Film-pore-concentration-dependent surface diffusion model for the adsorption of dye onto palm kernel shell activated carbon

The rate of dye adsorption from aqueous effluents onto palm kernel shell (PKS) activated carbon has been studied experimentally using the batch adsorption method. The adsorption rates of methylene blue on PKS for systems of different initial dye concentrations are modeled using a film-pore-concentration dependent surface diffusion (FPCDSD) model. The FPCDSD model is sufficiently general and can be reduced easily to describe other simplified models. Using the FPCDSD model, only a single set of mass transfer parameters is required to describe the methylene blue/PKS system for different initial concentrations. A different set of mass transfer parameters are needed to obtain the best fitting if the pore diffusion is not included in the model.     

New model of surface diffusion in reversed-phase liquid chromatography

A new model of surface diffusion in reversed-phase liquid chromatography (RPLC) was derived by assuming a correlation between surface and molecular diffusion. Analysis of surface diffusion data under different conditions of sample compounds, mobile and stationary phases, and temperature in RPLC systems validates this assumption and shows that surface diffusion should be regarded as a molecular diffusion restricted by the adsorptive interactions between the adsorbate molecule and the stationary phase surface. A surface-restricted molecular diffusion model was proposed as a first approximation for the mechanism of surface diffusion. The model is formulated according to the absolute rate theory. The activation energy of surface diffusion (Es) was quantitatively interpreted assuming that Es consists of the contributions of two processes, a hole-making and a jumping one. The former contribution is nearly equal to the activation energy of molecular diffusion and is correlated with the evaporative energy of the mobile phase solvent. The latter contribution is a fraction of the isosteric heat of adsorption. An appropriate explanation based on this new model of surface diffusion is provided for two contradictory results related to the relationship between retention equilibrium and surface diffusion in RPLC and to the surface diffusion coefficient for weakly retained sample compounds.     

Long-jump probabilities in a BGK model for surface diffusion

The jump-length probability distribution (JLPD) in a periodic system is studied using the solution of the linearized Boltzmann equation with BGK collision kernel. The equation is solved both by the matrix-continued-fraction method and by direct numerical simulations. The JLPDs obtained by the BGK equation are compared to those derived from other kinetic models, such as the Langevin (Fokker–Planck) model.     

氢原子在镍台阶面上吸附、振动和表面扩散行为的理论研究

本文用对势方法研究了氢原子在Ni(510)台阶面上的吸附和振动, 计算结果与实验符合得很好。并考察了氢原子在Ni(997)台阶面上的吸附和扩散, 结果表明,台阶对下台面上扩散的氢原子开成捕获势阱, 对上台面扩散的氢原子形成反射势,这也很好地支持了实验结果。     

Generalized overlap amplitudes for the lithium atom

Generalized overlap amplitudes (GOAS) are calculated between the lithium atom and several states of Li⁺. An examination of the long-range behavior of the GOAS indicates that they are coupled, appearing to have the same exponential decay at large r. At intermediate distances from the nucleus, the GOAS decay with their unique exponential rate and the decay rates only merge at large r. Although many of the GOAS appear to be similar, their distinctness indicates that they may, in fact, be linearly independent. © 1996 John Wiley & Sons, Inc.     

氢原子在金属锂表面台阶附近吸附和表面扩散行为的ab initio研究

取Li7H和Li9H两个原子簇模拟氢原子与含台阶的金属锂表面的相互作用, 以小基组用ab initip方法计算了体系的吸附和表面扩散势能面(或势能曲线)。结果表明: (1)对Li7H体系, 台阶面附近沿垂直边棱方向存在三种不同的桥位吸附位, 最稳定的吸附位在上台面接近台阶边棱处, 台阶面显著地改变了表面扩散活化能, 台阶边棱处有一个较高的势垒。于是, 迁移原子将会在台阶边棱处受到反射, 并可被捕获于台阶面上及其附近。由势能面确定了最低能量表面扩散途径。(2)对Li9H体系, 在Li7H原子簇基础上增加次表面层两个锂原子后, 表面扩散活化能略有减小, 氢原子在上台面的桥位吸附更趋稳定, 各吸附位相对稳定性及势垒内何位置几无改变, 这些结果显示了台阶面对氢原子的化学吸附和表面扩散发生扰动, 台阶边棱对表面扩散起着重要作用。     

Contribution of concentration-dependent surface diffusion in ternary adsorption kinetics of ethane, propane and n-butane in activated carbon

The role of concentration-dependent surface diffusion in the adsorption kinetics of a multicomponent system is investigated in this paper. Ethane, propane and n-butane are selected as the model adsorbates and Ajax activated carbon as the model adsorbent. Adsorption equilibrium isotherm and dynamic parameters extracted from single-component systems are used to predict the ternary adsorption equilibria and kinetics. The effect of concentration-dependent surface diffusion on the adsorption kinetics predictions is studied by comparing the results of two mathematical models with the experimental data. Three diffusion mechanisms, macropore, surface and micropore diffusions are incorporated in both models. The distinction between these two models is the use of the chemical potential gradient as the driving force for the diffusion of the adsorbed species in one model and the concentration gradient in the other. It was found that the model using the chemical potential gradient provides a better prediction of the ternary adsorption kinetics data, suggesting the importance of the concentration dependency of the surface diffusion, which is implicitly reflected in the chemical potential gradient. The kinetic model predictions are also affected by the way how single-component adsorption equilibrium isotherm data are fitted.     

