A polymer is any molecule constructed by linking together chemical units or monomers to form a long-chain molecule. The molecule is called a homopolymer if all the monomers are identical, whereas it is called a copolymer if it involves two or more chemically distinct monomers. If in the latter case the like monomers are grouped together in long sequences, the molecule is termed a block copolymer. The topic of our group consists three parts: one is simulation of phase separation in homopolymer system. One is phase separation in block copolymer system by means of self-consistent field theory. Another is phase transition between metastable state in block copolymer system. Phase separation in polymer solutions or polymer blends has attracted great interests of scientists in recent years. Due to long relaxation time and large scale of polymer molecules, the morphology of phase separation in polymer systems can exhibit many special features such as volume shrinking and phase inversion phenomenon compared with that in small molecule systems. We study phase separation from mesoscopic view based on two-fluid model derived from Doi and Onuki. Compared with the original two-fluid model, our model makes energy dissipation hold and can also recover experimental observations. For copolymer system, the repulsive interaction between the chemically different blocks drives the system to phase separate, whereas the connectivity of the copolymer chains prevents macroscopic phase separation. As a result of these competing trends, block copolymer systems self-organize into many complex structures. For diblock copolymers, these structures range from lamellar, hexagonal-packed cylinder and body-centered cubic sphere phases to complex bicontinuous cubic phase. These structures can be controlled by varying the chemical composition of the block copolymer or the segregation between blocks. Lots of methods were developed to simulate this phenomenon, and one of the most successful methods is the self-consistent mean field theory (SCFT). The SCFT can predict the phase diagram well over almost the whole temperature region. Nucleation is the decay of a metastable state via the thermally activated formation and subsequent growth of droplets of the equilibrium phase. The study of nucleation is challenging when ordered, periodic phases are present. Here we will focus on diblock copolymer melts, whose equilibrium phase behavior is well understood. Besides the disordered phase, the system has several ordered periodic structures---lamellar, hexagonally packed cylindrical, body-centered-cubic spherical, and gyroid. Employing the Landau-Brazovskii model, we will study the nucleation from a metastable lamellar phase to a stable cylindrical phase, which is the simplest order-order transition. We apply a new numerical method, called the string method, to compute the transition path and then find the size and shape of the critical droplet and the free-energy barrier to nucleation from the path. |
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Pattern-evolution process in polymer blends of 20wt\% polystyrene\\ (M: 1.01$\times{10^{5}}$) and polystyrene(methyl-ethyl)(M: 9.4$\times{10^{4}}$) given by Tanaka H |
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| Simulation results in polymer solution($\phi_0=0.4$) |
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| Phase diagram of triblock copolymer given by G. Fredrickson and F. S. Bates |
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The configurations of the states in the MEP of the nucleation from a metastable lamellar phase to a stable cylindrical phase in 2D. |
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The configurations of the states in the MEP of the nucleation from a metastable lamellar phase to a stable cylindrical phase in 3D. |
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