Relative Vapor Pressure and Food Stability

Food stability and p/p0 are closely related in many situations. The data in Figure 23 and Table 6 provide examples of these relationships. Shown in Table 6 are various common microorganisms and the range of RVP permitting their growth. Also shown in this table are common foods categorized according to their RVP. Data in Figure 23 are typical qualitative relationships between reaction rate and p/p0 in the FIGURE 23 Relationships among relative water vapor pressure, food stability and sorption isotherms. (A) Microbial g rowth versus p/p 0. (B) Enzymic hydrolysis versus p/p0. (C) Oxidation (nonenzymic) versus p/p0. (D) Maillard browning versus p/p 0. (E) Miscellaneous reaction rates versus p/p 0. (F) W ater content versus p/p0. All ordinates are “relative rate” except for F. Data from various sources. Pag e 53 TABLE 6 Relative Vapor Pressure and Growth of Microorg anisms in Food Rang e of p/p0 Microorg anisms g enerally inhibited by lowest p/p 0 in this rang e Foods g enerally within this rang e 1.00–0.95 Pseudomonas, Escherichia, Proteus, Shigella, Klebsiella, Bacillus, Clostridium perfringens, some yeasts Hig hly perishable (fresh) foods and canned fruits, veg etables, meat, fish, and milk; cooked sausag es and breads; foods containing up to approximately 40% (w/w) sucrose or 7% sodium chloride 0.95–0.91 Salmonella, Vibrio parahaemolyticus, C. botulinum, Serratia, Lactobacillus, Pediococcus, some molds, yeasts (Rhodotorula, Pichia) Some cheeses (Cheddar, Swiss, Muenster, Provolone), cured meat (ham), some fruit juice concentrates; foods containing up to 55% (w/w) sucrose or 12% sodium chloride 0.91–0.87 Many yeasts (Candida, Torulopsis, Hansenula), Micrococcus Fermented sausag e (salami), spong e cakes, dry cheeses, marg arine; foods containing up to 65% (w/w) sucrose (saturated) or 15% sodium chloride 0.87–0.80 Most molds (mycotoxig enic penicillia), Staphylococcus aureus, most Saccharomyces (bailii) spp., Debaryomyces Most fruit juice concentrates, sweetened condensed milk, chocolate syrup, maple and fruit syrups; flour, rice, pulses containing 15–17% moisture; fruit cake; country-style ham, fondants, hig h-ratio cakes 0.80–0.75 Most halophilic bacteria, mycotoxig enic asperg illi Jam, marmalade, marzipan, g lacé fruits, some marshmallows 0.75–0.65 Xerophilic molds (Aspergillus chevalieri, A. candidus, Wallemia sebi), Saccharomyces bisporus Rolled oats containing approximately 10% moisture; g rained noug ats, fudg e, marshmallows, jelly, molasses, raw cane sug ar, some dried fruits, nuts 0.65–0.60 Osmophilic yeasts (Saccharomyces rouxii), few molds (Aspergillus echinulatus, Monascus bisporus) Dried fruits containing 15–20% moisture; some toffees and caramels; honey 0.50 No microbial proliferation Pasta containing approximately 12% moisture; spices containing approximately 10% moisture 0.40 No microbial proliferation W hole eg g powder containing approximately 5% moisture 0.30 No microbial proliferation Cookies, crackers, bread crusts, etc. containing 3–5% moisture 0.20 No microbial proliferation W hole milk powder containing 2–3% moisture; dried veg etables containing approximately 5% moisture; corn flakes containing approximately 5% moisture; country style cookies, crackers Source: Ref. 6 Pag e 54 temperature range 25–45°C. For comparative purposes a typical isotherm, Figure 23F, is also shown. It is important to remember that the exact reaction rates and the positions and shapes of the curves (Fig. 23A-E) can be altered by sample composition, physical state and structure of the sample, composition of the atmosphere (especially oxygen), temperature, and by hysteresis effects. For all chemical reactions in Figure 23, minimum reaction rates during desorption are typically first encountered at the boundary of Zones I and II of the isotherm (p/p0 0.20–0.30), and all but oxidative reactions remain at this minimum as p/p0 is further reduced. During desorption, the water content at the first-encountered rate minimum is the “BET monolayer” water content. The unusual relationship between rate of lipid oxidation and p/p0 at very low values of p/p0 deserves comment (Fig. 23C). Starting at the extreme left of the isotherm, added water decreases the rate of oxidation until the BET monolayer value is attained. Clearly, overdrying of samples subject to oxidation will result in less than optimum stability. Karel and Yong [48] have offered the following interpretative suggestions regarding this behavior. The first water added to a very dry sample is believed to bind hydroperoxides, interfering with their decomposition and thereby hindering the progress of oxidation. In addition, this water hydrates metal ions that catalyze oxidation, apparently reducing their effectiveness. Addition of water beyond the boundary of Zones I and II (Fig. 23C and Fig. 23F) results in increased rates of oxidation. Karel and Yong [48] suggested that water added in this region of the isotherm accelerates oxidation by increasing the solubility of oxygen and by allowing macromolecules to swell, thereby exposing more catalytic sites. At still greater p/p0 values (> ~ 0.80) the added water may retard rates of oxidation, and the suggested explanation is that dilution of catalysts reduces their effectiveness. It should be noted that curves for the Maillard reaction, vitamin B1 degradation, and microbial growth all exhibit rate maxima at intermediate to high p/p0 values (Fig. 23A, D, E). Two possibilities have been advanced to account for the decline in reaction rate that sometimes accompanies increases in RVP in foods having moderate to high moisture contents [20,54]. 