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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Examining Graphite Degradation in Molten Salt Environments: A Chemical, Physical, and Material Analysis

Molten-salt reactors (MSRs) are Generation IV nuclear reactors that use liquid salt as a coolant and/or fuel. In several MSR designs, graphite serves as a moderator and/or reflector. However, due to limited experimental data and operational experience, our understanding of graphite behavior in molten salt environments remains incomplete. This report aims to identify the degradation mechanisms of nuclear graphite in MSRs, detail the mechanisms of each factor, and provide an initial assessment of their impact on the structural integrity of graphite components. This assessment is based on an extensive literature review and insights from subject matter experts. Furthermore, given the limited data, a modeling strategy using existing Grizzly software is proposed for a more thorough analysis where appropriate. Additionally, it presents mitigation strategies where applicable. The report covers physical degradation mechanisms such as infiltration, erosion, and abrasion, as well as chemical degradation mechanisms including fluorination, intercalation, corrosion, and oxidation. Molten salt can infiltrate the porous structure of graphite, leading to several detrimental effects. Entrapment of fissile products within the graphite pores can cause radiation damage and could pose challenges in the handling and disposal of contaminated components. The differential thermal expansion between the infiltrated salt and graphite, along with internal stress from pressurized molten salt and volumetric heating, can compromise the structural integrity of graphite. To mitigate these effects, employing ultra-fine graphite grades and applying sealants and coatings are effective strategies. A computational model based on coupled solid mechanics and heat transfer phenomena could be used to predict the internal stresses using Grizzly software. In pebble-bed MSRs, graphite fuel pebbles can cause abrasion against reactor components due to friction and wear. The severity of wear is influenced by various factors such as temperature, environment, and the presence of lubricants. Tribological studies reveal that higher temperatures and molten salt environments, such as FLiBe, significantly reduce wear rates compared to dry conditions. Additionally, the chemical composition of the salt can further optimize graphite's tribological performance. Long-term wear effects can be modeled by incorporating surface defects into the geometry and predict stresses under thermal and radiation effects using Grizzly software. Chemical degradation of graphite in a molten salt environment can occur through fluorination and intercalation. Fluorination can occur via replacement of hydrogen or oxygen atoms, or at the active sites, but does not cause structural degradation. Intercalation, on the other hand, can lead to exfoliation, where layers of graphite separate and peel away, damaging the graphite. Protective coatings can enhance graphite's resistance to intercalation. Graphite generally exhibits good chemical stability in molten salt environments, though it can corrode under specific conditions, particularly in the presence of impurities or oxidants. Studies have shown that protective coatings, such as plasma-sprayed partially stabilized zirconia (PSZ), can effectively prevent such degradation. Corrosion behavior varies significantly with different graphite grades and coating applications, underscoring the need for detailed studies on uncoated and coated graphite to understand and mitigate corrosion mechanisms in MSRs. Research indicates that the presence of oxidants and impurities can accelerate graphite degradation in molten salts, making it essential to explore acceptable impurity limits. Oxidation is another critical degradation mechanism, leading to weight loss and structural damage due to the formation of CO and CO 2 from the reaction of carbon atoms with oxygen. This process creates new porosity and compromises graphite's integrity. While extensive research on graphite oxidation has been conducted for gas-cooled reactors, studies specific to MSRs are limited. Findings from the coal industry suggest that molten alkali metal salts can significantly accelerate graphite oxidation, a hypothesis worth exploring for fluoride salts in MSRs. Understanding oxidation behavior in MSRs is vital for developing protective measures. The analysis of post-irradiated graphite from the MSRE experiment demonstrated exceptional chemical compatibility with molten fluoride salt, suggesting that the extent of chemical attack on graphite largely depends on the salt's infiltration capability. Therefore, the use of ultra-fine grade graphite could help mitigate chemical degradation effects. Existing oxidation modeling capabilities in Grizzly, which use reaction-diffusion equations to model graphite-air interactions, could be adapted to simulate the chemical degradation effects of graphite in molten salt environments.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Developing the Science Basis for Understanding Polymer Encapsulant Degradation Mechanisms: DuraMAT 2.0 Final Project Report

Polymeric encapsulants are essential materials in photovoltaic modules, protecting sensitive electronics from the environment while providing mechanical integrity to the multilayered assembly. However, these polymeric materials are susceptible to degradation processes driven by the ingress of environmental species, ultraviolet radiation, thermal stresses, and mechanical loading. In this study, we employ a combined atomistic simulation and accelerated aging experimental approach to study the molecular-scale mechanisms of encapsulant degradation. Classical molecular dynamics simulations quantify the diffusion of environmental and degradation species through the polymer matrix, producing composition-specific diffusion coefficients. Reactive simulations characterize activation energy barriers and reaction rate constants for key chemical pathways. In parallel, thermal-desorption analyses coupled with mass spectrometry monitor the emergence and concentration profiles of degradation products under controlled stressor conditions. By integrating simulation and experiment, we establish quantitative correlations between polymer composition, species diffusivity, and chemical reactivity. We anticipate that these relations and quantitative values could serve as high-fidelity inputs to reaction-diffusion models, enabling physics-informed lifetime predictions and guiding the design of more durable encapsulant materials for solar energy applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking

Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. Focusing on the decohered cluster state – a mixed-state symmetry-protected topological state protected by a combined strong and weak symmetry – we construct a parent Lindbladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical and numerical methods, we find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. However, when perturbations introduce only weak symmetry defects, the steady-state mixed-state symmetry-protected topological order remains stable. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.

Shah, Jeet [University of Maryland, College Park, ↗
DOE OSTI2026

Reaction Diffusion Modelling of 3D Pillar Electrodes in Single-Catalyst CO 2 Reduction Cascades

Effective electrochemical CO 2 reduction to liquid fuels requires that the local catalytic environment facilitates the desired reactivity, yet a microscopic understanding of this environment is difficult to achieve from experiment alone. In this work, a 3D reaction-diffusion model was developed to explore the effects of electrode surface area and local geometry on the performance of a heterogeneous catalyst that performs a two-step CO 2 reduction cascade reaction to CO and then CH 3 OH under aqueous conditions. Kinetic parameters for the model were inspired by experimental results using a cobalt phthalocyanine (CoPc) catalyst. Three-dimensional architectures composed of arrays of square pillars with varying dimensions and either smooth or periodically modulated surfaces were tested, revealing the extent to which geometry modulates the performance of the cascade reactions. Although structural variations modulate local concentration gradients, we find that electrochemically active surface area predominantly governs the overall cascade reaction. Moreover, the results suggest that supersaturation of CO, with concentrations up to ten-fold higher than the equilibrium solubility limit, might be critical for more efficient conversion to CH 3 OH. For any given geometry, the spatially averaged ratio of [CO] to [CO 2 ] is dictated by the electrochemically active surface area and determines the yield of CH 3 OH. For a fixed surface area, geometries that spatially confine the electrolyte yield moderate local [CO] to [CO 2 ] ratios within small volumes. In contrast, less confining geometries result in a broader distribution of local ratios spread over larger volumes, with both configurations yielding the same spatially averaged [CO] to [CO 2 ] ratio. These insights provide valuable design principles—highlighting the critical importance of surface area and possibly CO supersaturation—for engineering advanced electrode architectures that leverage intermediate trapping and CO supersaturation to enhance overall performance in tandem CO 2 reduction systems.

COMSOL↗
NASA NTRS1983

Numerical solution of the problem of flame propagation by the use of the random element method

A numerical, grid-free algorithm is presented for one-dimensional reaction-diffusion model of laminar flame propagation in premixed gases. It is based on the random element method we developed for the analysis of diffusional processes. The effect of combustion is taken into account by applying the principle of fractional steps to separate the process of diffusion, modeled by the random walk of computational elements, from the exothermic effects of chemical reaction, monitoring their strength. The validity of the algorithm is demonstrated by application to flame propagation problems for which exact solutions exist. The flame speed evaluated by its use oscillates around the exact value at a relatively small amplitude, while the temperature and species concentration profiles are self-correcting in their convergence to the exact solution. A satisfactory resolution is obtained by the use of quite a small number of computational elements which automatically adjust their distribution of fit sharp gradients.

Ghoniem, A. F.↗
NASA NTRS1986

Multi-dimensional initial-boundary value problems with strong nonlinearities

Initial boundary value problems for the general scalar singularly perturbed parabolic equation in a cylindrical domain are studied. The one-dimensional reaction-diffusion equation is considered in the absence of convection. Then, the general one-dimensional and N-dimensional reaction-convection-diffusion equations are analyzed.

Howes, F. A.↗
NASA NTRS1987

The thermal stability of coronal loops by nonlinear diffusion asymptotics

A nonlinear reaction-diffusion equation and some additional constraints are derived which describe the time-dependent behavior of the temperature structure of the plasma in coronal loops. The equation is analyzed using nonlinear diffusion asymptotics, in particular singular perturbation techniques, and the results are interpreted in the context of the physical problem of the thermal stability and temporal behavior of the plasma. The results are consistent with the possibility of cyclic thermal behavior of the plasma, as suggested by Kuin and Martens (1982).

