Surface Diffusion Flux Research Articles

Can Nanowires Coalesce?

Coalescence of nanowires and other three-dimensional structures into continuous film is desirable for growing low-dislocation-density III-nitride and III-V materials on lattice-mismatched substrates; this is also interesting from a fundamental viewpoint. Here, we develop a growth model for vertical nanowires which, under rather general assumptions on the solid-like coalescence process within the Kolmogorov crystallization theory, results in a morphological diagram for the asymptotic coverage of a substrate surface. The coverage is presented as a function of two variables: the material collection efficiency on the top nanowire facet a and the normalized surface diffusion flux of adatoms from the NW sidewalls b. The full coalescence of nanowires is possible only when a=1, regardless of b. At a>1, which often holds for vapor-liquid-solid growth with a catalyst droplet, nanowires can only partly merge but never coalesce into continuous film. In vapor phase epitaxy techniques, the NWs can partly merge but never fully coalesce, while in the directional molecular beam epitaxy the NWs can fully coalesce for small enough contact angles of their droplets corresponding to a=1. The growth kinetics of nanowires and evolution of the coverage in the pre-coalescence stage is also considered. These results can be used for predicting and controlling the degree of surface coverage by nanowires and three-dimensional islands by tuning the surface density, droplet size, adatoms diffusivity, and geometry of the initial structures in the vapor-liquid-solid, selective area, or self-induced growth by different epitaxy techniques.

Sulfur-enhanced dynamics of coinage metal(111) surfaces: Step edges versus terraces as locations for metal-sulfur complex formation

The propensity of trace amounts of sulfur adsorbed on coinage metal(111) surfaces to dramatically enhance surface dynamics has been demonstrated by STM observations of accelerated 2D island decay for Cu and Ag. It is generally accepted that this enhancement is due to the formation of adsorbed metal-sulfur complexes, which facilitate surface mass transport of the metal. These complexes were originally proposed to form on terraces following the extraction of metal atoms from step edges and subsequent combination with sulfur on the terraces. However, even when thermodynamically feasible, this mechanism may not be kinetically viable for some complexes due to limited coupling of the complex concentration to the surface diffusion flux of metal atoms. Focusing on the case of Cu, we assess various scenarios where complexes are formed either on terraces or instead directly at step edges, the latter being a new paradigm. A new pathway is proposed for the formation on terraces. A rich variety of structures incorporating S at step edges exist, which could provide a viable source for complexes, at least from a thermodynamic perspective. However, it is necessary to also assess the activation barrier for complex formation and detachment from step edges. This is facilitated by the nudged-elastic-band analysis of the minimum energy path for this process utilizing machine-learning derived potentials based on density functional theory energetics for the metal-sulfur system.

Three-dimensional mass transport modeling of pharmaceuticals adsorption inside ZnAl/biochar composite

Three-dimensional Pore Volume and Surface Diffusion Model (3D-PVSDM) was implemented to predict the adsorption of acetaminophen, ketoprofen, and ibuprofen inside ZnAl/biochar composite. The experimental results revealed that ZnAl/biochar composite presented a remarkable potential as adsorbent in the studied adsorption systems since the maximum adsorption capacity was 1,108.43 mg/g for acetaminophen, 1,081.35 mg/g for ketoprofen, and 1,032.81 mg/g for ibuprofen. The equilibrium adsorption of acetaminophen was well fitted by Freundlich isotherm, while Henry isotherm properly adjusted the equilibrium adsorption of ketoprofen and ibuprofen. The 3D-PVSDM simulations indicated that the surface diffusion flux was the priority transport mechanism during the adsorption of acetaminophen, ketoprofen, and ibuprofen onto ZnAl/biochar composite. Therefore, it was possible to neglect the pore volume diffusion and apply the simplified three-dimensional Surface Diffusion Model (3D-SDM) to accurately simulate the mass transport of pharmaceutical compounds on ZnAl/biochar composite. The surface diffusion coefficients ranged from 2.58 × 10−9 to 9.52 × 10−9 cm²/s for acetaminophen, from 1.87 × 10−9 to 8.21 × 10-9 cm²/s for ibuprofen, and from 1.15 × 10-9 to 1.65 × 10−9 cm²/s for ketoprofen.