1. For those reactions in which water is a product, an increase in water content can result in product inhibition. 2. When the water content of the sample is such that solubility, accessibility (surfaces of macromolecules), and mobility of rateenhancing constituents are no longer rate-limiting, then further addition of water will dilute rate-enhancing constituents and decrease the reaction rate. Since the BET monolayer value of a food provides a good first estimate of the water content providing maximum stability of a dry product, knowledge of this value is of considerable practical importance. Determining the BET monolayer value for a specific food can be done with moderate ease if data for the low-moisture end of the MSI are available. One can then use the BET equation developed by Brunauer et al. [8] to compute the monolayer value (8) where aw is water activity, m is water content (g H2O/g dry matter), m1 is the BET monolayer value, and C is a constant. In practice, p/p0 values are used in Equation 8 rather than aw values. From this equation, it is apparent that a plot of aw/m(1-aw) versus aw, known as a BET plot, should yield a straight line. An example for native potato starch, with aw replaced by p/p0, is shown in Figure 24. The linear relationship, as is generally acknowledged, begins to deteriorate at p/p0 values greater than about 0.35. Pag e 55 FIGURE 24 BET plot for native potato starch (resorption data, 20°C). (Data from Ref. 125.) The BET monolayer value can be calculated as follows: From Figure 24, the y intercept is 0.6. Calculation of the slope from Figure 24 yields a value of 10.7. Thus, In this particular instance the BET monolayer value corresponds to a p/p0 of 0.2. The GAB equation yields a similar monolayer value [81]. In addition to chemical reactions and microbial growth, p/p0 also influences the texture of dry and semidry foods. For example, suitably low RVPs are necessary if crispness of crackers, popped corn, and potato chips is to be retained; if caking of granulated sugar, dry milk, and instant coffee is to be avoided; and if stickiness of hard candy is to be prevented [53]. The maximum p/p0 that can be tolerated in dry materials without incurring loss of desirable properties ranges from 0.35 to 0.5, depending on the product. Furthermore, suitably high water activities of soft-textured foods are needed to avoid undesirable hardness. 2.11 Molecular Mobility (Mm) and Food Stability 2.11.1 Introduction Even though the RVP approach has served the food industry well, this should not preclude consideration of other approaches that can supplement or partially replace RVP as a tool for predicting and controlling food stability and processability. In recent years, evidence has become increasingly compelling that molecular mobility (Mm; translational or rotational motion) may Pag e 56 be an attribute of foods that deserves attention because it is related causally to many important diffusion-limited properties of food. Luyet and associated in the United States and Rey in France were apparently the first to draw attention to the relevance of Mm (glassy states, recrystallization, collapse temperatures during freeze drying) to properties of biological materials [74, 76, 78, 94]. John D. Ferry, a professor of chemistry at the University of Wisconsin, and his associates formulated many of the basic concepts pertaining to Mm in nonequilibrium systems consisting of synthetic, amorphous polymers [27,130]. In 1966, White and Cakebread [129] described the important role of glassy and supersaturated states in various sugar-containing foods and suggested that the existence of these states has an important influence on the stability and processability of many foods. Duckworth et al. [17] demonstrated the relevance of Mm to rates of nonenzymic browning and ascorbic acid oxidation, and thereby provided further evidence that the relationship between Mm and food stability is one of considerable importance. Widespread recent interest in the relationship between Mm and food properties was created primarily by Felix Franks [29] and the team of Louise Slade and Harry Levine [60–67, 112–118]. They showed that important basic principles underlying the behavior of synthetic, amorphous polymers, as developed by Ferry’s group and others, apply to the behavior of glass-forming foods. Slade and Levine used the phrase “food polymer science approach” to describe the interrelationships just mentioned; however, the term “molecular mobility” (Mm) seems preferable because