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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Tank Waste LDR Organics Data Summary for Sample-and-Send (Rev.1A)

The presence of organic chemicals regulated under the Resource Conservation and Recovery Act (RCRA) Land Disposal Restrictions (LDR) adds complexity to treating and disposing of the low activity fraction of Hanford tank waste if a low temperature treatment method such as grouting is used (SRNL-STI-2020-00228). The complexity arises from the fact that the baseline vitrification method is considered by the Washington State Department of Ecology (Ecology) as providing adequate thermal treatment for organics; a status not automatically extended to a lowtemperature process, such as solidifying the waste in a cementitious waste form. In addition, the Environmental Protection Agency (EPA) LDR program is intended to ensure that wastes are properly treated prior to disposal. Proper treatment makes hazardous waste less harmful to groundwater by reducing the mobility and/or toxicity of the hazardous constituents in the waste. EPA guidance indicates that stabilization/solidification of waste for organics could be considered impermissible dilution under the LDR dilution prohibition. In addition, waste storage activities at Hanford have required transferring and blending waste within the tank system and these activities have potentially altered the concentrations of the hazardous constituents. The LDR dilution prohibition found in 40 Code of Federal Regulations (CFR) 268.3 states that “… no generator, transporter, handler, or owner or operator of a treatment, storage, or disposal facility shall in any way dilute a restricted waste or the residual from treatment of a restricted waste as a substitute for adequate treatment …”. Hence, if LAW is to be treated using low temperature stabilization (such as cementation), then it is important to demonstrate both how past storage activities have contributed to the removal (by vacuum evaporation), or destruction (by in situ decomposition) of the LDR organics and how future retrieval and waste feed preparation will contribute to their removal (by filtration and ion exchange). Demonstrating these processes helps validate that cementation without additional organic treatment does not necessarily represent impermissible dilution. To aid in implementing cementitious solidification of Low Activity Waste (LAW), WRPS has been developing a regulatory and processing LDR treatment variance strategy termed “Sampleand-Send” that relies, in part, on demonstrating that in situ decomposition reactions along with historic evaporation of tank waste has destroyed or removed most of the LDR organics possibly associated with Hanford Tank Waste (SRNL-STI-2020-00582, SRNL-STI-2021-00453, SRNL-STI-2022-00391). Under the Sample-and-Send concept, Hanford tank waste would be retrieved, processed through a Tank-Side Cesium Removal-like system, and staged as a candidate feed that would then be sampled to confirm the waste acceptance criteria is met for solidification in an LAW cementitious treatment facility. If it can be shown that LDR organics are at concentrations below the waste acceptance criteria (WAC) for cementitious stabilization and have been sufficiently removed (by historic evaporation or by filtration and ion exchange during Cs removal), destroyed (by historic in situ decomposition), or are not soluble in LAW above the WAC then additional organic treatment is not needed prior to creating a cementitious final waste form and the concept of Sample-and-Send would be proposed to establish a non-rulemaking site-specific treatment variance using the specified method of treatment “STABL” to remove sampling requirements of the waste form after treatment. Waste not meeting the WAC could either be routed to the Hanford Waste Treatment and Immobilization Plant for LAW vitrification, or further processed by evaporation or chemical oxidation before solidifying in a cementitious waste form. A key component in implementing the Sample-and-Send strategy is identifying which of the 207 LDR organic compounds associated with the RCRA Part A permit application waste codes for the Double Shell Tanks (DSTs) and Single Shell Tanks (SSTs) and any applicable Underlying Hazardous Constituents (UHCs) from 40 CFR 268.48 should be considered as potentially present and thus subject to regulation. In addition, it is also necessary to understand the solubility volatility, and reactivity of these compounds in LAW to identify which of the potentially present LDR organic compounds are not soluble above regulatory levels or are likely to have been removed by historic evaporation or destroyed by in situ decomposition reactions. If there are potentially present LDR organic compounds that have not been removed or destroyed and are soluble above regulatorily significant concentrations then a treatability variance may be needed for these species to eliminate any concerns pertaining to impermissible dilution. The spreadsheet accompanying this calculation report contains the data and logic computations needed to screen the list of 207 LDR organics associated with Hanford tank waste to identify those potentially present and to indicate which compounds may need to be included in a treatability variance.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2012

