Microphase-separated State Research Articles

Phase Separation of FUS with Poly(ADP-ribosyl)ated PARP1 Is Controlled by Polyamines, Divalent Metal Cations, and Poly(ADP-ribose) Structure.

Fused in sarcoma (FUS) is involved in the formation of nuclear biomolecular condensates associated with poly(ADP-ribose) [PAR] synthesis catalyzed by a DNA damage sensor such as PARP1. Here, we studied FUS microphase separation induced by poly(ADP-ribosyl)ated PARP1WT [PAR-PARP1WT] or its catalytic variants PARP1Y986S and PARP1Y986H, respectively, synthesizing (short PAR)-PARP1Y986S or (short hyperbranched PAR)-PARP1Y986H using dynamic light scattering, fluorescence microscopy, turbidity assays, and atomic force microscopy. We observed that biologically relevant cations such as Mg2+, Ca2+, or Mn2+ or polyamines (spermine4+ or spermidine3+) were essential for the assembly of FUS with PAR-PARP1WT and FUS with PAR-PARP1Y986S in vitro. We estimated the range of the FUS-to-PAR-PARP1 molar ratio and the cation concentration that are favorable for the stability of the protein's microphase-separated state. We also found that FUS microphase separation induced by PAR-PARP1Y986H (i.e., a PARP1 variant attaching short hyperbranched PAR to itself) can occur in the absence of cations. The dependence of PAR-PARP1-induced FUS microphase separation on cations and on the branching of the PAR structure points to a potential role of the latter in the regulation of the formation of FUS-related biological condensates and requires further investigation.

Phase behavior of mixtures of hard colloids and soft coarse-grained macromolecules.

Effective "soft" interactions between macromolecules such as polymers, amphiphilic dendrimers, and suitably designed DNA based dendritic molecules have been shown to be purely repulsive and non-diverging. We report the structure and phase behavior of a mixture of hard colloids and soft coarse-grained macromolecules. Through the use of Reference Interaction Site Model theory and molecular dynamics simulations we find that hard colloids and soft macromolecules act as depletants toward each other, generating a medium-induced effective attraction. This effective attraction leads to the formation of non-dispersed phases at high densities. At low and high fractions of hard colloids the system macrophase separates into two disparate regions of hard colloids and soft macromolecules. However, this system microphase separates into a hard-rich and soft-rich self-assembled domains at intermediate compositions. The formation of microphase separated structure in this system of isotropic, disconnected, and purely repulsive colloids is surprising and quite novel. This behavior is likely due to a softening of the interface between hard-rich and soft-rich self-assembled domains. Molecular dynamics simulations have revealed that the microphase separated state has an overall disordered bicontinuous morphology. The hard-rich domain forms an ordered FCC structure and the soft-rich domain forms a disordered cluster-fluid, making the structure simultaneously ordered and disordered.

Effect of the counterion size on microphase separation in charged-neutral diblock copolymers.

In this work, the question of the influence of the counterion size on the self-assembly in melts of diblock copolymers with one charged block was studied using coarse-grained molecular dynamics simulations. It was assumed that the blocks were fully compatible, i.e., the Flory-Huggins parameter χ between them was equal to 0. Due to the presence of correlation attraction (electrostatic cohesion) between the charged species, the systems with all types of counterions underwent transitions to ordered states, forming various morphologies, including lamellae, perforated lamellae, and hexagonally packed cylinders. Phase diagrams were constructed by varying the chain composition fc and locating the order-disorder transition positions in terms of the electrostatic strength parameter λ (dimensionless Bjerrum length). Despite having a rather large ion size mismatch, the systems with smaller counterions demonstrated an even better tendency to form microphase separated states than the systems with larger ones. It was found that the differences between the phase diagrams of the systems with different counterions can be roughly rationalized by using coordinates (volume fraction of the charged block φc-modified interaction parameter λ*). The latter parameter assumes that the electrostatic energy is simply inversely proportional to the characteristic distance between the ions of different signs. Such an approach appeared to be rather effective and allowed the diagrams obtained for different counterion sizes to almost coincide. The results of this work suggest that the counterion size can be used as a tool to control the system morphology as well as the effective incompatibility between the blocks.

Capillary Interfacial Tension in Active Phase Separation.

