Predicting Steady-state Oxygen Concentrations in Modified ...

J. AMER. SOC. HORT. SCI. 119(3):546–550. 1994.

Predicting Steady-state Oxygen Concentrations in Modified-atmosphere Packages of Tomatoes Sannai Gong and Kenneth A. Corey Department of Plant and Soil Sciences, University of Massachusetts, Amherst, MA 01003 Additional index words. packaging ratio, film permeability, Lycopersicon esculentum Abstract. Mathematical procedures for predicting steady-state O2 concentrations for a range of packaging conditions for modified-atmosphere packages (MAP) of ‘Heinz 1370’ tomato (Lycopersicon esculentum) were developed and tested. The relationship between O2 consumption rate and O2 concentration was determined using O2 depletion data collected by enclosing tomatoes in jars and sampling head space O2 concentration over time. The fitted function was then used in conjunction with the input variables film permeability to O2 (PO ), film surface area (A), and fruit weight in packages (Wp) to develop an equation to predict steady-state O2 concentrations for different packaging ratios (A/Wp) and film permeabilities. Prediction curves showing steady-state O2 concentration for packaging ratios in the range of 1 to 12 closely resembled best-fit curves of experimental data. Increasing temperature from 20 to 28C had little effect on in-package O2 concentration, but decreasing temperature from 28 to 10C led to higher in-package O2 concentrations. The predictive equation developed can be used to select appropriate films and optimize packaging ratios to achieve desired steady-state O2 concentrations for MAP of tomatoes. 2

Delaying tomato fruit ripening is desirable during distribution and for short-term storage before marketing. Commercially, tomatoes intended for distant markets are usually harvested at mature-green or breaker stages so that fruit can endure the rigors of handling while maximizing shelf life. Fruit harvested at mature-green and breaker stages will ripen to the firm-red stage in 7 to 10 days and 2 to 3 days, respectively, when kept in air at 20C (Hobson, 1987; Ryall and Lipton, 1979; Stenvers and Bruinsma, 1975). These times are often not sufficient for transport of fruit from production sites to distant retail markets. The incidence of over-ripe fruit often leads to increased mechanical damage in transit and has been reported as a serious problem associated with long-distance shipments taking more than a week (Geeson et al., 1985). Refrigeration and controlled atmosphere (CA) storage are effective tools for delaying ripening for long durations in transit, but are limited due to high costs and fruit sensitivity to chilling injury at temperatures below 12.5C (Cheng and Shewfelt, 1988; Hobson, 1987; Ryall and Lipton, 1979). Alternatively, an inexpensive way to delay fruit ripening is the use of modified atmosphere packaging (MAP), where fruit are sealed in semipermeable plastic packages that enable the development of a beneficial gas atmosphere created and maintained by the interaction of fruit respiration and gas diffusion through the packaging film. An appropriate MAP for unripe tomatoes delays changes in color, acidity, soluble solids concentration, and firmness (Nakhasi et al., 1991; Yang and Chinnan, 1987). In addition, fruit kept in MAP also benefit from reduced weight loss due to maintenance of high relative humidity (Anderson and Poapst, 1983). Maximum benefits for tomatoes in MAP were obtained when the O2 concentration inside the package was maintained in the range of 3% to 5% (Dennis et at., 1979; Geeson et al., 1985; Kader et al., 1980). For a MAP design to achieve and maintain an O2 concentration in the desired range, it is necessary to select the appropriate combinations of film composition and thickness, film surface area, and fruit weight. Mathematical procedures for predicting and optimizing Received for publication 15 Apr. 1993. Accepted for publication 3 July 1993. Paper no. 3069 of the Massachusetts Agricultural Experiment Station. The cost of publishing this paper was defrayed in part by the payment of page charges. Under postal regulations, this paper therefore must be hereby marked advertisement solely to indicate this fact.

