Phase Separation Morphologies And Phase Diagrams Of Block Copolymers By Self-consistent Mean Field Theory

Copolymers are composed of two or more different type of monomers. According to their connection types, one can classify them into four categories: alternating copolymers, graft copolymers, random copolymers and block copolymers. Because of the covalent bond between different blocks, only microscopic phase separation can occur, block copolymer melts can self-assemble to form dizzying morphologies, and these morphologies (with length scales between 5-100nm) present as complex nanostructures. The phase behavior is quite different between block copolymers with different chain topologies, such as chains with linear, star, comb and ring structures. The studies of phase behavior of block copolymers are very important to design the final property of polymer materials.In this thesis, by using self consistent mean field theory, we have carried on a comprehensive study of phase behaviors of ring shape ABC triblock copolymer melt system. We have also proposed an improved spectral method to solve the modified diffusion equation, which has the advantage of being able to predict new phases with high computational accuracy. There are two chapters in this thesis:The first part: compared with AB diblock copolymer, the prediction of phase behavior of ABC triblock copolymer is more difficult and complex. According to previous theoretical and experimental studies, one can find factors that influence the phase behavior of ABC triblock copolymers, including: volume fractions, Flory-Huggins interaction parameters, chain topology, and the sequences of ABC blocks. In this part, we comprehensively studied the phase behavior of ring ABC triblock copolymer systems which haven't been investigated by other group yet.Different from linear, star, andÏ€shape ABC triblock copolymers, there is no end point in the ring ABC triblock copolymer chains. According to previous studies of AB ring shape diblock copolymer systems, we find that the major differences between the ring ABC triblock copolymers and copolymers with other topology are the phase transition point and domain spacing.In this chapter, we systematically studied the phase behavior of ring ABC triblock copolymer melt systems by real-space implementation of SCFT, and compared it with linear, star ABC triblock copolymer to find the major influences of different chain topology. Nine ordered morphologies have been observed during the simulation. They are (a) hexagonal lattice phase (HEX); (b) "three-color" lamellae phase (LAM3); (c) core-shell hexagonal lattice phase (CSH); (d) "three-color" hexagonal honeycomb phase (HEX₃); (e) lamellae phase with beads at the interface (LAM+BD-I) ;(f) lamellae phase with alternating beads (LAM+BD); (g) octagon-octagon-tetragon phase (OOT); (h) octagon-tetragon-tetragon phase (OTT); (i) decagon-hexagon-tetragon phase (DEHT). Most of them present in the simulation of linear or star ABC copolymers, however, the OTT is particular in ring ABC copolymers.Triangle phase diagrams are constructed for four classes of typical triblock polymers in terms of the relative strengths of the interaction energies: 1)χ_ABN =χ_BCN =χ_ACN = 35 ; 2)χ_ABN=χ_BCN=χ_ACN= 45; 3)χ_ABN =χ_BCN = 50,χ_ACN = 25;4)χ_ABN =χ_BCN = 30,χ_ACN = 50.When both volume fractions and interaction energies of the threespecies are comparable, the hexagonal honeycomb phase (HEX3) is found to be the most stable. By using the same method, we selectively studied the linear ABC copolymers and compared the morphologies of ring ABC triblock copolymers with them in the same conditions. Both of them form the same morphologies in general, but microdomain periods of ring ABC triblock copolymers are found to be smaller than that of their linear. That's because free ends chains are easier to interpenetrate and lead to small domains, but no end chains less easy to interpenetrate and lead to larger domains. This assumption needs more experimental and theoretical evidences to support.With the morphologies and phase diagrams of ring ABC triblock copolymers, our present may help the design and the synthesis of the ring ABC block copolymers.The second part: currently, there are three different efficient numerical implementations of SCMFT; (1) the spectral method introduced by Matsen and Schick. This method is extremely efficiency and accuracy for the calculation of the free energies and phase diagram, but it demands the symmetries of the phases to be calculated. (2) A combinatorial screening real space implementation of SCMFT has been suggested by Drolet and Fredrickson. This method does not require the assumption of the micro-phase symmetry, thus can explore the phase structures of various copolymer melts. However, the free energies and the phase boundaries calculated in phase diagram is not so precise as that in the spectral method. (3) An efficient algorithm named pseudo-spectral method has been proposed by Rasmussen et al. Instead of using a Crank-Nicholson scheme, they used a split-step Fourier algorithm to solve the modified diffusion equations. This method is more precise than real space method and does not need a prior assuming symmetry of the phase. In this chapter, we propose an improved spectral method which extends all spatial dependent parameter by complete Fourier series. The advantages include no need of a prior symmetry assumption and the energy calculation is very precise. The largest relative difference of the free energy between the improved spectral method and classic spectral method is less than 1%. To illustrate this is a very general method, we have study the Frustration 2 system of linear ABC triblock copolymers, and find the knitting pattern which has been reported by Stadler et al recently. This method will be useful in the field of exploring new morphologies in complex block copolymers.