**1. Introduction**

Cassava (*Manihot esculenta* Crantz), belonging to the *Euphorbiaceae* family, is a highly popular crop in the tropical zones of the globe, likewise, e.g., wheat in European countries [1]. It is one of the most often cultivated crops worldwide, providing starch for foodstuff and feedstuff production [2,3]. It is of particular importance to the economies of such countries as Nigeria, Thailand, Ghana, Brazil, and Indonesia, as it plays the role of a strategic raw material [4–6]. In the years 2000–2018, its production increased by approximately 100 million tons only in the countries claimed to be its main producers [7], which points to the growing demand for this crop.

Cassava (*Manihot esculenta* Crantz) roots are used to manufacture various starch products with a different fraction size composition, the common feature of which is a high dehydration degree. Water content reduction enables a radical decrease in water activity, and by this means, achieves enzymatic and microbiological stability, which, in turn, ensures adequate storage stability [8,9]. This form of preservation and storage of cassava products is driven by its higher susceptibility to spoilage compared to other tuber roots (potato, sweet potato, yam) [10]. Consequently, the cassava root, which is a storage organ, like other tuberous organs, does not fall into dormancy even under favorable conditions [11]. Granulated products obtained from cassava starch in the form of uneven, polyhedral, or spherical granules are called tapioca [12,13].

Tapioca is becoming more and more popular and is also used in European countries. There are three basic forms of this starch available on the market: starch powder, starch

**Citation:** Ocieczek, A.; Mesinger, D.; Toczek, H. Hygroscopic Properties of Three Cassava (*Manihot esculenta* Crantz) Starch Products: Application of BET and GAB Models. *Foods* **2022**, *11*, 1966. https://doi.org/10.3390/ foods11131966

Academic Editors: Jianhua Xie, Yanjun Zhang and Hansong Yu

Received: 29 May 2022 Accepted: 27 June 2022 Published: 2 July 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

granulate, and fermented starch powder produced in the lactic fermentation process. Fermented starch is used as an additive to some baked products, both sweet and dry ones. In Ghana, fermented starch is used to produce six groups of products traditionally consumed in African countries, including: fermented pulps—fufu and akpu; fermented flours—lafun, kanyanga, and luku; smoked fermented balls—kumkum and pupuru; steamed and fermented chips—chikwangue and ntuka; baked grits—gari, agbelima, kapok, and popogari; steamed grits—attieke.

Lactic acid fermentation of edible cassava roots is extremely important as it removes cyanogenic glycosides, linamarin, and lotaustralin, which are present in the plant in various proportions. Cyanogenic glycosides are toxic because their hydrolytic degradation releases hydrogen cyanide. Therefore, the fermentation of cassava is strongly recommended [14].

The food industry extensively uses cassava starch (tapioca) in each of the three mentioned forms. However, starch powder and granules are the most common in the European market, whereas fermented starch cannot be commonly purchased in Poland yet. Tapioca starch (non-fermented) is used as, e.g., a stabilizer or a thickener due to its favorable technological properties and very neutral or utterly neutral taste. Tapioca-based food products are recommended to persons susceptible to allergens, especially those allergic to wheat and/or maize proteins. In addition, the starch of this type is increasingly often applied in food products intended for children, owing to its beneficial physical properties, texture, stability, and neutral taste. However, the most popular food products available on the European market are Asian-style noodles, Asian-style crispy bread, gluten-free bread, or the very popular molecular caviar (used in the production of Bubbletea, i.e., tapioca starch in the form of balls soaked in a fruit-flavored syrup and added in this form to lemonade or tea). Tapioca can also be used to prepare, e.g., pancakes, cakes, or puddings [15–17].

Edible cassava starch, i.e., tapioca, is also used in pharmaceutical products as an excipient and a filling substance. In the native form, it is a constituent of many pharmaceutical formulations—a binder, disintegrant, and a diluent of the active substance. In turn, the modified tapioca starch has an even more comprehensive range of applications, depending on the type of modification and intended use, etc. [18].