Optimal Solar PV Arrays Integration for Distributed Generation

Solar photovoltaic (PV) systems hold great potential for distributed energy generation by installing PV panels on rooftops of residential and commercial buildings. Yet challenges arise along with the variability and non-dispatchability of the PV systems that affect the stability of the grid and the economics of the PV system. This paper investigates the integration of PV arrays for distributed generation applications by identifying a combination of buildings that will maximize solar energy output and minimize system variability. Particularly, we propose mean-variance optimization models to choose suitable rooftops for PV integration based on Markowitz mean-variance portfolio selection model. We further introduce quantity and cardinality constraints to result in a mixed integer quadratic programming problem. Case studies based on real data are presented. An efficient frontier is obtained for sample data that allows decision makers to choose a desired solar energy generation level with a comfortable variability tolerance level. Sensitivity analysis is conducted to show the tradeoffs between solar PV energy generation potential and variability.

Omitaomu, Olufemi A↗
DOE OSTI2016

Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number R i and predict a saturation of flux Richardson number ( R f → R fm ) at sufficiently large R i . The CSB approach further predicts the value of R fm and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing R i . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as R fm is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Maps of the Magellanic clouds from combined South Pole Telescope and Planck data

Here, we present maps of the Large and Small Magellanic Clouds from combined South Pole Telescope (SPT) and Planck data. Both instruments are designed to make measurements of the cosmic microwave background but are sensitive to any source of millimeter-wave (mm-wave) emission. The Planck satellite observes in nine mm-wave bands, while the SPT data used in this work were taken with the three-band SPT-SZ camera. The SPT-SZ bands correspond closely to three of the nine Planck bands, namely those centered at 1.4, 2.1, and 3.0 mm. The angular resolution of the Planck data in these bands ranges from 5 to 10 arcmin, while the SPT resolution in these bands ranges from 1.0 to 1.7 arcmin. The combined maps take advantage of the high resolution of the SPT data and the long-timescale stability of the space-based Planck observations to deliver high signal-to-noise and robust brightness measurements on scales from the size of the maps down to ~1 arcmin. In each of the three bands, we first calibrate and color-correct the SPT data to match the Planck data, then we use noise estimates from each instrument and knowledge of each instrument's beam, or point-spread function, to make the inverse-variance-weighted combination of the two instruments' data as a function of angular scale. Furthermore, we create maps assuming a range of underlying emission spectra (for the color correction) and at a range of final resolutions. We perform several consistency tests on the combined maps and estimate the expected noise in measurements of features in the maps. Finally, we compare the maps of the Large Magellanic Cloud (LMC) from this work to maps from the Herschel HERITAGE survey, finding general consistency between the datasets. Furthermore, the broad wavelength coverage provides evidence of different emission mechanisms at work in different environments in the LMC.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

QTL Mapping of Seed Fatty Acid Contents in Camelina sativa Under Heat Stress

Heat stress alters oil quality in oilseed crops, yet its genetic underpinnings in Camelina sativa remain unclear. This study investigated the genetic basis of heat-induced changes in seed fatty acids using a recombinant inbred line (RIL) population derived from a cross between two camelina varieties, Suneson and Pryzeth. Exposure to high temperature during reproductive growth led to increased proportions of saturated (C16:0, C18:0) and monounsaturated (C18:1) fatty acids, whereas polyunsaturated C18:3, total unsaturated fatty acids (UFA) and the PUFA/MUFA ratio were decreased, suggesting an inhibition of the C18:1 → C18:2 → C18:3 desaturation pathway. A high-density linkage map (4981 bins across 20 chromosomes) was built, and 25 QTLs for fatty acids were detected, with hotspots on chromosomes 1, 9, 12, 13, 16, and 20. A major QTL on chromosome 1 (~ 80 cM) explained the largest variance component for PUFA/MUFA under heat. Three desaturase genes (FAD2, FAD7, FAD8) were located within key QTL intervals, nominating them as candidates for modulating unsaturation under elevated temperature. These results provide a genetic basis for fine mapping and functional validation, supporting future molecular and breeding efforts to stabilize oil quality under warming conditions.

