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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Twist-engineered phonon polaritons in α − V 2 O 5

The advent of layered materials has unveiled new opportunities for tailoring electromagnetic waves at the subwavelength scale, particularly through the study of polaritons, a hybrid light–matter excitation. In this context, twist-optics, which investigates the optical properties of twisted stacks of van der Waals (vdW) layered specimens, has emerged as a powerful tool. Here, we explore the tunability of phonon polaritons in α-V 2 O 5 via interlayer twisting using scanning nano-infrared (IR) imaging. We show that the polaritonic response can be finely adjusted by varying their interlayer electromagnetic coupling, allowing for precise control over the propagation direction and phase transition from open unidirectional iso-frequency contours to closed elliptic geometries. Furthermore, our experimental results, in conjugate with theoretical modeling, reveal the mechanisms underpinning this tunability, highlighting the role of twist-induced nano-light modifications for advanced nanophotonic control at the nanoscale.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Self-Assembly of a Triblock Copolymer in the Presence of a Rigid Conjugated Polyelectrolyte

The properties of conducting polymers are strongly influenced by structural changes induced by long-range order, which can be achieved by using block copolymers that self-assemble into crystalline structures. These blends result in unique mesophases distinct from the pure components with self-assembly behavior modulated by solution conditions and polymer architectures. High-throughput small-angle X-ray scattering data of aqueous Pluronic P123 (PEO 20 –PPO 70 –PEO 20 ) and conjugated polyelectrolyte poly[3-(potassium-4-butanoate) thiophene-2,5-diyl] (PPBT) blends at various concentrations and temperatures were automatically classified into phase maps by autophasemap, an unsupervised statistical analysis algorithm. The outlined phase boundaries revealed that adding PPBT to high P123 concentrations induced a transition from cubicly ordered spherical micelles to hexagonally packed cylindrical micelles. Shear alignment via rheological small-angle neutron scattering of the blends produced monolithic oriented cubic and hexagonal crystal gels. Furthermore, these insights into the self-assembly of conductive polymer blends will aid in the design of soft materials with tunable structural and electronic properties.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Polytype selection in the antisolvent-free crystallization of formamidinium lead iodide using alkylammonium chlorides

This work presents a systematic study of how the size of the C 0 –C 4 alkylammonium chloride additive directs the crystallization pathway in antisolvent-free FAPbI 3 films. We find that larger cations promote the intermediate formation of hexagonal polytypes, correlating with enhanced film crystallinity. Understanding the nucleation, crystallization, and phase transition mechanisms in perovskite thin films produced without antisolvent quenching is crucial for improving phase stability and optoelectronic performance at scale. By means of in situ grazing incidence wide-angle X-ray scattering experiments, we show that the nature of alkylammonium chloride (RACl) additives significantly influences the crystallization dynamics and temperature-dependent stability of formamidinium lead iodide (FAPbI 3 ) perovskite films formed using antisolvent-free processes. The in situ experiments reveal that the effective radius of the RA + cation and the vapor pressure of the RA 0 conjugate base are critical factors affecting the crystallization pathway and film morphology. C 2 –C 3 additives with moderate chain lengths may strike a balance between promoting the early crystallization of the cubic 3C phase while suppressing unwanted phases. This balance promotes the formation of highly crystalline cubic perovskite phase with well-oriented structure and better optoelectronic properties. These findings provide guidance regarding the design of additives to crystallize more stable and efficient perovskite films for optoelectronic applications.

Marchezi, Paulo E↗
DOE OSTI2025

Revisiting the Role of Entropy for Charge Separation in 1D Pi-Conjugated Semiconductors

Free carrier generation in organic donor/acceptor heterojunctions and redox-doped organic semiconductors is poorly understood, since assumed tight electron-hole binding conflicts with observed high free carrier yields. Cornerstone analyses that have guided the field for over 15 years predict that entropy can stabilize free charges in 2D and 3D pi-conjugated semiconductors but not in 1D systems. Here, the impact of entropy on charge generation in 1D pi-conjugated semiconductors is revisited by exploiting a greatly simplified system where enthalpy considerations alone should not allow for free charge generation. Noncontact solution-phase microwave conductivity is used to investigate the carrier density-dependent conductivity and dielectric constant in isolated chemically doped semiconducting single-walled carbon nanotubes in a low-dielectric solvent. Dopant chemical structure dramatically influences the carrier density-dependent complex conductivity, with bulky dopants facilitating carrier escape even at carrier densities below one carrier per nanotube. Three distinct numerical calculations show that entropic stabilization dramatically lowers the Gibbs energy barrier for free charge generation, explaining the high yield of free carriers, even in 1D. This renewed understanding of entropy's role in carrier generation has important implications for designing organic electronic devices-such as solar cells and thermoelectric energy harvesters-for enhanced carrier yield, conductivity, and performance.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Real-time simulation of asymmetry generation in fermion-bubble collisions