ЕЛЕМЕНТАРНА МОДЕЛЬ ПРЯМОГО З’ЄДНАННЯ МАТЕРІАЛІВ ПРИ НИЗЬКІЙ ТЕМПЕРАТУРІ

The simplest model of the joining kinetics at the stage of isolated interface voids shrinking is developed. The model basic assumptions are described, as well as also the kinetic equations in the mono-size approximation are derived. There are tThree main stages of the process can be represented distinguished when two surfaces with a small roughness are in contact with each other (tens-of-nanometer-order irregularities) and fall under pressure: 1. At the first stage, several isolated contacts are formed. Their number and contact area increases with time due to the capillary pressure and external pressure effect. 2. At the next stage, the formation of a two-phase quasi-directional contact zone, consisting of two interpenetrating percolation clusters – a contact cluster and a pore cluster – can be expected. 3. At the third stage, one can expect the formation of almost complete contact aside from a certain number of isolated pores at the interface. These pores ripen and selfheal (recover) withover time, mainly due to the capillary pressure effect. The present article is devoted to a simple model of the third stage. The Gibbs-Thomson equations for capillary effect is reformulated for the case of rectangular voids. Chemical potentials for various facets of finite sizes are found. Difference of the surface diffusivities along different facets is taken into account. Balance of grain-boundary diffusion fluxes and surface diffusion fluxes are also taken into account. The proposed model is only the first step to describe the compound joining kinetics at its last stage. Subsequent research will focus on: 1. Accounting for evolving pore size distribution. The ripening of interfacial poresPore coalescence proceeds due to vacancy exchangeexchange by by diffusion via theacross their outer surface (cont contact interface.) 2. Designing a model with a rigorous solution for the ‘real’ stress distribution (the real contact stress distribution) around realistic pore structures (irregular, nont-rectangular shape) 3. Detailed and comprehensive three-stage compound analysis.

Formation of vertically oriented graphenes: what are the key drivers of growth?

Vertically oriented graphenes have been grown for more than a decade, but until now the chemical and physical mechanisms underlying their growth have not been fully defined and understood. For this reason, we build a multi-scale, multi-factor model which is thoroughly verified using a large body of experimental data to provide a significant insight into the chemical and physical processes that determine nucleation, growth and structure formation of vertically aligned graphenes in plasma environments. Roles of chemical and physical processes that cannot be directly characterized using presently available experimental techniques, e.g. surface diffusion of adatoms and radicals, are also studied using this model. The leading role of surface diffusion fluxes, rather than direct influx from the gas phase, is confirmed, with ion bombardment being a key factor in ‘switching’ the growth modes by generating surface defects and hence, increasing the surface adsorption energy. Thus, the hydrocarbon radicals generated on a substrate as a result of bombardment are shown to diffuse to the nanoflakes and catalyze the reactions, and serve as the primary source of material to build the nanoflakes.

Dynamically imaging collision electrochemistry of single electrochemiluminescence nano-emitters.

The quest for new techniques to measure single nanomaterials is a great impetus to research efforts to understand individual behaviours. Here, we develop an electrochemiluminescence (ECL) microscopy for visualization of stochastic collision electrochemistry of single nano-emitters without the interference of current and optical background. This design uses a water-immersion objective to capture the ECL emission of nanoparticles near the specular electrode surface for enhancing light collection efficiency. The approach enables us to trace the collision trajectory of multiple nanoparticles and spatially distinguish simultaneous collisions. Results reveal that collision types, frequencies and ECL intensities significantly depend on surface natures, particle concentrations, and diffusion fluxes. By recording successive collisions, we develop a "relay probe" sensing platform for long-term research. This imaging technique displays great potential for applications in single-particle electrochemical and analytical research.

