Enthalpy-Entropy Compensation in Food Vapor Adsorption

Cesar I. Beristain,” Hugo S. Garcia,” & Ebner Azuara”

“Institute de Cicncias BBsicas, Universidad Veracruzana, Apartado Postal 575, Xalap:~, Vcracruz. Mexico

“Depto. Ing. Quimica y Bioquimica Institute Tccnobgico de Veracrus, Apartado Postal 1420, Veracruz. Ver. Y 1860, Mexico

(Received 26 Scptemhcr lYY4: revised IS May 19%: accepted 5 February lOY6)

ARSTRA CT

Enthulpy-entropy compensution was an~dysed for sorption isotherms of potatoes, rnacadamiu nuts, upricots, figs. currunts, prunes and raisins. Plots of (AH,,;,) , 1-s (AS,,,,) ,. ,for potrrtocs and macadamirr nuts presented two isokinetic temperatures: Tn, = 272.0 i 57.7 K ( - I’C) for potutoes, T,,, = 265.0 _+ 18.8 K (-8°C) ,for mucadcrmicr nuts und TI, = 382.5 F 7.3 K (109.5”C) ,fbr both products. The ,first isokinetic temperature (TRI) uppeured only at the upper portion of the temperature mnge tested (50, 60 und 7PC for potatoes und 50 und 60°C for macadamiu nuts). The two isokinetic temperatures observed ,f;~r potatoes and macndamiu nuts suggested that during the initiul stages at low N IU Tijl is controlled by chqqes in the entropy of’ wuter; whereas the second isokinetic temperuture (Tnz) is considered to be enthalpy-controlled. Dried @its presented only one isokinetic curve T,, = J/5.7+ 3.5 K (42.7”C), ,for misin,s, currunts and ,figs (75.2-c)2..3%~ d.b. sugars) and Tn = 317.7k4.6 K (44.7”(‘) ,for prunes und apricots (S/.5-54.57~ d.b. sugux), indicating an enthnlp!- controlled adsorption pro0c’es.s for the whole range of moisture contents co\.ered. Copyright 0 1996 Elsevier Science Limited

INTRODUCTION

Over the past few years research on the thermodynamics of dehydrated foods has increased. This is because a good understanding of the thermodynamic relationships between water and foodstuffs allows food engineers to estimate heat requirements for certain processes, and to predict optimum storage conditions for maximum stability of food products (Nunes & Rotstein, 1991; Beristain et al., 1994). Addition- ally, good estimates of some thermodynamic properties such as enthalpy, Gibb’s fret energy and entropy are of utmost importance for design and optimization of ulnit

406 C. I. Beristain et al.

operations such as dehydration and humidification (Tsami, 1991). Changes in some thermodynamic properties with respect of the moisture content can provide a good description of the sorption mechanisms, and can be used to estimate points of transition between mechanisms (Rizvi & Benado, 1984). Conversely, determination of the thermodynamic parameters, allows for a more thorough interpretation of the sorption isotherms and provides a better insight into the sorption mechanisms.

Changes in enthalpy (AH), may provide a measure of the energy changes occur- ring upon the mixing of water molecules with sorbent during sorption processes. Entropy changes (As) may be associated with the binding or repulsive forces in the system. Entropic changes (AS) may also be associated with the spatial arrangements during adsorption at the water interface in a defined state. AS is related to the degree or order of randomness existing in the water-sorbent system and is useful in the interpretation of processes such as dissolution, crystallization and swelling. Finally, AC based on its sign may be indicative of the affinity of sorbents for water and provides a criterion whether water sorption occurs as a spontaneous process (Apostolopoulos & Gilbert, 1990).

The kinetic compensation effect has been widely observed in various areas such as physics, chemistry, biology and thermal analysis. Labuza (1980) reviewed the basis for AS/AT compensation and described the problems that can be encountered in applying the concept of a linear enthalpy-entropy compensation plot in food-related reactions such as thermal inactivation of microrganisms, protein denaturation and ascorbic acid degradation. Ferro-Fontan et af. (1982) suggested the existence of a linear relationship between enthalpy and entropy for water sorption in some foods. Aguerre et al. (1986) applied enthalpy-entropy compensation to derive a two- parameter sorption equation which took into account the effect of temperature on water sorption isotherms of some food products.

The purpose of the present work was to analyze the enthalpy-entropy compensa- tion for water adsorption in two starchy foods: potatoes and macadamia nuts, and five dried fruits: sultana raisins, currant, figs, prunes and apricots, to obtain informa- tion on the usefulness of this effect in food water vapor adsorption.

