Model Polymer Research Articles

Molecular Dynamics Analysis of the Scattering Phenomena of Oxygen Molecules on an Ionomer Surface in Catalyst Layer of Fuel Cell

As energy demand increases and global warming progresses, expectations for fuel cells, which generate electricity through chemical reactions between hydrogen and oxygen, are rising. There are various types of fuel cells, which are classified according to the electrolyte. Polymer electrolyte fuel cells (PEFCs) are expected to be used in stationary power sources for home use and fuel cell vehicles because of their low operating temperature, short start-up time, and ease of miniaturization. The cost has been an issue in the widespread use of fuel cells. The amount of platinum used in the catalyst layer (CL) must be reduced to reduce costs. However, it increases the current density per unit area of platinum. There are three factors that contribute to voltage drop: ohmic polarization, activation polarization, and diffusion polarization. At high current densities, the voltage drop due to diffusion polarization is dominant. The main cause of diffusion polarization is the transport resistance of oxygen molecules in the CL, and improving the oxygen transport properties in the CL will lead to lower cost PEFCs. In this study, we analyzed the transport properties of oxygen molecules in the CLs of PEFCs using the Monte Carlo (MC) method. The effect of oxygen scattering on the overall oxygen transport properties was investigated by considering the behavior on the surface of the ionomer film (surface diffusion) into the MC method, which simulates the overall transport in the PEFC CL. The objective of this study is to reproduce accurate oxygen transport by comparing the results of MC and molecular dynamics (MD) methods. First, we used the MC method to analyze oxygen scattering phenomena. In this study, we used the 3D structure data of CL in the MC simulations. The three-dimensional structure of the sample was reconstructed from sequential slice images. Molecules were assumed to reflect specularly on the boundaries of the simulation domain. Oxygen molecules were randomly placed in the simulation system. The time step was set at 5 ps and the simulation time was set at 4 μs. In order to examine the effect of surface diffusion on the transport properties of oxygen molecules, the simulation was performed using various conditions of surface diffusion. We calculated the effective diffusion coefficient of oxygen in the CL as the transport property of oxygen molecules in the MC method. As the surface diffusion coefficient increases, the effective diffusion coefficient of oxygen increases. When the surface diffusion coefficient is small, the effective diffusion coefficient of oxygen increases due to a decrease in the time constant, which determines the probability distribution of the surface residence time. However, when the surface diffusion coefficient is large, a different trend emerges. As the time constant increases, the effective diffusion coefficient has a peak value and then decreases. Next, to verify the model of surface diffusion in the MC method, we analyzed the scattering phenomenon of oxygen molecules in a simulation system that simulates the pores in the CL using the MD method. We modeled the nano pores in the CL as a slit between the ionomer walls in the MD method. Nafion with the equivalent weight (EW) of 1146 was used as polymer model. The number of Nafion chains is set at 4, and the water content λ is set at 7. Three-dimensional periodic boundary conditions were applied to the simulation domain. After the system was equilibrated, 1 ns of NVT simulation was performed for production. The temperature was set at 297 K. The behavior of oxygen molecules impacting on the ionomer wall was analyzed. We analyzed the behavior of oxygen molecules colliding with the ionomer membrane using the MD method. The average residence time of surface diffusion on the ionomer thin film was of the order of 10-10s. When the calculation results were compared with the MC results, it was found that the average residence time obtained by the MD method was the value where the surface diffusion coefficient affects much on the effective diffusion coefficient. Comparing the results of the MD method with the surface diffusion model used in the MC method, there are some discrepancies between the results and the model. For example, the MC method used a model in which oxygen molecules reflect diffusively on the ionomer surface. However, in the MD method, it was found that oxygen molecules tend to reflect in the direction of travel (Fig. 1). Therefore, a more accurate model of the MC method needs to be developed in the future. Figure 1

Modeling Electrical Conductivity of Injection-Molded Polymer Composite Bipolar Plates

