Soft quasicrystals - Why are they stable?

In the last two years we have witnessed the exciting experimental discovery of soft matter with nontrivial quasiperiodic long-range order---a new form of matter termed a \emph{soft quasicrystal}. Two groups have independently discovered such order in soft matter: The first in a system of dendrimer liquid crystals [1]; and the second in a system of ABC star-shaped polymers [2]. These newly discovered soft quasicrystals not only provide exciting platforms for the fundamental study of both quasicrystals and of soft matter, but also hold the promise for new applications based on self-assembled nanomaterials with unique physical properties that take advantage of the quasiperiodicity, such as complete and isotropic photonic band-gap materials [3]. Here we provide a concise review of the emerging field of soft quasicrystals [4], and invoke an old theory [5] suggesting that the existence of two natural length-scales, along with 3-body interactions, may constitute the underlying source of their stability.\par\noindent [1] Zeng \emph{et al.}, Nature {\bfseries 428} (2004) 157.\par\noindent [2] Takano \emph{et al.}, J.\ Polym.\ Sci.\ Polym.\ Phys.{\bfseries 43} (2005) 2427.\par\noindent [3] Zoorob \emph{et al.}, Nature {\bfseries 404} (2000) 740.\par\noindent [4] Lifshitz \& Diamant, preprint (cond-mat/0611115).\par\noindent [5] Lifshitz \& Petrich, Phys.\ Rev.\ Lett.\ {\bfseries 79} (1997) 1261.