Adsorption integral equation via complex approximation with constraints: kernel of general form

For the monolayer adsorption on a homogeneous surface, including arbitrary range lateral interactions, the isotherm can be written as a power series of the Langmuir isotherm. If this isotherm is used as the kernel in the adsorption integral equation, this integral equation can be solved in an analytical form. Because the global isotherm is usually known as a set of experimental values, the use of a numerical method is inevitable. A new numerical method for solving the adsorption integral equation with a kernel of general form is developed. It is based on recent results concerning the structure of the local isotherm and on the ideas of complex approximation with constraints, and allows reduction of the problem under consideration to a linear‐quadratic programming problem. Results of numerical experiments are presented. The method can be useful for the evaluation of the adsorption energy distribution from experimental data. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1058–1066, 2001     

A simplified integral equation for adsorption of gas mixtures on heterogeneous surfaces

Summary The multiple integral representing the overall isotherm for adsorption of gas mixtures on heterogeneous surfaces is transformed to a single integral, which is promising for predicting the mixed-gas adsorption by means of single-gas adsorption parameters. This transformation is possible when the adsorption energies of components for various adsorption sites show a certain type of correlation.

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Eine vereinfachte Integralgleichung für die Adsorption von Gasmischungen auf heterogenen Oberflächen

Zusammenfassung Das multiple Integral, das die Adsorption von Gasmischungen auf heterogenen Oberflächen darstellt, wurde zu einem einfachen Integral transformiert, das zur Voraussage der Adsorption von Gasgemischen mittels der Einzelgas-Adsorptionsparameter geeignet sein sollte. Diese Transformation ist dann möglich, wenn die Adsorptionsenergien der Komponenten einem bestimmten Korrelationstyp angehören.

     

Langmuir Analysis of Nanoparticle Polyvalency in DNA‐Mediated Adsorption

Many nanoparticle adsorption processes are dictated by the collective interactions of surface‐bound ligands. These adsorption processes define how nanoparticles interact with biological systems and enable the assembly of nanoparticle‐based materials and devices. Herein, we present an approach for quantifying nanoparticle adsorption thermodynamics in a manner that satisfies the assumptions of the Langmuir model. Using this approach, we study the DNA‐mediated adsorption of polyvalent anisotropic nanoparticles on surfaces and explore how deviations from model assumptions influence adsorption thermodynamics. Importantly, when combined with a solution‐based van’t Hoff analysis, we find that polyvalency plays a more important role as the individual interactions become weaker. Furthermore, we find that the free energy of anisotropic nanoparticle adsorption is consistent across multiple shapes and sizes of nanoparticles based on the surface area of the interacting facet.     

超临界氢在活性炭上的吸附等温线研究

通过７７－２９８Ｋ范围内氢在ＡＸ－２１活性炭上的吸附数据，探讨如何用普通Ｉ－型等温线模型处理超临界条件下的吸附等温线，以获取关于超临界吸附系统的正确信息，结果表明，Ｌａｎｇｍｕｉｒ方程虽然可用来表达实验数据，但不能提供关于该吸附系统的任何可靠信息，Ｖｉｒｉａｌ方程虽不是整组数据的最好模型，但却能够可靠地确定Ｈｅｎｒｙ定律常数，然后可从ｖａｎｔＨｏｆｆ标绘决定等量吸附热，通过将实验数据拟合到Ｄｕｂｉ     

SAPO-34上甲醇及二甲醚吸附等温线及吸附热测量与分析(英文)

在25,60和100°C下分别测定了甲醇及二甲醚在SAPO-34分子筛上的吸附等温线,同时用微量热法测定了微分吸附热与覆盖率的关系曲线(量热线),提出了吸附数据需要利用双吸附位Langmuir方程拟合,并获取了相应的吸附参数.对比测得的吸附等温线与量热线发现,在一定压力下,当甲醇及二甲醚在SAPO-34上达到一定吸附量后,随着吸附质分压增加,量热线快速下降,而吸附等温线显示出吸附量仍然继续增加.由此推断,在SAPO-34分子筛上存在两种吸附位——常规吸附位及弱吸附位,其中弱吸附位在高分压下继续吸附.如缺乏量热数据提供的常规吸附位饱和吸附量数据,对吸附等温线进行单吸附位拟合获取吸附参数极易导致错误结果,尤其是当吸附质分压较高时.建议采用双吸附位Langmuir方程,参照量热线提供的常规吸附位的饱和吸附量,通过拟合可以获得两种吸附位的吸附参数.     

