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Journulo1‘ Food Engineen’ng 28 (lYY6) l(lY- I 19 Copyright 0 1996 Elsevier Science Limited

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Enthalpy-Entropy Compensation Models for Sorption and Browning of Garlic

P. S. Madamba,‘” R. H. Driscoll & K. A. Buckle

Department of Food Science and Technology, The University of New South Wales, Sydney, 2052, Australia

(Received 18 February 1994; revised version received 15 August 1994; accepted 21 November 1994)

ABSTRACT

The enthalpy-entropy compensation theory was applied to both the sorption and non-enzymic browning of garlic. The theory was found to explain sorption well but gave a non-linear relationship for browning. The resulting power law model for sorption was compared with the Guggenheim-Anderson-de Boer (GAB) model and found to predict higher moisture contents at high water activity levels. Copyright 0 1996 Elsevier Science Limited.

A a, B AG h Ah

k” M eqGAB

M e‘Jp”Wcr M n

NOTATION

Constant in eqn (13) Water activity Constant in eqn (13) Change in Gibb’s free energy function (J/mol) Specific enthalpy (J/mol) Change in enthalpy (J/mol) Reaction rate constant Boltzmann’s constant Predicted values for the GAB model Predicted values for the power model Dry basis moisture content (7%) Number of isotherms

*Present position and address: Assistant Professor and Chairman, Department of Agricultural Process Engineering and Technology (AGPET), College of Engineering and Agro-Industrial Technology (CEAT), University of the Philippines at Los BaAos. College, Laguna, The Philippines 4031.

109

110 tl S. Madamba, R. H. Driscoll, K. A. Buckle

R AS T

A4

Universal gas constant (8314 Pa m3/mol K) Change in specific entropy (J/km01 K) Absolute temperature (K) Change in heat content (J/mol)

r Intercept defined in eqn (7)

G(M)

Standard error (%) Empirical function of moisture content

<D Temperature correction factor

Superscript 0 Isoteric variables

Subscripts

fY Isokinetic Dry basis

eq Equilibrium net Net hm Harmonic mean

INTRODUCTION

Heat of sorption data were collected as a component of a research project into the drying properties of garlic (cv. Early Californian). Collection of data on non-enzymic browning rates (NEB) of garlic was reported in a previous paper (Driscoll & Madamba, 1994). Fitting models to the data is an essential step in its utilisation in design and optimisation studies of a commercial dehydration unit. Finding an applicable theory to explain the variance in results would be of benefit in selecting an appropriate model for the sorption properties of garlic, and a time saving step in investigating future products. Food products are complex chemical mixes, where competing reactions often obscure experimental balance between the dehydrating air stream and the vaporisation of moisture from the product surface.

Browning is an irreversible reaction in foods that reduces quality as well as consumer acceptability of dehydrated products. Rates of browning reactions are necessary for predicting (using dehydration models) the quality consequences of applying specific processing strategies.

A promising theory which has been widely applied to investigate physical and chemical phenomena (Leffler, 1965; Heyrovsky, 1970; Aguerre et al., 1986) is enthalpy-entropy compensation or isokinetic theory, applied by Bell (1937) and others subsequently to a range of sorption and chemical reactions. This theory states that compensation arises from changes in the nature of the interaction between solute and solvent causing the reaction and that the relationship between enthalpy and entropy for a specific reaction is linear (Laidler, 1959). Labuza (1976) applied the equation to the thermal death curves of microorganisms, protein denaturation and ascorbic acid degradation in various food systems. Aguerre et al. (1986) applied the concept to water sorption in foods, deriving an equation relating equilibrium

Enthalpy-entropy compensation models for sorption and browning of garlic III

moisture content (EMC), water activity and temperature, obtaining a correlation between Ah” and AS of 0.997 over a range of food substances (thermodynamic quantities expressed on a molar basis).

