`
`159
`
`Differential Scanning Calorimetry Study of Phase Transitions Affecting
`the Quality of Dehydrated Materials’
`
`Yrjo Roos and Marcus Karel*
`Department of Food Science, Rutgers-The State University of New Jersey, P.O. Box 231,
`New Brunswick, New Jersey 08903
`
`Differential scanning calorimetry was used to determine the phase transitions of dried
`and rehumidified amorphous lactose, sucrose, and a mixture of sucrose and Amioca.
`Glass-transition, crystallization, and melting temperatures decreased with increasing
`moisture content. The time to crystallization of amorphous lactose held isothermally
`above the glass-transition temperature decreased as the temperature was increased.
`Isothermal crystallization time of lactose was a function of the temperature difference
`between the holding temperature and the glass-transition temperature independently
`of moisture content. Amorphous biological materials are metastable showing temper-
`ature, moisture content, and time-dependent phase transitions that affect their dry-
`ing behavior, stickiness, storage stability, and quality.
`
`Introduction
`The water content of biological materials can be reduced
`by concentration, freezing, and drying. Both freezing and
`drying reduce the water activity to levels at which the
`growth of microorganisms is inhibited. Therefore, water
`is not available to microorganisms but may have an effect
`on physical and chemical changes in the material. Usu-
`ally the separation of water leads to the formation of a
`highly viscous, metastable, amorphous state, which can
`be either a “glass” or a “rubber” depending on the final
`temperature and moisture content. The physical state
`and its effect on various changes have been discussed by
`White and Cakebread (I), Karel (2), Levine and Slade
`( 3 , 4 ) , and Simatos and Karel (5).
`During freezing, evaporation, or sublimation pro-
`cesses, the material is in a continuously changing state,
`which is determined by temperature, moisture content,
`and time. In various studies, the physical changes, e.g.,
`collapse and stickiness during drying, have been proved
`to affect the quality of the final product (6-10). Carbo-
`hydrate materials, especially mono- and disaccharides and
`products in which these are the main components like
`fruit juices, are difficult to dry because of their sensitiv-
`ity to temperature and moisture (11, 12).
`At low moisture contents, both carbohydrates and pro-
`teins may exist in an amorphous state. This state is
`extremely sensitive to water, which plasticizes the amor-
`phous structure ( I , 3). The temperature at which the
`structure changes from the glass to the more liquidlike
`rubber is a function of molecular weight and the amount
`of plasticizer (3). This change, known as glass transition
`( T J , is specific to each amorphous material and compo-
`sition. At the glass-transition temperature, the free vol-
`ume and the mobility of the molecules of the amorphous
`matrix increase at a rapid rate (13). This causes an
`endothermal change in the apparent specific heat that
`can be detected by using differential scanning calorime-
`try. Also, changes in the physical properties such as vis-
`
`+ Paper No. 159c presented at the AIChE Annual Meeting, San
`Francisco, November 5-10, 1989.
`
`cosity occur at the glass-transition temperature. The tem-
`perature dependence of mechanical relaxation processes
`in amorphous polymers above the glass-transition tem-
`perature follows the Williams-Landel-Ferry (WLF) equa-
`tion (13).
`During dehydration, physical changes that may have
`a profound effect on technological properties and the qual-
`ity of the materials occur. These changes are related to
`the molecular mobility and glass-transition temperature
`during and after dehydration. The glass-transition tem-
`perature is affected by various factors of which the com-
`position of the material, molecular weight, and plasticiz-
`ers are most important. These effects have been exten-
`sively discussed in the literature (3-5,14,15). Plasticizers
`decrease the glass-transition temperature, and thus, e.g.,
`water in dried sugars affects also diffusional properties.
