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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 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Locally Engineering and Interrogating the Photoelectrochemical Behavior of Defects in Transition Metal Dichalcogenides

Transition metal dichalcogenides (TMDs) are attractive materials for a variety of applications in solar energy conversion and electrocatalysis, due to their favorable optical and electrical properties and their unique two-dimensional structures which facilitate the fabrication of wide-area, ultrathin layers. Unfortunately, the basal planes which make up the majority of these materials are relatively inert, and thus a great deal of effort has been directed to engineering favorable, catalytically active defects into these materials. In this paper, we demonstrate how probe-based electrochemical techniques can be employed as multifunctional tools for locally modifying TMD materials and probing the electrochemical behavior of the resulting defects. Scanning Electrochemical Cell Microscopy (SECCM) was employed to locally anodize exfoliated p-type WSe 2 nanosheets, creating hole-like defects within individual basal planes in a highly controllable fashion. Photoelectrochemical SECCM imaging was then employed to characterize the chemical behavior of these engineered defects, revealing significantly enhanced activity toward the Hydrogen Evolution Reaction (HER). Atomic force microscopy studies are presented which suggest these enhancements result from an increased density of monolayer-high step features within the anodized defects. Analysis of the SECCM data in the context of finite element simulations revealed that these enhancements increased with increasing anodization time, with local kinetic rates over 2 orders of magnitude higher than unaltered basal planes.

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

Confinement-mediated phase behavior of hydrocarbon fluids: Insights from Monte Carlo simulations

The phase behavior of hydrocarbon fluids confined in porous media has been discussed to deviate significantly from that in the bulk environment due to the existence of sub-10nm pores. Though experiments and simulations have measured the bubble/dew points and sorption isotherms of hydrocarbons confined in both natural and synthetic nanopores, the confinement effects in terms of the strength of fluid-pore interactions tuned by surface wettability and chemistry have received comparably less discussion. More significantly, the underlying physics of confinement-induced phenomena remain obfuscated. In this work, we studied the phase behavior and capillary condensation of n-hexane to understand the effects of confinement at the molecular level. To systematically investigate the pore effects, we constructed two types of wall confinements; one is a structureless virtual wall described by the Steele potential and the other one is an all-atom amorphous silica structure with surface modified by hydroxyl groups. Our numerical results demonstrated the importance of fluid-pore interaction, pore size, and pore morphology effects in mediating the pressure-volume-temperature (PVT) properties of hydrocarbons. The most remarkable finding of this work was that the saturation pressure predicted from the van der Waals-type adsorption isothermal loop could be elevated or suppressed relative to the bulk phase, as illustrated in the graphical abstract. As the surface energy (i.e., fluid-pore interaction) decreased, the isothermal vapor pressure increased, indicating a greater preference for the fluid to exist in the vapor state. Sufficient reduction of the fluid-pore interactions could even elevate the vapor pressure above that of the bulk fluid.

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

On the Interfacial Behavior of Catenated Poly(l-lactide) at the Air–Water Interface

Interfacial properties of polymeric materials are significantly influenced by their architectural structures and spatial features, while such a study of topologically interesting macromolecules is rarely reported. Here, we reported, for the first time, the interfacial behavior of catenated poly(l-lactide) (C-PLA) at the air–water interface and compared it with its linear analogue (L-PLA). The isotherms of surface pressure–area per repeating unit showed significant interfacial behavioral differences between the two polymers with different topologies. Isobaric creep experiments and compression–expansion cycles also showed that C-PLA demonstrated higher stability at the air–water interface. Interestingly, when the films at different surface pressures were transferred via the Langmuir–Blodgett method, successive atomic force microscopy imaging displayed distinct nanomorphologies, in which the surface of C-PLA exhibited nanofibrous structures, while that of the L-PLA revealed a smoother topology with less fiber-like structures.

