Session F26: Machine Learning and Advanced Computational Methods in Polymer Physics

Bicontinuous microemulsion in binary blends of complimentary diblock copolymers

The phase behavior of binary blends of AB diblock copolymers of compositions f and 1-f is examined using field theoretic simulations (FTSs). Highly asymmetric compositions (i.e., f ≈ 0) behave like homopolymer blends macrophase separating into coexisting A- and B-rich phases as the segregation is increased, whereas more symmetric diblocks (f ≈ 0.5) microphase separate into an ordered lamellar phase. In self-consistent field theory, these behaviors are separated by a Lifshitz critical point at f= 0.2113. However, its lower critical dimension is believed to be four, which implies that the Lifshitz critical point should be destroyed by fluctuations. Consistent with this, the FTSs find that it transforms into a tricritical point with a lower critical dimension of three. Furthermore, the highly swollen lamellar phase near the mean-field Lifshitz critical point is transformed into a bicontinuous microemulsion (BμE), consisting of large interpenetrating A- and B-rich microdomains. The BμE has been previously reported in ternary blends of AB diblock copolymer with its parent A- and B-type homopolymers, but in that system the homopolymers have a tendency to macrophase separate from the microemulsion. Our alternative system for creating BμE should be less prone to this macrophase separation.   

Complex Solutions of Self-Consistent Field Theory

For the past few decades, self-consistent field theory (SCFT) has proven to be a powerful tool for the exploration of polymeric nanostructures. It provides a mean field solution to the physical system, and thus one naturally assumes that the fields and ensemble average densities of SCFT solution must be real-valued functions. However, we unveil an intriguing possibility that the saddle-point approximation in SCFT may result in complex solutions. In this study, we demonstrate that for each real saddle-point solution, there may exist an infinite number of complex solutions sharing the same free energy, and thus the concept of "saddle-point" in the functional space can be generalized as "saddle-line" in the complex world. Focusing on AB homopolymer mixtures and AB diblock copolymer systems, we explore the conditions for obtaining such complex solutions and their unique characteristics. In the case of the AB homopolymer mixture, we derive an analytic expression for the complex solution in the high χN limit. These findings offer valuable insights for comprehending and analyzing results from complex Langevin field theoretic simulations, where these complex solutions are readily accessible.   

Preserving Positivity: Developments in Density-Explicit Field-Theoretic Simulations

Field-theoretic simulations (FTS) are numerical treatments of polymer field theory models that go beyond the mean-field level and account for composition fluctuations. Such simulations have successfully captured a range of mesoscopic phenomena. Modern field-based simulations of polymeric fluids rely upon the auxiliary field theory framework that uses Hubbard-Stratonovich transformations to invoke the particle-to-field transformation; the transform introduces an inverse potential limiting the functional form of the non-bonded potentials. Lifting the restriction on non-bonded potentials will facilitate studies of a broad range of systems whose description requires higher-body or more complex potentials. A candidate field theory is the hybrid density-explicit auxiliary field (DE-AF) theory, which retains each species' density field in addition to a conjugate auxiliary field. Although the DE-AF theory is not new, FTS simulations in the DE-AF framework have yet to be realized up to this point. A significant challenge is maintaining the nonnegative character of the density field during stochastic evolution. For this purpose, we utilize positivity-preserving schemes that allow for the first stable and efficient FTS simulations of the DE-AF theory.   

Bridging Particle and Field-Theoretic Simulations of Polymers with Deep Learning

Polymer science holds a pivotal role in areas such as advanced materials design, drug delivery systems, and biological systems. In these applications, being able to efficiently predict polymer thermodynamics and self-assembly is crucial. Self-consistent field theory (SCFT) offers a theoretical framework with many successful predictions that have guided experiments. However, there are many examples where SCFT is challenging to apply due to its computational expense, such as systems with broad polydispersity or polymers with semiflexible backbones. Given the intrinsic limitations of SCFT in capturing dynamic behaviors, this study proposes a machine-learning approach that aims to bridge the gap between field-based and particle-based simulations. By integrating convolutional neural networks into SCFT, we aspire to utilize data from particle-based simulations for more informed training and enhanced predictive purposes. This SCFT informed by deep learning (SCFT-DL) strategy not only combines the strengths of both methods but also extends the classes of systems that can be efficiently described by SCFT. In this talk, I will describe how we have integrated CNNs, particle-based simulations, and field-theoretic simulations to extend the range of materials that can be modeled with SCFT. I will compare the efficiency of our method to existing methods and discuss numerous potential future applications for SCFT-DL.   

