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. 2020 May 13;57(7):2758–2763. doi: 10.1007/s13197-020-04490-7

Dielectric properties of litchi fruit (Litchi chinensis Sonn) at microwave frequencies

Richard Torrealba-Melendez 1,✉, Edna Iliana Tamariz-Flores 2, María Elena Sosa-Morales 3, Edgar Colín-Beltran 4, José Eduardo Miranda-Díaz 1, Luis Hernández-Ruíz 1
PMCID: PMC7270439  PMID: 32549626

Abstract

The dielectric properties of litchi fruit were determined using the open-ended coaxial probe method. The measurements were performed in the frequency range from 0.5 to 20 GHz during 3 days of storage at room temperature (~  24 °C). The dielectric properties increased with storage time. Additionally, measurements at different temperatures (24, 30, 40 and 50 °C) were determined. The dielectric constant (ε′) decreased with increasing temperature in a frequency range of 0.5–5 GHz; at higher frequencies, ε' increased with increasing temperature. The loss factor (ε″) value increased at frequencies higher than 2 GHz and decreased with increasing temperature. The results will be useful for further applications using microwaves, such as microwave-assisted drying, sensing of quality parameters, modeling, and heating to protect against molds or insects, among other applications.

Keywords: Litchi, Dielectric properties, Open-ended coaxial technique

Introduction

Litchi (Litchi chinensis Sonn.) is a delightful subtropical fruit native to China and Southeast Asia. It belongs to the Sapindaceae family (Jiang et al. 2013). The annual world production of litchi is estimated to be approximately 2.6 million tons, growing in areas 1100 m above sea level (Chen and Huang 2014). Litchi fruit is mainly consumed fresh, but some litchi products have been introduced, such as juice, wine, canned and dried litchi (Wu et al. 2009). Litchi is known as “the queen of fruits” due to its delicious flavor, abundant nutrients, and several benefits for health (Cabral et al. 2014). According to the United States Department of Agriculture (USDA 2019), every 100 g of fruit pulp contains 1.3 g of fiber, 171 mg of potassium, 71.5 mg of vitamin C and 14 μg of folate. Zhao et al. (2007) reported significant amounts of flavonoids ((−)-epicatechin, proanthocyanidin B2 and proanthocyanidin B4) in the pericarp of litchi fruits, with anticancer activity in in vitro and in vivo assays. Lv et al. (2014) reported phenolic compounds in litchi pulp, such as (−)-epicatechin and procyanidin, with potential hypoglycemic effects. For these reasons, litchi fruit has been widely accepted by consumers worldwide, and its commercial value has increased. Unfortunately, litchi has a short shelf life. Vijayanand et al. (2010) reported a shelf life of 4–6 days at temperatures of approximately 25–32 °C, while only 2 to 3 days at ambient temperature—with loss of the natural red color of its pericarp—according to Jiang et al. (2004). Pericarp browning is the most common postharvest problem in litchi, caused by temperature stress, decay and senescence (Bhushan et al. 2015). Unsuitable relative humidity conditions around litchis result in water loss from membranes, allowing the interaction of substrates with deteriorative enzymes, such as peroxidase, lipoxygenase, polyphenol oxidase, anthocyanase and phenylalanine ammonia lyase (Sun et al. 2006). The products of these reactions include o-quinones as browning precursors (Wang et al. 2010). Additionally, nonenzymatic browning may occur throughout hydrolytic reactions with the production of derivatives of aglycone or chalcone (Bhushan et al. 2015). These effects reduce the possibility of market litchi at the international level. In addition, the wide international production of litchi occurs in a short season, between mid-May and July (Janjai et al. 2010).

Several aspects of litchi fruit have been reported, for example, pharmacological aspects (Besra et al. 1996), chemical structure of polysaccharides in the pulp (Yang et al. 2016), flavonoid identifications (Wen et al. 2014) and biotechnological studies (Kumar et al. 2017). Moreover, with the objective of increasing the shelf life of litchi fruit, diverse postharvest and storage techniques have been developed (Tran et al. 2016), and several techniques for controlling pericarp browning in litchi fruit have been proposed (Bhushan et al. 2015). On the other hand, the commercial value of dried peeled litchi has increased and has become an important sector of food technology, preserving the taste and the availability outside of the litchi season. Coupled microwave–hot air drying (MWAD) and microwave-assisted vacuum drying (MWVD) are some of the commonly employed methods for drying the pulp (Fang et al. 2015).