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

Wetting Behavior of A -block- (B- random -C) Copolymers with Equal Block Surface Energies on Surfaces Functionalized with B- random -C Copolymers

To form nanopatterns with self-assembled block copolymers (BCPs), it is desirable to have through-film domains that are oriented perpendicular to the substrate. The domain orientation is determined by the interfacial interactions of the BCP domains with the substrate and with the free surface. Here, we use thin films of two different sets of BCPs with A-block-(B-random-C) architecture matched with a corresponding B-random-C copolymer nanocoating on the substrate to demonstrate two distinct wetting behaviors. The two sets of A-b-(B-r-C) BCPs are made by using thiol–epoxy click chemistry to functionalize polystyrene-block-poly(glycidyl methacrylate) with trifluoroethanethiol (TFET) and either 2-mercaptopyridine (2MP) or methyl thioglycolate (MTG). For each set of BCPs, the composition ratio of the two thiols in the BCP (φ 1 ) is found that results in the two blocks of the modified BCP having equal surface energies (Δγ air = 0). The corresponding B-r-C random copolymers were synthesized and used to modify the substrate, and the composition ratio (φ 2 ) values that resulted in the two blocks of the BCP having equal interfacial energy with the substrate (Δγ sub = 0) were determined with scanning electron microscopy. The correlation between each block’s γ sub value and the interaction parameter, χ, is employed to explain the different wetting behaviors of the two sets of BCPs. For the thiol pair 2MP and TFET, the values of φ 1 and φ 2 that lead to Δγ air = 0 and Δγ sub = 0, respectively, are significantly different. A similar difference was observed between the φ 1 and φ 2 values that lead to Δγ air = 0 and Δγ sub = 0 for the BCPs made with the thiol pair MTG and TFET. In the latter case, for Δγ sub = 0 two windows of φ 2 are identified, which can be explained by the thermodynamic interactions of the specific thiol pair and the A-b-(B-r-C) architecture.

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

Comparing Experimental Phase Behavior of Ion-Doped Block Copolymers with Theoretical Predictions Based on Selective Ion Solvation

The effects of salt-doping on the morphological behavior of block copolymers are well established but remain poorly understood, partially because of the challenge of resolving electrostatics in a heterogeneous medium with low average permittivity. By employing a recently developed field theory, we analyze the phase behavior of polystyrene-b-poly(ethylene oxide) (SEO) copolymers doped with lithium bis(trifluoromethanesulfonyl)imide salts (LiTFSI). Using a single fitting parameter, the ionic solvation radius, we obtain qualitative agreement between our theory and experimental data over a range of polymer molecular weights and copolymer compositions. Such agreement supports and highlights the need of solvation free energy to accurately describe the self-assembly of ion-doped block copolymers and demonstrates that experimentally observed dependence on molecular weight, not present in neutral block copolymers, can be rationalized by solvation effects. Overall, morphological variations are stronger than those predicted by the leading, linear order theory but can be captured by the full model.

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

Investigation of the Self-Assembly Behavior of Statistical Bottlebrush Copolymers via Self-Consistent Field Theory Simulations

Bottlebrush copolymers, a class of high-density side-chain-grafted copolymers with high molecular weights, have recently attracted extensive research attention due to the dramatic reduction of chain entanglement in these copolymers, unique self-assembly behaviors, and distinctive physical properties. In this study, we employ self-consistent field theory simulations to systemically investigate the phase behavior of statistical bottlebrush copolymers A-stat-B, an intriguing subclass of bottlebrush copolymers with random or alternating sequences of A and B side chains. We find that a broader variety of ordered mesophases can be stabilized in the melts of these copolymers relative to the more extensively studied bottlebrush block copolymers. In particular, we observe that these statistical copolymers can stabilize sphere phases over a larger range of species volume fractions than their diblock and tetrablock counterparts but require much higher segregation strength to achieve this. The sphere and hexagonally packed cylinder phases formed by conformationally symmetric statistical bottlebrush copolymers possess interesting discrete core–shell structures with the backbone and lower volume fraction side-chain species forming shells and cores, respectively. Moreover, we uncover a new strategy of stabilizing the Frank–Kasper phase A15 by introducing conformational asymmetry through different side-chain lengths and also observe deflection of order–order phase boundaries and significant mixing between the backbones and short side chains as conformational asymmetry is introduced.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Simulations of Glass Transition and Mechanical Behavior of Off-Stoichiometric Crosslinked Polymers

