Product desorption rate influence on catalytic reactivity of spatially inhomogeneous surfaces

We investigate numerically a phenomenological mathematical model of unimolecular reactions proceeding on inhomogeneous planar surfaces in the two-dimensional space case taking into account: the bulk diffusion of the reactant from the bounded vessel toward the adsorbent and the product bulk one from the adsorbent into the same vessel, the adsorption and desorption of reactant particles, long-range surface diffusion of the adsorbate, and a slow product desorption from the adsorbent. Simulations were performed using the finite difference technique. The influence of the long-range surface diffusion and product desorption rate on the kinetics of processes catalysed by inhomogeneous surfaces with different arrangements of reactive and nonreactive adsorption sites are studied.     

Numerical study of the kinetics of unimolecular heterogeneous reactions onto planar surfaces

In this paper we investigate two-dimensional in space mathematical models of the kinetics of unimolecular heterogeneous reactions proceeding onto planar surfaces. The models are based on Langmuir-type kinetics of the adsorption, desorption, and reaction including the surface diffusion of the adsorbate, surface diffusion of the product before its desorption, and slow desorption of the product from the adsorbent. It is also assumed that the reactant diffuses towards an adsorbent from a bounded vessel and the product diffuses from the adsorbent into the same vessel. Diffusivity of all species and kinetic coefficients are constants. The numerical simulation was carried out using the finite difference technique for four models: one model neglects the surface diffusion of the adsorbate and product, the second one includes the surface diffusion of the adsorbate and product, the third of them includes the surface diffusion of the adsorbate and neglects diffusion of the product along the surface, and the last one neglects the surface diffusion of the adsorbate and includes diffusion of the product along the adsorbent. By changing input parameters effects of the surface diffusion of the adsorbate and product and the slow desorption of the product are studied numerically.     

Spillover in monomer–monomer reactions on supported catalysts: dynamic mean-field study

The kinetics of a $A_1+A_2\rightarrow A_1A_2$ reaction on supported catalysts is investigated numerically using a phenomenological model which includes: the bulk diffusion of reactants from a bounded vessel towards the adsorbent and the product bulk one into the same vessel, adsorption and desorption of reactants molecules, and surface diffusion of adsorbed particles. The model is based on the Langmuir–Hinshelwood surface reaction mechanism coupled with the Eley–Rideal step. The model based only on the Langmuir–Hinshelwood mechanism is also studied. Simulations were performed using the finite difference technique. Three cases of reactants adsorption are considered: each reactant can adsorb on the active in reaction catalyst surface and inactive support, one of reactants adsorbs on the catalyst surface while the other one adsorbs on the support, both reactants adsorb only on the support. The surface diffusion and catalytic surface size influence on the catalytic reactivity of a supported catalyst is studied.     

Non-equilibrium adsorption at solid/liquid interfaces from polyelectrolyte solutions

The poly(2-vinylpyridine) layer was established at the Pyrex glass/water interface with periodic phases of adsorption/desorption runs observed over several days. This was evidenced by determining the concentration of radio-labelled molecules in the solution equilibrating the glass beads as a function of time (the effluent) while the same radio-labelled polymer was slowly supplied by injecting the polymer solution into the reactor containing the adsorbent at a controlled extremely slow rate. Although the adsorption (or the desorption) steps seemed to present some periodic character, they were better correlated with the successive bulk concentration thresholds that were established with time when the initial surface was free of polymer at time zero. Even when the adsorbent was coated at different degrees, desorption steps were correlated to the overstepping of decreasing concentration thresholds. Adsorption and desorption runs were attributed to the existence of different typical interfacial conformations of the adsorbed macromolecules that only can be stabilised in the adsorbed state when the layer was equilibrated with the polymer solution of a certain concentration. Macromolecule were definitely adsorbed when the reconformation process led to a flat conformation (trains). Macromolecules adsorbed with a conformation close to their solution conformation may be desorbed as a result of the reconformation process affecting previously adsorbed neighbour molecules (in the case of partially coated surfaces at time zero of injection). Macromolecules with loops and tails were retained on the surface when the polymer concentration in the bulk was progressively increased (for uncoated surfaces at time zero of injection). All these effect were attributed to the combined influence of topological effects on adsorption and reconformation of adsorbed macromolecules that characterise the non-equilibrium adsorption processes.     

