Optimization and Kinetic Modelling of Hydroxycinnamic Acid Extraction from Anethum graveolens Leaves

Abstract

This study focused on optimizing key extraction parameters (ethanol concentration, temperature, and time) to enhance the extraction of hydroxycinnamic acids from A. graveolens leaves, applying a replicated 2³ full factorial design. The experimental results demonstrated that extraction conditions significantly influenced the yield of hydroxycinnamic acids. The optimum conditions were 50% ethanol for 80 min at 50 °C, yielding 103.75 µg/g of chlorogenic acid (ChA), 6.05 µg/g of ferulic acid (FA), and 2.19 µg/g of sinapic acid (SA). Therefore, the extract obtained with 50% ethanol showed the highest levels of polyphenols, flavonoids, and antioxidant potential, highlighting its suitability for use in both food-related products and pharmaceutical formulations. Additionally, the applicability of different mathematical models (unsteady-state diffusion, parabolic diffusion, and power law models, as well as Ponomaryov’s and Elovich’s equations) to describe and better understand the kinetics of hydroxycinnamic acid extraction from dill leaves was evaluated. The fit of each kinetic model to the experimental data was assessed using the root mean square error and the coefficient of determination. Among the five kinetic models, the unsteady-state diffusion model and Ponomaryov’s equation provided the best fit, exhibiting the highest accuracy. The activation energy for the extraction process was determined to be 5.85, 6.46, and 7.59 kJ/mol for ChA, FA, and SA, respectively. The extraction of hydroxycinnamic acids from dill leaves was found to be endothermic, irreversible, and spontaneous.

1. Introduction

Herbs and spices used in cooking have long served as natural preservatives and flavor enhancers. Their distinctive sensory qualities make them widely appreciated in various food applications. In recent years, they have also gained attention as dietary sources of antioxidant polyphenols, prompting growing scientific interest in their phenolic composition and biological activity [1]. Among aromatic herbs, Anethum graveolens L.—commonly known as dill—has been valued for generations for both its culinary uses and traditional medicinal properties. Native to the Mediterranean basin and southeastern Europe, dill is particularly rich in phenolic constituents [2,3]. Traditionally, dill leaves have been used as a diuretic and to relieve digestive ailments such as flatulence, indigestion, stomach discomfort, and colic [4,5]. These leaves are also a notable source of hydroxycinnamic acids, compounds known for their capacity to neutralize free radicals and contribute to antioxidant defense. Their activity is primarily linked to the interruption of free radical chain reactions through hydrogen or electron donation [6].

Polyphenols found in plant materials are typically isolated using a solid–liquid extraction technique. This method relies on mass transfer principles to separate and recover the target bioactive compounds from plant tissues using an appropriate solvent. Key parameters such as temperature, extraction time, and the ratio between the solvent and plant material substantially influence the efficiency of the extraction process [7].

To optimize this type of extraction, the initial step involves selecting appropriate process conditions that influence extraction efficiency, including solvent choice and operational parameters. Process modeling and optimization can help maximize extraction efficiency and improve yields. A combination of mathematical modeling and experimental approaches is often used to assess how extraction yields change over time or how various operational parameters influence both the amount of compound extracted and the efficiency of the extraction process. Widely used approaches for this purpose include response surface methodology (RSM) and factorial design. Additionally, various kinetic models—including first-order, second-order, hyperbolic, and Elovich equations—have been applied to characterize the extraction kinetics of phenolic compounds from plant sources [8,9,10]. Despite this, data on the kinetics of hydroxycinnamic acid extraction specifically from dill leaves are still lacking in the current literature.

This research explores how solvent concentration, extraction time, and temperature influence the extraction of hydroxycinnamic acids from dill leaves, applying a factorial design approach. To better understand the extraction mechanism, experimental results were analyzed using five kinetic models: unsteady-state diffusion, parabolic diffusion, power law, Ponomaryov’s model, and the Elovich equation. The adequacy of each model was evaluated using the coefficient of determination (R²) and the root mean square error (RMS). To further interpret the extraction process, key thermodynamic indicators—enthalpy, entropy, and Gibbs free energy—were also determined.

2. Materials and Methods

2.1. Plant Materials

Fresh dill leaves were manually collected in the early morning during peak flowering from three different sites in southeastern Serbia. Immediately after harvesting, the plant material was air-dried for 15 days in a shaded, well-ventilated space to preserve its active compounds. Once dried, the samples were stored in paper bags and kept in a dark, dry, and cool environment until further use. Prior to extraction, the dried leaves were ground using a hammer mill and passed through a 6 mm sieve to obtain a uniform particle size.

2.2. Chemicals and Reagents

Folin-Ciocalteu reagent, aluminum chloride, gallic acid, 2,2-diphenyl-1-picrylhydrazyl (DPPH), 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS), Trolox (6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid), potassium persulfate, catechin, and gallic acid were purchased from Sigma Chemical Corporation (St. Louis, MO, USA). Analytical standards (ChA, FA, and SA) were sourced from Sigma-Aldrich (St. Louis, MO, USA) and Alfa Aesar (Karlsruhe, Germany). High-purity solvents, including acetonitrile, ethanol, methanol, and formic acid, were obtained from Aldrich Chemical Company (Steinheim, Germany).

The vessels used were washed sequentially with ethanolic KOH solution, followed by HCl solution (1:1), and then rinsed with tap water, distilled water, and deionized water. Deionized water with a conductivity of 0.05 μS/cm was used for the preparation of all aqueous solutions.

2.3. Initial Content of Phenolic Compounds in Dill Leaves (q₀)

A 2.5 g portion of ground dill leaves was placed into a 250 mL Erlenmeyer flask with a ground-glass stopper and mixed with 100 mL of extraction solvent—either 50% aqueous ethanol (v/v) or absolute ethanol. The first extraction step was performed via maceration for 120 min at room temperature. After this period, the liquid phase was separated by filtration through Whatman No. 1 filter paper (Whatman, Maidstone, UK). To increase extraction efficiency, the plant residue underwent two additional extractions with fresh solvent, each lasting 30 min. All three filtrates were combined for further analysis.

