Title: Self-assembly of Nanoparticles on Fluid and Elastic Membranes
Description: This dissertation presents studies on self-assembly of nanoparticles adsorbed onto fluid and elastic membranes. It focuses on particles that are at least one order of magnitude larger than the surface thickness, in which case all chemical details of the surface can be ignored in favor of a coarse-grained representation, and the collective behavior of many particles can be analyzed. We use Monte Carlo and molecular dynamics simulations to study the phase behavior of these systems, and its dependence on the mechanical and geometrical properties of the surface, the strength of the particle-surface interaction and the size and the concentration of the nanoparticles. We present scaling laws and accurate free-enegy calculations to understand the occurrence of the phases of interest, and discuss the implications of our results. Chapters 3 and 4 deal with fluid membranes. We show how fluid membranes can mediate linear aggregation of spherical nanoparticles binding to them for a wide range of biologically relevant bending rigidities.

This result is in net contrast with the isotropic aggregation of nanoparticles on fluid interfaces or the expected clustering of isotropic insertions in biological membranes. We find that the key to understanding the stability of linear aggregates resides in the interplay between bending and binding energies of the nanoparticles. Furthermore, we demonstrate how linear aggregation can lead to membrane tubulation and determine how tube formation compares with the competing budding process. The development of tubular structures requires less adhesion energy than budding, pointing to a potentially unexplored route of viral infection and nanoparticle internalization in cells. In Chapters 5 - 8, we shift focus to elastic membranes and study self-assembly of nanoparticles mediated by elastic surfaces of different geometries, namely planar, cylindrical and spherical. Again, a variety of linear aggregates are obtained, but their spatial organization can be controlled by changing the stretching rigidity of the elastic membrane, the strength of the particle adhesion, the curvature of the surface, as well as by introducing surface defects.

Furthermore, we show how a fully flexible filament binding to a cylindrical elastic membrane may acquire a macroscopic persistence length and a helical conformation. We find that the filaments helical pitch is completely determined by the mechanical properties of the surface, and can be easiliy tuned. Moreover, we study the collapse of unstretchable (thin) hollow nanotube due to the collective behavior of nanoparticles assembling on its surface, resulting in an ordered nanoparticle engulfment inside the collapsed structure. Our hope is that the results presented in this Dissertation will stimulate further experimental studies of the mechanical properties of fluid and cross-linked membranes, in particular the long range correlations arising due to the particle binding.