Adsorption kinetics of protein mixtures. A tentative explanation of “the vroman effect”

A model for protein adsorption kinetics is presented. This model includes diffusion limited adsorption, adsorption and desorption rate constants which are dependent on the surface concentration and an interaction term for the mutual influence of the adsorbed protein molecules. It is shown that, in first approximation, the values of the adsorption and desorption rate constants are exponential functions of the surface concentration. Assuming an adequate interaction term it is possible to show with this model for the adsorption kinetics of a mixture of proteins that the ratio of the adsorbed proteins is strongly dependent on the overall surface concentration even if the ratio of the bulk concentrations of these proteins is kept constant. Differences in interaction terms for the different proteins offer a possible explanation for the peculiar behaviour of plasma protein adsorption on a surface at different dilutions of the plasma, the so called “Vroman effect”.     

Desorption of oxygen and nitrogen from iron surfaces Application of X-ray photoelectron spectroscopy to surface analysis

The patterns of desorption of oxygen and nitrogen from metal surfaces were examined and applied in the determination of gaseous elements in metal samples. The abundance of gaseous elements on metal surfaces is controlled by thermal desorption and diffusion to or from the surface. A heat treatment suitable for the separation of adsorbed gases from those in the bulk sample is discussed. Preheating of the metal samples at ca. 300 degrees in a vacuum reduces the residual adsorbates to a minimum and retards the diffusion of the gaseous elements from the bulk to the surface.     

Modelling of the NO + CO reaction over inhomogeneous surfaces

A phenomenological model of \(\mathrm {CO}\) oxidation with \(\mathrm {NO}\) reaction proceeding over composite (supported) catalysts is proposed and solved numerically using the finite difference method. The model is based on the coupled system of PDEs subject to nonclassical conjugate conditions at the catalyst-support interface and includes: the bulk diffusion of reactants from a bounded vessel towards the catalyst surface and the bulk one of the reaction products from the surface into the same vessel, adsorption and desorption of particles of reactants, and surface diffusion of adsorbed molecules. The readsorption of the reaction product N\(_2\)O is also taken into account. The influence of the rate constants of the adsorbed particle jumping via the catalyst-support interface and reaction rate constants on the surface reactivity is investigated. It is shown that the turnover rates of the CO and NO into products N\(_2\)O, CO\(_2\), and N\(_2\) are nonmonotonic time functions and depending on values of the kinetic parameters may possess one or two maxima. The N\(_2\)O readsorption in case of the existence of two maxima essentially increases the turnover rates and extends the duration of their high values. The mechanism and conditions for arising of the second maximum is discussed. It is also shown that the variation of the particle jumping rate constants influences differently the size of the jump discontinuity of concentrations of different adsorbates at the catalyst-support interface.     

法拉第吸脱附偶联过程循环伏安行为的有限元分析

法拉第吸脱附偶联过程的电化学行为较为复杂,难以定量获得其表界面反应动力学信息. 本文通过COMSOL有限元软件对法拉第吸脱附偶联过程的循环伏安行为进行数值分析,研究了反应物或产物不同吸附条件下的循环伏安行为. 结果表明：当反应物或产物弱吸附时,可通过阴、阳极峰电流之差实现饱和吸附量的定量表征. 随着吸附平衡常数的增大,反应由弱吸附向强吸附过渡,峰电流由扩散峰与吸脱附峰相互重叠过渡到相互分离的吸脱附“前波”或“后波”特征. 该吸脱附特征峰的形状和位置与电势依赖的吸附平衡常数有关. 吸附平衡常数及其电势依赖程度越大,吸脱附峰偏离扩散峰越远,吸脱附峰越尖锐. 该模型为法拉第吸脱附偶联过程的循环伏安研究提供了一种定量研究方法,能够帮助研究者从复杂的吸脱附伏安行为中定量获得饱和吸附量和吸附平衡常数等信息,并对涉及吸脱附的电催化研究具有一定指导意义.     

