Sequential phase transitions and transient structured fluctuations in two-dimensional systems with a high-density...

We report studies of (i) the isothermal density dependent sequences of phases in two-dimensional systems of particles with repulsive pair potentials devised by Truskett [J. Chem. Phys. 145, 054901 (2016)] and Torquato [Phys. Rev. E 88, 042309 (2013)] to support a high-density Kagome lattice phase and (ii) transient structured fluctuations close to a transition to a Kagome lattice. The commonalities in the sequences of phases in these systems and other 2D systems suggest the existence of a universal mechanism driving all to favor similar packing arrangements as the density is increased, but the simulations also show that the only such general rule proposed, namely, the Süto theorem, is not a necessary condition for the support of multiple distinct lattice structures by a particular pair potential. The transient fluctuations in the liquid close to the liquid-to-Kagome phase transition have Kagome symmetry, whereas deeper in the liquid phase, the fluctuations have hexagonal symmetry. When the transition is string-to-Kagome phase, the transient structured fluctuations in the string phase have both six-fold and other than six-fold symmetries. The path of the string-to-Kagome transition in the Truskett system involves intermediate honeycomb configurations that subsequently buckle to form a Kagome lattice. The path of the string-to-Kagome transition in the Torquato system suggests that the Kagome phase is formed by coiled strings merging together; increasing density generates a Kagome phase with imperfections such as 8-particle rings.