Friction and diffusion of a Brownian particle in a mesoscopic solvent

Abstract

The friction and diffusion coefficients of a massive Brownian particle in a mesoscopic solvent are computed from the force and the velocity autocorrelation functions. The mesoscopic solvent is described in terms of free streaming of the solvent molecules, interrupted at discrete time intervals by multiparticle collisions that conserve mass, momentum, and energy. The Brownian particle interacts with the solvent molecules through repulsive Lennard-Jones forces. The decays of the force and velocity autocorrelation functions are analyzed in the microcanonical ensemble as a function of the number N of solvent molecules and Brownian particle mass and diameter. The simulations are carried out for large system sizes and long times to assess the N dependence of the friction coefficient. The decay rates of these correlations are confirmed to vary as N(-1) in accord with earlier predictions. Hydrodynamic effects on the velocity autocorrelation function and diffusion coefficient are studied as a function of Brownian particle mass and diameter.

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

“…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.…”

Simulation of DNA electrophoresis in systems of large number of solvent particles by coarse‐grained hybrid molecular dynamics approach

“…By using < k B T >¼ ms 6ðMÀ1Þ h P i v 2 i i and central limit theorem, < v >¼ ffiffiffiffiffiffiffi ffi 6kBT Mms q v 0 in which v 0 is a unit vector of random rotation in the range of 3608 or 1808 away from or at the inner planer surface of the solvent container. 19,20,31 As \v[ is approximately given as a time-independent quantity, the friction coefficient f 0 can also be estimated by as a constant f 0 5 m b s 21 . 14,32,36 f i (t) is the random force exerted by the surrounding solvent upon the ith solvent particle, which is given in terms of the Gaussian white noise and obeys the fluctuation-dissipation theorem:…”

“…[17][18][19][20][21][22] In particular, coarse-grained molecular dynamics (CG-MD) with explicit hydrodynamics has been used for studying the friction and the collision of polymers and the tethered polymers in shear flow, [17][18][19] and the dissipative particle dynamics (DPD) method has been used for studying the mobility of DNA electrophoresis in a well-studied nano-fluidic device in explicit solvent. 22 Nonetheless, the computing cost of these explicit solvent methods tends to become prohibitively high for systems of very large number of solvent particles, primarily because of the need in computing pair-wise interactions among solvent particles by these methods.…”

“…25 The second combines MD with lattice Boltzmann for studying electrophoretic properties of highly charged colloids, [26][27][28] and the third combines MD with mesoscale treatment of solvent-solvent interactions for studying solvent effect on polymer dynamics. 20,[29][30][31] By combining the advantages of the coarsegained treatment in CG-MD 17,18 and DPD 22 with the efficient modeling of solvent-solvent interactions of the hybrid MD approach, 23,24,[26][27][28] we introduced and tested a new coarsegrained hybrid MD (CGH-MD) approach as a potentially useful method for complementing the more rigorous methods to simulate systems of larger number of solvent particles without substantially losing simulation accuracy.…”

“…22 The bonding and excluded volume interactions between polymer beads are modeled by the finitely extensible nonlinear elastic potential (FENE) and Lennard-Jones potential, 20,[29][30][31] the excluded volume interaction between polymer bead and solvent are described by the Lennard-Jones potential, and the solvent-solvent interaction is represented by a frictional force and random force that obey the fluctuation-dissipation theorem. 5,14,15,32 In this work, we tested whether the CGH-MD is capable of simulating a system of large number of particles in explicit solvent at substantially lower computing cost and at accuracy levels comparable to those of coarse-grained MD.…”