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packaging variables for tomatoes and other commodities have been developed (Beaudry et al., 1992; Cameron et al., 1989, 1990; Hayakawa et al., 1975; Henig and Gilbert, 1970; Yang and Chinnan, 1988). However, the equations were not tested for their predictive powers under a wide range of packaging situations to include diverse films and packaging ratios (ratio of film surface area to fruit weight). The objectives of this work were to develop and test mathematical and experimental procedures for predicting steady-state O2 concentrations in MAP systems for tomato for a range of packaging variables. In the development and testing of our procedures, we introduce the concept of the packaging ratio (PR). Materials and Methods Mathematical procedures. Modeling of gas concentrations in a MAP of fresh produce is based on the concept that, at steady-state, the amount of O2 diffused into the package equals the amount of O2 consumed by commodity respiration. The amount of O2 diffused into the package from the surrounding atmosphere (JO ) is calculated from Fick’s law of gas diffusion, 2

JO = PO A(0.208 – [O2]p) 2

[1]

2

where PO is the film permeability to O2 (ml•cm–2•h–1 per atm), A is the film surface area (cm2), 0.208 is the ambient partial pressure of O2 (atm), assuming the package was kept in air, and [O2]p is the partial pressure of O2 in the package (atm). Oxygen consumption by a commodity in a MAP (CO ) is calculated by multiplying the O2 consumption rate at in-package O2 concentrations (RRO , ml•kg–1•h–1) and commodity weight (Wp, kilograms). 2

2

2

CO = RRO Wp 2

[2]

2

For a MAP system at steady state, the following equation can be established from Eqs. [1] and [2]: PO A(0.208 – [O2]p) = RRO Wp 2

[3]

2

For this study, PO , for two, polyethylene + ethyl-vinyl acetate 2

J. AMER. SOC. HORT. SCI. 119(3):546–550. 1994.

additive (PEVA) films (MaxPak Industries, Somerville, Mass.), with respective thicknesses of 0.033 and 0.041 mm, were determined to be 0.0620 and 0.0426 ml•cm–2•h–1 per atm at 20C using a steady-state technique (Gong, 1992). Oxygen consumption rates were derived from O2 depletion data. The best-fitting function was found to be a second-order polynomial, expressed [O2] = at2 + bt + c

[4]

where [O2] is the O2 concentration in the sealed jars (percent), t is the time from sealing the jar (h), and a, b, and c are constants. Equation [4] was then used to derive the input variable RRO by the following three steps. The first derivative of Eq. [4] represents the O2 consumption rate at any time. Second, the respiration rate of fruit at any time was calculated as 2

d[O2]/dt = 2at + b

[5]

by incorporating into Eq. [5] the fruit weight, WR (kilograms), used in the respiration measurements, and void volume, V (liter), which was calculated by subtracting the volume taken by fruit from the total volume of the respiration jar. A factor of 10 is needed for the resulting unit to be ml•kg–1•h–1. RRO = 10(2at + b)WR–1V

[6]

2

Finally, a solution for t is obtained from Eq. [4] and then substituted into Eq. [6] to yield the input variable RRO : 2

2

RRO2 = 10[2a

–b± b –4a(c–[O2])

–1

+b]WR V

2a

[7]

2

–1 R

=10( b –4a(c–[O2]) W V The predictive equation was developed by substituting Eq. [7] into Eq. [3] to give 2

–1

PO2A(0.208 – [O2]p) = (10 b –4a(c–[O2]) WR V)Wp.

[8]

