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DOE OSTI2015

Continuum model of tensile fracture of metal melts and its application to a problem of high-current electron irradiation of metals

A continuum model of the metal melt fracture is formulated on the basis of the continuum mechanics and theory of metastable liquid. A character of temperature and strain rate dependences of the tensile strength that is predicted by the continuum model is verified, and parameters of the model are fitted with the use of the results of the molecular dynamics simulations for ultra-high strain rates (≥1–10/ns). A comparison with experimental data from literature is also presented for Al and Ni melts. Using the continuum model, the dynamic tensile strength of initially uniform melts of Al, Cu, Ni, Fe, Ti, and Pb within a wide range of strain rates (from 1–10/ms to 100/ns) and temperatures (from melting temperature up to 70–80% of critical temperature) is calculated. The model is applied to numerical investigation of a problem of the high-current electron irradiation of Al, Cu, and Fe targets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1990

A new continuum model for suspensions of gyrotactic micro-organisms

A new continuum model is formulated for dilute suspensions of swimming micro-organisms with asymmetric mass distributions. Account is taken of randomness in a cell's swimming direction, p, by postulating that the probability density function for p satisfies a Fokker-Planck equation analogous to that obtained for colloid suspensions in the presence of rotational Brownian motion. The deterministic torques on a cell, viscous and gravitational, are balanced by diffusion, represented by an isotropic rotary diffusivity Dr, which is unknown a priori, but presumably reflects stochastic influences on the cell's internal workings. When the Fokker-Planck equation is solved, macroscopic quantities such as the average cell velocity Vc, the particle diffusivity tensor D and the effective stress tensor sigma can be computed; Vc and D are required in the cell conservation equation, and sigma in the momentum equation. The Fokker-Planck equation contains two dimensionless parameters, lambda and epsilon; lambda is the ratio of the rotary diffusion time Dr-1 to the torque relaxation time B (balancing gravitational and viscous torques), while epsilon is a scale for the local vorticity or strain rate made dimensionless with B. In this paper we solve the Fokker-Planck equation exactly for epsilon = 0 (lambda arbitrary) and also obtain the first-order solution for small epsilon. Using experimental data on Vc and D obtained with the swimming alga, Chlamydomonas nivalis, in the absence of bulk flow, the epsilon = 0 results can be used to estimate the value of lambda for that species (lambda approximately 2.2; Dr approximately 0.13 s-1). The continuum model for small epsilon is then used to reanalyse the instability of a uniform suspension, previously investigated by Pedley, Hill & Kessler (1988). The only qualitatively different result is that there no longer seem to be circumstances in which disturbances with a non-zero vertical wavenumber are more unstable than purely horizontal disturbances. On the way, it is demonstrated that the only significant contribution to sigma, other than the basic Newtonian stress, is that derived from the stresslets associated with the cells' intrinsic swimming motions.

NASA Discipline Number 28-20↗

DOE OSTI2012

Sensitivity of the Properties of Ruthenium “Blue Dimer” to Method, Basis Set, and Continuum Model

The ruthenium “blue dimer” [(bpy)2RuIIIOH2]2O4+ is best known as the first well-defined molecular catalyst for water oxidation. It has been subject to numerous computational studies primarily employing density functional theory. However, those studies have been limited in the functionals, basis sets, and continuum models employed. The controversy in the calculated electronic structure and the reaction energetics of this catalyst highlights the necessity of benchmark calculations that explore the role of density functionals, basis sets, and continuum models upon the essential features of blue-dimer reactivity. In this paper, we report Kohn-Sham complete basis set (KS-CBS) limit extrapolations of the electronic structure of “blue dimer” using GGA (BPW91 and BP86), hybrid-GGA (B3LYP), and meta-GGA (M06-L) density functionals. The dependence of solvation free energy corrections on the different cavity types (UFF, UA0, UAHF, UAKS, Bondi, and Pauling) within polarizable and conductor-like polarizable continuum model has also been investigated. The most common basis sets of double-zeta quality are shown to yield results close to the KS-CBS limit; however, large variations are observed in the reaction energetics as a function of density functional and continuum cavity model employed.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2023

Modeling the Environment-Dependent Kinetics of Oxygen Reduction Reaction – a Continuum Model for Electric Double Layer