The entropy of a material is proportional to the log of the number of available states corresponding to a specific energy level, and so increases with heat. From this it can be shown that:

(1)

where A9 is an inexact differential and AS is exact. Reaction rates will proceed faster when more states are available. In the case of sorption, for example, the latent heat of vaporisation and heat of wetting are released, the rate of sorption exhibiting an Arrhenius form of temperature dependence:

From eqns (1) and (2) and the definition of entropy, k is thus proportional to the number of available system states in the absence of internal work. Plots of enthalpy versus entropy (mollier charts) yield lines with slopes of dimension temperature, the slope at a point being called the isokinetic temperature, which is constant if the theory is valid (Heyrovsky, 1970). Thus, the enthalpy-entropy compensation is also called the isokinetic theory. Enthalpy-entropy data for organic reactions are available in the literature (Leffler, 1955; Leffler & Grunwald, 1963). More recently Ferro Fontan et al. (1982) applied the isokinetic model to a range of food products, obtaining a coefficient of determination (r2) of 0.988. Labuza (1976) analysed the data of Hendel et al. (1955) and Mizrahi et al. (1970) on non-enzymic browning of potatoes and cabbage, reporting linear compensation with isokinetic temperatures of 355 K and 350 K, respectively. To predict the reaction rate constant at equilibrium, the Gibb’s free energy function may be used:

G=h -TS (1’)

This function always decreases for a spontaneous reaction at constant temperature and pressure in the absence of internal work:

AG=Ah - TAS (‘4)

For ideal reactants (both idea1 gases and reacting species in solution):

AC= -RT InK,, ( .5 )

where K,, is the rate constant at equilibrium, given by the concentrations of reacting species to their stoichiometric powers. Thus a plot of the logarithm of the equilibrium rate constant against the reciprocal absolute temperature is linear, with a slope of -Ah/R and intercept of ASIR, respectively (Aguerre et al., 1986; Krug et al ., 1976~). This assumes that Ah remains constant with temperature (Wang & Brennan, 1991; Kiranoudis et al., 1993).

112 P S. Madamba, R. H. Driscoll, K. A. Buckle

and that errors associated with measurement of the rate constant are normally distributed (Krug et al., 1976~).

The objective of this paper was to model the effect of temperature on the sorption and browning reaction of garlic using the isokinetic theory.

MATERIALS AND METHODS

Raw materials

Freshly harvested garlic bulbs (cv. Early Californian) were obtained from Bidgee Valley Product Pty Ltd, Whitton, NSW, a commercial variety with a high solids content. The cloves were cured by blowing ambient air (25 f 3°C) through the bulbs for a minimum of 14 days per batch. The cloves were sorted and peeled manually and were stored at 0°C for not more than 28 days until all experiments could be performed.

Equilibrium moisture properties

The equilibrium moisure properties of garlic (desorption branch) were determined in a previous study using a static equilibrium method. Saturated salt solutions were prepared (Young, 1967; Greenspan, 1977) at a 2 cm depth and placed into 2-litre glass jars. The garlic samples were placed on petri dishes on glass tripods inside the jars, which were then sealed and placed in a temperature-controlled chamber. The variable range tested was from 20 to 70°C and 11 to 85% relative humidity. Weights were measured daily for the first 7 days and then 2 days thereafter until the difference between subsequent weighings was less than or equal to 0.01 g; see Madamba et al. (1994) for further details.

Browning rates

The browning rates were measured in a previous study using the same apparatus as above, but with a temperature range of 50 to 90°C. The sample slices were placed in wire mesh baskets and the colour was determined as CIE L, a and b using a Minolta Chroma meter II at different time intervals depending on the temperature; see Driscoll and Madamba (1994) for further details.

Enthalpy and entropy of sorption and browning

The data described above were fitted to equations of the form:

Ah0 AS” In K_=---

RT R (6)

where for sorption, K,, is the water activity a, and for browning K,, is the rate constant k. The curve fitting was performed using the statistical package SAS on a VAX-VMS mainframe computer.

