Session K16: Block Copolymer Self-Assembly

Self-consistent field theory study of self-assembly of bottlebrush diblock copolymers

Bottlebrush block copolymers are characterized by densely grafted side chains onto a long polymeric backbone, and this feature enables unique self-assembly properties which are hard to achieve with conventional diblock copolymers. Recent advances of molecular synthesis techniques and designing lamella forming bottlebrush polymers for photonic crystals have led to interests in bottlebrush molecular design for achieving advanced network nanostructure materials. In this talk, we present our recent study on the self-assembly behaviors of bottlebrush diblock copolymers using self-consistent field theory, focusing on the stability of the double gyroid phase in various bottlebrush architectures including coil-bottlebrush copolymers. We found that the dominant effect of increasing side chain length in the architecturally symmetric bottlebrush copolymers is increasing segregation strength by adding segment volumes on the backbones, and the gyroid regions of the phase diagram are almost identical to linear diblock copolymers at equivalent segregation. In contrast, architecturally asymmetric coil-bottlebrush copolymers significantly deflect the gyroid region due to the conformational asymmetry, promoting the spontaneous curvature toward the coil block.   

Modeling chain packing in triply periodic networks of self-assembled block copolymers

Triply periodic network (TPN) phases belong to the natural forms of soft matter self-assembly and underlie a range of attractive function properties. Understanding how a TPN phase is equilibrium among its competitor phases is intricately tied to packing frustration or extension of molecules into centers of the domains, a notion which is ambiguous for TPN phases and confounds attempts to predict thermodynamically optimal packing of molecules. Here, we examine the double gyroid (DG) network phase of block copolymer (BCP) melts, a prototypical amphiphilic system and test the link between terminal boundaries of individual blocks to lie along medial sets, a generic and purely geometric definition of the center of complex domain shapes and the thermodynamics of BCP assembly using geometric formulation of the strong stretching theory of BCP melts. We show that medial packing is essential for equilibrium DG in strongly segregated BCP melts and importantly revise long held notions of packing frustration which assume that terminal boundaries of tubular blocks are constrained to lie along  one-dimensional skeletal graphs. Additionally, we find a previously unrecognized dependence of DG stability on the entropic stiffness asymmetry between tubular and matrix blocks.   

Efficient back-mapping between particle-based and field-theoretic simulations

Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complimentary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct multi-resolution simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models which are then simulated subject to the constraint that their density operators are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. We envision that this method will be useful for whenever free energies, rapid equilibration, molecular configurations and dynamic information are all simultaneously desired.   

Effect of conformational asymmetry on self-assembly of linear–brush block copolymers

Control over morphology and nanostructure size of linear–linear AB block copolymers is achieved by varying the Flory-Huggins interaction parameter, χ, overall degree of polymerization, N, and composition of the block copolymer, f. For nonlinear AB block copolymers, conformational asymmetry also comes into play as the relative sizes of monomers A and B may induce shifts in phase transitions and thermodynamically favor morphologies with curved interfaces at equal f values. We synthesized a series of linear–brush BCP and explored the effect of conformational asymmetry as function of side-chain length on their self-assembly in bulk. We built the corresponding phase diagrams by small-angle X-ray scattering experiments and found that a subtle variation in side-chain length from 5 to 9 units dramatically changes self-assembly behavior. Our findings were confirmed by coarse-grained simulations. By coupling experiments and simulations we will set out to better understand the molecular underpinnings controlling self-assembly in these systems, which will help to finely tune morphology and nanostructure size at mesoscale through molecular architecture design.   

Melt Self-Assembly of Bottlebrush Block Copolymers

Bottlebrush block copolymers are comprised of densely grafted sidechains arranged in chemically distinct blocks along a linear polymer backbone. It is well known experimentally that bottlebrush block copolymers differ from their linear counterparts in the scaling of domain spacing with backbone length; we study this using both self-consistent field theory (SCFT) and fully fluctuating simulations (FTS).  Using SCFT, we map the phase behavior for both symmetrical and asymmetrical arm bottlebrush block copolymers and observe a shifted order-disorder transition. We show that the shift in order-disorder transition in SCFT solely depends on a molecular architecture parameter. The SCFT results show conventional 2/3 scaling of domain size with backbone length, while FTS results to date hint at domain expansion. These studies were performed with varying chain statistics such as continuous Gaussian, discrete Gaussian, and freely-jointed chains; the particular choice having little impact on structure and phase behavior.   

How extreme conformational asymmetry alters the diblock copolymer phase diagram

Conformational asymmetry due to differences in chain flexibility and monomer packing in block copolymers frequently leads to skewing of the phase diagram, and in some cases, entirely new phases of block copolymers. One particularly extreme case of conformational asymmetry is that of a block copolymer consisting of a simple linear block, and a bottlebrush-like polymer block. In systems such as these it has been demonstrated through both strong stretching theory and experiment that the typical diblock phase diagram is drastically altered due to interfacial bending that occurs in order to accommodate the bottlebrush block at the interface. However, existing studies have thus far not examined two key areas of the phase diagram: the order disorder transition, and how it shifts in these extreme cases of asymmetry, and distortion of the phase diagram where the bottlebrush volume fraction is much smaller than the linear block fraction. In this talk I present results answering both of these questions obtained through a simulation study of a model copolymer with asymmetric bottlebrush component.   