this term is simple and emphasizes the underlying aspect of importance. The work of Slade and Levine has been relied on heavily during preparation of this section on Mm. The importance of the Mm concept, which lay unappreciated by food scientists for many years, lends support to an important principle: For those in applied sciences who aspire to engage in pioneering work, much more can be gained from scientific literature that underlies or is peripheral to their primary field of endeavor than from literature that is central to it. Evidence now suggests that Mm is causally related to diffusion-limited properties of foods that contain, besides water, substantial amounts of amorphous, primarily hydrophilic molecules, ranging in size from monomers to polymers. The key constituents with respect to Mm are water and the dominant solute or solutes (solute or solutes comprising the major fraction of the solute portion). Foods of this type include starch-containing foods, such as pasta, boiled confections, protein-based foods, intermediate-moisture foods, and dried, frozen, or freeze-dried foods. Some properties and behavioral characteristics of food that are dependent on Mm are shown in Table 7. When a food is cooled and/or reduced in moisture content so that all or part of it is converted to a glassy state, Mm is greatly reduced and diffusion-limited properties become stable. It is important to note the qualifying term “diffusion-limited.” Most physical properties/changes are diffusion-limited, but some chemical properties/reactions are controlled more by chemical reactivity than diffusion. Approaches to predicting whether rates of chemical reactions are limited by diffusion or chemical reactivity are available but calculations are not simple. This matter will be discussed further in Section Even if future work establishes that the Mm approach applies to virtually all physical properties of foods but only to some chemical properties, the importance of this approach remains sufficient to justify careful study. It is appropriate at this point to suggest that the RVP and Mm approaches to food stability are, for the most part, complementary rather than competitive. Although the RVP approach focuses on the “availability” of water in foods, such as the degree to which it can function as a solvent, and the Mm approach focuses on microviscosity and diffusibility of chemicals in foods, the latter, of course, is dependent on water and its properties [83]. Because several terms used in the following discussion will be unfamiliar to many readers of this book and/or have been poorly defined in other works, a glossary appears at the end of this chapter. Many readers will find it useful to study the glossary before proceeding further. Pag e 57 TABLE 7 Some Properties and Behavioral Characteristics of Foods That Are Governed by Molecular Mobility (Diffusion-Limited Chang es in Products Containing Amorphous Reg ions) Dry or semidry foods Frozen foods Flow properties and stickiness Crystallization and recrystallization Moisture mig ration (ice crystallization, formation of inpackag e ice) Sug ar bloom in chocolate Cracking of foods during drying Lactose crystallization (”sandiness” in frozen desserts) Texture of dry and intermediate moisture foods Enzymatic activity Collapse of structure during secondary (desorption) phase of freeze-drying Structural collapse of amorphous phase dur- ing sublimation (primary) phase of freeze-drying Escape of volatiles encapsulated in a solid, amorphous matrix Shrinkag e (partial collapse of foam-like frozen desserts) Enzymatic activity Maillard reaction Gelatinization of starch Staling of bakery products caused by retrog radation of starch Cracking of baked g oods during cooling Thermal inactivation of microbial spores Source: Adapted from Ref. 114. 2.11.2 State Diagrams Consideration of “state” diagrams is highly pertinent to the discussion of Mm and stability of foods that are frozen or have reduced moisture contents. State diagrams are much more suitable for this purpose than conventional phase diagrams. Phase diagrams pertain solely to equilibrium conditions. State diagrams contain equilibrium information as well as information on conditions of nonequilibrium and metastable equilibrium “states.” State diagrams are, therefore, supplemented phase diagrams, and they are appropriate because foods that are dried, partially dried, or frozen do not exist in a state of thermodynamic equilibrium. A simplified temperature-composition state diagram for a binary system is shown in Figure 25. Important additions to the standard phase diagram are the glass transition curve (Tg) and the line extending from TE to , with both lines representing metastable conditions. Samples located above the glass transition curve and not on any line exist, with few exceptions, in a state of nonequilibrium, as will be discussed subsequently. State diagrams of this format will be used several times during the following discussion of Mm in foods. When using these diagrams, it is assumed that pressure is constant and the time dependency