Adsorption and Surface Diffusion of Supercritical Methane in Shale

The primary objective of this study is to investigate the adsorption and surface diffusion of supercritical methane in shale. An adaptive Dubinin–Astakhov (ADA) model, with a term taking the adsorbed phase density, was introduced to interpret measured excess adsorption isotherms and obtain temperature-independent characteristic curves. The ADA model can also predict adsorption isotherms at different temperatures. Combining with the ADA model and the Maxwell–Stefan equation, a new model was developed to describe the surface diffusion of supercritical methane in shale. The model was successfully validated against experimental data. We also studied the effect of fugacity and temperature on the surface diffusion. With increasing temperature, the surface diffusion flux reaches a maximum and then decreases, which is the result of a trade off between the amount adsorbed and the effective Maxwell–Stefan surface diffusivity. The driving force for surface diffusion is the chemical potential gradient, which can be r...

Modelling of catalytic reactivity of inhomogeneous surfaces in monomer-monomer reactions

The kinetics of a A1 + A2 -> A1A2 reaction on inhomogeneous surfaces with continuously distributed adsorption sites is investigated numerically using two phenomenological models. One of them includes: the bulk diffusion of reactants from a bounded vessel towards the adsorbent and the product bulk one from the adsorbent into the same vessel, adsorption and desorption of molecules of both reactants, and surface diffusion of adsorbed and product particles before their desorption. The other model describes surface reaction provided that concentrations of both reactants at the surface are given. Both models are based on the Langmuir–Hinshelwood reaction mechanism coupled with the Eley–Rideal step. Two surface diffusion mechanisms are used. According to one of them, the diffusion flux of the adsorbed and product particles is described by the standard Fick law, while in the other one the surface diffusion flux is based on the particle jumping into a nearest vacant adsorption site. Simulations were performed using the finite difference technique. The kinetic rate constants, Eley–Rideal steps, and surface diffusion mechanisms influence on the catalytic reactivity of surf aces is studied.

Sharp Interface Limits of the Cahn-Hilliard Equation with Degenerate Mobility

In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving exponentially large and small terms and multiple inner layers. In contrast to some results found in the literature, our analysis reveals that the interface motion is driven by a combination of surface diffusion flux proportional to the surface Laplacian of the interface curvature and an additional contribution from nonlinear, porous-medium type bulk diffusion, For higher degenerate mobilities, bulk diffusion is subdominant. The sharp interface models are corroborated by comparing relaxation rates of perturbations to a radially symmetric stationary state with those obtained by the phase field model.

The Nanoscale Implications of a Molecular Gas Beam during Electron Beam Induced Deposition

The gas flux direction in focused electron beam induced processes can strongly destabilize the morphology on the nanometer scale. We demonstrate how pattern parameters such as position relative to the gas nozzle, axial rotation, scanning direction, and patterning sequence result in different growth modes for identical structures. This is mainly caused by nanoscale geometric shadowing, particularly when shadowing distances are comparable to surface diffusion lengths of (CH3)3-Pt-CpCH3 adsorbates. Furthermore, two different adsorbate replenishment mechanisms exist and are governed by either surface diffusion or directional gas flux adsorption. The experimental study is complemented by calculations and dynamic growth simulations which successfully emulate the observed morphology instabilities and support the proposed growth model.

Multi-scale kinetic surface roughening of reactive-sputtered TaN thin films characterized by wavelet transform approach

Kinetic surface roughening of TaN thin films deposited by reactive sputtering was investigated by using atomic force microscopy. Wavelet transform method incorporating power spectrum density analysis was applied to extract the global and local surface morphologies of the films. Then the dynamical exponents of global and local surface roughening were calculated in terms of dynamic scaling theory. The results show that the kinetic surface roughening of TaN thin films exhibits multi-scale characteristics, where a set of local dynamical exponents (αl=0.95, βl=0.24) and global dynamical exponents (αg=1.56, βg=0.71) was obtained. The local surface roughening is dominated by the competition between linear surface diffusion and deposition flux noise, while the global surface roughening displays anomalous rapid-roughening behavior due to the preferred grain growth.

