Understanding the phase behaviour of colloidal systems is relevant to designing new colloid-based nanostructured materials. One common platform for studying the colloidal system is the model of hard spheres. Over the last few decades, different hard-sphere models have been developed. We study the phase behaviour of three hard-sphere models: the lattice gas model, the local density approximation model, and the white bear version of the fundamental measure theory, with short-range attractive and long-range repulsive (SALR) interactions. The competition between the attraction and repulsion results in the formation of clusters composed of many particles, whereas the spatial arrangement of these clusters leads to the formation of long-range ordered phases. Phase diagrams containing the commonly observed body-center-cubic (BCC) and hexagonally close-packed (HCP) phases, as well as the novel Frank-Kasper $\sigma$ and A15 phases, have been constructed using the density functional theory applied to hard spheres with SALR interactions. Similar phase transition sequences have been predicted for the three hard-sphere models, implying a universality of the observed phase behaviour for hard spheres interacting with SALR potentials. However, the details of the phase diagrams could vary significantly. The results obtained from our study shed light on understanding the emergence of complex phases from simple systems. / Thesis / Master of Science (MSc) / Soft condensed matter physics, a sub-field of condensed matter physics, primarily concerns the investigation of physical properties of pliable, deformable materials such as plastics, gels, and colloidal suspensions. One particularly intriguing feature of these soft materials is their ability to self-assembly, leading to the spontaneous formation of ordered structures, including but not limited to body-centered cubic and face-centered cubic phases. In particular, a group of complex spherical phases, known as the Frank-Kasper phases, has been identified in various soft matter systems, encompassing polymeric blends, colloidal suspensions, and more. Notably, in colloidal systems, when nanoparticles are grafted with polymer chains, the Frank-Kasper phases could become stable. However, the emergence of these complex phases from the diverse soft matter systems have not been fully understood. In this thesis, we employ the classical density functional theory based on three different hard-sphere models to probe the formation of the Frank-Kasper phases in colloidal systems. Our results provide insights into the formation mechanism of the Frank-Kasper phases in a simple system and demonstrate the universality of different hard-sphere models.
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/28897 |
| Date | 11 1900 |
| Creators | LI, YU |
| Contributors | Shi, An-Chang, Physics and Astronomy |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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