Titolo della tesi: Mix, Match, and Assemble: an inverse design approach to tailor materials
Inverse self-assembly seeks to design building units, through their shape and interactions, that spontaneously organise into a target structure. This is challenging due to kinetics pathways and the emergence of alternative, often unforeseen, structures. A promising route employs multiple building units with simple shapes and interaction potentials, achieving selectivity through specific, directional interactions. However, mixtures introduce a combinatorial challenge in exploring the space of candidate designs and add thermodynamic complexity: phase behaviour and self-assembly become more intricate, the latter often occurring via non-classical nucleation pathways. The SAT-assembly approach addresses the first challenge by mapping a patchy particle design problem into Boolean equations. Here, we focus on the second challenge: using theoretical analysis and numerical simulations, we study the thermodynamics of mixtures, identify optimal self-assembly conditions, and encode them directly into the design. Crystallisation often proceeds via a two-step nucleation process. While liquid-vapour metastability is known to enhance nucleation through density fluctuations, its coupling with composition fluctuations in mixtures remains poorly understood. We find that higher nucleation rates and larger assemblies emerge when the species concentration in the liquid phase matches that of the target structure. However, during phase separation, mixtures do not preserve the initial component ratio, making it difficult to identify starting conditions for optimal self-assembly. Our strategy is to design azeotropes and incorporate them into the nucleation pathway, since at the azeotrope vapour and liquid phases coexist at the same starting composition, mimicking one-component systems. We derive design rules linking bond connectivity and energy to locate the azeotrope at a desired concentration, integrating these as supplementary clauses into SAT-assembly. In this way, we extend inverse self-assembly into an inverse-thermodynamic framework, capable of engineering not only structural but also thermodynamic properties. Beyond design identification, SAT-assembly enumerates all possible ways to populate a lattice with particles of a given design, thereby listing all polymorphs, which interestingly share the same free energy. We use them to build a falsifiability test for classical nucleation theory (CNT), challenging the assumption that macroscopic properties alone predict nucleation outcomes. These polymorphs can also have distinct photonic properties, motivating us to explore how to design chiral crystals using the SAT-assembly framework. Ultimately, we outline a protocol from the design to the experimental realisation with DNA nanotechnology, towards creating colloidal photonic crystals. DNA is a perfect construction material due to its predictable and selective base-pairing, and the SAT-assembly naturally integrates the concept of complementarity to control interactions.