4. Influence of temperature on moisture sorption isotherms

Temperature affects the mobility of water molecules and the dynamic equilibrium between the vapor and the adsorbed gases [13]. If water activity is kept constant, an increase in temperature causes a decrease in the amount of sorbed water [20] (Figure 9). This indicates that the food becomes less hygroscopic. Iglesias and Chirife [72] pointed out that increase of temperature represents a condition unfavorable to water sorption.

An exception to this rule is shown by certain sugars and other low molecular weight food constituents, which become more hygroscopic at higher temperature because they dissolve in water. Temperature shifts can have an important practical effect on the chemical and microbiological reactivity related to quality deterioration of a food in a closed container [73]. An increase of temperature at constant moisture content causes increase in water activity (Figure 10). This increases the rate of reactions and leads to deterioration [74–76]. Weisser [31] studied the effect of temperature on the sorption isotherms of roasted coffee and reported that the product showed consistent separation of the isotherms at different temperatures. However, not all foods exhibit such consistency. In the work reported by Saravacos et al. [12], crossing over occurred at high water activity (aw = 0.78) in the 20 and 30°C adsorption isotherms of sultana raisins and 5, 20 and 45°C adsorption and desorption isotherms of Chilean papaya shown in Figure 11 [77]. Such crossing over has earlier been observed by Saravacos and Stinchfield [78] on model systems of starch-glucose, Audu et al. [79] on sugars, Weisser et al. [80] on sugar and alcohols

and Silverman et al. [81] on 20 and 37°C isotherms of precooked bacon. These substances contain large amounts of low molecular weight constituents in a mixture of high molecular weight biopolymers. At lower water activity values, the sorption of water is due mainly to the biopolymers, and an increase of temperature has the normal effect of lowering the isotherms [13]. As water activity is raised beyond the intermediate region, moisture begins to be sorbed primarily by the sugars and other low molecular constituents leading to the swinging up of the isotherm. Dissolution, which is favored by higher temperature, offsets the opposite effect of temperature on higher molecular weight constituents. The net result is an increase of moisture content (crossing over) of the isotherms. This has bearing on the sign and magnitude of the binding energy [13]. The binding energy of sultana raisin decreased as the temperature increased from 22 to 32°C in the low moisture region [12], but the effect of temperature showed a crossing over of the lines at higher moisture

Changes in water activity at constant moisture content and in moisture content at constant water activity with

Adsorption EMC of hydroxypropylated cassava starch showing variation of MSI with temperature. Source:

Moisture Sorption Isotherms and Isotherm Model Performance Evaluation for Food…

DOI: http://dx.doi.org/10.5772/intechopen.87996

Figure 10.

155

Figure 9.

Aviara [20].

changes in temperature. Source: Rizvi [6].

Moisture Sorption Isotherms and Isotherm Model Performance Evaluation for Food… DOI: http://dx.doi.org/10.5772/intechopen.87996

#### Figure 9.

3.5 AquaLab instrument

Figure 8.

Sorption in 2020s

Inc. [71].

154

condition unfavorable to water sorption.

AquaLab is the fastest, most accurate and most reliable instrument available for measuring water activity, giving readings in 5 min or less [71]. It is easy to use and provides accurate and timely results. Its readings are reliable, providing 0.003 aw accuracy. The instrument is easy to clean and checking calibration is simple. The

4TE model AquaLab moisture content—water activity measuring instrument. Source: METER Group,

