The absorption process of water molecules in of Matricaria recutita L. "chamomile", Calendula officinalis L. "marigold" and Plantago major L. "plantain" seeds is characterized through mathematical modeling. The method used was the static method according to the analytical technique of hygroscopic equilibrium at 27 ± 2 °C. The experimental values were fitted to six mathematical models and the curve was classified according to its shape and levels of absorption. The seeds reached equilibrium starting from 144 hours after the experiment began and described the absorption process above 82.6% relative moisture. The Halsey model was the one that best described the sorption for all species. The GAB model established the range of moisture content that the seeds must have in order to guarantee maximum durability during the storage stage.

Introduction

In Cuba, where high temperatures and relative humidity prevail, seed moisture content is a determining factor in long-term preservation. The moisture content of this biological material varies depending on the surrounding environment; therefore, the organic processes that occur during exposure to the specific atmosphere can change depending on the species, morphological characteristics, and even chemical composition.

In this sense, hygroscopicity is defined as the ability of a product to absorb or release moisture until it reaches equilibrium with the surrounding environment (Rovelli) et al., 2020). Hence, the knowledge of the hygroscopic properties of seeds of species such as Matricaria recutita L. "chamomile", Calendula officinalis L. "calendula" and Plantago Major L. "plantain" are of great value for proper long-term preservation, since this property is the abiotic factor that most effects quality with respect to temperature (Prieto-Díaz et al., 2022). These properties allow the establishment of optimal storage conditions, since equilibrium moisture primarily regulates the metabolic activity and longevity of the seed (Villanueva and Rojas, 2020). Seed quality is the starting point for obtaining plant materials of high pharmacopoeial value. Matricaria recutita L. "chamomile" is widely valued for its secondary metabolites with anti-inflammatory, antispasmodic, and anxiolytic properties, mainly essential oils such as chamazulene, bisabolol , and flavonoids (El Joumaa and Borjac , 2022; Dai et al., 2023). Calendula Calendula officinalis L. is valued for its triterpenoids, saponins, and flavonoids, which are attributed with healing, anti-inflammatory, antimicrobial, and antioxidant activities, and is widely used in dermal and cosmetic formulations (Shahane et al., 2023; Chauhan et al., 2022). Plantago, for its part, Plantain L. major "plantain" is recognized for its iridoids ( aucubin and catalpol), flavonoids and polysaccharides (mucilage), which give it demulcent, expectorant, anti-inflammatory and healing properties, supported by recent pharmacological studies (Adom et al., 2022; Najafi et al., 2020). Preserving the viability and biochemical integrity of these seeds is therefore a critical step to ensure the traceability and efficacy of the phytopharmaceuticals derived from them, which underlines the importance of studies focused on optimizing their storage.

For this reason, much research has focused on obtaining optimal conditions for proper storage, such as studying seed sorption processes at different temperatures and in different types of containers, among other factors. This underscores the importance of studies focused on optimizing storage, with absorption isotherm modeling being a fundamental tool for this purpose. The objective of this work was to describe the moisture absorption process in seeds of medicinal species.

Postharvest Biology and Technology Laboratory of the "Alejandro de Humboldt" Institute of Fundamental Research in Tropical Agriculture (INIFAT), located in Santiago de las Vegas, Boyeros municipality, Havana, Cuba.

Experimental development: 

The initial moisture content of the seeds was determined in triplicate, according to the gravimetric method (2 hours at 130 °C) and for this purpose an OHAUS Explorer brand analytical balance with a precision of 0.0001 g and a MEMMERT brand oven were used.

The hygroscopic equilibrium analytical technique was used to determine the absorption isotherm. For this purpose , 1.0 g of Matricaria recutita L. "chamomile" and Plantago seeds were placed in a container. major L. "plantain", as well as 0.5 g of Calendula seed officinalis L. "calendula" in triplicate in desiccators with different saturated saline solutions at room temperature (27 ± 2 °C) until equilibrium was reached (Table 1). The weight of the sample was determined daily, until a constant weight was obtained (when the difference between two consecutive weighings was less than 0.001 g) and subsequently the moisture contents were calculated using the AOAC method (1990).

                                                                                         Table 1: Saline solutions used in hygroscopic equilibrium

The experimental equilibrium data were fitted using the equations in Table 2. The quality of the fit was assessed from the linear correlation coefficient (R 2 ) and the relative mean error percentage (% E).

No.	Equation	Model name
1		Peleg
2		Halsey
3		GAB
4		Adam and Shove
5		Caurie
6		D' Arcy - Watt

                                                               Table 2: Mathematical models applied to absorption isotherms (Cárdenas and Ramírez, 2021).

Where:

X e : Equilibrium moisture content ( gag -1 m s)

a w : Water activity.

X m : Moisture content of the monolayer (gg -1 m s )

X s : Safety constant ( gg -1 ms)

K and K' of the DAW model: Represent the number of absorption sites with strong bonds.

k, k' of the DAW model: Number of absorption sites with multi -molecular bonds.

A of the Peleg model: Represents mass transfer.