The pooled extracts were then concentrated under reduced pressure at 45 °C using a rotary evaporator (Rotavapor R-200, BÜCHI Labortechnik AG, Flawil, Switzerland). The dry residues were re-dissolved in the same solvent prior to analysis. All extractions were conducted in triplicate to ensure data reproducibility. Quantification of hydroxycinnamic acids was performed using the HPLC-DAD method. The initial concentrations of chlorogenic acid (ChA), ferulic acid (FA), and sinapic acid (SA) in dill leaves extracted with 50% ethanol were 128.52 µg/g, 7.92 µg/g, and 2.93 µg/g, respectively.

Total phenolics (TPs), total flavonoids (TFs), and antioxidant activity (via DPPH, ABTS, FRP, and CUPRAC assays) were assessed spectrophotometrically using a Shimadzu UV-1800 spectrophotometer (Kyoto, Japan). All measurements were performed on triplicate samples, and average values were reported.

2.4. HPLC-DAD Analysis of Extracts

Individual hydroxycinnamic acids were quantified by reverse-phase HPLC using an Agilent 1200 Series (Santa Clara, CA, USA) chromatographic system coupled with a diode array detector (DAD). Sample separation was performed on a C-18 column (4.6 × 150 mm) maintained at 25 °C with a 5 µL injection volume. Gradient elution was performed with solvent A (water with 2% formic acid) and solvent B (80% acetonitrile, 2% formic acid, and water). The gradient progressed from 0% to 80% B over 40 min, then returned to initial conditions.

Phenolic compounds were characterized by comparing their retention times and UV-Vis spectra with those of reference standards. Quantification was performed using calibration curves generated from standard solutions (5 mg/10 mL methanol, HPLC grade).

Table 1. Analytical parameters for hydroxycinnamic acids used for HPLC-DAD analysis.

Compound	Calibration Curve	(R2)	Range (µg/mL)	LOD 1 (µg/mL)	LOQ 2 (µg/mL)
ChA	$y=\mathrm{10,481.8}x-0.52$	0.9994	50–900	1.23	3.73
FA	$y=\mathrm{18,346.2}x+0.38$	0.9996	100–1000	3.41	10.33
SA	$y=\mathrm{38,685.6}x-0.50$	0.9992	20–500	0.33	1.10

¹ LOD—limit of detection; ² LOQ—limit of determination.

summarizes the calibration data, including the correlation coefficients (R²), limits of detection (LOD), and limits of quantification (LOQ). The contents of hydroxycinnamic acids were expressed as micrograms per gram of dried plant material (µg/g).

2.5. Determination of TPC and TFC in Extracts

The total phenolic content (TPC) in the extracts was assessed using the Folin–Ciocalteu colorimetric method as previously described [11]. The concentration of phenolics was determined by fitting the absorbance of the sample to a gallic acid calibration curve constructed over a range of 1.0 to 5.0 μg/mL (y = 0.147C + 0.002, R² = 0.9992). Results were expressed as milligrams of gallic acid equivalents (mg GAEs) per gram of dry plant material (d.w.) ± standard deviation.

Total flavonoid content (TFC) was quantified according to an established spectrophotometric protocol [12]. Absorbance values were interpolated from a standard curve prepared with catechin in the concentration range of 5.0 to 25.0 μg/mL (A = 0.046C − 0.005, R² = 0.9972). Flavonoid levels were reported as milligrams of catechin equivalents (mg CEs) per gram of dry weight ± standard deviation.

2.6. Determination of the Antioxidant Activity of the Extracts

The antioxidant capacity of the extracts was evaluated through several spectrophotometric assays. The ability of the samples to neutralize the DPPH• free radical (2,2-diphenyl-1-picrylhydrazyl) was assessed following the method described by Siddartha Baliyan et al. (2022) [13]. Sample absorbance values were interpolated into a Trolox calibration curve established across the range of 1.0–10.0 μmol/L (y = 0.022C + 0.005, R² = 0.9984) to determine DPPH radical scavenging activity.

The scavenging activity against the ABTS•⁺ radical cation (2,2′-azinobis-(3-ethylbenzothiazoline-6-sulfonic acid)) was measured according to the protocol of Yasmin Cunha-Silva et al. (2024) [14]. The activity was calculated using a standard Trolox curve (1.0–10.0 μmol/mL, y = 0.025C − 0.001, R² = 0.9977).

The total reducing power (TRP) of the dill leaf extracts was evaluated using the method of Suresh Mickymaray and Mohammed Saleh Al Aboody (2019) [15], based on a calibration curve spanning 1.0–10.0 μmol/mL (y = 0.070C + 0.022, R² = 0.9988).

The cupric ion reducing antioxidant capacity (CUPRAC) assay was performed following the procedure developed by Apaket et al. [16] using a Trolox standard curve in the range of 10.0–80.0 μmol/mL (y = 0.190C − 0.015, R² = 0.9992).

In all assays, Trolox served as the reference compound and the results were expressed as milligrams of Trolox equivalents (mg TEs) per gram of dry weight (d.w.) ± standard deviation (S.D.).

2.7. Optimization of the Extraction Procedure Using Experimental Design and Statistical Analysis

At the initial phase of the study, extractions were carried out under varying conditions of solvent concentration (50% and 100%), extraction time (20 and 80 min), and temperature (30 and 50 °C), using a solvent-to-solid ratio of 1:20 g/mL, as higher ratios did not lead to improved yields. Hydroxycinnamic acids were extracted from dill leaves using a maceration technique.

