Non-equilibrium Material Research Articles

Extracting non-equilibrium material properties in visco-hyperelastic polymers based on analytical stress solution

This study extracts non-equilibrium material properties in the visco-hyperelastic polymers using an analytical stress solution. At first, the analytical stress solution of visco-hyperelastic polymers is obtained from finite-strain creep test data based on the generalized Maxwell’s rheological model. The solution uses the low-computational-cost exponential generalized pseudospectral method and analytically brings the stress components in terms of time and unknown non-equilibrium material properties of Maxwell’s elements. The solution invokes the Ogden hyperelastic model for the elastic element of the generalized Maxwell’s model. The exponential generalized pseudospectral method, based on exponential–rational Lagrange functions suitable for the semi-infinite time interval [Formula: see text] and the rational Chebyshev roots as the collocation points, is applied to derive the stress components. The non-equilibrium properties are derived by minimizing a residual, which is obtained by making the derivatives of the residual in terms of the non-equilibrium properties as zero. Notably, the proposed analytical method requires a small number of exponent–rational Lagrange basis functions and collocation points. Besides, the proposed method does not require integration, discretization, or linearization. Two case studies are considered: the moderate-stretched ETFE polymer with the neo-Hookean model as the elastic element and the large-stretched rubber with the six-parameter Ogden hyperelastic model as the elastic branch. The results are validated using uniaxial creep modeling in ANSYS and available reports in the literature.

Melting and solidification dynamics during laser melting of reaction-based metal matrix composites uncovered by in-situ synchrotron X-ray diffraction

Laser additive manufacturing (AM) of reaction-based metal matrix composites (MMCs) involves highly complex and non-equilibrium material transformation behavior, including melting, dissolution, precipitation, and solidification. Yet, the dynamics and interplay of these phase transformation processes remain poorly understood, posing substantial challenges in identifying the microstructure formation mechanism, and predicting and controlling the microstructure in the printed parts. Here we performed the in-situ X-ray diffraction experiment to characterize the phase evolution dynamics of the 316L + 10 vol.%TiC system during laser melting, which provides direct and quantitative insights of the complex phase reaction and evolution dynamics under rapid heating and cooling conditions relevant to additive manufacturing of reaction-based MMCs. Further in-depth thermodynamic and kinetic calculations revealed that most of the phase evolution behavior observed in the in-situ X-ray diffraction experiment cannot be solely explained by widely used equilibrium thermodynamic models, and diffusion-controlled nonequilibrium dissolution and precipitation kinetics must be considered to elucidate the complex phase evolution behavior, including incomplete TiC dissolution, and three-step TiC precipitation. The three distinct types of precipitates generate unique hierarchical TiC micro- and nanostructures, which enhances the yield strength from 513 MPa to 877 MPa by 71 %, tensile strength from 628 MPa to 1054 MPa by 68 %, and Young's modulus from 193 GPa to 221 GPa by 14 %. The findings of our research provide the knowledge foundation for the design of unique microstructures and advanced MMC materials through laser AM.

Long-term creep monitoring of composite wing leading edge using embedded fiber Bragg grating

The creep behavior of composite wing leading edges resulting from nonequilibrium residual stresses and material viscoelasticity needs to be evaluated comprehensively as it significantly affects assembly. In this study, long-term creep monitoring of a composite wing leading edge used in an actual airplane for 710 h is conducted using embedded fiber Bragg grating arrays and a creep extraction algorithm. The spectra and Bragg wavelength shifts of two embedded arrays, which involve temperature, thermal expansion, and creep, are recorded and analyzed. The creep curve of the composite wing leading edge is reconstructed and further predicted using the creep extraction algorithm based on multiparameter decoupling and the Burgers model. This study elucidates the enlargement of the opening size in the composite wing leading edge by measuring the tensile strain above the neutral axis. The predicted creep time serves as a valuable reference for determining the appropriate assembly timing.

Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries1 and electrocatalysts2. Experimental characterizations of such materials by operando microscopy produce rich image datasets3–6, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation7. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

High thermal stability of residual amorphous regions in metallic glasses

As a thermodynamic non-equilibrium material, metallic glasses have a spontaneous tendency to crystallize, commonly accompanied by a degradation of mechanical properties. In this work, the thermal stability of a composition Zr60Co27Al13 under both a monolithic amorphous state and symbiotic primary crystal-glass state was intensively analyzed to uncover the origination of the thermal stability. It shows that the symbiotic metallic glass is much more stable than that of the monolithic metallic glass, which can be attributed to the consumption of short-range order clusters, the relaxation in atomic dimensions, and the more homogenous elemental distribution in the residual amorphous regions. Revealing the effect of the primary crystal on the residual amorphous phase in the symbiotic state may be beneficial for developing metallic glasses with high thermal stability.

