Coverage-dependent Activation Energy Research Articles

Kinetic model for hydrogen absorption in tungsten with coverage dependent surface mechanisms

In this work, a kinetic model is presented to describe hydrogen absorption and desorption from tungsten at different surface coverages. Activation energies for hydrogen absorption into the bulk and desorption from the surface of tungsten are modelled by functions that depend explicitly and continuously on the hydrogen surface coverage. A steady-state model is developed to derive these activation energies from experimental data. The newly developed coverage dependent activation energies are then implemented in the non steady-state rate-equation code MHIMS. Published experimental results on D uptake and retention of self-damaged tungsten exposed to 0.28 eV deuterium atoms at different temperatures ranging from 450 K to 1000 K can be successfully described with this approach. Finally, the steady-state model is applied to determine surface concentration, bulk concentration and migration depths of hydrogen isotopes in tungsten exposed to various atomic fluxes and temperatures ranging from milder conditions in laboratory experiments to divertor strike point conditions in tokamaks.

Interactions of Atomic and Molecular Hydrogen with a Diamond-like Carbon Surface: H2 Formation and Desorption

Abstract The interactions of atomic and molecular hydrogen with bare interstellar dust grain surfaces are important for understanding H2 formation at relatively high temperatures (>20 K). We investigate the diffusion of physisorbed H atoms and the desorption energetics of H2 molecules on an amorphous diamond-like carbon (DLC) surface. From temperature-programmed desorption experiments with a resonance-enhanced multiphoton ionization (REMPI) method for H2 detection, the H2 coverage-dependent activation energies for H2 desorption are determined. The activation energies decrease with increasing H2 coverage and are centered at 30 meV with a narrow distribution. Using a combination of photostimulated desorption and REMPI methods, the time variations of the surface number density of H2 following atomic and molecular hydrogen depositions are studied. From these measurements, we show that H2 formation on a DLC surface is quite efficient, even at 20 K. A significant kinetic isotope effect for H2 and D2 recombination reactions suggests that H-atom diffusion on a DLC surface is mediated by quantum mechanical tunneling. In astrophysically relevant conditions, H2 recombination due to physisorbed H-atoms is unlikely to occur at 20 K, suggesting that chemisorbed H atoms might play a role in H2 formation at relatively high temperatures.

Inclusion of surface heterogeneity in bridging PEM fuel cell electrode contamination kinetics and transport via a competitive Langmuir-Freundlich isotherm

This paper reports the development of mathematical model that bridges PEMFC transport phenomena with surface reaction kinetics in rough and heterogeneous electrodes, in which specifically the anode is modeled under carbon monoxide contamination. The mathematical bridging is done by converting surface concentration of reactants and contaminant into surface coverage of relevant adsorbates using the Langmuir-Freundlich isotherm to statistically include heterogeneity in binding site energetics. Thermodynamically optimized kinetic rate and equilibrium constants are calculated using coverage-dependent activation energies and provided as input to the HOR, ORR, and a kinetic-based limiting current model developed to solve for the distribution of activation overpotential. A novel model for a closed-form calculation of activation overpotential is proposed to allow numerical investigation via a galvanostatic approach. The kinetic reaction models are highly coupled with three-dimensional transport equations and solved iteratively under single-phase and steady-state conditions. Comparison is done with respect to two sets of available literature data in order to test the kinetic model validity under variation of CO concentrations and cell operating temperatures, in which good agreement is found. The results confirm that a Langmuir-Freundlich isotherm could be a more suitable isotherm compared to the extensively used Langmuir-specific isotherm for rough heterogeneous surfaces physically found in PEMFC catalysts. Results from the model show that rate of HOR is higher under the ribs of the cell since most of the active sites under channel are blocked with CO, with the effect exacerbated at lower temperatures.

ChemInform Abstract: Effect of the Size of Platinum Particles on the Chemisorption of Oxygen.

