Correlation of the Diffusion Parameters and the Biological Activities in the Formulation of Pinus halepensis Essential Oil in Phosphogypsum Material

Abstract

The use of natural biopesticides, specifically essential oils, is being explored as an alternative solution to protect stored foodstuffs. This study focuses on a formulation of phosphogypsum–Pinus halepensis essential oil as a pesticidal product. First, the essential oil chemical composition was determined using gas chromatography with mass spectrometry (GC-MS), while the phosphogypsum (waste from the phosphate mining industry) was analyzed using scanning electron microscopy, X-ray fluorescence, X-ray diffraction, Fourier-transform infrared spectroscopy, and thermogravimetric–differential thermal analysis; thus, physico-chemical properties and heavy metal contents were determined. In a second step, the preparation of the formulation consists in grafting the essential oil on the phosphogypsum (adsorption) in a cylindrical geometric shape adapted to the models applied in the bioprocesses of storage. The study of essential oil transfers in the material in the case of desorption along the axis (Oz) was carried out using analytical and numerical models of the Fickian diffusion process to understand the behavior of the oil and determine physicochemical parameters such as diffusivity (D) and evaporation flux (F). By using statistical methods such as experimental design and principal component analysis, these parameters can help explain the mechanisms involved in the insecticidal activities against the primary pest of lentils (Bruchus signaticornis) and in the parameters of lentil seed germination.

1. Introduction

Leguminous crops are an important source of protein and other essential nutrients in many diets around the world. In Morocco, leguminous crops are widely cultivated and play a key role in the country’s agriculture and food security [1]. One of the most important leguminous crops in Morocco is lentils, which are grown in many regions throughout the country. However, once harvested, lentils and other leguminous crops are susceptible to damage from insects and other pests. In order to protect these crops during storage, farmers and other agricultural professionals often use insecticides and other control measures to prevent infestations and preserve the quality of the crops [2,3]. Some of the most commonly used insecticides for leguminous crops in Morocco include pyrethroids, organophosphates, and neonicotinoids. While insecticides can be effective at controlling pests in stored leguminous crops, they also have some drawbacks. For example, some insecticides may be harmful to humans and other animals if ingested or inhaled [4,5,6,7]. Additionally, some insects may develop resistance to certain types of insecticides over time, which can reduce their effectiveness. As a result, some farmers and other agricultural professionals in Morocco have begun to explore alternative methods of controlling insect pests in stored leguminous crops. One promising approach is the use of essential oils as pesticides [8,9,10].

Essential oils are highly concentrated liquids that are extracted from plants using a variety of methods. Some essential oils have been shown to have insecticidal properties, which makes them potentially useful for controlling pests in stored leguminous crops [11,12,13,14]. For example, essential oils from plants such as peppermint, thyme, and clove have all been shown to have insecticidal properties [15]. Using essential oils as insecticides has several potential advantages over traditional insecticides. For one, many essential oils and other natural compounds from plants are safe for humans and other animals, which makes them a potentially attractive option for farmers and other agricultural professionals who are concerned about the potential health risks associated with traditional insecticides [16]. Additionally, insects may be less likely to develop resistance to essential oils than they are to traditional insecticides, which can help to ensure their effectiveness over time. However, there are also some potential drawbacks to using essential oils as insecticides. For one, essential oils can be expensive, which can make them less practical for some farmers and other agricultural professionals. Additionally, essential oils may not be as effective at controlling pests as traditional insecticides, particularly in cases where infestations are severe [17,18,19].

This study aimed to investigate natural and sustainable methods for controlling insect infestations in stored leguminous crops. Specifically, this study focused on a natural insecticide formulation comprising Pinus halepensis essential oil (EOPH) and phosphogypsum (PG). This work begins with a physicochemical characterization of the essential oil and phosphogypsum, followed by an examination of the desorption process of the previously absorbed essential oil in PG. This study analyzes the behavior of the essential oil and establishes correlations between specific physicochemical parameters and biological parameters by utilizing experimental and analytical models.

