Effect of attractions on the hard-sphere dynamic universality class

The fundamental understanding of the dynamic and transport properties of liquids is crucial for the better processing of most materials. The usefulness of this understanding increases when it involves general scaling rules, such as the concept of the hard-sphere dynamic universality class, which provides a unifying scaling of the dynamics of soft-sphere repulsive systems. A relevant question is how far this concept extends to systems that also involve attractive interactions. To answer this question, in this work we performed systematic molecular and Brownian dynamics simulations with the Lennard-Jones system in a wide range of temperatures and densities and verify the extent to which its static and dynamic properties map onto those of the hard-sphere system. We determine that in most of the fluid regime, the Lennard-Jones liquid exhibits the same dynamic equivalence with the hard-sphere system as most purely repulsive fluids, thus establishing the degree of its inclusion in the hard-sphere dynamic universality class.

Figure 1

Phase diagram of the Lennard-Jones fluid. The black plus symbols connected with a line represent the binodal line obtained in Ref. [16], whereas the stars with lines indicate the freezing and melting lines of the liquid-solid transition taken from Ref. [17]. The other symbols (in different colors) represent the state points $(\varphi ,T)$ that we investigated and at which we could document the structural and dynamical equivalence of the LJ fluid with the HS system. The dotted lines are iso-${\varphi }_{HS}$ lines (defined in the text) corresponding, from left to right, to ${\varphi }_{HS}=0.2$, 0.3, and 0.45.

Figure 2

Radial distribution function for Lennard-Jones systems at the equivalent volume fraction ${\varphi }_{HS}=0.45$. The solid lines correspond to the solution of PYVW theory for hard spheres. (a) State point $(\varphi ,T)=(0.6,4.5)$. (b) State point $(\varphi ,T)=(0.5,1.89)$. (c) State point $(\varphi ,T)=(0.45,1.25)$. (d) RDFs after transforming to HS units.

Figure 3

(a) Mean squared displacement of the LJ system for several state points with the same effective volume fraction ${\varphi }_{HS}=0.2$ $\left[\right(\varphi ,T)=(0.10,1.6)$, (0.20,4.5), and (1.5,11454)], ${\varphi }_{HS}=0.45$ $\left[\right(\varphi ,T)=(0.50,1.6)$, (0.60,4.5), and (4.0,11454)], and ${\varphi }_{HS}=0.56$ $\left(\right[\varphi ,T)=(0.54,1.89)$ and (0.78,4.5)]. Main panel: MSDs in units of ${\sigma }_{HS}^2$, plotted as a function of the scaled time $D_{0}t/{\sigma }_{HS}^2$. Inset: MSDs in units of ${\sigma }^2$, plotted as a function of the scaled time $D_{0}t/{\sigma }^2$. (b) Self-intermediate scattering function $F_S(k,t)$ at the wave vector $k=k_{\max }$, the position of the main peak of the static structure factor, plotted as a function of $t$ in the same fashion and for the same systems as in (a). The circles in (a) and (b) represent the data for HS fluids, determined as described in Ref. [12]. (c) Main panel: $D^{*}=D_L/D_0$ as a function of ${\varphi }_{HS}$ for BD and MD simulations. Inset: $\alpha$-relaxation time ${\tau }^{*}=k^2{D}_0{\tau }_{\alpha }$ as a function of ${\varphi }_{HS}$ for the same cases as the main panel. (d) Main panel: Long-time self-diffusion coefficient $D_L$ scaled with $\sigma \sqrt{k_{B}T/M}$. Inset: $\alpha$-relaxation time ${\tau }_{\alpha }$ in the format ${\tau }^{*}=k^2{D}_0{\tau }_{\alpha }$.