Adsorption isotherm models and error analysis for single and binary adsorption of Cd(II) and Zn(II) using leonardite as adsorbent

Leonardite, a by-product from coal mines, was applied to adsorb Cd(II) and Zn(II) from aqueous solutions. Individual and simultaneous adsorptions of the two metal ions were investigated. In a single-component adsorption system, Langmuir and Freundlich isotherms were fitted to the adsorption data. Linear and nonlinear regression methods were used for the assessment of the optimum adsorption isotherm. Error functions including root-mean-square error, sum of the squares of the errors, mean absolute percentage error, Marquardt’s percent standard deviation (MPSD), and Chi-square were applied in the nonlinear regression. The most suitable model for the adsorption of Cd(II) and Zn(II) in the single system is the Freundlich isotherm. The isotherm parameters calculated by MPSD provided the lowest sum of normalized error (SNE) value. The adsorption capacity was found to be 23.89 mg/g for Cd(II) and 16.86 mg/g for Zn(II). It was observed that the adsorption of Cd(II) on leonardite is greater than that of Zn(II). For binary component adsorption systems, Cd(II) and Zn(II) showed antagonistic behavior. The presence of the other metal ions could decrease the amount of metal adsorbed. Binary adsorption of Cd(II) and Zn(II) was tested with regard to four multi-component isotherms: Extended Langmuir, Modified Langmuir, Sheindorf–Rebuhn–Sheintuch, and Extended Freundlich. The Extended Freundlich isotherm proved to be a good fit for the experimental data.     

Equilibrium sorption of crude oil by expanded perlite using different adsorption isotherms at 298.15 k

During the past decades, a significant increase occurred in accidental oil spill in the aquatic environments. In this regard, oil spill in Marine freshwater is still considered as a major environmental hazard. In this research, the experimental data on the sorption capacity of expanded perlite to crude oil were correlated with the equilibrium isotherm of Langmuir, Freudlich, Tempkin and the three parameter Redlich-Peterson isotherms. The results obtained from each specified isotherms were compared and accuracy of the models were favorably discussed. Accuracy of each model using the error function were evaluated. Moreover, the effect of type of objective function on the final results was investigated. To bring up the idea; the sum of square of the average squares of the errors, the sum of the squares of the errors, the hybrid fractional error function, Marquardt’s percent standard deviation and Chi-Square objective function were used and the accuracy was obtained using each objective function. The results showed that the Redlich-Peterson model can better represent the equilibrium isotherm data for the crude oil to be up taken on the expanded perlite.     

Comparison of linear and nonlinear forms of isotherm models for Zn(II) and Cu(II) sorption on a kaolinite

The most appropriate method in designing the adsorption systems and assessing the performance of the adsorption systems is to have an idea on adsorption isotherms. Comparison analysis of linear least square method and nonlinear method for estimating the isotherm parameters was made using the experimental equilibrium data of Zn(II) and Cu(II) onto kaolinite. Equilibrium data were fitted to Freundlich, Langmuir, and Redlich–Peterson isotherm equations. In order to confirm the best-fit isotherms for the adsorption system, the data set using the chi-square (χ ²), combined with the values of the determined coefficient (r ²) was analyzed. Nonlinear method was found to be a more appropriate method for estimating the isotherm parameters. The best fitting isotherm was the Langmuir and Redlich–Peterson isotherm. The Redlich–Peterson is a special case of Langmuir when the Redlich–Peterson isotherm constant g was unity. The sorption capacity of kaolinite to uptake metal ions in the increasing order was given by Cu (4.2721 mg/g)?<?Zn (4.6710 mg/g).     

Removal of lead from aqueous solution using low cost abundantly available adsorbents

The removal of poisonous Pb (II) from wastewater by different low-cost abundant adsorbents was investigated. Rice husks, maize cobs and sawdust, were used at different adsorbent/metal ion ratios. The influence of pH, contact time, metal concentration, adsorbent concentration on the selectivity and sensitivity of the removal process was investigated. The adsorption efficiencies were found to be pH dependent, increasing by increasing the solution pH in the range from 2.5 to 6.5. The equilibrium time was attained after 120 min and the maximum removal percentage was achieved at an adsorbent loading weight of 1.5 gm. The equilibrium adsorption capacity of adsorbents used for lead were measured and extrapolated using linear Freundlich, Langmuir and Temkin isotherms and the experimental data were found to fit the Temkin isotherm model.     

