Nitrogen adsorption on silica surfaces of nonporous and mesoporous materials

We present an accurate comparative analysis of N 2 adsorption at 77 K on nonporous silica and the pore wall surface of MCM-41 materials. The analysis shows that in the low-pressure region of N 2 adsorption obeys a peculiar mechanism governed by short-ranged forces, which makes the surface curvature effect on the N 2 adsorption in mesopores nearly negligible. We used this observation to define more exactly compared to the BET technique the specific surface area of the reference adsorption isotherm on nonporous silica basing on XRD data and linear sections of t-plots. Calculation of the capillary evaporation and condensation pressures seems to confirm our previous finding that the capillary condensation pressure corresponds to the equilibrium transition rather than spinodal condensation at least for pore sizes less than 7 nm. It allowed us to provide more reliable pore size distribution (PSD) analysis of mesoporous silica materials. For example, the PSDs of MCM-41 samples do not show artificial peaks in the micropore range that we obtained in our earlier publications.     

Irreversible adsorption of particles on heterogeneous surfaces

Methods of theoretical and experimental evaluation of irreversible adsorption of particles, e.g., colloids and globular proteins at heterogeneous surfaces were reviewed. The theoretical models were based on the generalized random sequential adsorption (RSA) approach. Within the scope of these models, localized adsorption of particles occurring as a result of short-ranged attractive interactions with discrete adsorption sites was analyzed. Monte-Carlo type simulations performed according to this model enabled one to determine the initial flux, adsorption kinetics, jamming coverage and the structure of the particle monolayer as a function of the site coverage and the particle/site size ratio, denoted by lambda. It was revealed that the initial flux increased significantly with the site coverage theta(s) and the lambda parameter. This behavior was quantitatively interpreted in terms of the scaled particle theory. It also was demonstrated that particle adsorption kinetics and the jamming coverage increased significantly, at fixed site coverage, when the lambda parameter increased. Practically, for alpha = lambda2theta(s) > 1 the jamming coverage at the heterogeneous surfaces attained the value pertinent to continuous surfaces. The results obtained prove unequivocally that spherically shaped sites were more efficient in binding particles in comparison with disk-shaped sites. It also was predicted that for particle size ratio lambda < 4 the site multiplicity effect plays a dominant role, affecting significantly the structure of particle monolayers and the jamming coverage. Experimental results validating main aspects of these theoretical predictions also have been reviewed. These results were derived by using monodisperse latex particles adsorbing on substrates produced by covering uniform surface by adsorption sites of a desired size, coverage and surface charge. Particle deposition occurred under diffusion-controlled transport conditions and their coverage was evaluated by direct particle counting using the optical and electron microscopy. Adsorption kinetics was quantitatively interpreted in terms of numerical solutions of the governing diffusion equation with the non-linear boundary condition derived from Monte-Carlo simulations. It was proven that for site coverage as low as a few percent the initial flux at heterogeneous surfaces attained the maximum value pertinent to homogeneous surfaces. It also was demonstrated that the structure of larger particle monolayers, characterized in terms of the pair correlation function, showed much more short-range ordering than predicted for homogeneous surface monolayers at the same coverage. The last part of this review was devoted to detection of polyelectrolyte multilayers on various substrates via particle deposition experiments.     

Pressure-induced effects in the heterogeneous adsorption of insulin on chromatographic surfaces

The effect of increasing the average column pressure (ACP) on the heterogeneous adsorption of insulin variants on a C18-bonded silica was studied in isocratic reversed-phase HPLC. Adsorption isotherm data of lispro and porcine insulin obtained for values of the ACP ranging from 57 to 237 bar were fitted to the Langmuir-Freundlich and the Tóth equation. The resulting isotherm parameters, including the equilibrium adsorption constant and the heterogeneity index, were next used for the calculation of distribution functions characterizing the energy of interactions between the adsorbed insulin molecules and the stationary phase. It was observed that increasing the pressure by 180 bar causes a broadening of the distribution functions and a shift of the position of their maximum toward lower interaction energies. These findings suggest that, under high pressures, the insulin molecules interact with the stationary phase in a more diversified way than under low pressures. Additionally, the most probable value of the energy of the insulin-surface interactions becomes lower when the ACP increases. The pressure-induced changes in the interaction of insulin variants with the hydrophobic surface are attributed to a possible conformational flexibility of the molecular structure of this protein.     

