AW and Glass Transistion Review - Labuza

LITERATURE REVIEW onWATER ACTIVITY andGLASS TRANSITION

Dr. Ted Labuza

University of MinnesotaDept. of Food Science

and Nutrition1354 Eckles Ave.St Paul MN 55108

[email protected]

water activity and glass transition page # 2

In the mid 1970s, water activity came to the forefront as a major factor in understanding thecontrol of the deterioration of reduced moisture and dry foods, drugs and biological systems.1,2 It

was found that the general modes of deterioration, namely physical and physicochemicalmodifications, microbiological growth, and both aqueous and lipid phase chemical reactions, were

all influenced by the thermodynamic availability of water (aw, relative vapor pressure(p/po), orwater activity) as well as the total moisture content of the system. It is the difference in the

chemical potential of water (µ) between two systems that results in moisture exchange and abovea certain chemical potential as related to the aw of a system there is enough water present to

result in physical and chemical reactions.Water activity or the equilibrium relative humidity of a system is defined as:

aw = p/po= %ERH (1)

where p = vapor pressure of water in equilibrium with the dry systempo = saturation vapor pressure of pure water at the same temperature.It must be noted that the use of the water activity term signifies that the system is at equilibriumwith its surrounding vapor which may not be true in all cases. The water activity is related tochemical potential by:

µ = µo + RT ln aw (2)

Note that the chemical potential is the true driving force for the transfer of energy or matter andin this case at constant temperature is exponentially related to the water activity.

The physical structure of a food or biological product, important from both functional andsensory standpoints, is often altered by changes in water activity due to moisture gain or loss. Forexample, the caking of powders is attributed to the amorphous-crystalline state transfer of sugarsand oligosaccharides that occurs as water activity increases above the glass transition point whichis close to 0.3 to 0.4 at room temperature.3 This caking interferes with the powder's ability todissolve or be free flowing and phase transitions can lead to volatile loss or oxidation ofencapsulated lipids. The desirable crispiness of crackers, dry snack products such as potato chips,and breakfast cereals is lost if a moisture gain results in a water activity above 0.40-0.45.4, againabove the glass transition. Conversely, raisins and other dried fruits may harden due to the loss ofwater associated with decreasing water activity, usually below 0.55. Thus, raisins or other fruitsin breakfast cereals are sugar coated to reduce the moisture loss rate or are modified with glycerolto reduce the water activity thereby preventing moisture loss. These procedures inhibit the netmoisture transfer rate from the raisins to the cereal, therefore maintaining the cereal's crisp natureand the softness of the fruit pieces in the presence of a chemical potential driving force. Finally, asaw increases, the permeability of packaging films to oxygen and water vapor increases, due toswelling in the rubbery state.

Like physicochemical phenomena, the growth and death of microorganisms are alsoinfluenced by water activity. It has been repeatedly shown that each microorganism has a criticalwater activity below which growth cannot occur.5 For example, Aspergillus parasiticus doesnot grow below a water activity of 0.82 while the production of aflatoxin, a potent toxin, fromthe same organism is inhibited below a water activity of 0.87.6 For growth or toxin production tocease, key enzymatic reactions in the microbial cell must cease. Thus, the lowering of water


activity inhibits these biochemical reactions which in turn restricts microbial functioning as awhole. With spores, the lower the water activity, the more resistant they are to heat kill..Microbially stable dry foods generally are defined as those with a water activity of less than 0.6, alevel below which no known microbe can grow.5

Water activity has been shown to influence the kinetics of many chemical reactions such asthe loss of vitamin C in the dry state.7 Except for lipid oxidation reactions where the rateincreases as water activity decreases at very low water activities, the rates of chemical reactionsgenerally increase with increasing water activity as depicted in Figure 1.8

1.00.80.60.40.20.00

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40

50

relative rate

moisture

water activity

rela

tive

rea

ctio

n r

ate

Water Activity

Moi

stu

re g

wat

er/1

00 g

sol

ids

Figure 1The influence of water activity on chemical reaction rates in the aqueous phase overlaid ona sorption isotherm. Generally, the minimum reaction rate for aqueous phase reactions is found at themonolayer moisture content which is the point where theoretically all polar groups have adsorbedone molecule of water vapor.8 It is at or just above this point that an aqueous phase just begins toform such that chemical species can dissolve, diffuse and react. From moisture sorption isothermdata, the monolayer can be determined from either the BET equation, using data below a wateractivity of 0.5 or the GAB equation which is based on the thermodynamics of multilayer moistureadsorption and uses all the data. The GAB equation can be written as

m = mokbCaW/[(1 - kbaW)(1 - kbaW + kbCaW)] (3)

where m is the moisture content, aW is the water activity, mo is the monolayer, kb is a multilayer

factor, and C is a heat constant. Either a polynomial solution or non-linear regression is used tosolve for the constants in this equation so as to determine the monolayer value. This is currentlythe most accepted equation to generate an isotherm. It can generate the whole curve from fivedata points at different water activities

It is thus important from a shelf life testing standpoint to evaluate the moisture sorptionisotherm of each system and then to calculate the monolayer water activity to determine theoptimum point for stability. from either the BET equation and the GAB equation. From this, awindow for initial moisture content can then be set to be used as a production goal so as tomaximize shelf life. The rationale for this determination will be discussed and then the methods todetermine the monolayer will be presented.

There are many examples of the influence of water activity above the monolayer value onthe rates of chemical reactions in the dry state which lead to loss of shelf life or biological activity.


For example, the rate of ascorbic acid degradation increases dramatically as water activityincreases from the dry state.7 Similarly, the rate of glucose utilization during non-enzymaticbrowning increases as water activity increases.9 Below the monolayer, the rate of lipid oxidationincreases again, thus for systems which also contain unsaturated lipids, such as in the membranesof all biological systems, the shelf life is at a maximum near the monolayer. 8 Since many of thereactions in the aqueous phase are acid-base catalyzed, the amount of water and the availability of

H+ and OH- ions in the reduced moisture state will also significantly influence reaction rates.One of the most studied reactions in our laboratory which can be used as an excellent

example of reaction kinetics and stability is that of the acid-base catalyzed degradation ofaspartame in both liquid and dry state systems.10 The influence of the system water activity stateon aspartame degradation can be used to illustrate many shelf life related chemical phenomena inreduced moisture systems. Figure 2 shows the simple case where water activity is the only factorwhich is varied to determine the effect on aspartame degradation in the dry state. An increase inwater activity from the dry state, increases the aspartame degradation rate.

200100010

100

Days

% A

spar

tam

e re

mai

nin

g

Aw = 0.34

Aw = 0. 57

Aw = 0.66

Figure 2.Degradation of aspartame in model systems asa function of water activity at pH 5 and 30 °C

These results can be depicted as a water activity versus half-life plot as shown in Figure 3,which also shows the complex influence of the initial pH of the system. From the slope of theline in Figure 3, the QA at each pH can be determined. The QA is defined as the ratio between thehalf-life at one water activity and the half-life at a water activity 0.1 units higher. The QA's foraspartame degradation range from 1.3 to 2, which means that for an increase in water activity of0.1 the rate of aspartame degradation increases by 30-100%. For most aqueous phase chemicalreactions in the dry state for aw= 0 to 0.7 , the QA is between 2 to 3, which emphasizes the needfor maintaining the water activity as close as possible to the monolayer.


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1

10

100

1000 pH 3

pH 5pH 7

pH 3

Aw

Hal

f L

ife

in D

ays

Figure 3.Log half life vs water activity plot for aspartame

degradation at aw 0.33 and 30 °C.

As was seen in Figure 1, above about aw 0.6 to 7, reaction rates fall again . In general thepattern of a linear rise and fall of reaction rate with water activity on a semilog plot is found asshown in Figure 4 .