Reversible adsorption of spherical particles from binary mixtures: long-time behaviour

Formation of monolayers of spherical particles in processes with reversible adsorption from mixtures of large and small particles was simulated in computer experiments. Computer program was based on an algorithm that took into account random sequential adsorption, desorption and lateral diffusion of adsorbed particles (RSA–DLD model). Computer experiments were performed for systems with rate constants of particle adsorption at least 10³ times higher than rate constants of desorption. In processes with very fast adsorption and slow desorption, formation of monolayer can be divided into two stages. During the first stage, the total surface coverage (the coverage with particles of both types) increases very fast and becomes very close to that at equilibrium. During the second stage, the total coverage changes very slowly and the system approaches equilibrium mainly by the replacement of large particles with the small ones. A simple kinetic model for evolution of the monolayer composition during the second stage has been proposed. Kinetic equations related to this model allow the determination of large particles’ desorption rate constants on the basis of changes in the surface concentrations of adsorbed large and small microspheres. The validity of the model has been tested comparing large particles’ desorption rate constants values that had been used for simulations with values of the corresponding rate constants determined using analytical equations, with a view to analysing the simulation results. To cite this article: S. Slomkowski et al., C. R. Chimie 6 (2003).     

Molecular macrocluster formation on silica surfaces in phenol-cyclohexane mixtures

The adsorption of phenol, an aromatic compound with a hydrogen-bonding group, onto a silica surface in cyclohexane was investigated by colloidal probe atomic force microscopy (AFM), attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), and adsorption isotherm measurements. ATR-FTIR measurements on the silica surface indicated the formation of surface macroclusters of phenol through hydrogen bonding. The ATR-FTIR spectra were also measured on the H-terminated silicon surface to observe the effect of the silanol groups on the phenol adsorption. The comparison of the ATR-FTIR spectra for both the silicon oxide and H-terminated silicon surfaces proved that the silanol groups are necessary for the formation of phenol clusters on the surface. The surface force measurement using colloidal probe AFM showed a long-range attraction between the two silica surfaces in phenol-cyclohexane mixtures. This long-range attraction resulted from the contact of the adsorbed phenol layers for the phenol concentrations below 0.6 mol %, at which no significant phenol clusters formed in the bulk solution. The attraction started to decrease at 0.6 mol % phenol due to the exchange of the phenol molecules between the clusters in the bulk phase and on the surface. The surface density of phenol in the adsorbed layer was calculated on the basis of the long-range attraction and found to be much smaller than the liquid phenol density. The plausible structure of the adsorbed phenol layer was drawn by referring to the crystal structure of the bulk phenol and orientation of the phenol molecules on the surface, estimated by the dichroic analysis of ATR-FTIR spectroscopy. The investigation of the phenol adsorption on the silica surface in a nonpolar solvent using this novel approach demonstrated the effect of the aromatic ring on the surface packing density.     