2. Materials and Methods

2.1. Plant Material and Essential Oil

Between March and April of 2022, aerial parts of P. halepensis plants were collected from the Middle Atlas region of Morocco. The P. halepensis essential oil (EOPH) was obtained by extracting the dried aerial parts for 3 h (in triplicate) using a Clevenger extractor. The resulting oil was collected through a simple operation of decantation and subsequently dried over anhydrous sodium sulfate (Na₂SO₄) prior to the analysis of composition. The oil was analyzed using GC-MS at the CNRST (Rabat, Morocco). The GC-MS apparatus utilized for analysis was a Hewlett Packard 5971A. Quantitative analyses were carried out to calculate the relative proportions of the different compounds using GC/FID (gas chromatography coupled with flame ionization) under the same operational conditions. A DB-5 type column was used for the GC/MS, with dimensions of 250 μm diameter, 30 m length, and a 0.2 mm film thickness. Helium gas was used as the carrier with a flux of 1 mL/min. The temperature protocol used consisted of a detector temperature of 300 °C and an oven temperature that was programmed to ramp up from 50 °C to 150 °C at a rate of 3 °C per minute and then ramp up from 150 °C to 250 °C at a rate of 5 °C per minute. After reaching 250 °C, the temperature was held constant for 5 min, while the initial temperature was set to 280 °C. To identify the constituents of the essential oil, retention indices were compared with data from the literature, and mass spectra were analyzed using a computer library search [20].

2.2. Phosphogypsum: Preparation and Analysis

Raw phosphogypsum (PG) was obtained from Jorf Lasfar (El Jadida, Morocco). The material was crushed, ground, washed with distilled water, dried at 105 °C, and sieved to obtain a homogeneous powder with a particle size of 0.5 mm. Initially, physico-chemical analyses were conducted on the material using commonly used techniques such as SEM (scanning electron microscopy, JSM-6700F, JEOL Ltd., Tokyo, Japan), XRF (X-ray fluorescence, Axios, Overijssel, PANalytical, Almelo, The Netherlands), XRD (X-ray diffraction, using a D8 Advance diffractometer with Cu Kα radiation at 1.54 Å, Bruker Corporation, Billerica, MA, USA), TGA-DT (thermogravimetric analysis and differential thermal analysis, using a DTG-60H system, Shimadzu, Kyoto, Japan), and FTIR (Fourier-transform infrared spectroscopy, using a Vertex 70, Bruker Corporation, Billerica, MA, USA). Subsequently, a set of physico-chemical properties such as density (pycnometer), pH (HI2210 pH-meter, HANNA Instruments, Woonsocket, RI, USA), conductivity (HI 99300 Conductimeter, HANNA Instruments, Woonsocket, RI, USA), organic matter content, mineral matter content (calcination method in an oven), specific surface area (V-Sorb 2800S Analyzer, Japan) and heavy metal contents (Thermo 7400 ICP-OES Analyzer, Thermo Fisher Scientific, Waltham, MA, USA) were determined.

2.3. Formulation Essential Oil—Phosphogypsum

A specific volume of essential oil (EO) was combined with a measured amount of phosphogypsum powder (PG) at concentrations ranging from 10% to 50% (v/w) to ensure complete absorption of the oil by the powder. The resulting EO–PG formulations were then transferred to metal cylinders with diameters of 1 cm for subsequent experimental analysis [21].

2.4. Mathematical Theory of Transfer

The following assumptions are being made:

• In the cylindrical coordinate system, mass transfer from EO happens through one-dimensional diffusion along the (Oz) axis.
• Under transient conditions, the diffusion process takes place with a constant diffusivity and flux.
• Once the EO–PG formulation is mixed with the material, the concentration of EO on the surface of the material reaches an equilibrium value.
• The concentration of EO within the material remains constant at the beginning of desorption. Fick’s second law for diffusion in cylindrical coordinates can be formulated as [22]:

$$\frac{\partial C}{\partial t}=\frac{1}{r}\times \left\{\frac{\partial }{\partial r}\left(r\times D_r\times \frac{\partial C}{\partial r}\right)+\frac{\partial }{\partial \theta }\left(\frac{D_{\theta }}{r}\times \frac{\partial C}{\partial \theta }\right)+\frac{\partial }{\partial z}\left(r\times D_z\times \frac{\partial C}{\partial z}\right)\right\}$$

(1)

where C is the concentration of the diffusing species, t is time, r is the radial distance from the axis of the cylinder, θ is the azimuthal angle, z is the axial coordinate, and D is the diffusivity of the species.

