Velocity Autocorrelation Function Research Articles

Longitudinal, transverse, and single-particle dynamics in liquid Zn:Ab initiostudy and theoretical analysis

We perform ab initio molecular dynamics simulations of liquid Zn near the melting point in order to study the longitudinal and transverse dynamic properties of the system. We find two propagating excitations in both of them in a wide range of wave vectors. This is in agreement with some experimental observations of the dynamic structure factor in the region around half the position of the main peak. Moreover, the two-mode structure in the transverse and longitudinal current correlation functions had also been previously observed in high pressure liquid metallic systems. We perform a theoretical analysis in order to investigate the possible origin of such two components by resorting to mode-coupling theories. They are found to describe qualitatively the appearance of two modes in the dynamics, but their relative intensities are not quantitatively reproduced. We suggest some possible improvements of the theory through the analysis of the structure of the memory functions. We also analyze the single-particle dynamics embedded in the velocity autocorrelation function, and explain its characteristics through mode-coupling concepts.

Single particle Brownian motion with solid friction.

We study the Brownian dynamics of a solid particle on a vibrating solid surface. Phenomenologically, the interaction between the two solid surfaces is modeled by solid friction, and the Gaussian white noise models the vibration of the solid surface. The solid friction force is proportional to the sign of relative velocity. We derive the Fokker-Planck (FP) equation for the time-dependent probability distribution to find the particle at a given location. We calculate analytically the steady state velocity distribution function, mean-square velocity and diffusion coefficient in d-dimensions. We present a generic method of calculating the autocorrelations in d-dimensions. This results in one dimension in an exact evaluation of the steady state velocity autocorrelation. In higher dimensions our exact general expression enables the analytic evaluation of the autocorrelation to any required approximation. We present approximate analytic expressions in two and three dimensions. Next, we numerically calculate the mean-square velocity and steady state velocity autocorrelation function up to d = 3 . Our numerical results are in good agreement with the analytically obtained results.

Single Particle Dynamics at the Intrinsic Surface of Various Apolar, Aprotic Dipolar, and Hydrogen Bonding Liquids As Seen from Computer Simulations.

We investigate the single molecule dynamics at the intrinsic liquid/vapor interface of five different molecular liquids (carbon tetrachloride, acetone, acetonitrile, methanol, and water). After assessing that the characteristic residence times in the surface layer are long enough for a meaningful definition of several transport properties within the layer itself, we characterize the dynamics of the individual molecules at the liquid surface by analyzing their normal and lateral mean-square displacements and lateral velocity autocorrelation functions and, in the case of the hydrogen bonding liquids (i.e., water and methanol), also the properties of the hydrogen bonds. Further, dynamical properties as well as the clustering of the molecules residing unusually long in the surface layer are also investigated. The global picture emerging from this analysis is that of a noticeably enhanced dynamics of the molecules at the liquid surface, with diffusion coefficients up to 4 times larger than in the bulk, and the disappearance of the caging effect at the surface of all liquids but water. The dynamics of water is dominated by the strong hydrogen bonding structure also at the liquid surface.

Study of cage effect and subdiffusion in Pickering emulsions from Molecular Dynamics simulations

In this work, we study the diffusion laws of oil-droplets dispersed in water onto which are strongly adsorbed charged point-like particles (Pickering emulsions). This diffusion that originates from multiple collisions with the molecules of water, is anomalous, due to the presence of relatively strong correlations between the moving oil-droplets. Using Molecular Dynamics simulation, with a pair-potential of Sogami-Ise type, we first observe that the random walkers execute a normal diffusion, at intermediate time, followed by a slow diffusion (subdiffusion) we attribute to the presence of cages, formed by the nearest neighbors (traps). In the cage-regime, we find that the mean-square-displacement increases according to a time-power law, with an anomalous diffusion exponent, α (between 0 and 1). This exponent and the generalized diffusion coefficient are computed varying the relevant parameters (surface charge, density, salt-concentration). We remark that the subdiffusion is significant only for strong surface charges and densities, and low-salt concentrations. The existence of a cage effect is shown computing the velocity auto-correlation function of the random walker. It is found that, in a cage, this function is governed by an underdamped (oscillatory) behavior, for strong densities and surface charges, and low-salt concentration. In the inverse situation, however, we observe that this correlation-function is rather overdamped (non-oscillatory). In the two cases, at large-time, this function fails according to a time-power law, with the exponent α−2. To validate our simulation data, we propose a memory diffusion theory that is based essentially on a generalized Langevin equation. Finally, we demonstrate that the results from simulations are in good agreement with the predictions of the elaborated theory.

