Correlating the Diffusion of Water to Performance in Model Reverse Osmosis Polyamides with Controlled Crosslink Densities.

We systematically reduce the cross-link density of a PA network based on m-phenylene diamine by substituting a fraction of the trifunctional trimesoyl chloride cross-linking agent with a difunctional isophthaloyl analog that promotes chain extension, in order to elucidate robust design cues for improving the polyamide (PA) separation layer in reverse osmosis (RO) membranes for desalination. Thin films of these model PA networks are fully integrated into a composite membrane and evaluated in terms of their water flux and salt rejection. By incorporating 15 mol % of the difunctional chain extender, we reduce the cross-link density of the network by a factor of two, which leads to an 80 % increase in the free or unreacted amine content. The resulting swelling of the PA network in liquid water increases by a factor of two accompanied by a 30 % increase in the salt passage through the membrane. Surprisingly, this leads to a 30 % decrease in the overall permeance of water through the membrane. This conundrum is resolved by quantifying the microscopic diffusion coefficient of water inside the PA network with quasi-elastic neutron scattering. In the highest and lowest cross-link density networks, water shows strong signatures of confined diffusion. At short length scales, the water exhibits a translational diffusion that is consistent with the jump-diffusion mechanism. This translational diffusion coefficient is approximately five times slower in the lowest cross-linked density network, consistent with the reduced water permeance. This is interpreted as water molecules interacting more strongly with the increased free amine content. Over longer length scales the water diffusion is confined, exhibiting mobility that is independent of length scale. The length scales of confinement from the quasi-elastic neutron scattering experiments at which this transition from confined to translational diffusion occurs is on the order of (5 to 6) Å, consistent with complementary X-ray scattering, small angle neutron scattering, and positron annihilation lifetime spectroscopy measurements. The confinement appears to come from heterogeneities in the average inter-atomic distances, suggesting that diffusion occurs by water bouncing between chains and occasionally sticking to the polar functional groups. The results obtained here are compared with similar studies of water diffusion through both rigid porous silicates and ion exchange membranes, revealing robust design cues for engineering high-performance RO membranes.

CyRSoXS: a GPU-accelerated virtual instrument for polarized resonant soft X-ray scattering.

Polarized resonant soft X-ray scattering (P-RSoXS) has emerged as a powerful synchrotron-based tool that combines the principles of X-ray scattering and X-ray spectroscopy. P-RSoXS provides unique sensitivity to molecular orientation and chemical heterogeneity in soft materials such as polymers and biomaterials. Quantitative extraction of orientation information from P-RSoXS pattern data is challenging, however, because the scattering processes originate from sample properties that must be represented as energy-dependent three-dimensional tensors with heterogeneities at nanometre to sub-nanometre length scales. This challenge is overcome here by developing an open-source virtual instrument that uses graphical processing units (GPUs) to simulate P-RSoXS patterns from real-space material representations with nanoscale resolution. This computational framework - called CyRSoXS (https://github.com/usnistgov/cyrsoxs) - is designed to maximize GPU performance, including algorithms that minimize both communication and memory footprints. The accuracy and robustness of the approach are demonstrated by validating against an extensive set of test cases, which include both analytical solutions and numerical comparisons, demonstrating an acceleration of over three orders of magnitude relative to the current state-of-the-art P-RSoXS simulation software. Such fast simulations open up a variety of applications that were previously computationally unfeasible, including pattern fitting, co-simulation with the physical instrument for operando analytics, data exploration and decision support, data creation and integration into machine learning workflows, and utilization in multi-modal data assimilation approaches. Finally, the complexity of the computational framework is abstracted away from the end user by exposing CyRSoXS to Python using Pybind. This eliminates input/output requirements for large-scale parameter exploration and inverse design, and democratizes usage by enabling seamless integration with a Python ecosystem (https://github.com/usnistgov/nrss) that can include parametric morphology generation, simulation result reduction, comparison with experiment and data fitting approaches.

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.

Role of nanoparticle size and surface chemistry on ion transport and nanostructure of perfluorosulfonic acid ionomer nanocomposites.