`The purpose of this study was to determine glass-
`transition, crystallization, and melting temperatures of
`amorphous lactose, sucrose, and a gelatinized mixture of
`sucrose (80%) and Amioca (20%) as a function of mois-
`ture content and to determine the temperature depen-
`dence of the crystallization time with use of differential
`scanning calorimetry. These transitions are of impor-
`tance to drying behavior, water sorption, and storage sta-
`bility. It will be shown that glass-transition, crystalliza-
`tion, and melting temperatures of the amorphous mate-
`rials decrease with increasing water content and are
`affected by the composition of the material. Crystalli-
`zation of amorphous sugars is a temperature-dependent
`phenomenon having a relaxation time dependent on the
`mobility of the crystallizable molecules above Tg. The
`crystallization of amorphous sugars occur isothermally
`from the rubbery state above T being faster as the hold-
`ing temperature is increased. %herma1 transitions give
`information of temperature, moisture content, and time-
`dependent changes in the amorphous materials during
`drying and storage.
`Materials and Methods
`Amorphous Food Models. The model food materi-
`als used were a-lactose (Fisher Scientific; Certified ACS),
`
`8756-7938/90/3006-0159$02.50/0 0 1990 American Chemical Society and American Institute of Chemical Engineers
`
`Amneal v. Cubist
`IPR2020-00193
`Cubist Ex. 2003
`
`
`
`sucrose/ Amioca
`Tg, "C
`H,O g/100 g
`58.4 f 4.3
`0.0
`32.6 f 3.6
`0.5
`1.1
`20.4 1.4
`4.4
`10.5 f 1.0
`-5.1 f 1.5
`6.5
`
`Lactose
`
`
`l
`g
`J
`LL w u c r o s e
`w 2 O\
`
`Biotechnol. Prog., 1990, Vol. 6, No. 2
`160
`Table I. Glass-Transition Temperatures (T f Standard Deviation) for Amorphous a-Lactose, Sucrose, and a Gelatinized
`Mixture of Sucrose (80%) and Amioca (20%? Equilibrated to Varying Moisture Contents over Saturated Salt Solutions
`material
`sucrose
`a-lactose
`a, *
`T,, "C
`T,, "C
`H,O 9/100 g
`H,O g/100 g
`salt
`p20,
`101.2 f 0.9
`56.6 f 3.4
`0.00
`0.0
`0.0
`LiCl
`65.0 f 1.6
`0.11
`1.2
`1.4
`37.4 f 8.0
`CH,COOK
`43.7 f 2.6
`0.23
`3.4
`3.8
`27.9 f 2.4
`MgCl,
`29.1 f 6.4
`0.33
`5.9
`4.7
`12.6 f 0.9"
`W O ,
`17.5 & 1.1"
`0.44
`8.0
`a
`" Moisture content allows crystallization at room temperature. ' Water activity at 25 "C.
`sucrose (Sigma Chemical Co.; anhydrous, grade 11), and
`a mixture of sucrose (80%) and Amioca (20%) (a high
`amylopectin starch (1.8% amylose); National Starch and
`Chemical Corp.). The materials were dissolved into dis-
`tilled water as a 10% solution, and the mixture contain-
`ing sucrose and Amioca was gelatinized. Weighing bot-
`tles containing 10 g of respective solutions were subse-
`quently frozen at -20 "C overnight, tempered over dry
`ice for 3 h, and freeze dried on shelves for 24 h at a pres-
`sure below 0.1 mbar with a laboratory freeze drier (Vir-
`tis, Benchtop 3 1). After the samples were freeze dried,
`the vacuum was broken with dry nitrogen, and the weigh-
`ing bottles were transferred into a vacuum desiccator and
`dried over P205 (Fisher; Certified ACS) for at least 1
`week.
`Differential Scanning Calorimetry. Differential
`scanning calorimetry (DSC) was used to determine the
`glass transition, crystallization, and melting of the amor-
`phous model foods and to determine the isothermal crys-
`tallization time of amorphous lactose at varying mois-
`ture contents above respective glass-transition tempera-
`tures. The DSC used was a Perkin Elmer Model DSC-2
`equipped with Intracooler I1 and Perkin-Elmer Model
`3600 data station. Dynamic measurements were made
`using the Perkin-Elmer TADS standard software and iso-
`thermal measurements using the isothermal software. Per-
`kin-Elmer hermetically sealable 20-pL aluminum sam-
`ple pans were used in all measurements with an empty
`aluminum pan as the reference sample. The DSC was
`calibrated for temperature and heat flow with distilled
`water (distilled several times, mp = 0.0 "C, AH, = 333
`J/g), gallium (mp = 29.8 "C, Aldrich Chemical Co.), and
`indium (mp = 156.6 "C, A H m = 28.45 J/g; Perkin-Elmer
`standard). The drybox of the DSC was dried with des-
`iccant and a flush of dry nitrogen. The sample head was
`purged with a flow of dry nitrogen (20 mL/min) to avoid
`condensation of moisture.