Camelina↗
DOE OSTI2014

The iterative thermal emission method: A more implicit modification of IMC

For over 40 years, the Implicit Monte Carlo (IMC) method has been used to solve challenging problems in thermal radiative transfer. These problems typically contain regions that are optically thick and diffusive, as a consequence of the high degree of “pseudo-scattering” introduced to model the absorption and reemission of photons from a tightly-coupled, radiating material. IMC has several well-known features that could be improved: a) it can be prohibitively computationally expensive, b) it introduces statistical noise into the material and radiation temperatures, which may be problematic in multiphysics simulations, and c) under certain conditions, solutions can be nonphysical, in that they violate a maximum principle, where IMC-calculated temperatures can be greater than the maximum temperature used to drive the problem. We have developed a variant of IMC called iterative thermal emission IMC, which is designed to have a reduced parameter space in which the maximum principle is violated. ITE IMC is a more implicit version of IMC in that it uses the information obtained from a series of IMC photon histories to improve the estimate for the end of time step material temperature during a time step. A better estimate of the end of time step material temperature allows for a more implicit estimate of other temperature-dependent quantities: opacity, heat capacity, Fleck factor (probability that a photon absorbed during a time step is not reemitted) and the Planckian emission source. We have verified the ITE IMC method against 0-D and 1-D analytic solutions and problems from the literature. These results are compared with traditional IMC. We perform an infinite medium stability analysis of ITE IMC and show that it is slightly more numerically stable than traditional IMC. We find that significantly larger time steps can be used with ITE IMC without violating the maximum principle, especially in problems with non-linear material properties. The ITE IMC method does however yield solutions with larger variance because each sub-step uses a different Fleck factor (even at equilibrium)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

The role of cool-flame fluctuations in high-pressure spray flames, studied using high-speed optical diagnostics and Large-Eddy Simulations

Here this work investigates the low- and high-temperature ignition and combustion processes, applied to the Engine Combustion Network Spray A flame, combining advanced optical diagnostics and large-eddy simulations (LES). Simultaneous high-speed (50 kHz) formaldehyde (CH 2 0) planar laser-induced fluorescence (PLIF) and line-of-sight OH* chemiluminescence imaging were used to measure the low- and high-temperature flame, during ignition as well as during quasi-steady combustion. While tracking the cool flame at the laser sheet plane, the present experimental setup allows detection of distinct ignition spots and dynamic fluctuations of the lift-off length over time, which overcomes limitations for flame tracking when using schlieren imaging. After significant development to improve LES prediction of the low-and high-temperature flame position, both during the ignition processes and quasi-steady combustion, the simulations were analyzed to gain understanding of the mixture variance and how this variance affects formation/consumption of CH 2 0. Analysis of the high-temperature ignition period shows that a key improvement in the LES is the ability to predict heterogeneous ignition sites, not only in the head of the jet, but in shear layers at the jet edge close to the position where flame lift-off eventually stabilizes. The LES analysis also shows concentrated pockets of CH 2 0, in the center of jet and at 20 mm downstream of the injector (in regions where the equivalence ratio is greater than 6), that are of similar length scale and frequency as the experiment (approximately 5–6 kHz). The periodic oscillation of CH 2 0 match the frequency of pressure waves generated during auto-ignition and reflected within the constant-volume vessel throughout injection. The ability of LES to capture the periodic appearance and destruction of CH 2 0 is particularly important because these structures travel downstream and become rich premixed flames that affect soot production.

