Diffusion-limited Regime Research Articles

In-phase step wandering on vicinal Si(1 1 1) surfaces

The step structure transition between a regular step and a bunched step on vicinal Si(1 1 1) surfaces induced by DC is studied by the kinetic Monte Carlo simulation in a terrace-adatom-step-kink (TASK) model. In the TASK model, effective force due to DC is taken into account explicitly on the mass transport of Si adatoms. In the diffusion-limited regime corresponding to the experimental temperature range II, step bunching is induced by step-up force and in-phase wandering of a regular step is formed by step-down force. The in-phase wandering of a regular step is formed by nucleation growth mode and the amplitude of wandering grows with time in proportion to t . The period of in-phase wandering decreases as the effective force increases, consistent with the recent experimental results.

Surface Concentration of Defects at Grain Boundaries in Sintered Alumina Determined by Positron Annihilation Lifetime Spectroscopy

Sintered alumina samples of grain diameters spanning from 1.2 to 4.5 μm have been investigated by positron annihilation lifetime spectroscopy. One series of samples was produced from material containing about 150 ppm impurities (mainly SiO 2 ). The second one was made from material having about 2700 ppm of various elements (SiO 2 , MgO, CaO). Two models of positron trapping at grain boundaries are compared: The first one relates to the diffusion-limited regime; and the other one - to the transition-limited regime of trapping. As a result the relative change of surface concentration of defects at grain boundaries is determined. Additionally, the positron diffusion constant in bulk alumina at room temperature, D + = 0.36 ′ 10 cm 2 /s, is estimated.

Colloid Polymer Interactions and Aggregation in Aqueous Mixtures of Polystyrene Latex, Sodium Dodecyl Sulfate, and a Hydrophobically Modified Polymer: A Dynamic Light Scattering Study

The kinetics of clusters formed in the flocculation process of polystyrene latex particles (PSL) in the presence of hydrophobically modified ethyl(hydroxyethyl)cellulose (HM-EHEC) and sodium dodecyl sulfate (SDS) in the concentration interval of 2−4 mmolal have been investigated with the aid of dynamic light scattering measurements at different temperatures. For this system (HM-EHEC/SDS/PSL) we observe an intriguing time-dependent cluster growth over a restricted (2−4 mmolal) surfactant concentration range. The rate of flocculation and the aggregation mechanism are affected by both the level of surfactant addition and temperature. The value of the homogeneity exponent λ, used to characterize the aggregation mechanism, depends on temperature and concentration of surfactant. Flocculation behaviors between the reaction-limited and diffusion-limited regimes are observed. The picture that emerges is that polymer−surfactant complexes are adsorbed onto the PSL particles in form of fuzzy layers with hydrophobic s...

The generation of concentration gradients using electroosmotic flow in micro reactors allowing stereoselective chemical synthesis.

The stereoselective control of chemical reactions has been achieved by applying electrical fields in a micro reactor generating controlled concentration gradients of the reagent streams. The chemistry based upon well-established Wittig synthesis was carried out in a micro reactor device fabricated in borosilicate glass using photolithographic and wet etching techniques. The selectivity of the cis (Z) to trans (E) isomeric ratio in the product synthesised was controlled by varying the applied voltages to the reagent reservoirs within the micro reactor. This subsequently altered the relative reagent concentrations within the device resulting in Z/E ratios in the range 0.57-5.21. By comparison, a traditional batch method based on the same reaction length, concentration, solvent and stoichiometry (i.e., 1.0:1.5:1.0 reagent ratios) gave a Z/E in the range 2.8-3.0. However, when the stoichiometric ratios were varied up to ten times as much, the Z/E ratios varied in accordance to the micro reactor i.e., when the aldehyde is in excess, the Z isomer predominates whereas when the aldehyde is in low concentrations, the E isomer is the more favourable form. Thus indicating that localised concentration gradients generated by careful flow control due to the diffusion limited non-turbulent mixing regime within a micro reactor, leads to the observed stereo selectivity for the cis and trans isomers.