`Sample Preparation for Differential Scanning
`Calorimetry. The amorphous materials dried over
`P205 were extremely hygroscopic, and samples were placed
`in the DSC pans (2-3 mg) in the-dry box and hermeti-
`cally sealed before weighing. Samples of varying water
`contents were prepared by weighing 2-3 mg of the dried
`material into open DSC pans. Samples in the open pans
`were equilibrated over saturated salt solutions in vac-
`uum desiccators for 24 h. The salts used were LiC1,
`CH,COOK, MgCl,, and K2C03 (Fisher; Certified ACS)
`giving the following water activities respectively: 0.11,
`0.23, 0.33, and 0.44 (Table I). After equilibration, the
`pans were hermetically sealed and weighed. The water
`content of the samples was obtained from the increase
`in weight (16).
`Dynamic Measurements. The samples were scanned
`at a rate of 5 "C/min from -50 "C until melting was com-
`pleted. The thermograms obtained were typical of amor-
`phous materials (Figure 1) and were analyzed for Tg (deter-
`
`(endo)
`5
`50
`-50
`0
`2 00
`100
`150
`TEMPERATURE
`( O C )
`Figure 1. Dynamic DSC curves for dried amorphous lactose,
`sucrose, and a gelatinized mixture of sucrose and Amioca. The
`thermograms show glass transition, crystallization, and melt-
`ing. Scanning rate was 5 OC/min.
`mined as the onset temperature of an endothermic shift
`in the apparent specific heat), T,, (determined as the
`onset temperature of an exothermic peak), and Tm (deter-
`mined as the peak temperature of the broad melting
`endotherm). At least four replicates were used, and the
`results were calculated as the mean value f the stan-
`dard deviation.
`Isothermal Measurements. The isothermal crystal-
`lization time @,,)
`of amorphous lactose at varying tem-
`peratures and moisture contents was determined to obtain
`the temperature dependence of the crystallization time
`and its dependence on the T,. Samples of varying mois-
`ture contents were heated from ambient temperature to
`a predetermined final temperature at 40 "C/min, and
`isothermal data was collected at 5 "C intervals below T,,
`until a crystallization exotherm was completed (Figure
`2). O,, was determined as the time at the peak of the
`exotherm. At least four replicates were used at each tem-
`perature and moisture content, and the results were cal-
`culated as the mean value for each experimental point.
`Temperature Dependence of Crystallization
`Time. O,, of amorphous lactose at different tempera-
`tures was used to determine the temperature depen-
`dence of the crystallization time a t each relative humid-
`ity. The dynamic measurements showed that crystalli-
`zation occurs at a constant value for T,, - T,. Therefore,
`the temperature dependence of Ocr was assumed to fol-
`low the WLF equation (l), which is proved to establish
`
`ucrose/Amioca
`
`I
`
`51.6 + (T - Tg)
`the temperature dependence of mechanical relaxation pro-
`cesses above T of amorphous polymers (13). $, used to
`calculate the &F curve was obtained by solving the equa-
`
`
`
`Biotechnol. Prog., 1990, Vol. 6, No. 2
`
`t
`
`181
`
`U Lactose
`.-..iJ--
`Sucrose
`
`- - * - SucroseiAmioca
`
`1 1
`0
`
`1
`
`2
`
`3
`
`6
`
`I
`
`7
`
`4
`5
`(103s)
`TIME
`Figure 2. Isothermal DSC curves for amorphous lactose at var-
`ious temperatures after equilibration at 0% and 23% relative
`humidity. The thermograms show exothermal crystallization
`of amorphous lactose having a peak at Bcr that is specific to
`each T - TB.
