Polymer adsorption on heterogeneous surfaces

The adsorption of polymers on an energetically heterogeneous surface can be modelled using a self-consistent field lattice theory. The surface consists of sites having different adsorption energies. It turns out that the distribution of the sites over the surface is one of the main parameters determining the adsorption behaviour.     

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.     

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.     

A site energy distribution function from Toth isotherm for adsorption of gases on heterogeneous surfaces

A site energy distribution function based on a condensation approximation method is proposed for gas-phase adsorption systems following the Toth isotherm. The proposed model is successfully applied to estimate the site energy distribution of three pitch-based activated carbons (PA, PFeA and PBA) developed in our laboratory and also for other common adsorbent materials for different gas molecules. According to the proposed model the site energy distribution curves of the activated carbons are found to be exponential for hydrogen at 77 K. The site energy distribution of some of the activated carbon fibers, ambersorb, Dowex optipore, 13X Zeolite for different adsorbate molecules represents a quasi-Gaussian curve with a widened left hand side, indicating that most sites have adsorption energies lower than a statistical mean value.     

Isotope exchange kinetics at heterogeneous solid surfaces (solid-liquid interfaces)

A system of equations describing isotope exchange kinetics at heterogeneous solid surfaces (solid-liquid interfaces) is studied numerically. The theoretical kinetic curves, characterizing the isotope exchange, are calculated for different discrete distributions of the isotope exchange rate constant.

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Isotopenaustauschkinetik an heterogenen Festkörperoberflächen (Fest-flüssig Grenzflächen)

Zusammenfassung Ein die Kinetik des Isotopenaustausches an heterogenen Festkörperflächen (fest-flüssig Grenzflächen) beschreibendes Gleichungssystem wird einer numerischen Auswertung unterzogen. Die theoretischen kinetischen Kurven des Isotopenaustausches werden für verschiedene diskontinuierliche Verteilungen der Isotopenaustausch-Geschwindigkeitskonstante berechnet.

     

Structural controls on OH site availability and reactivity at iron oxyhydroxide particle surfaces

Iron oxyhydroxides (FeOOH) are highly reactive minerals of widespread occurrence in natural and industrial settings. These minerals chiefly occur as nano- to submicron-sized particles and are covered by hydroxyl functional groups coordinated to one (-OH), two (μ-OH), or three (μ(3)-OH) underlying iron atoms. These groups are reaction centers for gases, solutes as well as solvents and thereby play important roles in the fate and transformation of natural and industrial compounds. In this work we provide tools to identify hydroxyl groups on distinct crystallographic planes of two important FeOOH polymorphs, namely lepidocrocite (γ-FeOOH) and goethite (α-FeOOH). Fourier transform infrared spectroscopy was used to monitor O-H stretching vibrations of groups on particles with well-defined and distinct morphologies. Spectral responses to proton loadings and thermal gradients were used to assign bands to hydroxyl groups. These efforts were facilitated by the extraction of pure spectral components obtained by multivariate curve resolution. Molecular dynamics simulations of dominant crystallographic planes of the particles guided band assignment procedures by identifying feasible hydrogen bond networks between surface groups. Our findings provide new possibilities for molecular-scale resolution of important gas-phase processes on the surfaces of these important minerals.     

Friction and adsorption of aqueous polyoxyethylene (Tween) surfactants at hydrophobic surfaces

The nanotribological responses of a series of nonionic polyoxyethylene surfactants (Tween 20, Tween 40, Tween 60, and Tween 80) were investigated after they were adsorbed from aqueous solution onto atomically smooth hydrophobic substrates. The hydrophobic surfaces were composed of a condensed monolayer of octadecyltriethoxysilane (OTE; contact angle theta>110 degrees ). The nanorheological measurements were performed using a modified surface forces apparatus after coating atomically smooth mica with these OTE monolayers, while adsorption measurements were performed using phase-modulated ellipsometry on silicon wafers coated with these same monolayers. The minimum surface-surface separation observed under high load in friction studies agreed quantitatively with the thickness obtained from ellipsometry. For Tweens 20, 40, and 60, the thickness of the adsorbed film increases with increasing alkyl chain length. Systematic investigations of the nanorheological response showed that there is a "solid-like" elastic response from confined surfactant layers, which is the case for the smallest separations to separations up to slightly larger than twice the adsorbed film thickness. In kinetic friction, these confined layers are characterized by a shear stress of approximately 3 MPa with minimal dependence on shear rate. The magnitude of the sliding shear stress is the same as the apparent yield stress at approximately 3 MPa; it is independent of alkyl chain length within the Tween family of surfactants and corresponds to a nominal friction coefficient of mu approximately 1. A similar friction coefficient is observed for boundary lubrication on the macroscopic scale in a tribometer utilizing hydrophobic surfaces and mu approximately 1.1 for Tweens 20, 40, and 60. These results suggest that while Tween molecules adsorb onto hydrophobic surfaces to form a robust separating layer, the lubricating properties of these layers are dominated by a highly dissipative slip plane, the same for all alkyl chain lengths.     

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.     

