Static Energy Barrier Research Articles

Detailed mass transfer studies of a ternary system in the presence of unidirectional ejections coupled with unconfined density convection in both phases

Experiments were carried out to transfer acetic acid from toluene to water under static conditions (inside a 50 cm3 buret) for a fixed initial concentration of 1 mol dm−3 of acid in toluene. The phase volumes (i.e., 5 and 10 cm3) were equal for the separate sets of runs at different extraction times. The extraction experiments were carried out for up to 60 min. Complete concentration profiles of the solute in both phases were developed, leading to variable solute concentrations on both sides of the interface at different extraction times. In the ternary system, intermittent ejection phenomena were only visible from the organic to the aqueous phase, over a fraction of the total interfacial area. Two theories of energy instability were verified experimentally through numerical calculations of the instability criteria at different extraction times. The molecular energy of acetic acid in toluene was estimated to be 3000 J mol−1. In both the phases, the Rayleigh number ranged from 108 to 109 due to the unstable density gradients. The interfacial mass transfer coefficient, calculated under static conditions, was one-fifth of that under stirred conditions, where the Marangoni instability was superimposed on the energy instability. The interfacial mass transfer coefficient was higher than the bulk phase transfer coefficient in the raffinate phase, even in the presence of density convection. The dynamic interfacial energy barrier was found to be higher than the static energy barrier, i.e., the free energy of the interface.

Uncovering the influence of Cu on the thickening and strength of the δ′/θ′/δ′ nano-composite precipitate in Al–Cu–Li alloys

Nanoscale δ′/θ′/δ′ composite precipitate, as another important strengthening phase in the latest generation of Al–Li alloys, exhibits excellent resistance to coarsening. Here, we propose two thickening models for an anomalous δ′/θ′/δ′ that is discovered recently, by analyzing various influencing factors, including the static energy barrier, aging temperature-dependent nucleation conditions, and the elastic distortion suffered during growth. It indicates that the thickness of the δ′/θ′/δ′ composite precipitate seems to depend on the nucleation of the δ′. At elevated aging temperatures, θ′ precipitates can grow and thicken rapidly until the δ′ nucleates on them. This is strikingly different from the dislocation-induced growth mechanism. Subsequently, we propose a vacuum-added methodology to accurately extract the interfacial energy. The results show that this nano-composite precipitate can realize supra-nanostructure in thickness at low aging temperatures due to the spontaneous nucleation of the δ′ upon the pre-precipitate θ′. Cu atoms segregated at the interface suppress the nucleation of the δ′, but release the lattice distortion to some extent. Using Griffith fracture model-assisted ab-initio uniaxial tensile tests, the cohesion strength and fracture process of this composite precipitate with and without Cu segregation have been captured. It indicates that the Cu atoms induced interfacial expansion and the fracture of strong Al–Al covalent bond, resulting in a reduction of fracture strength of this nano-composite precipitate.

Ab initio study of H, B, C, N, O, and self-interstitial atoms in hcp-Zr

In this work, we investigate the stabilities of H, B, C, N, O, and Zr atoms at various interstitial sites in hcp-Zr using a first-principles theoretical approach. The formation energy of each interstitial atom at each site in the hcp crystal was determined, and the difference in the energy at different sites were considered as a static energy barrier to predict energetically favored diffusion pathways. Linear and non-linear prediction models for the interstitial formation energy were developed using readily accessible chemical and structural input parameters. We show that a simple linear model predicts the formation energies of the interstitial atoms with an R2 of 97%.

Potential Energy Surfaces and Charge Transfer of PAH-Sodium-PAH Complexes.

To further understanding of the role of sodium in carbon cathode degradation in Hall-Héroult cells, potential-energy surfaces and charge-transfer curves are presented for finite-size complexes of sodium intercalated between various polycyclic aromatic hydrocarbons. Calculations for lithium and potassium are included to highlight the disparate intercalation behaviour of the alkali metals in graphite intercalation compounds. Static energy barriers from DFT are used to compute macroscopic diffusion coefficients according to transition-state theory. Comparing the calculated diffusion coefficient to experimental values from the literature sheds light on the role of lattice diffusion of sodium-graphite intercalation compounds in sodium intrusion in graphitic carbon cathodes.

Numerical study of self‐ and heterodiffusion on clean unreconstructed and missing‐row reconstructed Pt(110) surfaces

This article sheds light on the investigation of the diffusion and the adsorption of Pt and Au adatoms on the ideal (1 × 1) and the missing‐row structures ((1 × 2), (1 × 3), and (1 × 4)) of Pt(110) surfaces. This study is performed by using quenched molecular dynamics simulations combined with an interatomic potential derived from the embedded‐atom method (EAM). For each geometry, we have considered the homo‐ and heterogeneous systems: Pt/Pt and Au/Pt. The multilayer and adatom relaxation trends and adatom bond lengths with the first nearest neighbors were examined. We have found that the atomic relaxation is quantitatively different for all configurations. The static energy barriers for hopping and adsorption energy were calculated for all configurations and both systems. Thus, the analysis of our results provides interesting insights and a tentative idea about the geometry influence on the adsorption and the diffusion on the missing‐row reconstructed surfaces. Our numerical results were compared with some experimental and theoretical data available in the literature and a good agreement was achieved.

