Polydispersity-induced macrophase separation in diblock copolymer melts

Low Tg, strongly segregated, ABA triblock copolymers: a rheological and structural study

ABA triblock copolymers can form microphase separated structures where the B blocks form bridges between A domains, leading to reversible networks interesting for a variety of applications such as pressure sensitive adhesives or thermoplastic elastomers. However, a major drawback of these systems is their rapid loss of mechanical properties upon temperature increase. A potential way to circumvent this limitation would be to design ABA triblock copolymers that keep their microphase separation at high temperatures. In this paper, we report on all-soft ABA triblock copolymers having a poly(n-butyl acrylate) (PnBA) central block and poly(heptafluorobutyl acrylate) (PHFBA) outer blocks. By introducing fluorinated units, the incompatibility between the blocks is largely increased, allowing strong segregation between the block domains, which preserve the microphase separation up to high temperatures despite the low glass transition temperature of the blocks, as shown by temperature dependent SAXS measurements. We study the properties of different copolymers, with similar PHFBA volume fractions but different block lengths. Linear shear rheology measurements revealed the presence of a second, low frequency, plateau whose onset and length depend on the PnBA and PHFBA length, respectively. This plateau also persists up to higher temperatures for longer PHFBA blocks.

Stability and Elasticity of Ultrathin Sphere-Patterned Block Copolymer Films

Sphere-patterned ultrathin block copolymer films are potentially interesting for a variety of applications in nanotechnology. We use self-consistent field theory to investigate the elastic response of sphere monolayer films with respect to in-plane shear, in-plane extension, compression deformations, and bending. The relations between the in-plane elastic moduli are roughly compatible with the expectations for two-dimensional elastic systems with hexagonal symmetry, with one notable exception: The pure shear and the simple shear moduli differ from each other by roughly 20%. Even more importantly, the bending constants are found to be negative, indicating that free-standing block copolymer membranes made of only a sphere monolayer are inherently unstable above the glass transition. Our results are discussed in view of the experimental findings.

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.

Effects of a Nanophase-Separated Structure on Mechanical Properties and Proton Conductivity of Acid-Infiltrated Block Polymer Electrolyte Membranes under Non-Humidification

Acid-infiltrated block polymer electrolyte membranes adopting a spherical or lamellar nanophase-separated structure were prepared by infiltrating sulfuric acid (H₂SO₄) into polystyrene-b-poly(4-vinylpyridine)-b-polystyrene (S-P-S) triblock copolymers to investigate the effects of its nanophase-separated structure on mechanical properties and proton conductivities under non-humidification. Lamellae-forming S-P-S/H₂SO₄ membranes with a continuous hard phase generally exhibited higher tensile strength than sphere-forming S-P-S/H₂SO₄ membranes with a discontinuous hard phase even if the same amount of Sa was infiltrated into each neat S-P-S film. Meanwhile, the conductivities of lamellae-forming S-P-S/H₂SO₄ membranes under non-humidification were comparable or superior to those of sphere-forming S-P-S/H₂SO₄ membranes, even though they were infiltrated by the same weight fraction of H₂SO₄. This result is attributed to the conductivities of S-P-S/H₂SO₄ membranes being greatly influenced by the acid/base stoichiometry associated with acid-base complex formation rather than the nanophase-separated structure adopted in the membranes. Namely, there are more free H₂SO₄ moieties that can release free protons contributing to the conductivity in lamellae-forming S-P-S/H₂SO₄ membranes than sphere-forming S-P-S/H₂SO₄, even when the same amount of H₂SO₄ was infiltrated into the S-P-S.

Sedimentation path theory for mass-polydisperse colloidal systems

Both polydispersity and the presence of a gravitational field are inherent to essentially any colloidal experiment. While several theoretical works have focused on the effect of polydispersity on the bulk phase behavior of a colloidal system, little is known about the effect of a gravitational field on a polydisperse colloidal suspension. We extend here the sedimentation path theory to study sedimentation-diffusion-equilibrium of a mass-polydisperse colloidal system: the particles possess different buoyant masses but they are otherwise identical. The model helps to understand the interplay between gravity and polydispersity on sedimentation experiments. Since the theory can be applied to any parent distribution of buoyant masses, it can also be used to study the sedimentation of monodisperse colloidal systems. We find that mass-polydispersity has a strong influence in colloidal systems near density matching for which the bare density of the colloidal particles equals the solvent density. To illustrate the theory, we study crystallization in sedimentation-diffusion-equilibrium of a suspension of mass-polydisperse hard spheres.

