Equilibrium Surface Coverage Research Articles

Near Equilibration Times in the Diffusion-Controlled Adsorption.

A model of the Frumkin isotherm following adsorption on the surface of the rotating disk is developed with the purpose to calculate the time that is needed for the establishment of the near equilibrium state between the amount of adsorbate and the bulk concentration of surfactant. The "near" is quantified as 99% of the proper equilibrium surface coverage. The near equilibration time depends on the bulk concentration and on the coefficient of molecular attraction in the adsorbed layer. In the vicinity of the inflection point of the isotherm, this time exhibits sharp spike. It is caused by the diminished flux that increases surface coverage very slowly but continues for a long time. Eventually, both the flux and the surface coverage increase with time drastically under the influence of the exponential part of the Frumkin isotherm.

Surface coverage dynamics for reversible dissociative adsorption on finite linear lattices.

Dissociative adsorption onto a surface introduces dynamic correlations between neighboring sites not found in non-dissociative absorption. We study surface coverage dynamics where reversible dissociative adsorption of dimers occurs on a finite linear lattice. We derive analytic expressions for the equilibrium surface coverage as a function of the number of reactive sites, N, and the ratio of the adsorption and desorption rates. Using these results, we characterize the finite size effect on the equilibrium surface coverage. For comparable N's, the finite size effect is significantly larger when N is even than when N is odd. Moreover, as N increases, the size effect decays more slowly in the even case than in the odd case. The finite-size effect becomes significant when adsorption and desorption rates are considerably different. These finite-size effects are related to the number of accessible configurations in a finite system where the odd-even dependence arises from the limited number of accessible configurations in the even case. We confirm our analytical results with kinetic Monte Carlo simulations. We also analyze the surface-diffusion case where adsorbed atoms can hop into neighboring sites. As expected, the odd-even dependence disappears because more configurations are accessible in the even case due to surface diffusion.

Role of Hydride Formation in Electrocatalysis for Sustainable Chemical Transformations

The electrochemical potential of numerous reduction reactions corresponds to hydrogen pressures that thermodynamically favor the formation of many metal hydrides. Whether a catalyst remains metallic with hydrogen on the surface (Hads) or absorbs hydrogen into its lattice (Habs), forming a metal hydride, results from a balance between not only this thermodynamic driving force but also the kinetics of concurrent surface reactions and equilibrium surface coverage. Drawing parallels with thermal catalytic processes, we provide examples of how hydride formation impacts electrocatalysis in H2 evolution, organic and CO2 reduction, and N2 and NO3– reduction reactions. Hydride formation not only changes catalyst activity and selectivity but also can impact durability. We highlight techniques capable of identifying hydride formation under reaction conditions, imperative for an understanding of electrocatalyst kinetics. Hydrides offer many possibilities in electrocatalysis, including unique reaction mechanisms involving the catalyst lattice and innovative reactor architectures, beneficial for applications in chemical transformations and energy.

Platinum Graphene Catalytic Condenser for Millisecond Programmable Metal Surfaces.

Accelerating catalytic chemistry and tuning surface reactions require precise control of the electron density of metal atoms. In this work, nanoclusters of platinum were supported on a graphene sheet within a catalytic condenser device that facilitated electron or hole accumulation in the platinum active sites with negative or positive applied potential, respectively. The catalytic condenser was fabricated by depositing on top of a p-type Si wafer an amorphous HfO2 dielectric (70 nm), on which was placed the active layer of 2-4 nm platinum nanoclusters on graphene. A potential of ±6 V applied to the Pt/graphene layer relative to the silicon electrode moved electrons into or out of the active sites of Pt, attaining charge densities more than 1% of an electron or hole per surface Pt atom. At a level of charge condensation of ±10% of an electron per surface atom, the binding energy of carbon monoxide to a Pt(111) surface was computed via density functional theory to change 24 kJ mol-1 (0.25 eV), which was consistent with the range of carbon monoxide binding energies determined from temperature-programmed desorption (ΔBECO of 20 ± 1 kJ mol-1 or 0.19 eV) and equilibrium surface coverage measurements (ΔBECO of 14 ± 1 kJ mol-1 or 0.14 eV). Impedance spectroscopy indicated that Pt/graphene condensers with potentials oscillating at 3000 Hz exhibited negligible loss in capacitance and charge accumulation, enabling programmable surface conditions at amplitudes and frequencies necessary to achieve catalytic resonance.

