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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Confined Crystal Melting in Edgeless Poly( L -lactic acid) Crystalsomes

Polymer single crystals tend to be quasi two-dimensional (2D) lamellae and their small lateral surfaces are the starting points of lamella melting and thickening. However, the recently discovered crystalsomes, which are defined for hollow single crystal-like spherical shells, are edgeless, self-confined, and incommensurate with translational symmetry. Here, this work concerns the structure and melting behavior of these edgeless crystalsomes. Poly(l-lactic acid) crystalsomes were grown using a miniemulsion solution crystallization method. Differential scanning calorimetry and in situ wide-angle X-ray diffraction were used to follow the structural evolution of the crystalsomes upon heating. Our results demonstrated that the structure and melting behavior of crystalsomes are curvature-dependent and significantly different from their flat crystal counterpart.

36 MATERIALS SCIENCE↗
NASA NTRS2020

Characterization of SiC/SiC Composites Subjected to Sequential Tensile Creep and Dwell Fatigue in Air under Thermal Gradient Conditions

Uncoated SiC/SiC composites, with 2D and 3D fiber architectures, were investigated under steady state thermal gradient conditions with sequential tensile creep and dwell fatigue. Melt infiltration (MI), chemical vapor infiltration (CVI), polymer impregnation and pyrolysis (PIP), and hybrid (CVI and PIP) techniques were used to fabricate ceramic matrix composites (CMCs) with a 2D balanced fiber architecture. CMCs with 3D fiber weaves were also fabricated using MI and hybrid methods. Steady state through the thickness thermal gradients were generated for the tensile specimens using laser heating on the front (hot side) and forced air cooling on the back (cold side). Hot side and cold side temperatures of 2400 and 2200 °F, respectively, were used for testing CMCs fabricated with the MI process, whereas hot side and cold side temperatures of 2700 and 2400 °F, respectively, were used for CMCs fabricated with CVI, PIP, and hybrid processes. Each CMC specimen was initially tested under tensile creep at 69 MPa (10 ksi) for 80 hours, which was then followed by tensile dwell fatigue testing at a maximum stress of 69 MPa (10 ksi) for another 80 hours for a total of 160 hours. This type of sequential tensile creep followed by tensile dwell fatigue testing was performed to ascertain the integrity of uncoated CMCs under steady state thermal gradient conditions. Tensile creep and dwell fatigue test results, generated under steady state thermal gradient conditions on different types of SiC/SiC composites, are compared with corresponding creep behaviors observed under isothermal conditions to determine the influence of both monotonic creep (static fatigue) and dwell fatigue on accumulated strains and deformation behaviors of the CMCs.

Kalluri, Sreeramesh↗
DOE OSTI2026

Henry’s Solubility and Diffusion Coefficients for 29 Volatile Organic Compounds in Polydimethylsiloxane Sylgard 184 at 293 K

Two-dimensional (2D) inverse gas chromatography (IGC) enables simultaneous determination of Henry’s solubility and Fickian diffusion coefficients for volatile organic compounds (VOCs) in polymer films. This technique offers a significant advantage over traditional cylindrical column IGC by providing precise control and measurement of the film thickness (here, 0.064 ± 0.002 mm), which is the critical length scale for accurate diffusivity determination. We apply this methodology to characterize VOC transport in Sylgard 184, a widely used polydimethylsiloxane (PDMS)-based polymer containing substantial silica filler content. At room temperature (20 °C), we measured solubility and diffusion coefficients for 29 common VOCs spanning diverse chemical functionalities, including alkanes, aromatics, chlorinated solvents, ketones, esters, and alcohols. Comparison with literature data for pure PDMS reveals that VOC solubility in Sylgard 184 is generally higher; for most non-hydrogen-bonding compounds it remains within a factor of 2 of pure PDMS, whereas alcohols are enhanced by roughly 1.8 to 3.7 times, which we attribute to favorable interactions with residual silanol groups on the silanized silica filler. Diffusion coefficients range from 1.0 × 10 –6 cm 2 /s (n-undecane) to 8.9 × 10–5 cm 2 /s (acetonitrile) and align well with extrapolated literature values for PDMS. This study provides essential thermodynamic and transport data for predicting VOC permeation in Sylgard 184 while demonstrating the utility of 2D IGC as a robust technique for characterizing rubbery polymer membranes across diverse industrial applications.