Novel Transition Mechanism of Surface Electromigration Induced Step Structure on Vicinal Si(111) Surfaces

The step structure transition between a regular step and a bunched step structure on Si(111) induced by DC is studied, using a terrace-adatom-step-kink (TASK) model in which the mass transport of Si adatoms is taken into account explicitly. The step structure transformation dynamics were calculated by the dynamical Monte Carlo simulation in the TASK model, and the adatom flux was analyzed by the generalized Burton-Cabrela-Frank (BCF) theory. The step bunching was generated by the step-down directed force in capture-limited regime and by the step-up directed force in diffusion-limited regime. For a regular step structure in the diffusion-limited regime, in-phase wandering of steps was induced by the step-down force.

Rate-limiting steps during nitrogen incorporation in furnace-grown silicon oxynitrides: effects on wafer-to-wafer uniformity

Incorporation of nitrogen yields better electrical properties to silicon oxynitrides as compared to oxides. But the amount and profile of nitrogen in these films need to be carefully monitored and controlled. This study focuses on a fundamental understanding of film properties uniformity in the silicon oxynitridation process along the furnace length. Gas-phase N 2O decomposition is monitored using real-time mass spectrometry. Secondary ion mass spectrometry is used to obtain the O and N depth profiles in silicon oxynitrides fabricated at different loading positions in the furnace. Films are grown in N 2O starting with both bare Si and a pre-grown oxide. It is found that at 900°C and 1 atm, the amount and concentration profile of N in the oxynitride depend strongly upon gas-phase composition from the entrance to the exit of the furnace. Furthermore, at low N 2O gas-phase decomposition, N incorporation is seen to be limited by the reaction at the substrate/oxynitride interface. At higher N 2O gas-phase decomposition, the incorporation of N shifts to the solid-phase diffusion-limited regime. Effects of these findings on uniformity of N concentration profiles from wafer-to-wafer are of particular importance in designing furnaces for silicon oxynitridation and in determining wafer loading positions for uniform film properties throughout such systems.

A continuum model for non-dense growth

We present a continuum model for diffusion-limited non-dense growth. Our approach leads to a set of two coupled partial differential equations which describe the time evolution of the (spherically) averaged aggregation density and concentration of growth units in the liquid phase. For time-independent parameters the solution of the equations yields a constant (non-fractal) aggregation density. The model gives a phenomenological description of non-fractal unstable growth, e.g. non-fractal spherulitic growth, on a macroscopic scale in terms of a minimal number of parameters and can be used in combination with experimental data, such as the front velocity and the width of the growth front, for both a qualitative and quantitative interpretation of the growth process. The analytical solution of the equations in the diffusion-limited regime leads to simple relations involving the aggregation density and the velocity and width of the growth front. This allows for an easy quantitative analysis of experimental data.

An analysis of the reaction-diffusion mechanism governing the chlorination process of poly(vinyl chloride)

Chlorinated poly(vinyl chloride) (CPVC) obtained through a dry chlorination of PVC films or grains can show a heterogeneous repartition of its chlorine atoms because the reaction process is limited by the mass transfer of the chlorine gas in the material. In order to describe the evolution of such a system, a set of coupled equations is derived where only two dimensionless constants have to be determined: KS, which depends on the solubility of the chlorine gas in the PVC, and KT, the ratio between the diffusion and the reaction characteristic times. The kinetics of chlorination obtained for the different regimes matches the available experimental data, and the corresponding concentration profiles for the chlorinated PVC chains are displayed to demonstrate how a heterogeneous chlorination can arise from this dual process. In particular, a sharp interface appears in the diffusion-limited regime that separates the chlorinated region from an unchlorinated core and is shown to progress deeper into the film with the square root of time. To a larger extent, this analysis shows how heterogeneity of reaction and nonlinear effects can arise from a coupling between a diffusive phenomenon and a reactive phenomenon. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3201–3209, 2000

Evolution of the morphological structure of a two-dimensional cluster obtained with a linear microparticle trajectory in the diffusion-limited aggregation regime

Two-dimensional diffusion-limited aggregation of spherical microparticles was achieved experimentally as a result of their rectilinear motion (“ballistic aggregation”) at a “water-air” interface. A percolation cluster was obtained and the evolution of its morphological parameters was studied under compression. A change in the orientation of the cluster pores and a nonlinear coalescence and breakup process were observed. A fabrication technology is proposed for monolayer films similar to the Langmuir method.

