Analysis of Water Sorption Isotherms of Superabsorbent Polymers by Solution Thermodynamics

NII-Electronic Library Service

Biosci. Biotech. Biochem .. 61 (6), 936~94 L 1997

Analysis of Water Sorption Isotherms of Superabsorbent Polymers by Solution Thermodynamics

Hitoshi KUMAGAI, t Akinori MIZUNO, Hitomi KUMAGAI, * and Toshimasa Y ANO tt

Department of Applied Biological Chemistry, Division of Agriculture and Agricultural L(fe Sciences, The University of Tokyo, 1-1-1 Yayoi. Bunkyo-ku, Tokyo 113, Japan * Department (l Agricultural and Biological Chemistry, Nihon University, 3-34-1 Shimouma, Setagaya-ku, Tokyo 154, Japan Received November 13, 1996

Water sorption isotherms of superabsorbent polymers were measured, and their affinity for water was evaluated by solution thermodynamics. The results provide basic data for the functional packaging of food to control the water content of food during its transportation or storage. Water activity above 0.9 was measured by adding a specific amount of water to the samples, while that below 0.9 was measured with apparatus for evaluating water sorption isotherms. Thus, water sorption isotherms for super absorbent polymers were obtained up to a water activity of approximately 0.98. The amount of water sorbed by the superabsorbent polymers was influenced by the type of functional groups in the polymers, and not by the degree of cross-linking in the polymers. The integral Gibbs free energy, which is the most suitable parameter for evaluating the affinity of a material for water, was evaluated from the water sorption isotherms by using solution thermodynamics.

Key words: water activity; water sorption isotherm; superabsorbent polymer; solution thermodynamics; Gibbs free energy

Water sorption isotherms give information on the interaction between water and such material as food. The state of water in a food can be qualitatively evaluated by the shape of the water sorption isotherm of the material. Thermodynamic analysis of a water sorption isotherm gives further quantitative information on the interaction between the material and water. However, only the thermodynamic function of water can be obtained by a conventional thermodynamic analysis 1 ~ 10) based on the Clapeyron-Clausius equation 11) (hereafter referred to as adsorption thermodynamics) because it does not take account of any change in the solid. The solid state sometimes changes (e.g., swells) during water sorption by a material. Therefore, adsorption thermodynamics is not often adequate for evaluating the affinity of a material for water. On the other hand, solution thermodynamics based on the GibbsDuhem equation 1 1) gives thermodynamic parameters on both water and a material by considering the solid change during water sorption. Le Maguer 12) has applied solution thermodynamics to the water sorption isotherms of potato starch. Kumagai et al. 13) have corrected the errors in the theory of Le Maguer's paper and applied the modified theory to the water sorption isotherms of defatted and extruded rice flour: they have shown that the "integral Gibbs free energy" physically means the change in Gibbs free energy by water sorption and that it was an appropriate parameter for evaluating the affinity of food for water. As a result, the enhanced affinity of rice flour for water after defatting and extruding was quantitatively evaluated by solution thermodynamics.

In the works of Le Maguer12J and Kumagai et al.,13) only sigmoidal water sorption isotherms that fitted well

t To whom correspondence should be addressed.

with the GAB (Guggenheim, Anderson, and de Boer) equation 14~ 16) were analyzed by solution thermodynamics. Water sorption isotherms of materials which swell greatly through water sorption could not be fitted by the GAB equation. In principle, thermodynamic functions in solution thermodynamics can be numerically calculated without using the GAB equation, although solution thermodynamics has not been applied to the water sorption isotherms of such materials.

Superabsorbent materials such as polyacrylate polymer and acrylate-vinylalcohol copolymer possess hydrophilic parts and cross-linking parts in their molecules: they absorb and retain a large amount of water. 1

7 - 23) Superabsorbent polymers have recently been used for functional packaging to control the water content of foods during their transportation and storage: e.g., vegetables and raw fish.23 28) To choose an appropriate polymer, two basic items of information would be necessary: one is the water sorption isotherms for the packaging being used, because water transfers between food and the package in proportion to the water vapor pressure difference; the other is the affinity of the polymer for water, because water should not leak from the package during storage. Therefore, it is necessary to measure the water sorption isotherms of superabsorbent polymers up to a high water activity (aw) and to evaluate their affinity for water by thermodynamics. However, the water sorption isotherms of superabsorbent polymers have not previously been measured.