Based on the design presented in

Table 2. Experimental values and coded levels of the independent variables used for the Experimental design with the observed response values for ChA, FA, and SA.

No	Design Matrix			ChA		FA		SA
	x1 (%)	x2 (min)	x3 (°C)	qex 1 (µg/g)	qpre 2 (µg/g)	qex 1 (µg/g)	qpre 2 (µg/g)	qex 1 (µg/g)	qpre 2 (µg/g)
1	50 (−1)	20 (−1)	30 (−1)	72.34 ± 0.54 a	72.09	2.89 ± 0.06	2.94	1.06 ± 0.05	1.05
2	100 (+1)	20 (−1)	30 (−1)	65.66 ± 0.33	65.91	2.63 ± 0.07	2.58	0.87 ± 0.06	0.88
3	50 (−1)	80 (+1)	30 (−1)	92.08 ± 0.48	92.33	4.62 ± 0.10	4.61	1.85 ± 0.10	1.84
4	100 (+1)	80 (+1)	30 (−1)	84.95 ± 0.55	84.70	4.25 ± 0.18	4.26	1.68 ± 0.08	1.68
5	50 (−1)	20 (−1)	50 (+1)	77.44 ± 0.39	77.69	3.56 ± 0.12	3.59	1.12 ± 0.08	1.15
6	100 (+1)	20 (−1)	50 (+1)	71.76 ± 0.50	71.51	3.26 ± 0.20	3.23	1.03 ± 0.07	0.99
7	50 (−1)	80 (+1)	50 (+1)	103.75 ± 0.66	103.50	6.05 ± 0.28	5.98	2.19 ± 0.12	2.17
8	100 (+1)	80 (+1)	50 (+1)	95.61 ± 0.54	95.86	5.55 ± 0.20	5.62	1.99 ± 0.15	2.01

x₁—ethanol concentration; x₂—time; x₃—temperature; ^a mean values (n = 3) ± standard deviation; ¹ experimental results; ² predicted results.

, plant samples (2.5 g) were extracted using different solvent concentrations, extraction times, and temperatures. The extraction process was carried out using a bath thermostat. After filtration through filter paper with a 6 μm pore size (Whatman, Maidstone, Kent, UK), the extracts were stored in a flask.

A first-order polynomial model (Equation (1)) was applied to fit the experimental data using linear regression, establishing a mathematical correlation between the process variables x₁, x₂, and x₃ and the responses y₁ (content of ChA), y₂ (content of FA), and y₃ (content of SA):

$$y=b_o+b_1{x}_1+b_2{x}_2+b_3{x}_3+b_{12}{x}_1{x}_2+b_{13}{x}_1{x}_3+b_{23}{x}_2{x}_3+b_{123}{x}_1{x}_2{x}_3$$

(1)

where $x_1$, $x_2$, and $x_3$ are identified as the ethanol concentration, time, and temperature, respectively. Terms $x_1{x}_2$, $x_1{x}_3$, and $x_2{x}_3$ each describe the combined effect of two variables and $x_1{x}_2{x}_3$ establishes the interaction of three idenpendent variables. $b_o$ is the constant regression coefficient, $b_i$ is the linear regression coefficient, and $b_{ij}$ and $b_{ijk}$ are the regression coefficients of 2- and 3-factor interactions, respectively.

2.8. The Kinetics of Extraction

Measured amounts of dill leaves and extraction solvent (solvent-to-solid ratio of 1:20 g/mL) were combined in a series of 250 mL Erlenmeyer flasks. The mixtures were macerated for varying durations—5, 10, 15, 20, 40, 60, and 80 min. The temperature was precisely regulated at 30 ± 0.1 °C using a Julabo MP 5A Open Bath Circulator (JULABO, Allentown, PA, USA). At the end of each extraction interval, one vessel was removed from the water bath and the liquid phase was isolated from the plant residue using vacuum filtration. The concentration of hydroxycinnamic acids in the resulting extracts was analyzed by HPLC-DAD. The entire process was repeated at two additional temperatures: 40 ± 0.1 °C and 50 ± 0.1 °C.

2.9. Kinetic Models

Five kinetic models involving two parameters each were evaluated: the unsteady-state diffusion model, parabolic diffusion model, power law model, Ponomaryov’s equation, and Elovich’s equation—all commonly applied in the recovery of solutes from various plant materials [10,17,18].

Table 3. Equations of extraction kinetic models and thermodynamics parameters.

	Non-Linear	Linear
Kinetic Model
Unsteady-state diffusion model	$q_i/q_o=\left(1-b\right)e^{-kt}$	$ln\left(q_i/q_o\right)=ln\left(1-b\right)-kt$
Parabolic diffusion model		$\overline{q}=A_o+A_1{t}^{1/2}$
Power law model	$\overline{q}=B{t}^n$	$ln\overline{q}=lnB+nlnt$
Ponomaryov’s equation		$1-q_i/q_o=b^{’}+k^{’}t$
Elovich’s equation		$\overline{q}=E_o+E_{1}lnt$
Thermodynamic parameters and units
Activation energy (kJ/mol)	$k=A{e}^{{-E}_a/RT}$	$lnk=lnA-{\displaystyle \frac{E_a}{R}}{\displaystyle \frac{1}{T}}$
$\mathrm{Standard} \mathrm{entropy} ∆H^0$(kJ/mol)		$ln{K}_e=-{\displaystyle \frac{∆H^0}{R}}{\displaystyle \frac{1}{T}}+{\displaystyle \frac{∆S^0}{R}}$
$\mathrm{Standard} \mathrm{entropy} ∆S^0$(J/mol K)		$ln{K}_e=-{\displaystyle \frac{∆H^0}{R}}{\displaystyle \frac{1}{T}}+{\displaystyle \frac{∆S^0}{R}}$
$\mathrm{Gibbs} \mathrm{free} \mathrm{energy} ∆G^0$(kJ/mol)	$∆G^0=∆H^0-T∆S^0$
Temperature extraction coefficient γ	${\overline{q}}_T={\overline{q}}_{T_o}{\gamma }^{T/10}$	$ln{\overline{q}}_T=ln{\overline{q}}_{T_0}+{\displaystyle \frac{T}{10}}ln\gamma$