Herein, we present a systematic investigation of the impact of silica nanoparticle (SiNP) size and surface chemistry on the nanoparticle dispersion state and the resulting morphology and vanadium ion permeability of the composite ionomer membranes. Specifically, Nafion containing a mass fraction of 5% silica particles, ranging in nominal diameters from 10 nm to >1 µm and with both sulfonic acid- and amine-functionalized surfaces, was fabricated. Most notably, an 80% reduction in vanadium ion permeability was observed for ionomer membranes containing amine-functionalized SiNPs at a nominal diameter of 200 nm. Further, these membranes exhibited an almost 400% increase in proton selectivity when compared to pristine Nafion. Trends in vanadium ion permeability within a particular nominal diameter were seen to be a function of the surface chemistry, where, for example, vanadyl ion permeability was observed to increase with increasing particle size for membranes containing unfunctionalized SiNPs, while it was seen to remain relatively constant for membranes containing amine-functionalized SiNPs. In general, the silica particles tended to exhibit a higher extent of aggregation as the size of the particles was increased. From small-angle neutron scattering experiments, an increase in the spacing of the hydrophobic domains was observed for all composite membranes, though particle size and surface chemistry were seen to have varying impacts on the spacing of the ionic domains of the ionomer.

Addressing the challenges of modeling the scattering from bottlebrush polymers in solution.

Small-angle scattering measurements of complex macromolecules in solution are used to establish relationships between chemical structure and conformational properties. Interpretation of the scattering data requires an inverse approach where a model is chosen and the simulated scattering intensity from that model is iterated to match the experimental scattering intensity. This raises challenges in the case where the model is an imperfect approximation of the underlying structure, or where there are significant correlations between model parameters. We examine three bottlebrush polymers (consisting of polynorbornene backbone and polystyrene side chains) in a good solvent using a model commonly applied to this class of polymers: the flexible cylinder model. Applying a series of constrained Monte-Carlo Markov Chain analyses demonstrates the severity of the correlations between key parameters and the presence of multiple close minima in the goodness of fit space. We demonstrate that a shape-agnostic model can fit the scattering with significantly reduced parameter correlations and less potential for complex, multimodal parameter spaces. We provide recommendations to improve the analysis of complex macromolecules in solution, highlighting the value of Bayesian methods. This approach provides richer information for understanding parameter sensitivity compared to methods which produce a single, best fit.

Bottlebrush polymers in the melt and polyelectrolytes in solution share common structural features.

Uncharged bottlebrush polymer melts and highly charged polyelectrolytes in solution exhibit correlation peaks in scattering measurements and simulations. Given the striking superficial similarities of these scattering features, there may be a deeper structural interrelationship in these chemically different classes of materials. Correspondingly, we constructed a library of isotopically labeled bottlebrush molecules and measured the bottlebrush correlation peak position [Formula: see text] by neutron scattering and in simulations. We find that the correlation length scales with the backbone concentration, [Formula: see text], in striking accord with the scaling of ξ with polymer concentration cP in semidilute polyelectrolyte solutions [Formula: see text] The bottlebrush correlation peak broadens with decreasing grafting density, similar to increasing salt concentration in polyelectrolyte solutions. ξ also scales with sidechain length to a power in the range of 0.35-0.44, suggesting that the sidechains are relatively collapsed in comparison to the bristlelike configurations often imagined for bottlebrush polymers.

The Concentration Dependence of the Size and Symmetry of a Bottlebrush Polymer in a Good Solvent.

