Freezing of two-length-scale systems: complexity, universality and prediction

Two-length-scale pair potentials arise ubiquitously in condensed matter theory as effective interparticle interactions in molecular, metallic and soft matter systems. The existence of two different bond lengths generated by the shape of potential causes complex behavior in even one-component systems: polymorphism in solid and liquid states, water-like anomalies, the formation of quasicrystals and high stability against crystallization. Here we address general properties of freezing in one-component two-length-scale systems and argue that the formation of solid phases during cooling a liquid is essentially determined by the radial distribution function (RDF) of the liquid. We show that different two-length-scale systems having similar RDF freeze into the same solid phases. In most cases, the similarity between RDFs can be expressed by the proximity of two dimensionless effective parameters: the ratio between effective bond lengths, $\lambda$, and the fraction of short-bonded particles $\phi$. We validate this idea by studying the formation of different solid phases in different two-length-scale systems. The method proposed allows predicting effectively the formation of solid phases in both numerical simulations and self-assembling experiments in soft matter systems with tunable interactions.