MATERIALS AND METHODS

Sorption isotherms

Experimental water sorption data available in the literature were used to test the validity of the enthalpy-entropy compensation. The experimental isotherms selected were of those products for which equilibrium data at four temperatures were avail- able, to avoid excessive error in the determination of the enthalpy and entropy of sorption. Experimental sorption data for sultana raisins, currants, figs, prunes and apricots at 1.5, 30, 45 and 60°C were reported by Tsami (1991) and are presented in Table 1.

Dried fruits data were divided into two sets for their analysis: (a) raisins (82.3% d.b. sugars), currants (79.5% d.b. sugars) and figs (75.2% d.b. sugars) and (b) prunes (54.5% d.b. sugars) and apricots (51.5% d.b. sugars).

Isotherms for potatoes at 40, 50, 60 and 70°C and macadamia nuts at 20, 30, 50 and 60°C corresponding to Wang and Brennan (1991); and Palipane and Driscoll

TABLE1 Water Activity of Dried Fruits Adsorption Data (from Tsami. IYY I )

liwpcratrirc~ (“C’) Water contrrlt (%d. h.) a H __-._

Raisim C’urrarits Figs Prurxs Apricot t

30

4s

IS 5 10 IS 20 30 40 so ho 70 80

5 IO 15 20 30 40 so 60 70 80

5 IO I5 20 30 40 50 ho 70 x0

I;: 15 20 30 40 so 60 70 80

(,O

0.08 0.25 0.43 0.48 0.55 0.57 0.62 0.65 0.72 0.74 0.78 0.80 0.83 0.84 0.87 0.87 0.‘) I O.YO 0.03 0.0 I 0.3 I 0.3h 0.46 0.5 I 0.55 0.60 0.61 O.hS 0.70 0.73 0.7(1 0.7x 0.x0 0.83 0.84 0.86 0.87 0.88 0.X’) 0.90 0.33 0.36 0.47 0,s I 0.56 O.SY 0.62 0.64 0.7 I 0.72 0.77 0.77 0.82 0.x1 0.84 0.85 0.86 0.87 0.87 0.88 0.37 0.35 0.50 0.48 0.58 0.55 Oh4 0.63 0.72 0.7 I 0.78 0.77 0.82 0.80 0.84 0.x.3 0.85 0.84 0.86 0.84

0.08 0.46 0.58 0.64 0.73 0.80 0.84 0.X8 NY I O.Y.3 0.12 0.4x 0.57 0.64 0.73 0.7x 0.x2 0.X6 0.x’) 0.0 I 0.37 0.52 0.60 o.Ki 0.72 0.77 0.x2 0.x5 0.87 0.X8 0.40 0.54 0.63 0.68 0.75 0.7’) 0.x2 OXi 0.86 0.86

408 C. I. Beristuin et al.

TABLE 2 Estimated Parameters of the GAB Equation for Potato (from Wang and Brennan, 1991)

Parameter Temperature (“C)

40 50 60 70

c 13.73 13.41 21.18 17.75 K 0.83 0.82 0.86 0.90

0.052 0.048 0.036 0.029 5.62 4.08 3.41 5.69

(1992) respectively, were reproduced using the GAB constants estimated by these authors (see Tables 2 and 3) according the following equation:

M= M,CKaw

(1 -Kaw)(l-Kaw+CKaw) (1)

where M is the moisture content, a w is the water activity and M,, C and K are constants. Theoretically M, is the monolayer moisture content and C and K are relate to temperature as follows:

C = c exp[(h, - =h,)/RTz,] (2)

K = k exp[(hi -h,)/RT,] (3)

where c and k stand for entropic accommodation factors; h,, h, and hi are the molar sorption enthalpies of the monolayer, multilayer and bulk liquid respectively; R and T, stand for the ideal gas constant and the absolute temperature.

An Arrhenius-type relationship between the monolayer moisture content and temperature can be assumed and an equation of the following form could be written:

M,, = b exp(e/TJ (4)

where b and e are constants. Goodness of fit was evaluated using the average of the relative percentage differ-

ence between the experimental and predicted values of the moisture content or mean relative deviation modulus (P) defined by the following equation (Lomauro et al., 1985):

TABLE 3 Estimated Parameters of the GAB Equation for Macadamia Nuts (from Palipane and Dris-

~011, 1992)

Parameters

c 0.0212

h,,-h,lR 2059.7

k 0.8502

hi-h,iR 10.168

h 0.4847

e 607.1

100 P= ---Ix

Mi -MPi

II Mi (5)

where M, is the moisture content at observation i; MI,, is the predicted moisture content at that observation: and n is the number of observations.

