Molecular simulations of the self-assembly of sno-cone-shaped patchy colloids with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self assemble into clusters and that clusters comprised of particular numbers of cones (e.g. 4 - 17, 20, 27, 32, 42) have a unique and precisely packed structure that is robust over a range of cone angles [1,2]. These precise clusters form a sequence of structures at specific cluster sizes – a “precise packing sequence” -- that for small sizes is identical to that observed in evaporation-driven assembly of colloidal spheres [3-6]. We discuss the effect of cone angle on the stability and metastability of clusters [2].

We further show that this "magic number" sequence is reproduced and extended in simulations of two simple models of spheres self-assembling from random initial conditions subject to convexity constraints, including an initial spherical convexity constraint for moderate- and large-sized clusters, demonstrating that the clusters are best described as minimal second moment clusters on a convex hull. This sequence contains six of the most common virus capsid structures obtained in vivo including large chiral clusters, and a cluster that may correspond to several non-icosahedral, spherical virus capsid structures obtained in vivo. Our findings suggest this precise packing sequence results from free energy minimization subject to convexity constraints and is applicable to a broad range of assembly processes.

Finally, we discuss a phenomenological model in which the simulated packing of hard, attractive spheres on a prolate spheroid surface with convexity constraints produces structures identical to those of prolate virus capsid structures [7]. Our simulation approach combines the traditional Monte Carlo method with a modified method of random sampling on an ellipsoidal surface and a convex hull searching algorithm. Using this approach we identify the minimum physical requirements for non-icosahedral, elongated virus capsids, such as two aberrant flock house virus particles and the prolate prohead of bacteriophage phi-29. Our predicted structures may potentially be experimentally realized by evaporation-driven assembly of colloidal spheres under shear.

[1] T. Chen, Z.L. Zhang and S.C. Glotzer, “A Precise Packing Sequence of Self-Assembled Convex Structures,” Proc. Natl. Acad. Sci., 104(3) 717-722 (2007).

[2] T. Chen, Z.L. Zhang and S.C. Glotzer, “Simulation studies of self-assembly of cone-shaped particles,” Langmuir, in press.

[3] Manoharan, V. N., Elsesser, M. T. & Pine, D. J. (2003) Science 301, 483-487.

[4] Yi, G. R., Manoharan, V. N., Michel, E., Elsesser, M. T., Yang, S. M. & Pine, D. J. (2004) Adv. Mater. 16, 1204-1208.

[5] Cho, Y. S., Yi, G. R., Lim, J. M., Kim, S. H., Manoharan, V. N., Pine, D. J. & Yang, S. M. (2005) J. Am. Chem. Soc. 127, 15968-15975.

[6] Cho, Y. S., Yi, G. R., Kim, S. H., Pine, D. J. & Yang, S. M. (2005) Chem. Mater. 17, 5006-5013.

[7] T. Chen and S.C. Glotzer, “Simulation studies of a phenomenological model of prolate virus assembly,” Phys. Rev. E, in press.