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Dielectric properties of in-shell and shelled sunower seeds
(Helianthus annuus L.) and pine nuts (Pinus pinea L.) at dierent
temperatures for radio and microwave frequencies
Ruth Hernández-Nava
a
, Juan Mateo Meza-Arenas
b
, Diego Sarmiento-Narvaez
b
, Tejinder Kaur
c
,
Alonso Corona-Chavez
b
, Roberto Rojas-Laguna
d
, and María Elena Sosa-Morales
e
a
Departamento de Ingeniería Química, Alimentos y Ambiental, Universidad de las Américas Puebla, San Andrés
Cholula, Mexico;
b
Departamento de Electrónica, Instituto Nacional de Astrofísica, Óptica y Electrónica, Tonanzintla,
Mexico;
c
Departamento de Sistemas Electrónicos y de Telecomunicaciones, Universidad Autónoma de la Ciudad de
Mexico, CDMX, Mexico;
d
Departamento de Ingeniería Electrónica, División de Ingenierías, Campus Irapuato-
Salamanca, Universidad de Guanajuato, Salamanca, Mexico;
e
Departamento de Alimentos, División de Ciencias de la
Vida, Campus Irapuato-Salamanca, Universidad de Guanajuato, Irapuato, Mexico
ABSTRACT
The bulk permittivity (ε
bulk
) and particle permittivity (ε
part
) of in-shell and
shelled sunower seeds (Helianthus annuus L) and pine nuts (Pinus pinea L.)
were determined in a temperature range of 20–60°C and a frequency range
of 27–5000 MHz using the transmission line method. Additionally, the sam-
ples were analyzed for moisture content, water activity (a
w,
), fat content,
color, and densities (bulk, tapped, and particle). The dielectric constant (ε’)
decreased with increasing temperature for sunower seeds (from 3.04 to 2.63
for in-shell samples) and increased with temperature for pine nuts (from 4.41
to 5.48, also for in-shell seeds), due to the dierences in the a
w
values. For all
samples, the ε’ and loss factor (ε’”) decreased with increasing frequency. ε”
and ε’” values increased with higher bulk density; for instance, at frequency
of 915 MHz, in-shell sunower seeds (ρ
bulk
= 0.341 g/cm
3
) had ε” = 1.49 and
ε’” = 0.02 at 20°C, while in-shell pine nuts (ρ
bulk
= 0.601 g/cm
3
) had ε” = 2.53
and ε’’ = 0.03 at 20°C. Higher penetration depth (d
p
) values were found at
lower frequencies, for example, shelled sunower seeds at 60°C exhibited d
p
= 7.52 at 27 MHz, but d
p
= 1.20 m at 5000 MHz. Results are valuable for
designing further radiofrequency and microwave treatments for these
seeds and nuts.
ARTICLE HISTORY
Received 30 December 2024
Revised 29 March 2025
Accepted 31 March 2025
KEYWORDS
Dielectric properties;
penetration depth;
physicochemical properties;
pine nuts; sunflower seeds
Introduction
Edible seeds and nuts are a group of foods commonly consumed for their rich content of proteins
(higher than 20% w.b.), vitamins, minerals, and fatty acids, which also exhibit antioxidant properties
due to their bioactive compounds.
[1,2]
Bioactive compounds are secondary metabolites from plant
materials whose exhibit antioxidant activity with valuable and positive effects on human health.
Among the edible seeds traditionally consumed worldwide are sunflower (Helianthus annuus L.),
macadamia nuts (Macadamia integrifolia), almonds (Prunus dulcis), pine nut (Pinus pinea L.), and
walnut (Juglans regia L.).
[1–3]
Sunflower seed is a native oilseed of North America. It is among the most important oilseed crops
because of its oil content, which had polyunsaturated fatty acids.
[4,5]
Sunflower seeds are made of
around 8% water, 6% dietary fiber, 19% carbohydrates, 20% protein, and 48% crude fat,
[6]
almost
CONTACT María Elena Sosa-Morales msosa@ugto.mx Departamento de Alimentos, División de Ciencias de la Vida, Campus
Irapuato-Salamanca, Universidad de Guanajuato, Carretera Irapuato-Silao km. 9, Irapuato 36500, Mexico
INTERNATIONAL JOURNAL OF FOOD PROPERTIES
2025, VOL. 28, NO. 1, 2489489
https://doi.org/10.1080/10942912.2025.2489489
© 2025 Ruth Hernández-Nava, Juan Mateo Meza-Arenas, Diego Sarmiento-Narvaez, Tejinder Kaur, Alonso Corona-Chavez, Roberto Rojas-Laguna and
María Elena Sosa-Morales Published with license by Taylor & Francis Group, LLC.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this
article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.
a third part of the fat content consists of essential fatty acids, including linoleic acid.
[7]
The composi-
tion of sunflower seeds has been reviewed by Zhang et al.
[5]
highlighting important benefits for health.
The pine nut is one of the nine main nut species worldwide and holds significant economic
importance, primarily growing in Mediterranean countries.
[8]
Pine nuts are composed by unsaturated
fatty acids, proteins, vitamins, minerals, and bioactive compounds.
[9]
The oil extracted from pine nuts
is known for its bioactive compounds and antioxidant properties due to its high levels of phenols and
vitamins.
[10]
Regular consumption of pine oil has been associated with various health benefits, such as
reduction of inflammation, regulation of immune disorders, appetite control, and reducing blood fat
levels.
[10,11]
However, sunflower seeds and pine nuts, when exposed to high relative humidity during storage,
are prone to fungal attacks that can lead to the development of aflatoxins.
[12]
Additionally, their high
oil content makes them susceptible to oxidative reactions, such as rancidity, which reduces the
nutritional value of foods and produces compounds that generate undesirable odors and
flavors.
[8,13]
Both aflatoxins and rancidity products can negatively impact human health due to their
mutagenic and carcinogenic effects.
