On numerical classification of solution adsorption isotherms

To numerically classify solution adsorption isotherms, a difference or deviation measure, DS(mc) (the relative difference between two sums of the adsorption maximum's characteristics of selectivity isotherms x 100), is derived. The measure is applicable to completely miscible binary solutions on solids. This quantity evaluates the difference between an adsorption system and the ideal adsorption system (ideal adsorbed and bulk phases, homogeneous surface, and equal molar area solution components) at the point of maximum adsorption. For model systems, DS(mc)s are calculated at several levels of surface heterogeneity (Gaussian distribution of surface energy) and for different signs of phase nonideality (regular solution phases) on a homogeneous surface and on a simple two-site-type heterogeneous surface. All heterogeneous surfaces have negative DS(mc) values, but nonideal phases have DS(mc)s with signs opposite to the sign of deviation from Raoult's law. DS(mc)s from both U- and S-shape isotherms are reported for 16 experimental systems consisting of hydrocarbon mixtures and both alcohol + hydrocarbon and alcohol + water solutions or acetone + carbon tetrachloride on several silica gels and a variety of carbons.     

Ideal nonideality in adsorption of 2-aminoethanethiol and 2-mercaptoethane sulfonic acid to form electrostatically stabilized binary self-assembled monolayers on Au(111)

In formation of binary self-assembled monolayers (SAMs) composed of 2-aminoethanethiol (AET) and 2-mercaptoethane sulfonic acid (MES) by adsorption from an ethanol solution on Au(111), the adsorption shows nearly ideal nonideality in that the surface ratio of MES to AET in the SAM is unity and does not depend on the mixing ratio of MES to AET in the bathing ethanol solution used for preparing SAMs, chi(soln)MES, over the wide range of chi(soln)MES between 0.01 and 0.95. X-ray photoelectron spectroscopy confirms that at least 80% of AET molecules adsorbed are protonated in this range of chi(soln)MES, indicating that the electrostatic interaction between positively charged AET and negatively charged MES is responsible to the observed nonideality. Correspondingly, there appears only one cathodic peak in a linear-sweep voltammogram of the reductive desorption of the SAM, having a narrow full width at half-maximum of about 20 mV. This suggests the presence of strong lateral attractive interaction between the adsorbed thiolates.     

Application of the vacancy solution theory to describe the enthalpic effects accompanying mixed-gas adsorption

The possibility of utilizing vacancy solution theory (VST) to study the enthalpic effects accompanying mixed-gas adsorption equilibria is presented. Besides heterogeneity, the interaction effects by using the regular adsorbed solution, Flory-Huggins, and Wilson models of nonideality in the adsorbed phase are taken into account. To predict adsorption phase diagrams and calorimetric effects in the mixed-gas adsorption system, only a knowledge of the single-gas adsorption isotherms and accompanying calorimetric effects is required. The possibility of simplification of the obtained theoretical expressions is shown. The obtained agreement between theory and experiment is very satisfactory.     

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.     

A quasi-equilibrium theory of protein adsorption

A model is developed to describe the adsorption and desorption of proteins to and from a surface film under quasi-equilibrium conditions. Starting from Fick's first law of diffusion, an equation for the flux of molecules to a surface is derived assuming a gradient in the chemical potential from the bulk to the surface and a potential barrier due to an existing surface film. Protein molecules are modeled as components with varying surface areas to depict the different orientations of molecules with respect to the film. For concentrated solutions, formation of multilayer protein films is described by allowing components with small minimum surface areas. The thermodynamic analysis is based on Butler's equation for the chemical potentials of the components of a Gibbs surface layer and a first-order model for the nonideality of the surface layer enthalpy and entropy. The model assumes reversible adsorption, consistent with globular proteins that show little denaturation or flexible-chain proteins that reversibly denature at the interface. The model predicts the behavior of five different experiments measuring film properties of the serum protein albumin in quasi-equilibrium and equilibrium conditions at over 2 orders of magnitude in concentration using a single set of parameters. This provides a new framework for analyzing interactions and adsorption of protein films. The key new features of this model are an extension of the classical Smoluchowski analysis to calculate the adsorption and desorption rate, a model of multilayers with decreased molecular areas to allow effective densities greater than a close-packed monolayer, and a concentration-dependent layer thickness.     

