Phase Behavior Of Copolymers Research Articles

Lyotropic Phase Behavior of Coil-Bottlebrush Diblock Copolymers in Alkylimidazolium-Based Ionic Liquids

Lyotropic Phase Behavior of Coil-Bottlebrush Diblock Copolymers in Alkylimidazolium-Based Ionic Liquids

Molecular Simulations Revealing Effects of Non-concatenated Ring Topology on Phase Behavior of Symmetric Diblock Copolymers

Molecular Simulations Revealing Effects of Non-concatenated Ring Topology on Phase Behavior of Symmetric Diblock Copolymers

Phase behavior of triblock copolymer and homopolymer blends: Effect of copolymer topology

Two distinct linear triblock copolymers with different block sequences, ABA or BAB, are obtained when two identical AB diblock copolymers are jointed at their B or A ends, respectively, resulting in three homologous, AB diblock, ABA, and BAB triblock copolymers with the same chemical composition but different topologies. We demonstrate that the topological effect on the phase behaviors of these copolymers is amplified when A homopolymers are added to the system. Specifically, the phase behaviors of binary blends composed of ABA or BAB linear triblock copolymers and A homopolymers are studied by using the random-phase approximation (RPA) and self-consistent field theory (SCFT). The RPA analysis predicts that the Lifshitz point for the ABA/A blends behaves like a second-order transition but that for the BAB/A blends behaves like a first-order transition. The Lifshitz point of the BAB/A mixtures is found to occur at a much lower homopolymer concentration than that of the ABA/A mixtures, indicating a poorer miscibility of the A homopolymers into the BAB than ABA triblocks, which is also confirmed by SCFT. For sphere-forming triblock copolymers mixed with homopolymers, the poorer miscibility and the more diffused distribution of the A homopolymers in the BAB/A blends result in a phase behavior drastically different from that of the ABA/A and AB/A blends. The ABA/A blends stabilize the Frank-Kasper (FK) phases similar to the AB/A blends, but the stability window of FK phases becomes negligibly small in the corresponding BAB/A blends. Our results demonstrate that the topological effect of block copolymers on the equilibrium phase behaviors can be more prominent in multicomponent systems and thus more attention should be paid to copolymer topologies in the design of polymeric blends. Published by the American Physical Society 2024

Phase behavior of symmetric diblock copolymers under 3D soft confinement.

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using self-consistent field theory. Soft confinement is realized in binary blends composed of AB diblock copolymers and C homopolymers, where the copolymers self-assemble to form a droplet embedded in a homopolymer matrix. The phase behavior of the confined block copolymers is regulated by the degree of confinement and the selectivity of the homopolymers, resulting in a rich variety of novel structures. When the C homopolymers are neutral to the A- and B-blocks, stacked lamellae (SL) are formed where the number of layers increases with the droplet volume, resulting in a morphological transition sequence from Janus particles to square SL. When the C homopolymers are strongly selective for the B-blocks, a series of non-lamellar morphologies, including onion-, hamburger-, cross-, ring-, and cookie-like structures, are observed. A detailed free energy analysis reveals a first-order reversible transformation between SL and onion-like (OL) structures when the selectivity of the homopolymers is changed. Our results provide a comprehensive understanding of how various factors, such as the copolymer concentration, homopolymer chain length, degree of confinement, and homopolymer selectivity, affect the self-assembled structures of diblock copolymers under soft 3D confinement.

The mechanism underlying the transitions between stripes, helices, and stacked toroids in the cylindrical shell formed by AB diblock copolymers on a long nanocylinder.

The self-assembly of block copolymers on nanocylinders has attracted a lot of interest due to its potential application in biomedicine and other fields. In this study, the self-assembly phase behavior of AB diblock copolymers on long nanocylinders in soft confinement has been studied by using a simulated annealing method. A square phase diagram of the morphology was constructed by increasing the number of chains of copolymers (cn) and the cylindrical diameter (D). As a result, morphological transitions from striped to helical and axially stacked toroids, as well as reversible transitions, started to appear. By analyzing the chain packing in a fan-shaped region and calculating the mean-square end-to-end distance (DEE2) of the copolymers and number of AB contacts, both types of transitions were found to be driven by the competition between conformational entropy and AB interfacial energy. The number of stripes increased and the helical angle decreased with the increase in cylinder diameter. The chirality of the helix was found to be random.