`tion (1) for all experimental points of each moisture con-
`tent, and the average time obtained for crystallization at
`T, was used. Thus, O,, to the WLF-type behavior could
`be calculated:
`-17.44(T - Tg)
`log o,, = log og +
`51.6 + ( T - Tg)
`Both experimental and calculated values of Ocr were used
`to show the temperature dependence of the crystalliza-
`tion time.
`
`(2)
`
`Results
`Glass-Transition Temperature. The drying of the
`materials studied led to the formation of an amorphous,
`glassy state, which could be analyzed and proved by using
`DSC (Figure 1). T, was found to be affected by water
`plasticizing the materials studied. Te was found to be a
`function of moisture content, decreasing with increasing
`moisture. Tg and the respective moisture content of the
`materials studied are given in Table I. The effect of mois-
`ture content on T, is shown in Figure 3.
`Crystallization and Melting. The T,, and T , are
`given in Table 11. They were found to be functions of
`moisture content decreasing with increasing moisture. The
`increase in moisture content caused about an equal
`decrease in T, and Tcr.
`Temperature Dependence of Crystallization
`Time. The time to crystallization of amorphous lactose
`at temperatures T,, > T > T was found to be a func-
`tion of temperature (Figure 27. O,, for amorphous lac-
`tose followed the WLF equation at the temperature range
`studied, and the Ocr values were plotted against T - T,
`(Figure 4 ) . However, a linear temperature dependence
`of the crystallization time on T - T, of the data points
`also gives a good correlation and is consistent with an
`Arrhenius-type temperature dependence.
`Discussion
`The properties of amorphous food materials during and
`after dehydration depend on a number of factors. Many
`of these are similar to those well-defined for polymers
`(3,15). The important factors related to food materials
`have been reviewed by Karel and Flink (17) and King et
`al. (18). The glass-transition temperature is related to
`molecular mobility, and the quantitative aspects of the
`
`-20
`0
`
`’
`
`2
`8
`6
`4
`MOISTURE CONTENT (g/lOOg dry matter)
`Figure 3. Effect of moisture content on the glass-transition
`temperature of amorphous lactose, sucrose, and a gelatinized
`mixture of sucrose and Amioca.
`
`I
`1 0
`
`dependence of the mobility of amorphous sugars as mea-
`sured by time to recrystallization under isothermal con-
`ditions above T, have not been reported.
`The glass-transition temperature of amorphous food
`materials has been reported to have an effect on drying
`behavior and properties of the dried products (16, 19).
`It has been shown in various studies that the final qual-
`ity, flavor retention, and stickiness as well as the final
`moisture content are functions of the drying tempera-
`ture, structure of the material, including its molecular
`weight, and time. Lactose crystallization is an impor-
`tant defect in dried dairy products. This can be pre-
`dicted by the relationship between the glass-transition
`temperature, moisture content, and time to crystalliza-
`tion. In this study various carbohydrate materials were
`dried, and the thermal behavior was determined for sam-
`ples of different moisture contents. The results showed
`similar dependence of T on moisture content as Tsour-
`ouflis et al. (11) reporteckfor the collapse temperature of
`freeze-dried materials and Downton et al. (20) for the
`sticky point in spray drying. These temperatures are
`decreased by the presence of moisture, which plasticizes
`the amorphous materials (Figure 3).
`Ts decreases with increasing moisture content and the-
`oretically reaches the T of pure water. Most of the work
`on food-related materials has been done with frozen solu-
`tions, and the glass-transition temperatures for the freeze
`concentrated solutions have been reported (4). How-
`ever, estimation of drying conditions and storage stabil-
`ity requires knowledge of the effects of very small amounts
`of moisture on T,. The effects of moisture on T, of wheat
`gluten has been reported by Hoseney et al. (21) and on
`dried strawberries by Roos (16). For the carbohydrate
`materials in this study, an increase in water content from
`“zero” to 1% decreased T, 20-40 “C. As the T, is decreased
`below ambient temperature, collapse and, in some cases,
`crystallization of amorphous sugars occur during stor-
`age. In sorption isotherms of amorphous sugars, this is
`shown as loss of moisture.
