Misleading information on homogeneity and heterogeneity obtained from sorption isotherms

In this paper, the applications and the differences among the widely applied sorption isotherms (Langmuir isotherm for adsorption, competitive adsorption, ion exchange, Freundlich isotherm) are shown. The misleading information obtained by the formal applications of the isotherms is demonstrated using a simple mathematical model of homovalent ion exchange on homogeneous surface. This model calculation clearly reveals that when studying surface accumulation processes, the mechanism of the sorption process has to be determined. The correct thermodynamic interpretation of the data of sorption experiments is possible only if the isotherm is adapted to the sorption mechanism. It is emphasized that the regression values of the applied models themselves provide correct information neither on the surface heterogeneity nor the interactions among the sorbed species. The curved shape of an inadequate applied isotherm gives no information about the heterogeneity. In order to study the energy distribution of surface sites, the thermodynamic equations, including isotherms, has to be selected on the basis of sorption mechanism. All variable quantities involved in the given model (concentrations of the competing substances in all phases) have to be measured experimentally and included into the isotherm.     

Application of linear regression analysis for iron and copper removal process using natural zeolites

Natural zeolites (zeolitic volcanic tuffs) cropped out from three regions of Transilvania, Vultureni (V), Pagli?a (P) and M?cica? (M), were evaluated in the process of iron (V, P, M) and copper (M) removal from wastewaters. Iron and copper removal process was studied using a fixed bed column, when equilibrium and kinetic data were acquired. Four isotherms, Langmuir, Freundlich, Langmuir?CFreundlich and Redlich?CPeterson, were used to fit the experimental data obtained for each natural zeolite sample. Parameters of the adsorption isotherms were estimated from the experimental equilibrium data using MATLAB. Using these data the best fit with one of the chosen isotherm can be found. Isotherm constants were determined by linear regression analysis of the experimental data. We concluded that the mathematical model based on Freundlich isotherm is the most appropriate to describe the iron and copper exchange on our natural zeolite samples.     

Adsorption of Methylene Blue from Aqueous Solution on High Lime Fly Ash: Kinetic,Equilibrium, and Thermodynamic Studies

Kinetic, equilibrium, and thermodynamic studies were performed for the batch adsorption of methylene blue (MB) on the high lime fly ash as a low cost adsorbent material. The studied operating variables were adsorbent amount, contact time, dye concentration, and temperature. The kinetic data were analyzed using the pseudo-first order and pseudo-second order kinetic models and the adsorption kinetic was followed well by the pseudo-second order kinetic model. The equilibrium data were fitted with the Freundlich, Langmuir, and Dubinin Radushkevich (D–R) isotherms and the equilibrium data were found to be well represented by the Freundlich and D–R isotherms. Based on these two isotherms MB is taken by chemical ion exchange and active sites on the high lime fly ash have different affinities to MB molecules. Various thermodynamic parameters such as enthalpy of adsorption (ΔH°), free energy change (ΔG°), and entropy change (ΔS°) were investigated. The positive value of ΔH° and negative value of ΔG° indicate that the adsorption is endothermic and spontaneous. The positive value of ΔS° shows the increased randomness at the solid–liquid interface during the adsorption. A single-stage batch adsorber was also designed based on the Freundlich isotherm for the removal of MB by the high lime fly ash.     

Removal of methyl violet from aqueous solution by perlite

The use of perlite for the removal of methyl violet from aqueous solutions at different concentration, pH, and temperature has been investigated. Adsorption equilibrium is reached within 1 h. The capacity of perlite samples for the adsorption of methyl violet was found to increase with increasing pH and temperature and decrease with expansion and increasing acid-activation. The adsorption isotherms are described by means of the Langmuir and Freundlich isotherms. The adsorption isotherm was measured experimentally at different conditions and the experimental data were correlated reasonably well by the adsorption isotherm of Langmuir. The order of heat of adsorption corresponds to a physical reaction. It is concluded that the methyl violet is physically adsorbed onto the perlite. The removal efficiency (P) and dimensionless separation factor (R) have shown that perlite can be used for removal of methyl violet from aqueous solutions, but unexpanded perlite is more effective.     

