GAB Equation Research Articles

Morphology and functional properties of corn, potato and tapioca starches

In this study, morphology and functional properties of commercial native corn, potato and tapioca starches were evaluated. Morphological study with light and scanning electron microscopy revealed that these starches had unique granule characteristics. The starches were observed to be almost insoluble in water at 20 °C but upon heating to 70 °C, they were solubilized in water to an extent of 3.89, 13.49 and 14.36% for corn, potato and tapioca starches, respectively. Among these, corn starch held less water as compared to potato and tapioca starches. The viscosity of starches was almost same at low concentration (0.1%, w/v) but increased curvilinearly with the increase in concentration to 0.5% in ascending order for tapioca, corn and potato starches and at high concentration (5%, w/v) they showed shear thinning behaviour. Corn starch exhibited high viscosity stability to shear. The pasting curves of starches during cooking, using rapid visco-amylograph indicated that corn showed higher degree of crystallinity since it gelatinized apparently at higher temperature. Other pasting properties of starches like peak viscosity, final viscosity and breakdown were higher for potato compared to corn followed by tapioca but the setback tendency gave an opposite trend. Potato starch gelled at lower concentration followed by corn and then tapioca starches. Texture profile analysis results showed that potato starch gel was harder, sticky, gummy and chewy than that of corn and tapioca starch gels. The moisture sorption isotherm described with the help of GAB equation revealed that potato starch had higher heat sorption and monolayer moisture content compared to corn and tapioca starches.

Modeling of the Equilibrium Moisture Content (EMC) of Tarragon (Artemisia Dracunculus L.)

The equilibrium moisture content of tarragon, Artemisia dracunculus L. (stem and leaf separately) was determined by using the saturated salt solutions method at three temperatures (25, 50 and 70°C) within a range of 5 to 90% relative humidity. Both adsorption and desorption methods were used for stem and leaf of two varieties: Russian and French tarragon. Experimental curves of moisture sorption isotherms were fitted by modified Henderson, modified Halsey, modified Oswin, modified Chung-Pfost and GAB equations and evaluated by residual sum squares, standard error of estimate and mean relative deviation. The modified Halsey and GAB equations were found to be the most suitable for describing the relationship among equilibrium moisture content, relative humidity and temperature. There was no significant difference between the equilibrium moisture content of the Russian and French tarragon.

The derivation of the GAB adsorption equation from the BDDT adsorption theory

SummaryThe BET‐like adsorption equation, popularly known as the GAB equation, was derived from the BDDT adsorption equation without changes to the bulk liquid properties of multilayer molecules. Without these changes the third parameter K in the GAB equation cannot be said to measure changes in the bulk liquid properties of the multilayer molecules. Instead K measures the range of application of the GAB equation and differentiates multilayer adsorption, when K > 0.5, from singular layer adsorption, when K ≤ 0.5. The GAB equation, derived from and based on the BDDT theory is argued, in this paper, to provide a greater insight into the mechanism of water adsorption than the same equation derived from and based on the BET theory.

Description of organic compound vapor-phase sorption by geosorbents: Adequacy of the isotherm approximation

The approximation of isotherms of vapor-phase sorption of organic compounds (OC) is a long-standing problem. It is especially difficult to solve in case of natural heterogeneous sorbents (soils, sediments, aquifers, etc.) since these sorbents contain sites with different sorption activity. The aim of this work was the statistical evaluation of the adequacy of the approximation of isotherms of vapor-phase sorption of OC by geosorbents in water-unsaturated conditions by employing various fitting equations. Vapor sorption isotherms were measured by the static headspace gas-chromatographic analysis method for 27 various organic sorbates (13 hydrocarbons and 5 chlorinated hydrocarbons, 7 oxygenated and 2 nitrogenated OC) on geosorbents (6 soils typical for Middle Russia regions, separate soil layers of 2 dark-gray forest soils, natural zeolite-containing material and bentonite clay, and two clay-humic complexes). The computer-assisted special sorption database with the corresponding software was created, and on the whole, 103 experimental sorption isotherms (86 isotherms measured and 17 taken from the literature) were used for the approximation. The adequacy of isotherm approximation by different sorption models was compared: Brunauer–Emmett–Teller (BET), modified BET (MBET), Pickett–Dellyes (PD), Guggenheim–Anderson–De Boer (GAB), Aranovich–Donohue (AD), Hinz (HZ) and polynomial (PN) equation. For the comparison of the adequacy of isotherm approximation by different equations, the following three criteria were used: (a) s 5%—the average probability of the location of experimental sorption values within the range of 5% of the theoretical curve; (b) two interconnected parameters: R 2—the square of correlation coefficient and k—the slope tangent for the linear regression ( V E; V T) at various sorbate activities; (c) D ¯ —relative sample variance as a characteristics of the optimal ratio between numbers of parameters of the fitting equation and its approximation quality. For the description of the vapor sorption of OC by geosorbents, the new MGAB equation (the modified GAB equation) was suggested. It is characterized by the optimal ratio between the ‘complexity’ of an equation (MGAB is a four-parametrical equation) and its approximation quality (MGAB shows one of the best isotherm approximations). The following rank of the decrease of the adequacy (upon D ¯ criterion) of examined fitting equations in relation to the OC sorption isotherm approximation in the whole isotherm range was formed: MGAB > HZ > PD > GAB > AD > PN.

