Direct imaging and mesoscale modelling of phase transitions in a nanostructured fluid

Mesoscale Simulation Based on the Dynamic Mean-Field Density Functional Method on Block-Copolymeric Ionomers for Polymer Electrolyte Membranes

Block copolymers generally have peculiar morphological characteristics, such as strong phase separation. They have been actively applied to polymer electrolyte membranes for proton exchange membrane fuel cells (PEMFCs) to obtain well-defined hydrophilic regions and water channels as a proton pathway. Although molecular simulation tools are advantageous to investigate the mechanism of water channel formation based on the chemical structure and property relationships, classical molecular dynamics simulation has limitations regarding the model size and time scale, and these issues need to be addressed. In this study, we investigated the morphology of sulfonated block copolymers synthesized for PEM applications using a mesoscale simulation based on the dynamic mean-field density functional method, widely applied to investigate macroscopic systems such as polymer blends, micelles, and multi-block/grafting copolymers. Despite the similar solubility parameters of the monomers in our block-copolymer models, very different morphologies in our 3D mesoscale models were obtained. The model with sulfonated monomers, in which the number of sulfonic acid groups is twice that of the other model, showed better phase separation and water channel formation, despite the short length of its hydrophilic block. In conclusion, this unexpected behavior indicates that the role of water molecules is important in making PEM mesoscale models well-equilibrated in the mesoscale simulation, which results in the strong phase separation between hydrophilic and hydrophobic regions and the ensuing well-defined water channel. PEM synthesis supports the conclusion that using the sulfonated monomers with a high sulfonation degree (32.5 mS/cm) will be more effective than using the long hydrophilic block with a low sulfonation degree (25.2 mS/cm).

Nanoparticle-induced morphological transformation in block copolymer-based nanocomposites

By controlling the chemical composition and the spatial organization of nanoparticles, hybrid nanocomposites incorporating ordered arrangements of nanoparticles could be endowed with exotic physical and chemical properties to fulfill demands in advanced electronics or energy-harvesting devices. However, a simple method to fabricate hybrid nanocomposites with precise control of nanoparticle distribution is still challenging. We demonstrate that block copolymer-based nanocomposites containing well-ordered nanoparticles with various morphologies can be readily obtained by adjusting the nanoparticle concentration. Moreover, the structural evolution of nanocomposite thin films as a function of nanoparticle loading is unveiled using grazing-incidence transmission small-angle X-ray scattering and atomic force microscopy. The morphological transformation proceeds through a phase transition from perforated lamellae to in-plane cylinder layout, followed by structural changes. The successful achievement of a variety of morphologies represents an effective and straightforward approach to producing functional hybrid nanocomposites for potential applications in various functional devices.

Integration of Machine Learning and Coarse-Grained Molecular Simulations for Polymer Materials: Physical Understandings and Molecular Design

In recent years, the synthesis of monomer sequence-defined polymers has expanded into broad-spectrum applications in biomedical, chemical, and materials science fields. Pursuing the characterization and inverse design of these polymer systems requires our fundamental understanding not only at the individual monomer level, but also considering the chain scales, such as polymer configuration, self-assembly, and phase separation. However, our accessibility to this field is still rudimentary due to the limitations of traditional design approaches, the complexity of chemical space along with the burdened cost and time issues that prevent us from unveiling the underlying monomer sequence-structure-property relationships. Fortunately, thanks to the recent advancements in molecular dynamics simulations and machine learning (ML) algorithms, the bottlenecks in the tasks of establishing the structure-function correlation of the polymer chains can be overcome. In this review, we will discuss the applications of the integration between ML techniques and coarse-grained molecular dynamics (CGMD) simulations to solve the current issues in polymer science at the chain level. In particular, we focus on the case studies in three important topics—polymeric configuration characterization, feed-forward property prediction, and inverse design—in which CGMD simulations are leveraged to generate training datasets to develop ML-based surrogate models for specific polymer systems and designs. By doing so, this computational hybridization allows us to well establish the monomer sequence-functional behavior relationship of the polymers as well as guide us toward the best polymer chain candidates for the inverse design in undiscovered chemical space with reasonable computational cost and time. Even though there are still limitations and challenges ahead in this field, we finally conclude that this CGMD/ML integration is very promising, not only in the attempt of bridging the monomeric and macroscopic characterizations of polymer materials, but also enabling further tailored designs for sequence-specific polymers with superior properties in many practical applications.