Benchmarking the diffusion and viscosity of H-He mixtures in warm dense matter regime by quantum molecular dynamics simulations

Quantum molecular dynamics simulations for self-diffusion, mutual-diffusion, and viscosities of hydrogen-helium (H-He) mixtures are investigated to benchmark the standard theoretical models in the warm dense matter regime. We carefully examine the differences in velocity autocorrelation functions (VACFs) between the mixtures and pure hydrogen or helium. The VACFs for the mixtures exhibit oscillatory features, which however are absent for pure species. At low temperatures, the VACFs of H in H-He mixtures have a negative correlation region, which results in an obviously smaller self-diffusion of H in H-He mixtures compared to that in a pure H system. The calculated self-diffusion coefficients of H and He in H-He mixtures show much different behaviors with the variation of the composition of He (XHe): the self-diffusion coefficients of He increase monotonously with increasing XHe, whereas the self-diffusion coefficients of H generally decrease with the increase in XHe. The viscosities are smaller for the H-He mixtures with a more helium content. These diffusion and viscosity coefficients are used as a benchmark to check some analytical models based on the one component plasma or the Yukawa one component plasma.

Memory effects in the velocity relaxation process of the dust particle in dusty plasma

In this paper, by comparing the timescales associated with the velocity relaxation and correlation time of the random force due to dust charge fluctuations, memory effects in the velocity relaxation of an isolated dust particle exposed to the random force due to dust charge fluctuations are considered, and the velocity relaxation process of the dust particle is considered as a non-Markovian stochastic process. Considering memory effects in the velocity relaxation process of the dust particle yields a retarded friction force, which is introduced by a memory kernel in the fractional Langevin equation. The fluctuation-dissipation theorem for the dust grain is derived from this equation. The mean-square displacement and the velocity autocorrelation function of the dust particle are obtained, and their asymptotic behavior, the dust particle temperature due to charge fluctuations, and the diffusion coefficient are studied in the long-time limit. As an interesting feature, it is found that by considering memory effects in the velocity relaxation process of the dust particle, fluctuating force on the dust particle can cause an anomalous diffusion in a dusty plasma. In this case, the mean-square displacement of the dust grain increases slower than linearly with time, and the velocity autocorrelation function decays as a power-law instead of the exponential decay. Finally, in the Markov limit, these results are in good agreement with those obtained from previous works on the Markov (memoryless) process of the velocity relaxation.

Why there is no Newtonian backreaction

In the conventional framework for cosmological dynamics the scale factor $a(t)$ is assumed to obey the `background' Friedmann equation for a perfectly homogeneous universe while particles move according to equations of motions driven by the gravity of the density fluctuations. It has recently been suggested that the emergence of structure modifies the evolution of $a(t)$ via Newtonian (or `kinematic') backreaction and that this may avoid the need for dark energy. Here we point out that the conventional system of equations is exact in Newtonian gravity and there is no approximation in the use of the homogeneous universe equation for $a(t)$. The recently proposed modification of Racz et al.\ (2017) does not reduce to Newtonian gravity in the limit of low velocities. We discuss the relation of this to the `generalised Friedmann equation' of Buchert and Ehlers. These are quite different things; their formula describes individual regions and is obtained under the restrictive assumption that the matter behaves like a pressure-free fluid whereas our result is exact for collisionless dynamics and is an auxiliary relation appearing in the structure equations. We use the symmetry of the general velocity autocorrelation function to show how Buchert's $\cal Q$ tends very rapidly to zero for large volume and that this does not simply arise `by construction' through the adoption of periodic boundary conditions as has been claimed. We conclude that, to the extent that Newtonian gravity accurately describes the low-$z$ universe, there is no backreaction of structure on $a(t)$ and that the need for dark energy cannot be avoided in this way.

Thermal neutron scattering cross section of liquid FLiBe

The molten salt material Li2BeF4 (FLiBe) has been widely proposed as a moderator and coolant material in nuclear applications. Its usage and impact on neutron thermalization in the system requires accurate generation of FLiBe thermal neutron scattering libraries. In this work, liquid FLiBe is modeled using the classical molecular dynamics code LAMMPS. Experimental limits of liquid FLiBe properties are determined from reported databases. Predicted properties of FLiBe from molecular dynamics simulations including density, viscosity, and atomic species diffusivities are computed and compared to experimental data. To initiate the calculation of the thermal neutron scattering law, the velocity autocorrelation functions are calculated from molecular dynamics trajectories and subjected to Fourier transformation to obtain the density of states of possible excitations. Bound modes and diffusive modes of the density of states are separated to calculate the corresponding scattering law Sbound(α,β) and ,Sdiff(α,β) respectively. Thermal neutron scattering cross section libraries of F, Li, Be in FLiBe are generated at temperatures of 873 K, 923 K and 973 K in ENDF/B VII.1 format.

