  Superhydrophobic materials are often inspired by nature, whereas
metamaterials are engineered to have properties not usually found in naturally
occurring materials. In both cases, the key that unlocks their unique
properties is structure. Here, we show that a negative Poisson's ratio
(auxetic) mechanical metamaterial is capable of transforming into a unique type
of superhydrophobic material. When stretched its surface has the
counterintuitive property that it also expands in the orthogonal lateral
direction. We model the change in the solid surface fraction as strain is
applied and show it decreases as the space between solid elements of the
auxetic lattice expands. This results in a unique dependence of the
superhydrophobicity on strain. We construct experimental models illustrating
the relationship between different states of strain and superhydrophobicity as
the lattice structure transitions from an auxetic to a conventional (positive
Poisson's ratio) one. The principles we have discovered offer a new approach to
designing superhydrophobic materials for self-cleaning surfaces, droplet
transportation, droplet encapsulation and oil-water separation.