An unambiguous particle-size effect has been observed in the desorption of oxygen from a faujasite-embedded platinum dispersion with distinctly different and narrow particle-size distributions. A kinetic analysis of the desorption spectra revealed a relative increase in the activation energy for desorption by about 60 kJ mol–1 as the Pt particle size decreased from 5 to 1 nm. A coverage-dependent activation energy has to be assumed for a consistent interpretation of the experimental results.

Heat of adsorption for NH 3, NO 2 and NO on Cu-Beta zeolite using microcalorimeter for NH 3 SCR applications

Microcalorimetry is a powerful technique with which to measure the heat of adsorption (Δ H), producing values that are very important when developing kinetic models. The method provides a way of determining these parameters independently. For kinetic models describing NH 3 SCR it is critical to be able to accurately describe the storage of ammonia and NO x in order to simulate rapid transients occurring in the experiments. The objective of our study is to measure the heat of adsorption of NH 3, NO 2 and NO on Cu-Beta. An ammonia TPD experiment was conducted at 150 °C using the microcalorimeter, resulting in the observation of an exotherm when introducing ammonia due to adsorption. This resulted in an average heat of adsorption of −100 kJ/mol. A good reproducibility was found when using a second sample, resulting in −97 kJ/mol. In order to investigate the coverage dependence of the heat of adsorption, an ammonia stepwise experiment was conducted. First, the catalyst was exposed to NH 3 at 500 °C, resulting in the adsorption of strongly bound ammonia and obtaining a heat of adsorption of −110 kJ/mol. Thereafter, the catalyst was cooled in Ar and at 400 °C, NH 3 was again introduced. Due to that the temperature is lower the ammonia that adsorbed was weaker. The procedure was repeated at 300, 200 and 100 °C, resulting in a coverage dependent activation energy for ammonia desorption (if assuming zero activation for adsorption) according to the following formula: E d e s o r p t i o n , N H 3 = 120.0 ( 1 − 0.38 θ N H 3 ) where θ N H 3 is the coverage of ammonia on the surface. The NO and NO 2 adsorption and desorption were investigated using NO and NO 2 TPD experiments, respectively. For the NO 2 TPD experiment, approximately three NO 2 were stored for each NO produced, corresponding to the disproportionation mechanism. This resulted in Δ H of −65 kJ/mol per NO 2 consumed. The NO TPD experiment resulted in that only small amounts of NO was adsorbed.

Adsorption, desorption, and diffusion of nitrogen in a model nanoporous material. I. Surface limited desorption kinetics in amorphous solid water

The adsorption and desorption kinetics of N2 on porous amorphous solid water (ASW) films were studied using molecular beam techniques, temperature programed desorption (TPD), and reflection-absorption infrared spectroscopy. The ASW films were grown on Pt(111) at 23 K by ballistic deposition from a collimated H2O beam at various incident angles to control the film porosity. The experimental results show that the N2 condensation coefficient is essentially unity until near saturation, independent of the ASW film thickness indicating that N2 transport within the porous films is rapid. The TPD results show that the desorption of a fixed dose of N2 shifts to higher temperature with ASW film thickness. Kinetic analysis of the TPD spectra shows that a film thickness rescaling of the coverage-dependent activation energy curve results in a single master curve. Simulation of the TPD spectra using this master curve results in a quantitative fit to the experiments over a wide range of ASW thicknesses (up to 1000 layers, approximately 0.5 microm). The success of the rescaling model indicates that N2 transport within the porous film is rapid enough to maintain a uniform distribution throughout the film on a time scale faster than desorption.

Effect of coverage and temperature on the kinetics of nitrogen desorption from Rh(111) surfaces

The kinetics of molecular nitrogen desorption from Rh(111) single-crystal surfaces covered with atomic nitrogen were characterized by both isothermal and temperature-programmed experiments. A complex kinetic behavior was observed for this system not describable by typical Arrhenius expressions even if coverage-dependent activation energies are considered. In fact, the possibility of developing an analytical expression for those desorption rates is voided by the fact that they depend not only on surface temperature and nitrogen coverage but also on the mode of preparation of the system. Isotope labeling experiments support the idea of the formation of surface nitrogen islands and of preferential recombination and desorption at their edges. Coadsorbed oxygen, a typical by-product in NO reduction catalysis, behaves kinetically in a way similar to surface nitrogen as far as N2 desorption is concerned. The recombination of two surface nitrogen atoms is typically slower than the reaction between one nitrogen and one adsorbed NO molecule, and therefore the catalytic reduction of NO most likely occurs via the latter pathway.