Consistent approach to adsorption thermodynamics on heterogeneous surfaces using different empirical energy distribution models

Adsorption on heterogeneous surfaces with three basic energy distribution models (uniform model, exponential model, and normal-like model) is studied. Exact analytical solutions of the adsorption isotherms and the heats of adsorption are derived for the uniform and exponential models, and, with these solutions including a numerical solution for the normal-like model, the behavior of the differential heat of adsorption and the "apparent" standard adsorption entropy concerning the overall surface is described as a function of coverage and temperature. The approximations underlying the isotherms and heats of adsorption in the Temkin, Freundlich, and Langmuir-Freundlich types of adsorption are rationalized. By comparing these empirical formulas to the exact solutions, the level of these approximations is found to be identical, which is similar to the "condensation approximation". Their preconditions are that either the temperature is low enough, or the surface is strongly heterogeneous. Generally, they are suitable for the middle coverage range. The exact solutions provide a method to obtain more information on the heats, entropy, and heterogeneity of the catalyst surface from the calorimetric measurement of the heat of adsorption.     

Entropy of adsorption of carbon monoxide on energetically heterogeneous surfaces

Standard entropies of adsorption (Δs ⁰) of CO on different materials (Cu catalysts, Au catalysts, ZnO and to TiO₂) are obtained from static adsorption microcalorimetry, adsorption isobars and temperature-programmed desorption, based on the thermodynamics of adsorption on energetically heterogeneous surfaces. Vibrational entropies of the surfaces s _vib^α are normally between the rotational and the standard translational entropy of CO in gas phase, and decrease with increasing adsorption energy, which agrees with the explanation of statistical thermodynamics. Δs ⁰ reflects both the mobility of adsorbates and the specific adsorbate-adsorbent interaction. Limits for reasonable values of the entropy of adsorption are proposed.     

Monte Carlo study of surfactant adsorption on heterogeneous solid surfaces

The equilibrium between free surfactant molecules in aqueous solution and adsorbed layers on structured solid surfaces is investigated by lattice Monte Carlo simulation. The solid surfaces are composed of hydrophilic and hydrophobic surface regions. The structures of the surfactant adsorbate above isolated surface domains and domains arranged in a checkerboard-like pattern are characterized. At the domain boundary, the adsorption layers display a different behavior for hydrophilic and hydrophobic surface domains. For the checkerboard-like surfaces, additional adsorption takes place at the boundaries between surface domains.     

Surfactant adsorption on solid surfaces: recognition between heterogeneous surfaces and adsorbed surfactant aggregates

We study the possibility of the recognition of surface heterogeneities with surfactant adsorption by performing Monte Carlo simulations. It is found that when each patch size of a heterogeneous surface is capable of being commensurate with the size of aggregates adsorbed on the constituent homogeneous surfaces, the adsorption isotherm of the system will display both adsorption characteristics for each homogeneous surface. Otherwise, one or more adsorption characteristics will be spoiled or destroyed. Therefore, the adsorption isotherm of surfactants on a heterogeneous surface provides a signal of recognition.     

Modeling of binary adsorption on heterogeneous surfaces characterized by a quasi-gaussian adsorption energy distribution

The integral equation (IE) approach coupled with a quasi-Gaussian adsorption energy distribution is used to model the adsorption of single gases and their binary mixture on a heterogeneous solid surface. The adsorbing surface is assumed to be characterized by two, generally different in width, quasi-Gaussian distribution functions, each of them related to a single component of the mixture. The influence of correlations between the distribution functions associated with different components on the corresponding adsorption isotherms and phase diagrams is discussed. In particular, it is demonstrated that a lack of microscopic correlations between the adsorption energies of the components may lead to the formation of an azeotropic mixture. The predictions of the theory are also compared with the results of the grand canonical Monte Carlo (GCMC) simulations carried out for the system studied.     

Al-promoted increase of surface area and adsorption capacity in ordered mesoporous silica materials with a cubic structure

The structure of ordered mesoporous materials presenting a cubic structure undergoes a strong modification after adding aluminium alkoxides to the synthesis gel. As a result, an outstanding increase in the surface area and pore volume is observed, together with changes in the mesopore ordering. Hydrated aluminium species influence the chemical environment of the micelles during synthesis, which seems to induce the accumulation of stacking faults in the mesopore framework, and give rise to closer structural packing. The adsorption and release of ibuprofen as a test molecule correlates well with the textural changes observed.     

A new approach to the adsorption kinetics of gas mixtures on heterogeneous surfaces

An attempt is made to develop a general theory for describing the adsorption kinetics of gaseous mixtures on heterogeneous surfaces. This can be made by generalization of the equations obtained for equilibrium adsorption of gas mixtures.

