Anisotropic particles with tetrahedral symmetry

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Artists impression of a tetrahedral patchy particle

Anisotropic particles with tetrahedral symmetry

Kern and Frenkel model[edit]

Phase diagram[edit]

The phase diagram of the tetrahedral Kern and Frenkel patchy model exhibits the following solid phases[1][2]: diamond crystal (DC), body centred cubic (BCC) and face centred cubic (FCC). The gas-liquid critical point becomes metastable with respect to the diamond crystal when the range of the interaction becomes short (roughly less than 15% of the diameter).

In contrast to isotropic models, the critical point becomes only weakly metastable with respect to the solid as the interaction range narrows (from left to right in the figure).


Tetrahedral Kern-Frenkel patchy particles crystallise spontaneously into open tetrahedral networks for narrow patches (solid angle < 30). The interaction range does not play an important role in crystallisation [3]

Interaction range, , versus patch angular width. Diamonds correspond to crystallising and circles to glass–forming models. The point studied in Ref. [4] is included.

When the patches in this model are made even wider (while still enforcing the limit of a single bond per patch), the diamond phase becomes metastable with respect to a liquid phase, which is stable even in the zero-temperature limit [5].

Modulated patchy Lennard-Jones model[edit]

The solid phases of the modulated patchy Lennard-Jones model has also been studied [6]

Lattice model[edit]


See also[edit]


Related reading