The absence of the C36 Laves phase in diblock polymer melts and blends

Under specific conditions, spherical diblock polymer micelles self-assemble into complex spatially periodic packings called Frank-Kasper phases that mimic the packing of atoms in certain metal alloys. Two recently observed examples include the C14 and C15 Laves phases, which are stable phases in AB diblock polymer/core-homopolymer blends. In metals, the C36 Laves phase is also commonly observed in systems similar to those that form C14 and C15. However, C36 has not been observed in any form of soft matter. To provide an explanation for this phenomenon, we used self-consistent field theory to examine the morphology and free energy of Laves phases in both neat diblock polymer melts, where Laves phases are predicted to be metastable, and diblock polymer/core-homopolymer blends. We find that the free energy of the C36 morphology bisects the free energies of C14 and C15 as a result of the structures of these phases, in which C36 is composed of half C14-type layers and half C15-type layers. The presence of this apparent "interfacial energy" penalty between layers, combined with the fact that transitions between Laves phases are expected to be facile in block polymers, suggests that C36 is unlikely to form as a stable self-assembled morphology in diblock polymer systems.   

Determining Structure of Lamellar A-b-(B-r-C) Copolymers with Soft X-ray Reflectivity

Nanostructured polymer thin films have been studied for a variety of applications including electronic transistors, membranes for separations, and bit-patterned media. We have devised a model block copolymer system to systematically tune the interaction parameter, χ, through use of modular A-b-(B-r-C) copolymers. The nanostructure can be tuned by changing the chemical identities of blocks B and C, as well as the molar ratio of component B to C, φ. This modular polymer architecture allows for precise tuning of the block copolymer periodicity, L₀, for a prescribed value of segregation strength, χN. Through resonant soft X-ray reflectivity (RSoXR), we have determined the effect of φ on the interface width and lamellar spacing on thin films of lamellar block copolymers oriented parallel to the substrate. It is hypothesized that the interface width is directly related to the line edge roughness of patterned block copolymers, an important property for applications in directed self-assembly. We will compare the results from reflectivity to measurements of line-edge and width roughness of perpendicular oriented polymer thin films via image analysis of SEM micrographs. Our results provide insights into how copolymer structure affects block copolymer self-assembly and roughness in polymer thin films.   

The effect of structural isomerism on block copolymer self-assembly

The impact of structural isomerism on the self-assembly of block copolymers (BCPs) is generally demonstrated. However, to date, the precise control over structural isomerism of BCPs (SI-BCPs) and a systematic investigation on its effect on thermodynamics have not been fully realized. Here we demonstrate a high throughput platform for a library of well-defined SI-BCPs with identical dispersity and molecular weight. The isomerism is precisely controlled by manipulating the number and position of fluorine atoms of one block. A significant difference in domain periodicities of SI-BCPs was observed. The Flory-Huggins interaction parameter was estimated using self-consistent mean-field theory. The chain conformation of SI-BCPs was measured using scattering techniques. Finally, we believe this systematic investigation of SI-BCPs may lead to a better understanding of the structure-property relationship of polymeric materials and broaden the scope for new polymeric materials.   

Frank-Kasper Phases of Diblock Copolymer Melts Studied with the DPD Model

We have included the dissipative particle dynamics (DPD) model (i.e., compressible melts of discrete Gaussian chains with the DPD potential) into the newly released C++/CUDA version of PSCF¹, and performed real-space self-consistent field (SCF) calculations of the Frank-Kasper (FK) phases formed by diblock copolymer (DBC) melts based on the DPD model. Comparisons with the SCF results based on the “standard” model (i.e., incompressible melts of continuous Gaussian chains with the Dirac d-function potential) clearly reveal the effects of model differences on the stability of FK phases. This also enables us to unambiguously quantify, using DPD simulations, the fluctuation/correlation effects inherently neglected by the SCF theory, which are important to the low-molecular weight DBCs forming such phases in experiments.   

Apex-dependent Frank-Kasper phases from simple second-generation dendron assemblies

The pioneering structures from molecular self-assembly demand the non-classical sphere-packing such as Frank-Kasper (FK) phases to explore self-assembly behaviors. To facilitate these phases, the simple second-generation dendrons were used to perform the rich development of FK phases. This optimal structures of dendrons allow the high potential on apex functionalities which attune the core interactions. These sphere-packing phases are measured and tracked by in-situ small-angle X-ray scattering and FT-IR spectroscopy. The electron density maps of sphere-packing phases are reconstructed from X-ray scattering data to analyze the characteristics of each phase. To establish the phase stability regime from the free energy balance of dendron assemblies, we apply enthalpic/entropic effects which accommodate the core interactions of apex functionalities. Our approach to modulating the core interactions in a basic second-generation dendron assembly envisions a feasible strategy and primitive platform for manipulating diverse sphere-packing FK assemblies and quasiperiodic arrays.   

Lattice Transition of Sphere-forming Block Copolymer Thin Films under Solvent Vapor Annealing

Block copolymer (BCP) can self-assemble into various nanostructures depending on the relative ratio of each block length. Especially, sphere-forming BCPs can exhibit various interesting structures beyond the classical lattice structure, such as the Frank-Kasper phase and Laves phase.

In this study, we report the lattice transition behavior of the sphere-forming BCP thin films under the solvent vapor annealing (SVA) process. Generally, sphere-forming BCP thin films have a hexagonally close-packed (HEX) symmetry. However, we found that the HEX symmetry developed at low solvent fraction transforms into face-centered orthorhombic (FCO) symmetry with increasing the solvent fraction. This structural transformation can be observed consistently in the thickness of 2-8 layers. We found that FCO symmetry can be a stable structure in the solvent swollen state and can be trapped with rapid solvent removal. Furthermore, we show that the transition path is varied with the solvent quality and discuss the overall lattice transitions that the sphere-forming BCP can experience from the interface to the bulk.