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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2026

FY26 Progress on Demonstration of a Multiphysics Steady State Capability for Modeling Core Radial Expansion in SFRs

Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism in liquid metal-cooled fast reactors and involves multiphysics effects including radiation transport, fluid flow, heat transfer, and mechanical response to temperature and flux gradients. This report summarizes recent progress on developing a multiphysics, MOOSE-based workflow to predict core bowing and associated reactivity feedback. Significant new capabilities in the reactor physics code Griffin - sodium backfill and pin power reconstruction for deformed geometries - were applied in this effort. This year’s work included verification, code comparisons, sensitivity studies, and coupled demonstrations that advance the state of MOOSE-based core bowing workflow. Griffin’s sodium backfill capability was verified by demonstrating that its automated treatment of geometry expansion and material-density updates reproduces manual calculations exactly, confirming solid mass conservation and proper coolant backfilling in expanded geometries. Reconstructed pin powers were compared for Griffin’s ductheterogeneous and ring-heterogeneous treatments in single-, seven-, and nineteen-assembly cases, with best agreement observed in lower-leakage configurations and the duct-heterogeneous approach offering substantially lower computational cost. Thermal-hydraulic sensitivity sensitivities showed that MOOSE SCM, SAM, and CFD are expected to produce similar deformation predictions despite variances in their temperature predictions, and that explicit treatment of inter-assembly flow becomes increasingly important as gap flow rate increases. Finally, coupled demonstrations on small multi-assembly configurations using Griffin, MOOSE Solid Mechanics, MOOSE SCM, and Heat Conduction produced physically consistent reactivity feedback from thermal expansion and bowing. The coupled demonstrations simulated grid plate expansion as well as resultant core bowing at full power conditions. Simplifications were made in current workflow, namely the assumption of instantaneous full power conditions following hot zero power, and pre-expanding the Griffin geometry axially due to lack of an axial fuel pin expansion model and temperature feedback to Griffin.

Wozniak, Nicholas↗
DOE OSTI2018

Thermo-mechanical performance assessment of selected plates from MP-1 low power experiments

Monolithic plate-type fuel is a fuel form that is being developed for the conversion of high performance research and test reactors to low-enrichment uranium fuels. These fuel-plates are comprised of a high density, low enrichment, U-Mo alloy based fuel foil encapsulated in an aluminum cladding. To benchmark this new design, number of plates has been irradiated with satisfactory performance. As a part of continuing evaluation efforts, a set of plates covering range of operational parameters is scheduled to be tested during MP-1 irradiation experiments. It is necessary to evaluate the thermo-mechanical performance of plates during irradiation. For this, selected plates with distinct operational histories; covering low power, high power and high fission density were simulated. Fully coupled three-dimensional models of plates with a capability to evolve mechanical and thermal properties of constituent materials with irradiation time and burn-up were developed. The models input used projected parameters, including plate geometry, irradiation history and coolant conditions as input. The model output included temperature, displacement and stresses in the fuel, cladding and diffusion barrier. The fuel behavioral model considered inelastic behavior including volumetric swelling due to solid and gaseous products, irradiation induced creep, thermal expansion, conductivity degradation and plasticity. A visco-plastic behavioral model was used for the cladding that included thermal creep, irradiation hardening, growth due to fast neutrons and Mises plasticity. The plates were then simulated by using projected irradiation parameters. The resulting temperature, displacement and stress-strains were comparatively evaluated on the selected paths. The results were then compared with those of plates from previous RERTR experiments.

42 ENGINEERING↗
DOE OSTI2018

Validation and optimization of batch and continuous particle separation processes

Recent advances in simulation capabilities coupled with advanced manufacturing can be leveraged to create highly efficient compact reactors with low emissions, low cost, high reliability, and high flexibility for energy conversion. This type of reactor is especially important for conversion of bio-mass, a storable, renewable and fast-growing energy source, considering the distributed nature of raw material and cost of biomass collection and transportation. To achieve this goal, it is critical to developing new process technologies that are significantly more efficient than traditional processes for which the added manufacture provides a fast way of realization and evaluation. Based upon the flagship MFiX multiphase computational fluid dynamic software suite, NETL has developed an Optimization Toolset to facilitate the CFD simulation based reactor design and optimization, and process intensification. This technical report presents the recent development and application of the Optimization Toolset and the framework for process optimization of particle separation in batch and continuous processes. In these processes, a fluidized bed reactor under proper operating condition was used to separate particles of different physical properties. MFiX-DEM simulations were conducted for a batch system to simulate the process covering a wide range of superficial gas velocities from which the optimal operational parameter can be determined through analyzing the system response. After successful demonstration of the framework, a continuous system for particle separation was designed based on CFD simulations. Similar optimization exercises were conducted for the continuous particle separation considering multiple operating parameters. The design was then fabricated in the laboratory through 3D printing for testing. The particle separation performance was carefully measured through high-speed video for particle tracking. Quantitative comparison between numerical results and experimental measurements were conducted for confirmation and validation.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2022

