Brunauer Emmett Teller Equation Research Articles

Unveiling the non-equilibrium process in multilayer mixture adsorption

The Brunauer–Emmett–Teller (BET) theory [S. Brunauer et al., “Adsorption of gases in multimolecular layers,” J. Am. Chem. Soc. 60, 309–319 (1938)] constitutes a cornerstone in gas-adsorption physics. Recently, the kinetic BET equation of single-kind adsorbate has been proposed [H. Yu and X. Zhang, “Molecular-kinetic study of multilayers gas-adsorption in a rarefied gas environment,” Phys. Fluids 34, 123106 (2022)], while its counterpart of mixed adsorbates is currently unknown. Gas mixtures are commonly found in both natural and artificial systems. To address this limitation, we have proposed a kinetic BET theory for adsorbate mixtures in this paper. Moreover, we gave an analytical solution addressing low gas pressure conditions. In this condition, we predicted the “over-adsorption” of one species in the mixture with a higher desorption rate over time, and the “inertia effect” during the crowed-out process of the fast-desorbing species. Further, we also simulated the reciprocal influence of multilayer gas adsorption on the non-equilibrium fluids. Our findings provide valuable insights into gas-adsorption experiments and can facilitate technological advancements.

Jerapan Isotermal Fosfat Pada Tanah Ultisol

The distribution area of mineral soil in Indonesia reaches 148 million ha. The acid mineral soil in South Kalimantan for Ultisol reaches 886.186 ha. Ultisols have low fertility and P availability. The low availability of P in the soil is caused by P being absorbed. Isothermal absorption is very useful for measuring P adsorption in the soil due to strong P fixation by Fe and Al in Ultisol soils. Many researchers have suggested determining the amount of P required to reach an optimum level for maximum crop yield to quantitatively describe isothermal adsorption, the most popular of which are Langmuir, Freundlich, and the Brunauer-Emmett-Teller (BET) equations. The purpose of this study was to determine the isothermal adsorption limit of P and describe quantitatively the isothermal adsorption in Ultisols in Banjarbaru City using the Langmuir, Freundlich, and BET equations. From the research results, it can be concluded that P adsorption on Ultisols in Gunung Kupang Village, Cempaka District, Banjarbaru City follows the BET Equation. The high and low P adsorption indicated the availability of P. In other words, the fixation activity of acid mineral soils could result in a smaller amount of available P for plants.

Soil water isotherm model for particle surface sorption and interlamellar sorption

AbstractSoil–water retention curve (SWRC) describes the relationship between soil matric potential and soil water content, which is recognized as the most important constitutive function for unsaturated soil that governs many hydrological and mechanical properties, such as fluid flow, hydraulic conductivity, chemical transport, and soil freezing and thawing, etc. Soil–water isotherm (SWI) measured from vapor adsorption technique captures the SWRC at medium to high matric potential range, where three physical mechanisms of soil–water retention (SWR) with distinct free energy levels are involved: adsorption on external particle surface, adsorption in interlamellar space, and capillarity. So far, there is not a single SWI model that can take all three mechanisms into full consideration in full matric potential range. Here a closed‐form SWI model is formulated as the mathematical sum of three independent SWIs, which are external sorptive SWI, internal sorptive SWI, and capillary SWI; each corresponds to one of the aforementioned SWR processes. The generality and effectiveness of the proposed model are experimentally validated through a suite of 21 soils, covering all common soil types with plasticity index (PI) of 4–132. The proposed SWI model shows excellent performance as it nearly perfectly (R2 > 0.99) fits both the adsorption isotherm and the desorption isotherm for each soil, validating the generality of the model. The external specific surface area (SSA) obtained from the external sorptive SWI correlates well with that determined from the classic Brunauer–Emmett–Teller equation, while the internal SSA obtained from the internal sorptive SWI also coincides with that measured independently; both further confirm the capability of the proposed SWI model to distinguish between external surface adsorption and interlamellar adsorption.