Phase behavior in thin films of weakly segregated block copolymer/homopolymer blends

We have demonstrated the phase behavior of substrate-supported films of a symmetric weakly segregated polystyrene-block-poly (methyl methacrylate), P(S-b-MMA), block copolymer and its blends with homopolymer polystyrene (PS) at different compositions. Upon increasing the content of added PS in the blends, lamellae (L), perforated layers (PL), double gyroid (DG) and cylinders (C) are obtained in sequence for films. Among these nanodomains, PL and DG only exist in a narrow ϕ_PS region (ϕ_PS denotes the volume fraction of PS). At ϕ_PS = 64%, tuning film thickness and annealing temperature can produce parallel PL or DG with {121}_DG lattice planes being parallel to the substrate surface. The effects of annealing temperature and film thickness on the formation of PL and DG are examined. In thin films with n ≈ 3 (n denotes the ratio of initial film thickness to inter-domain spacing), the PL phase solely exists regardless of temperature. However, for thick films with n ≈ 6 and 10, thermal annealing at the most accessible temperature produces films containing both PL and DG of various fractions, but a low temperature tends to favor a greater fraction of PL. The PL phase becomes the only discernible phase if thick films are shortly annealed at 230 °C.

Influence of Osmotic Pressure on Nanostructures in Thin Films of a Weakly-Segregated Block Copolymer and Its Blends with a Homopolymer

We studied the influence of osmotic pressure on nanostructures in thin films of a symmetric weakly-segregated polystyrene-block-poly (methyl methacrylate), P(S-b-MMA), block copolymer and its mixtures with a polystyrene (PS) homopolymer of various compositions. Thin films were deposited on substrates through surface neutralization. The surface neutralization results from the PS mats, which were oxidized and cross-linked by UV-light exposure. Thus, thermal annealing produced perpendicularly oriented lamellae and perforated layers, depending on the content of added PS chains. Nevertheless, a mixed orientation was obtained from cylinders in thin films, where a high content of PS was blended with the P(S-b-MMA). A combination of UV-light exposure and acetic acid rinsing was used to remove the PMMA block. Interestingly, the treatment of PMMA removal inevitably produced osmotic pressure and consequently resulted in surface wrinkling of perpendicular lamellae. As a result, a hierarchical structure with two periodicities was obtained for wrinkled films with perpendicular lamellae. The formation of surface wrinkling is due to the interplay between UV-light exposure and acetic acid rinsing. UV-light exposure resulted in different mechanical properties between the skin and the inner region of a film. Acetic acid rinsing produced osmotic pressure. It was found that surface wrinkling could be suppressed by reducing film thickness, increasing PS content and using high-molecular-weight P(S-b-MMA) BCPs.

Kinetic Monitoring of Block Copolymer Self-Assembly Using In Situ Spectroscopic Ellipsometry

Understanding the kinetic pathways of self-assembly in block copolymers (BCPs) has been a long-standing challenge, mostly due to limitations of in situ monitoring techniques. Here, we demonstrate an approach that uses optical birefringence, determined by spectroscopic ellipsometry (SE), as a measure of domain formation in cylinder- and lamellae-forming BCP films. The rapid experimental acquisition time in SE (ca. 1 sec) enables monitoring of the assembly/disassembly kinetics of BCP films during solvent-vapor annealing (SVA). We demonstrate that upon SVA, BCP films form ordered domains that are stable in the swollen state, but disorder upon rapid drying. Surprisingly, the disassembly during drying strongly depends on the duration of solvent exposure in the swollen state, explaining previous observations of loss of order in SVA processes. SE thus allows for decoupling of BCP self-assembly and disordering that occurs during solvent annealing and solvent evaporation, which is difficult to probe using other, slower techniques.