b and $b^{’}—$ washing coefficient according to the unsteady-state diffusion model and the model Ponomaryov, respectively; $k$ and $k^{’}—$ slow extraction coefficient according to the unsteady-state diffusion model and the model Ponomaryov, min⁻¹; $A_0$ and $A_1$—parameters of the parabolic diffusion model: washing coefficient and diffusion rate constant (min^−0.5); B—parameter of the power law model incorporating the characteristics of the extraction system (min⁻ⁿ); n—diffusion exponent of the power law model (L); E₀ and E₁—parameters of the Elovich equation, respectively; q—the hydroxycinnamic acid content in the plant material after the period t (mg/g of dry plant material); $q_0—$ the hydroxycinnamic acid amount in the plant material (mg/g dm); $\overline{q}—$ extraction yield ($=q/q_0$); t—time, min; T—absolute temperature (K); K_e—equilibrium constant; m_L/m_S—m_L is the amount of hydroxycinnamic acid in liquid at equilibrium temperature (T) and m_S is the amount of these acids in solid at T; R—gas constant.

presents an overview of the empirical equations along with their linearized forms.

2.10. Validity Kinetic Models

$$-R^2={\displaystyle \frac{\sum _{i=1}^N{\left(q_{ex}-q_{pre}\right)}^2}{\sum _{i=1}^N{\left(q_{ex}-q_m\right)}^2}}$$

(2)

$$RMS=\sqrt{{\displaystyle \frac{1}{N}}{\sum }_{i=1}^N\left({\displaystyle \frac{q_{ex}-q_{pre}}{q_{ex}}}\right)}$$

(3)

In these equations, $q_{ex}$ and $q_{pre}$ represent the experimentally observed and predicted concentrations of hydroxycinnamic acids, respectively, $q_m$ denotes the average experimental value, and N is the total number of experimental data points. A higher R² value alongside a lower RMS indicates a better agreement between the model and experimental results.

2.11. Thermodynamic Study

The temperature dependence of the extraction process was assessed using the Arrhenius equation to determine the activation energy based on the k coefficient from the unsteady-state diffusion model (

Table 4. ANOVA of the first order polynomial model for the response variables (actual values).

HA	SOV	x1	x2	x3	x1x2	x1x3	x2x3	x1x2x3	Error	Total
ChA	SS 1	95.4271	994.3557	140.5326	1.0585	0.00001	15.4846	0.5050	1.5537	1248.918
	Df 2	1	1	1	1	1	1	1	8	15
	MS 3	95.4271	994.3557	140.5326	1.0585	0.00001	15.4846	0.5050	0.19422	83.2612
	F-Value	491.33	5119.74	723.57	5.4500	0.4000	79.727	2.6001
	p-Value	<0.00001 4	<0.00001	<0.00001	0.047823	0.544737 a	0.00002	0.145522
FA	SS	0.2556	8.2621	2.0301	0.0120	0.0036	0.2556	0.0010	0.0194	10.8394
	Df	1	1	1	1	1	1	1	8	15
	MS	0.2556	8.2621	2.0301	0.0120	0.0036	0.2556	0.0010	0.00242	0.7226
	F-Value	105.61	3414.0	838.88	4.9586	1.4876	105.61	0.4132
	p-Value	<0.00001	<0.00001	<0.00001	0.056579	0.257324	<0.00001	0.538333
SA	SS	0.0528	1.6471	0.0946	0.0010	0.0006	0.02311	0.0021	0.00416	1.8255
	Df	1	1	1	1	1	1	1	8	15
	MS	0.0528	1.6471	0.0946	0.0010	0.0006	0.02311	0.0021	0.00052	0.12169
	F-Value	101.53	3167.5	181.92	1.9230	1.1538	44.442	4.0384
	p-Value	<0.00001	<0.00001	<0.00001	0.202942	0.314082	0.000158	0.07933

$x_1$, $x_2$, and $x_3$ represent ethanol concentration, time, and temperature, respectively. SOV: source of variation; ¹: sum of squares; ²: degree of freedom; ³: mean of square; ⁴: <0.00001, highly significant; ^a: p ≥ 0.05, not significant.

). In addition, key thermodynamic parameters (∆H⁰, ∆S⁰, and ∆G⁰) were calculated from the van’t Hoff and Gibbs equations to evaluate the spontaneity and energetic nature of the extraction [10,19].

3. Results and Discussion

3.1. Optimization of the Hydroxycinnamic Acid Extraction Process

Analysis of the ethanol extracts of dill leaves revealed the presence of chlorogenic, ferulic, and sinapic acids. These metabolites were documented in dill leaves in prior investigations [20]. Among the phenolic acids quantified in this work, ChA was the most prevalent, followed by FA and SA. A comparable trend was reported by Vallverdú-Queralt et al. [1] and Shan et al. [21].

To fully utilize these compounds in cosmetic formulations, dietary supplements, and functional foods, the extraction process must first be optimized to maximize the recovery of hydroxycinnamic acids from natural sources.

The influence of certain extraction variables can sometimes be more significant than others. The use of insignificant variables in the extraction process may lead to incorrect or inappropriate results. Thus, factor screening is essential for optimizing the extraction process. The identification of extraction parameters that significantly impact the recovery yield of chlorogenic acid (ChA), ferulic acid (FA), and sinapic acid (SA) from dill leaves was performed using a 2³ factorial design. A total of eight experimental combinations were tested, with each extraction performed twice.