Here, for proton-exchange-membrane fuel cells (PEMFCs) to achieve broad commercialization, improved energy-conversion efficiency with minimal Pt-based electrocatalyst is required. Because the sluggish rate of oxygen reduction reaction (ORR) limits the efficiency of PEMFCs, the efficiency improvement requires a better understanding of ORR kinetics and mechanism to design better catalyst. To understand the ORR mechanism, theoretical and experimental analyses have been conducted. While previous studies reasonably explained the catalyst-dependent activity on single crystal catalysts in 0.1 M perchloric acid solution, the explicit effect of electrolyte and related microenvironments is not thoroughly understood. The change in the electrolyte alters the electric-double-layer (EDL) structure and thus the local microenvironment at the electrode/electrolyte interface. Thus, the structure of the EDL should be carefully analyzed to uncover the electrolyte-dependent reaction kinetics. In this talk, we propose a multiscale continuum model to predict the EDL structure and examine the effect of perchloric acid concentration on ORR activity on Pt (111). The model includes Density Potential Functional Theory (DPFT) for electron density and Modified Poisson Boltzmann equation for species’ density and electric potential. Also, the interaction between adsorbents and electric field is taken into account by minimizing the grand potential. After model validation with experimentally measured double-layer capacity data as a function of applied potential and concentration, the effect of the perchloric acid concentration (0.02 M – 0.2 M) on ORR activity is analyzed and discussed. It is shown that the model reproduces the specific activity obtained in the experiments when assuming the oxygen adsorption is limiting the rate, which can be attributed to the large energetic barrier for solvent reorganization. Then, extension of the model to PEMFC ionomer electrolytes will be introduced. Overall, the model framework and findings provide insights into the ORR mechanism and guidance on how to tailor catalyst materials for increased PEMFC performance.

30 DIRECT ENERGY CONVERSION↗

NASA NTRS1988

Continuum modeling of large lattice structures: Status and projections

The status and some recent developments of continuum modeling for large repetitive lattice structures are summarized. Discussion focuses on a number of aspects including definition of an effective substitute continuum; characterization of the continuum model; and the different approaches for generating the properties of the continuum, namely, the constitutive matrix, the matrix of mass densities, and the matrix of thermal coefficients. Also, a simple approach is presented for generating the continuum properties. The approach can be used to generate analytic and/or numerical values of the continuum properties.

Noor, Ahmed K.↗

NASA NTRS1988

Continuum modeling of large lattice structures - Status and projections

Noor, Ahmed K.↗

NASA NTRS2001

Equivalent-Continuum Modeling of Nano-Structured Materials

A method has been developed for modeling structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with an equivalent-continuum model. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As an important example with direct application to the development and characterization of single-walled carbon nanotubes, the model has been applied to determine the effective continuum geometry of a graphene sheet. A representative volume element of the equivalent-continuum model has been developed with an effective thickness. This effective thickness has been shown to be similar to, but slightly smaller than, the interatomic spacing of graphite.

Odegard, Gregory M.↗

NASA NTRS1989

A continuum model of continental deformation above subduction zones - Application to the Andes and the Aegean

A continuum model of continental deformation above subduction zones was developed that combines the viscous sheet and the corner flow models; the continental lithosphere is described by a two-dimensional sheet model that considers basal drag resulting from the viscous asthenosphere flow underneath, and a corner flow model with a deforming overlying plate and a rigid subducting plate is used to calculate the shear traction that acts on the base of the lithosphere above a subduction zone. The continuum model is applied to the Andes and the Aegean deformations, which represent, respectively, compressional and extensional tectonic environments above subduction zones. The models predict that, in a compressional environment, a broad region of uplifted topography will tend to develop above a more steeply dippping slab, rather than above a shallower slab, in agreement with observations in the various segments of the central Andes. For an extensional environment, the model predicts that a zone of compression can develop near the trench, and that extensional strain rate can increase with distance from the trench, as is observed in the Aegean.

Wdowinski, Shimon↗

DOE OSTI2016

A semi-continuum model on vibration frequency of silicon nanowires in <111> orientation

In this article, a new semi-continuum model is built to describe the fundamental vibration frequency of the silicon nanowires in <111> orientation. The Keating potential model and the discrete nature in the width and the thickness direction of the silicon nanowires in <111> orientation are applied in the new semi-continuum model. Based on the Keating model and the principle of conservation of energy, the vibration frequency of the silicon nanowires with the triangle, the rhombus, and the hexagon cross sections are derived. It is indicated that the calculation results based on this new model are accordant with the simulation results of the software based on molecular dynamics (MD).

