Misapplication of the Clausius–Clapeyron equation for estimating heats of adsorption in foods

It has been pointed out that the Clausius–Clapeyron equation which is currently used to measure isosteric heat of adsorption in reality measures the latent heat of evaporation. The usual Clausius–Clapeyron plot that decays rapidly to low values at low Aws has been compared with a suggested alternative equation derived directly from an expanded form of Caurie's unimolecular adsorption equation. The plot of the proposed equation is higher than that of the Clausius–Clapeyron equation, and it has the shape of an inverse sigmoid isotherm. Two discontinuities in the proposed plots are stated to demarcate three energy levels corresponding to three states of bound water recognised to exist along sigmoid food isotherm plots.     

Sorption isotherms,GAB parameters and isosteric heat of sorption

The diffusion–sorption drying model has been developed as a physics‐based way to model the decreasing drying rate at low moisture contents. This new model is founded on the existence of different classes of water: free and bound water. The transition between these classes and the corresponding thermodynamics form distinct components of the drying model. This paper shows that the characteristics of the different classes of water and of the transition between them can be deduced from the GAB sorption isotherm. The parameters in the GAB sorption isotherm support the theory of localised sorption, establishing the existence of different classes of water. Moreover, the sorption mechanism retrieved from the GAB parameters is in accordance with the sorption mechanism, which is obtained from the moisture dependence of the net isosteric heat of sorption. This holds for experimental sorption data of corn and starch as well as for literature data on five vegetables and four fortified cassava products. An extremum in the net isosteric heat of sorption coincides with the transition between bound and free water, and the partition moisture content corresponds with the monolayer value derived from the GAB equation. This confirms that the GAB monolayer value can be chosen as model boundary between bound and free water. Moreover, it reveals that this method can be developed into a technique to estimate the bound water content in foods. Copyright © 2005 Society of Chemical Industry     

A new method for predicting sorption isotherms at different temperatures: Extension to the GAB model

In this work, the new methodology for parameter estimation using less experimental data proposed in Staudt et al. (2013) is extended to be used with the GAB model. In addition, a modification in the Arrhenius form for temperature dependency of the energetic constant C is proposed in order to avoid numerical instabilities during parameter estimation. When compared to the original work, one additional parameter, k needs to be estimated but still only one isotherm and one value of net isosteric heat of sorption is required to build the whole set of sorption isotherms. Different food materials were successfully tested providing good fitting and prediction results attesting that the advantages of the methodology originally developed for the BET model are kept with the GAB model.     

The unimolecular character of the classical Brunauer, Emmett and Teller adsorption equation and moisture adsorption

A reformulation of the classical Brunauer, Emmett and Teller multimolecular adsorption equation resulted in a unimolecular equation in which a third parameter was introduced into general statements. The third parameter represented adsorption centres on the unimolecular surface. This parameter modified the constant C in the BET equation to C^1/n which, on analysis, was found to measure the density of the most strongly adsorbed molecules. The new equation, which was shown to apply to all isotherm shapes, delineated limits between which three states of unimolecularly adsorbed molecules could be identified along the isotherm. It also provided a new method for calculating the net heat of adsorption, which is identical with the Clausius–Clapeyron equation at low values of Aw. The equation also explained the phenomenon of adsorption compression in sorption studies and this was because of the increased density of primary adsorbate molecules at low values of Aw.     

Thermodynamic properties of moisture adsorption of whole wheat flour. Calculation of net isosteric heat

The moisture sorption isotherms of whole wheat flour were determined at 10, 20 and 30 °C over a relative humidity range of 10–90%. Two models were applied to the sorption experimental data: the Guggenheim–Anderson–de Boer (GAB) and the Caurie models. The goodness of fit of the mathematical models was statistically evaluated by means of the root mean square per cent error (%RMS), obtaining values between 1.44 and 1.05 for GAB, and between 2.69 and 2.57 for the Caurie model. Hence, both models provided a good fit to the experimental data. The isosteric heat of sorption was calculated using two methods: the Clausius–Clapeyron expression and the Caurie equations, showing in both cases maximum values (11.03 and 12.39 kJ mol^?1, respectively) when moisture content was minimum (2.5 g H₂O per 100 g dry matter), and gradually diminishing to the value of the heat of vaporisation of pure water when moisture content reached a maximum value.     

Water vapour sorption behaviour of original and defatted wheat gluten

The water vapour sorption isotherms of original and defatted gluten samples, prepared from two wheat cultivars (Spring and Taurus) with good and poor baking performance, respectively, were investigated at 25 and 40°C. The GAB isotherm equation described the isotherms well up to a relative humidity of at least 84% at 25°C and up to 75% at 40°C. The GAB constants of Spring gluten indicated an increased number of adsorption sites and a decreased average interaction energy per binding site at increased defatting (petroleum ether, chloroform). This tendency was also observed for Taurus, however, here no significant differences were found between the solvents. When comparing both cultivars the isotherm analysis indicated less available active sites for water adsorption with a stronger interaction energy per site for Taurus gluten. This stronger interaction is in accord with the higher isosteric heat of adsorption (Clausius-Clapeyron analysis) found at low relative humidities. These findings are related to bread baking performance.     

