Review Isotermas

0960–3085/02/$10.00+0.00# Institution of Chemical Engineers

Trans IChemE, Vol 80, Part C, June 2002

MOISTURE SORPTION ISOTHERM CHARACTERISTICSOF FOOD PRODUCTS: A REVIEWA. H. AL-MUHTASEB, W. A. M. McMINN and T. R. A. MAGEE

Food Process Engineering Research Group, School of Chemical Engineering, Queen’s University Belfast, Northern Ireland, UK.

K nowledge of the sorption properties of foods is of great importance in fooddehydration, especially in the quantitative approach to the prediction of the shelflife of dried foods. Equations for modelling water sorption isotherms are of special

interest for many aspects of food preservation by dehydration, including evaluation of thethermodynamic functions of the water sorbed in foods. Knowledge of the thermodynamicproperties associated with sorption behaviour of water in foods is important to dehydration inseveral respects, especially in the design and optimization of unit operation.

Keywords: sorption isotherm; water activity; hysteresis; mathematical models; isosteric heat ofsorption.

INTRODUCTION

Controlling the moisture content during the processing offoods is an ancient method of preservation. This is achievedby either removing water, or binding it such that the foodbecomes stable to both microbial and chemical deteriora-tion1. For this reason much attention has been given to thesorption properties of foods. Sorption characteristics have,and are currently being examined in light of their in� uence onthe storage stability of dehydrated products, as well as theireffect on the diffusion of water vapour2. Walter3 in 1924 wasprobably the � rst researcher to relate relative water vapourpressure to microbial growth, the main cause of food spoil-age. A decade afterwards, Scott4 and Salwin5 independentlyapplied this relationship and introduced the concept of wateractivity (aw). This is a term indicating the ‘quality’ of thewater content of food. It describes the degree of ‘boundness’of water and hence, its availability to participate in physical,chemical, and microbiological reactions. Since then, experi-mental and theoretical studies of the water associated withfoods have been intensi� ed in an attempt to understand andinterpret water behaviour. Such endeavourshavebeen fraughtwith dif� culties because foods are heterogeneousmixtures ofsoluble organic and inorganic materials6.

The properties of water, in relation to biological system,can be classi� ed into three categories6.

(1) Structural Aspects: the position and orientation ofwater molecules in relation to each other and tomacromolecules;

(2) Dynamic Aspects: molecular motions of water and theircontribution to the hydrodynamic properties of thesystem;

(3) Thermodynamic Aspects: water in equilibrium with itssurroundings, at a certain relative humidity andtemperature.

WATER ACTIVITY

Water, the most abundant constituent of natural foods, hasmany roles in food processing and, while the chemistry issimple, the impact on food reactions and food quality isgreater than any other chemical component7. Karel8 consid-ered water to be the most important plasticizer ‘mobilityenhancer’ for hydrophilic food component, i.e. its lowmolecular weight leads to a large increase in mobility, dueto increased free volume (the volume of the polymer-plasticizer mixture that is not occupied by molecules) anddecreased local viscosity9.

In biological systems, such as foods, water is believed toexist with either unhindered or hindered mobility, referred toas free and bound water, respectively. The amount of waterheld by the food product, under a speci� c set of conditions, istraditionally referred to as the water-holding or water-bindingcapacity of the material. The often ill-de� ned term, ‘boundwater’ is usually considered as that portion of water held inthe material which exhibits physical properties signi� cantlydifferent from those of free, or bulk, water10. It has beensuggested that the water is bound to stronger hydrogen bondacceptors than liquid water (possibly with favoured hydrogenbond angles) as well as water-solvating nonpolar groups.According to Luck11, bound water has a reduced solubilityfor other compounds, causes a reduction in the diffusion ofwater-soluble solutes in the sorbent, and exhibits a decreasein diffusion coef� cient with decreasingmoisture content.Thedecreased diffusion velocity impedes drying processesbecause of slower diffusion of water to the surface.

Some of the characteristics of bound water are lowervapour pressure, high binding energy as measured duringdehydration, reduced mobility as seen by nuclear magneticresonance (NMR), unfreezability at low temperature, andunavailability as a solvent12. Although each of these char-acteristics has been used to de� ne bound water, each gives a

118

different value for the amount of water which is bound. As aresult of this, as well as the complexities and interactions ofthe binding forces involved, no universal de� nition of boundwater has been adopted.

The concept of water activity, that is used most commonlyby researchers in the food industry, can be de� ned as:

aw ˆ p=p0 ˆ relative humidiy100

…1†

where p is the partial pressure of water in the food (atm),and p0 the vapour pressure of pure water at the sametemperature (atm).

MOISTURE SORPTION ISOTHERM

The relationship between total moisture content and thewater activity of the food, over a range of values, and at aconstant temperature, yields a moisture sorption isothermwhen expressed graphically. This isotherm curve can beobtained in one of two ways (see Figure 1):

(i) an adsorption isotherm is obtained by placing a com-pletely dry material into various atmospheres of increas-ing relative humidity and measuring the weight gain dueto water uptake;

(ii) a desorption isotherm is found by placing an initiallywet material under the same relative humidities, andmeasuring the loss in weight2.

