The fitting of various models to water sorption isotherms of tea stored in a chamber under controlled temperature and humidity

The moisture sorption characteristics of tea stored in a chamber regulated by an atomizing humidification system were investigated at 25, 35 and 45 °C for water activity ranging from 0.1 to 0.9. The sorption isotherms of tea were typical type II sigmoidal curves according to BET classification. In both adsorption and desorption, an increase in temperature resulted in lower equilibrium moisture contents at corresponding values of water activity. The sorption isotherms exhibited hysteresis over the whole water activity range. GAB, BET, Henderson, Iglesias and Chirife, Oswin, Peleg, Smith and Caurie models were applied for analysing the experimental data. Nonlinear regression analysis was used for the determination of the parameters in the equations. Estimated parameters and fitting ability for sorption models were evaluated. The Peleg model was found to be the most suitable for describing the relationship between equilibrium moisture content and water activity for the whole range of temperatures and relative humidities studied. The surface area of monolayer was calculated. The BET equation was solved for the monolayer moisture content and the corresponding a_w values at which monolayer forms were presented. Sorption isotherm data were used to determine the thermodynamic functions such as isosteric heat of sorption, sorption entropy, spreading pressure, net integral enthalpy and entropy. The Clausius-Clapeyron equation was used to evaluate the isosteric heats of sorption. The isosteric heats of sorption and sorption entropy decreased with increasing moisture content. The heat of desorption was little higher than that of adsorption at low moisture content. The enthalpy-entropy compensation theory could be successfully applied to water sorption by tea. This theory showed that the moisture sorption of tea was governed by enthalpy-controlled mechanisms. The spreading pressure increased with increase in water activity and decreased with increasing temperature. The net integral enthalpy decreased with moisture content while the net integral entropy increased.     

Water Sorption Isotherms and Crispness of Fried Yam Chips in the Temperature Range from 293K to 313K

Water sorption isotherms of fried yam chips were determined using a static gravimetric method with saturated salt solutions in the range of water activity between 0.22 and 0.85 at 293, 303 and 313K. Four sorption models namely GAB, Peleg, modified Mizrahi, and BET were fitted with the sorption data generated. The GAB model followed by Peleg and modified Mizrahi models were found to best represent the experimental data in the a_w range of 0.22–0.85. However, the BET model was more applicable between a_w range of 0.22–0.55. The adsorption isotherm of fried yam chips clearly showed the influence of temperature, decreasing the moisture content at a fixed water activity value with higher temperature. The net isosteric heats of sorption of water were estimated by applying the Clausius–clapeyron equation to the adsorption isotherms at different temperatures. The net isosteric heat of sorption was observed to be decreasing as moisture content increases. Samples stored in desiccators of 0.44 and 0.55 a_w at 303 and 313K, respectively, were rated higher in terms of textural properties investigated.     

MOISTURE SORPTION CHARACTERISTICS of STARCH GELS. PART II: THERMODYNAMIC PROPERTIES

A thermodynamic approach was used to interpret the experimental adsorption and desorption isotherm data for potato starch gel. Calculation of the thermodynamic properties (differential enthalpy, integral enthalpy, differential entropy and integral entropy) provides an understanding of the properties of water and energy requirements associated with the sorption behavior. Isosteric heats (differential enthalpies) were calculated through direct use of moisture isotherms by applying the Clausius‐Clapeyron equation. the differential enthalpy and entropy decreased with increasing moisture content and were adequately characterized by an exponential model. A plot of differential heat versus entropy satisfied the enthalpy‐entropy compensation theory. the spreading pressure increased with increasing water activity, and decreased with increasing temperature. the net integral enthalpy increased with moisture content to a maximum value (around the monolayer moisture content) and then decreased. In a reverse manner, the net integral entropy decreased with moisture content to a minimum value and then increased.     

