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In this second paper the authors study the transport properties of the lattice-gas cellular automaton presented in Paper I [J. Chem. Phys. 126, 194709 (2007)] to model adsorption and dynamics of particles in a lattice of confining cells. Their work shows how a surprisingly simple parallel rule applied to a static network of cells joined by links set in space and time can generate a wide range of dynamical behaviors. In their model the cells are the elementary constituent objects of the network. They are a portion of space structured in sites which are energetically different. Each cell can accommodate a given maximum number of particles, and each pair of neighboring cells can exchange at most one particle at a time. The predictions of the model are in qualitative agreement with both experimental observations and molecular dynamics simulation results. [ABSTRACT FROM AUTHOR]

The present paper provides direct noncircumstantial evidence in support of the existence of a diffuse flux of volume jv in mixtures. As such, it supersedes an earlier paper [H. Brenner, J. Chem. Phys. 132, 054106 (2010)], which offered only indirect circumstantial evidence in this regard. Given the relationship of the diffuse volume flux to the fluid's volume velocity, this finding adds additional credibility to the theory of bivelocity hydrodynamics for both gaseous and liquid continua, wherein the term bivelocity refers to the independence of the fluid's respective mass and volume velocities. Explicitly, the present work provides a new and unexpected linkage between a pair of diffuse fluxes entering into bivelocity mixture theory, fluxes that were previously regarded as constitutively independent, except possibly for their coupling arising as a consequence of Onsager reciprocity. In particular, for the case of a binary mixture undergoing an isobaric, isothermal, external force-free, molecular diffusion process we establish by purely macroscopic arguments-while subsequently confirming by purely molecular arguments-the validity of the ansatz jv=(v1-v2)j1 relating the diffuse volume flux jv to the diffuse mass fluxes j1(=-j2) of the two species and, jointly, their partial specific volumes v1,v2. Confirmation of that relation is based upon the use of linear irreversible thermodynamic principles to embed this ansatz in a broader context, and to subsequently establish the accord thereof with Shchavaliev's solution of the multicomponent Boltzmann equation for dilute gases [M. Sh. Shchavaliev, Fluid Dyn. 9, 96 (1974)]. Moreover, because the terms v1, v2, and j1 appearing on the right-hand side of the ansatz are all conventional continuum fluid-mechanical terms (with j1 given, for example, by Fick's law for thermodynamically ideal solutions), parity requires that jv appearing on the left-hand side of that relation also be a continuum term. Previously, diffuse volume fluxes, whether in mixtures or single-component fluids, were widely believed to be noncontinuum in nature, and hence of interest only to those primarily concerned with transport phenomena in rarefied gases. This demonstration of the continuum nature of bivelocity hydrodynamics suggests that the latter subject should be of general interest to all fluid mechanicians, even those with no special interest in mixtures. [ABSTRACT FROM AUTHOR]

We previously reported comprehensive density functional theory-molecular dynamics (DFT-MD) at 400 K to determine the composition and structure of the solid electrolyte interface (SEI) between a Li anode and [Pyr14][TFSI] ionic liquid. In this paper, we examined diffusion rates in both the Li-electrode region and SEI compact layer in smaller 83Li/2[TFSI] and larger 164Li/4[TFSI] systems. At 400 K, the Li-diffusion constant in the Li-region is 1.35 × 10−10 m2/s for 83Li/2[TFSI] and 5.64 × 10−10 m2/s for 164Li/4[TFSI], while for the SEI it is 0.33 × 10−10 m2/s and 0.22 × 10−10 m2/s, thus about one order slower in the SEI compared to the Li-region. This Li-diffusion is dominated by hopping from the neighbor shell of one F or O to the neighbor shell of another. Comparing the Li-diffusion at different temperatures, we find that the activation energy is 0.03 and 0.11 eV for the Li-region in the smaller and larger systems, respectively, while for the SEI it is 0.09 and 0.06 eV. [ABSTRACT FROM AUTHOR]

The diffusion map is a dimensionality reduction method. The reduction coordinates are associated with the leading eigenfunctions of the backward Fokker–Planck operator, providing a dynamic meaning for these coordinates. One of the key factors that affect the accuracy of diffusion map embedding is the dynamic measure implemented in the Gaussian kernel. A common practice in diffusion map study of molecular systems is to approximate dynamic proximity with RMSD (root-mean-square deviation). In this paper, we present a hybrid geometry-energy based kernel. Since high energy-barriers may exist between geometrically similar conformations, taking both RMSD and energy difference into account in the kernel can better describe conformational transitions between neighboring conformations and lead to accurate embedding. We applied our diffusion map method to the β-hairpin of the B1 domain of streptococcal protein G and to Trp-cage. Our results in β-hairpin show that the diffusion map embedding achieves better results with the hybrid kernel than that with the RMSD-based kernel in terms of free energy landscape characterization and a new correlation measure between the cluster center Euclidean distances in the reduced-dimension space and the reciprocals of the total net flow between these clusters. In addition, our diffusion map analysis of the ultralong molecular dynamics trajectory of Trp-cage has provided a unified view of its folding mechanism. These promising results demonstrate the effectiveness of our diffusion map approach in the analysis of the dynamics and thermodynamics of molecular systems. The hybrid geometry-energy criterion could be also useful as a general dynamic measure for other purposes. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations were conducted to investigate the dynamic properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. The ring melts were found to diffuse faster than their linear counterparts, with both architectures approximately obeying a D ∼ N-2.4 scaling law for large N. The mean-square displacement of the center-of-mass of the rings follows a sub-diffusive behavior for times and distances beyond the ring extension g2>, neither compatible with the Rouse nor the reptation model. The rings relax stress much faster than linear polymers, and the zero-shear viscosity was found to vary as η0 ∼ N1.4 ± 0.2 which is much weaker than the N3.4 behavior of linear chains, not matching any commonly known model for polymer dynamics when compared to the observed mean-square displacements. These findings are discussed in view of the conformational properties of the rings presented in the preceding paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204904 (2011)]. [ABSTRACT FROM AUTHOR]

Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schätzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles. [ABSTRACT FROM AUTHOR]