The interplay of diffusional and electrophoretic transport mechanisms of charged solutes in the liquid film surrounding charged nonporous adsorbent particles employed in finite bath adsorption systems

A model that describes the diffusive and electrophoretic mass transport of the cation and anion species of a buffer electrolyte and of a charged adsorbate in the liquid film surrounding nonporous adsorbent particles in a finite bath adsorption system, in which adsorption of the charged adsorbate onto the charged surface of the nonporous particles occurs, is constructed and solved. The dynamic behavior of the mechanisms of this model explicitly demonstrates (a) the interplay between the diffusive and electrophoretic molar fluxes of the charged adsorbate and of the species of the buffer electrolyte in the liquid film surrounding the nonporous adsorbent particles, (b) the significant effect that the functioning of the electrical double layer has on the transport of the charged species and on the adsorption of the charged adsorbate, and (c) the substantial effect that the dynamic behavior of the surface charge density has on the functioning of the electrical double layer. It is found that at equilibrium, the value of the concentration of the charged adsorbate in the fluid layer adjacent to the surface of the adsorbent particles is significantly greater than the value of the concentration of the adsorbate in the finite bath, while, of course, the net molar flux of the charged adsorbate in the liquid film is equal to zero at equilibrium. This result is very different than that obtained from the conventional model that is currently used to describe the transport of a charged adsorbate in the liquid film for systems involving the adsorption of a charged adsorbate onto the charged surface of nonporous adsorbent particles; the conventional model (i) does not consider the existence of an electrical double layer, (ii) assumes that the transport of the charged adsorbate occurs only by diffusion in the liquid film, and (iii) causes at equilibrium the value of the charged adsorbate in the liquid layer adjacent to the surface of the particles to become equal to the value of the concentration of the charged adsorbate in the liquid of the finite bath. Furthermore, it was found that a maximum can occur in the dynamic behavior of the concentration of the adsorbate in the adsorbed phase when the value of the free molecular diffusion coefficient of the adsorbate is relatively large, because the increased magnitude of the synergistic interplay between the diffusive and electrophoretic molar fluxes of the adsorbate in the liquid film allows the adsorbate to accumulate (to be entrapped) in the liquid layer adjacent to the surface of the adsorbent particles faster than the concentrations of the electrolyte species, whose net molar fluxes are significantly hindered due to their opposing diffusive and electrophoretic molar fluxes, can adjust to account for the change in the surface charge density of the particles that arises from the adsorption of the charged adsorbate. The results presented in this work also have significant implications in finite bath adsorption systems involving the adsorption of a charged adsorbate onto the surface of the pores of charged porous adsorbent particles, because the diffusion and the electrophoretic migration of the charged solutes (cations, anions, and charged adsorbate) in the pores of the adsorbent particles will depend on the dynamic concentration profiles of the charged solutes in the liquid film surrounding the charged porous adsorbent particles. The results of the present work are also used to illustrate how the functioning of the electrical double layer could contribute to the development of inner radial humps (concentration rings) in the concentration of the adsorbate in the adsorbed phase of charged porous adsorbent particles.     

Water adsorption and desorption pretreatment of surfaces increases the maximum amount of adsorbed water molecules by a multiple

The amount of adsorbed water on surfaces in an atmosphere with 100 % relative humidity can be increased by a multiple, if the surfaces are pretreated by cycles of adsorption and desorption of water. This was observed on surfaces of diamond, titanium dioxide and silicon dioxide at temperatures around 22 °C. With a sufficient number of such cycles a faster and stronger adsorption of water molecules was obtained, if compared with untreated surfaces. This also means an increased energy transfer from the atmosphere to the surface. Due to the pretreatment the amount of adsorbed water was more than three times increased. The observed effect is explained by small amounts of specially arranged water molecules, which remain on the surface after the desorption process and which support the adsorption of water. The observed effect can be used to moisten surfaces of small particles very efficiently from the gas phase.     