organic↗
DOE OSTI2025

Elucidating the modes of incorporation of the ferulic acid amides feruloyltyramine and feruloyloctopamine into the lignin-suberin fraction of potato periderms

Ferulic acid amides are naturally present in the cell walls of potato (Solanum tuberosum) periderms. In this study, we investigated their modes of incorporation into the periderm cell wall polymers. A lignin/suberin-enriched fraction was isolated and analyzed by GPC, DFRC, and 2D-NMR. The analyses revealed that the lignin domain of this fraction was predominantly composed of G-lignin units, with an H:G:S ratio of 2:70:28 (S/G ratio of 0.40). More importantly, the data also indicated the presence of two ferulic acid amides, feruloyltyramine and feruloyloctopamine, that are incorporated into the lignin/suberin structure of potato periderms through a variety of linkages, including 8-O-4' and 4-O-beta' ether linkages, as well as 8-5' linkages forming a phenylcoumaran structure involving the ferulate moiety. Although the phenolic groups of the tyramine and octopamine moieties could theoretically undergo oxidation, potentially creating additional sites for radical coupling, our research indicates that these groups remain predominantly as free phenolic entities that do not participate in radical coupling. On the other hand, all the phenolic groups of the ferulate moieties are bound through ether linkages reinforcing the conclusion that the feruloyltyramine and feruloyloctopamine moieties are linked to lignin/suberin within the cell wall via radical coupling reactions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Polymer-assisted transfer of MBE-grown van der Waals materials

Molecular beam epitaxy (MBE) has been used to create high-quality, large-scale two-dimensional van der Waals (2D vdW) materials. However, due to the strong adhesion between the substrate and deposited materials, the peel-off and dry transfer of MBE-grown vdW films onto other substrates has been challenging. This limits the study and use of MBE films for heterogeneous integration including stacked and twisted heterostructures. In this work, we develop a polymer-assisted dry transfer method and successfully perform full-film transfer of various MBE-grown 2D vdW materials including transition metal dichalcogenides (TMD), topological insulators (TI) and 2D magnets. In particular, we transfer air-sensitive 2D magnets, characterize their magnetic properties, and compare them with as-grown materials. The results show that the transfer technique does not degrade the magnetic properties, with the Curie temperature and hysteresis loops exhibiting similar behaviors after the transfer. Our results enable further development of heterogeneous integration of 2D vdW materials based on MBE growth.

Li, Ziling [The Ohio State University]↗
DOE OSTI2025

Full-film dry transfer of MBE-grown van der Waals materials

Abstract Molecular beam epitaxy (MBE) has been used to create high-quality, large-scale two-dimensional van der Waals (2D vdW) materials. However, due to the strong adhesion between the substrate and deposited materials, the peel-off and dry transfer of MBE-grown vdW films onto other substrates has been challenging. This limits the study and use of MBE films for heterogeneous integration including stacked and twisted heterostructures. In this work, we develop a polymer-assisted dry transfer method and successfully perform full-film transfer of various MBE-grown 2D vdW materials including transition metal dichalcogenides, topological insulators and 2D magnets. In particular, we transfer air-sensitive 2D magnets, characterize their magnetic properties, and compare them with as-grown materials. The results show that the transfer technique does not degrade the magnetic properties, with the Curie temperature and hysteresis loops exhibiting similar behaviors after the transfer. Our results enable further development of heterogeneous integration of 2D vdW materials based on MBE growth.

