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

Self-assembly in soft matter with multiple length scales