Benchmarking Simulated Precipitation Variability Amplitude across Time Scales

Here, objective performance metrics that measure precipitation variability across time scales from subdaily to interannual are presented and applied to Historical simulations of Coupled Model Intercomparison Project phase 5 and 6 (CMIP5 and CMIP6) models. Three satellite-based precipitation estimates (IMERG, TRMM, and CMORPH) are used as reference data. We apply two independent methods to estimate temporal variability of precipitation and compare the consistency in their results. The first method is derived from power spectra analysis of 3-hourly precipitation, measuring forced variability by solar insolation (diurnal and annual cycles) and internal variability at different time scales (subdaily, synoptic, subseasonal, seasonal, and interannual). The second method is based on time averaging and facilitates estimating the seasonality of subdaily variability. Supporting the robustness of our metric, we find a near equivalence between the results obtained from the two methods when examining simulated-to-observed ratios over large domains (global, tropics, extratropics, land, or ocean). Additionally, we demonstrate that our model evaluation is not very sensitive to the discrepancies between observations. Our results reveal that CMIP5 and CMIP6 models in general overestimate the forced variability while they underestimate the internal variability, especially in the tropical ocean and higher-frequency variability. The underestimation of subdaily variability is consistent across different seasons. The internal variability is overall improved in CMIP6, but remains underestimated, and there is little evidence of improvement in forced variability. Increased horizontal resolution results in some improvement of internal variability at subdaily and synoptic time scales, but not at longer time scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

A Subgrid Approach for Modeling Microtopography Effects on Overland Flow

Microtopography, or heterogeneities in the elevation across scales much smaller than the domain of interest, plays a critical role in surface water retention, surface/subsurface interactions, and runoff. Resolving microtopographic influences on flow requires high–resolution simulations, which are computationally demanding even when considering the surface system in isolation and even more so when surface flow is one component in integrated simulations that couple surface flow with unsaturated subsurface flow. There is thus significant motivation for models that allow the effects of subgrid microtopography to be better represented. Subgrid models modify coarsened models to capture the microtopography–induced nonlinear effects on hydrologic processes. We present a subgrid model that alters the water storage and flow terms in the diffusion wave equation for surface flow. Stochastically generated microtopography with strongly contrasting spatial structure, high–resolution digital elevation maps from a polygonal tundra site on the North Slope of Alaska and a hummocky microtopography from a field site in Northern Minnesota are used to assess the accuracy and applicability of the subgrid model to disparate landscapes. Approaches for determining subgrid model parameters are tested and simulation results using the subgrid model are compared to benchmark fine–scale simulations and to coarse simulations that ignore microtopography. Our findings confirm that a properly parameterized subgrid model greatly improves the coarse–scale representation of hydrographs and total water content in the system. Furthermore, using the polygonal tundra example, we propose and test a strategy for moving to application–relevant spatial scales by combining microtopography classification and a few fine–scale simulations on small subdomains.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

High Level Waste in Salt Repositories: Experiments and Simulations of Evaporation in the Underground - 17167

