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Phase Transition in Foods
CHAPTER 10
Phase Transition in Foods Camila Gambini Pereira
10.1 INTRODUCTION Most food products are complex materials composed of a large number of substances of different molecular weights and chemical structures. It is also known that each substance has different physical properties. The physical characteristics of these substances and of foods may vary greatly under certain operating conditions, with tendencies to form amorphous structures when cooled to temperatures below the melting point or when subjected to reduction of the water content present in the foods. Such structures are often desirable to provide the sensory attributes in the final materials, typically in products, such as prunes, raisins, and dried apricots. The mechanical and physical characteristics of amorphous materials are also related to the water activity and its influence in the molecular motion and food quality. The crunchiness of solid foods, cookies for example, is lost with water absorption and structural modification caused by the water plasticization. Phase transitions correspond to changes occurring in the phase and state of materials. These can be considered a first order transition, such as solidliquidvapor transitions, or a second order transition, such as glass transition, gelatinization, and denaturation. The importance of understanding the condition of glass transition is fundamental in the characterization of the physical behavior of food materials under processing and storage conditions, where amorphous materials are formed. Such events are found in steps such as crystallization and recrystallization, frozen storage, spray drying, extrusion, and candy formation. The determination of phase transition data has been performed for different foods since the 1980s, and some aspects of these data are discussed in this chapter. As a matter of fact, the phase transition data are presented as a reference factor for the determination of process performance in several aspects: (1) knowledge and control of the behavior of the amorphous state of food products during the processing and storage Thermodynamics of Phase Equilibria in Food Engineering
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Thermodynamics of Phase Equilibria in Food Engineering
of these materials; (2) evaluation of the quality of the final product and its relationship with consumer requirements; (3) analysis of the safety and shelf life of material, since factors such as microbiological action and enzymatic activity are directly related to the water activity present in the food and temperature of the material; and (4) optimization of the operational conditions to maintain the quality and characteristics of the product. In this sense, this chapter aims to present the main concepts of phase transition as well as an overview of glass transition studies in food.
10.2 FUNDAMENTAL CONCEPTS 10.2.1 Glassy Transition Glass is an amorphous (non-crystalline) solid of high viscosity (10101014 Pa/s). In this condition, the material is hard and brittle [1]. The main characteristic of this material is the high reduction in molecular mobility, offering a wide variety of applications, mainly in the food industry. Glassy materials can be obtained from the rapid cooling of the material below its melting point. Under these conditions, the physical and mechanical properties of the material are quite brittle and easily affected by external conditions [2]. When a liquid is slowly cooled in such a way that the system remains in equilibrium, it will crystallize at melting point (Tm). This transition is characterized by a rapid and significant decrease in the specific volume. However, if the process occurs at an extremely high cooling rate, 2(dT/ dt), i.e., cooled very quickly, the material arrives at the condition of noncrystalline solid (glass), in the vitreous state, whose specific volume resembles that of the crystalline state. The temperature that establishes the emergence of the vitreous state is called the glass transition temperature (Tg). This condition is presented in Fig. 10.1. Here it is also possible to observe the effect of the phase change on the apparent viscosity in both circumstances. In Fig. 10.1, the region between Tg and Tm is defined as glass transition. The melting transition, resulting from slow transition, is an equilibrium state. However, the fast cooling process propitiates the emergence of the glass transition region and vitreous state, considered as non-equilibrium and metastable states. Here, it is worth highlighting the differences in some terminologies. In Chapter 2, the concepts of equilibrium and nonequilibrium were defined, describing situations within the context observed for food systems and related processes. As well as this, the different forms of 422
Phase Transition in Foods
Specific volume
(A) Liquid
uid
Liq
Glass Crystal
log ηa
(B) Crystal
Glass
Liq
uid Liquid
Tg
Tm
Temperature
Figure 10.1. General representation of the phase transition in the formation of glass and crystal of a pure nonpolymeric component. (A) Specific volume as a function of temperature; (B) apparent viscosity (ηa), with slow cooling (—), and very fast cooling (- - -). Based on [2].
equilibrium (stable, unstable, metastable, and neutral) were explained from the thermodynamic point of view, and, when we talk about glass transition, these concepts reappear. Amorphous systems have atomic clusters, where the atom positions coincide with relative minima of the free energy, differently from the lattice positions, providing atomic relaxation motions toward equilibrium configurations, with very small atomic reorganization. This is a characteristic of metastable systems [3]. Therefore, amorphous materials, such as noncrystalline solids (glass) and supercooled liquids, are in a metastable state. 423
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However, it should be emphasized that the non-equilibrium states involve time-dependent changes. Since the glass transition is a region formed as a function of the rate 2dT/dt, whose properties and physical structures may vary according to the type of the processing applied, the transition is considered a non-equilibrium state. Accordingly, the glass transition region (TTg) is a non-equilibrium transition, which connects two different metastable conditions, i.e., the supercooled (or supersaturated) liquid and the glass. Note that amorphous materials (metastable systems) under non-equilibrium conditions exhibit time-dependent changes and, therefore, also tend to approach the equilibrium condition, that is, the crystalline state. As explained in Chapter 2, any system remains in equilibrium as long as the modifications in the vicinity do not affect its state. Thus, systems in metastable equilibrium condition, like amorphous materials, can move out of the equilibrium state if the neighbors in non-equilibrium are acting on the system. In food, this situation is commonly to be found: sweet confectionery, an amorphous solid (metastable material), suffers alteration over time with its texture, for instance, when exposed to environmental conditions with variances in relative humidity and temperature (non-equilibrium conditions). With such characteristics, amorphous materials exhibit particularities that depend on the processing and environment that surround them. During the food processing, particularly when water is removed and/ or temperature is reduced to conditions below the melting point, glass transition state (region) is achieved and amorphous or partially amorphous materials can be formed. Pure food compounds, such as carbohydrates and proteins, often show glass transition with variations in properties as indicated by Fig. 10.1 [47]. However, several food systems may present such partially amorphous substances. This status is affected by water presence and temperature changes, as will be discussed in Section 10.2. Glass transition may be present in both low-moisture/dehydrated foods, such as snack foods or breakfast cereals, and high-moisture foods, such as frozen foods. In all these cases, the food is characterized by having amorphous or partially amorphous profile. The transition region is also accompanied by a variation in viscosity that influences the characteristics of the material. This change is quite perceptible in solid amorphous materials (vitreous state) that, when absorbing water or increasing temperature in the region of glass transition, came to have a different texture characteristic of rubbery materials. This change in the viscosity in amorphous materials through the effect of temperature is evidenced in Fig. 10.2 by the variations 424
Log modulus log ηa
Phase Transition in Foods
Glassy
“Rubbery”
Tg
Liquid
Tm
Temperature Figure 10.2. Schematic viscoelastic behavior of partially crystalline synthetic polymers, indicated by the elastic shear modulus—log Modulus (—), and apparent viscosity, ηa (- - -). Based on [2].
of elasticity modulus of the material at temperatures below the melting point, between the amorphous glassy state and the fluid. The diagram represented in Fig. 10.2 provides information on the rheological characteristics of the polymeric systems as a function of the effect of the variation of temperature during the glass transition. The term “rubbery” state is employed to describe the highly viscoelastic characteristic of polymers when they are in the amorphous state limited by the temperatures Tg and Tm. It is a term used generally to describe the rheological nature of these materials. The phase transition from glassy to liquid states in polymers is characterized by the rapid fall of the elasticity modulus (from about 109 to 106 Pa), by the effect of a small increase in temperature, resulting in a significant change in the rigidity of the material, followed by a plateau region indicating a long-range elasticity of the material over a wide temperature range. The final decline of the modulus is characteristic of linear polymers and has both rubber elasticity and flow properties [1]. In general, the glass transition temperature (Tg) occurs at 100150 K below the compound melting temperature [2], as observed in Table 10.1. 425
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Table 10.1. Physical properties of food components in the glass transition [10,11] Compound
M (g/mol) Tm (K)
Maltohexaose Maltotetraose Maltotriose Sucrose Maltose Glucose Fructose
990.9 666.6 504.4 342.3 342.3 180.1 180.1
461.5 6 0.5 421 6 2 397.15
Tg (K)
Tg0 (K)a
w10 b
388.15 384.15 349.15408.15 325.15343.15 316.15368.15 294.15312.15 278.15290.15
258.65 252.65253.65 244.15249.65 227.15241.15 232.15243.65 216.15230.15 220.15231.15
0.670.76 0.640.81 0.690.82 0.640.84 0.740.80 0.670.83 0.510.85
Tg0 is the glass transition temperature in the maximally freeze-concentrated solution. w10 is the mass fraction of the solute in the condition of maximally freeze-concentrated solution. The meaning of these terms is discussed in Section 10.3.
a
b
Although glass transition temperature (Tg) is often indicated by a single value, it can vary. Indeed, Tg depends on the experimental conditions used in its determination, the type of apparatus employed, and interpretive ability of the operator. As well as this, the value of Tg depends on the thermal history, that is, even applying the same method, a certain sample can present different values of Tg. One of the features of glass transition is that similar to synthetic polymers, the glass transition temperatures of amorphous food compounds increase with increasing molecular weight, as observed in Table 10.1.
10.2.2 Plasticization and Molecular Mobility According to Platzer [12], plasticization is the process in which the plasticizer substances neutralize intermolecular bonds of the van der Waals type between the polymer molecules to make it easier to bend. It increases the mobility of the polymer and decreases the crystallinity. In the case of foods, a similar effect can be observed. Foods are heterogeneous systems composed of different substances, such as carbohydrates, proteins, lipids, other minor components, and water. Polymers such as carbohydrates and proteins also undergo the effect of plasticization, which occurs mainly due to the water presence. In these, water acts as plasticizer, and, as it has lower molecular weight than the bulk material, it causes an increase in free volume, resulting in plasticization. Also, when present in concentrated foods, carbohydrates and proteins are generally in the amorphous state. As explained, one of the main characteristics of amorphous materials is the reduced molecular mobility. When the temperature increases above the temperature of glass transition (Tg), the 426
Phase Transition in Foods
473
Temperature (K)
423
373 Starch 323 Glutenin Maltose Fructose 273
223 0
5
10
15
20
25
30
Water content (g/100g of solids) Figure 10.3. Plasticization effect by water of amorphous carbohydrates: fructose (K), maltose (x), glutenin (’), starch (▲). Adapted with permission from [7].
molecular mobility increases causing a decrease in the viscosity of the material. In such situations, the plasticization is a result of the temperature effect. In addition, the plasticizing effect is also described by the dependence of the glass transition temperature on either weight or volume fraction of water. The plasticization of amorphous materials by water affects the temperature of glass transition (Tg). When water is absorbed by the material, it increases the free volume, and the increase in the water content results in the decrease of the glass transition temperature, as observed in Fig. 10.3. Therefore, changes in amorphous food properties can be the result of thermal plasticization, due to the increase in temperature, or water plasticization, by increasing the amount of water. Indeed, low molecular weight components decrease the Tg of polymers by increasing the free volume available to the polymer. In food, besides water, substances of low molecular weight, such as salts, alcohols, sugars, acids and others, also act as a plasticizer. This effect can be additive. One example is the glass transition of amylopectin in the presence of water and fructose. It is known that the glass transition of carbohydrates (in this case: amylopectin) decreases with an increasing amount of water 427
Thermodynamics of Phase Equilibria in Food Engineering
in the system. The analysis of the ternary system amylopectin waterfructose indicated that the addition of fructose in the mixture amylopectinwater drastically reduces the temperature value of Tg of the system. The effect of fructose on the Tg of the amylopectinwater system was higher when the water content was lower, due to the greater volume fraction of fructose in the systems at reduced water content. Whats is more, it has been observed that as the molecular weight of water is less than that of fructose, the plasticizing effect of water dominates the effect of fructose when the water content is increased. This additive effect of low weight molecules has been observed in other food mixtures [1315]. Moreover, especially when talking about proteins, the molecule of globular proteins may be considered as hydrophilic glassy state, encapsulating a hydrophobic central part [16]. Since food compounds of low molecular weight such as essential oils, fatty acids, surfactants absorbed by aqueous media can decrease the conformational stability of proteins and cause the swelling and dissociation of certain protein molecules, they also are considered “internal plasticizers”.
