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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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At least 163 records · Page 9

Magnetic-Confinement Fusion—Plasma Theory: Tokamak Magnetohydrodynamic Equilibrium and Stability

Magnetohydrodynamics (MHD) provides a useful model to describe the crucial plasma macroscopic equilibrium and stability behaviors in toroidal tokamak devices by considering the plasma as a conducting fluid interacting with a surrounding confining electromagnetic field. MHD is the most basic plasma model, incorporating most large-scale phenomena, including plasma equilibrium and all major instabilities. MHD equations are obtained by taking moments of the Boltzmann equations for different plasma species. They provide a set of comprehensive physics constrains to compute and optimize the equilibrium plasma shape and pressure and current profiles that are critical to its stability and performance. In the ideal case, the equations have special properties that lead to efficient numerical calculation schemes, the most important of which is the ideal MHD energy principle for linear stability against small departures from equilibrium. In a tokamak plasma, equilibrium pressure is mostly destabilizing for MHD modes, whereas equilibrium current is also often a major driving force. Plasma resistivity creates new freedom for a MHD instability to grow, but there are also cases where the plasma resistivity plays a stabilizing role. Equilibrium toroidal flow and/or flow shear can affect MHD instabilities. Principal MHD instabilities include the internal kink mode, sawtooth, fishbone, external kink, resistive wall mode, resistive interchange, tearing and neoclassical tearing modes (NTMs), locked modes, toroidal Alfven eigenmodes (TAEs), and edge localized modes (ELMs). Fast-growing MHD instabilities can lead to an abrupt plasma disruption and termination that can potentially damage the device plasma facing components (PFCs) and in-vessel structures. Furthermore, an important MHD application is to develop robust techniques to mitigate and control MHD instabilities.

Dispersive pellet injection↗

Braiding Majorana fermions and creating quantum logic gates with vortices on a periodic pinning structure

We show how vortices that support Majorana fermions when placed on a periodic pinning array can be used for vortex exchange and independent braiding by performing a series of specific moves with a probe tip. Using these braiding operations, we demonstrate realizations of a Hadamard and a CNOT gate. We specifically consider the first matching field at which there is one vortex per pinning site, and we show that there are two basic dynamic operations, move and exchange, from which basic braiding operations can be constructed in order to create specific logic gates. The periodic pinning array permits both control of the world lines of the vortices and freedom for vortex manipulation using a set of specific moves of the probe during which the probe tip strength and height remain unchanged. We measure the robustness of the different moves against thermal effects and show that the three different operations produce distinct force signatures on the moving tip.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Basic Design Layout of a Modular Pumped Hydro Teaching Unit

This work was originally completed in July 2015 as a proposal to Santa Fe Community College (SFCC) for their engineering program and a follow up to a feasibility study completed for the Community College the year earlier as indicated below. The work was ahead of its time and funding was hard to obtain to implement a project. This work is now being formally released for distribution to a wider audience based on the evolving circumstances in greater society that now favor this approach with funding more readily available. Due to the distribution outside of SFCC, specific architectural drawing sets of the pertinent buildings called out in the design have been removed. No changes to the design have been made. The design layout utilizing a building is not meant to limit the implementation of the design. The elevation difference required may be obtained with a building, a small hill, jacking up the upper tank, or similar means. The design presented is a basic design, identifying major components and how they are connected together. The user may change components under their own liability. All local applicable codes and standards must be followed when building an actual unit, under the authority of a responsible engineer or owner. Appropriate measures must be followed to protect people from hazards such as electricity, water pressure, and general construction. A leak test to verify water tightness of the system should be conducted prior to any operations. The vision of this design is to allow a class of 10 to 15 students to construct the assembly within a month or so time period, and then learn to operate the assembly at their school location under the guidance of their instructor. This will allow the students to learn about the practical concept of storing electricity with water, and gain a hands on experience of the real world challenges faced with full Modular Pumped Hydro Projects.

13 HYDRO ENERGY↗

Morphological Characters Can Strongly Influence Early Animal Relationships Inferred from Phylogenomic Data Sets