Calculation of sorption enthalpy and entropy

The method of Othmer (1940) was used, which is based on the Claussius-Clapcyron equation and obtained from the expression:

HI (T) InP,.= ~ I 1 H:!(T) M

InPl!+A (6)

where P, = vapor pressure of water in the food, Py = vapor pressure of pure wal.el at the same temperatue H,.(T) = Isosteric heat for water adsorption, H’,!(T) = Heat of condensation of pure water, M = moisture, and A = adsorption constant. The isosteric net heat of adsorption or enthalpy of adsorption (AH,,if) is given by:

17)

where H:!(T) can be obtained from steam tables or from eqn (8) (Wexler, 1976).

H!,)(T) [J/mol.K] = 6.15 x lO’-94.14 T+17.74 x 10 ’ T’-2.03 x 10 ’ T3 118)

Then, the change in molar differential entropy of adsorption (ASdlt).,- can be cal- culated from Gibbs-Helmontz equation as used by Rizvi (1986) and Apostolopoulos & Gilbert (1990):

The free energy AC was calculated from Gibb’s equation (Rockland, 1969: Iglesias ct al., 1976):

AC = RT In u,~ (10)

where a, is the water activity and T is the absolute temperature (K). The effect of a change in water adsorption on free energy is usually accompanied

by changes on both the enthalpy and the entropy.

RESULTS AND DISCUSSION

A plot of (AHdit.).l. vs (ASdit),r was prepared for each of the sorption data. From the figures we observe that the law of compensation is applicable in the range of moistures studied. Values for (AHdif)l. were correlated with Eq. 1 1.

(AHt,,th = TR(ASclit)T+AGH (11)

where TH = Isokinetic temperature, and AGF3 = measure of the free energy at T,,.

410 C. I. Beristain et al.

All the calculated regression coefficients are acceptable, however, in order to confirm the existence of compensation, the test of Krug et al. (1976a, 1976b) must be used. This test compares TB with the mean harmonic temperature (T,,,), which is defined as:

T,,,,,= ’

$ (l/T)

(12)

where n = total number of isotherms used. An approximate (l-r)100 percent confi- dence interval for TB may be calculated from:

Tn = Tn *t,,, ~ 2,x/2\ Wr3) (13)

where:

T R

= C((AHdir),-(AHdir)T) ((ASdir)T- (ASdir)T) (14)

C((ASdif)T - (ASdir)T)’

VT,) = C((AH,if)~-AGB-TB(ASdif)T)2

(15) (m_2)C((ASdif)~-(ASdif)~)’

and = number of ((AHdif)T , (ASdir)T) data pairs, (AHdir)T = average enthalpy and (ASdir)T = average entropy.

According to Krug et al. (1976a, 1976b), a linear chemical compensation pattern exists only if T,#T,,,. If Thm falls within the Ts interval, the observed distribution of data in the (AHdir)T , -(ASdirT)) plane is a reflection solely of the propagation of experimental errors, not chemical factors. In this work a 95% confidence interval for TB was calculated for all data sets.

Data for macadamia nuts and potatoes presented 2 straight lines as seen in Fig. 1; one at low moisture contents, with T,, = 272.Ok57.7 K, AG,, = -9132.4 Jimol and r2 = 0.987 for potatoes (1.8-3.5 g H,O/lOO g dry solids) and T,, = 265.0_+ 18.8 K, AGn, = -6665.1 Jimol and r2 = 0.999 for macadamia nuts (1.8 to 2.6 g Hz01100 g dry solids), and the second line, which covers most of the range studied (moisture contents >3.5 g H,O/lOO g dry solids for potatoes and >2.6 g H,O/lOO g dry solids for macadamia nuts), with TB2 = 382.5 f7.3 K, AGB2 = -298.7 J/mol and r2 = 0.997 for both sets of data. Foods with high sugar content were fitted to a single curve and are presented in Figs 2 and 3. Data for set (a) (raisins, currants and figs) presented one straight line (see Fig. 2) with TB = 315.7k3.5 K, AGn = 19.5 J/mol and r2 = 0.996, and data for prunes and apri- cots show a similar behavior (see Fig. 3) with TR = 317.6k4.6 K, AG, = 80.9 J/mol and r* = 0.996. In this work, Thm = 319.7 for starchy foods and 309.6 K for sugar- rich foods. When this value is compared to the calculated Tes, we confirm the existence of the linear chemical compensation.

According to Leffler (1955), if TB > T,,, the process is enthalpy driven, and if the contrary condition exists (TB<Thm), then the process is entropy-controlled. There- fore, water vapor adsorption in starchy foods (Ts2 = 382.5 ) 7.3 K, T,,,,, = 319.7 K) and sugar-rich foods (T,, set (a) = 315.7k3.5 K, Ts, set (b) = 317.6k4.6 K, Thm = 309.6 K) may be considered as mainly enthalpy-driven. The straight lines

o 333 K ”

313 K Potatoes

= 272 0t57.7 K

_+_.