Moisture sorption characteristics of rice flour

Moisture equilibrium data (adsorption and desorption) of rice flour were determined using the static gravimetric method of saturated salt solutions at three storage temperatures: 10, 20 and 30 degrees C. The range of water activities for each temperature was from 0.11 to 0.85. Equilibrium moisture content decreased with increase in storage temperature at any given water activity. The experimental data were fitted to four mathematical models (modified Oswin, modified Halsey, modified Chung-Pfost and modified Henderson). The monolayer moisture content was estimated from sorption data using the Brunauer-Emmett-Teller (BET) equation. The isosteric heats of sorption were evaluated using Clausius-Clapeyron equation.     

Desorption isotherms of shelled maize: whole, dehulled and hulls

Water vapour desorption isotherms of whole kernel maize were determined at 40, 50 and 60°C, and those of dehulled kernels and hulls at 50 and 60°C. It was found that while whole and dehulled kernels show similar equilibrium moisture contents, the hull gives lower values. Equilibrium data were modelled with two-parameter equations. It was found that the Henderson equation is best for describing the equilibrium data for whole kernels, while the Halsey equation was more appropriate for hulls. A simple semi-theoretical equation was used to model the effect of temperature on the equilibrium values of whole maize kernels for the three temperatures investigated. BET heats of desorption and the isosteric heat curves were calculated for whole kernels and hull. It was found that the BET heat values correlate quite well with the isosteric heat values at the monolayer moisture content.     

Moisture sorption and the applicability of the Brunauer-Emmet-Teller (BET) equation for blanched and unblanched mushrooms

Moisture sorption isotherms of blanched and unblanched mushrooms over 0.11–0.75 a_w were determined at 27°C and 37°C by using the static gravimetric method. Adsorption and desorption behaviors of blanched and unblanched mushrooms were compared. The unblanched material adsorbed more water than that of the blanched. In desorption isotherms, the equilibrium moisture contents of the unblanched material were found to be higher than those of the blanched throughout the entire a_w range. The BET equation was tested to fit the experimental moisture sorption data over the 0.11–0.43 a_w, 0.11–0.55 a_w, 0.11–0.64 a_w, and 0.11–0.75 a_w. Nonlinear regression analysis was used for the determination of the parameters in the equation. The quality of the fit of the BET model over each a_w range was judged from the value of the relative percent root mean square (% RMS). The moisture sorption behavior over 0.11–0.43 a_w of mushrooms has indicated that the BET equation is applicable generally up to 0.43 a_w. Monolayer moisture contents and C constants in the BET equation obtained for each a_w interval were reported. The water activities corresponding to the monolayer values have been determined and discussed related to mushroom storage. The net isosteric heats of adsorption and desorption were estimated from equilibrium sorption data, using the integrated form of the Clausius-Clapeyron equation. The heats of adsorption/desorption decreased with increase in moisture content and approached to a constant value. It was concluded that moisture adsorption/desorption occurred by physical mechanisms at high moisture contents, but at low moisture contents, besides physical adsorption, chemisorption was also observed.     

Adsorption isotherms of pinhão (Araucaria angustifolia seeds) starch and thermodynamic analysis

The seeds of Araucaria angustifolia, commonly known as pinhão, are widely consumed in both Southern and Southeastern Brazil due to their high nutritious value comprised basically by starch. The literature on the technological aspects of this seed is still very scarce. Moisture adsorption isotherms of pinhão starch were determined at 10, 20, 30 and 40 °C using the gravimetric method. Results show that the Peleg model most appropriately represents the experimental data. Other models (Chung–Pfost, GAB, Henderson, BET and Chirife) also were found to adjust well. The isosteric heat of sorption (differential enthalpy) was calculated by using the moisture adsorption isotherm and decreased as moisture content increased. The enthalpy–entropy compensation theory was applied to adsorption isotherms and the isokinetic temperature for pinhão starch was calculated by plotting the differential enthalpy versus differential entropy. It was found that the adsorption process investigated was enthalpy-controlled and spontaneous.     

