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DOE OSTI2021

Analysis of the Amorphous and Interphase Influence of Comononomer Loading on Polymer Properties toward Forwarding Bioadvantaged Copolyamides

In this paper we present an approach for selectively modifying the properties of semicrystalline polymers by introducing “bioadvantaged” counits. With this approach, the unique functionality of biomass can be leveraged to tailor the properties of the amorphous phase of semicrystalline polymers with minimal impact on crystallinity and thermomechanical properties. As a model case, PA 6,6 copolyamides were produced using the bioadvantaged monomer trans-3-hexenedioic acid (t3HDA). The analogous structure of t3HDA to adipic acid, a PA 6,6 monomer, allows for seamless integration. Screening over the entire composition range identified the t3HDA loading (20 mol%) beyond which properties deviate appreciably from Nylon 6,6. Once identified, copolyamides of suitable compositions were upgraded to commercial quality and fully characterized to assess the influence of counit loading and polymer structure on thermal and mechanical properties. Samples were characterized using gel permeation chromatography (GPC), proton nuclear magnetic resonance spectroscopy (1H NMR), heteronuclear single quantum coherence spectroscopy (HSQC), wide-angle X-ray scattering (WAXS), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), dynamic mechanical analysis (DMA), tensile testing, flexural testing, and water absorption testing. t3HDA units were shown to hydrate during the harsh polycondensation to 3-hydroxyhexanedioic acid (3HHDA) and fully incorporate into the polymer backbone. Loading levels up to 20% were shown to have comparable thermal and mechanical properties in the dry state, yet moisture absorption—a known method for improving the toughness, yield strain, and elongation of polyamides—was enhanced by over 100% at 20% loading. This case study on bioadvantaged copolymers elucidates the governing structure-function principles that can be leveraged to forward value-added renewable polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Modelling galaxy cluster triaxiality in stacked cluster weak lensing analyses

Counts of galaxy clusters offer a high-precision probe of cosmology, but control of systematic errors will determine the accuracy of this measurement. Using Buzzard simulations, we quantify one such systematic, the triaxiality distribution of clusters identified with the redMaPPer optical cluster finding algorithm, which was used in the Dark Energy Survey Year-1 (DES Y1) cluster cosmology analysis. We test whether redMaPPer selection biases the clusters’ shape and orientation and find that it only biases orientation, preferentially selecting clusters with their major axes oriented along the line of sight. Modelling the richness–mass relation as log-linear, we find that the log-richness amplitude ln (A) is boosted from the lowest to highest orientation bin with a significance of 14σ, while the orientation dependence of the richness-mass slope and intrinsic scatter is minimal. We also find that the weak lensing shear-profile ratios of cluster-associated dark haloes in different orientation bins resemble a ‘bottleneck’ shape that can be quantified with a Cauchy function. We test the correlation of orientation with two other leading systematics in cluster cosmology – miscentering and projection – and find a null correlation. The resulting mass bias predicted from our templates confirms the DES Y1 finding that triaxiality is a leading source of bias in cluster cosmology. However, the richness-dependence of the bias confirms that triaxiality does not fully resolve the tension at low-richness between DES Y1 cluster cosmology and other probes. Our model can be used for quantifying the impact of triaxiality bias on cosmological constraints for upcoming weak lensing surveys of galaxy clusters.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Significance of radiative corrections on measurements of the EMC effect

Deep inelastic scattering (DIS) from nuclear targets probes the parton distribution functions (PDFs) in nuclei. Comparisons of the PDFs from heavy nuclei and the deuteron show deviations that demonstrate a non-trivial nuclear dependence to these distributions, referred to as the EMC effect. A global analysis of the worlds data on the EMC effect reveals tensions between different extractions. Precise measurements at Jefferson Lab, studying the dependence on both the quark momentum fraction, x, and nuclear mass, show systematic discrepancies among experiments, making the extraction of the A dependence of the EMC effect sensitive to the selection of datasets. Further, by comparing various methods and assumptions used to calculate radiative corrections, we have identified differences that, while not large, significantly impact the EMC ratios and show that using a consistent radiative correction procedure resolves this discrepancy, leading to a more coherent global picture, and allowing for a more robust extraction of the EMC effect for infinite nuclear matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Impact of cross-section uncertainties on supernova neutrino spectral parameter fitting in the Deep Underground Neutrino Experiment