On the generalized Kramers problem with exponential memory friction

The time-dependent transmission coefficient for the generalized Kramers problem with exponential memory friction has recently been calculated by Kohen and Tannor [D. Kohen, D.J. Tannor, J. Chem. Phys. 103 (1995) 6013] using a procedure based on the method of reactive flux and the phase space distribution function. Their analysis is restricted to the high friction regime or diffusion-limited regime. We recently developed a complementary theory for the low-friction energy-diffusion-limited regime in the Markovian limit [J.M. Sancho, A.H. Romero, K. Lindenberg, J. Chem. Phys. 109 (1998) 9888]. Here, we generalize our method to the case of an exponential dissipative memory kernel. We test our results, as well as those of Kohen and Tannor, against numerical simulations.

Crossover in the Kinetic Growth Process of Porphyrin Aggregation

By combining ultraviolet and visible absorption and elastic light scattering measurements we have studied the salt-induced aggregation kinetics of the porphyrin $t\ensuremath{-}{H}_{2}{P}_{\mathrm{agg}}$ in aqueous solution. The temporal evolution of the spectra, directly related to the time dependence of the monomer concentration and the mean cluster size, shows unambiguously the presence of an early stage driven by a reaction-limited aggregation. After a variable time (dependent on the salt concentration) a crossover to a diffusion-limited aggregation regime is observed. Elastic light scattering data confirm such a result.

Investigation of the Effects of Controlled Periodic Illumination on the Oxidation of Gaseous Trichloroethylene Using a Thin Film of TiO2

Enhancement of gas-phase photocatalytic oxidation by controlled periodic illumination (CPI) was investigated. The oxidation of trichloroethylene (TCE) was studied in a versatile reactor designed to provide periodic illumination of the TiO2 films. The reactor was operated in two different geometric configurations, tubular and annular. Multiple flow regimes were investigated: kinetic- and diffusion-limited. No enhancement on the rate or the selectivity of TCE oxidation was observed at any of the CPI conditions investigated in the kinetically limited flow regime. The ratio of TCE oxidized to dichloroacetyl chloride (DCAC) produced was 0.59 at all light and dark times investigated for kinetically limited operation. In diffusion-limited regimes, CPI increased the rate of oxidation and decreased the relative amount of DCAC in the product stream. In the kinetic-limited regimes the apparent quantum yield was constant at around 150%; however, in the diffusion-limited regimes the apparent quantum yield almost doub...

Monte-Carlo simulation of linear sweep voltammograms during redox switching of conducting polymers

We propose a derived approach from the model of the moving front, that includes ionic transport in the redox process of conducting polymers. The moving front is the border between the insulating and conducting zones, where oxidation takes place. In our approach, the conversion of a polymer site from reduced to oxidised state requires simultaneously an electron transfer with the electrode and the presence of a dopant ion. When both conditions are fulfilled, oxidation occurs: the dopant ion remains trapped and the front is shifted toward the neighbour site. Ionic motion inside the film is assumed to be one-dimensional diffusion, and is simulated by Monte-Carlo. Simulated voltammograms are thus obtained and analysed as a function of scan rate. A diffusion limited regime was actually observed at low scan rate, but the high scan rate behaviour is somewhat different from experimental profiles. This tends to show the necessity to include a migration component in the dopant transport, in order to improve the description of the redox process of conducting polymers.