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2014

Relaxation of a steep density gradient in a simple fluid: Comparison between atomistic and continuum modeling

We compare dynamical nonequilibrium molecular dynamics and continuum simulations of the dynamics of relaxation of a fluid system characterized by a non-uniform density profile. Results match quite well as long as the lengthscale of density nonuniformities are greater than the molecular scale (∼10 times the molecular size). In presence of molecular scale features some of the continuum fields (e.g., density and momentum) are in good agreement with atomistic counterparts, but are smoother. On the contrary, other fields, such as the temperature field, present very large difference with respect to reference (atomistic) ones. This is due to the limited accuracy of some of the empirical relations used in continuum models, the equation of state of the fluid in the present example.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Exploring chemical speciation at electrified interfaces using detailed continuum models

We present a local free-energy functional-based generic continuum model for material interfaces with a specific emphasis on electrified solid/liquid interfaces. The model enables a description of multicomponent phases at interfaces and includes the effects of specific non-electrostatic interactions (specific adsorption), ion size disparity, and the explicit presence of neutral species. In addition to the optimization of electrostatic, non-electrostatic, and steric forces, the model can be easily modified to explore the effects of other channels for equilibration, including local chemical transformations driven by equilibrium constants and electrochemical reactions driven by the electrode potential. In this way, we show that, upon accounting for these effects, local speciation in the vicinity of the interface can be drastically different from what is expected from restricted models and minor species (from the bulk perspective) may become dominant due to the effects of local pH. We evaluate the ionic contribution to the surface tension at the interface and show how this could impact the structure of air/liquid interfaces. On the same footing, an attempt to describe electrochemical metal dissolution is made. The model allows estimates of the mutual population of newly produced ions depending on their charge and size and could be useful for interpretation of electrochemical and spectroscopic measurements if the dissolution involves different metal ions (species). With these advances, the proposed model may be used as an ingredient within a hybrid ab initio-continuum methodology to model biased interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Derivation of a continuum model and the energy law for moving contact lines with insoluble surfactants

A continuous model is derived for the dynamics of two immiscible fluids with moving contact lines and insoluble surfactants based on thermodynamic principles. The continuum model consists of the Navier-Stokes equations for the dynamics of the two fluids and a convection-diffusion equation for the evolution of the surfactant on the fluid interface. The interface condition, the boundary condition for the slip velocity, and the condition for the dynamic contact angle are derived from the consideration of energy dissipations. Different types of energy dissipations, including the viscous dissipation, the dissipations on the solid wall and at the contact line, as well as the dissipation due to the diffusion of surfactant, are identified from the analysis. A finite element method is developed for the continuum model. Numerical experiments are performed to demonstrate the influence of surfactant on the contact line dynamics. The different types of energy dissipations are compared numerically.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1992

Multilevel optimization using a continuum model for structures

The new concept of using a continuum model in the multilevel decomposition of structural optimization problems is presented. The practicality of this concept is demonstrated by application in a scheme for the optimization of beam-like space structures. This scheme is tested against traditional optimization procedures for savings in computational cost. Results from both optimization methods are presented for comparison.

Yates, K.↗

DOE OSTI2021

Progress on continuum modeling of lithium–sulfur batteries

While lithium–sulfur batteries are a promising next-generation chemistry devices due to their high theoretical energy density, commercialization has been slow due to low coulombic efficiency and poor cycle life. This review explores the ways in which continuum modeling contributes to the understanding of lithium–sulfur (LiS) battery mechanisms and cell-level performance through the lens of micro- and macroscale phenomena. We examine different approaches to modeling important physical phenomena such as reaction mechanisms, cathode microstructure, shuttling, nucleation and precipitation, and transport limitations. This paper also emphasizes the significance and challenge of connecting typical modeling parameters and assumptions to systems-level metrics of a standard state-of-art high performing lithium–sulfur cell. Particularly important, the considerations for high energy density cells and the areas where continuum models can facilitate better collaboration are discussed. Here, we also summarize a few selected works to highlight experimentally-driven modeling, use of electroanalytical techniques, and parameter identification approaches to enable model-based design and advanced battery management systems.

