Experimental tools of modern nanoscience evoke the possibility of designing and manipulating patterned materials with nearly atomic precision. Many of the processes that generate nanoscale structure, however, are advanced by complex microscopic dynamics that are still poorly understood and thus challenging to control. We work to elucidate the mechanisms underlying pattern formation both within and among nanoparticles, focusing on the fluctuations and boundary effects that make these materials distinct from their bulk counterparts. To do so we construct coarse-grained models that permit thorough statistical study, and explore their dynamical landscapes using theory and computation. One current project examines the exchange of cation constituents in semiconductor nanocrystals, which surprisingly preserve lattice structure in the midst of wholesale compositional change. Simple models suggest that exchange trajectories may be shaped by phase transitions at intermediate composition, which result generically from spatially heterogeneous elastic fluctuations. Another project explores the statistical mechanics of ligands that passivate the surfaces of many nanoparticles. For these ligand shells, typical laboratory conditions lie near phase coexistence between ordered and disordered states. Much as in the well-known hydrophobic effect, nanoparticles’ association can therefore be accompanied by phase transitions that effect powerful forces of assembly.
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