Velocity autocorrelation function of a Brownian particle

Chakraborty, Dipanjan

doi:10.1140/epjb/e2011-20395-3

Cited by 20 publications

(29 citation statements)

References 25 publications

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“…In recent years, Brownian motion of spherical particles with uniform wettability was extensively studied by MD simulations [19][20][21][22][23][24][25][26]. It was shown that a number of parameters, e.g., the mass and size ratios of a particle and a solvent molecule, interaction potentials, boundary conditions and the system size, can influence the diffusion process.…”

Section: Introductionmentioning

confidence: 99%

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Diffusion of a Janus nanoparticle in an explicit solvent: A molecular dynamics simulation study

Kharazmi

Priezjev

2015

The Journal of Chemical Physics

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Molecular dynamics simulations are carried out to study the translational and rotational diffusion of a single Janus particle immersed in a dense Lennard-Jones fluid. We consider a spherical particle with two hemispheres of different wettability. The analysis of the particle dynamics is based on the time-dependent orientation tensor, particle displacement, as well as the translational and angular velocity autocorrelation functions. It was found that both translational and rotational diffusion coefficients increase with decreasing surface energy at the nonwetting hemisphere, provided that the wettability of the other hemisphere remains unchanged. We also observed that in contrast to homogeneous particles, the nonwetting hemisphere of the Janus particle tends to rotate in the direction of the displacement vector during the rotational relaxation time.

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Section: Introductionmentioning

confidence: 99%

“…However, if the particle consists of a cluster of atoms and their interaction energy with fluid molecules is sufficiently large, then stick boundary conditions apply at the particle surface [23,25].…”

Section: Introductionmentioning

confidence: 99%

Diffusion of a Janus nanoparticle in an explicit solvent: A molecular dynamics simulation study

Kharazmi

Priezjev

2015

The Journal of Chemical Physics

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“…The initial momentum of a tagged atom can also be rapidly carried away by propagating sound waves. Usually, this contributes only to the short time decay of the VAF [19]. As the system is confined, the long-time hydrodynamic tail is expected to be lost and this mechanism becomes important.…”

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confidence: 99%

Velocity autocorrelation function in supercooled liquids: Long-time tails and anomalous shear-wave propagation

2016

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Molecular dynamic simulations are performed to reveal the long-time behavior of the velocity autocorrelation function (VAF) by utilizing the finite-size effect in a Lennard-Jones binary mixture. Whereas in normal liquids the classical positive t −3/2 long-time tail is observed, we find in supercooled liquids a negative tail. It is strongly influenced by the transfer of the transverse current wave across the period boundary. The t −5/2 decay of the negative long-time tail is confirmed in the spectrum of VAF. Modeling the long-time transverse current within a generalized Maxwell model, we reproduce the negative long-time tail of the VAF, but with a slower algebraic t −2 decay. DOI: 10.1103/PhysRevE.94.060601 One of the simplest parameters for measuring liquid dynamics is the diffusion coefficient, which can be calculated from the mean-square displacement or from the single-particle velocity autocorrelation function (VAF) through the Green-Kubo relation [1,2]. In dilute fluids, where the correlation between binary collisions can be neglected, the time-dependent VAF decays exponentially. This has been validated by the kinetic theory for gases or granular media and Brownian dynamics [1,3]. It came as a surprise when Alder and Wainwright for the first time reported that the long-time tail of the VAF decays algebraically as t −d/2 , where d is the dimension of the system [4][5][6]. This long-lasting correlation is attributed to the well-known hydrodynamic vortex, or backflow, that supports the initial motion and develops a persistent long time tail [7,8].At high densities the initial direction of motion of an atom is, on average, soon reversed as the atom feels the surrounding neighbors, as a negative region. For the reversed velocity a t −5/2 decay has been reported for a hard-sphere fluid [9]. Interestingly, the same algebraic decay is observed in a Lorentz gas, where the long-time tail has been shown both theoretically [10] and by computer simulation (at low obstacle density) to decay as −t −d/2−1 [11]. A plausible conjecture is that they would have the same physical mechanism. Since the dynamic heterogeneity (both in space and time) manifests itself in the dynamics of high volume fraction of hard-sphere and of supercooled liquids [12][13][14], groups of immobile atoms might play the role of the fixed scatterers for mobile atoms as in the Lorentz gas. They then account for the negative long-time tail [9]. Actually frozen scatterers are not essential for the emergence of negative long-time tails. A more general approach using coarse graining has theoretically predicted a negative t −d/2−1 decay [15][16][17]. There are two mechanisms for the decay of the singleparticle momentum in atomic or molecular liquids: diffusion and sound propagation. By diffusion the momentum of a tagged atom is transferred into a region of typical length l = √ Dt (D is the diffusion coefficient) and the velocity decays * Corresponding author: hailong.peng@imr.tohoku.ac.jp, which is the classical long-time tail. In accordance with this mech...

