In recent years, the self-assembly of copolymer micelles has become an appealing frontier of supramolecular chemistry as a strategy to construct superstructures with multiple levels of complexity. The assembly of copolymer micelles is a form of higher-level self-assembly occurring at the nanoscale level where the building blocks are preassembled micelles. Compared to one-step hierarchical self-assembly, this assembly strategy is superior for manipulating multilevel architectures because the structures of the building blocks and higher-order hierarchies can be regulated separately in the first and higher-level assembly, respectively. However, despite the substantial advances in the self-assembly of copolymer micelles in recent years, universal laws have not been comprehensively summarized. This review article aims to provide an overview of the current progress and developing prospects of the self-assembly of copolymer micelles. In particular, the significant role of theoretical simulations in revealing the mechanism of copolymer micelle self-assembly is discussed.

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A theoretical approach combining self-consistent-field theory (SCFT) for fluids and density functional theory (DFT) for particles was applied to investigate the self-assembly behavior of amphiphilic diblock copolymer/nanoparticle mixture in dilute solution. Two kinds of hydrophobic nanoparticles are studied:  one is that the particles are selective to hydrophobic blocks but are incompatible with hydrophilic blocks, and the other is that the particles are nonselective to hydrophobic and hydrophilic blocks. For both cases, the self-association of amphiphilic block copolymer/nanoparticle mixture is observed, and the nanoparticles are spatially organized in the clusters. The aggregate morphologies can be tuned by the particle radius and particle volume fraction. For the selective particles, the aggregate morphologies of amphiphilic block copolymer/nanoparticle mixture can experience a transition from vesicles to mixture of circlelike and rod micelles as the particle radius and/or particle volume fraction increase. For the nonselective nanoparticles, the large compound micelles are produced instead of the vesicles. The large compound micelles transform to the mixture of large compound micelles and circlelike micelles with an increase in particle volume fraction and/or radius. The distribution of nanoparticles in the clusters is also affected by the particle radius and volume fraction. For both cases, when the values of nanoparticle radius and/or volume fraction are small, the nanoparticles are almost uniformly distributed in the cores of micelles. However, the particles tend to localize near the interfaces between the core and shell with increasing particle volume fraction and/or radius.

The effect of chain conformation change on the self-assembly behavior of poly(gamma-benzyl- l-glutamate)-block-poly(ethylene glycol) (PBLG-b-PEG) was studied both experimentally by transmission electron microscopy, laser light scattering, and circular dichroism and computationally using molecular dynamics (MD) simulation. It was found that, by introducing trifluoroacetic acid to the PBLG-b-PEG solution, the conformation of the PBLG chain transforms from alpha-helix to random coil, which results in a change of the micelle structures formed by PBLG-b-PEG from rod to sphere. Meanwhile, the MD simulations were performed by using Brownian dynamics on the self-assembly behavior of model AB-type diblock copolymers with various chain rigidities of the A-block. The results show that, by decreasing the fraction of rigid chain conformation of the A-block, which corresponds to the helix-coil transition in the PBLG-b-PEG sample, the aggregate structure transforms from rod to sphere. The MD simulations also provide chain packing information in the micelles. On the basis of both experimental and MD simulation results, the mechanism regarding the effect of the conformation change of the polypeptide block copolymer on its self-association behavior is suggested.

Using real-space self-consistent field theory, we explored hierarchical microstructures self-assembled from A(BC) n multiblock copolymers. The multiblock copolymers were classified into two types in terms of relative magnitude of A/B and A/C interaction strengths: one is that χAB N is less than or equal to χAC N, and the other is that χAB N is greater than χAC N. For both cases, the multiblock copolymers can self-assemble into hierarchically ordered microstructures with two different length scales. For χAB N ≤ χAC N, various hierarchical microstructures, such as cylinders-in-lamellae∥, lamellae-in-lamella∥, cylinders-in-cylinder∥, and spheres-in-sphere∥, were observed. In these microphases, the small-length-scale structures and the large-length-scale structures are packed in the doubly parallel forms. It was found the number of internal small-length-scale structures can be tailored by tuning the number of BC block and the interaction strength between A and BC blocks. For χAB N > χAC N, in addition to the parallel packed hierarchical structures, the multiblock copolymers can self-organize into perpendicular packed hierarchical structures, in which the structures with small periods are arranged perpendicular to structures with large periods. These perpendicular packed hierarchical structures were found to be only stable at higher value of χBC N.

Combining the self-consistent field theory (SCFT) and the density functional theory (DFT), we investigated the self-assembly behavior of AB diblock copolymer tethered single spherical particle P (ABP molecules). Two cases were studied: one is where the particles are chemically neutral to both A and B blocks, and the other is where the particles are unfavorable to neither of the two blocks. For neutral particles, the ABP molecules self-assemble to typical equilibrium microstructures, such as lamellae and cylinders. The P particles are localized in B block domains, and the size of particles can influence the phase behavior. For unfavorable particles, the ABP molecules microphase separate to form distinct ordered structures. Hierarchical structures, such as cylinders with cylinders at the interfaces and lamellae with cylinders at the interfaces, were observed. These resulting hierarchical structures are mainly determined by two parameters: A block fraction f(A) and particle size R(P). On the basis of the calculation results, phase diagrams were constructed.

We present a hybrid numerical method to introduce hydrodynamics in dynamic self-consistent field (SCF) studies of inhomogeneous polymer systems. It solves a set of coupled dynamical equations: The Navier-Stokes equations for the fluid flow, and SCF-based convection-diffusion equations for the evolution of the local monomer compositions. The Navier-Stokes equations are simulated by the lattice Boltzmann method and the dynamic self-consistent field equations are solved by a finite difference scheme. Two applications are presented: First, we study microphase separation in symmetric and asymmetric block copolymer melts with various values of shear and bulk viscosities, comparing the results to those obtained with purely diffusive dynamics. Second, we investigate the effect of hydrodynamics on vesicle formation in amphiphilic block copolymer solutions. In agreement with previous studies, hydrodynamic interactions are found to have little effect on the microphase separation at early times, but they substantially accelerate the process of structure formation at later times. Furthermore, they also contribute to selecting the pathway of vesicle formation, favoring spherical intermediates over aspherical (disklike) ones. 1

Morphologies and bridging properties of graft copolymers in the bulk state were studied by using a real-space algorithm of self-consistent field theory in two dimensions. The phase transition from cylindrical to lamellar phase can be triggered by changing the position of graft points and the number of branches. The fraction of bridged conformation, f(bridge), shows a tendency to decrease with increasing the length of free end blocks, tau1, and the number of branches, m. The value of f(bridge) has a discontinuous drop when the transition from cylindrical to lamellar phase takes place. The relationship between m and the number of bridged chains per unit area, nb, which is associated with the mechanical properties of copolymers, was also examined. It was found that nb increases with increasing m in the cylindrical phase. However, in the lamellar phase, nb decreases when m increases. It is proposed that the position of graft points and the number of branches are two important parameters for material design.