Bipolar plates can be responsible for up to 40% of the total stack cost and 80% of the weight of a polymer electrolyte membrane fuel cell [1]. To reduce these cost and weight limitations, this work explores injection molding of polymer composites. Injection molding is well-suited for mass production and polymeric materials can significantly reduce the weight of traditional metallic bipolar plates. While polymers lack electrical conductivity, fillers can be added to fabricate conductive polymer composites. The main objective of this research is to model and injection mold polymer composites that will meet the United States Department of Energy technical target for bipolar plate electrical conductivity (> 100 S/cm).A fiber contact model was developed to predict electrical conductivity based upon direction in the material, fiber alignment, fiber length and diameter, fiber concentration, and fiber conductivity [2]. Fiber alignment was measured experimentally by imaging cross sections of injection-molded nylon/carbon fiber composites. Imaging was performed on samples with different weight percentages of carbon fiber and from different mold designs to compare how fiber angles change based on mold geometry. To reduce the significant time required to measure fiber angles experimentally, computer recognition and processing of fiber alignment was developed. Nylon composites were injection molded with carbon fiber loadings ranging from 10 to 40 wt%. Modeling predictions show good correlation within 20% of experimental conductivity measurements. Samples with at least 20 wt% carbon fiber exceeded the US DOE technical target for bipolar plate conductivity, reaching 250 S/cm. In addition to modeling electrical conductivity, the Halpin-Tsai equations are used to model the elastic modulus and ultimate strain of the polymer composite. Tensile testing showed that the modulus of elasticity increases with carbon fiber loadings up to 30 wt%, reaching 7.3 GPa. At loadings above 30 wt%, the higher filler content can create voids which decrease the modulus of elasticity. De Las Heras, A.; Vivas, F. J.; Segura, F.; Andujar, J. M., From the cell to the stack. A chronological walk through the techniques to manufacture the PEFCs core. Renewable & Sustainable Energy Reviews 2018, 96, 29-45.Weber, M.; Kamal, M. R., Estimation of the volume resistivity of electrically conductive composites. Polymer Composites 1997, 18 (6), 711-725. Figure 1

Analysis of the Mullins effect in buckling instability of double-network hydrogel beams under swelling equilibrium

Due to their outstanding physical and mechanical properties, double-network (DN) hydrogels have gained a most attention among various synthetic tough hydrogels. The Mullins effect and buckling instability are two frequent phenomena that may occur simultaneously in slender DN hydrogel structures as high load-bearing candidates. The swelling/deswelling degree of the DN hydrogel affects the coupling phenomena. It is essential to understanding the interplay between these behaviors. In this work, a physically based damage constitutive model for a DN polymer under water-diffusion equilibrium and cyclic loadings is developed. This theory of coupled swelling and load-induced deformations show good capability in capturing the Mullins effect of swollen DN hydrogels and the corresponding swelling ratio. The model parameters are determined by fitting experimental data of a freely swollen DN hydrogel under cyclic compression. Based on the constitutive model and determined parameters, the buckling instability of DN hydrogel beams is studied via the analytical formula of incremental modulus. The stability diagrams of the DN hydrogel beams under virgin loading and reloading are presented. The influences of stress softening, strain stiffening and chemical potential on buckling conditions for compressive stress and slenderness ratio are thoroughly analyzed. It demonstrates that the stress softening is dramatically against the stability of the beam, but the strain-stiffening effect would conversely help widen the stable range. Besides, it is found that a DN gel beam immersed in a sufficient low chemical potential environment has better buckling stability. These theoretical results are valuable in the preparation and structural design of DN hydrogels for repeated use purpose.

Disentanglement of Surface and Confinement Effects for Diene Metathesis in Mesoporous Confinement.

We study the effects of a planar interface and confinement on a generic catalytically activated ring-closing polymerization reaction near an unstructured catalyst. For this, we employ a coarse-grained polymer model using grand-canonical molecular dynamics simulations with a Monte Carlo reaction scheme. Inspired by recent experiments in the group of M. Buchmeiser that demonstrated an increase in ring-closing selectivity under confinement, we show that both the interface effects, i.e., placing the catalyst near a planar wall, and the confinement effects, i.e., locating the catalyst within a pore, lead to an increase of selectivity. We furthermore demonstrate that curvature effects for cylindrical mesopores (2 nm < d < 12.3 nm) influence the distribution of the chain ends, leading to a further increase in selectivity. This leads us to speculate that specially corrugated surfaces might also help to enhance catalytically activated polymerization processes.

