Fast off-lattice Monte Carlo simulations of phase transitions in block copolymers and liquid crystals

Abstract

The basic idea of the so-called fast off-lattice Monte Carlo (FOMC) simulations is to perform particle-based Monte Carlo (MC) simulations in continuum with the excluded-volume interactions modeled by soft repulsive potentials that allow particle complete overlapping, where using soft potentials naturally arises from the application of coarse-grained models. This method is particularly suitable for the study of equilibrium properties of soft matter. One apparent advantage of FOMC is that using soft potentials can greatly improve the sampling efficiency in the simulations. Another advantage is that FOMC simulations can be performed in any statistical ensemble, and all the advanced off-lattice MC techniques proposed to date can be readily applied to further improve the sampling efficiency. Moreover, it provides a powerful methodology to directly compare theoretical results with simulation results without any parameter fitting. Last but not least, using FOMC is the only way to study experimentally accessible fluctuation/correlation effects in many-chain systems. This work makes use of FOMC simulations to study phase transitions in block copolymers and liquid crystals. To compare with the simulations results, various theoretical methods are also applied in the research. Chapter 2 is devoted to study the classic yet unsolved problem of fluctuation/correlation effects on the order-disorder transition (ODT) of symmetric diblock copolymer (DBC). In Chapter 3, we highlight the importance of quantitative and parameter-fitting-free comparisons among different models/methods. In Chapter 4, we investigate the effect of system compressibility on the ODT of DBC melts. In Chapter 5, we extend FOMC simulations to study the isotropic-nematic transition of liquid crystals. Finally, in Chapter 6, we briefly summarize all the studies in this dissertation and give some directions to future work.