Here, this work explores the influence of blend composition, network architecture, and hydrogen bonding on the material properties of crosslinked epoxy networks, focusing on the glass transition temperature (T g ) and Young’s modulus (Y). We used coarse-grained molecular dynamics simulations to simulate varying compositions of stiff and flexible components in epoxy monomer blends with varying excess of curative. We find that, without hydrogen bonding, networks of any composition show a monotonically increasing T g with decreasing excess curative, consistent with theory. In contrast, we find that when hydrogen bonding is introduced, the binary blend networks show significant enhancement in T g for lightly crosslinked systems. This result contributes to an explanation of the anomalous T g behavior observed experimentally in these systems. We further find that Y is generally enhanced by hydrogen bonds, especially below T g , demonstrating that hydrogen bonding has a significant influence on mechanical properties and can allow access to other desirable dynamic behavior, especially self-healing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Insight into the Competitive Adsorption Behavior of Polymer Chains in Silica Nanopores by Small-Angle Neutron Scattering

Processive hydrogenolysis catalysts, in which a metal nanoparticle (e.g., Pt) embedded at the bottom of a cylindrical silica nanopore can repeatedly cleave polymer chains and produce value-added hydrocarbon products, offer a potential solution for billions of tons of waste plastics. As the chain stays longer near the Pt catalysts, it would have a higher chance of getting cut, and therefore the molecular weight distribution of the product could be affected by the adsorption behavior of virgin chains (long polymers) versus cleaved chains (short polymers) into the nanopores. Further, this work reports a model study to understand the competitive adsorption behavior of the two different molecular weight polymers that are mixed, mimicking the reaction medium in the intermediate stage of the catalytic reaction. This study employs small-angle neutron scattering (SANS), which takes advantage of contrast differences between hydrogenous and deuterated polystyrenes to experimentally observe the relative composition of the two polymers in the silica nanopores. Our results reveal preferential adsorption of longer chains in the silica nanopores, which is consistent with the theoretical prediction in the literature for the case of the enthalpic attraction between polymers and pore walls.

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

Thermal Hysteresis and Ordering Behavior of Magnetic Skyrmion Lattices

The physics of phase transitions in two-dimensional (2D) systems underpins research in diverse fields including statistical mechanics, nanomagnetism, and soft condensed matter. However, many aspects of 2D phase transitions are still not well understood, including the effects of interparticle potential, polydispersity, and particle shape. Magnetic skyrmions are chiral spin-structure quasi-particles that form two-dimensional lattices. Here, in this study, we show, by real-space imaging using in situ cryo-Lorentz transmission electron microscopy coupled with machine learning image analysis, the ordering behavior of Néel skyrmion lattices in van der Waals Fe 3 GeTe 2 . We demonstrate a distinct change in the skyrmion size distribution during field-cooling, which leads to a loss of lattice order and an evolution of the skyrmion liquid phase. Remarkably, the lattice order is restored during field heating and demonstrates a thermal hysteresis. This behavior is explained by the skyrmion energy landscape and demonstrates the potential to control the lattice order in 2D phase transitions.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Probing the Effects of the First Atomic Layer on the Dynamic Behavior of Sub-2 nm MgO/Al 2 O 3 Memristors