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“…However, introducing compressibility in continuum hydrodynamics [27,28] does not improve the prediction for the VACF, even with an effective hydrodynamic radius adjusted to reproduce the calculated friction (see [19]), because it does not capture molecular scale effects. Finally, let us consider the implications of the present work for larger solutes.…”

Section: Figmentioning

confidence: 99%

Molecular Hydrodynamics from Memory Kernels

et al. 2016

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The memory kernel for a tagged particle in a fluid, computed from molecular dynamics simulations, decays algebraically as t −3/2 . We show how the hydrodynamic Basset-Boussinesq force naturally emerges from this long-time tail and generalize the concept of hydrodynamic added mass. This mass term is negative in the present case of a molecular solute, at odds with incompressible hydrodynamics predictions. We finally discuss the various contributions to the friction, the associated time scales and the cross-over between the molecular and hydrodynamic regimes upon increasing the solute radius.The Brownian motion of a particle in a fluid finds its origin in the fluctuating force exerted by the solvent molecules on the solute. It has long been known that the canonical description of this random force by a Gaussian Markov process is only valid in limiting cases. Even in the limit where the solute is much heavier than the solvent particles, for which multiple time-scale analysis allows to recover the Smoluchowski equation for diffusion [1], nonMarkovian effects are expected when the mass density ratio is close to unity [2] -a situation which is rather the rule than the exception e.g. in colloidal suspensions. These non-Markovian effects arise because of momentum conservation, leading to slow hydrodynamic modes that manifest themselves as long-time tails in the velocity autocorrelation function (VACF) [3][4][5][6]. Recent experiments have demonstrated that the force exerted by the bath includes a deterministic component [7], well described for large colloidal spheres by the Basset-Boussinesq (BB) hydrodynamic force [8,9]:where R is the sphere radius, η the solvent viscosity and ρ 0 its mass density. The first term is the usual Stokes friction. The other two account for the inertia of the displaced fluid and involve a finite added mass m BB 0 = 2 3 πR 3 ρ 0 and a viscosity-dependent retarded component describing the transient effects of momentum diffusion in the solvent. While continuous descriptions of steady-state flows appear to hold down to the nanoscale [10][11][12], possibly at the price of adapting the hydrodynamic radius R or the boundary conditions [13], their validity for the transient regimes should be questioned. The implicit assumption of a separation of time scales between the solvent and solute dynamics, which holds a priori for colloidal particles [14], is expected to break down with smaller solutes such as nanoparticles or biomolecules.Here we address the fundamental questions that arise when approaching the regime of molecular solutes by computing directly from Molecular Dynamics (MD) simulations the memory kernel and the random noise of the Generalized Langevin Equation (GLE). A novel algorithm based on the Mori-Zwanzig formalism with high numerical stability allows us to explore long time scales for the first time. We consider the extreme case of a tagged particle (identical masses and sizes) in a pure supercritical fluid.By examining the long-time behaviour of the memory kernel, we demonstrate the gen...

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Velocity autocorrelation function of a Brownian particle

Cited by 20 publications

References 25 publications

Diffusion of a Janus nanoparticle in an explicit solvent: A molecular dynamics simulation study

Diffusion of a Janus nanoparticle in an explicit solvent: A molecular dynamics simulation study

Velocity autocorrelation function in supercooled liquids: Long-time tails and anomalous shear-wave propagation

Molecular Hydrodynamics from Memory Kernels

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