Sorption Isosteric Heat Determination by Thermal Analysis and Sorption Isotherms

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1 JOURNAL OF FOOD SCIENCE ENGINEERING/PROCESSING Sorption Isosteric Heat Determination by Thermal Analysis and Sorption Isotherms A. Mulet, J. García-Reverter, R. Sanjuán, and J. Bon ABSTRACT A procedure based on thermal analysis thermogravimetry (TG) and differential-scanning calorimetry (DSC) was examined to compute isosteric heat of sorption for water. DSC measurements on samples with different moisture content allowed determining enthalpy variations due to water vaporization. Thermogravimetries performed on the same samples enabled a link to be made between enthalpic measurements and weight losses and thus compute isosteric heats. The procedure was applied to cauliflower and potato starch. From equilibrium isotherms by applying the Clausius-Clapeyron equation, the isosteric heats of sorption were calculated. The comparison of the values obtained through both procedures showed a good agreement. Key Words: Isotherms, cauliflower, potato starch, isosteric heat, calorimetry INTRODUCTION MASS TRANSFER DUE TO HEAT TREATMENTS IS QUITE COMMON IN the food industry. Thus knowing how heat affects the desorption of different constituents may be important. In drying operations water is removed, generally by heating, to stabilize the food by decreasing water activity. Then the equilibrium isotherms are important for dryer design. They help establish the final moisture contents and compute energy requirements. The isosteric heat of sorption is a measurement of the energy or intermolecular bonding between water molecules and absorbing surfaces. The moisture content, for which the heat of absorption is almost identical to that of vaporization for pure water, is often considered as an indicator of the free water content. An index of the nature of water sorption in foods is frequently obtained by applying the Clausius-Clapeyron equation to sorption isotherms at different temperatures (Iglesias and Chirife, 1976; Mc- Minn and Magee, 1997). This index has been considered more qualitative than quantitative because of measurement errors in determination of sorption isotherms and approximations in calculating the isosteric heat of sorption from the isotherms. Tolaba et al. (1997) showed that by using the integral or the differential form of the Clausius- Clapeyron equation the variation in computed heats of sorption could be in some instances >100%. Also it has been reported that the use of isotherms to compute isosteric heats of sorption could be very imprecise at moisture contents <15%. For example at 5% moisture the variability exceeds 100% (Chirife and Iglesias, 1992). This was one of the reasons for extensive work that has been carried out to improve the accuracy of sorption isotherms (Wolf et al., 1984; 1985). Among the difficulties are: lack of reversibility of change in a Authors Mulet and Bon are with the Depto. de Tecnología de Alimentos, Universidad Politécnica de Valencia, Camino Vera s/n 46071, Valencia, Spain. Authors Garcia-Reverter and Sanjuan are with AINIA Instituto Tecnológico Agroalimentario, Parc Tecnològic.-Apdo 103, Paterna (Valencia), Spain. Direct inquiries to Prof. Antonio Mulet. majority of food isotherms during moisture removal and temperature increases(mcminn and Magee, 1997). There is a need for better methods to compute isosteric heats of sorption. Many studies on evaluation of isosteric heat of water sorption have been reported (Iglesias and Chirife, 1976; Wang and Brennan, 1991, Tolaba et al., 1997). The isosteric heats of sorption were generally obtained from the water activity dependence on temperature. Some researchers have suggested using calorimetric techniques but not applied. Sanjuán et al. (1994) employed calorimetric techniques to determine isosteric heats in chufa (Cyperus esculentus,l.) and Sánchez et al. (1977) had used the same methodology on potato. Calorimetric techniques applied to different kinds of materials to determine heats of sorption are scarce and our objective was to use this approach on a homogeneous and a non homogeneous food product to provide more needed data for such assessments. THEORY THE ISOSTERIC HEAT OF SORPTION (Q st ) CAN BE DEFINED AS a partial molar property, derived from the isotherm dependency on temperature, (d lnp/dt) w = (Q st /RT 2 ) (1) where P is the partial pressure of water vapor, R is the gas constant and T the absolute temperature. Most of the studies previously cited, used the Clausius-Clapeyron equation to establish the isosteric heat of sorption because it provides a rapid computational