Modified BET Model Research Articles

Combined effects of pore structure and surface chemistry on water vapor adsorption characteristics of coal: Equilibrium, thermodynamic and kinetic studies

The combined effects of surface chemistry and pore structure on water vapor adsorption characteristics of coal were studied by evaluating the equilibrium, thermodynamic and kinetic properties. Four coal samples of different rank were fully characterized with gas (N2 and CO2) sorption and Fourier Transform infrared spectroscopy (FTIR) methods. Then measurements of water vapor adsorption equilibrium and kinetics were undertaken at elevated temperatures. Equilibrium and kinetic data were fitted by the modified BET model and the unipore model, respectively. The thermodynamic parameters, as well as diffusion activation energy were estimated based on the adsorption data. The results demonstrate that water vapor adsorption depends on the surface chemistry but unrelated to the pore structure, because the pore space is not completely filled by water molecules even at the saturation pressure. The monolayer adsorption capacity decreases with increasing coal rank. Moreover, water vapor needs lower work to attain equilibrium on high-ranked coal. Also, the binding affinity of water molecule with primary sites is stronger than secondary sites. Furthermore, the diffusion coefficient decreases with coal rank, and the diffusion activation energy for high-volatile bituminous is higher than the other coals, as a result of the complexity and poor connectivity of its pore network.

Phase diagram prediction and experimental verification of a binary hydrated salt mixture as phase change thermal storage materials

As an important inorganic phase change materials (PCMs), hydrated salts have many advantages such as high latent heat, moderate thermal conductivity, low cost and excellent fire safety compared with organic PCMs. The phase change process of hydrated salts has a significant effect on thermal storage performance. It is meaningful to predict the phase change process by the thermodynamic models. The modified BET model is an effective method to predict the phase diagram of water–salt system. In this work, an applicability of modified BET model used for Na2SO4·10H2O and KAl(SO4)2·12H2O binary hydrated salt mixture was confirmed. According to the BET parameters and solubility constants, the solubility phase diagram of this binary hydrated salt mixture was predicted with modified BET model, and Na2SO4·7H2O was found when Na2SO4·10H2O was lower than 44 wt%. Besides, the phase diagram and the existence of Na2SO4·7H2O were validated in the DSC and XRD measurements. The function of Na2SO4·7H2O to eliminate phase separation was interpreted as that it acts as a thickener to prevent water molecules from escaping from the liquid and avoids the formation of anhydrous Na2SO4. This work could guide the design of binary hydrated salt mixtures as thermal storage materials, and provide new insights for phase separation elimination of hydrated salt mixtures.

Adsorption Isotherms and Thermodynamic Properties of Dried Tomato Slices

Moisture adsorption isotherms and thermodynamic properties of dried tomato slices obtained from four tomato varieties were investigated. Freshly harvested tomatoes were pretreated with potassium metabisulphite solution (0.2%, weight/volume) before drying in a cabinet dryer at 60± 2° C. Moisture adsorption behavior of the dried tomato slices was determined using the static gravimetric method at 25, 30 and 40o C. The data fitted to GAB, M.BET, DLP, Smith and Oswin sorption models. The isosteric heat of sorption was also determined. Moisture adsorption isotherm of dried tomato slices from UC82B, Roma, Eva-F1 and Kerewa varieties exhibited a sigmoid isotherm curve typical of type II BET classification. Increase in temperature resulted into a decrease in the equilibrium moisture content. The GAB, DLP and modified BET model adequately modeled the isotherms of dried tomato slices. The relationship between isosteric heat of sorption and the equilibrium moisture of dried tomato slices were accurately described by exponential model.