As the dominant diffusion in the cylinder occurs in the height direction, which is significantly smaller than the diameter and lateral surface, the transfer of diffusion can be simplified and considered as one-dimensional. This simplifies the problem, and the diffusion equation can be expressed using Fick’s second law:

$$\frac{\partial C}{\partial t}=D_z\times \frac{{\partial }^{2}C}{\partial z^2}$$

(2)

or

$$D_z=D=cte$$

(3)

According to the chronological conditions of monitoring at the following limits:

$$\left\{\begin{array}{ccc}t=0& C=C_0& 0\le z\le h\\ t>0& C=C_t& z=h\end{array}\right.$$

(4)

Crank (1979) [23] derived an analytical solution to Equation (2) while taking into account the conditions specified in Equation (4). The resulting solution can be expressed as follows:

$$C\left(z,t\right)=\frac{4}{\pi }\times {\displaystyle \sum }_{n=0}^{\infty }exp\left(-D\times \frac{{\left(2n+1\right)}^2}{h^2}\times {\pi }^2\times t\right)\times cos\left(\frac{\left(2n+1\right)\pi }{2h}\times z\right)$$

(5)

The total mass of essential oils in the PG at an instant t can be obtained by integrating the concentration C over the volume of the material. Since the diffusion is assumed to be one-dimensional, the concentration C is only a function of the axial coordinate z, and the integration can be simplified to

$$M_t=S\times {{\displaystyle \int }}_0^{h}C\left(z,t\right)dz$$

(6)

where S is the cross-sectional area of the cylinder.

The solution to these equations has an analytical solution that takes into account the boundary conditions and assumes an infinite desorption time, which leads to equilibrium. This solution can be expressed as follows:

$$\frac{M_t-M_{\infty }}{M_0-M_{\infty }}=\frac{8}{{\pi }^2}\times {\displaystyle \sum }_{n=0}^{\infty }\frac{1}{{\left(2n+1\right)}^2}exp\left(-D\times \frac{{\left(2n+1\right)}^2}{h^2}\times {\pi }^2\times t\right)$$

(7)

The variables used in the analytical solution include M₀, which represents the initial mass of absorbed EO–PG; M_t, which represents the mass of desorbed EO–PG at a given aging time; and M_∞, which represents the final mass at equilibrium.

If we assume that M_∞ = 0 and take the first term of the series solution, Equation (7) can be simplified to

$$\frac{M_t}{M_0}=\frac{8}{{\pi }^2}\times exp\left(\frac{-D\times {\pi }^2\times t}{h^2}\right)$$

(8)

and if we assume that the term (8/π²) is equal to 1, then Equation (8) simplifies to

$$\frac{M_t}{M_0}=exp\left(\frac{-D\times {\pi }^2\times t}{h^2}\right)$$

(9)

As part of our modeling study and taking into account the theoretical considerations already mentioned, we will focus on two parameters that are relevant to the desorption process: diffusivity (D) and flux (F). These parameters can be respectively obtained through linear or logarithmic extrapolation of Equation (9) and the tangent of the kinetic curve of Equation (10).

$$F=F_0=\frac{1}{S}\times li{m}_{t\to 0}\frac{dM}{dt}$$

(10)

To obtain a deeper insight into the behavior and diffusion process of EOPH in PG material, two intermediate steps were conducted: a kinetic study and a simulation. The kinetic study involved analyzing the rate of desorption of the EOPH from the PG material over time. This allowed for a better understanding of the diffusion process and helped to determine the diffusion coefficient (D) and the evaporation flux (F) parameters. In addition, concentration profiles within the cylinder were simulated to further understand the behavior of EOPH in the PG material. These intermediate steps provided a more detailed understanding of the diffusion process and aided in the precise determination of important parameters.

Various kinetic models have been mentioned in previous literature to examine the desorption mechanism, and in this study, the Fickian model of diffusion was used [24,25,26]. The research methodology included two intermediate steps to analyze the behavior and diffusion process of EOPH in PG material, namely, the investigation of desorption kinetics and the simulation of concentration profiles within the cylinder. These steps aided in understanding the mechanism involved in the diffusion process and accurately determining parameters such as the diffusion coefficient (D) and the flux (F).

