Meijiao Liu

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.

Segmented helical structures formed by ABC star copolymers in nanopores

Self-assembly of ABC star triblock copolymers confined in cylindrical nanopores is studied using self-consistent mean-field theory. With an ABC terpolymer forming hexagonally-arranged cylinders, segmented into alternative B and C domains, in the bulk, we observe the formation in the nanopore of a segmented single circular and non-circular cylinder, a segmented single-helix, and a segmented double-helix as stable phases, and a metastable stacked-disk phase with fourfold symmetry. The phase sequence from single-cylinder, to single-helix, and then to double-helix, is similar as that in the cylindrically-confined diblock copolymers except for the absence of an equilibrium stacked-disk phase. It is revealed that the arrangement of the three-arm junctions plays a critical role for the structure formation. One of the most interesting features in the helical structures is that there are two periods: the period of the B/C domains in the helix and the helical period. We demonstrate that the period numbers of the B/C domains contained in each helical period can be tuned by varying the pore diameter. In addition, it is predicted that the period number of B/C domains can be any rational in real helical structures whose helical period can be tuned freely.

Origins of low-symmetry phases in asymmetric diblock copolymer melts

Significance We demonstrate that low-molecular weight asymmetric diblock copolymer melts can form multiple metastable liquid states at a common temperature, dependent on the processing history. Formation of ordered self-assembled micelles at low temperatures shapes the number density of the mesoscopic particles, which is preserved upon heating above the order–disorder transition temperature. Cooling returns the liquid to the same crystalline state reflecting a memory—a type of hidden symmetry—imprinted in the fluid. These surprising results are explained based on the large energetic penalty associated with fusing or fragmenting micelles in the highly structured liquid state. This work reveals concepts related to spontaneous symmetry breaking in self-assembled soft materials including surfactant-based systems. Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order–disorder transition temperature (TODT). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank–Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)-b-poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the TODT from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEXC) upon heating and cooling. The process-path–dependent formation of crystalline order shapes the number of particles per unit volume, n/V, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed n/V is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank–Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.

Order-order transitions of diblock copolymer melts under cylindrical confinement

The self-assembly behavior of AB diblock copolymers under cylindrical confinement is investigated using the self-consistent field theory. We focus on the impact of the confinement on the order-order transitions of three-dimensional morphologies by constructing two types of phase diagrams with continuously varying block compositions. One type is with respect to the block composition and the immiscibility parameter for various pore sizes, in which the order-order transitions are shown to be strongly impacted by the pore curvature and thus largely different from the bulk ones. Note that the morphologies are categorized by the intrinsical geometry of their domains, i.e., that helical morphologies are regarded as one type of cylindrical phase. Another type of phase diagram is with respect to the block composition and the pore diameter, which exhibits a number of interesting order-order transitions, especially the transition sequence from a straight line of spheres, to one straight cylinder and stacked disks as the pore diameter increases. A critical point is observed at which the stability region of the straight cylinder vanishes and thereby the spheres transform into the stacked disks continuously. The mechanism of these phase transitions is rationalized in the context of the bulk factors as well as an additional factor, i.e., the competition between the spontaneous curvature of the copolymer and the imposed curvature by the nanopore.