Adsorption of Chain Molecules

We analyze the influence of chain length on the adsorption isotherm using the framework of lattice theory. Each molecule is represented as a chain of segments occupying separate sites in the lattice. Adsorption equilibria (particularly adsorption isotherms) are analyzed for one-component and two-component mixtures of chain molecules. Copyright 1999 Academic Press.     

The effects of energy sites on adsorption of Lennard-Jones fluids and phase transition in carbon slit pore of finite length a computer simulation study

A Monte Carlo simulation method is used to study the effects of adsorption strength and topology of sites on adsorption of simple Lennard-Jones fluids in a carbon slit pore of finite length. Argon is used as a model adsorbate, while the adsorbent is modeled as a finite carbon slit pore whose two walls composed of three graphene layers with carbon atoms arranged in a hexagonal pattern. Impurities having well depth of interaction greater than that of carbon atom are assumed to be grafted onto the surface. Different topologies of the impurities; corner, centre, shell and random topologies are studied. Adsorption isotherms of argon at 87.3 K are obtained for pore having widths of 1, 1.5 and 3 nm using a Grand Canonical Monte Carlo simulation (GCMC). These results are compared with isotherms obtained for infinite pores. It is shown that the surface heterogeneity affects significantly the overall adsorption isotherm, particularly the phase transition. Basically it shifts the onset of adsorption to lower pressure and the adsorption isotherms for these four impurity models are generally greater than that for finite pore. The positions of impurities on solid surface also affect the shape of the adsorption isotherm and the phase transition. We have found that the impurities allocated at the centre of pore walls provide the greatest isotherm at low pressures. However when the pressure increases the impurities allocated along the edges of the graphene layers show the most significant effect on the adsorption isotherm. We have investigated the effect of surface heterogeneity on adsorption hysteresis loops of three models of impurity topology, it shows that the adsorption branches of these isotherms are different, while the desorption branches are quite close to each other. This suggests that the desorption branch is either the thermodynamic equilibrium branch or closer to it than the adsorption branch.     

Predicting isotherms in micropores for different molecules and temperatures from a known isotherm by improved Horvath-Kawazoe equations

Our improved Horvath-Kawazoe (H-K) equations (by considering the isotherm nonlinearity) for three pore geometries are first summarized. These equations apply to adsorption in microporous materials at subcritical temperatures. From a known isotherm at a given temperature, these equations are used to predict isotherms of the same adsorbate molecules at other temperatures, and also to predict isotherms for other adsorbate molecules at the same (or any subcritical) temperature. A reasonable agreement is obtained between predictions and experimental data. Since the H-K formulation only involves dispersion forces, it underpredicts for gas-solid systems in which other forces also exist. The N₂-zeolite system is one of these systems.     

π-Selective stationary phases: (II) Adsorption behaviour of substituted aromatic compounds on n-alkyl-phenyl stationary phases

The frontal analysis method was used to measure the adsorption isotherms of phenol, 4-chlorophenol, p-cresol, 4-methoxyphenol and caffeine on a series of columns packed with home-made alkyl-phenyl bonded silica particles. These ligands consist of a phenyl ring tethered to the silica support via a carbon chain of length ranging from 0 to 4 atoms. The adsorption isotherm models that fit best to the data account for solute–solute interactions that are likely caused by π–π interactions occurring between aromatic compounds and the phenyl group of the ligand. These interactions are the dominant factor responsible for the separation of low molecular weight aromatic compounds on these phenyl-type stationary phases. The saturation capacities depend on whether the spacer of the ligands have an even or an odd number of carbon atoms, with the even alkyl chain lengths having a greater saturation capacity than the odd alkyl chain lengths. The trends in the adsorption equilibrium constant are also significantly different for the even and the odd chain length ligands.     

