Self-assembly, modularity, and physical complexity.

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus, to any given type of physical structure that can be divided into building blocks. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by quantifying the physical complexity of molecules and protein complexes. This measure is particularly well suited for the detection of symmetry and modularity in the underlying structure, and allows for a quantitative definition of structural modularity. Furthermore we use our approach to show that symmetric and modular structures are favored in biological self-assembly, for example in protein complexes. Lastly, we also introduce the notions of joint, mutual and conditional complexity, which provide a useful quantitative measure of the difference between physical structures.

Phase diagram of model anisotropic particles with octahedral symmetry.

The phase diagram for a system of model anisotropic particles with six attractive patches in an octahedral arrangement has been computed. This model for a relatively narrow value of the patch width where the lowest-energy configuration of the system is a simple cubic crystal. At this value of the patch width, there is no stable vapor-liquid phase separation, and there are three other crystalline phases in addition to the simple cubic crystal that is most stable at low pressure. First, at moderate pressures, it is more favorable to form a body-centered-cubic crystal, which can be viewed as two interpenetrating, and almost noninteracting, simple cubic lattices. Second, at high pressures and low temperatures, an orientationally ordered face-centered-cubic structure becomes favorable. Finally, at high temperatures a face-centered-cubic plastic crystal is the most stable solid phase.

Evidence of kinetic trapping in clusters of C60 molecules.

Molecular dynamics simulations of the growth of nanoclusters of C60 provide convincing evidence that experimental magic numbers, which are associated with structures based on Mackay icosahedra, are of kinetic origin. This finding resolves a long-standing contradiction between the experimental observations and the theoretically predicted most stable structures. Our results show that, even if a sticky intermolecular potential energetically disfavors icosahedral structures, the latter are frequently produced because the stickiness of the potential itself enhances kinetic trapping phenomena.