Analytic solutions to the advective contaminant transport equation with non-linear sorption

This paper considers advective transport of a soluble contaminant through saturated soil with non-linear sorption of the contaminant onto a stationary porous media. The non-linear sorption isotherms considered in the transport analysis are the Langmuir and Freundlich sorption isotherms. A special case of the Freundlich sorption isotherm is the linear sorption isotherm, and it is shown that in this case transport through a homogeneous soil results in the initial concentration profile simply being translated in the direction of the groundwater flow. However, when the sorption isotherm is non-linear the initial concentration profile distorts as it is translated with the groundwater flow, leading to the development of concentration shock fronts and rarefactions. Analytic solutions to the non-linear first-order hyperbolic equations are developed for a number of contaminant transport problems of practical significance. It is shown that in the case of the Langmuir sorption isotherms, shock fronts develop at the leading edge of the concentration profile while for the Freundlich sorption isotherm shock fronts may develop at either the leading or trailing edge of the concentration profile. Copyright © 1999 John Wiley & Sons Ltd.     

Nitrate sorption by organosmectites

The use of organoclays as adsorbents in the remediation of polluted water has been the subject of many recent studies. In this present work, a Tunisian smectite modified by two cationic surfactants was used as a sorbent for the investigation of the adsorption kinetics, isotherms and thermodynamic parameters of nitrate ions at various contact time, initial concentrations and temperatures. Two simplified kinetic models, first-order and second-order, were used to predict the adsorption constants. It was found that the adsorption kinetics of nitrate was best described by the second-order model. Adsorption isotherms and equilibrium adsorption capacities were determined by the fittings of the experimental data to two well-known isotherm models including Langmuir and Freundlich. The results showed that Langmuir model appears to fit the adsorption better than Freundlich model. The equilibrium constants were used to calculate thermodynamic parameters, such as the change of free energy, enthalpy and entropy.     

Lead removal from wastewater using fluted pumpkin seed shell activated carbon: Adsorption modeling and kinetics

Activated carbon produced from fluted pumpkin (Telfairia occidentalis) seed shell was utilized for the removal of lead (II) ion from simulated wastewater. Adsorption tests were carried out in series of batch adsorption experiments. Several kinetic models (Bhattacharya-Venkobacher, Elovich, pseudo first and second order, intra-particle and film diffusion) were tasted for conformity to the experimental data obtained. The Langmuir and Freundlich adsorption models were also used to test the data. The amount of lead (II) ion adsorbed at equilibrium from a 200 mg/L solute concentration was 14.286 mg/g. The experimental data conform very well to the pseudo-second order equation where equilibrium adsorption capacities increased with increasing initial lead (II) concentration. The rate of the adsorption process was controlled by the film (boundary layer) diffusion as the film diffusion co-efficient values obtained from data analysis were of the order of 10 ⁶cm²/s. From the plots, the linear regression coefficient (R²) of the Langmuir model was higher than that of the Freundlich: the adsorption isotherm obeyed the Langmuir model better than the Freundlich model.     

Linearized and non-linearized isotherm models comparative study on adsorption of aqueous phenol solution in soil

Use of native soil in adsorption of phenol from industrial wastewater has been one of the attractive option for dephenolation, especially in view of low cost and ease in accessibility, as well as scope for regeneration (or, at least reuse). However, an effective usage of the adsorbent necessitates a deeper understanding of the adsorption characteristics. Most of the study of adsorption characteristics are confined to analysis of mono- and bi- parametric isotherm models (and rarely, linearized multi-parametric isotherm models), due to the difficulties in solving higher parametric models, as well as fairly satisfying results by lower-parametric models. In the present study, adsorption batch studies were carried out using a naturally and widely available common soil of south India (namely, Adhanur soil), for removal of phenol from the aqueous solution, with an explicit objective of comparison of linear and non-linear regression methods for finding variation in isotherm coefficients and fitness of the models. Six linearized isotherm models (including four linearized Langmuir models) and three non-linear isotherm model were discussed in this paper, and their coefficients were estimated. Although all the studied isotherm models showed fairly good fit to the experimental data, but Redlich—Peterson isotherm was found to be the best representative for phenol-sorption on the used soil adsorbent. Besides, it was observed that to determine the isotherm parameters non-linear isotherm models were found to be the best representative of adsorption characteristics, than their linearized counter-parts.     