Tuning conformational asymmetry in particle-forming diblock copolymer alloys

Self-consistent field theory is employed to compute the phase behavior of binary blends of conformationally asymmetric, micelle-forming diblock copolymers with miscible corona blocks and immiscible core blocks (a diblock copolymer "alloy"). The calculations focus on establishing conditions that promote the formation of Laves phases by tuning the relative softness of the cores of the two different Laves phase particles via independent control of their conformational asymmetries. Increasing the conformational asymmetry of the more spherical particles of the Laves structure has a stabilizing effect, consistent with the expectations of increased imprinting of the Wigner-Seitz cells on the core/corona interface as conformational asymmetry increases. The resulting phase diagram in the temperature-blend composition space features a more stable Laves phase field than that predicted for conformationally symmetric systems. The phase field closes at low temperatures in favor of macrophase separation between a hexagonally-packed cylinder (hex) phase and a body-centered cubic phase. Companion calculations, using an alloy whose components do not produce a hex phase in the neat melt state, suggest that the Laves phase field in such a blend will persist at strong segregation.

Emergence of Hexagonally Close-Packed Spheres in Linear Block Copolymer Melts

The hexagonally close-packed (HCP) sphere phase is predicted to be stable across a narrow region of linear block copolymer phase space, but the small free energy difference separating it from face-centered cubic spheres usually results in phase coexistence. Here, we report the discovery of pure HCP spheres in linear block copolymer melts with A = poly(2,2,2-trifluoroethyl acrylate) ("F") and B = poly(2-dodecyl acrylate) ("2D") or poly(4-dodecyl acrylate) ("4D"). In 4DF diblocks and F4DF triblocks, the HCP phase emerges across a substantial range of A-block volume fractions (circa f_A = 0.25-0.30), and in F4DF, it forms reversibly when subjected to various processing conditions which suggests an equilibrium state. The time scale associated with forming pure HCP upon quenching from a disordered liquid is intermediate to the ordering kinetics of the Frank-Kasper σ and A15 phases. However, unlike σ and A15, HCP nucleates directly from a supercooled liquid or soft solid without proceeding through an intermediate quasicrystal. Self-consistent field theory calculations indicate the stability of HCP is intimately tied to small amounts of molar mass dispersity (Đ); for example, an HCP-forming F4DF sample with f_A = 0.27 has an experimentally measured Đ = 1.04. These insights challenge the conventional wisdom that pure HCP is difficult to access in linear block copolymer melts without the use of blending or other complex processing techniques.

Rapid access to discrete and monodisperse block co-oligomers from sugar and terpenoid toward ultrasmall periodic nanostructures

Discrete block co-oligomers (BCOs) are gaining considerable attention due to their potential to form highly ordered ultrasmall nanostructures suitable for lithographic templates. However, laborious synthetic routes present a major hurdle to the practical application. Herein, we report a readily available discrete BCO system that is capable of forming various self-assembled nanostructures with ultrasmall periodicity. Click coupling of propargyl-functionalized sugars (containing 1-7 glucose units) and azido-functionalized terpenoids (containing 3, 4, and 9 isoprene units) afforded the discrete and monodisperse BCOs with a desired total degree of polymerization and block ratio. These BCOs microphase separated into lamellar, gyroid, and cylindrical morphologies with the domain spacing (d) of 4.2-7.5 nm. Considering easy synthesis and rich phase behavior, presented BCO systems could be highly promising for application to diverse ~4-nm nanofabrications.