Comparison of Coverage-Dependent Binding Energy Models for Mean-Field Microkinetic Rate Predictions.

The binding energies of adsorbates at catalytic surfaces are in general functions of adsorbate coverage, with corresponding consequences for equilibrium surface coverages and reaction rates under relevant conditions. This coverage dependence is commonly incorporated into mean-field microkinetic models by writing adsorption energies as an algebraic function of coverage and parametrizing against density functional theory models. In this work, we compare the performance of three different analytical coverage-dependent forms, including linear and piecewise models and a logarithmic form inspired by Wilson's activity model, against accurate results obtained from a lattice-based cluster expansion (CE) representation of adsorbate interactions combined with a Monte Carlo evaluation of reaction rates. We take as a model system O2 dissociation-limited NO oxidation to NO2 over Pt(111), parametrize all models against the same set of previously reported coverage-dependent NO and O binding energies, and solve kinetic models under the same set of assumptions. Steady-state coverages from the analytical models are similar to each other and the ensemble-averaged CE result, other than the discontinuities in O and NO coverages that appear in the piecewise model. Predicted steady-state rates differ more substantially, reflecting the sensitivity of the O2 dissociation activation energy to coverage-dependent binding energies. The activity model predicts reaction rates reliably at low temperatures and systematically deviates from CE rates at high temperatures, where minority surface sites, having low local coverage around vacant pairs, dominate overall reaction rates. The results highlight the challenges of developing coverage-dependent microkinetic models that are reliable across a range of conditions.

Critical Nucleus Size at Electrocrystallization

A new interpretation of critical nucleus, which is based on the kinetic analysis of nucleation, is proposed. By critical size of nucleus is meant the size that corresponds to the smallest flux of transition to the next size class. The relationship between the critical size and overpotential and equilibrium surface coverage with adatoms or between the critical size and the specific surface energy and adhesion energy is determined.

On the decisive role of the sulfur-based anchoring group in the electro-assisted formation of self-assembled monolayers on gold

A reproducible electro-assisted method is proposed to follow the influence of different sulfur-based anchoring groups on the adsorption kinetics and thermodynamics of SAM formation on gold electrodes. This has been made possible thanks to the preparation of several molecules containing various anchoring groups (thiol, thioester, acyclic and cyclic disulfides, thiosulfonate) while preserving the same spacer redox head group. In this paper we focus on the question of a substantial difference between SAMs derived from either alkylthiols or disulfides using cyclic voltammetry. The comparison of equilibrium surface coverage, affinity constant toward gold surface and stability suggest a decisive role of the nature of the anchoring group in the formation of the monolayers. Moreover, a significant difference of the desorption behavior of SAMs on gold, pre-formed from either thiol or disulfide, has clearly been demonstrated.

Adsorption isotherms for hydrogen chloride (HCl) on ice surfaces between 190 and 220 K.

The interaction of hydrogen chloride (HCl) with ice surfaces at temperatures between 190 and 220 K was investigated using a coated-wall flow-tube connected to a chemical ionization mass spectrometer. Equilibrium surface coverages of HCl were determined at gas phase concentrations as low as 2 × 10(9) molecules cm(-3) (∼4 × 10(-8) Torr at 200 K) to derive Langmuir adsorption isotherms. The data are described by a temperature independent partition coefficient: KLang = (3.7 ± 0.2) × 10(-11) cm(3) molecule(-1) with a saturation surface coverage Nmax = (2.0 ± 0.2) × 10(14) molecules cm(-2). The lack of a systematic dependence of KLang on temperature contrasts the behaviour of numerous trace gases which adsorb onto ice via hydrogen bonding and is most likely related to the ionization of HCl at the surface. The results are compared to previous laboratory studies, and the equilibrium partitioning of HCl to ice surfaces under conditions relevant to the atmosphere is evaluated.

Interfacial properties of asphaltenes at toluene-water interfaces.