Retention of a heavy metal by marl collected from aquifer substratum

One of the objectives of this work is to characterize marl samples collected from the bedrock aquifer (at 30 m depth) of Wadi Al Ghoula located in Draria southwest of Algiers. The other objective is to make a kinetics study, linear and non-linear isotherm study, and mass transfer study of the adsorption of copper onto marl in aqueous solution. The fitness of kinetics and isotherm models was evaluated by using some error analysis function. One of the major results using an XRF technique is an evidence of the presence of calcite in the weight of 13.82%. The XRD patterns of these samples confirmed the presence of montmorillonite, kaolinite, illite, calcite, and quartz. On the other hand, the FTIR analysis clarified the presence of calcite. The specific surface area of 20,999 m²/g was obtained using the BET, which indicates that the material has a predominance for the mesoporous character. The instrumental neutron activation analysis (INAA), a nondestructive method, gives the elemental composition of the adsorbent. Based on the value of the coefficient of determination, the adsorption kinetics of copper in aqueous solution using marl as adsorbent follows the pseudo-second-order model. And according to the value of the coefficient of determination obtained for the two models, the intraparticle diffusion and liquid film diffusion control the process of adsorption of copper onto marl with low predominance for the second model of diffusion in the first stage of adsorption. The linear and the non-linear treatments of the two-parameter isotherm models (Langmuir, Freundlish, Temkin) show that the fitting best model of isotherm is the empirical Freundlish isotherm. For the three-parameter isotherm models (Toth, Sips, and Redlish-Peterson), the Sips model is the more accurate fitting model than the two other isotherms in the non-linear approach. Some error analysis functions are used to choose the best results.     

Preparation and characterization of biosorbents and copper sequestration from simulated wastewater

This paper reports the potential of chemically treated wood chips to remove copper (II) ions from aqueous solution a function of pH, adsorbent dose, initial copper (II) concentration and contact time by batch technique. The wood chips were treated with (a) boiling, (b) formaldehyde and (c) concentrated sulphuric acid and characterized by Fourier transform infrared spectroscopy, scanning electron microscopy and energy dispersive analysis X-ray. pH 5.0 was optimum with 86.1, 88.5 and 93.9 % copper (II) removal by boiled, formaldehyde-treated and concentrated sulphuric acid-treated wood chips, respectively, for dilute solutions at 20 g L^?1 adsorbent dose. The experimental data were analysed using Freundlich, Langmuir, Dubinin–Radushkevich and Temkin isotherm models. It was found that Freundlich and Langmuir models fitted better the equilibrium adsorption data and the adsorption process followed pseudo-second-order reaction kinetics. The results showed that the copper (II) is considerably adsorbed on wood chips and it could be an economical option for the removal of copper from aqueous systems.     

Kinetic and equilibrium study of Ni(II) sorption from aqueous solutions onto Peganum harmala-L

In this study, the adsorption behavior of Ni(II) in an aqueous solution system using natural adsorbent Peganum harmala-L was measured via batch mode. The prepared sorbent was characterized by scanning electron microscope, Fourier transform infrared spectroscopy, N₂ adsorption–desorption and pH_zpc. Adsorption experiments were carried out by varying several conditions such as contact time, metal ion concentration and pH to assess kinetic and equilibrium parameters. The equilibrium data were analyzed based on the Langmuir, Freundlich, Temkin and Dubinin–Radushkevich isotherms. Kinetic data were analyzed using the pseudo-first-order, pseudo-second-order and intra-particular diffusion models. Experimental data showed that at contact time 60 min, metal ion concentration 50 mg/L and pH 6, a maximum amount of Ni(II) ions can be removed. The experimental data were best described by the Langmuir isotherm model as is evident from the high R ² value of 0.988. The adsorption capacity (q _m) obtained was 68.02 mg/g at an initial pH of 6 and a temperature of 25 °C. Kinetic studies of the adsorption showed that equilibrium was reached within 60 min of contact and the adsorption process followed the pseudo-first-order model. The obtained results show that P. harmala-L can be used as an effective and a natural low-cost adsorbent for the removal of Ni(II) from aqueous solutions.     