2.5. Biological Activities

2.5.1. Insecticidal Activity Test

In this test, a population of Bruchus signaticornis adult weevils susceptible to insecticides was used. The population was collected from the Biotechnology and Analysis Department (EST-Khenifra; USMS; Morocco). Lentil grains that were free of insecticide residue were used to rear the weevils in 1 L glass containers. The containers were placed within growth chambers maintained at a temperature of 25 ± 5 °C, a humidity of 70 ± 10%, and a 12:12 h photoperiod (dark: light).

For the experiments, EO or EO–PG was placed in cylinders (steel) with a height of 0.5 cm. The cylinders, along with 10 insects, were placed inside glass Petri dishes. A negative control without any product was also included in the experiment. The Petri dishes were then introduced into a fumigation chamber located within a temperature- and humidity-controlled experimental enclosure. The mortality of the bruchus was observed for a period of 24 h, and each trial was repeated three times to minimize errors.

The corrected mortality rate of the treated insects was determined using the following equation [27]:

$$M\%=\left(\frac{M_{test}-M_{control}}{100-M_{control}}\right)\times 100$$

(11)

M%—percentage of mortality; M_test—mortality observed during activity; M_control—mortality observed in the negative control.

The lethal dose required to cause 50% mortality (LD₅₀) was determined by using linear interpolation of curves that plotted the percentage of mortality against the logarithm of the tested concentration [28].

LD₅₀ values are widely recognized as a means of assessing the toxicity of a substance. In this study, the test population consisted of insects, and the LD₅₀ values were used to evaluate the efficacy of the EOPH and EO–PG formulations as insecticides.

2.5.2. Germination Test

Lens culinaris was used as a reference indicator for seed germination tests of the essential oil and formulation. Commercially available Lens culinaris seeds were washed with sterile deionized water and placed individually in Petri dishes. Each dish contained an agar layer of distilled water mixed with the test products. The Petri dishes were covered with parafilm and kept in a culture chamber at optimized temperatures of 25 °C and 30 °C in the dark for a specific time required to measure each parameter. Ten replicates were conducted for each treatment.

After the 24-h incubation period, the number of germinated seeds in each dish was counted, and the percentage of germination was calculated as the first parameter. A seed was considered germinated if the length of the radicle was at least 2 mm. After two weeks, the second reading was taken, and three parameters were calculated for each seedling: weight (W), length of the aerial part (L_A), and length of the root part (L_R). [29,30].

2.6. Statistical Analysis and Computer Processing of Transfer Conditions

We used statistical experimental designs as a method to minimize the experimental conditions for the diffusion transfer of EO in EO–PG. The transfer was presented as flux F. The design matrix used for this purpose was a full factorial design based on three factors, X_i:

• Factor 1 = T: temperature (25 °C and 30 °C);
• Factor 2 = H: humidity (50% and 70%);
• Factor 3 = C: concentration of the EO fixed on the PG (0.01 µL·g⁻¹·cm⁻³ and 0.02 µL·g⁻¹·cm⁻³).

Each factor with two levels: high level coded as +1 and low level coded as −1. The number of tests for k factors:

$$number of tests=2^k$$

(12)

$$Number of tests=2^3=8$$

(13)

This corresponds to 8 tests.

The polynomial model presents

$$F=a_0+{\displaystyle \sum }_{i=1}^n{a}_i{X}_i+{\displaystyle \sum }_{i=1}^n{\displaystyle \sum }_{j=1}^{n-1}{a}_{ij}{X}_i{X}_j+a_{ijk}{X}_i{X}_j{X}_k$$

(14)

or:

• Mean: a₀;
• 3 effects for each factor: a_i;
• 3 effects present the interactions of 2nd order: a_ij;
• 1 effect presents the interactions of 3rd order: a_ijk.

Various factors determine the behavior of essential oil in a porous material. On the one hand, diffusion parameters include flux (F) and diffusivity (D). The insecticidal activity is represented by the mortality (M%), and the germination parameters are presented by the weight (W), the length of the aerial part (L_A), and the length of the root part (L_R) of the lentils. However, the numerical values of the parameters are difficult to understand and interpret their meanings.

To investigate the interaction between EO behavior in porous media and biological activity, we utilized PCA (principal component analysis), a multivariate statistical analysis. We correlated the matter transfer by diffusion parameters with the biological activity.