Temperature affects the mobility of water molecules and the dynamic equilib-

An exception to this rule is shown by certain sugars and other low molecular weight food constituents, which become more hygroscopic at higher temperature because they dissolve in water. Temperature shifts can have an important practical effect on the chemical and microbiological reactivity related to quality deterioration of a food in a closed container [73]. An increase of temperature at constant moisture content causes increase in water activity (Figure 10). This increases the rate of reactions and leads to deterioration [74–76]. Weisser [31] studied the effect of temperature on the sorption isotherms of roasted coffee and reported that the product showed consistent separation of the isotherms at different temperatures. However, not all foods exhibit such consistency. In the work reported by Saravacos et al. [12], crossing over occurred at high water activity (aw = 0.78) in the 20 and 30°C adsorption isotherms of sultana raisins and 5, 20 and 45°C adsorption and desorption isotherms of Chilean papaya shown in Figure 11 [77]. Such crossing over has earlier been observed by Saravacos and Stinchfield [78] on model systems of starch-glucose, Audu et al. [79] on sugars, Weisser et al. [80] on sugar and alcohols

rium between the vapor and the adsorbed gases [13]. If water activity is kept constant, an increase in temperature causes a decrease in the amount of sorbed water [20] (Figure 9). This indicates that the food becomes less hygroscopic. Iglesias and Chirife [72] pointed out that increase of temperature represents a

photograph of 4TE model of the equipment is shown in Figure 8.

4. Influence of temperature on moisture sorption isotherms

Adsorption EMC of hydroxypropylated cassava starch showing variation of MSI with temperature. Source: Aviara [20].

#### Figure 10.

Changes in water activity at constant moisture content and in moisture content at constant water activity with changes in temperature. Source: Rizvi [6].

and Silverman et al. [81] on 20 and 37°C isotherms of precooked bacon. These substances contain large amounts of low molecular weight constituents in a mixture of high molecular weight biopolymers. At lower water activity values, the sorption of water is due mainly to the biopolymers, and an increase of temperature has the normal effect of lowering the isotherms [13]. As water activity is raised beyond the intermediate region, moisture begins to be sorbed primarily by the sugars and other low molecular constituents leading to the swinging up of the isotherm. Dissolution, which is favored by higher temperature, offsets the opposite effect of temperature on higher molecular weight constituents. The net result is an increase of moisture content (crossing over) of the isotherms. This has bearing on the sign and magnitude of the binding energy [13]. The binding energy of sultana raisin decreased as the temperature increased from 22 to 32°C in the low moisture region [12], but the effect of temperature showed a crossing over of the lines at higher moisture

#### Figure 11.

Moisture desorption isotherms of Chilean papaya showing isotherm crossing at higher water activities with increase in temperature. Source: Vega-Galvez et al. [84].

contents due to the endothermic dissolution of fruit sugars. Iglesias and Chirife [82] studied the equilibrium moisture contents of air-dried beef and found that the higher the drying temperature, the lower the sorption capacity of the dried beef. Similar results were reported for cookies and corn snacks [21] and apples [25]. Temperature changes also have effects on the water activity of saturated salt solutions, which are used in the determination of sorption isotherms. Labuza et al. [83] used experimental data and thermodynamic analysis to demonstrate that water activity of saturated salt solutions should decrease with increase in temperature.

span or extent is denoted by the water activity range covered. Kapsalis [13] grouped

Type I hysteresis: This type of hysteresis is normally pronounced mainly in the lower moisture content region, below the first inflection point of the isotherm. Although the total hysteresis may be large, no occurrence is normally observed above the 0.65 water activity or in the intermediate moisture range. The type I hysteresis is normally exhibited by high-sugar and high-pectin foods, exemplified

Type II: In this type, moderate hysteresis begins at high water activity, in the capillary condensation region, and extends over the rest of the isotherm to zero water activity. In both desorption and adsorption arms, the isotherm's sigmoidal shape is retained. This type of hysteresis is normally exhibited by high-protein

Type III: In this type, large hysteresis loop occurs with a maximum at about 0.70

Increasing temperature decreases the total hysteresis and limits the span of the loop along the isotherm [84]. Iglesias and Chirife [85] studied the effect of temperature on the magnitude of moisture sorption hysteresis of foods and reported that increasing temperature decreased or eliminated hysteresis for some foods, while for others, the total hysteresis size remained constant, or even increased. In the case where the hysteresis loop decreased, it did so more appreciably at high temperatures. The effect of temperature was found to be more pronounced on the desorp-

Several theories have been proposed to explain hysteresis phenomena in agricultural and food products. The most prominent of the theories are the ink bottle

water activity, which is within the capillary condensation region. This type of

hysteresis normally occurs in starchy foods such as freeze-dried rice.

moisture sorption hysteresis into three general types as follows:

Moisture Sorption Isotherms and Isotherm Model Performance Evaluation for Food…

by air-dried apple.