A Dopant Replacement-Driven Molten Salt Method toward the Synthesis of Sub-5-nm-Sized Ultrathin Nanowires

The high-temperature molten-salt method is an important inorganic synthetic route to a wide variety of morphological phenotypes. However, its utility is limited by the fact that it is typically incapable of producing ultrathin (<5 nm diameter) nanowires, which have a crucial role in novel nanotechnology applications. Herein, a rapid molten salt-based synthesis of sub-5-nm-sized nanowires of hexagonal tungsten oxide (h-WO₃ ) that is critically dependent on a substantial proportion of molybdenum (Mo) dopant is described. This dopant-driven morphological transition in tungsten oxide (WO₃ ) may be attributable to the collapse of layered structure, followed by nanocluster aggregation, coalescence, and recrystallization to form ultrathin nanowires. Interestingly, due to the structural properties of h-WO₃ , the thus-formed ultrathin nanowires are demonstrated to be excellent photocatalysts for the production of ammonia (NH₃ ) from nitrogen (N₂ ) and water. The ultrathin nanowires exhibit a high photocatalytic NH₃ -production activity with a rate of 370 µmol g^-1 h^-1 and an apparent quantum efficiency of 0.84% at 420 nm, which is more than twice that obtained from the best-performing Mo-doped W₁₈ O₄₉ nanowire catalysts. It is envisaged that the dopant replacement-driven synthetic protocol will allow for rapid access to a series of ultrathin nanostructures with intriguing properties and increase potential applications.

Real-time and in situ observation of structural evolution of giant block copolymer thin film under solvent vapor annealing by atomic force microscopy

An instrumentation technique for real-time, in situ and real space observation of microphase separation was proposed for ultra-high molecular weight block copolymer thin films (1010 kg mol⁻¹, domain spacing of 180 nm) under high solvent vapor swelling conditions. This is made possible by a combination of a homebuilt chamber which is capable of supplying sufficient amount of vapor, and force–distance curve measurements which gives real-time swollen film thickness and allow active feedback for controlling the degree of swelling. We succeeded in monitoring the domain coarsening of perpendicular lamellar structures in polystyrene-block-poly(methyl methacrylate) thin films for eight hours via tapping mode imaging. During the annealing process, the thickness reached a maximum of 8.5 times that of the original film. The series of temporal real space topographic images obtained via this method allowed us to study, for the first time, the growth exponent of the correlation length under solvent vapor annealing.

Real-time and in situ observation technique was proposed for ultra high molecular weight block copolymer thin films under solvent vapor annealing.

Time-spliced X-ray diffraction imaging of magnetism dynamics in a NdNiO3 thin film

Diffraction imaging of nonequilibrium dynamics at atomic resolution is becoming possible with X-ray free-electron lasers. However, there are unresolved problems with applying this method to objects that are confined in only one dimension. Here I show that reliable one-dimensional coherent diffraction imaging is possible by splicing together images recovered from different time delays in an optical pump X-ray probe experiment. The time and space evolution of antiferromagnetic order in a vibrationally excited complex oxide heterostructure is recovered from time-resolved measurements of a resonant soft X-ray diffraction peak. Midinfrared excitation of the substrate is shown to lead to a demagnetization front that propagates at a velocity exceeding the speed of sound, a critical observation for the understanding of driven phase transitions in complex condensed matter.

Scaling properties of ageing orientation fluctuations in stripe phases

We investigate the non-equilibrium dynamics of an ordered stripe-forming system free of topological defects. In particular, we study the ageing and the coarsening of orientation fluctuations parallel and perpendicular to the stripes via computer simulations based on a minimal phase-field model (model B with Coulomb interactions). Under the influence of noise, the stripe orientation field develops fluctuations parallel to the stripes, with the dominant modulation length λ*∥ increasing with time t as λ*∥ ∼ t1/4 and the correlation length perpendicular to the stripes ξ⊥θ increasing as ξ⊥θ ∼ t1/2. We explain these anisotropic coarsening dynamics with an analytic theory based on the linear elastic model for stripe displacements first introduced by Landau and Peierls. We thus obtain the scaling forms and the scaling exponents characterizing the correlation functions and the structure factor of the stripe orientation field. Our results reveal how the coarsening of orientation fluctuations prevents a periodically modulated phase free of topological defects from reaching equilibrium.