Biosorption of nickel(II) and copper(II) ions from aqueous solution by Streptomyces coelicolor A3(2)

The biosorption of nickel(II) and copper(II) ions from aqueous solution by dried Streptomyces coelicolor A3(2) was studied as a function of concentration, pH and temperature. The optimum pH range for nickel and copper uptake was 8.0 and 5.0, respectively. At the optimal conditions, metal ion uptake was increased as the initial metal ion concentration increased up to 250 mg l(-1). At 250 mg l(-1) copper(II) ion uptake was 21.8% whereas nickel(II) ion uptake was found to be as high as 7.3% compared to those reported earlier in the literature. Metal ion uptake experiments were carried out at different temperatures where the best ion uptake was found to be at 25 degrees C. The characteristics of the adsorption process were investigated using Scatchard analysis at 25 degrees C. Scatchard analysis of the equilibrium binding data for metal ions on S. coelicolor A3(2) gave rise to a linear plot, indicating that the Langmuir model could be applied. However, for nickel(II) ion, divergence from the Scatchard plot was evident, consistent with the participation of secondary equilibrium effects in the adsorption process. Adsorption behaviour of nickel(II) and copper(II) ions on the S. coelicolor A3(2) can be expressed by both the Langmuir and Freundlich isotherms. The adsorption data with respect to both metals provide an excellent fit to the Freundlich isotherm. However, when the Langmuir isotherm model was applied to these data, a good fit was obtained for the copper adsorption only and not for nickel(II) ion.     

Adsorption of Promethazine hydrochloride with KSF Montmorillonite

Adsorption of Promethazine hydrochloride (PHCl) onto KSF Montmorillonite from aqueous solution has been investigated. Experiments were conducted at various pH values, ionic backgrounds and solution temperatures. The pseudo-second-order equation successfully predicted the adsorption among the tried kinetics models (pseudo-first-order, pseudo-second-order and intraparticle diffusion). Langmuir, Freundlich and DR adsorption models were used to describe equilibrium isotherms and the isotherm constants were obtained. The increase in solution temperature caused a decrease in the adsorption capacity values found from Freundlich and DR isotherm. The adsorption type can be explained by combined ion exchange and physisorption. Thermodynamic parameters of adsorption of Promethazine hydrochloride (PHCl) onto KSF were also evaluated. The surface morphologies of KSF and PHCl loaded KSF were examined using a scanning electron microscope (SEM). FTIR measurements of samples were also conducted.     

Ion-exchange equilibria of lysozyme, myoglobin and bovine serum albumin. Effective valence and exchanger capacity

A series of ion-exchange equilibrium experiments were completed and analyzed by a mass action model. The isotherms at various counter-ion concentrations are regressed to determine the average number of binding sites, Z, the mass action constant, K, and the effective capacity of the exchanger, Pm. The estimates for Pm are 1-10 mmol of protein adsorbed per liter of packed Sepharose exchanger, in agreement with values determined from fitting the Langmuir isotherms. A geometric model, developed to relate the charge distribution of the exchanger and the size of the protein to the protein capacity, also confirms the estimates of Pm. The Z values estimated (and confirmed with an independent slope method) range from 0.8 to 3.6, indicating that most of the ionized sites on the protein do not undergo ion exchange. Geometric model estimates of exchanger sites covered by a protein at maximum surface coverage show that only 1-32% of the sites actually undergo ion exchange. This result indicates that adsorbed protein molecules "block" many exchanger sites, preventing other molecules from ion exchanging at those sites. This high degree of blocking by proteins also indicates that there is an excess of exchanger sites, as evidenced by Z showing no dependence on charge separation distance over the range 6-10 A. Scatchard pots of the equilibrium data indicate that there is competition between at least two different binding forms of each protein studied. For the high-affinity systems, cooperative binding was observed at low exchanger loading; the character then changed to heterogeneous competitive binding as the exchanger loading increased. The effect on an isotherm plot is a subtle but systematic deviation from the Langmuir and mass action models. More important, the competition means that Z represents an average for competing binding forms and, as such, Z can be fractional.     

Diffusion Mechanisms of Biosorption of Cr(VI) onto Powdered Cotton Stalk

The present study investigates biosorption diffusion mechanism for the removal of toxic hexavalent chromium from aqueous solution using powdered cotton stalk an agricultural waste biomass. The effects of pH, temperature, adsorption isotherms, adsorption kinetics, and thermodynamic on chromium biosorption were investigated. The results showed that a maximum removal efficiency of 95% was achieved at pH 2. The pH at zero point charge (pH_zpc) on biosorbent surface was 4.3. The adsorption kinetics showed that the pseudo-second order rate expression fitted well the biosrption process. The equilibrium isotherm was measured experimentally and results were analyzed by Langmuir, Freundlich, and Temkin isotherms using linearized correlation coefficients. The significant parameters for isotherms were determined. The Langmuir adsorption isotherm relative to two other isotherms was found to fit the equilibrium data best for chromium adsorption. Thermodynamic studies reveal that the biosorption of Cr(VI) on cotton stalk was endothermic, spontaneous and occurs with increase in disorder at solid-liquid interface. Adsorption diffusion kinetic was further analyzed and showed that biosorption mechanism was totally controlled by intraparticle diffusion mechanism.     