Motivated by the out-of-equilibrium dynamics during an early-Universe first-order phase transition, we perform real-time simulations of fermion-bubble scattering in 1 + 1 dimensions. This nonequilibrium process can generate a charge-conjugation C asymmetry outside the bubble wall, induced by the complex fermion mass profile. The resulting C asymmetry is the 1 + 1 -dimensional analog of the C P asymmetry in 3 + 1 dimensions, a key ingredient in baryon asymmetry generation at the electroweak scale. Using tensor network methods, we track the real-time evolution of the C asymmetry in the charge density as the fermion interacts with the bubble wall, a regime inaccessible to analytic calculations. We further introduce two observables to quantify the asymmetry in the asymptotic region where reflected particles are well separated from the scattering point: one based on the net charge outside the bubble wall, and the other on the spatial displacement between the reflected particle and antiparticle wave packets. Our study represents a first step toward nonperturbative, real-time computations of C P asymmetry in 3 + 1 dimensions for electroweak baryogenesis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Bulky Cation-Modified Interfaces for Thermally Stable Lead Halide Perovskite Solar Cells

Charged conjugated organic molecules offer promising prospects for reducing nonradiative recombination at interfaces in perovskite solar cells, while protecting the active layer from moisture. However, several studies have shown that the heat induced diffusion of these cations leads to irreversible solar cell degradation. Passivation molecules for perovskite can reconstruct the film surface into lower-dimensional phases when exposed to thermal stress, impeding charge extraction and affecting the photoconversion efficiency (PCE) of devices. In this work, we study how molecular interactions between passivation molecules and 3D CsFAPbI 3 perovskite impact stability and charge extraction at the perovskite/hole transport layer interfaces. Two model π- conjugated molecules are studied: 2-([2,2′-bithiophen]-5-yl)ethan-1-aminium iodide (2TI) and 2-(3‴,4′-dimethyl-[2,2′:5′,2″:5″,2‴- quaterthiophen]-5-yl)ethan-1-ammonium iodide (4TmI). We demonstrate that the speed of surface layer reconstruction under thermal stress can be controlled by the cation size and correlate these structural changes with the solar cell performance and stability. Devices treated with 2TI and 4TmI achieve PCEs over 21% and maintain their performance under thermal stress. Our findings demonstrate that thermal stability in PSCs can be achieved via the design engineering of passivation agents, offering a blueprint for developing next-generation passivation molecules.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Halogenated Dibenzo[ f , h ]quinoxaline Units Constructed 2D‐Conjugated Guest Acceptors for 19% Efficiency Organic Solar Cells

Abstract Halogenation of Y‐series small‐molecule acceptors (Y‐SMAs) is identified as an effective strategy to optimize photoelectric properties for achieving improved power‐conversion‐efficiencies (PCEs) in binary organic solar cells (OSCs). However, the effect of different halogenation in the 2D‐structured large π‐fused core of guest Y‐SMAs on ternary OSCs has not yet been systematically studied. Herein, four 2D‐conjugated Y‐SMAs (X‐QTP‐4F, including halogen‐free H‐QTP‐4F, chlorinated Cl‐QTP‐4F, brominated Br‐QTP‐4F, and iodinated I‐QTP‐4F) by attaching different halogens into 2D‐conjugation extended dibenzo[ f , h ]quinoxaline core are developed. Among these X‐QTP‐4F, Cl‐QTP‐4F has a higher absorption coefficient, optimized molecular crystallinity and packing, suitable cascade energy levels, and complementary absorption with PM6:L8‐BO host. Moreover, among ternary PM6:L8‐BO:X‐QTP‐4F blends, PM6:L8‐BO:Cl‐QTP‐4F obtains a more uniform and size‐suitable fibrillary network morphology, improved molecular crystallinity and packing, as well as optimized vertical phase distribution, thus boosting charge generation, transport, extraction, and suppressing energy loss of OSCs. Consequently, the PM6:L8‐BO:Cl‐QTP‐4F‐based OSCs achieve a 19.0% efficiency, which is among the state‐of‐the‐art OSCs based on 2D‐conjugated Y‐SMAs and superior to these devices based on PM6:L8‐BO host (17.70%) and with guests of H‐QTP‐4F (18.23%), Br‐QTP‐4F (18.39%), and I‐QTP‐4F (17.62%). The work indicates that halogenation in 2D‐structured dibenzo[ f , h ]quinoxaline core of Y‐SMAs guests is a promising strategy to gain efficient ternary OSCs.

