Calculating Pairwise Similarity of Polymer Ensembles via Earth Mover's Distance.

Synthetic polymers, in contrast to small molecules and deterministic biomacromolecules, are typically ensembles composed of polymer chains with varying numbers, lengths, sequences, chemistry, and topologies. While numerous approaches exist for measuring pairwise similarity among small molecules and sequence-defined biomacromolecules, accurately determining the pairwise similarity between two polymer ensembles remains challenging. This work proposes the earth mover's distance (EMD) metric to calculate the pairwise similarity score between two polymer ensembles. EMD offers a greater resolution of chemical differences between polymer ensembles than the averaging method and provides a quantitative numeric value representing the pairwise similarity between polymer ensembles in alignment with chemical intuition. The EMD approach for assessing polymer similarity enhances the development of accurate chemical search algorithms within polymer databases and can improve machine learning techniques for polymer design, optimization, and property prediction.

Scaling Relationship of Complex Coacervate Core Micelles: Role of Core Block Stretching.

The scaling relationship of complex coacervate core micelles (C3Ms) has been investigated experimentally and theoretically. The C3Ms are formed by mixing two oppositely charged block copolyelectrolyte solutions (i.e., AB + AC system) and are characterized by small-angle neutron (SANS) and X-ray scattering (SAXS). Scaling relationships for micellar structure parameters, including core radius, total radius, corona thickness, and aggregation number, all with respect to the core block length, are determined. A scaling theory is also proposed by minimizing the free energy per chain, leading to four regimes depending on the core and corona chain conformations. Although the corona block is significantly longer than the core block, the structure of our C3Ms is consistent with that of the crew-cut I regime. A highly swollen core by water enables the core blocks to be stretched significantly and corona chains to be minimally overlapped.

Emerging Trends in Machine Learning: A Polymer Perspective.

In the last five years, there has been tremendous growth in machine learning and artificial intelligence as applied to polymer science. Here, we highlight the unique challenges presented by polymers and how the field is addressing them. We focus on emerging trends with an emphasis on topics that have received less attention in the review literature. Finally, we provide an outlook for the field, outline important growth areas in machine learning and artificial intelligence for polymer science and discuss important advances from the greater material science community.

Community Resource for Innovation in Polymer Technology (CRIPT): A Scalable Polymer Material Data Structure.

The Community Resource for Innovation in Polymer Technology (CRIPT) data model is designed to address the high complexity in defining a polymer structure and the intricacies involved with characterizing material properties.

Leveraging Theory for Enhanced Machine Learning.

The application of machine learning to the materials domain has traditionally struggled with two major challenges: a lack of large, curated data sets and the need to understand the physics behind the machine-learning prediction. The former problem is particularly acute in the polymers domain. Here we aim to simultaneously tackle these challenges through the incorporation of scientific knowledge, thus, providing improved predictions for smaller data sets, both under interpolation and extrapolation, and a degree of explainability. We focus on imperfect theories, as they are often readily available and easier to interpret. Using a system of a polymer in different solvent qualities, we explore numerous methods for incorporating theory into machine learning using different machine-learning models, including Gaussian process regression. Ultimately, we find that encoding the functional form of the theory performs best followed by an encoding of the numeric values of the theory.

Structure-dilute solution property relationships of comb-like macromolecules in a good solvent.

The structural characterization of branched polymers still poses experimental challenges despite their technological potential. This lack of clarity is egregious in linear low-density polyethylene (LLDPE), a common industrial plastic. Here, we design a coarse-grain, implicit solvent molecular dynamics model for LLDPE in 1,2,4-trichlorobenzene, a canonical good solvent, that replicates all-atom simulations and experiments. We employ this model to test the relationship between the contraction factors, the ratios of branched to linear dilute solution properties. In particular, we relate the contraction factor of the radius of gyration to that of the intrinsic viscosity and the hydrodynamic radius. The contraction exponents are constant as we vary branch length and spacing in contrast to theoretical expectations. We use this observation to develop a general theory for the dilute solution properties of linear polymers with linear side-chain branches, comb-like macromolecules, in a good solvent and validate the theory by generating master curves for LLDPE.

Molecular Mass Dependence of Interfacial Tension in Complex Coacervation.

The interfacial tension of coacervates, the liquidlike phase composed of oppositely charged polymers that coexists at equilibrium with a supernatant, forms the basis for multiple technologies. Here we present a comprehensive set of experiments and molecular dynamics simulations to probe the effect of molecular mass on interfacial tension γ, far from the critical point, and derive γ=γ_{∞}(1-h/N), where N is the degree of polymerization, γ_{∞} is the infinite molecular mass limit, and h is a constant that physically corresponds to the number of monomers of one chain within the coacervate correlation volume.

Rheology of crystallizing polymers: The role of spherulitic superstructures, gap height, and nucleation densities.