10.3 STATE DIAGRAMS In the previous chapters, phase diagrams were used to indicate phase behavior of systems at a given condition of temperature, pressure, or composition, being important in processes whose equilibrium condition is the necessary requirement for the separation or obtaining of a particular component. Such diagrams provide information where phase transition (melting, boiling, subliming) occurs at equilibrium condition. However, as explained, the transition observed in the glass transition is in a nonequilibrium condition; for this reason, the diagrams that represent the behavior of a system in a glass transition are named “state diagrams”. State diagrams indicate the glass transition temperature (Tg) of a given solute, providing a boundary between regions of lower mobility (glassy) and increasing mobility (supersaturated liquid). The simplest form of state diagram is presented in Fig. 10.4. The liquidus and solidus curves denote the melting point and the solute solubility. The intersection of these two curves occurs in Te (eutectic point), under equilibrium conditions. Further crystallization and concentration of the solute in the solution may still occur along the pathway Te and Tg0 . In the last condition of this segment, the solution has a concentration of the solute indicated by w10 . This condition is the maximal-freezing concentration, where the water present in the mixture is 428
Phase Transition in Foods
313 293
Temperature (K)
273 253 233 213 193 173 153 133 0.00
0.20
0.40
0.60
0.80
1.00
w1 (%) Figure 10.4. State diagram of the system D-fructose (1)water (2), with equilibrium states (—); and metastable equilibrium states (- - -). Experimental data (x, K, &, Δ, 3 ) from [1719].
unfreezable. Even when the temperature is decreased, the amount of water (1 2 w10 ) remains unfrozen. Tg0 is the glass transition temperature of a maximally freeze-concentrated solution. Tg0 and w10 data of some food components are presented in Table 10.1. Solutions rapidly cooled to temperatures lower than glass transition curve show formation of glassy material. The main utility of state diagrams is to identify glassy regions, where the molecular mobility is minimal, and the supersaturated state, where the molecular mobility is increased (characteristic of the “rubbery” state). The passage of a glassy state to a supersaturated state can be performed either by increasing the temperature at a given fixed composition or increasing the plasticizer amount (generally water in foods) at a given fixed temperature or both. Moreover, different subregions can be found in the glass transition region, providing different behaviors when temperature or compositions are modified, as indicated in Fig. 10.5. State diagrams have been defined for several food components: sugars and starch [2124], milk powders [25,26], cereal and proteins [2729], general food systems such as fruits and vegetables [3032], and several others [3336], with some regions characterized as indicated in Fig. 10.5. 429
ve
Thermodynamics of Phase Equilibria in Food Engineering
lity
c ur
Liquid Solution
ubi
Super-
Temperature
saturated solution
S ol
Melting point cu
Tm2
rve
Tg1
Ice + Solution
Te
Ice + Supersaturated solution
Tg′
Ice + Glass
Glass n sitio tran Glass
0
ve cur
Glass
w1′
1
Solute mass fraction (%) Figure 10.5. Typical state diagram of food systems, with equilibrium curves (—), and metastable equilibrium curves (- - -).
10.4 GLASS TRANSITION AND THE QUALITY OF FOOD A general rule is that food is more stable at and below its glass transition. In thermodynamics, the term “stable” is given when the system is in a condition of minimum value in its energetic state. In the case of food science, most often the term “stable” is used to designate the quality of materials, providing information on the shelf life, from the sensorial (color, taste, texture) and microbiological point of view. Even systems in non-equilibrium conditions tend over time to achieve the stable equilibrium condition. In other words, amorphous foods tend to reach the condition of thermodynamic stability (solid, liquid, gas) after a prolonged storage period (usually after the shelf life of the product). The greater stability of food in the glass transition is due to the fact that molecular mobility is quite reduced. This happens due to the low water activity and value of the temperature range TTg. The dependence of chemical and biochemical reactions and microbial growth in food is directly related to the availability of water, expressed in terms of water 430
Phase Transition in Foods
Shelf life Stability
activity. Foods with higher availability of water may also have reduced mobility in two situations: (1) in the vitreous state (glassy), if the process of water removal is extremely fast avoiding the crystallization of water; or (2) in supersaturated solution state, providing a system with a rubbery state profile. It is important to note that even below the glass transition condition, small molecules generally still have a certain molecular mobility, although greatly reduced, allowing for some chemical reactions to possibly exist, although very slowly, as is the case of lipid oxidation. However, microbial growth usually stops in amounts of water above glass transition. As a matter of fact, nowadays, the stability of foods is assessed by considering both data: water activity and temperature. The conditions of glass transition temperatures (Tg and TTg) settled during the processing and temperature of storage have a direct effect on the stability and shelf life of foods, as illustrated in Fig. 10.6. Although the presence of water has a direct relation to the quality and deterioration of foods, today it is a consensus that Tg and the difference TTg have strong effects on the mobility of biomolecules in foods. A classic example is the loss of crispness from cookies when they remain exposed to the environment by absorbing the humidity from the air, which leads to changes in their texture (changing to the rubbery
glass
“rubber”
liquid Temperature aw
Figure 10.6. Effect of temperature and water activity (aw) in the shelf life and stability of foods.
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Thermodynamics of Phase Equilibria in Food Engineering
state). Another example is the recrystallization of ice in frozen foods. Ice creams are processed in such a way that the temperature is reduced rapidly to prevent water crystallization. When exposed to room temperature for a long time, the temperature of the environment causes melting of the ice cream. When this slightly or partially melted product returns to the freezer (e.g., in the consumer’s residence), freezing (normally slow) is not carried out properly, causing the emergence of ice crystals, or even, the separation of the mixture into two or more phases. As seen in both cases, the stability and shelf life of food are strongly affected by the temperature and presence of water in the food. In the case of ice creams, the use of stabilizers, such as guar gum, carrageenan, xanthan, and gelatin, act in the stabilization of ice crystals in the ice cream, improving the transport properties of the unfrozen part of the system, by increasing the viscosity in the rubbery region [37], as indicated in Fig. 10.7. The quality of foods is generally related to consumer demands (crispy crackers, stuffed confectionery, frozen food, etc.), and legislation requirements (food safety, identification, labeling, etc.). In both cases, quality is associated with microbial action, and sensory and physical changes observed during processing and storage of food. Besides the quality of food, several properties of amorphous materials change in the glass transition region. These variations are observed in both thermal (heat capacity,
Viscosity (millions of Pas)
6 5 4 3 2 1 0 238
Tg′
243
248
253
258
Temperature (K)
263
268
273
Tm
Figure 10.7. Effect of stabilizers on the viscosity and rubbery state of the ice creams mixes: with stabilizers (—), without stabilizers (- - -). Adapted with permission from [37].
432
Phase Transition in Foods
278
Temperature (K)
268
258
248
238
228 0
100
200
300
400
Pressure (MPa) Figure 10.8. Effect of pressure on freezing temperature for potato (K), compared with that for water (—). Metastable regions indicated by A, B, and C (hachured) associated with experimental data (K, &, ▲). Adapted with permission from [41].
thermal expansion, diffusivity) and rheological (viscosity, elastic shear modulus) properties [38]. In addition to the effect of temperature and water removal, studies have shown that the pressure applied during processing to obtain food systems by freezing also influences the phase transition [3945]. In studies of freezing of potato tissue, different ice alterations were observed during freezing processes at pressures ranging from 0 to 300 MPa, finding three metastable regions from 200 to 300 MPa [41], as shown in Fig. 10.8. As a consequence, pressure has a significant influence on the chemical, enzymatical, and structural changes in food processing.