procedure. From that equation, applied to pure water, the following was obtained: {[d ln(p/p o )]dt} w = (d lna w /dt) w = Q n st /RT 2 (2) where a w is the water activity and P o the saturation pressure at temperature T. The net isosteric heat of sorption Q n st represents the difference between the isosteric heat and pure water vaporization energy (L r ). This variable can be calculated according to Eq (2) by plotting the sorption isotherms as ln (a w ) at a specific moisture content vs 1/T and measuring the slope (Wang and Brennan, 1991). Equation (2) is based on the assumption that Q n st is invariant with T. Although not always true this assumption has often been accepted (Iglesias and Chirife, 1989). The application of this method requires the measurement of sorption isotherms at more than two temperatures. The isosteric heat may also be calculated from the integrated form of (Eq 2) applied to sorption isotherms measured at two temperatures (Wang and Brennan, 1991). Q n st = R{[(T 1 T 2 )/(T 2 - T 1 )]ln (a w2 /a w1 )} (3) Accuracy of experimental data is required in isosteric heat determination. Calorimetric techniques are a better alternative with available instrumentation. Values for the isosteric heats of sorption for cauliflower and starch could be obtained from desorption isotherms at several temperatures and calorimetric measurements (DSC and TG), to show their equivalence. Calorimetry is less cumbersome than sorption isotherm techniques and requires small samples. 64 JOURNAL OF FOOD SCIENCE Volume 64, No. 1, Institute of Food Technologists

2 MATERIALS & METHODS Raw material Fresh cauliflower (Snow March cultivar) was harvested, stored whole at 6 C and at 85% relative humidity and used within 2 wk of harvest. Potato starch (soluble ACS REAGENT, product number S9765, lot number 084h0198) was obtained from SIGMA Chemical Co. (St. Louis, MO). Starch samples were equilibrated to different water activities using saturated solutions. The salts (potassium nitrate, potassium bromide, ammonium chloride, sodium chloride, sodium bromide, magnesium chloride, potassium fluoride, potassium acetate, Lithium chloride, Potassium hydroxide) were provided by ACROS CHIMICA (Janssen Pharmaceutikalaan, Belgium), water activity for saturated solutions of these salts was reported by Lewis (1977) at 25 C. The amounts of salt used were those recommended by Wolf et al. (1985). Equilibrium RH varied from 100% for distilled water to 8.23±0.72 for potassium hydroxide. Salt solutions (200 cm 3 ) were prepared with distilled water, placed in 500 cm 3 closed crystal flasks and left at rest for 24h, then 500 mg samples of starch were placed in small open containers inside the flasks. The flasks were left at controlled temperature (25±1 C) for more than 30 days to allow equilibration of the material. Starch was also lyophilized for more than 48h to obtain near zero available water content samples. Sorption isotherms The sorption isotherms for cauliflower were established by using a Novasina TH-2 (Axain Ltd. Systems for Air Treatment, Pfäffikon, Switzerland) conductivity hygrometer. Samples were prepared by drying cauliflower to different moisture contents. The dried products were then ground and homogenized before being introduced in the Novasina measuring cell. Water activities were measured at 25, 35 and 45 C. Moisture content was determined according to the official method for dried fruits (JAOAC, 1996). For that purpose samples were kept in a vacuum heated cabinet at 70ºC until constant weight was reached. All measurements for water activity and moisture content were carried out at least twice, when values were different by >1%, the number of measurements was increased. Sorption isotherms considered for potato starch were taken from published data (Van der Berg, 1981). Isosteric heat of sorption from isotherms From the slope of the plot ln (a w ) vs 1/T (Eq 2), the net isosteric heat of sorption was determined. A least squares fitting was used to compute the slope (-Q n st/r). The net sorption heats were also determined according to Eq (3) by using the pairs a w -T and averaging. The value for Q st was obtained by adding the latent heat of vaporization (L r ), computed as the average value for the 3 temperatures considered (L r = J/g). Isosteric heat of sorption from calorimetric techniques Thermal analyses were carried out with a Mettler TA 4000 apparatus consisting of a TC11TA processor, a thermobalance M3 and a measurement cell DSC30. The analysis of the thermograms was accomplished using Mettler software Graphware TA72AT1. Samples with different moisture contents were used for DSC and TG measurements. The