A thermodynamically consistent explicit competitive adsorption isotherm model based on second-order single component behaviour

A competitive adsorption isotherm model is derived for binary mixtures of components characterized by single component isotherms which are second-order truncations of higher order equilibrium models suggested by multi-layer theory and statistical thermodynamics. The competitive isotherms are determined using the ideal adsorbed solution (IAS) theory which, in case of complex single component isotherms, does not generate explicit expressions to calculated equilibrium loadings and causes time consuming iterations in simulations of adsorption processes. The explicit model derived in this work is based on an analysis of the roots of a cubic polynomial resulting from the set of IAS equations. The suggested thermodynamically consistent and widely applicable competitive isotherm model can be recommended as a flexible tool for efficient simulations of fixed-bed adsorber dynamics.     

Separation mechanism of nortriptyline and amytriptyline in RPLC

The single and the competitive equilibrium isotherms of nortriptyline and amytriptyline were acquired by frontal analysis (FA) on the C18- bonded discovery column, using a 28/72 (v/v) mixture of acetonitrile and water buffered with phosphate (20 mM, pH 2.70). The adsorption energy distributions (AED) of each compound were calculated from the raw adsorption data. Both the fitting of the adsorption data using multi-linear regression analysis and the AEDs are consistent with a trimodal isotherm model. The single-component isotherm data fit well to the tri-Langmuir isotherm model. The extension to a competitive two-component tri-Langmuir isotherm model based on the best parameters of the single-component isotherms does not account well for the breakthrough curves nor for the overloaded band profiles measured for mixtures of nortriptyline and amytriptyline. However, it was possible to derive adjusted parameters of a competitive tri-Langmuir model based on the fitting of the adsorption data obtained for these mixtures. A very good agreement was then found between the calculated and the experimental overloaded band profiles of all the mixtures injected.     

Study of the competitive isotherm model and the mass transfer kinetics for a BET binary system

The competitive adsorption behavior of the binary mixture of phenetole (ethoxy-benzene) and propyl benzoate in a reversed-phase system was investigated. The adsorption equilibrium data of the single-component systems were acquired by frontal analysis. The same data for binary mixtures were acquired by the perturbation method. For both compounds, the single-component isotherm data fit best to the multilayer BET model. The experimental overloaded band profiles are in excellent agreement with the profiles calculated with either the general rate model or the modified transport-dispersive models. The competitive adsorption data were modeled using the ideal adsorbed solution (IAS) theory. The numerical values of the coefficients were derived by fitting the retention times of the perturbation pulses to those calculated using the IAS theory compiled with the coherence conditions. Finally, the elution profiles of binary mixtures were recorded. They compared very well with those calculated. As a characteristic feature of this case, an unusual retainment effect of the chromatographic band of the more retained component by the less retained one was observed. The combination of the General Rate Model and the adsorption isotherm model allowed an accurate prediction of the band profiles.     

Adsorption behaviour of sugars versus their activity in single and multicomponent liquid solutions

In this work the activity of three carbohydrates (sucrose, glucose and fructose) in highly concentrated aqueous solutions was studied along with its effect on the adsorption behaviour of the investigated compounds. Activities of individual sugars in aqueous solutions of single solute as well as in binary mixtures were quantified on the basis of solubility properties. Solid–liquid equilibria of sugars were correlated with the NRTL (nonrandom, two liquid) model of activity coefficient formulation. Activities of individual sugars were incorporated into the single component adsorption isotherm model, which reproduced accurately the course of the adsorption equilibria of sugars in aqueous solutions obtained experimentally in previous work using an ion-exchange resin. Activities of sugars determined in binary solute systems along with the single component isotherms were used to predict competitive adsorption equilibria. To calculate adsorbed phase concentrations of individual sugars in binary mixtures the adsorbed solution theory was adopted. The isotherm shapes calculated were compared to the data of competitive adsorption from the former study and found to be able to describe these experimental results.     