Li, Ziling (ORCID:0000000203537036)↗
DOE OSTI2020

Single-layer graphene as a highly selective barrier for vanadium crossover with high proton selectivity

In this paper, we report near-zero crossover for vanadium cross-permeation through single-layer graphene immobilized at the interface of two Nafion® polymer electrolyte membranes. Vanadium ion diffusion and migration, including proton mobility through membrane composites, were studied with and without graphene under diffusion and migration conditions. Single-layer graphene was found to effectively inhibit vanadium ion diffusion and migration under specific conditions. The single-layer graphene composites also enabled remarkable ion transmission selectivity improvements over pure Nafion® membranes, with proton transport being four orders of magnitude faster than vanadium ion transport. Resistivity values of 0.02 ± 0.005 Ω cm 2 for proton and 223 ± 4 Ω cm 2 for vanadium ion through single atomic layer graphene are reported. This high selectivity may have significant impact on flow battery applications or for other electrochemical devices where proton conductivity is required, and transport of other species is detrimental. Our results emphasize that crossover may be essentially completely eliminated in some cases, enabling for greatly improved operational viability.

2D nanomaterial↗
DOE OSTI2025

Determining the nanostructure of polymer foams using 3D ptycho-tomography for inertial fusion energy applications

Polymer foams play a critical role in contemporary inertial fusion energy (IFE) target designs by enhancing energy yield and optimizing implosion dynamics. However, the lack of high-resolution characterization of the nanostructure of these foams restricts progress in fusion science. In this work, we demonstrate the first high-resolution three-dimensional (3D) reconstruction of a low-density, Si-doped polymer foam fabricated via two-photon polymerization, using ptychographic x-ray computed tomography (PXCT) at an x-ray free electron laser (XFEL). This imaging method reconstructs two-dimensional (2D) attenuation and phase information at multiple sample angles that are combined into a 3D density map used to extract local mass density and determine structural dimensions. We achieve a 2D spatial resolution of 19 ± 3 nm on a high-contrast Ronchi pattern target and 78.7 ± 3 nm for low-contrast polymer foams, marking a significant advancement for XFEL-based ptychography of low-density materials. Furthermore, our experimental results reveal an average foam strut thickness of 1.17 ± 0.4 μm, consistent with fabrication expectations, and a reconstructed average mass density of 0.35 g/cc, aligning closely with the predicted density of 0.29 g/cc. These findings provide important insights for improving foam design and refining radiation hydrodynamics modeling in future IFE experiments. Our study establishes PXCT at an XFEL as a powerful tool for high-resolution characterization of fusion-relevant materials, paving the way for enhanced target performance in IFE research.

Hancock, Levi [Colorado State Univ., Fort Collins,↗
DOE OSTI2020

Highly-Cyclable Room-Temperature Phosphorene Polymer Electrolyte Composites for Li Metal Batteries

Despite significant interest toward solid-state electrolytes owing to their superior safety in comparison to liquid-based electrolytes, sluggish ion diffusion and high interfacial resistance limit their application in durable and high-power density batteries. Here, a novel quasi-solid Li + ion conductive nanocomposite polymer electrolyte containing black phosphorous (BP) nanosheets is reported. The developed electrolyte is successfully cycled against Li metal (over 550 h cycling) at 1 mA cm -2 at room temperature. The cycling overpotential is dropped by 75% in comparison to BP-free polymer composite electrolyte indicating lower interfacial resistance at the electrode/electrolyte interfaces. Molecular dynamics simulations reveal that the coordination number of Li + ions around (trifluoromethanesulfonyl)imide (TFSI - ) pairs and ethylene-oxide chains decreases at the Li metal/electrolyte interface, which facilitates the Li + transport through the polymer host. Here, density functional theory calculations confirm that the adsorption of the LiTFSI molecules at the BP surface leads to the weakening of N and Li atomic bonding and enhances the dissociation of Li + ions. This work offers a new potential mechanism to tune the bulk and interfacial ionic conductivity of solid-state electrolytes that may lead to a new generation of lithium polymer batteries with high ionic conduction kinetics and stable long-life cycling.