C in the Peleg model: Represents the absorption capacity.

a, b, c, d, K, A, B, V, C, D:Characteristic constants of the product and related to the heat of absorption.

Figure 1 shows that during exposure of the seeds to relative humidities between 52 and 100% at room temperature, the absorption process occurred, reaching maximum values of 1.0218 for Matricaria recutita L. "chamomile". From 144 h after the start of the process, for all environments, the Plantago seeds major L. "plantain" stabilized, followed by Calendula officinalis L. "calendula" at 168 h and Matricaria recutita L. "chamomile" at 300 h.

Figure 1: Variation in equilibrium moisture content of Matricaria recutita L. "chamomile" seeds, Calendula officinalis L. "marigold" and Plantago major L. "plantain" over time for different relative humidity values.

The equilibrium moisture content values for the three species under study are shown in Table 3. It can be seen that the highest values were obtained for water activities greater than 0.826; which corresponds to the beginning of the water molecule absorption process.

                                                                                       Table 3: Equilibrium moisture content of seeds at room temperature

The experimental data were fitted to different mathematical models as shown in Figure 2 and Table 4 reflects the coefficients of each evaluated model. According to Brunauer 's classification et al. (1940) and according to the C < 2>Flory - Huggins isotherms and are characteristic of low adsorbate -adsorbent interactions and are associated with a probable small absorption strength in the monolayer (Hernández et al., 2023).

Leyenda:

A&S: Modelo de Adam y Shove

DAW: Modelo de D´ Arcy-Watt 

X m : Moisture content of the monolayer (gg -1 m s)

X s : Safety constant ( gg -1 ms)

K and K' of the DAW model: Represent the number of absorption sites with strong bonds

k, k' of the DAW model: Number of absorption sites with multimolecular bonds 

A of the Peleg model: Represents mass transfer

C in the Peleg model: Represents the absorption capacity

a, b, c, d, K, A, B, V, C, D:Characteristic constants of the product and related to the heat of absorption.

Figure 2: Moisture absorption isotherms of Matricaria recutita L. "chamomile" seeds, Calendula officinalis L. "marigold" and Plantago major L. "plantain" adjusted to the Halsey model

The hygroscopic equilibrium experiment of the seeds of Matricaria recutita L. "chamomile", Calendula officinalis L. "marigold" and Plantago major L. "plantain", characterized the absorption processes of these species in the different environments to which they were exposed. The differences in the times required to reach hygroscopic equilibrium (144 h for P. major, 168 h for C. officinalis, and 300 h for M. recutita) reflect the influence of the morphological and structural characteristics of the seeds on the kinetics of water vapor absorption. The rapid stabilization of Plantago The high moisture content of plantain (144 h) is explained by the ability of its seeds to form a mucilaginous gel when hydrated. This mucilage, composed mainly of polysaccharides, acts as a hydrophilic matrix that considerably increases the surface area in contact with water vapor and accelerates moisture uptake until saturation is reached (Yang et al., 2012) In contrast, the seeds of Matricaria recutita L. "chamomile" , which are smaller (1-2 mm) and have a semipermeable seed coat, exhibit slower absorption kinetics, since water vapor must diffuse through structures that limit water exchange ( Pirkhezri et al., 2010). For their part, the seeds of Calendula officinalis L. "calendula”, with a rough and ornamented surface, show an intermediate behavior, where the irregularities of the testa facilitate capillary condensation and initial absorption, but without the speed conferred by the mucilage (Moreira et al., 2002; Al- Snafi , 2017).

The inflection point observed in the isotherms at a water activity (a _w) of 0.826 (82.6% RH) marks the transition to a predominance of the absorption process. For a _w values below 0.826, the seeds had a higher vapor pressure than the surrounding saline solution, resulting in a net loss of moisture (desorption) until the pressures equalized. Conversely, for a _w > 0.826, the ambient vapor pressure exceeded that of the seeds, favoring water uptake. This behavior has direct practical implications: under storage conditions with ambient relative humidity above 82.6% (approximately 83%), the seeds of these species will absorb moisture in a sustained manner, which could increase the water content to levels that promote metabolic activity, respiration and the development of fungi, compromising their viability and pharmacopoeial quality (Prieto et al., 2022).

The equilibrium moisture content reached by Matricaria recutita L. "chamomile" seeds was consistently higher than that of the other two species for the same a _w values (Table 3). This behavior suggests a greater affinity of the seed matrix for water molecules, possibly associated with its chemical composition and a higher proportion of hydrophilic components. The lack of previous reports on absorption isotherms for these specific species in the consulted literature highlights the novelty and usefulness of these data, although the values obtained can be contextualized with those reported for other small seeds. For example, Ellis (1988) reported lower values for onion seeds under similar conditions, which reinforces the specificity of hygroscopic behavior as a function of the composition and structure of each species. Fitting the experimental data to six mathematical models allowed us to identify the Halsey model as the most suitable for describing the absorption process in the three species. The Halsey model, originally developed to describe multilayer condensation at relatively large distances from the adsorbent surface, assumes that the absorption potential decreases with distance according to a power law.