Self-Assembly of Complex Multimetal Nanostructures from Perforated Lamellar Block Copolymer Thin Films

We introduce a facile and effective fabrication of complex multimetallic nanostructures through block copolymer self-assembly. Two- and three-dimensional complex nanostructures, such as "nanomesh," "double-layered nanomeshes," and "surface parallel cylinders on nanomesh," can be fabricated using the self-assembly of perforated lamellar morphology in block copolymer thin films. Simultaneous integration of various metallic elements, including Pt, Au, and Co, into the self-assembled morphologies generates multimetal complex nanostructures with highly interconnected morphology and a large surface. The resultant metal nanostructures with a large surface area, robust electrical connectivity, and well-defined alloy composition demonstrate a high-performance electrochemical catalysis for hydrogen evolution reaction (current density: 6.27 mA/cm²@0.1 V and Tafel slope: 43 mV/dec).

Analyzing spinodal decomposition of an anisotropic fluid mixture

Spinodal decomposition leads to spontaneous fluctuations of the local concentration. In the early stage, the resulting pattern provides explicit information about the material properties of the mixture. In the case of two isotropic fluids, the static structure factor shows the characteristic ring shape. If one component is a liquid crystal, the pattern is typically anisotropic and the structure factor is more complex. Using numerical methods, we investigate how structure factors can be used to extract information about material properties like the diffusion constant or the isotropic and the anisotropic contributions to the interfacial tension. The method is based on momenta taken from structure factors in the early stage of the spinodal demixing. We perform phase field calculations for an isotropic and an anisotropic spinodal decomposition. A comparison of the extracted results with analytic values is made. The calculations show that linear modes dominate in the beginning of the growth process, while non-linear modes grow monotonously in the region of the k-space for which damping is predicted by the linearized theory. As long as non-linear modes are small enough, linearized theory can be applied to extract material properties from the structure factor.

Asymmetric block copolymer membranes with ultrahigh porosity and hierarchical pore structure by plain solvent evaporation

Membranes with a hierarchical porous structure and an isoporous skin could be manufactured from a block copolymer blend by pure solvent evaporation (drying induced phase separation).

Microphase Separation of a PS-b-PFS Block CopolymerviaSolvent Annealing: Effect of Solvent, Substrate, and Exposure Time on Morphology

Block copolymer (BCP) lithography makes use of the microphase separation properties of BCPs to pattern ordered nanoscale features over large areas. This work presents the microphase separation of an asymmetric polystyrene-block-poly(ferrocenyl dimethylsilane) (PS-b-PFS) BCP that allows ordered arrays of nanostructures to be formed by spin casting PS-b-PFS on substrates and subsequent solvent annealing. The effects of the solvent annealing conditions on self-assembly and structural stability are discussed.

Aging of orientation fluctuations in stripe phases

Stripe patterns, observed in a large variety of physical systems, often exhibit a slow nonequilibrium dynamics because ordering is impeded by the presence of topological defects. Using computer simulations based on a well-established model for stripe formation, we show that a slow dynamics and aging occur also in stripe patterns free of topological defects. For a wide range of noise strengths, the two-time orientation correlation function follows a scaling form that is typical for systems exhibiting a growing length scale. In our case, the underlying mechanism is the coarsening of orientation fluctuations, ultimately leading to power-law spatial correlations perpendicular to the stripes. Our results show that even for the smallest amount of noise, stripe phases without topological defects do not reach equilibrium. This constitutes an important aspect of the dynamics of modulated phases.

Structural transitions in asymmetric poly(styrene)-block-poly(lactide) thin films induced by solvent vapor exposure

Successive structural transitions in thin films of asymmetric poly(styrene)-block-poly(lactide) (PS-PLA) block copolymer samples upon exposure to tetrahydrofuran (THF) vapors have been monitored using atomic force microscopy (AFM) and both in situ and ex situ grazing incidence small-angle X-ray scattering (GISAXS). A direct link was established between the structure in the swollen state and the morphology formed in the dried state post solvent evaporation. This was related to the high incompatibility between the constituting blocks of the copolymer that thwarted the system from reaching the homogeneous disordered state in the swollen state under the specific conditions utilized in this study. Upon rapid solvent removal, the morphologies formed in the swollen state were trapped due the fast evaporation kinetics. This work provides a better understanding of the mechanisms associated with block copolymer thin film morphology changes induced by solvent vapor annealing.