cauliflower samples were ground, sealed in a glass container at controlled temperature (25±1 C) and held 20h to allow moisture uniformity. Before measurements, starch samples were conditioned as above. All experiments were replicated at least 3. The experimental set up was established from a previous study: dynamic experiment (time varying temperature). The heating rate 2 C/ min, temperature range C. The temperature range was fixed to allow the loss of water and avoid carbohydrate pyrolysis (Raemy and Schweitzer, 1983). The heating rate was designed to eliminate any background signal from the equipment. Samples for DSC measurements were placed in sealed aluminum crucibles with lid (perforated). Care was taken to ensure good contact of the product with the bottom of the crucible to facilitate heat transfer. Then the crucible with the sample was placed inside the measuring cell along with another crucible with inert material (air). The enthalpy of the endotherms was determined from the peak areas. For thermogravimetry the samples were placed in aluminum crucibles without lids, placed in the thermobalance, and then the weight loss was recorded when the sample was heated. DSC and TG data were used to compute the enthalpy of vaporization of water at different moisture contents. The following steps were used: (1) At each moisture content (W), at least 3 DSC thermograms were obtained to calculate the enthalpy absorbed per unit mass. We assumed that the differential energy absorbed was utilized for water vaporization and an average value for that energy was obtained. (2) On samples with the same moisture content as those used for DSC, weight losses by TG were recorded within the same temperature ranges in the DSC measurements which were repeated 3. (3) From TG and DSC data the vaporization energy per unit mass was calculated. This average value is referred to as Cumulated Average Vaporization Enthalpy (E ci ). The Cumulated Average Vaporization Enthalpy associated with a particular moisture (E ci ) was defined as the enthalpy absorbed by the sample when heated from the initial moisture to complete dryness, divided by the weight loss (vaporized water). For computational purposes, E ci = 0 wi Q st (W)dW/ 0 w1 dw (4) where Q st represents the energy needed to vaporize a unit mass of water and W the product moisture dry basis. Thus the objective was to obtain the function Q st (W) from the experimental measurement of E ci values at different W i, since during dehydration it was only possible to measure average energy consumption. Modeling It was found (Riedel, 1977) that Eq (5) ln[a w (T 2 )/a w (T 1 )] w = Ae -bw [(1/T 1 ) - (1/T 2 )] (5) adequately described in foods the temperature influence on a w. Equation (5) involves two characteristic constants A and b. Combining with Eq (3) and rearranging, Q st = Ce -bw + L r (5) where C is RA. By substitution of Eq( 6) on the Cumulated Average Vaporization Enthalpy (Eq 4) and integrating, E ci = (C/b)[(1 - e -bw) /W)]+ L r (7) From E ci experimental data, values for the constants C and b (Eq 7) could be obtained. For that purpose the criteria shown in Eq. (8) was considered (Lomauro et al., 1985), Newton s method for multivariate minimization (EXCEL TM ) was used to carry out the calculations: N (Calculated Isoteric Heat - Experimental Isoteric Heat) ABS (8) i=0 Experimental Isoteric Heat where N was the total number of experimental points. Initial values for the constants were needed to start the computational procedure due to the fact that numerical optimization methods could only locate local optima. In order to obtain unbiased initial Volume 64, No. 1, 1999 JOURNAL OF FOOD SCIENCE 65

3 Sorption Isoteric Heat Determination... Table 1 Values of the constants C and b for different products Product C(J/g) B(kg water/100 kg d.m.) -1 Camomile Trout Chicken Thyme Marjoram Cinnamon Nutmeg Table 2 Parameters of the fitted GAB equation Temp (ºC) W m C g k tal data, the values for C and b for cauliflower were computed, then from Eq (6) the isosteric heats of absorption were obtained. The values achieved through parametric identification were 8070 (J/g) for C and 0,445 (kg water/100kg d.m.) -1 for b. The experimental and calculated values of E ci based on Eq. (7) were compared (Fig. 3A). The model fits the experimental data well (Root Mean Square Deviation 3.67, explained variance 85%). Once the constants C and b were established, the sorption isosteric heats were computed (Eq. 6) for each moisture content. Agreement of values measured by calorimetry and desorption isotherms was also found (Fig. 3B) (correlation coefficient 0.98, average difference 1.6%). The