Biosorption of lead from acid solution using chitosan as a supporting material for spore forming-fungal biomass encapsulation

Asexual spores of the filamentous fungus Rhizopus arrhizus were used as the resting biomass as they tolerate chitosan gelling for mycelia growing in chitosan beads. Biosorption of lead using the dead detergent pre-treated chitosan-immobilised and grown fungal beads was performed with initial lead (II) nitrate concentrations ranging from 9.02 to 281.65 mg/L. The adsorption data were best correlated with equilibrium adsorption isotherms in the order Redlich–Peterson, Langmuir, Freundlich and Fritz–Schlünder by non-linear regression. The biosorption kinetic model of pseudo second-order (R ² > 0.99) fitted better than pseudo first-order and modified pseudo first-order models. Among the four pseudo second-order kinetic models, the Blanchard model was the best fit for the experimental biosorption data. The rate-limiting step of biosorption of lead was shown to be intraparticle diffusion controlled according to Weber and Morris model fitting. The beads could be regenerated using 1 M nitric acid solution. This illustrated the good performance of the beads for regenerated sorption/desorption at least five cycles.     

Nonlinear kinetic analysis of phenol adsorption onto peat soil

Phenolic compounds are considered as a serious organic pollutant containing in many industrial effluents particularly vulnerable when the plant discharge is disposed on land. In the present study, the phenol removal potential of peat soil as adsorption media was investigated as the adsorption process are gaining popular for polishing treatment of toxic materials in industrial wastewater. Batch experiments were performed in the laboratory to determine the adsorption isotherms of initial concentrations for 5, 8, 10, 15, and 20 mg/L and predetermined quantity of peat soil with size ranges between 425 and 200 μm poured into different containers. The effects of various parameters like initial phenol concentration, adsorbent quantity, pH, and contact time were also investigated. From experimental results, it was found that 42 % of phenol removal took place with optimized initial phenol concentration of 10 mg/L, adsorbent dose of 200 g/L, solution pH 6.0 for the equilibrium contact time of 6 h. The result exhibits that pseudo-first-order (R ² = 0.99) and Langmuir isotherm models are fitted reasonably (R ² = 0.91). Adams–Bohart, Thomas, Yoon–Nelson, and Wolborska models were also investigated to the column experimental data of different bed heights to predict the breakthrough curves and to determine the kinetic coefficient of the models using nonlinear regression analysis. It was found that the Thomas model is the best fitted model to predict the experimental breakthrough curves with the highest coefficient of determination, R ² = 0.99 and lowest root mean square error and mean absolute performance error values.     

Multiscale estimation of the Freundlich adsorption isotherm

Adsorption plays an important role in water and wastewater treatment. The analysis and design of processes that involve adsorption rely on the availability of isotherms that describe these adsorption processes. Adsorption isotherms are usually estimated empirically from measurements of the adsorption process variables. Unfortunately, these measurements are usually contaminated with errors that degrade the accuracy of estimated isotherms. Therefore, these errors need to be filtered for improved isotherm estimation accuracy. Multiscale wavelet based filtering has been shown to be a powerful filtering tool. In this work, multiscale filtering is utilized to improve the estimation accuracy of the Freundlich adsorption isotherm in the presence of measurement noise in the data by developing a multiscale algorithm for the estimation of Freundlich isotherm parameters. The idea behind the algorithm is to use multiscale filtering to filter the data at different scales, use the filtered data from all scales to construct multiple isotherms and then select among all scales the isotherm that best represents the data based on a cross validation mean squares error criterion. The developed multiscale isotherm estimation algorithm is shown to outperform the conventional time-domain estimation method through a simulated example.     