混合气体中SAPO-34上单个物种的表面浓度简

运用Langmuir等温线方程和理想吸附溶液理论（IAST）两种方法计算了SAPO-34在混合气体中的单个物种表面浓度,并对比了计算值与实验值的吻合程度. 考察了两个二元混合体系,分别为80 ℃的甲醇和二甲醚以及25 ℃的二甲醚和乙烯混合气,发现IAST计算值在实验压力范围内均与实验结果吻合;但是Langmuir理论计算值仅在酸性位覆盖率低于1/3时与实验值吻合较好,随着压力增加严重偏离实验值,而且Langmuir理论不能描述随压力增加低饱和吸附量物种覆盖率降低的现象. 因此,针对包含不同饱和吸附量组分的混合气,Langmuir理论仅适用于描述表面浓度低时的反应动力学,当表面浓度高时应该采用IAST方法.     

Adsorption Isotherms of Quercetin and Catechin Compounds on Quercetin-MIP

A molecular imprinted polymer(MIP)was prepared with quercetin as the template and methacrylic acid(MAA)as the functional monomer.Acetonitrile and methanol were used as the porogen with ethylene glycol dimethacrylate(EGDMA)as the crosslinker and 2,2'-azobis(isobutyronitrile)(AIBN)as the initiator.The experimental parameters of the equilibrium isotherms were estimated via linear and nonlinear regression analyses.The linear equation as the functions of the adsorption concentration of the single compound in its solution and the competitive adsorption of the single compound in its mixed compounds solution was then expressed,and the adsorption equilibrium data were correlated to Langmuir and Freundlich isotherm models.The mixture compounds show competitive adsorption on the specific binding sites of quercetin-MIP.Furthermore,the competitive Langmuir isotherms were applied to the mixture compounds.The adsorption concentrations of quercetin,( )catechin( C),and(-)epicatechin(EC)on the quercetin molecular imprinted polymer were compared.The quercetin-imprinted polymer shows extraordinarily higher adsorption ability for quercetin than for the two catechin compounds that were also assessed.     

Comparison of Adsorption Isotherms of Methylxanthines on C18 Column

A comparison of the adsorption isotherms of caffeine, theophylline and theobromine and the competitive adsorption of the three compounds on a C 18 column were investigated. The experimental parameters of the equilibrium isotherms were estimated by linear and nonlinear regression analyses. The linear equation as a function of the adsorption concentration of the single compound in its solution and the competitive adsorption of a single compound in a mixed solution were then determined. The adsorption equilibrium data were then correlated to the linear, Langmuir, Freundlich, Langmuir-Freundlich and stoichiometric displacement theory for adsorption(SDT-A) isotherm models. The mixed compounds of the three compounds were competitively adsorbed on the C 18 particles. The expression of stoichiometric displacement theory for adsorption was found to be more suitable for adsorption of methylxanthines on a C 18 column.     

Dependence of the adsorption of polymer mixtures from solution on the amount of an adsorbent

Simultaneous competitive adsorption from solutions of mixtures of poly(butyl methacrylate) and polystyrene and adsorption of each component from binary solutions have been studied for three ratios of the adsorbent mass to the solution volume, A/V. It was found that adsorption from both binary and ternary solutions strongly depends on the amount of an adsorbent, adsorption of poly(butyl methacrylate) being preferential. The characteristic adsorption isotherms of both polymers were constructed under conditions of equal equilibrium concentration of each component to estimate the parameters of preferential adsorption and their dependence on the A/V ratio. It was found that the A/V effect plays an important role in adsorption from polymer mixtures and determines the peculiarities of adsorption from polymer mixtures as well as from solution of single polymers. Changing the A/V ratio may be one way to regulate the composition of an adsorption layer consisting of two chemically different polymers. The reasons for the A/V effect are considered in the framework of the concept of the plurality of adsorption equilibria between two chemically different components and between fractions of different molecular mass of each component having various absorbability.     