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This second of a series of four papers presents the results for the self-diffusion coefficient, and discusses and interprets the behavior of this transport coefficient in the fluid region of the phase diagram. The uncertainty of the self-diffusion data is estimated to be 1% in the gas region and 0.5% at high-density liquid states. With the very accurate data, even fine details in the shape of the self-diffusion isotherms are resolved, and the previously little-investigated behavior of the self-diffusion coefficient at low-density gaseous states is analyzed in detail. Finally, aspects of the mass transport mechanisms on the molecular scale are explored by an analysis of the velocity autocorrelation functions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Diffusion is one of the key subjects of molecular modeling and simulation studies. However, there is an unresolved lack of consistency between Einstein-Smoluchowski (E-S) and Green-Kubo (G-K) methods for diffusion coefficient calculations in systems of complex molecules. In this paper, we analyze this problem for the case of liquid n-triacontane. The non-conventional long-time tails of the velocity autocorrelation function (VACF) are found for this system. Temperature dependence of the VACF tail decay exponent is defined. The proper inclusion of the long-time tail contributions to the diffusion coefficient calculation results in the consistency between G-K and E-S methods. Having considered the major factors influencing the precision of the diffusion rate calculations in comparison with experimental data (system size effects and force field parameters), we point to hydrogen nuclear quantum effects as, presumably, the last obstacle to fully consistent n-alkane description. [ABSTRACT FROM AUTHOR]

Surface diffusion rates have been simulated using classical molecular dynamics in a model of CO adsorbed on Ni(111). This paper describes the energy distribution among adsorbate modes at the transition state, energy relaxation after crossing the transition state, and correlations among adsorbate modes near the transition state. The adsorbate bending (frustrated rotation) mode is strongly coupled to lateral translational motion. This molecular mode provides an important source of energy for reaching the transition state to diffusion, and an important frictional force that dissipates excess lateral translational energy. In this model, the molecular bending mode is a more important source (and sink) of lateral translational energy than the surface at short times. This result is interpreted as a consequence of directional bonding to the surface, and it should be generally important in surface diffusion of chemisorbed molecules. [ABSTRACT FROM AUTHOR]

Random walks including non-nearest-neighbor jumps appear in many real situations such as the diffusion of adatoms and have found numerous applications including PageRank search algorithm; however, related theoretical results are much less for this dynamical process. In this paper, we present a study of mixed random walks in a family of fractal scale-free networks, where both nearest-neighbor and next-nearest-neighbor jumps are included. We focus on trapping problem in the network family, which is a particular case of random walks with a perfect trap fixed at the central high-degree node. We derive analytical expressions for the average trapping time (ATT), a quantitative indicator measuring the efficiency of the trapping process, by using two different methods, the results of which are consistent with each other. Furthermore, we analytically determine all the eigenvalues and their multiplicities for the fundamental matrix characterizing the dynamical process. Our results show that although next-nearest-neighbor jumps have no effect on the leading scaling of the trapping efficiency, they can strongly affect the prefactor of ATT, providing insight into better understanding of random-walk process in complex systems. [ABSTRACT FROM AUTHOR]

Rotational diffusion processes are correlated with nanoparticle visualization and manipulation techniques, widely used in nanocomposites, nanofluids, bioscience, and so on. However, a systematical methodology of deriving this diffusivity is still lacking. In the current work, three molecular dynamics (MD) schemes, including equilibrium (Green-Kubo formula and Einstein relation) and nonequilibrium (Einstein-Smoluchowski relation) methods, are developed to calculate the rotational diffusion coefficient, taking a single rigid carbon nanotube in fluid argon as a case. We can conclude that the three methods produce same results on the basis of plenty of data with variation of the calculation parameters (tube length, diameter, fluid temperature, density, and viscosity), indicative of the validity and accuracy of the MD simulations. However, these results have a non-negligible deviation from the theoretical predictions of Tirado et al. [J. Chem. Phys. 81, 2047 (1984)], which may come from several unrevealed factors of the theory. The three MD methods proposed in this paper can also be applied to other situations of calculating rotational diffusion coefficient. [ABSTRACT FROM AUTHOR]

Measurements of diffusion and driven motion by probe particles in polymer solutions constrain theoretical models of polymer solution dynamics. In this paper, motions of large, intermediate (smaller than a polymer chain, larger than a solvent molecule), and small (solvent, ion) probes through polymer solutions and viscous small-molecule solvents are analyzed. The resulting constraints limit the physical models that can plausibly be used to describe polymer motion and separately limit the mathematical structures that might be used to obtain quantitative predictions from those models. A transition in small-molecule mobility through polymer solutions, at polymer concentrations near 400 g/l, is explained in terms of the size of a solvent molecule relative to the gaps between pairs of chain segments on adjacent polymer molecules. [ABSTRACT FROM AUTHOR]

We provide a systematic comparative analysis of various simulation methods for studying steady-state diffusive transport of molecular systems. The methods differ in two respects: (1) the actual method with which the dynamics of the system is handled can be a direct simulation technique [molecular dynamics (MD) and dynamic Monte Carlo (DMC)] or can be an indirect transport equation [the Nernst-Planck (NP) equation], while (2) the driving force of the steady-state transport can be maintained with control cells on the two sides of the transport region [dual control volume (DCV) technique] or it can be maintained in the whole simulation domain with the local equilibrium Monte Carlo (LEMC) technique, where the space is divided into small subvolumes, different chemical potentials are assigned to each, and grand canonical Monte Carlo simulations are performed for them separately. The various combinations of the transport-methods with the driving-force methods have advantages and disadvantages. The MD+DCV and DMC+DCV methods are widely used to study membrane transport. The LEMC method has been introduced with the NP+LEMC technique, which was proved to be a fast, but somewhat empirical method to study diffusion [D. Boda and D. Gillespie, J. Chem. Theor. Comput. 8, 824 (2012)]. In this paper, we introduce the DMC+LEMC method and show that the resulting DMC+LEMC technique has the advantage over the DMC+DCV method that it provides better sampling for the flux, while it has the advantage over the NP+LEMC method that it simulates dynamics directly instead of hiding it in an external adjustable parameter, the diffusion coefficient. The information gained from the DMC+LEMC simulation can be used to construct diffusion coefficient profiles for the NP+LEMC calculations, so a simultaneous application of the two methods is advantageous. [ABSTRACT FROM AUTHOR]