Mechanisms of aromatic molecule - Oxygen-containing functional group interactions on carbonaceous material surfaces

Surface oxygen-containing functional groups (OFGs) at different sites of carbonaceous materials showed different effects on the normalized monolayer adsorption capacity (QBET/A) obtained from the modified BET model. The OFGs on mesoporous surfaces inhibited the adsorption via the water competition, whereas those on the external surface promoted the adsorption due to the enhanced hydrophobic driving force and electrostatic forces, as analyzed from the adsorption molar free energy. Multiple linear relationships were established between the monolayer adsorption capacity QBET/A and the amounts of OFGs on mesoporous and the external surfaces ([O]meso and [O]external, respectively). The properties of aromatic adsorbate compounds, the polar area radio of aromatic molecule to water (PAad/w), and the log Kow together influenced the inhibition or promotion effects of OFGs. These results would allow predictions of adsorption behavior of aromatic compounds on carbonaceous materials on the basis of OFGs parameters. Theoretical calculations and simulations projected the configuration of aromatic molecules being parallel to the graphene sheets of carbonaceous materials. The symmetry-adapted perturbation theory (SAPT) energy decomposition showed that the electrostatic forces intensified with the increase of adsorbate polarity. These analyses revealed that the electrostatic forces were enhanced in the presence of OFGs and that the π-π EDA (electron donor-acceptor) was the main force.

Thermodynamic modeling and experimental verification of new eutectic salt mixtures as thermal energy storage materials

In this work, modified BET model was applied to obtain phase diagrams and to design new eutectic mixtures. As a result, the eutectic composition and the melting point of two mixtures based on salt hydrates: LiNO3·3H2O–NaNO3–Mn(NO3)2·6H2O and LiNO3·3H2O–Mn(NO3)2·6H2O–Mg(NO3)2·6H2O were predicted. Both mixtures present the same predicted melting temperature of 10.8 °C. Experimental verifications by T-history method showed satisfactory accordance of the predicted temperatures values with a difference of 0 °C and +2.3 °C for the mixtures, with sodium nitrate and magnesium nitrate, respectively. It is added that the thermal and physical properties such as density, the heat capacity for solid and liquid phases, as well as viscosity and volume change during the fusion of the new PCMs were evaluated. The results of the characterization, the energy storage density (about 300 MJ m−3) and material cost estimation show that both mixtures are promising candidates for use in low temperature energy storage systems.

Application of ANN Predictive Model for the Design of Batch Adsorbers - Equilibrium Simulation of Cr(VI) Adsorption onto Activated Carbon

Background: Escalation of industrial processes continues to increase the concentrations of Cr(VI) in wastewater above permissible discharge limits. Persistent exposure to Cr(VI)may result in deleterious effects on human health, aquatic life, and the environment. Laboratory-scale adsorption studies have proven effective in achieving the low treatment levels demanded by statutory authorities. The eventual design of the pilot and full-scale systems hinges on the ability to predict adsorption behavior mathematically. Objective: The objective of this study is to elucidate the mechanism of Cr(VI) adsorption and to develop an Artificial Neural Network (ANN) model capable of accurately simulating complex multi-layered adsorption processes. Methods: Batch equilibrium experiments were conducted for the removal of Cr(VI) by activated carbon. Conventional two and three-parameter equilibrium models such as the Langmuir, Freundlich, Sips, original BET and modified BET were used to simulate the data and expound the mechanism of adsorption. An ANN model was constructed with the built-in effect of the residual Cr(VI) concentration for the prediction of the equilibrium sorption capacity. Results: The modified BET model was most successful at predicting the monolayer coverage. However, the model failed to capture the complex shape of the isotherm at higher initial concentrations. The highest correlation to the equilibrium data was revealed by the ANN model (R2 = 0.9984). Conclusion: A batch adsorber was successfully designed using mass balance, and incorporating the predictive ability of the ANN model. In spite of the ANN’s ability to simulate the adsorption process, it provides little insight into the mechanism of adsorption. However, its ability to accurately predict Cr(VI) removal enables the up-scaling of the adsorption processes to pilot and full-scale design.