Carbohydrates are the most important and, at the same time, the dominant component of each starch, determining its technological usefulness as well as the stability of functional properties and consumer safety. In particular, attention is paid to the ratio of amylose to amylopectin, which in tapioca is at the level of 17–24% amylose and 76–83% amylopectin [19]. The ratio of these fractions may be necessary for shaping the sorption, including hygroscopicity. The crystalline form of granules of the dominant component of the cassava root causes the water present in it to be characterized by a high level of its activity, amounting to approximately 0.85 [20]. At the same time, it should be emphasized that the degree of its processing affects both the water content and its activity. At the same time, there are reports showing that the natural variety of cassava and the degree of its processing generally have a negligible or unclear effect on sorption behavior [21]. This statement had to be verified in the light of the growing interest in cassava products on the European market.

This study aimed to compare the sorption properties, in terms of hygroscopicity, of three cassava (*Manihot esculenta* Crantz) starch products (native, fermented, granulated), by comparing their sorption isotherms and the parameters of selected mathematical models used to describe these isotherms. The use of the *BET* (Brunauer, Emmett, and Teller) and *GAB* (Guggenheim, Anderson, and De Boer) models was conditioned by their theoretical nature, allowing for a physical interpretation of the parameters of these models. Moreover, its goal was to identify selected parameters describing the microstructure of the tested products. The study also assessed the differentiation of particle size and shape distributions of the studied starch samples. It was assumed that the analysis of the differentiation of the hygroscopic properties of starch, taking into account the variability of selected physical parameters of these starch particles, will be a source of new valuable information for the management of the production process, safety, and stability of these products.

#### **2. Material and Methods**

#### *2.1. Materials*

Three products made of cassava (*Manihot esculenta* Crantz) starch, also called tapioca, were studied: native starch powder (NS), starch granulate (SG), and fermented starch powder (FS). All three starches were produced under industrial conditions. Native tapioca powder (NS) and tapioca granulate (SG) were purchased in Poland, whereas fermented starch (FS) was imported from Brazil. Native tapioca powder was produced in Thailand and distributed in Poland by De Care Group Sp. z o.o. i wsp. Sp. Kom. Tapioca granulate was produced in Thailand by THAI WORLD IMPORT & EXPORT Co., Ltd. (Bangkok, Thailand) and distributed in Poland by KK Polska Sp. z o.o. Fermented tapioca was produced in Brazil and distributed by SUCOS DO BRASIL—PRODUCTOS LATINO GMB (Neuss, Germany) under the trademark YOKI™. When opened, the experimental material was kept in a tightly closed package, at room temperature, according to producers' recommendations.

The chemical reagents used to maintain appropriate relative humidity conditions in the desiccators were high-quality, pure, analytical compounds. The water used to prepare the saturated solutions of these reagents was distilled water.

### *2.2. Methods*

Differences in the physical properties of the analyzed starches were established by comparing value distributions of parameters characterizing the size and shape of their particles determined using a Morphology G3 automatic particle analyzer (Malvern Instruments, Malvern, UK). The analyzer enables determination of the size distribution of solid particles, with sizes ranging from 0.5 to 10,000 μm. Estimations were made for value distributions of such parameters as: diameter, circularity, convexity, elongation, shape coefficient, and solidity [22].

Water content was determined according to the Polish Standard (PN-ISO 712:2002) in the AquaLab apparatus series 4 model TE (Decagon Devices, Inc., Pullman, WA, USA), exact to ±0.003, at a temperature of 20 ± 1 ◦C.