[12,13]
Radio frequency and microwave treatments have gained
attention in research due to their diverse applications in disinfection, pest management, enzyme
inactivation, and processes like drying, roasting, and pasteurization.
[14]
Furthermore, understanding
dielectric properties is essential for designing treatments that use electromagnetic energy, as they
describe the interaction between electromagnetic energy and food.
[15]
Although several studies have
been conducted on the dielectric properties of edible seeds such as almonds,
[16]
walnuts,
[17]
and
peanuts,
[18]
there is not much information available in the literature on the dielectric properties of
sunflower seeds and pine nuts. Therefore, this research aimed to study the dielectric properties of in-
shell and shelled sunflower seeds and pine nuts at different frequencies and temperatures.
Additionally, this study examines two types of permittivity: bulk permittivity, representing the air-
sample mixture, and particle permittivity, which excludes air and reflects the permittivity of the
sample as a solid.
Materials and methods
Materials
In-shell and shelled samples of sunflower seeds (Helianthus annuus) and pine nuts (Pinus pinea) were
purchased from a local market (Central Supply of the Municipality, Irapuato, Guanajuato, Mexico).
They were stored in plastic bags at 15°C and no pre-treatment was applied to them.
Methods
Characterization of in-shell and shelled sunflower seeds and pine nuts
The sunflower seeds and pine nuts were characterized by their moisture content, water activity, fat
content, color, densities (bulk, tapped, particle), and porosity. The analyses were performed in
triplicate for both in-shell and shelled samples. Moisture content was determined following the
AOAC gravimetric method,
[19]
2.0 ± 0.001 g of each sample were dried at 103 ± 2°C for 20 h in
a convection oven (CE3F, Shel Lab, Cornelius OR, USA). Water activity (a
w
) was measured with
a dew point hygrometer (AquaLab Series 3, Decagon Devices, Pullman WA, USA) using 5.0 ± 0.01 g.
Diethyl ether extraction was used to determine the fat content using a Goldfish equipment (GF-6,
Novatech, Mexico City, CDMX, Mexico) during 5 h, with a sample of 2.0 ± 0.001 g.
[19]
Color para-
meters (L*a*b*) of a 20 ± 0.01 g sample were analyzed with a colorimeter (ColorFlex EZ, Hunter Lab,
Reston VA, USA), pre-calibrated with a black glass and a white tile. The bulk (ρ
bulk
) and tapped (ρ
tap
)
densities were determined with the modified method by Hernández-Nava et al.
[20]
The ρ
bulk
was
measured by recording the volume of in 5 ± 0.01 g of the sample inside of a 50-mL graduated cylinder.
Likewise, ρ
tap
was determined when the volume of the sample remained constant after being manually
2R. HERNÁNDEZ-NAVA ET AL.
compressed with a metallic tip. The particle density (ρ
part
) was obtained following method described
by Kaur et al.,
[21]
with slight modifications. A sample of 5 ± 0.01 g was placed in a 50 mL graduated
cylinder, followed by the addition of 15 mL of acetone, and the volume displacement was recorded.
The samples’ porosity was calculated using the relationship between the bulk and particle densities
according to Equation (1)
[22]
:
Dielectric properties
A modified version of the Thru-Reflect-Line method was used to measure the dielectric as described
by Engen and Hoer,
[23]
where two lines of similar impedance and different length are required. In this
method, measurement with both lines is required to obtain the matrix T according to Equation (2)
and (3).
where M
1
and M
2
are the measured T parameters from the sample, T
A
and T
B
are the T parameters of
the connectors, which are equal for both lines, and T
L1
and T
L2
are the T parameters of the lines. The
line T parameters are directly related to their propagation constant, and length as shown in Equation
(4) and (5).
where T
Γ
is the line reflection matrix and ϒ is the complex propagation constant of the lines, and
according to Equation (6):
where α is the attenuation constant and β is the phase constant. The latter one is related to the effective
permittivity of the line as shown in Equation (7):
where β is the phase constant, c is the speed of light in free space (3 × 10
8
m/s), and f is the
frequency (Hz).
The Thru-Reflect-Line method involved constructing two lines; however, to simplify the process,
only one line was physically built, while the second was simulated using a full-wave electromagnetic
simulator (High Frequency Structure Simulation software, HFSS v7, ANSYS Inc., Canonsburg PA,
USA). The sensor consisted of a microstrip transmission line designed with three layers. The top and
bottom layers were composed of a TMM6 substrate with a relative permittivity of εr = 6 and
a thickness of h = 0.76 mm. The microstrip line was etched on the top layer, and the bottom layer
functioned as the ground plane. The middle layer, which acted as a sample holder, was fabricated from
PLA material using a 3D printer (Finder2, FlashForge Ltd., ZhengJiang, China) as shown in Figure 1.
In microstrip lines, for good transmission, it is important that the dielectric height is less than
the wavelength (H < λ); this ensures a quasi-TEM transmission mode. Although perfect transmis-
sion is not required, maintaining the propagation mode is essential. Through electromagnetic
simulation, it was found that a maximum height of 3.5 mm preserved the line’s characteristics,
INTERNATIONAL JOURNAL OF FOOD PROPERTIES 3
allowing the method to be applied up to 5 GHz. For this reason, the sample holder was designed to
have H
sample
= 1.5 mm. Moreover, if whole samples were used, due to the large seed size, big air
gaps compared to the size of the transmission line would fill spaces between seeds; therefore, the
preferred method for measuring their dielectric properties would be cavity method or transmission
line method.
[24,25]
Calibration was carried out using five substrates with known properties (DiClad880, RO4003, FR4,
TMM6, TMM10i, purchased to Rogers Corporation (Chandler AZ, USA); calibration was done once
at the beginning of every experimental run. Then, the Thru-Reflect-Line method was applied to both
the physical measurement and the simulation. Each measurement was repeated five times, and
a calibration curve was generated through curve fitting.