Application of the modified BET model to concentrated salt solutions with relatively high water activities: Predicting solubility phase diagrams of NaCl + H2O, NaCl + LiCl + H2O, and NaCl + CaCl2 + H2O

Solubility phase diagrams of mixtures of salts and water are of interest in various application fields and can be calculated using the modified BET model. In comparison with other thermodynamic models, the modified BET model requires only two salt-specific model parameters and has shown to possess a predictive capability. In this work, the modified BET equations are extended in order to calculate solubility phase diagrams of concentrated salt solutions with relatively high water activities within the range of undersaturation. As an example, BET parameters of NaCl are determined and applied to calculate solubility phase diagrams of NaCl + H2O, NaCl + LiCl + H2O, and NaCl + CaCl2 + H2O within the temperature range of around 250–500 K. In the ternary systems, the best agreement with solubility data from literature is obtained using constant BET parameters of NaCl and an additional temperature-dependent regular solution parameter to account for salt-salt interaction.

Porosity induced thermoelectric performance optimization for antimony telluride

Sb2Te3 bulks with various porosities are synthesized via applying different pressures and processes. Pores defect variations are demonstrated by positron annihilation spectroscopy measurement. Through tuning sintering temperature and pressure exerted in one step or two steps, pores and interfaces of the materials are tailored, which enhances the Seebeck coefficient, simultaneously maintains high electrical conductivity and remarkably reduces thermal conductivity. A maximum ZT of 1.17 is obtained at 523 K for Sb2Te3 samples compacted in two steps under 10 kN, increasing by 54.1% as compared to corresponding sample under 1 kN. Lattice thermal conductivity calculation by modified BET model combining with effective medium theory fits with experiments data, revealing porosity manipulation plays a significant role in reducing thermal conductivity.

Correlation of swelling and sorption properties of block coal sample

The swelling and sorption experiments were carried out simultaneously for two block coal samples under CO2 and CH4 pressure (up to 16MPa) at three temperatures (25, 45 and 65°C). The absolute sorption isotherms present type-II pattern and can be described by a modified BET model. The swelling isotherms present L-type pattern and can be described by a modified Langmuir model. The relationship between swelling ratio and absolute sorption amount presents S-type pattern and can be described by a modified Gompertz function (a logistic function). It is interesting to find that the correlations of normalized properties have a single relationship that is independent of experimental conditions, coals and gases. When the sorption amount approaches to the monolayer sorption coverage (na/nm=1), the swelling ratio reaches ∼93% of the maximum swelling ratio. It implies the importance of the mutual contact between coal and sorbate. The differential characteristic of swelling process shows that the swelling rate with respect to sorption amount varies with the sorbate coverage; the swelling rate peaks at na/nm≈0.37 and approches zero at na/nm≈1.5. In addition, a theoretical model correlating swelling and sorption was established. The concept of reduction of surface free energy by sorption was taken into account. It is encouraged that the experiment data match of model is generally acceptable.

A comparison of desorption process of Chinese and Australian lignites by dynamic vapour sorption

ABSTRACTModified BET model and Do and Do (D.D.) model were chosen to interpret the desorption process of water on hard and soft lignites. The organic and inorganic hydrophilic sites were determined by X-ray photoelectron spectroscopy and X-Ray fluorescence spectroscopy. From the modified BET model, only a small part of hydrophilic sites (HSs) acted as effective primary sites due to space restraint, intramolecular hydrogen bond and maybe more than one hydrophilic site connecting with one water molecule. From the D.D. model, the total adsorption sites (St) of Loy Yang lignite (LY) is 18.7 mmol/g, which is higher than that of Shengli (SL) 17.0 mmol/g in spite of lower primary sites, and the saturation concentration of water (qus) in the micropore of LY is 33.7 mmol/g, which is much higher than that of SL (12.5 mmol/g). So the high moisture-holding capacity of LY is mainly determined by the high St and qus, and not the primary sites. The size of water clusters entering the micropores is 7 for SL and 6 for LY, which is related to relative location of HS. When dewatered, the higher total sites density and smaller water cluster size of LY both implied higher dewatering energy.

Validation of Using a Modified BET Model to Predict the Moisture Adsorption Behavior of Bituminous Coal

A good correlation exists between the amount of moisture adsorbed and the oxygen content of medium-rank B vitrinite-rich and medium-rank C inertinite-rich bituminous coal. Total mass moisture adsorbed per gram of coal determined from the modified BET model provides a better approximation than the BET model. The relationship between the modified BET moisture monolayer coverage and the area of surface oxygen groups suggests that moisture is adsorbed at these sites. Oxygen content is a good indicator of the amount of moisture adsorbed on bituminous coal. Open hysteresis loops indicate that moisture is retained on medium-rank C inertinite-rich bituminous coals.

