Phase behavior of colloidal superballs: Shape interpolation from spheres to cubes

Robert D. Batten, Frank H. Stillinger, Salvatore Torquato

Research output: Contribution to journalArticlepeer-review

101 Scopus citations


The phase behavior of hard superballs is examined using molecular dynamics within a deformable periodic simulation box. A superball's interior is defined by the inequality |x| 2q + |y| 2q + |z| 2q ≤1, which provides a versatile family of convex particles (q ≤ 0.5) with cubelike and octahedronlike shapes as well as concave particles (q<0.5) with octahedronlike shapes. Here, we consider the convex case with a deformation parameter q between the sphere point (q=1) and the cube (q=∞). We find that the asphericity plays a significant role in the extent of cubatic ordering of both the liquid and crystal phases. Calculation of the first few virial coefficients shows that superballs that are visually similar to cubes can have low-density equations of state closer to spheres than to cubes. Dense liquids of superballs display cubatic orientational order that extends over several particle lengths only for large q. Along the ordered, high-density equation of state, superballs with 1<q<3 exhibit clear evidence of a phase transition from a crystal state to a state with reduced long-ranged orientational order upon the reduction of density. For q≤3, long-ranged orientational order persists until the melting transition. The width of the apparent coexistence region between the liquid and ordered, high-density phase decreases with q up to q=4.0. The structures of the high-density phases are examined using certain order parameters, distribution functions, and orientational correlation functions. We also find that a fixed simulation cell induces artificial phase transitions that are out of equilibrium. Current fabrication techniques allow for the synthesis of colloidal superballs and thus the phase behavior of such systems can be investigated experimentally.

Original languageEnglish (US)
Article number061105
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
StatePublished - Jun 2 2010

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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