Theoretical Studies On Block Copolymers Assemble Under The Direction Of Patterned Substrates

Polymer is a kind of soft matter, a concept proposed by P.G. de Gennes on Nobel Prize Ceremony in1990. Today, polymer materials have been widely used in a number of industry areas. According to compositions, polymer can be divided into homo-polymer, block copolymer, grafted copolymer and random copolymer. Block copolymer consists of two or more different blocks of polymer in a chain. Because of the linkage of chemical bond, micro-phase separation could occur in the systems of block copolymer, which self-assemble into periodic ordered nano-structures. In semiconductor industry, conventional lithography cannot meet the demand of shrinkage length to sub-30nm. Block copolymer lithography (BCL), a new strategy to obtain a large scale of ordered periodic nano-structure via directed self-assembly of block copolymer, has been viewed as a promising alternative technique of conventional lithography to keep semiconductor industry forward. Now there are several methods developed to bring block polymer lithography into practice. Among them, the chemical-patterned substrate and topology confinement methods have attracted extensive research interest of scientists, and have made intensive progress. Due to increasing development of computer science, computer simulation has been a powerful research tool which can provide profound understanding to more and more systems. In this thesis, we take advantage of computer simulation and develop some appropriate models to study the self-assembling dynamics under the direction of the above two BCL methods. Aim of our work is to understand the underlined self-assembling mechanism of block copolymers under the direction of different environmental conditions, and try to find the answers to some problems encountered in experiments. In addition, we have developed a coarse-grained Monte-Carlo model to study the stretching mechanics of PAN carbon fibers. With the developed model, we have studied the influence of defects with various defect concentrations and shapes on the stretching mechanics of carbon fibers, including strength, breaking length and modulus.In chapter1, we give an introduction to the background of theoretical research in polymer physics, including widely used theoretical methods together with some achieved results. The advantage of theoretical research is also described.In chapter2, we focus on the two methods of block copolymer lithography, the self-assembly of block copolymers under the direction of the chemical patterned substrate and geometry-topology confinement. Time dependent Ginzburg-Landau equations have been used to simulate the dynamical process of self-assembly of block copolymers under the direction of various external conditions. In section1, the background as well as the frontier of block copolymer lithography are briefly introduced. In section2, we simulate the dynamical process that the lamella-formed diblock copolymers self-assemble on the stripe-patterned substrate. First, our results suggest that the correlation length in the assembled structures grows with a power-law function of the evolution time, which is consistent with the ordering behavior in bulk. This prediction can be readily used to answer the question that there is a density multiplication (DM) limit in related experiments. Second, a dynamical tolerance window for the perfect ordered structures has been determined by our simuations. It is a useful guide to fabricate large-scale ordered nano-structures by the block copolymer assembly under the chemical-patterned substrates in experiments. In section3, the nucleation phenomena are observed in the diblock copolymer/homo-polymer blends. Based on this important physical process, we have proposed a new strategy of block copolymer lithography which combines the advantages of the nucleation phenomena and the chemical-pattern direction for the fabrication of perfect ordered patterns. With our new strategy, the density multiplication has been improved up to at least128, an unprecedented high value. With this new strategy, it is hopeful to push the application of BCL closer to the real practice because of the highly improved efficiency. In the last section, we have studied the self-assembling behaviors of block copolymers under the hexagonal cylindrical confinement. The self-consistent mean field theory (SCMFT) and the time dependent Ginzburg-Landau equations (TDGL) have been used to study the thermodynamics and the ordering dynamics in the systems. Our results show that it is feasible to fabricate ordered nano-structure via the self-assembly of block copolymers under a large size hexagonal confinement in experiments, but the annealing time increases with respect to the size. In addition, much longer annealing time is required for the ordering process when the box size deviates from the interger multiple of the bulk period. Our theoretical prediction on the ordering time is helpful for experiments. In chapter3, a coarsen-grained Monte Carlo method has been developed and has been used to simulate the stretching mechanics of the PAN carbon fiber. Our simulation results give a systematic prediction on the influence of the defect concentration and the defect shapes on the stretching mechanics. While the defects do not destroy the whole net-structure, the introduction of defects is helpful to increase the breaking length of carbon fibers, and otherwise, the defects result in the breakage. The alignment of the long axis of defect along the stretching direction is more helpful for the mechanical properties of carbon fibers than the opposite case.