The work follow-up was carried out on matrices obtained from eight subjects during the optimization of the flow of evaporation in porous materials. Six variables were considered in the analysis, namely, F, D, M%, W, L_A, and L_R. The aim was to determine the relationships between the variables and to identify any patterns or trends that could provide insight into the behavior of EO–PG with respect to biological activities.

All the analysis was conducted using various computer tools, including MATLAB software for numerical modeling and other programs, such as EXCEL, XLSTAT, and DESIGN EXPERT, for specific calculations and graphical representations. The resulting data were compared with experimental results to identify relevant parameters and ensure maximum interpretation.

3. Results

3.1. Chemical Composition of the Essential Oil

Table 1. Identification of the EOPH.

KI	Compounds	Percentage (%)
939	α-pinene	88.62
953	Camphene	0.94
980	β-pinene	1.08
991	Myrcene	1.16
1005	α-phellandrene	0.01
1011	δ-3-carene	0.42
1189	α-terpineol	1.43

KI: Kovat index.

displays the GC-MS findings for the essential oil. The analysis of these chromatographic results of the EOPH allowed for the quantification and detection of about seven constituents. The analysis of the results showed that the EOPH is mainly composed of monoterpenes, with α-pinene as the main constituent.

3.2. Physico-Chemical Characterization of PG

SEM was utilized to examine the surface structure of the material and study the morphology of the PG. The image displayed an irregular and porous structure with heterogeneous pore shapes across the entire surface of the PG sample (Figure 1).

XRD was carried out to determine the structure of the PG. The results from XRD analysis revealed that all observed lines were attributed to calcium sulfate dihydrate (CaSO₄·2H₂O), with three main lines located at approximately 2θ = 12°, 20.5°, 23°, and 29°. The presence of a line attributed to quartz was also observed, located at 2θ = 26° (Figure 2) [31,32].

The XRF analysis confirmed the XRD results and identified significant percentages of sulfur trioxide (50.11%) and calcium oxide (38.52%) in the PG sample (

Table 2. The identified mineral components through XRD.

Mineral Components	SO3	CaO	SiO2	P2O5	F	Na2O	Al2O3	Fe2O3	MgO	SrO	K2O	Y2O3	TiO2	PAF
(%)	50.11	38.52	2.65	1.22	1.00	0.25	0.23	0.06	0.05	0.05	0.02	0.02	0.01	5.81

).

TGA analysis was used to investigate the thermal information of the PG sample. The results showed a total weight loss of approximately 21%, with DT analysis revealing two peaks. The first peak appeared around 134 °C and was attributed to the dehydration of gypsum, while the second peak appeared at 431 °C and was attributed to the oxidation of organic matter (Figure 3) [33,34].

FTIR analysis was used as a complementary analysis to all previous analyses. The spectrum of the PG sample showed the vibrations of the SO₄ bonds at bands: 608 cm⁻¹, 672 cm⁻¹, and 1150 cm⁻¹. The vibrations of the H₂O bonds appeared at the bands: 1640 cm⁻¹, 1692 cm⁻¹, and 3440 cm⁻¹ (Figure 4) [35,36].

Physicochemical properties of the PG material were determined, including density, pH, conductivity, organic matter content, mineral matter content, and specific surface area. These properties were measured and presented in

Table 3. Physicochemical properties of phosphogypsum.

Parameters	Value
Density (g/cm3)	2.87 ± 0.25
pH	5.18 ± 0.66
Conductivity (μS/cm)	2.356 ± 0.704
Organic matter content (%)	0.43 ± 0.11
Mineral content (%)	99.57 ± 0.11
Specific surface (cm2/g)	2.71 ± 0.32

.

Heavy metal content, including Cd, Hg, Pb, Cr, Zr, Zn, and Cu, was found to exceed material concentration limits [37]. However, subsequent use of this material in large volumes could reduce these concentrations (

Table 4. Heavy metal content.

Elements	Concentration (ppm)
Cd	1.27
Hg	0.67
Pb	1.95
Cr	9.8
Zr	15
Zn	47
Cu	6.1

).

3.3. Insecticidal Activities of EO and EO–PG

Table 5. LD₅₀ (μL/cm³) of the insecticidal tests of the EOPH and EO–PG.

