An-Chang Shi

Self-assembly of diblock copolymers under confinement

Block copolymers are a class of soft matter that self-assemble to form ordered morphologies at nanometer scales, making them ideal materials for various applications. The self-assembly of block copolymers is mainly controlled by the monomer–monomer interactions, block compositions and molecular architectures. Besides these intrinsic parameters, placing block copolymers under confinement introduces a number of extrinsic factors, including the degree of structural frustration and surface–polymer interactions, which can strongly influence the self-assembled morphologies. Therefore confinement of block copolymers provides a powerful route to manipulate their self-assembled nanostructures. In this review, we discuss the relationship between confining conditions and the resulting structures, focusing on principles governing structural formation of diblock copolymers under two-dimensional and three-dimensional confinement. In particular, the effects of commensurability condition, surface–polymer interactions, and confining geometries on the self-assembled morphologies are discussed.

Helical Vesicles, Segmented Semivesicles, and Noncircular Bilayer Sheets from Solution-State Self-Assembly of ABC Miktoarm Star Terpolymers

Multicompartment micelles, especially nanostructured vesicles, offer tremendous potential as delivery vehicles of therapeutic agents and nanoreactors. Solution-state self-assembly of miktoarm star terpolymers provides a versatile and powerful route to obtain multicompartment micelles. Here we report simulations of solution-state self-assembly of ABC star terpolymers composed of a solvophilic A arm and two solvophobic B and C arms. A variety of multicompartment micelles are predicted from the simulations. Phase diagrams for typical star terpolymers are constructed. It is discovered that the overall micelle morphology is largely controlled by the volume fraction of the solvophilic A arms, whereas the internal compartmented and/or segregated structures depend on the ratio between the volume fractions of the two solvophobic arms. The polymer-solvent and polymer-polymer interactions can be used to tune the effective volume fraction of the A-arm and, thereby, induce morphological transitions. For terpolymers with equal or nearly equal length of B and C arms, several previously unknown structures, including vesicles with novel lateral structures (helices or stacked donuts), segmented semivesicles, and elliptic or triangular bilayer sheets, are discovered. When the lengths of B and C arms are not equal, novel micelles such as multicompartment disks and onions are observed.

Self-assembly of diblock copolymers confined in cylindrical nanopores

Self-assembly of AB diblock copolymers confined in cylindrical nanopores is studied using a simulated annealing technique. The pore diameter and surface preference are systematically varied to examine their effects on the self-assembled morphologies and the chain conformations. For bulk lamella-forming and cylinder-forming diblock copolymers, novel structures such as helices and concentric (perforated) lamellae spontaneously form when the copolymers are confined in cylindrical pores. The observed equilibrium morphologies are compared with that obtained from experiments, theory, and other simulations. A simple model is proposed for symmetric diblock copolymers, which gives a reasonable description of the layer thickness for the concentric lamellae. It is found that chains near the pore surfaces are compressed relative to the bulk chains, which can be attributed to the existence of the surfaces. The dependence of the chain conformation on the degree of confinement and strength of the surface preference are reasonably explained. The energetics is discussed qualitatively and used to account for the appearance of the complex phase behavior observed for certain intermediate conditions.

Soft Confinement-Induced Morphologies of Diblock Copolymers

The self-assembly of diblock copolymers under soft confinement is studied systematically using a simulated annealing method applied to a lattice model of polymers. The soft confinement is realized by the formation of polymer droplets in a poor solvent environment. Multiple sequences of soft confinement-induced copolymer aggregates with different shapes and self-assembled internal morphologies are predicted as functions of solvent-polymer interaction and the monomer concentration. It is discovered that the self-assembled internal morphology of the aggregates is largely controlled by a competition between the bulk morphology of the copolymer and the solvent-polymer interaction, and the shape of the aggregates can be non-spherical when the internal morphology is anisotropic and the solvent-polymer interaction is weak. These results demonstrate that droplets of diblock copolymers formed in poor solvents can be used as a model system to study the self-assembly of copolymers under soft confinement.

The Observation of Highly Ordered Domains in Membranes with Cholesterol.

Rafts, or functional domains, are transient nano- or mesoscopic structures in the exoplasmic leaflet of the plasma membrane, and are thought to be essential for many cellular processes. Using neutron diffraction and computer modelling, we present evidence for the existence of highly ordered lipid domains in the cholesterol-rich (32.5 mol%) liquid-ordered () phase of dipalmitoylphosphatidylcholine membranes. The liquid ordered phase in one-component lipid membranes has previously been thought to be a homogeneous phase. The presence of highly ordered lipid domains embedded in a disordered lipid matrix implies non-uniform distribution of cholesterol between the two phases. The experimental results are in excellent agreement with recent computer simulations of DPPC/cholesterol complexes [Meinhardt, Vink and Schmid (2013). Proc Natl Acad Sci USA 110(12): 4476–4481], which reported the existence of nanometer size domains in a liquid disordered lipid environment.