Adsorption of carbon dioxide by X zeolites exchanged with Ni2+ and Cr3+: isotherms and isosteric heat

The adsorption of CO2, at intervals of 30 K from 303 K was carried out on M(n+)X zeolites (M(n+)=Ni2+ or Cr3+) exchanged at different degrees. The structural regularity of the zeolite lattice of NaX and the existence of well-defined cavities within which the adsorbate molecules are lodged suggest that it should be possible to use various isotherm equations. Several models were thus used to describe the experimental isotherms. The best fit of adsorption isotherm data is obtained with the Sips model. The Volmer model also describes satisfactorily the isotherms of CO2 adsorption by NaX, Ni(x)X, and Cr(x)X. Analysis of the isosteric heat reveals a character energetically heterogeneous for NaX and Ni(x)X samples exchanged at a higher degree of Ni2+ exchange and at low coverage. Specific interaction is also obtained between the adsorbate molecules and Cr(x)X exchanged at a lower degree. From these considerations, hypotheses will be advanced to describe the behavior of the adsorbed phase within zeolitic cavities.     

Pattern of adsorption isotherms in Ono-Kondo coordinates

The Ono-Kondo lattice density functional theory is used to analyze adsorbate-adsorbate interactions for supercritical systems. In prior work, this approach has been used to study intermolecular interactions in subcritical adsorbed phases, and this has included the study of adsorbate-adsorbate repulsions in the regime of adsorption compression. In this paper, we present the general pattern of adsorption isotherms in Ono-Kondo coordinates; this has not been done in the past. For this purpose, experimental isotherms for adsorption of supercritical fluids (including nitrogen, methane, and carbon dioxide) are plotted in Ono-Kondo coordinates. In addition, we performed Grand Canonical Monte Carlo simulations of adsorption for Lennard-Jones molecules and plotted isotherms in Ono-Kondo coordinates. Our results indicate a pattern of isotherms with regimes of adsorbate-adsorbate attractions at low surface coverage and adsorbate-adsorbate repulsions at high surface coverage. When the generalized Ono-Kondo model is used over a wide range of pressures - from low pressures of the Henry's law regime to supercritical pressures - the slope of the isotherm varies from positive at low pressures to negative at high pressures. The linear sections of these graphs show when the adsorbate-adsorbate interaction energies are approximately constant. When these linear sections have negative slopes, it indicates that the system is in a state of adsorption compression.     

Adsorption of square and rectangular plate-like molecules on a planar surface

A mean-field statistical thermodynamic analysis of monolayer adsorption of rigid square and rectangular plate-like molecules on a homogeneous planar surface is developed. The analysis is simplified by only considering facewise and edgewise modes of adsorption in restricted orthogonal orientations parallel to the surface. The free energy density, adsorbate population distribution and surface spreading pressure are obtained as a function of adsorbate density and compared for square plate molecules using three different sequences of adsorbate molecule placement on the surface to evaluate the configurational degeneracy. It is found that edgewise adsorbed molecules can be anisotropically ordered if the edge length of square and rectangular plate-like molecules exceeds three length units in the absence of anisotropic dispersion interactions. If intermolecular dispersion interactions are present and of sufficient strength, the spreading pressure-density isotherms can exhibit one or two van der Waals loops for square plate molecules with three van der Waals loops possible for rectangular plate adsorbate molecules. The phase transitions for the adsorbed monolayer corresponding to the appearance of these van der Waals loops are discussed.     

Nonionic surfactant sorption onto the bacterial cell surface: a multi-interaction isotherm

The adsorption of linear polyoxyethylene (POE) alcohol surfactants of the form CxEy onto the surface of a Sphingomonas sp. has been examined. For this study, the alkyl chain length (x) was fixed at 12 and the POE chain length (y) was varied, with y = 4, 7, 9, 10, and 23 ethylene oxide units. Langmuirian isotherms were observed for C12E4 and C12E23, and more complex isotherms were observed for the three intermediate POE chain length surfactants, with C12E7 and C12E9 exhibiting strong S-shaped isotherms. All isotherms showed plateaus near the critical micelle concentration (CMC) with the plateau decreasing with increasing POE chain length. A simple multi-interaction isotherm is proposed that models the sorption isotherm as the sum of two interactions. The first interaction describes monolayer adsorption, whereas the second interaction describes lateral interactions between sorbed surfactant molecules and the formation of surface aggregates. Varying ratios of these two interactions as a function of POE chain length gives rise to the variety of observed isotherm shapes. Results of the isotherm analysis suggest that lateral interactions dominate for surfactants with low POE chain lengths, and the lateral interactions decrease as the POE chain length is increased.     