Wetting transition of the ordered nanoporous matrix layer under impact and static pressure

In this study, a series of anodic aluminum oxide (AAO) ordered nanoporous matrix layers were prepared, and hydrophobic (perfluoroalkyltriethoxysilanes, PFO) and hydrophilic (3-aminopropyltrimethoxysilane, APTS) materials were modified on these surfaces. The static contact angle of these specimens was in the range of 30–153°. By using the f values in the theory equation and comparing with the experiment value, the wetting state of the surface was determined. Under impact pressure, the wetting states of the porous surface with the hydrophobic PFO-modified material were more stable, and the contact angle on these surfaces under external pressure remains constant. However, the hydrophobicity of the surface modified with APTS was metastable, and the surface hydrophobicity decreased as the impact pressure increased. Under sufficient hydraulic pressure, the liquid would wet a rough structure, and the hydrophobic state would be lost and not automatically restored. In addition, the change in the wettability of the APTS-modified surface occurs spontaneously due to the immersion conditions. Finally, the critical pressure of the PFO-modified surfaces was investigated. Although the critical pressure of the surface is on the micrometer level, which is similar to the static energy barrier (ΔP), our experimental data are smaller and on the nanometer scale, which is discussed in this study.

Atomic self-diffusion behaviors relevant to 2D homoepitaxy growth on stepped Pd(001) surface

Using molecular dynamics, nudged elastic band and modified analytic embedded atom methods, the diffusion behaviors of Pd adatom on stepped Pd(001) surface have been investigated. Lower than 975K, Pd adatom just hops along the perfect [110]-direction step. The diffusion dynamics equation is derived from the Arrhenius law between 875 and 975K, and the corresponding migration energy and prefactor are 0.76eV and 5.2×10−2cm2/s respectively, which shows that they adhere to the step in case of adatom moving to the step. The adatom diffuses across the perfect step with an Ehrlich–Schwoebel barrier of 0.09eV by exchange mechanism. Our calculations show the kink at step can markedly decrease the static energy barrier across the step with a negative Ehrlich–Schwoebel barrier, and it contributes to form layer-by-layer growth model in the epitaxial experiment. Our calculations show that the kink can also markedly improve the adatom's mass transport of interlayer, contributing to the formation of the compact film. Lastly, a quantitative result at 300K shows that the kink affects tremendously the diffusion mobility of adatom near it, which indicates that the kink plays a key role in the formation of the compact and uniform film on Pd(001) surface in an epitaxial growth experiment.

Molecular Transport through Surfactant-Covered Oil−Water Interfaces: Role of Physical Properties of Solutes and Surfactants in Creating Energy Barriers for Transport

Mechanisms of molecular transport across oil-water interfaces covered by nonionic surfactants are investigated using coarse-grained molecular dynamics simulations. Resistance of the surfactant monolayer to the solute transport is shown to be controlled by dense regions in the monolayer. The dense regions are formed on both sides of the dividing surface and the barrier to the solute transport is created by those of them experiencing unfavorable interactions with the solute. Resistance to the transport of a hydrophobic (hydrophilic) solute increases with the excess density of the head (tail) group region of the monolayer, which in turn increases with the length of the surfactant head (tail) group. Barriers for solute transport through surfactant monolayers are also influenced by the solute size. However, the extent of this influence is determined by the monolayer thickness and the solute structure and composition. For example, it is shown that resistance offered by thin monolayers to transport of linear oligomers is relatively insensitive to the solute length. The barrier sensitivity to the length of these solutes increases with the monolayer thickness. In addition to the static barriers, the solute transport is shown to be affected by dynamic barriers due to a nonadiabatic coupling of the monolayer surface with the solute position and configuration. This coupling leads to deviations of the system dynamics from the minimum energy path. The deviations are most significant in the neighborhood of the static energy barrier, which effectively leads to an increase of the barrier for the solute transport.

Dynamics diffusion behaviors of Pd small clusters on a Pd(1 1 1) surface

Using molecular dynamics, nudged elastic band and modified analytic embedded atom methods, the self-diffusion dynamics properties of palladium atomic clusters up to seven atoms on the Pd (1 1 1) surface have been studied at temperatures ranging from 300 to 1000 K. The simulation time varies from 20 to 75 ns according to the cluster sizes and the temperature ranges. The heptamer and trimer are more stable than the other neighboring clusters. The diffusion coefficients of the clusters are derived from the mean square displacement of the cluster's mass-center, and the diffusion prefactors D0 and activation energies Ea are derived from the Arrhenius relation. The activation energy of the clusters increases with the increasing atom number in the clusters, especially for Pd6 to Pd7. The analysis of trajectories shows the noncompact clusters diffuse by the local diffusion mechanism but the compact clusters diffuse mainly by the whole gliding mechanism, and some static energy barriers of the diffusion modes are calculated. From Pd2 to Pd6, the prefactors are in the range of the standard value 10−3 cm2 s−1, and the prefactor of Pd7 cluster is 2 orders of magnitude greater than that of the single Pd adatom because of a large number of nonequivalent diffusion processes. The heptamer can be the nucleus in the room temperature range according to nucleation theory.