However, to better understand and apply microwaves in the processing of litchi, it is necessary to determine the dielectric properties at microwave frequencies. The dielectric properties of a material determine the interaction between the material and the applied electromagnetic field; they include the dielectric constant (ε′) and the loss factor (ε″), the real and imaginary parts of the permittivity, respectively (Jha et al. 2011).

However, to understand the mechanisms that affect the dielectric properties, the Debye model is commonly used to describe them with a single relaxation time of the electromagnetic field (Decareau 1985):

ε=ε∞+εs-ε∞1+jωτ 1

where εs is the static dielectric constant, ε∞ is the dielectric constant at frequencies higher than the relaxation frequency, fr = 1/(2πτ), at which the polar molecules do not have time to contribute to the polarization, and τ is the relaxation time, which is commonly determined experimentally.

Moreover, the penetration depth of the microwaves at the frequency and temperature of the study defines the depth layer of fruit that must be reached to assure the action of the treatment. To the best of our knowledge, there are no available reports of the dielectric properties of litchi.

The objective of this work was to determine and analyze the dielectric properties and penetration depth of litchi pulp at microwave frequencies and temperatures between 20 and 50 °C during three consecutive days of storage.

Materials and methods

Litchi fruits

Samples of organic litchi (free of pesticides) were acquired from producers in Santa Clara Misantla, Veracruz, Mexico. The litchi fruits were harvested on May 19, 2018 (day 0). Fruits were transported to the city of Puebla by car in cardboard boxes and were stored at room temperature (24 °C).

Characterization of litchi fruits

The total soluble solids (°Brix) and pH were determined in the fruits by quintuplicate testing using a refractometer (Carl Zeiss, Germany) and a digital pH-meter (pH10, Conductronic, Mexico), respectively. Both instruments were previously calibrated (water for the refractometer and buffers 4 and 7 for the pH meter).

Open-ended coaxial technique and dielectric properties measurements

The open-ended coaxial probe has been widely used to measure the dielectric properties of semisolid and liquid foods (Rodríguez-Moré et al. 2018; Kataria et al. 2017; Fang et al. 2016) due to its broadband response and capacity for no invasive measurements (Komarov et al. 2016; Seo et al. 2018).

A hermetic stainless-steel borosilicate-glass-filled coaxial probe (kit 85070E, Keysight Technologies, USA) was employed for the measurements. The inner and outer radii of the coaxial aperture are 0.1 and 0.8 mm, respectively, and the radius of the probe is 4.75 mm. The frequency range for measurements is from 0.5 to 20 GHz. The probe was connected to a vector network analyzer, VNA (VectorStar, Anritsu, USA) with a high-precision test cable. The VNA was calibrated using the open-short-load calibration at the end of the high-precision cable. After connecting the open-ended coaxial probe, the reference plane of the measurement was defined by shorting the end of the probe with the short block (included in the dielectric probe kit 85070E) and adjusting the electrical delay of the VNA until a constant phase angle of 180° was observed (Misra et al. 1990). Afterward, the reflection coefficients for the probe of the air, distilled water and the short block for calibrating the measurement system were measured for calibration.

To obtain the litchi pulp, litchi was peeled by hand, and the seed was removed. After that, the pulp was ground using a glass mortar. For our measurements, the sample of pulp had a volume of 25 mL, and this sample was placed in a beaker of 30 mL. This volume of pulp was sufficient to satisfy the sample size requirements of the employed coaxial probe. With respect to temperature increase, the temperature of the sample was increased using a hot water bath.

Finally, to obtain the dielectric properties of the litchi pulp, the measurements collected in the VNA were processed in MATLAB (MathWorks, USA) for inversion of the admittance equation to the open-ended probe (Misra et al. 1990; Komarov et al. 2016). The graphics were generated using the MATLAB program. The measurements of the dielectric properties of litchi started on May 21 (day 2 after harvesting).

Determination of penetration depth

The penetration depth (dp) is the distance into a sample where the waves have dropped to 1/e (e is the Euler constant equal to 2.718), equal to 36.8% of the transmitted value. dp can be calculated based on the dielectric properties (von Hippel 1954):

dp=c2πf2ε′1+ε″ε′2-1 2

where c is the light speed in free space (3 × 108 m/s). The penetration depth, expressed in cm, was calculated after obtaining the dielectric properties at the ISM (International, Scientific, and Medical) frequencies (Datta and Davidson 2000) and at the four temperatures measured.

