Self-assembly of rod-coil-rod block copolymers in a coil-selective solvent: coarse-grained simulation results.

The solution self-assembly of amphiphilic polymers provides a versatile approach to design novel nanostructured materials. Multiblock polymers, particularly those composed of liquid crystalline and coil blocks, are of significant interest due to the potential display of nematic ordering in liquid crystalline domains, offering intriguing optical and mechanical properties. In this study, dissipative particle dynamics is used to investigate the solution self-assembly of rod-coil-rod copolymers in a coil-selective solvent. Extensive molecular simulations were conducted to elucidate the impact of polymer composition, concentration and flexibility on the self-assembly behavior. A quantitative analysis was performed to investigate how polymer conformations varied with changes in composition, concentration, and rigidity. Simulation results show that, at small rod compositions, rod-coil-rod polymers self-assemble into micelles at low concentrations, transitioning to network formation as concentration increases. An increase in rod composition leads to the formation of larger aggregates, resulting in cylindrical micelles and membranes. The results reported here also offer insights into the role of flexibility in shaping the self-assembly behavior of rod-coil-rod triblocks in selective solvents, thus, contributing to a comprehensive understanding of the factors governing the formation of diverse structures in the solution self-assembly of triblock copolymers.

Exploring conformations of comb-like polymers with varying grafting density in dilute solutions.

Comb-like polymers have shown potential as advanced materials for a diverse palette of applications due to the tunability of their polymer architecture. To date, however, it still remains a challenge to understand how the conformational properties of these polymers arise from the interplay of their architectural parameters. In this work, extensive simulations were performed using dissipative particle dynamics to investigate the effect of grafting density, backbone length, and sidechain length on the conformations of comb-like polymers immersed in a good solvent. To quantify the effect of these architectural parameters on polymer conformations, we computed the asphericity, radius of gyration, and backbone and sidechain end-to-end distances. Bond-bond correlation functions and effective Kuhn lengths were computed to quantify the topological stiffness induced by sidechain-sidechain interactions. Simulation results reveal that the effective Kuhn length increases as grafting density and sidechain length increase, in agreement with previous experimental and theoretical studies. This increase in stiffness results in comb-like polymers adopting extended conformations as grafting density and sidechain length increase. Simulation results regarding the radius of gyration of comb-like polymers as a function of grafting density are compared with scaling theory predictions based on a free energy proposed by Morozova and Lodge [ACS Macro Lett. 6, 1274-1279 (2017)] and scaling arguments by Tang et al. [Macromolecules 55, 8668-8675 (2022)].

Effect of Block Sequence on the Solution Self-Assembly of Symmetric ABCBA Pentablock Polymers in a Selective Solvent.

Solution self-assembly of multiblock polymers offers a platform to create complex functional self-assembled nanostructures. However, a complete understanding of the effect of the different single-molecule-level parameters and solution conditions on the self-assembled morphology is still lacking. In this work, we have used dissipative particle dynamics to investigate the solution self-assembly of symmetric ABCBA linear pentablock polymers in a selective solvent and examined the effect of the block sequence, composition, and polymer concentration on the final morphology and polymer conformations. We confirmed that block sequence has an effect on the self-assembled morphologies, and it has a strong influence on polymer conformations that give place to physical gels for the sequence where the solvophilic block is located in the middle of the macromolecule. Our results are summarized in terms of morphology diagrams in the composition-concentration parameter space.

Coarse-Grained Simulation of Bottlebrush: From Single-Chain Properties to Self-Assembly.

Bottlebrush polymers consist of a linear backbone with densely grafted side chains. They are known to have a range of properties of interest, such as enhanced mechanical strength and rapid self-assembly into large domains, and have attracted attention as promising candidates for applications in photonics, lithography, energy storage, organic optoelectronics, and drug delivery. Here, we present a coarse-grained model of bottlebrush polymers that is able to reproduce their experimentally observed persistence lengths and chain conformations in the melt. The model is then used to investigate the morphologies of this class of materials for various chain architectures and grafting densities.

Dynamics and phase behavior of two-dimensional size-asymmetric binary mixtures of core-softened colloids.

