  Functionalization of nanoparticles or colloids is increasingly being used to
develop customizable "atoms". Functionalization by attaching single strands of
DNA allows for direct control of the binding between nanoparticles, since
hybridization of double strands will only occur if the base sequences of single
strands are complementary. Nanoparticles and colloids functionalized by four
single strands of DNA can be thought of as designed analogs to tetrahedral
network forming atoms and molecules, with a difference that the attached DNA
strands allow for control of the length scale of bonding relative to the core
size. We explore the behavior of an experimentally realized model for a
nanoparticles functionalized by four single strands of DNA (a tetramer), and
show that this single-component model exhibits a rich phase diagram with at
least three critical points and four thermodynamically distinct amorphous
phases. We demonstrate that the additional critical points are part of the
Ising universality class, like the ordinary liquid-gas critical point. The
dense phases consist of a hierarchy of interpenetrating networks, reminiscent
of a woven cloth. Thus bonding specificity of DNA provides an effective route
to generate new nano-networked materials with polyamorphic behavior. The
concept of network interpenetration helps to explain the generation of multiple
liquid phases in single-component systems, suggested to occur in some atomic
and molecular network forming fluids, including water and silica.