On the Temperature‐Induced Equilibration of Phase Distribution and Microstructure in a Gas‐Atomized Titanium Aluminide Powder

Powder production by gas atomization of γ‐TiAl based alloys typically yields a highly nonequilibrium material regarding the occurring phases and their microstructural appearance. In particular, the equilibration of the powder and the associated phase transformations during heating are of great importance for the subsequently applied densification techniques. The present work employs in situ high‐energy X‐ray diffraction to investigate how this thermodynamic equilibration manifests itself in the resulting phase distribution, the ordering behavior of the disordered α and β phase, both evidenced in the powder, and the change of the γ lattice parameters during heating of a Ti–46.3Al–2.2W–0.2B (at%) powder up to 850 °C. Complementary microstructural characterization of the gas‐atomized powder and the heat‐treated material condition reveals that the temperature exposure predominately affects the dendritic parts of the microstructure, especially when the α phase is transformed into γ phase with small embedded grains of α2 and βo.

Generalized continuum mixture theory for multi-material shock physics

A long-standing area of research for computational shock physics has been the treatment of mixed materials. A mixed material volume is defined as a control volume space where two or more materials coexist as immiscible materials having separate densities and energies that have non-equilibrium stress and thermal states. In traditional computational shock physics framework, a mixture of materials can occupy a control volume having a common velocity corresponding to the mixture center of mass. In this work, this assumption is relaxed and separate densities, energies and velocities are used to characterize non-equilibrium material behavior. To accomplish this task, this work builds upon the original two-phase Baer and Nunziato model by extending the two-phase theory to N-phases. Specifically, this work is based on the development by Drumheller to derive a new N-phase mixture theory that incorporates deformation mechanics using the deformation gradient with a full stress tensor.

Dynamic interplay between phase transformation instabilities and reaction heterogeneities in particulate intercalation electrodes

Lithium-ion batteries rely on particulate porous electrodes to realize high performance, especially the fast-charging capability. To minimize the particle-wise reaction heterogeneities that may lead to local hot spots, deeper understandings of these electrodes at the mesoscale, i.e. hundreds of particles, have become an urgent need. This study reveals that the seemingly random reaction heterogeneities are actually controlled by the interplay between the non-equilibrium material thermodynamics and the external electrochemical driving force. Our operando experiments confirm the true working current density around a single particle that is much higher than the globally averaged current density, can change the behavior of phase transformation. The combined theoretical and experimental analyses reveal that unlike other phase-transforming porous electrodes, not all phase separation processes in graphite can be suppressed at high currents, due to the characteristics of the concentration-dependent exchange current density. The insights highlight the necessity to incorporate materials thermodynamics into electrochemical models to ensure self-consistent understandings of practical porous electrodes toward precision design and management.

Predicting the unobserved: A statistical mechanics framework for non-equilibrium material response with quantified uncertainty

Can far-from-equilibrium material response under arbitrary loading be inferred from equilibrium data and vice versa? Can the effect of element transmutation on mechanical behavior be predicted? Remarkably, such extrapolations are possible in principle for systems governed by stochastic differential equations, thanks to a set of exact relations between probability densities for trajectories derived from the path integral formalism (Chen and Horing, 2007; Nummela and Andricioaei, 2007; Kieninger and Keller, 2021). In this article, we systematically investigate inferences (in the form of ensemble-averages) drawn on system/process S based on stochastic trajectory data of system/process S̃, with quantified uncertainty, to directly address the aforementioned questions. Interestingly, such inferences and their associated uncertainty do not require any simulations or experiments of S. The results are exemplified over two illustrative examples by means of numerical simulations: a one-dimensional system as a prototype for polymers and biological macromolecules, and a two-dimensional glassy system. In principle, the approach can be pushed to the extreme case where S̃ is simply comprised of Brownian trajectories, i.e., equilibrium non-interacting particles, and S is a complex interacting system driven far from equilibrium. In practice, however, the “further” S̃ is from S, the greater the uncertainty in the predictions, for a fixed number of realizations of system S̃.

