Physics

Nanotechnology

Crystallization

Mathematics

Entropy (arrow of time)

Statistical physics

Valency

Colloidal crystal

Philosophy

Physical chemistry

Chemical physics

Chemistry

Materials science

Geometry

Molecule

Theoretical physics

Linguistics

Polyhedron

Colloid

Quantum mechanics

Thermodynamics

Statistical mechanics

Proceedings of the National Academy of Sciences

Significance Computer simulations of hard, polyhedrally shaped particles predict a great diversity of complex colloidal crystal structures via self-assembly. The structural similarities between colloidal crystals and atomic crystals suggest that they should be describable within analogous, although different, conceptual frameworks. Like the chemical bonds that hold atoms together in crystals, the statistical, emergent forces that hold together hard colloidal particles should be describable using the language of bonding. Whereas atomic crystals can be predicted a priori by solving Schrödinger’s equation, we present a theory of entropic bonding that permits prediction of colloidal crystals by solving a different eigenvalue equation, facilitated by the use of mathematically constructed shape orbitals analogous to atomic orbitals.

A theory of entropic bonding