Equilibrium studies on removal of lead (II) ions from aqueous solution by adsorption using modified red mud

In the present experimental study, solid waste was used as an adsorbent and the effectiveness of the adsorbent was increased by novel treatment methods. Red mud, acid-treated activated red mud and iron oxide-coated acid-treated activated red mud were used for the removal of lead (II). The structural and functional groups were identified to confirm the removal of lead (II) by powder X-ray diffraction and Fourier transform infrared spectroscopy analyses. The enhancement of surface area was confirmed by Brunauer–Emmett–Teller analysis. Batch adsorption experiment was also conducted, and various parameters such as the effect of adsorbent dosage, pH, contact time and initial ion concentration were analyzed and reported. Adsorption equilibrium data were investigated using Langmuir, Freundlich and Dubinin–Radushkevich isotherm models with three parameters, and the rate of reaction was examined through kinetic models. The results indicate that in particular a novel modified form of red mud, namely iron oxide-coated acid-treated activated red mud was well fitted in lead (II) removal compared with reported adsorbents. The Langmuir isotherm shows that the maximum adsorption of adsorbate per gram was greater than other adsorbents (27.02 mg/g). In Freundlich isotherm, the Freundlich constant n values lie between 1 and 10 indicate the favorable adsorption. The calculated n values for normal red mud, acid-treated activated red mud and iron oxide-coated acid-treated activated red mud were found to be 1.9, 2.1 and 2.0 respectively. The correlation coefficient value was higher and the rate of reaction follows the pseudo-second-order kinetic model.     

The Pre-concentration and determination of Iridium and Palladium in environmental water by imprinted polymer-based method

In this study, the imprinted aniline–formaldehyde was used as an adsorbent for removal of Iridium and Palladium ions from aqueous solutions through batch equilibrium. The sorbent was characterized by fourier transform infrared spectroscopy. The influence of pH, equilibrium time, temperature and initial concentration of metal ions on adsorbed amount of both ions were investigated. The maximum adsorption capacity in initial concentration of 100 mg/L was found to be 12.5 mg/g at pH 7.0 and 14.3 mg/g at pH 8.0 for Iridium and Palladium, respectively. In addition, the best desorption of the metal ions from resin was obtained by 0.5 mol/L nitric acid as eluting agent. The profile of both ions uptake on this sorbent reflects good accessibility of the chelating sites in the imprinted aniline–formaldehyde. Langmuir, Freundlich, Temkin and Redlich–Peterson isotherm models were applied to analyze the experimental data. Moreover, Langmuir linear method was used to obtain the isotherm parameters. However, Langmuir type II achieved the highest coefficient which led to the best fit for the palladium and the best fit for Iridium obtained from linear Redlich–Peterson. However, the thermodynamic parameters (ΔG°, ΔH°, and ΔS°) were also determined using the equilibrium constant values obtained at different temperatures. The results showed that the adsorption for Iridium and Palladium ions was spontaneous nature and endothermic. Moreover, the method was applied for the determination of both ions from tap water samples.     

Retention studies of chromium (VI) from aqueous solution on the surface of a novel carbonaceous material

In the present study, the retention capacity of carbonaceous material obtained from the diesel engine exhaust mufflers for Cr(VI) removal has been investigated. The physicochemical properties such as density, pH of aqueous slurry, pH at point of zero charge, ash content, moisture content, volatile matter, surface area, scanning electron microscopy and electron dispersive spectroscopy of the carbonaceous material were determined. The capacity of adsorbent for removal of Cr(VI) from aqueous solution was observed under different experimental condition like contact time, initial concentration of metal ions, pH and temperatures on the adsorption capacity of the adsorbent. Maximum adsorption of Cr(VI) ions was found at low pH. The adsorption process was found to follow second-order kinetics. The rate constant was evaluated at different temperatures along with other thermodynamic parameters like activation energy, Gibbs free energy change, enthalpy change and entropy change. Both Langmuir and Freundlich isotherms were used to describe the adsorption equilibrium of carbonaceous material at different temperatures. Langmuir isotherm shows better fit than Freundlich isotherm at given conditions. The result shows that low-cost carbonaceous material from diesel engine exhaust mufflers can be efficiently used for wastewater treatment containing Cr(VI) ions.     