157

Figure 12.

foods exemplified by freeze-dried pork.

Moisture sorption hysteresis loop. Source: Kapsalis [13].

DOI: http://dx.doi.org/10.5772/intechopen.87996

5.2 Effect of temperature on hysteresis

tion isotherms than the adsorption isotherms.

5.3 Theories of moisture sorption hysteresis

### 5. Moisture sorption hysteresis

A product which attains its moisture equilibrium with the surrounding by losing moisture at a given temperature is said to have reached the desorption EMC. When the relatively dry material absorbs moisture from a high humidity environment at the same temperature, it will eventually reach the adsorption EMC. The isotherm plots may indicate a significant difference at certain water activities and temperatures between desorption and adsorption EMC values, with the desorption values being higher than the adsorption counterpart. This difference is called moisture sorption hysteresis [13, 45]. A typical hysteresis loop presented in Figure 12 could occur within the region of monolayer moisture but could begin at a higher water activity and extend down to zero water activity, depending on its class according to Kapsalis [13] classification.

Moisture sorption hysteresis has important theoretical and practical implications in foods. These include the general aspects of the irreversibility of moisture sorption process and the question of validity of thermodynamic parameters derived from a particular arm of the isotherm. Moisture sorption hysteresis has effect on chemical and microbiological deterioration of low and intermediate moisture foods.

#### 5.1 Hysteresis classification

The hysteresis phenomenon in agricultural and food products varies in magnitude, shape and extent, depending on the type of food and temperature [13]. Hysteresis size or magnitude is depicted by the area enclosed by the loop, while the Moisture Sorption Isotherms and Isotherm Model Performance Evaluation for Food… DOI: http://dx.doi.org/10.5772/intechopen.87996

span or extent is denoted by the water activity range covered. Kapsalis [13] grouped moisture sorption hysteresis into three general types as follows:

Type I hysteresis: This type of hysteresis is normally pronounced mainly in the lower moisture content region, below the first inflection point of the isotherm. Although the total hysteresis may be large, no occurrence is normally observed above the 0.65 water activity or in the intermediate moisture range. The type I hysteresis is normally exhibited by high-sugar and high-pectin foods, exemplified by air-dried apple.

Type II: In this type, moderate hysteresis begins at high water activity, in the capillary condensation region, and extends over the rest of the isotherm to zero water activity. In both desorption and adsorption arms, the isotherm's sigmoidal shape is retained. This type of hysteresis is normally exhibited by high-protein foods exemplified by freeze-dried pork.

Type III: In this type, large hysteresis loop occurs with a maximum at about 0.70 water activity, which is within the capillary condensation region. This type of hysteresis normally occurs in starchy foods such as freeze-dried rice.

#### 5.2 Effect of temperature on hysteresis

Increasing temperature decreases the total hysteresis and limits the span of the loop along the isotherm [84]. Iglesias and Chirife [85] studied the effect of temperature on the magnitude of moisture sorption hysteresis of foods and reported that increasing temperature decreased or eliminated hysteresis for some foods, while for others, the total hysteresis size remained constant, or even increased. In the case where the hysteresis loop decreased, it did so more appreciably at high temperatures. The effect of temperature was found to be more pronounced on the desorption isotherms than the adsorption isotherms.