Moisture sorption characteristics of tropical fresh water crayfish ( Procambarus clarkii)

Moisture sorption characteristics of crayfish ( Procambarus clarkii) were investigated at 25E, 30E, 40E, and 50EC using gravimetric method and the results analyzed according to various sorption isotherm models. The heats of moisture adsorption and desorption were estimated from equilibrium sorption data using the Clausius–Clapeyron equation. Equilibrium moisture content decreased with increase in temperature but increased with increase in water activity. Both adsorption and desorption isotherms were sigmoidal in shape (type II). The Henderson, GAB and Oswin equations provided good fit to experimental data (<10%RMS) for adsorption and desorption. The heats of desorption were higher than the heats of adsorption, indicating a significant hysteresis in moisture sorption by crayfish. Net isosteric heats of adsorption and desorption varied from 21.1 to 2.4 kJ/mol and 28.9 to 3.5 kJ/mol respectively while entropy of adsorption and desorption varied from −0.053 to −0.006 kJ/mol °C and −0.076 to −0.009 kJ/mol °C respectively within moisture contents range of 2.0 to 12.0 g H 2O/100 g solids.

Water desorption characteristics of raw goat meat: Effect of temperature

Moisture desorption isotherms of raw goat meat were obtained at 10, 25 and 50 °C. Sigmoid desorption isotherms were observed for these samples. The sorption data were analyzed using mathematical equations of BET, Caurie, Halsey, modified Mizrahi, Oswin and GAB. The modified Mizrahi and GAB equations gave the best fit over the entire temperature range. The temperature dependence of GAB constants was evaluated and excellent fit was obtained. The net isosteric heats of sorption were calculated by applying Clausius–Clapeyron equations. The GAB and BET monolayer moisture values were not significantly different ( P > 0.01) and decreased with increasing temperature. Number of adsorbed monolayers, density and amount of bound water and surface area of adsorption (Caurie’s equations) also decreased as the sorption temperature increased. The pores, in general, enlarged with rising temperature.

Water adsorption isotherms of texturized soy protein

Texturized soy proteins (TSP) have been used for many years as a substitute of animal protein. In recent times, TSP was used as a functional ingredient in several food applications; its process involves a drying step. The water adsorption isotherms of TSP were determined using the static method of saturated salt solutions at 10, 20, 30 and 40 °C. The experimental data were fitted to Oswin, Halsey, BET, GAB, Peleg and Darcy Watt models. The equilibrium moisture content at water activities up to 0.9 decreased as the temperature was increased from 20 to 40 °C. At higher water activities, the moisture content showed an inverse behavior, resulting a crossover of the isotherms. The GAB and Peleg equation showed the best fit for the experimental curves. The total heat of sorption of TSP increased with decreased moisture content.

Sorption isotherms of shelled and unshelled kernels of candle nuts

The sorption isotherms of candle nuts, unshelled and shelled kernel samples, were measured at temperatures of 30, 40, 50, and 60 °C by a static gravimetric method. The unshelled kernel samples had a higher equilibrium moisture content than shelled kernel samples at all tested conditions. In both samples, hysteresis was pronounced and decreased as the temperature increased. The isosteric heat of desorption, calculated using Clausius–Clapeyron equation, was higher than the isosteric heat of adsorption. The GAB equation gave satisfactory goodness of fit to unshelled kernel samples data with the average of correlation coefficient, r 2, greater than 0.99 and the mean relative deviation, MRD, less than 0.05.

