Explaining complex metals with polymers

Analogies and metaphors are widespread in science. We use them to convey difficult concepts to colleagues or when popularizing science to communicate with the general public. Analogies also form an integral part of the scientific process itself (1). Some may even say that science is all about finding analogies between seemingly different phenomena, organizing them using unifying abstract concepts and common models, thereby generalizing these concepts and advancing their understanding. In PNAS, Lee et al. (2) draw a surprising analogy between the principles that govern the formation of ordered phases in soft-matter systems consisting of micelle-forming block copolymers (3), and those underlying the formation of hard solid-state metallic crystals. Lee et al. (2) study a system of nearly identical diblock copolymers. These are molecules that consist of a pair of different polymer chains of unequal lengths attached at a single point, forming one long double-block chain. Lee et al. (2) observe that under conditions that favor the segregation of the two blocks, groups of about 200 of these copolymer chains self-assemble into spherical micelles. Each micelle resembles a little ball with a core consisting mostly of one of the blocks, and a corona consisting of the other block. When an initially disordered liquid state, made up of these fuzzy little balls, is cooled down, one observes a phase transition into an ordered state with a simple body-centered cubic (bcc) structure. Upon further cooling, the system undergoes a secondary phase transition into a more complex structure with tetragonal symmetry (that of a square prism), called a Frank–Kasper σ phase (Fig. 1). It is the latter transition from a cubic phase to a lower-symmetry tetragonal phase—which is presumed to be the ground-state configuration that persists down to the lowest temperatures—that is the focus of Lee et al.’s (2) analogy with metals. (Left …