Liquid-solid adsorption from binary component mixture

Based on five thermodynamic equilibria among the components Ⅰ,Ⅱ,and adsorbent,astoichiometric displacement model of adsorption(SDM-A)from binary liquid mixture with completerange of concentration in liquid-solid system is proposed and tested by using data published in litera-tures.The two expressions of this model show the quantitative relationships between the activity of thecomponent Ⅰ on the surface and that in the bulk solution and between its partition coefficient in twophases and its equilibrium activity in bulk solution,respectively.In some cases,the two expressionsmay become two linear equations,from which the correspondingly linear slopes(i.e.the adsorptionparameters)are obtained with which the stoichiometric displacement relation and relative adsorptionability between components Ⅰ and Ⅱ can be elucidated.The effectiveness of these two expressions fordifferent adsorption systems and the similarity and difference between SDM-A and the Freundlich Em-pirical Equation are also investigated.A rule illustrating a parallel relationship between 2n/Z and theproperty of bulk solution is also found.And,having studied the quantitative relation of the adsorptionfrom either ideal or non-ideal liquid mixture and compaired their linear adsorption parameters,we findthat SDM-A is much better than the Langmuir's.     

Analysis of adsorption isosteres of gas and vapor on microporous adsorbents

The adsorption isosteres and isotherms of methane on the microporous carbon adsorbent PAU-10 were calculated using the Dubinin—Radushkevich equation taking into account nonideality of the gas phase. The conditions under which the adsorption isosteres are linear were outlined. The calculated and experimentally found adsorption isosteres were compared for the methane—PAU-10 system. The slope of the isosteres remains unchanged on going to the region of strong nonideality of the gas phase. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 382–385, March, 2007.     

Adsorption equilibria of binary gas mixtures on graphitized carbon black

Adsorption equilibria for binary gas mixtures (methane-carbon dioxide, methane-ethane, and carbon dioxide-ethane) on the graphitized carbon black STH-2 were measured by the open flow method at 293.2 K. The experimental pressure range was (0 to 1.6) MPa. The extended Langmuir (EL) model and the ideal adsorption solution theory (IAST) have been adopted to predict the equilibria of binary gas mixtures. The results indicate that gas mixtures adsorbed on the homogeneous surface of STH-2 exhibit the nonideal behavior, which is mainly induced by adsorbate-adsorbate interactions. The real adsorption solution theory (RAST) has been used to analyze the property of the adsorbed mixtures. The activity coefficients have been correlated with the Wilson equation. The investigation demonstrates that the nonideality of adsorbed phase is completely dissimilar with the bulk liquid phase. The adsorption of the heavier component would benefit the adsorption of the lighter component.     

The line adsorption equation: the one-dimensional counterpart of the Gibbs adsorption equation

The thermodynamic development for multiphase contact lines is analogous to that for surfaces or interfaces. However, for one of the most important equations in surface thermodynamics, the Gibbs adsorption equation, the one-dimensional analogue is missing. This paper derives such an analogue, the line adsorption equation. Similarly to the Gibbs adsorption equation, the line adsorption equation is derived from Gibbsian thermodynamics. For a three-phase, three-component contact line system (e.g. an oil lens on the surface of an aqueous solution), the line concentrations (excesses) of two immiscible solvents can be made vanish by appropriately placing the dividing line. Consequently, the line concentration of the solute can be evaluated through the line tension change with the volume concentration of the solute. Such an evaluation provides information about molecular adsorption at the contact line, which is important in physical chemistry of lines, but difficult to obtain by any other means.     