Phase behavior of AB/CD diblock copolymer blends via coarse-grained simulation

The phase diagram of equimolar blends of AB and CD diblock copolymers has been studied using dissipative particle dynamics. All unlike blocks interacted with the same χ, except for the B-C interaction, for which χ_BC < 0 in order to prevent macrophase separation. The BC interaction was able to prevent macrophase separation except for low volume fractions of B and C (φ_BC⪅ 0.1) and relatively equal fractions of A and D. For high φ_BC (φ_BC⪆ 0.92), a disordered state was obtained. For all microphase separated states the shapes/morphologies were described by the ratios of the eigenvalues of the radius of gyration tensor and their sphericity. These were used to classify the domains as forming sphere, cylinders, lamellae, or branched/gyroidal structures. For φ_BC < 0.5 the BC domains acted as an interfacial region which compatibilized the A and D domains, while for φ_BC > 0.5 the BC domain filled in the space between A and D domains. Several interesting structures were formed including a novel connected/branched spheres morphology, hierarchical lamellae, concentric spheres/cylinders, and a combination of cylinders/lamellae. Comparisons are made with the linear diblock and linear triblock phase diagrams.

On the nitroxide mediated polymerization of methacrylates derived from bio-sourced terpenes in miniemulsion, a step towards sustainable products

The typical use of toxic solvents, expensive control agents and the need of intermediate purification steps hinders the introduction of bio-sourced monomers into industrially viable block copolymers. This study aims at overcoming these limitations.

Block copolymers containing stable radical and fluorinated blocks with long-range ordered morphologies prepared by anionic polymerization

We report a facile synthetic approach to create stable radical block copolymers containing a secondary fluorinated block via anionic polymerization using a bulky, sterically hindered countercation composed of a sodium ion and di-benzo-18-crown-6 complex. The synthetic conditions described in this report allowed for controlled molecular weights and dispersity (<1.3) of both homopolymers: poly(2,2,6,6-tetramethyl-1-piperidinyloxy-methacrylate) (PTMA) and poly(2,2,2-trifluoroethyl methacrylate) (PTFEMA) as well as their block copolymers (PTMA-b-PTFEMA). The stable radical concentration of the polymers was determined by electron spin resonance (ESR) and showed radical content above 70%. An analysis of the microphase morphologies in PTMA-b-PTFEMA thin films via atomic force microscopy (AFM) and grazing incidence small angle X-ray scattering (GISAXS) showed clear evidence of long-range ordering of lamellar and cylindrical morphologies with 32 and 36 nm spacing, respectively. The long-range ordering of the morphologies was developed with the aid of two separate neutral layers: PTMA-ran-PTFEMA-ran-poly(hydroxyl ethyl methacrylate) (PHEMA) and poly(isobutyl methacrylate) (PiBMA)-ran-PTFEMA-ran-PHEMA, which helped us corroborate, along with the Zisman method, the surface energy estimation of PTMA to be 30.1 mJ/m2.

Self-assembly of highly asymmetric, poly(ionic liquid)-rich diblock copolymers and the effects of simple structural modification on phase behaviour

A series of ATRP-synthesized poly(IL) diblock copolymers exhibit morphological phase behavior with shifted phase boundaries and alkyl substituent dependent segregation.

Dispersity and architecture driven self-assembly and confined crystallization of symmetric branched block copolymers

Architectural variety in the form of branching combined with disparate dispersities in block polymers have been exploited to access microphase morphologies outside the conventional phase windows typically observed in uniform linear analogs.

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.

Block copolymer electrolytes for fuel cells and secondary batteries, the small angle neutron scattering inputs

This paper aims at giving an overview on the importance of scattering, and more specifically neutron scattering, for probing the nanomorphology of polymer electrolytes made of block copolymers. Two types of self-assembled polymer electrolyte materials will be discussed: (i) the ionomer membranes used in fuel cell and (ii) the solid polyelectrolytes used in secondary batteries. Both are used to physically separate the electrodes in the respective electrochemical devices and are expected to have a high ion transport capacity so as good chemical and mechanical stabilities. Unfortunately, in most cases improving one property leads to the degradation of the others. Nonetheless, through block copolymers selfassembly it is possible to tackle this issue; indeed, antagonist properties can be decoupled and associated within controlled nano-morphologies. This aspect will be discussed and supported by examples based on published studies; in parallel useful scattering analytical tools and models will be presented along the paper and detailed in annex.