Rearrangment of Eq. [8] to isolate the packaging ratio, A/Wp, gives 2 A = 100 b –4a(c–[O2]p 10V PO2 (20.8 – [O2]p WR Wp

was within 1% of the targeted packaging ratio. Fruit. ‘Heinz 1370’ tomato plants were grown at the Univ. of Massachusetts Research Farm, South Deerfield, in 1991. Maturegreen fruit were harvested and kept at 20C for 12 to 24 h before the experiments began. Fruit selected for experiments were uniform in size and free from obvious defects. Gas analysis. All gas samples were analyzed on a gas chromatograph (Varian Instruments, Walnut Creek, Calif.) equipped with a thermal conductivity detector. The column used to measure CO2 and O2 concentration was CTR I-3700, which was composed of a molecular sieve column and a Poropak-Q column. The column did not separate argon from O2; therefore, 0.95% argon was taken into consideration when calculating the O2 concentration for all samples. Temperature conditions used were column at 35C, detector at 150C, and injector at 150C. The flow rate of the carrier gas (He) was 60 ml•min–1. Respiration measurement. Two fruit with a total weight of 290 ± 5 g were enclosed into each of three, 1-liter gas-tight glass jars. Oxygen concentration in the head space of each jar was measured over time until it decreased below 1%. The O2 depletion function was used to develop a respiration rate function as described in the mathematical procedure. MAP package. To test the predictive power of the equation, pouches of surface areas (A), ranging from 700 to 1350 cm2, were made. Various weights of fruit (Wp), from 85 to 1400 g, were then sealed into those packages using an impulse sealer. The packaging ratio ranged from 1 to 12 cm2•g–1. A rubber septum was glued on the surface of each package for gas sampling. Gas samples in packages were removed with a syringe at time intervals and then analyzed for O2 concentration until steady-state was reached. Effect of temperature. Packages were kept initially at 20C until the O2 concentration reached steady-state, and then were successfully held for 4 days each at 28 and 10C. Changes in O2 concentrations in packages were monitored. Statistical analyses and predictions. Regression analyses were conducted using a statistical package (SAS Institute, 1985). Statistically fitted constants determined from O2 depletion data and O2 permeabilities measured previously for the two films were used as input variables in a PASCAL computer program (Gong, 1992) to generate predictions of steady-state O2 concentrations.

[9]

Results A second-order polynomial fit to the respiratory depletion of O2 data yielded an r2 of 0.999 (Fig. 1) The fitted coefficients (a = 7.07 × 10–3, b = –0.75, c = 20.64) were inserted into Eq. [7] along with [O2] values from 0% to 20% to generate a functional relationship of RRO to [O2] (Fig. 1, inset). Oxygen consumption rate decreased sharply below [O2] of ≈6%; the RRO at 3% being about one-third of the value at ambient [O2]. Steady-state O2 concentrations in packages of various packaging designs were determined. An example of typical patterns for changes in O2 and CO2 concentrations in tomato packages are shown in Fig. 2. Oxygen concentration decreased rapidly within a day to a minimum of ≈4%, then gradually increased to a steadystate concentration of ≈6%. Carbon dioxide followed a reverse pattern, with a resulting steady-state concentration of ≈4%. Packaging designs, for which steady-state O2 concentrations were measured, included two films, several film surface areas (A), and various weights of tomatoes packaged (Wp). The packaging ratio, A/Wp, was varied from 1 to 12 cm2•g–1 for one film (Fig. 3A) and 1 to 5 cm2•g–1 for the other (Fig. 3B). Steady-state O2 concentrations achieved in the different packages were plotted with their 2

2

For this study, V/WR = 0.71/0.29 = 2.45. Because the unit of [O2] on the left side of Eq. [8] is in atmospheres, a factor of 100 (1 atm = 100%) enabled the predicted steady-state O2 concentration to be expressed in volume percentage. This equation was used to predict steady-state O2 concentrations for various packaging ratios. Because the algebra required to obtain a solution for [O2] for a given packaging ratio was cumbersome, a computer program was written to solve the equation using iterative procedures (Gong, 1992). Oxygen concentrations from 1% to 20% at increments of 0.1% and O2 permeability of the packaging films were fed into the program to calculate the corresponding packaging ratio until an O2 concentration (solution) was found to satisfy the condition that the packaging ratio calculated J. AMER. SOC. HORT. SCI. 119(3):546–550. 1994.

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Fig. 1. Nonsteady-state respiratory depletion of O2 by tomatoes at 20C. Points are means of three replications ± 1 SD. Inset shows derived O2 consumption rates for various O2 concentrations. The curve was generated from Eq. [7] shown in the text.

