  Spontaneous self-assembly in molecular systems is a fundamental route to both
biological and engineered soft matter. Simple micellisation, emulsion
formation, and polymer mixing principles are well understood. However, the
principles behind emergence of structures with competing length scales in soft
matter systems remain an open question. Examples include the
droplet-inside-droplet assembly in many biomacromolecular systems undergoing
liquid-liquid phase separation, analogous multiple emulsion formation in
oil-surfactant-water formulations, and polymer core-shell particles with
internal structure. We develop here a microscopic theoretical model based on
effective interactions between the constituents of a soft matter system to
explain self-organization both at single and multiple length scales. The model
identifies how spatial ordering at multiple length scales emerges due to
competing interactions between the system components, e.g. molecules of
different sizes and different chemical properties. As an example of single and
multiple-length-scale assembly, we map out a generic phase diagram for a
solution with two solute species differing in their mutual and solvent
interactions. By performing molecular simulations on a block-copolymer system,
we further demonstrate how the phase diagram can be connected to a molecular
system that has a transition from regular single-core polymer particles to
multi-core aggregates that exhibit multiple structural length scales. The
findings provide guidelines to understanding the length scales rising
spontaneously in biological self-assembly, but also open new venues to the
development and engineering of biomolecular and polymeric functional materials.