Sol-gel processing of a covalent organic framework for the generation of hierarchically porous monolithic adsorbents

Sol-gel processing of a covalent organic framework for the generation of hierarchically porous monolithic adsorbents

Description of sigmoid adsorption isotherms of water pollutants by the Aranovich–Donohue equation

ABSTRACT In the field of adsorptive water remediation, the Brunauer–Emmett–Teller (BET) equation is often used to describe sigmoid type II isotherm data. A standard type II isotherm is a composite curve that comprises a type I and a type III curve at low and high concentrations, respectively. The BET equation uses a Langmuir-like function to describe the type I curve and a unique function to represent the type III curve. However, the ability of this mathematical combination to fit atypical type II isotherms is somewhat limited. The BET equation has been modified in various ways to improve its data fitting ability. The Aranovich–Donohue equation is an interesting modification in that it has a flexible equation structure that allows users to choose an isotherm model to describe the type I curve at low concentrations. It is shown here that the Aranovich–Donohue equation featuring the Sips equation is capable of accurately correlating anomalous acid red and acid black dye isotherm data, outperforming the original BET equation. Furthermore, the Aranovich–Donohue–Sips equation can accurately track a phenol isotherm characterized by a type V curve at low concentrations, demonstrating its versatility in fitting nonstandard type II isotherm data.

How Reproducible are Surface Areas Calculated from the BET Equation?

Porosity and surface area analysis play a prominent role in modern materials science. At the heart of this sits the Brunauer-Emmett-Teller (BET) theory, which has been a remarkably successful contribution to the field of materials science. The BET method wasdeveloped in the 1930s for open surfaces but is now the most widely used metric for the estimation of surface areas of micro- and mesoporous materials. Despite its widespread use, the calculation of BET surface areas causes a spread in reported areas, resulting in reproducibility problems in both academia and industry. To prove this, for this analysis, 18 already-measured raw adsorption isotherms wereprovided to sixty-one labs, who wereasked to calculate the corresponding BET areas. This round-robin exercise resulted in a wide range of values. Here, the reproducibility of BET area determination from identical isotherms is demonstrated to be a largely ignored issue, raising critical concerns over the reliability of reported BET areas. To solve this major issue, a new computational approach to accurately and systematically determine the BET area of nanoporous materials is developed. The software, called "BET surface identification" (BETSI), expands on the well-known Rouquerol criteria and makes an unambiguous BET area assignment possible.

Validating the Generality of a Closed-Form Equation for Soil Water Isotherm

Total soil water potential ψt is conventionally defined as the sum of matric potential ψm and osmotic potential ψo, i.e., ψt=ψm+ψo, when gravitational potential is ignored. Soil water isotherm (SWI) is the constitutive relationship between ψt and soil water content w, i.e., ψt(w)=ψm(w)+ψo, where ψm(w) is called soil water retention curve (SWRC) or soil water characteristic curve. SWI and SWRC are arguably the two most important soil constitutive relationships because they govern virtually all phenomena in soil such as flow, stress and deformation, and biological activities. A closed-form SWI, recast from a generalized SWRC equation for adsorption and capillarity, is experimentally validated for its generality in representing SWI. Adsorption isotherms of 49 soils, covering all spectrum of soil types with plasticity index up to 185% and specific surface area up to 600 m2/g, are used to validate the SWI equation. It is shown that the SWI equation can nearly perfectly represent the isotherms of these soils with almost all of the coefficients of determination R2≥0.99, validating the generality of the SWI equation. Comparative analysis is also conducted by using two existing SWI equations, namely, the Brunauer–Emmett–Teller (BET) equation and the augmented BET (A-BET) equation. It is demonstrated that the SWI equation is superior to the BET and A-BET equations in representing soil–water interactions by adsorption and capillarity, and in the full relative humidity range.

