Determination of the friction coefficient of a Brownian particle by molecular-dynamics simulation

Kaddour, F. Ould; Levesque, D.

doi:10.1063/1.1563593

Cited by 30 publications

(33 citation statements)

References 15 publications

(46 reference statements)

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“…Several studies have been devoted to the Brownian limit [1,2,4,6,8,11], some of them especially to the question, for which range of tracer mass and size this purely hydrodynamic relation also holds on the microscopic level [5,7]. Depending on whether the mass is changed at constant size ratio or not, the SE relation was found to hold for mass ratios larger than 10 [5] and larger than 100 [7], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…The dynamic properties of binary fluid systems where one particle species differs from the other only in size, mass or both of these parameters have been the subject of a large number of studies during the last years [1,2,3,4,5,6,7,8,9,10,11,12]. The increasing interest is, on the one hand, due to the fact that such systems serve as simple models for colloids and micellar solutions, which are of prime importance in many scientific areas such as biology or biochemistry, on the other hand it is sparked by the rapidly growing capabilities of modern computer hardware which allows us to investigate parameter ranges and system sizes that were not accessible before.…”

Section: Introductionmentioning

confidence: 99%

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Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

et al. 2009

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Correlation functions and transport coefficients of self-diffusion and shear viscosity of a binary Lennard-Jones mixture with components differing only in their particle mass are studied up to high values of the mass ratio µ, including the limiting case µ = ∞, for different mole fractions x. Within a large range of x and µ the product of the diffusion coefficient of the heavy species D2 and the total shear viscosity of the mixture ηm is found to remain constant, obeying a generalized Stokes-Einstein relation. At high liquid density, large mass ratios lead to a pronounced cage effect that is observable in the mean square displacement, the velocity autocorrelation function and the van Hove correlation function.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

et al. 2009

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“…Since MD simulations are carried out at finite N, the study of the N (and M) dependence of ζu(t) and the estimate of the friction coefficient from either the decay of the momentum or force autocorrelation functions is of interest. 4,5 Furthermore, in order to calculate the friction coefficients of the BP from Eqs. (6) and (7), the mass of the BP, M, becomes infinity, or the BP is fixed in space using a holonomic constraint method.…”

Section: Resultsmentioning

confidence: 99%

“…The decay rates of these correlations are confirmed to vary as N -1 in accord with earlier predictions. 4 The purpose of this paper is twofold: First, we investigate the issue discussed above by carrying out large scale simulations confirming the treatment of momentum conservation of the whole system related to the estimates of the friction coefficients. Second, we use these calculations to understand the effects of the size ratio of the BP and the solvent particle on the friction coefficient.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, the computation of the friction coefficient from MD simulations involves a number of subtle issues for finite-size systems as discussed in several recent papers. [2][3][4] The problems center around the definition of the friction coefficient in terms of the projected dynamics and its relation to the fixed-particle friction coefficient for a massive Brownian particle (BP). The estimates of the friction coefficients have been shown to depend on the order in which the mass of the BP and the solvent particle number N are taken to infinity.…”

Section: Introductionmentioning

confidence: 99%

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Friction of a Brownian Particle in a Lennard-Jones Solvent: A Molecular Dynamics Simulation Study

Lee¹

2010

Bulletin of the Korean Chemical Society

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In this work, equilibrium molecular dynamics (MD) simulations in a microcanonical ensemble are performed to evaluate the friction coefficient of a Brownian particle (BP) in a Lennard-Jones (LJ) solvent. The friction coefficients are determined from the time dependent friction coefficients and the momentum autocorrelation functions of the BP with its infinite mass at various ratios of LJ size parameters of the BP and solvent, σB/σs. The determination of the friction coefficients from the decay rates of the momentum autocorrelation functions and from the slopes of the time dependent friction coefficients is difficult due to the fast decay rates of the correlation functions in the momentumconserved MD simulation and due to the scaling of the slope as 1/N (N: the number of the solvent particle), respectively. On the other hand, the friction coefficient can be determined correctly from the time dependent friction coefficient by measuring the extrapolation of its long time decay to t=0 and also from the decay rate of the momentum autocorrelation function, which is obtained by time integration of the time dependent friction coefficient. It is found that while the friction coefficient increases quadratically with the ratio of σB/σs for all σB, for a given σs the friction coefficient increases linearly with σB.

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Multiparticle Collision Dynamics: Simulation of Complex Systems on Mesoscales

Kapral

2008

Advances in Chemical Physics

312

303

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Complex systems can display complex phenomena that are not easily described at a microscopic level using molecular dynamics simulation methods. Systems may be complex because some or all of their constituents are complex molecular species, such as polymers, large biomolecules, or other molecular aggregates. Such systems can exhibit the formation of patterns arising from segregation of constituents or nonequilibrium effects and molecular shape changes induced by flows and hydrodynamic interactions. Even when the constituents are simple molecular entities, turbulent fluid motions can exist over a range of length and time scales.Many of these phenomena have their origins in interactions at the molecular level but manifest themselves over mesoscopic and macroscopic space and time scales. These features make the direct simulation of such systems difficult because one must follow the motions of very large numbers of particles over very long times. These considerations have prompted the development of coarse-grain methods that simplify the dynamics or the system in different ways in order to be able to explore longer length and time scales. The use of mesoscopic dynamical descriptions dates from the foundations of nonequilibrium statistical mechanics. The Boltzmann equation [1] provides a field description on times greater than the time of a collision and the Langevin equation [2] replaces a molecular-level treatment of the solvent with a stochastic description of its properties.The impetus to develop new types of coarse-grain or mesoscopic simulation methods stems from the need to understand and compute the dynamical properties of large complex systems. The method of choice usually depends on the type of information that is desired. If properties that vary on very long distance and time scales are of interest, the nature of the dynamics can be altered, while still preserving essential features to provide a faithful representation of these properties. For example, fluid flows described by the Navier-Stokes equations will result from dynamical schemes that preserve the basic conservation laws of mass, momentum, and energy. The details of the molecular interactions may be unimportant for such applications. Some coarsegrain approaches constructed in this spirit, such as the lattice Boltzmann method [3] and direct simulation Monte Carlo [4], are based on the Boltzmann equation. In dissipative particle dynamics [5, 6], several atoms are grouped into simulation sites whose dynamics is governed by conservative and frictional 90 raymond kapral 92 raymond kapral

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Determination of the friction coefficient of a Brownian particle by molecular-dynamics simulation

Cited by 30 publications

References 15 publications

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

Friction of a Brownian Particle in a Lennard-Jones Solvent: A Molecular Dynamics Simulation Study

Multiparticle Collision Dynamics: Simulation of Complex Systems on Mesoscales

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