  The ability to design and synthesize ever more complicated colloidal
particles opens the possibility of self-assembling a zoo of complex structures,
including those with one or more self-limited length scales. An undesirable
feature of systems with self-limited length scales is that thermal fluctuations
can lead to the assembly of nearby, off-target states. We investigate
strategies for limiting off-target assembly by using multiple types of
subunits. Using simulations and energetics calculations, we explore this
concept by considering the assembly of tubules built from triangular subunits
that bind edge to edge. While in principle, a single type of triangle can
assemble into tubules with a monodisperse width distribution, in practice, the
finite bending rigidity of the binding sites leads to the formation of
off-target structures. To increase the assembly specificity, we introduce
tiling rules for assembling tubules from multiple species of triangles. We show
that the selectivity of the target structure can be dramatically improved by
using multiple species of subunits, and provide a prescription for choosing the
minimum number of subunit species required for near-perfect yield. Our approach
of increasing the system's complexity to reduce the accessibility of
neighboring structures should be generalizable to other systems beyond the
self-assembly of tubules.
