Self-Assembly of Octahedral Patchy Particles

In this thesis the equilibrium behaviour of colloidal particles decorated with patches in an octahedral arrangement have been studied through the use of Monte Carlo (MC) simulations. The patches of the particles have a patch-antipatch interaction type, i.e. each patch can only form bonds with a specific antipatch on other particles. For these particles the fluid, simple cubic (sc) crystal and body-centered-cubic (bcc) crystal phases have been studied. Through MC simulations in the constant number of particles, pressure and temperature ensemble the equation of state has been found and via Einstein integration the free energies of the phases have been found. Combining these two results the phase diagram of the particles has been determined for number densities between ρσ3 = 0 and ρσ3 = 1.2, where σ is the particle’s diameter. It has been found that three phases are stable for temperatures between kbT = 0.2 and kbT = 0.35, where kb is Boltzmann’s constant. It is expected that at higher temperatures the face-centered-cubic crystal (fcc) phase is expected to be stable, although this has not been explored in this paper. At higher temperatures (above kbT = 0.35) melting of both crystal phases has been observed.