The important role of liquid water in many areas of science from chemistry, physics, biology, geology to climate research, etc., has motivated numerous theoretical studies of its structure and dynamics. The significance of quantum effects on the properties of water, however, has not yet been fully resolved. In this paper we focus on quantum dynamical effects in liquid water based on the linearized semiclassical initial value representation (LSC-IVR) with a quantum version of the simple point charge/flexible (q-SPC/fw) model [Paesani et al., J. Chem. Phys. 125, 184507 (2006)] for the potential energy function. The infrared (IR) absorption spectrum and the translational diffusion constants have been obtained from the corresponding thermal correlation functions, and the effects of intermolecular and intramolecular correlations have been studied. The LSC-IVR simulation results are compared with those predicted by the centroid molecular dynamics (CMD) approach. Although the LSC-IVR and CMD results agree well for the broadband for hindered motions in liquid water, the intramolecular bending and O–H stretching peaks predicted by the LSC-IVR are blueshifted from those given by CMD; reasons for this are discussed. We also suggest that the broadband in the IR spectrum corresponding to restricted translation and libration gives more information than the diffusion constant on the nature of quantum effects on translational and rotational motions and should thus receive more attention in this regard. [ABSTRACT FROM AUTHOR]

This paper presents a method for simultaneously determining multiple trajectories of single molecules from sequential fluorescence images in the presence of photoblinking. The tracking algorithm is computationally nondemanding and does not assume a model for molecular motion, which allows one to determine correct trajectories even when a distribution of movement speeds is present. We applied the developed procedure to the important problem of monitoring surface motion of single molecules under ambient conditions. By limiting the laser exposure using sample scanning confocal microscopy, long-time trajectories have been extracted without the use of oxygen scavengers for single fluorescent molecules. Comparison of the experimental results to simulations showed that the smallest diffusion constants extracted from the trajectories are limited by detector shot noise giving error in locating the positions of the individual molecules. The simulations together with the single molecule trajectories and distributions of diffusion constants allowed us therefore to distinguish between mobile and immobile molecules. Because the analysis algorithm only requires a time series of images, the procedure presented here can be used in conjunction with various imaging methodologies to study a wide range of diffusion processes. [ABSTRACT FROM AUTHOR]

Diffusion of perdeuterated tempone (PDT) in various nonpolar hydrocarbon solvents on both the large and microscopic scales is examined through electron paramagnetic resonance spectroscopy. Spectral line broadening and hyperfine spacing are measured in order to extract both the Heisenberg spin-exchange rate as well as the average recollision times between spin-probe pairs. Probe recollision is responsible for a linear component to the dependence of the line shift on spectral broadening which has been identified in recent years. The present study extends the work of a previous paper by Kurban et al. [J. Chem. Phys. 129, 064501 (2008)], in which it was reported that recollision rates for PDT formed a common curve across n-alkanes when plotted with respect to free volume and to isothermal compressibility. It is now found that such common curves occur within distinct chemical families, in particular, the alkane and aromatic groups. Within each chemical family, the spin probe recollision rate correlates with free volume and compressibility independently of the geometry of the particular solvent. All solvents show significantly enhanced recollisional diffusion over the Stokes–Einstein (SE) prediction at high temperatures. The spin-exchange rate forms a common curve with respect to T/η for all alkanes except cyclohexane and another common curve in all three aromatic compounds. It is reasoned that although all spin-exchange rates are near to the SE prediction, the semblance of hydrodynamic behavior is superficial and arises incidentally from mathematical cancellation of terms in a generalized diffusion coefficient. As a collision pair coexists for a time within a solvation shell, the recollision time places a lower limit on the lifetime of the solvent cage. Although molecular dynamics simulations conducted thus far have yielded cage lifetimes lower than the measured recollision times, this is attributable to the fact that such simulations have mostly examined cage configurations too small to harbor a spin-exchange encounter, and is also likely due to restrictive mathematical definitions of cage lifetimes that are employed in such simulations. [ABSTRACT FROM AUTHOR]

The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is a variant of the stochastic simulation algorithm in which the spatially inhomogeneous volume of the system is divided into homogeneous subvolumes, and the chemical reactions in those subvolumes are augmented by diffusive transfers of molecules between adjacent subvolumes. The ISSA can be prohibitively slow when the system is such that diffusive transfers occur much more frequently than chemical reactions. In this paper we present the Multinomial Simulation Algorithm (MSA), which is designed to, on the one hand, outperform the ISSA when diffusive transfer events outnumber reaction events, and on the other, to handle small reactant populations with greater accuracy than deterministic-stochastic hybrid algorithms. The MSA treats reactions in the usual ISSA fashion, but uses appropriately conditioned binomial random variables for representing the net numbers of molecules diffusing from any given subvolume to a neighbor within a prescribed distance. Simulation results illustrate the benefits of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper the thermodiffusive behavior of an equimolar binary mixture subject to repulsive potentials of the form (σ/r)n is investigated by using nonequilibrium molecular dynamics (NEMD) and the thermodiffusion (Soret) coefficient, ST, is computed in a wide range of temperatures. With the aim to contribute to the study of the dependence of the Soret coefficient on the interaction potential, the exponent n of the potential is varied from 1 to 12, that is from a pseudocoulombian to a pseudohard-sphere interaction. The steady state equation is integrated for the composition function under reasonable assumptions and it is shown that in some cases the request for it to be linear cannot be satisfied. For this reason nonlinear functions are used to fit the NEMD composition data. The simulations indicate a negligible dependence of ST on the composition (in the composition range here considered) while the dependence on the temperature is more marked. The computed values of ST as a function of the temperature are fitted with analytical functions. It is found that with n≥3 (medium and short range interaction) the model system behaves like a dilute gas mixture with the Soret coefficient varying with the temperature almost like 1/T. In the case of n=1 (long range interaction), ST has a more complex dependence on T: in particular it shows a change of sign. The analytical fitting functions, ST(T), are used in the integrated steady state equation thus obtaining the steady state composition profile and its comparison with the NEMD results indicates the grounding of the approach here proposed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of the hydrocarbon chain length of lipid molecules on the permeation process of small molecules through lipid bilayers. We perform molecular-dynamics simulations using three kinds of lipid molecules with different chain length: dilauroylphosphatidylcholine, dimyristoylphosphatidylcholine, and dipalmiltoylphosphatidylcholine. Free-energy profiles of O2, CO, NO, and water molecules are calculated by means of the cavity insertion Widom method and the probability ratio method. We show that the lipid membrane with longer chains has a larger and wider energy barrier. The local diffusion coefficients of water across the bilayers are also calculated by the force autocorrelation function method and the velocity autocorrelation function method. The local diffusion coefficients in the bilayers are not altered significantly by the chain length. We estimate the permeability coefficients of water across the three membranes according to the solubility-diffusion model; we find that the water permeability decreases modestly with increasing chain length of the lipid molecules. [ABSTRACT FROM AUTHOR]

Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time t as t1/2 in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the one-dimensional Fick’s model of the diffusion equation is compared to the diffusivity calculated using the Darken equation from simulations of equilibrated solvent-polymer solutions. The diffusivity calculated using these two different approaches are in good agreement. The behavior of the diffusivity strongly depends on the state of the polymer and is related to the shape of the solvent concentration profile.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we study the propagation of a planar traveling wave in a nonisothermal autocatalytic reaction diffusion system. This is done by performing a series of molecular dynamics simulations for different densities and heat of reactions. In the special case where the reaction is isothermal, it is shown that the molecular dynamics simulation qualitatively resembles the approximative macroscopic description that is based on the reaction diffusion equation. Simulations for different densities and heat releases further show that the speed of propagation is not simply the minimum speed of the corresponding macroscopic equation and that the speed is always constant even though the Lewis number is greater than unity. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Anomalous self-diffusion in a single-file fluid under the influence of random background forces has been predicted theoretically for decades, but is far from well understood. In particular, one does not fully comprehend the nature of the random force that is necessary to produce the anomalous self-diffusion. For this reason, a molecular dynamics simulation method that can produce anomalous diffusion will be of interest. We propose, in this paper, a fluid scattering mechanism for particles against the confining wall that will be sufficient to induce anomalous self-diffusion. It is efficient and simple to implement. Molecular dynamics simulations of hard sphere fluids in narrow cylindrical pores are used to demonstrate the new method. [ABSTRACT FROM AUTHOR]

We propose, in this paper, a theoretical model to investigate surface self-diffusion of single adatoms on the face-centered-cubic metals. Calculations are performed on both close packed (111) and loosely packed (001) planes of rhodium and nickel. Two realistic model potentials are applied to describe the interatomic interaction of the adatom/substrate systems. The first model is a Morse-type potential, which involves several empirical fitting of bulk properties of solid. The second newly popular potential was introduced by Sutton and Chen, which incorporates with many-body effects. With these potentials, conventional molecular dynamics (MD) is employed to obtain trajectories of the atoms. The averaged square displacements are computed for a range of initial kinetic energies, and the surface diffusion constants can be obtained by means of the Einstein relation. The estimated random walk exponential prefactors and activation energies exhibit Arrhenius behavior, which are confirmed with the previous results. Surface migration by an exchange mechanism for self-diffusion on the Ni(001) plane is also discussed. [ABSTRACT FROM AUTHOR]

Rotations of the molecules about their long axis constitute an important part in the complex pattern of internal motions in the rhombohedral phase of perfluoro-n-eicosane (C20F42). Dynamical studies were performed by quasielastic and inelastic neutron scattering. Spectra were determined in a range of strong diffuse scattering. They show a superposition of librations (δE[bar_over_tilde:_approx._equal_to]1–2 meV) and rotational diffusion (δE[bar_over_tilde:_approx._equal_to]10–100 μeV). Reorientation rates exhibit a slowing down on approaching the transition to the low temperature phase (Tc=200 K). As indicated by this slowing down, by the nonexponential relaxation function, and also an intensity enhancement at the Bragg-positions, rotations occur correlated between neighboring molecules. The state of motion can be simulated by molecular dynamics calculations performed for a two-dimensional lattice of coupled rotators. [ABSTRACT FROM AUTHOR]

The translational motion of C20F42 helices is investigated using a combination of x-ray scattering and coherent quasielastic and inelastic neutron scattering techniques. In phase I, the helices are ordered with respect to their orientation and the dominating mode of motion is an acoustic phonon. In the high temperature phase R, the helices are disordered with respect to their longitudinal position and the angle of rotation around their main axis. Neutron scattering reveals for the longitudinal disorder a wide spectrum of relaxation times (10-12–10-9 s). The rotational ordering of the helices leads to increased correlations and a slowing down in the diffusive longitudinal dynamics already above the phase transition. [ABSTRACT FROM AUTHOR]

We have extended two previously introduced models of n-alkanes to numerically investigate the liquid-state dynamics of branched alkanes. We compare our results with new experimental measurements of diffusion and 13C-NMR T1 relaxation. Significant systematic and quantitative agreement is found between simulated and experimental values. We demonstrate the role of branching in controlling the temperature dependence of diffusion and point out the effect of global single-chain relaxation processes on the local intramolecular dynamics probed by the 13C-NMR experiment. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we study the motion of a molecule in a series of fluctuating bottlenecks. We solve explicitly the case of two bottlenecks and show that under steady state condition the problem can be formulated in terms of a two-dimensional reaction-diffusion equation. We present an analysis of the reaction-diffusion equation, with a sink term that depends on the coordinates of the two bottlenecks, and relate the solution to molecular motion through biomolecules. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Molecular Dynamics (MD) simulations based on the Effective Fragment Potential (EFP) method are utilized to provide a comprehensive assessment of diffusion in liquid n-hexane. We decompose translational diffusion into components along and orthogonal to the long axis of the molecule. Rotational diffusion is decomposed into tumbling and spinning motions about this axis. Our analysis yields four corresponding diffusion coefficients which are related to diagonal entries in the complete 6 × 6 diffusion tensor accounting for the three rotational and three translational degrees of freedom and for the potential coupling between them. However, coupling between different degrees of freedom is expected to be minimal for a natural choice of the molecular body-fixed axis, so then off-diagonal entries in the tensor are negligible. This expectation is supported by a hydrodynamic analysis of the diffusion tensor which treats the liquid surrounding the molecule being tracked as a viscous continuum. Thus, the EFP MD analysis provides a comprehensive characterization of diffusion and also reveals expected shortcomings of the hydrodynamic treatment, particularly for rotational diffusion, when applied to neat liquids. [ABSTRACT FROM AUTHOR]