The self-assembly of binary colloidal mixtures provides a bottom-up approach to create novel functional materials. To elucidate the effect of composition, temperature, and pressure on the self-assembly behavior of size-asymmetric mixtures, we performed extensive dynamics simulations of a simple model of polymer-grafted colloids. We have used a core-softened interaction potential and extended it to represent attractive interactions between unlike colloids and repulsions between like colloids. Our study focused on size-asymmetric mixtures where the ratio between the sizes of the colloidal cores was fixed at σBσA=0.5. We have performed extensive simulations in the isothermal-isobaric and canonical (NVT) ensembles to elucidate the phase behavior and dynamics of mixtures with different stoichiometric ratios. Our simulation results uncovered a rich phase behavior, including the formation of hierarchical structures with many potential applications. For compositions where small colloids are the majority, sublattice melting occurs for a wide range of densities. Under these conditions, large colloids form a well-defined lattice, whereas small colloids can diffuse through the system. As the temperature is decreased, the small colloids localize, akin to a metal-insulator transition, with the small colloids playing a role similar to electrons. Our results are summarized in terms of phase diagrams.

Mesoscale Simulations of Polymer Solution Self-Assembly: Selection of Model Parameters within an Implicit Solvent Approximation.

Coarse-grained modeling is an outcome of scientific endeavors to address the broad spectrum of time and length scales encountered in polymer systems. However, providing a faithful structural and dynamic characterization/description is challenging for several reasons, particularly in the selection of appropriate model parameters. By using a hybrid particle- and field-based approach with a generalized energy functional expressed in terms of density fields, we explore model parameter spaces over a broad range and map the relation between parameter values with experimentally measurable quantities, such as single-chain scaling exponent, chain density, and interfacial and surface tension. The obtained parameter map allows us to successfully reproduce experimentally observed polymer solution assembly over a wide range of concentrations and solvent qualities. The approach is further applied to simulate structure and shape evolution in emulsified block copolymer droplets where concentration and domain shape change continuously during the process.

Grain polydispersity and coherent crystal reorientations are features to foster stress hotspots in polycrystalline alloys under load.

The mechanical properties of metallic alloys are controlled through the design of their polycrystalline structure via heat treatments. For single-phase microstructures, they aim to achieve a particular average grain diameter to leverage stress hardening or softening. The stochastic nature of the recrystallization process generates a grain size distribution, and the randomness of the crystallographic orientation determines the anisotropy of a mechanical response. We developed a multiscale computational formalism to capture the collective mechanical response of polycrystalline microstructures at unprecedented length scales. We found that for an averaged grain size, the mechanical response is highly dependent on the grain size distribution. The simulations reveal the topological conditions that promote coherent grain texturization and grain growth inhibition during stress relaxation. We identify the microstructural features that are responsible for the appearance of stress hotspots. Our results provide the elusive evidence of how stress hotspots are ideal precursors for plastic and creep failure.

Kinetically-arrested single-polymer nanostructures from amphiphilic mikto-grafted bottlebrushes in solution: a simulation study.

Solution self-assembly of molecular bottlebrushes offers a rich platform to create complex functional organic nanostructures. Recently, it has become evident that kinetics, not just thermodynamics, plays an important role in defining the self-assembled structures that can be formed. In this work, we present results from extensive molecular dynamics simulations that explore the self-assembly behavior of mikto-grafted bottlebrushes when the solvent quality for one of the side blocks is changed by a rapid quench. We have performed a systematic study of the effect of different structural parameters and the degree of incompatibility between side chains on the final self-assembled nanostructures in the low concentration limit. We found that kinetically-trapped complex nanostructures are prevalent as the number of macromonomers increases. We performed a quantitative analysis of the self-assembled morphologies by computing the radius of gyration tensor and relative shape anisotropy as the different relevant parameters were varied. Our results are summarized in terms of non-equilibrium morphology diagrams.

Phase behavior of a two-dimensional core-softened system: new physical insights.

In this work, we report results of extensive computer simulations regarding the phase behavior of a core-softened system. By using structural and thermodynamic descriptors, as well as self-diffusion coefficients, we provide a comprehensive view of the rich phase behavior displayed by the particular instance of the model studied in here. Our calculations agree with previously published results focused on a smaller region in the temperature-density parameter space (Dudalov et al 2014 Soft Matter 10 4966). In this work, we explore a broader region in this parameter space, and uncover interesting fluid phases with low-symmetry local order, that were not reported by previous works. Solid phases were also found, and have been previously characterized in detail by (Kryuchkov et al 2018 Soft Matter 14 2152). Our results support previously reported findings, and provide new physical insights regarding the emergence of order as disordered phases transform into solids by providing radial distribution function maps and specific heat data. Our results are summarized in terms of a phase diagram.