10.5 MATHEMATICAL MODELING When it comes to process engineering, one of the key issues is process prediction and modeling. For the equilibrium condition (melting point and solubility curves), the prediction can be performed using the thermodynamic calculations procedures which make use of activity coefficient models, as described in Chapter 8. In the case of non-equilibrium conditions, this question becomes even more complicated due to the food 433
Thermodynamics of Phase Equilibria in Food Engineering
components involved and variations related to this state. In the glass transition, Tg is dependent on the technique used for its determination and the procedure of analysis, which could lead to different Tg values. However, some researchers have proposed equations that help predict the glass transition region based on the properties of the compounds present in the systems. Although similarities in vitreous behavior have been observed between polymers and some food compounds, such as proteins and carbohydrates, some models applied to predict the glass transition of polymer systems are not applicable in food systems, since they are based on the resemblance of the properties of the compounds of the mixture, which rarely happens when it comes to foods. One of the first equations that was successful in adjusting food systems was the Gordon and Taylor equation [46], in 1952, Eq. (10.1), originally developed to describe the dependence of Tg with the binary composition of miscible polymers. This equation presented good results in the prediction of Tg of compounds like amorphous sugars [22,23,47,48] and maltodextrin [22,49]. Tg 5
w1 Tg1 1 kw2 Tg2 w1 1 kw2
(10.1)
where wi is the mass fraction of the component i, Tgi is the glass transition temperature of the component i, and k is a function of the thermal expansion coefficient that is generally estimated using non-linear regression analysis. In 1978, Couchman and Karasz [50] relied on the thermodynamic theory of the glass transition of polymer mixtures, considering the individual values of the heat capacities (ΔCpi ), to propose a plasticization model, indicated by w2 ΔCp2 ln Tg2 =Tg1 Tg ln 5 (10.2) w1 ΔCp1 1 w2 ΔCp2 Tg1 or lnTg 5
w1 ΔCp1 lnTg1 1 w2 ΔCp2 lnTg2 w1 ΔCp1 1 w2 ΔCp2
(10.3)
Some authors use the Couchman and Karasz equations, Eqs. (10.2) or (10.3), in a simplified way, disregarding the logarithm effect, resulting in the approximate form indicated by Eq. (10.4). One should only take care that this approximation does not occur in an overestimation of the Tg condition of the mixture. 434
Phase Transition in Foods
Tg 5 or simply
w1 ΔCp1 Tg1 1 w2 ΔCp2 Tg2 w1 ΔCp1 1 w2 ΔCp2
w1 Tg1 1 w2 ΔCp2 =ΔCp1 Tg2 Tg 5 w1 1 w2 ΔCp2 =ΔCp1
(10.4)
(10.5)
Observe that Eqs. (10.1) and (10.5) are exactly the same, since k5
ΔCp2 ΔCp1
(10.6)
This equation has been used with success to predict the glass transition temperature of maltooligosaccharides [51]. However, in aqueous solutions, the experimental values of the heat capacity of water are quite dissimilar and have provoked great debates. Kalichevsky et al. [52] have generated an important discussion about this issue. As well as this, if the heat capacity of pure water is used in Eq. (10.6), it can lead to values of k less than 1, resulting in contradictory behavior in the glass transition curve when compared to what is observed experimentally [21,5255]. Another way to determine this constant is considering the information of glass transition of amorphous solid through the free volume theory [56]. Good results from this have been observed in different aqueous systems [55,5759]. According to this theory, when the multiplication between the variation of the thermal expansion coefficient (Δα 5 αL 2 αg) and Tg is approximately constant, the following relation provides good representation for the value of k: k5
ρ1 Tg1 ρ2 Tg2
(10.7)
The Couchman and Karasz equation in its approximated form, Eq. (10.4), was extended by Kalichevsky and Blanshard [60] in a study of the glass transition of the ternary system wateramylopectinsugar. This equation has been applied to ternary and quaternary systems containing sugar constituents [43,61,62] and other ternary systems, such as waterglutenglycerol [63], waterproteinglycerol, and waterproteinolive oil [64]. Pn i51 wi ΔCpi Tgi Tg 5 P (10.8) n i51 wi ΔCpi
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Thermodynamics of Phase Equilibria in Food Engineering
Analogously, the Kwei equation [65], Eq. (10.9), originally developed for polymer systems, has also been extended to predict the glass transition behavior of multicomponent systems, Eq. (10.10), such as systems of corn distiller dried grains with soluble compounds in water [66]. Tg 5
w1 Tg1 1 kw2 Tg2 1 qw1 w2 w1 1 kw2
P n w1 Tg1 1 ni52 ki21 wi Tgi Pn 1 q L wi Tg 5 w1 1 i52 ki21 wi i51
(10.9)
(10.10)
where q is a fitting constant that incorporates the dependence of intermolecular interaction between the components. Another equation with a similar proposal, based on the values of individual Tgi and individual values of the heat capacities, has shown good results to predict the glass transition temperatures of carbohydrates and proteins. The Huang equation [67], Eq. (10.11), was able to predict values of Tg for glucose, maltose, maltotriose, maltohexose, starch, and gluten with a good approximation of experimental data. " # w1 ΔCp1 Tg1 1 Tg2 1 2w2 ΔCp2 Tg2 Tg 5 Tg1 (10.11) w1 ΔCp1 Tg1 1 Tg2 1 2w2 ΔCp2 Tg1 Furthermore, the additive group-contribution method has been used to predict the glass transition temperature of proteins, carbohydrates, and their mixtures [15,6870]. The method provided very good results for all systems evaluated. For proteins, the calculated values were very close to experimental data in systems containing a weight fraction of water from 0.05 to 0.25. The largest difference was observed at low water content. The reason is the strong intermolecular interactions observed in the systems in these conditions, leading to a decrease in the macromolecular motion, which increases the chain rigidity and the distance in the predicted Tg value [15]. In the case of carbohydrates, the model provided good agreement with experimental data.
10.6 CASE STUDY Currently one of the most present ingredients in food is sucrose, with varied functions ranging from sweetening to texture and increasing the shelf life of foods. Its presence in frozen foods also promotes a change in 436
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the glass transition point. Due to its importance of application, experimental data on glass transition (Tg) have been presented in the literature, furthermore, correlating this information with mathematical models becomes quite useful when it comes to studying the optimization of an industrial process. In this sense, the present case study aims to correlate data of phase change of the system sucrose (1)water (2) in a state of equilibrium (melting point and solubility) and non-equilibrium (glass transition) with mathematical models to evaluate their applicability. For this end, experimental data collected from literature [71,72] were used. For melting point and solubility curves, UNIQUAC and UNIFAC models (described in Chapter 4) were applied, considering the parameters presented in Tables 10.2 and 10.3. For the glass transition, equations of Gordon and Taylor, Eq. (10.1), Couchman and Karasz, Eq. (10.4), and Kwei, Eq. (10.9), were applied, using Tg1 5 343K [71] and Tg2 5 134K [73]. For Eq. (10.1), k 5 5.2 [71] was applied. For Eq. (10.4), as the values of ΔCP1 5 218.88 J/mol.K [74] and ΔCP2 5 34.92 J/mol.K [73], the value of k obtained by Eq. (10.6) will be 0.16, and then the curvature of glass transition will be inverted, as expected based on the discussion presented in Section 10.5. In this way, Eq. (10.7) was used, considering ρ1 5 1.47 g/cm3 [74] and ρ2 5 0.94 g/cm3 [75]. For Eq. (10.8), k 5 5.2 [71] and the adjusted parameter q 5 3.79 K were used. The comparison between the calculated and experimental data is presented in Fig. 10.9.
Table 10.2 UNIQUAC parameters for the system sucrose (1)water (2) [76] Component
ri
qi
a012 =K
at12
a021 =K
at21
Sucrose (1) Water (2)
14.5496 0.92
13.764 1.4
89.3391
0.3328
118.995
0.3410
Table 10.3 UNIFAC parameters for the system sucrose (1)water (2) [77]
PYR FUR -OCH2 OHring H2 O
PYR
FUR
-O-
CH2
OHring
H2O
0 0 0 0 0 2599.043
0 0 0 0 0 2866.916
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 2102.546
243.2789 2169.231 0 0 591.9366 0
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Thermodynamics of Phase Equilibria in Food Engineering
400
Temperature (K)
350 300 250 200 150 100 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
w1 Figure 10.9 State diagram of the system sucrose (1)water (2). Experimental data ( , Δ, x) collected from [71,72], calculated values using UNIQUAC (—) and UNIFAC (- - -) for the melting point and solubility curves; and Gordon and Taylor ( ), Couchman and Karasz (a a), and Kwei (- e -) equations for the glass transition curve.
It can be observed that for the melting point and solubility, both models (UNIQUAC and UNIFAC) presented very good predictions, with slight deviations when the solution is concentrated (w1 . 0.73). For the glass transition, as Tg values are not precise, it becomes difficult to evaluate the models, nonetheless, all the equations applied provided values coherent to the experimental data.
10.7 CONCLUDING REMARKS The study of glass transition is very important in the food industry, since the formation of amorphous structures in such conditions is related to the quality characteristics of food products. Its application in food is extremely varied, being observed from dehydrated, frozen and crystallized products to the formation of microstructured materials and biopolymer films. However, although there has been some advance in the knowledge of the vitreous transition of food systems, it is still very small in the face of the variety of products, processes, and 438
Phase Transition in Foods
situations found in everyday life. Furthermore, studies to predict the behavior of such foods in vitreous conditions are still necessary in order to better understand the behavior of pure compounds in complex mixtures, and in foods in relation to the variables that affect this state, such as temperature, pressure, presence of water and other minority compounds.
REFERENCES [1] Sperling LH. Introduction to physical polymer science. New York, NY: John Wiley & Sons; 2006. [2] Walstra P. Physical chemistry of foods. New York, NY: Marcel Dekker; 2003. [3] Ossi OM. Disordered materials. An introduction. New York, NY: Springer; 2006. [4] Slade L, Levine H. Glass transitions and waterfood structure interactions. Adv Food Nutr Res 1995;38:103269. [5] Kalichevsky MT, Jaroszkiewicz EM, Ablett S, Blanshard JMV, Lillford PJ. The glass transition of amylopectin measured by DSC, DMTA and NMR. Carbohydr Polym 1992;18:7788. [6] Talja RA, Roos YH. Phase and state transition effects on dielectric, mechanical, and thermal properties of polyols. Thermochim Acta 2001;380:10921. [7] Roos YH, Drusch S. Phase transition. 2nd ed. Oxford: Elsevier; 2016. [8] Gleick J. Rubber physics. Slovakia: Alexander Dubcek University of Trencin; 2007. [9] Levine H, Slade L. Influences of the glass and rubbery states on the thermal, mechanical and structural properties of doughs and backed products. In: Faridi H, Faubion JM, editors. Dough rheology and baked product texture. New York, NY: Van Nostrand Rheinhold/AVI; 1989. [10] Slade L, Levine H, Finley JW. Proteinwater interactions: water as a plasticizer of gluten and other protein polymers. In: Phillips RD, Finley JW, editors. In: Protein quality and the effects of processing. New York, NY: Marcel Dekker; 1989. [11] NIST. National Institute of Standards and Technology. Available in: www.nist.gov. (Accessed in July 2017). [12] Platzer NAJ. Plasticization and plasticizer processes. Advances in chemistry. Washington, DC: American Chemical Society; 1965. [13] Kalichevsky MT, Blanshard JMV. The effect of fructose and water on the glass transition of amylopectin. Carbohydr Polym 1993;20(2):10713. [14] Kalichevsky MT, Blanshard JMV. A study of the effect of water on the glass transition of 1:1 mixtures of amylopectin, casein and gluten using DSC and DMTA. Carbohydr Polym 1992;19:2718. [15] Matveev YI, Grinberg VY, Tolstoguzov VB. The plasticizing effect of water on proteins, polysaccharides and their mixtures. Glassy state of biopolymers, food and seeds. Food Hydrocolloid 2000;14:42537. [16] Tolstoguzov V. Origins of globular structure in proteins hypothesis. FEBS Lett 1999;444(145-8):1. [17] Ablett S, Izzard MJ, Liliford PJ, Arvanitoyannis J, Blanshard JMV. Calorimetric study of the glass transition occurring in fructose solutions. Carbohyd Res 1993;246:1322. [18] Vasitko J, Smelfk A. Solubility of anhydrous BD-fructose in water. Chem Zvesti 1967;21:7368.