Experimental investigations and atomistic simulations are combined to study the cesium diffusion processes at high temperature in UO2. After 133Cs implantation in UO2 samples, diffusion coefficients are determined using the depth profile evolution after annealing as measured by secondary ion mass spectrometry. An activation energy of 1.8 ± 0.2 eV is subsequently deduced in the 1300–1600 °C temperature range. Experimental results are compared to nudged elastic band simulations performed for different atomic paths including several types of uranium vacancy defects. Activation energies ranging from 0.49 up to 2.34 eV are derived, showing the influence of the defect (both in terms of type and concentration) on the Cs diffusion process. Finally, molecular dynamics simulations are performed, allowing the identification of preferential Cs trajectories that corroborate experimental observations. [ABSTRACT FROM AUTHOR]

Heterostructures of 2D materials offer a fertile ground to study ion transport and charge storage. Here, we use ab initio molecular dynamics to examine the proton-transfer/diffusion and redox behavior in a water layer confined in the graphene-Ti3C2O2 heterostructure. We find that in comparison with the similar interface of water confined between Ti3C2O2 layers, the proton redox rate in the dissimilar interface of graphene-Ti3C2O2 is much higher, owing to the very different interfacial structure as well as the interfacial electric field induced by an electron transfer in the latter. Water molecules in the dissimilar interface of the graphene-Ti3C2O2 heterostructure form a denser hydrogen-bond network with a preferred orientation of water molecules, leading to an increase in proton mobility with proton concentration in the graphene-Ti3C2O2 interface. As the proton concentration further increases, proton mobility decreases due to increasingly more frequent surface redox events that slow down proton mobility due to binding with surface O atoms. Our work provides important insights into how the dissimilar interface and their associated interfacial structure and properties impact proton transfer and redox in the confined space. [ABSTRACT FROM AUTHOR]

The generalized Fick-Jacobs equation is widely used to study diffusion of Brownian particles in three-dimensional tubes and quasi-two-dimensional channels of varying constraint geometry. We show how this equation can be applied to study the slowdown of unconstrained diffusion in the presence of obstacles. Specifically, we study diffusion of a point Brownian particle in the presence of identical cylindrical obstacles arranged in a square lattice. The focus is on the effective diffusion coefficient of the particle in the plane perpendicular to the cylinder axes, as a function of the cylinder radii. As radii vary from zero to one half of the lattice period, the effective diffusion coefficient decreases from its value in the obstacle free space to zero. Using different versions of the generalized Fick-Jacobs equation, we derive simple approximate formulas, which give the effective diffusion coefficient as a function of the cylinder radii, and compare their predictions with the values of the effective diffusion coefficient obtained from Brownian dynamics simulations. We find that both Reguera-Rubi and Kalinay-Percus versions of the generalized Fick-Jacobs equation lead to quite accurate predictions of the effective diffusion coefficient (with maximum relative errors below 4% and 7%, respectively) over the entire range of the cylinder radii from zero to one half of the lattice period. [ABSTRACT FROM AUTHOR]

Atomic diffusion is at the basis of chemical ordering transformations in nanoalloys. Understanding the diffusion mechanisms at the atomic level is therefore a key issue in the study of the thermodynamic behavior of these systems and, in particular, of their evolution from out-of-equilibrium chemical ordering types often obtained in the experiments. Here, the diffusion is studied in the case of a single-atom impurity of Ag or Au moving within otherwise pure magic-size icosahedral clusters of Cu or Co by means of two different computational techniques, i.e., molecular dynamics and metadynamics. Our simulations reveal unexpected diffusion pathways, in which the displacement of the impurity is coupled with the creation of vacancies in the central part of the cluster. We show that the observed mechanism is quite different from the vacancy-mediated diffusion processes identified so far, and we demonstrate that it can be related to the presence of non-homogeneous compressive stress in the inner part of the icosahedral structure. [ABSTRACT FROM AUTHOR]

A novel approach to simulate simple protein–ligand systems at large time and length scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD lacks a mathematical framework to derive coupling schemes, is limited to isotropic ligands in a single conformational state, and lacks multiparticle extensions. In this work, we address these needs by developing a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes. Given enough data to parameterize the model, it is capable of modeling protein–protein interactions over large time and length scales, and it can be extended to handle multiple molecules. We derive the MSM/RD framework, and we implement and verify it for two protein–protein benchmark systems and one multiparticle implementation to model the formation of pentameric ring molecules. To enable reproducibility, we have published our code in the MSM/RD software package. [ABSTRACT FROM AUTHOR]

Polymerization induced phase separation (PIPS) in a three component thermoset is studied using molecular dynamics simulations of a new coarse-grained thermoset model. The system includes two crosslinker molecules, which differ in their glass transition temperatures (Tg) and chain length and thus have the potential for phase separation. One crosslinker has a high Tg corresponding to a rubbery behavior, and simulations were performed for a short length (4 beads) and a long length (33 beads). The resin and other crosslinker have low Tg. A coarse-grained model is developed with these features and with interaction parameters determined so that for either rubbery crosslinker length, the system is in the liquid state at the cure temperature. For sufficiently slow reaction rates, the long rubbery molecule exhibits PIPS into a bicontinuous array of nanoscale domains, but the short one does not, reproducing recent experimental results. The simulations demonstrate that the reaction rates must be slow enough to allow diffusion to yield phase separation. Particularly, the reaction rate corresponding to the secondary amine must be very slow, else the structure of crosslinked clusters and the substantially increased diffusion time will prevent PIPS. [ABSTRACT FROM AUTHOR]

