Frenkel Equation Research Articles

Coadsorption of Dioxygen and Carbon Monoxide on a Mg(100) Surface

The activation of carbon monoxide by oxygen on Mg(100) surface has been investigated by X-ray photoelectron spectroscopy (XPS). Carbon monoxide is only weakly adsorbed (dispersion-type forces) on a magnesium surface. The XPS result has shown that the dissociation of carbon monoxide leading to the formation of a metastable surface carbonate species occurs through the participation of an oxygen surface O¯(s). A stepwise mechanism involving a weakly adsorbed CO molecule present at very low surface coverage (<0.1) undergoing surface diffusion and interaction with the transient oxygen adatoms is suggested. The Frenkel equation has been used to estimate the mean residence time of CO molecule on the surface, and the residence time of a molecule on a specific surface site has also been estimated.

Influence of electrostatic fields on binding energy (NO on Rh)

Pulsed field desorption mass spectrometry (PFDMS) has been applied to measure binding energies of adsorbates on metal surfaces in the presence of a high electric field. The electric field modifies the charge state of adsorbed particles, i.e. it acts in a manner similar to work function changes or alkali coadsorption. Furthermore, it modifies the binding energy and possibly even the orbital configuration of the adsorbate. Recent progress in the theoretical treatment of the chemisorption of small molecules on metal clusters has made it possible to calculate electrostatic field influences on adsorbates. Comparison between experiment and quantum chemical calculations becomes possible. For this purpose, the adsorption/thermal desorption equilibrium of NO on Rh(111) is observed as a function of temperature (300–630 K) and field strength (0–3 V/nm). The PFDMS apparatus is merely used as a tool to measure the equilibrium coverage. The data treatment is performed according to Frenkel's equation so that the binding energy is obtained from an Arrhenius plot. In this way, the influence of the electric field on the kinetic energy of the impinging particles, as well as the diffusion from the shank towards the apex can be eliminated.

Mechanism of sintering between polypropylene beads

Using experimental results obtained by hot-stage light microscopy, the sintering behaviour of off-reactor spherical grades of polypropylene and poly(methyl methacrylate) were considered. Sintering rates were found to be strongly influenced by initial particle size, melt temperature and viscosity and could be modelled using the Frenkel equation. Examination of the microstructure between sintered polypropylene particles revealed a distinct transcrystalline zone, which was relatively insensitive to sintering temperature and cooling rate.

Scattering experiments with silver on NaCl, KBr, amorphous carbon and polycrystalline tungsten

Experimental results for the nucleation and growth of thin films from the vapour phase are commonly interpreted on the basis of a kinetic nucleation model. It is assumed that the adatoms form a quasi two-dimensional gas on the substrate surface and that nucleation takes place by collisions of single atoms. During the initial stages, comdensation is incomplete and a large fraction of adatoms may re-evaporate before being trapped by other adatoms or clusters. The mean residence time is determined by the adatom adsorption energy E a and the surface vibration frequency τ 0 −1 via the Frenkel equation. We investigated the residence times of silver atoms on various substrates by time-of-flight spectroscopy. In addition, the angular and velocity distributions of the scattered atoms were examined. For silver on NaCl and on KBr the residence time was below the detection limit of 40 μs for temperatures above 25 °C, leading to estimated adsorption energies below 0.6 eV and 0.46 eV respectively. Within the error limits, these data are consistent with results from nucleation experiments. For silver on amorphous carbon, two different binding states were indicated: a dominant state with E a=1.3 eV and a less populated state with E a=1.8 eV. For silver on polycrystalline tungsten, at a somewhat lowered detection limit, residence times in the range from 30 μs to 0.3 s were measured for temperatures between 1450 and 900 °C, resulting in E a=2.9 eV and τ 0=7.9×10 −14 s, in close agreement with data from other researchers. In all cases cosine distributions of the scattered atoms were found. This indicates, together with measured velocity distributions, almost complete accommodation of the adatoms.

ADSORPTION OF NO ON Pt STUDIED BY PULSED FIELD DESORPTION MASS SPECTROMETRY

Pulsed Field Desorption Mass Spectrometry (PFDMS) has been employed for studying thermal desorption kinetics of adsorbates. The adsorption of NO on a (100) oriented Pt field emitter has been studied. No+-ion intentities have been measured as a function of adsorption time. An analysis, using Frenkel's equation, results in the activation energy Ed = 139kJ/mol and the preexponential τ0=3,8x10-15s.

Intermolecular interactions and viscosity of petroleum oils

The temperature coefficient of viscosities of petroleum oils increases with decreasing temperature. This paper surveys attempts to explain the temperature dependence of oil viscosity, and in particular analyze the data to show that at temperatures above 150/sup 0/ oils and oil hydrocarbons follow Frenkel's equation (as specified) in the first approximation. The magnitude of the viscosity, the contribution of associates with polymeric additives to viscosity, and the concept that oils are supercooled liquids are also studied. The relationships among the parameters of association of such complex mixtures as petroleum oils have not been studied adequately.

