Effect of impermeable interfaces on apparent diffusion coefficient in heterogeneous media

It is known that the short-time behavior of the diffusion coefficient, which is measurable by nuclear magnetic resonance (NMR), provides an estimate of the specific surface of porous samples filled with an NMR-detectable fluid. This method is not directly applicable to the exploration of structure of impermeable restrictions in mixtures such as living tissues, in which the inherent microscopic structure in the bulk medium results in the same pattern of the temporal dynamics of the diffusion coefficient as the impermeable restrictions studied. Here, an approach to describe diffusion and the boundary effect in heterogeneous media is developed in the framework of a cumulant expansion of the NMR signal. The leading term of this expansion is determined by the velocity autocorrelation function which is expressed in terms of properties of microscopic transport in the medium. Given these properties, the apparent diffusion coefficient as measured by NMR can be found by a straightforward integration. Calculations are performed in one spatial dimension.     

Diffusion of atoms incorporated in the surface layer of the fcc(111) face

The kinetics of the migration of the impurity atom due to the diffusion of vacancies on the fcc(111) face was investigated. The study focused on the dependence of the diffusion coefficient of the impurity on the degree of surface coverage with vacancies. It was shown by molecular dynamics that this dependence is linear in the limit of the vanishingly small concentration of vacancies 1; the results of modeling coincided with the predictions of our analytical theory. The diffusion coefficient increased nonlinearly with and its growth correlated with that of the size of the percolation clusters. After the percolation threshold was overcome, the diffusion coefficient of the impurity quickly tended toward its value for the surface without hindrances.     

Diffusion of adsorbates on random alloy surfaces

In this work the diffusion of non-interacting adsorbates on a random AB alloy surface is considered. For this purpose a simple cubic (sc), body-centered cubic (bcc) or face-centered cubic (fcc) auxiliary metal lattice is introduced. The auxiliary lattice is truncated parallel to its (100) plane in such a way that the fourfold hollow positions of the metal surface form a regular net of adsorption sites with square symmetry. The adsorption energy of each adsorption site is determined by its own environment, i.e. by the numbers of direct A or B neighbors. The Monte-Carlo method has been utilized to simulate surface diffusion of adsorbates on such energetically heterogeneous alloy surfaces and to calculate the tracer, jump and chemical diffusion coefficients. The chemical diffusion coefficient was calculated via two different approaches: the fluctuation and the Kubo-Green method. The influence of energetical heterogeneities on the surface diffusion is largely pronounced at low temperatures and low surface coverages, where most of the adatoms are trapped by deep adsorption sites. It was found that at low temperatures the sequential occupation of the different types of adsorption sites can be observed. Received: 24 October 1997 / Accepted: 17 December 1997     

Diffusion in a heterogeneous medium for low concentrations

The equations describing diffusion on a heterogeneous lattice for low concentrations are considered taking into account lattice site blocking. It is shown that lattice site blocking cannot be disregarded in the case of a strongly heterogeneous lattice even for low concentrations. It is established that the equation with a fractional time derivative holds only in a bounded time interval. Anomalous diffusion, which is described by the equation with a fractional time derivative at the initial stage, must be described over long time periods by an ordinary diffusion equation with a concentration-dependent diffusion coefficient.     

非均匀生物组织中光子迁移的数值方法

导出了一种研究光子在非均匀生物组织中迁移规律的数值方法，并验证该方法的精确性，进一步研究了非均匀生物组织中扩散系数对反射和透射光通量的影响，结果表明扩散系数的非均匀性对光反射和透射的影响不可忽略。     

Molecular dynamics simulation of nanoscale surface diffusion of heterogeneous adatoms clusters

Molecular dynamics simulation employing the embedded atom method potential is utilized to investigate nanoscale surface diffusion mechanisms of binary heterogeneous adatoms clusters at 300 K, 500 K, and 700 K. Surface diffusion of heterogeneous adatoms clusters can be vital for the binary island growth on the surface and can be useful for the formation of alloy-based thin film surface through atomic exchange process. The results of the diffusion process show that at 300 K, the diffusion of small adatoms clusters shows hopping, sliding, and shear motion; whereas for large adatoms clusters(hexamer and above), the diffusion is negligible. At 500 K, small adatoms clusters, i.e., dimer, show almost all possible diffusion mechanisms including the atomic exchange process; however no such exchange is observed for adatoms clusters greater than dimer. At 700 K, the exchange mechanism dominates for all types of clusters, where Zr adatoms show maximum tendency and Ag adatoms show minimum or no tendency toward the exchange process. Separation and recombination of one or more adatoms are also observed at 500 K and 700 K. The Ag adatoms also occupy pop-up positions over the adatoms clusters for short intervals. At 700 K, the vacancies are also generated in the vicinity of the adatoms cluster,vacancy formation, filling, and shifting can be observed from the results.     