There are considerable phylogenetic incongruencies between morphological and phylogenomic data for the deep evolution of animals. This has contributed to a heated debate over the earliest-branching lineage of the animal kingdom: the sister to all other Metazoa (SOM). Here, we use published phylogenomic data sets ($\sim $45,000–400,000 characters in size with $\sim $15–100 taxa) that focus on early metazoan phylogeny to evaluate the impact of incorporating morphological data sets ($\sim $15–275 characters). We additionally use small exemplar data sets to quantify how increased taxon sampling can help stabilize phylogenetic inferences. We apply a plethora of common methods, that is, likelihood models and their “equivalent” under parsimony: character weighting schemes. Our results are at odds with the typical view of phylogenomics, that is, that genomic-scale data sets will swamp out inferences from morphological data. Instead, weighting morphological data 2–10$\times $ in both likelihood and parsimony can in some cases “flip” which phylum is inferred to be the SOM. This typically results in the molecular hypothesis of Ctenophora as the SOM flipping to Porifera (or occasionally Placozoa). However, greater taxon sampling improves phylogenetic stability, with some of the larger molecular data sets ($>$200,000 characters and up to $\sim $100 taxa) showing node stability even with $\geqq100\times $ upweighting of morphological data. Accordingly, our analyses have three strong messages. 1) The assumption that genomic data will automatically “swamp out” morphological data is not always true for the SOM question. Morphological data have a strong influence in our analyses of combined data sets, even when outnumbered thousands of times by molecular data. Morphology therefore should not be counted out a priori. 2) We here quantify for the first time how the stability of the SOM node improves for several genomic data sets when the taxon sampling is increased. 3) The patterns of “flipping points” (i.e., the weighting of morphological data it takes to change the inferred SOM) carry information about the phylogenetic stability of matrices. The weighting space is an innovative way to assess comparability of data sets that could be developed into a new sensitivity analysis tool.

59 BASIC BIOLOGICAL SCIENCES↗

X-ray CT Scans—Set 5

This report includes a collection of x-ray computed tomography scans of specimens from the Museum of Southwestern Biology.

59 BASIC BIOLOGICAL SCIENCES↗

MRT 7365: Power flow physics and key physics phenomena

The Z accelerator at Sandia National Laboratories conducts z-pinch experiments at 26 MA in support of DOE missions in stockpile stewardship, dynamic materials, fusion, and other basic sciences. Increasing the current delivered to the z-pinch would extend our reach in each of these disciplines. To achieve increases in current and accelerator efficiency, a fraction of Z’s shots are set aside for research into transmission-line power flow. These shots, with supporting simulations and theory, are incorporated into this Advanced Diagnostics milestone report. The efficiency of Z is reduced as some portion of the total current is shunted across the transmission-line gaps prior to the load. This is referred to as “current loss”. Electrode plasmas have long been implicated in this process, so the bulk of dedicated power-flow experiments are designed to measure the plasma environment. The experimental analyses are enhanced by simulations conducted using realistic hardware and Z voltage pulses. In the same way that diagnostics are continually being improved for sensitivity and resolution, the modeling capability is continually being improved to provide faster and more realistic simulations. The specifics of the experimental hardware, diagnostics, simulations, and algorithm developments are provided in this report. The combined analysis of simulation and data confirms that electrode plasmas have the most detrimental impact on current delivery. Experiments over the last three years have tested the theoretical current-loss mechanisms of enhanced ion current, plasma gap closure, and Hall-related current. These mechanisms are not mutually exclusive and may be coincident in the final feed as well as in upstream transmission lines. The final-feed geometries tested here, however, observe lower-density plasmas without dominant ion currents which is consistent with a Hall-related current. The picture of plasma formation and transport formed from experiment and simulation is informing hardware designs being fielded on Z now and being proposed for the Next-Generation Pulsed Power (NGPP) facility. In this picture, the strong magnetic fields that heat the electrodes above particle emission thresholds also confine the charged particles near the surface. Some portion of the plasmas thus formed is transported into the transmission-line gap under the force of the electric field, with aid from plasma instabilities. The gap plasmas are then transported towards the load by a cross-field drift, where they accumulate and contribute to a likely Hall-related cross-gap current. The achievements in experimental execution, model validation, and physical analysis presented in this report set the stage for continued progress in power flow and load diagnostics on Z. The planned shot schedule for Z and Mykonos will provide data for extrapolation to higher current to ensure the predicted performance and efficiency of a NGPP facility.

43 PARTICLE ACCELERATORS↗

Carbon Dioxide Conversion to Nanomaterials: Methods, Applications, and Challenges

Anthropogenic carbon dioxide (CO 2 ) emission is one of the biggest global threats that we are confronted with in the 21st century. A lack of prompt action to mitigate the atmospheric CO 2 level could lead to global catastrophic events. As a result of the significance of the aforementioned threat, multiple nations have agreed to enact carbon capture, storage, utilization, and sequestration (CCUS) technologies at academic and industrial scales with the aim of lowering the atmospheric CO 2 level. Although there are many reviews on CCUS technologies, there is a lack of comprehensive review on CO 2 conversion to more economically valuable products, such as nanomaterials. Carbon dioxide capture and conversion into nanomaterials is an interesting research topic in many ways because it contributes to our fundamental knowledge of material conversion, provides alternative ways to reduce atmospheric pollution, and yields lucrative products, which has not been explored broadly. Aside from the positive outcomes, we have a moral obligation to rectify a global threat caused by anthropogenic emission. Herein, we present current methods of converting CO 2 into organic and inorganic nanomaterials with a focus on operating conditions and challenges as well as the potential of nanomaterials in specifically biomedical applications as opposed to extensively reviewed energy-related uses. Furthermore, our review emphasizes the toxicity issues related to using such nanomaterials in biological settings based on literature and other comparable studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Epstein-Barr Virus Epitope–Major Histocompatibility Complex Interaction Combined with Convergent Recombination Drives Selection of Diverse T Cell Receptor α and β Repertoires