Surface and solution behavior of the mixed dialkyl chain cationic and nonionic surfactants

The surface and solution behavior of the mixed dialkyl chain cationic and nonionic surfactant mixture of dihexadecyldimethylammonium bromide, DHDAB, and hexaethylene monododecyl ether, C12E6, has been investigated, using primarily the scattering techniques of small-angle neutron scattering and neutron reflectivity. Within the time scale of the measurements, the adsorption of the pure component C12E6 at the air-solution interface shows no time dependence. In contrast, the adsorption of the DHDAB/C12E6 mixture and pure DHDAB has a pronounced time dependence. The characteristic time for adsorption varies with surfactant concentration, composition, and temperature. It is approximately 2-3 h for the DHDAB/C12E6 mixture, dependent upon concentration and composition, and approximately 50 min for DHDAB. At the air-solution interface, the equilibrium composition of the adsorbed layer shows a marked departure from ideal mixing, which is dependent upon both the solution concentration and the concentration of added electrolyte. In contrast, the composition of the aggregates in the bulk solution that are in equilibrium with the surface is close to ideal mixing, as expected for solution concentrations well in excess of the critical micellar concentration. The structure of the mixed adsorbed layer has been measured and compared with the structure of the equivalent pure surfactant monolayer, and no substantial changes in structure or conformation are observed. The extreme departure from ideal mixing in the adsorption behavior of the DHDAB/C12E6 mixture is discussed in the context of the structure of the adsorbed layer, changes in the underlying solution structures, and the failure of regular solution theory to predict such behavior.     

A complete experimental approach for synthesis gas separation studies using static gravimetric and column breakthrough experiments

In this work a combination of static gravimetric and inverse chromatographic techniques is used to study the adsorption and separation of the main synthesis gas components, i.e. CO₂, CO, CH₄ and H₂. The single component adsorption isotherms of CO₂, CO, CH₄ and H₂ on faujasite NaX were measured from 303 K to 473 K and over a large range of pressures (from 0 to 1200 kPa). Breakthrough curves of CO₂ and CO and their mixtures were determined at 323 K and 373 K and 100 kPa as an illustrative example. A nice agreement was noticed between the two above-mentioned techniques for single component adsorption. Binary mixture dynamics measurements were compared to the predictions of ideal adsorption solution theory (IAST) via the previously cited single component adsorption data.     

A high-throughput methodology for liquid phase adsorption experimentation

This article describes a novel application of high-throughput experimentation, namely in the field of liquid mixture separation through adsorption. Two separate setups are designed and extensively used to study multicomponent liquid phase adsorption: the first setup performs batch adsorption in static conditions to obtain adsorption isotherms while the latter carries out breakthrough experiments in dynamic conditions, which yield multicomponent breakthrough curves. The obtained data serves as an indicator of the separative qualities of an adsorbent exposed to a particular liquid mixture. The reliability of the obtained measurements is assessed using different validation techniques. Case studies pertaining to the competitive adsorption of binary alkane/alkene/aromatic mixtures on faujasites complete the validation process. A new model for batch adsorption isotherms is proposed based on the equilibrium conditions in liquid phase.     

The adsorption and self-assembly of mixtures of alkylbenzene sulfonate isomers and the role of divalent electrolyte

In this paper, the role of the different structural isomers of the anionic surfactant sodium para-dodecyl benzene sulfonate, LAS, on surface adsorption and solution self-assembly has been studied. Using a combination of neutron reflectivity, NR, and small angle neutron scattering, SANS, the effect of mixing an isomer with a short symmetric hydrocarbon chain with one which has an asymmetric hydrocarbon chain on both the equilibrium surface adsorption behavior and the solution microstructure of the mixtures, both in the presence and absence of a divalent cation (Ca(2+)), has been investigated. In the absence of electrolyte, the LAS isomer mixtures form small charged globular micelles throughout the composition range studied. The micelle aggregation number increases with the increase in the asymmetric isomer content, reflecting an increase in the packing efficiency within the micelle. The addition of calcium ions promotes the formation of planar aggregates, as multilamellar vesicles, but only when the symmetric LAS isomer is the major component of the mixture. At a surfactant concentration just above the critical micelle concentration, CMC, and in the absence of electrolyte, the variation in the surface composition is close to the solution composition. Regular solution theory, RST, calculations show that this variation is also close to what is expected for ideal mixing. The addition of Ca(2+) ions induces a different surface behavior, resulting in the formation of multilayer structures at the interface throughout the entire composition range.     