Measurement of the dielectric properties
All samples were ground using a commercial grinder (Model 80393, Hamilton Beach, Glen Allen VA,
USA). Then, 2.0 ± 0.01 g of the final powder was filled inside the sample holder and pressed to avoid
air gaps. All measurements were taken with a frequency range from 27 to 5000 MHz at three
temperatures (20, 40 and 60°C), the samples were heated up using a commercial microwave oven
(IOIO110MDI, Mabe, Querétaro, Mexico). The temperature was measured using an infrared thermo-
meter (GM550, Fei Niao, Beijing, China) at different spots on the sample. Based on the measurements
and because of the small size of sample (2 g), we get temperature uniformity. Then, their dielectric
properties were measured immediately. All results were measured in quintuplicate. Every time that the
sample was placed, it was tapped to avoid air. Since the experimental values consist of a sample/air
mixture, where air lowers the measured permittivity, the solid sample permittivity (particle permit-
tivity) was calculated using Equation (8).
[26]
where ε
part
is the particle permittivity, ε
bulk
is the bulk permittivity (air/sample mixture), and
v
s
=ρ
tap
/ρ
part
.
Penetration depth
The penetration depth (d
p
) is defined as the volume where the microwave power density drops to 1/e
(e = 2.718). Since food materials are usually nonmagnetic, Metaxas and Meredith’s model (Equation
(9))
[27]
can be used to calculate the dp:
Figure 1. Sensor design used in the modified Thru-Reflect-Line method.
4R. HERNÁNDEZ-NAVA ET AL.
where c is the speed of light in free space (3 × 10
8
m/s), f is the frequency (Hz), and ε′ and ε′′ the values
of the dielectric constant and loss factor, respectively.
Statistical analysis
The data were analyzed statistically using analysis of variance (ANOVA) and Fisher’s comparison tests
at a 95% confidence level, performed with Minitab software (version 17, Minitab Inc., State College
PA, USA). Using the same statistical software, the Pearson correlation coefficient (r) was calculated to
analyze the effect of frequency and temperature on dielectric properties at a 95% confidence level.
Results and discussion
Physicochemical properties
The physicochemical properties of in-shell sunflower seed (ISS), shelled sunflower seed (SSS), in-shell
pine nut (IPN), and shelled pine nut (SPN) are shown in Table 1. It was observed that, for sunflower
and pine nuts, the in-shell samples had higher moisture content values (p < .05) due to the lignin and
cellulolytic content in the shell that protect the kernels.
[28–30]
In the case of IPN, the difference in the
moisture content observed (9.60 ± 0.12% w.b.) is due to several factors such as freshness, storage and
harvesting conditions.
[31,32]
Regarding water activity (a
w
), the sample with the lowest value was SPN
(0.385 ± 0.002). The rest of the samples had a
w
values higher than 0.5 (p < .05). a
w
values above 0.5
might favor the lipid oxidation, potentially reducing the nutritional value and generating undesirable
flavors and odors.
[8,13]
For fat content, the shelled samples had higher values than the in-shell ones
(Table 1). The lower fat content values observed (p < .05) for in-shell samples is explained since shells
are primarily composed of lignin and cellulolytic materials, which can account for around 80% of the
seed’s total weight.
[28]
The color parameters (L*, a*, b*) values had a significant difference (p < .05)
between samples. The L* values of the in-shell samples were below 50 representing dark colors.
[33,34]
All the samples had positive values of a* and b*, with a tendency toward red and yellow,
respectively.
[33,35]
The in-shell samples had higher a* values, indicating a redder shade than shelled
ones. As for b* values, shelled samples had higher values than the in-shell ones, which means a more
yellow shade. The increase in L* and the decrease of a* values in the shelled samples are due to the
removal of phenolic compounds such as flavonoids, anthocyanins, and tannins present in the seed
shells of sunflowers and pine nuts.
[29,30]
The increase in b* values in the shelled samples is the result of
the prevalence of carotenoids, which give the characteristic colors of sunflower and pine nut
kernels.
[30,35]
For bulk density (ρ
bulk
) it was observed that in sunflower samples, the values slightly
increased when the shell was removed (p < .05); meanwhile, in pine nut samples, the opposite behavior
was observed (p < .05). The discrepancy in the behavior of sunflower seeds and pine nuts could be
related to the characteristics of the cellular structure in in-shell seeds, in-shell nuts, and their kernels,
Table 1. Physicochemical properties of in-shell and shelled sunflower seeds (Helianthus annuus L.) and pine nuts (Pinus pinea L.).
Samples ISS SSS IPN SPN
Moisture content (% w.b.) 6.59 ± 0.13
a
4.46 ± 0.09
b
9.60 ± 0.12
c
2.37 ± 0.23
d
a
w
(25°C) 0.527 ± 0.004
a
0.548 ± 0.004
b
0.616 ± 0.003
c
0.385 ± 0.002
d
Fat content (% w.b.) 26.44 ± 1.67
a
47.50 ± 1.83
b
21.27 ± 1.58
c
50.59 ± 1.75
b
L* 44.80 ± 0.95
a
54.43 ± 0.99
b
37.57 ± 0.15
c
60.87 ± 0.82
d
a* 2.65 ± 0.10
a
3.76 ± 0.25
b
10.92 ± 0.44
c
5.53 ± 0.20
d
b* 10.61 ± 0.35
a
16.15 ± 0.52
b
21.67 ± 0.61
c
28.47 ± 0.33
d
ρ
bulk
(g/cm
3
) 0.341 ± 0.010
a
0.464 ± 0.012
b
0.601 ± 0.007
c
0.518 ± 0.018
d
ρ
tap
(g/cm
3
) 0.390 ± 0.013
a
0.587 ± 0.008
b
0.637 ± 0.009
b
0.924 ± 0.118
c
ρ
part
(g/cm
3
) 0.764 ± 0.050
a
1.048 ± 0.045
b
1.135 ± 0.088
b
0.980 ± 0.039
b
Porosity 0.553 ± 0.017
a
0.557 ± 0.008
a
0.469 ± 0.035
b
0.472 ± 0.003
b
ISS: In-shell sunflower seed; SSS: Shelled sunflower seed; IPN: In-shell pine nut; SPN: Shelled pine nut.