A primary goal of the upcoming Deep Underground Neutrino Experiment (DUNE) is to measure the 𝒪⁡(10) MeV neutrinos produced by a Galactic core-collapse supernova if one should occur during the lifetime of the experiment. The liquid-argon-based detectors planned for DUNE are expected to be uniquely sensitive to the 𝜈 𝑒 component of the supernova flux, enabling a wide variety of physics and astrophysics measurements. A key requirement for a correct interpretation of these measurements is a good understanding of the energy-dependent total cross section 𝜎⁡(𝐸 𝜈 ) for charged-current 𝜈 𝑒 absorption on argon. In the context of a simulated extraction of supernova 𝜈 𝑒 spectral parameters from a toy analysis, we investigate the impact of 𝜎⁡(𝐸 𝜈 ) modeling uncertainties on DUNE’s supernova neutrino physics sensitivity for the first time. We find that the currently large theoretical uncertainties on 𝜎⁡(𝐸 𝜈 ) must be substantially reduced before the 𝜈𝑒 flux parameters can be extracted reliably; in the absence of external constraints, a measurement of the integrated neutrino luminosity with less than 10% bias with DUNE requires 𝜎⁡(𝐸 𝜈 ) to be known to about 5%. The neutrino spectral shape parameters can be known to better than 10% for a 20% uncertainty on the cross-section scale, although they will be sensitive to uncertainties on the shape of 𝜎⁡(𝐸 𝜈 ). A direct measurement of low-energy 𝜈𝑒-argon scattering would be invaluable for improving the theoretical precision to the needed level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1995

Development and applications of laser-induced incandescence

Several NASA-funded investigations focus on soot processes and radiative influences of soot in diffusion flames given their simplicity, practical significance, and potential for theoretical modeling. Among the physical parameters characterizing soot, soot volume fraction, f(sub v), a function of particle size and number density, is often of chief practical interest in these investigations, as this is the geometrical property that directly impacts radiative characteristics and the temperature field of the flame and is basic to understanding soot growth and oxidation processes. Diffusion flames, however, present a number of challenges to the determination of f(sub v) via traditional extinction measurements. Laser-induced incandescence (LII) possesses several advantages compared to line-of-sight extinction techniques for determination of f(sub v). Since LII is not a line-of-sight technique, similar to fluorescence, it possesses geometric versatility allowing spatially resolved measurements of f(sub v) in real time in nonaxisymmetric systems without using deconvolution techniques. The spatial resolution of LII is determined by the detector and imaging magnification used. Neither absorption by polycyclic aromatic hydrocarbons (PAH's) nor scattering contributes to the signal. Temporal capabilities are limited only by the laser pulse and camera gate duration, with measurements having been demonstrated with 10 ns resolution. Because of these advantages, LII should be applicable to a variety of combustion processes involving both homogeneous and heterogeneous phases. Our work has focussed on characterization of the technique as well as exploration of its capabilities and is briefly described.

Vanderwal, Randy L.↗

NASA NTRS2010

An Experimental Investigation of Silicone-to-Metal Bond Strength in Composite Space Docking System Seals

The National Aeronautics and Space Administration (NASA) is currently developing a new universal docking mechanism for future space exploration missions called the Low Impact Docking System (LIDS). A candidate LIDS main interface seal design is a composite assembly of silicone elastomer seals vacuum molded into grooves in an electroless nickel plated aluminum retainer. The strength of the silicone-tometal bond is a critical consideration for the new system, especially due to the presence of small areas of disbond created during the molding process. In the work presented herein, seal-to-retainer bonds of subscale seal specimens with different sizes of intentional disbond were destructively tensile tested. Nominal specimens without intentional disbonds were also tested. Tension was applied either uniformly on the entire seal circumference or locally in one short circumferential length. Bond failure due to uniform tension produced a wide scatter of observable failure modes and measured load-displacement behaviors. Although the preferable failure mode for the seal-to-retainer bond is cohesive failure of the elastomer material, the dominant observed failure mode under the uniform loading condition was found to be the less desirable adhesive failure of the bond in question. The uniform tension case results did not show a correlation between disbond size and bond strength. Localized tension was found to produce failure either as immediate tearing of the elastomer material outside the bond region or as complete peel-out of the seal in one piece. The obtained results represent a valuable benchmark for comparison in the future between adhesion loads under various separation conditions and composite seal bond strength.

