Non-linear Isotherm Models Research Articles

RETRACTED: Application of natural and modified hectorite clays as adsorbents to removal of Cr(VI) from aqueous solution–Thermodynamic and equilibrium study

A hectorite (H) clay sample has been modified with 2-mercaptobenzimidazole (MBI) using homogeneous and heterogeneous routes. Both modification methodologies resulted in similar products, named H(HOM) and H(HET), respectively. These materials were characterized by CO(2) gas adsorption, elemental analysis, nuclear magnetic nuclei of carbon-13 and silicon-29. The effect of two variables (contact time and metal concentration) has been studied using batch technique at room temperature and pH 2.0. After achieving the best conditions for Cr(VI) adsorption, isotherms of this adsorbate on using the chosen adsorbents were obtained, which were fitted to non-linear Sips isotherm model. The maximum number of moles adsorbed was determined to be 11.63, 12.85 and 14.01 mmol g(-1) for H, H(HOM) and H(HET), respectively, reflecting the maximum adsorption order of H(HET)>H(HOM)>H. The energetic effects (Delta(int)H degrees , Delta(int)G degrees and Delta(int)S degrees ) caused by chromium ion adsorption were determined through calorimetric titrations.

Sorption behavior of a synthetic antioxidant, polycyclic musk, and an organophosphate insecticide in wastewater sludge

Emerging contaminants (ECs) are chemicals that are currently unregulated due to limited understanding of health effects and limited data regarding occurrence. Wastewater treatment plants (WWTP) receive many ECs as components of influent waste and the removal of organic contaminants, such as ECs, occurs primarily by sorption to sludge. Therefore, it is important to develop measures of sorption behavior by ECs to sludge. This study evaluates sorption of three ECs: 3-tert-butyl-4-hydroxyanisole (BHA) a synthetic antioxidant, 1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexamethyl-cyclopenta(g)-2-benzopyrane (HHCB) a polycyclic musk, and chlorpyrifos a organophosphate insecticide. Twenty-four hour laboratory-scale sorption experiments were conducted for each compound individually and then in combination, which allowed the quantification of sorption onto wastewater sludge and the affects of multiple compounds. ECs in both the liquid and solid phases were analyzed using a gas chromatograph with flame ionization detector (GC/FID). Isotherms of individual sorption behavior followed a linear trend (R2 > 0.9) for individual ECs, while K(d) averaged 2,689 L kg(-1), 27,786 L kg(-1) and 31,402 L kg(-1) for BHA, chlorpyrifos and HHCB, respectively. Sorption behavior for BHA was linear during combined studies with K(d) of 1,766 L kg(-1) or a decrease of 34%, while HHCB and chlorpyrifos followed non-linear isotherm models. Synergistic effects were observed with spike concentrations > or =25 mg L(-1) for HHCB and > or =20 mg L(-1) for chlorpyrifos. K(d) values ranged from 16,984-6,000,000 L kg(-1) for HHCB and 19,536-3,000,000 L kg(-1) for chlorpyrifos. These distribution coefficients differed substantially from previously published values, mainly because few studies used sludge as the sorption media. Results suggest that HHCB and chlorpyrifos may be contained in the sludge unlike BHA, which is more available in the aqueous phase. Future investigations should evaluate WWTP processes for degrading ECs to harmless products and releases of ECs from sludge.

RETRACTED: Layer silicates modified with 1,4-bis(3-aminopropyl)piperazine for the removal of Th(IV), U(VI) and Eu(III) from aqueous media

Natural montmorillonite (M) and synthetic kanemite (K) have been functionalized with 1,4-bis(3-aminopropyl)piperazine reacted with methylacrylate to yield new inorganic-organic chelating materials. The original and modified materials were characterized by X-ray diffractometry, textural analysis, SEM and nuclear magnetic nuclei of carbon-13 and silicon-29. The chemically modified clay samples (M-APPMA and K-APPMA) showed modification of its physical-chemical properties including: specific area 45.0m(2)g(-1) (M) to 978.8 m(2)g(-1) (M-APPMA) and 23.5m(2)g(-1) (K) to 898.9 m(2)g(-1) (K-APPMA). The ability of these materials to remove thorium(IV), uranyl(VI) and europium(III) from aqueous solution was followed by a series of adsorption isotherms, which were fitted to non-linear Sips adsorption isotherm model. To achieve the best adsorption conditions the influence of pH and variation of metal concentration were investigated. The energetic effects (Delta(int)H degrees , Delta(int)G degrees and Delta(int)S degrees ) caused by metal ions adsorption were determined through calorimetric titrations.

