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DOE OSTI2022

Quantifying transport and electrocatalytic reaction processes in a gastight rotating cylinder electrode reactor via integration of Computational Fluid Dynamics modeling and experiments

Understanding the complexity of the multiple processes of mass, momentum, charge, and heat transport, and how these affect reaction kinetics at the electrode/electrolyte interface is one of the major challenges in the field of energy and catalysis. The rapid and rational scale-up of electrocatalytic systems to industrial scales require a detailed understanding of nonlinear transport-reaction processes, accessible only through the building of multi-physics models that capture with high fidelity the complexity of real-world devices. The gastight rotating cylinder electrode (RCE) reactor is a promising lab-scale tool that can decouple transport from intrinsic kinetics to generate data for first-principle models useful in the design of industrial, electrochemical reactors. Computational Fluid Dynamics (CFD) studies have previously been used to investigate the bulk flow in RCE reactors for simple corrosion and electroplating processes. However, the quantification of changes in local concentration within the viscous layer where catalysis takes place requires capturing the correct flow conditions inside the hydrodynamic boundary layer near the surface of the electrode. Further, this requires simulations with spatial resolution in the nm and μm scale and temporal resolutions between ms and s scales that are similar to the timescales for reactions on the electrode surface. In this study, experimental electrocatalysis is combined with CFD modeling to elucidate and parameterize the hydrodynamics in a gastight RCE reactor. CFD simulations of the electrochemical ferricyanide reduction reaction under mass transport limited conditions are used to evaluate the validity of the CFD model parameters by comparing calculated dimensionless mass transport descriptors to dimensionless correlations obtained experimentally. Justifications for assumptions and details of the simulation methods used in this study are presented to provide a detailed understanding of the effect that each model parameter has on the ability to accurately simulate electrocatalysis in RCE systems. The simulation methodology reported here is a first step towards the development of multi-scale models for the study of transport dependent electrocatalytic processes, such as the electrochemical transformation of CO 2 to fuels and chemicals.

42 ENGINEERING↗

DOE OSTI2022

Generalized Analysis of Dynamic Flow Fouling on Heat Transfer Surfaces

Several energy applications involve flow of untreated heat transfer fluids that contain trace amounts of mineral salts, such as calcium carbonate and calcium sulfate, which show reverse solubility with temperature. The gradual accretion of these salts onto the heat transfer surfaces causes fouling that degrades thermal performance over time. While fouling of bare surfaces has been extensively studied, fouling of nonwetting superhydrophobic or liquid-infused surfaces is less understood, especially under dynamic flow conditions. This study presents a systematic experimental analysis to elucidate dynamic flow fouling of calcium carbonate and calcium sulfate on smooth, superhydrophobic and liquid-infused surfaces in a generalized manner. Here, copper tubes with modified inner surface wettability are fabricated and subjected to forced convection at different flow rates and fouling salt concentrations. Fouling characteristics of the two salts on the different surfaces are examined through microstructural analysis, and quantified in terms of asymptotic fouling resistance that measures the total extent of fouling, and a threshold time, which correlates to the onset of significant fouling. Using Taguchi design of experiments, the study reports, for the first time, closed-form analytical relationships for the asymptotic fouling thermal resistance and threshold time on the Reynolds number, dimensionless concentration of fouling agent and dimensionless infused liquid viscosity that represents the different surface types in a unified manner. It is shown that the analytical model accurately predicts the fouling characteristics in up to about 97% of the data, based on which contour maps of optimum surface designs for minimizing fouling resistance are presented. The results provide information on designing surfaces for reduced fouling or for estimating the fouling characteristics for a given surface in applications.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Enhanced internal condensation of R1233zd(E) on micro- and nanostructured copper and aluminum surfaces

In-tube condensation of refrigerants is an important process which affects thermal efficiency in many applications, ranging from refrigeration and air conditioning to electronics thermal management. In-tube heat transfer and pressure drop are important to heat exchanger sizing and design. Here, in this work, micro- and nanostructured surfaces are applied to the internal wetted areas of copper and aluminum mini-channels to enhance the condensation heat transfer coefficient of hydrofluorocarbon R1233zd(E) refrigerant. To achieve scalable nanomanufacturing, surfaces were uniformly structured by relying on hydrochloric acid etching of aluminum and chemical oxidation of copper. The etched aluminum surfaces exhibited a 150% increase in heat transfer coefficient compared to smooth aluminum channels at specific qualities, with a 66% heat transfer coefficient improvement for complete phase change from saturated vapor to saturated liquid. Copper oxide structures showed no discernable difference in thermal-hydraulic performance when compared to smooth copper channels. Critical dimensionless parameters governing the heat transfer enhancement were identified by varying the tube internal diameter (2.3 mm to 4.7 mm), refrigerant mass flux (50 to 300 kg/(m 2 ·s)), and refrigerant quality (0 to 1). The dimensionless parameters include the Bond number normalized to the condensate film thickness, and the Weber number modified by the vapor friction factor. The relatively small increase in pressure drop (< 10%) associated with these surface enhancements further supports the promise of this method. The scalable and cost-effective techniques used to create these aluminum microstructures may reduce manufacturing cost when compared with current enhancement approaches such as extrusion, drawing, and welding.