Different letters in row indicate significant differences (p < .05) between samples according to ANOVA and Fisher’s comparison test.
INTERNATIONAL JOURNAL OF FOOD PROPERTIES 5
which influence the increase in mass and volume.
[36]
Tapped density (ρ
tap)
and particle density (ρ
part)
values were higher than those of ρ
bulk
. Since smaller particles occupy the voids between larger particles
due to the tapping process, a more compact packing arrangement results in higher ρ
tap
values.
[20,37]
Similarly, ρ
part
values are greater than ρ
bulk
values due to the presence of air in ρ
bulk
, which lowers
its overall value.
[38,39]
Regarding porosity, the removal of the shell showed no significant difference
(p > .05) in the porosity values of sunflower seed and pine nut samples. Furthermore, the sunflower
seed samples had higher values than those of pine nuts (p < .05). Regarding porosity, a slight increase
in the porosity values was observed with the removal of the shell, showing no significant difference
(p > .05) in sunflower seed and pine nut samples. Furthermore, the sunflower seed samples had higher
values than those of pine nuts (p < .05), suggesting a higher number of interparticle spaces. A larger
number of spaces between particles indicates an increased amount of oxygen available for degradation
reactions,
[40]
along with a decrease in dielectric properties caused by the presence of air.
[26]
Factors inuencing the dielectric constant using bulk permittivity
Frequency
The dielectric constant (ε
bulk
’) values, determined using the bulk permittivity, for in-shell and shelled
sunflower seeds and pine nuts were significantly affected by frequency (p < .05). ε
bulk
‘ decreased as the
frequency increased, regardless of the temperature (Figure 2). For the Pearson correlation (p < .05), the
average values of the samples when frequency increased at a fixed temperature were as follows: ISS
(−0.72), SSS (−0.70), IPN (−0.69), and SPN (−0.67). As frequency increases, the ε
bulk
’ tends to decrease;
however, the correlation is not extremely strong, as the values indicate a moderate to strong negative
linear relationship. This effect was more pronounced in the radio frequency band than in the
microwave band (Table 2). For example, at 20°C, when the frequency increased from 27 to 44 MHz,
the ε
bulk
’ of ISS decreased from 3.04 to 2.47. In contrast, when the frequency increased from 915 to
5000 MHz, the ε
bulk
’ decreased from 1.49 to 1.39. The higher dielectric constant is attributed to
interfacial and dipolar polarization. At low frequencies, this polarization follows the alternations of
the electric field without lag, resulting in a higher dielectric constant. However, as the frequency
increases, the dipoles are not able to follow the rapid changes in the polarity of the field, causing their
oscillations to lag, which leads to a decrease in the dielectric constant.
[41,42]
Temperature
When the temperature increased at a fixed frequency, the ε
bulk
” decreased for in-shell and shelled
sunflower seeds (p < .05). In contrast, the ε
bulk
‘ increased for in-shell and shelled pine nuts. ISS and SSS
had r values (p < .05) of −0.98 and −0.74, respectively, as the temperature rose while maintaining
a constant frequency. This strong negative correlation could be due to thermal depolarization, where
an increase in temperature disrupts dipole alignment, leading to a lower ε
bulk
.’
[43,44]
In the case of IPN
and SSS, the r values (p < .05) were 0.96 and 0.91, respectively, indicating a strong correlation where
the ε
bulk
‘ increases as temperature rises. This positive correlation could be because, in some materials,
increasing temperature enhances ionic mobility or space charge polarization, leading to a higher
dielectric constant.
[15]
The dielectric constant’s behavior with temperature is complex, as it can either
increase or decrease depending on the specific material.
[43,44]
This variable behavior can be explained
in terms of a
w
. As a
w
increases with rising temperature, it influences how water availability and
reactivity affect the dielectric properties.
[45]
For ISS and SSS, the ε
bulk
’ decreased with the increment of
a
w
due to water evaporation caused by moisture migration toward the surface, driven by pressure-
induced flow.
[45–47]
In the cases of IPN and SPN, the ε
bulk
” increased as a
w
augmented, resulting from
improved ion mobility due to more availability of free water molecules.
[15,48]
Moisture and fat content
Moisture and fat affect the dielectric constant, with free water increasing its value, while fat tends to
decrease it.
[42,43]
In the case of sunflower seeds, as the temperature increased at a fixed frequency, the
6R. HERNÁNDEZ-NAVA ET AL.
Figure 2. Dielectric constant (ε
bulk
’) and loss factor (ε
bulk
”) using the bulk permittivity (air/sample mix) of in-shell sunflower seed (a),
shelled sunflower seed (b), in-shell pine nut (c), and shelled pine nut (d).
INTERNATIONAL JOURNAL OF FOOD PROPERTIES 7
Table 2. Dielectric properties of in-shell and shelled sunflower seeds (Helianthus annuus L.) and pine nuts (Pinus pinea L.) using the bulk permittivity (air/sample mix).