Benzene Adsorption in Microporous Materials

The adsorption behaviour of benzene in silicalite-1, AlPO₄-5 and EU-1 has been investigated using gravimetric techniques and molecular simulation methods. For the one-dimensional, 12-membered ring (MR) channels of AlPO₄-5 and the unidirectional, 10-MR channels with 12-MR side pockets of EU-1, the isotherms of benzene show simple type I behaviour. For the three dimensional 10-MR channels of silicalite-1, an anomalous behaviour of the benzene molecules sorbed has been observed. Two steps at loadings of ca. 4 and 6 molecules per unit cell [m.(u.c.)⁻¹], respectively, and an hysteresis loop between loadings from 6 to 8 m.(u.c.)⁻¹ can be found in the isotherms of this system. These stepped isotherms can be classified as showing type VI isotherm behaviour but in this system the reasons behind the steps are of a new and novel nature. These abnormal adsorption properties have been ascribed to the subtle interplay of increased sorbate-sorbate interactions and decreases in the entropy of sorption due to the energetically heterogeneous surfaces which are present in silicalite-1. The composition and structure of the silicalite-1 samples also play an important role on the adsorption properties of this system.     

Theoretical and experimental investigation of morphology and temperature effects on adsorption of organic vapors in single-walled carbon nanotubes

Hexane adsorption on single-walled carbon nanotube (SWNT) bundles is studied by both simulation and experimentally using a previously developed computer-aided methodology, which employed a smaller physisorbed probe molecule, nitrogen, to explore the porosity of nanotube samples. Configurational-bias grand canonical Monte Carlo simulation of hexane adsorption on localized sites of the bundles is carried out to predict adsorption on their external surface and in their internal sites. These localized isotherms are then combined into a global isotherm for a given sample by using knowledge of its tube-diameter distribution and structural parameters, such as the fraction of open-ended nanotubes and the external surface area of bundles in samples, which have been independently determined from the standard nitrogen adsorption isotherm. The near-perfect replication of experimental isotherms demonstrates the validity of our method for structural characterization of SWNT samples. The effect of temperature on adsorption is also studied and the simulation results are extrapolated to predict the limiting hexane adsorption capacity of the samples. The similarity between the hexane adsorption isotherms and those of other organic molecules demonstrates that the adsorption mechanisms explored here are not specific to hexane, and that the proposed methodology can be potentially applicable to other sorbates with equal success.     

Equilibrium in an ideal adsorption layer during multiplet adsorption

The equilibrium in an ideal adsorption layer during adsorption of a mixture of substances whose molecules can occupy one or m elementary sites is examined. It is shown that the isotherm for any adsorbate in the mixture can be readily found if the isotherm is known for one of the adsorbed substances whose molecules occupy m elementary surface sites in the absence of other adsorbates. The form of the isotherm for multiplet adsorption depends on the distribution of the elementary sites on the surface.     

Analysis of van der Waals loops in the adsorption isotherms of porous systems

The properties of the van der Waals loops for isotherms of the adsorbate located in the slit-shaped and cylindrical pores of different width were analyzed. The adsorbate molecules are modeled by spherical Lennard-Jones type particles. The calculation was based on the latticegas model in the quasichemical approximation for intermolecular interactions. The accuracy of calculations of the adsorption hysteresis loops increases due to the use of distributed models, which reflect the spatial inhomogeneity of the distribution of molecules along the normal to the pore wall. The effect of the adsorbate-adsorbent interaction potential and pore width on the pattern of adsorption isotherms is considered. Taking into account the inhomogeneity of the spatial distribution of molecules changes the course of the spinodal sections of the adsorption isotherms.     