Phase Behavior and Structure of Poloxamer Block Copolymers in Protic and Aprotic Ionic Liquids.

Ionic liquids are promising media for self-assembling block copolymers in applications such as energy storage. A robust design of block copolymer formulations in ionic liquids requires fundamental knowledge of their self-organization at the nanoscale. To this end, here, we focus on modeling two-component systems comprising a Poly(ethylene oxide)-poly (propylene oxide)-Poly(ethylene oxide) (PEO-PPO-PEO) block copolymer (Pluronic P105: EO37PO58EO37) and room temperature ionic liquids (RTILs): protic ethylammonium nitrate (EAN), aprotic ionic liquids (1-butyl-3-methylimidazolium hexafluorophosphate (BMIMPF6), or 1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4). Rich structural polymorphism was exhibited, including phases of micellar (sphere) cubic, hexagonal (cylinder), bicontinuous cubic, and lamellar (bilayer) lyotropic liquid crystalline (LLC) ordered structures in addition to solution regions. The characteristic scales of the structural lengths were obtained using small-angle X-ray scattering (SAXS) data analysis. On the basis of phase behavior and structure, the effects of the ionic liquid solvent on block copolymer organization were assessed and contrasted to those of molecular solvents, such as water and formamide.

Tuning Cocrystallization, Microphase Separation, and Optical Property of All-Conjugated Triblock Copolymers by Molecular Engineering

Compared to the widely studied classical coil–coil block copolymers (BCPs) with well-established phase diagram and recent advances achieved in all-conjugated diblock copolymers, the investigation into the phase behavior of all-conjugated triblock copolymers is rather limited. In this work, we prepare a series of triblock copolymers containing various poly(3-alkylthiophene)s (P3ATs), interrogate their phase transition between cocrystallization and microphase separation adjusted by a set of molecular parameters (alkyl side chains, block ratios, and block sequences), and correlate these different structures strongly to their optical properties. Poly(3-butylthiophene) (P3BT), poly(3-hexylthiophene) (P3HT), poly(3-(2′-ethyl)hexylthiophene) (P3EHT), poly(3-octylthiophene) (P3OT), and poly(3-dodecylthiophene) (P3DDT) are selected, in which P3EHT has a much less crystalline capability than the other four components. Interestingly, when the P3EHT block is situated in the BCP middle position (P3BT-b-P3EHT-b-P3AT), a smaller side chain difference between the two outer P3BT and P3AT blocks and the P3EHT with a shorter main chain length favor cocrystallization in the triblock copolymers over microphase separation. Moreover, when changing the block sequence to place the P3EHT block at two terminals (P3OT-b-P3BT-b-P3EHT and P3BT-b-P3OT-b-P3EHT), they display stronger cocrystalline capability than P3BT-b-P3EHT-b-P3OT with the P3EHT in the central. At last, these various crystalline structures are related to their optical properties. This work demonstrates the tuning of the phase transition between cocrystalline and microphase-separated structures in conjugated triblock copolymers via molecular engineering, which correlate closely to their optical properties and may underpin their applications in optoelectronic devices.

Competitive Effects of Hydrogen Bonds and Molecular Weights on the Phase and Crystallization Behaviors of Binary Block Copolymers

Competitive Effects of Hydrogen Bonds and Molecular Weights on the Phase and Crystallization Behaviors of Binary Block Copolymers

Emergent Sequence Biasing in Step-Growth Copolymerization: Influence of Non-Bonded Interactions and Comonomer Reactivities.