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The kinetics and saturation of reversible adsorption on patterned (heterogeneous) surfaces

We analytically examine the time-dependent adsorption of analyte (solute) on a finite-sized adsorption region as a model for sensors utilizing patterned or heterogeneous surfaces. We account for both reversible adsorption (assuming first-order reaction) and saturation of the adsorption patch that may arise either from packing constraints (finite area) or because of a finite number of binding sites (ligands). Our main conclusions include the following: (1) Saturation effects, due to either finite patch size or finite number of binding sites, become significant at extremely short times. (2) Increasing the strength of binding between the analyte and the adsorption sites increases the adsorbed amount at short times, but, at long times, the mass adsorbed on a weakly binding patch is higher than that on a strongly binding one. (3) The sensitivity of detection, as defined by the adsorption of the minimal analyte mass required for signaling, over a fixed period of time, does not scale as 1/detection time. As a result, increasing the time over which adsorption occurs increases sensitivity, but not linearly. Sensitivity of detection also increases with increasing patch area and initial binding strength.     

Statistical thermodynamics of adsorption from multicomponent liquid mixtures on heterogeneous solid surfaces

The statistical thermodynamics of adsorption from multicomponent liquid mixtures on heterogeneous solid surfaces is discussed by assuming the cell adsorption model and ideal adsorbed phase.Two integral representations for the adsorption isotherm are proposed: one based onn-dimensional energy distribution function (i.e., each adsorption site is characterized by adsorption energies of all components), and the other based on distribution of differences of adsorption energies ofn-1 components in relation to adsorption energy of the chosen component (i.e., each adsorption site is characterized byn-1 differences of adsorption energies of the components in relation to adsorption energy of the chosen component).The expressions for differential adsorption heat for adsorption from binary liquid mixtures have been derived from both integral equations.

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Statistische Thermodynamik der Adsorption aus flüssigen Mehrkomponentenmischungen auf heterogenen festen Oberflächen

Zusammenfassung Die statistische Thermodynamik der Adsorption von aus mehreren Komponenten bestehenden flüssigen Mischungen auf heterogenen festen Oberflächen wird für das Modell der Zellenadsorption bei ideal adsorbierter Phase diskutiert.Zwei Integraldarstellungen der Adsorptionsisotherme werden vorgeschlagen: eine auf einen-dimensionale Verteilungsfunktion der Energie gestützte (das heißt, jede Adsorptionsstelle wird durch Adsorptionsenergien von allen Komponenten charakterisiert); die andere basiert auf der Verteilung der Unterschiede von Adsorptionsenergien dern-1-Komponenten in bezug auf die Adsorptionsenergie der ausgewählten Komponente (das heißt, jede Adsorptionsstelle wird durchn-1-Unterschiede charakterisiert. Formeln für differentiale Adsorptionswärmen für die Adsorption aus binären flüssigen Mischungen sind von beiden Integral-Gleichungen abgeleitet worden.

     

Density functional theory model of adsorption on amorphous and microporous silica materials

We present a novel quenched solid density functional theory (QSDFT) model of adsorption on heterogeneous surfaces and porous solids, which accounts for the effects of surface roughness and microporosity. Within QSDFT, solid atoms are considered as quenched component(s) of the solid-fluid system with given density distribution(s). Solid-fluid intermolecular interactions are split into hard-sphere repulsive and mean-field attractive parts. The former are treated with the multicomponent fundamental measure density functional. Capabilities of QSDFT are demonstrated by drawing on the example of adsorption on amorphous silica materials. We show that, using established intermolecular potentials and a realistic model for silica surfaces, QSDFT quantitatively describes adsorption/desorption isotherms of Ar and Kr on reference MCM-41, SBA-15, and LiChrosphere materials in a wide range of relative pressures. QSDFT offers a systematic approach to the practical problems of characterization of microporous, mesoporous, and amorphous silica materials, including an assessment of microporosity, surface roughness, and adsorption deformation. Predictions for the pore diameter and the extent of pore surface roughness in MCM-41 and SBA-15 materials are in very good agreement with recent X-ray diffraction studies.     

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.