Use of lipophilic ion adsorption isotherms to determine the surface area and the monolayer capacity of a chromatographic packing, as well as the thermodynamic equilibrium constant for its adsorption

A method that champions the approaches of two independent research groups, to quantitate the chromatographic stationary phase surface available for lipophilic ion adsorption, is presented. For the first time the non-approximated expression of the electrostatically modified Langmuir adsorption isotherm was used. The non approximated Gouy-Chapman (G-C) theory equation was used to give the rigorous surface potential. The method helps model makers, interested in ionic interactions, determine whether the potential modified Langmuir isotherm can be linearized, and, accordingly, whether simplified retention equations can be properly used. The theory cultivated here allows the estimates not only of the chromatographically accessible surface area, but also of the thermodynamic equilibrium constant for the adsorption of the amphiphile, the standard free energy of its adsorption, and the monolayer capacity of the packing. In addition, it establishes the limit between a theoretical and an empirical use of the Freundlich isotherm to determine the surface area. Estimates of the parameters characterising the chromatographic system are reliable from the physical point of view, and this greatly validates the present comprehensive approach.     

Adsorption of indole and 2-methylindole on ligand-exchange matrix

The adsorption of indole and its 2-methyl derivative from aqueous solutions onto cobalt(II)-carboxylated diaminoethane sporopollenin (CDAE-sporopollenin) was studied using a fixed-bed column at 25+/-0.1 degrees C. Minicolumn adsorption studies showed that the breakthrough and the total adsorption capacities of CDAE-sporopollenin in the concentration range we have studied increased with increasing external ligand concentration. The characteristics of the adsorption process were investigated using Scatchard plot analysis, where the equilibrium binding data for indole on ligand exchanger gave rise to a linear plot. However, for 2-methylindole, divergence from the Scatchard plot was evident, consistent with the participation of secondary equilibrium effects in the adsorption process. The adsorption behaviors of ligands on CDAE-sporopollenin were expressed by both the Langmuir and Freundlich isotherms. The adsorption isotherm data for these ligands on the resin can be satisfactorily fitted to the Freundlich isotherm within the concentration range studied. However, in the case of 2-methylindole, the experimental data did not fit the Langmuir model, especially when a high ligand concentration range is used; this is probably due to the nonspecific interactions between the ligand exchange matrix and the methyl group present. Ligand adsorption constants and correlation coefficients for the ligands were calculated from the Langmuir and Freundlich isotherms.     

Discrimination between adsorption isotherm models based on nonlinear frequency response results

A number of criteria are established for distinguishing between different adsorption isotherm types. These criteria are defined based on the adsorption isotherm derivatives up to the third order, which, on the other hand, can be estimated from nonlinear frequency response data. The criteria for five favourable (Langmuir, Freundlich, Sips, Toth and Unilan) isotherms and two complex isotherms (BET and quadratic) are presented. These criteria enable unique identification of the underlying adsorption isotherm relation if the values of the local first, second and third order isotherm derivatives at several points are known. The method is applied to experimental data from our previous publications, for one case of a favourable and one case of a complex isotherm.     

Potato peels as solid waste for the removal of heavy metal copper(II) from waste water/industrial effluent

A new sorbent potato peels, which are normally discarded as solid waste for removing toxic metal ion Cu(II) from water/industrial waste water have been studied. Potato peels charcoal (PPC) was investigated as an adsorbent of Cu(II) from aqueous solutions. Kinetic and isotherm studies were carried out by studying the effects of various parameters such as temperature, pH and solid liquid ratios. The optimum pH value for Cu(II) adsorption onto potato peels charcoal (PPC) was found to be 6.0. The thermodynamic parameters such as standard Gibb's free energy (Delta G degrees ), standard enthalpy (Delta H degrees ) and standard entropy (DeltaS degrees ) were evaluated by applying the Van't Hoff equation. The thermodynamics of Cu(II) adsorption onto PPC indicates its spontaneous and exothermic nature. The equilibrium data at different temperatures were analyzed by Langmuir and Freundlich isotherms.     

