasing rates varied with both time and temperature. Higher temperature resulted in higher increase in the rate. For the effect of cooking time, there was a common point that both L and ΔE values increased with the cooking time but the increase rate decreased with time until they reached the equilibrium values. According to this property, the fraction kinetic model (eq. (8)) was selected as a regression equation to fit the experimental results of both L and ΔE values. Based on the regression analysis, time kinetic parameters D and k as well as equilibrium values (L_max and ΔE_max) for L and ΔE values were determined and the values have been summarized in Table 2. These results were further used for regression analysis of temperature dependence to obtain z, D, E_a and s values that are listed in Table 2. For the time dependence kinetics, the high regression coefficients (R²≥0.94) for both L and ΔE indicated that the selected fractional conversion first-order model was adequate to describe the relationship between color parameters (L and ΔE values) and the cooking time. For the temperature dependence kinetics, the regression coefficient, R², for L was <0.9, while it was 0.99 for ΔE. This meant that the first order or the Arrhenius model could match better the temperature kinetics of ΔE rather than that of L. Thus, it would be better to use the regression equation of ΔE as a prediction model for the practical application purpose rather than that of L.

Figure 3:

Color change of potato sample with time at different cooking temperatures: (a) L value and (b) ΔE value.

3.3 Kinetics of ascorbic acid loss

With respect to ascorbic acid loss/degradation, a plot of log concentration (A_c) and time resulted in a straight line indicating that the loss/degradation with respect to time at a specific temperature followed the simple first order (Figure 4). Accordingly, reaction rate constants, D values and the temperature dependence z value were calculated and are presented in Table 3. The D values at different temperatures varied from 23 min at 100°C to 140 min at 70°C, giving a z value of 39°C and activation energy of 63 kJ/mol. These values obtained are slightly different from those reported in literature. Holdsworth [34] reported E_a between 30.6 and 49.9 kJ/mol, while Esteve et al. [35] found an E_a of 51 kJ/mol for samples of asparagus.

Figure 4:

Ascorbic acid concentration changes with time at different cooking temperatures.

3.4 Correlation matrix

In order to determine the relationship between all quality attributes investigated in this study, a set of data for F, S and H for texture properties, L and ΔE for color, as well as ascorbic acid under typical cooking conditions were generated by above kinetic models, and then was used to build up a correlation matrix of quality attributes, as shown in Table 4. From this table, it can be found that there were very high linear relationships (R²>0.95) between three texture properties F, S and H, especially between F and H. It means that it is feasible that anyone of properties can be used for representing the texture softening during the cooking process for the potato samples within the ranges of cooking conditions studied. The relationship coefficient between L and ΔE was 0.91, less than those for relationships between texture properties. This is because ΔE was calculated by total difference of color parameters including L, a and b, instead of only L. In addition, there was a very high relationship between ΔE and A_c (R² = −0.953) and between L and S (R² = −0.954). The negative indicated that ΔE or L increased with the decrease of A_c or S value.