42 ENGINEERING↗
DOE OSTI2018

Partially coherent ptychography by gradient decomposition of the probe

Coherent ptychographic imaging experiments often discard the majority of the flux from a light source to define the coherence of the illumination. Even when the coherent flux is sufficient, the stability required during an exposure is another important limiting factor. Partial coherence analysis can considerably reduce these limitations. A partially coherent illumination can often be written as the superposition of a single coherent illumination convolved with a separable translational kernel. This article proposes the gradient decomposition of the probe (GDP), a model that exploits translational kernel separability, coupling the variances of the kernel with the transverse coherence. An efficient first-order splitting algorithm ( GDP-ADMM ) for solving the proposed nonlinear optimization problem is described. Numerical experiments demonstrate the effectiveness of the proposed method with Gaussian and binary kernel functions in fly-scan measurements. Remarkably, GDP-ADMM using nanoprobes produces satisfactory results even when the ratio between the kernel width and the beam size is more than one, or when the distance between successive acquisitions is twice as large as the beam width.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

The Spatial and Temporal Variability of the Clear Convective Boundary Layer at the ARM SGP Supersite

The convective boundary layer (CBL), also known as the mixing layer, constitutes the critical lower segment of the atmosphere that significantly influences daily human activities. The growing demand for precise weather forecasts is driven by the requirements of agriculture, transportation, and routine societal functions. Here, to enhance understanding of the CBL, this study investigates the spatiotemporal variability in the CBL and its controlling factors using four-year Doppler lidar, surface flux, and profiling measurements at five ARM Southern Great Plains sites within a 100 km radius. This investigation utilizes data collected exclusively under clear-sky conditions or scattered low-cloud conditions. Results reveal significant spatial differences in CBL evolutions. Daily mixing layer heights (MLHs) vary up to 1 km (30% of the mean) in late afternoon. There is a clear east–west contrast: western sites (C1, E32, E37) exhibit higher summer MLH (1.9–2.1 km) and vertical velocity variances (1.0–1.2 m 2 s −2 ) than eastern sites (1.6–1.8 km), reversing in winter. Temporally, the MLH peaks at 70% of the sunrise–sunset interval, the lagging heat flux (HF) peaks at 50%; and the seasonal MLH maxima lag the HF by approximately one month, influenced by nighttime PBL (planetary boundary layer) properties. The HF and lower tropospheric stability are the main factors of influence for the CBL, but site-specific dependencies highlight the critical roles of local factors, underscoring the need for including them in CBL modeling.

ARM SGP site↗
DOE OSTI2023

Stability of Kuramoto networks subject to large and small fluctuations from heterogeneous and spatially correlated noise

Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise. In this article, we focus on the assessment of fluctuations resulting from heterogeneous and spatially correlated noise inputs on Kuramoto model networks. We evaluate the typical, small fluctuations near synchronized states and connect the network variance to the overlap between stable modes of synchronization and the input noise covariance. Going beyond small to large fluctuations, we introduce the indicator mode approximation that projects the dynamics onto a single amplitude dimension. Such an approximation allows for estimating rates of fluctuations to saddle instabilities, resulting in phase slips between connected oscillators. Statistics for both regimes are quantified in terms of effective noise amplitudes that are compared and contrasted for several noise models. In conclusion, bridging the gap between small and large fluctuations, we show that a larger network variance does not necessarily lead to higher rates of large fluctuations.

42 ENGINEERING↗
DOE OSTI2026

Techno-Economic Analysis of Recycling Strategies for Catalyst and Acid During Catalytic Graphitization

With the aim of meeting the urgent demand for active anode materials (AAM) in energy storage systems, bio-based graphite (biographite) emerges as an affordable solution to de-risk the turbulent supply chain of critical minerals. Anode grade biographite requires high crystallinity and purity, which can be achieved by catalytic graphitization with iron, followed by acid washing. Therefore, a well-conceived process integration that recycles catalyst can be the starting point to commercialization. This study evaluates closed-loop catalyst recovery, and byproducts valorization scenarios through a technoeconomic framework to help understand the scale-up potential of biographite. For the acid washing, three reactors in series meet the required biographite purity at 99.95%. Iron and acid recovery can reduce material consumption and waste generation by ~95%, albeit at the expense of ~80% increase in capital costs. Recovery scenarios present similar capital and operational expenses, yielding minimum selling prices (MSP) near $6 kg-1 of biographite. Monte Carlo methodology reveals that feedstock price accounts for ~60% of MSP variance, followed by plant capacity ~20%. The likelihood of reaching a competitive profit margin of 30% in the U.S. AAM market sits at 85% average for recovery scenarios, and 103% when iron oxide is sold as byproduct. Additionally, an IRR >= 15% can be achieved for half of Monte Carlo simulations, representing promising early-stage results. Biographite production offers a strategic pathway to stabilize the anode market beyond China by integrating established technologies for a scalable, economically viable, and sustainable process. The role of catalyst recovery and byproducts utilization is critical for advancing the biomaterials industry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