Gaier, James R.↗

NASA NTRS2012

An Assessment of the Surface Longwave Direct Radiative Effect of Airborne Dust in Zhangye China During the Asian Monsoon Year Field Experiment (2008)

Tiny suspensions of solid particles or liquid droplets, called aerosols, hover in earth's atmosphere and can be found over just about anywhere including oceans, deserts, vegetated areas, and other global regions. Aerosols come in a variety of sizes, shapes, and compositions which depend on such factors as their origin and how long they have been in the atmosphere (i.e., their residence time). Some of the more common types of aerosols include mineral dust and sea salt which get lifted from the desert and ocean surfaces, respectively by mechanical forces such as strong winds. Depending on their size, aerosols will either fall out gravitationally, as in the case of larger particles, or will remain resident in the atmosphere where they can undergo further change through interactions with other aerosols and cloud particles. Not only do aerosols affect air quality where they pose a health risk, they can also perturb the distribution of radiation in the earth-atmosphere system which can inevitably lead to changes in our climate. One aerosol that has been in the forefront of many recent studies, particularly those examining its radiative effects, is mineral dust. The large spatial coverage of desert source regions and the fact that dust can radiatively interact with such a large part of the electromagnetic spectrum due to its range in particle size, makes it an important aerosol to study. Dust can directly scatter and absorb solar and infrared radiation which can subsequently alter the amount of radiation that would otherwise be present in the absence of dust at any level of the atmosphere like the surface. This is known as radiative forcing. At the surface dust can block incoming solar energy, however at infrared wavelengths, dust acts to partially compensate the solar losses. Evaluating the solar radiative effect of dust aerosols is relatively straightforward due in part to the relatively large signal-to-noise ratio in the measurements. At infrared wavelengths, on the other hand, the effect is rather difficult to ascertain since the measured dust signal level is on the same order as the instrumental uncertainties. Although the radiative impact of dust is much smaller in the infrared, it can still have a noticeable influence on the distribution of energy in the Earth-atmosphere system. This is mainly attributed to the strong light-absorptive properties commonly found in many earth minerals.

Hansell, Richard A.↗

DOE OSTI2021

Designing Anion-Exchange Ionomers with Oriented Nanoscale Phase Separation at a Silver Interface

We report performance of polymer electrolyte-based energy systems is significantly impacted by transport within the electrode catalyst layer, where ionomer thin films coat catalyst particles. Proton exchange ionomer thin films have been thoroughly characterized, but few studies have critically examined anion-exchange ionomer (AEI) thin films. Further, none have reported nanoscale phase separation for hydrocarbon AEIs, which is critical to mitigate transport resistances. In this work, a set of hydrocarbon-based AEIs with nanoscale phase separation are developed from tunable block copolymer systems composed of polyisoprene (PIp) and polychloromethylstyrene (PCMS). The effect of the PIp/PCMS ratio, architecture, and thickness on the thin-film morphology of the neutral block copolymer precursors on silicon and silver substrates is investigated using grazing-incidence small-angle X-ray scattering (GISAXS) and atomic force microscopy (AFM). AEIs are prepared by quaternizing with trimethylamine or methylpiperidine and their cation-dependent morphology is characterized at 60 °C and 95% RH. A perpendicularly aligned morphology is observed on silver, while no phase separation is observed on silicon, indicating that silver-polymer interfacial interactions drive phase separation. After quaternization, dipole-dipole interactions induce some disorder, but nanoscale phase separation is still maintained. GISAXS patterns are modeled using a Unified Fit approach to understand water uptake and swelling, and recommendations for AEI design are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Shedding light on shadow generalized parton distributions