Simulating surface diffusion and surface growth in ceramics

We examine the movement of ion pairs on the surfaces of simple oxides. Using temperature-accelerated dynamics the elementary processes involved are identified and the activation energies of these used as input to kinetic Monte Carlo simulations. Results are presented for the motion of BaO and SrO ion pairs on the (100) surfaces of BaO and SrO, respectively, and the formation of island pairs on these surfaces is studied. The simulations reveal the importance of exchange mechanisms in surface diffusion and growth of oxides. The importance of such reactions has been recognised previously for metallic surfaces but not for ionic systems, where it has been assumed that ionic surface diffusion is surface diffusion via the hopping motion of ion pairs from one surface site to another. Exchange mechanisms can dominate transport processes both on terraces and steps for both homoepitaxial and heteroepitaxial growth. We suggest the unavoidable mixing when an exchange mechanism operates must be considered when attempting to grow sharp interfaces in oxide nanostructures.     

氢原子在平坦金属锂(100)面上表面扩散行为的ab initio研究

本文用Li7(4,3)-H和Li9(5,4)-H小原子簇模拟氢原子在平坦金属锂(100)面吸附体系, 取小基组作了各吸附位吸附势能曲线及相应分子轨道能级图、吸附和表面扩散势能面的ab initio研究。结果表明, 氢原子优先吸附在配位数较高的吸附位上, 并倾向于由高配位数吸附位向低配位数吸附位迁移, 表面扩散各向异性, 扩散跳跃步长与锂单晶晶格原子间距数量级相同。从吸附和表面扩散势能确定了最低能量表面扩散途径, 分析了原子在平坦金属表面上迁移的微观过程。     

Generalized diffusion equation of interacting brownian particles

Macroscopic behavior of a system of brownian particles interacting with each other through potential forces is described by a generalized diffusion equation (GDE) for the density of particles. The diffusion coefficient in the GDE is given by the generalized Stokes—Einstein relation and generally depends on the density. In the presence of long-range interactions, the GDE becomes non-local in space. When a Coulomb interaction exists, the GDE corresponds to an improvement of the Poisson—Boltzmann equation.     

Generalized reptation model

Summary The reptation model is generalized on the basis of a theory which accounts for hindered defect diffusion along the chain. A basic ingredient of the theory is a waiting time distribution for the hops of elementary defects which store length. Important rheological quantities are found to generally depend on fractional powers of the molecular mass rather than on integer powers as in the conventional reptation picture.Zusammenfassung Ein verallgemeinertes Reptationsmodell wird vorgestellt. Entlang einer Polymerkette berücksichtigt es die gehinderte Difussion von Defekten, die Länge speichern. Dieser Effekt wird beschrieben mittels einer Wartezeitverteilung für die Defektplatzwechselvorgänge. In der Folge findet man für wichtige rheologische Größen Molekulargewichtsabhängigkeiten in Form von Potenzgesetzen mit gebrochenen Exponenten an Stelle der ganzzahligen Exponenten des konventionellen Reptationsmodells.     

Collective surface diffusion measurements

The analysis of surface diffusion is more complicated in systems at finite coverage because different atomistic processes, depending on the local environment of an atom should be taken into account. The analysis is simplified under strongly non-equilibrium conditions if one of the processes becomes the dominant one. Different experiments will be reviewed which measure different atomistic processes depending on how far the system is from equilibrium.     

Mechanisms of surface diffusion

Mechanisms of surface diffusion of single atoms, molecules and atomic clusters on flat terraces (with and without a driving force) of metal and semiconductor surfaces are discussed, focusing on our recent scanning tunneling microscopy (STM) results. Experimental evidence leading to these conclusions is presented. Besides the commonly known hopping mechanism, there are many other mechanisms. In Arrhenius analysis, a linear behavior can be expected for only some of the simpler mechanisms.     

