Phase Transition And Phonon In Two-dimensional Colloidal Crystals

Two-dimensional colloidal systems are understanding systems to study two-dimensional melting and properties of two-dimensional crystals. In the last decade, extensive studies on theoretical model, simulations and experiments of two-dimensional colloidal system were carried out. In this thesis, we focus on two-dimensional melting and vibration modes of two-dimensional crystal via Brownian dynamics simulation.In the first chapter, we briefly introduced two-dimensional colloidal systems. Firstly, we introduced the entropy effect and the random fluc-tuations in soft matter, and then we introduced theoretical models of the interaction potential and experimental preparation of three kind of two-dimensional colloidal systems, such as hard disk systems, charged colloidal systems and super-paramagnetic colloidal systems.In the second chapter, we introduced theory on two-dimensional melt-ing of colloidal crystal. Firstly, quasi-long-range order in two-dimensional systems, such as XY model and two-dimensional crystal, is discussed. Secondly, we introduced vortex-induced phase transition of XY model, namely, Kosterlitz-Thouless transition, and we discussed the renormal-ization group method of two-dimensional phase transition. Finally, we introduced KTHNY theory of two-dimensional melting.In chapterⅢ, the melting scenario of two-dimensional colloidal crys-tal was studied. In this chapter, Brownian dynamics simulations of two-dimensional charged colloidal system and definition of configurational tem-perature are introduced, and then the simulation results of the melting of charged colloidal system are discussed. We first gave some classical crite-rion on the melting of two-dimensional charged colloidal, including order parameter and its correlation function, structure factor, Lindemann param-eter, susceptibility and the average potential energy function. Secondly, we present the simulation results of configurational temperature, and defects analysis is also performed. Thirdly, we calculated the core energy of dislo-cations in our simulation system. In addition, the disorder parameters are calculated to visualize the structural heterogeneity.In chapterⅣ, vibration modes or phonon of two-dimensional crystal were studied. In this chapter, we studied vibration modes, the density of states (DOS), Boson peak and cumulative DOS of two-dimensional charged colloidal crystals at different temperatures by Brownian dynamics simula-tions. By using the normalization methods, the DOS, Boson peak and cumulative DOS at different temperatures can be normalized by a par-ticular frequencyω* and the peak of p(ω*), and the data collapse fairly well. Cumulative DOS is also fitted. We have found that the cumulative DOS is satisfied Debye law at low frequency but not at high frequency. However, for the entire frequencies region, cumulative DOS follows the law that:N*(ω)～- exp[-α(ω/ω*)2]. Finally, a theoretical model is present to interpret the law that:N*(ω)～- exp[-α(ω/ω*)2], and an abnormal dispersion relation thatω2= 2C/ln|k2| is given by the theoretical model.We summary this dissertation in the last chapter and outlook re-searches in the future.