Single and Binary Dye Adsorption of Methylene Blue and Methyl Orange in Alcohol Aqueous Solution via Rice Husk Based Activated Carbon: Kinetics and Equilibrium Studies

The present work was mainly focused on the single and binary adsorption of methylene blue(MB) and methyl orange(MO) from alcohol aqueous solution over rice husk based activated carbon(RHAC). The study of single dye adsorption equilibrium experiments found that the Langmuir adsorption model was consistent with the adsorption behavior of RHAC on MB and MO, indicating that it was a single layer adsorption. The adsorption behavior conformed to the pseudo-second-order kinetic model. The binary dye adsorption experiments showed that the Langmuir-Freundlich model could be applied to describe the adsorption behavior of RHAC on MB and MO. Comparation with the single dye system, the adsorption capacity on the binary dye system was larger, and there was "competitive adsorption" and "synergistic adsorption" effects existed. Meanwhile, the pseudo-second-order kinetic model also fit for the binary dye adsorption behavior.     

Effect of temperature on competitive adsorption of the solute and the organic solvent in reversed-phase liquid chromatography

In analysis of the temperature effect on chromatographic separations the influence of the adsorption of organic solvent on the retention properties of solute is generally not taken into account. In fact, adsorption behavior of solutes is strongly affected by competitive adsorption of organic solvents, which is temperature dependent. In this work changes of adsorption equilibrium of an organic solvent as well as a solute with temperature have been analyzed. Data of the excess adsorption of methanol from aqueous solutions on octadecyl-bonded silica have been acquired at different temperature. Experiments have been performed over a relatively narrow temperature range corresponding to typical chromatographic conditions, i.e., 10-50 degrees C. The competitive adsorption equilibria of model solutes (i.e., two homologous compounds: cyclopentanone and cyclohexanone) have been measured at different temperature and composition of the mobile phase. Temperature alterations to the retention properties were found to result from combined effects of changes in adsorption behavior of the organic solvent and of the solute. The influence of temperature on the separation selectivity has been considered.     

Tensammetry with accumulation on the hanging mercury drop electrode : Part 5. The behaviour of mixtures of oxyethylated alcohols

The behaviour of the following mixtures of polydispersed oxyethylated alcohols having a well-defined n-alkyl radical was investigated: 18-14/6-14, 18-14/10-14, 18-14/18-10, 18-14/18-6, 18-6/18-10, 6-14/10-14 and 18-6/18-10/18-14 (the first number denotes the number of carbon atoms in the n-alkyl chain, and the second is the number of oxyethylene subunits). The influence of preconcentration potential in the range more negative than - 1.0 V vs. SCE is described in detail. The results are compared with the behaviour of model mixtures of poly(ethylene glycols). The surfactant mixtures 18-14/6-14 and 18-14/10-14 behave similarly to a model mixture of components having sufficiently different properties. Separate peaks for both components appear on the tensammetric curves of the mixtures, but only at certain preconcentration potentials are the peak heights similar to the peak heights for the individual components alone. The behaviour of the 18-14, 18-10 and 18-6 mixtures, in alt combinations, depends strongly on whether premicellar (associated) forms are present in the solution. These premicellar forms are indicated by a common very narrow peak on the tensammetric curves. If the monomeric forms predominate (i.e., at low-total surfactant concentrations) the peak heights for the mixtures are approximately additive after preconcentration at a suitable potential. If premicellar forms predominate (as at total concentrations > 0.1 mg l^?1), the behaviour of the mixtures is a result of competition between the monomeric and premicellar forms in the adsorption process. This behaviour approximates the behaviour of a mixture consisting of sufficiently different components; monomeric forms behave like the first component, and premicellar forms like the second component of the model mixture. For the surfactant mixture 18-14/18-10, which behaves additively under certain conditions, it is possible to determine the total concentration within the range 10-35μgl^?1. The 6-14/10-14 mixture forms a single nonadditive peak.     