Porogen effect on characteristics of banana pith carbon and the sorption of dichlorophenols

Banana pith was used as precursor material to prepare carbon with and without porogens. Characterization of the carbons showed higher BET surface area (1285 m 2/g) for ZnCl 2-treated carbon, comparatively. Adsorption experiments were conducted to study the removal of 2,4-dichlorophenol (DCP) from aqueous solutions using the carbons under varying experimental conditions. Decrease in pH increased the percentage removal. All the carbons studied showed greater percentage of DCP removal with decrease in the initial concentration of DCP. Kinetic studies showed that the adsorption of DCP on the carbons was a rapid process. Nonlinear forms of pseudo-first-order and pseudo-second-order models were used to fit the experimental data. Among these the pseudo-first-order model described the data with high correlation coefficients and low percentage error values. Four nonlinear isotherm models including the Langmuir, Freundlich, Toth, and Sips were used to analyze the experimental DCP isotherms under different pH (2–4) conditions. Adsorption capacities ( Q max ) from the Langmuir model were found to be 129.4, 67.7, and 49.9 mg/g for ZnCl 2-treated, KOH-treated, and porogen-free carbon, respectively, at pH 2. From desorption studies it seemed that chemisorption played a major role in the adsorption process. The results indicated that ZnCl 2-treated carbon could effectively remove phenols from wastewater.

Revised Ion Exchange Method for Estimation of Conditional Stability Constants of Metal−Dendrimer Complexes

This study reports a revised method for determination of the conditional stability constant (Kc) and the equilibrium metal-to-ligand molar ratio (n) for various metal−dendrimer complexes. The method employs a system containing an ion-exchange resin, a dendrimer, and a metal (Cu2+ or Pb2+) solution. It considers the multi-dentate nature of dendrimers and employs a nonlinear (Langmuir) isotherm model to interpret the ion exchange isotherm. For its minimal dendrimer uptake, a weak acid cation-exchange resin, IRC-50, was found most suitable for the study. For complexes of Cu2+ with a homologue of dendrimers with NH2 terminal groups Kc increased from 1016.2 to 1036.6, and n increased from 1 to 13 as the generation number rose from 0.0 to 4.0. Kc for complexes of Pb2+ with a generation-1 dendrimer with NH2 terminal groups was 1017.2 at pH 5, compared to 1020.9 for complexes of Pb2+ with a generation-1.5 dendrimer with carboxylate terminal groups.

Sorption Isotherms and KocS Estimation of Pyrethroids in Sediments

Laboratory sorption isotherm batch studies have been attempted to elucidate interaction of synthetic pyrethroids (bifenthrin and permethrin) with sediments and their fractions. As a nonlinear isothermal model, the Freundlich equation was applied to sorption results obtained from sediments to investigate the relationship between synthetic pyrethroids and sediments containing different amounts of organic carbon. Results demonstrated that the sorption capabilities of bifenthrin and cis- and trans-permethrin was in the order of bifenthrin, cis-permethrin and trans-permethrin, respectively, indicating that adsorbed bifenthrin was the most stable followed by cis- and trans-permethrin in all sediments. Their sorption capability was closely related to organic carbon contents in sediments. Higher sorption was observed in sediments containing higher organic carbon contents. Sorption study extended into the fractions, clay and humic acids, extracted from a sediment, indicated that higher sorption capacity in humic acids occurred than in the clay of both examined bifenthrin and permethrin. This study demonstrates the sorption of synthetic pyrethroids with sediments, and will help in the understanding of the transport and fate of synthetic pyrethroids existing in field sediments.

Experimental determination of adsorption energies, adsorption isotherms, probability density functions, and lateral molecular interactions on C XH Y/CaO systems

Reversed-flow gas chromatography (RF-GC) is extended to the measurements of the probability density function for the adsorption energies as well as the differential energies of adsorption due to lateral interactions of molecules adsorbed on different heterogeneous solid surfaces. All these calculations are based on a non-linear adsorption isotherm model as it is well accepted that the linear one is inadequate for substances such as these used in this work. Thus, some new important physicochemical parameters have been obtained for the characterization of the heterogeneous systems studied. The adsorbent used in this study was calcium oxide. The adsorption of many significant hydrocarbons was investigated. With these systematic experiments under conditions which are similar to the atmospheric ones, an extrapolation of the results obtained to “real” atmospheres with a high degree of confidence is possible.

