# softmatter:Cubically Ordered Spherical Micelles

Block Copolymers (BCPs) and Surfactants are known to phase separate into complex morphologies including **Cubically Ordered Spherical Micelles**, Hexagonally Packed Cylindrical Micelles, Double Gyroid, Perforated Lamella, and Lamella. Recent simulation results have shown that Tethered building blocks also can exhibit similar phases as a result of microphase separation.

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## Block Copolymers

Melts of assymmetric BCPs, with block fractions of ~0.1 or ~0.9, have been shown to form spherical micelles that order into Body Centered Cubic (BCC) arrangements, as well as close-packed spherical micelles as assymmetry is increased [1]. Here block fraction is defined as (*length of the A block*)/(*total length of polymer*).

## Surfactants

Simulations of symmetric Surfactants in selective solvent have also yielded BCC ordered spherical micelles for volume fractions of approximately 0.1 - 0.2 [2].

## Tethered Nanospheres

Tether-aggregating tethered nanospheres (TNS) were found to exhibit Hexagonally Close Packed (HCP) spherical micelles for volume fractions ~0.2-0.3, where the excluded volume ratio of head to tail F_{v} = 1.95 [2].

## References

- [1] Matsen and Bates, Macromolecules 29:1091, 1996
- [2] Iacovella CR, Horsch MA, Zhang Z, Glotzer SC, Phase diagrams of self-assembled mono-tethered nanospheres from molecular simulation and comparison to surfactants, LANGMUIR 21 (21): 9488-9494 OCT 11 2005