In passive fluid-fluid phase separation, a single interfacial tension sets both the capillary fluctuations of the interface and the rate of Ostwald ripening. We show that these phenomena are governed by two different tensions in active systems, and compute the capillary tension σ_{cw} which sets the relaxation rate of interfacial fluctuations in accordance with capillary wave theory. We discover that strong enough activity can cause negative σ_{cw}. In this regime, depending on the global composition, the system self-organizes, either into a microphase-separated state in which coalescence is highly inhibited, or into an "active foam" state. Our results are obtained for Active Model B+, a minimal continuum model which, although generic, admits significant analytical progress.

Dynamics of matrix-free nanocomposites consisting of block copolymer-grafted silica nanoparticles under elongation evaluated through X-ray photon correlation spectroscopy

X-ray photon correlation spectroscopy (XPCS) is a powerful tool for investigating the dynamics of polymer nanocomposites. In this study, XPCS was utilized to analyze the dynamics of a matrix-free nanocomposite consisting of poly(methyl methacrylate)-b-poly(butyl acrylate)-g-silica nanoparticles (PMMA-b-PBA-g-SiNPs) during uniaxial elongation and stress relaxation. The effect of the microphase-separated state of PMMA-b-PBA on the dynamics of the SiNP core in the PMMA-b-PBA-g-SiNPs was confirmed at the initial state with temperature-dependence. The SiNPs exhibited a hyperdiffusive and ballistic-like motion in the temperature range of 298–423 K, including at temperatures above and below the glass transition temperature (Tg) of the outer PMMA layer. The SiNPs velocity increased rapidly when the temperature approached the Tg of PMMA. During uniaxial elongation, the PMMA-b-PBA-g-SiNPs exhibited anisotropic dynamics between two directions, namely parallel and perpendicular to elongation. The SiNPs velocity in the direction perpendicular to elongation was faster than those parallel to elongation, despite the small strain, high weight ratio of SiNP, and the large size of SiNP in the PMMA-b-PBA-g-SiNPs. A decrease in the relaxation rate of the SiNPs was also observed by XPCS during stress relaxation at strain = 0.2, which is in the plastic deformation region.

The hierarchical packing of euchromatin domains can be described as multiplicative cascades.

The genome is packed into the cell nucleus in the form of chromatin. Biochemical approaches have revealed that chromatin is packed within domains, which group into larger domains, and so forth. Such hierarchical packing is equally visible in super-resolution microscopy images of large-scale chromatin organization. While previous work has suggested that chromatin is partitioned into distinct domains via microphase separation, it is unclear how these domains organize into this hierarchical packing. A particular challenge is to find an image analysis approach that fully incorporates such hierarchical packing, so that hypothetical governing mechanisms of euchromatin packing can be compared against the results of such an analysis. Here, we obtain 3D STED super-resolution images from pluripotent zebrafish embryos labeled with improved DNA fluorescence stains, and demonstrate how the hierarchical packing of euchromatin in these images can be described as multiplicative cascades. Multiplicative cascades are an established theoretical concept to describe the placement of ever-smaller structures within bigger structures. Importantly, these cascades can generate artificial image data by applying a single rule again and again, and can be fully specified using only four parameters. Here, we show how the typical patterns of euchromatin organization are reflected in the values of these four parameters. Specifically, we can pinpoint the values required to mimic a microphase-separated state of euchromatin. We suggest that the concept of multiplicative cascades can also be applied to images of other types of chromatin. Here, cascade parameters could serve as test quantities to assess whether microphase separation or other theoretical models accurately reproduce the hierarchical packing of chromatin.

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 χBC < 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 (φBC⪅ 0.1) and relatively equal fractions of A and D. For high φBC (φBC⪆ 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 φBC < 0.5 the BC domains acted as an interfacial region which compatibilized the A and D domains, while for φBC > 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.

Power Law Relaxations in Lamellae Forming Brush Block Copolymers with Asymmetric Molecular Shape

We report the linear viscoelasticity of densely grafted poly(styrene)-block-poly(ethylene oxide) (PS-b-PEO) diblock bottlebrush block copolymers (dbBB) of equal mass fraction over a wide range of backbone degree of polymerization (Nbb = 21–119). The difference in side chain length (PS Mn = 2.9 kg/mol, PEO Mn = 5 kg/mol) produces an asymmetry between the molecular shape of the two blocks despite their equal mass fractions. The dbBBs rapidly self-assemble into lamellar morphologies upon thermal annealing. Increasing Nbb results in an increase of domain spacing from d0 = 29 to 90 nm. In the microphase separated melt state, dbBBs are thermorheologically simple and remain unentangled up to large molecular weight (Mw > 500 kg/mol). Oscillatory shear rheology data shows distinct power law relationships analogous to critical gels across a wide range of time scales. The viscoelasticity is expressed by a dual power law relaxation time spectrum H(τ), consisting of relaxation processes at short (n1) and long (n2) tim...