of the metastable states, although real, is of little or no commercial importance (not true of nonequilibrium states). It also should be recognized that each simple system will have its own characteristic state diagram that differs quantitatively, but not qualitatively, from that in Figure 25, and that most foods are so complex that they cannot be accurately or easily represented on a state diagram. For all complex foods, both dry and frozen, accurate determination of a glass transition curve (or more properly zone, as will be discussed later) is difficult, but estimates are essential if the Mm approach to food stability is to be used effectively. Although estimates of Tg for complex foods are not easy to obtain, this can be done with accuracy sufficient for commercial use. Pag e 58 Fig ure 25 State diag ram of a binary system. Assumptions: maximal freeze concentration, no solute crystallization, constant pressure, no time dependence. is the melting point curve, T E is the eutectic point, is the solubility curve, T g is the g lass transition curve, and is the solute-specific g lass transition temperature of a maximally freeze concentrated solution. Heavy dashed lines represent conditions of metastable equilibrium. All other lines represent conditions of equilibrium. Establishing the equilibrium curves ( Fig. 25) for complex foods also can be difficult. For dry or semidry foods the curve, the major equilibrium curve of importance, usually cannot be accurately depicted as a single line. A common approach is to base the state diagram on water and a food solute of dominating importance to the properties of the complex food, then deduce properties of the complex food from this diagram. For example, a state diagram for sucrose-water is useful for predicting the properties and behavior of cookies during baking and storage [67]. Determining curves for dry or semidry complex foods that do not contain a dominating solute is a difficult matter that has not yet been satisfactorily resolved. For frozen foods, the situation is somewhat better because the melting point curve ( ), the major equilibrium curve of importance, is often known or easily determined. Thus, it is possible, with accuracy sufficient for commercial purposes, to prepare a state diagram for a complex frozen food. For binary systems, the effect of different solutes on the glass transition curve is shown schematically in Figure 26. Note that the left end of the Tg curve is always fixed at -135°C, the Tg of water. Thus, differences in location of the curve depend on and on Tg of the dry solute. Pag e 59 FIGURE 26 State diag ram of a binary system showing the influence of solute type on the position of the g lass transition curve. The extreme left position of the T g curve is always fixed at the vitrification temperature of pure water (-135°C), the midpoint at the solute’s , and the extreme rig ht position at the T g of the pure solute; a and b are curves for different solutes. Assumptions stated in Fig ure 25 apply here. 2.11.3 Nine Key Concepts Underlying the Molecular Mobility Approach to Food Stability Concept 1. Many Foods Contain Amorphous Components and Exist in a State of Metastable Equilibrium or Nonequilibrium Complex foods frequently contain amorphous (noncrystalline solid or supersaturated liquid) regions. Biopolymers are typically amorphous or partly amorphous. Examples include proteins such as gelatin, elastin, and gluten, and carbohydrates such as amylopectin and amylose. Many small molecules such as sugars also can exist in an amorphous state, and all dried, partially dried, frozen, and freeze-dried foods contain amorphous regions. Amorphous regions exist in metastable equilibrium or nonequilibrium. Attainment of thermodynamic equilibrium (minimum free energy) is not a goal during food processing, though this condition results in maximum stability. Thermodynamic equilibrium is incompatible with life, including that of fruits and vegetables postharvest, and is incompatible with satisfactory quality in foods. Thus, a major goal of food scientists/technologists, although they rarely view their duties in this manner, is to maximize the number of desirable food attributes that depend on metastable equilibrium states, and to achieve acceptable stability for those desirable attributes that must unavoidably depend on nonequilibrium states. Hard candy (amorphous solid) is a Pag e 60 common example of a metastable food, and emulsions, small ice crystals, and unsaturated lipids are examples of food components that exist in a state of unstable nonequilibrium. Metastable states of food components often can be achieved by drying or freezing. Concept 2. The Rates of Most Physical Events and Some Chemical Events Are Governed by Molecular Mobility (Mm) Because most foods exist in metastable or nonequilibrium states, kinetic rather than thermodynamic approaches are often more appropriate for understanding, predicting, and controlling their properties. Molecular mobility (Mm) is a kinetic approach considered appropriate for this purpose because it is causatively