Continuous polydispersity in a self-consistent field theory for diblock copolymers

The impact of intramolecular polydispersity on the self-assembly of ABn miktoarm star copolymers

The self-assembly behaviors of AB_n miktoarm star copolymers as one typical type of asymmetric architecture have been studied well in the past few decades due to their deflected phase boundaries. In particular, recently, they have attracted renewed theoretical interest due to their expanded spherical phase region that stabilizes complex Frank-Kasper spherical phases. However, previous theoretical studies have never considered AB_n copolymers with unequal arm lengths, which is more or less the case for synthesized copolymers. In this work, we investigate the self-assembly behaviors of AB_n miktoarm star copolymers with unequal B-arms using self-consistent field theory. We propose an intramolecular polydispersity index (iĐ) to quantify the distribution of unequal B-blocks. Accordingly, we further propose a simple quantity of an effective arm number n_equ = n/iĐ for quantitatively comparing the phase boundaries between various AB_n copolymer samples with different arm numbers or different distributions of B-blocks. Our results indicate that different AB_n copolymers with equal n_equ exhibit similar phase diagrams. On the other hand, we also found that the phase boundaries of two different samples with same n_equ are not exactly overlapped. We speculate that the effect of spontaneous curvature may be mainly controlled by n_equ, but the packing frustration of B-blocks may also be dependent on the other quantities that are closely related to the shape of the distribution of B-arms, such as higher order polydispersity indexes.

General weak segregation theory with an application to monodisperse semi-flexible diblock copolymers

A general theory has been developed for a polydisperse semi-flexible multi-block copolymer melt. Using the Bawendi-Freed approach to model semi-flexible chains, an expression for the Landau free energy is derived in the weak segregation regime, which includes density and orientation order-parameters. The orientation order-parameter is described in the smectic phase and in more complicated structures, such as the hexagonal phase. The Landau free energy contains contributions of two kinds of interactions. The first kind is the Flory-Huggins interaction, which describes the incompatibility of chemically different blocks and may induce microphase separation. The second kind is the Maier-Saupe interaction, which may induce nematic ordering. In the framework of the weak segregation limit, the Landau theory allows us to predict phase structures in the melt as a function of the composition, persistence length, and the strength of the Flory-Huggins and Maier-Saupe interaction. The general theory is applied to a simple system of monodisperse semi-flexible diblock copolymers. In several phase diagrams, a number of possible phase structures are predicted, such as the bcc, hexagonal, smectic-A, smectic-C, and nematic phase. The influence of the Maier-Saupe interaction on the microphase structure is thoroughly discussed.

Experimental and Computational Evaluation of Self-Assembled Morphologies in Diblock Janus Bottlebrush Copolymers

Diblock Janus-type "A-branch-B" bottlebrush copolymers (di-JBBCPs) consist of a backbone with alternating A and B side chains, in contrast to the side chain arrangement of conventional bottlebrush copolymers. As a result, A and B blocks of di-JBBCPs can microphase-separate perpendicular to the backbone, which is located at the interface between the two blocks. A reparametrized dissipative particle dynamics (DPD) model is used to theoretically investigate the self-assembly of di-JBBCPs and to compare with the experimental results of a range of polystyrene-branch-polydimethylsiloxane di-JBBCPs. The experimentally formed cylinder, gyroid, and lamellar morphologies showed good correspondence with the model phase diagram, and the effect of changing volume fraction and backbone length is revealed. The DPD model predicts a bulk-stable perforated lamella morphology together with two unconventional spherical phases, the Frank-Kasper A15 spheres and the hexagonally close-packed spheres, indicating the diversity of morphologies available from complex BCP molecular architectures.