From bulk to microphase separation in scalar active matter: a perturbative renormalization group analysis

We consider a dynamical field theory (Active Model B+) that minimally extends the equilibrium Model B for diffusive phase separation of a scalar field, by adding leading-order terms that break time-reversal symmetry. It was recently shown that such active terms can cause the bulk phase separation of Model B to be replaced by a steady state of microphase separation at a finite length scale. This phenomenon was understood at mean-field level as due to the activity-induced reversal of the Ostwald ripening mechanism, which provides the kinetic pathway to bulk phase separation in passive fluids. This reversal occurs only in certain ranges for the activity parameters. In this paper we go beyond such a mean-field analysis and develop a -loop renormalisation group (RG) approach. We first show that, in the parameter range where bulk phase separation is still present, the critical point belongs formally to the same (Wilson–Fisher) universality class as the passive Model B. In contrast, in a parameter range associated with microphase separation, we find that an unstable non-equilibrium fixed point of the RG flow arises for , colliding with the Wilson–Fisher point in and making it unstable in . At large activity, the flow in this region is towards strong coupling. We argue that the phase transition to microphase separation in active systems, in the physically relevant dimensions and , very probably belongs to a new non-equilibrium universality class. Because it is governed by the strong-coupling regime of the RG flow, our perturbative analysis leaves open the quantitative characterization of this new class.

Cluster Phases and Bubbly Phase Separation in Active Fluids: Reversal of the Ostwald Process

It is known that purely repulsive self-propelled colloids can undergo bulk liquid-vapor phase separation. In experiments and large scale simulations, however, more complex steady states are also seen, comprising a dynamic population of dense clusters in a sea of vapor, or dilute bubbles in a liquid. Here we show that these microphase-separated states should emerge generically in active matter, without any need to invoke system-specific details. We give a coarse-grained description of them, and predict transitions between regimes of bulk phase separation and microphase separation. We achieve these results by extending the $\phi^4$ field theory of passive phase separation to allow for all local currents that break detailed balance at leading order in the gradient expansion. These local active currents, whose form we show to emerge from coarse-graining of microscopic models, include a mixture of irrotational and rotational contributions, and can be viewed as arising from an effective nonlocal chemical potential. Such contributions influence, and in some parameter ranges reverse, the classical Ostwald process that would normally drive bulk phase separation to completion.

Diblock-Copolymer-Based Composites for Tire-Tread Applications with Improved Filler Network Topology

We present in this Letter the results of a study focusing on vulcanized poly(butadiene–styrene butadiene rubber) (PB–SBR) diblock copolymers in the microphase-separated state filled with various amounts of silica nanoparticles. It is demonstrated that the microphase separation of PB and SBR blocks is preserved in composites with a silica mass content of ≤60 parts per hundred rubber (phr). The only effect of silica incorporation is a more restricted long-range order of the block copolymer morphology. The most interesting finding is, however, that through mechanical mixing the silica nanoparticles are highly selectively incorporated in the SBR phase up to high filler contents. This opens new opportunities toward a rational design of the filler network in composites with self-assembled elastomer matrixes and results in advantageous mechanical properties for tire-tread applications.

Rheology in shear and elongation and dielectric spectroscopy of polystyrene-block-poly(4-vinylpyridine) diblock copolymers

We elucidate the influence of composition (weight ratios of 89/11, 76/24 and 49/51) and morphology (spherical, cylindrical and lamellar) on the dielectric and viscoelastic properties in shear and elongation of anionically synthesized polystyrene-block-poly(4-vinylpyridine) (PS-b-P4VP) diblock copolymers in the microphase-separated state. The temperature dependence of the response in both experiments is compared. The analysis of the linear regime shows the appearance of composition (superposition of moduli) and interfacial effects caused by microphase separation (low frequency shoulder, plateau and ω1/2 regime for dynamic moduli and Maxwell-Wagner-Sillars polarization in dielectric experiments). In shear and extensional flows with a constant deformation rate, a pronounced strain-softening behavior in case of a cylindrical and a lamellar morphology appears. For a high weight fraction of the majority phase and a spherical morphology, respectively, strain-softening is observed to a lesser extent. Consequently, strain-softening of diblock copolymer melts can be tuned by the weight/volume ratio of the two blocks.

