Brunauer–Emmett–Teller Model Research Articles

Thermo-physical characterization of Pharmacoat® 603, Pharmacoat® 615 and Mowiol® 4-98

Hydroxypropyl methylcellulose (HPMC) and polyvinyl alcohol (PVA) are important polymers in pharmaceutical, food and other industries being largely used as encapsulation agents. The characterization of two reference grades of HPMC (Pharmacoat® 603 and Pharmacoat® 615) and one reference grade of PVA (Mowiol® 4-98), through X-ray diffraction (XRD) and thermogravimetry (TG) is described. Specific analyses were performed by means of dynamic vapour sorption analysis of water adsorption/desorption from vapours at 10, 25, 40, 55 and 70 °C. Guggenheim–Anderson–de Boer (GAB), Brunauer–Emmett–Teller (BET), Park and n-layer BET models were successfully used to fit the experimental data. The glass transition temperature as function of water content was measured by means of differential scanning calorimetry (DSC). The experimental data were analysed according to Linear, Gordon–Taylor, Fox and Roos equations. XRD studies revealed amorphous structure for the Pharmacoat® 603 and Pharmacoat® 615 and crystalline for Mowiol® 4-98. Single and multi-step temperature degradation point was found for Pharmacoat® 603 and Pharmacoat® 615 and Mowiol® 4-98, respectively. The water uptake is higher for Pharmacoat® 603 and Pharmacoat® 615 than Mowiol® 4-98. The influence of temperature on water uptake is opposite for the two types of polymers. GAB and n-layer BET were found to better model Pharmacoat® 603 and Pharmacoat® 615 and Mowiol® 4-98 data, respectively. The water makes the glass transition to decrease quite drastically. Gordon–Taylor is better fitting the experimental data both for Pharmacoat® 603 and Pharmacoat® 615 and Mowiol® 4-98.

Organic vapor adsorption on in situ grown carbon nanotube films

Organic vapor adsorption isotherms are measured on in situ grown carbon nanotube (CNT) films using piezoelectric GaPO 4 crystal microbalances as mass sensing substrates. The isotherms are Type IV and show adsorption/desorption hysteresis, consistent with a porous material. The measured porosity is 2%, a value surprisingly low given an over 90% void volume in the film estimated from density considerations. At low pressures ( p/ p 0 < 0.25) the isotherm is well fit by the Freundlich model and at intermediate pressures ( p/ p 0 = 0.1–0.4) by the Brunauer, Emmett, Teller (BET) model. Monte Carlo simulations show three consecutive adsorption processes: filling of the intratube micropores at low pressures, monolayer coverage of the CNT external surface at intermediate pressures, and capillary condensation in the intertube mesopores at high pressures. The simulation results validate the use of the BET model for surface area analysis in the experimental system. The average total accessible surface area is found to be 180 ± 100 mm 2 and the specific surface area is estimated to be 45 ± 25 m 2/g. Further engineering of the CNT film microstructure should lead to much higher surface areas.

Effect of drying temperature and beeswax content on moisture isotherms of whey protein emulsion film

The objective of this investigation was to study the effect of drying temperature and beeswax (BW) content on moisture sorption behavior of whey proteins emulsion films. For this purpose, films were obtained by the casting method and dried at two selected temperatures (5 and 25°C) and constant relative humidity (RH) (58%). After drying, films were removed from the casting plates and were conditioned in the environmental chamber set at 25°C and 58% RH for 3 days. Subsequently, portions of 400mg of film were placed in glass bottles and pre-dried in desiccators containing drierite (aw=0) during 10 days. Then, the bottles were placed in hermetically sealed glass jars containing 10 different desiccants to achieve aw ranging from 0.11 to 0.90, and allowed to reach equilibrium. The analyses were made in quintuplicate at 25°C. The equilibrium moisture content (EMC) was determined by drying samples in an oven and the experimental data were fitted by the Brunauer-Emmett-Teller (BET) and the Guggenheim-Anderson-De Boer (GAB) models. The results showed that both models were effective to describe the moisture sorption behavior of the films. The GAB model gave better fit than the BET model. The increase of the drying temperature of 5 to 25°C and the incorporation of lipids reduced the EMC of whey protein emulsion films. Finally, data from experimental sorption isotherms are a useful tool to predict the effect of the environmental conditions that surround the film on its properties; particularly considering that the stability of an edible film is function of its mechanical and moisture barrier properties and both are strongly influenced by the presence of water, film formulation and drying and storage conditions.