A longstanding goal in polymer rheology is to develop a physical picture that relates the growth of mechanical moduli during polymer crystallization to that of a structure. Here, we utilize simultaneous mechanical rheology and optical microscopy, with augmentation by deterministic reconstruction and stochastic simulations, to study isothermal crystallization in isotactic polypropylene. We observe the nucleation and growth of the surface and bulk spherulites, which are initially isolated and then impinge to form clusters and superstructures that eventually span the gap. We find that spherulitic superstructures play a critical role in the rheology, especially in the characteristic sharp upturn in moduli. Both the rheology and the spherulitic superstructures show pronounced gap dependencies, which we explain via finite-size effects in percolation phenomena and via surface-induced nucleation. The modulus-crystallinity relationship can be described through a general effective medium theory. It indicates that for thicker gaps, the viscoelastic liquid to solid transition can be described via percolation, whereas for our thinnest gap, it is best described by the linear mixing rule. We describe our results in terms of dimensionless nucleation rates and spherulite size, which enable the estimation of when gap-dependent superstructure effects can be anticipated.

Valence, loop formation and universality in self-assembling patchy particles.

Patchy particles have emerged as an attractive model to mimic phase separation and self-assembly of globular proteins solutions, colloidal patchy particles, and molecular fluids where directional interactions are operative. In our previous work, we extensively explored the coupling of directional and isotropic interactions on both the phase separation and self-assembly in a system of patchy particles with five spots. Here, we extend this work to consider different patch valences and isotropic interaction strengths with an emphasis on self-assembly. Although the location of self-assembly transition lines in the temperature-density plane depend on a number of parameters, we find universal behavior of cluster size that is dependent only on the probability of a spot being bound, the patch valence, and the density. Using these principles, we quantify both the mass distribution and the shape for all clusters, as well as clusters containing loops. Following the logical implications of these results, combined with a simplified version of a mean-field theory that incorporates Flory-Stockmayer theory, we find a universal curve for the temperature dependence of cluster mass and a universal curve for the fraction of clusters that contain loops. As the curves are dependent on the particle valence, such results provide a method for parameterizing patchy particle models using experimental data.

Polymer Informatics: Opportunities and Challenges.

We are entering an era where large volumes of scientific data, coupled with algorithmic and computational advances, can reduce both the time and cost of developing new materials. This emerging field known as materials informatics has gained acceptance for a number of classes of materials, including metals and oxides. In the particular case of polymer science, however, there are important challenges that must be addressed before one can start to deploy advanced machine learning approaches for designing new materials. These challenges are primarily related to the manner in which polymeric systems and their properties are reported. In this viewpoint, we discuss the opportunities and challenges for making materials informatics as applied to polymers, or equivalently polymer informatics, a reality.

Blending Education and Polymer Science: Semi Automated Creation of a Thermodynamic Property Database.

Structured databases of chemical and physical properties play a central role in the everyday research activities of scientists and engineers. In materials science, researchers and engineers turn to these databases to quickly query, compare, and aggregate various properties, thereby allowing for the development or application of new materials. The vast majority of these databases have been generated manually, through decades of labor-intensive harvesting of information from the literature; yet, while there are many examples of commonly used databases, a significant number of important properties remain locked within the tables, figures, and text of publications. The question addressed in our work is whether, and to what extent, the process of data collection can be automated. Students of the physical sciences and engineering are often confronted with the challenge of finding and applying property data from the literature, and a central aspect of their education is to develop the critical skills needed to identify such data and discern their meaning or validity. To address shortcomings associated with automated information extraction, while simultaneously preparing the next generation of scientists for their future endeavors, we developed a novel course-based approach in which students develop skills in polymer chemistry and physics and apply their knowledge by assisting with the semi-automated creation of a thermodynamic property database.

Coupling of isotropic and directional interactions and its effect on phase separation and self-assembly.

The interactions of molecules and particles in solution often involve an interplay between isotropic and highly directional interactions that lead to a mutual coupling of phase separation and self-assembly. This situation arises, for example, in proteins interacting through hydrophobic and charged patch regions on their surface and in nanoparticles with grafted polymer chains, such as DNA. As a minimal model of complex fluids exhibiting this interaction coupling, we investigate spherical particles having an isotropic interaction and a constellation of five attractive patches on the particle's surface. Monte Carlo simulations and mean-field calculations of the phase boundaries of this model depend strongly on the relative strength of the isotropic and patch potentials, where we surprisingly find that analytic mean-field predictions become increasingly accurate as the directional interactions become increasingly predominant. We quantitatively account for this effect by noting that the effective interaction range increases with increasing relative directional to isotropic interaction strength. We also identify thermodynamic transition lines associated with self-assembly, extract the entropy and energy of association, and characterize the resulting cluster properties obtained from simulations using percolation scaling theory and Flory-Stockmayer mean-field theory. We find that the fractal dimension and cluster size distribution are consistent with those of lattice animals, i.e., randomly branched polymers swollen by excluded volume interactions. We also identify a universal functional form for the average molecular weight and a nearly universal functional form for a scaling parameter characterizing the cluster size distribution. Since the formation of branched clusters at equilibrium is a common phenomenon in nature, we detail how our analysis can be used in experimental characterization of such associating fluids.

Interplay of particle shape and suspension properties: a study of cube-like particles.