The Effect of Catalyst Calcination Temperature on Catalytic Decomposition of HFC-134a over γ-Al2O3

This paper explores the thermal and catalytic pyrolysis of HFC-134a over γ-Al2O3 calcined at temperatures of 550 °C (A550), 650 °C (A650), 750 °C (A750), and 850 °C (A850). The physicochemical properties of catalysts were studied through thermogravimetric analysis (TGA), Brunauer–Emmett–Teller equation for nitrogen physisorption analysis (BET), X-ray diffraction (XRD), and temperature-programmed desorption of ammonia (NH3-TPD). The non-catalytic pyrolysis of HFC-134a showed less than 15% decomposition of HFC-134a. Catalysts increased the decomposition as A650 revealed the highest decomposition efficiency by decomposing more than 95% HFC-134a for 8 h followed by A750, A850, and A550. The larger surface area and pore volume paired with a low amount of strong acidic sites were considered as the main contributors to the comparatively longer catalytic activity of A650.

WITHDRAWN: Magnetic polyazomethine-amide nanocomposites: Synthesis and characterization, and their application

The preparation of the Schiff base 5A-O ligand in this study was through an interaction between 2-Hydroxy-3-methoxybenzaldehyde and 5-aminoisophthalicacid, and the product was characterized by several techniques such as 1-HNMR, 13 CNMR, mass spectrometry and elemental analysis. With good yield (85percent) the monomer derivative reacted with 4.4′-diminodiphenyl ether and triphenylphosphite (TPP) to form an aromatic polyamide (P5A-O) These polymers were easily soluble in NMP, N, N-dimethylacetamide, dimethylsulfoxide, and pyridine, among other solvents. The polymerization reaction was carried out by using the polymerization process to modify the surface of magnetic nanoparticles (Fe3O4 MNPs). To confirm the composition of the prepared nanocomposite, various analytical techniques such as field-emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), X-ray, and vibrating sample magnetometer (VSM) tests were used. The effect of the polymerization process of the synthetic polymeric on the surface of a sphere shape was observed by FE SEM photographs. The Brunauer Emmett–Teller equation was used to determine the surface area of a magnetic polymer. The elimination of Ni(II) and Fe(III)ions from aqueous solutions using this novel magnetic nanocomposite was compared under a number Experimental conditions and criteria, including pH, adsorbent dose and touch time for removal of heavy metals. Antioxidant operations in vitro, such as DPPH radical scavenging, were analyzed and revealed that poly azomethine-amide possessed significant antioxidant properties.

Adsorption behavior of Pd(II) ions from aqueous solution onto pyromellitic acid modified-UiO-66-NH2

A new adsorbent was successfully fabricated by chemically linking pyromellitic acid onto a zirconium-based metal-organic framework composite for selective adsorption of Pd(II) from an aqueous solution. The adsorbent was characterized by Fourier transform infrared spectroscopy, Brunauer–Emmett–Teller equation and scanning electron microscope. The adsorption capacity, selectivity and repeatability of the adsorbent were tested by batch experiments. The optimum pH was 2.0, and the maximum adsorption capacity at room temperature was 226.1 mg/g. In the kinetic experiments, the adsorption process achieved equilibrium within 5 h and generally conformed to the quasi-second kinetics and Freundlich isotherm model. The N-H and OH groups on the adsorbent interacted with Pd(II) by electrostatic and coordination action. The adsorbent maintained excellent adsorption capacity after at least 5 cycles. At the same time, the selectivity of the adsorbent in aqueous solution is excellent from interfering ions. Therefore, the new adsorbent will have an obvious application prospect on the recovery of palladium.