14 SOLAR ENERGY↗
DOE OSTI2026

Solid-State Side-Chain Functionalization of Conjugated Polymers for Expanded Chemical and Functional Versatility

Conjugated polymers that integrate diverse chemical functionalities with high electronic performance are essential for advanced organic electronic, optoelectronic, and biointerfaced technologies. Achieving such multifunctionality typically requires grafting functional units onto polymer side chains. However, conventional solution-phase approaches remain constrained by solubility limitations, side-chain-induced packing disruptions, and challenges in preserving charge transport. Here, we introduce a solid-state side-chain functionalization strategy that exploits a swellable polar side-chain architecture and azide–alkyne click chemistry to enable efficient molecular diffusion and reaction throughout predeposited polymer thin films. This approach substantially broadens the chemical compatibility of graftable units and mitigates the adverse effects on the electrical property. Moreover, the method supports spatially selective functionalization within a continuous film, enabling the patterned incorporation of chemically distinct groups to produce spatially defined optical properties. Here, this solid-state strategy thus provides a versatile platform for constructing conjugated polymers with expanded chemical versatility, preserved electronic performance, and programmable spatial functionality.

Conjugated polymers↗
DOE OSTI2026

Tuning Thermal Stability through Dopant Size in Chemically Doped DPP–Thiophene Polymers

Molecular doping of conjugated polymers (CPs) is a key strategy for improving the performance of organic electronics devices, particularly thermoelectrics. Doped donor–acceptor (D–A) conjugated polymers, characterized by a tunable energy gap between the Fermi level and the transport band, show great promise in achieving high electrical conductivity (σ) while preserving a favorable Seebeck coefficient (S). Despite the promising performance enhancement of chemically doped D–A polymers, their thermal stability remains largely underexplored, a crucial consideration for the long-term operation of organic thermoelectric devices. In this study, we investigated the dopant size-dependent thermal stability of a diketopyrrolopyrrole-thiophene (DPP-T) D–A copolymer, utilizing two p-dopants: 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F 4 TCNQ) and Mo(tfd-CO 2 Me) 3 . Temperature-dependent UV–vis–NIR spectroscopy revealed that DPP-T/F 4 TCNQ is more prone to dedoping under a high temperature thermal stress than DPP-T/Mo(tfd-CO 2 Me) 3 . Although the F 4 TCNQ doped polymer shows higher initial in-plane conductivity than its Mo(tfd-CO 2 Me) 3 counterpart, it undergoes a conductivity loss of more than an order of magnitude after annealing at 120 °C for 30 min. In contrast, the in-plane conductivity of DPP-T/Mo(tfd-CO 2 Me) 3 remains stable under the same thermal conditions. Thermogravimetric analysis ruled out dopant sublimation as a primary contributor to dedoping, leading us to attribute the conductivity loss in F 4 TCNQ-doped DPP-T to dopant phase separation and migration. This observation was further confirmed by X-ray scattering studies and nanoscale infrared microscopy and spectroscopy studies. This work could provide further insights into the thermal stability of doped conjugated polymers and suggests that incorporating bulkier dopants is an effective strategy to enhance the thermal robustness of doped DPP-type systems.

Conjugated polymers↗
DOE OSTI2025

A Finite Element Method for Compressible and Turbulent Multiphase Flow Instabilities with Heat Transfer

We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Enhancing the Conductivity and Thermoelectric Performance of Semicrystalline Conducting Polymers through Controlled Tie Chain Incorporation

Abstract Conjugated polymers are promising materials for thermoelectric applications, however, at present few effective and well‐understood strategies exist to further advance their thermoelectric performance. Here a new model system is reported for a better understanding of the key factors governing their thermoelectric properties: aligned, ribbon‐phase poly[2,5‐bis(3‐dodecylthiophen‐2‐yl)thieno[3,2‐b]thiophene] (PBTTT) doped by ion‐exchange doping. Using a range of microstructural and spectroscopic methods, the effect of controlled incorporation of tie‐chains between the crystalline domains is studied through blending of high and low molecular weight chains. The tie chains provide efficient transport pathways between crystalline domains and lead to significantly enhanced electrical conductivity of 4810 S cm −1 , which is not accompanied by a reduction in Seebeck coefficient or a large increase in thermal conductivity. Respectable power factors of 173 µW m −1 K −2 are demonstrated in this model system. The approach is generally applicable to a wide range of semicrystalline conjugated polymers and could provide an effective pathway for further enhancing their thermoelectric properties and overcome traditional trade‐offs in optimization of thermoelectric performance.

