Phase behaviors of cyclic diblock copolymers

Blending Linear and Cyclic Block Copolymers to Manipulate Nanolithographic Feature Dimensions

Block copolymers (BCPs) consist of two or more covalently bound chemically distinct homopolymer blocks. These macromolecules have emerging applications in photonics, membrane separations, and nanolithography stemming from their self-assembly into regular nanoscale structures. Theory suggests that cyclic BCPs should form features up to 40% smaller than their linear analogs while also exhibiting superior thin-film stability and assembly dynamics. However, the complex syntheses required to produce cyclic polymers mean that a need for pure cyclic BCPs would present a challenge to large-scale manufacturing. Here, we employ dissipative particle dynamics simulations to probe the self-assembly behavior of cyclic/linear BCP blends, focusing on nanofeature size and interfacial width as these qualities are critical to nanopatterning applications. We find that for mixtures of symmetric cyclic and linear polymers with equivalent lengths, up to 10% synthetic impurity has a minimal impact on cyclic BCP feature dimensions and interfacial roughness. On the other hand, blending with cyclic BCPs provides a route to "fine-tune" linear BCP feature sizes. We analyze simulated blend domain spacings within the context of strong segregation theory and find significant deviations between simulation and theory that arise from molecular-level packing motifs not included in theory. These insights into blend self-assembly will assist experimentalists in rationally designing BCP materials for advanced nanolithography applications.

Highly Ordered Nanoscale Film Morphologies of Block Copolymers Governed by Nonlinear Topologies

Among many properties of cyclic block copolymers, the notable domain spacing (d-spacing) reduction offers nonlinear topology as an effective tool for developing block copolymers for nanolithography. However, the current consensus regarding the topology-morphology correlation is ambiguous and in need of more studies. Here we present the morphological investigation on nanoscale films of cyclic and tadpole-shaped poly(n-decyl glycidyl ether-block-2-(2-(2-methoxyethoxy)ethoxy)ethyl glycidyl ether)s and their linear counterpart via synchrotron grazing-incidence X-ray scattering. All copolymers form phase-separated nanostructures, in which only the nonlinear copolymers form highly ordered and unidirectional nanostructures. Additionally, d-spacings of cyclic and tadpole-shaped block copolymers are 49.3-53.7% and 25.0-32.5% shorter than that of their linear counterpart, respectively, exhibiting greater or comparable d-spacing reductions against the experimentally and theoretically achieved values from the literature. Overall, this study demonstrates that cyclic and tadpole topologies can be utilized in developing materials with miniaturized dimensions, high structural ordering, and unidirectional orientation for various nanotechnology applications.

Simplicity in mean-field phase behavior of two-component miktoarm star copolymers

Using self-consistent field theory, we systematically explore the microphase separation in the class of two-component miktoarm star copolymers containing a single conjunction point between different blocks by considering an extended list of candidate microphases. We plot mean-field phase diagrams in the plane of segregation strength and composition for an array of representative star copolymers. Three principal phase diagram topologies, dictated by different phase stabilities, are exposed, displaying a hierarchy in complexity by increasing the molecular asymmetry. Our investigation indicates that the phase diagram topology depends on the ratios of arm numbers and Kuhn segment lengths, which highlights the role of the coordination number ratio between different polymers at the domain interface. These findings reveal the simplicity of the general phase behavior and suggest a complete list of stable microphases for the entire class, which provide useful insight into studying copolymers with more complicated architectures and conformational properties.

Correlations of nanoscale film morphologies and topological confinement of three-armed cage block copolymers

Three-armed cage block copolymers composed of immiscible blocks in near equivalent volume fractions formed topologically controlled sub-10 nm cylindrical and lamellar nanostructures in nanoscale films.

Bicyclic Topology Transforms Self-Assembled Nanostructures in Block Copolymer Thin Films

Ongoing efforts in materials science have resulted in linear block copolymer systems that generate nanostructures via the phase separation of immiscible blocks; however, such systems are limited with regard to their domain miniaturization and lack of orientation control. We overcome these limitations through the bicyclic topological alteration of a block copolymer system. Grazing incidence X-ray scattering analysis of nanoscale polymer films revealed that bicyclic topologies achieve 51.3-72.8% reductions in domain spacing when compared against their linear analogue, which is more effective than the theoretical predictions for conventional cyclic topologies. Moreover, bicyclic topologies achieve unidirectional orientation and a morphological transformation between lamellar and cylindrical domains with high structural integrity. When the near-equivalent volume fraction between the blocks is considered, the formation of hexagonally packed cylindrical domains is particularly noteworthy. Bicyclic topological alteration is therefore a powerful strategy for developing advanced nanostructured materials for microelectronics, displays, and membranes.

Lattice self-consistent field calculations of confined symmetric block copolymers of various chain architectures

The effects of chain architecture and confinement on the structure and orientation of lamellae formed by incompressible and symmetric AB-type block copolymer melts confined between two parallel and identical surfaces are investigated using self-consistent field calculations on a simple cubic lattice. Five systems of various chain architectures (linear, ring, and star) and lengths are studied, with their bulk lamellar period L₀ chosen such that they have comparable L₀/R_g, where R_g denotes the ideal-chain radius of gyration. For thin films of thickness D = L₀ confined between two neutral surfaces, we define the rescaled volume fraction profiles of A, B, chain end, and joint segments in the parallel and perpendicular lamellae such that these profiles can be directly compared among the five systems to quantitatively reveal the interplay between the chain-end enrichment near confining surfaces and the surface-induced A-B compatibilization, and how such interplay is affected by the chain architectures (for example, the chain-crowding effects in the star block copolymers). The effects of D and surface preference for one of the blocks are also investigated.

Change in interfacial properties of the blends of linear homopolymers by adding a gradient copolymer with ring architecture

The change in interfacial properties of the blends of immiscible linear A and B homopolymers by the addition of A-B ring gradient copolymers is investigated through a self-consistent field theory. The length of the composition gradient along copolymer chain contours is signified by a gradient number λ spanning 0 to 1. It is shown that the ternary blends with the ring copolymers are affected by screening unfavorable A/B contacts, the doubling-back of copolymer conformations, and the solubility of copolymers in homopolymer-rich phases. Upon the interplay of these effects, interfacial tension and thickness along with the surface adsorption of the copolymer chains in the blends yield mostly a monotonic dependence on λ with some peculiar λ regions, where the former two properties reveal a reverse trend. Discrepancies in such interfacial properties between the blends with the ring copolymers and with the corresponding linear copolymers are attributed again to the action of those determining effects.