Asphaltenes are "n-alkane insoluble" species in crude oil that stabilize water-in-oil emulsions. To understand asphaltene adsorption mechanisms at oil-water interfaces and coalescence blockage, we first studied the behavior in aliphatic oil-water systems in which asphaltenes are almost insoluble. They adsorbed as monomers, giving a unique master curve relating interfacial tension (IFT) to interfacial coverage through a Langmuir equation of state (EoS). The long-time surface coverage was independent of asphaltene bulk concentration and asymptotically approached the 2-D packing limit for polydisperse disks. On coalescence, the surface coverage exceeded the 2-D limit and the asphaltene film appeared to become solidlike, apparently undergoing a transition to a soft glassy material and blocking further coalescence. However, real systems consist of mixtures of aliphatic and aromatic components in which asphaltenes may be quite soluble. To understand solubility effects, we focus here on how the increased bulk solubility of asphaltenes affects their interfacial properties in comparison to aliphatic oil-water systems. Unlike the "almost irreversible" adsorption of asphaltenes where the asymptotic interfacial coverage was independent of the bulk concentration, an equilibrium surface pressure, dependent on bulk concentration, was obtained for toluene-water systems because of adsorption being balanced by desorption. The equilibrium surface coverage could be obtained from the short- and long-term Ward-Tordai approximations. The behavior of the equilibrium surface pressure with the equilibrium surface coverage was then derived. These data for various asphaltene concentrations were used to determine the EoS, which for toluene-water could also be fitted by the Langmuir EoS with Γ∞ = 3.3 molecule/nm(2), the same value as that found for these asphaltenes in aliphatic media. Asphaltene solubility in the bulk phase only appears to affect the adsorption isotherm but not the EoS. Further support for these observations is provided by dilatational rheology experiments for the EoS and contraction experiments in which desorption to the equilibrium surface pressure was observed.

Quantitative Modeling of Fibrinogen Adsorption on Different Biomaterials

Adsorption processes of biological macromolecules on solid surfaces, e.g. on implant materials, are of scientific, medical and technological interest. The adsorption process of the blood plasma protein fibrinogen from aqueous solutions on biomaterial surfaces is simulated by solving the diffusion equation in one dimension in combination with a two dimensional cellular automaton model. The adsorption/desorption kinetics of fibrinogen on different metallic biomaterials is tracked until a dynamic equilibrium is reached. In addition to mass transfer towards the surface, adsorption of fibrinogen molecules and surface diffusion of single fibrinogen molecules and clusters the algorithm also accounts for the desorption of single molecules. By varying the desorption behavior in the simulation calculation, the equilibrium surface coverage changes in the range of 0.2–0.85, implying more flexible and higher surface coverage than previous models. The influences of surface properties of the biomaterials and of the initial concentration of fibrinogen on the adsorption process are quantified. Experimental results from the literature on fibrinogen adsorption kinetics are compared with our simulation results and illustrate good quantitative agreement that is only achievable using desorption as essential model component.

Surface Reaction Rate and Probability of Ozone and Alpha-Terpineol on Glass, Polyvinyl Chloride, and Latex Paint Surfaces

Ozone can react homogeneously with unsaturated organic compounds in buildings to generate undesirable products. However, these reactions can also occur on indoor surfaces, especially for low-volatility organics. Conversion rates of ozone with α-terpineol, a representative low-volatility compound, were quantified on surfaces that mimic indoor substrates. Rates were measured for α-terpineol adsorbed to beads of glass, polyvinylchloride (PVC), and dry latex paint, in a plug flow reactor. A newly defined second-order surface reaction rate coefficient, k(2), was derived from the flow reactor model. The value of k(2) ranged from 0.68 × 10(-14) cm(4)s(-1)molecule(-1) for α-terpineol adsorbed to PVC to 3.17 × 10(-14) cm(4)s(-1)molecule(-1) for glass, but was insensitive to relative humidity. Further, k(2) is only weakly influenced by the adsorbed mass but instead appears to be more strongly related to the interfacial activity α-terpineol. The minimum reaction probability ranged from 3.79 × 10(-6) for glass at 20% RH to 6.75 × 10(-5) for PVC at 50% RH. The combination of high equilibrium surface coverage and high reactivity for α-terpineol suggests that surface conversion rates are fast enough to compete with or even overwhelm other removal mechanisms in buildings such as gas-phase conversion and air exchange.