In this study, we measured the water sorption isotherms of commercial superabsorbent polymers up to a water activity (aw) of approximately 0.99, considering that the aw values for many foods are close to unity.29) In addi-

tt Present address: Deparrment of Material Science and Chemical Engineering, Faculty of Engineering, Yokohama National University, 156 Tokiwadai, Hodogaya-kll, Yokohama 240, Japan.


Water Sorption Isotherms of Superabsorbent Polymers 937

tion, solution thermodynamics was applied to the obtained water sorption isotherms, and the Gibbs free energy was numerically evaluated.

Analytical Description of Gibbs ji-ee energy by water activity

The equations of solution thermodynamics described here are almost the same as those in the work of Kumagai et al. 13) The "solution" means the condensed phase formed by water sorption to the adsorbent. The reference state for water is the liquid form under the solution temperature (T) and pressure (P), and that for the adsorbent is a pure solid at T and P. In addition, thermodynamic variables are expressed by mass units, because the water sorption data are usually obtained on a mass basis.

The chemical potentials based on mass units are defined by

(1)

and

, (8GS

) f.1s = ~ a - 8n1a T,P.ln

w

(2)

where as is the Gibbs free energy of the solution, mw is the mass of water, rna is the mass of the adsorbent, f.1~ is the chemical potential of water in solution at T and P, and f.1~ is the chemical potential of the solid in solution at Tand P.

Parameters L\G~v and L\G~ are defined by

1/* r'a

(3)

(4)

where f.1; is the chemical potential of pure water at T and P, and f.1; is the chemical potential of the pure solid at T and P.

The relationship between parameter L\G~ and water activity aw is

L\G~ R'Tln aw (5)

where R' is the modified gas constant (=0.462kJ/kg of water' K).

Parameter L\G~ is given by

I1Gs = -R'T -- da + -~-- w aD dP (6) Jaw W JPw VS (V + V )

a w w o aw 0 rna

where Wis the water content, i.e., mw/rna' V S is the solution volume, Vw is the volume of pure water, VaO is the adsorbent volume in the dry state, and P w is the vapor pressure. By using the swelling ratio (y) defined by VS/(Vw+ VaO ), Eq. (6) can be expressed as follows:

L\G~= R'Tfaw

W daw+fPW~! l)(Vw+ VaO ) dPw (7) o aw 0 ma

If the volume change of the system by water sorption is small, i.e., y ~ 1, the second term on the right side of Eq. (7) is negligible, enabling us to write

(8)

The change in integral Gibbs free energy per kg of adsorbent (L\GS) is

(9)

Physical meaning of L\G~ and L\G S

Parameter I1G~ is the same as that calculated by adsorption thermodynamics, being the difference between the chemical potential of water in solution and that of pure water. On the other hand, L\Gs in Eq. (9) is the change in Gibbs free energy due to water sorption per kg of solid, as stated in the preceding paper. 13

) Accordingly, L\G S is more suitable for evaluating the interaction between water and a solid than is L\G~.

Evaluation of I1G~, L\G~, and L\G S

Parameter I1G~ at a specific water content can be calculated from Eq. (5) by using the water sorption isotherm. Since the water sorption isotherms obtained in this study did not fit well with the GAB equation, especially in the region of high water activity, L\G~ could not be analytically calculated. Therefore, L\G~ was numerically evaluated by integrating Eq. (8) in this study. Note that the value of W/aw at aw 0 (W=O) can be evaluated from the slope of the water sorption isotherm at aw 0 by considering

lim W = d W I (10) aw-'O aw daw aw=O

Parameter L\GS can be calculated from Eq. (9) by using the values for L\G~ and L\G~ just obtained.

