Basic concepts in self-assembly

In this brief contribution we review the basic elements of self-assembly, calling attention on the competition between the energetic gain of forming a bond and the loss of translational entropy. We show how to calculate theoretically the distribution of cluster sizes, in the hypothesis of an ideal gas of cluster, and discuss how the cluster partition functions can be calculated numerically. Building on the thermodynamic formalism, we discuss some analytically soluble simple models of self-assembly: equilibrium and cooperative polymerization and micelle formation. Finally, we discuss the importance of directional interactions for self-assembly, its role in the bonding entropy reduction, in the suppression of the driving force for phase-separation and in the possibility of forming aggregates that do not expose attractive surfaces, thus minimizing inter-cluster attractive interactions.