Ab Initio atomic simulations of antisite pair recovery in cubic silicon carbide

The thermal stability of an antisite pair in cubic silicon carbide (3C-SiC) is studied using ab initio molecular dynamics within the framework of density functional theory. The lifetime of the antisite pair configuration is calculated for temperatures between 1800 and 2250K, and the effective activation energy for antisite pair recombination is determined to be 2.52eV. The recombination energy path and static energy barrier are also calculated using the nudged elastic band method along with the dimer method to accurately locate the transition states. The consistency of the results suggests that the antisite pair cannot be correlated with the DI photoluminescence center, as proposed previously by theoretical interpretations. An extended exchange mechanism is found for the antisite pair recombination.

Diffusion rates of Cu adatoms on Cu(111) in the presence of an adisland nucleated at fcc or hcp sites

The surface diffusion of Cu adatoms in the presence of an adisland at fcc or hcp sites on Cu(111) is studied using the embedded atom model potential derived by Mishin et al. [Phys. Rev. B 63, 224106 (2001)]. The diffusion rates along straight (with close-packed edges) steps with (100) and (111)-type microfacets (respectively, step $A$ and step $B$) are first investigated using the transition state theory in the harmonic approximation. It is found that the classical limit beyond which the diffusion rates follow an Arrhenius law is reached above the Debye temperature. The Vineyard attempt frequencies and the (static) energy barriers are reported. Then a comparison is made with the results of more realistic classical molecular dynamic simulations which also exhibit an Arrhenius-type behavior. It is concluded that the corresponding energy barriers are completely consistent with the static ones within the statistical errors and that the diffusion barrier along step $B$ is significantly larger than along step $A$. In contrast the prefactors are very different from the Vineyard frequencies. They increase with the static energy barrier in agreement with the Meyer-Neldel compensation rule and this increase is well approximated by the law proposed by Boisvert et al. [Phys. Rev. Lett. 75, 469 (1995)]. As a consequence, the remaining part of this work is devoted to the determination of static energy barriers for a large number of diffusion events that can occur in the presence of an adisland. In particular, it is found that the corner crossing diffusion process for triangular adislands is markedly different for the two types of borders ($A$ or $B$). From this set of results the diffusion rates of the most important atomic displacements can be predicted and used as input in kinetic Monte Carlo simulations.

Fast structural relaxation of polyvinyl alcohol below the glass-transition temperature

In order to obtain information about structural relaxations of polymers within a time window of several nanoseconds, the absorption, site-selective steady-state fluorescence and time-resolved fluorescence spectra have been measured for polyvinyl alcohol doped with rhodamine 640 in the 150–300 K temperature range. The temperature dependence of the absorption and fluorescence spectra has been analyzed on the basis of one- and two-dimensional configuration-coordinate models. In spite of the measurement below the glass-transition temperature of the matrix, the existence of a fast relaxation process which is completed within a few hundred ps has been clarified. The magnitude of this relaxation increases with increasing temperature, while the relaxation mechanism cannot be ascribed to the thermal crossing of static energy barriers. It has been found that the experimental results are not explained by the two-dimensional configuration coordinate model in which the fast and slow structural relaxations are assumed to occur independently along the two axes. A relaxation process triggered by temperature-dependent release from the constraint preventing the structural change is shown to account for the experimental results well using a one-dimensional configuration coordinate model.

Molecular dynamics simulation of cation motion in water-filled gramicidinlike pores

A model calculation is carried out to study the potential energy profile of a sodium ion with several water molecules inside a simplified model of the gramicidin ion channel. The sodium ion is treated as a Lennard-Jones sphere with a point charge at its center. The Barnes polarizable water model is used to mimic the water molecules. A polarizable and deformable gramicidinlike channel is constructed based on the model obtained by Koeppe and Kimura. Potential minima and saddle points are located and the static energy barriers are computed. The potential minima at the two mouths of the channel exhibit an aqueous solvation structure very different from that at any of the interior minima. These sites are approximately 23.6 and 24.4 A apart for binding of a sodium ion and a cesium ion, respectively. Ionic motion from these exterior sites to the first interior minimum requires substantial rearrangement of the waters of solvation; this rearrangement may be the hydration/dehydration step in ionic permeation through the channel. Based on these results, a mechanism by which the sodium ion moves from the exterior binding site to the interior of the channel is proposed. Our model channel accommodates about eight water molecules and the transport of the ion and water within the channel is found to be single file. Results of less extensive calculations for Cs+ and Li+ ions in a channel with or without water are also reported.