Enthalpy-entropy compensation models ,for sorption and browning of garlic 113

2.0 . 0 100%Md n 65.3%Md f 50.5%Md 0 35.1%Md

x 208Md + ll%Md A 3%Md

1.5 t .-c-A_

.-A-

3

2 1.0 t 0.5 *-- l -•- l -•----•

XpX-X-X- X-_-L-X

_c__mv- 0 Y Y

2.9 3.0 3.1 3.2 3.3 3.4

1 /T (XE- 3)

Fig. 1. Isostere plots of garlic at different temperature and moisture levels.

1

0 R +

-1 0 :\

2 -2

-1

I\ ‘\

n x\ -_I

q Aw=O.102-0.111 + Aw=O.241-0.305

-4 x Aw=O.650-0.690 9! . Aw=O.785-0.812

I I I I

2.8 2.9 3.0 3.1

l/T (XE-3)

Fig. 2. Plot In k versus l/T.

3.2

RESULTS AND DISCUSSION

Figures 1 and 2 show the isosteres for moisture sorption, and the rate constants for browning against the inverse of absolute temperature. The average coefficient of determination of sorption using eqn (6) was 0.999 and for browning was 0.989. Figure 3 is a plot of Ah” against AS. The adjusted rz value was O-991 for the Leffler and Grunwald (1963) equation:

Ah”=T,\AS”+x (7) Since there is a high degree of linear correlation between enthalpy and entropy, the compensation theory was assumed to be valid for sorption. The isokinetic temperature has an important physical meaning as it represents the temperature at which all reactions in the series proceed at the same rate (Heyrovsky, 1970). The isokinetic temperature for sorption was found to be 348_t9 K. This agrees well with the results of Aguerre et al. (1986) and

114 l? S. Madamba, R. H. Driscoll, K. A. Buckle

4

3 6 z E

s

6 2

z La

0

.

cw .

I I I I I

0

n 3.1%MC I- IlIMC A 20%MC 0 35%MC

x 5096MC 4 65%MC A 8046MC o lOO%MC 0

2 4 6 8

Entropy (Jlkmole K)

10 12

Fig. 3. Enthalpy-entropy diagram for sorption.

Ferro Fontan et al. (1982) who reported isokinetic temperatures for selected food products of 3805 K and 327 K, respectively.

Krug et al. (1976a,b) recommended a test for the compensation theory which Uinvolves‘ comparing mean temperature Thm:

the isokinetic temperature wiih the harmonic

Tt,m= ,, ’

c (l/T) i=l

(8)

For garlic sorption this gave a value of 317.2 for Thm, a value significantly different from T,j, and so confirming the isokinetic theory for garlic sorption.

However in the case of non-enzymic browning, no definite pattern could be observed between enthalpy and entropy, with a measured r2=0+321. Analysis of the NEB discolouration data of Samaniego-Esguerra et al. (1991) for onion was analysed and also gave a poor correlation (r2=0+83). Browning is a complex biochemical process resulting from a series of reactions. The resulting free energies in these reactions were not equal, and so together with the presence of more than one interaction mechanism results in a non-linear isokinetic relationship (Leffler, 1965; Ritchie & Sager, 1964). The possibility of true compensation following a non-linear pattern as described by Leffler (1965) and Krug et al. (1976b) will be studied in a separate paper.

Both Ah” and AS” show a strong dependence on moisture content (Fig. 4) showing that the energy required for sorption in excess of the latent heat associated with the phase change is much higher at low moistures, particularly in the monolayer moisture region (moistures below 8% from the Guggenheim Anderson deBoer (GAB) model; Madamba et al., 1993). Iglesias and Chirife (1976) explained that sorption occurs initially on available sites with high activation energies, but as these sites become progressively filled, sorption occurs on less active sites. The results agree well with reported isosteric heats of sorption for Australian paddy rice

Enthulpy-entropy comperuation models for sorption und browning of gurlic 115

I . Net isosteric heat

J 0 10 20 30 40 50 60 70 80 90 100

Moisture content (%db)

Fig. 4. The net isostcric heat of sorption as a function of moisture content.