Desulfurization of Low Sulfur Diesel by Adsorption Using Activated Carbon: Adsorption Isotherms

Adsorptive desulfurization was studied using diesel fuel with low sulfur content (72 ppmw) and four commercial activated carbons (CAA, CAB, CAC, and CAD). After the adsorption scheme, it was possible to obtain a diesel with 15 ppmw of sulfur content. The experiments were carried out in a batch system at 303.15 K, atmospheric pressure, and 5−200 g-A/L-D, with magnetic stirring over 18 h. The adsorption isotherms were correlated by the Freundlich, Langmuir, Sips and Brunauer−Emmett−Teller (BET) models. There was a good agreement between the experimental and calculated adsorption isotherms. The Sips and BET models give the best correlation for the experiment.

Study of equilibrium and thermodynamic adsorption of α-picoline, β-picoline, and γ-picoline by Jordanian zeolites: Phillipsite and faujasite

In the present study the ability of phillipsite and faujasite to remove α-picoline, β-picoline, and γ-picoline from aqueous solution in the broad range of concentrations (1–500 mg L −1) was investigated. Adsorption equilibrium was carried out at different initial concentrations, sorbent concentrations, and temperatures. Brunauer–Emmett–Teller (BET), the Harkins–Jura, the Smith, and the Halsey equations were applied to the experimental data. The data fitted the BET model best. The overall adsorption of α-, β-, and γ-picoline on phillipsite and faujasite followed the order: faujasite α-picoline < phillipsite α-picoline < faujasite β-picoline < phillipsite β-picoline < faujasite γ-picoline < phillipsite γ-picoline. The values of change in Gibbs free energy (Δ G°), enthalpy (Δ H°), and entropy (Δ S°) were calculated. Thermodynamic study revealed that the adsorption of picolines onto phillipsite and faujasite was an exothermic process. Isosteric heat of adsorption was found to decrease with the increase in surface loading.

Water Sorption Isotherms and Textural Properties of Biodegradable Starch-Based Superabsorbent Polymers

A series of biodegradable superabsorbent polymers (SAP) based on starch grafted with acrylic acid (AA) and crosslinked with N,N’-methylenebisacrylamide (MBIS) were obtained. The parameters that define SAPs properties, such as starch type, amount of initiator, acrylic acid and crosslinker concentrations, and degree of neutralization were varied according to an experimental design. The swelling rate, the degree of swelling, the water sorption isotherms and the texture profile of the new materials were determined. A new method was used to measure the swelling rate. The water sorption results were correlated using various isothermal models as the BET (Brunauer-Emmett-Teller) and GAB (Guggenheim-Andersson-DeBoer) models. Hydrogels obtained from regular cornstarch presented better absorption capacities than those from waxy cornstarch. Maximum swelling was observed for 70% neutralization of carboxylic acid groups. More rigid SAPs presented lower swelling rates, but not necessarily lower swelling degrees.