Rectangular Cylinders Formed by Compositionally Bidisperse ABC Triblock Terpolymer Blends: A Self-Consistent Field Theory Study

Compared with traditional cylinders that have circular cross-sections, cylinders with rectangular cross-sections can endow nanomaterials with various novel optical properties and functions. In this work, the formation of the rectangular cylinders self-assembled by compositionally bidisperse ABC triblock terpolymer blends has been investigated via numerical simulations based on self-consistent field theory. The specially designed blending systems are composed of two types of linear ABC triblock terpolymers that have the same total chain lengths and the middle B block chain lengths, but different chain lengths of the side A/C blocks. By tuning the chain length fractions and the interactions between different blocks, rectangular cylinders with a fourfold symmetry pattern were successfully obtained in our simulations. Each rectangular phase domain is self-assembled together by the short and long side blocks of the same species. The simulation results indicate that the selective aggregation of the short side blocks determines the formation of the rectangular cylindrical phase, i.e., the short side blocks prefer to aggregate at the four corners within a rectangular cylindrical phase domain. This simulation result reveals a formation mechanism that is different from the mechanism proposed in previous experiments [Asai ACS Macro Lett., 2014, 3, 166-169]. Moreover, under different middle B block chain length fractions, phase diagrams as a function of the interaction parameter between different blocks and the short side block chain length fraction have been constructed. The phase diagrams show that the parameter window of the rectangular cylinders is considerably expanded by increasing the chain length fraction of the middle B blocks. Our simulation works can provide a theoretical basis for molecular design to regulate and fabricate nanomaterials with nontraditional phase domains in future experiments.

Metallic Nanomeshes Fabricated by Multimechanism Directed Self-Assembly

The directed self-assembly of block copolymers (BCPs) is a powerful motif for the continued scaling of feature sizes for nanoscale devices. A multimechanism directed self-assembly (MMDSA) method is described that generates orthogonal meshes from a polystyrene-b-poly-2-vinylpyridine BCP that is subsequently metallized with Pt. The MMDSA process takes advantage of three different mechanisms, trench wall guidance, edge nucleation, and underlayer guidance, to align the mesh with respect to substrate features. The mechanisms and their interactions are investigated via both experiments and dissipative particle dynamics simulations. MMDSA is applied to produce well-aligned conductive nanomeshes and then is extended to fabricate multicomponent metallic structures with 2D/3D hybrid morphologies.

Tuning dispersity of linear polymers and polymeric brushes grown from nanoparticles by atom transfer radical polymerization

Molecular weight distribution imposes considerable influence on the properties of polymers, making it an important parameter, impacting morphology and structural behavior of polymeric materials.

Fine control of the molecular weight and polymer dispersity via a latent monomeric retarder

A latent monomeric retarder was used for a one-shot polymerization with a defined MW and Đ.

Predictive design of polymer molecular weight distributions in anionic polymerization

Polymer molecular weight distributions are targeted through kinetic modeled with high fidelity based on the temporal control of chain initiation in anionic polymerizations.

Molecular Weight Distribution Shape as a Versatile Approach to Tailoring Block Copolymer Phase Behavior

The molecular weight distributions (MWDs) of block copolymers significantly impact their morphological phase behavior, but exploiting these features as a means to tune material properties has been limited to the MWD breadth, or dispersity (Đ). Manipulation of the entire MWD has promising potential to address this challenge by providing a convenient and versatile route toward tailoring polymer nanostructure. Herein, we describe the self-assembly of poly(styrene)-block-poly(2-vinylpyridine) (PS-b-P2VP) where the PS blocks have systematically deviating compositions of molecular weights. We find that controlling the MWD shape, breadth and skew, afforded access to different morphologies in samples with the same molecular characteristics, including Đ. As such, we illustrate the generality and effectiveness of this strategy and anticipate that it will facilitate the increased deployment of disperse polymer compositions in advanced materials applications.

Domain swelling in ARB-type triblock copolymers via self-adjusting effective dispersity

We investigated the domain spacing of an ordered structure formed by polydisperse ARB-type triblock copolymers (triBCPs) with random middle R blocks consisting of A and B monomers. ARB-type triBCPs were synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization, and the dispersities of all samples were controlled as narrow as ∼1.2. From the bulk and film morphologies, it was found that the domain swelling increases as the content of middle R blocks increases, which implies that the middle R block even with a small content plays a critical role in dilating the domain spacing. Since the random middle R blocks are energetically neutral, they can be segregated into either A or B blocks. The strong stretching theory (SST) suggests that the dispersities of the resulting constituent blocks are maximized to reduce the elastic energy associated with chain stretching, thereby leading to the dilation of domain spacing.