#### 5.3 Theories of moisture sorption hysteresis

Several theories have been proposed to explain hysteresis phenomena in agricultural and food products. The most prominent of the theories are the ink bottle

contents due to the endothermic dissolution of fruit sugars. Iglesias and Chirife [82] studied the equilibrium moisture contents of air-dried beef and found that the higher the drying temperature, the lower the sorption capacity of the dried beef. Similar results were reported for cookies and corn snacks [21] and apples [25]. Temperature changes also have effects on the water activity of saturated salt solutions, which are used in the determination of sorption isotherms. Labuza et al. [83] used experimental data and thermodynamic analysis to demonstrate that water activity of saturated salt solutions should decrease with increase in temperature.

Moisture desorption isotherms of Chilean papaya showing isotherm crossing at higher water activities with

A product which attains its moisture equilibrium with the surrounding by losing moisture at a given temperature is said to have reached the desorption EMC. When the relatively dry material absorbs moisture from a high humidity environment at the same temperature, it will eventually reach the adsorption EMC. The isotherm plots may indicate a significant difference at certain water activities and temperatures between desorption and adsorption EMC values, with the desorption values being higher than the adsorption counterpart. This difference is called moisture sorption hysteresis [13, 45]. A typical hysteresis loop presented in Figure 12 could occur within the region of monolayer moisture but could begin at a higher water activity and extend down to zero water activity, depending on its class according to

Moisture sorption hysteresis has important theoretical and practical implications in foods. These include the general aspects of the irreversibility of moisture sorption process and the question of validity of thermodynamic parameters derived from a particular arm of the isotherm. Moisture sorption hysteresis has effect on chemical

The hysteresis phenomenon in agricultural and food products varies in magni-

and microbiological deterioration of low and intermediate moisture foods.

tude, shape and extent, depending on the type of food and temperature [13]. Hysteresis size or magnitude is depicted by the area enclosed by the loop, while the

5. Moisture sorption hysteresis

increase in temperature. Source: Vega-Galvez et al. [84].

Figure 11.

Sorption in 2020s

Kapsalis [13] classification.

5.1 Hysteresis classification

156

theory, the incomplete wetting theory, the open-pore theory, the shrinkage theory and the capillary condensation-swelling fatigue theory.

Ink bottle theory: This theory assumes that an agricultural and food product is a porous body having capillaries consisting of narrow, small-diameter necks with large bodies resembling ink bottles (Figure 13). It explains hysteresis on the basis of difference in the radii of the porous sorbent. During desorption, the small radii of necks control the emptying of the capillaries and result in a lowering of the relative humidity above the product; whereas during adsorption, the large area for the bodies needs to be filled, thus requiring higher relative humidity. The explanation can be better understood using the Kelvin equation which states that

$$Ln\left(\frac{P}{P\_o}\right) = \frac{-2\sigma V \cos\theta}{RT r\_m} \tag{4}$$

angle of the receding film upon desorption is smaller than that of the advancing film upon adsorption. Therefore, condensation along the adsorption branch of the isotherm will be at a higher vapor pressure resulting in open hysteresis as illustrated in Figure 14. However, in foods the most common type of hysteresis is the closed-end, retraceable loop showing that this theory is limited in its application to foods.

Moisture Sorption Isotherms and Isotherm Model Performance Evaluation for Food…

DOI: http://dx.doi.org/10.5772/intechopen.87996

Open-pore theory: this theory extends the ink bottle theory by including considerations of multilayer adsorption. It is based on the difference in vapor pressure between adsorption Pa and desorption Pd as affected by the shape of the meniscus. During adsorption, the meniscus is considered cylindrical and the Cohan equation (not presented here) applies, whereas during desorption, the shape is considered to

Incomplete wetting theory of hysteresis (A) contact angle and (B) open hysteresis. Source: Kapsalis [13].

Figure 14.

Figure 15.

159

Open-pore theory of hysteresis. Source: Kapsalis [13].

where P is the vapor pressure of liquid over the curved meniscus (Pa), Po is the saturation vapor pressure (Pa) at temperature T (K), σ is the surface tension (N/m), θ is the angle of contact (in complete wetting, θ is 0 and cosθ = 1), V is the molar volume of liquid (m<sup>3</sup> /mol) and rm is the mean radius of curvature of meniscus.