The adsorption and desorption processes are not fullyreversible, therefore a distinction can be made between theadsorption and desorption isotherms by determiningwhether the moisture levels within the product are increas-ing indicating wetting, or whether the moisture is graduallylowering to reach equilibrium with its surroundings, imply-ing that the product is being dried.

On the basis of the van der Waals adsorption of gases onvarious solid substrates, Brunauer et al.13 classi� ed adsorp-tion isotherms into � ve general types (see Figure 2). Type Iis the Langmuir, and Type II the sigmoid shaped adsorptionisotherm; however, no special names have been attached tothe other three types. Types II and III are closely related toTypes IV and V, except that the maximum adsorption occursat a pressure lower than the vapour pressure of the gas. If,

however, the solid is porous so that it has an internal surface,then the thickness of the adsorbed layer on the walls of thepores is necessarily limited by the width of the pores. Theform of the isotherm is modi� ed correspondingly; instead ofType II and III, Type IV and V exist14.

Moisture sorption isotherms of most foods are nonlinear,generally sigmoidal in shape, and have been classi� ed asType II isotherms. Caurie15 suggested that most of the waterin fresh food exerts a vapour pressure very close to that ofpure water, i.e. unity. This vapour pressure level is main-tained until the moisture content of the food decreases toabout 22%. The moisture level is then no longer able tosustain the vapour pressure of the food at unity, and there-fore, begins to show a lowered vapour pressure, as if insolution. The changes with atmospheric humidity of this lastfraction (22%) of water in dehydrated foods result in thecharacteristic sigmoid shape of water sorption isotherms.Rowland16 suggested that the direct plasticizing effect ofincreasing moisture content at constant temperature isequivalent to the effect of increasing temperature at constantmoisture and leads to increased segmental mobility ofchains in amorphous regions of glassy and partially crystal-line polymers.

Foods rich in soluble components, such as sugars,however, have been found to show Type III behaviour, thisis due to the solubility of sugars in water17. Chinachoti andSteinberg18 found that sucrose added to starch gels sharplyincreased the sorption of water at water activities higher than0.85.

The sorption isotherm characteristics of many food pro-ducts have been determined experimentally (see Table 1),and have been further characterized according to theBrunauer et al.13 classi� cation; a number of examples arepresented in Table 2.

For interpretation purposes, the generalized moisturesorption isotherm for a hypothetical food system may bedivided into three main regions, as detailed in Figure 1.Region A represents strongly bound water with an enthalpyof vaporization considerably higher than that of pure water.A typical case is sorption of water onto highly hydrophilicbiopolymers such proteins and polysaccharides. The moist-ure content theoretically, represents the adsorption of the� rst layer of water molecules. Usually, water molecules inthis region are unfreezable and are not available for chemicalreactions or as plasticizers. Most dried food products areempirically observed to display their greatest stability atmoisture contents comparable to the monolayer moisturecontent19.Figure 1. Generalized sorption isotherm for food products91.

Figure 2. Five types of van der Waals adsorption isotherm13.

MOISTURE SORPTION ISOTHERM CHARACTERISTICS 119


Region B, represents water molecules which are less � rmlybound, initially as multilayers above the monolayer. In thisregion, water is held in the solid matrix by capillary conden-sation. This water is available as a solvent for low-molecular-weight solutes and for some biochemical reactions. Thequantity of water present in the material that does notfreeze at the normal freezing point usually is within thisregion. In region C or above, excess water is present inmacro-capillariesor as part of the � uid phase in high moisturematerials This exhibits nearly all the properties of bulk water,and thus is capable of acting as a solvent. Microbial growthbecomes a major deteriorative reaction in this region20,21.

The variation in sorption properties of foods reported inthe literature is caused by biological variation in foods, pre-treatment of food, and differences in experimental techni-ques adopted (gravimetric, manometric or hygrometric)22.

EFFECT OF TEMPERATURE ON SORPTIONISOTHERMS

The effect of temperature on the sorption isotherm is ofgreat importance given that foods are exposed to a range oftemperaturesduring storage and processing and water activitychangeswith temperature.Temperature affects the mobilityofwater molecules and the dynamic equilibrium between thevapour and adsorbed phases. In general, researchers havefound that if the water activity is maintained constant, anincrease in temperature causes a decrease in the amount ofsorbed water. Iglesias and Chirife23considered this to indicatethat the food is becoming less hygroscopic. Palipane andDriscoll24 suggested that at higher temperatures some watermolecules are activated to energy levels that allow them tobreak away from their sorption sites, thus decreasing theequilibrium moisture content. A deviation from this beha-viour, however, has been shown by certain sugars (glucose)and other low molecular weight food constituents (salt),which become more hygroscopic at higher temperatures dueto their ability to dissolve in water25. Saravacos et al.22

observed the intersection of the 20¯C and 30¯C isothermcurves of sultana raisins at a water activity of approximately0.78. This was also reported by Saravacos and Stinch� eld26

for model systems containing starch and glucose. Similareffects of temperature on the isotherm characteristics havebeen observed by Audu et al.27 for sugars, and Weisseret al.28

for sugar alcohol.Tsami et al.29 found similar results for driedfruits, up to a water activity of 0.55–0.7. However, for water

Table 1. Summary of moisture sorption isotherm characteristics of food materials.