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.1

1

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100

ln k

water activity

rate

con

stan

t

Q = 3a

Figure 4. Influence of water activity on shelf life- QA Plot

Figure 5 shows the effect of the initial pH before drying on the stability of aspartame in asystem during storage at a water activity of 0.34. It is clear that even at low water activities, theinitial pH before drying is another important factor that influences acid-base catalyzed degradationrates in the dry state. This phenomenon should be important in controlling the stability of manydry food, drug and biological systems.


Figure 5 .Degradation of aspartame as a function of pH at an aw

of 0.34 and 30° C

Figure 6 shows the pH rate profile plot for aspartame degradation at a water activity of0.34. The slope of the inclines are much less than found in solution (slopes ~ 1 above theisoelectric point and -1 below in solutions) indicating that the actual pH in the aqueouscondensed phase may be different than that in the wet state or the buffer concentration is changeddue to the reduction in total water content.

8765432.001

.01

.1

pH

Rat

e co

nst

ant [

day

]

-1

Figure 6. pH rate profile plot at an aw of 0.34

Upon drying and rehydrating the model system, the buffer forms a super-saturatedsolution which changes the true pH in the condensed aqueous phase. Studies in our lab indicatethat a wet system (i.e. before drying and rehydration) containing phosphate buffer at pH 5 will endup at a pH of 3.5 after drying, if the same amount of dry buffer salts are present in the amount ofwater found after drying and then rehydrating the model system.11 Thus a super-saturated buffersolution is formed. Therefore, the actual pH of reduced-moisture systems is lower than theinitial pH used for preparation of the model system. Given the shape of the pH-rate profile thiscan either increase or decrease acid-base catalyzed reactions.

It has also been demonstrated that the rates of acid-base catalyzed reactions are a functionof total buffer concentration.10 Figure 7 shows this effect also holds true in a reduced-moisturesystem for aspartame stability at a water activity 0.34. If the buffer concentration increasesbecause of the drop in water content, the rate of aspartame degradation will increase. However,as the buffer concentration approaches saturation, the pH will drop, which could then increase ordecrease the rate of degradation depending upon which side of the isoelectric minimum the initialpH lies. Thus, the understanding of reaction rates of reactions which are pH and buffer dependentis much more complex at reduced moisture contents.


Figure 7. Aspartame loss at 30 °C and an aw of 0.34 in phosphate

buffer at two concentrations.

The important effect of temperature on reaction rates has long been recognized.12

Generally, reaction rates increase with increasing temperatures. The most prevalent and widelyused model to explain this effect is the Arrhenius relation, in which the rate constant isexponentially related to the reciprocal of the absolute temperature. This relationship can bederived from thermodynamic laws as well as from statistical mechanics principles and takes theform:

k = kA exp (-EART ) (4)

In this equation, k is the reaction rate constant, kA is equal to the Arrhenius pre-exponential constant and EA is the excess energy barrier that the reacting substance needs toovercome to proceed to degradation products, generally referred to as the activation energy . Inpractical terms this relationship shows that if values of the rate constant k ,determined at differenttemperatures, are plotted on semilog graph paper against the reciprocal absolute temperature,1/T, a straight line is obtained with a slope of -EA/2.303 R (R=1.987 cal/ mol, the universal gasconstant). An example is shown in Figure 8 for aspartame degradation in solution. The value ofthe activation energy is the slope of this line times 2.303 R.


Figure 8.Typical Arrhenius plot for aspartame degradation

To insure reliable results, the reaction rate should be determined at three or moretemperatures and then k is plotted vs. 1/T on a semilog graph and a linear regression fit isemployed to determine EA. Statistical analysis, is used to determine the 95% confidence limits ofthe Arrhenius parameters. If only three k values are available (ie. only three test temperatureswere used), the confidence range is usually wide since the Student ta/2 value is large. To obtainmeaningfully narrower confidence limits in EA and k , rates at more temperatures are required ormethods to apply non-linear regression of all the data simultaneously can be used. Between 5 or 6experimental temperatures would be the optimum but is not practical especially if several wateractivities are also to be tested.

An alternative way of expressing the temperature dependence, which has been extensivelyused by the food industry and in the food science and biochemistry literature, is the shelf life orQ10 approach. Q10 is defined as the ratio of the shelf lives at two temperatures differing by 10

°C. In essence, Q10 is defined as the relative change of shelf life qs, i.e., the time to reach anunacceptable quality level, when the product is stored at a temperature higher by 10 °C. The Q10approach introduces a temperature-dependence equation of the form

k(T) = ko e bT or qs = qo e-bT (5)log k(T) = log ko + bT or log qs =l og qo - bT (6)


which shows that if k or the shelf life, qs is plotted on semilog graph paper vs. temperature(instead of 1/T of the Arrhenius equation) a straight line is obtained. Figure 9 shows such asemilog plot of qs vs. temperature in which the time for 25% loss of thiamin in pasta was chosenas the end of shelf life.

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Temperature °C

Hal

f li

fe v

itam

in C

[w

eek

s]Aw 0.4 Q 2.2

10

Aw 0.5 Q 1.9310

Aw 0.6 Q 1.310

Figure 9.Shelf life plot for thiamin loss as a function

of temperature and water activity.

Such plots are often called shelf life plots, where -b is the slope of the shelf life plot andqo is the intercept. The shelf life plots are true straight lines only for narrow temperature rangesof 20 to 30 °C. For such a narrow interval, data from an Arrhenius plot will give a relativelystraight line in a shelf life plot. In other words Q10 and b are functions of temperature anddepend on the temperature range.. The activation energy of a food quality loss reaction, Q10 andb (slope of shelf life plot) are interrelated through the following equation:

ln Q10 = 10 b = EAR

10T(T+10) (7)

The variation of Q10 with temperature for reactions of different activation energies is shown inTable 1.

Table 1.Q10 Dependence on EA and Temperature

EA Q10 Q10 Q10

kcal/mol at 5° C at 20 °C at 40 °C10 1.87 1.76 1.6420 3.51 3.10 2.7030 6.58 5.47 4.45


There are many factors relevant to quality loss reactions that can cause significant

deviations from an Arrhenius behavior with temperature.13 The most important is a temperaturecaused change in the reaction conditions such as changes in pH and water activity that usually areassumed to be the same at all temperatures. Our lab has shown the magnitude of this upward shift

in the water activity for products in sealed packages going to higher temperatures.14 This shiftwould result in both a water activity and temperature acceleration of the chemical reactionsleading to increased loss of shelf life. It is thus important in the understanding of most biologicalsystems to determine the moisture sorption isotherm at least at two temperatures and then use theClausius-Clapeyron equation to predict changes for temperature shifts.

Phase changes may also be involved which can affect reaction rates. The influence ofglass transition state will be covered in a latter section. Fats may change into the liquid statecontributing to the mobilization of organic reactants. In frozen systems, the effect of phase changeof the water to ice can cause a pronounced rate increase in the immediate sub-freezing

temperature range because of increased reactant and H+ concentration and increased mobility ofthe proton through ice. The rate increase is especially notable for reactants of low initialconcentration and is related basically to the freeze-concentration effect. It is prominent in thetemperature zone of maximum ice formation, the width of which will depend on the type of food,but generally will be in the range of -1 °C to about -10°C. Other phase change phenomena arealso important. Carbohydrates in the amorphous state may collapse or crystallize, creating morefree water for other reactions. Denaturation of proteins as temperature increases can increase ordecrease the susceptibility to chemical reactions depending upon the stereochemical factors thataffect these reactions, another factor that can cause non-Arrhenius behavior.