Pakkert, J. W.↗
NASA NTRS1990

Computation of the unsteady facilitated transport of oxygen in hemoglobin

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Davis, Sanford↗
NASA NTRS1990

Asymptotic analysis of dissipative waves with applications to their numerical simulation

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Hagstrom, Thomas↗
NASA NTRS1994

Microwave heating and joining of ceramic cylinders: A mathematical model

A thin cylindrical ceramic sample is placed in a single mode microwave applicator in such a way that the electric field strength is allowed to vary along its axis. The sample can either be a single rod or two rods butted together. We present a simple mathematical model which describes the microwave heating process. It is built on the assumption that the Biot number of the material is small, and that the electric field is known and uniform throughout the cylinder's cross-section. The model takes the form of a nonlinear parabolic equation of reaction-diffusion type, with a spatially varying reaction term that corresponds to the spatial variation of the electromagnetic field strength in the waveguide. The equation is analyzed and a solution is found which develops a hot spot near the center of the cylindrical sample and which then propagates outwards until it stabilizes. The propagation and stabilization phenomenon concentrates the microwave energy in a localized region about the center where elevated temperatures may be desirable.

Booty, Michael R.↗
NASA NTRS1996

Effects of Material Degradation on the Structural Integrity of Composite Materials: Experimental Investigation and Modeling of High Temperature Degradation Mechanisms

It has previously been demonstrated that simple coupled reaction-diffusion models can approximate the aging behavior of PMR-15 resin subjected to different oxidative environments. Based on empirically observed phenomena, a model coupling chemical reactions, both thermal and oxidative, with diffusion of oxygen into the material bulk should allow simulation of the aging process. Through preliminary modeling techniques such as this it has become apparent that accurate analytical models cannot be created until the phenomena which cause the aging of these materials are quantified. An experimental program is currently underway to quantify all of the reaction/diffusion related mechanisms involved. The following contains a summary of the experimental data which has been collected through thermogravimetric analyses of neat PMR-15 resin, along with analytical predictions from models based on the empirical data. Thermogravimetric analyses were carried out in a number of different environments - nitrogen, air and oxygen. The nitrogen provides data for the purely thermal degradation mechanisms while those in air provide data for the coupled oxidative-thermal process. The intent here is to effectively subtract the nitrogen atmosphere data (assumed to represent only thermal reactions) from the air and oxygen atmosphere data to back-figure the purely oxidative reactions. Once purely oxidative (concentration dependent) reactions have been quantified it should then be possible to quantify the diffusion of oxygen into the material bulk.

Cunningham, Ronan A.↗
NASA NTRS1998

Critical Slowing Down in Time-to-Extinction: An Example of Critical Phenomena in Ecology

We study a model for two competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observe that the final outcome depends on the initial densities (uniformly distributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlation length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, there is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have developed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system.

Gandhi, Amar↗
NASA NTRS1999

Surface Tension and Fingering of Miscible Interfaces

Experiments on miscible, buoyantly unstable reaction-diffusion fronts and non-reacting displacement fronts in Hele-Shaw cells show a fingering-type instability whose wavelengths (lambda*) are consistent with an interfacial tension (sigma) at the front caused by the change in chemical composition, even though the solutions are miscible in all proportions. In conjunction with the Saffman-Taylor model, the relation sigma = K/tau, where tau is the interface thickness and K approximately equal 4 +/- 2 x 10(exp -6) dyne, enables prediction of our measured values of lambda* as well as results from prior experiments on miscible interfaces. These results indicate that even for miscible fluids, surface tension is generally a more significant factor than diffusion in interfacial stability and flow characteristics.