relatively uniform starch enabled the testing for errors of the procedure. Measurements (39) with different samples were conduct- Table 3 Isosteric heats of sorption for cauliflower a Moisture Isosteric heat of sorption (J/g) (kg H 2 O/100 kg d.m.) (1) (2) a Obtained from isotherms (1) by differential method, and (2) by integral method Eq (3) at different moisture contents. estimates for C and b, the isosteric sorption heats for different products were used (Iglesias and Chirife, 1976). Values for initial estimations were reported (Table 1). RESULTS & DISCUSSION Desorption isotherms The desorption isotherms for cauliflower were determined (Fig. 1A). As expected there was a slight increase of water activity with temperature. The shape of the curves was similar to desorption isotherms for other vegetables. Two models (GAB, Ferro-Fontan) were fitted to the experimental data using a Marquard procedure (Samaniego-Esguerra et al., 1991). The GAB model gave the best results in the whole interval considered. The average error on moisture was kg water/kg d.s. for GAB and for Ferro-Fontan. The parameters from fitting the GAB model were determined (Table 2). Isosteric heat of sorption Data from the isotherms at the 3 temperatures were plotted according to Eq (2)(Fig. 1B). Slopes of the lines and values of Q n st were determined (Table 3). The isosteric heats of sorption for cauliflower (Fig. 1C) showed an increase in sorption energy when the moisture content decreased. At high moisture contents the isosteric heat of desorption coincides with the pure water latent heat of vaporization. Plots from thermal analysis were made for the results for the fresh cauliflower (92,24 kg water/ 100 kg) DSC experiment (Fig. 2A). The total energy (per unit weight of the sample) necessary to lose water from fresh cauliflower was 2393 J/g. The corresponding TG values were also determined (Fig. 2B). By using DSC and TG data through the procedure described, the Cumulated Average Vaporization Enthalpy was obtained. From the initial estimates (Table 1), by fitting the model (Eq 7) to the experimen- Fig. 1 (A) Desorption isotherms for cauliflower, experimental points at 25 C, 35 C, and 45 C and GAB model fit at ( ) 25 C, 35 C and 45 C. (B) Calculation of isosteric heats at different moisture contents from equilibrium isotherms [(1) 9.98 kg water/kg d.m., (2) 3.46 kg water/kg d.m.; (3) 0.55 kg water/kg d.m., (4) 0.18 kg water/kg d.m., (5) kg water/kg d.m.; (6) 0.07 kg water/kg d.m.; (7) 0.05 kg water/kg d.m.); (C) Isosteric heat of water desorption in cauliflower obtained from the isotherms. 66 JOURNAL OF FOOD SCIENCE Volume 64, No. 1, 1999

4 Fig. 2 (A) DSC endotherm of a raw cauliflower sample (initial sample weight= mg, rate of scanning=2.0 C/min). (B) Weight losses obtained from TG of a raw cauliflower sample (initial sample weight= mg, rate of scanning=2.0 C/min). Fig. 3 (A) Experimental ( ) and calculated ( ) data of Cumulated Average Vaporization Enthalpy of cauliflower. (B) Isosteric heat of desorption in cauliflower obtained from equilibrium isotherms ( ) and thermal analysis ( ). (C) Experimental ( ) and calculated ( ) data of Cumulated Average Vaporization Enthalpy of potato starch. ed, the standard deviation for Cumulated Average Vaporization Enthalpy measured by DSC was 9.13 J/g and for moisture measured by TG kg water/kg product. These results showed that the procedure outlined was quite reliable when enough replicates were carried out. The calorimetric results for starch exhibited the same kinds of variation than that were found for cauliflower (Fig. 3C). For starch, the model (Eq 7) for calculating the Cumulated Average Vaporization Enthalpy was fitted to experimental data and the values for the constants C (3650 J/g)) and b [ (kg water/100 kg d.m.) -1 ] were obtained. Agreement between experimental and calculated values for the Cumulated Average Vaporization Enthalpy was found for starch (Fig. 4) (explained variance 98%). From sorption isotherms reported by Van der Berg (1981) for potato starch the values of isosteric heat of sorption were found to be similar to those obtained by calorimetry not only at high moisture content but also at low moisture contents. For instance at 6% d.b. moisture the value from isotherms was 2900 J/g and from calorimetric measurements 2720 J/g. As reported by Chirife and Iglesias (1992) the precision for this measurement from isotherms (here at 6% d.b. moisture) gave a lower value of 2580 J/g and a higher value of 3320 J/g. Thus it could be considered that the values obtained through both methods were then coincident within the limits of experimental errors. The use of calorimetric techniques could provide advantages due to the greater ease and speed in performing the experiments, as well as a greater accuracy at low moisture contents. This is because the direct measurements of the Cumulated Average Vaporization Enthalpy are always affected by the same error. When using isotherms the uncertainties greatly increase at low moisture (Chirife and Iglesias, 1992). Both physisorption and chemisorption may occur, linked to low and high interaction energy respectively. Some studies have linked the variation in sorption energies to chemical functions and pointed out Volume 64, No. 1, 1999 JOURNAL OF FOOD SCIENCE 67