The fundamentals of adsorption theory for a mixture of bulky molecules in slit-shaped pores with heterogeneous wall surfaces

The fundamentals of the adsorption theory for a mixture of bulky molecules blocking more than one adsorption site on the surface in slit-shaped pores with heterogeneous wall surfaces are outlined. The adsorbate—adsorbate lateral interactions are taken into account in the quasi-chemical approximation and in the mean-field approximation. The expressions for the partial adsorption isotherms and for the binary coefficients of mixture separation and the way of isolation of the partial contributions of molecules on heterogeneous adsorption sites on pore walls are discussed. A simplified variant of adsorption theory for a binary mixture of molecules of different sizes in two-layer pores with the assumption of complete coverage of the pores is considered. The influence of the energy of binding of molecules to pore walls, lateral interactions, and the ratio of the component sizes on the shape of adsorption isotherms is analyzed. The results of calculations are compared with the experimental data for the benzene—CCl₄—microporous AC carbon adsorbent system.     

Calculation of the adsorption-desorption hysteresis curves in narrow-pore systems

The gas and liquid spinodal branches for an adsorbate located in narrow slit-shaped, cylindrical, and spherocylindrical pores were calculated. The adsorbate is modeled by Lennard-Jones spherical particles. The calculation was based on the lattice gas model taking into account the intermolecular interactions of nearest neighbors in the quasichemical approximation. The density-temperature diagrams for the gas and liquid spinodal branches in the pores are similar to the equilibrium vapor-liquid phase diagrams: they have a common critical point; the dense-phase branches are shifted to lower pore fillings, while the rarefied-phase branches are shifted toward higher pore fillings. The width of adsorption-desorption hysteresis loop in the adsorption isotherms for Lennard-Jones particles was analyzed as a function of the pore size and the interaction potential of the adsorbate with the pore walls. The effect of pore wall roughness and the accuracy of isotherm calculation on the width of the adsorption-desorption hysteresis loop in cylindrical pores is discussed Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 813–823, May, 2007.     

An Adsorption Isotherm from a Micro-state Model

The present study is dedicated to the derivation of an alternative adsorption isotherm for liquid-solid interfaces from a micro-state model, where adsorption is predominantly of a chemical nature. We describe adsorption-desorption on a liquid-solid interface starting from a partition function. In the new model the surface site occupation number is controlled by the Pauli principle (monolayer condition) and additional an attractive or repulsive surface potential, which depends on the overall surface coverage (nonlinearity). The effective potential represents adsorbate adsorbent interaction, as well as an influence of adsorbate adsorbate interactions on the surface potential. A Langmuir equivalent isotherm is recovered in the limit of a weak potential. The proposed model and Langmuirs isotherm are compared using data of humic acid (HA) adsorption on Brazilian Oxisol soil samples. Both models parameterize the experimental data well, but only the new model seems to be self-consistent.     

Statistical lattice model for the bimolecular reaction on the dynamically changing surface of a body-centered metal crystal

A statistical lattice model has been constructed for the surface of a body-centered cubic (bcc) crystal whose morphology varies under the action of external factors (temperature and adsorbate coverage). Monomolecular and dissociative bimolecular adsorption on the bcc crystal surface has been investigated. In this model, adsorption smoothens the originally rough surface owing to adsorbate molecules stabilizing their flat adsorption areas, as distinct from adsorption on the primitive cubic lattice. Our model differs from the models with invariable surface morphology in that the number of its accessible adsorption sites is variable and depends on external conditions. The kinetics of a catalytic reaction proceeding by the Langmuir-Hinshelwood mechanism have been studied for the (100) face of a bcc crystal whose morphology varies under the action of the reaction medium.     