Flocculation of Hematite with Polyacrylic Acid: Fractal Structures in the Reaction- and Diffusion-Limited Aggregation Regimes

The structure of hematite aggregates in the presence of fairly monodisperse polyacrylic acid (PAA) with two different molecular weights (Mw= 1.36 × 106,Mw/Mn= 1.53;Mw= 3.69 × 104,Mw/Mn= 1.60) was studied using static light scattering (SLS). The fractal dimensions were calculated from the scattering exponents, after taking into account the finite size of aggregates, using exponential and Gaussian cutoff functions. Three flocculation regimes, namely, pre-DLA, DLA (diffusion-limited aggregation), and post-DLA, were defined based on the polymer concentration. In the DLA regime, fractal dimension values,Df= 1.84 ± 0.02 and 1.73 ± 0.02, were obtained using exponential and Gaussian cutoff functions, respectively. A fractal dimension of approximately 2.0 was found, as expected, in the pre-DLA regime (at PAA concentrations lower than the optimal dosage for a DLA regime) where the flocculation rate was reaction limited. In contrast, in the post-DLA regime, the flocculation was slow but the structure of aggregates was as tenuous as in the DLA regime with a fractal dimensionDf≈ 1.8. Moreover, for all three regimes, theDfvalues were independent of the molecular weights of PAA. The lower fractal dimension in post-DLA was probably due to the increased concentration of polymer chains between adjacent particles in aggregates. The steric hindrance favored tip-to-tip aggregation, leading to a more tenuous structure.

Low-pressure organometallic vapor phase epitaxy of coherent InGaAsP/InP and InGaAsP/InAsP multilayers on InP(001)

InGaAsP/InP and InGaAsP/InAsP multilayers were grown on InP(001) by low-pressure organometallic vapor phase epitaxy. Large growth rates of ≈0.4–0.6 nm s−1 and an increased element-V overpressure were used to limit the morphological evolution of the strained layers during growth and to compensate for the relatively high temperatures (≈630 °C) necessary for vapor phase epitaxy in a diffusion-limited regime. High-resolution x-ray diffraction and reciprocal lattice mapping analyses indicate fully strained multilayers of high crystalline quality. This structural information, combined with room-temperature photoluminescence (PL) measurements, allows us to determine accurately the thickness and the composition of the layers. Well-resolved excitonic transitions between the heavy- and light-hole valence bands and the conduction band are visible in the low-temperature optical absorption spectra for compressive InGaAsP/InP multilayers. The PL spectra for compressive InGaAsP/InP structures show sharp and intense transitions between the first confined levels in the conduction and the heavy-hole bands. The PL peaks for InGaAsP/InAsP heterostructures are slightly broader than for InGaAsP/InP multilayers due to the more complex (quaternary-ternary) interface but remain sharp and intense.

Derivation of an analytical model to calculate junction depth in HgCdTe photodiodes

An enhanced analytical model is derived to calculate the junction depth and Hg interstitial profile during n-on-p junction formation in vacancy-doped HgCdTe. The enhanced model expands on a simpler model by accounting for the Hg interstitials in the p-type, vacancy-rich region. The model calculates junction depth during both the initial, reaction-limited regime of junction formation and the diffusion-limited regime. It also calculates junction depth under conditions when the abrupt junction approximation of the simpler model fails. The enhanced model can be used to determine the limits of the annealing conditions and times for which the junction depth calculated analytically is valid. The decay length of interstitials into the p-type region estimated analytically places an upper bound on the grid spacing needed to accurately resolve the junction in a numerical simulation.

Evidence for a crossover region in the aggregation of PEO-coated polystyrene particle suspensions

The crossover region in the salt-induced aggregation processes occurring in polystyrene latex suspensions has been investigated by means of dynamic light scattering measurements. The possible existence of a region between reaction-limited and diffusion-limited regimes has been suggested in the last few years on the basis of various experiments and computer simulations, but no definitive agreement has been reached, since reaction-limited aggregation can be viewed as the initial regime crossing over towards diffusion-limited aggregation after a certain time and, in any case, in the long time limit. In the present work we have varied the overall interaction potential between particle monomers and thus the corresponding aggregation regime by varying the amount of adsorbed polymer [poly(ethylene oxide) (PEO), in this case] on the particle surface. The aggregation is induced by adding an appropriate simple salt (NaCl, 0.5 M) to the PEO-coated latex particles, at different polymer surface coverages, giving rise to different aggregation regimes, from fast aggregation in the absence of PEO, to slow aggregation at moderate PEO concentration, up to complete stabilization of the colloidal suspension at higher polymer concentration. In the present case, deviation from a reaction-limited regime extends for a period of time long enough to allow accurate analysis of the data. Comparison of the experimental data with the prediction of the Smoluchowski equation, modified by Tartaglia etal. (Phys. Rev. E, 1994, 50, 1649) to take into account the intermediate regime, is quite satisfactory and values of the parameters of the interaction potential between monomers have been evaluated. The present analysis gives support to the suggestion that slow, reaction-limited cluster aggregation is only a transient regime of the early stage of aggregation.