In general the rates of degradation reactions increase as temperature increases as wasshown in Figure 9 but the temperature sensitivity, ie Q10 or b from the shelf life plot decreases.Table 2 lists the activation energies for aspartame degradation for a dry model system made todifferent pH values initially and held at different water activities. As seen, the activation energydecreases as water activity increases , at both pHs.

Table 2. Activation Energies for Aspartame Degradation.

pH aw Activation Energyinitial Kcal/mole 3 0.33 25.43 0.55 22.13 0.65 22.3

5 0.33 27.8 5 0.55 24.9

5 0.65 22.3

The decrease in activation energy (a smaller negative value) as water activity increasesmay be based in part on the enthalpy/entropy compensation theory.15 For compound A,undergoing reaction to an activated intermediate state AX* before reacting to produce product B,

the change in Gibbs free energy DG* for the activated state is :A + X --> AX* ---> B + X (8)

where:


DG* = DH* - T DS* (9)In this case DH* is the system enthalpy change (a negative value for exothermic spontaneous

reactions), T is absolute temperature, and DS* is the system entropy. The enthalpy change isdirectly proportional to the activation energy by:

Ea = DH* + RT (10)

Thus the entropy should increase with increasing water activity as found since as water becomesless bound it is more available for reaction. Thus, as entropy increases to a more positive value,the activation energy should become a smaller negative value for the Gibbs free energy to remainunchanged. However, in some food systems the opposite occurs; the reason for this is unknown.

Physical Properties of the rubbery and glassy state and stabilityGlass transition theory from the study of polymer science may help to understand textural

properties of food systems and explain changes which occur during food processing and storagesuch as stickiness, caking, softening and hardening as was noted earlier. Figure 10 shows a glassrubber transition diagram, the line representing the glass temperature, Tg.

Figure 10.Representative glass-rubber transition

diagram for an amorphous material

From polymer science, if an amorphous material exists in the glassy state, it is hard andbrittle, eg for cereals it would represent a crisp product. In the rubbery state the material is softand elastic, for a fried snack or cereal this would represent an undesirable soggy state. Texture isan important sensory attribute for many cereal based foods and the loss of desired texture leads toa loss in product quality and a reduction in shelf life (Nielsen, 1979). The texture of crisp foodshas been studied as a function of water activity by Katz and Labuza (1981). They determined thatsaltine crackers, popcorn, puffed corn curls and potato chips lost crispness if the water activityexceeded 0.35 - 0.50. They attributed crispness to intermolecular bonding of starch forming smallcrystalline-like regions when little water was present. These regions require force to break apartwhich gives the food a crisp texture. Above a certain water activity, the water was presumed todisrupt these bonds allowing the starch molecules to slip past each other when chewed. Hsieh,Hu, Huff and Peng (1990) also observed that puffed rice cakes lost crispness at a water activityjust above 0.44. Vickers and Bourne (1976) showed that crisp perception of dry cereal snackswas the result of sounds generated when chewed which diminished as the water activity was


increased. Our lab has shown that loss of crispness is well explained by the transition from theglassy to the rubbery state.

Caking is another property that can be related to the glass diagram as noted above. Whena sugar is in solution and is dried, it is in the amorphous glassy state and the powder is freeflowing.. At a high enough moisture or temperature, is crossing over the Tg line in Figure 10, thematerial can enter the rubbery state. In the rubbery state, dried amorphous sugars tend tocrystallize rapidly because of increased diffusion rates above Tg, , a condition resulting inundesirable caking which inhibits free flow. Caking follows the steps shown below in Figure 11for particles that are wetted by water vapor.

Wetting

Caking

Wetting

Sticking

Drying

Hard

Wetting

Drying

Figure 11. Steps involved in caking and agglomeration

Thus glass transition theory provides a clearer approach to understanding the physical andtexture changes of crisp cereals or snacks as water content increases. The elastic modulus which

is related to flow, extendibility and bending is approximately 103 times higher in the glassy statethan the modulus in the rubbery state (Sperling, 1986). Dry cereal products when bakedextruded or fried generally are in the glassy state and are best described as hard, stiff, brittle andcrisp. As these foods gain moisture or increase in temperature, they may enter the rubbery stateand become soft. It is desirable to retain crisp foods such as fried snack products and breakfastcereals in the glassy state and to retain high sugar foods in the glassy state to prevent caking. Thechoice of ingredients and level of plasticizers such as water and other small molecular weightcomponents influences the glass transition temperature of a food product. In general, as themolecular weight of a polymer increases within a homologous series, the glass transitiontemperature increases (Sperling, 1986). The addition of plasticizers decreases the glass transitiontemperature (Roos and Karel, 1991). Sugars also cake at different rates with glucose and fructosebeing most susceptible thus it is hard to predict behavior without having established a glasstransition diagram.


Study of texture by glass transition theoryThe key to understanding texture using glass transition theory lies in the ability to measure

the glass transition temperature (Tg) for the food and to correlate this transition with a change intexture of the food as determined by sensory analysis or other means. The measurement of glasstransition temperature of multicomponent foods, however, is quite difficult. Methods includedifferential scanning calorimetry (DSC) and dynamic mechanical thermal analysis (DMTA). Foodsystems under analysis may yield multiple glass transitions, and the melting or crystallization ofcomponents such as fats or sugars within the system may obscure the observation of the glasstransition. In the case of multiple glass transitions, it is important to identify the specific transitionwhich correlates with the change in food texture.

Glass transition temperature measurementThere are several methods which are used to measure the glass transition temperature for

a material. The most common method reported in the literature for glass transition determinationin food is differential scanning calorimetry (DSC). DSC measures the change in heat capacitybetween the glassy and rubbery states and is indicated by a change in baseline in a DSCthermogram as shown below in Figure 12. DMTA on the other hand measures changes in elasticbehavior at the transition. It is much more difficult to perform but has a much higher sensitivity.

T g

Temperature

endo

ther

mic

T melt

Figure 12. Typical DSC thermogram

Point of Tg determinationIn the literature, researchers report glass transition temperature data as either the midpoint

or the onset Tg. As shown below in Figure 13 , the point chosen for the determination of Tg canaffect the value of the glass transition temperature. The onset Tg is generally considered the mostappropriate temperature to report. However, many researchers report midpoint Tg values since aplot of the first derivative of the glass transition curve shows a peak at the midpoint glasstransition temperature making this point easy to identify.


T g

T g

onset

midpoint

Temperature

Figure 13.Determination of Tg from DSC curve

The graph below (Figure 14) shows results using the DSC at 10°C/min and determining themidpoint temperature for native and pre-gelatinized starch.

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Native Wheat Starch

Pre-Gelatinized Wheat Starch

Moisture (g water/ g solid)

Tem

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ture

(°C

)

Wheat Starch

Figure 14.Zeleznak, K. J. and Hoseney, R.C. 1987. Glass transition in starch. Cereal Chem.

64(2):121-124.

Application of glass transition theory to the texture of cereal foodsIf textural changes in a cereal system can be correlated with a glass transition, and the

state diagram for the cereal food is known, then the processing and environmental conditions canbe controlled such that the desired state for the food is achieved and is also retained duringdistribution and storage. Little research has been performed to show the correlation betweenglass transition and the textural changes in foods. LeMeste, Huang, Panama, Anderson and Lentz(1992), for example, studied the texture of white pan bread by thermal mechanical analysis. Theglass transition associated with cookies has been studied (Doescher, Hoseney and Milliken, 1987),but was not related to the texture of cookies. Much research can still be done in this area.


Several examples can be used to relate the glass transition state diagram to the texture ofcereal foods. The observed transition from a crisp to a soggy texture as moisture is gained isobviously a glass transition. A benefit of knowing the state diagram for crisp snack foodsincludes the possibility of formulating a snack food with a higher glass transition temperaturecurve. A higher glass transition curve allows a food to reach a higher temperature or highermoisture content without losing its crisp texture. This would provide a longer shelf life for thecrisp snack food, improve the snack quality, necessitate less stringent control over storage anddistribution conditions, and reduce package film moisture barrier requirements.