On the Correct Use of the Dubinin-Astakhov Equation to Study the Mixed-Gas Adsorption Equilibria

This paper presents the possibilities of Integral Equation (IE) approach to study the mixed-gas adsorption equilibria. As a result, the generalizations of Dubinin-Astakhov equation for the case of mixed-gas adsorption are presented. These new equations are examined using a few adsorption systems recently published in literature.     

Estimation of Adsorption Capacity for Dissociating and Non Dissociating Aromatic Compounds on Activated Carbon with Different Models

The process of adsorption of two dissociating and two non-dissociating aromatic compounds from dilute aqueous solutions on an untreated commercially available activated carbon (B.D.H.) was investigated systematically. All adsorption experiments were carried out in pH controlled aqueous solutions. The experimental isotherms were fitted into four different models (Langmuir homogenous Models, Langmuir binary Model, Langmuir-Freundlich single model and Langmuir-Freundlich double model). Variation of the model parameters with the solution pH was studied and used to gain further insight into the adsorption process. The relationship between the model parameters and the solution pH and pK_a was used to predict the adsorption capacity in molecular and ionic form of solutes in other solution.A relationship was sought to predict the effect of pH on the adsorption systems and for estimating the maximum adsorption capacity of carbon at any pH where the solute is ionized reasonably well.N₂ and CO₂ adsorption were used to characterize the carbon. X-ray Photoelectron Spectroscopy (XPS) measurement was used for surface elemental analysis of the activated carbon.     

Determination of the Porous Structure of Activated Carbons Using the IAE Concept. Influence of the Local Adsorption Model

In this paper we study a method for the determination of the micropore volume distribution function of activated carbons. This method is based on the Integral Adsorption Equation concept (IAE). The micropore volume distribution function is assumed to be a Gaussian of which the parameters are unknown. These parameters are determined using adsorption isotherms of carbon dioxide on a given activated carbon (F30/470 CHEMVIRON CARBON) at 278, 288, 298, 303, 308, 318 and 328 K and for pressures up to 100 kPa. Several local adsorption models are used (Langmuir, Volmer, Fowler-Guggenheim, Hill-de Boer). The influence of the choice of the local model on the pore volume distribution function is discussed. The physical validity of this function and the performances of the different models are presented. It appears that the effect of the temperature on the adsorption isotherms is difficult to model over a wide range of relative pressure. The Hill-de Boer and the Langmuir local models are the most efficient (average errors respectively equal to 3.53% and 2.80% in the studied range of temperature and pressure). They provide the most meaningful parameters for the pore volume distribution function.     

Multicomponent Adsorption of Pesticides onto Activated Carbon Fibers

The adsorption equilibria of pesticides and metabolites (atrazine, deethylatrazine, deisopropylatrazine and simazine) are studied onto activated carbon fibers –ACF– with a broad pore size distribution (32% mesopore volume, 68% micropore volume). Mono-and multi-component isotherms have been determined for low concentrations, from 0.23×10⁻⁶ to 9.52×10⁻⁶ mol L⁻¹. Single solute isotherms, modeled by Freundlich and Langmuir models, tend to prove the influence of the adsorbate's solubility in the adsorption capacity of activated carbon fibers. Binary solute isotherms confirm the strong influence of pesticide solubility on the competitive adsorption mechanism: the competition is higher in the case of adsorbates of different solubilities (atrazine and DEA or DIA for example). Multicomponent experimental data were modeled by extended Langmuir-based equations and the Ideal Adsorbed Solution theory. Whereas the first ones failed to model accurately binary adsorption due to restrictive hypothesis, the IAS model showed a good agreement between experimental and predicted data. It emphasised also the difficulty in satisfying the hypothesis of the model in the case of highly adsorbed compounds. Finally, the simultaneous adsorption of atrazine and NOM (in a natural water, DOC = 18.2 mg L⁻¹) shows no adsorption competition effects between natural organic matter and atrazine. This is due to the presence of secondary micropores (0.8–2 nm) and mesopores in the ACF, which limit a pore blockage phenomenon by NOM.     