The phase behavior and material properties of copolymers are intrinsically dependent on their primary comonomer sequences. Achieving precise control over monomer sequence in synthetic copolymerizations is challenging, as sequence determination is influenced not only by the reaction conditions and the properties of the reactants but also by the statistical nature of the copolymerization process itself. Mayo-Lewis reactivity ratios are often used to predict copolymer composition and sequence and are based on ratios of static reactivity constants. However, prior results have demonstrated that in a generic, solution-based step-growth A,B-copolymerization, relatively weak non-bonded attractions between certain monomer pairs induce emergent microphase separations. Such polymerization-driven separations lead to deviations from standard kinetics due to the emergent heterogeneities in reactant concentrations, which can also cause significant shifts in the resulting copolymer sequences. Previously, these effects were observed in systems where the activation energies were equal for all reaction pathways, that is, between all monomer pair combinations. In this work, we explore the combined effects on copolymerization kinetics of differences in both activation energies and non-bonded attractions between monomers and examine the sequences produced within this same step-growth copolymerization model. Our results indicate that altering activation energies influences the kinetics and sequences in a manner that also depends on the non-bonded attractions, showing that these effects may work in concert or in opposition to one another to bias the sequences formed. Non-standard kinetic behaviors and long-range sequence biasing are observed under certain conditions, and the extent of each clearly shifts as the reaction proceeds. These findings provide insight into the complex interplay between sequence and nascent oligomer phase behavior, highlighting the potential for exploiting emergent phase properties in the informed design of advanced sequence-biased materials.

Synthesis, Molecular Characterization, and Phase Behavior of Miktoarm Star Copolymers of the ABn and AnB (n = 2 or 3) Sequences, Where A Is Polystyrene and B Is Poly(dimethylsiloxane)

Synthesis, Molecular Characterization, and Phase Behavior of Miktoarm Star Copolymers of the AB_<i>n</i> and A_<i>n</i>B (<i>n</i> = 2 or 3) Sequences, Where A Is Polystyrene and B Is Poly(dimethylsiloxane)

Random Forest Predictor for Diblock Copolymer Phase Behavior.

Physics-based models are the primary approach for modeling the phase behavior of block copolymers. However, the successful use of self-consistent field theory (SCFT) for designing new materials relies on the correct chemistry- and temperature-dependent Flory-Huggins interaction parameter χAB that quantifies the incompatibility between the two blocks A and B as well as accurate estimation of the ratio of Kuhn lengths (bA/bB) and block densities. This work uses machine learning to model the phase behavior of AB diblock copolymers by using the chemical identities of blocks directly, obviating the need for measurement of χAB and bA/bB. The random forest approach employed predicts the phase behavior with almost 90% accuracy after training on a data set of 4768 data points, almost twice the accuracy obtained using SCFT employing χAB from group contribution theory. The machine-learning model is notably sensitive toward the uncertainty in measuring molecular parameters; however, its accuracy still remains at least 60% even for highly uncertain experimental measurements. Accuracy is substantially reduced when extrapolating to chemistries outside the training set. This work demonstrates that a random forest phase predictor performs remarkably well in many scenarios, providing an opportunity to predict self-assembly without measurement of molecular parameters.

Sub-3-Nanometer Domain Spacings of Ultrahigh-χ Multiblock Copolymers with Pendant Ionic Groups.

We investigated the temperature-dependent phase behavior and interaction parameter of polyethylene-based multiblock copolymers with pendant ionic groups. These step-growth polymers contain short polyester blocks with a single Li+SO3- group strictly alternating with polyethylene blocks of x-carbons (PESxLi, x = 12, 18, 23). At room temperature, these polymers exhibit layered morphologies with semicrystalline polyethylene blocks. Upon heating above the melting point (∼130 °C), PES18Li shows two order-to-order transitions involving Ia3̅d gyroid and hexagonal morphologies. For PES12Li, an order-to-disorder transition accompanies the melting of the polyethylene blocks. Notably, a Flory-Huggins interaction parameter was determined from the disordered morphologies of PES12Li using mean-field theory: χ(T) = 77.4/T + 2.95 (T in Kelvin) and χ(25 °C) ≈ 3.21. This ultrahigh χ indicates that the polar ionic and nonpolar polyethylene segments are highly incompatible and affords well-ordered morphologies even when the combined length of the alternating blocks is just 18-29 backbone atoms. This combination of ultrahigh χ and short multiblocks produces sub-3-nm domain spacings that facilitate the control of block copolymer self-assembly for various fields of study, including nanopatterning.