Experimental Superabsorbent polymers. Three kinds of polyacrylate superabsorbent

polymers with different cross-linking density, (hereafter referred to as PA 1, PA2, and PA3) were supplied by Kao Co., Japan; the cross-linking density decreased in the order of PAl, P A2, and P A3. (Note that the absorbency of water is taken as the index of cross-linking density in this study, as stated later). Poly(vinyl alcohol)-acrylate copolymer (hereafter referred to as V A) and carboxymethylcellulose superabsorbent polymer (hereafter referred to as CMC) were respectively obtained from Sumitomo Chemical Co., Japan and Daicel Chemical Industries, Japan.

Measurement of the absorbency by superabsorbent polymers. The absorbency of water for the superabsorbent polymers (the amount of water absorbed by a superabsorbent polymer in water at equilibrium) is taken as the index of cross-linking density of the polymer in this study, since the cross-linking density greatly influences the absorbency.18.20.21) A specific amount of a polymer was immersed in water for one night at room temperature. Thereafter, the swollen polymer was transferred to a sieve (125 {1M mesh size), and the water was removed, the absorbency being calculated from the increase in weight.

Preparation of the moistened polymers. To ensure reliability of the data for the water sorption isotherms or sample density, a uniformly moistened sample is necessary. Therefore, moistened samples were prepared by using the apparatus illustrated in Fig. I. After a dry polymer sample had been placed on the sieve (10 cm diameter; 45,LlM mesh size), the polymer was moistened by passing through air saturated with water vapor. Samples with different water content were prepared by varying the retention time in the apparatus.

Measurement of water sorption isotherms. In the region of water activity aw above approximately 0.9, TH-2 apparatus for measuring water activity (Novasina, Switzerland) was used. A moistened sample prepared by the method just explained was placed in the chamber of the apparatus, and its water activity was measured at 25°C. The water content of the sample was then measured by drying it at 105°C.

In the region of Clw below approximately 0.9, apparatus for measuring


938 H. KUMAGAI et al.

Flow meter

Air pump

Bubbling bottle

Fig. 1. Apparatus for Preparing the Moistened Polymers.

Table Absorbency of Water by Superabsorbent Polymers

PAl PAl PA3 VA CMC

Absorbency of water [kg of water/kg of dry polymer]

143 586 880 497 108

water sorption isotherms (Shibata Kagaku, Tokyo, Japan) was used. After about 0.5 g of a sample in the quartz-glass cell suspended by a quartz spring had been vacuum-dried overnight in the chamber at SO°C, the dried weight was recorded. The chamber was then cooled to 25°C, and a small amount of degassed water vapor in the water vapor vessel was introduced into the chamber. The vapor pressure in the vacuum chamber was measured by a diaphragm pressure transducer (Toyota Kob. Tokyo, Japan). The change in the spring length was monitored by a line sensor camera and converted to the sample weight.

Evaluation of the sample density. To confirm the applicability of Eq. (8), the data for the density of a polymer~water system sample is neeessary. The sample density (Ps) was evaluated from the volume of the dispersed system containing the sample and an organic solvent (Vm) by using the following equation:

(11 )

where Ms is the mass of the sample. Vf is the volume of the organic solvent, and Ps is the sample density. As an organie solvent, hexane (Kanto Chemical Co .. Tokyo, Japan) was used in this study.

Results The values for the absorbency of water by the super

absorbent polymers are shown in the Table. One kg of each superabsorbent polymer absorbed more than 100 kg of water at equilibrium. The absorbency increased in the order of CMC, PAL VA, PA2, and PA3.

Figure 2 shows the dependence of the density of the polymer-water system on water content, only that for PA2 (Fig. 2a) and VA (Fig. 2b) being shown as typical data. The solid curves in Fig. 2 were calculated by the following equation to include the swelling ratio (y):

Mw+Mao

y(M wi Pw + MaO/ PaO) (12)

2.2 ~--------------..,

2f-

E 1.S -0) ~ 4 o 1.6 T"" x ~ 1.4 '00 c: (]) 1.2 J o "

(a)

y=O.S

y=0.9

1 ~"-_· __ ~ ______ Lv:==-1:..:..0-==----___ -e.I"

O,S I I I I

o 100 200 300 400 500 600

Water content [kg/kg of dry matter]

1 ,6 ~--------------.., (b)

1,5 Ii-

"'E 1.4 -0) ~

o 1.3 ~ X -- __ ~~ ____ ~. __ ~y~:=~O~.S=__ ___ __4

~ 1.2 '00 \ a5 1,1 • y=0.9

o 1 r y=1.0

0,9 I I I I

o 100 200 300 400 500

Water content [kg/kg of dry matter]

Fig. 2. Dependence of Density for a Polymer-Water System on Water Content at 25°C.

