Bachelor thesis – Markus Hoffmann
Michael Hoffmann
Classical Density Functional Theory for Particles with Hard Cores and Soft Square Shoulders
[PDF]
finished 2019-10
supervised by Michael Schmiedeberg
Abstract
Classical density functional theory is an excellent tool to investigate classical many-body systems from fundamental principles, in particular soft matter systems. Here we consider hard particles with soft square shoulders in two dimensions. Since two mesoscopic particles cannot be at the same position at the same time, hard particles are a suitable model system. We model the interaction of impenetrable particles via infinite potentials. By adding soft shoulders, which are modelled by finite step potentials, we obtain a second length scale in our system. Two different length scales often lead to interesting pattern formations such as simple quadratic phases and quasiperiodic crystals. In this bachelor’s thesis we recover the liquid-solid phase transition for hard particles and for soft particles.
Classical density functional theory is an excellent tool to investigate classical many-body systems from fundamental principles, in particular soft matter systems. Here we consider hard particles with soft square shoulders in two dimensions. Since two mesoscopic particles cannot be at the same position at the same time, hard particles are a suitable model system. We model the interaction of impenetrable particles via infinite potentials. By adding soft shoulders, which are modelled by finite step potentials, we obtain a second length scale in our system. Two different length scales often lead to interesting pattern formations such as simple quadratic phases and quasiperiodic crystals. In this bachelor’s thesis we recover the liquid-solid phase transition for hard particles and for soft particles.