The computationally expensive nature of molecular dynamics simulation limits the access to length (nanometer) and time scales (nanosecond) that are orders of magnitude smaller than the experiment it models. This limitation warrants a careful estimation of statistical uncertainty associated with the properties calculated from these simulations. The assumption that a simulation is long enough so that the ergodic hypothesis applies is often invoked in the literature for the computation of properties of interest from a single molecular dynamics simulation. Here, we demonstrate that making this assumption without validation results in poor estimates of the self-diffusion coefficient from a single molecular dynamics simulation of Lennard-Jones fluid. This problem is shown to be even more severe when the diffusion coefficient of macromolecules is calculated from a single molecular dynamics simulation. We have shown that conducting multiple independent simulations is necessary to obtain reliable estimates of diffusion coefficients and their associated statistical uncertainties. We show that even a “routine” calculation of the self-diffusion coefficient for a Lennard-Jones fluid, as determined from a linear fit of the mean squared displacement of particles as a function of time, violates the key assumptions of linear regression. A rigorous approach for addressing these issues is presented.

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The diffusion of fractal aggregates constructed with the method by Jullien [ J. Phys. A 27, 2953 (1994)] comprised of Np spherical primary particles was studied as a function of the aggregate mass and fractal dimension using molecular dynamics simulations. It is shown that finite-size effects have a strong impact on the apparent value of the diffusion coefficient (D), but these can be corrected by carrying out simulations using different simulation box sizes. Specifically, the diffusion coefficient is inversely proportional to the length of a cubic simulation box, and the constant of proportionality appears to be independent of the aggregate mass and fractal dimension. Using this result, it is possible to compute infinite dilution diffusion coefficients (Do) for aggregates of arbitrary size and fractal dimension, and it was found that Do∝N−1/dfp, as is often assumed by investigators simulating Brownian aggregation of fractal aggregates. The ratio of hydrodynamic radius to radius of gyration is computed and shown to be independent of mass for aggregates of fixed fractal dimension, thus enabling an estimate of the diffusion coefficient for a fractal aggregate based on its radius of gyration. Disciplines Biological Engineering | Chemical Engineering CommentsThis article is from Physical Review E 82 (2010) The diffusion of fractal aggregates constructed with the method by Thouy and Jullien ͓J. Phys. A 27, 2953 ͑1994͔͒ comprised of N p spherical primary particles was studied as a function of the aggregate mass and fractal dimension using molecular dynamics simulations. It is shown that finite-size effects have a strong impact on the apparent value of the diffusion coefficient ͑D͒, but these can be corrected by carrying out simulations using different simulation box sizes. Specifically, the diffusion coefficient is inversely proportional to the length of a cubic simulation box, and the constant of proportionality appears to be independent of the aggregate mass and fractal dimension. Using this result, it is possible to compute infinite dilution diffusion coefficients ͑D o ͒ for aggregates of arbitrary size and fractal dimension, and it was found that D o ϰ N p −1/d f , as is often assumed by investigators simulating Brownian aggregation of fractal aggregates. The ratio of hydrodynamic radius to radius of gyration is computed and shown to be independent of mass for aggregates of fixed fractal dimension, thus enabling an estimate of the diffusion coefficient for a fractal aggregate based on its radius of gyration.

Nanoparticle surface forces < 1 nm Quantum Chemistry Brownian aggregation 1-100 nm Molecular Simulations Shear-induced restructuring 0.1-10 μm Brownian Dynamics Shear-induced aggregation 0.01-10 mm Direct Numerical Simulations Turbulent reacting flow 0.01-1 m Large Eddy Simulations AFM Experiments Force between Nanoparticles Light Scattering Experiments Aggregate Size and Fractal Dimension

Abstract:A force matching technique based on previous work by Voth and co-workers is developed and employed to coarse grain intermolecular potentials for three common solvents: carbon tetrachloride, benzene, and water. The accuracy of the force-matching approach is tested by comparing radial distribution functions (RDF) obtained from simulations using the atomistic and coarse-grained potentials. Atomistic molecular dynamics simulations were performed using the effective fragment potential method (EFP). The RDFs obtained from molecular dynamics simulations of EFPs for carbon tetrachloride, benzene and water are in a good agreement with the corresponding experimental data. The coarse-grained potentials reproduce the EFP molecular dynamics center-of-mass RDFs with reasonable accuracy. The biggest discrepancies are observed for benzene, while the coarse-graining of water and spherically symmetric carbon tetrachloride is of better quality

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