Phase diagram of diblock copolymers confined in thin films.

The phase behaviors of diblock copolymers confined in thin films with two identical preferential surfaces are investigated using the self-consistent field theory. Around 20 morphologies, including centrosymmetric and non-centrosymmetric ones, are considered to construct the two-dimensional phase diagram with respect to the volume fraction and the film thickness, while the interaction parameter χN and the surface preferences are fixed. When these morphologies are classified into four categories of ordered phases--sphere, cylinder, perforated lamella (corresponding to gyroid phase in bulk), and lamella--the phase diagram directly reveals the impact of the film confinement on the order-order transitions as a function of volume fraction via the comparisons to those in bulk. Our results also provide a comprehensive understanding over the dependence of the structure formations on the film thickness for each volume fraction.

Macromolecular Metallurgy of Binary Mesocrystals via Designed Multiblock Terpolymers

Self-assembling block copolymers provide access to the fabrication of various ordered phases. In particular, the ordered spherical phases can be used to engineer soft mesocrystals with domain size at the 5-100 nm scales. Simple block copolymers, such as diblock copolymers, form a limited number of mesocrystals. However multiblock copolymers are capable to form more complex mesocrystals. We demonstrate that designed B1AB2CB3 multiblock terpolymers, in which the A- and C-blocks form spherical domains and the packing of these spheres can be controlled by changing the lengths of the middle and terminal B-blocks, self-assemble into various binary mesocrystals with space group symmetries of a large number of binary ionic crystals, including NaCl, CsCl, ZnS, α-BN, AlB2, CaF2, TiO2, ReO3, Li3Bi, Nb3Sn(A15), and α-Al2O3. This approach can be generalized to other terpolymers as well as to tetrapolymers to obtain ternary mesocrystals. Our study provides a new concept of macromolecular metallurgy for producing crystal phases in a mesoscale and thus makes multiblock copolymers a robust platform for the engineering of functional materials.

Confined self-assembly of cylinder-forming diblock copolymers: effects of confining geometries

The effects of confining geometries on the self-assembly of cylinder-forming asymmetric diblock copolymers are studied using a simulated annealing technique. Morphological transitions of block copolymers confined inside two parallel flat walls, cylindrical channels, as well as spherical and ellipsoidal cavities are systematically investigated. Depending on the copolymer composition, confining geometry and degree of structural frustration, a very rich array of confinement-induced morphologies is predicted by the simulations. The results reveal that the dimensionality of the confinement can affect the structure, symmetry and degeneracy of the self-assembled structures. In particular, the effect of spherical confinement is much stronger than that of thin film or cylindrical confinement.

Plateau-Rayleigh instability in a torus: formation and breakup of a polymer ring

A liquid jet can break up into a stream of droplets as a result of the Plateau-Rayleigh instability. The droplet formation decreases the jets surface area and hence its free energy. Here we present the results of experiments in an unconventional geometry where this instability can be observed: a toroidal section. We discuss the formation of these polystyrene toroids with nanometer length scales. The constraints imposed by this geometry affect its observed instability in comparison to a simple linear jet. Specifically, we show that the additional curvature imposed by the torus can have a significant impact on the energy minimization route.

Effects of confinement on the order-disorder transition of diblock copolymer melts

The effects of confinement on the order-disorder transition of diblock copolymer melts are studied theoretically. Confinements are realized by restricting diblock copolymers in finite spaces with different geometries (slabs, cylinders, and spheres). Within the random phase approximation, the correlation functions are calculated using the eigenvalues and eigenfunctions of the Laplacian operator inverted Delta(2) in the appropriate geometries. This leads to a size-dependent scattering function, and the minimum of the inverse scattering function determines the spinodal point of the homogeneous phase. For diblock copolymers confined in a slab or in a cylindrical nanopore, the spinodal point of the homogeneous phase (chiN)(s) is found to be independent of the confinement. On the other hand, for diblock copolymers confined in a spherical nanopore, (chiN)(s) depends on the confinement and it oscillates as a function of the radius of the sphere. Further understanding of the finite-size effects is provided by examining the fluctuation modes using the Landau-Brazovskii model.