(Putranon et al., 1980) tibres (Cadden, 1988) selected food materials and crops such as vegetables, grains and eggs (Cenkowski et al., 1992) potatoes (Wang & Brennan, 1991), macadamia nuts (Palipane & Driscoll, 1993) and some vegetables (Kiranoudis et al., 1993). However, this was different from the reported behaviour for starches such as amylo-maize and potato starch (Morsi et al., 1967) and high protein products such as chicken (Iglesias & Chirife, 1976); this behaviour was expounded by Igelsias and Chirife (1976). The values obtained for the net isosteric heat for garlic were lower than for all the materials reported, showing that the average bonding site activation energy is low for garlic. This is reflected in a relatively low equilibrium moisture content especially at higher temperatures and lower a, values (Madamba et al., 1993) compared to those of other similar materials such as vegetables (Cenkowski et al., 1992; Kiranoudis et ul., 1993).

A modified form of the model used by Iglesias and Chirife (1976) was applied to the isosteric heat-moisture content data:

Ah::,,=O.55 exp2.85M ,i”“’ (9)

Figure 4 shows the isosteric heat for garlic as a function of moisture content fitted to eqn (9). A satisfactory fit was obtained with low standard errors of estimates (SEE) of the parameters (0*12-0.16) and the mean square error (MSE) and r2 were found to be 0.008 and O-991, respectively.

Figure 5 shows the entropy production for garlic sorption as a function of moisture content, wtih a trend similar to the isosteric heat-moisture curve. Based on the second law of thermodynamics, a process is reversible when the sum of all entropy changes for all subsystems in a process is constant (Wang, 1971). The process of desorption in garlic is clearly irreversible because entropy is produced during the process. An almost constant entropy can be observed at the higher moisture contents suggesting that desorption is reversible until a critical moisture content is reached. An exponential model similar to eqn (9) was fitted to the data, and is shown below:

AS “= 1.3 x 10 ’ exp 12.3 M dmO.""; ( 10)

116 I? S. Madamba, R. H. Driscoll, K. A. Buckle

A Entropy - Predicted

0 I I

0 10 20 30 40 50 60 70 80 90 100

Moisture content (%db)

Fig. 5. The entropy production of sorption as a function of moisture content.

A 2oc 0 3oc x 4Oc l 5oc

z2 L- % 9 01,

oA*xo.A x

o- ’ ’ ’ ’ ’ ’ ’ ’ 0 ’ ’ .

- 0 5 10 1.5 20 25 30 35 40 45 50 55

Equilibrium moisture content (% db)

Fig. 6. Equilibrium data of garlic at different temperatures according to eqn (12).

A satisfactory fit was obtained with a mean square error (MSE) and r2 of 0.2 and 0.987, respectively.

The comparison law can be used to model the effect of temperature on the sorption characteristics of garlic by combining eqns (6) and (7) and assuming a negligible effect of the intercept (a, eqn (7)) on the enthalpy change :

The functionality of a, against moisture in eqn (11) is implicit since the net isosteric heat of sorption is related to moisture content. Equation (11) can be rewritten in the form suggested by Aguerre et al. (1986):

% lna,=Y(MJ (12)

Enthalpy-entropy compensation models for so@on and browning of garlic 117

Equilibrium relative humidity

Fig. 7. Comparison ot’ experimental data with predicted values for the eqn (I .3) and GAB models at 30°C.

where Qr is (l/T,j-l/T))‘, Y(M,) is an empirical function of equilibrium moisture content. Here a-,. can be considered as a temperature correction factor for the isotherm and if it is adequate, eqn (12) can characterise the temperature dependence of the moisture sorption isotherm of garlic. The equilibrium data were calculated to plot @Jn a, versus the equilibrium moisture content and is shown in Fig. 6. Upon examination of the graph, a power law function can adequately characterise the relationship of @,ln LI, and moisture content:

CD-r. In a,=A *R’“~j (1.3)

The values of A and B were 5062.7 K and 0.873, respectively, as determined by non-linear regression. The standard errors of estimate for constants .4 and B were found to be 3685 and 0.014, respectively, and were less than the acceptable + 10% error (Wang & Brennan, 1991).