As a breakfast cereal picks up moisture from milk, it loses its crisp texture and becomessoggy. This is known as a loss of bowl life and may be the result of a glass to rubber transition.In this case, if it were possible to raise the glass transition curve for the cereal, more moistureabsorption would be required before the cereal would become soggy and unacceptable. High-sugar cereals consumed by children tend to have short bowl lives. This may be the result of alower glass transition temperature for such cereals as the result of plasticization by the higherlevel of small molecular weight sugars which may lower the Tg curve (Roos and Karel, 1991).

For some cookie products, a soft texture makes the cookie seem freshly baked. A softtexture may be achieved through a number of means, including formulation such that the finalbaked cookie is in the rubbery state at room temperature. An interesting application of this is thedual- textured cookie based on a patent by Hong and Brabbs (1984). In this case, the outercookie layer containing sucrose ends up in the glassy state when baked giving a crisp outer crust.The inner cookie dough is based on fructose and has a lower glass transition curve than the outerdough. Thus, the inner cookie ends up in the rubbery state following baking and seems soft andfresh. In the rubbery state, however, there is the possibility that crystallization of the sugars in thecookie could lead to a harder or crisp texture over time.

Much work has been done to utilize sugar crystallization for the formation of a crisptexture for cookie products. This is discussed in patents by Martin and Furia (1990) and Gageand Mishkin (1990). Roos and Karel (1991) studied the rate of crystallization for several sugarsolutions as a function of temperature above the glass transition temperature. They found thatcrystallization rate increased as T-Tg increased. Thus, if the state diagram for a sugar within acookie product were known, the moisture and temperature conditions required to promotecrystallization of the sugar to produce a crisp cookie would be also be known. A soft texture canbe retained by adding ingredients to delay or prevent crystallization.

With respect to caking, Figure 15 shows the DSC measured Tg curve vs the measurementof caking for a protein - sugar mixture made by spray drying (infant formula) as compared to theampoule method (sealed sample heated slowly in a sealed glass ampoule at 1°C per 3 minutes andshaken every few minutes to see if it sticks to the wall) and the propeller method (same heatingrate but sample stirred with a propeller ). Generally the DSC Tg curve is below the other two asseen but does represent the moisture temperature line at which a sample will cake during longterm storage and thus can be used as a guideline.


20151050

0

50

100

150

200

moisture (g H O/ 100 g solids)2

Figure 15. Caking phenomenon for sugar protein system

mm represents the Tg curve done by DSC at 1°C/3 minutes ss represents the ampoule method ll represents the propeller method

Glass transition approach and reaction ratesGlass transition theory applies to amorphous polymers and has also been found to be

applicable to low molecular weight sugars (Slade et al., 1989). The glass transition temperature,Tg, is the temperature at which a glass to rubber transition takes place. Water, the most commonplasticizer in foods, acts to decrease the glass transition temperature. The system propertiesabove and below the glass transition temperature differ quite dramatically and such differenceshave been studied relative to the crystallization (Roos and Karel, 1991b) and the viscosity(Soesanto and Williams, 1981) of sugar solutions. The relationship between the rate of chemicalreactions which occur in food systems and the state of the system, either glassy or rubbery, hasalso been studied. The properties of glassy and rubbery systems may contribute to differences inchemical reaction rates in each of these states.

There is a dramatic change in the local movement of polymer chains at the glass transitiontemperature, resulting in a number of property differences between glassy and rubbery systems.As a system moves from the glassy to the rubbery state, viscosity drops dramatically fromapproximately 1012 to 103 Pa•sec at the glass transition temperature (Sperling, 1992). Thereduced viscosity allows for greater polymer chain and reactant mobility. Free volume, definedas the amount of space associated with a system which is not taken up by polymer chainsthemselves, also changes between the glassy and rubbery states. The free volume available withina glassy system has been estimated to be between 2% and 11.3% of the total volume (Ferry,1980), and is believed to increase substantially at the glass transition temperature due to adramatic increase in the thermal expansion coefficient (Ferry, 1980). This increase in free volumeshould allow for faster diffusion of reactants. Based on the free volume required for diffusion,the size of a diffusing molecule may also be an important factor affecting diffusion rates.Diffusion is a function of the probability of creating a hole within a matrix which is sufficiently


large for a molecule to occupy. When a molecule is large compared to the available free volume,the probability of creating such a hole is low. Thus, a greater degree of free volume redistributionis required in order for diffusion of large molecules to take place compared to smaller molecules(Mauritz et al., 1990). This makes diffusion of large molecules within a region of limited freevolume very slow. Reactions which are dependent upon the diffusion of such molecules may alsobe very slow.

In addition to translational mobility, short range mobility may also be important forchemical reactions. Using electron spin resonance, Roozen and coworkers (1990, 1991) found asignificant increase in the rotational mobility of spin probes within sucrose-water, glycerol-waterand maltodextrin-water mixtures at a temperature which corresponded to the glass transitiontemperature, as measured by differential scanning calorimetry. The mobility of protons, asmeasured by nuclear magnetic resonance, has also been found to be higher in the rubbery statecompared to the glassy state (Kalichevsky et al., 1992).

Based on the properties associated with the glassy state, it might be expected thatchemical reaction rates would be quite slow within the glassy state, or would not occur at all, butwould substantially increase in rate within the rubbery state. In fact, this may be the explanationfor cessation of reactions at the monolayer determined from moisture sorption isotherms. It ispossible that the observed monolayer is not actually a monolayer, but rather a moisture content atwhich the glass transition is observed at a particular temperature.

Lim and Reid (1991) studied the rate of diffusion-controlled processes within frozensystems. Maltodextrins, carboxymethylcellulose (CMC) and sucrose were used as model systemsto study the rate of protein aggregation, ascorbic acid degradation and enzymatic hydrolysis attemperatures above and below the Tg' value for each model system. Figure 16 shows the resultsof enzymatic hydrolysis above and below the Tg' of a maltodextrin DE10 system.

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-3.5-5.5-8.5-13-19

Time (hours)

Rel

ativ

e ab

sorb

ance Temperature (°C)

Figure 16Enzymatic hydrolysis of maltodextrin in the frozen state.

Lim and Reid (1991)

Note that at temperatures below the system Tg' (-10°C), the reaction was very slow, but the rateincreased above the Tg', with a large increase in hydrolysis rate occurring 4.5°C above the

reported Tg'. Similar results were found for other DE maltodextrins. Protein aggregation andascorbic acid degradation within the maltodextrin systems were also slow within the rubbery state,


but increased in rate above the system Tg'. It was concluded that the maltodextrin systemprovided good cryostability below Tg'.

For the CMC systems, Lim and Reid (1991) found that ascorbic acid degradation wasobserved below the system Tg', possibly due to the porous structure of the CMC matrix whichallowed oxygen diffusion even within the glassy state. It may also be possible that the limited freevolume within the glassy state was sufficient for oxygen diffusion to occur. CMC also failed tostabilize the system against protein aggregation within the glassy state. This was unexpectedconsidering the high Tg' value for CMC (-11°C) and that in order for aggregation to take place,the diffusion of large protein molecules through the matrix would be required.

Lim and Reid (1991) found that the Tg' for a sucrose model system was very low (-33°C)and that all study temperatures were above Tg', within the rubbery state. Despite this, it wasobserved that sucrose effectively stabilized the system against protein aggregation. The glasstransition approach failed to predict the stability of the sucrose system in this case. As expected,however, the sucrose system showed rapid rates of ascorbic acid degradation within the rubberystate of this system. Note, however, that as the temperature above the Tg' increased, the watercontent in the system probably increased due to the melting of ice. Thus, it is difficult to attributethese observed results, as well as the results from other studies involving frozen systems, solelyto a temperature effect.