Water sorption on coals

Water vapor adsorption/desorption isotherm studies were performed on high volatile bituminous B coal and lignite to investigate the behavior of water on coal. The characterization of water sorption was studied by kinetic and equilibrium data, at a temperature of 298 K and a relative vapor pressure up to 0.95. Water sorption isotherms have a standard type II sigmoid shape obeying the BET model in the relative pressure range 0.05–0.35. A modified BET model was used to estimate the water adsorbed on primary and secondary sites, respectively. The specific surface areas estimated with water and CO 2 were similar and about 95 and 52 m 2 g −1 for high volatile bituminous B coal and lignite, respectively. The adsorption capacity of water and CO 2 was related to the oxygen content of coal and the proportion of inorganic matter. The water adsorption and desorption isotherms produce a different hysteresis loop for the two coals. On the other hand, the diffusion coefficient of water adsorption was estimated at about 10 −16 m 2 s −1, by the unipore model. From the diffusion coefficient of water, which varied with increase in relative pressure, it is shown that water adsorbs first on primary sites, before formation of water clusters and their micropore filling which was a slow process.

Thermodynamic study of the system (LiCl + CaCl 2 + H 2O)

Solubility isotherms of the ternary system (LiCl + CaCl 2 + H 2O) were elaborately determined at T = (283.15 and 323.15) K. Several thermodynamic models were applied to represent the thermodynamic properties of this system. By comparing the predicted and experimental water activities in the ternary system, an empirical modified BET model was selected to represent the thermodynamic properties of this system. The solubility data determined in this work at T = (283.15 and 323.15) K, as well as those from the literature at other temperatures, were used for the model parameterization. A complete phase diagram of the ternary system was predicted over the temperature range from (273.15 to 323.15) K. Subsequently, the Gibbs free energy of formation of the solid phases CaCl 2 · 4 H 2O (s), CaCl 2 · 2 H 2O (s), LiCl · 2H 2O (s), and LiCl · CaCl 2 · 5H 2O (s) was estimated and compared with the literature data.

Thermodynamic study of the system (LiCl + LiNO3 + H2O)

The solubility of the binary system (LiNO3+H2O) from T=273.15K to T=333.15K and solubility isotherms of the ternary system (LiCl+LiNO3+H2O) were elaborately measured at T=273.15K and T=323.15K. These solubility data, as well as water activities in the binary systems from the literature, were treated by an empirically modified BET model. The isotherms of the ternary system (LiCl+LiNO3+H2O) were reproduced and a complete phase diagram of the ternary system in the temperature range from 273.15K to 323.15K predicted. It is shown that the solubility data for the binary system (LiNO3+H2O) measured in this work are slightly different from the literature data. Simulated results showed that the saturated salt solution of (2.8LiCl+LiNO3) is in equilibrium with the stable solid phase LiNO3(s) over the temperature range from 283.15K to 323.15K, other than the solid phases LiNO3·3H2O(s) and LiClH2O(s) as reported by Iyoki et al. [S. Iwasaki, Y. Kuriyama. T. Uemura, J. Chem. Eng. Data 38 (1993) 396–398].

Comparison of the Sorption Isotherm Characteristics of Two Cassava Products

The sorption characteristics of two cassava products were obtained using the gravimetric method at three temperatures, 20, 30, and 40°C. The GAB, BET, and the modified BET models were found to describe the data reasonably well. The heat of sorption, which varied from 39.47 kJ/mol at 1% moisture content to 4.92 kJ.mol−1 at 20% moisture content dry basis, was calculated for the garified product. Similar values for the ungarified product were found to vary from 26.98 kJ/mol at 1% moisture content to 4.97 kJ/mol at 20% moisture content. The shelf-life for both products were estimated from sorption data and recommendations on their packaging and storage conditions given. The garified product was found to have a higher capacity for moisture adsorption and also potentially stores longer than the ungarified product.