Material A=D T, ¯C Researchers

Starchy foodsCorn D 10–60 Chen and Clayton92, Kumar93, Iglesias and Chirife65, Iglesias and Chirife94, Duras and Hiver95.Potato A and D 10–80 Mazza96, Labuza97, Lomauro et al.32, Diamante and Murno98, Wang and Brennan37,

Kiranoudis et al.38, McLauglin and Magee39, McMinn and Magee40.Wheat Flour A 20–50 Becker and Sallans99, Hubbard et al.100, Bushuk and Winkler101.Rice A and D 20 Taylor102, Wolf et al.52, Iglesias and Chirife65.Sorghum A 10–35 Iglesias and Chirife94.Starch gel A and D 20–50 Fish103, Saravacos and Stinch� eld26, McMinn104.

High protein foodsBeef A 30–50 Salwin5, Iglesias and Chirife65.Chicken, raw D 5–60 Labuza97.Chicken, cooked A and D 5–60 Wolf et al.105, Iglesias and Chirife94.Eggs A 17–60 Iglesias and Chirife94.Milk A and D 2–40 Berlin et al.106, Labuza et al.72, Linko et al.82, Labuza97.Macadamia nuts A and D 20–60 Palipane and Driscoll24.Cheese A and D 25 Salwin5, Wolf et al.105, Iglesias and Chirife65, Lomauro et al.32.Yoghurt A and D 5–45 Wolf et al.105, Kim and Bhowmik81.

FruitsBanana A 25–60 Wolf et al.105, Iglesias and Chirife65.Pineapple A and D 25–60 Wolf et al.105, Hossain et al.107.Apple D 20–30 Wolf et al.52, Iglesias and Chirife65, Roman et al.108, Roman et al.109.Apricots A and D 15–60 Maroulis et al.110, Samaniego et al.111.Raisins A and D 20–35 Saravacos et al.16, Maroulis et al.110, Tsami et al.29.

VegetablesGreen pepper A and D 30–60 Lomauro et al.32, Kiranoudis et al.38, Kaymak-Ertekin and Sultanoglu41.Lentil A and D 5–60 Wolf et al.105, Menkov80.Tomato D 30–60 Kiranoudis et al.38.Onion A 20–40 Salwin5, Samaniego-Esguerra et al.111, Kiranoudis et al.38, Adam et al.112.Sugar Beet Root D 35–50 Iglesias et al.58.Carrot A 30–60 Taylor102, Kiranoudis et al.38.Celery A 5–60 Wolf et al.105.Cabbage A 37 Mizrahi et al.113.

A: adsorption; D: desorption; T: temperature range.

Table 2. Types of van der Waals adsorption isotherms observed for differentfood materials.

van der Waalsadsorption isotherm Food materials

Type II Starch Gel26,104, Corn94, Potato37, Macadamia nuts24,Carrot38, Tomato, Green pepper, Potato39,40,Lentil seeds80, Onion112, Green pepper41,Chestnut114, Hazelnut115, Cocoa beans116.

Type III Pineapple105, Banana65, sugars27, Apple108, Sugaralcohol28, Sucros-Starch18,55, Raisins16,Apricot110,111, Pineapple107, Cured beef117.


120 AL-MUHTASEB et al.

activity values greater than 0.7, there was an inversion of theeffect of temperature (equilibriummoisture content increasedwith temperature).This phenomenonwas attributedto the factthat, in general, at low aw values the sorption of water is duemainly to the biopolymers, with an increase of temperaturehaving the normal effect of lowering the isotherm. However,as aw is raised beyond the intermediate region,water begins tobe sorbed by the sugars and other low molecular weightconstituents (offsets the effect of temperature). The result isan increasing of the moisture content, i.e. intersection of theisotherms25. The intersection point depends on the composi-tion of the food and the solubility of sugars26.

MEASUREMENT OF SORPTION ISOTHERMS

Many methods are available for determining water sorp-tion isotherms30. These methods can be classi� ed into threecategories: (1) gravimetric; (2) manometric; (3) hygrometric.

° gravimetric method: involves the measurement of weightchanges. Weight changes can be determined both continu-ously and discontinuously in dynamic or static systems(i.e. air may be circulated or stagnant). Continuousmethods employ the use of electro-balances or quartzspring balances. In the discontinuous systems, salt orsulphuric acid solutions are placed in vacuum or atmo-spheric systems with the food material, to give a measureof the equilibrium relative humidity.

° manometric method: measures the vapour pressure ofwater in the vapour space surrounding the food. Toimprove accuracy the � uid selected for the manometeris often oil instead of mercury. The whole system ismaintained at constant temperature and the food samplewill lose water to equilibrate with the vapour space. Thiswill be indicated by the difference in height on themanometer.

° hygrometric method: measures the equilibrium relativehumidity of air in contact with a food material, at a givenmoisture content. Dew-point hygrometers detect thecondensation of cooling water vapour. Electric hygro-meters measure the change in conductance or capacitanceof hygrosensors. Most hygrosensors are coated with ahygroscopic salt, such as LiCl, which absorbs moisturefrom the food sample.

