Self-Assembly in Diverse and Changing Energy Landscapes

Self-assembly is the process in which complex structures form without external intervention due to the inter-particle interactions of the assembling components. Assembly heavily depends on the strength of the effective inter-particle interactions, which are known to be sensitive to the environment in which assembly processes occur. While self-assembly has been well studied within a static, homogeneous environment, assembly very often occurs within dynamic and heterogeneous environments, where the environment varies in time or space. As environments, and therefore the effective inter-particle interactions, change, an assembling system follows non-equilibrium pathways on a varying energy landscape. Significant questions remain as to how these non-equilibrium pathways influence self-assembly.

In this thesis, we utilize Langevin dynamics simulations to probe how a coarse-grained, 2D viral capsid-like model self-assembles in highly variable energy landscapes. Oscillating the strength of the effective interactions between particles changes the assembly behavior. We find that oscillations at periods that are equivalent to the time-scales needed for particles to diffuse away from one another shift the window of orderly assembly to stronger attractions, in a manner dependent upon the oscillation amplitudes. An analysis of the various aggregate species that form and break up during these oscillations suggest that temporal attractions can aid in error correction. Spatially variant interactions were also investigated. This spatial inhomogeneity could also shift the window of self-assembly and control where structures assembled. When oscillations of the inter-particle attractions are fast compared to diffusional time-scales of the system, the oscillatory interactions and the system dynamics can be described via a time-averaged effective potential over an oscillation period. Certain interactions between particles, such as Coulombic interactions, will average in a way that enables us to obtain structures via fast oscillations that would not be possible through static interactions, while varying other interactions, such as the strength of a depletion force, can only result in structures obtainable at some average interaction strength. We predict how different materials will behave at the fast oscillation limit depending on the functional form of the inter-particle potential and suggest how time-averaged attractive interactions can be leveraged to control the assembly of novel, non-equilibrium structures.

Our studies here provide new fundamental insights to non-equilibrium self-assembly on temporally and spatially variant energy landscapes and provide guidelines for determining which inter-particle potentials will yield novel non-equilibrium assemblies at the fast oscillation limit.