The feasibility of extracting generalized parton distributions (GPDs) from deeply virtual Compton scattering (DVCS) data has recently been questioned because of the existence of an infinite set of so-called “shadow GPDs” (SGPDs). These SGPDs depend on the process and manifest as multiple solutions (at a fixed scale 𝑄 2 ) to the inverse problem that needs to be solved to infer GPDs from DVCS data. SGPDs therefore pose a significant challenge for extracting GPDs from DVCS data. With this motivation we study the extent to which QCD evolution can provide constraints on SGPDs. This is possible because the known classes of SGPDs begin to contribute to observables after evolution, and can then be constrained (at the input scale 𝑄$^{2}_{0}$) by data that has a finite 𝑄 2 range. The impact that SGPDs could have on determining the total angular momentum, pressure and sheer force distributions, and tomography is also discussed. We find that 𝑄 2 evolution, given empirical data over a wide range of skewness (𝜉 ) and 𝑄 2 scales, constrains the SGPDs studied at low 𝑥 and low 𝜉. If this finding generalizes to all SGPDs—and we have not been able to find any SGPDs with qualitatively different behavior—then this potentially makes extraction of GPDs from DVCS possible over a limited range of 𝑥 and 𝜉.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Enhanced Monte Carlo Simulations for Electron Energy Loss Mitigation in Real-Space Nanoimaging of Thick Biological Samples and Microchips

High-resolution imaging using Transmission Electron Microscopy (TEM) is essential for applications such as grain boundary analysis, microchip defect characterization, and biological imaging. However, TEM images are often compromised by electron energy spread and other factors. In TEM mode, where the objective and projector lenses are positioned downstream of the sample, electron–sample interactions cause energy loss, which adversely impacts image quality and resolution. This study introduces a simulation tool to estimate the electron energy loss spectrum (EELS) as a function of sample thickness, covering electron beam energies from 300 keV to 3 MeV. Leveraging recent advances in MeV-TEM/STEM technology, which includes a state-of-the-art electron source with 2-picometer emittance, an energy spread of 3 × 10 -5 , and optimized beam characteristics, we aim to minimize energy spread. By integrating EELS capabilities into the BNL Monte Carlo (MC) simulation code for thicker samples, we evaluate electron beam parameters to mitigate energy spread resulting from electron–sample interactions. Based on our simulations, we propose an experimental procedure for quantitively distinguishing between elastic and inelastic scattering. The findings will guide the selection of optimal beam settings, thereby enhancing resolution for nanoimaging of thick biological samples and microchips.

36 MATERIALS SCIENCE↗

NASA NTRS1993

A picture of the moon's atmosphere

Atomic sodium is a useful tracer of the tenuous lunar atmosphere because of its high efficiency in scattering sunlight at the D1 (5896 angstroms) and D2 (5890 angstroms) wavelengths. In 1988, Earth-based instruments revealed the presence of sodium at a density of less than 50 atoms per cubic centimeter at lunar altitudes below 100 kilometers. Telescopic observations that are made with a coronograph technique to block out the disk of the moon allow a true picture of the circumlunar atmosphere to be obtained and show the presence of sodium out to a distance of several lunar radii. The distribution of sodium has a solar zenith angle dependence, suggesting that most of the sodium that reaches great altitudes is liberated from the moon's surface by solar photons (by heating or sputtering) or by solar wind impact, in contrast to a source driven by uniform micrometeor bombardment.

Flynn, Brian↗

NASA NTRS1999

Towards a Global Aerosol Climatology: Preliminary Trends in Tropospheric Aerosol Amounts and Corresponding Impact on Radiative Forcing between 1950 and 1990