A static gravimetric technique was developed and stan-dardized in the Water Activity Group of the European COST90 project31. Moisture sorption data for food productspublished in the literature have been obtained by applyingthis technique at various temperatures and water activitiesfor its following advantages32–41:

(1) determining the exact dry weight of the sample;(2) minimizing temperature � uctuation between samples

and their surroundings or the source of water vapour;(3) registering the weight change of the sample in equili-

brium with the respective water vapour pressures;(4) achieving hygroscopic and thermal equilibrium between

samples and water vapour source.

MOISTURE SORPTION HYSTERESIS

In the � eld of water vapour sorption by a solid sorbent,moisture sorption hysteresis is the phenomena by which two

different paths exist between the adsorption and desorptionisotherms42. In general, if the amount of water per unit massof solid is plotted as the ordinate and the correspondingrelative vapour pressure as the abscissa, the desorptionisotherm lies above the adsorption isotherm and a closedhysteresis loop is formed. This is illustrated in Figure 1.

The extent of hysteresis is related to the nature and stateof the components in a food. It may re� ect their structuraland conformational rearrangment, which alters the accessi-bility of energetically favourable polar sites, and thus, mayhinder the movement of moisture17.

The effect of hysteresis on food is important, even thoughit can be relatively low in magnitude. Labuza et al.43 showedthat lipid oxidation occurs 3–6 times faster in foodsprepared by desorption than in those prepared by adsorptionat constant aw. Labuza et al.44 suggested that, although moreexpensive, the preparation of intermediate moisture foodsvia adsorption following desorption, rather than desorptionalone, might be justi� ed in terms of increased shelf life.

Theories of Sorption Hysteresis

Several theories have been formulated to explain thephenomenon of hysteresis, and to date, no theory hasgiven a complete insight into the several mechanisms andno quantitative prediction of hysteresis is available in theliterature45. The interpretations proposed for sorption hys-teresis can be classi� ed into one, or more, of the followingcategories25,46:

° hysteresis on porous solids: this is observed in materialssuch as fruits, where the theory is based on capillarycondensation;

° hysteresis on non-porous solids: this is observed inmaterials such as protein, where the theory is based onpartial chemisorption, surface impurities, or phasechanges;

° hysteresis on non-rigid solids: this is observed in materi-als such as starchy food, where the theory is based onchanges in structure, as these changes hinder penetrationof the adsorbate.

Several theories have been postulated to explain hystere-sis on porous solids. Without exception, the explanationswere established on the basis of the capillary condensationphenomena, and therefore, interpretation of hysteresis canbe realized in terms of the Kelvin equation40. Kapsalis42

reviewed the theories, and accordingly, established thefollowing classi� cation:

° incomplete wetting theory: suggests a variation in thecontact angles between the solid and liquid duringadsorption and desorption;

° ink bottle theory: explains hysteresis on the basis of thecharacteristic sorbent structure, i.e. large-diameter poreswith narrow passages, simulated by an ‘ink bottle’;

° open-pore theory: extends the ink-bottle theory to includeconsideration of multi-layer adsorption and, hence, avariation in the pore menisci shape.

It has been realized that a capillary condensation mechan-ism alone is not capable of explaining the presence ofhysteresis in some food materials (ginger, coriander,cooked chicken and raw chicken), this is due to the factthat the hysteresis loop extends to low water activities; in



this region the capillary condensation mechanism is unlikelyto operate47. Iglesias and Chirife48 recognized that it is notpossible to give a single explanation of the hysteresisphenomena in foods; this is due to the fact that food is acomplex combination of various constituents, which can,not only sorb water independently but also, interact amongstthemselves.

In a discussion on hysteresis, Hill49 stated that theadsorption branch represents the true equilibrium up to acertain point in the isotherm, and that the desorption branchnever represents the true equilibrium. It was noted that forporous materials, such as foods, the region on the adsorptionbranch that represents equilibrium is limited or non-existent.This is due to the wide distribution of pore sizes rendering itimpossible to determine, with any certainty, where capillaryeffects begin to exert a signi� cant in� uence in vapourpressure lowering; for the smallest pores it probablyoccurs in the early stages of the adsorption process.Among the factors that play a role in hysteresis is thenature of the pore size distribution, and the driving forceinvolved in changing the water activity17,50. Gregg andSing14 disagreed with Hill, considering that the desorptionbranch, having the lower pressure and hence the lowerchemical potential, to more closely represent to equilibrium.Kapsalis42 commented on this controversial point by statingthat, in general, the type of changes encountered uponadsorption and desorption will depend on the initial stateof the sorbent (amorphose versus crystalline), the transitiontaking place during adsorption, and the speed of desorption.

Rao51 attributed the elimination of hysteresis to the elasticproperties of organogels. During adsorption, the capillarypores of the adsorbent become elastic and swell. Upondesorption, the removal of water causes shrinkage andgeneral collapse of the capillary porous structure. Alterationof structure causes subsequent elimination of hysteresis dueto the absence of capillary condensation.