Complex microstructures of ABC triblock copolymer thin films directed by polymer brushes based on self-consistent field theory

The morphology and the phase diagram of ABC triblock copolymer thin film directed by polymer brushes are investigated by the self-consistent field theory in three dimensions. The polymer brushes coated on the substrate can be used as a good soft template to tailor the morphology of the block copolymer thin films compared with those on the hard substrates. The polymer brush is identical with the middle block B. By continuously changing the composition of the block copolymer, the phase diagrams are constructed for three cases with the fixed film thickness and the brush density: identical interaction parameters, frustrated and non-frustrated cases. Some ordered complex morphologies are observed: parallel lamellar phase with hexagonally packed pores at surfaces (LAM3 (ll) -HFs), perpendicular lamellar phase with cylinders at the interface (LAM(⊥)-CI), and perpendicular hexagonally packed cylinders phase with rings at the interface (C2 (⊥)-RI). A desired direction (perpendicular or parallel to the coated surfaces) of lamellar phases or cylindrical phases can be obtained by varying the composition and the interactions between different blocks. The phase diagram of ABC triblock copolymer thin film wetted between the polymer brush-coated surfaces is very useful in designing the directed pattern of ABC triblock copolymer thin film.

An in situ grazing incidence X-ray scattering study of block copolymer thin films during solvent vapor annealing

In situ grazing-incidence small-angle X-ray scattering experiments on thin films of block copolymers during annealing in neutral solvent vapors are reported. By removing the solvent in a controlled manner, the period of the microphase separated morphology is found to increase with increasing block copolymer concentration in a power law manner with an exponent ∼ 2/3. By venting the systems at different rates during the solvent removal process, kinetically arresting the system, the period of the microphase separated morphology in the dried film can be varied.

Cyclical "flipping" of morphology in block copolymer thin films

We studied the kinetics of nanopattern evolution in (polystyrene-b-polyethylene oxide) diblock copolymer thin films. Using scanning force microscopy, a highly unexpected cylindrical flipping of morphology from normal to parallel to the film plane was detected during solvent annealing of the film (with average thickness of 30 nm) at high vapor pressure. Using an in situ time-resolved light scattering device combined with an environmental cell enabled us to obtain kinetic information at different vapor pressures. The data indicated that there is a threshold value for the vapor pressure necessary for the structural transition. We propose a swelling and deswelling mechanism for the orientation flipping of the morphology. The cyclic transition occurs faster in thick films (177 nm) where the mass uptake and solvent volume fraction is smaller and therefore the driving force for phase separation is higher. We induced a stronger segregation by confining the chains in graphoepitaxially patterned substrates. As expected, the cyclic transition occurred at higher rate. Our work is another step forward to understanding the structure evolution and also controlling the alignment of block copolymer nanocylinders independently of thickness and external fields.

Geometric frustration phases of diblock copolymers in nanoparticles

The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated.

Block copolymer nanocontainers

Using cell dynamics computer simulation, we perform a systematic study of thin block copolymer films around a nanoparticle. Lamellar-, cylinder-, and sphere-forming block copolymers are investigated with respect to different film thicknesses, particle radii, and boundary conditions at the film interfaces. The obtained structures include standing lamellae and cylinders, "onions", cylinder "knitting balls", "golf ball", layered spherical, "virus"-like and mixed morphologies with T-junctions and U-type defects. The kinetics of the structure formation and difference with planar thin films are discussed. Our simulations suggest that novel porous nanocontainers can be formed by the coating of a sacrificial nanobead by a block copolymer layer with a well-controlled nanostructure. In addition, first scanning force microscopy experiments on a model system reveal surface structures similar to those predicted by our simulations.

