Graphoepitaxy for directed self-assembly of particle monolayers
Many promising nanotechnologies, such as bit-patterned magnetic media, require highly ordered, defect-free monolayers of particles. Thus, there is a need for cost-efficient and robust manufacturing techniques to reliably fabricate such structures. Self-assembly of particles from suspensions has emerged as a promising nanomanufacturing method, and the tunability of nanoparticle interactions can lead to a diverse array of thermodynamically accessible structures. Nonetheless, particles deposited on surfaces in the absence of external bias often form highly defective structures. Recently, template-directed self-assembly techniques such as graphoepitaxy have been successfully applied to produce low-defectivity block copolymer morphologies with desired nanoscale features. The role of a template in directing the assembly of particulate systems, however, is still poorly understood. The use of larger scale patterned substrates to drive smaller scale assembly of particle monolayers can potentially expand the set of achievable lattices, and could be used in nanopatterning processes or in the manufacture of functional materials. In this dissertation, classical density functional theory (DFT), grand canonical Monte Carlo (GCMC) simulations, and cell theory are used to assess the suitability of graphoepitaxial assembly for particle monolayers and to predict the limits of pattern multiplication in three separate systems. The first two involve the assembly of hard sphere and hard rectangle particle monolayers on surfaces with closed square and closed rectangle template geometries, respectively. The third involves the assembly of spherical and rectangular particles on surfaces patterned with posts. Pattern multiplication limits for these systems (~10x) can be understood in terms of the balance between favorable enthaplically-driven structuring near the boundaries and unfavorable loss of configurational entropy upon forming the targeted structure.