related to rates of diffusion-limited events in foods. The WLF (Williams-Landel-Ferry) equation (see Section provides the means for estimating Mm at temperatures above the glass transition temperature and below or . State diagrams indicate conditions of temperature and composition that permit metastable and nonequilibrium states to exist. The utility of the Mm approach for predicting many kinds of physical changes has been reasonably well established. However, situations do exist where the Mm approach is of questionable value or is clearly unsuitable. Some examples are (a) chemical reactions whose rates are not strongly influenced by diffusion, (b) desirable or undesirable effects achieved through the action of specific chemicals (e.g., alteration of pH or oxygen tension), (c) situations in which sample Mm is estimated on the basis of a polymeric component (Tg of polymer) and where Mm of small molecules that can penetrate the polymer matrix is a primary determinant of the product attribute of interest [110,111], and (d) growth of vegetative cells of microorganisms (p/p0 is a more reliable estimator than Mm) [12,13]. Point (a) deserves further attention because most authors of papers on Mm and its relevance to food stability are strangely silent on this important topic. Some useful references are Rice [95], Connors [14], Kopelman and Koo [50], Bell and Hageman [2a], and Haynes [40]. It is appropriate to first consider chemical reactions in a solution at ambient temperature. In this temperature range, some reactions are diffusion-limited but many are not. At constant temperature and pressure, three primary factors govern the rate at which a chemical reaction will occur: a diffusion factor, D (to sustain a reaction, reactants must first encounter each other), a frequency-of-collision factor, A (number of collisions per unit time following an encounter), and a chemical activation-energy factor, Ea (once a collision occurs between properly oriented reactants the energy available must be sufficient to cause a reaction, that is, the activation energy for the reaction must be exceeded). The latter two terms are incorporated in the Arrhenius relationship depicting the temperature dependence of the reaction rate constant. For a reaction to be diffusion-limited, it is clear that factors A and Ea must not be rate-limiting; that is, properly oriented reactants must collide with great frequency and the activation energy must be sufficiently low that collisions have a high probability of resulting in reaction. Diffusion-limited reactions typically have low activation energies (8–25 kJ/mol). In addition, most “fast reactions” (small Ea and large A) are diffusionlimited. Examples of diffusion-limited reactions are proton transfer reactions, radical recombination reactions, acid-base reactions involving transport of H+ and OH- , many enzyme-catalyzed reactions, protein folding reactions, polymer chain growth, and oxygenation/deoxygenation of hemoglobin and myoglobin [89,95]. These reactions may involve a variety of chemical entities including molecules, atoms, ions, and radicals. At room temperature, diffusion-limited reactions occur with bimolecular rate constants of about 1010 to 1011 M-1s -1; therefore a rate constant of this magnitude is regarded as presumptive evidence of a diffusion-limited reaction. It is also important to note that reactions in solution can go no faster than the diffusion-limited rate; that is, the diffusion-limited rate is the maximum rate possible (conventional reaction mechanisms are assumed). Thus, reactions occurring at rates significantly slower than the diffusion-limited maximum are limited by A or Ea or a combination of these two. The theory describing diffusion-limited reactions was developed by Smoluchowski in 1917. For spherical, uncharged particles, the second-order diffusion-limited rate constant is where NA is Avogadro’s number, D1 and D2 are the diffusion constants for particles 1 and 2, respectively, and r is the sum of the radii of particles 1 and 2, that is, the distance of closest approach. This equation was subsequently modified by Debye to accommodate charged particles and by others to accommodate additional characteristics of real systems. Nonetheless, the Smoluchowski equation provides an order-of-magnitude estimate of kdif. Of considerable pertinence to the present discussion is the viscosity and temperature dependence of the diffusion constant. This relationship is represented by the Stokes-Einstein equation: D= kT/pbhrs where k is the Boltzmann constant, T is absolute temperature, b is a numerical constant (about 6), h is viscosity, and rs is the hydrodynamic radius of the diffusing species. This dependence of D (and therefore kdif) on viscosity is a point of special interest because viscosity increases dramatically as temperature is reduced in the WLF region. It appears likely that rates of some reactions in high moisture foods at ambient conditions are diffusion-limited and rates of others are not. Those that are would be expected to conform reasonably well to WLF kinetics