Infrared spectroscopic studies of monothiol ligand adsorption on CdS nanocrystal films in aqueous solutions

Probing the surface chemistry of thiol ligand binding to cadmium chalcogenide nanocrystals is important to clarify factors involved in quantum dot stability and surface functionalization. Deposited CdS nanocrystal films have been used in this work as model quantum dot surfaces for ligand adsorption studies. The adsorption of mercaptoacetic acid, mercaptopropionic acid, and mercaptoethanol, from aqueous solution to CdS thin films, has been studied by in situ infrared spectroscopy. The absence of a S-H stretch absorption for the adsorbed species shows that adsorption occurs via the deprotonated thiol group, and the spectrum of the adsorbed carboxylic acid species closely resembles those of the solution ligands. Adsorption of mercaptoacetic acid and of mercaptopropionic acid resulted in pKa(COOH) decreases of 1.5 and 0.5, respectively. Significant changes in the spectrum of mercaptoethanol upon adsorption have been observed, but the present uncertainty in mercaptoethanol spectral interpretation does not provide structural inferences. Adsorption isotherms determined from the spectral data indicate strong thiol adsorption to CdS. The adsorption isotherms have been fitted to both Langmuir and Freundlich equations, with the latter providing a better fit. This may be attributed to a change in the probability of adsorption to vacant surface sites due to the increased CdS surface negative charge as the surface coverage increases.     

A single-site model for divalent transition and heavy metal adsorption over a range of metal concentrations

Metal adsorption data over a range of surface coverages typically are characterized by curvilinear metal adsorption isotherms. These isotherms generally have a slope of 1 at low surface coverage and a shallower slope at higher surface coverages. The curvature of metal adsorption isotherms with increasing surface coverage is frequently interpreted in terms of sequential adsorption onto different types of surface sites, multinuclear surface complexation, or nonideality of metal adsorption. We demonstrate that the curvature of metal adsorption isotherms can also be attributed to changes in surface charge and potential that depend on the predominant type of metal surface complex. A single-site extended triple-layer model is used to reinterpret previously studied metal adsorption isotherms and pH edges for a wide variety of metals (Cd2+, Co2+, Cu2+, Pb2+, and Zn2+) and solids (goethite, hydrous ferric oxide, corundum, and magnetite) in different electrolyte solutions (NaNO3 and NaClO4). Only metal adsorption on ferrihydrite at very low surface coverages is not consistent with the single-site triple-layer model. This discrepancy might be explained if ferrihydrite is in fact not a single phase but a mixture of two or more phases. Metal surface coverages ranging from 10(-4) to 10.2 mmol/m2 on the other minerals can be accounted for with a single-site extended triple-layer model if appropriate metal adsorption reactions are chosen. In addition, several examples suggest that, within the context of the model, surface complexation schemes can be established that describe metal adsorption over both a wide range of surface coverage and a wide range of ionic strength.     

Study of surface tension and surface properties of binary alcohol/n-alkyl acetate mixtures

The Butler equation is employed to describe quantitatively the nature, properties, and compositions of surface layers in binary liquid mixtures. Bulk mole fraction, surface molar area, and surface tension of pure components are necessary inputs for this equation. In addition, the UNIFAC group contribution method is applied to account for the nonideality of the bulk liquid as well as that of the surface layer. The average relative error obtained from the comparison of experimental and calculated surface tension values for 12 binary systems is less than 1%. Therefore, the model has good accuracy in comparison with other predictive equations. In addition to finding more information about the surface structure of binary mixtures, surface mole fraction was calculated using relative Gibbs adsorption values and an extended Langmuir model (EL). The obtained results show a good consistency between two models employed, i.e., the Gibbs adsorption model and EL model, based on the UNIFAC method.     

Dynamic surface tension and adsorption kinetics of beta-casein at the solution/air interface

A diffusion model is proposed to describe the adsorption kinetics of proteins at a liquid interface. The model is based on the simultaneous solution of the Ward-Tordai equation and a set of recently developed equations describing the equilibrium state of the adsorption layer: the adsorption isotherm, the surface layer equation of state, and the function of adsorption distribution over the states with different molar areas. The new kinetics model is compared with dynamic surface tensions of beta-casein solutions measured with the drop/bubble profile and maximum bubble pressure methods. The adsorption process for low concentrations is governed by the diffusion mechanism, while at large protein concentrations this is only the case in the initial stage. The effective diffusion coefficients agree fairly well with literature data. The adsorption values calculated from the dynamic surface tension data agree very well with the used equilibrium adsorption model.     