(a), PA2; (b), VA. Solid curves are the best fitting of data to Eq, (12),

where Mao is the mass of dry superabsorbent polymer, M w

is the mass of water, PaO is the density of the dry superabsorbent polymer. and Pw is the density of water. Note that the change in density of the polymer by water sorption is negligible at y = I, the density being additive in a polymer-water system. As shown in Fig. 2, the values for the density of two polymers are similar to those predicted by Eq. (12) assuming y = I or y = 0.9, indicating that the change in density of the polymer was negligible by water sorption. The values of y for the other polymers were also about unity, although the data are not shown.

Figure 3 presents water sorption isotherms for polymers PAl, PA2, PA3, and CMC measured at 25°C. Data measured by the apparatus of Shibata (0 L D <> ) smoothly connect to those of Novasina ( ...... ), the sorption isotherms for the polymers being concave upwards. At the same water activity, the water content of polyacrylate superabsorbent polymers PAl, PA2, and PA3 was almost the same up to about aw 0.98, while the water content of CMC was lower.

The water sorption isotherm for V A measured at 25°C is shown in Fig. 4, the water content of the sample suddenly increasing at about aw 0.73. This water sorption behavior for VA can be explained by a poly(vinyl alcohol) polymer



~ 6.--------------,

~ E 5 ~

"'0

a 4 0) ::£ .........

E .$ c o ()

I.-

m

~

2

0.5

Water activity a w

Fig. 3. Water Sorption Isotherms of Superabsorbent Polymers PA 1, PA2. PA3, and CMC. Measured at 25'C.

060<>, data measured with the apparatus of Shibata; ...... , data measured with the apparatus of Novasina; 6 .... PAl; D., PA2; <>., PA3; 0., CMC.

6,---------------n

0.5

Water activity a w

Fig. 4. Water Sorption Isotherm of Superabsorbent Polymer VA Measured at 25''C.

0, data measured with the apparatus of Shibata; e, data measured with the apparatus of Novasma.

possessing a crystal region 18) in which water cannot enter. At a high water content, however, the polymer network would expand due to electrical repulsion between the carboxyl groups, causing the sudden enhancement in the amount of water sorbed.

Figure 5 shows Gibbs free energy values L\G~, L\G~, and L\Gs for superabsorbent polymers PA 1, PA2, and PA3 calculated from the water sorption data in Fig. 3, while Fig. 6 shows the values for CMC calculated from the water sorption data in Fig. 3. Tn Fig. 7, Gibbs free energy values LlG~, L\G~, and LlGs for VA calculated from the water sorption data in Fig. 4 are presented. In these figures, WL\G~ was used instead of LlG~ to clarify the magnitude of the contribution of L\G~ to L\GS (see Eq. (9)). As the water content increased, the value for WL\G~ approached zero, while the absolute value of LlG~ also increased. At higher water contents, the contribution of L\G~ to LlG S was smaller than that of L\G~ to L\G s. The absolute values of L\Gs for superabsorbent polymers PAl, P A2, and P A3 were almost

...:' 0.0r:l:------------.

.$ 1i1 ~ -20.0 "0

'0 -40.0 ~ ~ ~

-60.0

C,m -80.0 <J

(a)

~ '" -100. 0 ~_=_"=__-+--:_':_-=___=_"=____,! $ 0 3

Water content W [kg/kg of dry matter]

~ 0.0m:---------~...., fa E ~ -20.0 "0

'0 0) -40.0 ~ J =. ~ -60.0

6" <J -80.0

ci" ~ -1 00. 0 O.!:--~:---!-----,-L=---:!:-~I..:-==----:!


...:' 0.0 (])

m (c) E ~ -20.0 "0

'0 0) -40.0 ~ J =. t9 -60.0 <J

c.?" <J -80.0

~

CJ <J -100.0 3: 0 3


Fig. 5. Changes in Gibbs Free Energy Values for Superabsorbent Polymers PAl, PA2, and PA3 during Water Sorption at 25°C.