Moisture adsorption isotherms of Tarhana at 25 °C and 35 °C and the investigation of fitness of various isotherm equations to moisture sorption data of Tarhana

Moisture adsorption isotherms of Tarhana were determined at 25 °C and 35 °C. As the temperature increased, the adsorbed moisture content decreased at water activities between 0.2 and 0.9. The experimental sorption data obtained were applied to the Halsey, Harkins‐Jura, Smith, BET and Freundlich isotherm equations to test fitness of these equations to Tarhana. The order of best fit or sorption data obtained for Tarhana was Halsey > Harkins‐Jura > Smith > Henderson > BET > Freundlich. The obtained sorption data fitted the Halsey, Harkins‐Jura and Smith isotherm equations quite well in the 0.2–0.9 water activity range; However, the best fit was obtained in the Freundlich, BET and Henderson isotherm equations in this water activity range. © 2000 Society of Chemical Industry     

广义GAB方程拟合小麦和大米吸着等温线研究

测定粮食平衡水分的难度是在水分活度(aw)≥0.8时粮食易发霉.假定标准GAB方程的参数C不是常数,而是水分活度aw的多项式函数,提出广义GAB方程aw/M=a+∑biaw,式中n是多项式次数,a、bi(i=1,n)多项式的系数.该方程的优点是能够拟合aw在0～1范围的吸附数据.广义GAB方程适合拟合我国小麦和大米品种的平衡水分实测数据.这为粮食水分吸附光谱分析提供基础.     

采用离子交换吸附对蛹虫草中虫草素的提取研究

采用超声波法对蛹虫草中虫草素进行粗提,筛选得到了最佳吸附介质阳离子树脂001×16,该介质对虫草素的吸附特性,包括吸附等温线、吸附动力学条件等进行了探讨。结果表明,001×16对虫草素的吸附等温线符合Langmuir方程,最佳吸附条件为pH值为4.0,温度15℃,吸附时间3 h。在此优化条件下,虫草素最大吸附量可达到1.3 mg/g。     

Influence of Roasting on the Water Sorption Isotherms of Argentinean Algarroba (Prosopis alba Griseb) Pods

Prosopis alba is an arboreal legume that occurs naturally in Argentine. Its fruits (algarroba or Prosopis pods) are dried or roasted, ground and then used in foods and feeds. The influence of roasting process on the water sorption isotherms of Prosopis pod flour at three storage temperatures was studied. The equilibrium data for each sorption isotherm were determined by the standard static gravimetric method. Experimental values were fitted to the BET and GAB sorption models. Type II isotherms were obtained according to Brunauer classification. The calculated isosteric heats of sorption (Qs) near the monolayer moisture content were 7.30 and 7.68 kJ/mol for raw and roasted flour, respectively. The results showed that roasting did not significantly change the behavior of the products with regard to water adsorption, although a slight reduction of the tendency to humectation was observed, this being somewhat less spontaneous. In this aspect, the stability of Prosopis flour is similar in the raw and roasted states.     

Equilibrium Water Content and the State of Water in Dehydrated White Cabbage

The water sorption isotherms for freeze-dried cabbage were determined at 15°C and 23°C, and the state of the water was studied using differential scanning calorimetry (DSC). The water sorption capacity of the freeze-dried cabbage depended on the temperature. The effects of free sugars were clear in both adsorption and desorption. The thermal behavior of freeze-dried cabbage was highly moisture dependent. In the capillary condensation range (>0.9 a_w) solution of low molecular components of the freeze-dried cabbage affected its freezing behavior.     

Sorption isotherm of corn distillers dried grains with solubles (DDGS) and its prediction using chemical composition

Corn distillers dried grains with solubles (DDGS) has high feed value due to its nutritive contents. The ratio of wet distillers grains (WDG) and condensed distillers solubles (CDS) added during the production process determines the chemical composition of DDGS. Effect of changing this ratio on water sorption behaviour of DDGS, at different temperature, was studied. Five mathematical models were evaluated to explain the sorption behaviour of DDGS. Prediction of sorption isotherm from chemical composition using a four-component model was also investigated. DDGS followed a BET Type III isotherm with higher equilibrium moisture content at increasing relative humidity. Difference in the sorption isotherm curves of DDGS samples reduced as equilibrium relative humidity increased. Equilibrium moisture content of DDGS samples reduced with lowering of CDS quantity added during production process. Modified Halsey equation was found suitable for mathematically explaining the sorption behaviour of DDGS. Binding energy of water molecule with DDGS increased with lowering of CDS level. Sorption behaviour of DDGS can be predicted from the chemical composition of protein, sugar, minerals, starch, fibre and glycerol. Increase in CDS level increased the percent relative deviation of predicted values calculated using the modified four-component model and might be due to the interaction between the chemical compounds present in the samples.     