`In drying, the evaporation of water keeps the product
`temperature low. As the water content is reduced, a dried
`amorphous surface layer is formed. The moisture con-
`tent of the dried layer depends on the vapor pressure in
`the drying environment, which also determines the mois-
`ture content of the dried product and affects its physi-
`cal state. In a proper drying process, the dried surface
`is probably transformed into a very viscous glass directly
`from solution. Bellows and King (9) and Downton et al.
`
`
`
`Biotechnol. Prog., 1990, Vol. 6, No. 2
`162
`Table 11. Crystallization and Melting Temperatures (T,, and T, f Standard Deviation) for Amorphous a-Lactose, Sucrose,
`and a Gelatinized Mixture of Sucrose (80%) and Amioca (20%) Equilibrated to Varying Moisture Contents over Saturated
`Salt Solutions
`
`a-lactose
`
`material
`sucrose
`
`salt
`
`32
`
`T,,, "C
`162.5 f 1.1
`113.3 f 6.1
`CH,COOK
`93.3 f 1.1
`M d l ,
`74.7 f 5.6
`64.9 f 1.5"
`K$O;
`Moisture content allows crystallization at room temperature.
`
`T,, OC
`214.1 f 0.4
`
`T,,, 'C
`104.4 f 2.3
`83.7 f 7.6
`75.1 f 4.1
`57.4 f 1.2"
`a
`
`T,, "C
`183.5 f 1.2
`172.1 f 4.2
`165.0 f 2.1
`
`sucrose/ Amioca
`T,,, OC
`T,, "C
`129.5 f 8.1
`178.1 f 2.2
`167.6 f 2.0
`104.7 f 2.0
`156.7 f 1.8
`100.3 f 2.8
`144.2 f 2.8
`73.4 f 3.6
`138.4 f 2.6
`49.6 f 3.6
`
`W
`A
`A
`
`Lactose 23% rH
`Lactose 33% rH
`Lactose 44% rH
`
`12
`
`10
`
`6
`
`
`
`6
`
`
`
`3
`L
`$
`-
`m
`
`4
`
`2
`
`0
`0
`
`1 0
`
`2 0
`
`3 0
`
`(T - Tg) O C
`Figure 4. Time to crystallization of amorphous lactose rehu-
`midified to various moisture contents at varying relative humid-
`ities as a function of T - T . The solid lines show the time to
`crystallization as predictedgy the WLF equation.
`
`4 0
`
`5 0
`
`6 0
`
`(20) have related collapse in freeze drying and stickiness
`in spray drying to viscosity changes. Soesanto and
`Williams (22) showed that the viscosity of an amor-
`phous mixture of sucrose and fructose above T, is char-
`acterized by the WLF equation. Thus, if the moisture
`content and the product temperature are increased above
`the specific collapse temperature or sticky point, the vis-
`cosity of the material is rapidly decreased, and it dries
`into the rubbery state. This leads to collapse, decreased
`water removal, decreased drying rate, and increased stick-
`iness, and both product quality and flavor retention are
`impaired.
`To and Flink (12) reported the collapse temperatures
`for dried lactose and sucrose to be 101.1 and 55.6 OC,
`respectively. In this study, the Tg of the dried lactose
`and sucrose were found to be at about the same temper-
`atures. Samples having a glass-transition temperature
`below room temperature were both collapsed and sticky.
`The similarities of glass transition, collapse, and sticki-
`ness are obvious, and TB as a well-characterized transi-
`tion of amorphous materials could be used to predict dry-
`ing, agglomeration, and storage conditions.
`A t sufficient moisture contents above Tg, the molecu-
`lar mobility is rapidly increased, and some materials may
`crystallize during storage, probably due to decreased vis-
`cosity. Crystallization of amorphous sucrose and lac-
`
`tose occurred at room temperature above 0 . 3 3 ~ ~ and
`0.44aW, respectively. Crystallization was not observed for
`the mixture of sucrose and Amioca but may occur prob-
`ably at higher moisture contents or slowly during stor-
`age. It was also found that the Amioca increased the T,,
`of amorphous sucrose about 25 "C and decreased the melt-
`ing temperature. The crystallization exotherm was broad
`and was subsequently followed by the melting endotherm.
