Theoretical Studies On The Complex Structures Self-Assembled By Block Copolymers

Block copolymers, formed by two or more incompatible polymer chains covalently jointed end to end, have attracted considerable interest for the following two main reasons. One reason is that block copolymers exhibit unique properties compared with homopolymers or the simple blending of homopolymers. The other reason is that block copolymers are able to self-assemble into nanoscale ordered structures, whose length scale can be tuned readily by the molecular weight of block copolymers. Moreover block copolymers can self-assemble into many complex structures, such as helices which are commonly existing in nature, the knitting pattern (KP) with unusual nonuniform mean curvatures, the binary nanocrystals with exceptional performances in photoelectric applications. These complex structures further expand the potential applications of block copolymers. While, in the process of experimental exploration of these particularly interested complex structures self-assembled from block copolymers, there are a number of difficulties. Firstly, the relevant experiments, which are usually composed of three major steps including synthesis, annealing and characterization, are very time-consuming and costly. Secondly, there are a multitude of independent parameters (interactions, compositions, etc.) which limit the breadth and depth of the experimental explorations. Thirdly, there are technical difficulties in either precisely controlled synthesis or annealing or characterization for the formation of complex structures. These difficulties slow down the experimental research on the exploration of complex structures from the specifically designed block copolymers. With the establishment and development of the theory of block copolymer phase segregation, theoretical calculation methods were validly used to analysize and comprehend the stability of different phase structures. Additionally, with the rapid development of computer as well as the parallel computing technology, theoretical calculation methods become more and more efficient in studying the self-assembly behaviors of block copolymers, and they play an increasingly important role in unearthing the complex structures self-assembled by block copolymers. High efficient theoretical calculations can make up for the deficiencies in the experimental studies.In particular, theoretical calculation methods can be applied to systematically analysize and screen the stability of different structures, and thus used to look for interesting and specific ordered structures.Therefore, theoretical calculations can be utilized to screen out the targeting block copolymers for experimental studies, and is helpful in reducing the experimental cost and in enhancing the experimental efficiency.This thesis is focused on two different ways to enrich the stable structures self-assembled by block copolymers. One way is imposing various geometrical confinements on block copolymer melts.Due to the impact of the symmetry and surface interaction of the geometrical confinements, block copolymers can self-assemble into novel structures beyond those in the bulk. The other way is increasing the molecular complexity of block copolymers, such as adding a new component C into AB block copolymers to form ABC block terpolymers or more blocks to form multiblock copolymer, or varying the chain architectures among linear, star, ring, etc.Increasing species results in a rapid growth of the phase parameters, and thus acts as an effective way to enrich the phase behaviors. At the same time, in multicomponent block copolymer systems, there are more types of interfaces between separated domains whose formation and arrangement directly complicate the formation of structures by enriching the symmetry of the self-assembled phases.In addition, as the number of blocks as well as the chain architectures also significantly affects the formation and arrangement of the interfaces, they also play key roles on impacting the phase behaviors of multiblock copolymers. The main contents are listed as follows:In the first chapter, Firstly, a brief introduction on the basic concepts and the self-assembly properties of block copolymers is presented. Then the derivation of the self-consistent field theory (SCFT) as well as the description of its numerical solution is given.Besides the common phase parameters, such as the volume fraction and the interaction parameters,the flexibility of different blocks is specifically included into the SCFT derivation in order to describe the characteristics of the block copolymers more realistically. The different flexibilities between distinct blocks result in the conformational asymmetry,ε. So the unique quantity of ε is finally appeared in the SCFT equations based on the ideal Gaussian chain model. Finally the numerical methods to solve the SCFT equations is introduced. In particular, the pseudo-spectral method based on the fast Fourier transform (FFT), which is one of the most popular methods in SCFT calculations, is described. To improve the efficiency of the SCFT calculation in the search of complicated phases, designing special initial conditions for specific phases is proposed. In addition, the Anderson mixing iteration method is used to accelerate the converging speed during the iterating solution of SCFT equations.The second chapter is devoted to the examination of the self-assembly behaviors of block copolymers under various geometrical confinements. The first