Excess free energy of supercooled liquids at disordered walls

Using a thermodynamic integration scheme, we compute the excess free energy, $\gamma$, of a glass-forming, binary Lennard-Jones liquid in contact with a frozen amorphous wall, formed by particles frozen into a similar structure as the liquid. We find that $\gamma$ is nonzero, becoming negative at low temperature. This indicates that the thermodynamics of the system is perturbed by the effect of the amorphous wall.

Figure 1

Simulation set-up of supercooled liquid in contact with disordered walls along the $z$ direction, showing the two components of the binary liquid mixture by different colors (light and dark), with different (a) and same (b) color (shades) codes adopted for the mobile and pinned particles. The dashed vertical line, denotes the location of the flat walls. (c) Density profile averaged over 10 different wall configurations (black or dark curve) and those corresponding to two independent realizations (red and green or lighter curves). Density is in units of ${\sigma }_{\mathrm{AA}}^{-3}$. Data corresponds to $T=0.53$ and $N=6912$. In (a), (b) and (c), $\sigma$ refers to the size of the A particles, ${\sigma }_{\mathrm{AA}}$.

Figure 2

Thermodynamic integrand as a function of $\lambda$ for the first (in the inset) and second steps of the TI scheme at the temperature $T=0.53$ and $N=4000$.

Figure 3

Interfacial free energy as a function of the equilibration time corresponding to the first (a) and second (b) TI steps for $T=0.53$ and $N=4000$.

Figure 4

Interfacial free energy vs temperature for supercooled liquid in contact with a disordered wall from the sum of the two TI steps for $N=4000$.