Chemistry↗
DOE OSTI2024

Peptide programming of supramolecular vinylidene fluoride ferroelectric phases

Ferroelectric structures have spontaneous macroscopic polarization that can be inverted using external electric fields and have potential applications including information storage, energy transduction, ultralow-power nanoelectronics and biomedical devices. These functions would benefit from nanoscale control of ferroelectric structure, the ability to switch polarization with lower applied fields (low coercive field) and biocompatibility. Soft ferroelectrics based on poly(vinylidene fluoride) (PVDF) have a thermodynamically unstable ferroelectric phase in the homopolymer, complex semi-crystalline structures, and high coercive fields. Here, in this work, we report on ferroelectric materials formed by water-soluble molecules containing only six VDF repeating units covalently conjugated to a tetrapeptide, with the propensity to assemble into the β-sheet structures that are ubiquitous in proteins. This led to the discovery of ribbon-shaped ferroelectric supramolecular assemblies that are thermodynamically stable with their long axes parallel to both the preferred hydrogen-bonding direction of β-sheets and the bistable polar axes of VDF hexamers. Relative to a commonly used ferroelectric copolymer, the biomolecular assemblies exhibit a coercive field that is two orders of magnitude lower, as the result of supramolecular dynamics, and a similar level of remnant polarization, despite having a peptide content of 49 wt%. Furthermore, the Curie temperature of the assemblies is about 40 °C higher than that of a copolymer containing a similar amount of VDF. This supramolecular system was created using a biologically inspired strategy that is attractive in terms of sustainability and that could lead to new functions for soft ferroelectrics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Directed Self-Assembly of the Organic Semiconductor C8-BTBT-C8 in Anodic Aluminum Oxide Nanopores

Controlling the self-assembly of organic semiconductors at the nanoscale is critical for advancing high-performance electronic and photonic devices, yet it remains challenging due to their intrinsic anisotropic crystallization and sensitivity to processing conditions. Here, in this study, we demonstrate that cylindrical nanoconfinement within anodic aluminum oxide membranes provides a versatile platform to precisely tune the molecular orientation and phase behavior of the prototypical organic semiconductor 2,7-dioctyl[1]benzothieno[3,2-b][1]benzothiophene (C8-BTBT-C8). Combining temperature-dependent high-resolution synchrotron X-ray scattering with optical birefringence measurements, we uncover that confinement geometries (pore diameters 25–180 nm) and surface chemistry govern the emergence of distinct smectic A textures, featuring molecular layers either parallel or perpendicular to the pore axis. The competition between axial and radial smectic layering is modulated by pore size, surface hydrophilicity, and thermal history, enabling reversible control over domain orientations and transitions between liquid crystalline and crystalline states. Notably, nanoconfinement stabilizes the smectic phase over an expanded temperature range compared to bulk, while inducing complex multidomain configurations owing to geometric constraints and anchoring conditions. Our results elucidate fundamental mechanisms by which anisotropic nanoscale confinement directs the self-organization of highly conjugated organic molecules, with implications for optimizing directional charge transport and anisotropic optical responses in organic–inorganic hybrid nanoarchitectures. This study establishes nanoconfinement as a powerful strategy to engineer morphology and functional properties in organic semiconducting materials with nanoscale precision.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Study of self-assembly behavior and ionic conductivity of conjugated liquid crystals with T-shaped facial-polyphilic structure

The unique self-assembly of liquid crystals (LCs), combined with their potential application as organic semiconductors, has become a focus of recent research. Here, a joint experimental and computational study of the self-assembly and ionic conduction was carried out on a series of T-shaped conjugated LCs consisting of three incompatible components. By extending the EOn side-chain length, several experimental evaluations confirmed a decrease of the order-disorder transition temperature, while coarse-grained simulations revealed a structural evolution from a smectic phase to a columnar phase. Ionic conductivity of these molecules was achieved by adding Li salt, leading to a maximum conductivity of 1.1 × 10 −3 siemens per centimeter observed at 120°C. All-atom simulations were performed to examine the Li-ion solvation environment and to evaluate the intrachain and interchain Li-ion hopping mechanisms. The molecule with a long EOn side chain was found to generate a densely distributed network of Li-ion solvation sites, which can facilitate effective interchain hopping to promote ion transport.

