Self-assembly in soft matter with multiple length scales

TL;DR

This paper presents a microscopic theoretical model explaining how competing interactions in soft matter systems lead to the emergence of structures with multiple length scales, supported by phase diagram analysis and molecular simulations.

Contribution

It introduces a new model linking effective interactions to multi-scale self-assembly and demonstrates its application through phase diagram mapping and simulations of block-copolymer systems.

Findings

Emergence of multi-length-scale structures explained by competing interactions.

Phase diagram mapping connects molecular interactions to structural outcomes.

Simulations show transition from single-core to multi-core polymer aggregates.

Abstract

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.