Adsorption of Direct Red 80 dye from aqueous solution onto almond shells: Effect of pH, initial concentration and shell type

The adsorption of Direct Red 80 (DR 80) dye from aqueous solution on almond shells as an eco-friendly and low-cost adsorbent was studied. The effect of shell type (internal, external and mixture shells), pH and initial dye concentration were considered to evaluate the sorption capacity of almond shell adsorbent. The mixture type of almond shell showed to be more effective. The adsorption studies revealed that the mixture type of almond shells remove about 97% of the DR 80 dye from aqueous phase after 1 h of the adsorption process in a batch system. Although, pH changes did not appreciably affect the adsorption process but the maximum adsorption capacity of different types of almond shells (20.5, 16.96 and 16.4 mg/g for mixture, external and internal shells) were obtained at pH 2. However, in order to have a better control on the experimental conditions, pH 6 was selected for conducting all adsorption experiments. Initial dye concentration was varied from 50 to 150 mg/L. Higher concentrations of dye in aqueous solution reduced DR 80 dye adsorption efficiency of almond shells. Equilibrium data were attempted by various adsorption isotherms including Langmuir, Freundlich and Brunauer–Emmett–Teller (BET) models. It was found that the adsorption process by mixture type of almond shells follows the Langmuir non-linear isotherm. Furthermore, the experimental data by internal and external almond shells could be well described by the BET and Freundlich isotherm models, respectively. The pseudo-second-order kinetics provides the best correlation of the experimental data.

Moisture Sorption Behaviour and Thermodynamic Characteristics of Rice stored in a Chamber under Controlled Humidity

The moisture sorption isotherms of rice stored in a chamber, the relative humidity of which is controlled by an atomising humidification system were determined at 25, 35 and 45 °C and within the range of 0·1–0·9 water activity. The sorption isotherm curves of rice showed the characteristics of a type II isotherm. The equilibrium moisture content increased with a decrease in storage temperature at any given water activity. The sorption isotherms exhibited hysteresis over the whole water activity range. The mathematical description of the sorption data was obtained applying some of the most common sorption equations [Guggenheim–Anderson–de Boer (GAB), Brunauer–Emmett–Teller (BET), Henderson, Iglesias and Chirife, Oswin, Peleg, Smith and Caurie equations]. A non-linear regression analysis was used to evaluate the constants of the sorption equations. Among the various models tested to interpret sorption isotherms, the model having best statistical indicators was selected as the most appropriate model. The Peleg model gave the best fit to the experimental sorption data over the range of temperatures and water activity investigated. The agreement between experimental and predicted values of the Peleg model was found to be satisfactory. In the range of water activity 0–0·4, the BET model was shown to give the closest fit to the experimental data. The surface area of monolayer was calculated and the water activities corresponding to the monolayer values were determined. 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 isosteric heats of sorption were determined from the best-fitting equation using the Clasius-Clapeyron equation. Isosteric heat decreased with increase in moisture content and approached the latent heat of vaporisation of pure water at moisture contents above 0·2 kg [water] kg−1 [dry solids]. The spreading pressures increased with increasing water activity. Within the moisture range of 0·013–0·207 kg [water] kg−1 [dry solids], the net integral enthalpy decreased with increase in moisture content and net integral entropy increased with increase in moisture content. Net integral entropy was negative in value.

Water sorption and time-dependent crystallization behaviour of freeze-dried lactose–salt mixtures

Water sorption properties of freeze-dried lactose, lactose/CaCl 2, lactose/NaCl, lactose/MgCl 2, and lactose/KCl mixtures in their molar ratio of (9:1) were investigated. Brunauer–Emmett–Teller (BET) and Guggenheim–Anderson–de Boer (GAB) models were used to model water sorption properties. Water is known to function as a plasticizer, depressing the glass transition and facilitating crystallization. Crystallization in the present study resulted in loss of sorbed water from lactose. The crystallization of pure lactose and lactose/salt mixtures was observed at RVP⩾44.0% within 24 h. At RVP⩾54.4% water contents were higher in lactose/CaCl 2 and lactose/MgCl 2 mixtures than in pure lactose, lactose/NaCl, and lactose/KCl. Water content in pure lactose after crystallization was ⩽5.0%, suggesting that lactose crystallized as a mixture of α-lactose monohydrate and various anhydrous forms of α/ β-lactose crystals. Anhydrous lactose/CaCl 2 and lactose/MgCl 2 had higher glass transition temperatures than lactose, but other salts (NaCl and KCl) with lactose gave lower glass transition than amorphous lactose. It seems that bivalent salts in mixtures with lactose gave a higher T g than smaller monovalent ions. Salts delayed lactose crystallization. The effect on lactose crystallization was highest with calcium chloride (CaCl 2) and lowest with potassium chloride (KCl). It seems that different salts interacted with lactose to different extents. For water sorption, GAB model gave a better fit than BET model. Water sorption and time-dependent crystallization properties of lactose/salt mixtures should be considered in manufacturing and storage of dairy-based dehydrated materials.