42 ENGINEERING↗

DOE OSTI2021

Pulsating Poiseuille flow of a cement slurry

In this paper, we investigate the pulsatile flow of a cement slurry in a pipe. The constitutive relation for the viscous stress tensor is based on the power-law model, where the shear viscosity not only depends on the shear rate but also the volume fraction of the cement particles. To solve for the volume fraction field, a convection-diffusion equation is used. The dimensionless form of the governing equations and the boundary conditions are solved numerically at different pulsatile cycles. Further, a parametric study is conducted to study the effect of different dimensionless numbers at different cycles on the velocity and the volume fraction profiles.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Simulation of methanol synthesis in a membrane-contactor reactor

In a recent paper we investigated experimentally in the laboratory the methanol synthesis (MeS) reaction in a novel high-pressure membrane reactor (MR) using tetraethylene glycol dimethyl ether (TGDE) and an ionic liquid (IL) as the sweep liquids. We reported significantly higher carbon conversion (per single-pass) compared to a traditional packed-bed reactor (PBR), as a result of the in-situ removal of methanol by the sweep liquid. Here, in this paper, a steady-state model is developed to simulate the MR behavior during MeS and is validated by the experimental data. The model is then used to study the reactor behavior for a broader range of operating conditions beyond those that can be accessed and studied experimentally in the laboratory-scale reactor. Converting the model equations into their dimensionless form helps to identify the key dimensionless groups determining reactor performance, enables one to better evaluate the efficacy of the MR system, and guides further process design and scale-up.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Beam-energy dependence of correlations between mean transverse momentum and anisotropic flow of charged particles in Au+Au collisions at RHIC

The correlation between the mean transverse momentum, [ p T ], and the squared anisotropic flow, $v^2_n$, on an event-by-event basis has been suggested to be influenced by the initial conditions in heavy-ion collisions. We present measurements of the variances and covariance of [ p T ] and $v^2_n$, along with their dimensionless ratio, for Au+Au collisions at various beam energies: $\sqrt{s_{NN}}$ = 14.6, 19.6, 27, 54.4, and 200 GeV. Our measurements reveal a distinct energy-dependent behavior in the variances and covariances. In addition, the dimensionless ratio displays a similar behavior across different beam energies. We compare our measurements with hydrodynamic models and similar measurements from Pb+Pb collisions at the Large Hadron Collider (LHC). These findings provide valuable insights into the beam energy dependence of the specific shear viscosity ( η/s ) and initial-state effects, allowing for differentiating between different initial-state models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Scaling CFB risers: Maintaining microstructure dynamics

Over the years there have been numerous approaches to develop a scaleup methodology for circulating fluidized beds. Many of these past approaches have relied on macroscopic definitions of similitude to define dimensionless groups such as Reynolds number, Froude number, density ratios, and dimensional ratios involving different length scales. These approaches have demonstrated various levels of success, but often fail when used outside the bounds of experimental datasets. The issue with these methods is that they rely on macroscopic similitude with the hopes that those conditions would provide microscopic similitude as it does in single phase systems where the Buckingham Pi techniques have given reasonable success. Two of the main reasons for failure are 1) changing fluidization regimes and 2) changing material properties that result in the material falling into a different Geldart group. Both are certain to change the microstructure (local instantaneous volume solids fraction) and changes to the microstructure affect the interphase transport properties of the reactor system, namely the mass transfer and heat transfer. Here, this work presents a new approach towards scaling based upon maintaining similitude at the microscale. It reviews a novel dimensionless flow regime map developed from analysis of the deterministic chaos parameters and higher order moments to ensure microstructure similitude. The work then examines four cases from the literature to assess the scaling approach used: (1) same particle-different scale risers for Geldart Group B particles, (2) Glicksman scaling of atmospheric circulating fluidized bed combustor, (3) same particle-different scale risers for Geldart Group A particles and (4) Glicksman scaling for pressurized gasification. General findings are that none of the scaling approaches produced directly applicable microstructure similar behavior based upon the chaotic and higher moment analysis. The positive take away is that the approach can define scale conditions that will provide similar microstructure that can be us to predict transport behavior.

