Self-diffusion Coefficient Model Based on Activation Energy and Free Volume

A new model for self-diffusion coefficients was proposed based oil both the concepts of molecular free volume and activation energy. The unknown parameters of this model were clearly defined and compared with the Chapman-Enskog model. At the same time a new method for calculating activation energy was devised and applied to the new model. In addition, the free volume was defined by implementing the generic van der Waals equation of state, the radial distribution function of which was obtained by using the Morsali- Goharshadi empirical formula. Under the same conditions, the new model was better than the original free volume model.

Critical anomaly and finite size scaling of the self-diffusion coefficient for Lennard Jones fluids by non-equilibrium molecular dynamic simulation

We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ＊ = ρσ3 = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T＊ = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of a 〈 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations fronl the literature.

Self-diffusion coefficients of organic solvents in linear and branched high density polyethylene particles measured by PFG NMR

Pulsed field gradient nuclear magnetic resonance （PFG NMR） has been performed to study the diffusion of organic solvents into semicrystalline polyethylene particles. Self-diffusion coefficients in different domains of the sample can be extracted through a bi- exponential fit to the echo intensity attenuation, which allows the precise determination of the tortuosity of the polyethylene particles. Further exploration comes from the measurements with branched polyethylene particles and it was found that the diffusion in polymer phase contributed significantly to the slow component of the exponential decay curve. 2007 Jing Dai Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.

Molecular dynamics simulation of self-diffusion coefficients for liquid metals

The temperature-dependent coefficients of self-diffusion for liquid metals are simulated by molecular dynamics meth ods based on the embedded-atom-method （EAM） potential function. The simulated results show that a good inverse linear relation exists between the natural logarithm of self-diffusion coefficients and temperature, though the results in the litera ture vary somewhat, due to the employment of different potential functions. The estimated activation energy of liquid metals obtained by fitting the Arrhenius formula is close to the experimental data. The temperature-dependent shear-viscosities obtained from the Stokes-Einstein relation in conjunction with the results of molecular dynamics simulation are generally consistent with other values in the literature.

OXYGEN SELF-DIFFUSION AND INTERACTIONS BETWEEN DEFECTS IN Fe_3O_4

New experimental results on the self diffesion of oxygen in Fe3O4 obtained with a high precision SIMS at 1079K allow to conclude the eristence of oxygen vacancies and of oxygen iron vacancy pairs coexisting selectively with different kinds of iron defects.The possibility of measuring the isotopic effect of the two tracers O17 and O18 is also examined.

Dramatic change of the self-diffusions of colloidal ellipsoids by hydrodynamic interactions in narrow channels

The self-diffusion problem of Brownian particles under the constraint of quasi-one-dimensional(q1 D) channel has raised wide concern.The hydrodynamic interaction(HI) plays an important role in many practical problems and two-body interactions remain dominant under q1D constraint.We measure the diffusion coefficient of individual ellipsoid when two ellipsoidal particles are close to each other by video-microscopy measurement.Meanwhile, we obtain the numerical simulation results of diffusion coefficient using finite element software.We find that the self-diffusion coefficient of the ellipsoid decreases exponentially with the decrease of their mutual distance X when X < X0, where X0 is the maximum distance of the ellipsoids to maintain their mutual influence, X0 and the variation rate are related to the aspect ratio p = a/b.The mean squared displacement(MSD) of the ellipsoids indicates that the self-diffusion appears as a crossover region, in which the diffusion coefficient increases as the time increases in the intermediate time regime, which is proven to be caused by the spatial variations affected by the hydrodynamic interactions.These findings indicate that hydrodynamic interaction can significantly affect the self-diffusion behavior of adjacent particles and has important implications to the research of microfluidic problems in blood vessels and bones, drug delivery, and lab-on-chip.

Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method(DEM)modelling.The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions.A side wall node loading method is used to exert bi-directional shear of various angles.The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials.However,the relationship between bidirectional shear and mechanical responses relies on loading conditions,i.e.constant vertical stress or constant volume conditions.The stress states induced by static shear consolidation are affected by loading angles,which are enlarged by subsequent shear,consistent with the relationship between bidirectional shear and principal stresses.It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials.The presence of bi-directional principal stress rotation(PSR)is demonstrated,which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction.Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts,but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts.It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions.Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined,providing further insights into understanding granular behaviour under bi-directional shear.