Highly stretchable polymer semiconductor thin films with multi-modal energy dissipation and high relative stretchability

Stretchable polymer semiconductors (PSCs) have seen great advancements alongside the development of soft electronics. But it remains a challenge to simultaneously achieve high charge carrier mobility and stretchability. Herein, we report the finding that stretchable PSC thin films (<100-nm-thick) with high stretchability tend to exhibit multi-modal energy dissipation mechanisms and have a large relative stretchability (rS) defined by the ratio of the entropic energy dissipation to the enthalpic energy dissipation under strain. They effectively recovered the original molecular ordering, as well as electrical performance, after strain was released. The highest rS value with a model polymer (P4) exhibited an average charge carrier mobility of 0.2 cm2V−1s−1 under 100% biaxial strain, while PSCs with low rS values showed irreversible morphology changes and rapid degradation of electrical performance under strain. These results suggest rS can be used as a parameter to compare the reliability and reversibility of stretchable PSC thin films.

Influence of the polymer type of a microplastic challenge on the reaction of murine cells

Due to global pollution derived from plastic waste, the research on microplastics is of increasing public interest. Until now, most studies addressing the effect of microplastic particles on vertebrate cells have primarily utilized polystyrene particles (PS). Other studies on polymer microparticles made, e.g., of polyethylene (PE), polyvinyl chloride (PVC), polypropylene (PP), or poly (ethylene terephthalate) (PET), cannot easily be directly compared to these PS studies, since the used microparticles differ widely in size and surface features. Here, effects caused by pristine microparticles of a narrow size range between 1 - 4 µm from selected conventional polymers including PS, PE, and PVC, were compared to those of particles made of polymers derived from biological sources like polylactic acid (PLA), and cellulose acetate (CA). The microparticles were used to investigate cellular uptake and assess cytotoxic effects on murine macrophages and epithelial cells. Despite differences in the particles' properties (e.g. ζ-potential and surface morphology), macrophages were able to ingest all tested particles, whereas epithelial cells ingested only the PS-based particles, which had a strong negative ζ-potential. Most importantly, none of the used model polymer particles exhibited significant short-time cytotoxicity, although the general effect of environmentally relevant microplastic particles on organisms requires further investigation.

Study on Molecular Rheology Using Some Model Polymers Based on Precise Synthesis

Study on Molecular Rheology Using Some Model Polymers Based on Precise Synthesis

Relationships Between Defectivity and Porosity in High Surface Area Porous Aromatic Frameworks.

Porous aromatic framework (PAF) microporosity is known to be strongly dependent on synthetic approach but little is known about why certain reactions yield significantly and consistently more porous PAFs. This article explores the connections between synthetic pathway, PAF defectivity, and microporosity. Using a network disassembly strategy, we show that defectivity is highly dependent on synthetic approach and that more defective PAFs are associated with lower surface areas and pore volumes. This empirical association is corroborated through systematic introduction of defects to a modelPAF, which results in significant reduction of apparent surface area and pore volumes. Taken together, these data suggest that only highly efficient coupling reactions should be targeted for the synthesis of ultra-high surface area porous aromatic frameworks.

Connecting Structural Characteristics and Material Properties in Phase-Separating Polymer Solutions: Phase-Field Modeling and Physics-Informed Neural Networks.

The formed morphology during phase separation is crucial for determining the properties of the resulting product, e.g., a functional membrane. However, an accurate morphology prediction is challenging due to the inherent complexity of molecular interactions. In this study, the phase separation of a two-dimensional model polymer solution is investigated. The spinodal decomposition during the formation of polymer-rich domains is described by the Cahn-Hilliard equation incorporating the Flory-Huggins free energy description between the polymer and solvent. We circumvent the heavy burden of precise morphology prediction through two aspects. First, we systematically analyze the degree of impact of the parameters (initial polymer volume fraction, polymer mobility, degree of polymerization, surface tension parameter, and Flory-Huggins interaction parameter) in a phase-separating system on morphological evolution characterized by geometrical fingerprints to determine the most influential factor. The sensitivity analysis provides an estimate for the error tolerance of each parameter in determining the transition time, the spinodal decomposition length, and the domain growth rate. Secondly, we devise a set of physics-informed neural networks (PINN) comprising two coupled feedforward neural networks to represent the phase-field equations and inversely discover the value of the embedded parameter for a given morphological evolution. Among the five parameters considered, the polymer-solvent affinity is key in determining the phase transition time and the growth law of the polymer-rich domains. We demonstrate that the unknown parameter can be accurately determined by renormalizing the PINN-predicted parameter by the change of characteristic domain size in time. Our results suggest that certain degrees of error are tolerable and do not significantly affect the morphology properties during the domain growth. Moreover, reliable inverse prediction of the unknown parameter can be pursued by merely two separate snapshots during morphological evolution. The latter largely reduces the computational load in the standard data-driven predictive methods, and the approach may prove beneficial to the inverse design for specific needs.