Ion exchange properties of crystalline bismuth molybdenum hydrous oxide and its intercalates: Equilibrium and kinetics of UO 2 2+ ions on the crystals

The sorption of uranyl ions on crystalline bismuth molybdenum hydrous oxide and its intercalates were investigated from point of view of both equilibrium and kinetics. Ion exchange isotherms of uranyl ions on the crystals were obtained, and ionic sieve effect was employed to describe the characteristics of ion exchange isotherms. The best fitting for sorption of uranyl ions on BMHO was achieved by means of the Langmuir isotherm, while the Freundlich isotherm appeared to best fit for its intercalates. The slightly negative free-energy change indicates that, thermodynamically, the crystals behave less favourable for uranyl ions. The equation derived from S_N2 chemical reactions was proved to fit the rate curves, and the rate constants were determined. The comparison between the calculated and observed pH values as a function of time further verified the chemical reaction mechanism.     

自然水体生物膜吸附Co,Ni和Cu的特征研究

研究了在自然水体中培养的生物膜吸附Co,Ni和Cu等3种重金属的热力学和动力学特征,并对生物膜吸附各重金属的热力学数据进行了非线性拟合.结果表明,3种重金属的吸附过程均符合Langmuir吸附等温曲线.在溶液中重金属浓度<0.5μmol/L时,生物膜对3种重金属元素的吸附能力顺序是Co>Cu>Ni;在重金属浓度>0.5μmol/L时,顺序是Cu>Co>Ni.对动力学数据进行非线性拟合的结果表明,生物膜对Co,Ni和Cu的吸附均在数小时内达到平衡,吸附过程符合Langmuir等动力学曲线.     

Kinetics and equilibrium adsorption study of lead(II) onto activated carbon prepared from coconut shell

Removal of lead from aqueous solutions by adsorption onto coconut-shell carbon was investigated. Batch adsorption experiments were performed to find out the effective lead removal at different metal ion concentrations. Adsorption of Pb2+ ion was strongly affected by pH. The coconut-shell carbon (CSC) exhibited the highest lead adsorption capacity at pH 4.5. Isotherms for the adsorption of lead on CSC were developed and the equilibrium data fitted well to the Langmuir, Freundlich, and Tempkin isotherm models. At pH 4.5, the maximum lead adsorption capacity of CSC estimated with the Langmuir model was 26.50 mg g(-1) adsorbent. Energy of activation (Ea) and thermodynamic parameters such as DeltaG, DeltaH, and DeltaS were evaluated by applying the Arrhenius and van't Hoff equations. The thermodynamics of Pb(II) on CSC indicates the spontaneous and endothermic nature of adsorption. Quantitative desorption of Pb(II) from CSC was found to be 75% which facilitates the sorption of metal by ion exchange.     

Adsorption at liquid interfaces: the generalized Langmuir isotherm and interfacial structure

The thermodynamics of adsorption of amphiphilic surface-active compounds at the interface between two immiscible liquids is considered. At the interface, these molecules are supposed to replace a few of the adsorbed molecules of both solvents. Classical isotherms of adsorption (Frumkin, Langmuir, Henry) were based on the model of nonpenetrable interface, where an adsorbate can substitute only molecules of one solvent. However, at the interface between two immiscible electrolytes, like nonpolar oil-water interfaces, or liquid membrane amphiphilic molecules can substitute molecules of both solvents; therefore, classical isotherms are not applicable in these cases. The generalization of Langmuir and Frumkin isotherms for permeable and nonpermeable interfaces, known as the Markin-Volkov (MV) isotherm, gives the possibility to analyze adsorption and the interfacial structure in a general case. In the present paper, the adsorption isotherms of pentafluorobenzoic acid at the octane-water interface at various pH were measured by the drop-weight method. The thermodynamic parameters of pentafluorobenzoic acid (PFBA) adsorption at the octane-water interface were found. From the measurements of PFBA adsorption, the structure of the octane-water interface was determined. Substitution of one adsorbed octane molecule requires approximately three adsorbed PFBA molecules. This result shows that the orientation of solvent molecules at the interface is different from the bulk solution. Adsorbed octane molecules have a lateral orientation with respect to the interface. Gibbs free energy of adsorption equilibrium and thermodynamic parameters of PFBA adsorption show that the adsorption of PFBA at the octane-water interface is accompanied by a reduction in the attraction between adsorbed PFBA molecules as the pH decreases to the acidic region.     

Removal of methylene blue by seed-watermelon pulp-based low-cost adsorbent: Study of adsorption isotherms and kinetic models

Based on the abundance of seed-watermelon pulp (SWP) in Xinjiang, China, SWP was employed to prepare low-cost adsorbent toward the removal of methylene blue (MB). The effects of contact time at different initial concentration were studied. The widely used adsorption isotherm models including Langmuir, Freundlich, and Temkin isotherms were employed to depict the adsorption process. The Langmuir isotherm was best fitted to the experimental data. Batch kinetic studies showed that an equilibrium time of 300 minutes was needed for the adsorption. The adsorption properties can be well described by pseudo-second-order kinetic model and the MB uptake was not controlled by intraparticle diffusion mechanism.     