An algebraic method for constructing stable and consistent autoregressive filters

In this paper, we introduce an algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth. By stable, we refer to the classical stability condition for the AR model. By consistent, we refer to the classical consistency constraints of Adams–Bashforth methods of order-two. One attractive feature of this algebraic method is that the model parameters can be obtained without directly knowing any training data set as opposed to many standard, regression-based parameterization methods. It takes only long-time average statistics as inputs. The proposed method provides a discretization time step interval which guarantees the existence of stable and consistent AR model and simultaneously produces the parameters for the AR models. In our numerical examples with two chaotic time series with different characteristics of decaying time scales, we find that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. These encouraging results are robust across wide ranges of discretization times, observation times, and observation noise variances. Finally, we also find that the proposed model produces an improved short-time prediction relative to the linear regression-based AR-models in forecasting a data set that characterizes the variability of the Madden–Julian Oscillation, a dominant tropical atmospheric wave pattern.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Stochastic Analysis of Levee Stability Subject to Variable Seepage Conditions

© ASCE. Levee stability is highly influenced by seepage. Specifically, hydraulic conductivity distribution within a levee influences pore pressure distribution and controls the drained strength of the soil. In this study the influence of hydraulic conductivity and blanket layer thickness on failure probability is evaluated within the context of reliability analyses that also include soil strength and unit weight as random variables. First-Order Reliability Method (FORM) is used to evaluate reliability, rank random variables by importance and to obtain sensitivity of the solution to each random variable and its distribution parameters. Stability is computed using Spencer's method of slices coupled to a finite element seepage code to directly evaluate pore pressure. In addition, response surface method solutions are compared to the direct reliability solution to assess response surface accuracy. The results show that blanket layer thickness is more important than most strength parameters and that the uncertainty in hydraulic conductivity is less important to the variance in safety factor for the case of a low-permeability blanket layer. Numerical challenges caused by implementing a finite element limit-state function are discussed. Response surface methods are found to give a reasonable approximation to the direct reliability solution when the design point is between response surface fitting points.

Lanzafame, Robert↗
DOE OSTI2024

Scalable bottom-up synthesis of Co-Ni–doped graphene

Introducing heteroatoms into graphene is a powerful strategy to modulate its catalytic, electronic, and magnetic properties. At variance with the cases of nitrogen (N)– and boron (B)–doped graphene, a scalable method for incorporating transition metal atoms in the carbon (C) mesh is currently lacking, limiting the applicative interest of model system studies. This work presents a during-growth synthesis enabling the incorporation of cobalt (Co) alongside nickel (Ni) atoms in graphene on a Ni(111) substrate. Single atoms are covalently stabilized within graphene double vacancies, with a Co load ranging from 0.07 to 0.22% relative to C atoms, controllable by synthesis parameters. Structural characterization involves variable-temperature scanning tunneling microscopy and ab initio calculations. The Co- and Ni-codoped layer is transferred onto a transmission electron microscopy grid, confirming stability through scanning transmission electron microscopy and electron energy loss spectroscopy. This method holds promise for applications in spintronics, gas sensing, electrochemistry and catalysis, and potential extension to graphene incorporation of similar metals.