Equation (13) is a two parameter equation which can be used to model the relationship of a, and equilibrium moisture content, with (TX,. as a temperature correction constant. The model was then compared to the sorption data of garlic to validate the adequacy of the temperature correction factor. Figure 7 is a comparison of the isotherm data for garlic at 40°C using the power law model (eqn (13)) and the Guggenheim- Anderson-de Boer (GAB) model proposed by Madamba et al. (1993). The two-parameter power law model adequately characterised the desorption of garlic up to an a, of close to 0.6 after which it tended to over-estimate the data, whereas the GAB model continued to characterise the data well. The standard error of the power model compared with the GAB model was calculated by eqn (14) to be 7.3%.

(14)

118 l? S. Madamba, R. H. Driscoll, K. A. Buckle

For practical purposes, the power law model as given by eqn (13) gives an estimate of the sorption behaviour of garlic below a,=0=6, and although it has a lesser number of parameters, the superiority of the GAB model cannot be doubted. In addition, the GAB parameters are physically significant. The GAB model has been used recently to model sorption behaviour of many food products and is recommended by the European COST 90 project (Wolf et al., 1984).

CONCLUSIONS

Based on the results reported here, the following conclusions can be made:

(1) The enthalpy-entropy relationship or the isokinetic theory can be successfully applied to some food processes. Desorption in garlic revealed that a linear compensation existed, while a possibility of non- linear compensation due to multiple interactions may have existed for the more complex process of NEB.

(2) The isosteric heat of sorption of garlic can be characterised by an exponential model.

(3) Entropy production is evident showing that the desorption process is irreversible.

(4) A power law model was developed and can adequately characterise the sorption behaviour of garlic at lower a, ranges but tends to over- predict the equilibrium moisture content at higher a,. Overall the GAB model was superior.

ACKNOWLEDGEMENTS

Acknowledgement is made to the Bidgee Valley Product Pty Ltd (BVP) for the provision of garlic, and to BVP and the Horticultural Research and Development Corporation (HRDC) for financial assistance.

REFERENCES

Aguerre, R. J., Suarez, C. & Viollaz, P. E. (1986). Enthalpy-entropy compensation in sorption phenomena: application to the prediction of the effect of temperature on food isotherms. J: Food Sci., 51 (6), 1547-9.

Bell, R. P. (1937). Relation between the energy and entropy solution and their significance. Trans. Faraday Sot., 33, 496-9.

Cadden, A. M. (1988). Moisture sorption characteristics of several food fibers. J. Food Sci., 53 (4), 1150-5.

Cenkowski, S., Jayas, D. S. & Hao, D. (1992). Latent heat of vaporization of selected foods and crops. Can. Agric. Engng, 34 (3), 281-6.

Driscoll, R. H. & Madamba, P. S. (1994). Modelling the browning kinetics of garlic. Food Aust., 46 (2), 66-71.

Ferro Fontan, C., Chirife, J., Sancho, E. & Iglesias, H. A. (1982). Analysis of a model for water sorption phenomena in foods. J Food Sci., 47, 1590-4.

Greenspan, L. (1977). Humidity fixed points of binary saturated solutions. .T. Res.