On the adsorbates formed during the platinum catalyzed (electro)oxidation of ethanol, 1,2-ethanediol and methyl-α- d-glucopyranoside at high pH

The irreversible adsorbates of ethanol, 1,2-ethanediol and methyl-α- d-glucopyranoside (MGP) have been studied with FTIRS and cyclic voltammetry. Both ethanol and 1,2-ethanediol display full CC(OH) dissociative adsorption and dehydrogenation. In the case of ethanol adsorbed CO and C are formed of which the latter partially oxidizes further to adsorbed CO. In the case of 1,2-ethanediol CO is formed as the only adsorbate. The adsorption of MGP occurs similarly to the small alcohols; it decarbonylates to form adsorbed CO and a small fraction of C adatoms. It is shown that the catalytic alcohol oxidation can be regarded as an electrochemical process that consists of two independently acting half-reactions that determine the open circuit potential (o.c.p.). The roughness of the surface greatly affects the o.c.p. measured during catalytic alcohol oxidation; smooth platinum leads to high o.c.p. values and platinized platinum leads to low o.c.p. values. These low and high open circuit potentials correspond respectively to a diffusion limited regime where diffusion of oxygen is rate limiting and a kinetic regime. The reaction rate is considerably lower in the kinetic regime than in the diffusion limited regime. The surface is highly covered with adsorbed oxygen or hydroxyl during oxidation of ethanol and MGP in the kinetic regime, whereas the surface is devoid of adsorbed oxygen in the diffusion limited regime and is instead covered with a high steady state amount of CO and C species. The deactivation of the catalyst is found to occur both in the diffusion limited and in the kinetic regime of the MGP oxidation. Whereas in the diffusion limited regime, the deactivation is caused by a slow accumulation of carbonaceous residue, and in the kinetic regime, changes in the properties of adsorbed oxygen cause deactivation.

Molecular dynamics simulations of multilayer homoepitaxial thin film growth in the diffusion-limited regime

Molecular dynamics (MD) simulations permit multiple-layer thin film growth to be studied in detail, using reliable interatomic potentials for fcc metals from corrected effective medium theory. Results are presented for the homoepitaxial deposition of 50 monolayers on Pd(001) and Cu(001) near 0 K. We find that atoms in overhang sites are stable due to the absence of diffusion at very low temperature and the short time scale of MD simulations. This stability leads to interesting features in the film which may be observable in STM or other experiments near 0 K. The growth behavior of the thin film changes after deposition of the first 5–10 monolayers: more overhanging atoms are present, the surface is rougher, and multiple-layer events begin to occur. The formation of large voids in the film and the mechanism of multi-atom rearrangement events which decrease the surface roughness are discussed. Several simulation parameters have been varied (e.g. deposition rate, system size, random aiming points of the deposited atoms) to study their effects on the results. There is no clear difference between Pd and Cu thin film growth near 0 K.

On the Absorption of Isobutene and trans-2-Butene in Sulfuric Acid Solutions

In reactions in which alkenes react in the presence of homogeneous Bronstedt acid catalysts, the protonation step is rate determining. Existing reaction rate correlations for protonation of butenes in sulfuric acid solutions are not consistent and limited to sulfuric acid concentrations below 80 wt %. The absorption of isobutene and trans-2-butene in sulfuric acid solutions was studied in the range of 30-98 wt %. Reevaluation of literature data, completed with new data from this study, revealed a set of kinetic rate data which coincide satisfactorily. Experiments and modeling of the absorption experiments showed a strong dependence of the reaction rate on local mixture composition through the activity coefficient of the protonating agent. This strong dependence prevents the occurrence of a diffusion-limited absorption regime. Application of the usually used criteria for operating in the kinetic regime can lead to erroneous results.