Evaluation of the Moisture Sorption Behaviour of Several Excipients by BET, GAB and Microcalorimetric Approaches

Moisture content of solid-state pharmaceutical products is one of the main factors that affect drug stability, therefore suitable sorption studies need to be performed to assure drug quality throughout their shelf life. The Brunauer-Emmett-Teller (BET) and the Guggenheim-Anderson-de Boer (GAB) models are usually used for this purpose. Using gravimetrically obtained data, both methods were applied in the present work to evaluate the sorption characteristics of several excipients. Microcalorimetric analysis was also performed in order to evaluate the interaction between water and the substances. The results of these experiments show excellent agreement between data and the BET model up to 55% RH and the GAB model over the entire humidity range, confirmed by high values of the statistical determination coefficients. Furthermore, microcalorimetric measurements suggested that the hygroscopicity of solid materials could be estimated approximately using this approach.

Water Sorption and Plasticization Behavior of Spray‐dried Lactose/Protein Mixtures

ABSTRACT: Water sorption properties, effects of proteins on glass transition temperature, and time‐dependent lactose crystallization of spray‐dried lactose and lactose in lactose/WPI (3:1), lactose/Na‐caseinate (3:1), lactose/albumin (3:1), and lactose/gelatin (3:1) mixtures were investigated. Brunauer‐Emmett‐Teller (BET) and Guggenheim‐Anderson‐de Boer (GAB) models were used to model water sorption. Lactose/protein mixtures sorbed high amounts of water at low relative vapor pressure (RVP) up to 23.1%. Above 23.1% RVP levels, water sorbed by pure lactose was higher, up to 44.1% RVP, except in the case of the lactose/gelatin mixture. Lactose/ gelatin also sorbed a high amount of water at 33.2% RVP. Loss of sorbed water resulting from crystallization of amorphous lactose was observed. Crystallization of pure lactose and lactose crystallization in lactose/protein mixtures occurred at RVP ≥ 44.1% within 24 h. After crystallization at RVP ≥ 54.5%, water contents remained higher for lactose/protein mixtures than for pure lactose. The rate of lactose crystallization was less in all lactose/protein mixtures than was observed for pure lactose. WPI had the lowest effect on lactose crystallization. Crystallization occurred most slowly in lactose/gelatin mixtures. Both GAB and BET models fitted to water sorption data up to 0.441 aw. It seems that different proteins interact with lactose differently. Water sorption and time‐dependent lactose crystallization of lactose/protein mixtures have important consequences to processing and storage behavior of lactose‐protein based 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.

Multilayer Adsorption with Multisite Occupancy: An Improved Isotherm for Surface Characterization

In this work, an improved solution for multilayer adsorption of linear species is presented. The particular case of multilayer dimer adsorption is dealt with in detail, and a new adsorption isotherm is obtained for determination of surface area and adsorption energy from experiments. From the comparison between the new isotherm and the standard Brunauer−Emmett−Teller (BET) formalism, it arises that the monolayer volume, vm (or the surface area, A), can be up to 1.5 times larger than the one from the BET model. The proposed model is simple and easy to apply in practice and leads to new values of surface area and adsorption heat. Physically, these advantages are a consequence of properly considering the configurational entropy of the adsorbate.

