Self-Consistent Field Theoretical Study Of Complex Polymer Systems And Monte Carlo Simulation For Microtubule Dynamics

Soft matter is closely related to human's lives, which widely exists in nature, life body and daily life, such as polymer, colloid, membrane and protein. There is a close relation between organisms and polymers, for example, biological membrane can be regarded as vesicle consisting of amphiphilic molecules. The microdomain structure of block copolymer is determined mainly by the molecular architecture and the interaction between the different components, thus the study of phase behavior of polymer system which contains special molecular chain architecture is significant to research the morphologies of soft matters. Microtubules are essential component of the cytoskeleton and are widely spread throughout the cytoplasm of eukaryotic cells. They play critical roles in a variety of cell processes, including cell shaping, intracellular tracking, cell division, and cell migration. The polymerization of microtubule is accompanied with the depolymerization of tubulin dimers and the hydrolysis of GTP (Guansine Triphosphate) within the microtubules, thus the microtubule dynamic behavior is very complicated. In this thesis, we first study the phase behavior of the polymer system which contains star molecular chains based on self-consistent field theory, and then research the microtubule dynamics by using Monte Carlo methods. The study mainly includes the following four aspects: (i) the phase behavior of diblock copolymer and star homopolymer blends; (ii) the phase behavior of star triblock copolymers both in bulk and in selective solvents; (iii) the phase behavior of star triblock copolymer thin films; (iv) the Monte Carlo simulation for microtubule dynamics.In the first part, the compatibility between the components in polymeric blend system is an important factor which affects system structure and properties. For copolymer-homopolymer blends, the phase separation behavior is affected not only by the macrophase separation between block copolymers and homopolymers, the microphase separation of block copolymer chains, but also the competition between these two kinds of phase separations. In this part, we have interpreted the self-assembled morphologies of the blends of AB diblock copolymers and 3-arm star A homopolymers by using self-consistent mean field theory. We have focused on the condition that the copolymer composition is fixed while the chain length and volume fraction of the star homopolymer are varied. It is found that the phase behavior of the blend depends on both the chain length and volume fraction of the star homopolymer. The distribution of star homopolymer within the microphases is investigated based on enthalpic and entropic effects. By comparing the result of linear copolymer-homopolymer blend, we have discussed the difference between the effects of topological distinct polymers. The results of our study are supposed to be helpful for the design of novel nanomaterials involving architectural different polymers.In the second part, we have studied the phase separation behavior of star ABC triblock copolymers both in bulk and in selective solvents by self-consistent mean field theory. In traditional experiments, abundant efforts are made to synthesize new block copolymers with the aim of investigating the molecular parameters and topological effects on discovering new morphologies. Furthermore, 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, in this way the ordered structure can be controlled and designed. By systematically varying the volume fraction of the C block, one-dimensional phase diagrams are constructed for three classes of typical star ABC triblock copolymers in terms of the relative strengths of the interaction energies between different species. The differences in the phase behaviors between the bulk and the solution are compared and explained. With the introduction of the selective solvent, the effective volume fraction of the C block is increased and the effective interaction energy is reduced for the other blocks. Then, the order-order transition is induced with specific volume fraction. The results presented here can provide valuable insight into phase behavior of both bulk star triblock copolymer and star copolymer concentrated solutions.In the third part, thin film is a very common and important constrained system. In this part, we have described the complex phase behavior of a specific star ABC triblock copolymers confined between two identical parallel walls. To focus on the star architecture of the polymer chain, we have chosen the symmetric copolymer composition. By systematically changing the film thickness and surface field, the self-assemble structures of confined star ABC triblock copolymer melts with the symmetric and asymmetric interactions between polymer species are carried out by SCFT simulations. A variety of structures are found to be stable, such as cylinders, undulated cylinders, lamellae with cylinders, perforated lamellae and alternating versions of the sphere in matrix structures, etc. In particular, some new morphologies, such as cylinders with alternating helixes structure and complicated hybrid network structures are found in our studies. In the case of neutral walls, cylinder structures are commonly observed in thin films. Moreover, the cylinder radius and shapes are quite flexible in order to adjust themselves to different film thicknesses due to the junction point constraint of the star architecture. When surface field is weak, the cylinder phases are frequently observed because in this case the confinement effect is dominant. When surface field is strong, the effect of surface field on film morphologies is more significant. The surface field can break up the cylinder structure, and a variety of noncylindrical structures will be favored. Our results may provide a guide to understand the complex interplay between confinement effects, surface field and interaction parameters in thin films of star triblock copolymers.In the last part, microtubule can be formed by tubulin heterodimers under the suitable temperature and tubulin concentration. The polymerization of microtubule is accompanied with the depolymerization of tubulin dimers and the hydrolysis of GTP (Guansine Triphosphate) within the microtubules, thus the microtubule dynamic behavior is very complex. The dynamics of microtubule is always the hot topic in life science. In this part, we have used an iterative Monte Carlo method to simulate the growth of microtubules and the impact of nucleation rate, tubulin concentration, the polymerization rate and depolymerization rate on the dynamics of microtubule. Especially, we have studied the dynamic behavior of microtubule after coupling the hydrolysis process of GTP. The simulation results show that the increase of tubulin concentration could promote microtubule polymerization, when tubulin concentration below the critical value, the microtubule would not be formed. Under the most calculating parameters, the microtubule population could reach steady state. After coupling the hydrolysis process of GTP, the time varying dynamic process of individual microtubule is consistent with the experimental results. In the simulation, we find that the choice of the models for both microtubule dynamics and GTP hydrolysis play essential roles in the study of microtubule dynamics. Although our work only get some preliminary results, but it provided effective guidance and data accumulation for further research of microtubule dynamics. The results presented here can provide valuable insight into some biological processes.