Advances in simulation of coupled heat and mass transfer in granular salt using the Finite Element Heat and Mass Transfer Code (FEHM) is presented in this paper. The modeling focuses on reproducing the results of an in-situ subsurface evaporation experiment beginning during the summer of 2015 carried out in the underground at the Waste Isolation Pilot Plant (WIPP). Run-of-mine (granular) salt was placed in a metal pan, and sample mass, as well as ambient temperature and humidity, were measured continuously on a data logger through May 2016. Changes in moisture content of the salt are interpreted from the change in mass, and these data provide insight into evaporation and water retention characteristics from salt in the WIPP underground. To allow simulation of the experimental data, FEHM was modified to include a variable humidity boundary condition. The new humidity boundary condition can adjust streams of inflowing air to reflect fractions of air and water at prescribed temperature and pressure conditions that in turn represent relative humidity. Attributes for the flow such as temperature, air mass fraction, and humidity can be specified for inflowing air. The in-situ experiment provided data for validation of FEHM code development to accurately compute water-vapor pressure lowering due to dissolved salt and capillary pressure for pore water stored granular WIPP salt. Using this new boundary condition capabilities, a numerical representation of the pan experiment was created. The numerical domain is a 2-dimensional square grid of 30 by 30 cm axes. Salt and air properties are assigned based on measured values. A low flow rate of air is specified across the pile of salt to represent drift ventilation airflow. Humidity and temperature of the flowing air are fixed to measured values, and the simulated pile of salt is allowed to take up or release water based only on gradients in humidity and water-vapor pressure. Mass changes of the modeled salt pan were compared to measured mass changes in the bench-scale experiment. Directionality of the modeled changes tracks well with measured values, with good correlation between peak and valley inflection points. This shows that in situations with airflow where the relative humidity boundary can apply, FEHM can produce accurate values if humidity, air flow, and initial conditions are well established. Finally, this work supports phased-field-thermal testing in salt planned for the underground at WIPP that is expected to begin in early 2017. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics

Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion is treated on the same footing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Advances in Geologic Disposal System Modeling and Application to Crystalline Rock

The Used Fuel Disposition Campaign (UFDC) of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Fuel Cycle Technology (OFCT) is conducting research and development (R&D) on geologic disposal of used nuclear fuel (UNF) and high-level nuclear waste (HLW). Two of the high priorities for UFDC disposal R&D are design concept development and disposal system modeling (DOE 2011). These priorities are directly addressed in the UFDC Generic Disposal Systems Analysis (GDSA) work package, which is charged with developing a disposal system modeling and analysis capability for evaluating disposal system performance for nuclear waste in geologic media (e.g., salt, granite, clay, and deep borehole disposal). This report describes specific GDSA activities in fiscal year 2016 (FY 2016) toward the development of the enhanced disposal system modeling and analysis capability for geologic disposal of nuclear waste. The GDSA framework employs the PFLOTRAN thermal-hydrologic-chemical multi-physics code and the Dakota uncertainty sampling and propagation code. Each code is designed for massively-parallel processing in a high-performance computing (HPC) environment. Multi-physics representations in PFLOTRAN are used to simulate various coupled processes including heat flow, fluid flow, waste dissolution, radionuclide release, radionuclide decay and ingrowth, precipitation and dissolution of secondary phases, and radionuclide transport through engineered barriers and natural geologic barriers to the biosphere. Dakota is used to generate sets of representative realizations and to analyze parameter sensitivity.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

Electrical coupled Morris-Lecar neurons: From design to pattern analysis

In this study, an experimental electronic neuron based on Morris-Lecar model is presented, able to become an experimental unit tool to study collective association of robust coupled neurons. The circuit design is given according to the ionic currents of this model. A weak coupling of such neurons under Multisim Software can generate clusters based on the boundary conditions of the neurons and their initial conditions. For this study, we work in the region close to the fold bifurcation of limit cycles. In this region two limit cycles exist, one of the cycles is stable and another one is unstable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Application of Generic Disposal System Models

This report describes specific GDSA activities in fiscal year 2015 (FY2015) toward the development of the enhanced disposal system modeling and analysis capability for geologic disposal of nuclear waste. The GDSA framework employs the PFLOTRAN thermal-hydrologic-chemical multi-physics code (Hammond et al., 2011) and the Dakota uncertainty sampling and propagation code (Adams et al., 2013). Each code is designed for massively-parallel processing in a high-performance computing (HPC) environment. Multi-physics representations in PFLOTRAN are used to simulate various coupled processes including heat flow, fluid flow, waste dissolution, radionuclide release, radionuclide decay and ingrowth, precipitation and dissolution of secondary phases, and radionuclide transport through the engineered barriers and natural geologic barriers to a well location in an overlying or underlying aquifer. Dakota is used to generate sets of representative realizations and to analyze parameter sensitivity.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Roadmap for Molecular Benchmarks in Nonadiabatic Dynamics