Bottlebrush polymers consist of a linear backbone with densely grafted side chains which impact the rigidity of the molecule. The persistence length of the bottlebrush backbone in solution is influenced by both the intrinsic structure of the polymer and by the local environment, such as the solvent quality and concentration. Increasing the concentration reduces the overall size of the molecule due to the reduction in backbone stiffness. In this study we map out the size of a bottlebrush polymer as a function of concentration for a single backbone length. Small-angle neutron scattering (SANS) measurements are conducted on a polynorbornene-based bottlebrush with polystyrene side chains in a good solvent. The data are fit using a model which provides both the long and short axis radius of gyration (R g,2 and R g,1, respectively), providing a measure for how the conformation changes as a function of concentration. At low concentrations a highly anisotropic structure is observed (R g,2/R g,1 ≈ 4), becoming more isotropic at higher concentrations (R g,2/R g,1 ≈ 1.5). The concentration scaling for both R g,2 and the overall R g are evaluated and compared with predictions in the literature. Coarse-grained molecular dynamics simulations were also conducted to probe the impact of concentration on bottlebrush conformation showing qualitative agreement with the experimental results.

Leveraging Nanoparticle Dispersion State To Tune Vanadium Ion Selectivity of Nanophase-Segregated Ionomer Nanocomposites for Redox Flow Batteries.

Ionomer nanocomposites provide a promising solution to address ion crossover issues inherent to traditional ion-containing membranes used in batteries for grid-scale energy storage (e.g., vanadium redox flow batteries). Herein, we investigate the impact of nanoparticle surface chemistry on nanoparticle dispersion, membrane morphology, and vanadium ion permeability in a series of Nafion nanocomposites. Specifically, silica nanoparticles (SiNPs) were functionalized with various chemical moieties, seven in total, that electrostatically interact, either attractively or repulsively, with the sulfonic acid groups that coalesce to form the ionic network within Nafion. As seen from electron microscopy analysis of the nanocomposites, SiNPs with sulfonic acid end-functionality were, on average, well dispersed within the ionomer membrane, though increased vanadium ion permeability, as compared to pristine (or unmodified) Nafion, was observed and attributed to changes in the Donnan potential of the system. In contrast, SiNPs with amine end-functionality were, on average, observed to form large aggregates within the ionomer membrane. Surprisingly, nanocomposites containing a higher degree of nanoparticle aggregation demonstrated the lowest vanadium ion permeability. Fractal analysis of the low-Q small-angle neutron scattering data suggests that the interface between the ionomer and the SiNP surface transitions from rough to smooth when the nanoparticle surface is changed from sulfonic acid-functionalized to amine-functionalized.

pyPRISM: A Computational Tool for Liquid-State Theory Calculations of Macromolecular Materials.

The Polymer Reference Interaction Site Model (PRISM) theory describes the equilibrium spatial-correlations of liquid-like polymer systems including melts, blends, solutions, block copolymers, ionomers, liquid crystalline polymers, and nanocomposites. Using PRISM theory, one can calculate thermodynamic (second virial coefficients, Flory-Huggins χ interaction parameters, potentials of mean force) and structural (pair correlation functions, structure factors) data for these macromolecular materials. Here, we present a Python-based, open-source framework, pyPRISM, for conducting PRISM theory calculations. This framework aims to simplify PRISM-based studies by providing a user-friendly scripting interface for setting up and numerically solving the PRISM equations. pyPRISM also provides data structures, functions, and classes that streamline PRISM calculations, allowing pyPRISM to be extended for use in other tasks, such as the coarse-graining of atomistic simulation force-fields or the modeling of experimental scattering data. The goal of this framework is to reduce the barrier to correctly and appropriately using PRISM theory and to provide a platform for rapid calculations of the structure and thermodynamics of polymeric fluids and nanocomposites.

Effect of conjugation on phase transitions in thermoresponsive polymers: an atomistic and coarse-grained simulation study.