Generalized continuum mixture theory for multi-material shock physics

A long-standing area of research for computational shock physics has been the treatment of mixed materials. A mixed material volume is defined as a control volume space where two or more materials coexist as immiscible materials having separate densities and energies that have non-equilibrium stress and thermal states. In traditional computational shock physics framework, a mixture of materials can occupy a control volume having a common velocity corresponding to the mixture center of mass. In this work, this assumption is relaxed and separate densities, energies and velocities are used to characterize non-equilibrium material behavior. To accomplish this task, this work builds upon the original two-phase Baer and Nunziato model by extending the two-phase theory to N-phases. Specifically, this work is based on the development by Drumheller to derive a new N-phase mixture theory that incorporates deformation mechanics using the deformation gradient with a full stress tensor.

Drive-pressure optimization in ramp-wave compression experiments through differential evolution

Ramp-wave dynamic-compression experiments are used to examine quasi-isentropic loading paths in materials. The gradual and continuous increase in pressure created by ramp waves make these types of experiments ideal for studying nonequilibrium material behavior, such as solidification kinetics. In ramp-wave compression experiments, the input drive pressure to the experimental setup may be exerted through one of a number of different mechanisms (e.g., magnetic fields, gas-gun-driven impactors, or high-energy lasers) and is generally required for simulating such experiments. Yet, regardless of the specific mechanism, this drive pressure cannot be measured directly (measurements are generally taken at a location near the back of the experimental setup through a transparent window), leading to an inverse problem where one must determine the drive pressure at the front of the experimental setup (i.e., the input) that corresponds to the particle velocity (the output) measured near the back of the experimental setup. We solve this inverse problem using a heuristic optimization algorithm, known as differential evolution, coupled with a multiphysics, hydrodynamics code that simulates the compression of the experimental setup. By running many rounds of forward simulations of the experimental setup, our optimization process iteratively searches for a drive pressure that is optimized to closely reproduce the experimentally measured particle velocity near the back of the experimental setup. While our optimization methodology requires a significant number of hydrodynamics simulations to be conducted, many of these can be performed in parallel, which greatly reduces the time cost of our methodology. One novel aspect of our method for determining the drive pressure is that it does not require physical modeling of the drive mechanism and can thus be broadly applied to many types of ramp-compression experiments, regardless of the drive mechanism.

IR ns pulsed laser irradiation of Polydimethylsiloxane in vacuum

Polydimethylsiloxane (PDMS) has been irradiated by a ns pulsed IR laser in vacuum and the radiation effects induced by the coherent radiation, above a threshold fluence, produce a non-equilibrium plasma and material ablation. The laser absorption can be enhanced using gold nanoparticles (AuNPs) embedded in the polymer. The laser-generated plasma has been characterized, whereas the ion emission from both the virgin PDMS and the PDMS + AuNPs sheets has been analysed both in mass and energy. Morphological investigations, optical spectroscopy and compositional analyses have been performed. The adopted laser treatment can be employed to modify the properties of PDMS with and without AuNPs inducing a local enrichment of microcrystalline silicon in both cases.

Superconducting 3R-Ta1+xSe2 with Giant In-Plane Upper Critical Fields.

Molecular-beam epitaxy (MBE) enables the stabilization of a nonequilibrium material phase, providing a powerful approach to the exploration of emergent phenomena in condensed-matter research. Here we demonstrate that one of the metallic two-dimensional (2D) materials, TaSe2, grown by MBE crystallizes into the pure 3R phase with the self-intercalated Ta atoms, 3R-Ta1+xSe2, which is thermodynamically metastable and does not exist in nature as a pure material phase. Interestingly, the thick-enough 3R-Ta1+xSe2 film exhibits a superconducting (SC) critical temperature (Tc) of 3.0 K, which is the highest among all of the polymorphs in TaSe2. Thickness-dependence measurements reveal that Tc decreases with decreasing thickness, accompanied by the development of the charge-density wave phase. The 3R-Ta1+xSe2 films exhibit large in-plane upper critical fields (Hc2) in their SC states even in the thick-enough regime, most likely due to the suppression of the interlayer hopping associated with the unique 3R stacking. Moreover, the temperature dependence of the in-plane Hc2 evolves from linear to square-root behavior with decreasing thickness, indicating crossover behavior from anisotropic three-dimensional superconductivity to 2D superconductivity. Our results unveil intriguing SC properties of metastable 3R-Ta1+xSe2 distinct from those of thermodynamically stable 2H-TaSe2, demonstrating the essential importance of the MBE-based approach to the exploration of novel quantum phenomena in 2D materials research.