Fungal biomass with grafted poly(acrylic acid) for enhancement of Cu(II) and Cd(II) biosorption

The biomass of Penicillium chrysogenum was modified by graft polymerization of acrylic acid (AAc) on the surface of ozone-pretreated biomass. The sorption capacity for copper and cadmium increased significantly as a large number of carboxyl groups were present on the biomass surface, especially when the carboxylic acid group was converted to carboxylate ions using NaOH. When modeled using the Langmuir isotherm, the sorption capacities were 1.70 and 1.87 mmol g(-1) for copper and cadmium, respectively. The loaded biosorbent was regenerated using HCl solution and used repeatedly over five cycles with little loss of uptake capacity beyond the second cycle. The sorption of the two metals was time-dependent, and the kinetics fitted the pseudo-second-order equation well. The Freundlich, Langmuir, Temkin, and Dubinin-Redushkevich isotherms were used to model the metal sorption isotherms, and the thermodynamic parameters calculated show that the sorption was spontaneous and endothermic under the condition applied and that the biomass has similar sorption affinities for the two metals. Fourier transform infrared and X-ray photoelectron spectroscopy reveal that carboxyl, amide, and hydroxyl groups on the biomass surface were involved in the sorption of copper and cadmium and ion exchange and complexation dominated the sorption process.     

Adsorption at liquid interfaces: The generalized Frumkin isotherm and interfacial structure

The thermodynamics of adsorption of amphiphilic surface-active compounds at the interface between two immiscible liquids is considered. At the interface, these molecules are supposed to replace a few of the adsorbed molecules of both solvents. Classical isotherms of adsorption (Frumkin, Frumkin-Damaskin, Langmuir, Henry) were based on the model of non-penetrable interface, where an adsorbate can substitute only molecules of one solvent. At the interface between two immiscible electrolytes, nonpolar oil/water interfaces, and liquid membranes amphiphilic molecules can substitute molecules of both solvent and classic isotherms cannot be used. The generalization of Frumkin isotherm for permeable and non-permeable interfaces, known as the Markin-Volkov isotherm, gives the possibility to analyze adsorption in a general case. The adsorption isotherms of pentafluorobenzoic acid at the octane/water interface at different pHs were measured by the drop-weight method. The thermodynamic parameters of pentafluorobenzoic acid (PFBA) adsorption at octane/water interface were determined. From the measurements of PFBA adsorption, the structure of the octane/water interface was determined. Substitution of one adsorbed octane molecule requires approximately three adsorbed PFBA molecules. This result shows that the orientation of solvent molecules at the interface is different from the bulk. Adsorbed octane molecules have a lateral orientation with respect to the interface. Gibbs free energy of adsorption equilibrium and thermodynamic parameters of PFBA adsorption show that the adsorption of PFBA at the octane/water interface is accompanied by a reduction in the attraction between adsorbed PFBA molecules as the pH decreases to the acidic region. Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 10, pp. 1194–1200. The text was submitted by the authors in English.     

Cesium uptake from aqueous solutions by bentonite: a comparison of multicomponent sorption with ion-exchange models

The removal of cesium from concentrated aqueous solutions into Ca/Mg-bentonite for a wide range of bentonite-to-water (m/V) ratios was studied experimentally and theoretically. Using the batch technique, the equilibrium of Cs uptake was measured. The nonlinear character of cesium sorption substantially influenced by the m/V ratio was observed. The experimental data were evaluated using the multicomponent Langmuir isotherm and an ion-exchange model based on the ion-exchange reaction between Cs+ and M2+ (Ca2+/Mg2+) initially sorbed on bentonite. Constants k1,Cs = 0.521 mmol.g-1, k2,Cs = 968 L.mol-1, and k2,M = 592 L.mol-1 were obtained for Cs uptake described by multicomponent Langmuir isotherm. For the ion-exchange model, the thermodynamic equilibrium constant K = 75.5 mL.g-1 with a standard deviation of sK = 17.4 mL.g-1 was determined. Using the t test, the calculated data of multicomponent Langmuir and ion-exchange isotherms were fit to experimental data, and the best agreement was obtained for the ion-exchange model. The results show that Cs uptake by bentonite could be substantially decreased in systems with a high bentonite-to-water (m/V) ratio as a consequence of the presence of desorbed divalent cations in the liquid phase.