Solid–liquid equilibria in mixtures of molten salt hydrates for the design of heat storage materials

Abstract Enthalpy of melting can be used to store heat in a simple way for time periods of hours and days. Knowledge of the solid –liquid equilibria represents the most important presumption for systematic evaluations of the suitability of hydrated salt mixtures. In this paper, two approaches for predicting solid–liquid equilibria in ternary or higher component systems are discussed using the limited amount of thermodynamic data available for such systems. One method is based on the modified Brunauer–Emmett–Teller (BET) model as formulated by Ally and Braunstein. In cases of a strong tendency toward complex formation of salt components, the BET model is no longer applicable. Reaction chain models have been used to treat such systems. Thereby, the reaction chain represents a method to correlate step-wise hydration or complexation enthalpies and entropies and, thus, reduce the number of adjustable parameters. Results are discussed for systems containing MgCl2, CaCl2, ZnCl2, and alkali metal chlorides.

Soil pore surface properties in managed grasslands

Properties of pore surfaces control adsorption and transport of water and chemicals in soils. Parameters are needed to recognize and monitor changes in pore surfaces caused by differences in soil management. Data on gas adsorption in soils can be compressed into parameters characterizing (a) area available to a particular adsorbate, and (b) surface roughness or irregularity. Our objectives were to see (a) whether models of adsorption on fractal surfaces are applicable to water vapor adsorption in soils in the capillary condensation range, and (b) whether differences in long-term management of grasslands are reflected by soil pore surface properties. Water vapor adsorption was measured in Gray Forest soil (Udic Argiboroll, Orthic Greyezem, clay loam) samples taken at four plots, where a long-term experiment on grassing arable land had been carried out for 12 years. The experiment had 2×2 design. Factors were ‘harvest–no-harvest’ and ‘fertilizer–no-fertilizer’. The hay was cut after over-seeding in harvested treatments every year. Ammonium nitrate, superphosphate, and potassium chloride were applied annually after the snowmelt to get the total amount of nutrients of 60 kg ha −1. The monolayer adsorption capacity was estimated from the Brunauer–Emmett–Teller model. A fractal Frenkel–Halsey–Hill model of adsorption on a fractal surface, and a thermodynamic adsorption model were applied in the range of relative pressures from 0.7 to 0.98 and provided good fit of data. Values of the surface fractal dimension D s were in the range from 2.75 to 2.85. Removal of carbohydrates resulted in increase of D s. Differences in management practices did not affect values of D s in the scale range studied, whereas the monolayer capacity was affected. Both fertilization and harvesting resulted in an increase of the monolayer capacity, with the largest increase observed in soil that was fertilized but not harvested.

Water desorption isotherms for eleven varieties of dates

In this paper, we report on the water vapour desorption isotherms, at 25°C, of eleven date ( Phoenix dactylifera) varieties, from different locations, collected at full ripeness: Mech-Degla, Deglet-Nour and Haloua (Algeria), Barhi, Fardd, Khadrawi, Khalass, Madjol, Rizaz (Saudi Arabia), Madjhoul (Israël) and Kentichi (Tunisia). The static gravimetric method was used, according to the COST 90 recommendations. The overall shape of the curves describing the water content as function of the water activity was typical of sugar-rich materials. Experimental data were analysed using the Guggenheim–Anderson–Brunauer (GAB) and Brunauer–Emmett–Teller (BET) models, through direct non-linear regression without any transformation of data. Both models correctly fit the whole set of data, for water activity ranking from 0.11 to 0.90, but the BET model was preferred since the values of its parameters were more realistic.