5 Sorption Isoteric Heat Determination... Fig. 4 Experimental and calculated data of Cumulated Average Vaporization Enthalpy of potato starch. that chemisorption of polar groups could explain the increase observed at very low moisture contents (Tsami, 1991). Experimental evidence of the true mechanism is lacking. However the magnitude of the increase in the sorption energy indicates that for cauliflower at moisture >10 kg water/100 kg dry matter the water is physisorbed or retained by other means in the vegetable and it is chemisorbed at lower moisture contents. This is also true for potato starch, although the isosteric heats of sorption were higher for cauliflower. Since chemisorption involves higher energies this observation would indicate that physisorption was more important in potato starch than in cauliflower. REFERENCES AOAC Official Methods of Analysis, 16th ed. {JAOAC, 1934, 17,215; JAOAC, 1935, 18,80.] Assoc. of Official Analytical Chemists, Arlington, VA. Chirife, J. and Iglesias, H.A Estimation of the precision of isosteric heats of sorption determined from the temperature dependence of food isotherms. Lebensmittel Wissenchaft Technologie 25: EXCEL TM Spreadsheet User s Manual, Excel 4.0. Microsoft Corporation, Redmond, WA. Iglesias, H.A. and Chirife, J Isosteric heats of water sorption on dehydrated foods. Part I. Analysis of the differential heat curves. Lebensmittel Wissenchaft Technologie 9(2): Iglesias, H.A. and Chirife, J On temperature dependence of isosteric heats of water sorption in dehydrated foods. J. Food Sci. 54: Lewis, G Humidity fixed points of binary saturated aqueous solutions. J. Res. National Bureau of Standards, 81A (1): Lomauro, C.J., Bakshi, A.S. and Labuza,T.P Evaluation of food moisture sorption isotherm equations. Part I: Fruit, vegetable and meat products. Lebensmittel Wissenchaft Technologie, 18: McMinn, W.A.M. and Magee, T.R.A Moisture sorption characteristics of starch materials. Drying Technol. 15(5): Raemy, A. and Schweitzer, T.F Thermal behavior of carbohydrates studied by heat flow calorimetry. J. Thermal Analysis 28: Riedel, L Calorimetric measurements of heats of hydration of foods. Chemie Mikrobiologie und Technologie der Lebensmittel. 5: Samaniego-Esguerra, C.M., Boag, I.F., and Robertson, G.L Comparison of regression methods for fitting the GAB model to the moisture isotherms of some dried fruit and vegetables. J. Food Engr. 13: Sánchez, E.S., Sanjuán, N., Simal, S., and Rosselló, C Calorimetric techniques applied to the determination of isosteric heat of desorption for potato. J. Sci. Food Agric. 74: Sanjuán, R., Garcia-Reverter,J., Bon, J., and Mulet, A Moisture retention in chufa (Cyperus esculentus, L.), equilibrium isotherms and isosteric heats. Revista Española de Ciencia y Tecnologia de Alimentos 34(6): Tolaba, M.P., Suarez, C., and Violaz, P Heats and entropies of sorption of cereal grains: a comparison between integral and differential quantities. Drying Technol. 15(1): Tsami, E Net isosteric heat in dried fruits. J. Food Eng. 14: Van der Berg, C Vapor sorption equilibria and other water-starch; a physicochemical approach. P.d. dissertation, Agricultural University, Wageningen, The Netherlands (1981). Wang, N. and Brennan, J.G Moisture sorption isotherm characteristics of potatoes at four temperatures. J. Food Engr. 14: Wolf, W.,Spiess, W.E.L., Jung,G., Weisser,H., Bizot, H., and Duckworth The watervapour sorption isotherms of microcrystalline cellulose (MCC) and of purified potato starch. Results of a collaborative study. J. Food Engr. 3: Wolf, W., Speiss, W.E.L., and Jung, G Standardization of isotherm measurement in Properties of water in Foods, D.Simatos and J.L. Multon (Ed.), p Martinus Nijhoff Publ., Dordrecht, The Netherlands. Ms received 2/4/98; revised 7/15/98; accepted 7/21/98. We thank the Spanish Comisión Interministerial de Ciencia y Tecnologia (CICYT), Project ALI for financial support. 68 JOURNAL OF FOOD SCIENCE Volume 64, No. 1, 1999

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