Liquid-phase parametrization and solidification in many-body dissipative particle dynamics

Many-body dissipative particle dynamics (MDPD) is a mesoscale method capable of reproducing liquid-vapor coexistence in a single simulation. Despite having been introduced more than a decade ago, this method remains broadly unexplored, and as a result, relatively unused for modeling of industrially important soft matter systems. In this work, we systematically investigate the structure and properties of an MDPD fluid. We show that, besides the liquid phase, the MDPD potential can also yield a gas phase and a thermodynamically stable solid phase with a bcc lattice, but lacking a proper stress-strain relation. For the liquid phase, we determine the dependence of density and surface tension on the interaction parameters, and devise a top-down parametrization protocol for real liquids.

Figure 1

Representative density profiles of the MDPD depicting (a) gas phase at $r_{\mathrm{d}}=0.75,A=-5,B=25$; (b) liquid phase at $r_{\mathrm{d}}=0.75,A=-45,B=65$; and (c) solid phase at $r_{\mathrm{d}}=0.75,A=-95,B=100$. From the similarity of (b) and (c) it follows that the solid phase cannot reliably be identified by its density profile.

Figure 2

Density heat maps for (a) $r_{\mathrm{d}}=0.55$, (b) $r_{\mathrm{d}}=0.65$, (c) $r_{\mathrm{d}}=0.75$, and (d) $r_{\mathrm{d}}=0.85$. Dark regions at low values of $\left|A\right|$ show the gas phase, and yellow regions of high density shown at the top left corner reveal the no-go region with attractive force at zero interparticle distance.

Figure 3

Mean-square displacements for the representative density profiles observed in many-body DPD, depicting typical behavior of (a) gas phase at $r_{\mathrm{d}}=0.75,A=-5,B=25$; (b) liquid phase at $r_{\mathrm{d}}=0.75,A=-45,B=65$; and (c) solid phase at $r_{\mathrm{d}}=0.75,A=-95,B=100$.

Figure 4

Self-diffusivity heat maps for (a) $r_{\mathrm{d}}=0.55$, (b) $r_{\mathrm{d}}=0.65$, (c) $r_{\mathrm{d}}=0.75$, and (d) $r_{\mathrm{d}}=0.85$. Yellow regions at the top reveal the solid phase; dark regions at the bottom show the gas phase.

Figure 5

(a) Radial distribution function of the bcc phase for parameters $r_{\mathrm{d}}=0.75,A=-100,B=100$. (b) and (c) show lattice visualisations of the bcc phase.

Figure 6

Heat maps of the coordination numbers for various many-body cutoffs (a) $r_{\mathrm{d}}=0.55$, (b) $r_{\mathrm{d}}=0.65$, (c) $r_{\mathrm{d}}=0.75$, which contain a solid phase, with the lattice denoting a specific phase type.

Figure 7

Example density surface cuts at $r_{\mathrm{d}}=0.75$ (in reduced units), suggesting linear and power law variation with $A$ and $B$, respectively.

Figure 8

Examples of surface tension surface cuts for $r_{\mathrm{d}}=0.75$ (in reduced units).