as temperature is lowered or water content is reduced. Among those that are not diffusion-limited at ambient conditions (probably uncatalyzed, slow reactions), many probably become so as temperature is lowered below freezing or moisture is reduced to the point where solute saturation/supersaturation becomes common. This is likely because a temperature decrease would reduce the thermal energy available for activation and would increase viscosity dramatically, and/or because a reduction in water content would cause a pronounced increase in viscosity. Because the frequency-of-collision factor, A, is not strongly viscosity dependent, it probably is not an important determinant of the reaction-limiting mechanism under the circumstances described [9]. This likely conversion of some chemical reactions from non-diffusion-limited to diffusion-limited as temperature is lowered or water content is reduced should result, for those reactions behaving in this manner, in poor conformance to WLF kinetics in the upper part of the WLF region and much better conformance in the lower part of the WLF region. Concept 3. Free Volume Is Mechanistically Related to Mm As temperature is lowered, free volume decreases, making translational and rotational motion (Mm) more difficult. This has a direct bearing on movement of polymer segments, and hence on local viscosity in foods. Upon cooling to Tg, free volume becomes sufficiently small to stop translational motion of polymer segments. Thus, at temperatures Tg, resulting in much greater Mm and much poorer stability than that attainable at T Tg in the WLF region. For example, at any given T in the WLF zone, substances with small Tm/Tg values (e.g., fructose) Pag e 65 result in larger values of Mm and greater rates of diffusion-limited events than do substances with large Tm/Tg values (e.g., glycerol [113]). Small differences in the value of Tm/Tg result in very large differences in both Mm and product stability [113]. 4. Tm/Tg is highly dependent on solute type (Table 8). 5. For equal Tm/Tg at a given product temperature, an increase in solids content results in decreased Mm and increased product stability. At this point it is appropriate to mention two approaches that have been used to study the interrelations between Mm, Tg, and food properties/stability. One approach, as just discussed, involves testing whether physical and chemical changes in foods over the temperature range Tm-Tg conform to WLF kinetics. Some studies of this kind have resulted in good conformity (physical properties) to WLF kinetics and others poor (some chemical reactions) (Fig. 28). A second approach is simply to determine whether food stability differs markedly above and below Tg (or , with little attention given to characterization of kinetics. With this approach, the expectation is not so demanding and the results are often much more favorable; that is, it is found that desirable food properties, especially physical properties, are typically retained much better below Tg than they are above. Tg appears to be much less reliable for predicting stability of chemical properties than it is for physical properties. The temperature below which oxidation of ascorbic acid exhibits greatly reduced temperature dependency (practical termination temperature) appears to correspond fairly well to , at least under the conditions used in Figure 29. However, the same is not true for non enzymatic browning. In Figure 30, the practical termination temperature for non enzymatic browning is well above sample Tg, whereas in Figure 31 the termination temperature is well below sample Tg. Differences in sample composition probably account for the dissimilar results in the two browning studies. In closing this section, it is appropriate to note that an algebraic equation is available to interrelate food texture, temperature, and moisture content in the vicinity of Tg (or other critical temperatures) [88]. Although the equation cannot be used to predict textural changes, it can be used to create quantitative, three-dimensional graphs that effectively display these interrelationships near Tg. Large differences exist among products with respect to dependency of a given textural property on temperature and moisture, and these differences are clearly evident on graphs of this kind. Concept 6. Water is a Plasticizer of Great Effectiveness and it Greatly Affects Tg This is especially true with regard to polymeric, oligomeric, and monomeric food substances that are hydrophilic and contain amorphous regions. This plasticizing action results in enhanced Mm, both above and below Tg. As water increases, Tg decreases and free volume increases (Fig. 32). This occurs because the average molecular weight of the mixture decreases. In general, Tg decreases about 5–10°C per wt% water added [118]. One should be aware, however, that the presence of water does not assure that plasticization has occurred; water must be absorbed in amorphous regions to be effective. Water, because of its small molecular mass, can remain surprisingly mobile within a glassy matrix. This