碱性吸附剂稳定性及其在油脂脱酸中吸附平衡作用

分别探讨自制碱性吸附剂酸稳定性和热稳定性,并将其应用到油脂脱酸工艺中。试验结果表明,碱性吸附剂在pH<2时不稳定,150℃处理对其脱酸效果有较大影响;其直线型吸附等温线方程为:Xe/q=0.0046Xe+0.0177,饱和吸附容量达217.39 mg/g。     

豆粕平衡水分及吸着等热研究

采用静态称重法测定了国产6个豆粕样品的平衡水分吸附/解吸等温线,并采用修正MCPE、MHAE、MHE、MGAB、MOE及STYE 6个方程进行拟合,得出MGAB、MHAE、MOE均适合描述豆粕平衡水分-平衡相对湿度之间的关系,并可用于分析豆粕水分吸附/解吸等热。当水分小于15%时,豆粕吸附/解吸等热均随水分增大而快速减小,同温度下的解吸吸着等热显著高于吸附吸着等热。当水分大于15%时,豆粕吸附/解吸等热均随水分增大而变化平缓,同温度下的解吸吸着等热趋同于吸附吸着等热。当水分小于15%时,较低温度下的豆粕吸附吸着等热与解吸吸着等热均高于较高温度下的。在水分17.5%的游离水临界点,豆粕的吸着等热(汽化热)接近纯水的潜热,约为2 500 kJ/kg。由等温线分析的25℃豆粕绝对安全水分为12.48%,相对安全水分为13.90%。     

马铃薯全粉平衡水分吸附等温线与吸附等热研究

采用静态称重法在温度10～35℃、相对湿度11%～96%范围内测定了五种马铃薯全粉的平衡水分/平衡相对湿度(EMC/ERH)数据,确定了多项式方程、修正3参数Guggenheim-Anderson-de Boer(MGAB)、修正Halsey(MHAE)、修正Oswin(MOE)为适合的等温线拟合方程,采用多项式EMC方程分析马铃薯全粉的安全储运最大允许的含水率,在25℃、RH60%条件下,绝对安全水分是10.05%;在25℃、RH 70%条件,相对安全水分是12.64%。采用MHAE分析马铃薯全粉水分吸附等热,随着含水率增加到17.5%,马铃薯全粉水分吸附等热则以抛物线形式快速地减少,之后随着含水率增加,水分吸附等热则减少缓慢。在含水率22%,马铃薯全粉水分吸附等热接近纯水的吸附等热。     

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。     

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.     

面包吸附等温线的测定及测定方法比较

目的：研究不同方法对测定面包吸附等温线的影响及在25 ℃下面包含水率与水分活度的关系。方法：采用饱和盐溶液法（SSS）、动态水分转移规律分析仪法（DWT）和动态蒸汽吸附法（DVS）测定面包在25 ℃下和0.100～0.902水分活度范围内的水分吸附等温线,采用7种吸附模型拟合结果。结果：面包的吸附等温线属于Ⅱ型曲线。采用SSS法和DWT法测定整个面包吸附等温线的最佳拟合模型分别为Halsey模型和Peleg模型;采用DVS法测定面包瓤和面包皮吸附等温线的最佳拟合模型分别是Halsey模型和Oswin模型。同时,SSS法不限制面包体积和质量,但试验用时较长且高湿度下难以提供稳定湿度环境;DWT法不限制面包体积和质量且能提供稳定的湿度条件;相对于SSS法和DWT法,DVS法尽管可快速得到面包水分吸附等温线的结果,但该方法限制了面包的质量和体积且无法同时进行平行试验。结论：DWT法更适合面包吸附等温线的测定。     

Sorption isotherms and isosteric heat of sorption for grapes, apricots, apples and potatoes

Moisture sorption isotherms of grapes, apricots, apples and potatoes were determined at 30°C, 45°C, and 60°C using the standard, static-gravimetric method. Six two-parameter and five three-parameter sorption models were tested to fit the experimental data. A nonlinear regression analysis method was used to evaluate the constants of the sorption equations. The Halsey equation gave the best fit to the experimental sorption data for all materials tested over the range of temperatures and water activities investigated. The GAB model gave also the closest fit to the sorption data for potatoes and grapes. The agreement between experimental and predicted values of these models was found to be satisfactory. The isosteric heat of desorption and adsorption of water determined from the equilibrium data using the Clausius-Clapeyron equation.