Preserving positivity in density-explicit field-theoretic simulations.

Field-theoretic simulations are numerical methods for polymer field theory, which include fluctuation corrections beyond the mean-field level, successfully capturing various mesoscopic phenomena. Most field-theoretic simulations of polymeric fluids use the auxiliary field (AF) theory framework, which employs Hubbard-Stratonovich transformations for the particle-to-field conversion. Nonetheless, the Hubbard-Stratonovich transformation imposes significant limitations on the functional form of the non-bonded potentials.

Accelerated Prediction of Phase Behavior for Block Copolymer Libraries Using a Molecularly Informed Field Theory.

Solution formulations involving polymers are the basis for a wide range of products spanning consumer care, therapeutics, lubricants, adhesives, and coatings. These multicomponent systems typically show rich self-assembly and phase behavior that are sensitive to even small changes in chemistry and composition. Longstanding computational efforts have sought techniques for predictive modeling of formulation structure and thermodynamics without experimental guidance, but the challenges of addressing the long time scales and large length scales of self-assembly while maintaining chemical specificity have thwarted the emergence of general approaches.

Investigating microstructure evolution in block copolymer membranes.

Block copolymer self-assembly in conjunction with nonsolvent-induced phase separation (SNIPS) has been increasingly leveraged to fabricate integral-asymmetric membranes. The large number of formulation and processing parameters associated with SNIPS, however, has prevented the reliable construction of high performance membranes. In this study, we apply dynamical self-consistent field theory to model the SNIPS process and investigate the effect of various parameters on the membrane morphology: solvent selectivity, nonsolvent selectivity, initial film composition, and glass transition composition.

Phase Separation, Reaction Equilibrium, and Self-Assembly in Binary Telechelic Homopolymer Blends.

We study a binary blend of telechelic homopolymers that can form reversible AB-type bonds at the chain ends. Reversibly bonding polymers display novel material properties, including thermal tunability and self-healing, that are not found in conventional covalently bonded polymers. Previous studies of reversibly bonding polymer systems have been limited by the computational demand of accounting for an infinite number of possible reaction products in a spatially inhomogeneous, self-assembled structure.

Coarsening dynamics of ternary polymer solutions with mobility and viscosity contrasts.

Using phase-field simulations, we investigate the bulk coarsening dynamics of ternary polymer solutions undergoing a glass transition for two models of phase separation: diffusion only and with hydrodynamics. The glass transition is incorporated in both models by imposing mobility and viscosity contrasts between the polymer-rich and polymer-poor phases of the evolving microstructure. For microstructures composed of polymer-poor clusters in a polymer-rich matrix, the mobility and viscosity contrasts significantly hinder coarsening, effectively leading to structural arrest.

Emergence of a Spin Microemulsion in Spin-Orbit Coupled Bose-Einstein Condensates.

We report the first numerical prediction of a "spin microemulsion"-a phase with undulating spin domains resembling classical bicontinuous oil-water-surfactant emulsions-in two-dimensional systems of spinor Bose-Einstein condensates with isotropic Rashba spin-orbit coupling. Using field-theoretic numerical simulations, we investigated the melting of a low-temperature stripe phase with supersolid character and find that the stripes lose their superfluidity at elevated temperature and undergo a Kosterlitz-Thouless-like transition into a spin microemulsion. Momentum distribution calculations highlight a thermally broadened occupation of the Rashba circle of low-energy states with macroscopic and isotropic occupation around the ring.

Assessment of the partial saddle point approximation in field-theoretic polymer simulations.

Field-theoretic simulations are numerical treatments of polymer field theory models that go beyond the mean-field self-consistent field theory level and have successfully captured a range of mesoscopic phenomena. Inherent in molecularly-based field theories is a "sign problem" associated with complex-valued Hamiltonian functionals. One route to field-theoretic simulations utilizes the complex Langevin (CL) method to importance sample complex-valued field configurations to bypass the sign problem.

Improved Elastic Recovery from ABC Triblock Terpolymers.