Solvent Dependent Folding of an Amphiphilic Polyaramid.

A series of synthetic alternating and amphiphilic aromatic amide polymers were synthesized by a step growth polymerization. Alternating meta- and para-linkages were introduced to force the polymer chain into a helical shape in the highly polar solvent water. The polymers were analyzed by 1H NMR spectroscopy and SEC in polar aprotic solvents such as DMSO and DMF. However, the polymers also showed good solubility in water. 1H NMR spectroscopy, small-angle X-ray scattering, and dynamic light scattering provided clear evidence of polymer folding in water but not DMF. We employed parallel tempering metadynamics in the well-tempered ensemble (PTMetaD-WTE) to simulate the free energy surfaces of an analogous model polymer in DMF and water. The simulations gave a molecular model of an unfolded structure in DMF and a helically folded tubular structure in water.

Correlation functions for confined wormlike chains

Polymer models describing the statistics of biomolecules under confinement have applications to a wide range of single-molecule experimental techniques and give insight into biologically relevant processes in vivo. In this paper, we determine the transverse position and bending correlation functions for a wormlike chain confined within slits and cylinders (with one and two confined dimensions, respectively) using a mean-field approach that enforces rigid constraints on average. We show the theoretical predictions accurately capture the statistics of a wormlike chain from Monte Carlo simulations in both confining geometries for both weak and strong confinement. We also show that the longitudinal correlation function is accurately computed for a chain confined to a slit and leverages the accuracy of the model to suggest an experimental technique to infer the (often unobservable) transverse statistics from the (directly observable) longitudinal end-to-end distance.

Explainability and extrapolation of machine learning models for predicting the glass transition temperature of polymers

AbstractMachine learning (ML) offers promising tools to develop surrogate models for polymers' structure–property relations. Surrogate models can be built upon existing polymer data and are useful for rapidly predicting the properties of unknown polymers. The accuracy of such ML models appears to depend on the feature space representation of polymers, the range of training data, and learning algorithms. Here, we establish connections between these factors for predicting the glass transition temperature (Tg) of polymers. Our analysis suggests linear models with fewer fitting parameters are as accurate as nonlinear models with many hidden and unexplainable parameters. Also, the performance of a monomer topology‐based ML model is found to be qualitatively identical to that of a physicochemical descriptor‐based ML model. We find that the ML models's performance in the extrapolative region is enhanced as the property range of the training data increases. Moreover, we establish new Tg – polymer chemistry correlations via ML. Our work illustrates how ML can advance the fundamental understanding of polymer structure–property correlations and its efficacy for extrapolation problems.

Polymer Modeling Reveals Interplay between Physical Properties of Chromosomal DNA and the Size and Distribution of Condensin-Based Chromatin Loops.

Transient DNA loops occur throughout the genome due to thermal fluctuations of DNA and the function of SMC complex proteins such as condensin and cohesin. Transient crosslinking within and between chromosomes and loop extrusion by SMCs have profound effects on high-order chromatin organization and exhibit specificity in cell type, cell cycle stage, and cellular environment. SMC complexes anchor one end to DNA with the other extending some distance and retracting to form a loop. How cells regulate loop sizes and how loops distribute along chromatin are emerging questions. To understand loop size regulation, we employed bead-spring polymer chain models of chromatin and the activity of an SMC complex on chromatin. Our study shows that (1) the stiffness of the chromatin polymer chain, (2) the tensile stiffness of chromatin crosslinking complexes such as condensin, and (3) the strength of the internal or external tethering of chromatin chains cooperatively dictate the loop size distribution and compaction volume of induced chromatin domains. When strong DNA tethers are invoked, loop size distributions are tuned by condensin stiffness. When DNA tethers are released, loop size distributions are tuned by chromatin stiffness. In this three-way interaction, the presence and strength of tethering unexpectedly dictates chromatin conformation within a topological domain.