A global aerosol climatology is needed in the study of decadal temperature change due to natural and anthropogenic forcing of global climate change. A preliminary aerosol climatology has been developed from global transport models for a mixture of sulfate and carbonaceous aerosols from fossil fuel burning, including also contributions from other major aerosol types such as soil dust and sea salt. The aerosol distributions change for the period of 1950 to 1990 due to changes in emissions of SO2 and carbon particles from fossil fuel burning. The optical thickness of fossil fuel derived aerosols increased by nearly a factor of 3 during this period, with particularly strong increase in eastern Asia over the whole time period. In countries where environmental laws came into effect since the early 1980s (e.g. US and western Europe), emissions and consequently aerosol optical thicknesses did not increase considerably after 1980, resulting in a shift in the global distribution pattern over this period. In addition to the optical thickness, aerosol single scattering albedos may have changed during this period due to different trends in absorbing black carbon and reflecting sulfate aerosols. However, due to the uncertainties in the emission trends, this change cannot be determined with any confidence. Radiative forcing of this aerosol distribution is calculated for several scenarios, resulting in a wide range of uncertainties for top-of-atmosphere (TOA) forcings. Uncertainties in the contribution of the strongly absorbing black carbon aerosol leads to a range in TOA forcings of ca. -0.5 to + 0.1 Wm (exp. -2), while the change in aerosol distributions between 1950 to 1990 leads to a change of -0.1 to -0.3 Wm (exp. -2), for fossil fuel derived aerosol with a "moderate" contribution of black carbon aerosol.

Tegen, Ina↗

DOE OSTI2022

Modeling and experimental validation of dynamical effects in Bragg coherent x-ray diffractive imaging of finite crystals

Bragg coherent diffractive imaging (BCDI) is a noninvasive microscopy technique that can visualize the shape and internal lattice deviations of crystals with nanoscale spatial resolution and picometer deformation sensitivity. Its strain imaging capability relies on Fourier transform–based iterative phase retrieval algorithms, which are mostly developed under the kinematical approximation. Such approximation prohibits the application of BCDI on larger crystals, which are commonly seen in most emerging functional materials. Understanding the dynamical effect in BCDI, as well as developing a validated method for modeling BCDI at the dynamical diffraction limit, is crucial for applying BCDI to hierarchical systems that contain micron-sized crystals and grains. Thus we report a comparative study on the impact of dynamical diffraction effects by comparing the reconstruction results from two measurements of the same crystal. Forward simulation is implemented to show subtle changes of interference fringes in the diffraction pattern due to the dynamical diffraction, and is compared directly with the experimental data.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Clustering Effects on the Structure of Ionomer Solutions: A Combined SANS and Simulations Study

Ionic assemblies, or clusters, determine the structure and dynamics of ionizable polymers and enable their many applications. Fundamental to attaining well-defined materials is controlling the balance between van der Waals interactions that govern the backbone behavior and the forces that drive the formation of ionic clusters. Here, using small angle neutron scattering and fully atomistic molecular dynamics simulations, the structure of a model ionomer, sulfonated polystyrene in toluene solutions, was investigated as the cluster cohesion was tweaked by the addition of ethanol. The static structure factor was measured by both techniques and correlated with the size of the ionic clusters as the polymer concentration was varied. The conjunction of SANS results and molecular insight from MD simulations enabled the determination of the structure in these inhomogeneous networks on multiple length scales. Additionally, we find that across the entire concentration range studied, a network driven by the formation of ionic clusters was formed, where the size of the clusters drives the inhomogeneity of these systems. Tweaking the ionic clusters through the addition of ethanol impacts the packing of the sulfonated groups, their shape, and their size distribution, which in turn, affects the structure of these networks.

36 MATERIALS SCIENCE↗

DOE OSTI2025

New Measurements of the Deuteron-to-Proton 𝐹 2 Structure-Function Ratio

Nucleon structure functions, as measured in lepton-nucleon scattering, have historically provided a critical observable in the study of partonic dynamics within the nucleon. However, at very large parton momenta, it is both experimentally and theoretically challenging to extract parton distributions due to the probable onset of nonperturbative contributions and the unavailability of high-precision data at critical kinematics. Extraction of the neutron structure and the d quark distribution have been further challenging because of the necessity of applying nuclear corrections when utilizing scattering data from a deuteron target to extract the free neutron structure. However, a program of experiments has been carried out recently at the energy-upgraded Jefferson Lab electron accelerator aimed at significantly reducing the nuclear correction uncertainties on the d quark distribution function at large partonic momentum. This allows leveraging the vast body of deuterium data covering a large kinematic range to be utilized for d quark parton distribution function extraction. In this Letter, we present new data from experiment E12-10-002, carried out in Jefferson Lab Experimental Hall C, on the deuteron to proton cross section ratio at large Bjorken 𝑥. These results significantly improve the precision of existing data and provide a first look at the expected impact on quark distributions extracted from parton distribution function fits.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2012