Pore-Size Distributions and Tortuosity in Heterogeneous Porous Media

The diffusion coefficient, measured at long observation times by pulsed-held-gradient NMR, can in principle be used to estimate the tortuosity of a porous medium. This method is useful for glass-sphere packs, but we find that it does not generally work for porous sedimentary rock. Natural sedimentary rocks are characterized by complex microgeometries and broad distributions of pore sizes, which cannot be adequately sampled by diffusing molecules in experimentally accessible observation times. The time-dependent diffusion coefficient D(t) can be distinctly irregular for rocks with very large pores. In heterogeneous porous media, determination of pore-size distribution by relaxation-time measurements and tortuosity by PFG diffusion measurements are mutually exclusive.     

Diffusion of interacting particles in one-dimensional heterogeneous systems

The equilibrium and transport properties of interacting ad-particles on bivariate heterogeneous chains are studied by combining analytical and simulation approaches. Heterogeneity is introduced in the way of patches of shallow and deep adsorbing sites distributed in a deterministic alternating way. Adsorption isotherms and mean-square fluctuations of the surface coverage, as well as the jump and collective diffusion coefficients, are calculated for different values of lateral interactions between ad-particles and substrate heterogeneity. In addition, different elementary jump mechanisms are introduced and their influence in the coverage dependence of the collective diffusion coefficient is investigated.     

Acquisition of pure-phase diffusion spectra using oscillating-gradient spin echo

Oscillating-gradient spin echo (OGSE) diffusion experiments have long been used to measure the short-time apparent diffusion coefficient, D(app)(t), in the presence of restricted diffusion, as well as the spectrum of the slow-motion velocity autocorrelation function. In this work, we focus on two previously unexplored aspects of OGSE experiments: convection compensation and acquisition of pure-phase diffusion spectra in the presence of homonuclear scalar couplings. We demonstrate that convection compensation afforded by single-echo OGSE compares well with that in double-echo convection-compensated PGSE experiments. We also show that, in the presence of homonuclear scalar couplings, setting the OGSE echo time to 1/2J enables acquisition of pure-phase diffusion spectra and yields more reliable D estimates than mixed-phase PGSE or OGSE spectra. Pure-phase OGSE acquisition is also compatible with measurements of the apparent diffusion coefficient at an arbitrary diffusion time. These features of OGSE can be valuable in diffusion measurements of scalar-coupled small-molecule probes in cellular and other heterogeneous systems.     

Background gradient suppression in pulsed gradient stimulated echo measurements

Pulsed gradient spin echo (PGSE) experiments can be used to measure the probability distribution of molecular displacements. In homogeneous samples this reports on the molecular diffusion coefficient, and in heterogeneous samples, such as porous media and biological tissue, such measurements provide information about the sample's morphology. In heterogeneous samples however background gradients are also present and prevent an accurate measurement of molecular displacements. The interference of time independent background gradients with the applied magnetic field gradients can be removed through the use of bipolar gradient pulses. However, when the background gradients are spatially non-uniform molecular diffusion introduces a temporal modulation of the background gradients. This defeats simple bipolar gradient suppression of background gradients in diffusion related measurements. Here we introduce a new method that requires the background gradients to be constant over coding intervals only. Since the coding intervals are typically at least an order of magnitude shorter than the storage time, this new method succeeds in suppressing cross-terms for a much wider range of heterogeneous samples.     

Surface exchange reactions and fast grain boundary diffusion in polycrystalline materials: Application of a spherical grain model

Laplace transforms of the solution functions to the diffusion equations for surface exchange reactions and fast grain boundary diffusion in polycrystalline materials of finite thickness have been derived by applying a spherical grain model. Diffusion profiles have been calculated for semi-infinite diffusion systems as well as thin films by application of numerical Laplace inversion. The surface exchange reaction at the surface of the sample (e.g. oxide ceramics) in contact with the constant diffusion source (e.g. gas phase) is assumed to be fairly slow such that the diffusion source is not in equilibrium with the surface during the diffusion anneal. Two limiting cases for the surface conditions are taken into account, viz. fast surface diffusion and a uniform ratio of the surface exchange coefficient/diffusion coefficient. The calculated profiles refer to Harrison's type-A diffusion kinetics. Apart from expressions for the effective diffusion coefficient, analogous relations for the effective surface exchange coefficient are proposed. Relaxation curves for the total amount of diffusant exchanged with the diffusion source are discussed in terms of the diameter of the spherical grains (average grain size), surface exchange coefficient, bulk and grain boundary diffusion coefficient, respectively.     

Contrasting friction and diffusion in molecularly thin confined films

We study, using fluorescence correlation spectroscopy, translational diffusion in molecularly thin liquids confined within a surface forces apparatus. The diffusion coefficient decreases exponentially from the edges towards the center of the Hertzian contact and further suggests the presence of a small number of distinct diffusion processes. This holds alike a crystallizable fluid (OMCTS) and a glass-former (1,2-propane diol), both of which displayed static friction. We conclude that friction, the average of an ensemble of molecules, masked massively heterogeneous molecular mobility.     

Chaotic wave trains in an oscillatory/excitable medium

We study the chaotic dynamics of a heterogeneous reaction–diffusion medium composed of two uniform regions: one oscillatory, and the other excitable. It is shown that, by altering the diffusion coefficient, local chaotic oscillations can be induced at the interface between regions, which in turn, generate different chaotic sequences of pulses traveling in the excitable region. We analyze the properties of the local chaotic driver, as well as the diffusion-induced transitions. A procedure based on the abnormal frequency-locking phenomenon is proposed for controlling such sequences. Relevance of the obtained results to cardiac dynamics is briefly discussed.     