Hierarchical complex self-assembly in binary nanoparticle mixtures.

Hierarchical self-assembly of soft matter provides a powerful route to create complex materials with enhanced physical properties. The understanding of the fundamental processes leading to such organization can provide design rules to create new functional materials. In this work, we use a simple model of polymer-grafted nanoparticles to explore the self-assembly of binary mixtures. By using Monte Carlo simulations we study the interplay of composition, density and particle sizes on the self-organization of such nanoparticle systems. It is found that complex hierarchical organization can take place for conditions where one-component systems form simple lattices. In particular, a mixture where one component forms a structure with 18-fold symmetry in a sea of an apparent disordered phase of the second component is observed to emerge for certain parameter combinations.

Enzyme-Induced Kinetic Control of Peptide-Polymer Micelle Morphology.

In this paper, experiment and simulation were combined to provide a view of the molecular rearrangements underlying the equilibrium and nonequilibrium transitions occurring in stimuli-responsive block copolymer amphiphile self-assemblies. Three block copolymer amphiphiles were prepared, each consisting of a hydrophilic peptide brush, responsive to proteolytic enzymes, and containing one of three possible hydrophobic blocks: (1) poly(ethyl acrylate), (2) poly(styrene), or (3) poly(lauryl acrylate). When assembled, they generate three spherical micelles each responsive to the addition of the bacterial protease, thermolysin. We found core-block-dependent phase transitions in response to the hydrophilic block being truncated by the stimulus. In one example, we found an unexpected, well-defined, pathway-dependent spherical micelle to vesicle phase transition induced by enzymatic stimulus.

Defect Annihilation Pathways in Directed Assembly of Lamellar Block Copolymer Thin Films.

Defects in highly ordered self-assembled block copolymers represent an important roadblock toward the adoption of these materials in a wide range of applications. This work examines the pathways for annihilation of defects in symmetric diblock copolymers in the context of directed assembly using patterned substrates. Past theoretical and computational studies of such systems have predicted minimum free energy pathways that are characteristic of an activated process. However, they have been limited to adjacent dislocations with opposite Burgers vectors. By relying on a combination of advanced sampling techniques and particle-based simulations, this work considers the long-range interaction between dislocation pairs, both on homogeneous and nanopatterned substrates. As illustrated here, these interactions are central to understanding the defect structures that are most commonly found in applications and in experimental studies of directed self-assembly. More specifically, it is shown that, for dislocation dipoles separated by several lamellae, multiple consecutive free energy barriers lead to effective kinetic barriers that are an order of magnitude larger than those originally reported in the literature for tightly bound dislocation pairs. It is also shown that annihilation pathways depend strongly on both the separation between dislocations and their relative position with respect to the substrate guiding stripes used to direct the assembly.

Directly Observing Micelle Fusion and Growth in Solution by Liquid-Cell Transmission Electron Microscopy.

Amphiphilic small molecules and polymers form commonplace nanoscale macromolecular compartments and bilayers, and as such are truly essential components in all cells and in many cellular processes. The nature of these architectures, including their formation, phase changes, and stimuli-response behaviors, is necessary for the most basic functions of life, and over the past half-century, these natural micellar structures have inspired a vast diversity of industrial products, from biomedicines to detergents, lubricants, and coatings. The importance of these materials and their ubiquity have made them the subject of intense investigation regarding their nanoscale dynamics with increasing interest in obtaining sufficient temporal and spatial resolution to directly observe nanoscale processes. However, the vast majority of experimental methods involve either bulk-averaging techniques including light, neutron, and X-ray scattering, or are static in nature including even the most advanced cryogenic transmission electron microscopy techniques. Here, we employ in situ liquid-cell transmission electron microscopy (LCTEM) to directly observe the evolution of individual amphiphilic block copolymer micellar nanoparticles in solution, in real time with nanometer spatial resolution. These observations, made on a proof-of-concept bioconjugate polymer amphiphile, revealed growth and evolution occurring by unimer addition processes and by particle-particle collision-and-fusion events. The experimental approach, combining direct LCTEM observation, quantitative analysis of LCTEM data, and correlated in silico simulations, provides a unique view of solvated soft matter nanoassemblies as they morph and evolve in time and space, enabling us to capture these phenomena in solution.

