  We consider the self-assembly of composite structures from a group of
nanocomponents, each consisting of particles within an $N$-atom system.
Self-assembly pathways and rates for nanocomposites are derived via a
multiscale analysis of the classical Liouville equation. From a reduced
statistical framework, rigorous stochastic equations for population levels of
beginning, intermediate, and final aggregates are also derived. It is shown
that the definition of an assembly type is a self-consistency criterion that
must strike a balance between precision and the need for population levels to
be slowly varying relative to the time scale of atomic motion. The deductive
multiscale approach is complemented by a qualitative notion of multicomponent
association and the ensemble of exact atomic-level configurations consistent
with them. In processes such as viral self-assembly from proteins and RNA or
DNA, there are many possible intermediates, so that it is usually difficult to
predict the most efficient assembly pathway. However, in the current study,
rates of assembly of each possible intermediate can be predicted. This avoids
the need, as in a phenomenological approach, for recalibration with each new
application. The method accounts for the feedback across scales in space and
time that is fundamental to nanosystem self-assembly. The theory has
applications to bionanostructures, geomaterials, engineered composites, and
nanocapsule therapeutic delivery systems.