Molecular Dynamics Simulation of the Self-Assembly of Rigid Sphere-Rod Amphiphilic Marcomolecules into Onion-Like Assemblies

Self-assembly behaviors of amphiphilic block copolymers have been well explored. When both hydrophilic and hydrophobic domains are rigid, the common rule of self-assembly based on the packing parameter is not applicable because the solvophobic domain cannot collapse into a globule state. Recently, it was found that the T-shaped sphere-rod shaped amphiphiles with the long rods being hydrophobic domains show intriguing self-assembly behavior. In polar solvents they first stack to each other face to face, then such units would further assemble into onion-like structures with uniform size and strictly identical interlayer distance. They respond to the external condition change by changing the number of layers, but not the overall morphology. The self-assembly of these marcomolecules in organic solvent and water mixed solvent results in the spontaneous organization of bilayer structures. Using all-atom molecular dynamics simulations, we investigated the initial stages of the self-assembly process of amphiphilic molecules which will be the focus of this presentation. The investigation is also expanded through coarse-grained simulations and our findings will be discussed as well.   

Coil-helix Block Copolymers Can Exhibit Divergent Thermodynamics

Recent advances in polymer synthesis have led to the development of chiral block copolymers, which are capable of exhibiting several interesting phenomena arising from self-assembly. Several thermodynamic factors play a role in the self-assembly such as the entropy, enthalpy, and fluctuation effects arising from the helical conformation. In particular, thermodynamic properties such as order-disorder transition temperature appear to depend on the particular chemistry of the chiral block. In this work, we utilized a particle-based simulation model to evaluate distinct thermodynamic metrics and to compute the conformational statistics of chiral molecules. Five distinct parameters produce a wide range of helical conformations of varying pitch, resulting in two distinct thermodynamic behaviors. Specifically, we aimed to understand (1) the relationship between the helical conformation and entropy, and (2) the effect of the conformation on the Flory–Huggins interaction parameter, χ, when chemical disparity was introduced. Commonly used conformational metrics for flexible or stiff block copolymers do not capture the effective block repulsion because helical blocks are semiflexible and aspherical. Instead, pitch can quantitatively capture the effective block repulsion. Quite remarkably, the shift in χ for chemically dissimilar block copolymers can switch sign with small changes in the pitch of the helix.   

Chemical Potential of a Flexible Polymer Liquid in a Coarse-grained Representation

While the excess chemical potential is the key quantity in determining phase diagrams, its direct computation for high-density liquids of long polymer chains has posed a significant challenge. Computationally, the excess chemical potential is calculated using the Widom insertion method, which involves monitoring the change in internal energy as one incrementally introduces individual molecules into the liquid. However, when dealing with dense polymer liquids, inserting long chains requires generating trial configurations with a bias that favors those at low energy on a unit-by-unit basis: a procedure that becomes more challenging as the number of units increases. Thus, calculating the excess chemical potential of dense polymer liquids using this method becomes computationally intractable as the degree of polymerization exceeds 30. Here, we adopt a coarse-grained model derived from integral equation theory, for which inserting long polymer chains becomes feasible. This integral equation theory of coarse-graining (IECG) represents a polymer as a sphere or a collection of blobs interacting through a soft potential. We employ the IECG approach to compute the excess chemical potential using Widom's method for polymer chains of increasing length and varying density. We demonstrate that the excess chemical potential remains nearly constant across various levels of coarse-graining, offering valuable insights into the consistency of this type of procedure.   

MolSets: Molecular graph deep sets model for mixture property modeling

Recent advances in machine learning (ML) have expedited materials discovery and design. One significant challenge faced by ML for materials is the expansive combinatorial space of potential materials formed by diverse constituents and their possible configurations. This complexity is particularly evident in molecular mixtures, a space frequently explored in search of electrolytes, fuels, and coolants, among other applications. Due to the complex structures of molecules and the permutation-invariant nature of mixtures, conventional ML methods have difficulties in modeling such systems. In this work, we propose MolSets, a specialized ML model for molecular mixtures. Representing individual molecules as graphs and their mixture as a set, MolSets leverages graph neural network and the deep sets architecture to extract information at the molecule level and aggregate it at the mixture level, thus addressing local complexity while retaining global flexibility. We demonstrate the efficacy of MolSets in predicting the transport properties of lithium battery electrolytes, and highlight its broader applicability across various mixture property modeling tasks and other problems with combinatorial complexity.   