Edelfosine—A new antineoplastic drug based on a phospholipid-like structure: The Langmuir monolayer study

Edelfosine (1-O-octadecyl-2-O-methyl-rac-glycero-3-phosphocholine, Et-18-OCH₃), an anticancer drug based on a phospholipid-like structure, was spread and investigated at the aqueous solution/air interface by means of surface pressure–area (π–A) and electric surface potential–area (ΔV–A) isotherms in addition to Brewster angle microscopy (BAM). The influence of such factors as subphase temperature, ionic strength, speed of compression and number of molecules spread at the surface on the characteristics of the π–A isotherms was studied. Edelfosine was found to form stable Langmuir monolayers which are nearly not influenced by the experimental conditions. The relative reflectivity measurements proved that the thickness of monolayer in the vicinity of collapse is 2.4 nm, which corresponds to length of a vertically oriented molecule. Perpendicular orientation of edelfosine molecules just before the film collapse has been confirmed with the apparent dipole moment value, which attains the maximum value in this region.     

Cross-Linked Ionic Liquid Polymer for the Effective Removal of Ionic Dyes from Aqueous Systems: Investigation of Kinetics and Adsorption Isotherms

In the current study, we have synthesized an imidazolium based cross-linked polymer, namely, 1-vinyl-3-ethylimidazolium bis(trifluoromethylsulfonyl)imide (poly[veim][Tf₂N]-TRIM) using trimethylolpropane trimethacrylate as cross linker, and demonstrated its efficiency for the removal of two extensively used ionic dyes—methylene blue and orange-II—from aqueous systems. The detailed characterization of the synthesized poly[veim][Tf₂N]-TRIM was performed with the help of ¹H NMR, TGA, FT-IR and FE-SEM analysis. The concentration of dyes in aqueous samples before and after the adsorption process was measured using an UV-vis spectrophotometer. The process parameters were optimised, and highest adsorption was obtained at a solution pH of 7.0, adsorbent dosage of 0.75 g/L, contact time of 7 h and dye concentrations of 100 mg/L and 5.0 mg/L for methylene blue and orange-II, respectively. The adsorption kinetics for orange-II and methylene blue were well described by pseudo-first-order and pseudo–second-order models, respectively. Meanwhile, the process of adsorption was best depicted by Langmuir isotherms for both the dyes. The highest monolayer adsorption capacities for methylene blue and orange-II were found to be 1212 mg/g and 126 mg/g, respectively. Overall, the synthesized cross-linked poly[veim][Tf₂N]-TRIM effectively removed the selected ionic dyes from aqueous samples and provided >90% of adsorption efficiency after four cycles of adsorption. A possible adsorption mechanism between the synthesised polymeric adsorbent and proposed dyes is presented. It is further suggested that the proposed ionic liquid polymer adsorbent could effectively remove other ionic dyes and pollutants from contaminated aqueous systems.     

Adsorption from solutions of nonelectrolytes on heterogeneous solid surfaces: A four-parameter equation for the excess adsorption isotherm

A four-parameter single-solute adsorption isotherm equation is generalized to the adsorption of binary liquid mixtures of nonelectrolytes. This equation comprises all isotherms being a simple extension of theEverett isotherm to liquid adsorption on heterogeneous solid surfaces. The benzene—cyclohexane excess adsorption data on silica gel are studied by using this new equation.

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Adsorption aus Lösungen von Nichtelektrolyten an heterogenen festen Oberflächen: Eine Vierparametergleichung für die Excess-Adsorptions-Isotherme

Zusammenfassung Es wird eine Vierparameter-Isothermengleichung für binäre Lösungen von Nichtelektrolyten diskutiert. Diese Gleichung umfaßt alle Isothermen vom Typ der einfachen Erweiterung derEverett-Isotherme für Flüssig-Adsorption auf heterogenen festen Oberflächen. Die Daten für die Adsorption von Benzol—Cyclohexan werden mittels dieser neuen Gleichung behandelt.