For desorption, by substituting r1 in Figure 13 for rm in Eq. (4) with cosθ = 1 (complete wetting), Eq. (4) becomes transformed into Eq. (5):

$$P\_d = P\_o \exp\left(\frac{-2\sigma V}{RTr\_1}\right) \tag{5}$$

In adsorption with condensation first taking place in the large diameter cavity, Eq. (4) becomes

$$P\_a = P\_o \exp\left(\frac{-2\sigma V}{RTr\_2}\right) \tag{6}$$

From the above, it follows that for a given amount of water sorbed, the pressure will be higher during adsorption than during desorption.

Incomplete wetting theory: This theory is also dependent on capillary condensation based on Eq. (4), but it notes that due to the presence of impurities, the contact

#### Figure 13.

Ink bottle neck theory of moisture sorption hysteresis (left, schematic representation and, right, actual pore). Source: Kapsalis [13].

Moisture Sorption Isotherms and Isotherm Model Performance Evaluation for Food… DOI: http://dx.doi.org/10.5772/intechopen.87996

angle of the receding film upon desorption is smaller than that of the advancing film upon adsorption. Therefore, condensation along the adsorption branch of the isotherm will be at a higher vapor pressure resulting in open hysteresis as illustrated in Figure 14. However, in foods the most common type of hysteresis is the closed-end, retraceable loop showing that this theory is limited in its application to foods.

Open-pore theory: this theory extends the ink bottle theory by including considerations of multilayer adsorption. It is based on the difference in vapor pressure between adsorption Pa and desorption Pd as affected by the shape of the meniscus. During adsorption, the meniscus is considered cylindrical and the Cohan equation (not presented here) applies, whereas during desorption, the shape is considered to

theory, the incomplete wetting theory, the open-pore theory, the shrinkage theory

Ink bottle theory: This theory assumes that an agricultural and food product is a porous body having capillaries consisting of narrow, small-diameter necks with large bodies resembling ink bottles (Figure 13). It explains hysteresis on the basis of difference in the radii of the porous sorbent. During desorption, the small radii of necks control the emptying of the capillaries and result in a lowering of the relative humidity above the product; whereas during adsorption, the large area for the bodies needs to be filled, thus requiring higher relative humidity. The explanation

> <sup>¼</sup> �2σVcos<sup>θ</sup> RTrm

/mol) and rm is the mean radius of curvature of meniscus.

RTr<sup>1</sup> 

RTr<sup>2</sup> 

where P is the vapor pressure of liquid over the curved meniscus (Pa), Po is the saturation vapor pressure (Pa) at temperature T (K), σ is the surface tension (N/m), θ is the angle of contact (in complete wetting, θ is 0 and cosθ = 1), V is the molar

For desorption, by substituting r1 in Figure 13 for rm in Eq. (4) with cosθ = 1

Pd <sup>¼</sup> Po exp �2σ<sup>V</sup>

Pa <sup>¼</sup> Po exp �2σ<sup>V</sup>

In adsorption with condensation first taking place in the large diameter cavity,

From the above, it follows that for a given amount of water sorbed, the pressure

Incomplete wetting theory: This theory is also dependent on capillary condensation based on Eq. (4), but it notes that due to the presence of impurities, the contact

Ink bottle neck theory of moisture sorption hysteresis (left, schematic representation and, right, actual pore).

(4)

(5)

(6)

and the capillary condensation-swelling fatigue theory.

volume of liquid (m<sup>3</sup>

Sorption in 2020s

Eq. (4) becomes

Figure 13.

158

Source: Kapsalis [13].

can be better understood using the Kelvin equation which states that

Ln <sup>P</sup> Po 

(complete wetting), Eq. (4) becomes transformed into Eq. (5):

will be higher during adsorption than during desorption.

Incomplete wetting theory of hysteresis (A) contact angle and (B) open hysteresis. Source: Kapsalis [13].