Intrinsically Hierarchical Nanoporous Polymers via Polymerization-Induced Microphase Separation

The synthesis of microporous polymers generally requires postpolymerization modification via hyper-cross-linking to trap the polymeric network in a state with high void volume. An alternative approach utilizes rigid, sterically demanding monomers to inhibit efficient packing, thus leading to a high degree of free volume between polymer side groups and main chains. Herein we combine polymers of intrinsic microporosity with polymerization-induced microphase separation (PIMS), a versatile methodology for the synthesis of nanostructured materials that can be rendered mesoporous. Copolymerization of various styrenic monomers with divinylbenzene in the presence of a poly(lactide) terminated with a chain-transfer agent (PLA-CTA) results in kinetic trapping of a microphase-separated state. Subsequent etching of PLA provides a bicontinuous mesoporous network. Using equilibrium and kinetic nitrogen sorption experiments as well as positron annihilation lifetime spectroscopy (PALS), we demonstrate that variations in ...

Self-assembly of polymer-linked nanoparticles and scaling behavior in the assembled phase

An entropic depletion-driven phase separation is known to be observed for mixtures of polymers and nanoparticles. While polymer-linked nanoparticles have been synthesized, their phase behavior has only been predicted for chemically specific interactions. We use integral equation theory to determine the structure and phase behavior of chemically isotropic polymer-linked nanoparticles at high densities. When each end of a linear polymer is grafted to a nanoparticle, we predict an entropy-driven microphase separation of locally segregated polymer-rich and nanoparticle-rich domains. The formation of these self-assembled structures is purely a consequence of the shape of the polymer-linked particle species. The depletion-driven demixing of ungrafted polymer-nanoparticle composites (with small amounts of nanoparticles) is enhanced as particle diameter (D) grows compared to the polymer radius of gyration (Rg). However, this study shows that for polymer-linked nanoparticle systems, the transition from a liquid to microphase separated state shifts to higher densities (i.e. is inhibited) as D/Rg increases. The transition volume fractions attain a unique value (of ∼0.69) at D/Rg ∼ 1.13. The repeating length scale (L*) is 1.4-2.2 times the size of the entire species (D + Rg). Surprisingly, L*/(D + Rg) is a non-monotonic function of the polymer radius of gyration. The repeating length scale also displays a remarkable scaling behavior, as a function of the particle diameter and the polymer density. Additionally, our study implies that two different mechanisms of transitioning to the microphase separated state are possible for these systems, which has important implications for the transition density and the kinds of structures formed.

Complex liquid-crystal nanostructures in semiflexible ABC linear triblock copolymers: A self-consistent field theory.

We show that two series of ABC linear triblock copolymers possess sequences of order-to-order phase transitions between microphase-separated states, as the degree of flexibility of the semiflexible middle B-blocks varies. The spatial and orientational symmetries of these phases, some of them containing liquid-crystal ordering, are analysed in comparison with related structures previously determined experimentally and theoretically. A theoretical framework based on the self-consistent field treatment of the wormlike-chain model, which incorporates the Flory-Huggins and Maier-Saupe interactions in the free energy, is used here as a basic foundation for numerical calculations. We suggest that tuning the flexibility parameter, which reduces to the concept of degree of polymerization in the coil-like limit and characterizes the chain-persistency in the rod-like limit, provides a promising approach that can be used to design the resulting microphase-separated structures in semiflexible copolymer melts.

INTERRELATIONS BETWEEN MORPHOLOGY AND SOFTENING BEHAVIOR IN SELF-ASSEMBLED POLY (BUTADIENE-BLOCK-(STYRENE-STAT-BUTADIENE)) COPOLYMERS