portion is focused on the study of AB diblock copolymer melts under the thin film confinements. The main research goal is to reveal the impact of the film confinement on the order-order transitions (OOTs) by comparing them with those in the bulk. Accordingly we fixed some less important phase parameters, such as the interaction between two blocks, the uniform flexibility of distinct blocks and the preferential interaction of two film surfaces on the two blocks. The reduced parameter space enables us to concentrate on the exploration of stable phases and their OOTs of diblock copolymers with varying volume fraction confined between thin films with variable film thickness. Systematical comparison of OOTs between the confined system and the bulk system (including sphere/cylinder, cylinder/gyriod and gyriod/lamella) readily reveals the influence of the one-dimension confinement on the OOTs. Here we focus on the case of thin films where one or two layer of structures is formed. In our SCFT calculations,20 stable structures are observed. By comparing the free energy of these structures, the phase diagram with respect to the volume fraction and the film thickness is constructed, which is composed of 200 determined phase transition points. In practice, thin films of block copolymers are usually prepared by spin coating from dilute solution on substrates for realizing specific applications of targeting structures. Therefore, this phase diagram provides a direct guide for relevant experiments or manufactures. And then, the phase behaviors of AB diblock copolymers under cylindrical confinements are investigated. Compared with the film confinement, under cylindrical confinements, the block copolymers are not only influenced by one more dimensional confinements, but also by the surface curvatures from the cylindrical shape. As a result, there are a rich diversity of phases self-assembled by cylindrically confined block copolymers. The helical structures, which are attractive because they broadly exist in nature, can also be spontaneously formed from achiral block copolymers under cylindrical confinements. So we systematically study the stability of the helical structures impacted by the phase parameters, such as the volume fraction of diblock copolymers (f), strength of segregation (χN), and the diameter of confining nanopores. Our calculations predict a number of stable phases, including single/double helical phases, stacked disk, and perforated circular layer phase, and determine their stability regions. Our results are helpful in understanding the self-assembly mechanism of block copolymers under cylindrical confinements, especially, in revealing the impact of the cylindrical confinement on the corresponding OOTs. Furthermore, the self-assembly mechanism of helical structures in achirality block copolymers under cylindrical confinements can inspire us to understand the helix formation in biological systems. In order to further comprehend the universal mechanism of the formation of helical structures in cylindrically confined block copolymers, we move on to a more complex block copolymer, ABC star block copolymer. In ABC star copolymer systems, the phase parameters are dramatically increased, and thereby exploring the full parameter space of the phase behaviour is formidable. Specifically, we choose ABC star copolymers that self-assembles into hierarchical hexagonal cylinders where each cylinder is composed of alternatively stacking B/C domain in the bulk. After imposed by the cylindrical confinement, the self-assembly of the ABC star copolymer is expected to be varied to ensemble a similar feature as that in the cylindrically confined AB diblock copolymer, i.e., to form hierarchical helical structures consisting of alternative B/C segments. This speculation is justified in our calculations. In this confined ABC star copolymer systems, we observed the segmented single/double helical structures that the B/C domains are alternatively stacked similar to those stacked into cylinders in the bulk. In our calculation, the periodic boundary condition is employed along the cylindrical axis, which induces that the number of the B/C domains contained in each helical period is not a consecutive rational number but is the "quantized" integer, nB/C. Analyzing the stability of these quantized helices and their neighbour structures is helpful to reveal the the universality of the formation of helical structures in block copolymers imposed by cylindrical confinements.In the third chapter, we mainly study the self-assembly of "frustrated" ABC linear triblock copolymers in the bulk. Here, we focus on probing the emergence and stability of the complex phase structure, knitting pattern (KP), which had been observed but its stability still had not been identified in experiments. We systematically examine the impact of diverse phase parameters, including the volume fraction of each block(fκ,κ∈(A,B,C)) and the interaction parameters (χABN,χBCN and χACN),as well as the parameters characterizing the conformational asymmetry between blocks (εκ,κ∈A,B,C)), on the stability of the KP phase. At the same time, a comparison between our calculated results and the relevant experimental results is conducted, which provides the theoretical explanation for the experimental observations. In addition, by selecting a specific set of parameters according to the extensively studied experimental triblock copolymer of SEBM, we identify the stable region of KP and its neighbouring phase regions in the