Repulsive Reference Potential Reproducing the Dynamics of a Liquid with Attractions

A well-known result of liquid state theory is that the structure of dense fluids is mainly determined by their repulsive forces. The Weeks-Chandler-Andersen potential, which cuts intermolecular potentials at their minima, is therefore often used as a reference. However, this cannot reproduce the viscous dynamics of the Kob-Andersen binary Lennard-Jones liquid [Berthier and Tarjus, Phys. Rev. Lett. 103, 170601 (2009)]. This paper shows that repulsive inverse-power-law potentials provide a reference for this liquid that reproduces its structure, dynamics, and isochoric heat capacity.

Figure 1

(a) The IPL exponent is estimated to $n=3\times 5.16=15.48$ by evaluating the slope of a scatter plot of the virial and potential energy fluctuations of the KABLJ liquid at three state points with same density (open symbols, $NVT$ simulations of 1000 particles). Average values of the state points are indicated by (yellow) $\times$’s. (b) The IPL prefactor is estimated to $A=1.945$ from the slope in a scatter plot of $\sum _{i>j}{\epsilon }_{ij}(r_{ij}/{\sigma }_{ij}{)}^{-n}$ and potential energy fluctuations. The number $R$ gives the relevant correlation coefficient.

Figure 2

Radial distribution functions of the $AA$, $AB$, and $BB$ particle pairs of the KABLJ, KABIP, and KABWCA liquids at one state point.

Figure 3

Incoherent intermediate self-scattering function for the $A$ particles of the KABLJ, KABIP, and KABWCA liquids along the $\rho =1.20$ isochore for five temperatures. At the highest temperature the three models have the same dynamics, but at lower temperatures only the KABLJ and KABIP liquid have the same dynamics; the KABWCA liquid is considerably faster. Asterices (KABWCAIP) denote the IPL approximation to the KABWCA liquid (at each state point the parameters $A$ and $n$ are uniquely determined from the equilibrium virial and potential energy fluctuations, resulting in at $\rho =1.20$ for $T=\{0.45,0.5,0.6,0.8,2.0\}$: $n=\{20.67,20.28,19.59,18.69,16.38\}$ and $A=\{1.176,1.205,1.231,1.267,1.471\}$).

Figure 4

(a) Structural relaxation time ${\tau }_{\alpha }$ as a function of inverse temperature [defined as the time when the $AA$ incoherent intermediate scattering function is $1/e$ at wave vector $q=7.25(\rho /1.2{)}^{1/3}$]. Lines between isochoric points are shown for clarity. (b) The reduced structural relaxation time of the KABLJ and KABIP liquids is a function of the variable ${\rho }^{\gamma }/T$, confirming density scaling [17, 18]. In both (a) and (b) the small (red) symbols give the KABWCA results at densities 1.15, 1.20, and 1.30.

Figure 5

(a) Isochoric specific heat per particle, $c_V$, in units of $k_B$. Lines between isochoric points are shown for clarity. The KABIP $c_V$ is closer to the KABLJ than is the KABWCA. (b) The same data scaled according to the density scaling recipe in conjunction with the Rosenfeld-Tarazona $c_V$ scaling [22], which is indicated by the (blue) dashed line (the number 1.25 being a fitting parameter).