How to Make the Stress Relaxation Experiment for Polymers More Informative.

Different viscoelastic models and characteristics are commonly used to describe, analyze, compare and improve the mechanical properties of polymers. A time-dependent linear relaxation modulus next to frequency-domain storage and loss moduli are the basic rheological material functions of polymers. The exponential Maxwell model and the exponential stretched Kohlrausch-Williams-Watts model are, probably, the most known linear rheological models of polymers. There are different identification methods for such models, some of which are dedicated to specific models, while others are general in nature. However, the identification result, i.e., the best model, always depends on the specific experimental data on the basis of which it was determined. When the rheological stress relaxation test is performed, the data are composed of the sampling instants used in the test and on the measurements of the relaxation modulus of the real material. To build a relaxation modulus model that does not depend on sampling instants is a fundamental concern. The problem of weighted least-squares approximation of the real relaxation modulus is discussed when only the noise-corrupted time-measurements of the relaxation modulus are accessible for identification. A wide class of models, that are continuous, differentiable and Lipschitz with respect to parameters, is considered for the relaxation modulus approximation. The main results concern the models that are selected asymptotically as the number of measurements tends to infinity. It is shown that even when the true relaxation modulus description is completely unknown, the approximate optimal model parameters can be derived from the measurement data that are obtained for sampling instants that are selected randomly due to the appropriate randomization introduced whenever certain conditions regarding the adopted class of models are satisfied. It is shown that the most commonly used stress relaxation models, the Maxwell and Kohlrausch-Williams-Watts models, satisfy these conditions. Since the practical problems of the identification of relaxation modulus models are usually ill posed, Tikhonov regularization is applied to guarantee the stability of the regularized solutions. The approximate optimal model is a strongly consistent estimate of the regularized model that is optimal in the sense of the deterministic integral weighted square error. An identification algorithm leading to the best regularized model is presented. The stochastic-type convergence analysis is conducted for noise-corrupted relaxation modulus measurements, and the exponential convergence rate is proved. Numerical studies for different models of the relaxation modulus used in the polymer rheology are presented for the material described by a bimodal Gauss-like relaxation spectrum. Numerical studies have shown that if appropriate randomization is introduced in the selection of sampling instants, then optimal regularized models of the relaxation modulus being asymptotically independent of these time instants can be recovered from the stress relaxation experiment data. The robustness of the identification algorithm to measurement noises was demonstrated both by analytical and numerical analyses.

Atomistic Modeling of Charge Injection Into Dielectric Polymers

Atomistic Modeling of Charge Injection Into Dielectric Polymers

Francis Comets’ Gumbel last passage percolation

In 2015, Francis Comets shared with me a clever way to relate a model of directed last passage percolation with i.i.d. Gumbel edge weights to a special case of the log-gamma directed polymer model. To my knowledge, he never wrote this down. In the wake of his recent passing I am recording Francis’ observation along with some associated asymptotics and discussion. This note is dedicated in memory of Francis whose work in the study of directed polymers defined and refined the field immensely.

Role of Polymer Concentration on the Release Rates of Proteins from Single- and Double-Network Hydrogels

Controlled delivery of proteins has immense potential for the treatment of various human diseases, but effective strategies for their delivery are required before this potential can be fully realized. Recent research has identified hydrogels as a promising option for the controlled delivery of therapeutic proteins, owing to their ability to respond to diverse chemical and biological stimuli, as well as their customizable properties that allow for desired delivery rates. This study utilized alginate and chitosan as model polymers to investigate the effects of hydrogel properties on protein release rates. The results demonstrated that polymer properties, concentration, and crosslinking density, as well as their responses to pH, can be tailored to regulate protein release rates. The study also revealed that hydrogels may be combined to create double-network hydrogels to provide an additional metric to control protein release rates. Furthermore, the hydrogel scaffolds were also found to preserve the long-term function and structure of encapsulated proteins before their release from the hydrogels. In conclusion, this research demonstrates the significance of integrating porosity and response to stimuli as orthogonal control parameters when designing hydrogel-based scaffolds for therapeutic protein release.