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[19] Young FE, Jones FT, Lewis HJ. D-Fructosewater phase diagram. J Phys Chem 1952;56:1093109. [20] Young FE, Jones FT, Lewis HJ. D-Fructosewater phase diagram. J Phys Chem 1952;56(9):10936. [21] Blond G, Simatos D, Catte´ M, Dussap CG, Gros JB. Modeling of the water-sucrose state diagram below 0 ˚C. Carbohyd Res 1997;298:13945. [22] Roos Y, Karel M. Water and molecular weight effects on glass transitions in amorphous carbohydrates and carbohydrate solutions. J Food Sci 1991;56:167681. [23] Roos Y. Melting and glass transitions of low molecular weight carbohydrates. Carbohydr Res 1993;238:3948. [24] Ruiz-Cabrera MA, Rivera-Bautista C, Grajales-Lagunes A, Gonza´lez-Garcı´a R, Schmidt SJ. State diagrams for mixtures of low molecular weight carbohydrates. J Food Eng 2016;171:18593. [25] Jouppila K, Roos YH. Glass transitions and crystallization in milk powders. J. Dairy Sci 1994;77:290715. [26] Vuataz G. The phase diagram of milk: a new tool for optimizing the drying process. Lait 2002;82:485500. [27] de Graaf EF, Madeka H, Cocero AM, Kokini JL. Determination of the effect of moisture on gliadin glass transition using mechanical spectrometry and differential scanning calorimetry. Biotechnol Prog 1993;9:21013. [28] Sablani S, Bruno L, Kasapis S, Symaladevi RM. Thermal transitions of rice: development of a state diagram. J Food Eng 2009;90(1):11018. [29] Asherie N. Protein crystallization and phase diagrams. Methods 2004;34:26672. [30] Sa´ MM, Sereno AM. Glass transitions and state diagrams for typical natural fruits and vegetables. Thermochim Acta 1994;246(2):28597. [31] Guizani N, Al-Saidi GS, Rahman MS, Bornaz S, AliAl-Alawi A. State diagram of dates: glass transition, freezing curve and maximal-freeze-concentration condition. J Food Eng 2010;99(1):927. [32] Witczak T, Witczak M, Ste˛pie´n A, Bednarz A, Grzesik M. State diagrams of candied orange peel obtained using different hypertonic solutions. J Food Eng 2017;212:23441. [33] Fonseca F, Obert JP, Be´al C, Marin M. State diagrams and sorption isotherms of bacterial suspensions and fermented medium. Thermochim. Acta 2001;366(2):16782. [34] Ohkuma C, Kawai K, Viriyarattanasak C, Mahawanich T, Tantratian S, Takaia R, et al. Glass transition properties of frozen and freeze-dried surimi products: effects of sugar and moisture on the glass transition temperature. Food Hydrocolloids 2008;22 (2):25562. [35] Shi Q, Wang X, Zhao Ya, Fang Z. Glass transition and state diagram for freezedried Agaricus bisporus. J Food Eng 2012;111:66774. [36] Rahman MS, Kasapis S, Guizani N, Al-Amri OS. State diagram of tuna meat: freezing curve and glass transition. J Food Eng 2003;57(4):3216. [37] Goff HD, Caldwell KB, Stanley DW, Maurice TJ. The influence of polysaccharides on the glass transition in frozen sucrose solutions and ice cream. Dairy Sci 1993;76:126877. [38] Pereira CG. Vitreous transition in foods: an analysis under the thermodynamic and technological view. In: IX Brazilian Congress of Applied Thermodynamics and V School of Thermodynamics, October, 2017. [39] LeBail A, Boillereaux L, Davenel A, Hayert M, Lucas T, Monteau JY. Phase transition in foods: effect of pressure and methods to assess or control phase transition. Innov Food Sci Emerg Technol 2003;4:1524. [40] Benet GU, Schlu¨ter O, Knorr D. High pressurelow temperature processing. Suggested definitions and terminology. Innov Food Sci Emerg Technol 2004;5 (4):41327. 440
Phase Transition in Foods
[41] Schluter O, Benet GU, Heinz V, Knorr D. Metastable states of water and ice during pressure-supported freezing of potato tissue. Biotechnol Prog 2004;20:799810. [42] Zhu S, Le Bail A, Ramaswamy HS. High-pressure differential scanning calorimetry: Comparison of pressure-dependent phase transition in food materials. J Food Eng 2006;75:21522. [43] Benet GB, Chapleau N, Lille M, Le Bail A, Autio K, Knorr D. Quality related aspects of high pressure low temperature processed whole potatoes. Innov Food Sci Emerg Technol 2006;7(12):329. [44] Benet GU, Balogh T, Schneider J, Knorr D. Metastable phases during high-pressure low-temperature processing of potatoes and their impact on quality-related parameters. J Food Eng 2007;78(2):37589. [45] Otero L, Ousegui A, Benet GU, Elvira C, Havet M, Le Bail, et al. Modelling industrial scale high-pressure-low-temperature processes. J Food Eng 2007;83(2):13641. [46] Gordon M, Taylor JS. Ideal copolymers and the second-order transitions of synthetic rubbers. I. Non-crystalline copolymers. J Appl Chem 1952;2:493500. [47] Roos YH. Water activity and physical state effects on amorphous food stability. J Food Processes Preserv 1993;16(6):43347. [48] Truong V, Bhandari BR, Howes T, Adhikari B. Analytical model for the prediction of glass transition temperature of food systems. In: Levine H, editor. Amorphous foods and pharmaceutical systems. Cambridge, UK: RSC Publishing; 2002. p. 3147. [49] Roos Y, Karel M. Plasticizing effect of water on thermal behavior and crystallization of amorphous food models. J Food Sci 1991;56(1):3843. [50] Couchman PR, Karasz FE. A classical thermodynamic discussion of the effect of composition on glass-transition temperatures. Macromolecules 1978;11:11719. [51] Orford PD, Parker R, Ring SG, Smith AC. Effect of water as a diluent on the glass transition behaviour of malto-oligosaccharides, amylose and amylopectin. Int J Biol Macromol 1989;11:916. [52] Kalichevsky MT, Laroszkiewicz EM, Blanshard IMV. The glass transition of gluten. 1. Gluten and gluten-sugar mixtures. Int J Biol Macromol 1992;14:25766. [53] Katkov II, Levine F. Prediction of the glass transition temperature of water solutions: comparison of different models. Cryobiology 2004;49:6282. [54] Weng L, Vijayaraghavan R, MacFarlane DR, Elliott GD. Application of the Kwei Equation tomodel the Tg Behavior of Binary Blends of Sugars and Salts. Cryobiology 2014;68(1):1558. [55] Polamarasetty VK, Rao J, Das M, Das SK. Effect of moisture content on glass transition and sticky point temperatures of sugarcane, palmyra-palm and date-palm jaggery granules. Int J Food Sci Tech 2010;45:94104. [56] Simha R, Boyer RF. On a General Relation Involving the Glass Temperature and Coefficients of Expansion of Polymers. J Chem Phys 1962;37:10037. [57] Hancock BC, Zografi G. The Relationship between the Glass Transition Temperature and the water content of Amorphous Pharmaceutical Solids. Pharm Res 1994;11(4):4717. [58] Constantin JG, Schneider M, Cort HR. Glass Transition Temperature of Saccharide Aqueous Solutions Estimated with the Free Volume/Percolation Model. J Phys Chem B 2016;120:504755. [59] Hadjikinova R, Marudova M. Thermal behaviour of confectionary sweeteners’ blends. Bulg Chem Comm 2016;48(E):44650. [60] Kalichevsky MT, Jaroszkiewicz EM, Blanshard JMV. A study of the glass transition of amylopectin—sugar mixtures. Polymer 1993;34(2):34658. [61] Roos YH. Glass transition-related physicochemical changes in foods. Food Technol 1995;49:97102.
441
Thermodynamics of Phase Equilibria in Food Engineering
[62] Arvanitoyannis I, Blanshard JMV, Ablett S, Izzard MJ, Lillford PJ. Calorimetric study of the glass transition occurring in aqueous glucose: Fructose solutions. J Sci Food Agric 1993;63:17788. [63] Gontard N, Ring S. Edible wheat gluten film: influence of water content on glass transition temperature. J Agric Food Chem 1996;44:34748. [64] Ghanbarzadeh B, Oromiehi AR. Studies on glass transition temperature of mono and bilayer protein films plasticized by glycerol and olive oil. J Appl Polym Sci 2008;109:284854. [65] Kwei TK. The effect of hydrogen bonding on the glass transition temperature of polymer mixtures. J Polym Sci 1984;22:30713. [66] Kingsly ARP, IIeleji KE. Glass transition behavior of corn distillers dried grains with solubles (DDGS). J Cereal Sci 2011;54:3328. [67] Huang V.T. Mathematical modeling on the glass transition curves of glassy polymers. Paper No. 911. Presented at the Annual Meeting of the Institute of Food Technologists, Chicago, IL, 1993, p. 104. [68] Tolstoguzov V. Functional properties of food proteins and role of proteinpolysaccharide interaction. Food Hydrocolloid 1991;4:42968. [69] Matveev YI, Grinberg VY, Sochava IV, Tolsoguzov VB. Glass transition temperature of proteins. Calculation based on the additive contribution method and experimental data. Food Hydrocolloid 1997;11(2):12533. [70] Matveev YI, Slade L, Levine H. Determination of the main technological parameters of food substances by means of additive contribution method. Food Hydrocolloid 1999;13:3818. [71] Roe KD, Labuza TP. Glass Transition and Crystallization of Amorphous ThehaloseSucrose Mixtures. Int J Food Prop 2005;8(3):55974. [72] Starzak M, Mathlouthi M. Temperature dependence of water activity in aqueous solutions of sucrose. Food Chem 2006;96:34670. [73] Sugisaki M, Suga H, Seki S. Calorimetric Study of the Glassy State. IV. Heat Capacities of Glassy Water and Cubic Ice. Bull. Chem. Soc. Jpn 1968;41 (11):25919. [74] Zhang J, Zografi G. Water Vapor Absorption Into Amorphous Sucrose-Poly(Vinyl Pyrrolidone) and Trehalose 6 Poly(Vinyl Pyrrolidone) Mixtures. J Pharm Sci 2001;90(9):137585. [75] Jenniskens P, Blake D. Structural transitions in amorphous water ice and astrophysical implications. Science 1994;265:7536. [76] Peres AM, Macedo EA. Thermodynamic properties of sugars in aqueous solutions: correlation and prediction using a modified UNIQUAC model. Fluid Phase Equilib 1996;123:7195. [77] Peres AM, Macedo EA. A modified UNIFAC model for the calculation of thermodynamic properties of aqueous and non-aqueous solutions containing sugars. Fluid Phase Equilib 1997;139:4774.