Mesoscale martensitic transformation in single crystals of topological defects.

Liquid-crystal blue phases (BPs) are highly ordered at two levels. Molecules exhibit orientational order at nanometer length scales, while chirality leads to ordered arrays of double-twisted cylinders over micrometer scales. Past studies of polycrystalline BPs were challenged by the existence of grain boundaries between randomly oriented crystalline nanodomains. Here, the nucleation of BPs is controlled with precision by relying on chemically nanopatterned surfaces, leading to macroscopic single-crystal BP specimens where the dynamics of mesocrystal formation can be directly observed. Theory and experiments show that transitions between two BPs having a different network structure proceed through local reorganization of the crystalline array, without diffusion of the double-twisted cylinders. In solid crystals, martensitic transformations between crystal structures involve the concerted motion of a few atoms, without diffusion. The transformation between BPs, where crystal features arise in the submicron regime, is found to be martensitic in nature when one considers the collective behavior of the double-twist cylinders. Single-crystal BPs are shown to offer fertile grounds for the study of directed crystal nucleation and the controlled growth of soft matter.

Segregation of liquid crystal mixtures in topological defects.

The structure and physical properties of liquid crystal (LC) mixtures are a function of composition, and small changes can have pronounced effects on observables, such as phase-transition temperatures. Traditionally, LC mixtures have been assumed to be compositionally homogenous. The results of chemically detailed simulations presented here show that this is not the case; pronounced deviations of the local order from that observed in the bulk at defects and interfaces lead to significant compositional segregation effects. More specifically, two disclination lines are stabilized in this work by introducing into a nematic liquid crystal mixture a cylindrical body that exhibits perpendicular anchoring. It is found that the local composition deviates considerably from that of the bulk at the interface with the cylinder and in the defects, thereby suggesting new assembly and synthetic strategies that may capitalize on the unusual molecular environment provided by liquid crystal mixtures.

A multi-chain polymer slip-spring model with fluctuating number of entanglements: Density fluctuations, confinement, and phase separation.

Coarse grained simulation approaches provide powerful tools for the prediction of the equilibrium properties of polymeric systems. Recent efforts have sought to develop coarse-graining strategies capable of predicting the non-equilibrium behavior of entangled polymeric materials. Slip-link and slip-spring models, in particular, have been shown to be capable of reproducing several key aspects of the linear response and rheology of polymer melts. In this work, we extend a previously proposed multi-chain slip-spring model in a way that correctly incorporates the effects of the fluctuating environment in which polymer segments are immersed. The model is used to obtain the equation of state associated with the slip-springs, and the results are compared to those of related numerical approaches and an approximate analytical expression. The model is also used to examine a polymer melt confined into a thin film, where an inhomogeneous distribution of polymer segments is observed, and the corresponding inhomogeneities associated with density fluctuations are reflected on the spatial slip-spring distribution.

Demixing by a Nematic Mean Field: Coarse-Grained Simulations of Liquid Crystalline Polymers.

Liquid crystalline polymers exhibit a particular richness of behaviors that stems from their rigidity and their macromolecular nature. On the one hand, the orientational interaction between liquid-crystalline motifs promotes their alignment, thereby leading to the emergence of nematic phases. On the other hand, the large number of configurations associated with polymer chains favors formation of isotropic phases, with chain stiffness becoming the factor that tips the balance. In this work, a soft coarse-grained model is introduced to explore the interplay of chain stiffness, molecular weight and orientational coupling, and their role on the isotropic-nematic transition in homopolymer melts. We also study the structure of polymer mixtures composed of stiff and flexible polymeric molecules. We consider the effects of blend composition, persistence length, molecular weight and orientational coupling strength on the melt structure at the nano- and mesoscopic levels. Conditions are found where the systems separate into two phases, one isotropic and the other nematic. We confirm the existence of non-equilibrium states that exhibit sought-after percolating nematic domains, which are of interest for applications in organic photovoltaic and electronic devices.