`
`The time to crystallization of amorphous lactose seems
`to be determined by the temperature difference between
`the holding temperature and glass-transition tempera-
`ture (T - T ). The crystallization rate is probably deter-
`mined by t i e mobility of lactose molecules. Viscosity is
`known to decrease with increasing temperature accord-
`ing to the WLF equation, and it is likely that the diffu-
`sivity of lactose in our system behaves similarly. The
`results of this study show that a completely dry lactose
`is more difficult to crystallize than amorphous lactose
`plasticized by water even when compared at the same T
`- Tg value. This observation may be due to the follow-
`ing process: the formation of crystals releases water since
`the isotherm for amorphous sugars shows moisture con-
`tents, at the same activity, that are much higher than
`those for crystalline materials (23-25). This water plas-
`ticizes the remaining amorphous material and facilitates
`crystallization. In the case of anhydrous lactose, this does
`not occur.
`The crystallization time of amorphous food materials
`depends on T - Tg, which makes their sorption behavior
`time-dependent as shown in Figure 5. This is of impor-
`tance to the quality of dried food products, which often
`contain crystallizable and noncrystallizable amorphous
`solids, as has been already noted for the case of sucrose-
`containing foods by Karel (26), who constructed a time-
`dependence diagram based on the data of Makower and
`Dye (23). They showed that crystallization time of amor-
`phous sucrose at room temperature depends on mois-
`ture content. Crystallization time was increased with
`decreasing moisture content, and at a, = 0.12, sucrose
`remained amorphous at least almost 3 years. The crys-
`tallization of amorphous sucrose at a, = 0.24 and 25 "C
`was noticed after about 300 days. According to our results,
`the T, of sucrose at a, = 0.24 is very close to 25 "C, and
`if we combine this with the data of Makower and Dye
`(23), we note that crystallization is clearly a function of
`T - T, following the WLF-type temperature depen-
`dence. At higher a, values above Tg, amorphous sucrose
`was reported to become sticky. In this study crystalli-
`zation of amorphous lactose occurred above T,, and it
`was faster the higher was the isothermal holding temper-
`ature. The results also indicated that the temperature
`dependence of Bcr is close to Arrhenius type when stud-
`ied at temperatures well above Tg. However, Bcr closer
`to T should be determined, since it appears that the
`WL# equation predicts Br better than the Arrhenius rela-
`tion extrapolated to Tg.
`Glass-transition temperature seems to be one of the
`most important factors governing the stability of amor-
`phous materials. Because of their high sensitivity to mois-
`ture content and temperature, both water sorption prop-
`erties and the temperature and time-dependent changes
`in the physical state determine the drying behavior and
`storage stability of most biological materials.
`
`
`
`Biotechnol. frog., 1990, Vol. 6, No. 2
`
`WATER ACTIVITY
`Figure 5. Effect of temperature dependence of crystallization
`time on the sorption isotherm of amorphous lactose at 25 OC.
`Crystallization may occur at varying a, values, depending on
`time. The a, values were obtained by using a linear relation-
`ship between a, and T g of amorphous lactose (16).
`
`Conclusions
`Amorphous food models show temperature, time, and
`moisture content dependent phase transitions that can
`be related to collapse and stickiness during drying and
`storage. The glass-transition temperature, collapse tem-
`perature, and sticky point are closely related. The glass-
`transition temperature can be fairly easily determined,
`and it may be useful in the evaluation of proper drying
`conditions and storage requirements. The crystalliza-
`tion of amorphous materials occurs above T, and depends
`on moisture content and time. More information is needed
`about the effects of the physical state and composition
`on temperature- and time-dependent changes during dry-
`ing and storage.