Moisture adsorption–desorption isotherms of Citrus reticulata leaves at three temperatures

The equilibrium moisture contents of Citrus reticulata leaves were measured by the gravimetric static method. The equilibrium was achieved after 12 days for desorption and 10 days for adsorption at 30, 40 and 50 °C with water activity ranging from 5% to 90%. The sorption isotherms of C. reticulata leaves decreased with increase in temperature at constant relative humidity. An hysteresis effect was observed. The experimental data of sorption were fitted by six models (Modified Henderson, Modified Chung-Pfost, Modified Oswin, Modified Halsey, GAB and Modified BET). Only the GAB and modified BET models were found to be the most suitable for describing the sorption curves. The net isosteric heat of sorption of C. reticulata leaves decreases with an increase in moisture content and was found to be a polynomial function of moisture content for adsorption and desorption.

Use of Sorption Isotherms for the Estimation of Shelf Life of Two Zimbabwean Flours

AbstractThe water sorption characteristics of two Zimbabwean flours, i.e. maize‐meal and millet, were obtained using the gravimetric method at temperatures of 20, 30 and 4Od̀C. The GAB, BET and the modified BET models were found to describe the data reasonably well. The heat of sorption, which varied from 1.915 kJ.mol−1 at 20% moisture content to 30.5 kJ.mol−1 at 1% moisture content dry‐basis was calculated for the maize meal. Similar values for the millet were found to vary from 1.87 kJ.mol−1 at 20% moisture content to 18.3 kJ.mol−1 at 1% moisture content. The shelf lives for both materials were estimated from the sorption data, and recommendations on packaging and storage conditions are suggested.

Quantum Effects on Hydrogen Adsorption in Internal Nanospaces of Single-Wall Carbon Nanohorns

Hydrogen adsorption isotherms in single-wall carbon nanohorns (SWNHs) have been measured at 20 K. The pore volume from hydrogen adsorption is compared with that from nitrogen adsorption at 77 K to determine the density of confined hydrogen in the internal space of SWNHs; it indicates that the average density of confined hydrogen inside SWNHs at 20 K is higher than that of liquid hydrogen in the bulk and nearly approaches the density of solid hydrogen at the triple point. The surface area from hydrogen adsorption using the BET theory is anomalously large compared with that for nitrogen; however, an alternative method (modified BET theory), in which an assumption is made that the energy of a molecule in the second layer is larger than that in the liquid, gives a reasonable surface area, especially when the adsorbed hydrogen in the first layer is assumed to be in a solid state. In the modified BET model, a packing constraint of the second layer due to the cylindrical geometry of SWNH is also taken into accou...

Moisture sorption isotherms and heat of sorption of bitter orange leaves ( Citrus aurantium)

Moisture adsorption–desorption isotherms (EMC/e.r.h.) of Citrus aurantium leaves were determined at 30, 40, and 50 °C using the standard gravimetric static method over a range of relative humidity from 0.05 to 0.9. The experimental sorption curves were fitted by six equations: modified Chung–Pfost, modified Halsey, modified Oswin, modified Henderson, modified BET, and GAB. The modified Halsey and the modified BET models were found to satisfactorily describe the desorption isotherms of Citrus aurantium leaves. For adsorption, GAB and modified BET models were the best fit. The net isosteric heats of sorption of water were determined from the equilibrium data at different temperatures.

Equilibrium moisture content and heat of sorption of Gelidium sesquipedale

Moisture equilibrium data for adsorption and desorption of water from Gelidium sesquipedale were investigated at temperatures in the range of 30–50°C and water activity ranging from 0.05 to 0.9. The experimental procedure used was based on the gravimetric static method. The sorption curves of Gelidium sesquipedale decreased with increase in temperature at constant relative humidity. The hysteresis effect was observed. The experimental data of sorption were described by six models. The GAB and modified BET models were found to be the most suitable for describing the sorption curves. The isosteric heats of desorption and adsorption of water were determined from the equilibrium data at different temperatures.