Heat of sorption of water in dried fruits

The heats of moisture adsorption and desorption in four dried fruits (sultana raisins, figs, prunes and apricots) were estimated from equilibrium sorption data, using the Clausius-Clapeyron equation in the temperature range 15–60°C. The net isosteric heat of sorption ( q st) decreased sharply from about 20 kJ mol⁻¹ water to near zero when the moisture content was increased from 0.05 to 0.50kg water kg⁻¹ dry matter. An exponential function was fitted to the experimental q st values at various moisture contents (X) , yielding two characteristic constants ( q 0 and X 0) for each fruit. Mean and total heats of sorption were calculated from the proposed empirical equation, which are useful for enthalpy prediction in food dehydration. The heats of desorption were higher than the heats of adsorption, indicating significant hysteresis in the sorption of water, especially in dried apricots.     

Moisture sorption and thermodynamic properties of cassava starch and soy protein concentrate based edible films

Moisture sorption isotherms and thermodynamic properties of cassava starch and soy protein concentrate–based edible films were investigated. Equilibrium moisture content was determined at various temperatures (10, 20, 30 and 40 °C) and relative humidities (17–83%) using gravimetric method, and the results were analysed using four sorption isotherm models. The equilibrium moisture of edible films (both adsorption and desorption modes) decreased with soy protein concentrate addition and temperature at constant water activity. The monolayer moisture content values of cassava starch–soy protein concentrate edible films decreased with increase in temperature and soy protein level. GAB and Oswin models (%RMS ≤10) best described the isotherms of the biofilms with the monolayer moisture contents, isosteric enthalpy and entropy higher for adsorption with significant kinetic compensations. The moisture sorption and thermodynamic properties of cassava starch–soy protein concentrate edible films showed that they are suitable for packaging applications.     

MOISTURE ADSORPTION ISOTHERMS AND ISOSTERIC ENERGY FOR ALMOND

The equilibrium moisture contents of almond were determined using the gravimetric‐static method at 15, 30, 55 and 75C for powder and 15, 55 and 75C for nut state of almond for water activity (a_w) ranging from 0.11 to 0.87. At a given a_w, the results show that the moisture content decreases with increasing temperature. The experimental sorption curves are then described by the BET, GAB, Henderson, Oswin, Smith and Halsey models. A nonlinear regression‐analysis method was used to evaluate the constants of equations. The GAB model was found to be the most suitable for describing the sorption curves; the monolayer‐content values for the sorption at different temperatures are calculated. Also, the isosteric heats of adsorption of water were determined as a function of moisture content from the equilibrium data at different temperatures using the Clasius‐Clapeyron equation.     

Equilibrium moisture content and sorption isosteric heats of five wheat varieties in China

The moisture sorption isotherm data of five Chinese wheat varieties were investigated via the gravimetric static method at five different temperatures (10, 20, 25, 30, and 35 °C) and relative humidity ranging from 11.3 to 96.0%. The sorption data of wheat decreased with an increase in temperature at a constant relative humidity (r.h.). The hysteresis effect was observed between adsorption and desorption isotherms. The width and span of the hysteresis loop decreased with increased temperature, but was not influenced by the hardness of wheat varieties. Six models, namely the Chen-Clayton (CCE), Modified BET (BET), Modified-Chung-Pfost (MCPE), Modified-Henderson (MHE), Modified-Oswin (MOE) and Strohman-Yoerger (SYE), were employed to describe the experimental data. The BET, MCPE and MOE models were selected to best describe the sorption isotherms of wheat in the ranges of 11.3-49.9, 11.3-96.0 and 11.3-96.0% r.h., respectively. The hygroscopic property difference between hard wheat (cv. ‘Longyuan’ and ‘Nanduan’) and soft wheat (cv. ‘Zhaozhuang’ and ‘Lumai’) was very small. The sorption isosteric heat of wheat decreased with an increase in moisture content until the dry bulb moisture content (m.c.) of 20% was reached, and then decreased smoothly with increasing moisture content. A big difference was found between adsorption and desorption isosteric heats of wheat below 20% m.c., but the sorption isosteric heat difference between hard and soft wheat isotherms was small.     

