Fundamentally, all sciences reason in the same way and aim at the same object. They all try to reach knowledge of the law of phenomena, so as to foresee, vary, or master phenomena.

Claude Bernard, Experimental Medicine

From the engineering perspective, the best understood and most highly developed engineered self-assembling systems are the static self-assembling systems. Static self-assembling systems are those that operate via a principle of energy minimization. A collection of particles slides down an energy gradient reaching a global or local minimum, ending in some final ordered configuration. The system then remains at this thermodynamic equilibrium and the end product is clear for all to see. The closest counterparts in the natural world of engineered static self-

assembling systems are crystals. In fact, many of the systems examined in this chapter are often discussed and sometimes dismissed as examples of artificial crystallization. While the criticism of these systems as examples of “mere crystallization” does have some merit, and while our ultimate goals in designing future systems are loftier than those achieved here, it is amazing to see just how much can be and has already been accomplished via a study of artificial crystallization. The relative wealth of examples of static self-assembling systems in the

literature means that in this chapter we must make difficult choices. There is simply not room to cover the entire spectrum of what has been accomplished. So, here, we will focus on four broad themes: systems that bond using capillary forces, template driven systems, systems that create structures by minimizing surface energy, and systems that assemble by folding. We begin in Section 6.2 with a discussion of systems that use capillary

forces to create particle-particle bonds. Of course, we’ve already encountered systems like these before, specifically the bubble raft of Chapter 2 and the Cheerios system of Chapter 5. The systems of this section operate in much

the same way that the bubble raft and the Cheerios system operate and we’ll find that the analysis of those systems allows us to understand the systems presented here quite easily. However, the examples of Section 6.2 go far beyond breakfast cereal. We’ll see how adding structure to floating particles, the “Cheerios,” allows for the formation of patterns much richer than a hexagonal bubble raft. We’ll also see how the idea of assembling via capillary forces can be extended to allow the creation of three dimensional functional devices. Finally, at the end of Section 6.2, we’ll explore two systems that push the use of capillary forces to their limits. The first allows for reconfiguration of assembled structures in response to changes in the environment. The second explores how capillary binding can be used to produce systems that compute. In Section 6.3 we examine systems that use templates. We focus on two

different systems. In this first, the use of the capillary bond is coupled with the use of a template to produce finite arrays of particles with a predefined shape. Here, the use of a template allows one to deal with the backward problem of self-assembly. The configuration of the final structure is specified by the shape of the template. The challenge is then reduced to designing particles that will fit into this template. In the second, a template is used as an intermediate step in a self-assembly process. Here, the template is used first to create, and then to align artificial amphiphiles. The amphiphiles selfassemble in a process mimicking that of micelles, but here, the alignment by the template turns out to be necessary in order for self-assembly to occur. In Section 6.4 we examine efforts to create structures such as microchan-

nels, waveguides, and microlenses, using nature’s tendency to minimize surface area. This brings the subject of self-assembly into contact with the mathematical theories of minimal surfaces and constant mean curvature surfaces. We’ll explore one of the simplest examples of a minimal surface, the catenoid, and show how its shape may be computed from an energy minimization principle. We then discuss experimental efforts in this area, discuss how they connect to the mathematical theory, and finally, we’ll encounter the phenomenon of symmetry breaking. In the final section of this chapter, Section 6.5, we examine self-assembled

systems that take inspiration from nature’s folding of proteins. We saw in Chapter 3, that nature utilized folding to create complex functional structures such as the ribosome. In Section 6.5 we’ll examine a simple system that uses folding and that has been both analyzed theoretically and realized experimentally. We’ll see how constraining the system and introducing the idea of linear sequential folding allows one to effectively solve the forward, backward, and yield problems of self-assembly.