Sample Temperature (°C)
Dielectric constant (ε
bulk
’) Loss factor (ε
bulk
’’)
Frequency (MHz) Frequency (MHz)
27 44 915 2400 5000 27 44 915 2400 5000
ISS 20 3.04 ± 0.03
A,a
2.47 ± 0.02
B,a
1.49 ± 0.01
C,a
1.40 ± 0.01
D,a
1.39 ± 0.01
D,a
0.19 ± 0.02
A,a
0.13 ± 0.01
B,a
0.02 ± 0.00
C,a
0.01 ± 0.00
C,a
0.01 ± 0.00
C,a
40 2.84 ± 0.02
A,b
2.31 ± 0.02
B,b
1.39 ± 0.02
C,b
1.30 ± 0.02
D,b
1.29 ± 0.02
D,b
0.27 ± 0.02
A,b
0.17 ± 0.01
B,b
0.01 ± 0.00
C,b
0.01 ± 0.00
C,b
0.01 ± 0.00
C,a
60 2.63 ± 0.05
A,c
2.12 ± 0.04
B,c
1.26 ± 0.02
C,c
1.17 ± 0.02
D,c
1.16 ± 0.02
D,c
0.17 ± 0.02
A,a
0.11 ± 0.01
B,c
0.01 ± 0.00
C,c
0.01 ± 0.00
C,c
0.01 ± 0.00
C,b
SSS 20 4.06 ± 0.14
A,a
3.39 ± 0.12
B,a
2.25 ± 0.10
C,a
2.18 ± 0.10
C,a
2.20 ± 0.10
C,a
0.51 ± 0.04
A,a
0.33 ± 0.02
B,a
0.02 ± 0.00
C,a
0.01 ± 0.00
C,a
0.01 ± 0.00
C,a
40 3.85 ± 0.12
A,b
3.22 ± 0.10
B,b
2.13 ± 0.07
C,b
2.07 ± 0.07
C,b
2.08 ± 0.07
C,b
0.47 ± 0.03
A,a,b
0.31 ± 0.02
B,a,b
0.02 ± 0.00
C,b
0.01 ± 0.00
C,b
0.01 ± 0.00
C,b
60 3.68 ± 0.12
A,c
3.09 ± 0.10
B,b
2.07 ± 0.07
C,b
2.01 ± 0.07
C,b
2.01 ± 0.07
C,b
0.45 ± 0.02
A,b
0.30 ± 0.01
B,b
0.02 ± 0.00
C,c
0.01 ± 0.00
C,b
0.01 ± 0.00
C,a,b
IPN 20 4.41 ± 0.05
A,a
3.73 ± 0.05
B,a
2.53 ± 0.06
C,a
2.48 ± 0.06
C,a
2.50 ± 0.06
C,a
0.52 ± 0.05
A,a
0.35 ± 0.03
B,a
0.03 ± 0.00
C,a
0.01 ± 0.00
C,a
0.01 ± 0.00
C,a
40 5.15 ± 0.09
A,b
4.40 ± 0.08
B,b
3.09 ± 0.07
C,b
3.05 ± 0.07
C,b
3.07 ± 0.06
C,b
0.53 ± 0.04
A,a
0.36 ± 0.02
B,a
0.03 ± 0.00
C,a
0.01 ± 0.00
C,b
0.01 ± 0.00
C,b
60 5.48 ± 0.15
A,c
4.72 ± 0.14
B,c
3.40 ± 0.13
C,c
3.37 ± 0.13
C,c
3.38 ± 0.13
C,c
0.75 ± 0.05
A,b
0.51 ± 0.03
B,b
0.03 ± 0.00
C,b
0.02 ± 0.00
C,c
0.01 ± 0.00
C,c
SPN 20 6.62 ± 0.13
A,a
5.80 ± 0.11
B,a
4.40 ± 0.08
C,a
4.39 ± 0.09
C,a
4.42 ± 0.09
C,a
0.94 ± 0.04
A,a
0.64 ± 0.02
B,a
0.04 ± 0.00
C,a
0.02 ± 0.00
C,D,a
0.01 ± 0.00
D,a
40 7.00 ± 0.11
A,b
6.18 ± 0.11
B,b
4.75 ± 0.10
C,b
4.74 ± 0.10
C,b
4.78 ± 0.10
C,b
1.24 ± 0.03
A,b
0.82 ± 0.02
B,b
0.04 ± 0.00
C,b
0.02 ± 0.00
D,b
0.01 ± 0.00
D,b
60 8.02 ± 0.33
A,c
7.03 ± 0.32
B,c
5.37 ± 0.30
C,c
5.36 ± 0.30
C,c
5.38 ± 0.30
C,c
1.47 ± 0.11
A,c
0.99 ± 0.06
B,c
0.06 ± 0.00
C,c
0.03 ± 0.00
C,c
0.02 ± 0.00
C,c
ISS: In-shell sunflower seed; SSS: Shelled sunflower seed; IPN: In-shell pine nut; SPN: Shelled pine nut.
Different lowercase letters in the column indicate significant differences (p < .05) between samples with the same characteristics at different temperatures according to ANOVA and Fisher’s
comparison test.
Different capital letters in row show significant differences (p < .05) between samples at different frequencies of the same dielectric property according to ANOVA and Fisher’s comparison test.
8R. HERNÁNDEZ-NAVA ET AL.
ISS sample, with higher moisture content and lower fat content (Table 1), showed a greater decrease in
the ε
bulk
” than the SSS sample, which had a lower moisture content and higher fat content. For
example, for the ISS sample, at a frequency of 27 MHz, as the temperature increased from 20 to 60°C,
the ε
bulk
” decreased by 0.41, compared to the SSS sample, where the value decreased by 0.38. On the
contrary, for the pine nut samples, the sample with higher moisture content and lower fat content
(IPN) showed a smaller increase in the ε
bulk
’ as the temperature increased at a fixed frequency,
compared to the SPN sample, which had a lower moisture content and higher fat content. For
example, when the temperature increased from 20 to 60°C at a frequency of 27 MHz, the increase in
the IPN sample was 1.07, while for SPN, it was 1.4.
Density and porosity
Overall, ε
bulk
’ values for in-shell and shelled pine nuts were higher than those for in-shell and shelled
sunflower seeds at a fixed temperature and frequency. The dependence of the dielectric constant on
density can explain this difference. It has been reported that, in agricultural products, an increase in
ρ
bulk
also increases ε
bulk
’ ,higher ρ
bulk
values indicate denser packing, which reduces porosity.
