  Self-assembly is a fundamental concept in biology and of significant interest
to nanotechnology. Significant progress has been made in characterizing and
controlling the properties of the resulting structures, both experimentally and
theoretically. However, much less is known about kinetic constraints and
determinants of dynamical properties like time efficiency, although these
constraints can become severe limiting factors of self-assembly processes. Here
we investigate how the time efficiency and other dynamical properties of
reversible self-assembly depend on the morphology (shape) of the building
blocks for systems in which the binding energy between the constituents is
large. As paradigmatic examples, we stochastically simulate the self-assembly
of constituents with triangular, square, and hexagonal morphology into
two-dimensional structures of a specified size. We find that the constituents'
morphology critically determines the assembly time and how it scales with the
size of the target structure. Our analysis reveals three key structural
parameters defined by the morphology: The nucleation size and attachment order,
which describe the effective order of the chemical reactions by which clusters
nucleate and grow, respectively, and the growth exponent, which determines how
the growth rate of an emerging structure scales with its size. Using this
characterization, we formulate an effective theory of the self-assembly
kinetics, which we show exhibits an inherent scale invariance. This allows us
to identify general scaling laws that describe the minimal assembly time as a
function of the size of the target structure. We show how these insights on the
kinetics of self-assembly processes can be used to design assembly schemes that
could significantly increase the time efficiency and robustness of artificial
self-assembly processes.