42 ENGINEERING↗

DOE OSTI2022

Enhancing $\phi$-sensitivity of ignition delay times through dilution of fuel-air mixture

The high $\phi$-sensitivity (η) of ignition delay time (τ IDT ) is one of the desirable fuel properties for the high-load extension of advanced compression ignition engine. Recent studies revealed the effectiveness of a high dilution rate (x D ) for enhancing η at the engine-relevant conditions. This study aims to quantify the effect of dilution on the η of isooctane using a combined experiment-simulation approach. The ignition delay of the isooctane/air mixture was measured with an Advanced Fuel Ignition Delay Analyzer (AFIDA) over the temperature range of 623 - 923 K at 10 bar pressure with global $\phi$ = 0.3 - 0.6, with and without 28.6% of additional N 2 dilution. For precise evaluation of experimental η, the facility effect of the AFIDA experiment was characterized with three-dimensional computational fluid dynamics (3-D CFD) simulation. The temperature in the combustion chamber from 3-D CFD indicated a substantial temporal dependency, varying up to ~52 K by charge-cooling of fuel injection and heat transfer from the wall. We introduced the dimensionless number θ(t) for characterizing the temporal profile of chamber temperature. Consideration of the facility effect using θ(t) resulted in better agreement between the experimental ..eta.. and zero-dimensional (0-D) kinetics simulation. The refined η were then further utilized to quantify the effectiveness of dilution to η The extent of η enhancement with dilution strategy was maximized at the low-temperature chemistry regime, increasing η by 77% with a 28.6% dilution rate. Further analysis on the dilution effect was carried out using 0-D kinetics simulation, revealing the critical dimensionless numbers relevant to the effectiveness of dilution to η enhancement. Here, this study is the first experiment-simulation combined research to quantify the effect of dilution on η, facilitating the kinetics model refinement for better reproduction of $\phi$-sensitivity.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2024

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

Here, we analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call “complexity reduction”. In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature T g of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2–6 nm at T g . Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

cancer↗

DOE OSTI2020

Microscopic Theory of Long-Time Center-of-Mass Self-Diffusion and Anomalous Transport in Ring Polymer Liquids

We construct a microscopic theory at the level of segment-scale correlated space–time intermolecular forces for the long-time center-of-mass (CM) diffusion constant and intermediate-time non-Fickian transport in dense solutions and melts of ring polymers. The approach combines ideas of polymer, colloid, and liquid-state statistical mechanics to quantify how the multifractal intra-ring conformational structure and inter-ring packing correlations determine dynamic caging constraints and time-dependent friction. Breakdown of Rouse theory is predicted to occur due to length scale-dependent temporal correlation of forces exerted on pairs of tagged ring segments from surrounding polymers. At large enough degrees of polymerization (N), a stronger scaling of the CM diffusion constant (D ∝ N –2 ) is predicted, with a crossover N D proportional to the product of the system-specific macromolecular volume fraction and dimensionless compressibility. In analogy with caging effects in glass-forming fluids, the theory does appear to begin to fail at sufficiently high N/N D for the center-of-mass diffusivity, likely due to another crossover to an even slower activated transport regime. However, use of N/N D with the theoretically predicted N D , in conjunction with dynamic blob scaling ideas for local Rouse friction, collapses semidilute and concentrated solution simulation data onto a master curve. Based on the same physical ideas employed to predict the diffusion constant, a generalized Langevin equation description is formulated for intermediate-time CM transport. It predicts two subdiffusive regimes that emerge due to the self-similar nature of internal ring structure. Analytic and numerical predictions for the apparent non-Fickian exponent as a function of time, N/N D and dimensionless compressibility, the evolution of the maximum degree of subdiffusive motion with N/N D , and the time scale for recovering Fickian diffusion are made, all of which are in good accordance with melt simulations. Furthermore, the present work sets the stage to address activated dynamics and glass formation on the macromolecular scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Impacts of Permeability Heterogeneity and Background Flow on Supercritical CO 2 Dissolution in the Deep Subsurface