This approach was used to determine the contribution of each selected individual parameter and their combined effects on the responses. Moreover, the effect of each parameter and the interplay between them was evaluated based on their significance levels (p < 0.05).

The selection of factor levels was guided by preliminary screening results, defined parameter ranges, and information from the literature. For temperature, 50 °C was set as the upper limit due to the potential degradation of phenolic compounds at elevated temperatures, while 30 °C was chosen as the lower limit to assess extraction efficiency at a lower temperature. The upper time limit was set at 80 min, as longer extraction times (>80 min) did not significantly influence the hydroxycinnamic acid content.

For ethanol concentration, 50% ethanol was selected as it has been reported to be the optimal extraction solvent for chlorogenic acid [22,23]. The upper limit was set at 100% ethanol to evaluate extraction efficiency in a pure solvent.

In Table 2, the experimental design parameters are listed alongside the measured and model-predicted outcomes.

The suitability of the linear first-order model was assessed through analysis of variance (ANOVA) and multiple regression techniques. The corresponding results are summarized in Table 4. The significance of the regression model was evaluated using the F-statistic and associated p-values.

The analysis showed that both linear and interaction terms were statistically significant (p < 0.05). The F-values for ethanol concentration (x₁), extraction time (x₂), and temperature (x₃) ranged from 101.54 to 5119.74, confirming strong effects on extraction yield. Extraction time (x₂) had the greatest impact, followed by temperature (x₃) and ethanol concentration (x₁). Among two-factor interactions, the combination of time and temperature (x₂x₃) notably influenced the yield of all hydroxycinnamic acids, while x₁x₂ was especially important for ChA extraction. The three-way interaction (x₁x₂x₃) was not significant (p > 0.05). These findings highlight the dominant role of extraction time in optimizing recovery efficiency.

An increase in extraction time from 20 to 80 min led to a marked rise in the content of hydroxycinnamic acids. This observation aligns with Fick’s second law of diffusion, which suggests that prolonged extraction enhances the release of polyphenolic compounds [24]. However, it is important to note that the optimal duration of extraction can vary depending on the specific characteristics of the plant material [25].

As shown in Table 1, the extraction of hydroxycinnamic acids was more efficient at 50 °C compared to 30 °C. These findings are consistent with previously published studies reporting that elevated temperatures enhance extraction, particularly from water–ethanol mixtures, in Lamiaceae herbs [26]. Temperature is a key factor influencing polyphenol extraction from plant matrices, as elevated temperatures typically enhance the solubility and diffusion rates of target compounds. Additionally, elevated temperatures decrease the viscosity and surface tension of the solvent system, leading to faster mass transfer and improved extraction efficiency [27]. However, excessive heating can result in solvent loss through evaporation and potential thermal degradation of sensitive polyphenols, negatively impacting yield [28]. Therefore, we selected a temperature range of 30–50 °C, where the interaction between extraction temperature and time (x₂x₃) was found to significantly increase the concentration of hydroxycinnamic acids.

Choosing a suitable solvent or solvent mixture plays an essential role in optimizing the extraction of polyphenols from plant sources. This decision is affected by a number of factors, including solvent polarity, the solubility of the target compounds, chemical reactivity, safety considerations, and economic viability. Studies have shown that binary mixtures of alcohol and water are generally more effective for extracting phenolic compounds than single-solvent systems [29]. The effect of ethanol–water solvent composition (50% and 100% v/v) on extraction of hydroxycinnamic acids from dill leaves was studied. It can be seen that the ChA, FA, and SA content increased from 65.66 µg/g, 2.63 µg/g, and 0.87 µg/g for 100% ethanol to 72.34 µg/g, 2.89 µg/g, and 1.06 µg/g for 50% ethanol, given an extraction time of 20 min and an extraction temperature of 30 °C (Table 1). Therefore, 50% ethanol is the optimal solvent. The likely explanation for the higher recovery of hydroxycinnamic acids using 50% ethanol is that the presence of water increases the solvent’s polarity and disrupts hydrogen bonds, thereby enhancing the extraction process [30]. In addition, incorporating water into the solvent system promotes swelling of the plant tissue, which increases the surface area available for solvent penetration and improves mass transfer. This may explain the higher efficiency of 50% ethanol in extracting hydroxycinnamic acids. Similar trends were observed by Cunha-Silva et al. [31], who reported that a 50% ethanol solution was most effective for recovering antioxidant polyphenols from Thymus lotocephalus. Consistent results were also reported by Jovanović et al. [32], where a 50% ethanol–water mixture yielded the highest levels of total polyphenols from Thymus serpyllum leaves.

It is also important that the regression models developed (Table 4) accurately represent the behavior of the system under real conditions.

Analysis of variance (ANOVA) was undertaken to analyze the significance of the regression models applied to the three response variables, considering both individual linear effects and interaction terms. The statistical relevance for every model component was determined by the F-test and corresponding p-values. Terms with larger F-values and smaller p-values were considered more significant, with p-values below 0.05 indicating statistically significant model terms.

The quality of the model fit was evaluated using the coefficient of determination (R²), which reflects how well the polynomial model (Equation (1)) represents the experimental data. The R² values for the responses y₁, y₂, and y₃ were 0.9987, 0.9982, and 0.9977, respectively, indicating that the model accounted for over 99% of the variability in the observed responses. Further validation was supported by the adjusted R² values—0.9976 for y₁, 0.9962 for y₂, and 0.9957 for y₃—demonstrating strong model performance after accounting for the number of predictors. The coefficient of variation (CV) was also calculated to assess the precision of the model predictions. The CV values for y₁, y₂, and y₃ were 0.53%, 1.20%, and 1.55%, respectively, all of which fall well below the 10% threshold, confirming the high reproducibility and reliability of the experimental data.