Results and discussion

Physicochemical properties of litchi fruit

The total soluble solids and pH in the litchi fruits on day 2 were 16.9 ± 0.05°Bx and 4.11 ± 0.08, respectively. Although litchi has been reported as a nonclimacteric fruit, a slight increase in total soluble solids and in pH was observed during the storage time. Three days after harvesting (May 22), the total soluble solids had a value of 17.7 ± 0.26, while after 4 days (May 23), the value was 17.9 ± 0.2236. For the pH, 3 and 4 days after harvesting, the obtained values were 4.46 ± 0.089 and 4.63 ± 0.0045, respectively. The pH values are in concordance with reported data, which range from 4.1 to 5 (Vijayanand et al. 2010; Joas et al. 2005). Furthermore, the obtained value for total soluble solids is consistent with reported data, which range from 16 to 17°Bx (Babbar et al. 2015; Vijayanand et al. 2010).

Frequency and storage time effects on dielectric properties of litchi fruit

The dielectric properties of litchi pulp on three different days are shown in Fig. 1. The dielectric constant (ε') decreased with respect to the frequency (Fig. 1a), being in the range of 74–76 at 0.5 GHz and falling to 24–26 at 20 GHz. This effect of frequency on ε' has been reported for other subtropical and tropical fruits, such as cherimoya, longan, passion fruit and white sapote (Wang et al. 2005). On the other hand, ε' values increased with storage time. This effect of storage time is in agreement with the results reported by Kataria et al. (2017) for other fruits, such as guava fruit, mamey sapote, and prickly pears, associated with the ripening process (increasing in both total soluble solids and pH values).

Fig. 1.

Fig. 1

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a Dielectric constant and b loss factor of litchi fruit 2, 3 and 4 days after harvesting

In the case of the loss factor (Fig. 1b), ε″ presented a “U” shape behavior in the frequency range of 0.5–2 GHz, having a minimum value of approximately 1.8 GHz, for the 3 days. Above this frequency, the loss factor increased with increasing frequency and reached its maximum value at approximately 13 GHz and then decreased at higher frequencies. This effect of frequency on ε″ has been reported for other fruits by Wang et al. (2005) for frequencies less than 1.8 GHz and by Kataria et al. (2017) for frequencies less than 3 GHz.

Temperature effect on the dielectric properties of litchi fruit

Figure 2 shows the effect of temperature on the dielectric properties of litchi; as an example, the presented results correspond to the sample 4 days after harvesting (May 23). The results for the other 2 days were similar (data not shown). In Fig. 2a, the variation of ε′ with respect to the temperature over the frequency range is shown; ε′ increased from 24 to 50 °C. ε′ presented a higher value for 24 °C than the ones obtained at 30 and 40 °C over a frequency range of 0.5–4 GHz, and it was even higher in the frequency range of 0.5–6 GHz compared with the one at 50 °C. The decrease in ε′ in the frequency range of 0.5–6 GHz occurred because increasing temperature in the material intensifies the movement of the molecules, causing the polarization of the medium to become less effective (Franco et al. (2017); additionally, this behavior was explained by Debye's model, as shown in the last section (Decareau 1985). Above these values, the dielectric constant increased with increasing temperature due to the effect of relaxation frequency. This effect has been reported by González-Monroy et al. (2018) and Zhu et al. (2012).

Fig. 2.

Fig. 2

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a Dielectric constant and b loss factor of litchi fruit 3 days after harvesting at different temperatures

In Fig. 2b, the variation of ε″ with frequency for temperatures from 24 to 50 °C over the frequency range from 0.5 to 20 GHz is presented. ε″ decreased with increasing temperature. In addition, ε″ increased with increasing frequency for all temperatures, reaching its maximum value at approximately 12 GHz at 30 °C and 14 GHz at 40 °C. A slight decrease with increasing frequency was observed above 14 GHz. At 50 °C, ε'' reached its maximum value at approximately 14 GHz and remained constant until higher frequencies. Nelson and Bartley (2002) reported that this behavior is associated with the two mechanisms that advocate heating: dipolar rotation is the main source of dielectric loss at higher microwave frequencies, while ionic conduction is the dominant mechanism at lower frequencies.