EOPH	EO–PG	Humidity	Temperature
0.2251	0.1978	H1 = 50%	T1 = 25 °C
0.1245	0.1230		T2 = 30 °C
0.1254	0.1155	H2 = 70%	T1 = 25 °C
0.0258	0.0194		T2 = 30 °C

presents the LD₅₀ values for the insecticidal tests of EOPH essential oil and the EO–PG formulation at different temperature and humidity conditions. The findings indicate that the EO–PG formulation is generally more potent as an insecticide than the EOPH alone. This observation is supported by the lower LD₅₀ values observed for the EO–PG formulation. This enhanced potency is likely due to the diffusion effect of the essential oil in the gypsum material in the formulation, which can amplify the insecticidal properties of the product. The insecticidal activity of the EOPH and EO–PG formulation is substantially affected by two factors: temperature and humidity.

3.4. Test of Germination

Figure 5 presents the results of a lentil seed germination test conducted after 24 h. The percentage of germination was measured for three treatments, including a control group with no added products, a treatment with EOPH at a concentration of 0.01 µL·cm⁻³, and a treatment with EO–PG at a concentration of 0.01 µL·g⁻¹·cm⁻³. The results show that the control group had a germination rate of 85%, the EOPH treatment had a germination rate of 80%, and the EO–PG treatment had the highest germination rate of 94%.

3.5. Optimization of Transfer

Table 6. Flux F obtained for each test in all experiments.

	Factor 1	Factor 2	Factor 3	Response
Run	T	H	C	Flux
	°C	%	µL·g−1·cm−1	(×104) (g·h−1·cm−1)
1	1	1	−1	8.41
2	−1	1	1	5.46
3	1	−1	−1	7.22
4	1	1	1	9.23
5	−1	−1	−1	5.87
6	−1	−1	1	5.72
7	−1	1	−1	6.42
8	1	−1	1	8.76

presents the matrix of all experiments and the corresponding flux obtained as part of the complete factorial design used for optimizing the flux parameter of EOPH fixed in the porous medium PG.

Based on the results obtained, the first-degree polynomial mathematical model is presented with the factors, second-order interactions, and third-order interactions of these three factors. Equation (14) shows the coefficients of the flux model of the EOPH fixed on the PG medium. The average flux obtained from the optimization route was found to be 7.14 × 10⁻⁴ g·h⁻¹·cm⁻¹. It can be concluded that all three factors—temperature (T), humidity (H), and concentration (C)—significantly increase the flux when studied individually on the support.

$$F \left(\times {10}^4)(\mathrm{g}·{\mathrm{h}}^{-1}·\mathrm{c}{\mathrm{m}}^{-1}\right)=7.14+\left(1.27\times T\right)+\left(0.24\times H\right)+\left(0.16\times C\right)+\left(0.17\times T\times H\right)+\left(0.43\times T\times C\right)-\left(0.19\times H\times C\right)$$

(15)

Figure 6 displays a collection of 3D plots representing the flux as a function of two of the three factors. The flux increases with the temperature and humidity (TH) and temperature and concentration (TC), while it decreases with the interaction of humidity and concentration (HC).

In

Table 7. Statistical parameters of the design experiments model.

Model	Mean of Flux (g·h−1·cm−1)	Standard Deviation (g·h−1·cm−1)	Coefficient of Variation (%)
Full Factorial Design	7.14	0.03	0.47
Coefficient of Determination R2	Adjusted R2	Predicted R2	Adeq Precision
0.9999	0.9995	0.9954	120.161

and

Table 8. Statistical parameters of the polynomial model of flux.

Model or Parameter (s)	dll	Ftest	Ptest
Model	6	2335.34	0.0158
T	1	11,577.67	0.0059
H	1	429.77	0.0307
C	1	174.89	0.0480
TH	1	211.30	0.0437
TC	1	1355.86	0.0173
HC	1	262.55	0.0392

, R² (coefficients of determination) for both media indicate that the optimized models explain the data accurately. The predicted R² value of 0.9954 is in agreement with the adjusted R² value of 0.9995, with a difference of 0.036, which is less than 0.2. The A_deq Precision, which measures the signal-to-noise ratio, is desirable when greater than 4, and the ratio of 120.161 suggests an adequate signal. This model can be used to explore the design space.

The significant model F-value of 2335.34 indicates that the model is noteworthy. A p-value of less than 0.05 implies that the model variables have statistical significance, and in this instance, all factors and their interactions have significant model terms.