(a), PAl; (b). PA2; (c), PA3. 0. WLlG~; 0, LlG!; 6, LlG'.

0.0 n----------------,

-20.0

-40.0

-60.0

-80.0

-100.0 1...-._.1..-_-'--_.....1-_--'-_--'-_--'

o 0.5 1.5 2 2.5 3


Fig. 6. Changes in Gibbs Free Energy Values for Superabsorbent Polymer CMC during Water Sorption at 25°C.

0, WLlG~; 0, LlG:; 6. LlG'.


940 H. KUMAGAI et al.

0.0c::t--------------, 03

:t::: C'O E ~

-20.0

"0

15 0> -40.0

.::¥:. -J 6 Q; -60,0 <l

OJ

C..9 <l -80.0 -;;

C..9

~ -100.0 L--_.L-_..L-_...J......._-'-__ ........l-_---'

o 0.5 1.5 2 2.5 3


Fig. 7. Changes in Gibbs Free Energy Values for Superabsorbent Polymer VA during Water Sorption at 25"C.

0, WLlG:,; 0. LlG~; D. ,.1G',

the same, but smaller than those for CMC and VA. This result indicates that the affinity of PA 1, PA2, and PA3 for water was larger than that of CMC and VA, and that the affinity of those superabsorbent polymers for water could be quantitatively evaluated by 8Gs.

Discussion Water sorption isotherms have mainly been measured

below aw 0.9, especially with foods,30) probably because the rate of water sorption was too low in humid air to attain equilibrium. However, as basic data for functional packaging to control the water content of foods during storage, aw data up to approximately unity is necessary, since aw value for many fresh foodstuffs is close to unity.29) In this study, data at high water activity were obtained by adding a specific amount of water to the samples and using the apparatus of Novasina. Thus, water sorption isotherms up to approximately aw 0.98 were obtained as shown in Figs. 3 and 4.

As can be seen from Figs. 3 and 4, the plots of the water sorption isotherms for superabsorbent polymers are concave upwards. On the other hand, the shape of the water sorption isotherms for most foods is sigmoidal. 30) According to adsorption theory,16.31) the shape of the isotherm for a material is concave upwards at a low water content if the monolayer adsorption heat is smaller than that of the condensation heat of the adsorbate, which means water here. From this aspect, the value of monolayer adsorption heat for a superabsorbent polymer is smaller than that for most foods. In other words, the affinity of a superabsorbent polymer for water is lower than that for foods in the vicinity of zero water content.

As shown in Fig. 3, the amount of water sorbed by polyacrylate superabsorbent polymers PAL PA2, and PA3 was identical at the same water content up to approximately aw 0.98, although their absorbency of water was influenced by the cross-linking density (see Table). Moreover, as shown in Figs. 3 and 4, the amount of water sorbed by PAl, PA2, or PA3 was different from that sorbed by CMC or VA. These results indicate that the superabsorbent polymers sorbed water by interaction between the functional groups

on the polymers and water, up to about aw 0.98, suggesting that not the cross-linking density of the polymer, but the type of functional groups in the polymer was important for a superabsorbent polymer to be used as a material for functional packaging.

We used Eq. (8) for calculating 8G!, assuming that the second term on the right of Eq. (7) would be negligible . The magnitude of the second term of Eq. (7) will be estimated here. Since the volume of a liquid or solid is almost independent of pressure below 100atm,32)

IPw~y-:-l)(Vw+ VaO) dPw

' . (y-l)(Vw+ VaO) IPw dPw

o rna rna 0

(y-I)(Vw + VaO) P w

rna

(y-I)(Vw + VaO) P~ (13)

rna

where P~ is the vapor pressure of water. Next, the value on the right of Eq. (13) will be calculated by substituting the following values into Eq. (13): P~ (25°C)==: 3.17 [kPa]; rna=: 5 x 10~4 [kg]; VaO 3.3 X 10~7 [m3]; and Vw =:3.0 x 10- 6 [m3]. Thus,