[49,50]
In
the present study, pine nut samples exhibited higher ρ
bulk
values than sunflower seed samples (p < .05),
which corresponded to lower porosity values (Table 1), resulting in higher ε
bulk
’ values.
Values of dielectric constant for shelled sunflower seeds at 915 and 2400 MHz at 20°C (2.25 and
2.18, respectively) are close to the reported by Li et al.
[16]
for almonds at the same frequencies and
temperature (1.8 and 1.55, respectively). Similarities are due to near moisture content between them
(4.46% w.b. for in-shell sunflower seeds and 4.2% w.b. for almonds). Also, the average value of shelled
sunflower seeds at 915 MHz, 20°C (ε
bulk
’ = 2.25) is similar to the reported for almonds (1.7) and
walnuts (2.2) at same conditions, reported by Wang et al.
[17]
Both reports
[16,17]
employed the open-
ended coaxial probe method, thus, the Thru-Reflect-Line method from our study shows equivalent
data and applicability for the dielectric properties measurements in this kind of seeds.
Factors inuencing the loss factor using bulk permittivity
Frequency
The loss factor (ε
bulk
”), calculated with the bulk permittivity, decreased with increasing frequency
(Figure 2). The average values of the samples for the Pearson correlation (p < .05), when the frequency
increased at a fixed temperature, were as follows: ISS (−0.69), SSS (−0.70), IPN (−0.71), and SPN
(−0.71). The correlation values indicate a moderate to strong negative relationship: as the frequency
increases, the ε
bulk
” decreases. This can be attributed to the material’s inability to efficiently follow
high-frequency oscillations, resulting in lower energy dissipation at higher frequencies.
[41,42]
This
decreasing effect was more noticeable in the radio frequency band compared to the microwave band
(Table 2). For instance, at 20°C, as the frequency increased from 27 to 44 MHz, the ε
bulk
” of ISS
dropped from 0.19 to 0.13. In contrast, when the frequency rose from 915 to 2400 MHz, the ε
bulk
”
decreased from 0.02 to 0.01. This phenomenon is linked to the microscopic response mechanism of
dielectric behavior: in the radio frequency band, dielectric loss is primarily due to the movement of
free charges (ions, electrons), while in the microwave band, it is mainly caused by the rotation of polar
molecules under an electric field.
Temperature
In the case of temperature increase, similar to the dielectric constant, the loss factor of the sunflower
samples tends to decrease. In contrast, the values for pine nut samples increase with rising tempera-
ture. Additionally, as the frequency increases, these decreases or increases become smaller. The
average r value (p < .05), for the sunflower seed samples was −0.65, and for the pine nut samples, it
was 0.77. These correlation values suggest a moderate negative relationship for the sunflower samples
and a strong positive relationship for the pine nut samples. The decrease in the loss factor as
temperature rises could indicate that conduction losses are decreasing, possibly because the ions
INTERNATIONAL JOURNAL OF FOOD PROPERTIES 9
lack a suitable solvation medium, reducing charge carrier mobility at higher temperatures.
[51]
This
may be a result of water evaporation caused by the increase in water activity with rising
temperature.
[45–47]
On the other hand, for the pine nut samples, the increase in temperature causes
a decrease in the viscosity of biomaterials, which results in higher oscillation of the dipoles and
increased ionic mobility, leading to an increase in the loss factor.
[52,53]
Moisture and fat content
Similar to the dielectric constant, the loss factor is affected by the moisture and fat content present in
food.
[42,43]
It was observed that, for both sunflower seed and pine nut samples, those with higher
moisture content and lower fat content showed a lower decrease in the loss factor as the frequency
increased. For example, at a temperature of 40°C and with a frequency increase from 27 to 5000 MHz,
the ISS sample exhibited a decrease of 0.26, while the SSS sample showed a decrease of 0.46.
Density and porosity
Overall, the ε
bulk
” values for pine nut samples were higher than those for sunflower seed samples at
a fixed temperature and frequency. Similar to ε
bulk
,’ ε
bulk
” is dependent on density, where an increase
in ρ
bulk
also increases ε
bulk
” due to denser packing and a reduction in porosity.
[49,50]
Loss factor values for shelled sunflower seeds at 915 and 2400 MHz at 20°C were 0.02 and 0.01,
equal to those reported for almonds by Li et al.
[16]
at same conditions. However, the ε
bulk
’’ value for
shelled sunflower seeds at 915 MHz (0.02) was lower than the reported by Wang et al.
[17]
for almonds
and walnuts, found as 5.7 and 2.9, respectively.
Penetration depth
For penetration depth (d
p
) values, calculated with ε
bulk
’ and ε
bulk
”, a constant decrease was observed
with the increment of frequency (Table 3). Overall, the d
p
values in the radio frequency band were
higher than those in the microwave band for all samples. This can be explained by the more
pronounced difference in the modification rates of ε
bulk’
and ε
bulk’
in the radio frequency band,
whereas in the microwave band, this difference was smaller, affecting the behavior of d
p
.
[52]
Greater
penetration depths at lower frequencies promote uniform heating, while reduced penetration at higher
frequencies primarily leads to surface heating.
[15,44]
Thus, radio frequency technology may be more
Table 3. Penetration depth of in-shell and shelled sunflower seeds (Helianthus annuus L.) and pine nuts (Pinus pinea L.) at different
frequencies and temperatures using the bulk permittivity (air/sample mix).
