Complexity, disorder, and functionality of nanoscale materials

The world of biology created a wealth of complex materials intertwining order, disorder, and hierarchy. They are produced with minimal energy expenditures and display combinations of properties that surpass materials aimed to be perfectly ordered crystals or perfectly disordered glasses. De novo engineering of biomimetic materials with “impossible” combination of properties necessary for multiple technologies becomes possible considering complexity as a design parameter but this methodology lacks foundational principles. This article delineates the concept of complexity in the context of materials science. It examines the pathway to quantitative complexity–functionality relations and explores pragmatic approaches to scalable complex materials guided by discrete mathematics of nanoassemblies from imperfect components.