魔芋葡甘聚糖及其衍生物保湿性能研究

考察魔芋葡甘聚糖(KGM)及其衍生物魔芋超强吸水剂(KSAP)的吸湿、保湿性能,并与甘油、丙二醇进行对比。测定KGM 和KSAP 的水分吸附等温线,采用回归分析建立数学模型。结果表明：KSAP 的吸湿、保湿性能优于甘油和丙二醇。水分吸附等温线属于第Ⅲ型,在给定的水分含量下,KSAP 的水分活度最低,保湿性能最好。Peleg 模型拟合效果最好,BET 模型和GAB 模型拟合显示KSAP 的单分子层水分含量最高,分别为14.59%和15.42%。     

Effect of Cooking on Moisture Sorption Isotherms of Shea Nut (Vitellaria paradoxa Gaertn.) Kernels Part II: Modelling and Properties of Sorbed Water

An investigation was undertaken in this work to model the sorption isotherms of cooked and raw shea nut kernels determined by the standard static gravimetric method. The GAB, Halsey and Caurie models were validated and used in describing the sorption behaviour of the kernels. The monolayer moisture contents derived from Caurie’s equation for the desorption of cooked and raw kernels at 40, 50 and 60 °C were 5.49, 4.40 and 2.65 % and 5.22, 3.68 and 2.47 %, respectively. Monolayer moisture contents obtained from the GAB model showed a similar variation. As the temperature of sorption increased from 40 to 60 °C, the number of adsorbed monolayers (N), the surface area of adsorbent (A) and the percent bound water decreased significantly (p?<?0.05). It is suggested that the sorption process at all temperatures is multilayered. Desorption isosteric heats were lower for cooked kernels than the raw ones, while the reverse phenomenon was obtained for the adsorption process. It was established that, during storage, cooked kernels adsorbed moisture more slowly, suggesting that they could be stored for a longer period compared to the raw ones.     

Desorption isotherms for fresh beef: An experimental and modeling approach

Desorption isotherms for fresh beef were determined at 30, 40 and 50 °C by the static gravimetric method. The resulting isotherms exhibited a type II sigmoid shape. The BET, GAB and Halsey models were used to fit these experimental data. The GAB model was most accurate for all temperatures and all levels of water activity, followed by the BET and Halsey models. The temperature dependence of GAB constants was estimated. The isosteric heat of desorption and its evolution in relation to moisture content were calculated using Clausius–Clapeyron equations. The monolayer moisture content was determined using the GAB model: it decreased as the temperature increased. The density of bound water, the number of adsorption sites, the sorption surface area and the percentage of bound water were calculated using the Caurie equation: all these quantities decreased as the temperature increased. The Kelvin and Halsey equations were used for calculation of pore size, which increases with an increase in moisture levels and sorption temperature.     

Moisture sorption characteristics of dried acid casein from buffalo skim milk

Adsorption and desorption isotherms of dried acid casein prepared from buffalo skim milk were determined at 25°, 35° and 45 °C over a water activity range of 0.11-0.97 using static moisture gain/loss from test samples. Both the adsorption and desorption isotherms exhibited sigmoid shape corresponding to type II, typical to many foods. There was generally a negative temperature effect on equilibrium moisture content. The effect of temperature was, however, statistically not significant over the temperature range of 25-45 °C. Of the seven sorption models tested for fitting the sorption data, the GAB model gave the best fit at all the three temperatures. The temperature dependence of GAB parameters has been determined in the form of Clausius-Clapeyron equation. The calculated values of monolayer moisture content from BET isotherm equation have been found to be lower than the corresponding values found by using GAB equation. However, in both cases the monolayer moisture was higher in desorption than the adsorption and deceased with increase in temperature. The net isosteric heat of sorption decreased exponentially with increasing moisture content and approached a constant value of 0.331 kJ/mol at moisture content 28 g/100 g (d.b.). The moisture sorption hysteresis observed at 25°, 35° and 45 C was statistically significant. The extent of hysteresis was negligible in monolayer moisture content region, occurred predominantly in the water activity range 0.35-0.60 and decreased at higher water activities. Total hysteresis energy was evaluated from the sorption data using Everett and Whitton plot. The effect of increase in temperature was to decrease the amount of hysteresis.     

