Molecular collisions and self-diffusion in liquids

The velocity autocorrelation function and coefficient of self-diffusion are derived for a hard-sphere fluid. An earlier quasi-lattice model of self-diffusion in liquids is re-examined and a less restrictive expression for the self-diffusion coefficient is derived. The coefficient of self-diffusion of a light or heavy isotope in the normal liquid is considered both for hard spheres and in the quasi-lattice approximation. An experiment is proposed to clarify the nature of the isotope effect in self-diffusion.     

Self-diffusion of aluminium in the intermetallic compound Fe-48 at.% Al

The self-diffusion coefficient of Al in the B2-type intermetallic compound Fe-48 at.% Al has been determined using the intrinsic diffusion coefficients of Fe and Al and the self-diffusion coefficient of Fe with the help of the Darken-Manning relation. The self-diffusion coefficient of Al in Fe-48 at.% Al is estimated to be a factor of about 0.6 smaller than that of Fe, and the activation energy for the self-diffusion of Al is obtained to be 280 kJ mol^?1 which is a little larger than the value of 262 kJ mol^?1 for the self-diffusion of Fe, indicating that the diffusion mechanisms for both components are nearly equal.     

Study of molecular mobility of fluid in zeolite NaX.

The self-diffusion of n-decane in zeolite NaX was studied by NMR PFG method. The situation when the liquid was only in the crystalline channels was studied in details. The restricted molecular motion of liquid in the crystalline channels was observed. The reasons of the anomalous self-diffusion of n-decane in zeolite bed were stated. The technique of the determination of the genuine self-diffusion coefficient in such porous systems was proposed. The genuine self-diffusion coefficients for system NaX/n-decane were obtained.     

Einsatz von deuterierten Molekülen zur Bestimmung von Selbstdiffusionskoeffizienten bei der Zweikomponentenadsorption in Zeolithen unter Anwendung der NMR-Meßtechnik

The nmr pulsed field gradient technique is an efficient tool for measuring molecular self-diffusion in sorplion systems. Applying alternatively perdeutcrated substances, in this way for the first lime the self-diffusion coefficients of the individual components at mullicomponent adsorption could be measured. Examples of self-diffusion results for mixtures of water, ammonia and liydrocarbons adsorbed on different types of zeolites are given.     

Application of random walk concept to the cyclic diffusion mechanisms for self-diffusion in intermetallic compounds

Huntington–Elcock–McCombie (HEM) mechanism involving six consecutive and correlated jumps, a triple-defect mechanism (TDM) involving three correlated jumps and an anti-structure bridge (ASB) mechanism invoking the migration of an anti-structure atom are the three mechanisms currently in vogue to explain the self- and solute diffusion in intermetallic compounds. Among them, HEM and TDM are cyclic in nature. The HEM and TDM constitute the theme of the present article. The concept of random walk is applied to them and appropriate expressions for the diffusion coefficient are derived. These equations are then employed to estimate activation energies for self-diffusion via HEM and TDM processes and compared with the available experimental data on activation energy for self-diffusion in intermetallic compounds. The resulting activation energies do not favour HEM and TDM for the self-diffusion in intermetallic compounds. A comparison of the sum of experimentally determined activation energies for vacancy formation and migration with the activation energies for self-diffusion determined from radioactive tracer method favours the conventional monovacancy-mediated process for self-diffusion in intermetallic compounds.     

Effect of alloying on the self-diffusion activation energy in γ-iron

The experimental data on the self-diffusion coefficient of austenite with different chemical compositions obtained by the radioactive isotope method have been analyzed quantitatively. The self-diffusion activation energy in pure γ-iron is shown to be ∼312 kJ/mol. Alloying of austenite with such elements as Mn, Mo, Nb, Ti, and Si (to a lower degree) increases the self-diffusion activation energy, and alloying with C, V, or Cr (for the element content ≥3 at %) decreases it. The empirical formula is derived for calculation of the self-diffusion activation energy in austenite solid solutions with complex composition.     

Water self-diffusion in Chlorella sp. studied by pulse field gradient NMR

The water self-diffusion behavior in chlorella water suspension was investigated by pulsed field gradient NMR technique. Three types of water was determined, which differs according to the self-diffusion coefficients; bulk water, extracellular and intracellular water. Intracellular and extracellular water self-diffusion were restricted, and the sizes of restriction regions were 3.4 microm and 17 microm, respectively. The water molecular exchange process between these three diffusion regions was investigated. The residence time and exchange rate constant for chlorella cells were obtained. The cell wall permeability determined from the rate constant as 3 x 10(-6) m/s agreed with the permeability 10(-6) m/s obtained from time dependence of intracellular water self-diffusion coefficient. The structural cluster model of chlorella cell is estimated to describe the extracellular water self-diffusion in chlorella water suspension.     