EUV Lithography optics contamination and lifetime studies

In this paper we discuss surface phenomena leading to contamination of multilayer optics designed for Extreme Ultraviolet (EUV) lithography. Experimental data supported by calculations indicate dramatic influence of resonance structure of EUV mirror on the secondary electron yield. These low energy electrons play an important role in radiation chemistry at the mirror surface. We also discuss the dependence on the partial pressure of admitted gas of equilibrium surface coverage and contamination rate under EUV irradiation.

The interaction of H2O2 with ice surfaces between 203 and 233 K

The interaction of H(2)O(2) with ice surfaces at temperatures between 203 and 233 K was investigated using a low pressure, coated-wall flow tube equipped with a chemical ionisation/electron impact mass spectrometer. Equilibrium surface coverages of H(2)O(2) on ice were measured at various concentrations and temperatures to derive Langmuir-type adsorption isotherms. H(2)O(2) was found to be strongly partitioned to the ice surface at low temperatures, with a partition coefficient, K(linC), equal to 2.1 × 10(-5) exp(3800/T) cm. At 228 K, this expression results in values of K(linC) which are orders of magnitude larger than the single previous determination and suggests that H(2)O(2) may be significantly partitioned to the ice phase in cirrus clouds. The partition coefficient for H(2)O(2) was compared to several other trace gases which hydrogen-bond to ice surfaces and a good correlation with the free energy of condensation found. For this class of trace gas a simple parameterisation for calculating K(linC)(T) from thermodynamic properties was established.

Chemical Control of the Photoluminescence of CdSe Quantum Dot−Organic Complexes with a Series of Para-Substituted Aniline Ligands

Replacement of the native (as-synthesized) ligands of colloidal CdSe QDs with varying concentrations of a series of para-substituted anilines (R-An), where R ranges from strongly electron-withdrawing to strongly electron-donating, decreases the PL of the QDs. The molar ratio of R-An to QD ([R-An]:[QD]) at which the PL decreases by 50% shifts by 4 orders of magnitude over the series R-An. The model employed to describe the data combines a Freundlich binding isotherm (which reflects the dependence of the binding affinity of the amine headgroups of R-An on the substituent R) with a function that describes the response of the PL to R-An ligands once they are bound at their equilibrium surface coverage. The latter function includes as a parameter the rate constant, k(nr), for nonradiative decay of the exciton at a site to which an R-An ligand is coordinated. The value of this parameter reveals that the predominant mechanism of QD-ligand interaction is passivation of Cd(2+) surface sites through sigma-donation for R-An ligands with R = H, Br, OCF(3), and reductive quenching through photoinduced hole transfer for R = MeO, (Me)(2)N.

Surface Self-Diffusion and Mean Displacement of Hydrogen on Graphite and a PEM Fuel Cell Catalyst Support

Quasielastic neutron scattering (QENS) measurements together with equilibrium molecular dynamic (EMD) simulations have been performed to investigate the surface interaction between hydrogen molecules and a carbon material commonly used in polymer electrolyte membrane fuel cells (PEMFC), called XC-72. Half a monolayer of molecular hydrogen was adsorbed on to the carbon material at 2 K. QENS spectra were recorded at the time-of-flight spectrometer IN5 at 40, 45, 50, 60, 70, 80, and 90 K. Simultaneously the pressure was measured as a function of time to monitor the equilibrium surface coverage at each temperature. By using the Chudley and Elliott model for jump diffusion we found the diffusion coefficient at each temperature. At 350 K, a typical fuel cell temperature, the temperature function was extrapolated to a self-diffusion coefficient of 2.3 × 10−7 m2/s. We simulated graphite in contact with hydrogen molecules using EMD simulation. We simulated the system at different temperatures from 70 to 350 K in 2...

Wetting and spreading

Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating ``wet'' regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.

Adsorption and Desorption of Nonionic Surfactants on Silica from Toluene Studied by ATR-FTIR

The adsorption and desorption kinetics and equilibrium surface coverages for a range of poly(ethylene glycol) monoalkyl ether nonionic surfactants (C(n)E(m)s) from toluene onto silica were studied using attentuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) coupled with a constant-flow liquid cell. The initial adsorption rate appears to be transport controlled, and broadly independent of molecular structure, whereas equilibrium adsorbed amounts are dependent on surfactant head group size (which controls both surface interactions and the surface-bulk partitioning). Desorption kinetic data are fitted to a simple two-step model based upon Langmuir-type kinetics. The results are interpreted in terms of a simple model comprising two modes of surfactant adsorption, each with a characteristic adsorbed amount and desorption rate constant; a possible physical basis for this observation is presented. Trace water levels appear to have a strong impact on the equilibrium surface coverages in these systems, possibly by influencing both surfactant interactions and solubility.

