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If particles interact according to isotropic pair potentials that favormultiple length scales, in principle a large variety of different complexstructures can be achieved by self-assembly. We present, motivate, and discussa conjecture for the occurrence of non-trivial (i.e., non-triangular) orderingsbased on newly-introduced enthalpy-like pair potentials, the capability ofwhich we demonstrate for the specific example of colloid-polymer mixtures. Uponexamining the phase behavior of two-dimensional colloid-polymer mixtures, whichcan also be realized in experiments, we observe that non-trivial structuresonly occur in the vicinity of selected densities where triangular ordering issuppressed by the pair potential. Close to these densities, a large number ofdifferent phases self-assemble that correspond to tilings containingtriangular, rhombic, square, hexagonal, and pentagonal tiles, and includingsome of the Archimedean tilings. We obtain the ground-state energies byminimizing the corresponding lattice sums with respect to particle positions ina unit cell as well as cell geometry and verify the occurrence of selectedphases at finite temperatures by using Brownian Dynamics simulations. Allreported phases should be accessible in experiments and, in addition, our workprovides a manual on how to find the regions of non-trivial phases in parameterspace for complex pair interactions in general.

Self-assembly of complex structures in colloid-polymer mixtures