Karmas et al. (1992) found that nonenzymatic browning within the glassy state ofcarbohydrate model systems was very slow below the system Tg. Depending on the compositionand moisture content of the carbohydrate system, the rate of nonenzymatic browning increasedsubstantially at about 20-75°C above the Tg. Figure 17 shows typical results of their work.

0 25 50 75 1000

2

4

6

8

10

T-T g

d(O

D)/

dt

a w=0.12

a w=0.33

Figure 17Nonenzymatic browning in the glassy and rubbery state

Karmas et al (1992)

For systems at aw=0.12 and aw=0.75, dramatic changes in the rate of nonenzymatic browningoccurred at 50°C and 75°C above the Tg, respectively. They stated that the temperature at whicha large increase in browning rate occurred could be related to the temperature for which thediffusion coefficient within the system rapidly increased based on changes in free volume. This


would be expected to occur at the glass transition temperature, but could occur at temperaturesabove the Tg depending on the system free volume and the size of the diffusing molecules.

A study of the oxidation of orange oil within a maltodextrin M100 encapsulating matrixshowed that oxidation occurred rather rapidly within the maltodextrin glassy state (Ma et al.,1992; Nelson and Labuza, 1992). As the water content of the matrix increased, but was stillwithin the glassy state, reaction rates increased, as shown in Figure 18.

302520151050

0

5

10

15

20

Time (days)

00.11

0.33

0.44

0.56

0.75

water activity

Lim

on

ene

oxi

de

(mg

/g o

ran

ge

oil)

Figure 18Oxidation of limonene as a function of water activity

Nelson and Labuza (1992)

In contrast to the expected rate increase within the rubbery state, the system at 75% relativehumidity was within the rubbery state, but showed the greatest stability to oxidation. Thesefindings were attributed to collapse of the matrix within the rubbery state which prevented oxygendiffusion through the matrix. Collapse occurs when a matrix can no longer support itself againstgravity and collapses upon itself forming a compact system. Caking and sticking are examples ofcollapse (Downton et al., 1982).

A rubbery system is characterized as a metastable state. In addition to collapse,crystallization may occur which may subsequently influence chemical reaction rates.Crystallization can occur within the rubbery state where viscosity is low such that molecules havesufficient mobility for crystallization to take place. Roos and Karel (1991b) found that the timefor crystallization decreased dramatically as temperature above the glass transition temperature(T-Tg) increased for sucrose and lactose solutions. Crystallization leads to a cross-linking effectwhich results in reduced polymer chain flexibility and mobility. Michaels et al. (1963) reportedlower gas diffusion rates within glassy and crystalline synthetic polymer matrices compared torubbery matrices. Crystalline regions were found to impede diffusion since molecules wererequired to pass through regions of low polymer chain mobility.

Labrousse et al. (1992) found that the collapse and crystallization of a lactose-gelatinmatrix containing methyl linoleate oil led to an increased rate of oil oxidation. They attributed thisto the reduction in free volume upon crystallization which forced the oil to the surface whereprotection from oxidation was minimal. Numerous researchers have examined the relationshipbetween the collapse and the retention of encapsulated oils and volatiles (Omatete and King,1978; Flink and Karel, 1972). The extent and rate of collapse or crystallization has been found toplay a part in the retention and the subsequent stability of these materials.

Based on the properties of glassy and rubber systems, it would be expected that reactionrates would be very slow within a glassy state and increase within a rubbery system. However,


based on the studies reported in the food science literature, it should not be assumed that glassysystems are completely stable, or that rubbery systems are less stable than glassy systems.Molecular size, matrix porosity and changes within the metastable rubbery state such as collapseand crystallization, may contribute to other, more complicated results.

Water activity and the glass transition approach both have strengths and weaknesses indefining the relationship between moisture content and chemical reaction rates. It is important torecognize, however, that it is a relatively simple task to measure the water activity of foodsystems. A number of instrumental methods are available for such determinations (Stamp et al.,1984). With the use of controlled relative humidity chambers, specific water activities can also beachieved for a particular food system. The measurement of glass transition temperature, on theother hand, requires more effort. Differential scanning calorimetry has been used extensively tomeasure the Tg of simple food systems, but this method lacks the sensitivity required to measurethe Tg of complex food systems. Other methods have, therefore, been examined as a means tomeasure glass transition temperatures (Kalichevsky et al., 1992; Bruni and Leopold, 1991).Without the ability to accurately and rapidly determine the Tg for a food system as a function ofmoisture content, it is difficult to correlate glass transition temperatures and reaction rates withincomplex food systems. Much work can still be done in this area.

Arrhenius vs WLF temperature modelIn addition to the effect of moisture on reaction rates, it is also useful to understand the

temperature dependence of chemical reactions in order to predict product shelf life as we havenoted. Often, shelf life studies are performed at elevated temperatures in order to expedite datacollection. In order to predict the rates of degradative chemical reactions at other temperatures, arelationship between the reaction rate and temperature must be established. The Arrheniusrelationship has traditionally been used to describe the temperature dependence of chemicalreactions (Glasstone, 1946). However, when reactions are diffusion-limited, an alternativeapproach by Williams, Landel and Ferry (1955) may be appropriate.

The Arrhenius relationship is the major mathematical model used to describe thetemperature dependence of most chemical reactions (Glasstone, 1946). Arrhenius originallydeveloped this empirical relationship for glucose hydrolysis (1889). Subsequently, the basis forthe relationship has been derived from thermodynamic and quantum mechanical principles and hasbeen found applicable to many chemical and physical processes such as diffusion. As notedearlier, the Arrhenius relationship shown in eq. 4 is:

k == ko

exp( −−Ea

/RT ) (4)

where k is the rate constant at temperature T, ko is a pre-exponential factor, R is the ideal gasconstant and Ea is the activation energy. The reference temperature, according to this equation, isabsolute zero. Of course, one cannot measure reactions at this temperature.

Kinetic data at several temperatures over a fairly large temperature range are required inorder to test the applicability of the Arrhenius model. A plot of ln(k) vs. 1/T, if a straight line,indicates the applicability of the Arrhenius model and that the activation energy over the specifictemperature range is constant. If the plot deviates from a straight line, either the test methodswere poor, or other reactions begin to become critical above some temperature and influence thereaction rate being studied.


It has been stated that the Arrhenius model is applicable for describing the temperaturedependence of reactions within the glassy state of a food matrix and also at 100°C above the glasstransition temperature, but is not applicable within the rubbery state (Slade et al. 1989). Thisassumption can be tested by applying the Arrhenius relationship to rates of chemical reactionswithin glassy and rubbery systems to determine whether the Arrhenius model provides a good fitof the data. von Meerwall and Ferguson (1979b) studied the rate of oil diffusion in natural rubber usingNMR spectroscopy. They found that an Arrhenius plot of the diffusion coefficient of oil withinthe rubbery state of the system showed the expected curvature above the glass transitiontemperature. A broad temperature range from -10°C to 140°C was used in their study. Based onseveral kinetic models, the Arrhenius plot would be expected to be curved if such a largetemperature range were used (Labuza, 1980) due to the extra temperature dependence at hightemperatures which is not accounted for in the Arrhenius model.

Ollett and Parker (1990) reported that the viscosity of anhydrous glucose and fructosemeasured at temperatures above the system Tg did not show Arrhenius-type temperaturedependence. Although the correlation coefficients for the Arrhenius plots for glucose andfructose were 0.98 and 0.99, respectively, slight curvature in the Arrhenius plots for both systemswas observed, possibly due to the large temperature range for this data (approximately 50°C).