Sample Temperature (°C)
Frequency (MHz)
27 44 915 2400 5000
Penetration depth (m)
ISS 20 16.03 ± 1.86
A,a
13.00 ± 1.22
B,a
4.04 ± 0.02
C,a
1.93 ± 0.01
D,a
1.02 ± 0.01
E,a
40 10.91 ± 0.73
A,b
9.82 ± 0.49
B,b
4.36 ± 0.03
C,b
1.94 ± 0.02
D,a
0.98 ± 0.01
E,b
60 16.86 ± 1.49
A,c
14.38 ± 1.02
B,c
4.41 ± 0.07
C,c
1.91 ± 0.02
D,b
0.96 ± 0.01
E,c
SSS 20 7.09 ± 0.40
A,a
6.04 ± 0.39
B,a
3.45 ± 0.10
C,a
2.08 ± 0.06
D,a
1.23 ± 0.04
E,a
40 7.36 ± 0.47
A,b
6.29 ± 0.36
B,b
3.57 ± 0.07
C,b
2.11 ± 0.04
D,b
1.23 ± 0.03
E,a
60 7.52 ± 0.40
A,b
6.46 ± 0.29
B,b
3.63 ± 0.10
C,c
2.10 ± 0.05
D,a,b
1.20 ± 0.03
E,b
IPN 20 7.19 ± 0.62
A,a
5.46 ± 0.44
B,a
3.21 ± 0.05
C,a
2.17 ± 0.03
D,a
1.41 ± 0.02
E,a
40 7.67 ± 0.48
A,b
6.36 ± 0.34
B,b
3.52 ± 0.08
C,b
2.46 ± 0.04
D,b
1.65 ± 0.03
E,b
60 5.54 ± 0.33
A,c
4.63 ± 0.26
B,c
2.91 ± 0.09
C,c
2.27 ± 0.06
D,c
1.68 ± 0.04
E,c
SPN 20 4.86 ± 0.19
A,a
4.07 ± 0.14
B,a
2.73 ± 0.05
C,a
2.43 ± 0.05
D,a
2.14 ± 0.07
E,a
40 3.79 ± 0.09
A,b
3.28 ± 0.07
B,b
2.63 ± 0.05
C,b
2.26 ± 0.04
D,b
1.81 ± 0.04
E,b
60 3.43 ± 0.22
A,c
2.92 ± 0.18
B,c
2.10 ± 0.09
C,c
1.77 ± 0.06
D,c
1.41 ± 0.04
E,c
ISS: In-shell sunflower seed; SSS: Shelled sunflower seed; IPN: In-shell pine nut; SPN: Shelled pine nut.
Different lowercase letters in the column indicate significant differences (p < .05) between samples with the same characteristics at
different temperatures according to ANOVA and Fisher’s comparison test.
Different capital letters in row show significant differences (p < .05) between samples at different frequencies according to ANOVA
and Fisher’s comparison test.
10 R. HERNÁNDEZ-NAVA ET AL.
suitable for heating agricultural products due to its better heating uniformity. On the other hand, at
lower frequencies, an increase in temperature led to a rise in d
p
values of sunflower samples, while
the d
p
of pine nut samples showed a tendency to decrease as the temperature rose. In contrast, at
higher frequencies, the d
p
of sunflower samples decreased with increasing temperature, while the d
p
of
pine nut samples exhibited different trends: IPN showed a tendency to increase as the temperature
rose, whereas SPN maintained its tendency to decrease as temperature increased. This discrepancy in
the behavior of sunflower and pine nut samples is due to the combined effect of temperature,
frequency, and sample composition on ε
bulk’
and ε
bulk’’
, resulting in a characteristic tendency in d
p
for each sample.
Modied values of the dielectric properties and d
p
applying the particle permittivity
The plots showing the corrected values of the dielectric constant (ε
part
’) and loss factor (ε
part
‘) for all
samples, after applying the particle permittivity, are shown in Figure 3. ε
part
’ and ε
part
” exhibited the
same tendencies as ε
bulk
’ and ε
bulk
” when increasing the frequency and temperature for all samples.
Nevertheless, the effect of fat content in the pine nuts samples is more pronounced for ε
part
’ and ε
part
”
when applying the particle permittivity (Table 4). It was observed that the ε
part
‘ and ε
part
’‘ values for
IPN (fat content: 21.27 ± 1.58%) were higher than those for SPN (fat content: 50.59 ± 1.75). The
presence of fat decreases the dielectric properties values because the increase in fat content dilutes the
water ratio within the food system.
[42,43]
In contrast, the sunflower seed samples exhibited a behavior
opposite to that of the pine nut samples regarding fat content and its effect on dielectric properties.
Although fat content could serve as a means to predict the dielectric properties, it is not always
accurate due to the complex interactions with other components, such as protein, that also affect the
dielectric properties.
[42,44]
A higher protein content increases the dielectric properties of food products
such as meat
[54]
and milk.
[55]
The shelled sunflower seeds are richer in protein than the in-shell
sunflower seeds,
[56,57]
and thus their dielectric properties are modified by the interaction with proteins
and fats, giving the samples their particular behavior. Overall, ε
part
’ and ε
part
” were higher than ε
bulk
’
and ε
bulk
” for all samples, resulting from the elimination of the air effect in the agricultural
products.
[21,49]
The d
p
values obtained with the particle permittivity were lower compared to those
obtained with the bulk permittivity (Table 4). This decrease in d
p
values is due to the combined
increase in both the dielectric constant and the loss factor across all samples.
[58]
Furthermore,
although the d
p
values reported in the literature are typically on the order of centimeters, they are
generally associated with foods that have high moisture content.
[44]
However, the d
p
values of foods
with low moisture content tend to be higher, on the order of meters, due to the small values of ε’ and ε”
resulting in very low loss, which increases d
p
.
[51,53,59]
Higher d
p
values for all samples at 40°C and 60°C
were observed at 44 MHz for radio frequency and 915 MHz for microwaves. This information could be
useful for developing heat treatments for these agricultural products using radio frequency or
microwaves.
Conclusions
Moisture content was higher in in-shell samples, due to the lignin and cellulolytic materials in the shells.