Modeling diffusion limitation in solid-oxide fuel cells

Effect of surface diffusion on the performance of solid-oxide fuel cell is investigated. A methodical approach for the evaluation of surface diffusion coefficients of various adsorbed species based on bond-order conservation Morse potential (BOC-MP) method is presented. The surface diffusion fluxes are used for the evaluation of temporal changes in surface coverages. Our analysis shows that surface diffusion does not lead to the concentration losses in solid oxide fuel cells. Further analysis is carried out and results are presented to substantiate the significance of interface diffusion on the behavior of voltage at limiting current.

A new method of modification of inorganic membranes with pyrocarbon nano-sized crystallites

Gas-separating membranes were obtained according to an original method of directed modification of ultra filtration membranes having 50 nm pores by means of pyrocarbon nano-sized crystallites (PNCs). For the first time, the size of the pores was reduced not along the entire depth of the selective layer but only at the pore orifice, increasing their productivity by several orders of magnitude. PNC deposition was done at 800 and 650°C using methane and propane as a pyrolyzed gas at 90–100 kPa, respectively. The depth of PNC deposition was determined by scanning electron microscopy and energy dispersive spectrometry. It was demonstrated that at the used pressure, the depth of deposition was 1.5 μm, i.e., PNCs were deposited in the pore orifices. Gas permeability analysis for a membrane with rpore ∼ 0.8 nm allowed us to estimate the Knudsen ratio and surface diffusion. The Knudsen and surface diffusion fluxes were estimated. The advantages and challenges of the proposed approach are discussed; these are mainly related to the thermal stability of the porous structure and the compatibility of the thermal expansion coefficients of the porous substrate and deposited PNCs. An analysis of the obtained results is presented, along with an outline for further studies.

Measurement of surface diffusivities in mesoporous Vycor glass membranes using a modified Wicke–Kallenbach cell with variable cell volume

The purpose of this paper is to suggest a new experimental method for the measurement of surface diffusivities in porous membranes and to demonstrate its applicability in a case study. So far only indirect methods are applied. Hereby the flux contributions due to surface diffusion are extracted from the total fluxes by subtracting calculated gas phase contributions. Since gas and adsorbed phases are coupled by adsorption equilibrium, surface diffusivities cannot be extracted from surface diffusion fluxes without knowing sorption isotherms. Thus, the quality of surface diffusivity data then depends on the quality of the adsorption data. Therefore, it might be worthwhile to look for another method, which allows the direct measurement of surface diffusivities without knowing the adsorption isotherm. We propose to use a modified Wicke–Kallenbach cell (WKC) with a variable chamber volume and to run pressure response experiments with one inert gas and the counter-diffusing adsorbable gas, for which one wants to determine the surface diffusivity.

A possible mechanism of uncatalyzed growth of carbon nanotubes

In this Letter, the uncatalyzed edge growth of carbon nanotubes (CNTs) is investigated by first principles calculations and using tight-binding molecular dynamics simulations. Both heptagon and pentagon have been found to be the stable defective configurations at the growing edge. However, the activation energy of pentagon formation is rather high in comparison with that of heptagon. The heptagons can be annealed out by reaction with adatoms transported to the tube edge. The edge of the open-ended NT may remain stable, if it is fed by a sufficiently large surface diffusion flux.

Application of the general rate model with the Maxwell–Stefan equations for the prediction of the band profiles of the 1-indanol enantiomers

The adsorption isotherm data of R- and S-1-indanol and of their racemic mixture on cellulose tribenzoate were measured by frontal analysis. These experimental data were fitted to the single-component and the modified competitive Bilangmuir isotherms. The overloaded elution profiles of bands of the pure enantiomers and of the racemic mixture were calculated for different sample sizes, using the best competitive isotherm model and the General Rate Model of chromatography coupled with the generalized Maxwell–Stefan equation that describes the surface diffusion flux. The calculated and the experimental profiles were found to be in excellent agreement in all cases. The parameters of the model of the mass transfer kinetics were derived from the band profiles obtained for the pure enantiomers. The same values of these parameters give an excellent prediction of the profiles of multicomponent bands. The new model described here allows a satisfactory interpretation of the competitive mass transfer kinetics.