Liu, Ziwei [Cornell Univ., Ithaca, NY (United Stat↗
DOE OSTI2025

Binding the Power of Cycloaddition and Cross-Coupling in a Single Mechanism: An Unexpected Bending Journey to Radical Chemistry of Butadiynyl with Conjugated Dienes

What if an experiment could combine the power of cycloaddition and cross-coupling with the in situ formation of an aromatic molecule in a single collision? Crossed molecular beam experiments augmented with electronic structure and statistical calculations provided compelling evidence on a novel radical route involving 1,3-butadiynyl (HCCCC; X 2 Σ + ) radicals synthesizing (substituted) arylacetylenes in the gas phase upon reactions with 1,3-butadiene (CH 2 CHCHCH 2 ; X 1 Ag) and 2-methyl-1,3-butadiene (isoprene; CH 2 C(CH 3 )CHCH 2 ; X 1 A'). Furthermore, this elegant mechanism de facto merges two previously disconnected concepts of cross-coupling and cycloaddition–aromatization in a single collision event via the formation of two new C(sp 2 )–C(sp 2 ) bonds and bending the 180° moiety of the linear 1,3-butadiynyl radical out of the ordinary by 60° to 120°. In addition to its importance to fundamental organic chemistry, this unconventional mechanism links two previously separated routes of gas-phase molecular mass growth processes of polyacetylenes and polycyclic aromatic hydrocarbons (PAHs), respectively, in low-temperature environments such as in cold molecular clouds like the Taurus Molecular Cloud (TMC-1) and in hydrocarbon-rich atmospheres of planets and their moons such as Titan, what revises the established understanding of low-temperature molecular mass growth processes in the Universe.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Continuous Counter‐Current Microfluidic Liquid–Liquid Extraction Achieved Using a Pair of Wettable Screen Meshes

Continuous counter‐current microfluidic liquid–liquid extraction performs separations by flowing immiscible liquids in opposing directions within a single flow channel. In principle, this flow arrangement enables a large number of theoretical separation units in a small footprint, without using interstage valving, pumping, and phase separation. Despite its potential for excellent separation performance, this microfluidic scheme rarely appears in literature due to the requirement for capillary forces to be greater than hydrodynamic forces for stable flow. We present a novel microfluidic device and flow approaches that overcome this force‐balance challenge, enabling stable, long‐duration continuous counter‐current flow. Additionally, we cover a suite of methodologies for quantifying the performance of the microfluidic device, revealing the number of theoretical equilibrium stages achieved. The enabling technologies include a woven mesh screen‐based microfluidic device architecture that is easily fabricated outside of a clean room, surface functionalization strategies to promote conjugate (organic/aqueous) wettability, flow approaches to eliminate bubbles and carryover, and computer‐aided flow automation with optical measurement of extraction performance. The reported experiments lasted for over 36 h, terminated only at experiment conclusion, where the device still exhibited good performance. Automated Raman spectroscopy was used for solute quantitation of the ternary system tert‐butanol in a toluene/water matrix, a ternary system that was specifically chosen to analyze the device's performance with a small solute partition ratio and to enable in‐line Raman measurements of solute concentrations in both phases. The microfluidic device possessed a 55 mm contact length and a 38.5 µL internal volume. During counter‐current flow, we observed approximately 37 equilibrium stages (37 ± 13) based on a best‐fit of the solute fraction remaining in the aqueous phase using a Kremser Group Method analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Topological solitons in square-root graphene nanoribbons controlled by electric fields

Conjugational defects, also known as solitons, play an important role in the electronic, magnetic, and optical properties of materials. Understanding solitons can uncover intriguing physics and provide insights for designing quantum materials with tailored band structures and electronic properties. Here we propose a framework to create and control solitons via topological phase transitions in a class of graphene nanoribbons (GNRs) called square-root GNRs, using a transverse electric field. To demonstrate the experimental feasibility, we design and synthesize a representative GNR with a bottom-up approach, with first-principles calculations revealing topological soliton states at the domain wall induced by the electric field. In conclusion, the framework introduced in this work can potentially enable direct manipulation of solitons and provide a platform to study them systematically.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Cahn–Hilliard–Navier–Stokes (CHNS) systems describe flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism (Morrison and Updike, 2024) achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the concentration variable and its thermodynamics conjugate, the chemical potential, are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. Furthermore, this general CHNS system reduces to cases in the literature, to which we can compare.

Cahn–Hilliard↗