Fig. 2. Typical pattern of changes in O2 and CO2 concentrations in tomato packages at 20C (A/Wp=1.35 ± 0.02 cm2•g–1, PO = 0.0426 ml•cm–2•h–1 per atm). Points are means of four replications ± 1 SD. 2

respective packaging ratios and compared to predicted values obtained from Eq. [9] (Fig. 3, inset). Plots of predicted O2 concentrations ([O2]p) from Eq. [9] vs. those achieved experimentally ([O]E) showed excellent predictability, with correlation coefficients of r = 0.95 and 0.99, respectively.Closeness between the predictive curve and the best nonlinear fit (dashed curves) of data using the equation [O2] = a[1 – e–b(A/W )] also demonstrated the high predictive power of the procedures. Temperature fluctuations resulted in changes in steady-state O2 concentration (Fig. 4). When fruit were initially packaged and kept at 20C, the in-package O2 concentration decreased rapidly to a minimum of ≈4% within a day and then gradually increased to a p

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Fig. 3. Comparisons of predicted steady-state O2 concentration (solid line) with those achieved experimentally (o) in tomato packages using two films: A) 0.033mm-thick PEVA film, PO = 0.062 ml•cm–2•h–1 per atm, and B) 1.6 ml PEVA film, PO2 = 0.0426 ml•cm–2•h–1 per atm. The dashed curve is the best nonlinear fit of data using the equation [O2] = a[1 – e–b(A/W )], r2 ≥ 0.90. Insets are plots of predicted steady-state oxygen concentrations ([O2]P) vs. those achieved experimentally ([O2]E). Correlation coefficients were highly significant (P < 0.01), as denoted by **. Note that the x and y axes of A and B differ in scale. 2

p

steady-state level of ≈6%. When packages were transferred from 20 to 28C, the O2 concentration increased gradually (≈3 days) to a new steady state of ≈ 7.3%. In-package O2 concentration increased rapidly when packages were transferred from 28 to 10C, reaching a steady-state concentration of 10.5% within 3 days. Generalized sets of steady-state [O2] prediction curves were developed for various packaging ratios (Fig. 5). Based on the desired steady-state [O2], these curves will aid in selecting films and optimizing packaging ratios for a wide range of packaging J. AMER. SOC. HORT. SCI. 119(3):546–550. 1994.

Fig. 4. Effects of temperature on steady-state O2 concentrations in MAP of tomatoes. Points represent means of four replications ± 1 SD. Arrows indicate where packages were transferred to a different temperature.

Fig. 5. Relationships of steady-state O2 concentrations in MAP of tomato with film permeability to O2 (PO ) for a range of packaging ratios (A/Wp) at 20C. Numbers to the left of each curve denote the packaging ratio (A/Wp) in cm2•g–1. 2

situations. Suppose 3% O2 concentration is targeted for tomato MAP. Further, consider a range of realistic packaging ratios of 0.8, 1.0, 1.2, 1.5, and 2.0 cm2•g–1. The appropriate film permeability (PO ) will be 0.045, 0.036, 0.030, 0.024, and 0.018 m•cm–2•h–1 per atm for those respective packaging ratios. 2

Discussion Modified-atmosphere packaging has been demonstrated to be an economical and effective way to delay ripening and extend shelf life of tomatoes (Geeson et al., 1985; Nakhasi et al., 1990; Parsons et al., 1970). We observed that mature-green ‘Heinz 1370’ tomaJ. AMER. SOC. HORT. SCI. 119(3):546–550. 1994.