Statistical mechanics of a two-dimensional lattice model of benzene adsorption in zeolites

In this Letter, we present a mean field calculation of the statistical mechanics of a lattice model of benzene adsorption in the quasi two-dimensional network of pores in zeolites. A lattice fluid model is introduced with monomer states to represent molecules standing perpendicular to the principle axis of the pore, dimer states to represent molecules lying flat against the pore wall, and vacant sites or holes. For a wide range of interaction parameters the model gives steps in adsorption isotherms similar to those observed experimentally for benzene adsorption in silicalite. Our treatment attributes the experimentally observed steps in the level of adsorption with rising pressure, to orientational transitions amongst molecules in the adsorbed phase with two possible ground states arrangements of the benzene molecules in the zeolite pores energetically competing with each other.     

A Modular Approach To Study Protein Adsorption on Surface Modified Hydroxyapatite

Biocompatible inorganic nano‐ and microcarriers can be suitable candidates for protein delivery. This study demonstrates facile methods of functionalization by using nanoscale linker molecules to change the protein adsorption capacity of hydroxyapatite (HA) powder. The adsorption capacity of bovine serum albumin as a model protein has been studied with respect to the surface modifications. The selected linker molecules (lysine, arginine, and phosphoserine) can influence the adsorption capacity by changing the electrostatic nature of the HA surface. Qualitative and quantitative analyses of linker‐molecule interactions with the HA surface have been performed by using NMR spectroscopy, zeta‐potential measurements, X‐ray photoelectron spectroscopy, and thermogravimetric analyses. Additionally, correlations to theoretical isotherm models have been calculated with respect to Langmuir and Freundlich isotherms. Lysine and arginine increased the protein adsorption, whereas phosphoserine reduced the protein adsorption. The results show that the adsorption capacity can be controlled with different functionalization, depending on the protein–carrier selections under consideration. The scientific knowledge acquired from this study can be applied in various biotechnological applications that involve biomolecule–inorganic material interfaces.     

Revision of adsorption models of xyloglucan on microcrystalline cellulose

Interactions among cellulose, hemicellulose and pectins are important for plant cell wall assembly and properties and also for industrial applications of these polysaccharides. Therefore, binding of pectin and xyloglucan on microcrystalline cellulose was investigated in this experiment by adsorption isotherms, zeta potential and scanning electron microscopy (SEM). Analysis of three isotherm models (Langmuir, Freundlich and Fowler-Guggenheim isotherms) showed that the experimental adsorption isotherm was well described via the Fowler-Guggenheim model, which includes lateral interaction between the adsorbate. The adsorption isotherm and zeta potential measurement showed that at temperature 25 °C only xyloglucan adsorbed on the microcrystalline cellulose. In case of xyloglucan on cellulose, the equilibrium was reached in about 3–4 h, and the kinetics of adsorption were well described by the multiexponential equation. Analysis of the model suggests that two steps can be distinguished: diffusion and reconformation in an adsorbed layer. No adsorption of pectin was observed in this study. SEM study showed that xyloglucan may prevent cellulose from aggregation.     

Adsorption of alkanes on a bismuth electrode from an alcoholic medium

The adsorption of higher alkanes (from C₁₀H₂₂ to C₂₁H₄₄) on a polarized bismuth electrode was studied from methanolic, ethanolic and n-butanolic solutions of LiClO₄ by differential capacity measurements. Alkane molecules, which do not contain either polar groups or double bonds, are compounds of low chemical activity. The adsorption of this group of compounds is purely physical. Nevertheless, a considerable difference in their adsorption activity on the various areas of the electrode surface caused by the two types of bond (metallic and covalent) between the atoms in the bismuth crystal lattice was discovered. Such a large difference indicates the different wettabilities of the separate single-crystal faces by alkanes. A weak dependence of the interaction parameter in the Frumkin isotherm on the length of the alkane molecule as well as on the length of the hydrocarbon chain of the solvent molecule was established. Various adsorption effects at high bulk concentrations of adsorbate (desolvation of the cations of the supporting electrolyte, thickening of the adsorption layer, maximum in the isotherm) were analysed.