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Active Self-Assembly

Periodic Report Summary 1 - ACTSA (Active Self-Assembly)

Self-assembly is the process in whereby components spontaneously come together to form ordered structures. Biomolecules such as proteins and DNA naturally assemble and disassemble depending on what functions they want to perform. In this project we investigate self-assembly in various environments (different interactions) through theory, computer simulations and collaboration with experimentalists. Specifically, the current research is split into three main themes all interconnected: dense packings and self-assembly of continuously deformed polyhedra, assembly of actively rotated shapes and swimmers, assembly of concave shapes.

1. how densely-packed structures change as a function of shape of the constituent particles.
2. the relationship between densely-packed structures in the limit of infinite pressure and self-assembled structures at finite pressure.
3. to relate local packing and motifs to global structure through the study of concave shapes
4. to design active building blocks and study far-from equilibrium dynamic assemblies.
5. to study active swimmers in fluids.

- A description of the work performed since the beginning of the project
The objectives all fall under the same umbrella of active self-assembly. In (1) we vary the shape continuously through truncation and study changes in the packing density and structure. Experimentally, this may be useful for switching between structures with different properties, by externally deforming the shape. Studying whether there is a clear correlation between the densest global packing at infinite pressure and the self-assembly at finite pressure, in (2), we aim to give a conclusive answer. In (3) we study the role of entropy in self-assembly of hard shapes and how it gives rise to emergent (effective) directional forces. In (4) we model actively-rotated shapes and find emergent forces that result from the constant input of energy into the system. In (5) we continue work on a novel propulsion mechanism of a model swimmer in a Newtonian fluid at moderate Reynolds numbers, through a collaboration with experimentalists.

- A description of the main results achieved so far

1. Complexity in surfaces of densest packings for families of polyhedra
Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, granular and colloidal matter, and biology. In all these fields, particle shape is important for structure and properties, especially upon crowding. Here, we explore packing as a function of shape. By combining simulations and analytic calculations, we study three 2-parameter families of hard polyhedra and report an extensive and systematic analysis of the densest packings of more than 55,000 convex shapes. The three families have the symmetries of triangle groups (icosahedral, octahedral, tetrahedral) and interpolate between various symmetric solids (Platonic, Archimedean, Catalan). We find that optimal (maximum) packing density surfaces that reveal unexpected richness and complexity, containing as many as 130 different structures within a single family. Our results demonstrate the utility of thinking of shape not as a static property of an object in the context of packings, but rather as but one point in a higher dimensional shape space whose neighbors in that space may have identical or markedly different packings. Finally, we present and interpret our packing results in a consistent and generally applicable way by proposing a method to distinguish regions of packings and classify types of transitions between them.

Unified Theoretical Framework for Shape Entropy in Colloids
Entropy has long been known to lead to the ordering of colloidal systems ranging from dense suspensions of hard particles to dilute suspensions of spheres in the presence of smaller polymeric depletants. Entropic ordering of hard anisotropic particles into complex structures has been demonstrated in simulations and experiments. It has been proposed that nonspherical particles order due to the emergence of directional entropic forces that depend upon particle shape, yet these forces have not been rigorously quantified, hindering their use in the understanding of entropic self assembly. We present a framework for treating entropic forces in systems of colloidal shapes. Through the introduction of an effective potential of mean force and torque (PMFT) we demonstrate quantitatively that the microscopic origin of entropic ordering of anisotropic shapes is the emergence of DEFs tending to align neighboring particles. We rigorously define and compute these forces and show they are at least several kT at the onset of ordering, placing DEFs. We provide a means through which the role of shape can be quantified and determined in experimental systems in which other forces also contribute to assembly.

Emergent collective phenomena in a mixture of hard shapes through active rotation
We investigate collective phenomena with rotationally driven spinners of concave shape. Each spinner experiences a constant internal torque in either a clockwise or counterclockwise direction. Although the spinners are modeled as hard, otherwise non-interacting rigid bodies, we find that their active motion induces an effective interaction that favors rotation in the same direction. With increasing density and activity, phase separation occurs via spinodal decomposition, as well as self-organization into rotating crystals. We observe the emergence of cooperative, super-diffusive motion along interfaces, which can transport inactive test particles. Our results demonstrate novel phase behavior of actively rotated particles that is not possible with linear propulsion or in non-driven, equilibrium systems of identical hard particles.

The expected final results and their potential impact and use
We are continuing work on the above projects. Projects that are currently close to publication include the study of swimmers at finite Reynolds numbers and relating densest packings to self-assembly for various shapes.