Theoretical studies of surface diffusion: Self-diffusion in the bcc (211) system

Surface self-diffusion in the bcc (211) system is studied using numerical molecular dynamics simulations. Calculations based on Lennard-Jones pair potentials extracted from fits to bulk thermodynamic data produce self-diffusion constants in excellent agreement with available experimental data. These same potentials have been shown previously to yield similar agreement with experimental self-diffusion data for the bcc (110) system.     

超高压水的分子动力学模拟

 采用平衡分子动力学（EMD）方法,模拟研究了温度范围为243~348 K、压强范围为0.1~400 MPa条件下水的热力学性质、结构和动力学性质,模拟结果与实验值吻合较好。模拟结果表明,随着压强的增大,水分子间的氢键作用增强,扩散系数减小;随着温度的升高,水分子间的氢键作用减弱,有序程度下降,扩散系数增大。但在过冷水中,扩散系数随压强的增大有增加的趋势。     

Self-diffusion of water and benzene molecules adsorbed in synthetic opal samples

The self-diffusion of adsorbed molecules of water and benzene in porous synthetic opals has been studied by pulsed field gradient nuclear magnetic resonance. The study indicates two “phases” of water molecules differing by the self-diffusion coefficients, indicating two types of porosities existing in the synthetic opals. The smallest self-diffusion coefficient characterizes water in ultramicropores found on the surface of nanospheres. The form of the diffusion decay depends on temperature in the region of high temperatures as a result of exchange between pores of different sizes. The ultramicropores are inaccessible for the largest benzene molecules. Water adsorption and self-diffusion data confirm that annealing of the opal samples at 1293 K caused the collapse of ultramicropores.     

Self-Diffusion in Cell Membranes in the Long Time Regime

We consider the process of self-diffusion in the cellular structure in the presence of permeable barriers in long time regime. Based on the most general concepts of the translation mobility and geometry of a heterogeneous system, an expression for the self-diffusion coefficient of liquid molecules in such a medium in a long time regime was derived. We have shown that the value of the self-diffusion coefficient in the long-time limit is determined by the probability of interaction of the diffusant molecule with an obstacle. We obtained an expression for the probability of such interaction as a function of the surface-to-volume ratio (S/V). Comparing the obtained analytical expression with the results of computer simulation was performed. Shown the exponential dependence of the self-diffusion coefficient on the barrier pinning density.     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.     

Dynamical properties of strongly interacting Brownian particles : II. Self-diffusion

The self-diffusion process of Brownian particles is theoretically investigated for concentrated systems in the presence of strong potential interactions between particles. Starting from an N-particle diffusion equation, a formalism is developed to calculate the self-diffusion coefficient and the velocity autocorrelation function on the basis of the superposition approximation for the three-particle distribution function of non-equilibrium states. Explicit calculations are carried out for model systems of hard spheres with a screened Coulomb potential. Calculated time-dependent self-diffusion coefficients are compared with available data of the Brownian dynamics. Without introducing any phenomenological or adjustable parameters, quantitative agreement is achieved.     

Determination of water self-diffusion coefficient in complex food products by low field 1H PFG-NMR: comparison between the standard spin-echo sequence and the T1-weighted spin-echo sequence

In 1990, Van Den Enden et al. proposed a method for the determination of water droplet size distributions in emulsions using a pulsed-field-gradient nuclear magnetic resonance (PFG-NMR) T1-weighted stimulated-echo technique. This paper describes both the T1-weighted spin-echo sequence, an improved method based on this earlier work, and, the standard PFG spin-echo sequence. These two methods were compared for water self-diffusion coefficient measurement in the fatty protein concentrate sample used as a 'cheese model.' The transversal and longitudinal relaxation parameters T1 and T2 were determined according to the temperature and investigated for each sample; fat-free protein concentrate sample, pure anhydrous milk fat, and fatty protein concentrate sample. The water self-diffusion in fat-free protein concentrate samples followed a linear behavior. Consequently, the water self-diffusion coefficient could be easily characterized for fat-free protein concentrate samples. However, it seemed more complicated to obtain accurate water self-diffusion in fatty protein concentrate samples since the diffusion-attenuation data were fitted by a bi-exponential function. This paper demonstrates that the implementation of the T1-weighted spin-echo sequence, using the different T1 properties of water and fat phases, allows the accurate determination of water self-diffusion coefficient in a food product. To minimize the contribution of the 1H nuclei in the fat phase on the NMR echo signal, the fat protons were selectively eliminated by an additional 180 degrees pulse. This new method reduces the standard errors of diffusion data obtained with a basic spin-echo technique, by a factor of 10. The effectiveness of the use of the T1-weighted spin-echo sequence to perform accurate water self-diffusion coefficients measurement in fatty products is thus demonstrated.     

Ionic and molecular Self-Diffusion in Ion-Exchange materials for fuel energetics studied by pulsed field gradient NMR

Pulsed field gradient nuclear magnetic resonance technique was applied to investigate the self-diffusion mechanism of water, alcohol molecules and Li⁻ counterions in sulfocation exchangers with different structures of the polymeric matrix. It was shown that in the homogeneous perfluorinated sulfocation exchange membranes the ionic and water translation motions are controled by the hydrogen bond network forming in ionogenic channels at the high water content. At the low solvent content, the self-diffusion coefficients of methanol and ethanol are higher than the water self-diffusion coefficients. The influence of non-ion-exchange sorbed electrolyte on Li⁺ self-diffusion coefficients was observed in the heterogeneous sulfocation exchanger KU-23.     

