Frustrated phases under three-dimensional confinement simulated by a set of coupled Cahn-Hilliard equations

Controlling the Formation of Polyhedral Block Copolymer Nanoparticles: Insights from Process Variables and Dynamic Modeling

This study delves into the formation of nanoscale polyhedral block copolymer particles (PBCPs) exhibiting cubic, octahedral, and variant geometries. These structures represent a pioneering class that has never been fabricated previously. PBCP features distinct variations in curvature on the outer surface, aligning with the edges and corners of polyhedral shapes. This characteristic sharply contrasts with previous block copolymers (BCPs), which displayed a smooth spherical surface. The emergence of these cornered morphologies presents an intriguing and counterintuitive phenomenon and is linked to process parameters, such as evaporation rates and initial concentration, while keeping other variables constant. Using a system of coupled Cahn-Hillard (CCH) equations, we uncover the mechanisms driving polyhedral particle formation, emphasizing the importance of controlling relaxation parameters for shape variable u and microphase separation v. This unconventional approach, differing from traditional steepest descent method, allows for precise control and diverse polyhedral particle generation. Accelerating the shape variable u proves crucial for expediting precipitation and aligns with experimental observations. Employing the above theoretical model, we achieve shape predictions for particles and the microphase separation within them, which overcomes the limitations of ab initio computations. Additionally, a numerical stability analysis discerns the transient nature versus local minimizer characteristics. Overall, our findings contribute to understanding the complex interplay between process variables and the morphology of polyhedral BCP nanoparticles.

Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement

We investigate the solution landscapes of the confined diblock copolymer and homopolymer in two-dimensional domain by using the extended Ohta-Kawasaki model. The projection saddle dynamics method is developed to compute the saddle points with mass conservation and construct the solution landscape by coupling with downward and upward search algorithms. A variety of stationary solutions are identified and classified in the solution landscape, including Flower class, Mosaic class, Core-shell class, and Tai-chi class. The relationships between different stable states are shown by either transition pathways connected by index-1 saddle points or dynamical pathways connected by a high-index saddle point. The solution landscapes also demonstrate the symmetry-breaking phenomena, in which more solutions with high symmetry are found when the domain size increases.

Pathways connecting two opposed bilayers with a fusion pore: a molecularly-informed phase field approach

A phase field model with two phase fields, representing the concentration and the head-tail separation of amphiphilic molecules, respectively, has been constructed using an extension of the Ohta-Kawasaki model (Macromolecules, 1986, 19, 2621-2632). It is shown that this molecularly-informed phase field model is capable of producing various self-assembled amphiphilic aggregates, such as bilayers, vesicles and micelles. Furthermore, pathways connecting two opposed bilayers with a fusion pore are obtained by using a combination of the phase field model and the string method. Multiple fusion pathways, including a classical pathway and a leaky pathway, have been obtained depending on the initial separation of the two bilayers. The study shed light on the understanding of the membrane fusion pathways and, more importantly, laid a foundation for further investigation of more complex membrane morphologies and transitions.

Theoretical prediction of morphological selection in amphiphilic systems

Biological and synthetic amphiphilic systems exhibit a wide range of morphologies. A density functional model for amphiphilic polymer phase mixtures is utilized to quantify localized equilibria and their stability, and ultimately predict and explain morphological preference. This is done by utilizing matched asymptotic expansions, which produces explicit connections between model parameters and macroscopic properties of equilibrium structures. Bilayers, cylindrical, and spherical micelle and vesicle configurations are found, and formulas which connect their geometry to ambient chemical potential are derived. Dynamics are studied in the context of a free boundary problem which describes the evolution of the hydrophobic-solvent domain interface. Linearization of this problem is used to explicitly determine growth rates and parameter regions of stability. All equilibria are found to have two branches of solutions terminating at a fold in the bifurcation diagram which signals the crossover from competitive stability to instability leading to ripening behavior. Ideally flat bilayers are determined to always possess a long wavelength buckling instability, suggesting that curved structures should be generically preferred. Spherical micelles exhibit morphological instabilities which are suppressed by large enough surface tension. Cylindrical micelles may have short-wavelength pearling and long-wavelength Rayleigh-Plateau-type instabilities. In addition, ideally infinite cylinders have an undulatory instability, suggesting that only finite length structures should be observed. A morphological phase diagram can be assembled which takes into account both existence and stability of different geometries. Consistent with experimental evidence, a bifurcation sequence from spheres to cylinders to vesicles is found as either surface tension or polymer composition increases. Coexistence of different stable morphologies is also observed.

Effects of the homopolymer molecular weight on a diblock copolymer in a 3D spherical confinement

The morphologies of a diblock copolymer spherically confined within a homopolymer were investigated by using the static self-consistent field theory method. A homogeneous A-B diblock copolymer sphere was surrounded by a homopolymer C. Upon changing the diblock volume fraction, homopolymer molecular weight and the interaction between the copolymer and its surrounding environment, different morphologies of the sphere were observed. Our calculations confirmed that when the homopolymer molecular weight was high a complete macrophase separation between the copolymer and the homopolymer was obtained. However, when the homopolymer molecular weight was low the homopolymer penetrated into the copolymer microdomains, diluting the diblock copolymer and reduced the interaction between the diblock copolymer segments and hence preventing them from segregating.