Nanostructured solvation in mixtures of protic ionic liquids and long-chained alcohols.

The structural and dynamical properties of bulk mixtures of long-chained primary and secondary alcohols (propanol, butanol, and 2-pentanol) with protic ionic liquids (ethylammonium and butylammonium nitrate) were studied by means of molecular dynamics simulations and small angle X-ray scattering (SAXS). Changes in the structure with the alcohol concentration and with the alkyl chain length of the alcohol moieties were found, showing variations in the radial distribution function and in the number of hydrogen bonds in the bulk liquids. Moreover, the structural behaviour of the studied mixtures is further clarified with the spatial distribution functions. The global picture in the local scale is in good agreement with the nanostructured solvation paradigm [T. Méndez-Morales et al. Phys. Chem. B 118, 761 (2014)], according to which alcohols are accommodated into the hydrogen bonds' network of the ionic liquid instead of forming clusters in the bulk. Indeed, our study reveals that the alcohol molecules are placed with their polar heads at the interfaces between polar and nonpolar nanodomains in the ionic liquid, with their alkyl chains inside the nonpolar organic nanodomains. The influence of alcohol chain length in the single-particle dynamics of the mixtures is also reported calculating the velocity autocorrelation function and vibrational densities of states of the different species in the ionic liquid-alcohol mixtures, and a weak caging effect for the ethylammonium cations independent of the chain size of the alcohols was found. However, the SAXS data collected for the studied mixtures show an excess of the scattering intensities which indicates that there are also some structural heterogeneities at the nanoscale.

Dynamical and transport properties in plasmas including three-particle spatial correlations

In this work, we study the two and triplet static correlation functions in plasma when the ions interact via the Debye screened potential and via the Deutsch screened potential. The latter takes into consideration the possible quantum effects at short distances. The ratio of the mean distance between two ions and the thermal De Broglie wavelength r_{i}/lambda_{mathrm{T}} gives the measure of these effects. Our investigation is developed in the conditions of weak coupling parameter (varGamma <1). The pair and the triplet correlation functions are calculated numerically and compared to the correlation functions due to the Kirkwood superposition approximation (KSA). Some applications to the ion velocity auto-correlation function D(t) and the electric field auto-correlation function C(t) at an ion (assumed to be an impurity) and the diffusion coefficient D are calculated for the two kinds of potentials in different plasma conditions. The comparison with other results found in the literature shows a well satisfactory agreement, for the static as well as the dynamic properties.

A study of the Brownian motion of the non-spherical microparticles on fluctuating lattice Boltzmann method

In this paper, the fluctuating lattice Boltzmann (FLB) model is used to simulate the Brownian motion of spherical and non-spherical particles directly on 3D. The FLB model is validated by comparing the simulation results with theoretical and experimental results. And then the Brownian motion characteristics of different shapes of non-spherical particles are analyzed, which includes some ellipsoidal and cylindrical particles with different aspect ratios. It is found that, although the ellipsoidal and cylindrical particles are anisotropic, they still obey the energy equalization theorem. The velocity and angular velocity autocorrelation functions of the particles still have the “long-time tail” effect. Moreover, the velocity and angular velocity autocorrelation functions are independent of the particle shape, and the diffusion coefficient is insensitive to the shape under a low aspect ratio. This work is a fundamental study for the further research of the motion of microparticles based on Brownian motion.