2D materials↗
NASA NTRS2025

The Shape Effect: Influence of 1D and 2D Boron Nitride Nanostructures on the Radiation Shielding, Thermal, and Damping Properties of High-Temperature Epoxy Composites

In space exploration, lightweight multifunctional materials capable of shielding neutron radiation, dissipating heat, and providing damping are essential. Polymer composites reinforced with boron nitride (BN) nanomaterials—specifically one-dimensional boron nitride nanotubes (BNNTs) and two-dimensional boron nitride nanoplatelets (BNNPs)—offer promising solutions. This study investigates how BN nanomaterial morphology influences the performance of high-temperature (HT) epoxy composites. We developed ultralightweight, three-dimensional BN foams comprising 1D BNNTs, 2D BNNPs, and hybrid 1D BNNT/2D BNNP structures via freeze-drying, then infiltrated them with HT epoxy to form dense composites. The BNNT foam exhibited the highest neutron radiation shielding, with a mass absorption coefficient of 26.64 cm2 g −1 , outperforming the hybrid foam (18.18 cm 2 g −1 ) and the BNNP foam (11.12 cm 2 g −1 ). A similar trend was observed in the HT epoxy composites; incorporating these foams at least doubled the mass absorption coefficient compared to the neat polymer. In terms of thermal conductivity, the BNNT/BNNP foam-epoxy composite achieved the highest value of 0.34 W m −1 K −1 , a 2.13-fold increase over neat HT epoxy. The BNNT/BNNP foam-epoxy composites also improved by 1.88 and 1.75 times, respectively. Mechanical testing revealed that BNNP foams withstood the highest loads during nanoindentation (3.53 kN), followed by BNNT/BNNP foams (1.93 kN) and BNNT foams (1.56 kN). All BN foam-epoxy composites exhibited enhanced damping properties, with tan δ increasing by at least 30 % compared to neat HT epoxy. These findings elucidate the impact of BN nanomaterial morphology on the multifunctional performance of HT epoxy composites, offering insights for developing high-performance, tailorable materials for demanding environments.

Kazue Orikasa↗
DOE OSTI2023

Engineering Functionalized 2D Metal-Organic Frameworks Nanosheets with Fast Li + Conduction for Advanced Solid Li Batteries

Solid-state batteries can ensure high energy density and safety in lithium metal batteries, while polymer electrolytes are plagued by slow ion kinetics and low selective transport of Li + . Metal-organic frameworks (MOFs) are proposed as emerging fillers for solid-state poly(ethylene oxide)(PEO) electrolytes, however, developing functionalized MOFs and understanding their roles on ion transfer has proven challenging. Herein, combining computational and experimental results, the functional group regulation in MOFs can effectively change surficial charge distribution and limit anion movement is revealed, providing a potential solution to these issues. Specifically, functionalized 2D MOF sheets are designed through molecular engineering to construct high-performance composite electrolytes, where the electron-donating effect of substituents in 2D-MOFs effectively limits the movement of ClO 4 - and promotes mechanical properties and ion migration numbers (0.36 up to 0.64) of PEO. As a result, Li/Li cells with composite electrolyte exhibit superior cyclability for 1000 h at a current density of 0.2 mA cm -2 . Meanwhile, the solid LiFePO 4 /Li battery delivers highly reversible capacities of 148.8 mAh g -1 after 200 cycles. In conclusion, these findings highlight a new approach for anion confinement through the use of functional group electronic effects, leading to enhanced ionic conductivity, and a feasible direction for high-performance solid-state batteries.

25 ENERGY STORAGE↗
DOE OSTI2023

Structure and dynamics of ILs-based gel polymer electrolytes and its enhanced conductive properties with the incorporation of Al 2 O 3 nanofibers

Here, this work reports the enhanced mobility of ions in ionic liquid (IL)-based gel polymer electrolytes (GPEs) with the incorporation of Al 2 O 3 nanofibers. A combination of PVDF-HFP, EMIMTFSI and LiTFSI with 3 wt% Al 2 O 3 nanofibers has been prepared through solution casting technique. The room temperature ionic conductivity of PVDF-HFP: ILs electrolyte (45:55, weight ratio of 0.82) (GPE) is found to be 2.7 × 10 –5 S cm –1 , which increases up to 7.8 × 10 –5 S cm –1 in Al 2 O 3 containing GPE (Al-GPE). Pulsed field gradient (PFG) NMR results validate the increased ionic conductivity observed in Al-GPE. We found that the diffusivity of Li + , TFSI – and EMIM + increases when Al 2 O 3 nanofibers are well-distributed in the GPE matrix. The surface morphology and the amorphicity of GPEs are examined through SEM and XRD analyses. Lastly, the local structure of Al 2 O 3 fibers and the molecular-level interactions of ions with polymer, and their effect on the diffusivity of ions are established through solid-state NMR detecting 27 Al, 1 H, 13 C, 19 F nuclei including 2D 13 C{ 1 H} HETCOR NMR experiments. The 13 C DPMAS and CPMAS experiments highlight the dynamic heterogeneity associated with the ions that are embedded in the rigid and the mobile phase of GPEs. While some of the ionic species strongly interact with polymer chains in the rigid environment, the majority of them reside in the mobile phase and contribute to the overall increased conductivity. Most importantly, Al 2 O 3 nanofibers significantly affect the dynamics of ionic species that are present in the mobile phase between the polymer chains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Electronically Coupled 2D Polymer/MoS 2 Heterostructures