`
`Notation
`water activity
`a,
`AHm
`latent heat of melting
`T
`temperature
`glass-transition temperature
`Tt3
`crystallization temperature
`Tcr T m
`melting temperature
`Greek Letters
`crystallization time
`ecr
`crystallization time at T,
`0,
`Acknowledgment
`We thank the Academy of Finland and the Center for
`Advanced Food Technology, at Rutgers University, for
`
`183
`their financial support, and M&M Mars, Inc., for dona-
`tion of some of the equipment used in this study. This
`is contribution no. D-10209-13-89 from New Jersey Agri-
`cultural Experiment Section.
`
`Literature Cited
`(1) White, G. W.; Cakebread, S. H. J. Food Technol. 1966, 1,
`73-82.
`(2) Karel, M. In Properties of Water in Foods; Simatos, D.,
`Multon, J. L., Eds.; Martinus Nijhoff Publishers: Dordrecht,
`The Netherlands, 1985.
`(3) Levine, H.; Slade, L. Carbohydr. Polym. 1986, 6, 213-244.
`(4) Levine, H.; Slade, L. J. Chem. SOC., Faraday Trans. 1
`1988,84, 2619-2633.
`(5) Simatos, D.; Karel, M. In Food Preseruation by Water Actiu-
`ity Control; Seow, C. C., Ed.; Elsevier: Amsterdam, 1988.
`(6) Flink, J.; Karel, M. J. Food Sci. 1970, 35, 444-446.
`(7) Holdsworth, S. P. J. Food Technol. 1971, 6, 331-370.
`(8) Thijssen, H. A. C. J. Appl. Chem. Biotechnol. 1971, 21,
`372-377.
`(9) Bellows, R. J.; King, C. J. AIChE Symp. Ser. 1973,69 (132),
`33-41.
`(10) Chirife, J.; Karel, M. J. Food Technol. 1974, 9, 13-20.
`(11) Tsourouflis, S.; Flink, J. M.; Karel, M. J. Sci. Food Agric.
`1976,27, 509-519.
`(12) To, E. C.; Flink, J. M. J. Food Technol. 1978,13,583-594.
`(13) Williams, M. L.; Landel, R. F.; Ferry, J. D. J. Am. Chem.
`SOC. 1955, 77,3701-3707.
`(14) Hopfenberg, H. B.; Stannett, V. In The Physics of Glassy
`Polymers; Haward, R. N., Ed.; John Wiley and Sons: New
`York, 1973.
`(15) Tant, M. R.; Wilkes, G. L. Polym. Eng. Sci. 1981,21,874-
`895.
`(16) Roos, Y. H. J. Food Sci. 1987,52, 146-149.
`(17) Karel, M.; Flink, J. M. In Aduances in Drying; Mujum-
`dar, A., Ed.; Hemisphere Publishing Corp.: Washington, DC,
`1983.
`8) King, C. J.; Kieckbusch, T. G.; Greenwald, C. G. In
`Aduances in Drying; Mujumdar, A., Ed.; Hemisphere Pub-
`lishing Corp.: Washington, DC, 1983.
`9) Berg van den, C. In Concentration and Drying of Foods;
`MacCarthy, D., Ed.; Elsevier Applied Science Publishers: Lon-
`don, 1985.
`(20) Downton, G. E.; Flores-Luna, J. L.; King, C. J. Ind. Eng.
`Chem. Fundam. 1982,21,447-451.
`(21) Hoseney, R. C.; Zeleznak, K.; Lai, C. S. Cereal Chem.
`1986,63,285-286.
`(22) Soesanto, T.; Williams, M. C. J. Phys. Chem. 1981, 85,
`3338-3341.
`-,. --
`(23) Makower, B.; Dye, W. B. J. Agric. Food Chem. 1956, 4,
`'lZ-'I'l.
`(24) Bushill, J. H.; Wright, W. B.; Fuller, C. H. F.; Bell, A. V.
`J . Sci. Food Agric. 1965, 16, 622-628.
`(25) Berlin, E.; Anderson, B. A.; Pallansch, M. J. J. Dairy Sci.
`1968,51, 1339-1344.
`(26) Karel, M. CRC Crit. Reu. Food Technol. 1973,3,329-313.
`
`Accepted February 28, 1990.
`
`