Mesoscale simulation approach for the dynamics and assembly of deformable objects

Abstract

The dynamics and self-assembly of small, deformable objects are investigated in this study.These objects are represented as deformable spheres in contact, with the geometry of the spheres representing the interactions of repulsive soft particles in nature, using a method inspired by the Kelvin packing problem (minimizing contact area of equal-sized polyhedra). A mesoscale approach known as ‘vertex models’ is used to track the geometries of spheres and polyhedra, where the number and positions of the vertices indicate the geometry of the object. Monte-Carlo steps are used to ’move’ the deformable objects. The behavioral difference between droplets in dilute and concentrated suspensions emphasizes the context in which this model is used. Surfactant micelles and emulsion droplets, in particular, frequently take spherical shapes in dilute suspensions. However, at high enough concentrations, contact between micelles or droplets results in non-spherical shapes. The dynamics and assembly of the suspension are more dependent on the interfaces between objects than on the bulk objects themselves at this limit. Self-assembled particle domains, such as block copolymers, and electron clouds of atoms are other examples of deformable objects. In this project, the term ”balloon model” refers to the novel application of vertex models to the dynamics and assembly of soft, deformable objects. The balloon model is based on the hypothesis that the periodic, aperiodic, and disordered structures observed in a material are primarily determined by the surface area of the material’s deformable particles. This contradicts the current widely held belief that these structures have more to do with the particle volume fraction. As a result, this research project has two objectives in order to investigate this hypothesis. The first goal is to use the balloon model to investigate the equilibrium structures of various simulated materials. The effects of thermal fluctuation and particle size variability on the equilibrium structure will be quantified here. The second goal of the research project is to demonstrate the dynamic evolution of the structures or states over time, which includes investigating the roles of metastable states. This structure evolution study includes the nucleation of ordered states from disordered states as well as diffusionless transformations from one aperiodically or periodically ordered state to another. Because the balloon model is based on the evolution of deformable object surface areas, comparing surface energy and material transfer between particles to thermal energy is critical to achieving these project goals. These variables govern the presence and movement of defects, as well as the dynamics of metastable states. The use of the balloon model in this project demonstrated that multiple ordered states are possible in 3D from disordered or other ordered states. These ordered states’ metastability has been quantified, and a ”diffusionless transformation” between them has been observed. These transformations are well-known in metallic systems but have only recently been discovered in soft material experiments. In this work, the method of studying soft materials is similar to that of foams and biological tissues, in which the interfaces between deformable objects (gas bubbles or cells) play an important role. As a result, the goal of this research is to create a unifying framework for understanding micelles, emulsions, biological tissues, and possibly small molecule metals and glasses.