Sorption isotherms, GAB parameters and isosteric heat of sorption

AbstractThe 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

입자크기에 따른 분말 녹차의 흡습특성

분말녹차의 저장안정성을 알아보고자 200 mesh이상, 200~140 mesh, 100~140 mesh로 입자크기에 따라 분급하여 흡습특성을 조사하고 수분활성도 예측 모델식을 수립하였다. 단분자층 수분함량은 BET식보다 GAB식이 더 높은 유의성을 보여 전구간에서 0.99~1.00으로 높은 적합도를 보였으며 그 함량은 0.024~0.052 g H₂O/g dry solid로 계산되었다. 평형수분함량은 입자크기에 작을수록, 낮은 온도에서 높은 평형수분함량을 나타내었다. 입자크기에 따른 흡습엔탈피도 큰 차이가 없었으나 수분활성도가 증가함에 따라 낮은 흡습에너지를 보였다. 등온흡습곡선의 적합도는 Halsey 모델이 R2가 0.96 이상으로 높은 적합도를 나타내었고 Oswin, Khun, Caurie 모델의 순으로 높은 적합도를 나타내었으며, 편차도 Halsey 모델이 2.1~4.0%로 가장 낮게 나타나 분말 녹차의 흡습특성에 적용가능함을 보였다. 수분활성도 예측모델의 수립을 위해 각 독립변수의 최적함수로 시간은 ln 함수, 상대습도와 온도는 일차식을 선정하였으며 수분활성도 예측 모델식은 입자의 크기에 관계없이 상대습도와 시간으로 수립한 모델식의 적합도가 적절한 것으로 나타났다.

An improved experimental and regression methodology for sorption isotherms

AbstractSorption isotherms of corn and starch cylinders with immobilised catalase are experimentally determined at different temperatures for use in drying models in optimal control studies. This application of the sorption isotherm requires an accurate prediction of the sorption data at different temperatures for the low water activity range. The GAB equation is used for the prediction of the sorption isotherms. Two major problems are encountered by employing standard procedures, ie prediction of sorption at aw &lt; 0.11 and sensitivity of the GAB parameters to the applied data range. An improved methodology is developed, consisting of extending the standard experimental procedure with additional data points in the low water activity range and changing the criterion in the regression procedure in the sum of squares, which is weighed by the variance of the experimental data. The new methodology leads to accurate, consistent and physically relevant parameters of the GAB equation, which are independent of the applied data range in the regression analysis and which result in accurate predictions of the sorption behaviour at low water activity. The sorption data at different temperatures at low water activity can be predicted in the best way with parameters obtained after direct regression based on weighed SSQ. Copyright © 2004 Society of Chemical Industry

Moisture adsorption behaviour of semolina and farina

Moisture adsorption isotherms of semolina (from hard wheat) and farina (from soft wheat) were determined at 20, 35, 50 and 60 °C using the isopiestic method. The adsorbed moisture content significantly affected ( p < 0.05) product type, temperature and water activity. Moisture up-take accelerated about 0.75 water activity. The experimental sorption data obtained in this study were applied to Halsey, Harkins-Jura, Henderson, Iglesias-Chirife, Smith BET, GAB isotherm equations to predict the sorption behaviour of semolina and farina. Henderson, Halsey and GAB equations were found to be the most suitable model to describe the isothermal water sorption of semolina and farina at 0.1–0.9 water activity range. Monolayer moisture contents ( m 0) for two products were calculated from BET and GAB equations. The m 0 values of both models decreased with increasing temperature. The values of m 0 of semolina and farina at 20 °C were 11.8 and 9.16 g/100 g calculated with GAB, respectively. Adsorption isosteric heat ( Q s) decreased; the maximum heat of adsorption was obtained in the moisture content 6–7% and was higher for semolina (15.2 kJ/mol) than farina (14.34 kJ/mol). The Q s value quickly decreased with increase in moisture content to approximately 15% and then was plateau on axis of moisture content. Semolina and farina must be storage below 75% relative humidity at 20 °C prevents caking and deterioration because moisture sorption acceleration was increased after 0.75 a w. The moisture content of the products in this storage conditions could be approximately 12.5%.