A detailed surface reaction mechanism for CO oxidation on Pt

A detailed surface reaction mechanism for oxidation of CO on polycrystalline Pt surfaces, capable of predicting various available experimental features, has been developed using a multistep methodology. First, thermodynamically consistent, coverage-dependent activation energies and heats of reactions were derived from the application of the unity bond index-quadratic exponential potential formulation. Next, initial estimates of pre-exponentials were obtained from transition state theory or available experiments. Important feature identification analysis was performed to determine key reaction parameters for each experiment. Model responses were then parameterized in terms of these important parameters by simple polynomials and factorial design techniques and subsequently used in simultaneous optimization through simulated annealing against different sets of literature and new experimental data from our laboratory. Model validation with independent experiments shows that the proposed surface reaction mechanism performs very well. The potential of our approach for developing surface reaction mechanisms for catalytic combustion of more complex fuels is also discussed.

Reactive scattering study of etching dynamics: Cl 2 on GaAs(100)

Pulsed supersonic molecular beam scattering has been used to study of the inelastic scattering, trapping desorption and reactive channels for the Cl 2+GaAs(100) thermal etching reactions. Temperature profiles of the reactive products GaCl, GaCl 3, AsCl 3, As 4 and As 2 are reported in the range 340 to 825 K. Angular and time-of-flight (TOF) distributions of inelastically scattered and trapped+desorbed Cl 2 are also reported. The translational inelasticity has been measured as a function of final scattering angle at two initial translational energies, 18 and 53.4 kJ mol −1. Angular distribution of all reaction products are described by a cos n ( θ) form with 1.1≤ n≤1.3. The TOF distributions of GaCl, GaCl 3 and AsCl 3 reveal prompt production but with measurable time delays (50 μs–5 ms). The As 4 and As 2 signals are effectively demodulated and correspond to delayed production on the surface with a time constant >1 s. The surface time profiles for GaCl and GaCl 3 are each well described by double-exponential decays for production desorption from the surface. The temperature dependence of the time constants for each product yield pairs of Arrhenius plots with common activation energies but different pre-exponential factors. It is argued that these do not correspond to two separate processes but reflect single product desorption with a coverage-dependent activation energy.

Self-Assembled Chromophoric NLO-Active Structures. Second-Harmonic Generation and X-ray Photoelectron Spectroscopic Studies of Nucleophilic Substitution and Ion Exchange Processes on Benzyl Halide-Functionalized Surfaces

The progress and extent of nucleophilic substitution and ion exchange reactions of self-assembled chromophoric monolayers are studied by X-ray photoelectron (XPS) and second harmonic generation (SHG) spectroscopy. Self-assembled monolayers prepared from 2-[4-(chloromethyl)phenyl]ethyl trichlorosilane (1) on glass substrates are susceptible to nucleophilic substitution of ∼90% of the surface-confined benzylic chloride functionalities with the “hypernucleophile” 4-(dimethylamino)pyridine; however, only ∼60% of the densely packed benzyl chloride groups undergo reaction with the high-β chromophore precursor 4‘-[4-[N,N-bis(3-hydroxypropyl)amino]styryl]pyridine (2a). Quaternization of a benzylic monolayer with this molecule yields a monolayer having a bulk second-order NLO response (χ(2)) of 3 × 10-7 esu at λ0 = 1064 nm, corresponding to a near-maximum chromophore coverage of ∼2 × 1014 molecules/cm2. The kinetics of this substitution reaction and associated structural modifications are studied in real time by in situ polarized SHG techniques, which reveal non-Langmuirian kinetics and a rapidly increasing chromophore tilt angle with increasing coverage. The quaternization kinetics can be fit to a phenomenological biexponential rate equation with k‘1 ≈ 2 × 10-2 L mol-1 s-1 and k‘2 ≈ 2 × 10-3 L mol-1 s-1 and to a coverage-dependent activation energy model (EA = E0 + Ebθ), yielding a perturbative energy Eb of 6−8 kJ mol-1. Both models are compatible with increasing repulsive interactions between chromophores at high coverages. The charge-compensating chloride counterions within monolayers having dense chromophore packing can be ion exchanged with iodide, up to a maximum of ∼40% of available chloride ions. The introduction of larger anions (sulfanilate, ethyl orange, eosin B) is observed in less densely packed films; however, the ion exchange process is completely inhibited in monolayers capped with a siloxane overlayer. In all cases, exchange of the chloride leads to significant increases in the second-harmonic generation efficiency, up to 45% on exchange with eosin B. In the case of iodide and sulfanilate substitution for chloride, the increase in the second-order response upon ion exchange is attributable to the incoming anion assuming a position within the monolayer microstructure different from that of the displaced anion.