The relationships between responses and the three tested variables are presented in the following equations (Equations (4)–(6)):

$$y_1{=82.948-3.454x}_1+11.148x_2+4.191x_3-0.364x_1{x}_2+1.391x_2{x}_3$$

(4)

$$y_2=4.101-0.179x_1+1.016x_2+0.505x_3+0.179x_2{x}_3$$

(5)

$$y_3=1.474-0.081x_1+0.454x_2+0.109x_3+0.054x_2{x}_3$$

(6)

Predicted outcomes for the respective variables can be found in Table 2. Table 2 demonstrates that the polynomial regression models align well with the experimental data. The observed data were matched against the model-predicted values, demonstrating that the utilized models successfully pinpointed the optimal conditions for the targeted extraction of hydroxycinnamic acids from dill leaves. As noted by Aklilu et al. [33], positive coefficients in the model suggest synergistic effects, while negative coefficients imply antagonistic effects among the variables. In this study, the negative coefficient for ethanol concentration (x₁) suggests it had an inhibitory effect on the yield of hydroxycinnamic acid. Conversely, the positive coefficients for extraction time (x₂) and temperature (x₃) indicate that increases in these parameters contributed to enhanced extraction yields.

The highest yield of hydroxycinnamic acids from dill leaf extract was achieved under the following optimized conditions: 50 °C extraction temperature, 80 min extraction time, and 50% ethanol concentration.

The response values projected by the model for the selected conditions are chlorogenic acid (103.50 μg/g), ferulic acid (5.98 μg/g), and sinapic acid (2.17 μg/g), while the experimental values were chlorogenic acid (103.75 μg/g), ferulic (6.05 μg/g), and sinapic acid (2.19 μg/g). The close match between the predicted and observed values supports the validity of the 2³ factorial design for modeling the extraction process.

3.2. Phenolic Content and Antioxidant Activity of Prepared Extracts

The prepared extracts were tested by TPC, TFC, DPPH, ABTS, FRP, and CUPAC spectrophotometric assays, and the results showed that dill extract is a rich source of polyphenolic compounds and has potential antiradical and antioxidant effects.

The results (

Table 5. Total phenolic content (TPC), total flavonoid content (TFC), and antioxidant activity dill leaves extracts established by different assays.

Ethanol %	TPC mg GAEs/g	TFC mg CEs/g	DPPH μmol TEs/g	ABTS μmol TEs/g	FRP μmol TEs/g	CUPRAC μmol TEs/g
50	2.859 ± 0.105	0.728 ± 0.011	14.92 ± 0.22	18.22 ± 0.38	26.55 ± 0.68	38.77 ± 1.05
100	2.532 ± 0.098	0.655 ± 0.032	13.11 ± 0.30	15.48 ± 0.33	24.43 ± 0.52	35.66 ± 0.88

) showed different content of target compounds and antioxidant activity depending on the extraction solvent.

According to the results obtained, lower values for TPC and TFC were found in extracts prepared using 100% ethanol as a solvent. Additionally, antioxidant tests followed the trends of previous analyses, wherein the 50% ethanol extract showed greater activity. Comparable findings have previously been reported regarding the antioxidant potential of dill extracts obtained using various solvents. Earlier DPPH studies on water, ethanol, and acetone extracts revealed that water extracts showed the highest DPPH• radical scavenging activity, followed by the ethanol extracts, while the extracts obtained with acetone demonstrated minimal activity [4].

3.3. Kinetics of Hydroxycinnamic Acid Extraction

3.3.1. Hydroxycinnamic Acid Variation with Extraction Time

The effect of different extraction times (5, 10, 15, 20, 30, 40, 60, and 80 min) on ChA, FA, and SA extraction from dill leaves are presented in Figure 1. Extraction was conducted at 30, 40, and 50 °C using 50% ethanol. A longer extraction duration, ranging from 5 to 80 min, resulted in higher yields of hydroxycinnamic acids.

The extraction of hydroxycinnamic acids from dill leaves appears to follow two distinct phases: an initial rapid phase often referred to as surface washing and a slower phase driven by diffusion. During the early stage of extraction, especially within the first 10 min, ethanol efficiently dissolves compounds located on or near the surface of the plant particles. This is reflected in the sharp rise in extracted compounds, where ChA, FA, and SA reached 69.96, 2.20, and 1.06 μg/g, corresponding to 76.0%, 62.5%, and 57.3% of their final concentrations (at 30 °C). Beyond this point, the extraction rate slows down considerably, suggesting that internal diffusion governs the process. This two-phase kinetic profile is in line with diffusion-limited extractions observed in other plant systems, such as grape seeds, pumpkin seeds, and leafy materials [34,35,36].

3.3.2. Kinetic Modeling of Hydroxycinnamic Acid Extraction

Mathematical modeling serves as a valuable tool in extraction process engineering, particularly for analyzing extraction kinetics and optimizing process design to optimize resource use and reduce both time and chemical demands. Various kinetic models have been reported in the literature to describe the transfer of target compounds from solid matrices into solvents during solid–liquid extraction.

Within this research, five widely used models were applied to fit the experimental data and assess the overall extraction behavior. These included the unsteady-state diffusion model, parabolic diffusion model, power law model, Ponomaryov’s model, and Elovich’s model. The performance of each model was evaluated to identify which one most closely matched the experimental observations.

Table 6. Values of kinetics parameters for hydroxycinnamic acid extraction.