Equilibrium Study, Modeling and Optimization of Model Drug Adsorption Process by Sunflower Seed Shells

The adsorption capacity of the medication methylthioninium chloride (MC) from aqueous solution onto sunflower seed shells (SSS), a low cost and abundant alternative adsorbent, was investigated in a batch system. The surface properties of the adsorbent were characterized by Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM), specific surface area (by using the Brunauer–Emmett–Teller equation), the liquid displacement method and pHPZC. The ability of SSS to remove the medication was assessed through kinetic, thermodynamic and equilibrium investigations. The adsorption efficiency of the SSS adsorbent for the removal of MC was evaluated considering the effects of its concentration, temperature, adsorption contact time, and the pH of the medium. The results obtained from the kinetic and isotherm studies show that the adsorption of the MC on SSS follows pseudo-second-order kinetics (R² > 0.99) and the Temkin isotherm model (R² = 0.97), respectively. The thermodynamic study showed that the adsorption was endothermic and spontaneous, according to its physisorption mechanism. The mathematical modeling of this process was carried out by using the surface response methodology of Box–Behenken. It was possible to deduce a statistically reliable regression equation that related the adsorption yield to the chosen operating parameters, that is, the initial MC concentration, the adsorbent dosage and the pH. Analysis of the variance indicated that the most influential parameters were the SSS dosage, the pH and their interaction and showed the optimal values for ensuring the best adsorption capacity of 95.58%.

Augmenting the adsorption parameters of palladium onto pyromellitic acid-functionalized nanosilicas from aqueous solution

Many industrial wastewaters contain large amounts of palladium and the recovery of palladium from wastewater has great significance. Here, a new adsorbent (PMA-SNP) was synthesized by modifying nano-silica with pyromellitic anhydride to selectively adsorb Pd(II) in wastewater. Fourier transform infrared spectroscopy, scanning electron microscopy, Brunauer–Emmett–Teller equation, X-ray photoelectron spectroscopy and transmission electron microscopy were employed to characterize the adsorbent. At 25 °C, the adsorbent has the higher adsorption rate in the pH range of 2 to 5. The adsorption equilibrium is reached in 480 min and the maximum adsorption capacity is 53.61 mg/g. The adsorption kinetics and isotherms accord with pseudo-second-order and Langmuir models, respectively. The results show that the adsorption process is monolayer adsorption and the rate-limiting step is chemical adsorption. After five cycles, the removal rate of Pd(II) by PMA-SNP decreased slightly from 71.18% to 66.11% with good reusability. The thermodynamic data revealed that the adsorption was a spontaneous exothermic process. PMA-SNP can selectively adsorb palladium from wastewater containing various coexisting ions. Adsorption mechanism is based on the electrostatic and chelation interaction between Pd(II) ion and the O and N atoms. It can be concluded that PMA-SNP is an effective and promising adsorbent for the recovery of palladium from wastewater.

A modified BET equation to investigate supercritical methane adsorption mechanisms in shale

Although the Brunauer-Emmett-Teller (BET) equation is a classic adsorption model for describing the adsorption of gases in adsorbents, it cannot be applied in supercritical conditions because the saturation vapor pressure ( p 0 ) in this equation is not defined when T > T c . In this study, a modified BET equation is proposed, and can be applied to investigate supercritical methane adsorption mechanisms in shale by using density instead of pressure in this equation. The observed (excess) high-pressure methane adsorption isotherms always can be well-fitted by the modified BET model when the adsorbed-phase density ( ρ a ) is not fixed. The fitted results show that the number of adsorption layers ( n ) ranges from 1.79 to 2.42, with an average value of 2.12, indicating a double-layer adsorption mechanism approximately. Moreover, we compare this novel model with the commonly used Langmuir and DR models, and find that all the three models can fit the excess adsorption isotherms equally well. However, a critical advantage of this new model is that it can calculate the number of adsorption layers ( n ), while other models cannot. It is this advantage that makes it possible to analyze the shale gas adsorption mechanism experimentally. Moreover, the average number of adsorption layers ( θ ) is much smaller than the number of adsorption layers ( n ), indicating that there are many empty adsorption sites in the adsorption space and the density of the second layer must be less than the first layer, which is consistent with the molecular simulation results. • A modified BET equation is proposed to investigate methane adsorption mechanisms in shale. • The experimental high-pressure adsorption isotherms can be well-fitted by the new model. • Supercritical methane is found to be approximately double-layer adsorbed in shale.

