Generalized Langmuir Equation Research Articles

Mesoporous Carbons and Highly Cross-Linking Polymers for Removal of Cationic Dyes from Aqueous Solutions-Studies on Adsorption Equilibrium and Kinetics.

This study presents the results of applying the methods of synthesizing mesoporous carbon and mesoporous polymer materials with an extended porous mesostructure as adsorbents for cationic dye molecules. Both types of adsorbents are synthetic materials. The aim of the presented research was the preparation, characterisation, and utilisation of obtained mesoporous adsorbents. The physicochemical properties, morphology, and porous structure characteristics of the obtained materials were determined using low-temperature nitrogen sorption isotherms, X-ray diffraction (XRD), small angle X-ray scattering (SAXS), and potentiometric titration measurements. The morphology and microstructure were imaged using scanning electron microscopy (SEM). The chemical characterisation of the surface chemistry of the adsorbents, which provides information about the surface-active groups, the elemental composition, and the electronic state of the elements, was carried out using X-ray photoelectron spectroscopy (XPS). The adsorption properties of the mesoporous materials were determined using equilibrium and kinetic adsorption experiments for three selected cationic dyes (derivatives of thiazine (methylene blue) and triarylmethane (malachite green and crystal violet)). The adsorption capacity was analysed to the nanostructural and surface properties of used materials. The Generalized Langmuir equation was applied for the analysis of adsorption isotherm data. The adsorption study showed that the carbon materials have a higher sorption capacity for both methylene blue and crystal violet, e.g., 0.88-1.01 mmol/g and 0.33-0.44 mmol/g, respectively, compared to the polymer materials (e.g., 0.038-0.044 mmol/g and 0.038-0.050 mmol/g, respectively). The kinetics of dyes adsorption was closely correlated with the structural properties of the adsorbents. The kinetic data were analysed using various equations: first-order (FOE), second-order (SOE), mixed 1,2-order (MOE), multi-exponential (m-exp), and fractal-like MOE (f-MOE).

Chitosan Deposited onto Fumed Silica Surface as Sustainable Hybrid Biosorbent for Acid Orange 8 Dye Capture: Effect of Temperature in Adsorption Equilibrium and Kinetics.

Chitosan was deposited on fumed silica without the addition of cross-linkers or activating agents. The chitosan surface layer has a high affinity toward organic molecules, e.g., Acid Orange 8 (AO8) dye, robust to a broad range of simulated conditions (variance with respect to temperature, time, and concentration of solute). Experimental equilibrium data were analyzed by the generalized Langmuir equation taking into consideration the energetic heterogeneity of the adsorption system. The effect of temperature on dye uptake and adsorption rate was studied. According to the calculated thermodynamic functions ΔG°, ΔH°, and ΔS° from the equilibrium data at different temperatures, the adsorption of AO8 onto chitosan–fumed silica composite is exothermic and spontaneous. The studies of temperature effect on adsorption equilibrium show that the maximum adsorption capacity (determined from the Langmuir–Freundlich equation) of synthesized composite toward AO8 is about one-third higher in the case of an isotherm measured at 5 °C than this value obtained for the isotherm measured at 45 °C. The quantitative binding of dye molecules to chitosan coating on the surface of silica was proved by 1H MAS NMR. The deep kinetics study through the application of various theoretical models—the first-order equation, pseudo-first-order equation, second-order equation, pseudo-second-order equation, mixed first, second-order equation, and multiexponential equation—was applied for getting inside the mechanism of AO8 binding to the chitosan coating. Structural characteristics of chitosan-coated silica were obtained from the low-temperature adsorption/desorption isotherms of nitrogen and imaging by scanning electron microscopy. The effects of a synthetic route for polymer coating on thermal stability and the ability to degrade were studied by differential scanning calorimetry.

Chitosan-Silica Hybrid Composites for Removal of Sulfonated Azo Dyes from Aqueous Solutions.