Motivated by CO 2 capture and sequestration (CCS) design considerations, we consider the coupled effects of permeability heterogeneity and background flow on the dissolution of a supercritical CO 2 lens into an underlying deep, confined aquifer. We present the results of a large-scale Monte Carlo simulation study examining the interaction of background flow rate and three parameters describing multi-Gaussian log-permeability fields: mean, variance, and correlation length. Hundreds of high-resolution simulations were performed using the PFLOTRAN finite volume software to model CO 2 dissolution in a kilometer-scale aquifer over 1,000 years. Predictive dimensionless scaling relationships relating CO 2 dissolution rate to heterogeneity statistics, Rayleigh (Ra) and Péclet (Pe) numbers were developed for both gravitationally dominated free convection to background flow-dominated forced convection regimes. An empirical criterion, Pe = Ra 3/4 , was discovered for regime transition. All simulations converged quickly to a quasi-steady, approximately linear dissolution rate. However, this rate displayed profound variability between permeability field realizations sharing the same heterogeneity statistics, even under mild permeability heterogeneity. In general, increased heterogeneity was associated with a lower mean and higher variance of dissolution rate, undesirable from a CCS design perspective. The relationship between dissolution rate and background flow was found to be complex and nonlinear. Dimensionless scaling relationships were uncovered for a number of special cases. Results call into question the validity of the Boussinesq approximation in the context of modest-to-high background flow rates and the general applicability of numerical simulations without background flow.

42 ENGINEERING↗

DOE OSTI2024

Sinuosity‐Driven Hyporheic Exchange: Hydrodynamics and Biogeochemical Potentials

Abstract Hydrologic exchange processes are critical for ecosystem services along river corridors. Meandering contributes to this exchange by driving channel water, solutes, and energy through the surrounding alluvium, a process called sinuosity‐driven hyporheic exchange. This exchange is embedded within and modulated by the regional groundwater flow (RGF), which compresses the hyporheic zone and potentially diminishes its overall impact. Quantifying the role of sinuosity‐driven hyporheic exchange at the reach‐to‐watershed scale requires a mechanistic understanding of the interplay between drivers (meander planform) and modulators (RGF) and its implications for biogeochemical transformations. Here, we use a 2D, vertically integrated numerical model for flow, transport, and reaction to analyze sinuosity‐driven hyporheic exchange systematically. Using this model, we propose a dimensionless framework to explore the role of meander planform and RGF in hydrodynamics and how they constrain nitrogen cycling. Our results highlight the importance of meander topology for water flow and age. We demonstrate how the meander neck induces a shielding effect that protects the hyporheic zone against RGF, imposing a physical constraint on biogeochemical transformations. Furthermore, we explore the conditions when a meander acts as a net nitrogen source or sink. This transition in the net biogeochemical potential is described by a handful of dimensionless physical and biogeochemical parameters that can be measured or constrained from literature and remote sensing. This work provides a new physically based model that quantifies sinuosity‐driven hyporheic exchange and biogeochemical reactions, a critical step toward their representation in water quality models and the design and assessment of river restoration strategies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids

For the Rayleigh–Taylor unstable arrangement of a viscous fluid sphere embedded in a finite viscous fluid spherical shell with a rigid boundary and a radially directed acceleration, a dispersion relation is developed from a linear stability analysis using the method of normal modes. [Formula: see text] is the radially directed acceleration at the interface. ρ i denotes the density, μ i is the viscosity, and R i is the radius, where i = 1 is the inner sphere and i = 2 is the outer sphere. The dispersion relation is a function of the following dimensionless variables: viscosity ratio [Formula: see text], density ratio [Formula: see text], spherical harmonic mode n, [Formula: see text], [Formula: see text], and the dimensionless growth rate [Formula: see text], where σ is the exponential growth rate. We show that the boundedness provided by the outer spherical shell has a strong influence on the instability behavior, which is reflected not only in the modulation of the growth rate but also in the selection of the most unstable modes that are physically possible. This outer boundary effect is quantified by the relative magnitude of the radius ratio H. We find that when H is close to unity, lower order harmonics are excluded from becoming the most unstable within a vast region of the parameter space. In other words, the effect of H has precedence over the other controlling parameters d, B, and a wide range of s in establishing what the lowest most unstable mode can be. When H ~ 1, low order harmonics can become the most unstable only for s >> 1. However, in the limit when s → ∞, we show that the most unstable mode is n = 1 and derive the dispersion relation in this limit. The exclusion of most unstable low order harmonics caused by a finite outer boundary is not realized when the outer boundary extends beyond a certain threshold length-scale in which case all modes are equally possible depending on the value of B.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Exploring the parameter space of MagLIF implosions using similarity scaling. I. Theoretical framework