From data of Lim and Reid (1991), the Arrhenius plot for an enzyme hydrolysis reactionwithin a partially frozen maltodextrin DE 25 above the system Tg' was constructed and is shownin Figure 19.

0.00390.00380.0037-4

-3

-2

-1

0

1/T (K-1)

ln(k

)

y = 79.497 - 2.1621E+4x R2 = 0.999

Figure 19Arrhenius plot of Lim and Reid results (1991)

The data spans a very limited temperature range of about 10°C above the Tg' (-13.3°C). The curvature expected within the rubbery state was not observed, and the Arrheniusplot is quite linear (r2=0.99) for this reaction, with a calculated activation energy of 42.9kcal/mole (10.3 kJ/mole). In order to observe the curvature expected in the Arrhenius plot withinthe rubbery state, data over a broader temperature range above the system Tg may be required.However, this is impossible for frozen systems since the system melts at slightly highertemperatures, and is essentially a liquid above 0°C.


A shift in the slope of an Arrhenius plot indicates a change in the activation energy for areaction. Due to the property differences between glassy and rubbery systems, a break in theArrhenius plot at the glass transition temperature of a system would be expected. Figure 20shows an Arrhenius plot which spans a temperature range which included a glass to rubbertransition from work by Karmas et al. (1992) on nonenzymatic browning within a carbohydratematrix.

0.00330.00320.00310.00300.00290.00280.0027-10

-8

-6

-4

-2

0

2

1/T (K-1)

ln(k

)rubbery

glassy

Tg

Ea = 45.1 kcal/mol

Ea = 20.8 kcal/mol

Figure 20Arrhenius plot of data of Karmas et al (1992)

They referred to the temperature at which a break in the Arrhenius plot was observed as thesystem-dependent “critical temperature.” They attributed this break in the Arrhenius plot tocollapse of the carbohydrate matrix above the system glass transition temperature. In the case ofthe lactose/CMC/trehalose/xylose/lysine model system in Figure 6, the break in the Arrhenius plotis observed near the glass transition temperature (Tg=50°C). As generally expected, theactivation energy calculated for nonenzymatic browning within the rubbery system was higherthan the activation energy within the glassy state. Note that despite the 40°C temperature rangewithin the rubbery state, the Arrhenius plot is quite linear within this region (r2= 0.99). If all thedata, both below and above the Tg, are included in the regression, the activation energy is 42.3

kcal/mole (10.1 kJ/mole) and the r2=0.985, which is still very good.In some cases, knowing the glass transition temperature may be useful in understanding

and explaining breaks observed in Arrhenius plots. However, a break in an Arrhenius plot may bedue other changes in a system, and is not always the result of a glass to rubber transition.Because the activation energy for reactions in glassy and rubbery systems may be different,caution should be applied when extrapolating rates of reactions within glassy systems to systemswithin the rubbery state. Although it has been stated that the Arrhenius model is not applicablefor describing the temperature dependence of reaction rates within systems in the rubbery state, ithas been seen that over small temperature ranges, the Arrhenius model may adequately predictchanges in reaction rate. However, the WLF model has been stated to be a more appropriateapproach for modeling the temperature dependence within rubbery systems.

An approach to model the temperature dependence of mechanical and dielectricrelaxations within the rubbery state, where it is assumed that the Arrhenius model does not


theoretically apply, was suggested by Williams, Landel and Ferry (1955). This approach is knownas the WLF approach and has the following form:

log aT =

−C1(T − Tref )

C2 + T − Tref

(11)

where C1 and C2 are system-dependent coefficients (Ferry, 1970) and aT is defined as the ratio ofthe relaxation phenomenon at T to the relaxation at the reference temperature, Tref (i.e., h/href forviscosity). It has been suggested in the literature that WLF kinetics may also describe thetemperature dependence of chemical reaction rates within amorphous matrices above their glasstransition temperature (Slade et al., 1989). For systems where diffusion is free volume dependent,it was shown by Sapru and Labuza (1993) that the rate of reaction can be expressed using theWLF equation with a shift factor of aT= (kref/k):

logkref

k=

−C1(T − Tref )

C2 + (T − Tref )(12)

Average values for the WLF coefficients were calculated by Williams et al. (1955) using theavailable values for many synthetic polymers. It is quite common in the literature to use theaverage coefficients, which have the values of C1=17.44 and C2=51.6, for establishing theapplicability of the WLF model (Roos and Karel, 1991b; Soesanto and Williams, 1981). Peleg(1992) discussed several problems associated with the use of average coefficients in the WLFequation. He found disagreement between the use of the average coefficients and literature valuesfor actual coefficients for prediction purposes 20-30°C above the glass transition temperature.

Typical proof of the applicability of the WLF model, as cited in the food science literature,is made based on fitting the WLF equation to kinetic data shown as in a plot of log(k) vs. T-Tg.The first step in such a proof involves determining the rate constant at the glass transitiontemperature, since this is generally not known. An average value of kg is calculated by solvingequation 12 for all experimental data and using the measured Tg and the average WLFcoefficients. The calculated average kg value is then used along with the average WLFcoefficients to calculate values of the rate constant over the experimental temperature range usingequation 12. A reasonable fit of the line to the data is stated as proof of the applicability of theWLF model. This was done for establishing the applicability of the WLF approach for thecrystallization of sugars (Roos and Karel, 1991b) and for the viscosity of sugar solutions(Soesanto and Williams, 1981). The disadvantage of this approach is that it assumes that theaverage WLF coefficients are appropriate for a particular data set, although this may not be thecase. Roos and Karel (1990) measured the time for lactose crystallization at several moisture andtemperature conditions. They reported that the average WLF coefficients adequately describedthe temperature dependence of their lactose crystallization data. However, an adequate fit of thecrystallization data in the temperature range of the measurements can also be made by utilizingother WLF coefficients. Several different values for the WLF coefficients were used to determinean average value for the time for crystallization at the Tg using lactose data for systems initiallyequilibrated to water activities between 0.11 and 0.44, as was done by Roos and Karel (1990)using the average WLF coefficients. The average value of the time for crystallization at Tg (θg)


was then be used to predict the time to crystallization at a specific temperature. This procedurewas followed for several different sets of WLF coefficients to construct the lines shown in Figure21.

0 10 20 30 40 50 600

2

4

6

8

10

12

0.11 0.22 0.33 0.44

aw

17.44 51.6 20.0 60.0 15.0 45.0 10.0 30.0

log

(θ)

T-Tg (°C)

C1 C2

Figure 21WLF plot for lactose crystallizationfrom data of Roos and Karel (1990)

As observed in Figure 21, all predicted lines visually fit the crystallization data for the systemsequilibrated to water activities between 0.11 and 0.44 about equally well. However, the time forcrystallization at the glass transition temperature, qg, was very different, depending on the set ofWLF coefficients used. This can be observed as the difference in the intersection of the predictedcurves with the y axis at T-Tg=0. This is the danger of utilizing the average WLF coefficients, aswell as the danger of making predictions at the glass transition temperature using data far aboveTg (Peleg, 1992). Alternative approaches will be suggested for accessing the applicability of theWLF model.

According to the WLF equation and using the average coefficients, a 10°C increase abovethe Tg should correspond to a reaction rate increase of approximately 600 times (Slade et al.,1989). Table 3 shows the rate increase expected for other temperature changes above Tg.Karmas et al. (1992) found that the increase in nonenzymatic browning rate within a carbohydratemodel system above the Tg was not as large as that predicted using the average WLF coefficients,as shown in Table 1. A simple check of this involves calculating kT values at temperatures abovethe Tg using equation 14 and the average coefficients, and comparing these to measured values.It is evident that the rate increases predicted from use of the average WLF coefficients did notdescribe the temperature dependence of nonenzymatic browning within this system. This may notmean that the WLF model is not applicable for this reaction, but rather that other WLFcoefficients, rather that the average values, must be used for this system.