The promise of ABC triblock terpolymers for improving the mechanical properties of thermoplastic elastomers is demonstrated by comparison with symmetric ABA/CBC analogs having similar molecular weights and volume fraction of B and A/C domains. The ABC architecture enhances elasticity (up to 98% recovery over 10 cycles) in part through essentially full chain bridging between discrete hard domains leading to the minimization of mechanically unproductive loops. In addition, the unique phase space of ABC triblocks also enables the fraction of hard-block domains to be higher ( ≈ 0.

Machine learning and polymer self-consistent field theory in two spatial dimensions.

A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional extension of the framework introduced in the work of Xuan et al. [J.

Predicting surfactant phase behavior with a molecularly informed field theory.

Hypothesis: The computational study of surfactants and self-assembly is challenging because 1) models need to reflect chemistry-specific interactions, and 2) self-assembled structures are difficult to equilibrate with conventional molecular dynamics. We propose to overcome these challenges with a multiscale simulation approach where relative entropy minimization transfers chemically-detailed information from all-atom (AA) simulations to coarse-grained (CG) models that can be simulated using field-theoretic methods. Field-theoretic simulations are not limited by intrinsic physical time scales like diffusion and allow for rigorous equilibration via free energy minimization.

Modeling Microstructure Formation in Block Copolymer Membranes Using Dynamical Self-Consistent Field Theory.

Block copolymers have attracted recent interest as candidate materials for ultrafiltration membranes, due to their ability to form isoporous integral-asymmetric membranes by the combined processes of self-assembly and nonsolvent-induced phase separation (SNIPS). However, the dependence of surface layer and substructure morphologies on the processing variables associated with SNIPS is not well understood nor is the interplay between microphase and macrophase separation in block copolymers undergoing such coagulation. Here, we use dynamical self-consistent field theory to simulate the microstructure evolution of block copolymer films during SNIPS and find that such films form the desired sponge-like asymmetric porous substructure only if the solvent and nonsolvent have opposite block selectivities and that otherwise they form a dense nonporous microphase-separated film.

Ionic Compatibilization of Polymers.

The small specific entropy of mixing of high molecular weight polymers implies that most blends of dissimilar polymers are immiscible with poor physical properties. Historically, a wide range of compatibilization strategies have been pursued, including the addition of copolymers or emulsifiers or installing complementary reactive groups that can promote the formation of block or graft copolymers during blending operations. Typically, such reactive blending exploits reversible or irreversible covalent or hydrogen bonds to produce the desired copolymer, but there are other options.

Field-Theoretic Simulation Method to Study the Liquid-Liquid Phase Separation of Polymers.

Liquid-liquid phase separation (LLPS) is a process that results in the formation of a polymer-rich liquid phase coexisting with a polymer-depleted liquid phase. LLPS plays a critical role in the cell through the formation of membrane-less organelles, but it also has a number of biotechnical and biomedical applications such as drug confinement and its targeted delivery. In this chapter, we present a computational efficient methodology that uses field-theoretic simulations (FTS) with complex Langevin (CL) sampling to characterize polymer phase behavior and delineate the LLPS phase boundaries.

Molecularly Informed Field Theories from Bottom-up Coarse-Graining.

Polymer formulations possessing mesostructures or phase coexistence are challenging to simulate using atomistic particle-explicit approaches due to the disparate time and length scales, while the predictive capability of field-based simulations is hampered by the need to specify interactions at a coarser scale (e.g., χ-parameters).

Direct free energy evaluation of classical and quantum many-body systems via field-theoretic simulation.

Free energy evaluation in molecular simulations of both classical and quantum systems is computationally intensive and requires sophisticated algorithms. This is because free energy depends on the volume of accessible phase space, a quantity that is inextricably linked to the integration measure in a coordinate representation of a many-body problem. In contrast, the same problem expressed as a field theory (auxiliary field or coherent states) isolates the particle number as a simple parameter in the Hamiltonian or action functional and enables the identification of a chemical potential field operator.

Interfacial reaction-induced roughening in polymer thin films.