Hydrophobic deep eutectic solvents (HDESs) have gained immense popularity because of their promising applications in extraction processes. Herein, we employ atomistic molecular dynamics simulations to unveil the dynamics of DL-menthol (DLM) based HDESs with hexanoic (C6), octanoic (C8), and decanoic (C10) acids as hydrogen bond donors. The particular focus is on understanding the nature of dynamics with changing acid tail length. For all three HDESs, two modes of hydrogen bond relaxations are observed. We observe longer hydrogen bond lifetimes of the inter-molecular hydrogen bonding interactions between the carbonyl oxygen of the acid and hydroxyl oxygen of menthol with hydroxyl hydrogen of both acids and menthol. We infer strong hydrogen bonding between them compared to that between hydroxyl oxygen of acids and hydroxyl hydrogens of menthol and acids, marked by a faster decay rate and shorter hydrogen bond lifetime. The translational dynamics of the species in the HDES becomes slower with increasing tail length of the organic acid. Slightly enhanced caging is also observed for the HDES with a longer tail length of the acids. The evidence of dynamic heterogeneity in the displacements of the component molecules is observed in all the HDESs. From the values of the α-relaxation time scale, we observe that the molecular displacements become random in a shorter time scale for DLM-C6. The analysis of the self-van Hove function reveals that the overall distance covered by DLM and acid molecules in the respective HDES is more than what is expected from ideal diffusion. As marked by the shorter time scale associated with hole filling, the diffusion of the oxygen atom of menthol and the carbonyl oxygen of acid from one site to the other is fastest for hexanoic acid containing HDES. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) have a wide range of applications in nanotechnology engineering. This research aims to quantify the effect of wall vibration on n-decane molecules' diffusion in double-walled CNTs (DWNTs) with different diameters and determine the diffusion mechanisms behind it. Molecular dynamics simulations are performed to generate mass density profiles of confined n-decane molecules. The root mean square fluctuation and mean squared displacement analyses show that the confinement suppresses n-decane molecules' fluctuations. A self-diffusion coefficient of n-decane molecules in a 13.6 Å-diameter DWNT is the largest. However, the vibration enhancement of the n-decane molecules' diffusion in a 27.1 Å-diameter DWNT is 207%, more extensive than that in 13.6 Å-diameter and 10.8 Å-diameter DWNTs. The n-decane–CNT attractive interactions, extreme confinement, and surface friction affect the n-decane molecules' diffusion in CNTs with vibration. [ABSTRACT FROM AUTHOR]

In this article, we investigate, through molecular dynamics simulations, the diffusion behavior of the TIP4P/2005 water confined in pristine and deformed carbon nanotubes (armchair and zigzag). To analyze different diffusive mechanisms, the water temperature was varied as 210 ≤ T ≤ 380 K. The results of our simulations reveal that water presents a non-Arrhenius to Arrhenius diffusion crossover. The confinement shifts the diffusion transition to higher temperatures when compared with the bulk system. In addition, for narrower nanotubes, water diffuses in a single line, which leads to its mobility independent of the activation energy. [ABSTRACT FROM AUTHOR]

Nanoparticle diffusion in polymer melts is studied by the combination of Molecular Dynamics (MD) simulations and Mode-Coupling Theory (MCT). In accord with earlier experimental, simulation, and theoretical studies, we find that the Stokes–Einstein (SE) hydrodynamic relation Dn ∼ 1/Rn holds when the nanoparticle radius Rn is greater than the polymer gyration radius Rg, while in the opposite regime, the measured nanoparticle diffusion coefficient Dn exceeds the SE value by as much as an order of magnitude. The MCT values of Dn are found to be consistently higher than the MD simulation values. The observed discrepancy is attributed to the approximations involved in constructing the microscopic friction as well as to the approximate forms for dynamic structure factors used in MCT. In a thorough test of underlying MCT assumptions and approximations, various structural and dynamical quantities required as input for MCT are obtained directly from MD simulations. We present the improved MCT approach, which involves splitting of the microscopic time-dependent friction into two terms: binary (originating from short-time dynamics) and collective (due to long-time dynamics). Using MD data as input in MCT, we demonstrate that the total friction is largely dominated by its binary short-time term, which, if neglected, leads to severe overestimation of Dn. As a result, the revised version of MCT, in agreement with the present MD data, predicts 1 / R n 2 scaling of the probe diffusion coefficient in a non-hydrodynamic regime when Rn < Rg. If the total friction is dominated by the collective long-time component, one would observe 1 / R n 3 scaling of Dn in accordance with previous studies. [ABSTRACT FROM AUTHOR]

To what extent can a 'bottom-up' mesoscale fluid model developed through systematic coarse-graining techniques recover the physical properties of a molecular scale system? In a previous paper [C.-C. Fu, P. M. Kulkarni, M. S. Shell, and L. G. Leal, J. Chem. Phys. 137, 164106 (2012)], we addressed this question for thermodynamic properties through the development of coarse-grained (CG) fluid models using modified iterative Boltzmann inversion methods that reproduce correct pair structure and pressure. In the present work we focus on the dynamic behavior. Unlike the radial distribution function and the pressure, dynamical properties such as the self-diffusion coefficient and viscosity in a CG model cannot be matched during coarse-graining by modifying the pair interaction. Instead, removed degrees of freedom require a modification of the equations of motion to simulate their implicit effects on dynamics. A simple but approximate approach is to introduce a friction coefficient, γ, and random forces for the remaining degrees of freedom, in which case γ becomes an additional parameter in the coarse-grained model that can be tuned. We consider the non-Galilean-invariant Langevin and the Galilean-invariant dissipative particle dynamics (DPD) thermostats with CG systems in which we can systematically tune the fraction [lowercase_phi_synonym] of removed degrees of freedom. Between these two choices, only DPD allows both the viscosity and diffusivity to match a reference Lennard-Jones liquid with a single value of γ for each degree of coarse-graining [lowercase_phi_synonym]. This friction constant is robust to the pressure correction imposed on the effective CG potential, increases approximately linearly with [lowercase_phi_synonym], and also depends on the interaction cutoff length, rcut, of the pair interaction potential. Importantly, we show that the diffusion constant and viscosity are constrained by a simple scaling law that leads to a specific choice of DPD friction coefficient for a given degree of coarse-graining. Moreover, we find that the pair interaction distance cutoffs used for DPD random and dissipative forces should be considered separately from that of the conservative interaction potential. [ABSTRACT FROM AUTHOR]

