Phase Separation Of Multi-Block Copolymers And Shape Transformation Of Vesicles Simulated By Self-Consistent Field Theory

Biological membranes and polymers are two important kinds of soft matter which are investigated in this thesis. Biological membranes are not only the basic unit of cells, but also the structural foundation to provide the life activity. In recent years, there has been increased interest on functions and shapes of membranes. Block copolymers have received considerable attention, both experimentally and theoretically, due to their fascinating ability to self-assemble into a variety of ordered nanoscale morphologies. The exploration, design and control of the ordered structures are highlight in the research and development of novel materials. However, in real experiments, there are many defects in the microphases of block copolymers. Then, the function and property of these materials can be damaged. Based on the above ideas, the following four topics are investigated in this thesis: (i) the shape of fluid vesicles anchored by a rigid rod; (ii) parallel algorithm of the real space numerical method for self-consistent mean field theory simulation of block copolymer structures and morphologies; (iii) the mechanism of defect trapping in lamellar phase of triblock copolymers; (iv) the phase separation behaviors of triblock copolymers in a selective solvent.In the first part, the system of a fluid vesicle anchored by a rigid rod is studied. In biological systems, membranes are usually "decorated" by glycolipids and glycoproteins which are semiflexible or even rigid macromolecules. Vesicles anchored by rigid rod can be an important model for real cell membranes. A method is developed which combines self-consistent field theory and Helfrich curvature elasticity theory to determine the stable and metastable shapes of rod anchored vesicles. Both the deformation of the vesicle and the density distribution of the rod segments can be obtained. Because of the vesicle's impenetrability, the rod segmentsexert an inhomogeneous entropic pressure on the vesicle and induce a change of the vesicle shape. The interaction between the rod segments and the vesicle membrane exerts an extra tension to the membrane. In addition, the rod length and the bending rigidity of the vesicle are investigated as important factors to the shape transformation of vesicles. The behavior of vesicle deformation is different when the rod is anchored outside or inside of the vesicle. The shape of the vesicle is determined by three key factors, i.e. curvature elasticity energy, the surface tension energy and the inhomogeneous entropic pressure. Due to the rigidity of the rod and the continuity of the vesicle curvature, the exhibited behaviors are very different from that of the Gaussian chain anchored vesicles. The results presented here can provide valuable insight into some biological processes. Meanwhile, it is possible to extend this method to more complicated and real biological systems, such as polymers with different topological architectures/vesicle, multiple chains/vesicle, protein inclusions, etc.In the second part, we develop a parallel algorithm of the real space numerical method for self-consistent mean field theory simulation. The most successful theoretical framework for the phase separation of the block copolymers is the self-consistent mean field theory (SCMFT). There are three efficient numerical approaches to solving the SCMFT. The real space method is more flexible than the spectral method and has a greater predictive capability. However, the real space method is computationally intensive and requires large memory resources. Hence, we develop a parallel algorithm of the real space numerical calculations. This parallel algorithm is a new algorithm base on the serial algorithm and suit to implement on cluster. After massive tests, we find our parallel algorithm is more efficient and suits for calculation of large system. Moreover, it can be easily extended to other algorithms for solving diffusion equations. With this parallel algorithm, the phase separation of a linear ABC triblock copolymer is studied in three-dimensional space. By systematically varying the volume fraction of the middle block, one dimensional phase diagrams are constructed for four classes of typical triblock polymers in terms of the relative strengths of the interaction energies between different species. Our parallel algorithm can boost the completeness of phase diagrams and contribute to the design of ordered structures in complex block copolymers.In the third part, the mechanism of defects trapping in lamellar phase of triblock copolymers is studied by dynamics density functional theory. In general, there are various defects in the ordered microphases of triblock copolymers. Then, the functionand property of these materials can be damaged. Hence, understanding the mechanism of defects trapping is critical to the development of novel materials based on triblock copolymers. We focus on two types of defects found in experiment. In the system of triblock polymers, there are two kinds of chain configurations which are loop and bridge configurations. The bridge configuration is the original for the first type defect. For the second type defect, the loop configure is the key factor and converted to the bridge configuration finally in the process of phase separation. In addition, the second type defect only exists with some specific parameters. Our research will contribute to the design and control of ordered structures in block copolymers.In the last part, we study the phase separation behaviors of linear ABC triblock copolymers in selective solvents with our parallel algorithm of the real space numerical method for self-consistent mean field theory. According to the theoretical result, our experiment phenomena are explained. The introduction of selective solvent into a block copolymer melt renormalizes the segment-segment interaction and gives rise to a wide range of self-assembled structures. The segment-segment interaction can be changed with changing the concentration of copolymer or different solvents. Hence, the ordered structure can be controlled and designed by this method. By systematically varying the volume fraction of the middle block, one-dimensional phase diagrams are constructed for four classes of typical triblock polymers in terms of the relative strengths of the interaction energies between different species. The difference in the behaviors between the bulk and the solution are compared and explained. With the introduction of the selective solvent, the effective volume fraction of the middle block is increased and the effective interaction energy is reduced for the two end blocks. Then, order-order transition is induced with specific volume fraction. The results presented here can provide valuable insight into phase behaviors of triblock copolymer concentrated solutions.