Thermo-viscoelastic Modeling of Nonequilibrium Material Behavior of Glass in Nonisothermal Glass Molding

Nonisothermal Glass Molding (NGM) has become a viable replicative manufacturing technology for the cost-efficient production of complex precision optical components made of glass. During the pressing stage in NGM, glass materials undergo a huge temperature change in the glass transition range. In this range, glass exhibits thermo-viscoelastic responses, and the temperature drop through the glass transition leads glass structure to depart from an equilibrium to a nonequilibrium state. Thermo-viscoelastic properties of the nonequilibrium glass material greatly depend on temperature and thermal history. This paper presents a phenomenological constitutive model developed for modeling the thermo-viscoelastic responses of nonequilibrium glass. We propose a direct incorporation of the temperature -and thermal history effects into each parameter of the phenomenological model. This novelty allows the model to describe the nonequilibrium phenomena and to study temperature-dependent viscoelasticity of glass without assuming thermo-rheologically simple characteristics. Furthermore, the phenomenological model enables the coupling of structural -and stress relaxation phenomena. The model validation conducted for creep experiments demonstrates an enhancement in numerical predictions of the nonequilibrium material behaviors of glass over wide ranges of temperature and thermal history.

46 MODELLING THE SCHIZOPHRENIA-ASSOCIATED LOSS-OF-FUNCTION MUTATION OF SETD1A IN HUMAN STEM CELL-DERIVED BRAIN ORGANOIDS

Polydimethylsiloxane (PDMS) has been irradiated by a ns pulsed IR laser in vacuum and the radiation effects induced by the coherent radiation, above a threshold fluence, produce a non-equilibrium plasma and material ablation. The laser absorption can be enhanced using gold nanoparticles (AuNPs) embedded in the polymer. The laser-generated plasma has been characterized, whereas the ion emission from both the virgin PDMS and the PDMS + AuNPs sheets has been analysed both in mass and energy. Morphological investigations, optical spectroscopy and compositional analyses have been performed. The adopted laser treatment can be employed to modify the properties of PDMS with and without AuNPs inducing a local enrichment of microcrystalline silicon in both cases.

Recent advances in the physics of polymer systems

Recent advances in the physics of polymer systems

Influence of the Nonequilibrium Material State on Wear Resistance

The influence of the nonequilibrium state of a material on its wear resistance is investigated in this study. Using methods of non-equilibrium thermodynamics and the theory of self-organization, a non-equilibrium material is shown to possess an overall lower wear rate than a material in an equilibrium state. This was experimentally demonstrated to be the case in different materials and tribosystems, such as Babbit operating in complete lubrication conditions, copper in the current collector and a cutting tool with a coating applied on it.

A Window on Polymer Science

On behalf of the Macromolecular Chemistry and Physics (MCP) team, I wish our readers, authors, referees, and board members a happy new year. “Polymers have influenced our modern technological society like few other materials. MCP covers the chemical and physical underpinnings and advances in these wonderful materials at the highest level since the early days of the discipline…”. – Miriam M. Unterlass (TU Vienna, MCP Board Member) When the German organic chemist Hermann Staudinger published the first Communication on polymerization in 1920, he caused great turmoil within the scientific community.1 His new concept had a great impact on the development of synthetic polymers such as thermoplastics, thermosets, rubbers, and biopolymers. The pioneering era of polymer science ended in the 1970s and the following decades saw a rapid growth in commodity polymer production, new polymerization methods, and process development.2 Since the end of the 20th century, modern polymer science has seen the development of advanced polymeric materials tailored to fulfill specific requirements for applications in technology, energy and biomedicine. Many challenges and new fascinating questions are waiting to be dealt with. Among others, the understanding of non-equilibrium systems is a topic that fascinates many researchers. As stated by Volker Abetz and co-authors in their Trend article in this celebration issue, “…traditional material science mostly focuses on the exploration and explanation of equilibrium states […] If we wish to fundamentally advance material properties, we must understand the principles underlying kinetically controlled processes […]”3 The authors then explain how self-assembling polymer materials are a class of soft matter ideal to study non-equilibrium material systems. Readers approaching this area of science will surely find this contribution inspiring. The importance of understanding the principles of self-assembly and how to tailor the properties of self-assembling polymer materials is underlined by the great number of articles on this topic published in Macromolecular Chemistry and Physics in the past years. The tag cloud provides the keywords most frequently used in papers published in the journal since 2013: larger letter size indicates higher usage frequency. Self-assembly plays an important role among the most published topics, along with block copolymers, particles, conjugated polymers, radical polymerization, hydrogels, catalysts, and many others. As polymer science develops, Macromolecular Chemistry and Physics undergoes continuous changes. The renewal of the editorial board is part of this process. We are grateful to the board members who have supported us in the past and are very excited to have gained many highly motivated scientists. Wolfgang Binder (Martin-Luther-University Halle-Wittenberg, Germany), Laura Hartmann (Heinrich-Heine-University Düsseldorf, Germany), Richard Hoogenboom (Ghent University, Belgium), Takashi Ishizone (Tokyo Institute of Technology, Japan), Daniel Savin (University of Florida, USA), Yanming Sun (Beihang University, Beijing, China), Ophelia Kwan Chui Tsui (Hong Kong University of Science and Technology, Hong Kong), Miriam M. Unterlass (Technical University, Vienna, Austria), and Jiayin Yuan (Clarkson University, USA) joined the journal’s board in early 2018. We have already had the honor of working with many of the new board members, and we look forward to collaborating with them all in the future. Macromolecular Chemistry and Physics new board members. From top left: Jiayin Yuan, Ophelia Kwan Chui Tsui, Takashi Ishizone, Wolfgang Binder, Yanming Sun, Miriam M. Unterlass, Laura Hartmann, Richard Hoogenboom, Daniel Savin. In particular, I am grateful to Takashi Ishizone and Holger Frey for organizing two special issues celebrating 60 years of living anionic polymerization (Issues 12/2017 and 1/2018) and to Ophelia Kwan Chui Tsui, Miriam M. Unterlass, and Shinji Ando for their help in assembling a great issue on polymer morphology and characterization (Issue 3/2018). In addition, Stefan Zechel, Stephanie Schubert, Ian Manners, and Ulrich S. Schubert guest-edited two parallel issues in Macromolecular Chemistry and Physics (Issue 22/2018) and Macromolecular Rapid Communications (Issue 22/2018) on metal containing polymers and metallo-supramolecular polymers in honor of George R. Newkome. More recently, we published an issue dedicated to Prof. Hatsuo Ishida and guest-edited by Pablo Froimowicz, Kan Zhang, and Qichao Ran. New special issues are in the pipeline for 2019: an issue honoring Reimund Stadler, guest-edited by Volker Abetz; and an issue on bioinspired and biobased materials, guest-edited by Frédéric Guittard, Hernando S. Salapare III, and Sonia Amigoni. We look forward to reading the contributions. Finally, I want to thank our authors for entrusting their work to us and our referees for their valuable time. I look forward to what new exciting polymer science the year 2019 will bring us.