Understanding Atomic-Scale Behavior of Liquid Crystals at Aqueous Interfaces.

The ordered environment presented by liquid crystals at interfaces enables a range of novel functionalities that is only now beginning to be exploited in applications ranging from light focusing devices to biosensors. One key feature of liquid crystals is that molecular events occurring at an interface propagate over large distances through the bulk. In spite of their importance, our fundamental understanding of liquid crystal-water and liquid crystal-air interfaces remains limited. In this work, we present results from large-scale atomistic molecular dynamics simulations on the organization of the nematic and isotropic phases of the nitrile-containing mesogenic molecule 4-cyano-4'-pentylbiphenyl (5CB) in the vicinity of vacuum and aqueous interfaces. Hybrid boundary conditions are imposed by confining 5CB films between vacuum and an aqueous medium to examine how those two types of interfaces influence the specific structural arrangement and ordering of 5CB. Consistent with experiments, our results indicate that 5CB exhibits homeotropic anchoring at the vacuum interface, and planar alignment at aqueous interfaces. Two-dimensional molecular dynamics potential of mean force calculations and average polarization densities show that the polar nitrile group of 5CB remains hydrated near the aqueous interface, where it modulates the orientation of water molecules. Estimates of the anchoring strength reveal an oscillatory decay and a semilinear decay with distance from the interface in vacuum and water, respectively.

Molecular pathways for defect annihilation in directed self-assembly.

Over the last few years, the directed self-assembly of block copolymers by surface patterns has transitioned from academic curiosity to viable contender for commercial fabrication of next-generation nanocircuits by lithography. Recently, it has become apparent that kinetics, and not only thermodynamics, plays a key role for the ability of a polymeric material to self-assemble into a perfect, defect-free ordered state. Perfection, in this context, implies not more than one defect, with characteristic dimensions on the order of 5 nm, over a sample area as large as 100 cm(2). In this work, we identify the key pathways and the corresponding free energy barriers for eliminating defects, and we demonstrate that an extraordinarily large thermodynamic driving force is not necessarily sufficient for their removal. By adopting a concerted computational and experimental approach, we explain the molecular origins of these barriers and how they depend on material characteristics, and we propose strategies designed to overcome them. The validity of our conclusions for industrially relevant patterning processes is established by relying on instruments and assembly lines that are only available at state-of-the-art fabrication facilities, and, through this confluence of fundamental and applied research, we are able to discern the evolution of morphology at the smallest relevant length scales-a handful of nanometers-and present a view of defect annihilation in directed self-assembly at an unprecedented level of detail.

Characterizing the Three-Dimensional Structure of Block Copolymers via Sequential Infiltration Synthesis and Scanning Transmission Electron Tomography.

Understanding and controlling the three-dimensional structure of block copolymer (BCP) thin films is critical for utilizing these materials for sub-20 nm nanopatterning in semiconductor devices, as well as in membranes and solar cell applications. Combining an atomic layer deposition (ALD)-based technique for enhancing the contrast of BCPs in transmission electron microscopy (TEM) together with scanning TEM (STEM) tomography reveals and characterizes the three-dimensional structures of poly(styrene-block-methyl methacrylate) (PS-b-PMMA) thin films with great clarity. Sequential infiltration synthesis (SIS), a block-selective technique for growing inorganic materials in BCPs films in an ALD tool and an emerging technique for enhancing the etch contrast of BCPs, was harnessed to significantly enhance the high-angle scattering from the polar domains of BCP films in the TEM. The power of combining SIS and STEM tomography for three-dimensional (3D) characterization of BCP films was demonstrated with the following cases: self-assembled cylindrical, lamellar, and spherical PS-b-PMMA thin films. In all cases, STEM tomography has revealed 3D structures that were hidden underneath the surface, including (1) the 3D structure of defects in cylindrical and lamellar phases, (2) the nonperpendicular 3D surface of grain boundaries in the cylindrical phase, and (3) the 3D arrangement of spheres in body-centered-cubic (BCC) and hexagonal-closed-pack (HCP) morphologies in the spherical phase. The 3D data of the spherical morphologies was compared to coarse-grained simulations and assisted in validating the simulations' parameters. STEM tomography of SIS-treated BCP films enables the characterization of the exact structure used for pattern transfer and can lead to a better understating of the physics that is utilized in BCP lithography.