Effects of Tailored Dispersity on the Self-Assembly of Dimethylsiloxane-Methyl Methacrylate Block Co-Oligomers

The effect of dispersity on block polymer self-assembly was studied in the monodisperse limit using a combination of synthetic chemistry, matrix-assisted laser desorption ionization spectroscopy, and small-angle X-ray scattering. Oligo(methyl methacrylate) (oligoMMA) and oligo(dimethylsiloxane) (oligoDMS) homopolymers were synthesized by conventional polymerization techniques and purified to generate an array of discrete, semidiscrete, and disperse building blocks. Coupling reactions afforded oligo(DMS-MMA) block polymers with precisely tailored molar mass distributions spanning single molecular systems (Đ = 1.0) to low-dispersity mixtures (Đ ≈ 1.05). Discrete materials exhibit a pronounced decrease in domain spacing and sharper scattering reflections relative to disperse analogues. The order-disorder transition temperature (T_ODT) also decreases with increasing dispersity, suggesting stabilization of the disordered phase, presumably due to the strengthening of composition fluctuations at the low molar masses investigated.

Universality between Experiment and Simulation of a Diblock Copolymer Melt

The equivalent behavior among analogous block copolymer systems involving chemically distinct molecules or mathematically different models has long hinted at an underlying universality, but only recently has it been rigorously demonstrated by matching results from different simulations. The profound implication of universality is that simple coarse-grained models can be calibrated so as to provide quantitatively accurate predictions to experiment. Here, we provide the first compelling demonstration of this by simulating a polyisoprene-polylactide diblock copolymer melt using a previously calibrated lattice model. The simulation successfully predicts the peak in the disordered-state structure function, the position of the order-disorder transition, and the latent heat of the transition in excellent quantitative agreement with experiment. This could mark a new era of precision in the field of block copolymer research.

"Shaping" the Future of Molecular Weight Distributions in Anionic Polymerization

Varying molecular weight distributions (MWDs) have the potential to precisely tune polymer properties, but this approach remains relatively unexplored owing to a lack of synthetic methods that provide control over the exact makeup of a distribution. Herein, we report a simple and highly efficient strategy for addressing this challenge through temporal regulation of initiation in the anionic polymerization of styrene. This method yields unprecedented control over the shape of the polymer MWD and facilitates the synthesis of diblock copolymers with controlled MWD compositions. Importantly, we show that the MWD symmetry has a marked influence on the stiffness of poly(styrene-block-isoprene) copolymers, which demonstrates that varying MWD shape is an effective method for altering polymer properties.

Density functional theory of equilibrium random copolymers: application to surface adsorption of aggregating peptides

We generalize a recently developed polymer density functional theory (PDFT) for polydisperse polymer fluids to the case of equilibrium random copolymers. We show that the generalization of the PDFT to these systems allows us to obtain a remarkable simplification compared to the monodispersed polymers. The theory is used to treat a model for protein aggregation into linear filaments in the presence of surfaces. Here we show that, for attractive surfaces, there is evidence of significant enhancement of protein aggregation. This behaviour is a consequence of a surface phase transition, which has been shown to occur with ideal equilibrium polymers in the presence of sufficiently attractive surfaces. For excluding monomers, this transition is suppressed, though an echo of the underlying ideal transition is present in the sudden change in the excess adsorption.

Disorder to Order Transition and Ordered Morphology of Coil-Comb Block Copolymer by Self-Consistent Field Theory

The disorder to order transition and the ordered patterns near the disordered state of coil-comb copolymer A-b-(B m + 1-g-C m ) are investigated by the self-consistent field theory. The phase diagrams of coil-comb copolymer are obtained by varying the composition of the copolymer with the side chain number m = 1, 2, and 3. The disorder to order transition is far more complex compared with the comb copolymer or linear block copolymer. As the side chain number m increases, the Flory-Huggins interaction parameter of disorder to order transition (DOT) increases and the lowest DOT occurs when the volume fractions of blocks A, B, and C are approximately equal. When one component is the minority, the disorder to order transition curve is similar with binary copolymer, but the curve shows the asymmetric property. The comb copolymer is more stable with larger side chain number m and shorter side chain. The ordered patterns from the disordered state are discussed. The results are helpful for designing coil-comb copolymers and obtaining the ordered morphology.