Analysis of the Variability of Parameters in the Brunauer−Emmett−Teller Solution Model for the Nitric Acid−Water System

The Brunauer−Emmett−Teller (BET) model was applied to the nitric acid−water system in order to determine the variability of the model constants. The available data were interpreted to obtain values for the entropic and energetic parameters from 9 to 225 m. The values of those parameters and the manner in which they vary are entirely consistent with the known chemistry of the system. The main conclusion is that the BET model should be modified in a fashion which maintains its simplicity and chemical significance. The possibility of such a simple approach to model highly nonideal systems forms the basis for future study.

Solute and Solvent Activities of CaCl2(aq) Solutions from the Adsorption Isotherm Treatment

The values of the two Brunauer−Emmett−Teller (BET) parameters calculated by Stokes and Robinson (1948) are reevaluated using recent experimental data on the activity coefficients of CaCl2(aq) reported by Rard and Clegg (1997). At the 95% confidence level, no significant statistical differences are observed in the values of the BET parameters reported in this work and those reported by Stokes and Robinson (1948). The water activities aw, osmotic coefficients φ, and mean ionic activity coefficients, γ± of CaCl2(aq) are then calculated from saturation to dilute solution. Since the standard state of the solute in the BET model is the anhydrous liquid electrolyte rather than the infinitely dilute solution, the technique of Ally and Braunstein (1996) is utilized to obtain the mean ionic activity coefficients of CaCl2(aq) over the entire concentration range. The differences between the chemical potentials of the solute in the infinitely dilute solution standard state (hypothetical) and the anhydrous liquid elect...

Statistical mechanics of multilayer adsorption: electrolyte and water activities in concentrated solutions

Approximately 33 years after Stokes and Robinson's modification of the Brunauer– Emmett–Teller (BET) adsorption isotherm paved the way for experimental investigations of the water activities and properties of concentrated aqueous electrolytes, Abraham derived an equation giving the activity of a salt on the basis of the same model, but restricted his result to a binary aqueous system consisting of one salt only. Many investigators have used Stokes and Robinson's modification to show good agreement between experimental and calculated water activities even for ternary and quaternary aqueous solutions, if the system is treated as a pseudobinary. However, no previous (theoretical) attempt has been made to go beyond the single salt or pseudobinary restriction of Abraham. In this paper, we categorically prove that there is no fundamental limitation that restricts the BET model to a single electrolyte. We verify the consistency of our results through satisfaction of the Gibbs–Duhem relationships and by showing agreement between the calculated and experimental data of Iyoki on water vapor pressures for {x(2.8LiCl + LiNO3)+(1−x)H2O}, wherex=ωMw/{ωMw+ (1−ω)Ms}; ω denotes the mass fraction of lithium salts; andMwandMsdenote the molar masses of H2O and of (2.8LiCl + LiNO3), respectively. In predicting activities of the components of {x(2.8LiCl + LiNO3)+(1−x)H2O}, no experimental data on this ternary system are utilized. This fact underlies the predictive quality of the theoretical model presented in our paper. By induction, we extend our results to the case of (water + N electrolytes).

Adsorption studies of water on copper, nickel, and iron using the quartz‐crystal microbalance technique: Assessment of BET and FHH models of adsorption

AbstractIn the atmospheric corrosion of copper, nickel, and iron, the adsorption of water affects the corrosion rates. Knowledge of water adsorption and metal oxyhydroxide formation is important in understanding the atmospheric corrosion process. The purposes of the present research were (1) to measure the adsorption of water on metal surfaces as a function of temperature and relative humidity (RH) and (2) to assess Brunauer‐Emmett‐Teller (BET) model and Frenkel‐Halsey‐Hill (FHH) model for water adsorption. In the present research, the quartz‐crystal microbalance (QCM) technique was used to measure the mass changes of copper, nickel, and iron at 0 to 100% RH and 7–90°C under nitrogen environments. Less water was adsorbed on copper, nickel, and iron which formed oxides than on gold. BET and FHH models could not fit the data points with single functional relationships. ΔH values were calculated using modified BET method and they decreased with temperature.