Effect of pH on Adsorption of Cephalosporin C by A Nonionic Polymeric Sorbent

Adsorption of cephalosporin C in a column charged with a nonionic polymeric sorbent, SP850, was studied at various pH values to assess the effect of pH on the dynamic behavior in column adsorbers. Since cephalosporin C is amphoteric, the fractions of each ionic form were calculated from the pK values at a given solution pH. Single-species isotherm parameters for each ionic form were simultaneously extracted from all sets of adsorption equilibrium data measured at several pH values. The mutual interaction between different ionic forms on SP850 was described by a competitive adsorption, namely the ideal adsorbed solution theory (IAST). This treatment made it possible to simulate the dynamic behavior of cephalosporin C at low pH values properly by a dynamic model which was incorporated with the mutual competitive adsorption.     

Equilibrium surface adsorption behavior in complex anionic/nonionic surfactant mixtures

Neutron reflectivity (NR) and small angle neutron scattering (SANS) have been used to investigate the equilibrium surface adsorption behavior and the solution microstructure of mixtures of the anionic surfactant sodium 6-dodecyl benzene-4 sulfonate (SDBS) with the nonionic surfactants monododecyl octaethylene glycol (C12EO8) and monododecyl triiscosaethylene glycol (C12EO23). In the SDBS/C12EO8 and SDBS/C12EO23 solutions, small globular mixed micelles are formed. However, the addition of Ca2+ ions to SDBS/C12EO8 results in a transition to a vesicle phase or a mixed vesicle/micellar phase for SDBS rich compositions. In contrast, this transition hardly exists for the SDBS/C12EO23 mixture, and occurs only in a narrow composition region which is rich in SDBS. The adsorption of the SDBS/C12EO8 mixture at the air-solution interface is in the form of a mixed monolayer, with a composition variation that is not consistent with ideal mixing. In water and in the presence of NaCl, the nonideality can be broadly accounted for by regular solution theory (RST). At solution compositions rich in SDBS, the addition of Ca2+ ions results in the formation of multilayer structures at the interface. The composition range over which multilayer formation exists depends upon the Ca2+ concentration added. In comparison, the addition of a simple monovalent electrolyte, NaCl, at the same ionic strength does not have the same impact upon the adsorption, and the surface structure remains as a monolayer. Correspondingly, in solution, the mixed surfactant aggregates remain as relatively small globular micelles. In the presence of Ca2+ counterions, the variation in surface composition with solution composition is not well described by RST over the entire composition range. Furthermore, the mixing behavior is not strongly correlated with variations in the solution microstructure, as observed in other related systems.     

Band splitting in overloaded isocratic elution chromatography II. New competitive adsorption isotherms

The equations of two new binary competitive isotherms models are derived. The first of these models assumes that the isotherms of the two pure, single compounds have distinct monolayer capacities. Its derivation is based on kinetic arguments. The ideal adsorbed solution (IAS) framework was applied to derive the second model that is a thermodynamically consistent competitive isotherm. This second model predicts the competitive adsorption isotherm behavior of a mixture of two compounds that have single-component adsorption behavior following a BET and/or a Langmuir isotherms. Both models apply well to the binary adsorption of ethylbenzoate and 4-tert.-butylphenol on a Kromasil-C18 column (with methanol-water, 62:38, v/v, as the mobile phase). The best single-solute adsorption isotherms of these two compounds are the liquid-solid extended multilayer BET and the Langmuir isotherms, respectively. The kinetic and thermodynamic new competitive models were compared, regarding the accuracy of their prediction of the elution band profiles of mixtures of these two compounds. A better agreement between experimental and calculated profiles was observed with the kinetic model. The IAS model failed because the behavior of the ethylbenzoate/4-tert.-butylphenol adsorbed phase mixture is probably non-ideal. The most striking result is the qualitative prediction by these models of the peak splitting of 4-tert.-butylphenol during its elution in presence of ethylbenzoate.     

Mixtures of charged colloid and neutral polymer: influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.