-80 60 -40 -20 0

Entropy (J/molK)

Fig. 1. Enthalpy-entropy relationship for water sorption in potatoes and macadamia nuts. Straight lines rcprcscnt the tits obtained using cqn (1 I).

observed in Fig. 1 for potatoes at low moisture contents (1.8-3.5 g H20/100 g (~I?/ solids) and macadamia nuts (1.8-2.6 g HzO/lOO g dry solids) for isokinetic tem- peratures lower than T,,,,, (272.0157.7 K and 265.0-L- 18.8 K) correspond to a zone of adsorption controlled by entropy and appear only in starchy foods at the higher temperatures tested (50, 60 and 70°C for potatoes, and SO and 60°C for macadamia

0 E ‘7

-5000 Tg=3157k35K

r2= 0 996

-10000

15000 t

0 318K m 333K + 288 K Currants A 303 K .

318 K x

333K m f

288 K S. 1

Rmms

0 303 K

318 K

.+--____. 7 -.333 K ( .__ i

100 -80 -60 -40 -20 0 20

Entropy (JimolK)

Fig. 2. Enthalpy-entropy relationship for water sorption in dried fruits (figs. currants .\nd sultana raisins).

412 C. I. Be&ah et al.

-100 -80 -60 -40 -20 0 20

Entropy (J/molK)

Fig. 3. Enthalpy-entropy relationship for water sorption in dried fruits (prunes and apricots).

nuts). This suggests a microstructural change induced by the temperature in these products. Because of this the isosteric heat of adsorption increases in the lower moisture content range (see Figs 4 and 5). The straight lines that appear at low moisture contents in Fig. 1 run in the opposite direction with respect to the longer line in the same figure (the moisture contents increase is indicated by arrows). This may indicate the effect of an endothermic process; contrary to the heat of adsorp-

x 15000

10000

5000

0 L 6

X. 6

:.

x .

.

343 K (70%) t

t 0 2 4 6 8 10 12 14

Moisture Content, % d.b.

Fig. 4. Enthalpy of adsorption as a function of moisture content for potatoes.

5000 1

. 293 K (20%)

. 303 K (30%)

o 323 K (50%)

x 333 K (60°C) /

i

0 c__ __+__---c_-, -_--+-_ _+a 0 2 4 6 8 IO 12

Moisture Content, % d.b.

Fig. 5. Enthalpy of adsorption as a function of moisture content for macadamia nuts.

tion, which is known to be exothermic. It is understandable that adsorption in this zone is controlled by entropy, because the interaction between water molecules and the food material is mainly restricted by structural external factors, which are in turn independent of the ionic or polar affinity between the water molecules and the foodstuff matrix.

Figures 2 and 3 show the enthalpy-entropy compensation in sugar-rich foods (prunes, apricots, figs, raisins and currants). Only one mechanism of adsorption is evident in the entire range of moisture studied. This mechanism is enthalpy-con- trolled. This relationship suggests that the microstructure of sugar-rich foods is more stable and does not suffer any changes in mechanisms of water adsorption in the temperatures range from 15 to 60°C. Additionally, the isosteric heat does not show any maxima in the low moisture range as readily observed in Fig. 6.

It is interesting to note that the enthalpy-entropy compensation line in Figs 2 and 3 for sugar-rich foodstuffs cross the (0,O) point. This would indicate sugar solubiliza- tion at high moisture contents (>30 g H,O/lOO g dry solids) as well as conversion of water sorption from an exothermic to an endothermic process.

CONCLUSIONS

From this work, we conclude that the linear plot of compensation between (AHd,,.).,. and (A~,i~)l. correlates well for water adsorption in starchy and sugar-rich foods. Water adsorption occurs primarily by enthalpy-controlled mechanisms. However, it was possible to find entropy-controlled adsorption processes at low moisture con- tents in foodstuffs which had their microstructure modified by temperature. Information on the enthalpy-entropy compensation could be an important tool to recognize different mechanisms for water adsorption under varying conditions.

414 C. I. Beristain et al.

-0 25000 -:

be o 288K (15’C) :

20000 -: a 303 K (30%) A

0 318 K (45%)

15000 -r

o 333 K (60%)

-5000 I I / 1 I r 0 10 20 30 40 50 60

Moisture Content, % d.b.

Fig. 6. Enthalpy of adsorption as a function of moisture content for sultana raisins.

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