As electronic devices continue to scale down from the current sub-5 nm range, atomic-scale control of defects becomes increasingly crucial to suppressing their impact on the physical properties of the devices. Memristors present an excellent example as a nonlinear and dynamic device with high speed and endurance required for electronic applications ranging from neuromorphic computing to nonvolatile memories. Herein we investigate the impact of atomic defects in sub-2 nm thick MgO/Al 2 O 3 atomic layer stack (ALS) memristors that use an M1 (switching layer)/M2 (oxygen vacancy reservoir layer) bilayer structure grown using in vacuo atomic layer deposition (iALD). Intriguingly, we revealed a direct correlation of the atomic defects in the M2 layer with the memristor dynamic behavior using a combined analysis of in situ scanning tunneling spectroscopy (iSTS) on the M2 layer and ex situ characterization on the memristors. Specifically, incomplete coverage of the 1st ALD atomic layer of M2 on the electrode yields defects at the M2/electrode interface. Despite the monotonic increase of ALD coverage, by almost three-fold from ~30% to >90%, at completion of the M2 layer of ~ 0.7 nm in thickness, the impact of the defects on the M2/electrode interface has been found detrimental to both memristor switching speed and endurance. Guided by atomistic simulation, we addressed the issue of interface defects via tuning of the Al surface hydroxylation to increase the first atomic layer ALD coverage to ~75%, leading to improved memristor switching speed and endurance by several orders of magnitude. In conclusion, these findings shed light on the correlation between the atomic defects and the dynamic behavior of sub-2 nm memristors and the importance of minimizing the atomic defects in memristors for future electronic applications.

Atomic Layer Deposition↗
DOE OSTI2025

Electrochemical Behavior of Cerium at an Indium Tin-Doped Oxide Electrode in Acidic Media

The redox behavior and speciation of cerium at mesoporous thin films composed of nanoparticles of indium tin-doped oxide (nITO) electrodes were characterized in pH 4.8, 0.1 M acetate buffer and both 0.1 and 1 M HNO 3 using electrochemical techniques and X-ray photoelectron spectroscopy. Anodic deposition of ceria species from Ce(III) to the nITO electrode was achieved under all solvent conditions via spontaneous condensation of electrochemically generated ceric hydroxide species. In 1 M nitric acid, the rate of CeO 2 dissolution is on the same order as CeO 2 deposition, resulting in negligible amounts of CeO 2 electrodeposited at the nITO surface. The cathodic stripping of CeO 2 from the nITO substrate deposited in 0.1 M nitric acid or pH 4.8 acetate buffer follows a 2-step process where Ce(IV)-oxide is initially reduced to an unstable Ce(III)-oxide species that rapidly undergoes acid catalyzed dissolution to yield soluble Ce(III) (aq) . These findings provide a foundation for the pH and anodic potential controlled deposition of CeO 2 thin films to ITO substrates, which can aid in the development of materials composed of ceria. As a result, they can also be used to infer likely analogous actinide redox behavior and speciation at these electrodes.

Cerium↗
DOE OSTI2021

Influence of Charge Fraction on the Phase Behavior of Symmetric Single-Ion Conducting Diblock Copolymers

A series of symmetric poly[(oligo(ethylene glycol) methyl ether methacrylate-co-oligo(ethylene glycol) propyl sodium sulfonate methacrylate)]-block-polystyrene (PsOEGMA-PS) diblock copolymers were synthesized as a model system to probe the effect of charge fraction on the phase behavior of charged-neutral single-ion conducting diblock copolymers. Small-angle X-ray scattering (SAXS) experiments showed that increasing the charge fraction does not alter the ordered phase morphology (lamellar) but increases the order–disorder transition temperature (T ODT ) significantly. Additionally, the effective Flory–Huggins interaction parameter (χ eff ) was found to increase linearly with the charge fraction, similar to the case of conventional salt-doped diblock copolymers. This indicates that the effect of counterion solvation, attributed to the significant mismatch between the dielectric constant of each block, provides the dominant effect in tuning the phase behavior of this charged diblock copolymer. Lastly, we therefore infer that electrostatic cohesion (local charge ordering induced by Coulombic interactions), which is predicted to suppress microphase separation and lead to asymmetric phase diagrams, only plays a minor role in this model system.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Influence of Charge Block Length on Conformation and Solution Behavior of Polyampholytes