Figure 15. Open-pore theory of hysteresis. Source: Kapsalis [13].

be hemispherical in which the Kelvin equation is applied. The open-pore theory is illustrated in Figure 15.

performance with R<sup>2</sup> ranging from 0.92 to 0.99. It, however, lacked the temperature term and was modified to incorporate the term. Other commonly used models include modified Henderson, modified Chung-Pfost, modified Halsey and modified Oswin and the GAB. The modified Henderson [96] and modified Chung-Pfost [97] models have been adopted as the standard equations by the American Society of Agricultural and Biological Engineers (ASABE) for describing the EMC-aw data for cereals and oil seeds [98]. The modified Halsey [85] has been reported as the best model for predicting the EMC-aw relationships of several tropical crops [99] and alongside with the modified Oswin [100] has been shown to describe the EMC-aw data of many seed satisfactorily [101, 102]. The Guggenheim-Anderson-de Boer (GAB) model has been recognized as the most satisfactory theoretical isotherm Equation [103–106] and has been recommended as the standard model for use in food laboratories in Europe [105] (1985) and the USA [107]. The GAB does not incorporate a temperature term; therefore, the determination of the effect of temperature on isotherms using the model usually involves the evaluation of up to six constants. Jayas and Mazza [108], however, developed a modified form of the GAB, which incorporates the temperature term. The MSI models considered in this study

Moisture Sorption Isotherms and Isotherm Model Performance Evaluation for Food…

were selected from the above list and presented as follows:

2.Guggenheim-Anderson-de Boer (GAB) model

<sup>M</sup> <sup>¼</sup> MmCaw

<sup>M</sup> <sup>¼</sup> CKMmaw

<sup>M</sup> <sup>¼</sup> AB <sup>C</sup>

<sup>M</sup> <sup>¼</sup> <sup>A</sup> aw

<sup>M</sup> <sup>¼</sup> <sup>T</sup> <sup>A</sup>

<sup>M</sup> <sup>¼</sup> �<sup>1</sup>

aw þ B 

<sup>M</sup> <sup>¼</sup> �Lnaw

<sup>C</sup> Ln � ð Þ <sup>T</sup> <sup>þ</sup> <sup>B</sup>

exp ð Þ <sup>A</sup> <sup>þ</sup> BT �1=<sup>C</sup>

ð Þ 1 � aw ½ � 1 þ ð Þ C � 1 aw

ð Þ 1 � Kaw ½ � 1 � Kaw þ CKaw

T aw

þ B � Caw �<sup>1</sup>

�<sup>1</sup>

� C <sup>T</sup><sup>n</sup> aw

<sup>A</sup> Lnaw

<sup>T</sup> Baw

(9)

(12)

ð Þ <sup>1</sup> � Baw <sup>1</sup> � Baw <sup>þ</sup> <sup>C</sup>

(7)

(8)

(10)

(11)

(13)

1.Brunauer-Emmett-Teller (BET) model

DOI: http://dx.doi.org/10.5772/intechopen.87996

3.Modified GAB model

4.Hailwood-Horrobin model

5.Modified Hailwood-Horrobin model

6.Modified Chung-Pfost model

7.Modified Halsey model

161

Shrinkage theory: This states that while agricultural and food product is drying out, the force of attraction causes water-holding spaces to shrink (molecular shrinkage). This permanent shrinkage reduces the water-binding polar sites and water-holding capacity of the material; hence less amount of water is absorbed during the adsorption process.

Capillary condensation and swelling fatigue theory: In this theory proposed by Ngoddy-Bakker-Arkema [86], the sorption hysteresis is considered linked with condensation and evaporation in irregular voids (capillary condensation) and influence of adsorbed water molecules on such physical properties of agricultural and food products as strength, elasticity, rigidity, swelling and evolution of heat (swelling fatigue). The above combination was simulated by adopting the Cohan theory of capillary condensation with modifications and combining it with the ink bottle theory in the first approximation. The theory presented expressions for calculating the desorption isotherms of biomaterials from corresponding adsorption isotherm using bulk moduli determined as a function of moisture content.