triangular phase diagram of compositions. Our calculated results suggest that a particular linear triblock copolymer, such as SEBM, with the appropriate parameters is able to self-assemble into stable KP morphologies. Moreover, our results also speculate the reason that the stable KP phase is not observed in experiments, which is that the volume fraction of the synthesized SEBM copolymers is deviating from the stability region of KP phase. This is the first time to predict the stability of the KP phase in theoretical studies, that serves as a direct theoretical guide for experiments to prepare the nonuniform curvature morphologies.The forth chapter is focusing on the exploration of binary nanocrystal structures formed by specifically designed ABC block terpolymers. Taking advantage of that block copolymers are able to self-assemble into nanoscale ordered structures and the length scale of the structures can be readily tuned by varying the molecular weight of polymers, nanoscale structures resembling the symmetries of inorganic binary atomic crystals can be obtained by reasonably designing the architecture of block terpolymers. This not only fills the gap of feature size between the small atomic crystals (0.1-1 nm) and the large colloidal crystals (0.1-1 micron), but also widens the range of applications of block copolymers in nanoscale functional materials. In order to effectively design block terpolymers for the formation of intriguing binary nanocrystals, we start with the design of block terpolymers which can self-assemble into simple symmetrical binary nanocrystals composed of two types of equal-number and equal-size spheres. Through extensive theoretical calculations on the stability of a variety of symmetric nanocrystals formed in block terpolymers with diverse molecular architectures, we summarize the self-assembling mechanism of symmetric nanocrystals. And then we extend the knowledge of the self-assembling mechanism in symmetric nanocrystals in that of more complex nanocrystals, such as asymmetric binary nanocrystals and even ternary nanocrystals. Our calculations and analysis suggest that the symmetrical B1AB2CB1 linear pentablock terpolymers is suitable to generate a multitude of symmetric binary nanocrystals, which are composed of A- and C-blocks formed spheres in the B matrix. The symmetry of stacking lattice of A and C spheres can be modulated by modifying the relative length of three B blocks while keeping the total B composition fixed. Obviously, the size of A/C spheres is directly determined by the length of B1 blocks, and the distance of the nearest-neighbour A/C spheres is significantly influenced by the length of the middle B2 bridging-block. We can speculate that the distance of A/C spheres tends to be reduced to minish the stretching penalty arising from the middle B2 block when shortening the middle B2 block for fixed total B composition of three blocks, and thus the shrunk crystal lattice would induce more crowded packing of B blocks. The above two irreconcilable contradictions enforce the third factor to be modified, i.e., the crystal lattice. In order to release the packing frustration of B blocks, a loser piling of A/C spheres is required. In other words, a new crystal lattice with smaller coordination numbers (CNs). With the fixed interaction parameters as χABN=XBCN=χACN=80,and the equal volume fraction of A and C blocks as fA=fC=f, a number of symmetric binary nanocrystals are observed by changing f and fB2.The observed symmetric binary nanocrystals include stable ones, such as CsCl, NaCl, ZnSc(sphalerite), and metastable ones, such as ZnSH (wurtzite), NiAs, PtS. In addition, a number of interesting none-crystal structures are explored in our calculations. By comparing the free energy of these phases, we construct the phase diagrams containing these stable phases of binary nanocrystals. It has been well known that only the CsCl binary nanocrystal structure is formed by the simple ABC linear triblock copolymers except that the NaCl structure occupies a very tiny phase region, therefore, our results greatly enrich the nanocrystals serf-assembled by block terpolymers. Additionally, the phase diagram can serve as a useful guide for experiments in synthesizing the relevant block terpolymers for the formation of distinct stable binary nanocrystals.In summary, the self-assembly behaviors of a variety of block copolymers both in the bulk and under geometric confinements are systematically studied by SCFT calculations. On the one hand, the process of exploring new structures is drastically improved by generating the special initial fields for targeting structures in the SCFT solution. In our calculations, a series of interesting structures are explored, and the stability of these structures are identified, such as the segmented helices where each helix is composed of alternatively stacked B/C segments, the knitting pattern, a variety of binary nanocrystals.Our results expand the applications of block copolymers in the fabrication of nanoscale functional materials. On the other hand, the usage of the high-efficient and accurate pseudo-spectral method and the Anderson mixing method enable us to systematically study the stability of a multitude of structures, and thus to construct their phase diagrams.In particular, we choose appropriate phase parameters to model the extensively studied experimental block terpolymer of SEBM as real as possible, and therefore our results can provide a direct theoretical guide for experimental studies.