Quantifying Similarity between Polymer Ensembles

Synthetic polymers are typically stochastic in nature, which means that instead of having a single well-defined structure, they are ensembles with distributions across molecular mass, topology and sequence. Thus, determining the similarity between polymers is significantly more challenging than for small molecules where a number of established methods exist. When dealing with polymer ensembles, a typical approach is to compute the embedding vector or fingerprint for monomer or polymer and then take the weighted average to yield a single embedding vector for the ensemble. This pre-averaging can obfuscate differences between ensembles and can erroneously yield predictions of perfect similarity for two dissimilar ensembles. Using inspiration from the informatics community, we adopt the Earth Mover's Distance (EMD) along with explicit calculation of distances between all constituents. As its name implies, EMD allows for computing the cost of moving an entity, earth or probability, from one location to another. We demonstrate the utility of this technique with a number of case studies ranging from copolymers to experimentally measured molecular mass distributions. Ultimately, similarity can be used for enhanced search in data resources such as a Community Resource for Innovation in Polymer Technology and to accelerate machine learning enabled polymer design.   

Identifying promising anions for superionic single-ion conducting polymer electrolytes using data-science approaches

Polymer electrolytes are one of the most promising materials for next-generation energy systems due to their high stability, flexibility, and processibility. A major challenge is the development of highly conductive polymers with high cation transport number since polymeric electrolyte have yet to achieve the necessary properties for large-scale applications. We seek to use data-science approaches to provide insights into ion transport and expedite the design of superionic single ion conductors. Using ionic conductivity data collected from the literature and our own data, we test different methods of extracting the energy barrier for ion transport. The traditional Arrhenius fit to the temperature dependent ionic conductivity data indicates that the Meyer-Neldel rule holds true for single-ion conductors, but the values of fitting parameters do not provide physical explanation. Our modified method using fixed preexponent factor suggests that energy barriers should be temperature dependent, which may be characteristic for a broad range of temperature. With this in mind, we further use data-driven approaches and density functional theory (DFT) based calculations to connect the chemical structures of anions, binding energy of cation-anion pairs, and ionic conductivity. These approaches will assist in identifying promising chemical structures that lead to enhanced conductivity and guide the design of novel superionic single ion conducting polymer electrolytes.   

Predicting Nanoparticle Dispersion State in Polymer Films via Machine Learning

The addition of nanoparticles into polymers can change the properties of the films. An important parameter in these nanocomposites is the aggregation state of the nanoparticles within the polymer matrix. Due to a large parameter space which may have an impact on the nanocomposite’s aggregation state, it is difficult to develop a physics based predictive model. In order to pin down which physical parameters are most important in predicting the nanoparticle dispersion in polymer films, we construct a machine learning model to predict the dispersion state of polymer nanocomposites which are produced via drop casting. Using this machine learning model, we can determine how much each individual parameter contributes to the prediction of the final aggregation state, and begin to design a physics based model using the most impactful parameters.   

Nucleation patterns of polymer crystals analyzed by machine learning models

The understanding of polymer crystallization is a longstanding challenge within the field of polymer science. We employ machine learning (ML) algorithms to analyze conformation patterns during nucleation of early crystallites in undercooled melts based on molecular dynamics simulation data. Our focus is on data-driven techniques that establish decision boundaries to detect the crystalline state of individual monomers without prior knowledge instead of 'classical' methods that manually position these boundaries [C. Luo and J.-U. Sommer, Macromolecules 44 (2011), 1523]. In particular, we utilize self-supervised auto-encoders to compress the local fingerprint information and apply a Gaussian mixture model to distinguish between ordered and disordered states. The high specificity of the method allows us to uncover the intricate temporal patterns related to crystalline order, even before any clear indications of the transition became evident in thermodynamic properties, such as specific volume. We identify a pre-transition point characterized by the highest crystallization efficiency, determined by the fraction of monomers preserved in the crystalline phase as compared to those entering that phase.