Interaction between water molecules and zinc sulfide nanoparticles studied by temperature-programmed desorption and molecular dynamics simulations

We have investigated the bonding of water molecules to the surfaces of ZnS nanoparticles (approximately 2-3 nm sphalerite) using temperature-programmed desorption (TPD). The activation energy for water desorption was derived as a function of the surface coverage through kinetic modeling of the experimental TPD curves. The binding energy of water equals the activation energy of desorption if it is assumed that the activation energy for adsorption is nearly zero. Molecular dynamics (MD) simulations of water adsorption on 3 and 5 nm sphalerite nanoparticles provided insights into the adsorption process and water binding at the atomic level. Water binds with the ZnS nanoparticle surface mainly via formation of Zn-O bonds. As compared with bulk ZnS crystals, ZnS nanoparticles can adsorb more water molecules per unit surface area due to the greatly increased curvature, which increases the distance between adjacent adsorbed molecules. Results from both TPD and MD show that the water binding energy increases with decreasing the water surface coverage. We attribute the increase in binding energy with decreasing surface water coverage to the increasing degree of surface under-coordination as removal of water molecules proceeds. MD also suggests that the water binding energy increases with decreasing particle size due to the further distance and hence lower interaction between adsorbed water molecules on highly curved smaller particle surfaces. Results also show that the binding energy, and thus the strength of interaction of water, is highest in isolated nanoparticles, lower in nanoparticle aggregates, and lowest in bulk crystals. Given that water binding is driven by surface energy reduction, we attribute the decreased binding energy for aggregated as compared to isolated particles to the decrease in surface energy that occurs as the result of inter-particle interactions.     

Determination of Isotherm for Acetate and Formate Adsorption at Pt(111) Electrode by Fast Scan Voltammetry (cited: 3)

Fast scan voltammetry is an efficient tool to distinguish oxidative/reductive adsorp-tion/desorption from that for bulk reaction. In this work, we provide a methodology that the isotherm of oxidative/reductive adsorption desorption processes at electrode surface canbe obtained using just one solution with relatively low reactant concentration, by taking the advantage of varying the potential scan rate (relative of the diffusion rate) to tune the adsorption rate and proper mathematic treatment. The methodology is demonstrated bytaking acetate adsorption at Pt(111) in acidic solution as an example. The possibility for ex-tension of this method toward mechanistic studies of complicated electrocatalytic reactions is also given.     

Parallel pore and surface diffusion of levulinic acid in basic polymeric adsorbents

The equilibrium and kinetics of levulinic acid (LA) adsorption on two basic polymeric adsorbents, 335 (highly porous gel) and D315 (macroreticular), were investigated. Experimental adsorption rates in batch stirred vessels under a variety of operating conditions were described successfully by the parallel pore and surface diffusion model taking into account external mass transfer and nonlinear Toth isotherm. The film-pore diffusion model was matched with the rate data and the resulting apparent pore diffusivities were strongly concentration-dependent and approached to a constant value for 335 adsorbent. Thus, the constant value was taken as the accurate pore diffusivity, while the pore diffusivity in D315 was estimated from the particle porosity. The surface diffusivities decreased with increasing initial bulk concentration for both adsorbents. The inverse concentration dependence was correlated reasonably well to the change of isosteric heat of adsorption as amount adsorbed.     

The special features of equilibrium adsorption of argon on homogeneous and inhomogeneous surfaces

Comparative patterns of equilibrium adsorption of argon on the surface of graphitized thermal carbon black (GCB) and the inhomogeneous surfaces of nongraphitized carbon black and silica at 77 and 87.3 K were considered. It was shown that argon acquires the properties of a special phase with a layered structure and exhibits two-dimensional phase transitions with the formation of crystal-like layers near the homogeneous surface of GCB even at a temperature exceeding the triple point. However, already at a distance of three-four molecular diameters from the surface, adsorbed argon behaves as a bulk phase in a weak external field. The defect surface of nongraphitized carbon black and the amorphous surface structure of silica destroy the longrange order of adsorbed argon and lower its solidification temperature. Therefore, argon adsorbed at a temperature of 77 K, i.e., below the triple point, exhibits the properties of a supercooled liquid. The applicability of density functional theory to describe argon isotherms and heat of adsorption on inhomogeneous surfaces was demonstrated.     