Sorption isotherms were plotted using the static-desiccator method at ambient temperature of 20 ± 1 ◦C, in a water activity (*aw*) range from 0.07 to 0.98, and the time (30 days) required to reach the dynamic equilibrium between the analyzed samples and saturated solutions of respective substances was: NaOH·H2O (0.0698); LiCl·H2O (0.1114); KC2H3O7·1.5H2O (0.231); MgCl2·6H2O (0.3303); K2CO3·2H2O (0.440); Na2Cr2O7·2H2O (0.548); KJ (0.6986); NaCl (0.7542); KCl (0.8513); KNO3 (0.932); and K2Cr2O7 (0.9793). Equilibrium water contents were determined based on the initial masses of the analyzed samples with established water content, and then their changes triggered by the incubation process in desiccators. The values achieved allowed plotting of the isotherms of water vapor sorption in the tested range of water activities. Each point on each of the plotted isotherms was the arithmetic mean from three parallel determinations. Differences in the course of the sorption isotherms in the entire *aw* range were analyzed statistically using the Student's *t*-test of differences between mean values for dependent variables. Differences were considered statistically significant at *p* < 0.05.

The course of sorption isotherms was analyzed mathematically using the *BET* Equation (1):

$$v = \frac{\upsilon\_{\text{w}} \cdot \upsilon\_{BET} \cdot a\_{\text{w}}}{(1 - a\_{\text{w}}) \cdot \left[1 + (c\_{BET} - 1) \cdot a\_{\text{w}}\right]} \tag{1}$$

where:

*v*—adsorption, g H2O/100 g d.m.;

*vm*—maximal adsorption value corresponding to the complete coverage of the surface with a monomolecular layer of the adsorbate, g H2O/100 g d.m.;

*cBET*—energy constant *BET*, describing the difference between the chemical potential of crude adsorbate molecules and those in the first adsorption layer, kJ/mol;

*aw*—water activity at the adsorption temperature [23].

The analysis also used the *GAB* Equation (2):

$$v = \frac{v\_m \cdot c\_{GAB} \cdot k \cdot a\_w}{(1 - k \cdot a\_w) \cdot (1 - k \cdot a\_w + c\_{GAB} \cdot k \cdot a\_w)} \tag{2}$$

where:

*v*—adsorption, g H2O/100 g d.m.;

*vm*—maximal adsorption value corresponding to the complete coverage of the surface with a monomolecular layer of the adsorbate, g H2O/100 g d.m.;

*cGAB*—energy constant *GAB*, describing the difference between the chemical potential of adsorbate molecules in the first adsorption layer and higher layers, kJ/mol;

*k*—constant correcting properties of multilayer molecules compared to the liquid phase; *aw*—water activity at the adsorption temperature [23].

The characterization of the sorption properties, in terms of hygroscopicity, using the *BET* and *GAB* models consisted of determining the maximal adsorption value corresponding to the complete coverage of the surface with a monomolecular layer of the adsorbate, called the monolayer (*vm*). Estimation of the monolayer allowed computing of the specific adsorption area (*asp*) using Equation (3):

$$a\_{sp} = \omega \cdot \frac{\upsilon\_m}{M} \cdot N \tag{3}$$

where:

*asp*—specific sorption area, m2/g;

*<sup>N</sup>*—Avogadro number, 6.023 × <sup>10</sup><sup>23</sup> molecules/mol;

*M*—molecular weight of water, 18 g/mol;

*<sup>ω</sup>*—water cross-section area, 1.05 × <sup>10</sup>−<sup>19</sup> <sup>m</sup>2/molecule [24].

In addition, energy constants *cBET* and *cGAB* were determined, and the *k* constant in the *GAB* equation was estimated.

Sizes and volumes of capillaries of the examined starch samples were determined for the area of capillary condensation using Kelvin's Equation (4), assuming the cylindrical shape of the capillaries.

$$
tau\_w = -\frac{2\cdot\sigma \cdot V}{r\_c \cdot R \cdot T} \tag{4}
$$

where:

*V*—molar volume of the liquid, g/mol;

*σ*—surface tension of the liquid, N/m;

*R*—universal gas constant, J/(mol K);

*T*—temperature, K;

*rc*—capillary radius, nm [24].

The *BET* equation parameters were identified based on empirical data in the water activity range of 0.07 < *aw* < 0.50 [25]. In turn, *GAB* equation parameters were identified based on empirical data from the entire *aw* range studied [26].