Propagation of nonlinear reactive contaminants in porous media

A study on the effect of nonlinear reactions on the space and time distribution of contaminant plumes governed by the advective‐dispersive equation in porous media was conducted. Several models of nonlinear reactions were considered: the irreversible nonlinear first‐order kinetic sorption model, the nonlinear Freundlich sorption isotherm model, the nonlinear Langmuir sorption isotherm model, and the reversible nonlinear kinetic sorption model. Each of these models was coupled with the advective‐dispersive equation with dimensionless concentration and an approximate analytical series solutions was obtained. Comparison between linear and nonlinear plumes indicated that nonlinear reactions may have a significant effect on the shape and spatial distribution of a contaminant at a given time and in certain cases may explain quantitatively the occurrence of scaled (e.g., concentration change while preserving shape), retarded, and nonsymmetric plumes as well as the presence of back tails and sharp front ends usually observed in the field. By adopting a nonlinear model of contaminant migration a more realistic representation of contaminant propagation is possible than that obtained with a linear model.

Author Index for Volume 211

Casuarina equisetifolia pines are degradable biopolymeric substance with dye-sequestering property was utilized as biosorbent to expel a cationic dye; methylene blue dye from simulated wastewater. The prepared adsorbent material was characterized for their structural, morphological and elemental features to understand their suitability in augmenting in dye-wastewater remediation. The results infer that 0.5 g/L biosorbent was proficient in removing 100 mg/L methylene blue (pH 7.0 ± 0.2) when agitated at 150 rpm for 120 min. Isothermal behavior were evaluated using non-linear isotherm models like Temkin, Langmuir and Freundlich models while the rate-limiting steps were found using kinetic models. Temkin isotherm and pseudo-first order model explained the removal mechanism among the models evaluated, which infers that the biosorption followed physisorption with the maximum adsorption capacity of 41.35 mg/g. Thermodynamic behavior of methylene blue removal by C. equisetifolia pines powder described the feasibility of biosorption as well as the type of heat involved. Equilibrium sorption capacities, rate constants and correlation coefficients explains that MB dye removal by C. equisetifolia pines is presumably physisorption, spontaneous and endothermic in nature.

Comparison of Equilibrium and Nonequilibrium Models in the Simulation of Multicomponent Sorption Processes

A mathematical model has been developed to describe the process of equilibrium adsorption from a finite bath. A nonlinear Fritz-Schluender isotherm model was used to describe the equilibrium between solid and liquid phases. Finite-difference numerical solutions for single, binary, and ternary systems were obtained and shown to match previously published experimental data satisfactorily. These solutions were also compared with nonequilibrium models for the three cases. It was shown that the nonequilibrium model is superior to the equilibrium one since 1) it is applicable to both equilibrium and nonequilibrium conditions, 2) its computer program is general and can be used for any number of sorbates, 3) it can be used for any type of linear or nonlinear equilibrium isotherms without the need to any modifications in the program, and 4) its numerical solutions are of high accuracy compared to experimental data.

Sorption of hydrophobic organic pollutants in saturated soil systems

Sorption equilibria and rates were characterized for a matrix of four aquifer sands and two slightly to moderately hydrophobic organic solutes (nitrobenzene and lindane), and the effects of sorption on the behavior of these solutes in saturated systems of the soils were determined. Experimental data were used to test and evaluate a variety of mathematical models for predicting contaminant fate and transport in groundwater systems. Observed equilibrium relationships between soil and solution phase solute concentrations were found to be described best by the nonlinear Freundlich isotherm model. It was further determined that the sorption process in the systems tested is rate controlled, requiring several days to approach equilibrium in completely mixed batch reactors. Subsequent modeling of solute transport in continuous flow soil column reactors was found to be most successful when rate-controlled models were used, the best results were obtained with a dual-resistance model incorporating the coupled mass transport steps of boundary-layer and intraparticle diffusion.

A Non-Linear Isothermal Model for Migration of Drugs in Wet Granulations

AbstractA non-linear isothermal model for migration of drugs during drying period in wet granulations is proposed and some of its important properties are introduced. The mathematical expression is derived from physical fundamentals in such a way that computer implementation is feasible. The model includes the well-known Rumpf and Washburn equations, and it can be used as a suitable starting point for numerical simulation experiments.