Study on the combined effects of solvent evaporation and polymer flow upon block copolymer self-assembly and alignment on topographic patterns

Microphase separation of a polystyrene-block-polyisoprene-block-polystyrene triblock copolymer thin film under confined conditions (i.e., graphoepitaxy) results in ordered periodic arrays of polystyrene cylinders aligned parallel to the channel side-wall and base in a polyisoprene matrix. Polymer orientation and translational ordering with respect to the topographic substrate were elucidated by atomic force microscopy (AFM) while film thickness and polymer profile within the channel were monitored by cross-sectional transmission electron microscopy (TEM) as a function of time over a 6 h annealing period at 120 degrees C. Upon thermal annealing, the polymer film simultaneously undergoes three processes: microphase separation, evaporation of trapped solvent, and mass transport of polymer from the mesas into the channels. A significant volume of solvent is trapped within the polymer film upon spin coating arising from the increased polymer/substrate interfacial area due to the topographic pattern. Mass transport of polymer during this process results in nonuniform films, where subtle changes in the film thickness within the channel have profound effects on the microphase separation process. The initially disordered structure within the film underwent an orientation transition via an intermediate formation of perpendicular cylinders (nonequilibrium) to a parallel (equilibrium) orientation with respect to the channel base. Herein, we present a time-resolved study of the cylinder reorientation process detailing how changing film thickness during the annealing process dramatically affects both the local and lateral orientation of the observed structure. Finally, a brief mathematical model is provided to evaluate spin coating over a complex topography following a classical asymptotic approximation of the Navier-Stokes equations for the as-deposited films.

Chemical interactions and their role in the microphase separation of block copolymer thin films

The thermodynamics of self-assembling systems are discussed in terms of the chemical interactions and the intermolecular forces between species. It is clear that there are both theoretical and practical limitations on the dimensions and the structural regularity of these systems. These considerations are made with reference to the microphase separation that occurs in block copolymer (BCP) systems. BCP systems self-assemble via a thermodynamic driven process where chemical dis-affinity between the blocks driving them part is balanced by a restorative force deriving from the chemical bond between the blocks. These systems are attracting much interest because of their possible role in nanoelectronic fabrication. This form of self-assembly can obtain highly regular nanopatterns in certain circumstances where the orientation and alignment of chemically distinct blocks can be guided through molecular interactions between the polymer and the surrounding interfaces. However, for this to be possible, great care must be taken to properly engineer the interactions between the surfaces and the polymer blocks. The optimum methods of structure directing are chemical pre-patterning (defining regions on the substrate of different chemistry) and graphoepitaxy (topographical alignment) but both centre on generating alignment through favourable chemical interactions. As in all self-assembling systems, the problems of defect formation must be considered and the origin of defects in these systems is explored. It is argued that in these nanostructures equilibrium defects are relatively few and largely originate from kinetic effects arising during film growth. Many defects also arise from the confinement of the systems when they are 'directed' by topography. The potential applications of these materials in electronics are discussed.

Specific features of defect structure and dynamics in the cylinder phase of block copolymers

We present a systematic study of defects in thin films of cylinder-forming block copolymers upon long-term thermal or solvent annealing. In particular, we consider in detail the peculiarities of both classical and specific topological defects, and conclude that there is a strong "defect structure-chain mobility" relationship in block copolymers. In the systems studied, representative defect configurations provide connectivity of the minority phase in the form of dislocations with a closed cylinder end or classical disclinations with incorporated alternative, nonbulk structures with planar symmetry. In solvent-annealed films with enhanced chain mobility, the neck defects (bridges between parallel cylinders) were observed. This type of nonsingular defect has not been identified in block copolymer systems before. We argue that topological arguments and 2D defect representation, sufficient for lamellar systems, are not sufficient to determine the stability and mobility of defects in the cylindrical phase. In-situ scanning force microscopy measurements are compared with the simulations based on the dynamic self-consistent mean field theory. The close match between experimental measurements and simulation results suggests that the lateral defect motion is diffusion-driven. In addition, 3D simulations demonstrated that the bottom (wetting) layer is only weakly involved into the structure ordering at the free surface. Finally, the morphological evolution is considered with the focus on the motion and interaction of the representative defect configurations.