We use molecular dynamics simulations to study the diffusion of water inside deformed carbon nanotubes with different degrees of deformation at 300 K. We found that the number of hydrogen bonds that water forms depends on nanotube topology, leading to enhancement or suppression of water diffusion. The simulation results reveal that more realistic nanotubes should be considered to understand the confined water diffusion behavior, at least for the narrowest nanotubes, when the interaction between water molecules and carbon atoms is relevant. [ABSTRACT FROM AUTHOR]

A coarse-grained model previously used to simulate Nafion using dissipative particle dynamics (DPD) is modified to describe sulfonated Diels-Alder poly(phenylene) (SDAPP) polymers. The model includes a proton-hopping mechanism similar to the Grotthuss mechanism. The intramolecular parameters for SDAPP are derived from atomistic molecular dynamics (MD) simulation using the iterative Boltzmann inversion. The polymer radii of gyration, domain morphologies, and cluster distributions obtained from our DPD model are in good agreement with previous atomistic MD simulations. As found in the atomistic simulations, the DPD simulations predict that the SDAPP nanophase separates into hydrophobic polymer domains and hydrophilic domains that percolate through the system at sufficiently high sulfonation and hydration levels. Increasing sulfonation and/or hydration leads to larger proton and water diffusion constants, in agreement with experimental measurements in SDAPP. In the DPD simulations, the proton hopping (Grotthuss) mechanism becomes important as sulfonation and hydration increase, in qualitative agreement with experiment. The turning on of the hopping mechanism also roughly correlates with the point at which the DPD simulations exhibit clear percolated, hydrophilic domains, demonstrating the important effects of morphology on proton transport. [ABSTRACT FROM AUTHOR]

The structural and dynamical properties of hydration water in aqueous solutions of trehalose are studied with molecular dynamics simulation. We simulate the systems in the supercooled region to investigate how the interaction with the trehalose molecules modifies the hydrogen bond network, the structural relaxation, and the diffusion properties of hydration water. The analysis is performed by considering the radial distribution functions, the residence time of water molecules in the hydration shell, the two body excess entropy, and the hydrogen bond water-water and water-trehalose correlations of the hydration water. The study of the two body excess entropy shows the presence of a fragile to strong crossover in supercooled hydration water also found in the relaxation time of the water-water hydrogen bond correlation function, and this is in agreement with predictions of the mode coupling theory and of previous studies of the oxygen-oxygen density correlators [A. Iorio et al., J. Mol. Liq. 282, 617 (2019); Sci. China: Phys., Mech. Astron. 62, 107011 (2019)]. The water-trehalose hydrogen bond correlation function instead evidences a strong to strong crossover in the relaxation time, and this crossover is related to a trehalose dynamical transition. This signals the role that the strong interplay between the soluted molecules and the surrounding solvent has in determining the dynamical transition common to both components of the system that happens upon cooling and that is similar to the well known protein dynamical transition. We connect our results with the cryoprotecting role of trehalose molecules. [ABSTRACT FROM AUTHOR]

Ab initio-based charge partitioning of ionic systems results in ions with non-integer charges. This charge-transfer (CT) effect alters both short- and long-range interactions. Until recently, the effects of CT have been mostly neglected in molecular dynamics (MD) simulations. The method presented in this paper for including charge transfer between ions and water is consistent with ab initio charge partitioning and does not add significant time to the simulation. The ions of sodium, potassium, and chloride are parameterized to reproduce dimer properties and aqueous structures. The average charges of the ions from MD simulations (0.900, 0.919, and -0.775 for Na+, K+, and Cl-, respectively) are consistent with quantum calculations. The hydration free energies calculated for these ions are in agreement with experimental estimates, which shows that the interactions are described accurately. The ions also have diffusion constants in good agreement with experiment. Inclusion of CT results in interesting properties for the waters in the first solvation shell of the ions. For all ions studied, the first shell waters acquire a partial negative charge, due to the difference between water-water and water-ion charge-transfer amounts. CT also reduces asymmetry in the solvation shell of the chloride anion, which could have important consequences for the behavior of chloride near the air-water interface. [ABSTRACT FROM AUTHOR]

The slow dynamics of glass-forming liquids is generally ascribed to the cage jump motion. In the cage jump picture, a molecule remains in a cage formed by neighboring molecules and, after a sufficiently long time, it jumps to escape from the original position by cage breaking. The clarification of the cage jump motion is therefore linked to unraveling the fundamental element of the slow dynamics. Here, we develop a cage jump model for the dynamics of supercooled water. The caged and jumping states of a water molecule are introduced with respect to the hydrogen-bond (H-bond) rearrangement process and describe the motion in supercooled states. It is then demonstrated from the molecular dynamics simulation of the TIP4P/2005 model that the characteristic length and time scales of cage jump motions provide a good description of the self-diffusion constant that is determined in turn from the long-time behavior of the mean square displacement. Our cage jump model thus enables the connection between H-bond dynamics and molecular diffusivity. [ABSTRACT FROM AUTHOR]

The Stokes-Einstein (SE) relation is examined for hard-sphere (HS) and Weeks-Chandler-Andersen (WCA) fluids by the molecular dynamics method on temperatures and densities corresponding to the saturated vapor line of Lennard-Jones (LJ) liquids. While the self-diffusion coefficient, D, and shear viscosity, ηsv, increases and decreases, respectively, with increasing steepness in interaction potentials, the same SE relation holds for HS and WCA fluids as that obtained for LJ liquids, i.e., Dηsv = (kBT/C)(N/V)1/3, where kB is the Boltzmann constant, T is the temperature, and N is the particle number included in the system volume V. The coefficient C is almost constant at about 6 to 2π for η > 0.3, where η is the packing fraction. The results show that the SE relation for simple liquids and fluids does not need to bear any concepts of both the hydrodynamic particle size and the boundary condition. In light of this SE relation, the Enskog, Eyring-Ree, and Zwanzig theories are quantitatively tested. In addition, the cause of deviation from unity of the exponent in the fractional SE relation for simple fluids is clearly accounted for. The present results show that applying both the original and the fractional SE relations to simple liquids and fluids does not lead to any meaningful discussions. [ABSTRACT FROM AUTHOR]