Capillary Phase-Transition and Self-Diffusion of Ethylene in the Slit Carbon Pores

The grand canonical Monte Carlo (GCMC), the canonical Monte Carlo by using equal probability perturbation, and the molecular dynamics (MD) methods were used to study the capillary phase-transition (capillary condensation and evaporation) and self-diffusion for a simple Lennard-Jones model of ethylene confined in slit carbon pores of 2.109 nm at temperatures between 141.26 K and 201.80 K. The critical point of capillary phase-transition was extrapolated by the critical power law and the law of rectilinear diameter from the capillary phase-transition data in the near critical region. The effects of temperature and fluid density on the parallel self-diffusion coefficients of ethylene molecules confined in the slit carbon pores were examined. The results showed that the parallel selfdiffusion coefficients in the capillary phase transition area strongly depended on the fluids local densities in the slit carbon pores.

Enhancement of water self-diffusion at super-hydrophilic surface with ordered water

It has been well acknowledged that molecular water structures at the interface play an important role in the surface properties, such as wetting behavior or surface frictions. Using molecular dynamics simulation, we show that the water self-diffusion on the top of the first ordered water layer can be enhanced near a super-hydrophilic solid surface. This is attributed to the fewer number of hydrogen bonds between the first ordered water layer and water molecules above this layer, where the ordered water structures induce much slower relaxation behavior of water dipole and longer lifetime of hydrogen bonds formed within the first layer.

Anisotropic self-diffusion of fluorinated poly(methacrylate) in metal-organic frameworks assessed with molecular dynamics simulation

Utilizing the periodically structured metal-organic framework （MOF） as the reaction vessel is a promising technique to achieve the aligned polymer molecular chains, where the diffusion procedure of the polymer monomer inside MOF is one of the key mechanisms. To investigate the diffusion mechanism of fluorinated polymer monomers in MOFs, in this paper the molecular dynamics simulations combined with the density functional theory and the Monte Carlo method are used and the all-atom models of TFMA （trifluoroethyl methacrylate） monomer and two types of MOFs,[Zn2（BDC）2（TED）]n and[Zn2（BPDC）2（TED）]n, are established. The diffusion behaviors of TFMA monomer in these two MOFs are simulated and the main influencing factors are analyzed. The obtained results are as follows. First, the electrostatic interactions between TFMA monomers and MOFs cause the monomers to concentrate in the MOF channel, which slows down the monomer diffusion. Second, the anisotropic shape of the one-dimensional MOF channel leads to different diffusion speeds of monomers in different directions. Third, MOF with a larger pore diameter due to a longer organic ligand,[Zn2（BPDC）2（TED）]n in this paper, facilitates the diffusion of monomers in the MOF channel. Finally, as the number of monomers increases, the self-diffusion coefficient is reduced by the steric effect.

Molecular Dynamics Simulations of Self-diffusion Coefficients of Exponential-six Fluids

Self-diffusion coefficients of exponential-six fluids are studied using equilibrium molecular dynamics simulation technique. Mean-square displacements and velocity autocorrelation functions are used to calculate self-diffusion coefficients through Einstein equation and Green-Kubo formula. It has been found that simulation results are in good agreement with experimental data for liquid argon which is taken as exponential-six fluid. The effects of density, temperature and steepness factor for repulsive part of exponential-six potential on self-diffusion coefficients are also investigated. The simulation results indicate that the self-diffusion coefficient of exponential-six fluid increases as temperature increases and density decreases. In addition, the larger self-diffusion coefficients are obtained as the steepness factor increases at the same temperature and density condition.

Investigation on characteristics of liquid self-diffusion in slit nanopores using simple quasicrystal model of liquid

Dynamical properties of liquid in nano-channels attract much interest because of their applications in engineering and biological systems. The transfer behavior of liquid confined within nanopores differs significantly from that in the bulk. Based on the simple quasicrystal model of liquid, analytical expressions of self-diffusion coefficient both in bulk and in slit nanopore are derived from the Stokes–Einstein equation and the modified Eyring's equation for viscosity. The local self-diffusion coefficient in different layers of liquid and the global self-diffusion coefficient in the slit nanopore are deduced from these expressions. The influences of confinement by pore walls,pore widths, liquid density, and temperature on the self-diffusion coefficient are investigated. The results indicate that the self-diffusion coefficient in nanopore increases with the pore width and approaches the bulk value as the pore width is sufficiently large. Similar to that in bulk state, the self-diffusion coefficient in nanopore decreases with the increase of density and the decrease of temperature, but these dependences are weaker than that in bulk state and become even weaker as the pore width decreases. This work provides a simple method to capture the physical behavior and to investigate the dynamic properties of liquid in nanopores.