Parameters	Clorogenic Acid			Ferulic Acid			Sinapic Acid
	30 °C	40 °C	50 °C	30 °C	40 °C	50 °C	30 °C	40 °C	50 °C
Model 1
b	0.805	0.812	0.816	0.713	0.736	0.761	0.703	0.709	0.720
k (1/min)	1.86 × 10−3	1.88 × 10−3	2.15 × 10−3	2.91 × 10−3	3.10 × 10−3	3.41 × 10−3	3.42 × 10−3	3.77 × 10−3	4.12 × 10−3
RMS (%)	0.21	0.15	0.18	0.55	0.65	0.62	1.98	1.85	1.73
R2 (%)	99.81	99.84	99.89	99.44	99.27	99.51	99.02	99.32	99.50
Molel 2
A0	0.439	0.433	0.426	0.234	0.241	0.245	0.197	0.179	0.162
A1	2.87 × 10−2	3.38 × 10−2	4.05 × 10−2	3.78 × 10−2	4.50 × 10−2	5.63 × 10−2	4.56 × 10−2	5.30 × 10−2	6.23 × 10−2
RMS (%)	2.00	2.05	1.81	2.89	2.35	3.73	4.62	3.30	3.63
R2 (%)	95.20	96.00	97.71	97.63	98.43	98.13	94.73	97.83	97.83
Model 3
n	0.128	0.142	0.164	0.236	0.267	0.268	0.268	0.296	0.323
B	0.389	0.386	0.380	0.201	0.200	0.228	0.184	0.176	0.172
RMS (%)	2.21	1.17	2.60	3.88	3.84	4.34	5.82	4.10	4.88
R2 (%)	94.15	96.32	95.22	93.55	96.51	95.96	91.72	97.48	95.94
Equation (1)
b′	0.514	0.524	0.536	0.336	0.360	0.397	0.318	0.322	0.330
k′ (1/min)	2.44 × 10−3	2.81 × 10−3	3.36 × 10−3	3.12 × 10−3	3.79 × 10−3	4.65 × 10−3	3.81 × 10−3	4.39 × 10−3	5.16 × 10−3
RMS (%)	0.24	0.26	0.12	0.44	0.43	0.51	2.78	1.03	0.80
R2 (%)	99.66	99.60	99.95	99.69	99.74	99.88	98.21	99.78	99.82
Equation (2)
E0	0.346	0.320	0.380	0.104	0.085	0.052	0.045	0.003	0.050
E1	0.076	0.081	0.086	0.103	0.123	0.153	0.122	0.143	0.169
RMS (%)	3.07	3.44	4.58	4.81	4.74	5.73	7.12	6.30	6.79
R2 (%)	89.96	88.76	90.10	91.93	90.08	92.24	86.97	91.76	90.19

Model 1—unsteady-state diffusion; Model 2—parabolic diffusion; Model 3—power law; Equation (1)—Ponomaryov’s; Equation (2)—Elovich’s. RMS—root mean square; R²—coefficient of determination. Note: All coefficients and corresponding explanations are provided in Table 3.

shows the calculated kinetic parameters recorded at various temperatures using equations for the unsteady-state diffusion, parabolic diffusion, power law, Ponomaryov’s, and Elovich’s models summarized in Table 2. The kinetic parameters for the unsteady-state diffusion, parabolic diffusion, power law, Ponomaryov’s, and Elovich’s models were obtained by plotting $ln\left(q_i/q_o\right)$ against t, $\overline{q}$ versus $\sqrt{t}$, $ln\overline{q}$ versus $lnt$, $q_o-q_i/q_o$ versus t, and $\overline{q}$ versus $lnt$, respectively.

It is evident from Table 6 that the extraction temperature had a notable influence on nearly all parameters across the evaluated kinetic models.

The results showed that in both the unsteady-state diffusion and Ponomaryov models, the parameters b, k, b′, and k′ increased as the extraction temperature rose. This trend supports the observed enhancement in hydroxycinnamic acid yields at elevated temperatures. Higher temperatures likely accelerate the extraction process by improving solute solubility and increasing diffusion rates. In the early stages of extraction, mass transfer is notably rapid due to a strong concentration gradient between the interior of the plant matrix and the surrounding solvent. As temperature rises, molecular diffusion becomes more efficient and the solvent is more readily saturated with bioactive compounds. Additionally, heat may cause the plant tissue to soften and the cell wall structure to weaken, thereby facilitating the release of hydroxycinnamic acids into the solvent phase [36].

In contrast, the kinetic parameters E₀ and E₁ for the Elovich model followed different trends with temperature increases. A comparable observation was reported by Menkiti et al. [10], who investigated oil extraction from T. catappa using n-hexane as the solvent. While E₁ increased with the increase in temperature like the unsteady-state diffusion and Ponomarev models, E₀ did not have a definite trend, as can be observed in

Table 7. Thermodynamic parameters of hydroxycinnamic acid extraction from dill leaves.

	Temperature	Ea	K	∆G0	∆H0	∆S0	γ
	(°C)	(kJ/mol)		(kJ/mol)	(kJ/mol)	(K/Jmol)
ChA	30	5.85	2.53	−3.55	3.33	22.69	1.062
	40		3.13	−3.78
	50		4.19	−4.01
FA	30	6.46	1.40	−5.67	1.98	25.23	1.122
	40		1.90	−5.92
	50		3.23	−6.17
SA	30	7.59	1.71	−3.87	3.39	23.98	1.080
	40		2.08	−4.13
	50		2.80	−4.35

. This identified trend observed for the kinetic parameter E₀ also resulted in a generally lower linear correlation coefficient (R²) (Table 6) obtained for the Elovich model when compared which those of the unsteady-state diffusion and Ponomarev models. Additionally, when increasing the extraction temperature, the parameters A₁ and n increased, A₀ decreased, and B followed different trends.

3.3.3. Comparison of the Kinetic Models

To identify the most appropriate kinetic model for describing the extraction of hydroxycinnamic acids from dill leaves, the fit between experimental results and model predictions was assessed using the coefficient of determination (R²) and root mean square error (RMS). A strong model fit is indicated by a higher R² and a lower RMS value.

All five kinetic models applied under the given conditions successfully represented the extraction behavior, as evidenced by the high coefficient of determination (R² > 0.88) and low RMS values (<7.5). Nevertheless, in relation to the other models, the Elovich model exhibited the highest RMS values (3.07–7.12) in all experiments, making it the least suitable for fitting the experimental data.