     

Time separation of adsorption sites on heterogeneous surfaces by inverse gas chromatography

Summary The measurement of local (homogeneous) adsorption energiesε _i , local monolayer capacities,c _max ^* , local adsorption isotherms,θ _i (p, T, ε), and probability density functions for adsorption, f(ε) and ϕ(ε,t), can be used to study the mechanism of adsorption of five gaseous hydrocarbons on the heterogeneous surface of magnesium oxide. The method does not use analytical or numerical solutions of a classical integral equation comprisingf(ε) as unknown, but it depends on a time function of gas chromatographic peaks obtained by short flow-reversals of the carrier gas. The results for adsorption of ethane, ethylene, acetylene, propene, and l-butene on MgO, in the absence and presence of O₃ are given and discussed on the basis of a mechanism proposed earlier for argon on titatium dioxide.     

Chemistry of aqueous silica nanoparticle surfaces and the mechanism of selective peptide adsorption

Control over selective recognition of biomolecules on inorganic nanoparticles is a major challenge for the synthesis of new catalysts, functional carriers for therapeutics, and assembly of renewable biobased materials. We found low sequence similarity among sequences of peptides strongly attracted to amorphous silica nanoparticles of various size (15-450 nm) using combinatorial phage display methods. Characterization of the surface by acid base titrations and zeta potential measurements revealed that the acidity of the silica particles increased with larger particle size, corresponding to between 5% and 20% ionization of silanol groups at pH 7. The wide range of surface ionization results in the attraction of increasingly basic peptides to increasingly acidic nanoparticles, along with major changes in the aqueous interfacial layer as seen in molecular dynamics simulation. We identified the mechanism of peptide adsorption using binding assays, zeta potential measurements, IR spectra, and molecular simulations of the purified peptides (without phage) in contact with uniformly sized silica particles. Positively charged peptides are strongly attracted to anionic silica surfaces by ion pairing of protonated N-termini, Lys side chains, and Arg side chains with negatively charged siloxide groups. Further, attraction of the peptides to the surface involves hydrogen bonds between polar groups in the peptide with silanol and siloxide groups on the silica surface, as well as ion-dipole, dipole-dipole, and van-der-Waals interactions. Electrostatic attraction between peptides and particle surfaces is supported by neutralization of zeta potentials, an inverse correlation between the required peptide concentration for measurable adsorption and the peptide pI, and proximity of cationic groups to the surface in the computation. The importance of hydrogen bonds and polar interactions is supported by adsorption of noncationic peptides containing Ser, His, and Asp residues, including the formation of multilayers. We also demonstrate tuning of interfacial interactions using mutant peptides with an excellent correlation between adsorption measurements, zeta potentials, computed adsorption energies, and the proposed binding mechanism. Follow-on questions about the relation between peptide adsorption on silica nanoparticles and mineralization of silica from peptide-stabilized precursors are raised.     

Grafted ionomer complexes and their effect on protein adsorption on silica and polysulfone surfaces

We have studied the formation and the stability of ionomer complexes from grafted copolymers (GICs) in solution and the influence of GIC coatings on the adsorption of the proteins β-lactoglobulin (β-lac), bovine serum albumin (BSA), and lysozyme (Lsz) on silica and polysulfone. The GICs consist of the grafted copolymer PAA₂₈-co-PAPEO₂₂ {poly(acrylic acid)-co-poly[acrylate methoxy poly(ethylene oxide)]} with negatively charged AA and neutral APEO groups, and the positively charged homopolymers: P2MVPI₄₃ [poly(N-methyl 2-vinyl pyridinium iodide)] and PAH?HCl₁₆₀ [poly(allylamine hydrochloride)]. In solution, these aggregates are characterized by means of dynamic and static light scattering. They appear to be assemblies with hydrodynamic radii of 8 nm (GIC-PAPEO₂₂/P2MVPI₄₃) and 22 nm (GIC-PAPEO₂₂/PAH?HCl₁₆₀), respectively. The GICs partly disintegrate in solution at salt concentrations above 10 mM NaCl. Adsorption of GICs and proteins has been studied with fixed angle optical reflectometry at salt concentrations ranging from 1 to 50 mM NaCl. Adsorption of GICs results in high density PEO side chains on the surface. Higher densities were obtained for GICs consisting of PAH?HCl₁₆₀ (1.6?÷?1.9 chains/nm²) than of P2MVPI₄₃ (0.6?÷?1.5 chains/nm²). Both GIC coatings strongly suppress adsorption of all proteins on silica (>90%); however, reduction of protein adsorption on polysulfone depends on the composition of the coating and the type of protein. We observed a moderate reduction of β-lac and Lsz adsorption (>60%). Adsorption of BSA on the GIC-PAPEO₂₂/P2MVPI₄₃ coating is moderately reduced, but on the GIC-PAPEO₂₂/PAH?HCl₁₆₀ coating it is enhanced.