Simulating the coupled electronic and nuclear response of a molecule to light excitation requires the application of nonadiabatic molecular dynamics. However, when faced with a specific photophysical or photochemical problem, selecting the most suitable theoretical approach from the wide array of available techniques is not a trivial task. The challenge is further complicated by the lack of systematic method comparisons and rigorous testing on realistic molecular systems. This absence of comprehensive molecular benchmarks remains a major obstacle to advances within the field of nonadiabatic molecular dynamics. A CECAM workshop, Standardizing Nonadiabatic Dynamics: Towards Common Benchmarks, was held in May 2024 to address this issue. This Perspective highlights the key challenges identified during the workshop in defining molecular benchmarks for nonadiabatic dynamics. Specifically, this work outlines some preliminary observations on essential components needed for simulations and proposes a roadmap aiming to establish, as an ultimate goal, a community-driven, standardized molecular benchmark set.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Model-based analysis of environmental controls over ecosystem primary production in an alpine tundra dry meadow

We investigated several key limiting factors that control alpine tundra productivity by developing an ecosystem biogeochemistry model. The model simulates the coupled cycling of carbon (C), nitrogen (N), and phosphorus (P) and their interactions with gross primary production (GPP). It was parameterized with field observations from an alpine dry meadow ecosystem using a global optimization strategy to estimate the unknown parameters. The model, along with the estimated parameters, was first validated against independent data and then used to examine the environmental controls over plant productivity. Our results show that air temperature is the strongest limiting factor to GPP in the early growing season, N availability becomes important during the middle portion of the growing season, and soil moisture is the strongest limiting factors by late in the growing season. Overall, the controls over GPP during the growing season, from strongest to weakest, are soil moisture content, air temperature, N availability, and P availability. This simulation provides testable predictions of the shifting nature of physical and nutrient limitations on plant growth. The model also indicates that changing environmental conditions in the alpine will likely lead to changes in productivity. For example, warming eliminates the control of P availability on GPP and makes N availability surpass air temperature to become the second strongest limiting factor. In contrast, an increase in atmospheric nutrient deposition eliminates the control of N availability and enhances the importance of P availability. Furthermore, these analyses provide a quantitative and conceptual framework that can be used to test predictions and refine ecological analyses at this long-term ecological research site.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence

The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the “dimensionality” of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuations in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

A continuum framework for coupled solid deformation–fluid flow through anisotropic elastoplastic porous media

We present a continuum framework for coupled solid deformation–fluid flow in anisotropic elastoplastic porous media. A thermodynamic formulation of the coupled processes gives rise to an anisotropic Biot tensor that is a function of drained elastic tangent moduli tensor of the solid skeleton and the intrinsic bulk modulus of the solid constituent. Two effective stress measures emerge from the formulation, namely, σ', which is energy-conjugate to the elastic strain, and σ'', which is energy-conjugate to the plastic strain. For the special case of transverse isotropy that is commonly encountered in natural rocks, the Biot tensor can be expressed in terms of its normal and tangential components to the bedding plane, along with a microstructure tensor. Apart from its thermodynamic consistency, an advantage of this new formulation is that standard mixed finite element formulation can be employed to discretize the domain and solve initial boundary-value problems. We conduct plane strain simulations of coupled solid deformation–fluid flow in a transversely isotropic porous medium to demonstrate the impacts of material anisotropy, stress history, and the Biot tensor on the system response.

42 ENGINEERING↗
DOE OSTI2024

HL-2A's ELM cycle simulations by integrating BOUT++'s drift MHD and transport code

A new integrating model has been developed to couple tokamak edge multiscale magnetohydrodynamic (MHD) events and transport simulations, such as edge-localized mode (ELM) cycles. As a proof of principle, we first start from a set of three-field two-fluid model equations, which includes the pressure, current, and vorticity. Here, the equations are separated into the slowly evolving part of the axisymmetric component by taking a time average of the axisymmetric component. The time-averaged fluxes, which are quadratic in fluctuating quantities, act as driven terms for the time-averaged axisymmetric quantities that determine the plasma transport, and therefore the large-scale evolution of the plasma profiles. Then the HL-2A's ELM cycles are simulated using the model. Good agreements of ELM size and pedestal recovery time have been achieved for the solutions obtained from the coupled simulation compared with experiment. For one ELM cycle simulation, the coupled code can achieve a speedup of a factor of up to 30 over standalone code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1999