Non-equilibrium exchange kinetics in sequential non-ionic surfactant adsorption: Theory and experiment

Vastly different characteristic times of adsorption and desorption of surfactants in multi-component systems can cause non-uniform changes in interfacial concentration and surface tension. The rate constants for these processes can be determined by experiments in pendant drops in which the interface adjacent to a surfactant solution is removed from equilibrium by replacement of the drop subphase. Experiments using two n-alkyl (C 10 and C 14) dimethyl phosphine oxides are presented which measure the desorption coefficients of each in single component experiments and show the impact desorption kinetics have on the dynamic surface tension which occurs during sequential replacement of a surfactant at the air–water interface by exchanging the bulk phase for solution of a second surfactant. Because of finite sorption kinetics, non-equilibrium surface densities prevail during the exchange process. When C 10 DMPO is replaced by C 14 DMPO, the desorption of C 10 DMPO is more rapid than the adsorption of C 14 DMPO and the surface coverage at intermediate times is less than the equilibrium surface coverage, causing the surface tension to exhibit a maximum. When the more slowly desorbing C 14 DMPO is replaced by C 10 DMPO, the surface density displays a maximum at intermediate times. This overcrowding causes the surface tension to exhibit a temporary minimum. The presence of these extrema can be described using theoretical framework which includes finite sorption kinetics. Reasonable agreement between theory and experiment for the surfactants in this study is achieved using only equilibrium adsorption parameters from each of the unary systems and independent measurements of the desorption kinetic coefficients; i.e. no adjustable parameters. These simple paradigms suggest a chemical strategy for temporal control of Marangoni stresses, which could be important in a variety of technologies including foam and emulsion formation and microfluidic applications.

Kinetic Monte Carlo study of proton binding at the metal oxide/electrolyte interface

The kinetics of proton binding at the metal oxide/electrolyte interface is studied using the kinetic Monte Carlo method. The influence of system properties (surface site density, interfacial dielectric constant, surface energetic heterogeneity) on the equilibrium and kinetic surface coverage is shown. It is shown that the kinetic properties are much more sensitive to lateral interactions than the equilibrium ones. The assumption of energetic heterogeneity rapidly changes the time scales of the processes as well as the time interval between two subsequent elementary processes. In this paper, the atomistic insight into the kinetics of H + ion uptake at the metal oxide/electrolyte interface is presented for the first time.

Nitric acid condensation on ice: 2. Kinetic limitations, a possible “cloud clock” for determining cloud parcel lifetime

Measurements of NOY condensation on cirrus particles found in stratospherically influenced air sampled during the SOLVE‐I mission are analyzed and compared with data from other field studies of HNO3 or NOY condensation on ice. Each field study exhibits an order of magnitude data spread for constant HNO3 pressures and temperatures. While others assumed this distribution is due to random error, the data spread exceeds instrument precision errors and instead suggests HNO3 removal had not attained equilibrium at the time of sampling. During the SOLVE‐I mission, condensation on ice was a significant sink for HNO3 despite submonolayer surface coverages; we therefore propose condensation of HNO3 on lower‐stratospheric cirrus particles is controlled by kinetics and will occur at a kinetically limited rate. Furthermore, we suggest the low accommodation coefficient for HNO3 on ice combined with relatively short‐lived clouds causes highly scattered, limited HNO3 uptake on cirrus particles. We couple laboratory data on the accommodation coefficient of HNO3 on ice with field surface coverage data in order to generate a “cloud clock”: a calculation to determine the age of a cloud parcel. Data from the aforementioned field studies are compared to theoretical models for equilibrium surface coverage on the basis of laboratory data extrapolated to atmospheric temperatures and HNO3 pressures. This comparison is difficult because most of the atmospheric data are probably not at equilibrium and follow a condensation time curve rather than an equilibrium surface coverage curve. Finally, we develop a simple mathematical solution for the time required for HNO3 condensation on ice.