(y-I)(Vw + VaO ) P~ 2.1 X 10- 2 x (y-l) (14) rna

The values of the right of Eq. (14) are 2.1 x 10- 3 and 2.1 x 10- 2 kJ /kg of dry matter for y 1.1 and y 2, respectively. The value of y for the superabsorbent polymers used in this study was about 1.0 as shown in Fig. 2. On the other hand, the values of 8G! were below -2kJ/kg as shown in Figs. 5,6, and 7, indicating that the second term on the right of Eq. (7) was negligible, so that 8G! for the superabsorbent polymers could be calculated by Eq. (8). Le Maguer has stated 12) that 8G~ could be calculated by Eq. (8) at constant total pressure P and that independent data for the swelling of the material were necessary if the solution was under its own vapor pressure P = P w like that in this study. However, for a superabsorbent polymer, the value of 8G~ can be calculated by Eq. (8) without the swelling data of the material even at P = P w' Kumagai et af. 13) have shown that the value of 8G! for rice flour could be calculated at P = P w without using the swelling data of the flour: the value of y for starch is almost unity. It was thus confirmed that the value of 8G! for a material with a value of y similar to unity could be calculated by Eq. (8), even if the material swells by water sorption.

Conventional adsorption thermodynamics only gives 8G~, which is the difference in the chemical potential of water between a solution and pure water, as the Gibbs free energy from water sorption data. On the other hand, solution thermodynamics gives not only 8G~ but also the difference in chemical potential between the solute in solution and the pure solid (~G~), 8Gs being the reflection of both 8G~ and 8G~. From this aspect and the physical meaning of ~GS explained in the analytical section of this study, 8GS is considered to be the most suitable parameter for evaluating the affinity of a material for water. The influence of ~G~ on ~Gs would be larger when the solid state changes during water sorption, e.g., swelling. As for



superabsorbent polymers, the amount of water sorbed increased drastically at a high water content (see Figs. 3 and 4). In addition, the contribution of ~G: to ~Gs was larger than that of ~G~, especially at a high water content. Therefore, the sorption isotherms of samples like superabsorbent polymers should be analyzed by solution thermodynamics.

Water sorption isotherms at temperatures below 25°C are necessary as basic data for suitable storage and transportation of foods at low temperature. In addition, water sorption isotherms for other materials should be analyzed by the procedure shown in this study.

Nomenclature aw : water activity (dimensionless) G' : Gibbs free energy in solution [kJJ

f...G': change in integral Gibbs free energy per kg of adsorbent [kJ/kg of matterJ

mass of adsorbent [kgJ mass of water [kg] pressure [kPaJ vapor pressure [kPaJ gas constant on a kg of water basis (=0.462 [kJ/kg of water' KJ)

T: absolute temperature [KJ VaO: V':

volume of adsorbent in the dry state [m}J volume of solution [m 3J volume of pure water [m3J water content (=mw/ma) [kg/kg of dry matterJ

y: swelling ratio defined by VS/( Vw Vao) (dimensionless)

II' . t"'w'

chemical potential of the adsorbent in solution at P and T [kJ/kg of dry matter] chemical potential of water in solution at P and T [kJ/kg of water] chemical potential of pure water at P and T [kJ/kg of water] chemical potential of the pure adsorbent at P and T [kJ/kg of dry matter]

The following parameters were used in the measurement of density for a polymer-water system:

M,\o: mass of the dry superabsorbent polymer [kgJ M, : mass of the polymer-water system [kg] M w : mass of water [kg]

Vf : volume of the organic solvent [m 3]

Vm: volume of the dispersed system [m 3J PolO: density of the dry superabsorbent polymer [kg/m3] Ps: density of the polymer-water system [kg/m 3J p,,: density of water [kg/m3]

Acknowledgments. We express our thanks to Dr. T. Kobayashi ofKao Co. for supplying the polyacrylate superabsorbent polymers. Part of this work was financially supported by Grant-in-Aid for Scientific Research from the Ministry of Education, Science, and Culture of Japan.