Giant Enhancement of Diffusion in a Tilted Egg-Carton Potential

Diffusion of a particle on a tilted periodic surface such as the egg-carton potential is investigated using Langevin Monte Carlo simulations.It is found that the effective diffusion coefficient of the particle related to the onedimensional case can be greatly enhanced,when the local minima of such potential along the x and y directions are close to vanishing.A relation between the group diffusion and the phase diffusion is used to analyze the enhancement mechanism of the diffusion.     

Depth distributions of implanted atoms under the influence of surface erosion and diffusion

Shallow range distributions are altered significantly by diffusion and surface erosion. It will be shown here that the simultaneous processes of implantation, diffusion, and surface erosion can be described by a second order differential equation which is mathematically tractable and yields general results in terms of analytical functions. The resulting depth distributions depend on one parameter only which is a combination of the mean particle range, the diffusion coefficient, and the velocity of surface erosion (e.g. sputtering). The theory is applied to practical cases, e.g. implantation of plasma particles in the wall of fusion reactors, or solar wind ions in the surface of meteorite materials.     

Diffusion-influenced reactions

We summarize three of our recent results on diffusion-influenced reactions in solutions. All deal with the concentration dependence of the reaction rate when the reactants must first diffuse together before reaction can occur. When one species (the sink species) is not dilute, the rate cannot be obtained by solution of a pair diffusion equation; the correlations among the sinks for the diffusing species must be accounted for. First, we consider fluorescence quenching when the quenchers are not dilute. For charged quenchers and fluorophores we discuss how the solution dielectric constant and ionic strength can strongly influence the deviations from the linear Stern-Volmer behavior (the dilute sink result) which arise due to the sink correlations. Second, we consider heterogeneous catalysis where a reactive species is adsorbed onto a surface and must surface diffuse to reactive sites (the sinks). We find that surface diffusion can be an important factor contributing to the rate of reaction; especially when surface diffusion is rapid relative to the adsorption/desorption rate. Third, we discuss diffusion influenced reactions with sinks which are long ellipsoids. Dilute long ellipsoids provide a large rate enhancement relative to a spherical sink; we show that this rate enhancement survives when nondilute ellipsoids are considered.     

异质原子在Cu（001）表面扩散的分子动力学模拟

采用分子动力学方法模拟单个增原子Ag,Pd和Cu在Cu（001）表面上的扩散过程.通过对自扩散和异质扩散过程中扩散机制的观察,统计三种不同的增原子在不同温度下的扩散频率,拟合给出扩散势垒和扩散频率的指前因子,并与扩散势垒的静力学计算结果进行比较.结果表明：在800 K以下时,三种增原子均以简单跳跃机制为主扩散,与衬底不互溶的Ag增原子的跳跃频率最大,与衬底互溶的Pd增原子的跳跃频率最小.同质增原子与异质增原子的扩散频率和温度的关系均较好地符合Arrhenius公式,由Arrhenius公式拟合给出的三种不同增原子的扩散势垒与表面结构和增原子表面结合能有关.Pd和Cu增原子从跳跃机制为主向交换机制为主的转换温度分别在825和937 K左右. 关键词： 表面扩散 分子动力学模拟     

Effect of magnetic field gradients induced by microvasculature on NMR measurements of molecular self-diffusion in biological tissues

Presence of induced mesoscopic gradients of magnetic field in magnetically heterogeneous samples affects the measured value of apparent diffusion coefficient. This effect is investigated theoretically in the context of diffusion measurements in perfused biological tissues with blood as the paramagnetic compartment. It is shown that the apparent diffusion coefficient is sensitive to mutual correlations in vessel positions. Neglect of these correlations results in a failure of the commonly used model of microvasculature in which vessels are described as independently placed cylinders. The model is modified to account for intervessel correlations. The results indicate an underestimation of apparent diffusion coefficient in proportion to the magnetic susceptibility of intravascular compartment in agreement with published experimental data. The proportionality coefficient depends on the microvascular architecture. Comparison with experimental data yields a numerical value for a new model parameter that characterises the correlation in mutual positions of blood vessels.     

Electrochemical study of silver thiosulphate reduction in the absence and presence of ultrasound

The electrochemical reduction of silver thiosulphate was studied potentiostatically on platinum electrodes in the absence and presence of ultrasound (20 kHz). This system is irreversible and the reaction is both diffusion and kinetically controlled. The slowest step is the kinetic reaction especially the chemisorption of ions at the electrode surface. Ultrasound greatly improves the mass transport, which can be explained by changing from diffusion to mainly convection. This paper reports the effect of ultrasound upon electrode kinetic and mass-transport parameters at various RDE rotation speeds and ultrasonic intensities. It was found that the heterogeneous rate constant (kf) is improved in the presence of ultrasound due to the increase in the formal or standard heterogeneous rate constant (k0) (approximately by 10-fold under sonication).