In this paper, we investigate the effect of charge block length on polyampholyte chain conformation and phase behavior using small-angle X-ray scattering (SAXS) and implicit-solvent molecular simulations. To this end, we use solid phase peptide synthesis to precision-tailor a series of polyampholytes consisting of l-glutamic acid (E) and l-lysine (K) monomers arranged in alternating blocks from 2 to 16 monomers. We observe that the polyampholytes tend to phase separate as block size increases. With addition of NaCl, phase separated polyampholytes exhibit a salting-in effect dependent on charge block length. Fourier-transform infrared (FTIR) spectroscopy reveals the presence of intramolecular hydrogen bonds that are disrupted upon the addition of NaCl, implicating both electrostatic interactions and hydrogen bonding in the phase behavior. SAXS spectra at no-added salt conditions show minimal dependence of charge block length on the radius of gyration (R g ) for soluble polyampholytes, but local chain stiffening is found to be dependent on charge block length. With increasing NaCl, consistent with electrostatic screening, all polyampholytes expand and behave as neutral or swollen chains in good solvent conditions. Molecular simulations are qualitatively consistent with experiments. Implications for understanding intracellular condensates and material design are noted.

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

Role of Decomposition Product Ions in Hysteretic Behavior of Metal Halide Perovskite

Ion migration is one of the most debated mechanisms and credited with multiple observed phenomena and performance in metal halide perovskites (MHPs) semiconductor devices. However, to date, the migration of ions and their effects on MHPs are not still fully understood, largely due to a lack of direct observations of temporal ion migration. In this work, using direct observation of ion migration in-operando, we observe the hysteretic migration behavior of intrinsic ions (i.e., CH 3 NH 3 + and I – ) as well as reveal the migration behavior of CH 3 NH 3 + decomposition ions. We find that CH 3 NH 3 + decomposition products can be affected by light and accumulate at the interfaces under bias. These MHP decomposition products are tightly related to the device performance and stability. Complementary results of time-resolved Kelvin probe force microscopy (tr-KPFM) demonstrate a correlation between dynamics of these interfacial ions and charge carriers. Overall, we find that there are a number of mobile ions including CH 3 NH 3 + decomposition products in MHPs that need to be taken into account when measuring MHP device responses (e.g., charge dynamics) and should be considered in future optimization studies of MHP semiconductor devices.

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

Selective Methane Oxidation to Methanol on ZnO/Cu 2 O/Cu(111) Catalysts: Multiple Site-Dependent Behaviors

Due to the abundance of natural gas in our planet, a major goal is to achieve a direct methane to methanol conversion at medium to low temperatures using mixtures of methane and oxygen. Here, we report an efficient catalyst, ZnO/Cu 2 O/Cu(111), for this process investigated using a combination of reactor testing, scanning tunneling microscopy, ambient-pressure x-ray photoemission spectroscopy, density functional calculations, and kinetic Monte Carlo simulations. The catalyst is capable of methane activation at room temperature and transforms mixtures of methane and oxygen to methanol at 450 K with a selectivity of ~30%. This performance is not seen for other heterogenous catalysts which usually require the addition of water to enable a significant conversion of methane to methanol. The unique coarse structure of the ZnO islands supported on a Cu 2 O/Cu(111) substrate provides a collection of multiple centers that display different catalytic activity during the reaction. ZnO-Cu 2 O step sites are active centers for methanol synthesis when exposed to CH 4 and O 2 due to an effective O-O bond dissociation, which enables a methane-to-methanol conversion with a reasonable selectivity. Upon addition of water, the defected O-rich ZnO sites, introduced by Zn vacancies, show superior behavior towards methane conversion and enhance the overall methanol selectivity to over 80%. Thus, in this case, the surface sites involved in a direct CH 4 → to CH 3 OH conversion are different from those engaged in methanol formation without water. Furthermore, the identification of the site-dependent behavior of ZnO/Cu 2 O/Cu(111) opens a design strategy for guiding efficient methane reforming with high methanol selectivity.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Characterizing Drought Behavior in the Colorado River Basin Using Unsupervised Machine Learning