Ultrafast removal of heavy metals by tin oxide nanowires as new adsorbents in solid-phase extraction technique

In the present research, the removal of lead(II) and copper(II) from aqueous solutions is studied, using SnO₂ nanowires as new adsorbent on solid-phase extraction disk and compared with pine core and buttonwood as biosorbents. Batch adsorption experiments were performed as a function of pH, adsorption time, solute concentration and adsorbent dose for biosorbents. Also, the pH, transfer rate of solution and metal concentration were selected as experimental parameters for the removal of heavy metals by SnO₂ nanowires. All of the parameters were optimized by experimental design method for sorbents. The experimental equilibrium adsorption data are tested for the Langmuir and Freundlich equations. Results indicate the following order to fit the isotherms: Langmuir > Freundlich, in case of lead and copper ions. The removal of Cu(II) and Pb(II) was performed by selected sorbents in the presence of interferences ions. This led to no remarkable decrease in the removal efficiency of SnO₂ nanowires. Using the SnO₂ nanowires in the wastewater treatment indicated 96.8 and 85.28% removal efficiency in only 7 min for Pb(II) and Cu(II), respectively. SnO₂ nanowires were found as reusable sorbent. Therefore, SnO₂ nanowires have a good potential for application in environmental protection.     

Adsorption of aqueous Pb(II), Cu(II), Zn(II) ions by amorphous tin(VI) hydrogen phosphate: an excellent inorganic adsorbent

Amorphous tin(VI) hydrogen phosphate (ATHP) was synthesized using the liquid phase precipitation method and served as an adsorbent to remove Pb(II), Cu(II), and Zn(II) from aqueous solutions. The ATHP was characterized by powder X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and nitrogen adsorption–desorption techniques. Adsorption properties were evaluated as a function of pH, reaction time, concentration of reactants, and salinity. Their equilibrium adsorption data were modeled using Freundlich, Langmuir, and Dubinin–Kaganer–Radushkevich isotherms, respectively. The results revealed that adsorption equilibrium reached within 180 min. ATHP indicated good adsorption even below the pH_ZPC, and best adsorption at pH 5 for Pb(II) and Cu(II) and at pH 5.5 for Zn(II) was observed. Equilibrium data fitted better to the Langmuir model for Pb(II) and Cu(II) and fitted better to the Freundlich model for Zn(II). The saturated adsorption capacities deduced from the Langmuir model were 2.425, 1.801, and 0.600 mmol/g for Cu(II), Pb(II), and Zn(II), respectively, indicating an adsorption affinity order of Cu > Pb > Zn. There is a negative correlation between the concentration of NaCl and adsorption capacity of ATHP, yet ATHP still exhibited excellent adsorption having an adsorption capacity of 19.35, 15.16, 6.425 mg/g when the concentration of NaCl was 0.6 mol/L. The free energy (E) was 12.33, 10.70, and 14.74 kJ/mol for Pb(II), Cu(II), and Zn(II), respectively. An adsorption mechanism based on ion exchange between heavy metal ions and H⁺ in the ATHP is proposed. Furthermore, the used ATHP was regenerated by HCl solution and the adsorbent was used repeatedly.     

Biosorption of Cd(II) from synthetic wastewater using dry biofilms from biotrickling filters

Biofilms wasted from biotrickling filters was dried and used as biosorbent for Cd(II) removal from aqueous solutions. The adsorption condition and effect, adsorption isotherms and kinetics of Cd(II) removal were investigated, and the effects of competitive metal ions on Cd(II) removal were also examined. Results showed that the dry waste biofilms reached the maximum adsorption capacity of 42 mg/g of Cd(II) at 25 °C for 120 min when the initial concentration of Cd(II) and their pH were 50 mg/L and 6.0, respectively. Under these conditions, the removal efficiency of Cd(II) reached to 89.3% when the biosorbent dosage was 2.0 g/L. The Langmuir isotherm model correlated with the isotherm data better than the Freundlich isotherm model, and the pseudo-second-order model fitted the kinetic data better than the pseudo-first-order model. These results indicated that the adsorption was monolayer accompanied with chemical adsorption. In the presence of other metal ions, divalent metal ions of Ca and Zn inhibited the performance of Cd(II) biosorption significantly, while Na(I), K(I) and Fe(III) which had a higher or lower valence than Ca(II) affected slightly when containing 50 mg/L Cd(II), 0.5 g/L adsorbent dosage and pH 6.0. The analyses of scanning electron microscopy and Fourier transform infrared spectroscopy illuminated that the biosorbent had porous structures and the amide group was the majorly responsible for Cd(II) removal. Dry biofilms were novel sorbents for effective removal Cd(II), and it could be reused and recycled if necessary.