Block-Random Copolymer-Micellization-Mediated Formation of Polymeric Patches on Gold Nanoparticles.

Patchy colloidal nanoparticles are important for a broad range of applications, especially as building blocks for complex and functional structural materials, but the controllable generation of chemical patches on as-synthesized nanoparticles remains a challenge. This article describes a robust strategy for the scalable synthesis of high-quality patchy nanoparticles in high yield and solid content. A simple thermal treatment of a mixture of gold nanoparticles and thiol-terminated block-random copolymers in selected solvents produced a variety of patchy nanoparticles with a controlled morphology and number of polymeric patches (e.g., beanlike patch, one patch, two patches, three patches, multiple patches, and open-configuration patch). We show in experiments and simulations that the dynamic detachment/attachment of copolymers and the exchange of copolymers between the nanoparticle surface and free micelles in the solution-which are dictated by the architecture of copolymers-govern the formation of polymeric patches. This work not only offers an effective approach to patchy nanoparticles but also provides new insights into the phase behaviors of copolymers on nanoscale surfaces.

Biological Stimuli-Induced Phase Transition of a Synthesized Block Copolymer: Preferential Interactions between PNIPAM-b-PNVCL and Heme Proteins.

The beguiling world of functional polymers is dominated by thermoresponsive polymers with unique structural and molecular attributes. Limited work has been reported on the protein-induced conformational transition of block copolymers; furthermore, the literature lacks a clear understanding of the influence of proteins on the phase behavior of thermoresponsive copolymers. Herein, we have synthesized poly(N-isopropylacrylamide)-b-poly(N-vinylcaprolactam) (PNIPAM-b-PNVCL) by RAFT polymerization using N-isopropylacrylamide and N-vinylcaprolactam. Furthermore, using various biophysical techniques, we have explored the effect of cytochrome c (Cyt c), myoglobin (Mb), and hemoglobin (Hb) with varying concentrations on the aggregation behavior of PNIPAM-b-PNVCL. Absorption and steady-state fluorescence spectroscopy measurements were performed at room temperature to examine the copolymerization effect on fluorescent probe binding and biomolecular interactions between PNIPAM-b-PNVCL and proteins. Furthermore, temperature-dependent fluorescence spectroscopy and dynamic light scattering studies were performed to get deeper insights into the lower critical solution temperature (LCST) of PNIPAM-b-PNVCL. Small-angle neutron scattering (SANS) was also employed to understand the copolymer behavior in the presence of heme proteins. With the incorporation of proteins to PNIPAM-b-PNVCL aqueous solution, LCST has been varied to different extents owing to the preferential, molecular, and noncovalent interactions between PNIPAM-b-PNVCL and proteins. The present study can pave new insights between heme proteins and block copolymer interactions, which will help design biomimetic surfaces and aid in the strategic fabrication of copolymer-protein bioconjugates.

Comment on “Quantify the contribution of chain length heterogeneity on block copolymer self-assembly”

The effects of molecular weight distribution on the self-assembly of lamella-forming AB-diblock copolymers with polydisperse A-blocks are examined using the self-consistent field theory applied to the freely-jointed chain (FJC) model of polymers. The experimentally observed domain spacing and order-disorder transition point are well described by the theory. The excellent agreement between experiments and theory indicates that the FJC model is capable of describing the phase behaviour of low-molecular block copolymers. A combination of experimental techniques and theoretical modelling offers exciting opportunities to engineering desirable block copolymer morphologies using block copolymers with designed chain length heterogeneities.

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.

Composition-dependent phase transformation in side-chain liquid crystalline copolymers with mesogenic groups at different substituent positions.

