Monte Carlo Simulation On Physical Gelation In Triblock Copolymer Solutions

In our daily life, the polymeric gel exists extensively, which is a system constituted by three-dimensional polymeric compounds and solution. The cross-linking point of polymeric gels can be chemical, which constituted by covalent bonds and also can be physical cross-link. Since a gel has a kind of three-dimensional structure, it can not be resolved by solvent and maintains a approximatively solid state when dispersing in the solvent. In the microcosmic aspect, it is concomitance of extensive consecutive solid and liquid components and in the macroscopical aspect, it has anti-sheer resistance and can have elastic deformation. Therefore, a polymeric gel is a system of two-component, which is filled with liquids and has semi-solid properties. Polymeric gels can be divided into to chemical gels which are cross-linked by covalent bond through the irreversible gelation processes, and physical gels which are trapped by physical interactions such as van der Waals interaction, electrostatic interaction, hydrophobic force and hydrogen bond etc., formed through reversible physical gelation processes. Despite widespread industrial applications of polymeric gels due to their obvious importance as well as their strong response to surroundings, there are significant gaps in the understanding of how physical gels are formed in polymer solutions in the presence of various interaction terms and their principles and the gelation process is difficult to describe in the experimentally and theoretically.For the time being, the computational simulation has become the third chief method which is as essential as theoretical and experimental method due to rapid development of computational theory and its technology. People begin to use random sampling consciously and systematically to settle a large amount of mathematical and physical problems. The Monte Carlo simulation is used widely in polymer science and other disciplines as a unique computational method. For example, it is used to simulate chain radius of gyration, sequences problems of copolymers, conformation statistics of polymer chains and polymerization reactions. Monte Carlo simulation can simulate microcosmic stages to describe static and dynamic performances of a system so that evolutive process can be detected in molecular levels, which differs from other experimental methods. A model system can be defined exactly merely by computational simulation and internal and external parameters in the system can be controlled freely so that relationships between desired factors and statistical properties in the model system can be studied. Therefore, it is one of the most effective methods to study formation principles, structures and properties relationships by computational simulations in conjunction with experiments and theoretical methods. This thesis mainly applies Monte Carlo simulation to study the physical gelation process of symmetrical tri-block copolymer solutions, introduces properties and formation principles of physical gels in the polymer solutions briefly and applications of Monte Carlo simulation in the polymer science. The simulation model is the developed eight-site bond fluctuation algorithm. The developed eight-site bond fluctuation algorithm is more efficient and adaptable to simulate complex systems than the original one.In the first place, scaling theory of de Gennes is applied. Scaling relationships between random walk (RW) and self-avoid walk (SAW) and chain length are validated by two-dimensional model of single-site bond fluctuation algorithm. For the random walk chains, R 2f∝N1.02, Rg2∝N1.04; while for the self-avoid walk chains, R 2f∝N1.53, Rg2∝N1.51. The results coordinate the theroy of de Gennes approximatively.In the second place, hole diffusion algorithm of the bond fluctuation with snakelike movement and without snakelike movement is simulated respectively. The mean-square end-to-end distance got by the former method is much shorter that by the latter method. And the scale index by the former method is 0.434, which is much smaller than the ideal result of de Gennes while that is 0.61 by the latter method, which is similar with the ideal result. We conjecture that the snakelike movement of middle chains is responsible for extra shrinkage of polymer chains so that the mean-square end-to-end distance simulated turns small.In the third place, we studied the temperature effect on the physical gelation process of telechelic tri-block copolymer solutions and adopt simple cubic lattice Monte Carlo simulation in conjunction with the percolation theory. Therefore a statistical thermodynamics model to determine the sol-gel phase diagram has been established. The percolation theory we used here is based on the theory introduced by Stauffer and Aharony, and the bond-site and spot-site percolation was applied to studying the gelation in our simulation system. Furthermore, the temperature and concentration of polymer chain effect on sol-gel transition in tri-block copolymer solutions is discussed and the phase diagram based on upon percolation theory to decide sol-gel transition is established. The study indicates that sol-gel transition is accelerated by both enhancing temperature and increasing the concentration of molecular chains in solutions.Finally, in order to explore the process of sol-gel transition further, we studied different distributions of the polymer chains with different conformations in the gelation process. The study indicates that in the initial state of gelation it is the bridge chain that makes the cluster aggregate, but during and in the termial state of gelation it is the loop chain that makes the cluster growing and percolating.