In this study, the influence of the chitosan immobilization method on the properties of final hybrid materials was performed. Chitosan was immobilized on the surface of mesoporous (ChS2) and fumed silica (ChS3) by physical adsorption and the sol-gel method (ChS1). It was found that physical immobilization of chitosan allows to obtain hybrid composites (ChS) with a homogeneous distribution of polymer on the surface, relatively wide pores, and specific surface area of about 170 m2/g, pHPZC = 5.7 for ChS3 and 356 m2/g and pHPZC = 6.0 for ChS2. The microporous chitosan-silica material with a specific surface area of 600 m2/g and a more negatively charged surface (pHPZC = 4.2) was obtained by the sol-gel reaction. The mechanisms of azo dye adsorption were studied, and the correlation with the composite structure was distinguished. The generalized Langmuir equation and its special cases, that is, Langmuir-Freundlich and Langmuir equations, were applied for the analysis of adsorption isotherm data. The adsorption study showed that physically adsorbed chitosan (ChS1 and ChS2) on a silica surface has a higher sorption capacity, for example, 0.48 mmol/g for the acid red 88 (AR88) dye (ChS2) and 0.23 mmol/g for the acid orange 8 (AO8) dye (ChS1), compared to the composite obtained by the sol-gel method [ChS1, 0.05 mmol/g for the AO8 dye]. For a deeper understanding of the behavior of immobilized chitosan in the adsorption processes, various kinetic equations were applied: first-order, second-order, mixed 1,2-order (MOE), multiexponential, and fractal-like MOE as well as intraparticle and pore diffusion model equations. In the case of AO8 dye, the adsorption rates were differentiated for three composites: for ChS3, 50% of the dye was removed from the solution after merely 5 min and almost 90% after 80 min. The slowest adsorption process controlled by the diffusion rate of dye molecules into the internal space of the pore structure was found for ChS1 (225 min halftime). In the case of ChS2, the rates for various dyes change in the following order: acid orange (AO7) > orange G (OG) > acid red 1 (AR1) > AR88 > AO8 (halftimes: 10.5 < 15.7 < 23.7 < 34.9 < 42.9 min).

Evaluation of the SBA-15 materials ability to accumulation of 4-chlorophenol on carbon paste electrode

The adsorption of 4-chlorophenol (4-CP) from an aqueous solution on three ordered mesoporous silica materials (commercial unmodified SBA-15-Sigma, synthesized unmodified SBA-15 and amino-functionalized SBA-15-NH2) was studied. The adsorption isotherms were analyzed using the Generalized Langmuir equation taking into account the energetic heterogeneity. The adsorption capacities of the mesoporous silicas increased in order: SBA-15 < SBA-15-Sigma < SBA-15-NH2. The materials were used for the modification of the carbon paste electrodes (CPEs) for detection of 4-CP based on differential pulse voltammetry. Different parameters that affects the DPV signal such as scan rate, accumulation time and paste composition were investigated. Compared with the bare (graphite) CPE, the SBA-15 modified electrodes greatly increased the oxidation peak current of 4-CP, showing strong signal enhancement effects. The SBA-15-NH2 modified CPE showed a larger peak current and higher sensitivity for the 4-CP in comparison with the SBA-15 and SBA-15-Sigma modified carbon paste electrodes. The results showed high usefulness of the ordered mesoporous silica materials as an electrode modifiers in the electroanalytical techniques.

A non-equilibrium thermodynamics model for combined adsorption and diffusion processes in micro- and nanopores

A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation, and the adsorbed phase governed by a generalized Langmuir equation. It is shown that the combination of diffusion and adsorption can be treated as diffusion in an effective medium, with an effective diffusion coefficient depending on the characteristics of the adsorption kinetics. The interplay between these effects leads to the appearance of different regimes in which the effective diffusion coefficient exhibits peculiar behaviours such as a decrease due to the presence of the adsorption process and a non-monotonous behavior resulting from particle interactions. We outline applications of the model developed to diffusion in porous materials such as zeolites and bentonites, and to engineered highly porous materials.

Gas chromatographic, quentum-chemical, and molecular statistical studies of cluster adsorption of water and methanol molecules on hydrophilic surface sites of hydrophobic adsorbents

The comprehensive theoretical and experimental study of the adsorption of water and methanol molecules on active sites (carboxyl and phenol hydroxyl groups) on the graphitized thermal carbon black is performed. It is shown that microclusters formed upon the adsorption of these molecules on such sites are characterized by the cyclic structure comprising 4–5 molecules similar to that whose existence was revealed previously in liquid water and on the surface of silver iodide. The analysis of the studied adsorption clusters demonstrated that the formation of such cycles is governed primarily by the hydrogen bonding; however, a definite role is played also by energy effects associated with the changes in the state of molecular motion during adsorption. It is shown that the generalized Langmuir equation derived from molecular statistical considerations provides for better reproducing of the experimental isotherm within a wider surface coverage range, thus making it possible to consistently interpret data on structural and energetic characteristics of adsorption systems obtained by gas chromatography and quentum-chemical method.

