Soft quasicrystals–Why are they stable?

Abstract

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 soft quasicrystal. Two groups have independently discovered such order in soft matter: Zeng et al. [Nature 428 (2004) 157] in a system of dendrimer liquid crystals; and Takano et al. [J. Polym. Sci. Polym. Phys. 43 (2005) 2427] in a system of ABC star-shaped polymers. 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. Here we provide a concise review of the emerging field of soft quasicrystals, suggesting that the existence of two natural length-scales, along with 3-body interactions, may constitute the underlying source of their stability. BackgroundThe discovery of quasicrystals by Shechtman more than two decades ago We know today that quasicrystals are more common than one had originally expected. Scores of binary and ternary metallic alloys are known to form quasicrystalline phases [22]-mostly with icosahedral or decagonal point-group symmetry-and more are being discovered all the time. Nevertheless, it is only in the last couple of years that quasicrystals have been discovered (independently) in two 1

Three-Dimensional Icosahedral Phase Field Quasicrystal

“…The ratio k 2 =k 1 must be close to certain special values; e.g., for dodecagonal QCs the value is 2 cosðπ=12Þ. Second, strong reinforcing (i.e., resonant) nonlinear interactions between these two characteristic density waves are required [17,19,20]. Earlier work on quasipatterns observed in Faraday wave experiments reveals similar requirements [19,[21][22][23].…”

“…Phase field crystal models have been employed to simulate the growth of 2D QCs [13] and the adsorption properties on a quasicrystalline substrate [14]. The ingredients for 2D quasipattern formation are, first, a propensity towards periodic density modulations with two characteristic wave numbers k 1 and k 2 [15][16][17][18]. The ratio k 2 =k 1 must be close to certain special values; e.g., for dodecagonal QCs the value is 2 cosðπ=12Þ.…”

Structural complexity in monodisperse systems of isotropic particles

“…It has been suggested [29] that their complex arrangements originates from the competition of two length scales, which appear due to soft repulsion and strong interpenetration. The micelles forming the dodecagonal quasicrystal in [15] have two natural length scales: the inner one corresponds to the backbone of the dendrons and the outer one to the end of the tethered chains.…”

Quasicrystals: diversity and complexity

“…Changhong Xiao [61] presented a newly discovered dodecagonal quasicrystal that self-assembles in mesoporous silica (Figure 2), adding yet another example to the growing number of mesoscale systems that form 12-fold quasicrystals. Theories of the growth and thermodynamic stability of these quasicrystals are only beginning to appear [62][63][64]. Tomonari Dotera added important insight to these theories by describing the dynamics of structural transitions in ABC-star polymeric quasicrystals [65].…”