Types of Hysteresis

A variety of hysteresis loop shapes have been observed infood systems. Wolf et al.52 reported wide differences in themagnitude, shape and extent of hysteresis of dehydratedfoods; the characteristics are dependent on the type of foodand the temperature. Variations can be grouped into threegeneral categories, as shown in Figure 325:

° high-sugar and high pectin foods—this phenomena ispronounced in the lower moisture content region53;

° high-protein foods—hysteresis begins at high water activ-ity, in the capillary condensation region, and extends overthe isotherm to zero water activity;

° starchy foods—a large loop is reported, with the maxi-mum deviation between the curves occuring at about aw

0.7 (or within the capillary condensation region )54.

Investigations have indicated decreased total hysteresisand limited loop span along isotherms developed at elevatedtemperatures48. Chinachoti and Steinberg55 found hysteresisin sugar containing starch up to a water activity of 0.6, andBolin56 up to 0.3 in raisins (very high sugar content). Tsamiet al.29 observed signi� cant hysteresis below 0.5–0.6 infruits, and suggested that the absence of hysteresis at hightemperature was due to the dissolution of sugars. Wolfet al.52 found a decrease of the hysteresis magnitude with

increasing temperature for pork, apple and rice. A similarbehaviour was found by Benson and Richardson57 for ethylalcohol sorption onto egg albumin. Although McLaughlinand Magee39 and McMinn and Magee40 found a decrease inthe total hysteresis with increasing temperature for potato,Wang and Brennan37 observed an increase in the totalhysteresis with increasing temperature (for potato).

MATHEMATICAL DESCRIPTION OF MOISTURESORPTION ISOTHERMS

Although several mathematical models exist to describewater sorption isotherms of food materials2,58, no oneequation gives accurate results throughout the whole rangeof water activities, and for all types of foods59. Labuza50

noted that no sorption isotherm model could � t data over theentire range of relative humidity because water is associatedwith the food matrix by different mechanisms in differentwater activity regions. Of the large number of modelsavailable in the literature60, some of those more commonlyused are discussed below.

The Brunauer-Emmett-Teller (BET) Equation

The Brunauer, Emmett and Teller (BET) sorption equa-tion, formulated in 1938, represents a fundamental mile-stone in the interpretation of multilayer sorption isotherms,particularly Type II and III61; it provides an estimation ofthe monolayer value of moisture adsorbed on the surface.The monolayer moisture content of many foods has been

Figure 3. Examples of sorption hysteresis in foods42.



reported to correspond with the physical and chemicalstability of dehydrated foods47,62. However, in almostall cases the so-called BET plots are only linear over thelower relative pressure region (aw) of the sorbate(0.05< aw< 0.35). The theory behind the BET equationhas been faulted on many grounds, including the assump-tions that: (1) the rate of condensation on the � rst layer isequal to the rate of evaporation from the second layer; (2)the binding energy of all of the adsorbate on the � rst layer isequal; (3) the binding energy of the other layers is equal tothose of the pure adsorbate. However, the equation has beenuseful in de� ning an optimum moisture content for dryingand storage stability of foods, and in the estimation of thesurface area of a food19. The BET equation is generallyexpressed in the form:

MM0

ˆ Caw

…1 ¡ aw†…1 ¡ aw ‡ Caw†…2†

where M is the moisture content (kg=kg dry solid), M0 ismonolayer moisture content (kg=kg dry solid), aw is thewater activity, and C is a constant related to the net heat ofsorption. The estimation of the constants is based onlinearization of equation (2). In their study on the reliabilityof the methods used to evaluate the constants, Iglesiaset al.63 proposed that a weighted least squares analysis isnecessary and should be applied when the linear BET plot isstudied.

Halsey Equation

The following equation, developed by Halsey64, providesan expression for condensation of multilayers at a relativelylarge distance from the surface:

aw ˆ exp…¡A=RTyr† …3†

where A and r are constants, y ˆ M=M0, R is the universalgas constant (8.314 kJ mol¡1 K¡1), and T is the absolutetemperature (K). Halsey assumed that the potential energyof a molecule varies as the inverse rth power of its distancefrom the surface. He also stated that the magnitude of theparameter r characterizes the type of interaction between thevapour and the solid. This equation was shown by Halsey64

to be a good representation of adsorption data that conformto Type I, II, or IIII isotherms19. Iglesias et al.58 and Iglesiasand Chirife65 reported that the Halsey equation could beused to describe 220 experimental sorption isotherms of 69different foods in the range of 0.1 < aw< 0.8.

Smith Equation

Smith66 developed an empirical model to describe the� nal curved portion of the water sorption isotherm of a highmolecular weight bio-polymer. He theorized that there aretwo fractions of water sorbed onto a dry surface; the � rstexhibits a higher than normal heat of condensation andwould be expected to follow the Langmuir model. Smithbased his model on the second fraction, which can formonly after the � rst fraction has been sorbed. He consideredthe second fraction to consist of multilayers of condensedwater molecules, which effectively prevent any possibleevaporation of the initial layer. He theorized that themoisture content in the second fraction was proportional

to the logarithm of the difference between the aw of thesample and pure water. The Smith model can be written as:

M ˆ A ‡ B log…1 ¡ aw† …4†where M is the moisture content (kg=kg dry solid), A thequantity of water in the � rst sorbed fraction, and B thequantity of water in the multilayer moisture fraction.

