Definitions

# Self-assembly

[uh-sem-blee]

Self-assembly is a term used to describe processes in which a disordered system of pre-existing components forms an organized structure or pattern as a consequence of specific, local interactions among the components themselves, without external direction.

Self-assembly can be classified as either static or dynamic. In static self-assembly, the ordered state forms as a system approaches equilibrium, reducing its free energy, whereas inpatterns of pre-existing components organized by specific, local interactions, and are not commonly described as "self-assembled" by scientists in the associated disciplines. These structures are better described as "self-organized".

## Self-assembly in chemistry and materials science

Self-assembly (SA) in the classic sense can be defined as the spontaneous and reversible organization of molecular units into ordered structures by non-covalent interactions. The first property of a self-assembled system that this definition suggests is the spontaneity of the self-assembly process: the interactions responsible for the formation of the self-assembled system act on a strictly local level—in other words, the nanostructure builds itself. At this point, one may argue that any chemical reaction driving atoms and molecules to assemble into larger structures, such as precipitation, could fall into the category of SA. However, there are at least three distinctive features that make SA a distinct concept.

First, the self-assembled structure must have a higher order than the isolated components, be it a shape or a particular task that the self-assembled entity may perform. This is generally not true in chemical reactions, where an ordered state may proceed towards a disordered state depending on thermodynamic parameters.

The second important aspect of SA is the key role of weak interactions (e.g. Van der Waals, capillary, $pi-pi$, hydrogen bonds) with respect to more "traditional" covalent, ionic or metallic bonds. Although typically less energetic of a factor 10, these weak interactions play an important role in materials synthesis. It can be instructive to note how weak interactions hold a prominent place in materials, but especially in biological systems, although they are often considered marginally with respect to "strong" (i.e. covalent, etc.) interactions. For instance, they determine the physical properties of liquids, the solubility of solids, the organization of molecules in biological membranes.

The third distinctive feature of SA is that the building blocks are not only atoms and molecules, but span a wide range of nano- and mesoscopic structures, with different chemical compositions, shapes and functionalities. These nanoscale building blocks (NBBs) can in turn be synthesised through conventional chemical routes or by other SA strategies.

Important examples of SA in materials science include the formation of molecular crystals, colloids, lipid bilayers, phase-separated polymers, and self-assembled monolayers. The folding of polypeptide chains into proteins and the folding of nucleic acids into their functional forms are examples of self-assembled biological structures.

Therefore, we can say that SA extends the scope of chemistry aiming at synthesising products with order and functionality properties, extending chemical bonds to weak interactions and encompassing the self-assembly of NBBs on all length scales. In covalent synthesis and polymerisation, the scientist links atoms together in any desired conformation, which does not necessarily have to be the energetically most favoured position; self-assembling molecules, on the other hand, adopt a structure at the thermodynamic minimum, finding the best combination of interactions between subunits but not forming covalent bonds between them. In self-assembling structures, the scientist must predict this minimum, not merely place the atoms in the location desired.

Another characteristic that is common to nearly all self-assembled systems is their thermodynamic stability: in order for SA to take place without the intervention of external forces, the process must lead to a lower Gibbs free energy, thus self-assembled structures are thermodynamically more stable than the single, unassembled components. A direct consequence is the general tendency of self-assembled structures to be relatively free of defects. An example is the formation of two-dimensional superlattices composed of an orderly arrangement of micrometre-sized polymethylmethacrylate (PMMA) spheres, starting from a solution containing the microspheres, in which the solvent is allowed to evaporate slowly in suitable conditions. In this case the driving force is capillary interaction, which originates from the deformation of the surface of a liquid caused by the presence of floating or submerged particles.

These two properties—weak interactions and thermodynamic stability—can be recalled in order to rationalise another property which is often found in self-assembled systems: the sensitivity to perturbations exerted by the external environment: small fluctuations that alter the thermodynamic variables might lead to marked changes in the structure and even compromise it, either during or after SA. The weak nature of interactions is responsible for the flexibility of the architecture and allows for rearrangements of the structure in the direction determined by thermodynamics. If fluctuations bring the thermodynamic variables back to the starting condition, the structure is likely to go back to its initial configuration. This leads us to identify one more property of SA, which is generally not observed in materials synthesised by other techniques: reversibility.

From what we have written so far, it should be evident that SA is a process which is easily influenced by external parameters: if this can make synthesis more problematic due to the many free parameters that require control, on the other hand it has the exciting advantage that a large variety of shapes and functions on many length scales can be obtained.

Generally speaking, the fundamental condition in order to have NBBs to self-assemble into an ordered structure is the simultaneous presence of long-range repulsive and short-range attractive forces. Figure [fig_sa_scheme] exemplifies SA occurring from building blocks made up of two different units (A and B) which are covalently linked (short-range attraction) and repel each other by long-range interactions (e.g. because A is hydrophobic and B is hydrophilic). Since the energy of the system will unfavour configurations where A is close to B, and still no macrophase separation is possible due to A--B covalent bonds, the system will adopt a configuration where the contact area between A and B is minimised. This results in a periodic ordered structure (in figure [fig_sa_scheme] this is exemplified by a lamellar structure). For a list of repulsive-attractive competing forces which can give rise to SA phenomena, see .

By choosing precursors with suitable physicochemical properties, it is possible to exert a fine control on the formation processes in order to obtain complex architectures. Clearly, the most important tool when it comes to designing a synthesis strategy for a material, is the knowledge of the chemistry of the building units.