ABSTRACTTwo series of poly(butadiene-block-(styrene-stat-butadiene) (PB-SBR) diblock copolymers were synthesized to study interrelations between microphase-separated state and relaxation dynamics. Series I consists of six symmetric PB-SBR samples (ΦSBR ∼ 0.50) with different styrene contents in the random SBR block (21 mol% ≤ xS,SBR ≤ 52 mol%). Series II contains six asymmetric PB-SBR diblock copolymers with almost constant styrene content in the SBR block (xS,SBR = 32 ± 4 mol%) and SBR volume fractions in the range of 0.20 ≤ ΦSBR ≤ 0.69. All PB-SBR diblock copolymers have a total molecular weight of about 200 kg/mol with 1,2-vinyl content of about 8.5 and 15.8 mol% in the soft PB and in the hard SBR block, respectively. A novel synthesis route has been developed so as to maintain low 1,2-vinyl contents in both blocks and a random distribution of the styrene units in the SBR block. The softening behavior of non–cross-linked PB-SBR diblocks was investigated by differential scanning calorimetry, providing first information about miscibility. The morphology of cross-linked PB-SBR diblock copolymers, which have been vulcanized with sulfur at 150 °C using standard procedures, was studied by atomic force microscopy. Dynamic shear measurements aimed at understanding the influence of morphological changes on the segmental dynamics of both phases, αPB and αSBR, were performed on vulcanized samples. Atomic force microscopy results and shear data indicate that symmetric diblock copolymers with styrene content higher than 27 mol% in the SBR block are well microphase separated. Strongly segregated states are also observed for asymmetric diblock copolymers with volume fractions 0.28 ≤ ΦSBR ≤ 0.60 showing cylindrical and lamellar morphologies. The origin of changes in the αPB and αSBR dynamics depending on morphology and segregation strengths is considered. Implications for the use of rubbery PB-SBR block copolymers in composites for tire treads are discussed.

Multiple Glass Transitions of Microphase Separed Binary Liquids Confined in MCM-41

The confinement of fluids in channels of nanometer size presents unprecedented opportunities to reveal emergent physicochemical properties that have no equivalent in the corresponding bulk system. We present an experimental study of fully miscible binary low-molecular weight liquids confined in nanopores. Under these conditions, the mixtures form a microphase-separated state with two regions of different compositions forming the core and the shell of a concentric tubular nanostructure. We combine neutron diffraction and DSC measurements to assess the thermal behavior of this unusual phase. These results show that crystallization is suppressed, leading to glassy behaviors characterized by anomalies in the density and the heat capacity. We reveal the coexistence of two different glass transitions, providing the direct proof for two different enthalpic relaxation times. It leads to the conclusion that the subcomponents of the microphase-separated mixture each obey distinct dynamical behaviors. This phenomeno...

Fluids density functional theory and initializing molecular dynamics simulations of block copolymers.

Classical, fluids density functional theory (fDFT), which can predict the equilibrium density profiles of polymeric systems, and coarse-grained molecular dynamics (MD) simulations, which are often used to show both structure and dynamics of soft materials, can be implemented using very similar bead-based polymer models. We aim to use fDFT and MD in tandem to examine the same system from these two points of view and take advantage of the different features of each methodology. Additionally, the density profiles resulting from fDFT calculations can be used to initialize the MD simulations in a close to equilibrated structure, speeding up the simulations. Here, we show how this method can be applied to study microphase separated states of both typical diblock and tapered diblock copolymers in which there is a region with a gradient in composition placed between the pure blocks. Both methods, applied at constant pressure, predict a decrease in total density as segregation strength or the length of the tapered region is increased. The predictions for the density profiles from fDFT and MD are similar across materials with a wide range of interfacial widths.

Microphase separation in polydisperse rod-rod diblock copolymer melt

The stability limits of the isotropic state of melt of rod-rod AB polydisperse diblock copolymer have been studied within weak segregation theory. The number of units in A block is assumed to be a random variable distributed by the Schulz-Zimm distribution. Inspection of the spinodal curves shows that the copolymer melt with polydisperse rigid blocks is less stable with respect to formation of the nematic and microphase separated states than the monodisperse melt. The values of ratios between strengths of isotropic and anisotropic interactions in the system strongly influences the forms of isotropic-nematic boundary curves.

Fast diffusion-limited lyotropic phase transitions studied in situ using continuous flow microfluidics/microfocus-SAXS.

Fast concentration-induced diffusion-limited lyotropic phase transitions can be studied in situ with millisecond time resolution using continuous flow microfluidics in combination with microfocus small-angle X-ray scattering. The method was applied to follow a classical self-assembly sequence where amphiphiles assemble into micelles, which subsequently assemble into an ordered lattice via a disorder/order transition. As a model system we selected the self-assembly of an amphiphilic block copolymer induced by the addition of a nonsolvent. Using microchannel hydrodynamic flow-focusing, large concentration gradients can be generated, leading to a deep quench from the miscible to the microphase-separated state. Within milliseconds the block copolymers assembly via a spinodal microphase separation into micelles, followed by a disorder/order transition into an FCC liquid-crystalline phase with late-stage domain growth and shear-induced domain orientation into a mesocrystal. A comparison with a slow macroscopic near-equilibrium kinetic experiment shows that the fast structural transitions follow a direct pathway to the equilibrium structure without the trapping of metastable states.