Halsey 's B parameter (0.719 in Matricaria recutita L. "chamomile”, 0.8626 in Calendula officinalis L. "marigold" and 0.918 in Plantago major L. "plantain”) indicated that the predominant attractive forces in the water-seed surface interaction are weak, of the Van der Waals type ( Alpizar et al., 2018; Castro, 2022). This thermodynamic characteristic implies that the absorbed water is relatively loosely bound to the solid matrix, which would facilitate its removal during drying processes, allowing the moisture content of the seeds to be reduced in short periods without requiring a high energy input. GAB (Guggenheim-Anderson-de Boer) model provided additional information about the energetic interactions in the system. The parameter K, which reflects the difference in chemical potential between water molecules in the multilayer and pure liquid water, showed values close to unity (0.84–0.92). K values < 1>et al. (2021).

monolayer moisture content (X _m), estimated using the GAB model, represents the amount of water strongly bound to the active sites on the seed surface and is generally considered the optimum value to ensure maximum stability during storage, since below this level the water is not available for deterioration reactions ( Labuza and Altunakar , 2020). The X _m values obtained (0.123 g·g^-1 ms for Matricaria recutita L. "chamomile", 0.046 g·g^-1 ms for Calendula) officinalis L. "marigold" and 0.109 g·g⁻¹ ms for Plantago major L. "plantain") suggest that calendula has a lower availability of primary absorption sites, which could give it a relative advantage in terms of stability, by requiring less water to saturate its monolayer .

The classification of isotherms as Type III, according to Brunauer 's nomenclature et al. (1940), is consistent with the values of the C parameter of the GAB model (less than 2 for Matricaria recutita L. "chamomile" and Plantago major L. "plantain" , and slightly above 2 for Calendula officinalis L. "calendula”). Type III isotherms, also called Flory-Huggins isotherms , are characteristic of systems where the adsorbate -adsorbent interaction is weak compared to the adsorbate-adsorbate interacción.

monolayer formation is not a clearly distinguishable event, and absorption increases progressively as water activity increases, accelerating markedly at high water activity (Hernández et al., 2023). This behavior is typical of materials with low surface energy and a predominance of nonpolar components or with limited absorption sites, which appears to be the case for the seeds studied. Caurie model allowed us to estimate the safety moisture (X s), defined as the moisture content with which maximum stability is achieved during shelf life, corresponding to the inflection point of the isotherm where multilayer absorption begins (Choque et al., 2018).

X s values obtained were slightly lower than the X m values of the GAB model, which is methodologically expected. Integrating the information from both models, along with the experimentally observed inflection points at a w = 0.826, safe moisture ranges for storing each species at 27 °C can be established: for Matricaria recutita L. "chamomile", between 0.053 and 0.1886 g·g⁻¹ ms; for Calendula officinalis L. "calendula", between 0.046 and 0.1066 g·g⁻¹ ms; and for Plantago major L. "plantain", between 0.044 and 0.0998 g·g⁻¹ ms. These ranges delimit the zone where water is predominantly in the initial monolayer or multilayers, without reaching levels that favor the mobility of reactants and accelerated deterioration. The first term of the DAW model, which relates the parameters K and K', represents the number of absorption sites with strong bonds, that is, the maximum absorption at primary sites (Socorro et al., 2010). The values obtained indicated that these seeds contain few absorption sites with relatively strong bonds; a result that confirmed what was obtained for the coefficient B of the Halsey equation, and A and C of the Peleg model .

D'Arcy -Watt (DAW) model, designed to describe absorption in heterogeneous biological materials, distinguishes between primary (strong bonds) and secondary (multilayer) absorption sites. The low values obtained for the K and K' parameters (which represent the contribution of absorption sites with strong bonds) confirm that the studied seeds have few high-energy absorption points, which is consistent with the Halsey B parameter values and the Type III classification of the isotherms (Socorro et al., 2010).

Additionally, the Peleg model provided information on absorption kinetics and capacity. The Peleg parameter C, representing absorption capacity, reached high values (1.859–4.974), indicating a high overall affinity for water once the initial barrier was overcome. The parameter A , related to mass transfer, was highest for Plantago. major L. "plantain" (A=5,796), corroborating the rapid water uptake mediated by the mucilage (Hernández et al., 2021). Taken together, the results demonstrate that the seeds of M. recutita, C. officinalis, and P. major exhibit marked hygroscopicity, characterized by Type III isotherms and a predominance of weak water-substrate interactions. This property makes efficient post-harvest drying imperative to reduce moisture content to the identified safe ranges (below 0.19 g·g⁻¹ ms in all cases), followed by storage under controlled relative humidity conditions (< 80>

The Halsey model characterizes the nonlinear behavior of the isotherms, classified as Type III according to Brunauer 's nomenclature , indicating a weak adsorbate -adsorbent interaction in the seeds ofMatricaria recutita L. "chamomile", Calendula officinalis L. "marigold" and Plantago major L. "plantain”.