Hemoglobin S Polymerization Effect on Water Self-Diffusion Coefficient

The transversal relaxation time, the effective transversal relaxation time and the water self-diffusion coefficient are evaluated during hemoglobin S polymerization. One homogeneous permanent magnet and one inhomogeneous and portable unilateral magnet with a very strong and constant static magnetic field gradient were utilized. The Carr-Purcell-Meiboom-Gill method was used before and after placing the studied samples 24 hours at 36&deg;C to guarantee the polymerization. The transversal relaxation shows two exponents after polymerization supporting the concept of partially polymerized hemoglobin. The effective transversal relaxation time decreases around 40%, which can be explained by the increase of water self-diffusion coefficient 1.8 times as a main value. This result can be explained considering the effects of the agglutination process on the obstruction and hydration effects in a partially polymerized solution.

The Relation between the Heat of Melting Point, Boiling Point, and the Activation Energy of Self-Diffusion in Accordance with the Concept of Randomized Particles

On the example of typical metals, it’s found that the activation energy of self-diffusion is above of the melting heat and below of vaporization heat. This corresponds to the existence of liquid-mobile particle classification based on the concept of randomized particles. A formula for estimating the activation energy of self-diffusion by which it is approximately half of the heat of evaporation of the substance is recommended. We derive the temperature dependence for a fraction self-diffusion’s particles.

Cyclic shear behavior of en-echelon joints under constant normal stiffness conditions

To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)conditions.We analyzed the evolution of shear stress,normal stress,stress path,dilatancy characteristics,and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles.The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle,with the shear strength at a positive angle exceeding that at a negative angle during shear cycles.As the number of cycles increases,the shear strength decreases rapidly,and the difference between the varying angles gradually decreases.Dilation occurs in the early shear cycles(1 and 2),while contraction is the main feature in later cycles(310).The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles.The joint angle determines the asperities on the rupture surfaces and the block size,and thus determines the subsequent shear failure mode(block crushing and asperity degradation).At positive angles,block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles.Therefore,the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.

Investigation of Self-Diffusion and Structure in Calcium Aluminosilicate Slags by Molecular Dynamics Simulation

Molecular dynamics simulation is applied to investigate the mechanism and variation of self-diffusion in calcium aluminosilicate slags. The self-diffusion coefficients are calculated for eleven slag compositions with varying Al2O3/SiO2 ratios at a fixed CaO content. In practice, the results of the study are relevant to the significant changes in transport phenomenon caused by the changes in chemical composition during continuous casting of steels containing high amounts of dissolved aluminum. The cooperative movement between O atoms and network formers is discussed since [AlO4] and [SiO4] tetrahedra are the elementary structural units in the CaO-Al2O3-SiO2 (CAS) slag system. The diffusivities for four atomic types are affected by the degree of polymerization (DOP) of slag network characterized by the proportions of non-bridging oxygen (NBO) and Qn species in the system. On the other hand, a sudden increase in 5-coordinated Al as network modifiers in high alumina regions slightly increases the self-diffusion coefficient for Al. As another structural defect, oxygen tricluster plays an important role in the behavior of self-diffusion for O atoms, while the diffusivity for Ca is deeply influenced by its bonding and coordinating conditions.

Gedankenexperiment for Modified ZPE and Planck’s “Constant”, h, in the Beginning of Cosmological Expansion, Partly Due to NLED

We initially look at a non singular universe representation of entropy, based in part on what was brought up by Muller and Lousto. This is a gateway to bringing up information and computational steps (as defined by Seth Lloyd) as to what would be available initially due to a modified ZPE formalism. The ZPE formalism is modified as due to Matt Visser’s alternation of k (maximum) ~ 1/(Planck length), with a specific initial density giving rise to initial information content which may permit fixing the initial Planck’s constant, h, which is pivotal to the setting of physical law. The settings of these parameters depend upon NLED.

Elementary Fermions: Strings, Planck Constant, Preons and Hypergluons

Using real fields instead of complex ones, it is suggested here that the fermions are pairs of coupled strings with an internal tension. The interaction between the two coupled strings is due to an exchange mechanism which is proportional to Planck’s constant. This may be the result of two massless bosons (hypergluons) coupled by a preon (prequark) exchange. It also gives a physical explanation to the origin of the Planck constant, and origin of spin.

ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR

In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.

Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.