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Phase Transition in Foods Camila Gambini Pereira
10.1 INTRODUCTION Most food products are complex materials composed of a large number of substances of different molecular weights and chemical structures. It is also known that each substance has different physical properties. The physical characteristics of these substances and of foods may vary greatly under certain operating conditions, with tendencies to form amorphous structures when cooled to temperatures below the melting point or when subjected to reduction of the water content present in the foods. Such structures are often desirable to provide the sensory attributes in the final materials, typically in products, such as prunes, raisins, and dried apricots. The mechanical and physical characteristics of amorphous materials are also related to the water activity and its influence in the molecular motion and food quality. The crunchiness of solid foods, cookies for example, is lost with water absorption and structural modification caused by the water plasticization. Phase transitions correspond to changes occurring in the phase and state of materials. These can be considered a first order transition, such as solidliquidvapor transitions, or a second order transition, such as glass transition, gelatinization, and denaturation. The importance of understanding the condition of glass transition is fundamental in the characterization of the physical behavior of food materials under processing and storage conditions, where amorphous materials are formed. Such events are found in steps such as crystallization and recrystallization, frozen storage, spray drying, extrusion, and candy formation. The determination of phase transition data has been performed for different foods since the 1980s, and some aspects of these data are discussed in this chapter. As a matter of fact, the phase transition data are presented as a reference factor for the determination of process performance in several aspects: (1) knowledge and control of the behavior of the amorphous state of food products during the processing and storage Thermodynamics of Phase Equilibria in Food Engineering
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of these materials; (2) evaluation of the quality of the final product and its relationship with consumer requirements; (3) analysis of the safety and shelf life of material, since factors such as microbiological action and enzymatic activity are directly related to the water activity present in the food and temperature of the material; and (4) optimization of the operational conditions to maintain the quality and characteristics of the product. In this sense, this chapter aims to present the main concepts of phase transition as well as an overview of glass transition studies in food.
10.2 FUNDAMENTAL CONCEPTS 10.2.1 Glassy Transition Glass is an amorphous (non-crystalline) solid of high viscosity (10101014 Pa/s). In this condition, the material is hard and brittle [1]. The main characteristic of this material is the high reduction in molecular mobility, offering a wide variety of applications, mainly in the food industry. Glassy materials can be obtained from the rapid cooling of the material below its melting point. Under these conditions, the physical and mechanical properties of the material are quite brittle and easily affected by external conditions [2]. When a liquid is slowly cooled in such a way that the system remains in equilibrium, it will crystallize at melting point (Tm). This transition is characterized by a rapid and significant decrease in the specific volume. However, if the process occurs at an extremely high cooling rate, 2(dT/ dt), i.e., cooled very quickly, the material arrives at the condition of noncrystalline solid (glass), in the vitreous state, whose specific volume resembles that of the crystalline state. The temperature that establishes the emergence of the vitreous state is called the glass transition temperature (Tg). This condition is presented in Fig. 10.1. Here it is also possible to observe the effect of the phase change on the apparent viscosity in both circumstances. In Fig. 10.1, the region between Tg and Tm is defined as glass transition. The melting transition, resulting from slow transition, is an equilibrium state. However, the fast cooling process propitiates the emergence of the glass transition region and vitreous state, considered as non-equilibrium and metastable states. Here, it is worth highlighting the differences in some terminologies. In Chapter 2, the concepts of equilibrium and nonequilibrium were defined, describing situations within the context observed for food systems and related processes. As well as this, the different forms of 422
Phase Transition in Foods
Specific volume
(A) Liquid
uid
Liq
Glass Crystal
log ηa
(B) Crystal
Glass
Liq
uid Liquid
Tg
Tm
Temperature
Figure 10.1. General representation of the phase transition in the formation of glass and crystal of a pure nonpolymeric component. (A) Specific volume as a function of temperature; (B) apparent viscosity (ηa), with slow cooling (—), and very fast cooling (- - -). Based on [2].
equilibrium (stable, unstable, metastable, and neutral) were explained from the thermodynamic point of view, and, when we talk about glass transition, these concepts reappear. Amorphous systems have atomic clusters, where the atom positions coincide with relative minima of the free energy, differently from the lattice positions, providing atomic relaxation motions toward equilibrium configurations, with very small atomic reorganization. This is a characteristic of metastable systems [3]. Therefore, amorphous materials, such as noncrystalline solids (glass) and supercooled liquids, are in a metastable state. 423
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However, it should be emphasized that the non-equilibrium states involve time-dependent changes. Since the glass transition is a region formed as a function of the rate 2dT/dt, whose properties and physical structures may vary according to the type of the processing applied, the transition is considered a non-equilibrium state. Accordingly, the glass transition region (TTg) is a non-equilibrium transition, which connects two different metastable conditions, i.e., the supercooled (or supersaturated) liquid and the glass. Note that amorphous materials (metastable systems) under non-equilibrium conditions exhibit time-dependent changes and, therefore, also tend to approach the equilibrium condition, that is, the crystalline state. As explained in Chapter 2, any system remains in equilibrium as long as the modifications in the vicinity do not affect its state. Thus, systems in metastable equilibrium condition, like amorphous materials, can move out of the equilibrium state if the neighbors in non-equilibrium are acting on the system. In food, this situation is commonly to be found: sweet confectionery, an amorphous solid (metastable material), suffers alteration over time with its texture, for instance, when exposed to environmental conditions with variances in relative humidity and temperature (non-equilibrium conditions). With such characteristics, amorphous materials exhibit particularities that depend on the processing and environment that surround them. During the food processing, particularly when water is removed and/ or temperature is reduced to conditions below the melting point, glass transition state (region) is achieved and amorphous or partially amorphous materials can be formed. Pure food compounds, such as carbohydrates and proteins, often show glass transition with variations in properties as indicated by Fig. 10.1 [47]. However, several food systems may present such partially amorphous substances. This status is affected by water presence and temperature changes, as will be discussed in Section 10.2. Glass transition may be present in both low-moisture/dehydrated foods, such as snack foods or breakfast cereals, and high-moisture foods, such as frozen foods. In all these cases, the food is characterized by having amorphous or partially amorphous profile. The transition region is also accompanied by a variation in viscosity that influences the characteristics of the material. This change is quite perceptible in solid amorphous materials (vitreous state) that, when absorbing water or increasing temperature in the region of glass transition, came to have a different texture characteristic of rubbery materials. This change in the viscosity in amorphous materials through the effect of temperature is evidenced in Fig. 10.2 by the variations 424
Log modulus log ηa
Phase Transition in Foods
Glassy
“Rubbery”
Tg
Liquid
Tm
Temperature Figure 10.2. Schematic viscoelastic behavior of partially crystalline synthetic polymers, indicated by the elastic shear modulus—log Modulus (—), and apparent viscosity, ηa (- - -). Based on [2].
of elasticity modulus of the material at temperatures below the melting point, between the amorphous glassy state and the fluid. The diagram represented in Fig. 10.2 provides information on the rheological characteristics of the polymeric systems as a function of the effect of the variation of temperature during the glass transition. The term “rubbery” state is employed to describe the highly viscoelastic characteristic of polymers when they are in the amorphous state limited by the temperatures Tg and Tm. It is a term used generally to describe the rheological nature of these materials. The phase transition from glassy to liquid states in polymers is characterized by the rapid fall of the elasticity modulus (from about 109 to 106 Pa), by the effect of a small increase in temperature, resulting in a significant change in the rigidity of the material, followed by a plateau region indicating a long-range elasticity of the material over a wide temperature range. The final decline of the modulus is characteristic of linear polymers and has both rubber elasticity and flow properties [1]. In general, the glass transition temperature (Tg) occurs at 100150 K below the compound melting temperature [2], as observed in Table 10.1. 425
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Table 10.1. Physical properties of food components in the glass transition [10,11] Compound
M (g/mol) Tm (K)
Maltohexaose Maltotetraose Maltotriose Sucrose Maltose Glucose Fructose
990.9 666.6 504.4 342.3 342.3 180.1 180.1
461.5 6 0.5 421 6 2 397.15
Tg (K)
Tg0 (K)a
w10 b
388.15 384.15 349.15408.15 325.15343.15 316.15368.15 294.15312.15 278.15290.15
258.65 252.65253.65 244.15249.65 227.15241.15 232.15243.65 216.15230.15 220.15231.15
0.670.76 0.640.81 0.690.82 0.640.84 0.740.80 0.670.83 0.510.85
Tg0 is the glass transition temperature in the maximally freeze-concentrated solution. w10 is the mass fraction of the solute in the condition of maximally freeze-concentrated solution. The meaning of these terms is discussed in Section 10.3.
a
b
Although glass transition temperature (Tg) is often indicated by a single value, it can vary. Indeed, Tg depends on the experimental conditions used in its determination, the type of apparatus employed, and interpretive ability of the operator. As well as this, the value of Tg depends on the thermal history, that is, even applying the same method, a certain sample can present different values of Tg. One of the features of glass transition is that similar to synthetic polymers, the glass transition temperatures of amorphous food compounds increase with increasing molecular weight, as observed in Table 10.1.
10.2.2 Plasticization and Molecular Mobility According to Platzer [12], plasticization is the process in which the plasticizer substances neutralize intermolecular bonds of the van der Waals type between the polymer molecules to make it easier to bend. It increases the mobility of the polymer and decreases the crystallinity. In the case of foods, a similar effect can be observed. Foods are heterogeneous systems composed of different substances, such as carbohydrates, proteins, lipids, other minor components, and water. Polymers such as carbohydrates and proteins also undergo the effect of plasticization, which occurs mainly due to the water presence. In these, water acts as plasticizer, and, as it has lower molecular weight than the bulk material, it causes an increase in free volume, resulting in plasticization. Also, when present in concentrated foods, carbohydrates and proteins are generally in the amorphous state. As explained, one of the main characteristics of amorphous materials is the reduced molecular mobility. When the temperature increases above the temperature of glass transition (Tg), the 426
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473
Temperature (K)
423
373 Starch 323 Glutenin Maltose Fructose 273
223 0
5
10
15
20
25
30
Water content (g/100g of solids) Figure 10.3. Plasticization effect by water of amorphous carbohydrates: fructose (K), maltose (x), glutenin (’), starch (▲). Adapted with permission from [7].
molecular mobility increases causing a decrease in the viscosity of the material. In such situations, the plasticization is a result of the temperature effect. In addition, the plasticizing effect is also described by the dependence of the glass transition temperature on either weight or volume fraction of water. The plasticization of amorphous materials by water affects the temperature of glass transition (Tg). When water is absorbed by the material, it increases the free volume, and the increase in the water content results in the decrease of the glass transition temperature, as observed in Fig. 10.3. Therefore, changes in amorphous food properties can be the result of thermal plasticization, due to the increase in temperature, or water plasticization, by increasing the amount of water. Indeed, low molecular weight components decrease the Tg of polymers by increasing the free volume available to the polymer. In food, besides water, substances of low molecular weight, such as salts, alcohols, sugars, acids and others, also act as a plasticizer. This effect can be additive. One example is the glass transition of amylopectin in the presence of water and fructose. It is known that the glass transition of carbohydrates (in this case: amylopectin) decreases with an increasing amount of water 427
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in the system. The analysis of the ternary system amylopectin waterfructose indicated that the addition of fructose in the mixture amylopectinwater drastically reduces the temperature value of Tg of the system. The effect of fructose on the Tg of the amylopectinwater system was higher when the water content was lower, due to the greater volume fraction of fructose in the systems at reduced water content. Whats is more, it has been observed that as the molecular weight of water is less than that of fructose, the plasticizing effect of water dominates the effect of fructose when the water content is increased. This additive effect of low weight molecules has been observed in other food mixtures [1315]. Moreover, especially when talking about proteins, the molecule of globular proteins may be considered as hydrophilic glassy state, encapsulating a hydrophobic central part [16]. Since food compounds of low molecular weight such as essential oils, fatty acids, surfactants absorbed by aqueous media can decrease the conformational stability of proteins and cause the swelling and dissociation of certain protein molecules, they also are considered “internal plasticizers”.
