Pressure and energy behavior of the Gaussian core model fluid under shear

The pressure and energy behavior of the Gaussian core model (GCM) fluid as a function of strain-rate are obtained from nonequilibrium molecular dynamics simulations for a wide range of thermodynamic state points. An analytical dependence of pressure on strain-rate is observed which is in agreement with a Taylor series expansion of pressure in terms of the strain-rate tensor. In contrast, the energy as a function of strain rate is found to be dependent on temperature and density. The different behavior of pressure and energy contradicts mode-coupling theory, which requires the same variation of pressure and energy with respect to the strain-rate. The results for the GCM fluid do not support the hypothesis that the strain-rate exponent for both pressure and energy can be universally represented by a simple linear function of temperature and density.

Figure 1

Pressure as a function of strain-rate at densities of (a) $\rho =0.1$ and (b) $\rho =1.0$ for different temperatures $T=0.002$ (◼), 0.1 (●), 0.5 (▲), 1.0 (▼), 2.0 (◆) and 3.0 (◀) (data from simulations). $\rho \text{TF}$ fits are shown as thin continuous lines. The $T=0.02$, 0.1, 0.5, 1.0, and 2.0 pressure isotherms are shifted by 100, 80, 60, 40, and 20 in Fig. 1a and by 150, 120, 90, 60, and 30 in Fig. 1b, respectively, in order to avoid overlap.

Figure 2

Parameters (a) $p_0$, (b) $p_{\dot{\gamma }}$, and (c) $\alpha$ of the $\rho \text{TF}$ fit as a function of temperature for densities $\rho =0.1$ (◼), 0.2 (●), 0.3 (▲), 0.4 (▼), and 1.0 (◆). Data obtained from the $\rho \text{TF}$ fit with the pressure data from simulations as a function of strain-rate. In Fig. 2a, 2b the pressure isochor for $\rho =1.0$ is shifted by $-2$ and in Fig. 2c the $\alpha$ isochors are shifted by $-0.1$ each starting at $\rho =0.2$ in order to avoid overlap.

Figure 3

Comparison of the relative percentage difference of the zero-shear pressure obtained from the $\rho \text{TF}$ fit with EMD calculations (Ref. [31]) as a function of temperature and densities of $\rho =0.1$ (◼), 0.2 (●), 0.3 (▲), 0.4 (▼), and 1.0 (◆).

Figure 4

Comparison of the relative percentage difference of hydrostatic pressures obtained from simulation with the hydrostatic pressures calculated from the AB fit as a function of strain-rate for the state points $\left(\rho =0.1,T=0.015\right)$ (●) and $\left(\rho =1.0,T=3.0\right)$ (○).

Figure 5

Potential energy per particle as a function of strain-rate at densities of (a) $\rho =0.1$ and (b) $\rho =0.4$ for different temperatures $T=0.015$ (◼), 0.02 (●), 0.03 (▲), 0.04 (▼), 0.06 (◆), and 0.08 (◀) (data from simulations). The $\rho$TF fits are shown as thin continuous lines. The energy isotherms in Fig. 5b for temperatures $T=0.015$, 0.02 and 0.03 are shifted by $-0.03$, $-0.02$, and $-0.01$, respectively, in order to avoid overlaps.

Figure 6

Values of (a) $E_0$, (b) $E_{\dot{\gamma }}$, and (c) $\alpha$ as functions of temperature obtained from the simulation data via a least-squares $\rho \text{TF}$ fit for densities $\rho =0.1$ (◼), 0.2(●), 0.3 (▲), 0.4 (▼), and 1.0 (◆). In Fig. 6a the $E_0$ isochor for $\rho =1.0$ is shifted by $-1.5$.

Figure 7

Values of (a) $E_0$, (b) $E_{\dot{\gamma }}$, and (c) $\alpha$ as functions of density obtained from the simulation data via a least-squares $\rho \text{TF}$ fit

Figure 8

Comparison of the relative percentage difference of the zero-shear potential energy per particle $E_0$ obtained from a $\rho \text{TF}$ fit with EMD calculations (Ref. [31]) as a function of temperature and densities of $\rho$=0.1 (◼), 0.2 (●), 0.3 (▲), 0.4 (▼), and 1.0 (◆).

Figure 9

Comparison of the relative percentage difference of potential energies per particle obtained from simulation with the energies calculated from an $\rho \text{TF}$ fit as a function of strain-rate for the state points $\left(\rho =0.1,T=0.015\right)$ (●) and $\left(\rho =0.4,T=0.1\right)$ (○).