Table 3


Rate increases predicted using the WLF equation with average values for C1 and C2, andobserved by Karmas et al. (1992) for nonenzymatic browning within alactose/CMC/trehalose/xylose/lysine model system at initial aw=0.12.

Temperature range Relative rate increase Relative rate increase predicted observed Tg ∅ Tg + 10°C 678 21.8Tg + 10°C ∅ Tg + 20°C 110 7.39Tg + 20°C ∅ Tg + 30°C 3.5 4.06Tg + 30°C ∅ Tg + 40°C 1.58 2.82

One approach to determine the applicability of the WLF equation fordescribing the temperature dependence of a chemical reaction would first be to determine the rateof reaction at the Tg, if possible. Once kg is known, equation 12, with Tg as the referencetemperature, can be rearranged to the following form:

logkg

k

−1

=−C2

C1(T − Tg )−

1

C1

(13)

such that a plot of

logkg

k

−1

vs. 1

T − Tg

(14)

gives a straight line with a slope equal to -C2/C1 and an intercept of -1/C1, if the WLF model isapplicable. For many systems, however, it is not possible to utilize the Tg as the referencetemperature because the phenomena at the Tg is so slow that good kinetic rate constants cannotbe measured. In such situations, a reference temperature above the Tg should be used to evaluatethe applicability of the WLF model. In fact, this approach was originally suggested by Williams etal. (1955) for the same reason.

If the glass transition temperature is known, the WLF constants at the referencetemperature can be transformed to correspond to the glass transition temperature, as shown byPeleg (1992):

C1' =

C1C2

C2 − δC2

' = C2 − δ (15)

In these relationships, d is the temperature difference between Tref and Tg, and C1' and C2' are thetransformed WLF coefficients at the glass transition temperature. These values can then becompared to the widely used average WLF coefficients.

Figure 22 was constructed using the approach of equation 14 and nonenzymatic browning ratesobtained by Karmas et al. within a carbohydrate model system over a 50°C temperature rangeabove the glass transition temperature.


0.30.20.10.0-3

-2

-1

0

1/(T-Tref)

1/lo

g(k r

ef/k

)

y = - 5.557E-2 - 10.015x r2 = 0.994

C1 = 18.0

C2 = 180.2

Figure 22Proper WLF linear plot for the browning data of Karmas et al (1992)

Note that the line is quite linear (r2=0.99), indicating the applicability of the WLF model. Fromthe linear regression for the plot, the values of C1 and C2 were determined to be 18.0 and 180.2,respectively, using 55°C as the reference temperature. When transformed to correspond to theglass transition temperature, 50°C, using equation 6, the values for C1' and C2' were 18.5 and175.2, respectively. These are quite different from the average WLF coefficients often cited inthe food science literature.

An alternative method to determine the applicability of the WLF model for describing thetemperature dependence of a chemical reaction is possible when kinetic data at many temperaturesare available, the Tg is known, but kg cannot be measured. In this approach, it is first assumedthat the WLF relationship describes the temperature dependence of the reaction. Then, initialestimates of kg, C1 and C2 are made and iterative nonlinear regression is used to optimize thesevalues, according to the relationship of equation 12. If kinetic data are available at manytemperatures over a wide range (at least 30°C), it is probable that only one line fits the data setand that the values determined for kg, C1 and C2 are probably quite close to actual values. vonMeerwall and Ferguson (1979a) used this three parameter optimization method to fit the diffusionof a diluent within a rubbery matrix with the WLF equation. They found that experimentalprecision was very important for the accuracy of such a fit. An additional disadvantage of thismethod is that it assumes, rather than proves, that the WLF model applies to the system.

Understanding the physical properties of foods using glass transition theory may still be inits infancy; however, the potential for utilizing this theory for the improvement of food texture isgreat. It is important to note, however, that food ingredients cannot be chosen based solely ontheir affect on the glass transition temperature of a particular food. As an example, it may bedesirable to formulate soft foods to the rubbery state. However, the rate of degradative chemicalreactions and crystallization may be higher in the rubbery state compared to the glassy state whichmay adversely affect food stability and quality during distribution, especially caking.

In reviewing these concepts several principles are clear:


1. water activity is an important concept for stability2. moisture sorption isotherms help to understand stability3. the monolayer optimal stability moisture can be obtained

from the isotherm4. the glass transition curve is a critical factor needed to

understand physical changes5. a glass transition in the middle of the temperature range for a shelf

life test could lead to significant error.

In addition, if the sorption parameters for an equation for the isotherm is known, eg the BET,GAB, or a simple linear model of m = ba +c over a small water activity range, then moisture gainor loss for any given distribution system is possible.16 This greatly enhances the food productdevelopment scientist in predicting product shelf life.

General Water Activity Literature References1. R. B. Duckworth, ed., "Water Relations in Foods," Academic Press, London (1975).2. Labuza, T.P. Sorption phenomena in foods. 1975 in "Theory, determination and control of physical properties of

foods". C. Rha ed. D. Reidel Pub. Dordrecth Holland pp 197-219.3. M. Saltmarch and T. P. Labuza, Influence of relative humidity on the physicochemical state of lactose in spray- driedsweet whey powders, J. Food Sci. 45(5):1231-1236 & 1242 (1980).4. E. E. Katz and T. P. Labuza, The effect of water activity on the sensory crispness and mechanical deformation of snackfood products, J. Food Sci. 46:403-409, 815. L. Beuchat, Microbial stability as affected by water activity, Cereal Foods World. 26:345 (1981).6. M. D. Northolt, C. A. H. Verhulsdonk, P. S. S. Soentoro, and W. E.Paulsch, Effect of water activity and

temperature on aflatoxin production by Aspergillus parasiticus, J. Milk Food Technol. 39:170-174.7. S. Lee and T. P. Labuza, Destruction of ascorbic acid as a function of water activity, J. Food Sci. 40:370-373 (1975).8. T. P. Labuza, The effect of water activity on reaction kinetics of food deterioration, Food Technol. 34(1):36-41 & 59(1980).9. J. A. Kamman and T. P. Labuza, A comparison of the effect of oil vs. shortening on the rates of glucose utilization

in non - enzymatic browning, J. Food Proc. and Preserv. 9:217-222 (1985).10. Bell, L.N. and Labuza, T.P. Aspartame Degradation in limited water conditions in "Water Relationships in Foods"

H. Levine and L. Slade eds. Plenum Press N.Y. pp 337-349 (1991)11. Bell, L.N. and Labuza, T.P. Potential pH implications in the dry state. Cryo Letters 13:335-34412. Labuza,T.P. Applications of chemical kinetics to deterioration of foods. J. Chem. Ed. 61:348-358 (1985)13. Labuza, T.P. and Schmidl, M.K. Accelerated shelf life testing of foods. Food Technol 39(9):57-6214. Labuza, T.P., Kaanane, A. and Chen. J. Effect of temperature on moisture sorption isotherms and aw shift of two foods. J.Food Sci. 50:385-391(1985)15 . T. P. Labuza, Enthalpy entropy compensation in food reactions, Food Technol. 34(2):67-77 (1980).16. Taoukis, P.S, A. ElMeskine and Labuza, T.P. Moisture transfer and shelf life of packaged foods. in "Food PackagingInteractions" J. Hotchkiss ed. ACS Symposium Series ACS Press pp 244-261

Glass Transition ReferencesBailley, R.T., North, A.M. and Pethrick, B. 1981. “Molecular Motion in High Polymers.” Clarendon Press. Oxford.Bruni, F. and Leopold, A.C. 1991. Glass transitions in soybean seed. Plant Physiol. 96:660-663.Doescher, L.C., Hoseney, R.C. and Milliken, G.A. (1987). A mechanism for cookie dough setting. Cereal Chem.