Real-Time Assimilation of Goes-Derived Products into A Mesoscale Model and It's Impact on Short-Term (06-36hr) Forecasts from 17 October 1998 through the Present

As the parameterizations of surface energy budgets in regional models have become more complete physically, models have the potential to be much more realistic in simulations of coupling between surface radiation, hydrology, and surface energy transfer. Realizing the importance of properly specifying the surface energy budget, many institutions are using land-surface models to represent the lower boundary forcing associated with biophysical processes and soil hydrology. However, the added degrees of freedom due to inclusion of such land-surface schemes require the specification of additional parameters within the model system such as vegetative resistances, green vegetation fraction, leaf area index, soil physical and hydraulic characteristics, stream flow, runoff, and the vertical distribution of soil moisture. Spatial heterogeneity of these parameters makes correct specification problematic since measurements are not routinely available. A technique has been developed for assimilating GOES-IR skin temperature tendencies, solar insolation, and surface albedo into the surface energy budget equation of a mesoscale model so that the simulated rate of temperature change closely agrees with the satellite observations. The technique has been successfully employed in a number of mesoscale models in case-study mode. We have taken the next step and developed a study to determine if assimilating these types of data into mesoscale models in real-time can improve short-term (648h) forecasts of temperature, relative humidity, and QPF on a daily basis over relatively large regions. Therefore, an operational modeling/assimilation system has been developed at the GHCC during the past summer that allows us to produce simulations out to 48 hours in a timely manor. The PSU/NCAR MM5 is used in a nested configuration with a 25 km grid covering the southeastern third of the US. The model has been on-line since 1 July 1998 and forecast products are posted on our web site. The satellite algorithms that generate data to be assimilated came on-line 17 October 1998. Quantitative assessment of the forecast quality is performed via traditional verification statistics. In addition, invaluable qualitative information is obtained through close collaboration with several NWSFO's who are using the MM5 products in real-time on a daily basis. The assimilation technique has been applied in an off-line mode since 17 October. Results based on bulk statistical verification of surface meteorology over the entire Southeastern US show that assimilating the GOES-derived land surface tendencies and solar radiation results in a significant reduction of the shelter air temperature and RH bias on a daily basis. In fact, the assimilation technique has produced improved temperature and RH forecasts for 97% of the 100 simulations performed to date. Work is currently underway to determine the sensitivity of the assimilation procedure to the availability of satellite data, length of assimilation period, model initialization, and synoptic-scale meteorological conditions. In addition, results from a detailed energy budget analysis using the Early Eta, our operational MM5, and the assimilation runs will help us to better understand the satellite assimilation the land-surface energy budge. Research during the spring-summer of 1999 will focus on the impact of the assimilation technique during the warm season where it is hypothesized that it can have a positive impact on QPF during conditions of weak synoptic-scale forcing.

Lapenta, William M.↗
DOE OSTI2016

Linking density functional and mode coupling models for supercooled liquids

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Tensile Fracture of Welded Polymer Interfaces: Miscibility, Entanglements, and Crazing

Large-scale molecular simulations are performed to investigate tensile failure of polymer interfaces as a function of welding time t. Changes in the tensile stress, mode of failure and interfacial fracture energy G I are correlated to changes in the interfacial entanglements as determined from Primitive Path Analysis. Bulk polymers fail through craze formation, followed by craze breakdown through chain scission. At small t welded interfaces are not strong enough to support craze formation and fail at small strains through chain pullout at the interface. Once chains have formed an average of about one entanglement across the interface, a stable craze is formed throughout the sample. The failure stress of the craze rises with welding time and the mode of craze breakdown changes from chain pullout to chain scission as the interface approaches bulk strength. The interfacial fracture energy G I is calculated by coupling the simulation results to a continuum fracture mechanics model. As in experiment, G I increases as t 1/2 before saturating at the average bulk fracture energy G b . As in previous studies of shear strength, saturation coincides with the recovery of the bulk entanglement density. Before saturation, G I is proportional to the areal density of interfacial entanglements. Immiscibiltiy limits interdiffusion and thus suppresses entanglements at the interface. Even small degrees of immisciblity reduce interfacial entanglements enough that failure occurs by chain pullout and G I << G b .

36 MATERIALS SCIENCE↗