Magneto-inertial fusion concepts, such as the magnetized liner inertial fusion (MagLIF) platform, constitute an alternative path for achieving ignition and significant fusion yields in the laboratory. The space of experimental input parameters defining a MagLIF load is highly multi-dimensional, and the implosion itself is a complex event involving many physical processes. In the first paper of this series, we develop a simplified analytical model that identifies the main physical processes at play during a MagLIF implosion. Using non-dimensional analysis, we determine the most important dimensionless parameters characterizing MagLIF implosions and provide estimates of such parameters using typical fielded or experimentally observed quantities for MagLIF. Here, we then show that MagLIF loads can be “incompletely” similarity scaled, meaning that the experimental input parameters of MagLIF can be varied such that many (but not all) of the dimensionless quantities are conserved. Based on similarity-scaling arguments, we can explore the parameter space of MagLIF loads and estimate the performance of the scaled loads. Then, in the follow-up papers of this series, we test the similarity-scaling theory for MagLIF loads against simulations for two different scaling “vectors,” which include current scaling and rise-time scaling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

A convergence metric for counting statistics in time-resolved small angle neutron scattering

Here, this work introduces a model-independent, dimensionless metric for predicting optimal measurement duration in time-resolved small-angle neutron scattering using early-time data. Built on a Gaussian process regression framework, the method reconstructs scattering profiles with quantified uncertainty, even from sparse or noisy measurements. Demonstrated on the EQ-SANS instrument at the Spallation Neutron Source, the approach generalizes to general SANS instruments with a two-dimensional detector. A key result is the discovery of a dimensionless convergence metric revealing a universal power-law scaling in profile evolution across soft matter systems. When time is normalized by a system-specific characteristic time t*, the variation in inferred profiles collapses onto a single curve with an exponent between −2 and −1. This trend emerges within the first ten time steps, enabling early prediction of measurement sufficiency. The method supports real-time experimental optimization and is especially valuable for maximizing efficiency in low-flux environments such as compact accelerator-based neutron sources.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

DOE OSTI2024

The nontrivial effects of annealing on superconducting properties of Nb single crystals

The effect of annealing on the superconducting properties of niobium single crystals was studied using optical, magnetic, and scanning tunneling microscopy (STM) methods. Pieces of the same crystal boule were studied before and after the annealing at 800 ${^\circ}\textrm{C}$, 1400 ${^\circ}\textrm{C}$, and near the melting point of niobium (2477 ${^\circ}\textrm{C}$). The initial samples had a high hydrogen content and low-temperature imaging revealed large hydrides (hundreds of micrometers) appearing below 190 K. The formation of these large precipitates is already completely suppressed by annealing at 800 ${^\circ}\textrm{C}$. However, the overall superconducting properties of the annealed samples did not improve and, in fact, worsened. In particular, the superconducting transition temperature decreased, the upper critical field increased, and the pinning strength increased. In the STM study, the sample was annealed initially at 400 ${^\circ}\textrm{C}$, measured, annealed at 1700 ${^\circ}\textrm{C}$, and measured again. The STM revealed a ‘dirty’ superconducting gap with a significant spatial variation in tunneling conductance after annealing at 400 ${^\circ}\textrm{C}$. The clean gap was recovered after annealing at 1700 ${^\circ}\textrm{C}$. This is likely due to oxygen redistribution near the surface, which is always covered by oxide layers in as-grown crystals. Our results indicate that vacuum annealing at least up to 1400 ${^\circ}\textrm{C}$, while removing a large percentage of hydrogen, introduces additional nanosized defects, likely hydride precipitates, that act as efficient pair-breaking and pinning centers. The dimensionless scattering rate is estimated to have increased from $\Gamma = 0.2$ to about $\Gamma = 0.4$ after annealing at 1400 ${^\circ}\textrm{C}$. These results on single crystals differ drastically from those obtained in polycrystalline bulk niobium (i.e. cut from superconducting radio-frequency cavities), where annealing is known to have a significant positive effect that is attributed to the improvement of the crystalline structure masking the more subtle influence of the hydrides.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids

Here, we employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.

36 MATERIALS SCIENCE↗

DOE OSTI2021

WKB Estimate of Bilayer Graphene’s Magic Twist Angles

We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which we obtain analytically. Our analytic flatband twist angles correspond closely to those determined numerically in previous work.

36 MATERIALS SCIENCE↗