64(3),158-163Downton, G.E., Flores-Luna, J.L. and King. C.J. 1982. Mechanism of stickiness in hygroscopic, amorphous powders. Ind.

Eng. Chem. Fundam. 21:447-451.Ferry, J.D. 1980. “Viscoelastic Properties of Polymers.” 3rd edition. John Wiley & Sons, Inc.: New York. 264-320.Flink, J. and Karel, M. 1972. Mechanisms of retention of organic volatiles in freeze-dried systems. J. Fd. Technol. 7:199-211.Gage, D.R. and Mishkin, M.A. (1990). Texture equilibration in cookies. U.S. Patent 4,892,745Glasstone, S. 1946. “Textbook of Physical Chemistry.” 2nd edition. Van Nostrad: Princeton, NJ.Hsieh, F., Hu, L., Huff, H.E., and Peng, I.C. (1990). Effects of water activity on textural characteristics of puffed

rice cake. Lebensmittel Wissenschaft und Technologie. 23(6),471-473.Hong, C.A., and Brabbs, W.J. (1984). Doughs and cookies providing storage-stable texture variability.


U.S. Patent 4,455,333Kalichevsky, M.T., Jaroszkiewicz, E.M., Ablett, S., Blanshard, J.M.V., and Lilliford, P.J. 1992. The glass transition of

amylopectin measured by DSC, DMTA and NMR. Carbohydrate Polymers. 18:77-88.Karmas, R., Buera, M.P. and Karel, M. 1992. Effect of glass transition on rates of nonenzymatic browning in food systems. J.

Agric. Food Chem. 40(5):873-879.Katz, E.E. and Labuza, T.P. (1981). Effect of water activity on the sensory crispness and mechanical deformation of snackfood products. J. Food Science. 46(2), 403-409Labrousse, S., Roos, Y. and Karel, M. 1992. Collapse and crystallization in amorphous matrices with encapsulated

compounds. Science des Aliments. In press.Labuza, T.P., Maloney, J.F., Karel, M. 1966. Autoxidation of methyl linoleate in freeze-dried model systems. II. Effect of

water on cobalt-catalyzed oxidation. J. Food Sci. 31:885-891.Labuza, T.P. 1971. Kinetics of lipid oxidation in foods. CRC Critical Reviews in Food Technology. 10:355-405.Labuza, T.P. 1980. Enthalpy/entropy compensation in food reactions. Food Tech. 2:67-77.LaJolo, F.M. Tannenbaum, S.R. and Labuza, T.P. 1971. Reactions at limited water concentration. II. Chlorophyll

degradation. J. Food Sci. 36:850-853.LeMeste, M., Huang, V.T., Panama, J., Anderson, G. and Lentz, R. (1992). Glass transition of bread. Cereal Foods World.37(3), 264-267

Martin, A.J. and Furia, T.E. (1990). Shelf stable cookie. U.S. Patent 4,965,077Lim, M.H. and Reid, D.S. 1991. Studies of reaction kinetics in relation to the Tg' of polymers in frozen model systems. In

“Water Relationships in Foods.” H. Levine and L. Slade, editors. Plenum Press: New York. 103-122.Ma, Y., Reineccius, G.A., Labuza, T.P. and Nelson, K.A. 1992. The stability of spray-dried microcapsules as a function of

glass transition temperature. Presented at the IFT Annual Meeting, 1992. New Orleans, LA.Mauritz, K.A., Storey, R.F. and George, S.E. 1990. A general free volume based theory for the diffusion of large molecules in

amorphous polymers above Tg. 1. Application to di-n-alkyl phthalates in PVC. Macromolecules. 23:441-450.Michaels, A.S., Vieth, W.R. and Barrie, J.A. 1963. Diffusion of gases in polyethylene terephthalate. J. Applied Physics.

34(1):13-20.Nelson, K.A. and Labuza, T.P. 1992. Relationship between water and lipid oxidation rates: Water activity and glass transition

theory. In “Lipid Oxidation in Foods.” A.J. St. Angelo, ed. American Chemical Society: Washington, DC. 93-103.Nielsen, A.C. Company. 1979. Product and package performance: The consumers view. A.C. Nielsen Co ILOmatete, O.O. and King, C.J. 1978. Volatile retention during rehumidification of freeze dried food models. J. Fd. Technol.

13:265-280.Peleg, M. 1992. On the use of the WLF model in polymers and foods. CRC Critical Reviews in Food Sci. and Nutr. 32:59-

66.Roos, Y. and Karel, M. 1991a. Phase transitions of mixtures of amorphous polysaccharides and sugars. Biotechnol. Prog.

7:49-53.Roos, Y. and Karel, M. 1991b. Plasticizing effect of water on thermal behavior and crystallization of amorphous food models.

J. Food Sci. 56(1):38-43.Roos, Y. and Karel, M. (1991). Apply state diagrams to food processing and development. Food Technology.

45(12), 66-71Roozen, M.J.G.W. and Hemminga, M.A. 1990. Molecular motion in sucrose-water mixtures in the liquid and glassy state as

studied by spin probe ESR. J. Phys. Chem. 94:7326-7329.Roozen, M.J.G.W., Hemminga, MA. and Walstra, P. 1991. Molecular motion in glassy water-malto-oligosaccharide

(maltodextrin) mixtures as studied by conventional and saturation-transfer spin-probe e.s.r. spectroscopy.Carbohydrate Research. 215:229-237.

Sapru, V. and Labuza, T.P. 1993. Glassy state in bacterial spores predicted by polymer glass transition theory. J. Food Sci.58(2):445-448.

Slade, L. and Levine, H. 1988. Non-equilibrium behavior of small carbohydrate-water systems. Pure and Appl.Chem. 60(12):1841-1864.

Slade, L., Levine, H., and Finey, J. 1989. Protein-water interactions: Water as a plasticizer of gluten and other proteinpolymers. In “Protein quality and the effects of processing.” Phillips, R.D., Finlay, J.W., Editors. Marcel Dekker:New York. 9-123.

Soesanto, T. and Williams, M.C. 1981. Volumetric interpretation of viscosity for concentrated and dilute sugar solutions. J.Phys. Chem. 85:3338-3341.

Sperling, L.H. (1986). Introduction to Physical Polymer Science, pp. 224-295. New York, John Wiley & SonsStamp, J.A., Linscott, S. Lomauro, C. and Labuza, T.P. 1984. Measurement of water activity of salt solutions and foods by

several electronic methods as compared to direct vapor pressure measurement. J. Food Sci. 49:1139-1142.von Meerwall, E. and Ferguson, R.D. 1979a. Diffusion of hydrocarbons in rubber, measured by the pulsed gradient NMR

method. J. Applied Polymer Sci. 23:3657-3669.von Meerwall, E. and Ferguson, R.D. 1979b. Pulsed-field gradient NMR measurements of diffusion of oil in rubber. J.

Applied Polymer Sci. 23:877-885.Warmbier, H.C., Schnickles, R.A. and Labuza, T.P. 1976. Effect of glycerol on non-enzymatic browning in a solid

intermediate moisture model food system. J. Food Sci. 41:528-531.


Williams, M.L., Landel, R.F. and Ferry, J.D. 1955. The temperature dependence of relaxation mechanisms in amorphouspolymers and other glass-forming liquids. J. Chem. Eng. 77:3701-3707.

Vickers, Z.M. and Bourne, M.C. (1976). A psychoacoustical theory of crispness. J. Food Science. 41, 1158-1164

AW and Glass Transistion Review - Labuza

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