Physical adsorption of gases: the case for absolute adsorption as the basis for thermodynamic analysis

We discuss the thermodynamics of physical adsorption of gases in porous solids. The measurement of the amount of gas adsorbed in a solid requires specialized volumetric and gravimetric techniques based upon the concept of the surface excess. Excess adsorption isotherms provide thermodynamic information about the gas-solid system but are difficult to interpret at high pressure because of peculiarities such as intersecting isotherms. Quantities such as pore density and heats of adsorption are undefined for excess isotherms at high pressure. These difficulties vanish when excess isotherms are converted to absolute adsorption. Using the proper definitions, the special features of adsorption can be incorporated into a rigorous framework of solution thermodynamics. Practical applications including mixed-gas equilibria, equations for adsorption isotherms, and methods for calculating thermodynamic properties are covered. The primary limitations of the absolute adsorption formalism arise from the need to estimate pore volumes and in the application to systems with larger mesopores or macropores at high bulk pressures and temperatures where the thermodynamic properties may be dominated by contributions from the bulk fluid. Under these circumstances a rigorous treatment of the thermodynamics requires consideration of the adsorption cell and its contents (bulk gas, porous solid and confined fluid).     

Kinetic derivation of common isotherm equations for surface and micropore adsorption

The Langmuir equation is one of the most successful adsorption isotherm equations, being widely used to fit Type I adsorption isotherms. In this article we show that the kinetic approach originally used by Langmuir for 2D monolayer surface adsorption can also be used to derive a 1D analogue of the equation, applicable in ultramicropores with single-file diffusion. It is hoped that such a demonstration helps dispel the idea that the Langmuir isotherm equation cannot apply to some micropores as more than a mathematical correlation. We furthermore seek to extend the insight provided by the simple kinetic derivation of the Langmuir equation to other isotherm equations capable of modelling Type I isotherms. The same kinetic approach is thus also used to derive the Volmer, Fowler–Guggenheim and Hill–de Boer equations, both for surface (2D adsorbed phase) and micropore adsorption (1D and 3D adsorbed phases). It is hoped that this will help make more intuitively clear that these equations can be used as phenomenological models in some instances of adsorption in micropores.     

Nonequilibrium surface tension for mixed adsorption kinetics

Experimental nonequilibrium surface tension measurements of 1–9 nonanediol solutions obtained by the oscillating-jet method have been interpreted in terms of our theoretical predictions derived for a mixed-controlled adsorption kinetics of the surfactant. The surface tension values have been calculated from the Szyszkowski equation using the Langmuir model of surfactant adsorption. Our theoretical results, obtained by a numerical solution of the adsorption equations, agree well with experimental data giving a value of the kinetics Szyszkowski constant very similar to the thermodynamic equilibrium value determined from experimental measurements of the static surface tension of 1–9 nonanediol solutions of various concentration. The approximate kinetic equation derived by P. Joos, G. Bleys, and G. Petre (J. Chim. Phys.79, 387 (1982)) for purely barrier-controlled adsorption proved to be less accurate.     

Phenol adsorption on closed carbon nanotubes

We present the results of systematic studies of phenol adsorption on closed commercially available, unmodified carbon nanotubes. Phenol adsorption is determined by the value of tube-specific surface area, the presence of small amount of surface groups influence adsorption only in very small amount. Phenol can be applied as a probe molecule for comparative analysis of tube surface areas. Tube curvature influences adsorption from solution, i.e., we observe increasing adsorption energy (and slower desorption process) with the decrease in tube curvature. This is in full accordance with molecular simulation results.     

Reversible kinetics of physical adsorption on homogeneous surface

The kinetics of reversible polymolecular adsorption was studied theoretically in main terms of the BET model. A system of equations that describes the adsorption process is derived and the analytical solution of a given system for the finite number of adsorption sites is found. The effect of equilibrium and kinetic parameters of adsorption system on the kinetics of adsorption is analyzed.