10.3 STATE DIAGRAMS In the previous chapters, phase diagrams were used to indicate phase behavior of systems at a given condition of temperature, pressure, or composition, being important in processes whose equilibrium condition is the necessary requirement for the separation or obtaining of a particular component. Such diagrams provide information where phase transition (melting, boiling, subliming) occurs at equilibrium condition. However, as explained, the transition observed in the glass transition is in a nonequilibrium condition; for this reason, the diagrams that represent the behavior of a system in a glass transition are named “state diagrams”. State diagrams indicate the glass transition temperature (Tg) of a given solute, providing a boundary between regions of lower mobility (glassy) and increasing mobility (supersaturated liquid). The simplest form of state diagram is presented in Fig. 10.4. The liquidus and solidus curves denote the melting point and the solute solubility. The intersection of these two curves occurs in Te (eutectic point), under equilibrium conditions. Further crystallization and concentration of the solute in the solution may still occur along the pathway Te and Tg0 . In the last condition of this segment, the solution has a concentration of the solute indicated by w10 . This condition is the maximal-freezing concentration, where the water present in the mixture is 428
Phase Transition in Foods
313 293
Temperature (K)
273 253 233 213 193 173 153 133 0.00
0.20
0.40
0.60
0.80
1.00
w1 (%) Figure 10.4. State diagram of the system D-fructose (1)water (2), with equilibrium states (—); and metastable equilibrium states (- - -). Experimental data (x, K, &, Δ, 3 ) from [1719].
unfreezable. Even when the temperature is decreased, the amount of water (1 2 w10 ) remains unfrozen. Tg0 is the glass transition temperature of a maximally freeze-concentrated solution. Tg0 and w10 data of some food components are presented in Table 10.1. Solutions rapidly cooled to temperatures lower than glass transition curve show formation of glassy material. The main utility of state diagrams is to identify glassy regions, where the molecular mobility is minimal, and the supersaturated state, where the molecular mobility is increased (characteristic of the “rubbery” state). The passage of a glassy state to a supersaturated state can be performed either by increasing the temperature at a given fixed composition or increasing the plasticizer amount (generally water in foods) at a given fixed temperature or both. Moreover, different subregions can be found in the glass transition region, providing different behaviors when temperature or compositions are modified, as indicated in Fig. 10.5. State diagrams have been defined for several food components: sugars and starch [2124], milk powders [25,26], cereal and proteins [2729], general food systems such as fruits and vegetables [3032], and several others [3336], with some regions characterized as indicated in Fig. 10.5. 429
ve
Thermodynamics of Phase Equilibria in Food Engineering
lity
c ur
Liquid Solution
ubi
Super-
Temperature
saturated solution
S ol
Melting point cu
Tm2
rve
Tg1
Ice + Solution
Te
Ice + Supersaturated solution
Tg′
Ice + Glass
Glass n sitio tran Glass
0
ve cur
Glass
w1′
1
Solute mass fraction (%) Figure 10.5. Typical state diagram of food systems, with equilibrium curves (—), and metastable equilibrium curves (- - -).
10.4 GLASS TRANSITION AND THE QUALITY OF FOOD A general rule is that food is more stable at and below its glass transition. In thermodynamics, the term “stable” is given when the system is in a condition of minimum value in its energetic state. In the case of food science, most often the term “stable” is used to designate the quality of materials, providing information on the shelf life, from the sensorial (color, taste, texture) and microbiological point of view. Even systems in non-equilibrium conditions tend over time to achieve the stable equilibrium condition. In other words, amorphous foods tend to reach the condition of thermodynamic stability (solid, liquid, gas) after a prolonged storage period (usually after the shelf life of the product). The greater stability of food in the glass transition is due to the fact that molecular mobility is quite reduced. This happens due to the low water activity and value of the temperature range TTg. The dependence of chemical and biochemical reactions and microbial growth in food is directly related to the availability of water, expressed in terms of water 430
Phase Transition in Foods
Shelf life Stability
activity. Foods with higher availability of water may also have reduced mobility in two situations: (1) in the vitreous state (glassy), if the process of water removal is extremely fast avoiding the crystallization of water; or (2) in supersaturated solution state, providing a system with a rubbery state profile. It is important to note that even below the glass transition condition, small molecules generally still have a certain molecular mobility, although greatly reduced, allowing for some chemical reactions to possibly exist, although very slowly, as is the case of lipid oxidation. However, microbial growth usually stops in amounts of water above glass transition. As a matter of fact, nowadays, the stability of foods is assessed by considering both data: water activity and temperature. The conditions of glass transition temperatures (Tg and TTg) settled during the processing and temperature of storage have a direct effect on the stability and shelf life of foods, as illustrated in Fig. 10.6. Although the presence of water has a direct relation to the quality and deterioration of foods, today it is a consensus that Tg and the difference TTg have strong effects on the mobility of biomolecules in foods. A classic example is the loss of crispness from cookies when they remain exposed to the environment by absorbing the humidity from the air, which leads to changes in their texture (changing to the rubbery
glass
“rubber”
liquid Temperature aw
Figure 10.6. Effect of temperature and water activity (aw) in the shelf life and stability of foods.
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Thermodynamics of Phase Equilibria in Food Engineering
state). Another example is the recrystallization of ice in frozen foods. Ice creams are processed in such a way that the temperature is reduced rapidly to prevent water crystallization. When exposed to room temperature for a long time, the temperature of the environment causes melting of the ice cream. When this slightly or partially melted product returns to the freezer (e.g., in the consumer’s residence), freezing (normally slow) is not carried out properly, causing the emergence of ice crystals, or even, the separation of the mixture into two or more phases. As seen in both cases, the stability and shelf life of food are strongly affected by the temperature and presence of water in the food. In the case of ice creams, the use of stabilizers, such as guar gum, carrageenan, xanthan, and gelatin, act in the stabilization of ice crystals in the ice cream, improving the transport properties of the unfrozen part of the system, by increasing the viscosity in the rubbery region [37], as indicated in Fig. 10.7. The quality of foods is generally related to consumer demands (crispy crackers, stuffed confectionery, frozen food, etc.), and legislation requirements (food safety, identification, labeling, etc.). In both cases, quality is associated with microbial action, and sensory and physical changes observed during processing and storage of food. Besides the quality of food, several properties of amorphous materials change in the glass transition region. These variations are observed in both thermal (heat capacity,
Viscosity (millions of Pas)
6 5 4 3 2 1 0 238
Tg′
243
248
253
258
Temperature (K)
263
268
273
Tm
Figure 10.7. Effect of stabilizers on the viscosity and rubbery state of the ice creams mixes: with stabilizers (—), without stabilizers (- - -). Adapted with permission from [37].
432
Phase Transition in Foods
278
Temperature (K)
268
258
248
238
228 0
100
200
300
400
Pressure (MPa) Figure 10.8. Effect of pressure on freezing temperature for potato (K), compared with that for water (—). Metastable regions indicated by A, B, and C (hachured) associated with experimental data (K, &, ▲). Adapted with permission from [41].
thermal expansion, diffusivity) and rheological (viscosity, elastic shear modulus) properties [38]. In addition to the effect of temperature and water removal, studies have shown that the pressure applied during processing to obtain food systems by freezing also influences the phase transition [3945]. In studies of freezing of potato tissue, different ice alterations were observed during freezing processes at pressures ranging from 0 to 300 MPa, finding three metastable regions from 200 to 300 MPa [41], as shown in Fig. 10.8. As a consequence, pressure has a significant influence on the chemical, enzymatical, and structural changes in food processing.
