Weihua Li

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.

Molecular pathways for defect annihilation in directed self-assembly

Significance A molecular model is used to calculate the free energy of formation of ordered and disordered copolymer morphologies. We rely on advanced methodologies to identify the minimum free energy pathways that connect such states of the material. Our predictions for defect formation and annealing are compared with experimental observations. Our results provide a detailed molecular view of isolated block copolymer defects, which measure approximately 5 nm and represent isolated events in large areas. They are true “needles in the hay stack” that can only be studied by concerted molecular simulations and dedicated access to production-level fabrication tools. We show that defect annealing is an activated process, where defects are eliminated by operating near the order−disorder transition. Over the last few years, the directed self-assembly of block copolymers by surface patterns has transitioned from academic curiosity to viable contender for commercial fabrication of next-generation nanocircuits by lithography. Recently, it has become apparent that kinetics, and not only thermodynamics, plays a key role for the ability of a polymeric material to self-assemble into a perfect, defect-free ordered state. Perfection, in this context, implies not more than one defect, with characteristic dimensions on the order of 5 nm, over a sample area as large as 100 cm2. In this work, we identify the key pathways and the corresponding free energy barriers for eliminating defects, and we demonstrate that an extraordinarily large thermodynamic driving force is not necessarily sufficient for their removal. By adopting a concerted computational and experimental approach, we explain the molecular origins of these barriers and how they depend on material characteristics, and we propose strategies designed to overcome them. The validity of our conclusions for industrially relevant patterning processes is established by relying on instruments and assembly lines that are only available at state-of-the-art fabrication facilities, and, through this confluence of fundamental and applied research, we are able to discern the evolution of morphology at the smallest relevant length scales—a handful of nanometers—and present a view of defect annihilation in directed self-assembly at an unprecedented level of detail.

Defects in the Self-Assembly of Block Copolymers and Their Relevance for Directed Self-Assembly

Block copolymer self-assembly provides a platform for fabricating dense, ordered nanostructures by encoding information in the chemical architecture of multicomponent macromolecules. Depending on the volume fraction of the components and chain topology, these macromolecules form a variety of spatially periodic microphases in thermodynamic equilibrium. The kinetics of self-assembly, however, often results in initial morphologies with defects, and the subsequent ordering is protracted. Different strategies have been devised to direct the self-assembly of copolymer materials by external fields to align and perfect the self-assembled nanostructures. Understanding and controlling the thermodynamics of defects, their response to external fields, and their dynamics is important because applications in microelectronics either require extremely low defect densities or aim at generating specific defects at predetermined locations to fabricate irregular device-oriented structures for integrated circuits. In this review, we discuss defect morphologies of block copolymers in the bulk and thin films, highlighting (a) analogies to and differences from defects in other crystalline materials, (b) the stability of defects and their dynamics, and (c) the influence of external fields.

Self-Assembly of ABC Star Triblock Copolymers under a Cylindrical Confinement

Self-assembly of ABC star triblock copolymers confined in cylindrical nanopores is studied using real-space self-consistent mean-field theory. Specifically, the investigation focuses on the confined self-assembly of a triblock copolymer which forms hierarchical lamellae in the bulk. Generically, the hierarchical lamellae can be parallel or perpendicular to the pore surfaces. Concentric rings of A and B/C lamellae are formed in the parallel case. The B/C layers further form B/C domains. The number of B/C domains is controlled by the pore size. In the perpendicular case, the B/C layers are arranged alternatively along the pore axis. The stability of these observed structures is analyzed.

Real-space self-consistent mean-field theory study of ABC star triblock copolymers

The phase behavior of ABC star triblock copolymers is examined using real-space self-consistent mean-field theory. The central part of the triangular phase diagram for ABC triblock copolymers with equal A/B, B/C, and C/A interactions is determined by comparing the free energy of a number of candidate ordered phases. In this region of the phase diagram, the dominant microstructures are cylinders with polygonal cross sections or two-dimensional polygon-tiling patterns. Most of the known polygon-tiling patterns observed in experiments and simulations, plus some neighboring morphologies, are considered in the construction of the phase diagram. The resulting phase behavior is consistent with experiments and computer simulations.

New strategy of nanolithography via controlled block copolymer self-assembly

The self-assembly of block copolymer–homopolymer blends in bulk, as well as under the direction of periodic patterned surfaces, has been investigated by computer simulations of the time-dependent Ginzburg–Landau theory. Specifically, a small amount of homopolymers are added to regulate the spontaneous nucleation rate and substrate patterns are designed to control the position and orientation of the induced nuclei. The mechanism, validity and efficiency of this scheme is examined using 2D and 3D computer simulations of cylinder-forming block copolymer–homopolymer blends, demonstrating that large-scale perfectly ordered patterns can be produced by controlling the position and orientation of induced multiple nucleation events. This scheme, combining the nucleation event of block copolymer self-assembly with the direction of the patterned surface, can be used in the lithography technique of block copolymers to significantly improve the directing efficiency, i.e., the density multiplication.

Ordering kinetics of block copolymers directed by periodic two-dimensional rectangular fields.

The ordering kinetics of directed assembly of cylinder-forming diblock copolymers is investigated by cell dynamics simulation of the time-dependent Ginzburg-Landau theory. The directing field, mimicking chemically or topologically patterned surfaces, is composed of a rectangular array of potential wells which are attractive to the minority blocks. The period of the templating fields is commensurate with the hexagonal lattice of the block copolymer domains. The ordering kinetics is described by the time evolution of the defect concentration, which reveals that the rectangular field of [1 m] for a given density multiplication has the best directing effect, and the reversed case of [m 1] has the worst. Compared with a hexagonal directing field, the rectangular field provides a better directing efficiency for a fixed high density multiplication. The difference of the directing effect can be understood by analyzing the ordering mechanisms in the two types of directing fields. The study reveals that the rectangular pattern is an alternative candidate to direct block copolymer assembly toward large-scale ordered domains.

Formation of Nonclassical Ordered Phases of AB-Type Multiarm Block Copolymers.

The formation of ordered phases from block copolymers is driven by a delicate balance between the monomer-monomer interaction and chain configurational entropy. The configurational entropy can be regulated by designed chain architecture, resulting in a new entropy-driven mechanism to control the self-assembly of ordered phases from block copolymers. An effective routine to regulate the configurational entropy is to utilize multiarm architecture, in which the entropic contribution to the free energy could be qualitatively controlled by the fraction of bridging configurations. As an illustration of this mechanism, the phase behavior of two AB-type multiarm block copolymers, B0-(Bi-Ai)m and (B1-Ai-B2)m where the minority A blocks form cylindrical or spherical domains, are examined using the self-consistent field theory (SCFT). The SCFT results demonstrate that the packing symmetry of the cylinders or spheres can be controlled by the length of the bridging B blocks. Several nonclassical ordered phases, including a novel square array cylinder with p4mm symmetry, are predicted to form from the AB-type multiarm block copolymers.

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.