Atomic Iodine Desorption from Single Crystal Nickel Surfaces

Atomic iodine desorption from single crystal nickel surfaces, Ni(100) and Ni(111), has been monitored by temperature-programmed desorption (TPD). CF 3 I was used as a precursor molecule for iodine adsorption. At low coverages, θ iodine = 0.016 ML, the temperature of the desorption rate maximum (T max ) is near 1035 K for desorption from Ni(100) whereas at higher coverages, θ iodine = 0.20 ML, the temperature decreases to 970 K. There is a similar decrease in T max with increasing coverage for iodine desorption from Ni(111). Analysis ofthe TPD data shows that iodine desorption follows first-order reaction kinetics with a coverage-dependent activation energy. We have modeled the coverage-dependent activation energy of desorption, E des (θ), in terms of a repulsive dipole-dipole interaction, E dip (θ), in the adsorbed layer, where E des (θ) = E des (θ = θ) - E dip (θ). The activation energy of desorption at low coverages, E des (θ = 0), was determined to be 249 and 214 kJ/mol from Ni(100) and Ni(111), respectively. The activation energy decreases by approximately 7% in the coverage range studied, θ = 0 - 0.20 ML. Simulated desorption curves agree well with the experimental data.

Monte Carlo simulations of temperature programmed desorption spectra

We introduce a Monte Carlo algorithm which simulates first-order temperature programmed desorption spectra using the correct connection between Monte Carlo simulation time and real time. The TPD spectra obtained from the Monte Carlo simulations are exactly the same as those calculated from the governing continuum differential equation for a noninteracting system. We discuss in some detail the effects of lateral interactions between adsorbates on the temperature programmed desorption spectra. We find that peak splitting of the temperature programmed desorption spectra characterizes an adsorbate configuration transition on the surface. Furthermore, we analyze in detail the behavior of the coverage-dependent activation energy and preexponential factor for the case of a repulsive nearest-neighbor interaction and find that kinetic compensation occurs in this case.

Thermal desorption from hydrogenated and oxygenated diamond (100) surfaces

Low energy electron diffraction (LEED) has been used to study the effects of atomic and molecular species of hydrogen and oxygen on the reconstructed C(100)-(2×1) surface. Thermal desorption spectroscopy was also used to study desorption products and kinetics from hydrogenated and oxygenated surfaces. Atomic hydrogen appears relatively inefficient at breaking C–C dimer bonds on the (100)-(2×1) surface. Atomic oxygen, in contrast, readily converts the surface from the 2×1 state to the 1×1 state. This process is reversible for a limited number of cycles before degradation of the surface obscures the 2×1 LEED pattern. Oxygen is thought to adsorb in one of two configurations, bridging carbon atoms on the surface, or double bonded to a single carbon atom on the surface. Thermal desorption of molecular hydrogen from hydrogenated C(100)-(2×1):H surfaces occurs at approximately 900 °C for a heating rate of 20 °C/s. Molecular hydrogen is the major desorption product and the desorption temperature appears to be coverage independent. Thus the desorption kinetics are most likely first order. Thermal desorption of carbon monoxide from oxygenated C(100)-(1×1):O surfaces occurs at approximately 600 °C for a heating rate of 20 °C/s. Carbon monoxide is the major product seen, with small quantities of carbon dioxide also observed. For increasing oxygen coverages, the desorption peak is observed to shift to lower temperatures. A peak shift to lower temperatures can be interpreted as either first order kinetics with a coverage dependent activation energy or second order kinetics. The reaction order is not known in this case, but from analysis of the peak shapes and from the fact that CO can desorb without prepairing, the data suggest that the reaction is first order.