10.5 MATHEMATICAL MODELING When it comes to process engineering, one of the key issues is process prediction and modeling. For the equilibrium condition (melting point and solubility curves), the prediction can be performed using the thermodynamic calculations procedures which make use of activity coefficient models, as described in Chapter 8. In the case of non-equilibrium conditions, this question becomes even more complicated due to the food 433
Thermodynamics of Phase Equilibria in Food Engineering
components involved and variations related to this state. In the glass transition, Tg is dependent on the technique used for its determination and the procedure of analysis, which could lead to different Tg values. However, some researchers have proposed equations that help predict the glass transition region based on the properties of the compounds present in the systems. Although similarities in vitreous behavior have been observed between polymers and some food compounds, such as proteins and carbohydrates, some models applied to predict the glass transition of polymer systems are not applicable in food systems, since they are based on the resemblance of the properties of the compounds of the mixture, which rarely happens when it comes to foods. One of the first equations that was successful in adjusting food systems was the Gordon and Taylor equation [46], in 1952, Eq. (10.1), originally developed to describe the dependence of Tg with the binary composition of miscible polymers. This equation presented good results in the prediction of Tg of compounds like amorphous sugars [22,23,47,48] and maltodextrin [22,49]. Tg 5
w1 Tg1 1 kw2 Tg2 w1 1 kw2
(10.1)
where wi is the mass fraction of the component i, Tgi is the glass transition temperature of the component i, and k is a function of the thermal expansion coefficient that is generally estimated using non-linear regression analysis. In 1978, Couchman and Karasz [50] relied on the thermodynamic theory of the glass transition of polymer mixtures, considering the individual values of the heat capacities (ΔCpi ), to propose a plasticization model, indicated by w2 ΔCp2 ln Tg2 =Tg1 Tg ln 5 (10.2) w1 ΔCp1 1 w2 ΔCp2 Tg1 or lnTg 5
w1 ΔCp1 lnTg1 1 w2 ΔCp2 lnTg2 w1 ΔCp1 1 w2 ΔCp2
(10.3)
Some authors use the Couchman and Karasz equations, Eqs. (10.2) or (10.3), in a simplified way, disregarding the logarithm effect, resulting in the approximate form indicated by Eq. (10.4). One should only take care that this approximation does not occur in an overestimation of the Tg condition of the mixture. 434
Phase Transition in Foods
Tg 5 or simply
w1 ΔCp1 Tg1 1 w2 ΔCp2 Tg2 w1 ΔCp1 1 w2 ΔCp2
w1 Tg1 1 w2 ΔCp2 =ΔCp1 Tg2 Tg 5 w1 1 w2 ΔCp2 =ΔCp1
(10.4)
(10.5)
Observe that Eqs. (10.1) and (10.5) are exactly the same, since k5
ΔCp2 ΔCp1
(10.6)
This equation has been used with success to predict the glass transition temperature of maltooligosaccharides [51]. However, in aqueous solutions, the experimental values of the heat capacity of water are quite dissimilar and have provoked great debates. Kalichevsky et al. [52] have generated an important discussion about this issue. As well as this, if the heat capacity of pure water is used in Eq. (10.6), it can lead to values of k less than 1, resulting in contradictory behavior in the glass transition curve when compared to what is observed experimentally [21,5255]. Another way to determine this constant is considering the information of glass transition of amorphous solid through the free volume theory [56]. Good results from this have been observed in different aqueous systems [55,5759]. According to this theory, when the multiplication between the variation of the thermal expansion coefficient (Δα 5 αL 2 αg) and Tg is approximately constant, the following relation provides good representation for the value of k: k5
ρ1 Tg1 ρ2 Tg2
(10.7)
The Couchman and Karasz equation in its approximated form, Eq. (10.4), was extended by Kalichevsky and Blanshard [60] in a study of the glass transition of the ternary system wateramylopectinsugar. This equation has been applied to ternary and quaternary systems containing sugar constituents [43,61,62] and other ternary systems, such as waterglutenglycerol [63], waterproteinglycerol, and waterproteinolive oil [64]. Pn i51 wi ΔCpi Tgi Tg 5 P (10.8) n i51 wi ΔCpi
435
Thermodynamics of Phase Equilibria in Food Engineering
Analogously, the Kwei equation [65], Eq. (10.9), originally developed for polymer systems, has also been extended to predict the glass transition behavior of multicomponent systems, Eq. (10.10), such as systems of corn distiller dried grains with soluble compounds in water [66]. Tg 5
w1 Tg1 1 kw2 Tg2 1 qw1 w2 w1 1 kw2
P n w1 Tg1 1 ni52 ki21 wi Tgi Pn 1 q L wi Tg 5 w1 1 i52 ki21 wi i51
(10.9)
(10.10)
where q is a fitting constant that incorporates the dependence of intermolecular interaction between the components. Another equation with a similar proposal, based on the values of individual Tgi and individual values of the heat capacities, has shown good results to predict the glass transition temperatures of carbohydrates and proteins. The Huang equation [67], Eq. (10.11), was able to predict values of Tg for glucose, maltose, maltotriose, maltohexose, starch, and gluten with a good approximation of experimental data. " # w1 ΔCp1 Tg1 1 Tg2 1 2w2 ΔCp2 Tg2 Tg 5 Tg1 (10.11) w1 ΔCp1 Tg1 1 Tg2 1 2w2 ΔCp2 Tg1 Furthermore, the additive group-contribution method has been used to predict the glass transition temperature of proteins, carbohydrates, and their mixtures [15,6870]. The method provided very good results for all systems evaluated. For proteins, the calculated values were very close to experimental data in systems containing a weight fraction of water from 0.05 to 0.25. The largest difference was observed at low water content. The reason is the strong intermolecular interactions observed in the systems in these conditions, leading to a decrease in the macromolecular motion, which increases the chain rigidity and the distance in the predicted Tg value [15]. In the case of carbohydrates, the model provided good agreement with experimental data.
10.6 CASE STUDY Currently one of the most present ingredients in food is sucrose, with varied functions ranging from sweetening to texture and increasing the shelf life of foods. Its presence in frozen foods also promotes a change in 436
Phase Transition in Foods
the glass transition point. Due to its importance of application, experimental data on glass transition (Tg) have been presented in the literature, furthermore, correlating this information with mathematical models becomes quite useful when it comes to studying the optimization of an industrial process. In this sense, the present case study aims to correlate data of phase change of the system sucrose (1)water (2) in a state of equilibrium (melting point and solubility) and non-equilibrium (glass transition) with mathematical models to evaluate their applicability. For this end, experimental data collected from literature [71,72] were used. For melting point and solubility curves, UNIQUAC and UNIFAC models (described in Chapter 4) were applied, considering the parameters presented in Tables 10.2 and 10.3. For the glass transition, equations of Gordon and Taylor, Eq. (10.1), Couchman and Karasz, Eq. (10.4), and Kwei, Eq. (10.9), were applied, using Tg1 5 343K [71] and Tg2 5 134K [73]. For Eq. (10.1), k 5 5.2 [71] was applied. For Eq. (10.4), as the values of ΔCP1 5 218.88 J/mol.K [74] and ΔCP2 5 34.92 J/mol.K [73], the value of k obtained by Eq. (10.6) will be 0.16, and then the curvature of glass transition will be inverted, as expected based on the discussion presented in Section 10.5. In this way, Eq. (10.7) was used, considering ρ1 5 1.47 g/cm3 [74] and ρ2 5 0.94 g/cm3 [75]. For Eq. (10.8), k 5 5.2 [71] and the adjusted parameter q 5 3.79 K were used. The comparison between the calculated and experimental data is presented in Fig. 10.9.
Table 10.2 UNIQUAC parameters for the system sucrose (1)water (2) [76] Component
ri
qi
a012 =K
at12
a021 =K
at21
Sucrose (1) Water (2)
14.5496 0.92
13.764 1.4
89.3391
0.3328
118.995
0.3410
Table 10.3 UNIFAC parameters for the system sucrose (1)water (2) [77]
PYR FUR -OCH2 OHring H2 O
PYR
FUR
-O-
CH2
OHring
H2O
0 0 0 0 0 2599.043
0 0 0 0 0 2866.916
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 2102.546
243.2789 2169.231 0 0 591.9366 0
437
Thermodynamics of Phase Equilibria in Food Engineering
400
Temperature (K)
350 300 250 200 150 100 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
w1 Figure 10.9 State diagram of the system sucrose (1)water (2). Experimental data ( , Δ, x) collected from [71,72], calculated values using UNIQUAC (—) and UNIFAC (- - -) for the melting point and solubility curves; and Gordon and Taylor ( ), Couchman and Karasz (a a), and Kwei (- e -) equations for the glass transition curve.
It can be observed that for the melting point and solubility, both models (UNIQUAC and UNIFAC) presented very good predictions, with slight deviations when the solution is concentrated (w1 . 0.73). For the glass transition, as Tg values are not precise, it becomes difficult to evaluate the models, nonetheless, all the equations applied provided values coherent to the experimental data.
10.7 CONCLUDING REMARKS The study of glass transition is very important in the food industry, since the formation of amorphous structures in such conditions is related to the quality characteristics of food products. Its application in food is extremely varied, being observed from dehydrated, frozen and crystallized products to the formation of microstructured materials and biopolymer films. However, although there has been some advance in the knowledge of the vitreous transition of food systems, it is still very small in the face of the variety of products, processes, and 438
Phase Transition in Foods
situations found in everyday life. Furthermore, studies to predict the behavior of such foods in vitreous conditions are still necessary in order to better understand the behavior of pure compounds in complex mixtures, and in foods in relation to the variables that affect this state, such as temperature, pressure, presence of water and other minority compounds.
REFERENCES [1] Sperling LH. Introduction to physical polymer science. New York, NY: John Wiley & Sons; 2006. [2] Walstra P. Physical chemistry of foods. New York, NY: Marcel Dekker; 2003. [3] Ossi OM. Disordered materials. An introduction. New York, NY: Springer; 2006. [4] Slade L, Levine H. Glass transitions and waterfood structure interactions. Adv Food Nutr Res 1995;38:103269. [5] Kalichevsky MT, Jaroszkiewicz EM, Ablett S, Blanshard JMV, Lillford PJ. The glass transition of amylopectin measured by DSC, DMTA and NMR. Carbohydr Polym 1992;18:7788. [6] Talja RA, Roos YH. Phase and state transition effects on dielectric, mechanical, and thermal properties of polyols. Thermochim Acta 2001;380:10921. [7] Roos YH, Drusch S. Phase transition. 2nd ed. Oxford: Elsevier; 2016. [8] Gleick J. Rubber physics. Slovakia: Alexander Dubcek University of Trencin; 2007. [9] Levine H, Slade L. Influences of the glass and rubbery states on the thermal, mechanical and structural properties of doughs and backed products. In: Faridi H, Faubion JM, editors. Dough rheology and baked product texture. New York, NY: Van Nostrand Rheinhold/AVI; 1989. [10] Slade L, Levine H, Finley JW. Proteinwater interactions: water as a plasticizer of gluten and other protein polymers. In: Phillips RD, Finley JW, editors. In: Protein quality and the effects of processing. New York, NY: Marcel Dekker; 1989. [11] NIST. National Institute of Standards and Technology. Available in: www.nist.gov. (Accessed in July 2017). [12] Platzer NAJ. Plasticization and plasticizer processes. Advances in chemistry. Washington, DC: American Chemical Society; 1965. [13] Kalichevsky MT, Blanshard JMV. The effect of fructose and water on the glass transition of amylopectin. Carbohydr Polym 1993;20(2):10713. [14] Kalichevsky MT, Blanshard JMV. A study of the effect of water on the glass transition of 1:1 mixtures of amylopectin, casein and gluten using DSC and DMTA. Carbohydr Polym 1992;19:2718. [15] Matveev YI, Grinberg VY, Tolstoguzov VB. The plasticizing effect of water on proteins, polysaccharides and their mixtures. Glassy state of biopolymers, food and seeds. Food Hydrocolloid 2000;14:42537. [16] Tolstoguzov V. Origins of globular structure in proteins hypothesis. FEBS Lett 1999;444(145-8):1. [17] Ablett S, Izzard MJ, Liliford PJ, Arvanitoyannis J, Blanshard JMV. Calorimetric study of the glass transition occurring in fructose solutions. Carbohyd Res 1993;246:1322. [18] Vasitko J, Smelfk A. Solubility of anhydrous BD-fructose in water. Chem Zvesti 1967;21:7368.
