High Efficient Methods For The Self-consistent Model Of Semiflexible Macromolecule System And The Phase Behavior Of Rod-coil Diblock Copolymer Melt

Macromolecule is a very large molecule created by jointing many similar momentsthrough covalent bond. Macromolecular compound would self-assemble into differentmicro structures in different circumstance. Numerical simulation is one of the mostimportant approaches to study these self-assembly behaviors. So far, study for flexiblediblock copolymers is quite rich, while researches on the self-assemble behavior ofsemiflexible diblock are limited. In this thesis, we employ the Wormlike-Gaussianchain model to investigate the self-assemble behaviors of rod-coil diblock copolymers.Self-consistent mean field theory (SCMFT) is one of the most successful theo-ries for investigating the equilibrium phase behavior of block copolymers. Wormlike-Gaussian chain model, has a computational problem when applied to the investigationof rod-coil copolymer melts. A full space simulation with SCFT has to solve a set ofequations in a six-dimension(position3d+orientation2d+contour1d) space, which isa great challenge for numerical methods. In this article, we present high efficient al-gorithms to solve the SCFT equations of rod-coil diblock copolymer systems. Pseudo-spectral methods are hired and two new iterative schemes are developed. One is asemi-implicit scheme developed by employing the asymptotic expansion, and the otheris a hybrid scheme combining the robustness of steepest descend method and the effi-ciency of conjugate gradient method. These two schemes are demonstrated to be muchmore efficient than the steepest descend scheme in our numerical experiments.In the wormlike model, a parameter λ was introduced to measure the stiffness ofthe macromolecule. When λ→∞, the wormlike chain becomes a hard rod, and whenλ→0, it reduces to the flexible chain model. Here we study the influence of λ on thephase behavior of semiflexible-coil by changing the λ of the semiflexible chain from∞to0. We find that when the semiflexible block is softened, stable region for isotropicand Smectic-C will become larger in the phase diagram. Furthermore, when λ→0,the phase diagram exhibit some kind of symmetry with respect to the coil fraction. In our simulation, we find two new smectic phases: Smectic-OB and Smectic-P. Theyare different from Smectic-A and Smectic-C for the orientation of rods. Moreover,with the help of weak inhomogeneity expansion, we analyze the phase behavior ofrod(λ=∞)-coil theoretically. Here, isotropic, nematic and Smectic-A are considered.These theoretical results are in good agreement with our numerical results.At last, we investigate the nonlamella behavior of rod-coil copolymer melt in theposition-2d simulation and present a position-2d phase diagram. Nine different struc-tures are included in this phase diagram: Isotropic, Nematic, Smectic-A, Smectic-C,zigzag-A, zigzag-C, wavy, Rectangular arranged Cylinder and Hexagonally arrangedCylinder. We find that zigzag structure can be a stable state, which is the first time innumerical simulation, and its formation depends on the aspect ratio of the rod block,i.e., larger aspect ratio of the rod makes it easier for rod-coil diblock copolymers toorganize in a zigzag fashion.