Prediction and Design of Self-Assembling Systems with Isotropic Potentials

Abstract: With technological advancement comes a growing interest in complex structures on the nano-scale. We as consumers desire new materials with interesting structural properties and smaller electronic components at a low price. Self-assembly is an easily scalable alternative to conventional manufacturing. Instead of arranging the constituent particles by external influence like etching or by directed forces, we design the particles to arrange themselves into desired structures by energy minimization. While significant progress has been made on the experimental side of self-assembly, there is a dearth of theoretical results. This thesis presents key results, of theoretical nature, from recently published papers on self-assembly. In the first paper we derive a limited number of universal morphologies that can be expected to emerge in aggregating two dimensional particle systems. The other papers concerns self-assembling crystals: the second paper describes an analytical method to design interactions that causes a particle system to self-assemble into desired crystals and the third paper is an observation of symmetry-breaking in maximally symmetric systems. The common divisor for the papers is that they all apply Fourier analysis of particle structures, connecting isotropic potentials to an energy spectrum.