Molecular Dynamics Simulations of Hydroxyapatite Nanopores in Contact with Electrolyte Solutions: The Effect of Nanoconfinement and Solvated Ions on the Surface Reactivity and the Structural, Dynamical, and Vibrational Properties of Water

Hydroxyapatite, the main mineral phase of mammalian tooth enamel and bone, grows within nanoconfined environments and in contact with aqueous solutions that are rich in ions. Hydroxyapatite nanopores of different pore sizes (20 Å ≤ H ≤ 110 Å, where H is the size of the nanopore) in contact with liquid water and aqueous electrolyte solutions (CaCl2 (aq) and CaF2 (aq)) were investigated using molecular dynamics simulations to quantify the effect of nanoconfinement and solvated ions on the surface reactivity and the structural and dynamical properties of water. The combined effect of solution composition and nanoconfinement significantly slows the self-diffusion coefficient of water molecules compared with bulk liquid. Analysis of the pair and angular distribution functions, distribution of hydrogen bonds, velocity autocorrelation functions, and power spectra of water shows that solution composition and nanoconfinement in particular enhance the rigidity of the water hydrogen bonding network. Calculation of the water exchange events in the coordination of calcium ions reveals that the dynamics of water molecules at the HAP–solution interface decreases substantially with the degree of confinement. Ions in solution also reduce the water dynamics at the surface calcium sites. Together, these changes in the properties of water impart an overall rigidifying effect on the solvent network and reduce the reactivity at the hydroxyapatite-solution interface. Since the process of surface-cation-dehydration governs the kinetics of the reactions occurring at mineral surfaces, such as adsorption and crystal growth, this work shows how nanoconfinement and solvation environment influence the molecular-level events surrounding the crystallization of hydroxyapatite.

Computer simulation studies of the influence of side alkyl chain on glass transition behavior of carbazole trimer

In this work, all-atom molecular dynamics simulations were employed to study the influence of the side alkyl chain on glass transition behavior of several carbazole trimers (CT) in a temperature range from 423 to 183 K. The glass transition temperatures were obtained from the break in the slope of the volume-temperature curves and found to agree with the experimental values. The short time dynamics of four CT molecules were probed by using velocity autocorrelation functions and mean-square displacements. The current studies showed that the dynamics of CT systems can be easily interpreted through the cage effect. Furthermore, the investigation of the torsional autocorrelation function and P2-state/P3-state functions showed that the rotational barriers of side chains can slow down the conformational relaxation and lead to stronger temperature dependence of conformational relaxation. The relaxation time, characteristic time of P2-state(t) and P3-state(t) functions were all found to have Arrhenius-type temperature dependence.

Impact of Vibrations and Electronic Coherence on Electron Transfer in Flat Molecular Wires

ABSTRACTElectron transfer in molecular wires are of fundamental importance for a range of optoelectronic applications. The impact of electronic coherence and ionic vibrations on transmittance are of great importance to determine the mechanisms, and subsequently the type of wires that are most promising for applications. In this work, we use the real-time formulation of time-dependent density functional theory to study electron transfer through oligo-p-phenylenevinylene (OPV) and the recently synthesized carbon bridged counterpart (COPV). A system prototypical of organic photovoltaics is setup by bridging a porphyrin-fullerene dyad, allowing a photo-excited electron to flow between the Zn-porphyrin (ZnP) chromophore and the C60 electron acceptor through the molecular wire. The excited state is described using the fully self-consistent ∆-SCF method. The state is then propagated in time using the real-time TD-DFT scheme, while describing ionic vibrations with classical nuclei. The charge transferred between porphyrin and C60 is calculated and correlated with the velocity autocorrelation functions of the ions. This provides a microscopic insight to vibrational and tunneling contributions to electron transport in linked porphyrin-fullerene dyads. We elaborate on important details in describing the excited state and trajectory sampling.

Specific properties of argon-like liquids near their spinodals

The work is devoted to the computer simulation study of the spinodal position for argon and low-molecular liquids having the averaged interparticle potentials similar to that for argon. For this purpose several new methods are developed: the study of the intersection points for pressure curves on pairs of two close isochors, specific changes for the isochoric behavior of the radial correlation functions near the spinodal, non-trivial changes of the temperature dependencies for isochoric values of the self-diffusion coefficient, kinematic shear viscosity and Maxwell relaxation time of argon at the intersection of its spinodal. The three last characteristics are determined with the help of analysis of long time tails for the velocity auto-correlation function. Obtained in such a way the position of spinodal is compared with that following from the experimental study and computer simulations of the isothermal compressibility.

Density of states from mode expansion of the self-dynamic structure factor of a liquid metal.