A macroscopic viscoelastic viscoplastic constitutive model for porous polymers under multiaxial loading conditions

A macroscopic constitutive model, the Porous Eindhoven Glass Polymer (Porous EGP) model, is presented to describe the deformation behavior of cavitated rubber toughened polymers under multiaxial loading conditions. It is shown that the proposed macroscopic constitutive model is able to describe the non-linear pre-yield regime, strain rate dependence, post-yield behavior (strain softening and hardening) and void evolution for loading conditions ranging from shear to equi-triaxial (pure triaxial) tension and compression. The Porous EGP model is a combination of a well established non-linear viscoelastic viscoplastic model, the Eindhoven Glassy Polymer (EGP) model, and the modified Gurson model. The Gurson model is adopted to determine the equivalent stress and plastic rate of deformation tensor making it depending on the void volume fraction, deviatoric and hydrostatic stress. The macroscopic constitutive model is developed based on the response of realistic 3D representative volume elements (RVEs) containing randomly positioned mono-disperse inclusions. The constitutive behavior of the matrix phase in this full-field model is described by the EGP model, and the cavitated inclusions are idealized as voids. Their response is studied for a range of void volume fractions, multiaxial loading conditions, strain rates and thermodynamic states. The yield behavior of the heterogeneous material depends non-linearly on the macroscopic hydrostatic stress. This response is well captured with the proposed macroscopic constitutive model.

Hi-BDiSCO: folding 3D mesoscale genome structures from Hi-C data using brownian dynamics.

The structure and dynamics of the eukaryotic genome are intimately linked to gene regulation and transcriptional activity. Many chromosome conformation capture experiments like Hi-C have been developed to detect genome-wide contact frequencies and quantify loop/compartment structures for different cellular contexts and time-dependent processes. However, a full understanding of these events requires explicit descriptions of representative chromatin and chromosome configurations. With the exponentially growing amount of data from Hi-C experiments, many methods for deriving 3D structures from contact frequency data have been developed. Yet, most reconstruction methods use polymer models with low resolution to predict overall genome structure. Here we present a Brownian Dynamics (BD) approach termed Hi-BDiSCO for producing 3D genome structures from Hi-C and Micro-C data using our mesoscale-resolution chromatin model based on the Discrete Surface Charge Optimization (DiSCO) model. Our approach integrates reconstruction with chromatin simulations at nucleosome resolution with appropriate biophysical parameters. Following a description of our protocol, we present applications to the NXN, HOXC, HOXAand Fbn2 mouse genes ranging in size from 50 to 100kb. Such nucleosome-resolution genome structures pave the way for pursuing many biomedical applications related to the epigenomic regulation of chromatin and control of human disease.

Interplay between dynamic heterogeneity and interfacial gradients in a model polymer film.

Glass-forming liquids exhibit long-lived, spatially correlated dynamical heterogeneity, in which some nm-scale regions in the fluid relax more slowly than others. In the nanoscale vicinity of an interface, glass-formers also exhibit the emergence of massive interfacial gradients in glass transition temperature Tg and relaxation time τ. Both of these forms of heterogeneity have a major impact on material properties. Nevertheless, their interplay has remained poorly understood. Here, we employ molecular dynamics simulations of polymer thin films in the isoconfigurational ensemble in order to probe how bulk dynamic heterogeneity alters and is altered by the large gradient in dynamics at the surface of a glass-forming liquid. Results indicate that the τ spectrum at the surface is broader than in the bulk despite being shifted to shorter times, and yet it is less spatially correlated. This is distinct from the bulk, where the τ distribution becomes broader and more spatially organized as the mean τ increases. We also find that surface gradients in slow dynamics extend further into the film than those in fast dynamics-a result with implications for how distinct properties are perturbed near an interface. None of these features track locally with changes in the heterogeneity of caging scale, emphasizing the local disconnect between these quantities near interfaces. These results are at odds with conceptions of the surface as reflecting simply a higher "rheological temperature" than the bulk, instead pointing to a complex interplay between bulk dynamic heterogeneity and spatially organized dynamical gradients at interfaces in glass-forming liquids.