Entropy versus energy: The phase behavior of a hard-disk mixture in a periodic external potential

The phase behavior of a 50% binary hard-disk mixture with diameter ratio ${\sigma }_B/{\sigma }_A=0.414$, which is exposed to a one-dimensional periodic potential, is examined via Monte Carlo simulations. We find an induced structural crossover in the modulated liquid. At higher densities, depending on the strength of the external potential, the system exhibits a tunable demixing transition, followed by fluid-solid coexistence of an equimolar mixture with the $S_1\left(AB\right)$ square lattice. We find a decoupled melting of the sublattices of the $S_1\left(AB\right)$ lattice. The melting of the small-component sublattice perpendicular to the external potential minima leads to fissuring in the large-component sublattice.

Figure 1

(Color online) Comparison of the total pair correlation functions (a) $h_{AA}\left(\vec{r}\right)$ and (b) $h_{BB}\left(\vec{r}\right)$ for the dimensionless number density $\varrho =1.6$. Insets show the corresponding 2D pair correlation functions at $V_0/k_{B}T=2.1$.

Figure 2

(Color online) Probability distribution of the shape factor $\zeta$ in the demixing regime at $V_0/k_{B}T=1.0$ and in the coexistence region at $V_0/k_{B}T=2.5$ at a dimensionless number density of $\varrho =1.68$. The insets show overlays of the positions of the larger component in the two regimes.

Figure 3

(Color online) Probability distribution of the order parameter $S_B$ at $V_0/k_{B}T=20.0$. For clarity the plots for the dimensionless number densities $\varrho =1.77$ and $1.76$ are shifted. The inset shows a typical fissure at $\varrho =1.74$.

Figure 4

(Color online) $\varrho \text{−}{V}_0$ plane of the phase diagram as obtained from the analysis of the order parameters $S_B$ and $S_A$ and the shape factor $\zeta$. Lines are a guide to the eye.