Strain and Band-Gap Engineering in Ge - Sn Alloys via P Doping

Ge with a quasi-direct band gap can be realized by strain engineering, alloying with Sn, or ultrahigh n-type doping. In this work, we use all three approaches together to fabricate direct-band-gap Ge-Sn alloys. The heavily doped n-type Ge-Sn is realized with CMOS-compatible nonequilibrium material processing. P is used to form highly doped n-type Ge-Sn layers and to modify the lattice parameter of P-doped Ge-Sn alloys. The strain engineering in heavily-P-doped Ge-Sn films is confirmed by x-ray diffraction and micro Raman spectroscopy. The change of the band gap in P-doped Ge-Sn alloy as a function of P concentration is theoretically predicted by density functional theory and experimentally verified by near-infrared spectroscopic ellipsometry. According to the shift of the absorption edge, it is shown that for an electron concentration greater than 1x10^20 cm-3 the band-gap renormalization is partially compensated by the Burstein-Moss effect. These results indicate that Ge-based materials have high potential for use in near-infrared optoelectronic devices, fully compatible with CMOS technology.

Effects of surface initial condition on aqueous corrosion of glass—A study with a model nuclear waste glass

AbstractBeing a nonequilibrium material, the structure of glass varies with the sample history. Thus, the initial surface condition of a glass can vary with the preparation condition and have a large impact on its reactivity. This paper shows that the aqueous corrosion behavior of international simple glass (ISG) varies depending on the initial surface state. The ISG glass samples were prepared as‐polished‐only and polished‐then‐annealed and they were immersed in aqueous solution saturated with soluble SiO2 at 30°C (modeling a mild condition) and at 90°C (modeling a severe condition). Molecular dynamics simulations were performed to obtain coordination numbers of network formers of ISG to assist oxygen speciation calculations. The surface structures of as‐prepared and corroded ISG samples were analyzed using various imaging and spectroscopic techniques. Among these analyses, only the oxygen speciation with x‐ray photoelectron spectroscopy showed discernable differences between two uncorroded surfaces with different preparation histories; all other methods could not differentiate the surface preparation history before aqueous corrosion. Such minor difference in chemical structures was found to have a profound impact on corrosion behaviors in the mild condition. In the harsh condition, the surface history dependence was not as drastic as the corrosion in the mild condition. The analysis results of the corroded surfaces suggested that the thickness and structure of the alteration layer formed on ISG in aqueous corrosion can vary with the initial surface state.