Dissipative particle dynamics study of velocity autocorrelation function and self-diffusion coefficient in terms of interaction potential strength

This research focuses on numerically investigating the self-diffusion coefficient and velocity autocorrelation function (VACF) of a dissipative particle dynamics (DPD) fluid as a function of the conservative interaction strength. Analytic solutions to VACF and self-diffusion coefficients in DPD were obtained by many researchers in some restricted cases including ideal gases, without the account of conservative force. As departure from the ideal gas conditions are accentuated with increasing the relative proportion of conservative force, it is anticipated that the VACF should gradually deviate from its normally expected exponentially decay. This trend is confirmed through numerical simulations and an expression in terms of the conservative force parameter, density and temperature is proposed for the self-diffusion coefficient. As it concerned the VACF, the equivalent Langevin equation describing Brownian motion of particles with a harmonic potential is adapted to the problem and reveals an exponentially decaying oscillatory pattern influenced by the conservative force parameter, dissipative parameter and temperature. Although the proposed model for obtaining the self-diffusion coefficient with consideration of the conservative force could not be verified due to computational complexities, nonetheless the Arrhenius dependency of the self-diffusion coefficient to temperature and pressure permits to certify our model over a definite range of DPD parameters.     

Model of grain-boundary self-diffusion in α- and β-phases of titanium and zirconium

A model of the grain-boundary self-diffusion process in metals undergoing phase transitions in the solid state is proposed. The model is based on the ideas and approaches of the theory of nonequilibrium grain boundaries. It is shown that the range of application of basic relations of this theory can be extended, and they can be used to calculate the parameters of grain-boundary self-diffusion in high-temperature and low-temperature phases of metals with phase transition. Based on the constructed model, activation energies of grainboundary self-diffusion in titanium and zirconium are calculated, and their anomalously low values in the low-temperature phase are explained. The calculated activation energies of grain-boundary self-diffusion are in good agreement with experimental data.     

Introduction to Quantum Statistical Mechanics, 2nd edn., by N.N. Bogolubov and N.N. Bogolubov Jr

The mobility and self-diffusion of polymer molecules in concentrated systems or in the molten bulk state is largely controlled by entanglements between the molecules. These entanglements are a result of the chain-like nature of the molecules and of their extended, coil-like configuration. The conformation and mobility of polymer molecules in dilute solution—which are relatively well understood—are discussed; this leads to a consideration of self-diffusion in the more concentrated states and in the bulk polymer melt, and several special properties of polymers which are controlled and modified by the molecular self-diffusion are examined.

Our current theoretical understanding of polymeric self-diffusion in highly entangled systems is outlined, and the ways in which such diffusion may be studied experimentally are briefly described. The final part of the review describes a recent experimental study of self-diffusion in a polymer melt; the results of this study may provide new insight into the motion of entangled, chain-like molecules.     

Correlation between film thickness and zinc defect distribution along the growth direction in an isotopic multilayer ZnO thin film grown by pulsed laser deposition analyzed using the internal diffusion method

Zinc self-diffusion along the growth direction was analyzed for the isotopic multilayer ZnO thin film ((⁶⁴ZnO/⁶⁸ZnO)₆⁶⁴ZnO) deposited by pulsed laser deposition. The isotopic distribution was measured using a secondary ion mass spectrometry. The amplitude of the ⁶⁴Zn abundance in the depth profile was reduced by annealing at 993 K for several hours due to interdiffusion between the ⁶⁴ZnO and ⁶⁸ZnO layers. The diffusion profiles at the isotopic interfaces were analyzed using a periodic equation. The obtained zinc self-diffusion coefficients at several isotopic interfaces along the growth direction showed that the self-diffusion coefficients increased towards the film/substrate interface. A similar trend was also found in the lateral direction. The variation among the self-diffusion coefficients was related to the film thicknesses at the analysis positions. Since zinc self-diffusion is controlled by a vacancy-mediated mechanism, the variation in zinc diffusivity along the growth direction can be attributed to the effect of compressive biaxial stress. These findings are useful for producing high-quality ZnO devices.     

液态纯铁自扩散系数研究

液态金属固有的良好导热性能和很好的流动性能,逐渐受到了工程领域越来越多的重视。但由于液相扩散系数的测量困难,目前未见液态纯铁的自扩散系数报道。本文以液态纯铁正则系综为研究对象,采用分子动力学模拟方法对其自扩散系数进行了模拟分析,研究结果表明液态纯铁自扩散系数随温度增加呈现出了较大的变化,应用自扩散系数与温度存在的Arrhenius关系拟合出了液态纯铁的自扩散系数经验公式,进一步获得了液态纯铁原子的平均自由程计算关系式。