Moisture sorption isotherms – Experimental and mathematical investigations of orange (Citrus sinensis) peel and leaves

The aims of this work were to determine chemical composition and sorption isotherms of Tunisian orange peel and leaves of the “Maltaise” variety. These by-products were found to be rich in fibre, soluble sugars, protein, minerals and phenols. The equilibrium moisture contents of “Maltaise” peel and leaves were measured using the static gravimetric method at three temperatures (40, 50 and 60 °C) and in wide range of water activity (0.109–0.891). Desorption and adsorption data of peel and leaves were best fitted by the Peleg model at 40, 50 and 60 °C. The net isosteric heats of desorption and adsorption were determined from sorption isotherms. For both peel and leaves, the net isosteric heat of desorption was higher than the net isosteric heat of adsorption and both decreased continuously with increasing of the equilibrium moisture content.     

Desorption Isotherms and Isosteric Heat of Three Tunisian Date Cultivars

The sorption isotherm of three Tunisian cultivars, Allig, Kentichi, and Deglet Nour, were obtained at 40, 60 and 80 °C. The static gravimetric method was used, according to the COST 90 recommendations. The overall shape of the curves describing the water content as a function of water activity was typical of sugar-rich materials. A difference between varieties exists for the sorption isotherm, thus for the drying behavior. Data were compared with respect to several isotherm models. It was found that the GAB and the BET equations could satisfactorily represent the sorption data up to about 0.9 relative humidity. Through the BET equation, monolayer moisture content was calculated for the isotherm zone corresponding to monomolecular adsorption. In addition, isosteric heat of sorption was determined from sorption data using the Clausius–Clapeyron equation.     

方便米粉的水分吸附和热力学特性

为了给方便米粉的加工和贮藏过程提供理论指导,根据吸附原理,在环境温度分别为15、25 ℃和35 ℃时,采用静态称量法研究方便米粉的吸附等温线。采用7 个常见的非线性回归方程对吸附实验进行拟合,以决定系数、平均相对偏差和标准估计误差为评价指标,确定最佳拟合模型及其参数,探讨方便米粉水分吸附过程中净等量吸附热、微分吸附熵和焓熵互补等热力学性质的变化。结果表明,方便米粉的水分吸附特性属于II型等温线,Peleg和GAB模型都适合描述方便米粉的水分吸附特性。用GAB模型拟合得到的单分子层水分含量X0在15、25 ℃和35 ℃下分别为9.23%、8.34%和7.65%（干基）。在水分吸附过程中,方便米粉的净等量吸附热和微分吸附熵都会随着平衡水分含量的升高而明显下降;同时,存在焓熵补偿现象;根据实验结果绘制净等量吸附热与微分吸附熵的关系图,计算获得方便米粉的吸附过程属于焓驱动和自发过程。本研究对方便米粉贮藏条件选择和进一步评估不同贮藏条件下方便米粉的贮藏期具有指导作用。     

Sorption Isosteric Heat Determination by Thermal Analysis and Sorption Isotherms

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.     

Sorption isotherms and thermodynamic properties of freeze‐dried colostral whey powders with different additives

Moisture adsorption isotherms of colostral whey (CW) powders with different additives (maltodextrin and sucrose) were determined using gravimetric static method at 15–35 °C in the water activity range of 0.067–0.76. The moisture adsorption isotherms obtained were typical sigmoid curves, and the modified‐Halsey and Guggenheim–Anderson–de Boer (GAB) equations gave the best fit to experimental data among five well‐known equations. Addition with maltodextrin into CW powders could effectively decrease equilibrium moisture content (EMC), whereas addition with sucrose increased EMC in the water activity of 0.43–0.76 at 15 and 25 °C and in the water activity of 0.21–0.76 at 35 °C, respectively. Thermodynamic properties including net isosteric heat of sorption and differential entropy were determined from adsorption data using Clausius–Clapeyron equation. The results showed that net isosteric heat of sorption of all the samples decreased exponentially with increasing EMC. Enthalpy–entropy compensation theory was applicable for adsorption process of all the samples, and the adsorption processes were enthalpy‐driven.