3.6. Modeling of the EOPH Diffusion

The optimal conditions (T = 25 °C, H = 70%, C = 0.01 µL·g⁻¹·cm⁻³) were employed to perform the kinetic study, which controlled the mass percentage of oil as a function of time through simulations of analytical treatments during desorption (Figure 7 and Figure 8). The research found a clear decrease in the mass percentage of essential oil, indicating the desorption mechanism. The diffusion coefficient (D) was estimated to be approximately 8.77·10⁻⁶ cm²·h⁻¹ under optimal conditions. Furthermore, the experimental results from the simulation showed that 96.6% of the EOPH was desorbed over a span of 15 days (360 h).

The results of the simulation closely match the experimental data, indicating that the developed analytical model is accurate and can be used to estimate other parameters.

3.7. Diffusion Behavior of EO–PG in Relation to Biological Activities

Table 9. Diffusion parameters and biological activities of EOPH desorption in the PG.

Test	Desorption Parameters		Insecticidal Parameter	Germination Parameters
	F (×104) (g·h−1·cm−1)	Dz (×106) (cm2·h−1)	M (%)	W (mg)	LA (cm)	LR (cm)
1	8.4152	12.40	33.33 ± 5.40	638.5 ± 0.2	3.4 ± 0.1	3.1 ± 0.1
2	5.4625	5.68	38.55 ± 5.64	999.0 ± 0.4	7.0 ± 0.2	8.2 ± 0.2
3	7.2241	7.92	20.20 ± 4.93	637.5 ± 0.2	4.3 ± 0.1	4.9 ± 0.1
4	9.2375	6.80	66.67 ± 7.21	515.5 ± 0.2	7.8 ± 0.2	4.0 ± 0.1
5	5.8732	14.64	21.84 ± 3.11	726.0 ± 0.3	7.8 ± 0.2	3.9 ± 0.1
6	5.7223	7.36	54.23 ± 6.29	909.5 ± 0.4	10.0 ± 0.2	5.5 ± 0.1
7	6.4254	8.77	50.41 ± 6.04	768.3 ± 0.3	5.2 ± 0.1	5.7 ± 0.1
8	8.764	6.24	30.21 ± 5.07	817.22 ±0.4	8.9 ± 0.1	5.1 ± 0.1

presents the values obtained for the parameters of diffusion and biological activities of desorption of the EOPH in the PG in all eight of the tests carried out.

In order to provide a comprehensive explanation of the findings, it was necessary to select the most pertinent axes for the analysis. The Kaiser criterion was used to select axes F1 and F2, which had eigenvalues greater than 1 (λ₁ = 2.79 and λ₂ = 1.64), corresponding to percentages of 46.56% and 27.27%, respectively. Together, these axes accounted for 73.83% of the information, and their eigenvalues represented a significant portion of the total inertia, indicating that the sum of the inertia explained by each axis was substantial.

The mapping displayed in Figure 9 provided several interpretations. First, the diffusion coefficient D and the flux F were perpendicular in the correlation circle, indicating that these two variables were not correlated and were independent. Second, the diffusion coefficient D was inversely correlated with the mortality M% and the length of the aerial part L_A, while the flux F was inversely correlated with the weight W and the length of the root part L_R.

4. Discussion

Biological formulations are becoming increasingly popular due to their potential to offer effective and environmentally friendly alternatives to chemical pesticides [38]. These formulations use natural ingredients, such as essential oils, to protect crops from pests and enhance their growth [39,40]. In this study, we explore the potential of a formulation of P. halepensis essential oil and phosphogypsum (EO–PG) as a biological formulation with high biological value.

The EO–PG formulation was prepared by fixing the EOPH onto the porous material of PG. The essential oil was characterized by GC-MS, which identified a composition of seven molecules, with α-pinene being the major compound at 88.62%. In fact, several authors have studied the compounds profile of genus Pinus essential oils. From their results, it appears that a high percentage of α-pinene is characteristic of most of this essential oil, except in the case of the essential oil of P. heldreichii and P. roxburghii [41]. For the essential oil of P. heldreichii, limonene is the majority constituent at 79.44% [42], and for the essential oil of P. roxburghii, δ-3-carene represents 50.6% [43]. Other studies have shown that the oils richest in α-pinene are those of P. wallichiana (90.7%) [44]. The essential oil of P. halepensis is distinguished by a lower content of β-pinene compared to that of P. pinaster, with levels of 1.08% and 6.35%, respectively [45]. This constituent presents higher contents for the essential oils of French and Portuguese P. pinaster, with respective levels of 17% and 26% [46]. Phosphogypsum was also characterized and found to be a porous material containing a high percentage of calcium sulfate dihydrate (CaSO₄·2H₂O) and a minor percentage of quartz.

