**3. FD Principle**

Water exists in three di fferent states: solid, liquid, or gas (vapor). Figure 1 presents the phase diagram of water (pressure versus temperature), where the curve lines show the passage from solid to vapor (sublimation), from liquid to vapor (evaporation), or from solid to liquid (fusion). Point T in Figure 1 represents the triple point of water (at 0.01 ◦C and 0.612 kPa) where the three phases (liquid, vapor, solid) coexist, and point C is the critical point of water (374 ◦C and 22060 kPa). Freeze-drying makes use of the sublimation phenomenon (at temperatures lower than 0.01 ◦C, and water vapor pressures below 0.612 kPa). In Figure 1, a product to be freeze-dried will follow the path from A to

point B (i.e., the product should be first frozen by decreasing its temperature, then the water vapor pressure should be lowered below the pressure corresponding to the triple point, and finally some heat should be supplied to help the ice to convert into vapor by sublimation).

During the FD process, the removal of solid-state water (ice) occurs in three steps: (a) freezing, where the sample should be completely frozen; (b) primary drying, when ice is sublimated, usually at sub-atmospheric pressure; and (c) secondary drying, when the remaining unfrozen/bound water is desorbed from the drier food matrix.

**Figure 1.** Phase diagram of water (T: triple point of water, C: critical point of water). "A" represents the starting point prior to freeze-drying (atmospheric pressure and ambient temperature), while "B", the desired final conditions during sublimation (below the triple point T).

Freezing is the first separation step in the FD process, which solidifies the food materials. The rate of freezing is important for the formation and size of ice crystals—slow rate of freezing forming bigger ice crystals and vice versa. Accordingly, the size of crystals affects the rate of drying, wherein large ice crystals are easier to sublimate and hence increase the rate of primary drying [22].

In primary drying, a vacuum is applied and the shelf temperature is increased to start the sublimation, such that the product temperature is 2–3 ◦C below the collapse temperature *Tc* [23,24]. Collapse temperature is the temperature above which the product has the risk of losing macroscopic structure during the FD process [24]. *Tc* could be determined with a freeze-drying microscope, but also may be estimated from the glass transition temperature (*Tg*). It should be noted that *Tc* could be 2 ◦C to 20 ◦C higher than *Tg*, depending mainly on sample composition [24,25]. However, very conservative predictions of the collapse temperature may only result in a much longer freeze-drying process, thus it can only be used in critical cases when the sample is difficult to freeze-dry. Figure 2 depicts the typical temperature profile of a product during each step of the freeze-drying process, where it can be observed that during primary drying the product temperature should be below the collapse temperature (represented as a dotted line T1 in Figure 2).

Secondary drying starts when sublimation is still in place, being a slow part of the freeze-drying process, which may take at least 30% longer to complete than the end of sublimation. This last step could be performed at an elevated shelf temperature to more efficiently remove the remaining unfrozen or bound water by desorption, but lower than the glass transition temperature of dry solids (represented as dotted line T2 in Figure 2). However, it is challenging to identify the endpoint of primary drying or the beginning of secondary drying phase. If temperature is increased before all the ice is sublimated (endpoint of primary drying phase), it could collapse the product and hence, affect the final quality. Patel et al. [23] have suggested some techniques to determine the endpoint of the primary drying such as Pirani pressure gauge, dew point monitor, tunable diode laser absorption spectroscopy (TDLAS), gas plasma spectroscopy, thermocouple (TC), and condenser pressure. Among these techniques, Pirani, dew point, TDLAS, and TC were found to be effective for determining the endpoint of the primary drying phase.

**Figure 2.** Temperature profile of product during freeze-drying process, where T1 (dotted line) is the collapse temperature and T2 (dotted line) is the glass transition temperature of dry solids (adapted from [22]).

#### **4. Characteristics of Plant-Based Foods, Their Advantages, and Challenges upon Freeze-Drying**

Plant-based foods are derived from vegetables, grains, nuts, seeds, legumes, and fruits [26]. Two types of plant-based foods are used in freeze-drying applications: solids and homogeneous solutions/suspensions such as juices or purees.