Complex investigation of cluster adsorbtion of water molecules on hydrophilic centers of graphite and graphitized thermal carbon black

A complex theoretical-experimental investigation has been carried out on the interaction of water with hydrophilic centers-phenolic and carboxyl groups-on the surface of graphite and graphitized thermal carbon black in low surface occupation range. It is shown that microclusters, formed by the absorption on such centers, have a cyclic structure of 4–5 molecules similar to those observed in liquid water and on the surface of silver iodide. The formation of such structures is shown to be energetically advantageous. It is shown that the generalized Langmuir equation, derived from molecular-statistical considerations, is considerably better over a wide range of relative pressure for the description of the experimental isotherm for the adsorption of water on graphitized thermal carbon black and allows for a better interpretation of structural and energetic characteristics of adsorbed systems obtained by a complex of methods.

Distribution function approach to irreversible adsorption of interacting colloidal particles

A statistical-mechanical description of the irreversible adsorption of interacting colloidal particles is developed. Our approach describes in a consistent way the interaction of particles from the bulk with adsorbed particles during the transport process towards the adsorbing surface. The macroscopic physical quantities corresponding to the actual process are expressed as averages over simpler auxiliary processes which proceed in the presence of a fixed number n of adsorbed particles. The adsorption rate verifies a generalized Langmuir equation, in which the kinetic resistance (the inverse of the kinetic coefficient) is expressed as the sum of a diffusional resistance and a resistance due to interaction with adsorbed particles during the transport process (blocking effect). Contrary to previous approaches, the blocking effect is not due to geometrical exclusion, instead it measures how the transport from the bulk is affected by the adsorbed particles. From the general expressions obtained, we have derived coverage expansions for the adsorption rate and the surface correlation function. The theory is applied to the case of colloidal particles interacting through DLVO potentials. This form of the kinetic coefficient is shown to be in agreement with recent experimental results, in which RSA fails.

Sorption of Strontium by Bacteria, Fe(III) Oxide, and Bacteria−Fe(III) Oxide Composites

This study provides the first quantitative comparison of the sorptive capacities of a bacteria--Fe oxide composite to its individual components. These results have enormous significance for understanding the fate and transport of inorganic contaminants in natural aqueous environments where heterogeneous bacteria--oxide composite solids are commonly found. The authors quantify Sr{sup 2+} sorption to the bacteria Shewanella alga, Shewanella putrefaciens, amorphous hydrous ferric oxide (HGO), and S. alga coated with HFO over a range of total Sr{sup 2+} concentrations and pH, under well controlled laboratory conditions. Significant Sr{sup 2+} sorption occurred at significantly lower pH values to the bacteria and S. alga-HFO composite compared to HFO. Geochemical modeling using a generalized Langmuir equation showed that the bacteria sorb significantly greater quantities of Sr{sup 2+} (maximum sorptive capacity: BSr{sub max} = 0.079 and 0.075 mmol{sm{underscore}bullet}g{sup {minus}1} for S. alga and S. putrefaciens, respectively) than the HFO (0.001 mmol{sm{underscore}bullet}g{sup {minus}1}). The observed BSr{sub max} for the S. alga-HFO composite was less than the combined sorptive properties of its components = 0.041 mmol{sm{underscore}bullet}g{sup {minus}1}, likely reflecting HFO masking of bacterial surface binding sites.

ChemInform Abstract: PHYSICAL ADSORPTION OF GASES ON ENERGETICALLY HETEROGENEOUS SOLIDS. I. GENERALIZED LANGMUIR EQUATION AND ITS ENERGY DISTRIBUTION

A generalizedLangmuir equation is proposed for describing the monolayer adsorption of single gases on heterogeneous solids. The special cases of this equation are:Langmuir-Freundlich, Toth andFreundlich type adsorption isotherms. The energy distribution function corresponding to this equation produces all types of simple energy distributions, i.e., symmetrical distribution, decreasing exponential distributions and asymmetrical distributions showing widening in the directions of low and high adsorption energies.

Physical adsorption of gases on energetically heterogeneous solids I. GeneralizedLangmuir equation and its energy distribution

A generalizedLangmuir equation is proposed for describing the monolayer adsorption of single gases on heterogeneous solids. The special cases of this equation are:Langmuir-Freundlich, Toth andFreundlich type adsorption isotherms. The energy distribution function corresponding to this equation produces all types of simple energy distributions, i.e., symmetrical distribution, decreasing exponential distributions and asymmetrical distributions showing widening in the directions of low and high adsorption energies.