toes in MAP containing 3% to 6% O2 can be kept 3 weeks at 20C without reaching the pink stage (data not shown). The accompanying steady-state CO2 concentrations in those packages usually ranged from 3% to 5%. No CO2 injuries on fruit were observed in this study, either when fruit were in packages for up to 4 weeks or when ripened subsequently in air at 20C. Our results indicate that packaging variables necessary for a MAP to achieve the desired O2 concentration can be predicted mathematically. Functions showing predicted steady-state O2 concentrations for a range of packaging ratios (Fig. 3) is a new approach, and, in this study, was tested comprehensively on two films and with various package sizes and packaging ratios. For predicting steady-state O2 concentrations in packages of tomato at 20C, the equations developed from O2 depletion data fitted with second-order polynomials had excellent predictive power. Fitting a relatively simple model to the O2 depletion data helped keep the final predictive equation from getting overly complex. The strong predictive power of Eq. [9] (see Fig. 3) will give versatility to practical applications and answer many questions concerning designing MAP systems without the need for much time spent on testing and development. For example, Fig. 3 will allow packers to know immediately the appropriateness of films based on the packaging ratio of a MAP design. Suppose it is desired that a package achieve an O2 concentration between 3% and 5% at a packaging ratio of about 1.0. Film B is clearly more appropriate than film A for this situation. Since permeability of selected films is often close to, but not exactly, the ideal value predicted, packaging ratio may be optimized by either varying film surface area or commodity weight to achieve the desired in-package O2 concentrations. Equation [9] can be used to make commercially useful predictions that will aid in selection of films and packaging ratios. For example, if one wanted to design a retail package of a specified size to hold a specified quantity of fruit, data such as those presented in Fig. 5 will help one to select a film with appropriate gas permeability based on the desired O2 concentration. Alternatively, an appropriate packaging ratio also can be selected, based on permeability of a packaging film and the desired steady-state O2 concentration from data such as those presented in Fig. 5. Effects of temperature on in-package steady-state O2 concentrations are important to know because packages will likely experience changes in temperature during distribution. A critical concern in transit is that increased temperature could lead to depletion of oxygen and the risk of fermentative reactions. In this study with tomato PEVA package, temperature changes from 20 to 28C resulted in only a small increase in steady-state O2 concentration (≈1.25%). This result suggests that the increase in respiration was largely offset by the increase in permeability of the film in this temperature range. A decrease in temperature from 28 to 10C caused a >3.0% increase in steady-state O2 concentration. This result indicates that a greater decrease in respiration rate than the decrease in film O2 permeability occurred when the temperature was dropped from 28 to 10C. A relatively large increase in steady-state O2 concentration (i.e., 3%) would have the effect of decreasing the benefits of a MAP. One limitation of the mathematical procedure is that it did not take into consideration the effect of CO2 on O2 consumption rate. Oxygen depletion data used for the derivation of the input variable RRO were collected in jars where CO2 was allowed to accumulate. However, the excellent prediction results achieved suggests that the effect of CO2 on O2 consumption rate of mature-green tomato was negligible. This finding is in agreement with previous reports 2

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(Henig and Gilbert, 1975; Kubo et al., 1989). Reduction in O2 consumption rate in response to CO2 concentration up to 20% is very low, although CO2 concentration above 9% decreased CO2 evolution rate from 18 to 12 ml•kg–1•h–1 in tomato (Henig and Gilbert, 1975). Refinement of the input variable (RRO ) in the prediction equation will become necessary for commodities where higher CO2 concentrations significantly affect O2 consumption rate. In conclusion, appropriate packaging variables that will maximize the benefits of MAP for tomato can be predicted with relatively straightforward mathematical procedures. With the help of a computer program, rapid simulations and predictions will allow one to know the appropriate packaging design in a matter of minutes. Rapid testing of the suitability of specific films and designs may be conducted using an active modification technique (Gong and Corey, 1992). If large temperature fluctuations during handling and distribution are expected to occur, the dependence of in-package O2 concentration on temperature should be evaluated and appropriate temperature control should be applied accordingly. Proper implementation of MAP for tomato will retard ripening processes and extend fruit shelf life, thereby facilitating handling and reducing waste. 2

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J. AMER. SOC. HORT. SCI. 119(3):546–550. 1994.