Characterization of soil particle surfaces using adsorption excess isotherms

Measurement of adsorption excess isotherms of methanol-benzene mixtures was applied to the characterization of soil particle surfaces. The sorption capacity and Gibbs energy of sorption of the solid-liquid interface were determined for montmorillonite, three types of soil, and their humin fractions. The soils were found to be less polar or less hydrophilic than the clay, and the humin fraction of soils was found to be less hydrophilic than the whole soils. The soil and humin samples have heterogeneous surfaces which can be divided in two regions on the basis of their relative polarity. The x-axis intersection of the straight section of isotherm assigns the relative proportions of the hydrophilic and hydrophobic regions of the surface.     

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.     

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.     

Poly(trifluoroethylene) adsorption and heterogeneous photochlorination reactions

Heterogeneous (gas-solid) photochlorination reactions of poly(trifluoroethylene) (PF 3E) films were studied as a function of reaction time and light intensity. The rate of chlorination was found to be faster in high-intensity light when compared to the reaction in ambient light. PF 3E irreversibly adsorbed to oxidized silicon and covalently attached amine monolayers supported on silicon, producing hydrophobic thin films in the thickness range of 8-40 A. Adsorption conditions such as polymer concentration and solvent composition were investigated. Radical grafting of maleic anhydride to the polymer backbone resulted in increased adsorption on oxidized silicon.     

Temperature-programmed surface reactions (TPSR) on heterogeneous surfaces

On the basis of calculations using a simple model of the energetic heterogeneity of a solid surface (assuming linear dependence of activation energy of desorption of the reactant on the degree of coverage), it is shown that both the degree of conversion and the course of desorption of the reactants are strongly influenced by the degree of heterogeneity assuming non-isothermal conditions. In contrast to a homogeneous solid surface, the degree of conversion for a heterogeneous surface depends strongly on the initial coverage of a catalyst by reactant. Possibilities for kinetic evaluation are indicated from the modelling calculations.     

Nanocomposite-based lignocellulosic fibers 3: polyelectrolyte adsorption onto heterogeneous fiber surfaces

Wood and natural fibers are composed of multiple polymeric components. Lignin, one primary component, is typically removed to various degrees during paper-making, but is present on thermomechanically isolated fibers. The effect of the residual lignin on the adsorption of poly(diallyldimethylammonium) chloride (PDDA) onto lignocellulosic fibers was investigated under varying solution conditions (electrolyte concentration and pH). Using nitrogen elemental analysis it was shown for the samples containing the highest concentration of lignin, PDDA adsorption to the fibers was reduced for all solution conditions. Upon extracting the alkali-soluble lignin, the samples showed the greatest amount of PDDA adsorption, achieving ~1.6% (w/w), under neutral solution conditions without the presence of added electrolyte. Furthermore, the influence of polyelectrolyte loading and electrokinetic potential on subsequent multilayer formation of PDDA and montmorillonite clay was quantified. It was revealed that electrokinetic potential of fiber after PDDA adsorption, rather than the amount of adsorbed PDDA layer, controlled the subsequent clay adsorption. Significant mass of PDDA/clay (up to ~75% of starting dry fiber mass for only 4 bi-layers) can be adsorbed onto steam-exploded wood fibers through the multilayer assembly process. This paper provides insight into how non-covalent modification of heterogeneous fibrous substrates offers a novel route for the creation of organic/inorganic fiber materials.     

Competitive adsorption from multicomponent non-electrolytic liquid mixtures on heterogeneous solid surfaces

Summary A simple model for competitive adsorption from multicomponent non-electrolytic liquid mixtures on energetically heterogeneous solid surfaces is discussed in terms of statistical thermodynamics. Integral equations are derived for the fundamental thermodynamic quantities that characterize competitive adsorption at the liquid-solid interface. Extensive model studies are presented in order to illustrate the influence of adsorbent heterogeneity on the behaviour of these thermodynamic quantities.on leave from Faculty of Chemistry, M. Curie-Sklodowska University, PL-20031 Lublin, Poland     

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.     

Irreversible adsorption of particles at random-site surfaces

Irreversible adsorption of negatively charged polystyrene latex particles (averaged diameter 0.9 microm) at heterogeneous surfaces was studied experimentally. The substrate bearing a controlled number of adsorption sites was produced by precovering mica sheets by positively charged polystyrene latex (averaged diameter of 0.45 microm). Positive latex (site) deposition was carried out under diffusion-controlled transport conditions and its coverage was determined by direct particle counting using the optical microscopy. Deposition kinetics of larger latex particles (averaged diameter 0.9 microm) at heterogeneous surfaces produced in this way was studied by direct optical microscope observations in the diffusion cell (under no-convection transport conditions). It was demonstrated that the structure of larger particle monolayers, characterized in terms of the pair correlation function, showed much more short-range ordering than it was predicted for homogeneous surface monolayers at the same coverage. This was found in agreement with theoretical predictions derived from the Monte Carlo simulations. On the other hand, particle adsorption kinetics was quantitatively interpreted in terms of numerical solutions of the governing diffusion equation with the nonlinear boundary condition derived from Monte Carlo simulations. From these kinetic measurements maximum (jamming) coverage of particles was determined in an accurate way by extrapolation. It was concluded that both the monolayer structure and jamming coverage were strongly influenced by the site multiplicity (coordination) effect.