Effects of skewing collision cells on transport properties in multiparticle collision dynamics simulations

TL;DR

Multiparticle collision dynamics (MPCD) models hydrodynamic interactions by momentum-exchanging collisions in local cells. This study extends MPCD to collision cells aligned with a triclinic (parallelepiped) box and analyzes how cell skewness affects transport properties of both solvent and solute particles, using VACF, MSD-derived diffusion, and viscosity measurements. The main findings are that skewed cells induce small changes in solvent transport but produce stronger, unphysical diffusion anisotropy for nearly hard-sphere solutes, with diffusion corrections and finite-size scaling behaving differently than in cubic-cell MPCD. These artifacts motivate caution in using skewed cells and suggest grid-free binning as a potential remedy to mitigate skewness-induced biases.

Abstract

Multiparticle collision dynamics (MPCD) is a mesoscale simulation technique that uses a simplified solvent to model hydrodynamic interactions. Rather than interact through pairwise forces, MPCD solvent particles undergo momentum-exchanging collisions within spatially localized cells according to prescribed rules. The conventional MPCD algorithm employs cubic collision cells, but this choice is not optimal for systems that are most naturally described using skewed simulation boxes. Here, we investigate the behavior of a modified MPCD scheme in which the collision cells are aligned with the vectors that define a triclinic (parallelepiped) simulation box. We find that skewing the collision cells has a small but statistically significant impact on the transport properties of the pure solvent. Similar, but more pronounced, effects are found for nearly hard spheres in solution, including a significant decrease in their nominal self-diffusion coefficient and unphysical anisotropy in their self-diffusion tensor. Thus, our analysis indicates that skewed MPCD collision cells may result in spurious behavior and should be used with caution. We posit that these artifacts may be mitigated by grid-free schemes for placing particles into collision cells.

Figures (8)

• Figure 1: Schematic of collision cells in two dimensions: (a) cubic and (b) skewed cells with $f_{xy} = 1.0$ ($45^\circ$ angle). Both representations describe the same underlying lattice.
• Figure 2: (a) Velocity autocorrelation function and (b) self-diffusion coefficient of the pure solvent with density $\rho = 5/\ell^3$ in Boxes A--D with $L=20\,\ell$. Percentages above bars in (b) indicate relative differences with respect to Box A.
• Figure 3: Shear viscosity of pure solvent with density $\rho = 5/\ell^3$ in Boxes A--C with $L = 20\,\ell$ obtained using RNES (filled bars) or force-driven simulations (hatched bars). The dotted line denotes the theoretically predicted viscosity for cubic collision cells.
• Figure 4: Self-diffusion coefficients of nearly hard spheres with density $\rho_{\rm s} = 0.2/\ell^3$ in solvent with density $\rho = 5/\ell^3$ in Boxes A--D with $L = 20\,\ell$. Percentages above bars indicate relative differences with respect to Box A.
• Figure 5: (a) Self-diffusion coefficients of nearly hard spheres with density $\rho_{\rm s} = 0.2/\ell^3$ in solvent with density $\rho = 5/\ell^3$ in Boxes A--D with $L = \{20, 25, 33, 50, 100\}\,\ell$. Solid symbols are simulated values, solid lines are linear fits to the simulated values, and dashed lines are linear extrapolation. (b) The same data as in (a) but with $D$ normalized by the self-diffusion coefficient extrapolated to infinite box size $D^{\infty}$. Uncertainties in the simulated data are approximately the size of or smaller than the symbols.