Hypernetted-chain-like closure of Ornstein-Zernike equation in multibody dissipative particle dynamics

We have derived a hypernetted-chain-like (HNC-like) approximate closure of the Ornstein-Zernike equation for multibody dissipative particle dynamics (MDPD) system in which the classic closures are not directly practicable. We first point out that the Percus's method is applicable to MDPD system in which particles interact with a density-dependent potential. And then an HNC-like closure is derived using Percus's idea and the saddle-point approximation of particle free energy. This HNC-like closure is compared with results of previous researchers, and in many cases, it demonstrates better agreement with computer simulation results. The HNC-like closure is used to predict the cluster crystallization in MDPD. We determine whether the cluster crystallization will happen in a system utilizing the widely applicable Hansen-Verlet freezing criterion and by observing the radial distribution function. The conclusions drawn from the results of the HNC-like closure are in agreement with computer simulation results. We evaluate different weight functions to determine whether they are prone to cluster crystallization. A new effective density-dependent pairwise potential is also proposed to help to explain the tendency to cluster crystallization of MDPD systems.

Figure 1

RDF results (a) and structure factor results (b) from different closures, compared with computer simulation results. $K=1, n=2, \rho =6, k_{B}T=1$.

Figure 2

RDF results (a) and structure factor results (b) from different closures, compared with computer simulation results. $K=0.1, n=3, \rho =6, k_{B}T=1$.

Figure 3

RDF results (a) and structure factor results (b) from different closures, compared with computer simulation results. Warren's MDPD model is used. $A=12.5, B=20, \rho =6, k_{B}T=1, r_d=0.75$.

Figure 4

RDF results (a) and structure factor results (b) from different closures, compared with computer simulation results. Warren's MDPD model is used. $A=-40, B=40, \rho =6, k_{B}T=1$.

Figure 5

RDF results (a) and structure factor results (b) from different closures, compared with computer simulation results. Parameters are the same as that of Merabia and Pagonabarraga [13]. Density is near the vapor-liquid coexistence density.

Figure 6

(a) Relations between the main peak of $S\left(k\right)$ and the system density. (b) Relations between the $g\left(0\right)$ and the system density. $K=0.05, n=2, k_{B}T=1$. Continuum lines are from solutions of the OZ equation, the dots are from computer simulations. The computer simulation data points marked by unfilled circles represent a system that is close to solidification or has already solidified.

Figure 7

(a) Relations between the main peak of $S\left(k\right)$ and the system density. (b) Relations between the $g\left(0\right)$ and the system density. $K=0.25, n=2, k_{B}T=1$. Continuum lines are from solutions of the OZ equation, the dots are from computer simulations. The computer simulation data points marked by unfilled circles represent a system that is close to solidification or has already solidified.

Figure 8

(a) Relations between the main peak of $S\left(k\right)$ and the system density. (b) Relations between the $g\left(0\right)$ and the system density. $K=0.05, n=2, k_{B}T=1$. Different line colors represent different weight functions.

Figure 9

The effective density-independent pairwise potentials computed from different weight functions. $K=0.05, n=2, k_{B}T=1, \rho =14$.