All nature... as it exists by itself, is founded on two things: there are bodies and there is void in which these bodies are placed and through which they move about.
Lucretius, Nature of Things
It is not diﬃcult to ﬁnd patterns in nature. In fact, quite the opposite is true. But, not all natural patterns are the result of a self-assembly process. In this chapter we examine four naturally occurring inorganic systems that are the result of some form of self-assembly. Our goal is to begin to understand the principles nature uses when she induces objects to self-assemble. We begin in Section 2.2 with bubble rafts. This very simple system is easily
observed in nature or in the laboratory and often used in the classroom to illustrate the bonding and packing of atoms that occurs in crystallization. We describe the bubble raft and take a ﬁrst look at the capillary forces driving the formation of the raft. We’ll revisit capillary forces in Part II when we examine engineered self-assembling systems. We also encounter the notion of packing. While understanding capillary forces allows us to understand why bubbles coalesce, understanding packing allows us to understand the global arrangement of bubbles in a bubble raft. This theme of packing as a minimal energy conﬁguration will reoccur throughout the text. Next, in Section 2.3 we turn to crystallization. With the bubble-raft model in hand, we describe the basics of crystallization and examine the order exhibited by crystals on both the atomic and macroscopic levels. We introduce the notion of diﬀusion limited aggregation (DLA). This serves as our ﬁrst computational model of a self-assembly process. In Section 2.4 we turn our attention to polymerization. Polymers are a class of materials of tremendous technological importance and in fact could be appropriately treated in this chapter, in Chapter 3 when we consider organic systems, or in Part II when we consider engineered systems. That is, there are naturally occurring inorganic polymers, naturally occurring organic polymers, and engineered polymers. We introduce polymers here in
order to be able to present a second model of a self-assembling system. We examine a simple reaction-kinetics type model based on the Law of Mass Action, solve this model, and consider the implications of this model for selfassembly. This type of model will arise again in Parts II and III of this text. Finally, in Section 2.5 we examine the remarkable self-assembling micelle. Micelles are structures formed in solution from amphiphilic molecules. These molecules consist of a water loving head group and an oil loving tail. When placed in water in the proper concentration, these molecules spontaneously assemble into spherical structures, tube-like structures, and eventually “living polymer” superstructures. When placed in oil, analogous reverse-micelles are formed. Both the process of micelle formation and the micelles themselves are the subject of much active research. Their similarity to biological membranes promises to make micelles of great use in applications as well as a great help in understanding the process of self-assembly.