Abib, Mohammed↗
NASA NTRS2001

The Cool Flames Experiment

A space-based experiment is currently under development to study diffusion-controlled, gas-phase, low temperature oxidation reactions, cool flames and auto-ignition in an unstirred, static reactor. At Earth's gravity (1g), natural convection due to self-heating during the course of slow reaction dominates diffusive transport and produces spatio-temporal variations in the thermal and thus species concentration profiles via the Arrhenius temperature dependence of the reaction rates. Natural convection is important in all terrestrial cool flame and auto-ignition studies, except for select low pressure, highly dilute (small temperature excess) studies in small vessels (i.e., small Rayleigh number). On Earth, natural convection occurs when the Rayleigh number (Ra) exceeds a critical value of approximately 600. Typical values of the Ra, associated with cool flames and auto-ignitions, range from 104-105 (or larger), a regime where both natural convection and conduction heat transport are important. When natural convection occurs, it alters the temperature, hydrodynamic, and species concentration fields, thus generating a multi-dimensional field that is extremely difficult, if not impossible, to be modeled analytically. This point has been emphasized recently by Kagan and co-workers who have shown that explosion limits can shift depending on the characteristic length scale associated with the natural convection. Moreover, natural convection in unstirred reactors is never "sufficiently strong to generate a spatially uniform temperature distribution throughout the reacting gas." Thus, an unstirred, nonisothermal reaction on Earth does not reduce to that generated in a mechanically, well-stirred system. Interestingly, however, thermal ignition theories and thermokinetic models neglect natural convection and assume a heat transfer correlation of the form: q=h(S/V)(T(bar) - Tw) where q is the heat loss per unit volume, h is the heat transfer coefficient, S/V is the surface to volume ratio, and (T(bar) - Tw ) is the spatially averaged temperature excess. This Newtonian form has been validated in spatially-uniform, well-stirred reactors, provided the effective heat transfer coefficient associated with the unsteady process is properly evaluated. Unfortunately, it is not a valid assumption for spatially-nonuniform temperature distributions induced by natural convection in unstirred reactors. "This is why the analysis of such a system is so difficult." Historically, the complexities associated with natural convection were perhaps recognized as early as 1938 when thermal ignition theory was first developed. In the 1955 text "Diffusion and Heat Exchange in Chemical Kinetics", Frank-Kamenetskii recognized that "the purely conductive theory can be applied at sufficiently low pressure and small dimensions of the vessel when the influence of natural convection can be disregarded." This was reiterated by Tyler in 1966 and further emphasized by Barnard and Harwood in 1974. Specifically, they state: "It is generally assumed that heat losses are purely conductive. While this may be valid for certain low pressure slow combustion regimes, it is unlikely to be true for the cool flame and ignition regimes." While this statement is true for terrestrial experiments, the purely conductive heat transport assumption is valid at microgravity (mu-g). Specifically, buoyant complexities are suppressed at mu-g and the reaction-diffusion structure associated with low temperature oxidation reactions, cool flames and auto-ignitions can be studied. Without natural convection, the system is simpler, does not require determination of the effective heat transfer coefficient, and is a testbed for analytic and numerical models that assume pure diffusive transport. In addition, mu-g experiments will provide baseline data that will improve our understanding of the effects of natural convection on Earth.

Pearlman, Howard↗
NASA NTRS1998

Spiral waves are stable in discrete element models of two-dimensional homogeneous excitable media

The spontaneous breakup of a single spiral wave of excitation into a turbulent wave pattern has been observed in both discrete element models and continuous reaction-diffusion models of spatially homogeneous 2D excitable media. These results have attracted considerable interest, since spiral breakup is thought to be an important mechanism of transition from the heart rhythm disturbance ventricular tachycardia to the fatal arrhythmia ventricular fibrillation. It is not known whether this process can occur in the absence of disease-induced spatial heterogeneity of the electrical properties of the ventricular tissue. Candidate mechanisms for spiral breakup in uniform 2D media have emerged, but the physical validity of the mechanisms and their applicability to myocardium require further scrutiny. In this letter, we examine the computer simulation results obtained in two discrete element models and show that the instability of each spiral is an artifact resulting from an unphysical dependence of wave speed on wave front curvature in the medium. We conclude that spiral breakup does not occur in these two models at the specified parameter values and that great care must be exercised in the representation of a continuous excitable medium via discrete elements.

NASA Discipline Cardiopulmonary↗
NASA NTRS2005

New Species of Fire Discovered: Fingering Flamelets Form a Dynamic Population

Poets and artists have long used fire as a metaphor for life. At the NASA Glenn Research Center, recent experiments in a subcritical Rayleigh number flow channel demonstrated that this analogy holds up surprisingly well when tools developed to characterize a biological population are applied to a class of fire that occurs in near-extinction, weakly convective environments (such as microgravity) or in vertically confined spaces (such as our apparatus). Under these conditions, the flame breaks into numerous 'flamelets" that form a Turing-type reaction-diffusion fingering pattern as they spread across the fuel. It is standard practice on U.S. spacecraft for the astronaut crew to turn off the ventilation to help extinguish a fire, both to eliminate the fresh oxygen supply and to reduce the distribution of the smoke. When crew members think that the fire is fully extinguished, they reactivate the ventilation system to clear the smoke. However, some flamelets can survive, and our experiments have demonstrated that flamelets quickly grow into a large fire when ventilation increases.

Olson, Sandra L.↗
DOE OSTI2025

Morphogenic Growth 3D Printing

Inspired by nature's morphogenesis, a new 3D printing process –growth printing (GP)– takes advantage of a self‐propagating curing front to produce 3D polymeric parts following a growth‐like development plan. The propagation of the curing front is driven by the exothermic polymerization of dicyclopentadiene (DCPD), which transforms the liquid resin into a stiff polymer as it propagates at 1 mm s −1 . GP is triggered when a heated initiator contacts the uncured liquid resin in an open container. The initiator nucleates the frontal polymerization reaction and the isotropic radial propagation of the growth front. Simultaneously, the initiator is moved up across the free surface of the resin, pulling the cured object out of the uncured resin. The motion trajectory of the initiator with respect to the free resin surface controls the growth morphology of the 3D part. An inverse design algorithm is developed to produce 3D parts by modeling the reaction‐diffusion‐driven solidification process. This process has substantial energy savings and high printing speeds.

3D printing↗