Copolymerization is an effective approach to tailor the thermal and structural properties of liquid crystalline polymer materials, which is essential for various applications. In this work, two series of polynorbornene copolymers, A-r-B and A-r-C, with the biphenyl mesogenic side group at different substituent positions were synthesized via ring-opening metathesis polymerization in various compositions. The corresponding homopolymers A and C are liquid crystalline polymers, exhibiting an oblique columnar structure (Colob/p2) and lamellar structure, respectively, while homopolymer B is amorphous. The composition-dependent phase behaviors of copolymers were systematically studied with the combination of SAXS, GISAXS, AFM, DSC and POM techniques. With increasing molar content of A (xA), the self-organzied structure of copolymer A-r-B follows the sequence from amorphous to lamellar, undulated lamellar, and Colob/p2 structures, and that of A-r-C follows the sequence of lamellar, undulated lamellar, and Colob/p2 structures. Then, copolymers with undulated lamellar or Colob/p2 structures tend to enter lamellar phase first at higher temperature and then change to the isotropic state during heating. The composition-induced transition from lamellar to supramolecular columnar organization is somewhat reminiscent of block copolymers and other soft matter systems that can form ordered structures. Furthermore, the subsitituent number and position of rigid mesogenic units in the side chain can further modify the morphologies of self-organized phases.

Modulating Microphase Separation of Lamellae-Forming Diblock Copolymers via Ionic Junctions.

We present a molecular dynamics simulation study investigating the phase behavior of lamellae-forming diblock copolymers with a single ionic junction on the backbone. Our results show qualitative agreement with experimental findings regarding enhanced microphase separation with the introduction of an ionic junction at the conjunction point, while further revealing nonmonotonic changes in domain spacing and order-disorder transition as a function of the electrostatic interaction strength. This highlights the dominant roles of entropic and binding effects of counterions under weak and strong ionic correlations, respectively. The location of the ionic junction is found to effectively modulate the charge distribution and chain conformation in the ordered domains; its presence in the middle of a block promotes folding of the block, leading to a smaller domain size. These findings demonstrate the interplay of ionic coupling with steric hindrance and chain end effects, which enhances our understanding of the delicate control over the microphase domain features.

Phase Behavior of Gradient Copolymer Melts with Different Gradient Strengths Revealed by Mesoscale Simulations.

Design and preparation of functional nanomaterials with specific properties requires precise control over their microscopic structure. A prototypical example is the self-assembly of diblock copolymers, which generate highly ordered structures controlled by three parameters: the chemical incompatibility between blocks, block size ratio and chain length. Recent advances in polymer synthesis have allowed for the preparation of gradient copolymers with controlled sequence chemistry, thus providing additional parameters to tailor their assembly. These are polydisperse monomer sequence, block size distribution and gradient strength. Here, we employ dissipative particle dynamics to describe the self-assembly of gradient copolymer melts with strong, intermediate, and weak gradient strength and compare their phase behavior to that of corresponding diblock copolymers. Gradient melts behave similarly when copolymers with a strong gradient are considered. Decreasing the gradient strength leads to the widening of the gyroid phase window, at the expense of cylindrical domains, and a remarkable extension of the lamellar phase. Finally, we show that weak gradient strength enhances chain packing in gyroid structures much more than in lamellar and cylindrical morphologies. Importantly, this work also provides a link between gradient copolymers morphology and parameters such as chemical incompatibility, chain length and monomer sequence as support for the rational design of these nanomaterials.

Rationalizing the Phase Behavior of Triblock Copolymers through Experiments and Molecular Simulations

In this paper, we develop a new coarse-grained model, under the MARTINI framework, for Pluronic block copolymers that is able to describe the self-assembly mechanism and reproduce experimental micelle sizes and shapes. Previous MARTINI-type Pluronic models were unable to produce realistic micelles in aqueous solution, and thus our model represents a marked improvement over existing approaches. We then applied this model to understand the effects of polymer structure on the cloud point temperature measured experimentally for a series of Pluronics, including both normal and reverse copolymers. It was observed that high polyoxypropylene glycol content leads to dominant hydrophobic interactions and a lower cloud point temperature, while high hydrophilic polyoxyethylene glycol content shields the micelles against aggregation and hence leads to a higher cloud point temperature. As the concentration increases, the effect of polymer architecture (normal versus reverse) starts to dominate, with reverse Pluronics showing a lower cloud point temperature. This was shown to be due to the increased formation of cross-links between neighboring micelles in these systems, which promote micelle aggregation. Our results shed new light on these fascinating systems and open the door to increased control of their thermal responsive behavior.