References 1) C. Van Den Berg, F. S. Kaper, J. A. G. Weldring, and 1. Wolters,

J. Food Techno!., 10, 589-602 (1975). 2) H. A. Iglesias and J. Chirife, J. Food Techno!., 11, 565-573 (1976). 3) J. Chirife, H. A. Iglesias, and R. Boquet, J. Food Techno!., 12, 605-613

(1977). 4) K. Hayakawa, J. Matas, and M. P. Hwang, J. Food Sci., 43,

1026-1027 (1978). 5) P. E. Hill and S. S. H. Rizvi, Lebensrn.-Wiss. u.-Technol., 15,185-190

(1982). 6) G. N. Roman, M. J. Urbicain, and E. Rotstein, J. Food Sci., 47,

1484-1488,1507 (1982). 7) J. C. Igbeka and J. L. Blaisdell, J. Food Techno!., 17, 37--46 (1982). 8) R. J. Aguerre, C. Suarez, and P. E. Viollaz, J. Food Techno!., 19,

325-331 (1984). 9) A. L. Benado and S. S. H. Rizvi, J. Food Sci., 50, 101-105 (1985).

10) G. D. Saravacos, D. A. Tsiourvas, and E. Tsami, J. Food Sci., 51, 381-383, 387 (1986).

11) W. J. Moore, in "Physical Chemistry," 3rd Ed., Prentice-Hall, New Jersey, 1972.

12) M. Le Maguer, in "Properties of Water in Foods," ed. by D, Simatos and J. L. Multon, Martinus NijhoffPublishers, Dordrecht, 1985, pp. 133-151.

13) H. Kumagai, M. Iwase, H. Kumagai, A. Mizuno, and T. Yano, Biosci. Biotech. Biochem., 58, 475-481 (1994).

14) R. B. Anderson, J. Am. Chem. Soc., 68, 686-691 (1946). 15) E. A. Guggenheim, in "Applications of Statistical Mechanics,"

Clarendon Press, Oxford, 1966, pp. 186-206. 16) J. H. de Boer, in "The Dynamic Character of Adsorption," 2nd Ed.,

Clarendon Press, Oxford, 1968, pp. 5-9. 17) T. Nakajima, E. Hayashi, and Y. Hirai, Rep. Prog. Polym. Phys.

Jpn., 29, 235-238 (1986). 18) F. Masuda, "Kokyusuisei Polymer" (in Japanese), Kyoritsu

Shuppan, Tokyo, 1987. 19) M. Yamaguchi, H. Watamoto, and M. Sakamoto, Carbohydrate

Polym., 9, 15-23 (1988). 20) S. A. Dubrovskii, M. V. Afanas'eva, M. A. Lagutina, and K. S.

Kazanskii, Polym. Bull., 24, 107-113 (1990). 21) F. L. Buchholz and N. A. Peppas (ed.), "Superabsorbent Polymers,"

American Chemical Society Symp. SeL, 573, 1994. 22) F. L. Buchholz, Chern. Br., 30, 652-656 (1994). 23) Y. Fujiura, Kagaku Kogyo (in Japanese), 45, 677-683 (1994). 24) H. Sasaki, Roso Gijutsu (in Japanese), 27, 287-290 (1988). 25) Y. Matsubara, Roso Gijutsu (in Japanese), 27, 858-863 (1988). 26) M. Furuta, S. Asano, and S. Imai, Japan Packaging Research (in

Japanese), 10, 1-9 (1989). 27) K. Mita and H. Hasegawa, Shokuhin Kogyo (in Japanese), 30,

57-65 (1990). 28) T. Morishita, K. Mita, T. Araki, and A. Matsushima, Japan

Packaging Research (in Japanese), 12, 35-45 (1991). 29) J. A. Troller and J. H. B. Christian, in "Water Activity and Food,"

Academic Press, New York, 1978. 30) H. A. Iglesias and J. Chirife, in "Handbook of Food Isotherms:

Water Sorption Parameters for Food and Food Components," Academic Press, New York, 1982.

31) D. M. Young and A. D. Crowell, in "Physical Adsorption of Gases," Butterworth & Co., London, 1962.

32) 1. Prigogine and R. Defay, in "Chemical Thermodynamics," Longmans Green and Co., London, 1954.

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Analysis of Water Sorption Isotherms of Superabsorbent Polymers by Solution Thermodynamics