Li在液态Al中扩散系数的测定研究

首次尝试利用开路电位-浓度曲线法测定合金的浓度, 并用阳极计时电位法快速测定Li在液态Al中的扩散系数。720℃下Li在液态Al中的扩散系数DLi/Al=4.94×10ˉ^5cm^2·gˉ^1,与根据Stokes-Einstein方程计算得到的理论值DLi/Al=4.85×10ˉ^5cm^2·sˉ^1相吻合。     

Semiclassical perturbation theory for diffraction in heavy atom surface scattering

The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ? the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics of the beam of incoming particles. Necessary conditions for observation of quantum diffraction are derived for the angular width of the incoming beam. An analytic expression for the angular distribution as a function of the angular and momentum variance of the incoming beam is obtained. We show both analytically and through some numerical results that increasing the angular width of the incident beam leads to decoherence of the quantum diffraction peaks and one approaches the classical limit. However, the incoherence of the beam in the parallel direction does not destroy the diffraction pattern. We consider the specific example of Ar atoms scattered from a rigid LiF(100) surface.     

The embedded atom model of liquid cesium

The embedded atom potential was calculated for cesium over the temperature range 323–1923 K at pressures up to 9.8 GPa from the diffraction data on the structure of the metal close to the temperature of fusion (T _f). The parameters of the embedded atom potential were adjusted using the data on the thermodynamic properties and structure of liquid cesium. The embedded atom potential well predicts the structural and thermodynamic characteristics of the liquid metal as the temperature increases along the liquid-vapor equilibrium line and under strong compression. The calculated potential energy and structure of liquid cesium closely agree with the experimental data at temperatures up to 1373 K. The calculated bulk compression modulus is close to its experimental values at all temperatures except 323 K. The self-diffusion coefficients increase as the temperature grows by a power law with an exponent close to 2 and satisfy the Stokes-Einstein equation. Deviations from experimental data at temperatures above 1400 K are explained by the metal-nonmetal transition that occurs as the density decreases.     

Modified surface chemistry of activated carbons

In this study, immersion calorimetry was used to characterise different samples of commercial granular activated carbon (GAC) which undergo oxidation with HNO₃ (GACOxN) and thermal treatments to modify its superficial group contents, as well as to determine the textural characteristics of the materials through nitrogen adsorption at 77 K and its superficial chemistry by Boehm titration and zero point of charge. Correlations between the immersion enthalpies and the results of the other techniques of characterisation were established. The immersion enthalpies in dichloromethane obtained were greater, which were found to be between ?88.36 and ?155.6 J g^?1, in contrast to those in carbon tetrachloride, which were found to be between ?50.21 and ?94.29 J g^?1. The dependence of the immersion enthalpies in water on the contents of total acidity and basicity surface groups was also established, and a good correlation between the accessible surface area determined by calorimetric technique and the BET area was found.     

The embedded atom model of molten lead

The method for calculating the embedded atom potential for liquid metals from the diffraction structural data close to the melting point was applied to lead at temperatures from 613 to 20000 K. The embedded atom potential parameters were adjusted using the data on the lead structure at 613–1173 K, the thermodynamic properties of lead over the temperature range 613–2000 K, and the results of shock wave experiments. The embedded atom potential and molecular dynamics method allowed the structural characteristics of the liquid metal to be successfully predicted up to 1173 K. The calculated bulk compression modulus at 613 K was close to its actual value. The self-diffusion coefficients along the liquid-vapor equilibrium line increased as the temperature rose following the power law with the exponent close to 2.03. The properties of lead under extremal conditions were calculated up to the temperature 20000 K and density 20.721 g/cm³. At 1000 K and a density of 18.156 g/cm³, close agreement with the experimental pressure (101.5 GPa) was obtained. The potential found fairly well described the properties of crystalline lead. At the same time, the embedded atom potential adjusted to describe the properties of the crystalline phase only poorly described the properties of liquid lead at increased densities.     

揭秘单原子催化:表面科学方法

理解单原子催化的基本机理对于设计高性能和高稳定性的催化剂体系至关重要.然而,这是个有待解决的问题,因为用现有的实验技术来表征单原子催化活性位极端困难.在过去的40年里,表面科学为理解多相催化提供了基础,但是有关反应温度下、已知结构金属氧化物上稳定的金属原子的模型体系罕见报道.本视角讨论了已知的、吸附在模型金属氧化物表面上的、孤立的金属原子,并探讨了如何利用这些信息去理解单原子催化.一个关键的问题是,尽管在表面科学研究中的高度理想化的模型体系可能无法代表真实反应条件下的催化剂,但是它们与采用理论模拟计算得出的模型非常相似.因此,表面科学有望成为评估单原子催化模型的方法.更令人兴奋的是,几个研究组已经发展出在升温条件下金属吸附原子仍保持稳定的模型体系.但到目前为止,还不能清楚地解释催化活性.最后,本文简要地讨论了在真实反应条件下扫描隧道显微镜的实验前景.