Electrospinning of PAN/Ag NPs nanofiber membrane with antibacterial properties

Abstract

Augmented Brunauer–Emmett–Teller Equation for Water Adsorption on Soils

Core Ideas We developed an augmented BET sorption isotherm equation for soils. We validated the equation through water adsorption isotherm data from a wide suite of soils. The equation can explicitly quantify soil's total SSA, particle SSA, and intra‐crystalline SSA. An augmented Brunauer–Emmett–Teller (BET) equation was developed for describing water adsorption on soils, overcoming the limitation of the original BET equation for describing only isotherms of materials with a homogeneous adsorption surface. The different physicochemical mechanisms underlying water adsorption in soils are synthesized, leading to a unique adsorption sequence dictated by two distinguishable free energy levels. The higher adsorption free energy level reflects the internal (intra‐crystalline) surface adsorption, whereas the lower adsorption free energy level reflects the external (particle) surface adsorption. This adsorption energy disparity is provided by the interlamellar energy barrier of van der Waals and electrostatic attractive forces. Consequently, an augmented BET equation was formulated as a combination of the individual BET equations for the internal (intra‐crystalline) surface adsorption and external (particle) surface adsorption. The augmented BET equation demonstrates excellent performance in representing measured water adsorption isotherms of a wide suite of silty and clayey soils, validating its applicability. The augmented BET equation excellently predicts the expected dominance of the external particle surface adsorption of the non‐polar N2 adsorption on clay soils, illustrating its ability in separating external and internal surface adsorption. Additionally, the specific surface area estimated by the augmented BET equation matches well the estimation by two independent methods, further confirming the validity of the augmented BET equation.

Drying kinetics and determination of water sorption isotherms of corn

The study was carried out for the purpose of determining the drying kinetics as well as moisture sorption isotherm of hybrid-81 corn. Corn at about 31% moisture content (wb) was dried in a forced convective hot air cabinet dryer at different drying conditions, such as variable air dry bulb temperature (40°C, 50°C and 60°C) and loading density (3.56 kg/m2, 7.12 kg/m2, and 10.68 kg/m2) as well as in shining sun at different layers (3.56 kg/m2, 7.12 kg/m2, and 10.68 kg/m2). The water sorption isotherm of the dried corn was developed using vacuum desiccators, which contained saturated salt solutions in the range of 11-93% RHs. The mono-layer moisture content calculated by the Brunauer–Emmett–Teller (BET) model (6.76 g/100 g solid) was lesser than that calculated by the Guggenheim–Anderson–De Boer (GAB) model (10.53 g/100 g solid). The energy constants were 10.45 and 4.64 as per BET and GAB equation, respectively. Both models gave suitable fits for corn. The activation energy (Ea) for diffusion of water was found to be 11.09 kcal/gm-mole for corn. Furthermore, it was noticed that, with the increase of corn layer, the drying rate decreased in case of both sun and mechanical drying. However, higher loading density resulted in efficient drying, at least up to 10.7 kg/m2. It was shown that the drying time to obtain stability was the lowest for moisture content (12.08 %) corresponding to aw of 0.65 in case of BET or GAB monolayer moisture content. This finding could be helpful in predicting the storage life of corn.J. Bangladesh Agril. Univ. 15(2): 309-317, December 2017

Esterification of guaiacol with octanoic acid over functionalized mesoporous silica