Emergent quantum phenomena in electronically coupled two-dimensional heterostructures are central to next-generation optical, electronic, and quantum information applications. Tailoring electronic band gaps in coupled heterostructures would permit control of such phenomena and is the subject of significant research interest. Two-dimensional polymers (2DPs) offer a compelling route to tailored band structures through the selection of molecular constituents. However, despite the promise of synthetic flexibility and electronic design, fabrication of 2DPs that form electronically coupled 2D heterostructures remains an outstanding challenge. Here, we report the rational design and optimized synthesis of electronically coupled semiconducting 2DP/2D transition metal dichalcogenide van der Waals heterostructures, demonstrate direct exfoliation of the highly crystalline and oriented 2DP films down to a few nanometers, and present the first thickness-dependent study of 2DP/MoS 2 heterostructures. In this work, control over the 2DP layers reveals enhancement of the 2DP photoluminescence by two orders of magnitude in ultrathin sheets and an unexpected thickness-dependent modulation of the ultrafast excited state dynamics in the 2DP/MoS 2 heterostructure. These results provide fundamental insight into the electronic structure of 2DPs and present a route to tune emergent quantum phenomena in 2DP hybrid van der Waals heterostructures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

All‐Liquid Reconfigurable Electronics Using Jammed MXene Interfaces

Abstract Rigid, solid‐state components represent the current paradigm for electronic systems, but they lack post‐production reconfigurability and pose ever‐increasing challenges to efficient end‐of‐life recycling. Liquid electronics may overcome these limitations by offering flexible in‐the‐field redesign and separation at end‐of‐life via simple liquid phase chemistries. Up to now, preliminary work on liquid electronics has focused on liquid metal components, but these devices still require an encapsulating polymer and typically use alloys of rare elements like indium. Here, using the self‐assembly of jammed 2D titanium carbide (Ti 3 C 2 T x ) MXene nanoparticles at liquid–liquid interfaces, “all‐liquid” electrically conductive sheets, wires, and simple functional devices are described including electromechanical switches and photodetectors. These assemblies combine the high conductivity of MXene nanosheets with the controllable form and reconfigurability of structured liquids. Such configurations can have applications not only in electronics, but also in catalysis and microfluidics, especially in systems where the product and substrate have affinity for solvents of differing polarity.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Seeking regularity from irregularity: unveiling the synthesis–nanomorphology relationships of heterogeneous nanomaterials using unsupervised machine learning

Nanoscale morphology of functional materials determines their chemical and physical properties. However, despite increasing use of transmission electron microscopy (TEM) to directly image nanomorphology, it remains challenging to quantify the information embedded in TEM data sets, and to use nanomorphology to link synthesis and processing conditions to properties. We develop an automated, descriptor-free analysis workflow for TEM data that utilizes convolutional neural networks and unsupervised learning to quantify and classify nanomorphology, and thereby reveal synthesis–nanomorphology relationships in three different systems. While TEM records nanomorphology readily in two-dimensional (2D) images or three-dimensional (3D) tomograms, we advance the analysis of these images by identifying and applying a universal shape fingerprint function to characterize nanomorphology. After dimensionality reduction through principal component analysis, this function then serves as the input for morphology grouping through unsupervised learning. We demonstrate the wide applicability of our workflow to both 2D and 3D TEM data sets, and to both inorganic and organic nanomaterials, including tetrahedral gold nanoparticles mixed with irregularly shaped impurities, hybrid polymer-patched gold nanoprisms, and polyamide membranes with irregular and heterogeneous 3D crumple structures. In each of these systems, unsupervised nanomorphology grouping identifies both the diversity and the similarity of the nanomaterial across different synthesis conditions, revealing how synthetic parameters guide nanomorphology development. Our work opens possibilities for enhancing synthesis of nanomaterials through artificial intelligence and for understanding and controlling complex nanomorphology, both for 2D systems and in the far less explored case of 3D structures, such as those with embedded voids or hidden interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A new approach to zip–lignin: 3,4–dihydroxybenzoate is compatible with lignification