Glass formation through hydrolysis of Si(OC 2H 5) 4 with NH 4OH and HCl solution

Monolithic silica glass was obtained by heating the gels prepared by hydrolyzing Si(OC 2H 5) 4 with NH 4OH and HCl solution. The effect of the condition of hydrolysis of Si(OC 2H 5) 4 on glass formation was examined by measuring the bulk density, the infrared spectra and the thermal shrinkage of the gel on heating. The gel prepared by hydrolysis with NH 4OH solution consisted of numerous spherical particles, the bulk density being about 0.8. This gel abruptly shrank at about 1050°C, being converted to the pore free material similar to fused silica. The conversion of the gel to glass followed the sintering model in which the viscous flow controlled the sintering process. The viscosity and the activation energy for viscous flow were calculated on the basis of the Frenkel equation. On the other hand, the spherical particles were not observed in the gel prepared by hydrolysis with HCl solution. The bulk density of the gel was about 1.8. This gel was converted to glass at about 700°C, which was lower than the temperature of glass formation for the gel obtained by hydrolysis with NH 4OH solution.

Mean residence time of potassium ions on tungsten as measured with reference to ionization efficiency

The mean residence time, τ i, of potassium ions on “clean” and oxygenated tungsten has been measured, together with the ionization efficiency, as a function of surface temperature T by using incident K beams of low intensity (10 9–10 12 atoms cm −2 s −1). For T higher than ~900 K the observed τ i followed Frenkel's equation τ i = τ i 0 exp ( Q i kT ) as usual and the agreement of the ionic desorption energy Q i and of the pre-exponential factor τ i 0 with the corresponding values of previous experiments was quite satisfactory. Below 830 ~ 910 K, where a steep drop of ionization efficiency began to be noticeable, Arrhenius plots of τ i deviated considerably from linearity. The apparent increment of the desorption energy was shown to be nearly equal to the decrement of thermionic work function of tungsten as obtained from the ionization efficiency and Saha-Langmuir equation. The increase of surface coverage by potassium was accordingly taken as the main cause of the departure of Arrhenius plots from linearity. Under certain conditions of incident beam intensity and surface temperature τ i was observed to make an abrupt change from a higher to a lower value — a difference expressed as 100–140 meV in terms of the difference in ionic desorption energy. This peculiar phenomenon was attributed to the phase change of adsorbed potassium on tungsten.

Analysis of adsorbate-substrate configuration by admolecule-probe field emission microscopy

By means of field electron emission microscopy with Faraday collector and magnetic deflection the emission current fluctuations between two or more levels caused by single Cu-phthalocyanine admolecules have been recorded. Relative abundance distribution functions of the times of sojourn in distinct adsorption states are given. From measurements at various temperatures in case of stationary fluctuations Arrhenius plots of the mean time of sojourn were obtained. They yield the energy differences E i between trough and saddle positions of single admolecules as well as the preexponential factors A i and the entropy differences Δ S i, respectively, according to the Frenkel equation τ i = A i exp( E i /kT ) = ( h kT ) exp(− ΔS i k ) exp ( E i kT ) . The average values and standard deviations of all measurements are E i = 0.22 eV, σ E i = = 0.11 eV, and log A i = −6.0, σ log A i = 1.6. The use of Cu-phthalocyanine as a molecular probe to investigate and characterize the adsorbate-substrate configuration, is discussed.

The Study of Mean Residence Time of Alkali Metal on Tungsten Surface by Means of Molecular Beam-An Attempt of Analysis of Experimental Values

Mean residence time of potassium atoms on polycrystalline tungsten filament surface has been studied. Beam pulse shorter than those of the measurements reported previously were used to improve time resolution. In order to measure the delay time of desorbed ions with an acceptable signal-to-noise ratio, sampling method was employed. From the dynamics of desorption of potassium atoms and ions, taking into consideration the shape of the gate function which has seldom been considered, the following formulas are obtained : G (p) /F (p) = (K+1/K) τ+p+ (1/β'+1) =θp+1/β : G (p) =α∫ ∞ 0 e-ptg (t) dt, F (p) =∫ ∞ 0 e-pt f (t) dt, where p is a parameter of Laplace transformation. G (t) and f (t) are gate function and intensity function of desorbed ions, respectively. The quantity a can be determined from the experiment. K is an equilibrium constant between the transient adatoms and adions : M (s) _??_ M+ (s) + e-β' is the degree of ionization and is considered to be constant under the same surface condition and temperature. A relation τ=βθ is introduced to make a comparison with the values in published papers. Scheer et al. estimated β by Saha-Langmuir equation using value of the work function of metals (Φ+) and the ionization potential (I) of alkali atoms, whereas β can be determined directly from experimental data. The temperature dependence of residence time of adions will be expressed by Frenkel equation of the formτ = τ0exp (l/kT).From this equation desorption energy (l) and the corresponding pre-exponential factor (τ0) are found to be 1.85 eV and 2.2×10-12 sec, respectively. These values are in good agreement with those of potassium ions on contaminated tungsten surface published by other authors.