Enthalpy-entropy compensation models for sorption and hrowning of garlic I .I9

Nat. Bur Stand., 81a, 89-96. Hendel, C. E., Silveria, V. G. & Harrington, W. 0. (1955). Rate of nonenzymatic

browning of white potato during dehydration. Food Technol., 9, 433-8. Heyrovsky, J. (1970). Determination of isokinetic temperature. Nature, 227, 66-7. Iglesias. H. A. & Chirife, J. (1976). Isosteric heats of water vapour sorption on

dehydrated foods. Part I - Analysis of differential heat curves. Lehen.sm.-wiss. II.- Technol., 9, 116-22.

Kiranoudis, C. T., Maroulis, Z. B., Tsami, E. & Marinos-Kouris, D. (19Y3). Equilibrium moisture content and heat of desorption of some vegetables. J. Food Engng, 20, 55-74.

Krug, R. R., Hunter, W. G. & Greigcr, R. A. (1976a). Enthalpy-entropy compensation. 1. Some fundamental statistical problems associated with the van‘t Hoff and Arrhenius data. J. Phys. Chem., 80 (21) 2335-42.

Krug, R. R., Hunter, W. G. & Greiger, R. A. (1976h). Enthalpy-entropy compensation. 2. Separation of the chemical from the statistical effect. .I. Ph_\s. Chem., 80 (21), 2335-42.

Labuza, T. P. (1976). Enthalpyientropy compensation in food reactions. Food Tech& ., 34, 67-77.

Laidler, K. J. (1959). Thermodynamics of the ionization proces. Part I - General theory of substituent effects. Trans. Faraday Sot., 5.5, 1725-30.

Leffler. J. E. (1955). The enthalpy-entropy relationship and its implications for organic chemistry. J. 0%. Chem., 20, 1202.

Leffler, J. E. (1965). Concerning the isokinetic relationship. Nafure, 205, 1101-2. Leffler, J. E. & Grunwald, E. (1963). Rates and Equilibria of Otganic Reactions. John

Wiley, New York. Madamba, P. S., Driscoll, R. H. & Buckle, K. A. (1994). Predicting the sorption

behaviour of garlic. Drying Technol., 11 (h), 1443-58. Morsi, M. K. S., Sterling, C. & Volman, D. H. (1967). Sorption of water vapor by B

pattern starch. J. Appl. Polymer Sci., 11, 1217-25. Palipane, K. B. & Driscoll, R. H. (1993). Moisture sorption characteristics of in-shell

macadamia nuts. .I. Food Engng, 18 (1) 63-76. Putranon, R., Bowrey, R. G. & Fowler, R. T. (1980). The effect of moisture content

on the heat of sorption and specific heat of Australian paddy rice. Food Techrrol. Aust ., 32, 56-9.

Ritchie, C. D. & Sager, W. F. (1964). An examination of structure-reactivity relationship. Prog. Phys. Org. Chem., 2, 323-400.

Samaniego-Esguerra, C. M., Boag, I. F. & Robertson, G. F. (1991). Kinetics of quality deterioration in dried onions and green beans as a function of temperature and water activity. Lebensm:wiss. u-Technol., 24 (l), 53-8.

SAS (1985). SAS User’s Guide: Statistics Ver 5 Ed. SAS Institute, Cary, NC. Wang, N. & Brennan, J. G. (1991). Moisture sorption characteristics of potatoes at

four temperatures. J. Food Engng, 14, 269-87. Wark, K. (1971). Thermodynamics, 2nd edn. McGraw-Hill, New York. Wolf, W., Spiess, W. E. L. & Jung, G. (1984). Standardisation of isotherm

measurements. In Properties of Water in Foods, eds D. Simatos & J. L. M&on. Martinus Nijhoff, Dordrecht.

Young, J. F. (1967). Humidity control in the laboratory using salt solutions -- a review. J. Appl. Chem ., 17, 241-5.

Zuritz, C., Singh, R. P., Moini, S. M. & Henderson, S. M. (1979). Desorption isotherm of rough rice from 10°C to 40°C. Trans. ASAE, 22 (2) 443-6.