mobility no doubt accounts, as previously noted, for the ability of some chemical reactions involving small molecules to continue at measurable rates somewhat below the Tg of a polymer matrix, and for water to be desorbable during the secondary phase of freeze drying at temperatures ~3,000 MW, , texture stability during frozen storage is often poor. One would expect that vegetables, with values that are typically quite high, would exhibit storage lives that are longer than those of fruits. This is sometimes but not always true. The quality attribute that limits the storage life of vegetables (or any kind of food) can differ from one vegetable to another, and it is likely that some of these attributes are influenced less by Mm than others.The values for fish (cod, mackerel) and beef in Table 11 were determined in 1996 and they differ markedly from earlier data (cod, -77°C [84]; beef, -60°C [91]). The earlier data are probably in error because the dominance of large protein polymers in muscle should result in values similar to those of other proteins (Table 10). Based on the muscle values in Table 11, one would be expect (as is generally observed) that all physical changes and all chemical changes that are diffusion limited would be effectively retarded during typical commercial frozen storage. Because storage lipids exist in domains separate from that of myofibrillar proteins, they probably are not protected by a glassy matrix during frozen storage and typically exhibit instability. Values of for several solutes are shown in Tables 8, 10, and 11, but these values are subject to some uncertainty. values determined recently using altered techniques tend to be smaller than earlier values (mainly those of Slade and Levine). Consensus on what type ofmeasurement yields values most relevant to food stability has not yet been achieved [39,92,97]. It is important to note, however, that the Slade and Levine values reported here were determined using initial sample compositions close to those of high-moisture foods, and this has an important influence on the value obtained. Two points need to be made about the term “unfrozen” as used in the definition of . First, unfrozen refers to a practical time scale. The unfrozen fraction will decrease somewhat over very long periods of time because water is not totally immobile at and equilibrium between the unfrozen phase and the glass phase is a metastable equilibrium, not a global one (not lowest free energy). Second, the term “unfrozen” has often been regarded as synonymous with “bound” water; however, bound water has been defined in so many other ways that the term has fallen into disrepute. A significant amount of water is engaged in interactions, mainly hydrogen bonds, that do not differ significantly in strength from water-water hydrogen bonds. This water is unfrozen simply because local viscosity in the glass state is sufficiently great to preclude, over a practical time span, the translational and rotation motions required for further ice and solute crystallization (formation of eutectics). Thus, most of the water should be regarded as metastable and severely “hindered” in mobility. Even though foods are frozen commercially at relatively slow rates (a few minutes to about 1 hr to attain -20°C) compared to typical rates for small samples of biological materials, maximal freeze concentration is unlikely. Increased rates of freezing affect the temperature-composition relationship, as shown schematically in Figure 36. This leads to the obvious question as to what is the appropriate reference temperature for foods frozen under commercial conditions—Tg or ? This is another area of disagreement. Slade and Levine [114] argue that is the appropriate value. However, choice of this value is open to question because initial Tg (immediately following freezing) will always be < and the approach of Tg to during frozen storage (caused by additional ice formation) will be slow and probably incomplete. The choice of initial Tg as the reference Tg, as some have suggested, is also open to question because (a) initial Tg is influenced not only by product type but also by freezing rate [43], and (b) initial Tg does not remain constant with time of frozen storage, but rather it increases at a commercially important rate at storage temperatures in the Tm-Tg zone, and more slowly, but at a significant rate, at storage temperatures < Tg [10,93,101]. The same considerations apply to Wg and . Unfortunately, the important matter of selecting an appropriate reference Tg for frozen foods cannot be resolved unambiguously because appropriate data are not available. In the meantime, the best that can be done is to suggest that be regarded as a temperature zone rather than as a specific temperature. The lower boundary of the zone will depend on freezing rate and time/temperature of storage, but in commercially important situations it is reasonable FIGURE 36 State diag ram of a binary system showing the effects of increasing rates of freezing (rate a

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