Science & Technology - Other Topics↗
DOE OSTI2024

Insights into Tetravalent Np Speciation in HNO 3 through Spectroelectrochemistry and Multivariate Analysis

In situ optical spectroscopy, spectropotentiometry, and multivariate analysis were applied to the Np(IV) nitrate system to better understand speciation and quantify HNO 3 concentration. Thin-layer spectropotentiometry, or spectroelectrochemistry, was leveraged to isolate and stabilize Np(IV) without compromising the solution conditions and generate representative Vis-NIR absorption spectra from 0.5 to 10 M HNO 3 and benchmark the corresponding Np(IV) molar absorptivity coefficients. Spectra were described with principal component analysis (PCA) to identify the purest Np(IV) absorbance spectra among other oxidation states [e.g., Np(V/VI)] at each acid concentration and then to identify the primary sources of variance within each Np(IV) spectrum with respect to Np(IV) nitrate complexes. Then, partial least-squares regression (PLSR) and support vector regression (SVR) models were built to predict HNO 3 concentration from the Np(IV) spectral data. The nonlinear SVR model outperformed the linear PLSR model for the HNO 3 concentration predictions. Finally, the inclusion of spectra collected in edge and center point HNO 3 concentrations in the calibration set was determined to be crucial for producing models with strong predictive capabilities. The multivariate approach used in this study makes it possible to quantify HNO 3 concentration solely based on Np(IV) absorption spectra, which is essential to quantifying processing streams in various online monitoring applications.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2016

Bond rupture between colloidal particles with a depletion interaction

The force required to break the bonds of a depletion gel is measured by dynamically loading pairs of colloidal particles suspended in a solution of a nonadsorbing polymer. Sterically stabilized poly(methyl methacrylate) colloids that are 2.7 μm diameter are brought into contact in a solvent mixture of cyclohexane-cyclohexyl bromide and polystyrene polymer depletant. The particle pairs are subject to a tensile load at a constant loading rate over many approach-retraction cycles. The stochastic nature of the thermal rupture events results in a distribution of bond rupture forces with an average magnitude and variance that increases with increasing depletant concentration. The measured force distribution is described by the flux of particle pairs sampling the energy barrier of the bond interaction potential based on the Asakura–Oosawa depletion model. A transition state model demonstrates the significance of lubrication hydrodynamic interactions and the effect of the applied loading rate on the rupture force of bonds in a depletion gel.

42 ENGINEERING↗
DOE OSTI2018

Machine Learning of Factors Influencing Damping and Frequency of Dominant Inter-area Modes in the WECC Interconnect

The stability of inter-area electromechanical oscillations are critical to power system reliability. Due to the complexities of power systems, relationships between system conditions and oscillation characteristics, such as damping and frequency, tend to be expressed only in generalities. In this study, a list of influential factors on Western Electricity Coordinating Council (WECC) interconnect modal characteristics are identified and evaluated with advanced machine learning techniques including principal component analysis, analysis of variance, random forest feature selection, support vector machine, and artificial neural network approaches.

Hou, Zhangshuan↗
DOE OSTI2012

Review of Rate Constants and Exploration of Correlations of the Halogen Transfer Reaction of Tri-substituted Carbon-centered Radicals with Molecular Halogens

Rate constants for the reaction (R 3C + X2 R 3CX + X ; X = F, Cl, Br, and I) are reviewed. Because of curved Arrhenius plots and negative EX values, empirical structure-reactivity correlations are sought for log kX,298 rather than EX. The well-known poor correlation with measures of reaction enthalpy is demonstrated. The best quantitative predictor for R 3C is p, the sum of the Hammett p constants for the three substituents, R . Electronegative substituents with lone pairs, such as halogen or oxygen, thus appear to destabilize the formation of a polarized pre-reaction complex and/or TS ( +R---X---X -) by -inductive/field electron withdrawal while simultaneously stabilizing them by -resonance electron donation. The best quantitative predictor of the reactivity order of the halogens, I2 > Br2 >> Cl2 F2, is the polarizability of the halogen, (X-X). For the data set of 60 rate constants which span 6.5 orders of magnitude, a modestly successful correlation of log kX,298 is achieved with only two parameters, p and (X-X), with a mean unsigned deviation of 0.59 log units. How much of this residual variance is the result of inaccuracies in the data compared with over-simplification of the correlation approach remains to be seen.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