Steering self-organisation through confinement

Abstract

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales in very different systems and scientific disciplines, from physics, materials science and robotics to biology, geophysics and astronomy. Recent research has highlighted how self-organisation can be both mediated and controlled by confinement. Confinement is an action over a system that limits its units' translational and rotational degrees of freedom, thus also influencing the system's phase space probability density; it can function as either a catalyst or inhibitor of self-organisation. Confinement can then become a means to actively steer the emergence or suppression of collective phenomena in space and time. Here, to provide a common framework and perspective for future research, we examine the role of confinement in the self-organisation of soft-matter systems and identify overarching scientific challenges that need to be addressed to harness its full scientific and technological potential in soft matter and related fields. By drawing analogies with other disciplines, this framework will accelerate a common deeper understanding of self-organisation and trigger the development of innovative strategies to steer it using confinement, with impact on, e.g., the design of smarter materials, tissue engineering for biomedicine and in guiding active matter.

Fig. 1. Emergence of structure from confined self-organising units. (a) Self-organisation is the emergence of large-scale structures and patterns from individual units. Confinement can act as a catalyst (as in the diagram) or inhibitor for a self-organising system. The arrows represent an external force field acting on the units. (b) Steering self-organisation through confinement requires encoding feedback loops in the process so that units and/or confining elements can adapt and evolve with the self-organising system. In the schematics, this is visualised by a change in both the confinement (solid lines and corresponding force field) and the units (here symbolically represented by a change in colour). As a consequence the emerging self-organisation patterns differ.

Fig. 2. Self-organisation at various length scales under different types of confinement. The diagram contains selected examples of self-organisation under different types of confinement occurring at different spatial (and time) scales in both natural and man-made systems. The horizontal axis represents the length scale of the self-organising units, from molecular up to astronomical scales. The vertical axis represents the type of confinement ordered based on its complexity and ability to be readily parameterised. At the bottom of the diagram, simpler and better understood forms of confinement are highlighted with blue shading. These include external boundaries and fields, e.g., small robots near walls or the gravitational field confining Earth's atmosphere for turbulent flows. At the top of the diagram, a different type of confinement is purposely separated from the other examples, as less understood but potentially more promising to steer self-organisation. These forms of confinement include feedback loops between the self-organising units and the confining features (e.g. in the quorum sensing that induces biofilm formation in microbes, in the information exchange among ants to generate structures such as bridges, or in the self-induced gravitational attraction that leads to harmonic orbit resonances).

Fig. 3. Example of hierarchical self-organisation under confinement in biology. Hierarchical organisation from molecules to tissue via the formation of macromolecules, cellular organelles and cells. At each stage, self-organised structures become units for further self-organisation subject to a different type of confinement, here illustrated at the molecular, cellular and tissue scale. Sources of confinement include, e.g., physical boundaries, mechanical forces (F) and chemical gradients. The emergence of complex functionality in biological systems relies on the existence of such hierarchical structures. Created with BioRender.com.