The EO–PG formulation showed a higher level of insecticidal activities than the essential oil alone against the pest Bruchus signaticornis of lentils. This can be explained by the desorption of the essential oil after its fixation on PG, which plays a role in the retention of the molecules. This retention allows for the sustained release of the essential oil and a longer-lasting effect on pests. The EO–PG formulation also had a positive effect on germination. This can be attributed to the phosphorus element in phosphogypsum, which has been shown to have a beneficial effect on plant growth. This indicates that the EO–PG formulation has potential as a growth-promoting agent as well as a pest control agent.

Optimal levels of parameters such as temperature, humidity, and concentration are critical for achieving effective insecticidal activity and controlling insect populations. These parameters should be carefully considered during the development of insecticidal formulations. Overall, the results suggest that the EO–PG formulation has the potential to be an effective and eco-friendly insecticide. However, further research is required to establish the optimal conditions [38].

The higher percentage of germination observed in the EO–PG treatment suggests that the addition of phosphorus through the EO–PG formulation may have contributed to improved germination compared to the control and EOPH treatments. It is important to note that the concentration of the EOPH and EO–PG treatments can affect their efficacy. The results of this study suggest that the EO–PG treatment with a concentration of 0.01 µL·g⁻¹·cm⁻³ was the most effective in promoting lentil seed germination. However, additional research is required to validate these findings and establish the ideal concentration of the EO–PG mixture for enhancing the germination process in lentil seeds [47].

The flux F, an important parameter for understanding the desorption phenomenon, was optimized using design plans. The results showed that temperature, humidity, and concentration all had a significant effect on this parameter. These findings suggest that the desorption of the EO–PG formulation can be optimized by controlling these factors. The EO–PG desorption kinetics were modeled using the Fickian model of diffusion, and concentration profiles were simulated at various time points, including t = 0 h, t = 1 h, t = 24 h, and t = 360 h. Based on the simulations, it was observed that the Fickian model was able to fit well with the experimental data, and therefore, it could be used to forecast the desorption kinetics of the EO–PG formulation. This simulation has important implications because it enables researchers to determine the amount of oil that remains during biological applications, which is critical for assessing the biological activities of the oil. These profiles provide information about the concentration of the oil at various heights and at different times, enabling researchers to obtain more precise data [48,49,50].

The correlations between the parameters of the diffusion model and the parameters of the biological activities were explored using principal component analysis (PCA). The diffusion coefficient D and the flux F were found to be perpendicular in the correlation circle, indicating that these two variables were not correlated and were independent. The diffusion coefficient D was inversely correlated with the mortality M% and the length of the aerial part L_A, while the flux F was inversely correlated with the weight W and the length of the root part L_R. These findings suggest that the diffusion parameters play an important role in the biological activities of the EO–PG formulation.

Finally, the EO–PG formulation shows promising potential as a biological formulation with high biological value. The sustained release of essential oils and the beneficial effects of phosphorus on plant growth make it an effective pest control and growth-promoting agent.

5. Conclusions

The development of a high-value biotechnological formulation of P. halepensis essential oil fixed on phosphogypsum is an important research focus in plant growth promotion and protection. The application of statistical tools such as the design of experiments, principal component analysis, and Fick’s second law modeling has enhanced our understanding of the correlations between diffusion and biological activities. In this study, the EO–PG formulation exhibited significant insecticidal activity against Bruchus signaticornis, a lentil pest, and demonstrated high performance in promoting lentil seed germination. Optimization of flux, considering critical parameters such as temperature, humidity, and concentration, was pivotal in determining the ideal profile of the EO–PG formulation and understanding its mechanism. The utilization of Pinus essential oil and phosphogypsum as a formulation for insect control and crop growth shows promising potential for providing sustainable and environmentally friendly alternatives to traditional chemical methods. Future research will further validate these results and improve the efficacy and versatility of this formulation.