Simulation study of the effect of molar mass dispersity on domain interfacial roughness in lamellae forming block copolymers for directed self-assembly

A coarse-grained molecular dynamics model was used to study the thin film self-assembly and resulting pattern properties of block copolymer (BCP) systems with various molar mass dispersities. Diblock copolymers (i.e. A-b-B type) were simulated in an aligned lamellar state, which is one of the most common patterns of potential use for integrated circuit fabrication via directed self-assembly of BCPs. Effects of the molar mass dispersity (Ð) on feature pitch and interfacial roughness, which are critical lithographic parameters that have a direct impact on integrated circuit performance, were simulated. It was found that for a realistic distribution of polymer molecular weights, modeled by a Wesslau distribution, both line edge roughness (LER) and line width roughness (LWR) increase approximately linearly with increasing Ð, up to ∼45% of the monodisperse value at Р= 1.5. Mechanisms of compensation for increased A-A and B-B roughness were considered. It was found that long and short chain positions were not correlated, and that long chains were significantly deformed in shape. The increase in LWR was due to the increase in LER and a constant correlation between the line edges. Unaligned systems show a correlation between domain width and local molecular weight, while systems aligned on an alternating pattern of A and B lines did not show any correlation. When the volume fraction of individual chains was allowed to vary, similar results were found when considering the Ð of the block as opposed to the Ð of the entire system.

Microphase separation in thin films of lamellar forming polydisperse di-block copolymers

Effects of polydispersity in chain lengths on microphase separation in thin films of di-block copolymers are studied using self-consistent field theory (SCFT) and neutron reflectivity experiments.

Phase diagrams of block copolymer melts by dissipative particle dynamics simulations

Phase diagrams for monodisperse and polydisperse diblock copolymer melts and a random multiblock copolymer melt are constructed using dissipative particle dynamics simulations. A thorough visual analysis and calculation of the static structure factor in several hundreds of points at each of the diagrams prove the ability of mesoscopic molecular dynamics to predict the phase behavior of polymer systems as effectively as the self-consistent field-theory and Monte Carlo simulations do. It is demonstrated that the order-disorder transition (ODT) curve for monodisperse diblocks can be precisely located by a spike in the dependence of the mean square pressure fluctuation on χN, where χ is the Flory-Huggins parameter and N is the chain length. For two other copolymer types, the continuous ODTs are observed. Large polydispersity of both blocks obeying the Flory distribution in length does not shift the ODT curve but considerably narrows the domains of the cylindrical and lamellar phases partially replacing them with the wormlike micelle and perforated lamellar phases, respectively. Instead of the pure 3d-bicontinuous phase in monodisperse diblocks, which could be identified as the gyroid, a coexistence of the 3d phase and cylindrical micelles is detected in polydisperse diblocks. The lamellar domain spacing D in monodisperse diblocks follows the strong-segregation theory prediction, D∕N(1∕2) ~ (χN)(1∕6), whereas in polydisperse diblocks it is almost independent of χN at χN < 100. Completely random multiblock copolymers cannot form ordered microstructures other than lamellas at any composition.

Phase Behavior of Tapered Diblock Copolymers from Self-Consistent Field Theory

Tapered diblock copolymers are similar to AB diblock copolymers, but the sharp junction between the A and B blocks is replaced with a gradient region in which composition varies from mostly A to mostly B along its length. The A side of the taper can be attached to the A block (normal) or the B block (inverse). We demonstrate how taper length and direction affect the phase diagrams and density profiles using self-consistent field theory. Adding tapers shifts the order-disorder transition to lower temperature versus the diblock, and this effect is larger for longer tapers and for inverse tapers. However, tapered systems' phase diagrams and interfacial profiles do not simply match those of diblocks at a shifted effective temperature. For instance, we find that normal tapering widens the bicontinuous gyroid region of the phase diagram, while inverse tapering narrows this region, apparently due to differences in polymer organization at the interfaces.