The pre-exponential factor in the desorption from glass of ionically pumped noble gases

A discussion regarding the value of τ 0 the pre-exponential factor in the Frenkel equation for the desorption from glass of ionically pumped noble gases is presented. Starting from an experimental desorption transient obtained by Konjević et al 1 by heating the glass according to a linear time schedule, the initial populations of a wide activation energy spectrum (34 values between 20 and 53 Kcallmole) were calculated, assuming τ 0=10 −13 seconds. Simulating on this spectrum the different previous heat treatments performed by the above quoted authors, there appeared a strong disagreement with their results. A relatively good agreement was obtained by assigning to the individual energies different values of τ 0 many orders of magnitude greater than 10 −13 seconds. This experimental fact confirms experimental results previously obtained by the authors.

Sur la détermination des chaleurs et des entropies d'adsorption par chromatographie d'élution gaz-solide

The two possible ways of deriving the relation between the retention volume of a gaseous sample in a Chromatographie column filled with a solid adsorbent and the thermodynamic quantities Δ H 0 and Δ S 0, of the adsorption equilibrium are critically reviewed. It is shown that the thermodynamic and the kinetic derivations do not lead to exactly the same relation, but the Frenkel equation, written more explicitly than is usually done, allows complete agreement between the two view-points. The significance of Δ S 0, the standard entropy of adsorption, is then stressed and its value is shown to depend tightly upon the choice of units which indirectly determine the standard states; these considerations are applied to a previous determination of Δ S 0 in the case of the adsorption of benzene on graphite.

Steady State Film Growth on Passive Iron in Neutral Solutions

AbstractThe steady state growth kinetics of the oxide film on passive iron in neutral solutions was studied by galvanostatic and potentiostatic techniques. There is a good correlation of results obtained at constant c. d. and at constant potential. The experimental expressions relating to potential, layer thickness and oxidation rate make it clear that the steady state kinetic follows the classical Frenkel equation. The constants appearing in this equation were determined and compared with existing data. The temperature dependences of the passive film conductivity and of the field coefficient are also in accord with the mechanism of field assisted ionic transport over a potential barrier, as expressed by the classical rate equation.

Adsorptionskinetik: II. Verweilzeiten adsorbierter edelgasatome an pyrexglas-oberflächen

Adsorption isotherms for Ar, Kr and Xe have been obtained from a study of transient molecular flow of these gases through a Pyrex glass capillary at temperatures in the vicinity of the relevant boiling points. At surface coverages θ between 10 −3 and 10 −1 a Dubinin-Radushkevich equation is obeyed. From the slope of the adsorption isotherms residence times of the adsorbed species have been obtained and are discussed on the basis of the Frenkel equation τ = τ 0 exp ( E ∗/ RT). The finding that τ 0 is significantly larger than the usual time of vibration of adsorbed molecules is explained by increasing surface mobility of the molecules with rising surface coverage. Entropy considerations are in agreement with this concept.

Mean Residence Times of Alkali Ions on Polycrystalline Wolfram Surfaces as Studied with a Pulsed‐Molecular‐Beam Mass Spectrometer

AbstractThe mean residence time τi of alkali ions on both atomically clean and strongly gas‐covered surfaces of polycrystalline wolfram has been studied with a recently developed technique of combining modulated atomic and/or molecular beams from vapors of alkali metals and alkali halides with phase‐sensitive mass‐spectrometic detection. The experimental arrangement allows the direct determination of the mean residence time τi of an ion on a metal surface under extremely clean surface conditions and at very small incident beam intensities (109− 1012 particles cm.−2 sec.−1) to avoid an influence of surface coverage by the beam material itself. In addition, it allows mass‐spectrometric determination of the effect of the composition of the incident beam on τi. The dependence of τi on the surface temperature T is given by Frenkel's equation τi = τ exp (Ei/kT), where Ei is the ion desorption energy. With alkali chloride sources, the values tabulated below were determined over ranges within the temperature region 1100 °K &lt; T &lt; 1700 °K. The atomic and molecular composition of the beam significantly affected τi, e.g., for an incident beam of neutral sodium atoms, τ = (0.85 ± 0.05) × 10−13 sec. Ei = 2.69 ± 0.03 eV for Na+ on clean W. magnified imageThe present experiments are being extended to determine the mean residence time τα of neutral alkali atoms on wolfram surfaces. Then with the aid of the more precisely determined values of Ei and Eα and with additional knowledge of the effective work function of the surface and of the ionization energy of the incident particle, it will be possible to decide such an important question as whether or not the surface states of adsorbed atoms differ from those for ions.

Sintering of synthetic latex particles

The sintering of synthetic latex particles takes place by the viscous flow of the polymer, the surface tension of the plastic furnishing the necessary shearing stress. The flow of the polymer under the influence of surface tension follows Frenkel's equation θ = 3γt 2πƞγ . The particle size distribution in the latex provided a method of experimentally observing the relationship between θ and r. η was varied by changing the temperature and by addition of plasticizer. The tensile strength of the material under these conditions was used as an indication of the voids in the material, or θ. Over a limited plasticizer range, the tensile strength increased with increasing plasticizer concentration. The conclusions drawn from observations of the sintering of pairs of particles and individual particles were shown to apply in a qualitative manner to the formation of films.