Molecular dynamics simulation study of binary fullerene mixtures

We report constant-pressure molecular dynamics (MD) simulations of binary ${\mathrm{C}}_{60}∕C_n$ fullerene-mixtures ($n=70$, 76, 84, 96) modeled in terms of a spherically symmetric two-body potential. By starting from a liquid configuration of the system, we cool mixtures down to freezing and beyond, until room temperature is reached, in order to verify the formation of solid solutions, namely, of configurations characterized by a unique crystalline lattice whose sites are randomly occupied by the two component fullerene species. We first explore the entire concentration range of the ${\mathrm{C}}_{60x}∕{\mathrm{C}}_{70(1-x)}(0<x<1)$ mixture and find fairly good agreement with experimental data, exhibiting partial reciprocal solubility of the two components into each other with an immiscibility gap at intermediate compositions. In fact, the system we simulate forms substitutional solid solutions over a wide range of concentrations except for $0.3⩽x⩽0.5$; over such an interval, it turns out that the initially liquid mixture can be supercooled down to relatively low temperatures, until eventually a glassy phase is formed. The study is then extended to fullerene mixtures of molecular diameter ratio $\alpha ={\sigma }_{{\mathrm{C}}_{60}}∕{\sigma }_{{\mathrm{C}}_n}$ smaller than in ${\mathrm{C}}_{60}∕{\mathrm{C}}_{70}$ (where $\alpha =0.93$), as is the case for ${\mathrm{C}}_{60}∕{\mathrm{C}}_{76}$ $(\alpha =0.89)$, ${\mathrm{C}}_{60}∕{\mathrm{C}}_{84}(\alpha =0.85)$ and ${\mathrm{C}}_{60}∕{\mathrm{C}}_{96}$ $(\alpha =0.79)$. The effect of the size mismatch between the two species is dramatic: The solid immiscibility region rapidly expands even upon a tiny reduction of $\alpha$, with formation of an amorphous phase at sufficiently low temperature, as found for the ${\mathrm{C}}_{60}∕{\mathrm{C}}_{70}$ mixture. For the smallest $\alpha ({\mathrm{C}}_{60}∕{\mathrm{C}}_{96})$ cocrystallization of the two components turns out to be forbidden over the whole concentration axis. A mapping of the MD evidences of the fullerene mixtures’ phase behavior onto the phase diagram of binary hard-sphere mixtures (determined by other authors) turns out to be worthwhile and enlightnening. In particular, size ratio effects and the onset of glassy phases emerge in qualitative good agreement with such studies, and with results of phase coexistence calculations in model binary colloidal systems.

Figure 1

Like (top) and unlike (bottom) fullerene-fullerene interaction in absolute distance and energy units.

Figure 2

Fullerene—fullerene interaction as in Fig. 1, in reduced distance units.

Figure 3

Volume of the ${\mathrm{C}}_{60}∕{\mathrm{C}}_{70}$ mixtures versus temperature at different ${\mathrm{C}}_{70}$ concentrations, appearing as labels beside the curves.

Figure 4

Same as Fig. 3 for the enthalpy of the ${\mathrm{C}}_{60}∕{\mathrm{C}}_{70}$ mixtures.

Figure 5

Room temperature rdfs. of the ${\mathrm{C}}_{60}{\mathrm{C}}_{70}$ solid solutions at different concentrations (labeling the curves). Rdfs. are displayed shifted by two units on the ordinate axis.

Figure 6

RT density (top) and enthalpy (bottom) of the ${\mathrm{C}}_{60}{\mathrm{C}}_{70}$ mixtures.

Figure 7

Temperature (top) and total packing (bottom) values for the isodiffusivity ($D={10}^{-5}{\mathrm{cm}}^2∕\mathrm{s}$) points of the ${\mathrm{C}}_{60}∕{\mathrm{C}}_{70}$ (circles) and ${\mathrm{C}}_{60}∕{\mathrm{C}}_{84}$ (squares) mixtures.

Figure 8

RT lattice constants $a$ (in nanometers) versus concentrations for the fullerene solid solutions: ${\mathrm{C}}_{60}∕{\mathrm{C}}_{70}$ (circles), ${\mathrm{C}}_{60}∕{\mathrm{C}}_{76}$ (squares), ${\mathrm{C}}_{60}∕{\mathrm{C}}_{84}$ (triangles), and ${\mathrm{C}}_{60}∕{\mathrm{C}}_{96}$ (diamond).

Figure 9

Eutectic phase diagram for binary hard sphere mixtures with diameter ratio $\alpha =0.9$ (solid line) and 0.85 (dashed line). Data have been extracted from Ref. 15.