25 ENERGY STORAGE↗

DOE OSTI2017

Continuum Model of Gas Uptake for Inhomogeneous Fluids

We describe a continuum model of gas uptake for inhomogeneous fluids (CMGIF) and use it to predict fluid adsorption in porous materials directly from gas-substrate interaction energies determined by first principles calculations or accurate effective force fields. The method uses a perturbation approach to correct bulk fluid interactions for local inhomogeneities caused by gas substrate interactions, and predicts local pressure and density of the adsorbed gas. The accuracy and limitations of the model are tested by comparison with the results of Grand Canonical Monte Carlo simulations of hydrogen uptake in metal-organic frameworks (MOFs). We show that the approach provides accurate predictions at room temperature and at low temperatures for less strongly interacting materials. As a result, the speed of the CMGIF method makes it a promising candidate for high-throughput materials discovery in connection with existing databases of nano-porous materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Interpreting Experimental Results from Shock Impacts on Single Crystal PETN in the Context of Continuum Models

Here we interpret previous experimental measurements of impacts on single crystal PETN in the context of a simple continuum model. Hugoniot calculations using the simple model framework under various limiting assumptions envelope measured Hugoniot states reasonably well and suggest that non-negligible deviatoric elastic strains may exist in the shock compressed state for weak impacts. An accompanying simple kinematic model for lattice deformation was used to estimate the expected shifts in X-ray diffraction peaks for the (211) plane under impacts normal to (110) planes. The results suggest that negligible relaxation of the deviatoric lattice deformation occurs on the short (10–20 ns) time and wave propagation (40–80 m) scales of laser-driven shock experiments, and that the corresponding elastic strains may be large. Because of the potentially large deviatoric elastic strains, the specific finite deformation strain measure used within thermomechanical single crystal models is of significant consequence, which is explored numerically by the comparison of isothermal purely elastic responses under uniaxial and simple shear deformations.

36 MATERIALS SCIENCE↗

NASA NTRS1988

The application of single particle hydrodynamics in continuum models of multiphase flow

A review of the application of single particle hydrodynamics in models for the exchange of interphase momentum in continuum models of multiphase flow is presented. Considered are the equations of motion for a laminar, mechanical two phase flow. Inherent to this theory is a model for the interphase exchange of momentum due to drag between the dispersed particulate and continuous fluid phases. In addition, applications of two phase flow theory to de-mixing flows require the modeling of interphase momentum exchange due to lift forces. The applications of single particle analysis in deriving models for drag and lift are examined.

Decker, Rand↗

DOE OSTI2014

Electronic excitation spectra of molecules in solution calculated using the symmetry-adapted cluster-configuration interaction method in the polarizable continuum model with perturbative approach

A perturbative approximation of the state specific polarizable continuum model (PCM) symmetry-adapted cluster-configuration interaction (SAC-CI) method is proposed for efficient calculations of the electronic excitations and absorption spectra of molecules in solutions. This first-order PCM SAC-CI method considers the solvent effects on the energies of excited states up to the first-order with using the zeroth-order wavefunctions. This method can avoid the costly iterative procedure of the self-consistent reaction field calculations. The first-order PCM SAC-CI calculations well reproduce the results obtained by the iterative method for various types of excitations of molecules in polar and nonpolar solvents. The first-order contribution is significant for the excitation energies. The results obtained by the zeroth-order PCM SAC-CI, which considers the fixed ground-state reaction field for the excited-state calculations, are deviated from the results by the iterative method about 0.1 eV, and the zeroth-order PCM SAC-CI cannot predict even the direction of solvent shifts in n-hexane for many cases. The first-order PCM SAC-CI is applied to studying the solvatochromisms of (2,2{sup ′}-bipyridine)tetracarbonyltungsten [W(CO){sub 4}(bpy), bpy = 2,2{sup ′}-bipyridine] and bis(pentacarbonyltungsten)pyrazine [(OC){sub 5}W(pyz)W(CO){sub 5}, pyz = pyrazine]. The SAC-CI calculations reveal the detailed character of the excited states and the mechanisms of solvent shifts. The energies of metal to ligand charge transfer states are significantly sensitive to solvents. The first-order PCM SAC-CI well reproduces the observed absorption spectra of the tungsten carbonyl complexes in several solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