Constraints on the Galactic Halo Dark Matter from Fermi-LAT Diffuse Measurements

We have performed an analysis of the diffuse gamma-ray emission with the Fermi Large Area Telescope (LAT) in the Milky Way halo region, searching for a signal from dark matter annihilation or decay. In the absence of a robust dark matter signal, constraints are presented. We consider both gamma rays produced directly in the dark matter annihilation/decay and produced by inverse Compton scattering of the e+/e− produced in the annihilation/decay. Conservative limits are derived requiring that the dark matter signal does not exceed the observed diffuse gamma-ray emission. A second set of more stringent limits is derived based on modeling the foreground astrophysical diffuse emission using the GALPROP code. Uncertainties in the height of the diffusive cosmic-ray halo, the distribution of the cosmic-ray sources in the Galaxy, the index of the injection cosmic-ray electron spectrum, and the column density of the interstellar gas are taken into account using a profile likelihood formalism, while the parameters governing the cosmic-ray propagation have been derived from fits to local cosmic-ray data. The resulting limits impact the range of particle masses over which dark matter thermal production in the early universe is possible, and challenge the interpretation of the PAMELA/Fermi-LAT cosmic ray anomalies as the annihilation of dark matter.

DIFFUSE MEASUREMENTS↗

NASA NTRS2022

The Impact of Inclination-dependent Attenuation on Ultraviolet Star Formation Rate Tracers

We examine and quantify how hybrid (e.g., UV+IR) star formation rate (SFR) estimators and the AFUV–β relation depend on inclination for disk-dominated galaxies using spectral energy distribution modeling that utilizes the inclination-dependent attenuation curves described in Doore et al. We perform this analysis on a sample of 133 disk-dominated galaxies from the CANDELS fields and 18 disk galaxies from the Spitzer Infrared Nearby Galaxies Survey and Key Insights on Nearby Galaxies: A Far-Infrared Survey with Herschel samples. We find that both the hybrid SFR estimators and the AFUV–β relation present clear dependencies on inclination. To quantify this dependence in the hybrid SFR estimators, we derive an inclination and a far-UV–near-IR color-dependent parametric relation for converting observed UV and IR luminosities into SFRs. For the AFUV–β relation, we introduce an inclination-dependent component that accounts for the majority of the inclination dependence with the scatter of the relation increasing with inclination. We then compare both of these inclination-dependent relations to similar inclination-independent relations found in the literature. From this comparison, we find that the UV+IR correction factor and AFUV for our hybrid and AFUV–β relations, respectively, result in a reduction in the residual scatter of our sample by approximately a factor of 2. Therefore, we demonstrate that inclination must be considered in hybrid SFR estimators and the AFUV–β relation to produce more accurate SFR estimates in disk-dominated galaxies.

Keith Doore↗

DOE OSTI2022

One-loop central-emission vertex for two gluons in $\mathcal{N}$ = 4 super Yang-Mills theory

A necessary ingredient for extending the BFKL equation to next-to-next-to-leading logarithmic (NNLL) accuracy is the one-loop central emission vertex (CEV) for two gluons which are not strongly ordered in rapidity. Here we consider the one-loop six-gluon amplitude in $\mathcal{N}$ = 4 super Yang-Mills (SYM) theory in a central next-to-multi-Regge kinematic (NMRK) limit, we show that its dispersive part factorises in terms of the two-gluon CEV, and we use it to extract the one-loop two-gluon CEV for any helicity configuration within this theory. This is a component of the two-gluon CEV in QCD. Although computed in the NMRK limit, both the colour structure and the kinematic dependence of the two-gluon CEV capture much of the complexity of the six-gluon amplitudes in general kinematics. In fact, the transcendental functions of the latter can be conveniently written in terms of impact factors, trajectories, single-emission CEVs and a remainder, which is a function of the conformally invariant cross ratios which characterise the six-gluon amplitudes in planar $\mathcal{N}$ = 4 SYM. Finally, as expected, in the MRK limit the two-gluon CEV neatly factorises in terms of two single-emission CEVs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