Reactive blending of immiscible polymers is an important process for synthesizing polymer blends with superior properties. We use a phase-field model to understand reaction dynamics and morphology evolution by diffusive transport in layered films of incompatible, end-reactive polymers. We thoroughly investigate this phenomenon over a large parameter space of interface shapes, layer thicknesses, reaction rates specified by a Damkohler number (Da), and Flory-Huggins interaction parameter (), under static conditions with no external fields.

A phase field model for dynamic simulations of reactive blending of polymers.

A facile way to generate compatibilized blends of immiscible polymers is through reactive blending of end-functionalized homopolymers. The reaction may be reversible or irreversible depending on the end-groups and is affected by the immiscibility and transport of the reactant homopolymers and the compatibilizing copolymer product. Here we describe a phase-field framework to model the combined dynamics of reaction kinetics, diffusion, and multi-component thermodynamics on the evolution of the microstructure and reaction rate in reactive blending.

Self-consistent field theory study of polymer-mediated colloidal interactions in solution: Depletion effects and induced forces.

Polymer-mediated colloidal interactions control the stability and phase properties of colloid-polymer mixtures that are critical for a wide range of important applications. In this work, we develop a versatile self-consistent field theory (SCFT) approach to study this type of interaction based on a continuum confined polymer solution model with explicit solvent and confining walls. The model is formulated in the grand canonical ensemble, and the potential of mean force for the polymer-mediated interaction is computed from grand potentials.

Open-source platform for block polymer formulation design using particle swarm optimization.

Facile exploration of large design spaces is critical to the development of new functional soft materials, including self-assembling block polymers, and computational inverse design methodologies are a promising route to initialize this task. We present here an open-source software package coupling particle swarm optimization (PSO) with an existing open-source self-consistent field theory (SCFT) software for the inverse design of self-assembling block polymers to target bulk morphologies. To lower the barrier to use of the software and facilitate exploration of novel design spaces, the underlying SCFT calculations are seeded with algorithmically generated initial fields for four typical morphologies: lamellae, network phases, cylindrical phases, and spherical phases.

Liquid-liquid phase separation of Tau by self and complex coacervation.

The liquid-liquid phase separation (LLPS) of Tau has been postulated to play a role in modulating the aggregation property of Tau, a process known to be critically associated with the pathology of a broad range of neurodegenerative diseases including Alzheimer's Disease. Tau can undergo LLPS by homotypic interaction through self-coacervation (SC) or by heterotypic association through complex-coacervation (CC) between Tau and binding partners such as RNA. What is unclear is in what way the formation mechanisms for self and complex coacervation of Tau are similar or different, and the addition of a binding partner to Tau alters the properties of LLPS and Tau.

Architecture Effects in Complex Spherical Assemblies of (AB)-Type Block Copolymers.

Molecular architecture plays a key role in the self-assembly of block copolymers, but few studies have systematically examined the influence of chain connectivity on tetrahedrally close-packed (TCP) sphere phases. Here, we report a versatile material platform comprising two blocks with substantial conformational asymmetry, A = poly(trifluoroethyl acrylate) and B = poly(dodecyl acrylate), and use it to compare the phase behavior of AB diblocks, ABA triblocks, and (AB) radial star copolymers with = 3 or 4. Each architecture forms TCP sphere phases at minority A block compositions ( < 0.

Mechanisms of Asymmetric Membrane Formation in Nonsolvent-Induced Phase Separation.

We report the first simulations of nonsolvent-induced phase separation (NIPS) that predict membrane microstructures with graded asymmetric pore size distribution. In NIPS, a polymer solution film is immersed in a nonsolvent bath, enriching the film in nonsolvent, and leading to phase separation that forms a solid polymer-rich membrane matrix and polymer-poor membrane pores. We demonstrate how mass-transfer-induced spinodal decomposition, thermal fluctuations, and glass-transition dynamics-implemented with mobility contrast between the polymer-rich and polymer-poor phases-are essential to the formation of asymmetric membrane microstructures.