Henderson Equation

One of the most widely used models relating wateractivity to the amount of water sorbed is the Hendersonequation67. This can be written as:

M ˆ ln…1 ¡ aw†¡A

µ ¶1=B

…5†

where M is the moisture content (kg=kg dry solid), A and Bare constants. A linearized plot of ln[¡ ln(1 7 aw)] versusmoisture content has been reported to give rise to three‘localized isotherms’68,69 which do not necessarily provideany precise information on the physical state of water, aswas originally thought67.

Oswin Equation

Oswin70 developed an empirical model which is a seriesexpansion for sigmoid shaped curves, and can be written as:

M ˆ Aaw

1 ¡ aw

µ ¶B

…6†

where M is the moisture content (kg=kg dry solid), A and Bare constants. Boquet et al.71 considered the Oswin equationto be the best one for describing the isotherms of starchyfood, and a reasonably good � t for meat and vegetables.This equation was also used by Labuza et al.72 to relate themoisture contents of non-fat dry milk up to awˆ 0.5.

Guggenheim-Anderson-de Boer (GAB) Equation

The three parameters GAB equation, derived indepen-dently by Guggenheim73, Anderson74, and de Boer75 is asemi-theoretical, multimolecular, localized, homogeneousadsorption model. It has been suggested to be the mostversatile sorption model available in the literature and hasbeen adopted by a group of West European food research-ers60,76. It can be written as:

M ˆ M0CKaw

…1 ¡ Kaw†…1 ¡ Kaw ‡ CKaw†…7†

where M is the moisture content (kg=kg dry solid), M0 is themonolayer moisture content; C and K are constants relatedto the energies of interaction between the � rst and furthermolecules at the individual sorption sites. Theoretically theyare related to the sorption enthalpies60:

C ˆ c0 expHm ¡ Hn

RT

µ ¶…8†

K ˆ k0 expH1 ¡ Hn

RT

µ ¶…9†

where c0 and k0 are entropic accommodation factors; Hm, Hn

and H1 are the molar sorption enthalpies of the monolayer,



multilayers and bulk liquid, respectively (kJ mol¡1). TheGAB model represents a re� ned extension of the BETtheory, postulating that the state of the sorbate moleculesin the second and higher layers is equal, but different fromthat in the liquid-like state. This assumption introduces anadditional degree of freedom (an additional constant, K) bywhich the GAB model gains its greater versatility. Incor-poration of the parameter K, however, assumes that multi-layer molecules have interactions with the sorbent that rangein energy levels somewhere between those of the monolayermolecules and the bulk liquid. If K is less than unity, lowersorption than that demanded by the BET model is predicted;this allows the GAB isotherm to be successful up to highwater activities (i.e. awº 0.9). In the special case whereK ˆ 1, the GAB equation reduces to the BET equation (ifK > 1, the sorption isotherm will become in� nite at a valueof aw less than unity, which is physically unsound)77.

The major advantages of the GAB model are78:

° viable theoretical background77 since it is a furtherre� nement of the Langmuir and BET theories of physicaladsorption;

° good description of sorption behaviour of almost all foodsfrom a water activity of zero to 0.9;

° parameters (c0, k0, Hm, Hn, and H1) have a physicalmeaning (as previously detailed) in terms of the sorptionprocesses;

° describes the greater part of the temperature effect onisotherms by means of Arrhenius type equations.

Table 3 provides a summary of the moisture sorptionisotherms models adopted by researchers for a variety offood materials. Even though, both BET and GAB isothermmodels are closely related, by postulating that the states ofwater molecules in the second and higher layers are of equalmagnitude but different from that in the liquid state, it hasbeen found that GAB parameters are more representativethan the corresponding BET parameters79. Of the modelsassessed, McLauglin and Magee39 reported that the GABmodel gave the best � t for the sorption isotherms ofpotatoes. A similar � nding was reported by Wang andBrennan37 for potato, Kiranoudis et al.38 for potato,carrot, tomato, green pepper and onion, and Menkov80 forlentil seeds. Kim and Bhowmik81 reported that the Hasleyand GAB models gave good � ts for the experimentalisotherms of yoghurt. Lomauro et al.32 reported that the

GAB model gave a good � t for over 75% of the foodisotherms (starchy foods, fruits, vegetables and meatproducts), while the Oswin model described 57% of thefood isotherms. Linko et al.82 reported that the Halseymodel gave a good � t for the experimental isotherms ofdried milk products. Starch-containing foods83 have alsoshown to be well described in their sorption behaviour bythis equation. In their comparison between Henderson andHalsey models, Chirife and Iglesias84 found that the Hender-son model was less versatile than the Halsey model.

ISOSTERIC HEAT OF SORPTION

Knowledge of the differential heat of sorption is of a greatimportance when designing equipment for dehydrationprocesses. This is due to the fact that the heat of vaporizationof sorbed water may increase to values above the heat ofvaporization of pure water as food is dehydrated to lowmoisture levels85.