The unsteady-state diffusion model and Ponomaryov’s equation yielded similar RMS values, indicating comparable predictive accuracy. The lowest RMS values were obtained from the unsteady-state diffusion model (0.15–1.98%), confirming it as the most accurate model.

Furthermore, the coefficient of determination (R²) was highest for the unsteady-state diffusion model, followed by Ponomaryov’s equation, the parabolic diffusion model, the power law model, and finally Elovich’s equation.

Based on these results, the unsteady-state diffusion model and Ponomaryov’s equation were identified as the best models for describing the kinetics of hydroxycinnamic acid extraction from dill leaves, as they exhibited the lowest RMS values and the highest R² values.

3.4. Thermodynamic Analysis

The temperature extraction coefficient (γ) was determined by linear regression of ln $\stackrel{-}{\mathrm{q}}$_T versus T/10. The activation energy (Ea) was calculated from the slope of the linear regression between ln k (based on the unsteady-state diffusion model) and 1/T. The Gibbs free energy change (∆G⁰), enthalpy change (∆H⁰), and entropy change (∆S⁰) were estimated using standard thermodynamic relationships involving ln K and 1/T. All equations used for these calculations are provided in Table 3, while the final calculated values of γ, Ea, K, ∆G⁰, ∆H⁰, and ∆S⁰ are presented in Table 7.

The yields of ChA, FA, and SA increased by factors of 1.062, 1.122, and 1.080, respectively, with each 10 °C rise in temperature. These temperature coefficients are in line with the values reported for oil extraction from Cannabis sativa seeds (1.012–1.025) [37] and from olive cake (1.02–1.14) [38].

The estimated activation energy values (Table 7) for the process with a slow extraction coefficient (k) (under the unsteady-state diffusion model) were 5.85 kJ/mol for ChA, 6.46 kJ/mol for FA, and 7.59 kJ/mol for SA. The data suggest that temperature had a greater impact on the extraction rate of sinapic acid compared to that of chlorogenic acid (ChA), which showed lower temperature sensitivity. There are no previous reports in the literature regarding the activation energy of hydroxycinnamic acid extraction from dill leaves. Nonetheless, the obtained values correspond closely with the findings reported for similar bioactive substances in the literature.

In the case of grape seed polyphenol extraction with 50% aqueous ethanol, activation energies between 1.10 and 7.70 kJ/mol have been documented [39]. For flavonoids extracted from rosemary leaves using 100% methanol, the activation energy was 5.35 kJ/mol [40]. The Ea for polyphenolic extraction from apple pomace with 50% ethanol was 10.2 kJ/mol [8], while for jamun seed extraction using water, the value was 9.48 kJ/mol [41].

An upward trend in the equilibrium constant (K_e) was observed with temperature elevation, reflecting higher equilibrium levels of ChA, FA, and SA (Table 7).

The values of enthalpy change (∆H⁰) and entropy change (∆S⁰) for the extraction of hydroxycinnamic acids from dill leaves using 50% ethanol were positive across the range of extraction temperatures. This confirms that the extraction process is endothermic and irreversible. This suggests that, for industrial applications, moderate heating can enhance extraction efficiency, although careful energy management would be required to maintain cost-effectiveness and process sustainability.

Comparable findings have been reported in studies involving the isolation of different biologically active substances employing diverse extraction solvents. For instance, the isolation of flavonoids from Phyllanthus emblica with water yielded an enthalpy change of 9.53 kJ/mol and an entropy change of 30.93 J/mol·K [42]. In another study, flavonoid extraction from rosemary leaves using ethanol resulted in values of 1.60 kJ/mol for enthalpy and 25.91 J/mol·K for entropy [35]. Similarly, for total phenolics extracted from hop with aqueous ethanol, the corresponding values were 7.32 kJ/mol and 60.74 J/mol·K, respectively [43].

The Gibbs free energy change (∆G⁰) values for the extraction process ranged from −3.55 to −4.01 kJ/mol for ChA, −5.67 to −6.17 kJ/mol for FA, and −3.87 to −4.35 kJ/mol for SA. Since the ∆G⁰ values were negative for all extractions, the process was confirmed to be feasible and spontaneous. Additionally, the spontaneity of hydroxycinnamic acid extraction increased with rising extraction temperature. A similar trend has been observed in vanillic acid extraction from pumpkin seeds (−5.38 to −5.91 kJ/mol) [40], total phenolics from hop (−11.99 to −10.78 kJ/mol) [43], and hempseed oil (−2.41 to −5.17 kJ/mol) [44].

4. Conclusions

To optimize extraction yield, a 2³ factorial experimental design was employed to evaluate the effects of key variables. ANOVA results confirmed that ethanol concentration, extraction time, and temperature all had statistically significant impacts. The developed linear regression models demonstrated strong correlations and effectively guided the optimization of chlorogenic (ChA), ferulic (FA), and sinapic (SA) acid extraction from dill leaves. All five kinetic models assessed—unsteady-state diffusion, parabolic diffusion, power law, Ponomaryov’s, and Elovich’s—provided a satisfactory fit to the experimental data, as evidenced by their high R² and low RMS values. Among them, the unsteady-state diffusion model exhibited the best performance, followed by Ponomaryov’s model. Thermodynamic parameters (∆G⁰, ∆H⁰, and ∆S⁰) further indicated that the extraction process was spontaneous (∆G⁰ < 0), irreversible, and endothermic (∆H⁰ > 0 and ∆S⁰ > 0). These findings support the potential application of this extraction approach in the food, pharmaceutical, and cosmetic industries. The use of ethanol–water mixtures and moderate operating conditions contributes to the advancement of green and sustainable strategies for recovering hydroxycinnamic acids.