Ashura Particles: Experimental and Theoretical Approaches for Creating Phase-Separated Structures of Ternary Blended Polymers in Three-Dimensionally Confined Spaces

Unique morphologies were found in binary and ternary polymer blended particles, including Ashura-type phase separation, which has three different polymer components on the particle surface. The morphologies of phase-separated structures in the binary polymer blended particles are discussed in terms of the surface tensions of the blended polymers. Structural control of ternary polymer blended particles was achieved based on the combination of polymers by examining binary polymer blended particles. A theoretical approach based on the Cahn-Hilliard equations gives identical morphologies with the experimental results. This work opens the way to creating polymer particles with sophisticated nanostructures by controlling their morphologies as predicted by theoretical simulations.

Nanoscale Effects in One-Dimensional Columnar Supramolecular Ferroelectrics

Organic ferroelectrics have been actively developed with the goal of fabricating environmentally friendly and low-cost memory devices. The remanent polarization of hydrogen-bonded organic ferroelectrics approaches that of the inorganic ones. Nanoscale fabrication of organic ferroelectrics is an essential aspect of high-density memory devices. A pyrene derivative with four tetradecylamide (-CONHC₁₄ H₂₉ ) chains (1) formed an amide-type N-H⋅⋅⋅O hydrogen-bonded one-dimensional (1D) column, which demonstrated ferroelectricity in the discotic hexagonal columnar (Col_h ) liquid crystalline phase through the inversion of the orientation of the hydrogen-bonded chains. On the contrary, similar chiral pyrene derivatives bearing 3,7-dimethyl-1-octhylamide chains (S-2 and R-2) did not indicate the Col_h phase and ferroelectricity. Homogeneous mixed liquid crystals (1)_1-x (S-2)_x (i.e., between the ferroelectric 1 and the non-ferroelectric S-2) enable the control of the nanoscale aggregation state of the organic ferroelectrics, resulting in a nanoscale effect of the 1D supramolecular ferroelectrics. Ferroelectric mixed liquid crystals (1)_1-x (S-2)_x were observed at x≦0.03, where one S-2 molecule was inserted after every thirty-three 1 molecule in the mixed liquid crystal (1)₃₃ (S-2). An average (1)₃₄ length of approximately 12 nm was required to maintain the 1D ferroelectricity, which was similar to the nanoscale limit of inorganic ferroelectrics, such as hafnium oxide thin film (≈15 nm).

Rotating robots move collectively and self-organize

Biological organisms and artificial active particles self-organize into swarms and patterns. Open questions concern the design of emergent phenomena by choosing appropriate forms of activity and particle interactions. A particularly simple and versatile system are 3D-printed robots on a vibrating table that can perform self-propelled and self-spinning motion. Here we study a mixture of minimalistic clockwise and counter-clockwise rotating robots, called rotors. Our experiments show that rotors move collectively and exhibit super-diffusive interfacial motion and phase separate via spinodal decomposition. On long time scales, confinement favors symmetric demixing patterns. By mapping rotor motion on a Langevin equation with a constant driving torque and by comparison with computer simulations, we demonstrate that our macroscopic system is a form of active soft matter.

Transformation of Block Copolymer Nanoparticles from Ellipsoids with Striped Lamellae into Onionlike Spheres and Dynamical Control via Coupled Cahn-Hilliard Equations

Annealing of block copolymers has become a tool of great importance for the reconfiguration of nanoparticles. Here, we present the experimental results of annealing block copolymer nanoparticles and a theoretical model to describe the morphological transformation of ellipsoids with striped lamellae into onionlike spheres. A good correspondence between the experimental findings and predictions of the model was observed. The model based on finding the steepest direction of descent of an appropriate free energy leads to a set of Cahn-Hilliard equations that correctly describe the dynamical transformation of striped ellipsoids into onionlike spheres and reverse onionlike particles, regardless of the nature of the annealing process. This universality makes it possible to describe a variety of experimental conditions involving nanoparticles underlying a heating process. A notable advantage of the proposed approach is that it enables selective control of the interaction between the confined block copolymer and the surrounding medium. This feature endows the model with a great versatility to enable the reproduction of several combined effects of surfactants in diverse conditions, including cases with reverse affinities for the block copolymer segments. A phase diagram to describe a variety of morphologies is presented. We employ the relationship between the temperature-dependent Flory-Huggins parameter and the width of the interfaces to account for changes in temperature due to the heating process. Simulation results correctly show how the transformation evolves as the temperature increases. This increment in temperature corresponds to progressively smaller values of the interfacial width. We anticipate that the proposed approach will facilitate the design and more precise control of experiments involving various kinds of annealing processes.

Soft Confinement-Induced Morphologies of the Blends of AB Diblock Copolymers and C Homopolymers

Self-assembly behavior of the blends of AB diblock copolymers and C homopolymers in soft confinement is studied by using a simulated annealing method. Polymer solution droplets in a poor solvent environment realize the soft confinement. Several sequences of soft confinement-induced copolymer aggregates with different shapes and internal structures are predicted as functions of the size of confinement, the number ratio of AB diblock copolymers to C homopolymers, the volume fraction of blocks, the selectivity of confinement's surface, the incompatibility between blocks, and the competition between two block-homopolymer interactions. Simulation results demonstrate that those factors are able to tune the morphology of the aggregates precisely. We anticipate the rules achieved here is helpful to fabrication of polymeric particle with predesigned morphology.

Mechanistic investigations of confinement effects on the self-assembly of symmetric amphiphilic copolymers in thin films

The self-assembly of a copolymer thin film, whose molecular structure is composed of one hydrophobic branch (denoted in green) and two hydrophilic branches (denoted in red), gives (a) cylindrical structure, (b) micellar structure, and (c) lamellar structure.