A differential heat of sorption greater than the heat ofvaporization, primarily indicates that the energy of interac-tion between the sorbate and sorption sites is greater thanthe energy that holds the sorbate molecules together in theliquid state. Consequently, the level of moisture content atwhich the differential heat of sorption approaches the heat ofvaporization of pure water is often taken as indicative of theamount of ‘bound’ water existing in the food86.

Two methods are available for measurement of the differ-ential heat of sorption. The � rst is direct calorimetricmeasurement of the heat evolved, and the second is applica-tion of the Clausius-Clayperon equation on the isostericequilibrium pressures at different temperatures (the ‘iso-steric’ heat of sorption). Sorption calorimetry is dif� cultbecause of the technique needed for precise measurement ofthe small quantities of heat evolved. For this reason,calorimetrical measured heats of sorption are much lesscommon than those calculated from the sorption isotherm,however, they offer a higher degree of accuracy whendetermined with care19.

The net isosteric heat (qst) is de� ned as the total heat ofsorption in the food minus the heat of vaporizationof water, atthe system temperature29. Conventionally, qst is a positivequantity when heat is evolved during adsorption, and nega-tive when heat is absorbed during desorption. The heat ofadsorption is a measure of the energy released on sorption,

Table 3. Summary of moisture sorption isotherm models used to � t experimental data.

Model aw range Food materials

GAB 0.05–0.95 Protein118, Starch119, Casein, Potato starch76, Fish90, Starchy food32, Raisins22, Raisins, Figs,and apricot110, Protein and starch food77, Potato37, Red pepper120, Macadamia nuts24,Pasta products121, Carrot, tomato, onion, and green pepper38, Yoghurt powder81, Potato39,40,Amaranth starch122, Lentil seeds80, Onion112, Pineapple107, Rice, Turkey, Chicken, Tomato,Potato starch, and Wheat starch79, Chestnut114 Hazelnut115, Cured beef117.

BET 0.05–0.35 Protein123, Chicken48, Peanut � akes62, Potato37,39, Lentil seed80, Onion112, Pineapple107, Rice,Turkey, Chicken, Tomato, Potato starch, and Wheat starch79.

Halsey 0.05–0.8 Starchy food, Proteins, Meats, and Fruits84, Milk82, Potato83,37,39, Raisin16, Yoghurt powder81,Lentil seeds80, Hazelnut115, Chestnut114, Cured beef117, Cocoa beans116

Oswin 0.05–0.9 Proteins123, Meats, and Fruits71, Starch food32, Potato37,39, Lentil seed80, Onion112,Hazelnut115, Chestnut114, Cured beef117

Smith 0.3–0.9 Wheat99, Corn starch124, Soy � our, Beef, and Casein125,126, Pineapple107, Hazelnut115,Chestnut114, Cocoa beans116

Henderson 0.05–0.8 Different food product69, Starchy food, Proteins, Meats, and Fruits84, Potato37, Lentil seeds80,Onion112, Pineapple107, Chestnut114, Cocoa beans116



and the heat of desorption the energy requirement to break theintermolecular forces between the molecules of water vapourand the surface of adsorbent17. Thus, the heat of sorption isconsidered as indicative of the intermolecular attractiveforces between the sorption sites and water vapour37.

For the most part, the heat of desorption has been observedto present a higher magnitude than the corresponding heat ofadsorption37–40,87–89. Iglesias and Chirife48 considered this tobe due to structural modi� cations which takes place duringdesorption; this modi� es the over-all energy of binding of thesorbate through co-operative binding or to entrapmenteffects. This picture of the phenomena not only explainsthe difference between the adsorption and desorption heatcurves, but it is also capable of explaining the differencebetween the moisture content of the adsorption and thedesorption branch of the isotherm for a given water activity.Iglesias and Chirife87 concluded that the heats of changeinvolved in irreversible processes are small compared withthe overall energy changes, so they may be neglected in ageneral qualitativedescription,or in the estimationof the heatrequirements for the dehydration process.

On the basis of thermodynamic principles, the net iso-steric heat of sorption may be determined from the equation:

qst ˆ ¡R@…ln aw†@…1=T†

…10†

where qst is the net isosteric heat of sorption at constantmoisture content (kJ mol¡1 water).

This relationship was derived from the Clausius-Clayperon equation, applied to the system and pure waterwith the following assumptions87–88:

(1) the heat of vaporization of pure water and excess heat ofsorption do not change with temperature;

(2) the moisture content of the system remains constant.

Labuza et al.90 mentioned that these assumptions could bemet for a pure system at low temperature, however, forcomplex systems like food, irreversible changes can occur inthe binding properties of the system.

The main advantage of the equation is that it gives theheat of adsorption and desorption for food materials whichis necessary to estimate the heat load during the drying offood materials45. Values of isosteric heat of sorption, ob-tained by adopting the Clausius-Clayperon equation, havebeen reported in the literature for several foods, includingmeat products, vegetables and fruits (see Table 4).