A qualitative approach to adsorption mechanism identification on microporous carbonaceous surfaces

The paper presents results of research on identification of localized and other adsorption mechanisms, on geometrically heterogeneous graphite-like carbonaceous surfaces. It attempts to get an insight into properties of individual adsorptive molecule movement near attractive adsorption sites, arising from adsorbent surface geometrical heterogeneities. In particular, a shape and volume of space occupied by the continuously moving molecule mass center are investigated. To this aim, kinematic equilibrium of the particle moving near a hypothetical microporous carbonaceous adsorbent wall is considered, and then compared with thermodynamic equilibrium. The proposed approach enables to examine effects of certain surface geometry on the shape and volume of space occupied by adsorbed particles, and so to outline temperature conditions for the localized adsorption mechanism predomination. Thus, it provides a cognitive basis to answer the question, what particular mechanism (localized or other—e.g. mobile) should be assumed for a class of adsorption systems in order to select the most appropriate mathematical adsorption model. Hence, it makes it possible for more reliable examination of real porous structures, based on adsorption measurements.     

Multilayer adsorption of water at a rutile TiO2)(110) surface: towards a realistic modeling by molecular dynamics

We present a model combining ab initio concepts and molecular dynamics simulations for a more realistic treatment of complex adsorption processes. The energy, distance, and orientation of water molecules adsorbed on stoichiometric and reduced rutile TiO(2)(110) surfaces at 140 K are studied via constant temperature molecular dynamics simulations. From ab initio calculations relaxed atomic geometries for the surface and the most probable adsorption sites were derived. The study comprises (i) large two-dimensional surface supercells, providing a realistically low concentration of surface oxygen defects, and (ii) a water coverage sufficiently large to model the onset of the growth of a bulk phase of water on the surface. By our combined approach the influence of both, the metal oxide surface, below, and the bulk water phase, above, on the water molecules forming the interface between the TiO(2) surface and the water bulk layer is taken into account. The good agreement of calculated adsorption energies with experimental temperature programmed desorption spectra demonstrates the validity of our model.     

Probe of NH3 and CO adsorption on the very outermost surface of a porous TiO2 adsorbent using photoluminescence spectroscopy

We report the first measurements of the kinetics of adsorption on the very outermost surface sites of a porous material compared to measurements made of adsorption on the interior sites. NH(3) and CO were employed in this study as representative of slow diffusion and fast diffusion, respectively, through porous TiO(2). Adsorption of NH(3) at 200 K occurs mainly at the very near surface (~20 nm) region as observed by photoluminescence (PL) spectroscopy, and its distribution by surface diffusion through the powder is highly retarded as judged by transmission IR spectroscopy. In contrast, the adsorption of CO in the near-surface region at 120 K is followed by the fast distribution of CO by surface diffusion into TiO(2) powder, causing the near-surface CO coverage to lag behind the coverage in the bulk. In the desorption process, the near-surface region delivers adsorbed CO molecules into the gas phase, accompanied by the supply of diffusing CO molecules from the interior. As a result, the adsorption/desorption processes for CO in the near-surface region of porous TiO(2) show a pronounced hysteresis effect. As surface diffusion is retarded at lower temperatures, the hysteresis effect gradually disappears.     

Time-resolved determination of surface diffusion coefficients for physically adsorbed or chemisorbed species on heterogeneous surfaces,by inverse gas chromatography

A new simple method is developed for measuring surface diffusion coefficients Ds of gases adsorbed on heterogeneous surfaces, using the reversed-flow version of inverse gas chromatography. The Ds values are found in a time-resolved way, together with the corresponding adsorption energy values, the local adsorbed concentrations, and the local adsorption isotherm values. A relative dynamic adsorption rate constant, an adsorption/desorption rate constant, and a surface reaction rate constant are also found in the same experiment, together with the total diffusion coefficient of the gas in the solid bed. The method has been applied for carbon monoxide, oxygen gas, and carbon dioxide as adsorbates on 75% Pt+25% Rh catalyst supported on SiO2, at 593.8 K.