     

New Type of an Adsorption Layer of Organic Molecules with a Cage Structure Condensed at the Electrode/Solution Interface: The Adsorption of Cubane Derivatives on a Mercury Electrode

A synthesis and a study by method of measuring the differential capacitance on a stationary mercury drop of the adsorption of a number of cubane derivatives in a surface-inactive electrolyte are performed. It is established that the compounds studied exhibit a high surface activity. For bromine derivatives of cubane (4-bromomethoxycarbonylcubane, 4-bromohydroxymethylcubane) the formation of two-dimensional adsorption layers is discovered. Values of adsorption parameters for these compounds are evaluated with use made of the Frumkin isotherm.     

An amphiphilic C60 derivative with a tris(2,2′-bipyridine)ruthenium(II) polar head group: synthesis and incorporation in Langmuir films

An amphiphilic C₆₀ derivative with a tris(2,2′-bipyridine)ruthenium(II) polar head group has been prepared. The Langmuir film of this compound has been characterized by its surface pressure versus molecular area (Π/A) isotherm and Brewster angle microscopy (BAM) observations.     

The volume of micropores and the Dubinin—Radushkevich equation

The substantiation and the area of applicability of the Dubinin—Radushkevich equation for determination of the micropore volume in microporous systems from experimental data on adsorption isotherms were examined. It was shown that the micropore volumes found using the standard procedure are overestimated. A more accurate method for determining the mircopore volumes based on the pressure of filling of micropores was proposed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 659–664, April, 1998.     

The Kinetics of Sorption–Desorption Phenomena: Local and Non-Local Kinetic Equations

The kinetics of adsorption phenomena are investigated in terms of local and non-local kinetic equations of the Langmuir type. The sample is assumed in the shape of a slab, limited by two homogeneous planar-parallel surfaces, in such a manner that the problem can be considered one-dimensional. The local kinetic equations in time are analyzed when both saturation and non-saturation regimes are considered. These effects result from an extra dependence of the adsorption coefficient on the density of adsorbed particles, which implies the consideration of nonlinear balance equations. Non-local kinetic equations, arising from the existence of a time delay characterizing a type of reaction occurring between a bulk particle and the surface, are analyzed and show the existence of adsorption effects accompanied by temporal oscillations.     

The Langmuirian Adsorption Kinetics Revised: A Farewell to the XXth Century Theories?

A brief historical review of the development of the theoretical approaches to the kinetics of gas adsorption/desorption on/from the solid surfaces is presented. The attention is focused on new approaches, challenging the classical theories based on the ideas of Absolute Rate Theory (ART). These new approaches relate the adsorption/desorption kinetics to the chemical potentials of the molecules in the gas and adsorbed states. Among them the so-called Statistical Rate Theory (SRT) has the most rigorous theoretical foundations. That new approach predicts that depending on experimental conditions one can have a variety of kinetic equations corresponding to the Langmuir equilibrium adsorption isotherm.     

Adsorption of 2,4-Dinitrotoluene on Dickite: The Role of H-Bonding

The adsorption of 2,4-dinitrotoluene (DNT) on the tetrahedral and octahedral surfaces of dickite (a clay mineral of the kaolinite group with a 1:1 dioctahedral structure characterized by the common chemical formula Al₂Si₂O₅(OH)₄) was studied using small representative mineral models. The calculations have been performed at the HF/3-21G level of theory. The orientation of DNT on the tetrahedral surface of dickite was found to be coplanar with the surface plane. In the case of the adsorption on the octahedral surface the DNT molecule is placed with an inclination about 30^∘ to the surface plane. This type of adsorption results in an electron density redistribution of DNT on the surface of the mineral that is more significant in the case of the adsorption on the tetrahedral surface. The interaction energies of DNT with the octahedral and tetrahedral surfaces corrected by the BSSE energy were found. The adsorption energy of a DNT-tetrahedral fragment amounts to −6.5 kcal/mol, and the interaction energy of the DNT-octahedral fragment system is −17.7 kcal/mol.