We present a systematic study of the self-diffusion coefficient for a fluid of particles interacting via the square-well pair potential by means of molecular dynamics simulations in the canonical (N, V, T) ensemble. The discrete nature of the interaction potential is modeled by the constant force approximation, and the self-diffusion coefficient is determined for several fluid densities at supercritical thermodynamic states. The dependence of the self-diffusion coefficient on the potential range λ is analyzed in the range of 1.1 ≤ λ ≤ 1.5. The obtained simulation results are in agreement with the self-diffusion coefficient predicted by the Enskog method. Additionally, we show that the diffusion coefficient is very sensitive to the potential range λ. Our results for the self-diffusion coefficient times density extrapolate well to the values in the zero-density limit obtained from the Chapman-Enskog theory for dilute gases. The constant force approximation used in this work to model the discrete pair potentials has shown to be an excellent scheme to compute the transport properties of square-well fluids using molecular dynamics simulations. Finally, the simulation results presented here are useful for improving theoretical approaches, such as the Enskog method. [ABSTRACT FROM AUTHOR]

We simulate the nonequilibrium ensemble dynamics of a biomolecule using the weighted ensemble method, which was introduced in molecular dynamics simulations by Huber and Kim and further developed by Zuckerman and co-workers. As the order parameters to characterize its conformational change, we here use the coordinates derived from the diffusion map (DM) method, one of the manifold learning techniques. As a concrete example, we study the kinetic properties of a small peptide, chignolin in explicit water, and calculate the conformational change between the folded and misfolded states in a nonequilibrium way. We find that the transition time scales thus obtained are comparable to those using previously employed hydrogen-bond distances as the order parameters. Since the DM method only uses the 3D Cartesian coordinates of a peptide, this shows that the DM method can extract the important distance information of the peptide without relying on chemical intuition. The time scales are compared well with the previous results using different techniques, non-Markovian analysis and core-set milestoning for a single long trajectory. We also find that the most significant DM coordinate turns out to extract a dihedral angle of glycine, and the previously studied relaxation modes are well correlated with the most significant DM coordinates. [ABSTRACT FROM AUTHOR]

The Fick diffusion coefficient matrix of ternary mixtures containing benzene + acetone + three different alcohols, i.e., methanol, ethanol, and 2-propanol, is studied by molecular dynamics simulation and Taylor dispersion experiments. Aiming to identify common features of these mixtures, it is found that one of the main diffusion coefficients and the smaller eigenvalue do not depend on the type of alcohol along the studied composition path. Two mechanisms that are responsible for this invariant behavior are discussed in detail, i.e., the interplay between kinetic and thermodynamic contributions to Fick diffusion coefficients and the presence of microscopic heterogeneities caused by hydrogen bonding. Experimentalwork alone cannot explain these mechanisms, while present simulations on the molecular level indicate structural changes and uniform intermolecular interactions between benzene and acetone molecules in the three ternary mixtures. The main diffusion coefficients of these ternary mixtures exhibit similarities with their binary subsystems. Analyses of radial distribution functions and hydrogen bonding statistics quantitatively evidence alcohol self-association and cluster formation, as well as component segregation. Furthermore, the excess volume of the mixtures is analyzed in the light of intermolecular interactions, further demonstrating the benefits of the simultaneous use of experiment and simulation. The proposed framework for studying diffusion coefficients of a set of ternary mixtures, where only one component varies, opens the way for further investigations and a better understanding of multicomponent diffusion. The presented numerical results may also give an impulse to the development of predictive approaches for multicomponent diffusion. [ABSTRACT FROM AUTHOR]

Self- and impurity diffusion coefficients are assessed in the liquid nickel system by the fundamental ab initio molecular dynamics approach. The impurity diffusion coefficients in the Ni-X systems (X=C, Co, N, Nb, Ta, Ti, W) are mostly not available in the current literature. The simulations are performed at four temperatures, in the range from 1903 to 2303 K, which allows to extract activation energies and frequency factors for the temperature dependent diffusion coefficient assuming an Arrhenius-type behavior in the liquid. In addition to the temperature dependence, the concentration-dependent impurity diffusion was investigated for the Ni-Co system. The data are of relevance for the development of the state-of-the art Ni-based superalloys and alternative binder systems in cemented carbides. The obtained theoretical results are in very good agreement with the limited experimental data for the diffusion in liquid Ni systems. [ABSTRACT FROM AUTHOR]

To clarify atomic diffusion in amorphous materials, which is important in novel information and energy devices, theoretical methods having both reliability and computational speed are eagerly anticipated. In the present study, we applied neural network (NN) potentials, a recently developed machine learning technique, to the study of atom diffusion in amorphous materials, using Li3PO4 as a benchmark material. The NN potential was used together with the nudged elastic band, kinetic Monte Carlo, and molecular dynamics methods to characterize Li vacancy diffusion behavior in the amorphous Li3PO4 model. By comparing these results with corresponding DFT calculations, we found that the average error of the NN potential is 0.048 eV in calculating energy barriers of diffusion paths, and 0.041 eV in diffusion activation energy. Moreover, the diffusion coefficients obtained from molecular dynamics are always consistent with those from ab initio molecular dynamics simulation, while the computation speed of the NN potential is 3-4 orders of magnitude faster than DFT. Lastly, the structure of amorphous Li3PO4 and the ion transport properties in it were studied with the NN potential using a large supercell model containing more than 1000 atoms. The formation of P2O7 units was observed, which is consistent with the experimental characterization. The Li diffusion activation energywas estimated to be 0.55 eV, which agrees well with the experimental measurements. [ABSTRACT FROM AUTHOR]