The net isosteric heat of sorption decreases considerablywhen the moisture content is increased. In an attempt todescribe the relationship between the net isosteric heat ofsorption and the moisture content, Tsami et al.29 proposed anempirical exponential correlation, which can be written as:

qst ˆ q0 exp…¡X =X0† …11†

where q0 is the net isosteric heat of sorption of the � rstmolecules of water in the food (kJ mol¡1), X is the equili-brium moisture content, (kg=kg dry solid), and X0 is thecharacteristic moisture content of the food material, (kg=kgdry solid). q0 provides important information on both thephysiochemical interactions of water with the major foodconstituents and the state of water within the food system,and it is an invaluable parameter, for estimation of theenergy requirements (q0, X0) during drying40. Values of

these parameters have been reported in the literature forseveral foods (see Table 5).

CONCLUSIONS

Moisture content control is an inherent feature of manyfood-processing operations. Moisture sorption isothermshave an important role to play in the quantitative approachto the prediction of the shelf life of dried foods due to theirsensitivity to moisture changes. The existence of hysteresisloops in the moisture sorption isotherms of food is indicativeof a non-equilibrium state, no matter how reproducible thedata. Equations for � tting water sorption isotherms in foodsare of special interest in many aspects of food preservation bydehydration; including the prediction of drying times andshelf life of a dried product in a packaging material. Besidesthis practical interest, the isotherm equation is also needed

Table 4. Isoteric heat of sorption of food materials.

Material qst (kJ kg¡1) Researcher

Apple 83.34–1112 Roman et al.109.Apricots ¡55.56–277.8 Tsami et al.89.Beef 356–1374 Iglesias and Chirife23.Carrot 566.7–1594.4 Kiranoudis et al.38.Celery 144–325 Iglesias and Chirife23.Cheese 365–780 Iglesias and Chirife23.Chicken 249–2661.7 Iglesias and Chirife23.Corn 111–425.5 Cenkowski et al.127, Iglesias and

Chirife23.Eggs 95.3–490.9 Iglesias and Chirife23.Milk 34–395 Iglesias and Chirife23.Onion 222.2–2111.3 Kiranoudis et al.38, Adam et al.112.Peppers 722.2–1961.1 Kiranoudis et al.38 and

Kaymak-Ertekin and Sultanoglu41.Pineapple 277.8–1666.8 Iglesias et al.48, Hossain et al.107.Potato 461.1–1933.3 Wang and Brennan37, Kiranoudis

et al.38, McLaughlin and Magee39,McMinn and Magee40.

Sugar beet 36.7–611.2 Iglesias et al.48, Iglesiasand Chirife23.

Raisins ¡55.5–944.5 Saravacos et al.22, Tsami et al.89.Rice 142.3–445.1 Iglesias and Chirife23,

Cenkowski et al.127.Squid 313–778 Castanon and Barral128.Starch (potato) 0–373.8 Iglesias and Chirife23.Starch (maize) ¡14.5–64.5 Iglesias and Chirife23.Tapioca 83.34–888.9 Soekarto and Steinberg129.Tomato 411.1–2383.3 Kiranoudis et al.38.

Table 5. Characteristic parameters for equation (11) for food materials.

Materialq0

(kJ mol¡1)X0 (kg=kgdry solid) Researcher

Adsorption dataApricot 10.3 0.06 Tsami et al.89.Potato 44 0.08 McMinn and Magee40.Raisin 94.7 0.03 Tsami et al.89.

Desorption dataApricot 109 0.03 Tsami et al.89.Carrot 40.5 0.2 Kiranoudis et al.38.Green pepper 61.1 0.19 Kiranoudis et al.38.Onion 65 0.18 Kiranoudis et al.38.Potato 74.6 0.08 Kiranoudis et al.38,

56 0.09 McMinn and Magee40.Raisin 131 0.03 Tsami et al.89.Tomato 114.2 0.12 Kiranoudis et al.38.



for evaluating the thermodynamic functions of the watersorbed in foods. To date, no one equation gives accurateresults throughout the whole range of water activities, and forall types of foods. The thermodynamic properties of foodsincluding enthalpy and entropy of sorption are essential forthe design and optimization of unit operations, and furtherhelp the understanding and interpretation of sorption mech-anisms and food-water interactions.

NOMENCLATURE

A constantaw water activityB constantC constantc0 entropic accommodation factorHm molar sorption enthalpies of monolayer, kJ mol¡1

Hn molar sorption enthalpies of multilayers, kJ mol¡1

H1 molar sorption enthalpies of bulk liquid, kJ mol¡1

DHvap latent heat of vaporization of pure water, kJ mol¡1

K constantk entropic accommodation factorM moisture content, kg=kg dry solidM0 monolayer moisture content, kg=kg dry solidp, pi water vapour pressure exerted by the food material, atmp0 vapour pressure of the pure water at the equilibrium temperature

of system, atmqst net isosteric heat of sorption, kJ mol¡1

r constantR universal gas constant, 8.314kJ mol¡1

T temperature, KX equilibrium moisture content, kg=kg dry solidX0 characteristic moisture content of the food material, kg=kg dry

solid

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ADDRESS

Correspondence concerning this paper should be addressed to ProfessorT. R. A. Magee, School of Chemical Engineering, Queen’s UniversityBelfast, David Keir Building, Belfast, BT9 5AG, Northern Ireland, UK.E-mail: [email protected]

The manuscript was received 9 July 2001 and accepted for publicationafter revision 11 March 2002.



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