Complex phases from spherically-symmetric repulsive pair-potentials

We report computer simulation studies and zero temperature analyses of two and three-dimensional systems of particles interacting via spherically symmetric, monotonically-repulsive pair-potentials. We have examined both bounded potentials and potentials with hard cores. We find that a very large class of potentials of this type display extraordinarily rich phase behavior. We observe a variety of complex modulated crystalline phases, commensurate and incommensurate phases solid phases (both achiral and chiral), structured isotropic liquids, micellar liquids and solids, and dodecagonal quasicrystals. These phases display a variety of phase transitions, including reentrant melting and freezing transitions, and commensurate-incommensurate phase transitions. The complexity arises because of multiple length scales due to the hard core (if present), the range of the potential, and spinodal length scales (Likos, et. al.$^1$) in the Fourier tranform of the pair potential. This rich polymorphism dramatically expands the range of possible models of colloidal self-assembly, and raises the interesting prospect of control of colloid self-assembly by rational design of pair potentials using grafted polymers or complex solvents. $^1$C.N. Likos, et. al, Phys Rev E 63, 031206 (1998).