Hagan Group

Anisotropic and Chiral Self-Assembly

The role of chirality and particle shape in self-assembly

As nanotechnology advances, it is becoming possible to design new and more complicated structures from a growing repertoire of building blocks. However, as the ensemble of building blocks becomes increasingly diverse and the desired products become more complex, understanding and directing the assembly kinetics of these components, and thus controlling what product they ultimately form, is correspondingly more complicated. While the viral capsid proteins that we study have evolved specific subunit shapes and directional interactions over millions of years to achieve particular structures, are there general classes of interactions or geometrical constraints which can be used to control assembly? We use computation in collaboration with experimental groups to examine the effect of chirality and particle anisotropy on assembly pathways of filamentous molecules or rod-like colloids, with a particular focus designing assembly reactions that self-terminate in one or more dimensions. Examples of these projects include:

Molecular chirality constrains the local packing geometries of assembling subunits and thus can frustrate long-range order. We demonstrated computationally that chiral interactions which drive subunits to assemble into filamentous bundles can result in regular self-limited bundles for moderate interaction strengths.  With stronger interactions, however, the frustration is relieved by defects that lead to irregular bundles or branched networks. [1]

Fig. 1: (a) Snapshots of regular chiral bundles. Free energy calculations and dynamics demonstrate that the optimal diameter decreases with increasing chirality. (b) Branched bundles form with strong interactions. Figure from [1].

Colloidal membranes are two dimensional (2D) surfaces composed of a one rod-length thick monolayer of aligned nanorods. Z. Dogic (Brandeis) recently discovered that suspensions of homogeneous rodlike viruses and non-adsorbing polymer form equilibrium colloidal membranes under some conditions. To understand the forces that drive assembly in two dimensions while limiting it in the third, we developed computer simulations and a density functional theory that describe the phase behavior of colloidal membranes formed by achiral hard rods. The calculations demonstrate that collective protrusion fluctuations stabilize colloidal membranes against stacking, but they predict that colloidal membranes are only stable above a threshold rod aspect ratio and below a threshold polymer radius of gyration. The latter prediction was qualitatively confirmed by new experiments in the Dogic lab, revealing geometrical requirements for self-limited assembly. [2-4]


Fig. 2: Simulations explain the phase behavior of achiral hard rods and depleting polymer [2]. A simulated colloidal membrane is shown; rods at the edge twist to minimize surface energy, as seen in experiments.


  1. Yang, Y., R.B. Meyer, and M.F. Hagan, Self-Limited Self-Assembly of Chiral Filaments. Physical Review Letters, 2010. 104(25): p. 258102.
  2. Gibaud, T., et al., Reconfigurable self-assembly through chiral control of interfacial tension. Nature, 2012. advance online publication.
  3. Yang, Y., et al., Self-assembly of 2D membranes from mixtures of hard rods and depleting polymers. Soft Matter, 2012. 8: p. 707-714.
  4. Yang, Y. and M.F. Hagan, Theoretical calculation of the phase behavior of colloidal memb Physical Review E, 2011. 84(5): p. E 051402.