A comparison of desorption rate parameters obtained by the variation of heating rate and the threshold temperature programmed desorption methods

Coverage dependent activation energies and preexponential factors for desorption of CO on Ni(110) have been obtained by the variation of heating rate and the threshold temperature programmed desorption (TTPD) methods. With the TTPD technique the initial coverage was varied by an adsorption and a desorption method. All three measurements yield nearly identical rate parameters at low coverages, but significant deviations are observed for higher coverages. In particular, abnormally low binding energies are observed in TTPD analysis of high coverages surfaces, where coverage is controlled by adsorption. These anamolous binding energies are attributed to desorption of CO which has not equilibrated to the tight binding sites on the surface. Better agreement is obtained between the variation of heating rate results and those obtained from TTPD analysis of surfaces where coverage is controlled by desorption. Remaining differences are considered to be a result of fundamental limitations in the TTPD technique as shown by comparison of the results with a calculated correction factor.

A comparison of desorption rate parameters obtained by the variation of heating rate and the threshold temperature programmed desorption methods

Coverage dependent activation energies and preexponential factors for desorption of CO on Ni(110) have been obtained by the variation of heating rate and the threshold temperature programmed desorption (TTPD) methods. With the TTPD technique the initial coverage was varied by an adsorption and a desorption method. All three measurements yield nearly identical rate parameters at low coverages, but significant deviations are observed for higher coverages. In particular, abnormally low binding energies are observed in TTPD analysis of high coverages surfaces, where coverage is controlled by adsorption. These anomalous binding energies are attributed to desorption of CO which has not equilibrated to the tight binding sites on the surface. Better agreement is obtained between the variation of heating rate results and those obtained from TTPD analysis of surface where coverage is controlled by desorption. Remaining differences are considered to be a result of fundamental limitations in the TTPD technique as shown by comparison of the results with a calculated correction factor.

Effect of the size of platinum particles on the chemisorption of oxygen

An unambiguous particle-size effect has been observed in the desorption of oxygen from a faujasite-embedded platinum dispersion with distinctly different and narrow particle-size distributions. A kinetic analysis of the desorption spectra revealed a relative increase in the activation energy for desorption by about 60 kJ mol–1 as the Pt particle size decreased from 5 to 1 nm. A coverage-dependent activation energy has to be assumed for a consistent interpretation of the experimental results.

Layer growth mechanism and dipole–dipole interactions of CH3Cl on Pd(100): An infrared and thermal desorption study

Fourier transform infrared spectroscopy (FTIRS) and temperature programmed desorption (TPD) have been used to study the layer growth mechanism of CH3Cl on a Pd(100) surface at 85 K. Methyl chloride adsorbs and desorbs in molecular form without decomposition. Three different adsorbed states are readily distinguishable by both methods. The chemisorbed state (first layer) saturates at Θ =0.5 coverage, with the characteristic C–H vibrations of 1011, 1330, 1426, 2927 cm−1. The desorption spectrum for this state suggests a coverage-dependent activation energy between 54.5 and 42 kJ/mol. Nearly the same amount of CH3Cl is bonded in the physisorbed state (second layer) with characteristic C–H vibrations at 1013, 1338, 1428, and 2925 cm−1. The activation energy of the desorption in this case is 40–35 kJ/mol. The condensation phase appears only after the completion of the first two layers and exhibits characteristic C–H vibrations at 1023, 1338/1346, 1444, and 2955 cm−1. In a model calculation {developed by Albano [J. Chem. Phys. 86, 1044 (1986)]} it is shown, that the intermolecular dipole–dipole interaction may explain correctly the coverage- dependent activation energy for desorption of methyl chloride.