Ester products, obtaining from guaiacol and octanoic acid which were the degeneration products of lignin, were tested over sulfonic acid-functionalized SiO2 materials. The results showed that the functionalized mesoporous SiO2 had a high activity and stability, resulting in ester yield of 62%. The ratio of S/phenyl played an important role in the activity and stability of SiO2-Phenyl-SO3H. Moreover, the optimal guaiacol to octanoic acid molar ratio is 8:1. The physicochemical, structural, textural and thermal stability characteristics of the synthesized mesoporous catalysts were investigated by X-ray diffraction (XRD), surface area analysis (Brunauer–Emmett–Teller equation), FT-IR and thermogravimetric analysis (TGA). The result of catalyst characterization and experiment of filtering catalysts from mixture showed that the SO3H- group incorporated with functionalized silica precursors. Moreover, the catalytic results indicated that SO3H-phenyl- group was the active part and the phenyl group increased the hydrophobicity of the catalyst surface, which accelerated the mobility of water, shifted the equilibrium, protected the acid sites and enhanced the activity of catalysts.

Post-functionalization of polymeric mesoporous C@Zn core–shell spheres used for methyl ester production

In the present study, the mesoporous carbon@zinc (C@Zn) core-shell spheres were hydrothermally synthesized, using polyethylene glycol (PEG) as the surfactant and d-glucose as the pore forming agent. Then, the post-sulfonation treatment was carried out to prepare polymeric mesoporous SO3H-ZnO catalyst. The physicochemical, structural, textural and morphological properties of the synthesized catalysts were characterized by X-ray powder diffraction (XRPD), surface area analysis (Brunauer–Emmett–Teller equation), temperature programed desorption (TPD), field emission scanning electron microscopy (FE-SEM), and transmission electron microscopy (TEM). The polymeric mesoporous SO3H-ZnO catalyst owned a high surface area of 396.56 m2/g with the average pore size of 3.45 nm and acid strength of 1.92 ± 0.05 mmol/g. The catalytic activity of the synthesized catalyst was further studied via esterification of the palm fatty acid distillate (PFAD), using a microwave-assisted technique. The biodiesel yield of 91.20% was achieved under the optimized esterification conditions as follows: the methanol to PFAD molar ratio of 9:1, catalyst concentration of 1.5 wt%, reaction temperature of 90 °C and reaction time of 15 min. The spent mesoporous catalyst was highly stable for reuse with nine continuous runs without further treatment.

Optimization of Kinetic Pore Size for Methane Storage Behavior of Pitch‐based Activated Carbon Fibers

Pitch‐based activated carbon fibers were prepared for application to methane storage. Chemical activation was accomplished by treatment with potassium hydroxide and heat, leading to increased specific surface area and micropore volume. Structural properties and morphology were evaluated by X‐ray diffraction and scanning electron microscopy, respectively. Textural properties and microporosity were determined from N2 /77 K adsorption–desorption isotherms using the Brunauer–Emmett–Teller equation and the Horvath–Kawazoe method. The methane storage capacity is influenced by activation time. This is attributed to the creation of a narrow distribution of micropores, which is a factor closely related to the methane storage capacity. This indicates that the methane storage behavior depends on the pore volume. Although a large pore volume is desirable for methane storage, the size of the pores in the activated carbon fibers that facilitate the activation process is also a significant factor.

Moisture sorption isotherm characteristics of Hemerocallis Fulva and Cymbopogon

AbstractThe moisture sorption isotherms of Hemerocallis Fulva and Cymbopogon are measured by the static gravimetric method at 25, 35, and 45 °C over a water activity range of 0.09 to 0.95 using standard saturated salt solutions. The sorption isotherms of H. fulva and Cymbopogon display type III (J‐shaped) and type II (nearly sigmoid shapes) isotherms. In addition, the adsorption and desorption data of H. fulva and Cymbopogon fit well with the White & Eiring model and the Oswin model, respectively. The Brunauer–Emmett–Teller equation is applied to determine the monolayer moisture content, and the surface area of a monolayer was calculated. The values of the net isosteric heat of sorption are found to increase with decreases in the equilibrium moisture content. Moreover, the net isosteric heat of desorption is higher than that of the adsorption heat. Copyright © 2016 Curtin University of Technology and John Wiley & Sons, Ltd.