A Model for the Surface Diffusion of Molecules on a Heterogeneous Surface

A new model to explain the effects of the variation of temperature and surface coverage on the surface diffusion of molecules on heterogeneous surfaces has been presented. In this model, the emphasis is placed on understanding the influence of surface structure and geometry on the surface diffusion process. The model is a multifractal version of the so-called “homotattic patch” model that is often used in studies of gas adsorption on heterogeneous surfaces. Some previous experimental results, reported in the literature, on the surface diffusion of benzene on a fumed silica, have been reanalyzed in the light of the new model. This reanalysis of past data has suggested that, at a given value of overall average surface coverage, the surface diffusion flux in this system is dominated by only a small fraction of the total number of molecules on the surface. In addition, the small fraction of molecules that are the predominant contributors to the surface diffusion flux are generally adsorbed within particular regions of the surface. The particular regions contained within the different surface patches in the model were found to have differing degrees of surface roughness, which could be characterized by different surface fractal dimensions. This work has also shown that it may be possible to use surface diffusion methods to determine the characteristic size and spatial distribution of the different surface patches with different adsorption energies in homotattic patch models of heterogeneous adsorbent surfaces.

Morphological stabilization, destabilization, and open-end closure during carbon nanotube growth mediated by surface diffusion

In this paper, the growth stability of open-ended carbon nanotubes mediated by surface diffusion on the lateral surface of the nanotube is considered in detail. Nanotube growth and destabilization is viewed as a competition of two processes at the open growth edge: (i) hexagon formation sustaining the continuous growth of the regular hexagonal network, and (ii) thermally activated pentagon formation, which causes inward bending of the nanotube wall resulting in end closure, i.e., growth termination. The edge of the open-ended nanotube, if it is fed by a sufficiently large surface diffusion flux, may remain stable even without extrinsic stabilizing effects. The closure of the open end of the growing nanotube is shown to happen whenever a change in the growth conditions (temperature, carbon vapor pressure, or surface area from which the open end is fed) decreases the surface diffusion flux, and the characteristic time for new atom arrival on the edge becomes larger than the characteristic time for pentagon defect formation. These kinetic effects are also shown to define the transition from single wall to multiwall nanotube growth. Additionally, the effect of surface diffusion feeding nanotube growth from behind the growth interface is shown to stabilize open edge morphology, effectively smoothing the growth perturbations which may be caused by diffusion-limited aggregation at the edge.

Mechanism of thermokinetical selection between carbon nanotube and fullerene-like nanoparticle formation

Open edge stability of carbon nanotube growth is suggested to depend on kinetically defined competition between pentagon and hexagon formation. Nanotube growth is possible when the time of hexagon formation, determined by the surface diffusion flux to the growth edge (proportional to carbon vapor pressure), is much lower than that of pentagon formation, which depends on the temperature. The competition of pentagon/hexagon formation at the growth edge together with thermal effects of condensation heat release and heat dissipation by radiation and collisions with inert gas (He), is shown to define selection between nanotube nucleus evolution into (i) continuous nanotube growth or (ii) fullerene- or cage-like nanoparticle formation. The involvement of catalyst nanoparticles enhances the formation of nanotubes by enhancing growth edge stability against pentagon formation under pressure-temperature conditions at which the open edge would otherwise become unstable closing nucleus into the fullerene-like nanoparticle.

Application of the general rate model and the generalized Maxwell–Stefan equation to the study of the mass transfer kinetics of a pair of enantiomers

The general rate model of chromatography can be coupled with the generalized Maxwell–Stefan equation that describes the surface diffusion flux. The resulting model is useful to describe the behavior of two enantiomers during their separation on chiral phases, cases in which the mass transfer kinetics is known to be sluggish. A case in point is the modeling of the elution profiles of the racemic mixture of the two enantiomers of 1-phenyl-1-propanol on cellulose tribenzoate coated on silica, a popular chiral stationary phase. The competitive equilibrium isotherm behavior of the two enantiomers on the chiral stationary phase was described using the competitive Tóth isotherm model. An excellent agreement between the experimental and the calculated profiles was observed in the whole range of experimental conditions investigated, at low and high column loadings.