Water activity was in the range of 0.385–0.616. Fat content was higher in shelled samples, likely because
of the lignin and cellulolytic materials present in the shells. The in-shell samples exhibited darker colors
and a redder shade compared to the shelled ones, which was attributed to the presence of phenolic
compounds. Tapped and particle densities were greater than bulk density values, resulting from the
rearrangement of particles in the available space and the removal of air. Sunflower seed samples had
higher porosity due to their lower bulk density. For all samples, the dielectric constant (ε’) and loss factor
(ε’”) calculated using ε
bulk
and ε
part
decreased as frequency increased, with a more pronounced effect in
the radio frequency range compared to the microwave band. As temperature increased, ε” decreased in
sunflower seed samples but increased in pine nut samples, likely due to differences in water activity
INTERNATIONAL JOURNAL OF FOOD PROPERTIES 11
Figure 3. Dielectric constant (ε
part
’) and loss factor (ε
part
”) using the particle permittivity (solid sample permittivity) of in-shell
sunflower seed (a), shelled sunflower seed (b), in-shell pine nut (c), and shelled pine nut (d).
12 R. HERNÁNDEZ-NAVA ET AL.
influencing evaporation and ion mobility. This effect was more evident in in-shell samples, which had
higher moisture content and lower fat content. The loss factor (ε”) increased with rising temperature
across all samples due to enhanced ionic mobility. Additionally, the dielectric properties were influenced
by density, as an increase in ρ
bulk
lead to higher ε
bulk
‘ and ε
bulk
” values, attributed to denser packing and
reduced porosity. These different results among samples regarding ε’ and ε”, reflected the influence of
density and food composition on dielectric behavior. Dielectric properties calculated with the particle
permittivity (ε
part
) were higher than those using bulk permittivity (ε
bulk
), due to the removal of air.
Penetration depth values were higher at lower frequencies, promoting uniform heating. The d
p
values
derived from ε
part
were smaller compared to those calculated from ε
bulk
, due to the simultaneous increase
in the dielectric constant and loss factor. The information obtained in this study could be useful for
developing heat treatments for sunflower seeds and pine nuts using radio frequency or microwave
technologies applied in food processing and safety. Furthermore, it is suggested that future studies vary
moisture content and water activity, as well as increase the temperature range to gather more informa-
tion about the effects of these factors on the dielectric properties of these agricultural products.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Funding
This research was funded by Consejo Nacional de Humanidades, Ciencias y Tecnologías (CONAHCYT, now SECIHTI),
research project [CBF2023-2024-1220].
ORCID
María Elena Sosa-Morales http://orcid.org/0000-0002-1197-2572
Table 4. Dielectric properties and penetration depth of in-shell and shelled sunflower seeds (Helianthus annuus L.) and pine nuts
(Pinus pinea L.) at three temperatures and five frequencies using the particle permittivity (solid sample permittivity).
Sample Frequency (MHz)
Temperature (°C)
20 40 60
ε
part
’ ε
part
’’ d
p
(m) ε
part
’ ε
part
’’ d
p
(m) ε
part
’ ε
part
’’ d
p
(m)
ISS 27 6.59 0.64 7.13 5.96 0.88 4.91 5.28 0.53 7.62
44 4.79 0.40 5.91 4.30 0.50 4.52 3.76 0.32 6.66
915 2.08 0.04 1.96 1.84 0.03 2.13 1.54 0.03 2.18
2400 1.86 0.03 0.94 1.63 0.03 0.96 1.35 0.02 0.95
5000 1.84 0.03 0.50 1.60 0.03 0.48 1.33 0.02 0.48
SSS 27 8.72 1.51 3.48 8.12 1.39 3.63 7.61 1.31 3.73
44 6.81 0.94 3.01 6.33 0.87 3.14 5.96 0.82 3.24
915 3.75 0.06 1.78 3.46 0.05 1.85 3.31 0.05 1.88
2400 3.58 0.04 1.07 3.30 0.03 1.10 3.16 0.03 1.09
5000 3.62 0.03 0.63 3.33 0.03 0.64 3.16 0.03 0.63
IPN 27 9.73 1.57 3.52 12.11 1.65 3.74 13.04 2.38 2.69
44 7.74 1.02 2.95 9.80 1.08 3.14 10.68 1.57 2.27
915 4.45 0.07 1.64 6.01 0.07 1.78 6.79 0.09 1.46
2400 4.32 0.04 1.11 5.88 0.04 1.25 6.70 0.05 1.14
5000 4.36 0.03 0.73 5.94 0.03 0.84 6.74 0.03 0.84
SPN 27 7.20 1.06 4.51 7.63 1.40 3.52 8.79 1.66 3.17
44 6.28 0.72 3.78 6.71 0.92 3.05 7.67 1.12 2.70
915 4.73 0.04 2.54 5.12 0.05 2.45 5.81 0.06 1.95
2400 4.72 0.02 2.26 5.11 0.02 2.10 5.79 0.03 1.64
5000 4.74 0.01 1.99 5.14 0.01 1.68 5.82 0.02 1.31
ISS: In-shell sunflower seed; SSS: Shelled sunflower seed; IPN: In-shell pine nut; SPN: Shelled pine nut.
Values are the average of analyses and calculations made by triplicate.
INTERNATIONAL JOURNAL OF FOOD PROPERTIES 13
Author contributions
R. Hernández-Nava performed the physicochemical experiments and wrote the draft of the manuscript.
D. Sarmiento-Narváez conducted experiments focused on dielectric properties. J.M. Meza-Arenas designed
the sensor for measuring dielectric properties and analyzed the data. T. Kaur and A. Corona-Chávez assisted in
interpreting the results and reviewing the manuscript. R. Rojas-Laguna performed the experiments for densities
and ran the statistical analysis. M.E. Sosa-Morales designed the study, performed experiments for density,
reviewed the data, and revised the manuscript.
Data availability statement
The datasets generated for this study are available upon request.
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