Drought is a pressing issue for the Colorado River Basin (CRB) due to the social and economic value of water resources in the region and the significant uncertainty of future drought under climate change. Here, we use climate simulations from various Earth System Models (ESMs) to force the Variable Infiltration Capacity hydrologic model and project multiple drought indicators for the sub-watersheds within the CRB. We apply an unsupervised machine learning (ML) based on Non-Negative Matrix Factorization using K-means clustering (NMFk) to synthesize the simulated historical, future, and change in drought indicators. The unsupervised ML approach can identify sub-watersheds where key changes to drought indicator behavior occur, including shifts in snowpack, snowmelt timing, precipitation, and evapotranspiration. While changes in future precipitation vary across ESMs, the results indicate that the Upper CRB will experience increasing evaporative demand and surface-water scarcity, with some locations experiencing a shift from a radiation-limited to a water-limited evaporation regime in the summer. Large shifts in peak runoff are observed in snowmelt-dominant sub-watersheds, with complete disappearance of the snowmelt signal for some sub-watersheds. The work demonstrates the utility of the NMFk algorithm to efficiently identify behavioral changes of drought indicators across space and time and to quickly analyze and interpret hydro climate model results.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Synaptic Zn2+ potentiates the effects of cocaine on striatal dopamine neurotransmission and behavior

Abstract Cocaine binds to the dopamine (DA) transporter (DAT) to regulate cocaine reward and seeking behavior. Zinc (Zn 2+ ) also binds to the DAT, but the in vivo relevance of this interaction is unknown. We found that Zn 2+ concentrations in postmortem brain (caudate) tissue from humans who died of cocaine overdose were significantly lower than in control subjects. Moreover, the level of striatal Zn 2+ content in these subjects negatively correlated with plasma levels of benzoylecgonine, a cocaine metabolite indicative of recent use. In mice, repeated cocaine exposure increased synaptic Zn 2+ concentrations in the caudate putamen (CPu) and nucleus accumbens (NAc). Cocaine-induced increases in Zn 2+ were dependent on the Zn 2+ transporter 3 (ZnT3), a neuronal Zn 2+ transporter localized to synaptic vesicle membranes, as ZnT3 knockout (KO) mice were insensitive to cocaine-induced increases in striatal Zn 2+ . ZnT3 KO mice showed significantly lower electrically evoked DA release and greater DA clearance when exposed to cocaine compared to controls. ZnT3 KO mice also displayed significant reductions in cocaine locomotor sensitization, conditioned place preference (CPP), self-administration, and reinstatement compared to control mice and were insensitive to cocaine-induced increases in striatal DAT binding. Finally, dietary Zn 2+ deficiency in mice resulted in decreased striatal Zn 2+ content, cocaine locomotor sensitization, CPP, and striatal DAT binding. These results indicate that cocaine increases synaptic Zn 2+ release and turnover/metabolism in the striatum, and that synaptically released Zn 2+ potentiates the effects of cocaine on striatal DA neurotransmission and behavior and is required for cocaine-primed reinstatement. In sum, these findings reveal new insights into cocaine’s pharmacological mechanism of action and suggest that Zn 2+ may serve as an environmentally derived regulator of DA neurotransmission, cocaine pharmacodynamics, and vulnerability to cocaine use disorders.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Scaling behavior of the quantum phase transition from a quantum-anomalous-Hall insulator to an axion insulator

The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase transition. Similar to the quantum Hall plateau to plateau transition, the QAH to axion insulator transition can also be understood by the Chalker–Coddington network model. We extract a critical exponent κ ~ 0.38 ± 0.02 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker–Coddington model at ν ~ 2.6, rather than the generally-accepted value of 2.33.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