We show that by exploiting multi-Lorentzian fits of the self-dynamic structure factor at various wave vectors it is possible to carefully perform the Q→0 extrapolation required to determine the spectrum Z(ω) of the velocity autocorrelation function of a liquid. The smooth Q dependence of the fit parameters makes their extrapolation to Q=0 a simple procedure from which Z(ω) becomes computable, with the great advantage of solving the problems related to resolution broadening of either experimental or simulated self-spectra. Determination of a single-particle property like the spectrum of the velocity autocorrelation function turns out to be crucial to understanding the whole dynamics of the liquid. In fact, we demonstrate a clear link between the collective mode frequencies and the shape of the frequency distribution Z(ω). In the specific case considered in this work, i.e., liquid Au, analysis of Z(ω) revealed the presence, along with propagating sound waves, of lower frequency modes that were not observed before by means of dynamic structure factor measurements. By exploiting ab initio simulations for this liquid metal we could also calculate the transverse current-current correlation spectra and clearly identify the transverse nature of the above mentioned less energetic modes. Evidence of propagating transverse excitations has actually been reported in various works in the recent literature. However, in some cases, like the present one, these modes are difficult to detect in density fluctuation spectra. We show here that the analysis of the single-particle dynamics is able to unveil their presence in a very effective way. The properties here shown to characterize Z(ω), and the information in it contained therefore allow us to identify it with the density of states (DoS) of the liquid. We demonstrate that only nonhydrodynamic modes contribute to the DoS, thus establishing its purely microscopic origin. Finally, as a by-product of this work, we provide our estimate of the self-diffusion coefficient of liquid gold just above melting.

Average-atom model for two-temperature states and ionic transport properties of aluminum in the warm dense matter regime

The average-atom model combined with the hyper-netted chain approximation is an efficient tool for electronic and ionic structure calculations for warm dense matter. Here we generalize this method in order to describe non-equilibrium states with different electron and ion temperature as produced in laser-matter interactions on ultra-short time scales. In particular, the electron-ion and ion-ion correlation effects are considered when calculating the electron structure. We derive an effective ion-ion pair-potential using the electron densities in the framework of temperature-depended density functional theory. Using this ion-ion potential we perform molecular dynamics simulations in order to determine the ionic transport properties such as the ionic diffusion coefficient and the shear viscosity through the ionic velocity autocorrelation functions.

Density of states and dynamical crossover in a dense fluid revealed by exponential mode analysis of the velocity autocorrelation function.

Extending a preceding study of the velocity autocorrelation function (VAF) in a simulated Lennard-Jones fluid [Phys. Rev. E 92, 042166 (2015)PLEEE81539-375510.1103/PhysRevE.92.042166] to cover higher-density and lower-temperature states, we show that the recently demonstrated multiexponential expansion method allows for a full account and understanding of the basic dynamical processes encompassed by a fundamental quantity as the VAF. In particular, besides obtaining evidence of a persisting long-time tail, we assign specific and unambiguous physical meanings to groups of exponential modes related to the longitudinal and transverse collective dynamics, respectively. We have made this possible by consistently introducing the interpretation of the VAF frequency spectrum as a global density of states in fluids, generalizing a solid-state concept, and by giving to specific spectral components, obtained through the VAF exponential expansion, the corresponding meaning of partial densities of states relative to specific dynamical processes. The clear identification of a high-frequency oscillation of the VAF with the near-top excitation frequency in the dispersion curve of acoustic waves is a neat example of the power of the method. As for the transverse mode contribution, its analysis turns out to be particularly important, because the multiexponential expansion reveals a transition marking the onset of propagating excitations when the density is increased beyond a threshold value. While this finding agrees with the recent literature debating the issue of dynamical crossover boundaries, such as the one identified with the Frenkel line, we can add detailed information on the modes involved in this specific process in the domains of both time and frequency. This will help obtain a still missing full account of transverse dynamics, in both its nonpropagating and propagating aspects which are linked through dynamical transitions depending on both the thermodynamic states and the excitation wave vectors.

Computing the non-Markovian coarse-grained interactions derived from the Mori-Zwanzig formalism in molecular systems: Application to polymer melts.

Memory effects are often introduced during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori-Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. More specifically, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. However, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function.

Velocity autocorrelation function in uniformly heated granular gas

In this paper we study aging of the velocity autocorrelation function of a uniformly heated granular gas using large scale event-driven molecular dynamics simulations in both 2 and 3 dimensional system. The system is heated by adding Gaussian white noise to each velocity component of all the particles. After a few collisions per particle, the system attains steady state. During early stages, the velocity autocorrelation function shows aging as there is explicit dependence of the function on τw but after steady state is reached, the velocity autocorrelation function become independent of τw and does not show any aging. Velocity correlations develop even after steady state is reached, these correlations are less pronounced in 3 dimensional system.