Tetragonal phase of cylinders self-assembled from binary blends of AB diblock and (A'B)n star copolymers

The phase behavior of binary blends composed of AB diblock and (A'B)_n star copolymers is studied using the polymeric self-consistent field theory, focusing on the formation and stability of the stable tetragonal phase of cylinders. In general, cylindrical domains self-assembled from AB-type block copolymers are packed into a hexagonal array, although a tetragonal array of cylinders could be more favourable for lithography applications in microelectronics. The polymer blends are designed such that there is an attractive interaction between the A and A' blocks, which increases the compatibility between the two copolymers and thus suppresses the macroscopic phase separation of the blends. With an appropriate choice of system parameters, a considerable stability window for the targeted tetragonal phase is identified in the blends. Importantly, the transition mechanism between the hexagonal and tetragonal phases is elucidated by examining the distribution of the two types of copolymers in the unit cell of the structure. The results reveal that the short (A'B)_n star copolymers are preferentially located in the bonding area connecting two neighboring domains in order to reduce extra stretching, whereas the long AB diblock copolymers are extended to further space of the unit cell.

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.

Stabilizing the Frank-Kasper Phases via Binary Blends of AB Diblock Copolymers

The emergence of the complex Frank-Kasper phases from binary mixtures of AB diblock copolymers is studied using the self-consistent field theory. The relative stability of different ordered phases, including the Frank-Kasper σ and A15 phases containing nonspherical minority domains with different sizes, is examined by a comparison of their free energy. The resulting phase diagrams reveal that the σ phase occupies a large region in the phase space of the system. The formation mechanism of the σ phase is elucidated by the distribution of the two diblock copolymers with different lengths and compositions. In particular, the segregation of the two types of copolymers, occurring among different domains and within each domain, provides a mechanism to regulate the size and shape of the minority domains, thus enhancing the stability of the Frank-Kasper phases. These findings provide insight into understanding the formation of the Frank-Kasper phases in soft matter systems and a simple route to obtain complex ordered phases using block copolymer blends.

Stability of the Frank-Kasper σ-phase in BABC linear tetrablock terpolymers

The phase behavior of B1AB2C tetrablock terpolymer melts is systematically studied using the self-consistent field theory, focusing on the emergence and stability of the complex Frank-Kasper σ-phase. Our study starts with an investigation of the stability region of the σ phase for a generic model of B1AB2C terpolymers, in which the C-blocks form spherical domains immersed in the A/B matrix. Then, we examine the stability of the σ phase for a model system with a specific set of parameters mimicking poly(styrene-b-isoprene-b-styrene-b-ethylene oxide) (SISO) block copolymers which were examined in recent experiments. Our results reveal that the formation of the σ phase is mainly governed by two factors. The first factor is the conformational asymmetry between the A/B-blocks and the C-block, similar to that in conformationally asymmetric AB-type block copolymers. The second factor is the specific chain architecture of B1AB2C. The tetrablock architecture with a specific set of interaction parameters and compositions leads to the formation of large core-shell spherical domains, which amplifies the effect of interfacial energy and thereby stabilizes the σ phase.

Synthesis and Self-Assembly of Discrete Dimethylsiloxane-Lactic Acid Diblock Co-oligomers: The Dononacontamer and Its Shorter Homologues

Most of the theoretical and computational descriptions of the phase behavior of block copolymers describe the chain ensembles of perfect and uniform polymers. In contrast, experimental studies on block copolymers always employ materials with disperse molecular makeup. Although most polymers are so-called monodisperse, they still have a molecular weight dispersity. Here, we describe the synthesis and properties of a series of discrete length diblock co-oligomers, based on oligo-dimethylsiloxane (oDMS) and oligo-lactic acid (oLA), diblock co-oligomers with highly noncompatible blocks. By utilizing an iterative synthetic protocol, co-oligomers with molar masses up to 6901 Da, ultralow molar mass dispersities (Đ ≤ 1.00002), and unique control over the co-oligomer composition are synthesized and characterized. This specific block co-oligomer required the development of a new divergent strategy for the oDMS structures by which both bis- and monosubstituted oDMS derivatives up to 59 Si-atoms became available. The incompatibility of the two blocks makes the final coupling more demanding the longer the blocks become. These optimized synthetic procedures granted access to multigram quantities of most of the block co-oligomers, useful to study the lower limits of block copolymer phase segregation in detail. Cylindrical, gyroid, and lamellar nanostructures, as revealed by DSC, SAXS, and AFM, were generated. The small oligomeric size of the block co-oligomers resulted in exceptionally small feature sizes (down to 3.4 nm) and long-range organization.