Inverse Design of Self-Folding 3D Shells.

Self-folding is an emerging paradigm for the inverse design of three-dimensional structures. While most efforts have concentrated on the shape of the net, our approach introduces a new design dimension-bond specificity between the edges. We transform this design process into a Boolean satisfiability problem to derive solutions for various target structures. This method significantly enhances the yield of the folding process. Furthermore, by linearly combining independent solutions, we achieve designs for shape-shifting nets wherein the dominant structure evolves with varying external conditions. This approach is demonstrated through coarse-grained simulations on two examples of triangular and square nets capable of folding into multiple target shapes.

Design strategies for the self-assembly of polyhedral shells.

The control over the self-assembly of complex structures is a long-standing challenge of material science, especially at the colloidal scale, as the desired assembly pathway is often kinetically derailed by the formation of amorphous aggregates. Here, we investigate in detail the problem of the self-assembly of the three Archimedean shells with five contact points per vertex, i.e., the icosahedron, the snub cube, and the snub dodecahedron. We use patchy particles with five interaction sites (or patches) as model for the building blocks and recast the assembly problem as a Boolean satisfiability problem (SAT) for the patch-patch interactions. This allows us to find effective designs for all targets and to selectively suppress unwanted structures. By tuning the geometrical arrangement and the specific interactions of the patches, we demonstrate that lowering the symmetry of the building blocks reduces the number of competing structures, which in turn can considerably increase the yield of the target structure. These results cement SAT-assembly as an invaluable tool to solve inverse design problems.

The Cell Adaptation Time Sets a Minimum Length Scale for Patterned Substrates.

The structure and dynamics of tissue cultures depend strongly on the physical and chemical properties of the underlying substrate. Inspired by previous advances in the context of inorganic materials, the use of patterned culture surfaces has been proposed as an effective way to induce space-dependent properties in cell tissues. However, cells move and diffuse, and the transduction of external stimuli to biological signals is not instantaneous. Here, we show that the fidelity of patterns to demix tissue cells depends on the relation between the diffusion (τD) and adaptation (τ) times. Numerical results for the self-propelled Voronoi model reveal that the fidelity decreases with τ/τD, a result that is reproduced by a continuum reaction-diffusion model. Based on recent experimental results for single cells, we derive a minimal length scale for the patterns in the substrate that depends on τ/τD and can be much larger than the cell size.

Random sequential adsorption on mobile patches.

An extension of the random sequential adsorption model has been proposed recently, motivated by the coverage of oil droplets by DNA-functionalized colloidal particles. Particles arrive to a flat substrate with a uniform flux F but they can only adsorb on patches. Patches diffuse on the substrate with a diffusion coefficient D if they are free and they remain immobile when attached to an adsorbed particle. The adsorption is considered irreversible and particles cannot adsorb on top of each other. Thus, the system reaches a jammed state, consisting of a monolayer where no more particles can adsorb. We performed Monte Carlo simulations to study the adsorption kinetics and jammed-state morphology on a one-dimensional lattice. We show that, while the time-dependence of the coverage depends on F and D, the jammed-state coverage depends solely on the ratio F/D. This result is grasped by a simple mean-field calculation. We also report two different regimes for the functional dependence of the jammed-state coverage on the size of the particles, for low and high density of patches.

Kinetic control of the coverage of oil droplets by DNA-functionalized colloids.

We report a study of reversible adsorption of DNA-coated colloids on complementary functionalized oil droplets. We show that it is possible to control the surface coverage of oil droplets using colloidal particles by exploiting the fact that, during slow adsorption, compositional arrest takes place well before structural arrest occurs. As a consequence, we can prepare colloid-coated oil droplets with a "frozen" degree of loading but with fully ergodic colloidal dynamics on the droplets. We illustrate the equilibrium nature of the adsorbed colloidal phase by exploring the quasi-two-dimensional phase behavior of the adsorbed colloids under the influence of depletion interactions and present simulations of a simple model that illustrates the nature of the compositional arrest and the structural ergodicity.