Using atomistic and coarse-grained molecular dynamics (MD) simulations, we explain the shifts in lower critical solution temperature (LCST)-like phase transitions exhibited by elastin-like peptides (ELPs) upon conjugation to other macromolecules (e.g. collagen-like peptides or CLPs). First, using atomistic simulations, we study ELP oligomers with the sequence (VPGFG)6 in explicit water, and characterize the LCST-like transition temperature as one at which the ELP oligomers undergo a change in "hydration state". In agreement with past experimental observations of Luo and Kiick, upon anchoring ELP oligomers to a point to mimic ELP oligomers conjugated to another macromolecule, there is an apparent slight shift in the transition temperature to lower values compared to free (unconjugated) ELP oligomers. However, these atomistic simulations are limited to small systems of short ELPs, and as such do not capture the multiple chain aggregation/phase separation observed in experiments of ELPs. Therefore, we utilize phenomenological coarse-grained (CG) MD simulations to probe how conjugating a block of generic-LCST polymer to another rigid unresponsive macromolecular block impacts the transition temperatures at concentrations and length scales larger than atomistic simulations. We find that when multiple LCST polymer chains are conjugated to a rigid unresponsive polymer block, the increased local crowding of the LCST polymers shifts the transition marked by onset of chain aggregation to smaller effective polymer-polymer attraction energies compared to the free LCST polymer chains. The driving force needed for aggregation is reduced in the conjugates compared to free LCST polymer due to reduction in the loss of polymer configurational entropy upon aggregation.

Wetting-Dewetting and Dispersion-Aggregation Transitions Are Distinct for Polymer Grafted Nanoparticles in Chemically Dissimilar Polymer Matrix.

Simulations and experiments are conducted on mixtures containing polymer grafted nanoparticles in a chemically distinct polymer matrix, where the graft and matrix polymers exhibit attractive enthalpic interactions at low temperatures that become progressively repulsive as temperature is increased. Both coarse-grained molecular dynamics simulations, and X-ray scattering and neutron scattering experiments with deuterated polystyrene (dPS) grafted silica and poly(vinyl methyl ether) PVME matrix show that the sharp phase transition from (mixed) dispersed to (demixed) aggregated morphologies due to the increasingly repulsive effective interactions between the blend components is distinct from the continuous wetting-dewetting transition. Strikingly, this is unlike the extensively studied chemically identical graft-matrix composites, where the two transitions have been considered to be synonymous, and is also unlike the free (ungrafted) blends of the same graft and matrix homopolymers, where the wetting-dewetting is a sharp transition coinciding with the macrophase separation.

Decreasing Polymer Flexibility Improves Wetting and Dispersion of Polymer-Grafted Particles in a Chemically Identical Polymer Matrix.

We present a molecular dynamics simulation study of nanocomposites containing homopolymer-grafted particles in a homopolymer matrix, where the graft and matrix chemistries are identical, to elucidate the effect of polymer flexibility on the wetting of the grafted layer by the matrix and the nanocomposite morphology. Decreasing flexibility of the graft and matrix causes increased wetting of the grafted layer by the matrix. This increased wetting of the grafted layer with decreasing flexibility is more significantly driven by decreasing the graft flexibility than by decreasing the matrix flexibility. This is due to a large increase in mixing entropy of the graft and matrix upon wetting rather than the reduction in conformational entropy loss of matrix upon wetting. Due to this improved wetting with decreasing flexibility of the graft and matrix, we observe increased particle dispersion in the polymer matrix.

Polydispersity for tuning the potential of mean force between polymer grafted nanoparticles in a polymer matrix.

We present an integrated theory and simulation study of polydisperse polymer grafted nanoparticles in a polymer matrix to demonstrate the effect of polydispersity in graft length on the potential of mean force between the grafted nanoparticles. In dense polymer solutions, increasing polydispersity in graft length reduces the strength of repulsion at contact and weakens the attractive well at intermediate interparticle distances, completely eliminating the latter at high polydispersity index. The reduction in contact repulsion is attributable to polydispersity relieving monomer crowding near the particle surface, especially at high grafting densities. The elimination of the midrange attractive well is attributable to the longer grafts in the polydisperse graft length distribution that introduce longer range steric repulsion and alter the wetting of the grafted layer by matrix chains. Dispersion of the grafted particles is stabilized by increased penetration or wetting of the polydisperse grafted layer by the matrix chains. This work demonstrates that at high grafting densities, polydispersity in graft length can be used to stabilize dispersions of grafted nanoparticles in a polymer matrix at conditions where monodisperse grafts would cause aggregation.