Assessment of two‐ and three‐parameter Lewicki models for description of sorption phenomena of starch materials

AbstractExperimental moisture sorption isotherm data for raw potato, starch gels (potato, starch–sugar and starch–salt) and starch powders (potato, highly amylopectin and highly amylose) were determined using a gravimetric static method at 30, 45 and 60 °C and over a relative humidity range 0.10–0.84. The raw potato, starch powders and starch gels exhibited type II behaviour, with type III form being observed on incorporation of sugar, or salt, into the starch gel matrix. The two‐parameter Lewicki relationship, and the three‐parameter Lewicki and GAB equations were considered for description of the experimental data. A nonlinear least square regression technique was used to evaluate the constants for the models. The three‐parameter Lewicki model was found to be the most suitable for describing the sorption characteristics of raw potato, potato starch, starch–sugar and starch–salt gels within the investigated temperature and water activity range. However, both Lewicki models gave an inadequate representation of the data for potato, high amylopectin and high amylose starch powders. Copyright © 2004 Society of Chemical Industry

Sorption isotherms for amaranth grains

Compiling of EMC–ERH data for amaranth grains ( Amaranthus cruentus L.) in the range of water activity from 0.029 to 0.979 and temperature from 25 to 90 °C was performed. Included data sets comprised experimental values of EMC–ERH that summarize 78 identified points for desorption, 53 for adsorption and 16 not discerned points that were considered for mean sorption. Five isotherm equations for grains included in the ASAE Standards (Modified Henderson, Modified Chung–Pfost, Modified Halsey, Modified Oswin and GAB) were evaluated for their ability to fit sorption data from the literature ( M e vs. a w for adsorption, desorption and mean sorption). The goodness of fit for each isotherm was quantified through the correlation coefficient ( R 2), the sum of squares (RSS), the standard error of the estimate ( S y ), the mean relative deviation (MRD) and the plots of residuals. The three-parameter GAB isotherm was the best and gave a good correlation ( R 2 > 0.9817, RSS < 0.0293, MRD < 0.1380, S y < 0.0141, and random residuals-plots) for the general data-fit in the range of a w from 0.1 to 0.9, of interest in seed storage and processing. The Modified Halsey equation was rejected because it gave poor statistic parameters of agreement and patterned residual plots. For desorption, the Modified Chung–Pfost model gave the lowest mean relative deviation; the Modified Henderson equation was the second best in describing the EMC–ERH data, followed by the Modified Oswin and GAB models. For adsorption, the GAB equation presented the lesser MRD, followed by the Modified Chung–Pfost, Henderson and Oswin models. When mean sorption data were analyzed, the Modified Chung–Pfost equation was the best. However, when the GAB isotherm was adjusted at each temperature, a higher quality of agreement was obtained compared with the other isotherms, demonstrating the adequacy of GAB model to describe the experimental data of EMC–ERH for amaranth.

Effect of water activity on glass transitions of date pastes

Water sorption isotherms of freeze dried and control (without freeze drying) date paste of cultivar Khalas were obtained at 20 °C using the static saturated salt solution method. The GAB equation fitted adequately for the whole range of water activity for both date paste samples. The monolayer moisture contents ranged between 0.102 and 0.12 for freeze dried and control samples respectively. The glass transition temperatures of saturated salt equilibrated paste samples were measured using a differential scanning calorimetry (DSC). Glass transition temperature of both samples decreased linearly with an increase in water activity. Water adsorption characteristics of freeze dried and control samples differed from each other and were supported by glass transition temperatures.

Grain sorption equilibria of quinoa grains

Quinoa has been identified as a promising source of food. Reports in the literature have focused mainly on agronomic potential, composition, nature of the starch and protein quality. Other aspects related with drying and storing of quinoa seed have received less attention. Moisture sorption isotherms constitute an essential part of the theory of drying and in the study of storage of dehydrated foods. Vapour water sorption of quinoa grains was determined at 20, 30 and 40 °C in the range of 0.089–0.851 water activity ( a w) by means of the gravimetric method. Experimental curves were fitted to one three-parameter equation (Guggenheim–Anderson–de Boer, GAB equation). The equilibrium values and temperature shifts were modelled with a three-parameter equation in the approximate moisture content range of 0.02–0.18 (g water/g dry matter). An analytical expression to calculate the isosteric heat of sorption and its moisture content dependence was used and the results were compared with the isosteric heat calculated from the experimental equilibrium data by means of the Clausius–Clapeyron equation. The GAB model describe the sorption isotherms of quinoa grains at different temperatures in the range of a w investigated, the sorption areas obtained from the GAB equation were comparable with other sorption areas reported in the literature for various cereal grains and the effect of temperature on water sorption isotherms is adequately describes by an equation based on the enthalpy-entropy compensation.