Renewed interests in the development of bioenergy, biochemicals, and biomaterials have elicited new strategies for engineering the lignin of biomass feedstock plants. Furthermore, this study shows, for the first time, that 3,4-dihydroxybenzoate (DHB) is compatible with the radical coupling reactions that assemble polymeric lignin in plants. We introduced a bacterial 3-dehydroshikimate dehydratase into hybrid poplar (Populus alba × grandidentata) to divert carbon flux away from the shikimate pathway, which lies upstream of lignin biosynthesis. Transgenic poplar wood had up to 33% less lignin with p-hydroxyphenyl units comprising as much as 10% of the lignin. Mild alkaline hydrolysis of transgenic wood released fewer ester-linked p-hydroxybenzoate groups than control trees, and revealed the novel incorporation of cell-wall-bound DHB, as well as glycosides of 3,4-dihydroxybenzoic acid (DHBA). Two-dimensional nuclear magnetic resonance (2D-NMR) analysis uncovered DHBA-derived benzodioxane structures suggesting that DHB moieties were integrated into the lignin polymer backbone. In addition, up to 40% more glucose was released from transgenic wood following ionic liquid pretreatment and enzymatic hydrolysis. This work highlights the potential of diverting carbon flux from the shikimate pathway for lignin engineering and describes a new type of ‘zip-lignin’ derived from the incorporation of DHB into poplar lignin.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

LigninGraphs: lignin structure determination with multiscale graph modeling

Lignin is an aromatic biopolymer found in ubiquitous sources of woody biomass. Designing and optimizing lignin valorization processes requires a fundamental understanding of lignin structures. Experimental characterization techniques, such as 2D-heteronuclear single quantum coherence (HSQC) nuclear magnetic resonance (NMR) spectra, could elucidate the global properties of the polymer molecules. Computer models could extend the resolution of experiments by representing structures at the molecular and atomistic scales. We introduce a graph-based multiscale modeling framework for lignin structure generation and visualization. The framework employs accelerated rejection-free polymerization and hierarchical Metropolis Monte Carlo optimization algorithms. We obtain structure libraries for various lignin feedstocks based on literature and new experimental NMR data for poplar wood, pinewood, and herbaceous lignin. The framework could guide researchers towards feasible lignin structures, efficient space exploration, and future kinetics modeling. Its software implementation in Python, LigninGraphs, is open-source and available on GitHub.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

SU(n) and Quantum SU(n) Symmetries in Physical Systems [Slides]

Presence of SU(n) or other Lie group symmetry in a physical system is its powerful, usually underutilized property. In many cases it allows for finding analytical solutions to nonlinear differential equations describing this system. Power of the method is presented on diversified examples from mathematical physics: Lie-group symmetries in finding solutions of generalized, multidimensional theory of gravity; analytical Dirac–equation solutions for description of conducting polymers; stability of qubit states in quantum computers; spatial defects in condensed matter; reconstruction of 3D object from its 2D tomographic image; significant improvement of numerical solutions stability for Euler equations. The next question after obtaining such Lie group symmetric solution is: does a generalized solution with appropriate quantum group symmetry exists for the given physical system, and if yes what is the physical meaning of the deformation parameter q introduced by such solution. In many cases it can be identified. Any SU(n) solution is by its nature singular, assuming a perfect symmetry of the physical system discussed. Such solution gives a powerful insight to theoretical physics, yet the assumption may be too demanding for experimental applications. Deformation parameter q from a quantum group symmetry allows for a continuum of solutions, more applicable to experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