Table 1 summarizes the values of the dielectric properties and penetration depth within the ISM range of frequencies with respect to the temperature of the litchi samples on the three storage days. These values are important for further applications of MW in processing, sensing, and modeling of litchi fruits.

Table 1.

Average dielectric constant (ε′), dielectric loss factor (ε″) and penetration depth of litchi at ISM (industrial, Scientific and Medical) frequencies 2, 3 or 4 days after harvesting

T (°C) Frequency (MHz) Day 2 Day 3 Day 4
915 2450 5800 915 2450 5800 915 2450 5800
24 ε′ 72.37 68.06 58.68 72.91 68.75 59.65 74.44 70.35 61.04
ε″ 13.2 16.56 25.11 14.64 17.07 25.72 14.82 14.99 21.81
dp (cm) 3.36 0.9743 0.2664 3.05 0.9503 0.2623 3.044 1.092 0.3109
30 ε′ 72.37 68.59 60.34 72.23 68.79 61.13 72.7 69.33 61.58
ε″ 14.77 16.1 24.5 14.95 14.6 23.49 15.37 15.94 23.75
dp (cm) 3.01 1.005 0.2763 2.974 1.109 0.2895 2.903 1.02 0.2874
40 ε′ 72.33 68.89 61.6 71.35 68.37 61.67 71.17 68.31 61.81
ε″ 14.7 14.44 23.14 15.4 14.6 21.39 16.06 14.99 21.81
dp (cm) 3.026 1.122 0.2948 2.871 1.105 0.3183 2.751 1.076 0.3127
50 ε′ 68.46 65.91 60.37 69.9 67.33 61.64 69.29 66.68 60.93
ε″ 15.62 13.92 20.02 16.32 14.16 20.13 16.87 14.47 20.38
dp (cm) 2.774 1.138 0.3361 2.684 1.131 0.3376 2.586 1.102 0.3318
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Penetration depth

In the case of litchi, the penetration depth decreased with increasing frequency (Table 1). The dp had a value of 3.36 cm at 915 MHz at a temperature of 24 °C, and it decreased to values between 3 and 2.7 cm at temperatures of 30 to 50 °C, respectively. In addition, with respect to storage time, dp presented a slight decrease of 0.3 cm at 24 °C.

For the frequencies of 2450 and 5800 MHz, dp showed a slight increase of 0.1 cm when the temperature increased. No significant effects were observed on dp with respect to storage time at these frequencies. With the dp values obtained, the microwave radiation at 915 MHz and 2450 MHz could reach the center of the peeled litchi (fruits had approximately 2–3 cm diameter) for all temperatures considered in this study. dp values will be useful for applications of microwave drying techniques. These values allow the determination of the maximum thickness of the sample needed for efficient drying. In comparison with other studies, the penetration of litchi fruit at 915 MHz and approximately 20 °C (3.36 cm) is similar to that reported for logan (3.3 cm) by Wang et al. (2005) and mangoes (3.35 cm) by Sosa-Morales et al. (2009), all of which are fruits with a stone in their center.

With the obtained data, it is now possible to design proper processes for litchi fruit, for example, MW-assisted disinfestation treatments or procedures against molds based on MW (the penetration depth ensures sufficient penetration of the waves), or MW drying for litchi pulp (the drying layer should not exceed the calculated penetration depth). Other quality tests may be developed based on the sensitivity of ε′ to the moisture content or ripening, and the results are also useful for modeling thermal processes associated with MW, as the dielectric properties values were obtained at different temperatures.

Conclusion

The dielectric properties increased with increasing storage time. On the other hand, in the case of temperature, the dielectric constant presented a decrease with increasing temperature in a frequency range of 0.5–5 GHz; for bigger frequencies, it increased with increasing temperature. The loss factor presented a “U” shape and decreased with increasing temperature. The results will be useful for further applications using microwaves, such as microwave-assisted drying, sensing of quality parameters, modeling, and heating against molds or insects, among others.

Acknowledgements

We thanks to the Laboratory of Characterization of Systems Based on Microwaves at FCE-BUAP (CONACyT Infraestructura 2016 #270761) and VIEP Projects 2018.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Footnotes

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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