Moisture sorption isotherm of fresh lean beef and external beef fat

The moisture sorption isotherm (MSI) of lean beef and fat beef was experimentally determined. The experimental procedure used was that of the COST 90 project with some modifications to accelerate equilibration. The procedure was validated with the standard reference material microcrystalline cellulose. The MSI of the beef at the highest humidity range was obtained by accelerating equilibration with changes of salts, using a low water activity salt for some time. This procedure was reliable for beef samples but not for the fat samples. No significant changes were found for lean beef in the temperature range 5–40 °C. Three models, GAB, Peleg and Lewicki, were used to fit the experimental data. The best fit was obtained with the GAB equation. The fat MSI was determined at 5, 15 and 25 °C and it was best fitted with the Lewicki model.

Drying kinetics of some vegetables

The effect of air conditions (air temperature, air humidity and air velocity) and characteristic sample size on drying kinetics of various plant materials (potato, carrot, pepper, garlic, mushroom, onion, leek, pea, corn, celery, pumpkin, tomato) was examined during air drying. A first-order reaction kinetics model was used, in which the drying constant is function of the process variables, while the equilibrium moisture content of dried products within the range of 0.10–0.90 water activity at two temperatures (30 and 70 °C) was fitted to GAB equation. The parameters of the model considered were found to be greatly affected by the air conditions and sample size during drying. In particular the temperature increment increases the drying constant and decreases the equilibrium moisture content of the dehydrated products.

Water sorption characteristics of six row barley malt ( Hordeum vulgare)

The water sorption isotherms of six-row Belgian barley malt (Plaisant) were determined for a temperature range between 15°C and 35°C. The results obtained showed that for water activity ( a w) values below 0.5 the effect of temperature on the sorption isotherms was negligible. For a w values above 0.5, an increase of the equilibrium moisture content with temperature at a given a w was observed, as reported by other authors in products rich in sugars. Due to the malting process, barley malt presents a higher simple sugar content than nonmalted barley. The experimental data was fit to various sorption models. The constants obtained for each equation and the correlation coefficients were presented. From these, it was found that the Brunauer–Emmett–Teller (BET) and Kuhn models showed the highest correlation coefficients for a w below 0.50. For a w values above 0.50, the best fitting was obtained for the models of Harkins–Jura, Smith and Henderson, although other models such as Freundlich, Chung–Pfost and Guggenheim–Anderson–De Boer (GAB) also showed good fitting. Due to the fact that the practical storage moisture content of barley malt is below 60 g/kg, the BET model (suitable for a w<0.50) would represent the best model to apply for this product. The monolayer water content calculated from the BET and GAB equations ranged between 42.5 and 43.9 g/kg (dry basis), and 46.0 and 51.0 g/kg (d.b.), respectively, for the range of temperature considered in this work (15–35°C). These values corresponded to a w values ranging from 0.16 to 0.19, according to the BET equation and from 0.19 to 0.21 using the GAB equation. The average sorption enthalpy ( Q s) and the total heat requirement (Δ H T) of this process (15–35°C) showed values of 7.787±0.262 and 51.834±0.275 kJ/gmol, respectively.

Water Sorption of Amaranthus cruentus L. Seeds Modelled by GAB Equation

The GAB (Guggenheim, Andersen, and de Boer) equation was adjusted to literature data of sorption of Amaranthus cruentus L. (M e vs. a w for adsorption and desorption) determined at 25, 30, 35, 40, 45, 50, 55, 65, 70, and 90°C, in the range of water activity from 0.029 to 0.979. To quantify the goodness of fit, the correlation coefficient (R 2), the sum of squares (RSS), the standard error of the estimate (S y ), the mean relative deviation (MRD) and the plots of residuals were analysed. The three theoretical parameters of the GAB model (M o , C, and K) gave a good correlation (R 2 > 0.9817, RSS < 0.0297, MRD < 0.138, S y < 0.0143, and random residuals‐plots) in the range of a w from 0.029 to 0.979, of interest in seed storage and processing. However this correlation does not consider the effect of temperature (T) on coefficient values. In a second stage, parameters M o and K were adjusted at each temperature. Very low variances were obtained in the range 25–65°C for desorption and in the range 25–55°C for adsorption. These results suggested that M o and K remain almost constant and a correlation with T is not justified. On the contrary sense, parameter C showed stronger variation with T. This was explained by the analysis of sensitivity for the influence of C on moisture content. On this basis, the relation C–T was proposed by an Arrhenius‐type relation [C = A.exp(B/T)] and this function was incorporated to the original GAB model to re‐estimate the parameters A, B, M o , and K. The developed modification provides a generalised and precise expression of GAB model for Amaranth.