Distributions of pore sizes and atomic densities in binary mixtures revealed by molecular dynamics simulations

We report on the results of a molecular dynamics simulation study of porous glassy media, formed in the process of isochoric rapid quenching from a high-temperature liquid state. The transition to a porous solid occurs due to the concurrent processes of phase separation and material solidification. The study is focused on topographies of the model porous structures and their dependence on temperature and average density. To quantify the pore-size distributions, we put forth a scaling relation that provides a satisfactory data collapse in systems with high porosity. We also find that the local density of the solid domains in the porous structures is broadly distributed, and, with increasing average density, a distinct peak in the local density distribution is displaced toward higher values.

Figure 1

Equilibrium instantaneous atomic configurations of the porous glass, computed at different values of $\rho {\sigma }^3$: (a) 0.3, (b) 0.5, (c) 0.7, and (d) 0.9 (from top to bottom). All the configurations are obtained at $T=0.05\varepsilon /k_B$. The left panels show the full three-dimensional plots of the atomic configurations, and the right panels display slices of the central parts of the simulation cell with thickness of $5\sigma$. Different colors mark atomic types $A$ and $B$.

Figure 2

The average pressure, $P$, in equilibrium systems as a function of temperature, $T$, for the indicated values of $\rho {\sigma }^3$. The inset shows the scaling collapse using $P/T\sim {\rho }^{\alpha }$ relation. See text for details.

Figure 3

The pore size distribution functions, $\mathrm{\Phi }\left(d_p\right)$, computed for systems with densities $\rho {\sigma }^3\in \left\{0.2,0.5,0.7,0.9\right\}$ and $T=0.05\varepsilon /k_B$. In the analysis, the original bin size is fixed at $\simeq 0.05\sigma$. Subsequent averaging was performed within $\simeq 0.5\sigma$; a reduced set of data points for each $\rho {\sigma }^3$ is shown for clarity. The dashed orange curve is a Gaussian fit to the $\rho {\sigma }^3=0.9$ data. The inset shows the data collapse for all densities according to Eq. (2). The same color code as in Fig. 2.

Figure 4

The maximum pore diameter, $d_m$, is plotted as a function of temperature for the tabulated values of $\rho {\sigma }^3$.

Figure 5

On-lattice local density distribution functions, ${\langle \rho \rangle }_R$, are shown for the normalized average density, $\rho {\sigma }^3$, values: (a) 0.2, (b) 0.3, (c) 0.4, (d) 0.5, (e) 0.6, (f) 0.7, (g) 0.8, (h) 0.9, and (i) 1.0. The distribution functions are computed using the bin size of ${\langle \rho \rangle }_R^{max}$/400 and $T=0.05\varepsilon /k_B$; no averaging of any kind is involved.

Figure 6

Average density of solid domains, ${\langle \rho \rangle }_S$, is plotted as a function of the porosity, $p$. The inset shows the porosity versus $\rho {\sigma }^3$ dependence (open circles). The power-law fit to the simulation data is indicated by the dashed curve. The fitting procedure is discussed in the text.