Effect of Rh particle size on CO desorption from Rh/alumina model catalysts

The adsorption of CO on small Rh particles on oxidized Al(100) was studied using temperature programmed desorption (TPD) and Auger electron spectroscopy (AES). The desorption data for CO were obtained for two Rh Al 2O 3 samples as well as for Rh(111). The supported Rh model catalysts were prepared from thermal decomposition of [Rh(CO 2Cl] 2 on an oxidized Al(100) substrate. By varying the substrate temperature and the amount of deposited Rh, samples were prepared with average Rh particles sizes of 20 and 70 Å. TPD data from the 70 Å Rh particles were similar to that from Rh(111), with a major peak at 500 K and a shoulder at 400 K for a saturation CO exposure. TPD from the small particles was very different from Rh(111) and the larger particles, showing a single broad peak centered at 415 K. The data show a particle size effect for the desorption on CO from supported Rh. Redhead analysis of the data for first-order desorption gave an activation energy of 30 kcal/mol for all of the samples at low CO coverages. A more detailed analysis using peak widths and peak temperatures was also performed. These calculations gave a very low activation energy, 19.8 kcal/mol, and preexponential, 1×10 8 cm 2 s for the small particles. These very low values were interpreted to mean that multiple desorption states, mobile precursors, or coverage dependent activation energies were affecting the data from the small particles. Calculations of first-order desorption rates showed that desorption states different than those on Rh(111) are the dominant species on the small particles at high CO coverages.

The compensation effect in thermal desorption of adsorbate systems with lateral interactions

Within the Polanyi–Wigner model of thermal desorption, lateral interactions are revealed by a coverage-dependent activation energy of desorption E(θ) and a preexponential factor ν(θ). Several experiments have shown that ν and E often satisfy the ‘‘compensation effect’’ ln ν(θ)=E(θ)/RTc+const. In this contribution we introduce this compensation effect into the rate expression for thermal desorption and present calculated thermal desorption spectra assuming pairwise lateral interactions and first- or second-order desorption kinetics. The results emphasize that simplified thermal desorption spectroscopy analysis procedures based on peak maximum temperatures and peak widths only will almost always lead to incorrect results.

Monolayer and multilayer surface diffusion, growth mode and thermal stability of indium on W {100}

Surface diffusion parameters, the thin film growth mode, and thermal stability of indium deposited on a W {100} single crystal have been studied using LEED, TDS and scanning AES, the surface diffusion studies being of central importance as part of a programme to examine the effect of lateral adatom-adatom interactions on diffusion parameters. A correlation of LEED, AES and secondary electron yield (SEY) measurements during stepwise deposition of indium point to completion of a pseudomorphic indium monolayer before subsequent growth occurs. Following layers grow in a long-range disordered fashion. First layer growth initially takes place via random occupation of surface sites, with two-dimensional islands forming at higher coverages. TDS indicates that evaporation from a thick film occurs down to two monolayers (ML) over the relatively narrow temperature range 700 to 800 K, the desorption energy, 240 kJ mol −1, being close to the reported sublimation energy for indium. Desorption of the second and first monolayers occurs between 800 and 1200 K, indicating a strongly coverage-dependent activation energy for desorption. Up to a monolayer coverage both the activation energy for diffusion ( E m) and the diffusivity ( D 0) are strongly coverage-dependent, indicating net repulsive lateral adatom-adatom interactions (for θ = 0.25 ML, E m∗ = 106 kJ mol −1 while for θ = 0.75 ML, E m∗ = 64 kJ mol −1) . The activation energy for diffusion is roughly a constant fraction of that for desorption (≈ 30%) in the monolayer region. Second and subsequent layers of indium diffused much more rapidly than the first; in this case E m∗ and D 0∗ are insensitive to coverage, and the diffusion energy barrier is only 10% of the desorption energy.