439
Thermodynamics of Phase Equilibria in Food Engineering
[19] Young FE, Jones FT, Lewis HJ. D-Fructosewater phase diagram. J Phys Chem 1952;56:1093109. [20] Young FE, Jones FT, Lewis HJ. D-Fructosewater phase diagram. J Phys Chem 1952;56(9):10936. [21] Blond G, Simatos D, Catte´ M, Dussap CG, Gros JB. Modeling of the water-sucrose state diagram below 0 ˚C. Carbohyd Res 1997;298:13945. [22] Roos Y, Karel M. Water and molecular weight effects on glass transitions in amorphous carbohydrates and carbohydrate solutions. J Food Sci 1991;56:167681. [23] Roos Y. Melting and glass transitions of low molecular weight carbohydrates. Carbohydr Res 1993;238:3948. [24] Ruiz-Cabrera MA, Rivera-Bautista C, Grajales-Lagunes A, Gonza´lez-Garcı´a R, Schmidt SJ. State diagrams for mixtures of low molecular weight carbohydrates. J Food Eng 2016;171:18593. [25] Jouppila K, Roos YH. Glass transitions and crystallization in milk powders. J. Dairy Sci 1994;77:290715. [26] Vuataz G. The phase diagram of milk: a new tool for optimizing the drying process. Lait 2002;82:485500. [27] de Graaf EF, Madeka H, Cocero AM, Kokini JL. Determination of the effect of moisture on gliadin glass transition using mechanical spectrometry and differential scanning calorimetry. Biotechnol Prog 1993;9:21013. [28] Sablani S, Bruno L, Kasapis S, Symaladevi RM. Thermal transitions of rice: development of a state diagram. J Food Eng 2009;90(1):11018. [29] Asherie N. Protein crystallization and phase diagrams. Methods 2004;34:26672. [30] Sa´ MM, Sereno AM. Glass transitions and state diagrams for typical natural fruits and vegetables. Thermochim Acta 1994;246(2):28597. [31] Guizani N, Al-Saidi GS, Rahman MS, Bornaz S, AliAl-Alawi A. State diagram of dates: glass transition, freezing curve and maximal-freeze-concentration condition. J Food Eng 2010;99(1):927. [32] Witczak T, Witczak M, Ste˛pie´n A, Bednarz A, Grzesik M. State diagrams of candied orange peel obtained using different hypertonic solutions. J Food Eng 2017;212:23441. [33] Fonseca F, Obert JP, Be´al C, Marin M. State diagrams and sorption isotherms of bacterial suspensions and fermented medium. Thermochim. Acta 2001;366(2):16782. [34] Ohkuma C, Kawai K, Viriyarattanasak C, Mahawanich T, Tantratian S, Takaia R, et al. Glass transition properties of frozen and freeze-dried surimi products: effects of sugar and moisture on the glass transition temperature. Food Hydrocolloids 2008;22 (2):25562. [35] Shi Q, Wang X, Zhao Ya, Fang Z. Glass transition and state diagram for freezedried Agaricus bisporus. J Food Eng 2012;111:66774. [36] Rahman MS, Kasapis S, Guizani N, Al-Amri OS. State diagram of tuna meat: freezing curve and glass transition. J Food Eng 2003;57(4):3216. [37] Goff HD, Caldwell KB, Stanley DW, Maurice TJ. The influence of polysaccharides on the glass transition in frozen sucrose solutions and ice cream. Dairy Sci 1993;76:126877. [38] Pereira CG. Vitreous transition in foods: an analysis under the thermodynamic and technological view. In: IX Brazilian Congress of Applied Thermodynamics and V School of Thermodynamics, October, 2017. [39] LeBail A, Boillereaux L, Davenel A, Hayert M, Lucas T, Monteau JY. Phase transition in foods: effect of pressure and methods to assess or control phase transition. Innov Food Sci Emerg Technol 2003;4:1524. [40] Benet GU, Schlu¨ter O, Knorr D. High pressurelow temperature processing. Suggested definitions and terminology. Innov Food Sci Emerg Technol 2004;5 (4):41327. 440
Phase Transition in Foods
[41] Schluter O, Benet GU, Heinz V, Knorr D. Metastable states of water and ice during pressure-supported freezing of potato tissue. Biotechnol Prog 2004;20:799810. [42] Zhu S, Le Bail A, Ramaswamy HS. High-pressure differential scanning calorimetry: Comparison of pressure-dependent phase transition in food materials. J Food Eng 2006;75:21522. [43] Benet GB, Chapleau N, Lille M, Le Bail A, Autio K, Knorr D. Quality related aspects of high pressure low temperature processed whole potatoes. Innov Food Sci Emerg Technol 2006;7(12):329. [44] Benet GU, Balogh T, Schneider J, Knorr D. Metastable phases during high-pressure low-temperature processing of potatoes and their impact on quality-related parameters. J Food Eng 2007;78(2):37589. [45] Otero L, Ousegui A, Benet GU, Elvira C, Havet M, Le Bail, et al. Modelling industrial scale high-pressure-low-temperature processes. J Food Eng 2007;83(2):13641. [46] Gordon M, Taylor JS. Ideal copolymers and the second-order transitions of synthetic rubbers. I. Non-crystalline copolymers. J Appl Chem 1952;2:493500. [47] Roos YH. Water activity and physical state effects on amorphous food stability. J Food Processes Preserv 1993;16(6):43347. [48] Truong V, Bhandari BR, Howes T, Adhikari B. Analytical model for the prediction of glass transition temperature of food systems. In: Levine H, editor. Amorphous foods and pharmaceutical systems. Cambridge, UK: RSC Publishing; 2002. p. 3147. [49] Roos Y, Karel M. Plasticizing effect of water on thermal behavior and crystallization of amorphous food models. J Food Sci 1991;56(1):3843. [50] Couchman PR, Karasz FE. A classical thermodynamic discussion of the effect of composition on glass-transition temperatures. Macromolecules 1978;11:11719. [51] Orford PD, Parker R, Ring SG, Smith AC. Effect of water as a diluent on the glass transition behaviour of malto-oligosaccharides, amylose and amylopectin. Int J Biol Macromol 1989;11:916. [52] Kalichevsky MT, Laroszkiewicz EM, Blanshard IMV. The glass transition of gluten. 1. Gluten and gluten-sugar mixtures. Int J Biol Macromol 1992;14:25766. [53] Katkov II, Levine F. Prediction of the glass transition temperature of water solutions: comparison of different models. Cryobiology 2004;49:6282. [54] Weng L, Vijayaraghavan R, MacFarlane DR, Elliott GD. Application of the Kwei Equation tomodel the Tg Behavior of Binary Blends of Sugars and Salts. Cryobiology 2014;68(1):1558. [55] Polamarasetty VK, Rao J, Das M, Das SK. Effect of moisture content on glass transition and sticky point temperatures of sugarcane, palmyra-palm and date-palm jaggery granules. Int J Food Sci Tech 2010;45:94104. [56] Simha R, Boyer RF. On a General Relation Involving the Glass Temperature and Coefficients of Expansion of Polymers. J Chem Phys 1962;37:10037. [57] Hancock BC, Zografi G. The Relationship between the Glass Transition Temperature and the water content of Amorphous Pharmaceutical Solids. Pharm Res 1994;11(4):4717. [58] Constantin JG, Schneider M, Cort HR. Glass Transition Temperature of Saccharide Aqueous Solutions Estimated with the Free Volume/Percolation Model. J Phys Chem B 2016;120:504755. [59] Hadjikinova R, Marudova M. Thermal behaviour of confectionary sweeteners’ blends. Bulg Chem Comm 2016;48(E):44650. [60] Kalichevsky MT, Jaroszkiewicz EM, Blanshard JMV. A study of the glass transition of amylopectin—sugar mixtures. Polymer 1993;34(2):34658. [61] Roos YH. Glass transition-related physicochemical changes in foods. Food Technol 1995;49:97102.
441
Thermodynamics of Phase Equilibria in Food Engineering
[62] Arvanitoyannis I, Blanshard JMV, Ablett S, Izzard MJ, Lillford PJ. Calorimetric study of the glass transition occurring in aqueous glucose: Fructose solutions. J Sci Food Agric 1993;63:17788. [63] Gontard N, Ring S. Edible wheat gluten film: influence of water content on glass transition temperature. J Agric Food Chem 1996;44:34748. [64] Ghanbarzadeh B, Oromiehi AR. Studies on glass transition temperature of mono and bilayer protein films plasticized by glycerol and olive oil. J Appl Polym Sci 2008;109:284854. [65] Kwei TK. The effect of hydrogen bonding on the glass transition temperature of polymer mixtures. J Polym Sci 1984;22:30713. [66] Kingsly ARP, IIeleji KE. Glass transition behavior of corn distillers dried grains with solubles (DDGS). J Cereal Sci 2011;54:3328. [67] Huang V.T. Mathematical modeling on the glass transition curves of glassy polymers. Paper No. 911. Presented at the Annual Meeting of the Institute of Food Technologists, Chicago, IL, 1993, p. 104. [68] Tolstoguzov V. Functional properties of food proteins and role of proteinpolysaccharide interaction. Food Hydrocolloid 1991;4:42968. [69] Matveev YI, Grinberg VY, Sochava IV, Tolsoguzov VB. Glass transition temperature of proteins. Calculation based on the additive contribution method and experimental data. Food Hydrocolloid 1997;11(2):12533. [70] Matveev YI, Slade L, Levine H. Determination of the main technological parameters of food substances by means of additive contribution method. Food Hydrocolloid 1999;13:3818. [71] Roe KD, Labuza TP. Glass Transition and Crystallization of Amorphous ThehaloseSucrose Mixtures. Int J Food Prop 2005;8(3):55974. [72] Starzak M, Mathlouthi M. Temperature dependence of water activity in aqueous solutions of sucrose. Food Chem 2006;96:34670. [73] Sugisaki M, Suga H, Seki S. Calorimetric Study of the Glassy State. IV. Heat Capacities of Glassy Water and Cubic Ice. Bull. Chem. Soc. Jpn 1968;41 (11):25919. [74] Zhang J, Zografi G. Water Vapor Absorption Into Amorphous Sucrose-Poly(Vinyl Pyrrolidone) and Trehalose 6 Poly(Vinyl Pyrrolidone) Mixtures. J Pharm Sci 2001;90(9):137585. [75] Jenniskens P, Blake D. Structural transitions in amorphous water ice and astrophysical implications. Science 1994;265:7536. [76] Peres AM, Macedo EA. Thermodynamic properties of sugars in aqueous solutions: correlation and prediction using a modified UNIQUAC model. Fluid Phase Equilib 1996;123:7195. [77] Peres AM, Macedo EA. A modified UNIFAC model for the calculation of thermodynamic properties of aqueous and non-aqueous solutions containing sugars. Fluid Phase Equilib 1997;139:4774.
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