With advances in anisotropic particle synthesis, particle shape is now a feasible parameter for tuning suspension properties. However, there is a need to determine how these newly synthesized particles affect suspension properties and a need to solve the inverse problem of inferring the particle shape from property measurements. Either way, accurate suspension property predictions are required. Towards this end, we calculated a set of dilute suspension properties for a family of cube-like particles that smoothly interpolate between spheres and cubes. Using three conceptually different methods, we numerically computed the electrical properties of particle suspensions, including the intrinsic conductivity of perfect conductors and insulators. We also considered hydrodynamic properties relevant to particle solutions including the hydrodynamic radius, the intrinsic viscosity and the intrinsic solvent diffusivity. Additionally, we determined the second osmotic virial coefficient using analytic expressions along with numerical integration. As the particles became more cube-like, we found that all of the properties investigated become more sensitive to particle shape.

Phase behavior of electrostatically complexed polyelectrolyte gels using an embedded fluctuation model.

Nanostructured, responsive hydrogels formed due to electrostatic interactions have promise for applications such as drug delivery and tissue mimics. These physically cross-linked hydrogels are composed of an aqueous solution of oppositely charged triblocks with charged end-blocks and neutral, hydrophilic mid-blocks. Due to their electrostatic interactions, the end-blocks microphase separate and form physical cross-links that are bridged by the mid-blocks. The structure of this system was determined using a new, efficient embedded fluctuation (EF) model in conjunction with self-consistent field theory. The calculations using the EF model were validated against unapproximated field-theoretic simulations with complex Langevin sampling and were found consistent with small angle X-ray scattering (SAXS) measurements on an experimental system. Using both the EF model and SAXS, phase diagrams were generated as a function of end-block fraction and polymer concentration. Several structures were observed including a body-centered cubic sphere phase, a hexagonally packed cylinder phase, and a lamellar phase. Finally, the EF model was used to explore how parameters that directly relate to polymer chemistry can be tuned to modify the resulting phase diagram, which is of practical interest for the development of new hydrogels.

Small angle neutron scattering study of complex coacervate micelles and hydrogels formed from ionic diblock and triblock copolymers.

A complex coacervate is a fluid phase that results from the electrostatic interactions between two oppositely charged macromolecules. The nature of the coacervate core structure of hydrogels and micelles formed from complexation between pairs of diblock or triblock copolymers containing oppositely charged end-blocks as a function of polymer and salt concentration was investigated. Both ABA triblock copolymers of poly[(allyl glycidyl ether)-b-(ethylene oxide)-b-(allyl glycidyl ether)] and analogous poly[(allyl glycidyl ether)-b-(ethylene oxide)] diblock copolymers, which were synthesized to be nearly one-half of the symmetrical triblock copolymers, were studied. The poly(allyl glycidyl ether) blocks were functionalized with either guanidinium or sulfonate groups via postpolymerization modification. Mixing of oppositely charged block copolymers resulted in the formation of nanometer-scale coacervate domains. Small angle neutron scattering (SANS) experiments were used to investigate the size and spacing of the coacervate domains. The SANS patterns were fit using a previously vetted, detailed model consisting of polydisperse core-shell micelles with a randomly distributed sphere or body-centered cubic (BCC) structure factor. For increasing polymer concentration, the size of the coacervate domains remained constant while the spatial extent of the poly(ethylene oxide) (PEO) corona decreased. However, increasing salt concentration resulted in a decrease in both the coacervate domain size and the corona size due to a combination of the electrostatic interactions being screened and the shrinkage of the neutral PEO blocks. Additionally, for the triblock copolymers that formed BCC ordered domains, the water content in the coacervate domains was calculated to increase from approximately 16.8% to 27.5% as the polymer concentration decreased from 20 to 15 wt %.

A facile synthesis of dynamic, shape-changing polymer particles.

We herein report a new facile strategy to ellipsoidal block copolymer nanoparticles that exhibit a pH-triggered anistropic swelling profile. In a first step, elongated particles with an axially stacked lamellae structure are selectively prepared by utilizing functional surfactants to control the phase separation of symmetric polystyrene-b-poly(2-vinylpyridine) (PS-b-P2VP) in dispersed droplets. In a second step, the dynamic shape change is realized by cross-linking the P2VP domains, thereby connecting glassy PS discs with pH-sensitive hydrogel actuators.

Striped, ellipsoidal particles by controlled assembly of diblock copolymers.

Control of interfacial interactions leads to a dramatic change in shape and morphology for particles based on poly(styrene-b-2-vinylpyridine) diblock copolymers. Key to these changes is the addition of Au-based surfactant nanoparticles (SNPs) which are adsorbed at the interface between block copolymer-containing emulsion droplets and the surrounding amphiphilic surfactant to afford asymmetric, ellipsoid particles. The mechanism of formation for these novel nanostructures was investigated by systematically varying the volume fraction of SNPs, with the results showing the critical nature that the segregation of SNPs to specific interfaces plays in controlling structure. A theoretical description of the system allows the size distribution and aspect ratio of the asymmetric block copolymer colloidal particles to be correlated with the experimental results.