Solid plant foods present intrinsic characteristics in terms of structure, anatomy, and composition, which may pose challenges on one hand, but otherwise occasionally help to ease the freeze-drying operation. To start, solid plant-based foods are mainly cellular solids. Gibson [27] reported that apples and potatoes are examples of a simple cellular tissue: parenchyma with thin-walled, polyhedral cells resembling an engineering closed-cell foam, as shown in Figure 3 for potato [28]. Unlike solutions and colloidal systems, cellular solids present stronger mechanical attributes related to the properties of the cell wall material and to the cell geometry—cellular materials allowing the simultaneous optimization of stiffness, strength, and overall weight in a given application [29]. Cellulose and noncellulosic (hemi-celluloses and pectic) polysaccharides are the main polymers forming the cell wall of plant-based foods. Cellulose is the single most abundant polysaccharide component of vegetable cell walls, presenting areas of crystallinity imparting a considerable tensile strength close to 1 GPa, and with a Young's modulus roughly 130 GPa [27,30]. Also, the mechanical response of cellular materials is enhanced by their arrangemen<sup>t</sup> and local geometry [31]. In this sense, if the freezing step is properly done at adequate low temperatures (without ice crystals destroying/weakening the cell walls), cellular materials are better prepared to stand during freeze-drying. It can be said that when freeze-drying solid cellular foods, mechanical properties and structural strength may play a more important role in keeping product integrity than glass transition temperature in order to avoid collapse during primary/secondary drying and storage of freeze-dried foods.

Most plants present an epidermis in their outer parts serving against water loss, regulating gas exchange, and secreting metabolic compounds to protect internal tissues against diseases and acting as a natural insect repellent as well. Figure 4 shows the cross section of the epidermal cuticle of *Vaccinium angustifolium* (lowbush) blueberries (magnified 250 times) [32]. This epidermis formed by a lipidic hydrophobic cuticle layer [33] constitutes an interface between the internal cells and the external environment, acting as a moisture barrier during growing, which enormously affects the water diffusion during subsequent processing, decreasing significantly the rate of freeze-drying when the whole plant-based material is dried (i.e., the case of berries/grapes). The outer surface of the cuticle is covered by epicuticular waxes (a lipid-soluble fraction) and consists of complex mixtures of long-chain aliphatic and cyclic components, including primary alcohols (C26, C28, C30), hydrocarbons (C29, C31), esters, fatty acids, and triterpenoids [34,35]. Intracuticular waxes are embedded in the cutin polymer matrix itself (a lipid-insoluble fraction), though little information is available on its composition [36]. This external waxy layer makes freeze-drying of whole fruits/vegetables challenging since vapor generated by ice sublimation during the primary step is trapped inside the product, increasing its pressure and thus, melting the ice. Finally, after a continuous pressure build-up, the product cracks or explodes inside the freeze-dryer, depending on the vacuum level. The quality of such freeze-dried product is therefore unacceptable, and thus, pretreatments are required to overcome this problem (please refer to Section 6).

**Figure 3.** Cellular structure of potato.

**Figure 4.** Optical microscope photo of a blueberry epidermis zone, where *C* is the proper cuticle, *E* is the epidermis, and *SE* is the sub epidermis.

For plant-based liquid solutions, sample composition may affect freeze-drying operation depending on one hand by the type of compound and its impact on overall glass transition temperature, but also on the total concentration of solids.

In a glass state, the viscosity of the matrix is high and the molecular movement is very limited. Glass transition occurs when a glassy matrix changes to a rubbery state, which is a more mobile amorphous structure. As explained previously, collapse temperature (related to the glass transition temperature *Tg*) represents the temperature above which the matrix loses its structure and the quality decreases, obviously related to the decrease in viscosity happening during glass transition. Therefore, when temperature during a process increases over the *Tg* of a product, the deterioration risk of many of its physical properties rises as well. Table 1 shows an example of the carbohydrate composition of apple and pear [37] together with literature values of the glass transition temperatures of pure sucrose, glucose, fructose, and D-sorbitol. As can be seen, pear juice has higher mass fractions of glucose and sorbitol than apple juice, and lower fractions of sucrose and fructose. Glass transition temperature of a multicomponent mixture could be roughly estimated using the following equation:

$$T\mathcal{g} = \sum\_{i=1}^{n} x\_i T\mathcal{g}\_i \tag{1}$$

where *xi* and *Tgi* are the mass fraction and individual glass transition temperature of each component, respectively. Water is a plasticizer, having a low glass transition temperature, and some authors have indicated a value of −137 ◦C [38]. Thus, while drying takes place, the glass transition temperature of a product increases as water content is reduced, as indicated in Equation (1). Equation (1) usually underestimates experimental glass transition values [25], however, it can be used in this manuscript to predict the effect of composition for comparison purposes. From this equation, and using the mass fractions of Table 1, the predictions of glass transition temperature for dry pear juice (≈ 60.9 ◦C) are approximately 16 degrees lower than for apple juice (≈ 77.1 ◦C), probably due to its lower mass fraction of fructose and higher mass fraction of sorbitol. Experimental values for dried apple and pear showed a similar difference in glass transition temperatures values of an average of 10 degrees [39], thus validating the general conclusions obtained from Equation (1).

**Table 1.** Juice carbohydrate composition and glass transition temperatures.


From the previous discussion, it can be said that pear juice would have less thermal stability than apple juice upon freeze-drying at similar operating conditions, provoking final freeze-dried pear juice with lower quality (i.e., darker, stickier, lower rehydration, etc.). These predictive results have been corroborated by experimental freeze-drying data [37]. In these cases, the product with lower glass transition has to be freeze-dried at lower shelf temperatures and under higher vacuum, making the process longer and increasing costs. This example aimed to illustrate the utmost importance that composition, and its influence in glass transition, has for freeze-drying of liquid plant-based foods, such as juices. As indicated in [41], the collapse temperature of pure orange juice is relatively low, the dry juice collapsing at 52 ◦C. This collapse temperature is very close to that of sucrose (55 ◦C), due to the higher sucrose content of this juice (more than 50% of the sugars). In the same study, it was shown that addition of macromolecules increases the collapse temperature of freeze-dried orange juice, thus providing better thermal stability.

In cellular solid foods, collapse during drying takes place when the natural turgidity of product is lost and cannot be restored. The impact of glass transition in this case is less important since structure plays a major role in understanding the collapse phenomena. In a freeze-drying study of potato, celery, and apple at temperatures below, near, and above their *Tg*, [42] pointed out that differences in plant tissues (structure, composition) may contribute together with glass transition to prevent collapse.

In particular for liquids (solutions, emulsions, suspensions), the matrix of the product to be freeze-dried provides for 'body', mechanical strength, and an attractive appearance [43]. Concentration of simple constituents of this matrix could thus have a significant impact on the freeze-drying operation since high levels of sugars or lipids may convert to low quality final freeze-dried products. For instance, when the sugar content is too high (i.e., concentrated orange juice, maple syrup), freezing temperatures should be set up at lower optimized levels for a successful freezing step. However, even if the temperature of the freezing step has been reduced, sugars might migrate to the surface of the product during freezing, building up a barrier for water di ffusion that will a ffect the further primary drying step, having a similar role as the epidermis of berries mentioned earlier. Thus, as water has di fficulty in escaping from the matrix, pressure builds up and the surface may crack, which is a positive solution for letting water to escape, but ice might melt, with goods exploding inside the freeze-dryer, producing final products with undesirable characteristics. Pretreatments should be used in such cases, as explained in Section 6.

Spray-drying is a continuous process considered industrially viable to produce powders out of fluids due to its lower costs compared to freeze-drying. However, when dealing with plant-based foods prone to collapse or containing valuable oxidative compounds, spray-drying at high temperatures and using enormous amounts of air is not as e ffective as a freeze-drying. Expensive complicated formulations are required to be added to solutions to be spray-dried in order to avoid quality problems related to oxidation, or important yield losses due to collapse and stickiness.

#### **5. Application of FD to Plant-Based Foods**