Recognition modes of individual T cell receptors (TCRs) are well studied, but factors driving the selection of TCR repertoires from primary through persistent human virus infections are less well understood. Using deep sequencing, we demonstrate a high degree of diversity of Epstein-Barr virus (EBV)-specific clonotypes in acute infectious mononucleosis (AIM). Only 9% of unique clonotypes detected in AIM persisted into convalescence; the majority (91%) of unique clonotypes detected in AIM were not detected in convalescence and were seeming replaced by equally diverse “de novo” clonotypes. The persistent clonotypes had a greater probability of being generated than nonpersistent clonotypes due to convergence recombination of multiple nucleotide sequences to encode the same amino acid sequence, as well as the use of shorter complementarity-determining regions 3 (CDR3s) with fewer nucleotide additions (i.e., sequences closer to germ line). Moreover, the two most immunodominant HLA-A2-restricted EBV epitopes, BRLF1 109 and BMLF1 280 , show highly distinct antigen-specific public (i.e., shared between individuals) features. In fact, TCRα CDR3 motifs played a dominant role, while TCRβ played a minimal role, in the selection of TCR repertoire to an immunodominant EBV epitope, BRLF1. This contrasts with the majority of previously reported repertoires, which appear to be selected either on TCRβ CDR3 interactions with peptide/major histocompatibility complex (MHC) or in combination with TCRα CDR3. Understanding of how TCR-peptide-MHC complex interactions drive repertoire selection can be used to develop optimal strategies for vaccine design or generation of appropriate adoptive immunotherapies for viral infections in transplant settings or for cancer.

59 BASIC BIOLOGICAL SCIENCES↗

Nanostructures for Electrical Energy Storage (NEES) (2020 Final Technical Report)

Nanostructures for Electrical Energy Storage (NEES, www.efrc.umd.edu) was an Energy Frontier Research Center supported by the DOE Office of Science, Basic Energy Sciences, from 8/1/2009 to 7/31/2020. Led by the University of Maryland, NEES enjoyed extensive collaborations with its funded partners, including two DOE Laboratories and six universities. The NEES vision has been to reveal a set of scientific insights and design principles that can underpin a next-generation electrical energy storage approach, building on advances in nanoscale science and technology to achieve simultaneous high power and high energy over extended charge/discharge cycling. The vision is motivated by the recognition that scaling into the nano regime opens the door to new physical phenomena and that the tools enlisted in nanoscale research provide major new opportunities for the synthesis not only of materials at molecular scale but for structures at nano scale and above. NEES has translated this vision into its research program based on two observations. First, while the behavior of ions and electrons in electrolytes and in electrode materials is crucial to electrical energy storage (or more appropriately electrochemical energy storage), it is the transport of ion and electron charge between different structural components of a storage device that ultimately determine its performance. With it well recognized that the choice of electrode materials typically constrain ion transport kinetics as well as maximum ion concentration, the search for better electrode materials has been a primary driver of battery research. At the same time the synthesis of electrodes is typically based on aggregation of particles with varying size, shape, and orientation in the electrode. Together with the presence of additional materials to impart electrical conductivity and cohesion to the composite electrode, change in electrode materials is necessarily accompanied by structural changes at the nano/micro scale that are difficult to categorize and manage. From the beginning, NEES’ vision has been to create and study simpler, highly controlled spatial arrangements of known materials as battery components (electrodes, current collectors, and electrolyte) and to understand how design and structure above the molecular scale determines the energy storage performance available from known materials. Second, advances in nanoscience dramatically expanded the portfolio of synthesis methods, structural motifs, and new phenomena available for research. Some of these gave rapid access to new building blocks at the deep nanoscale (e.g., carbon nanotubes grown by self-assembly, nanoscale arrays formed by electrochemical self-alignment, monolayer films controlled by self-limiting reaction). Such advances served as the enabler for the NEES vision to be pursued experimentally through study of 3D structures created and controlled at the nano, micro, and meso scales. Here, we use meso as in the BES MESO Report, implying not only intermediate or varying length scales, but very much the way behavior is influenced by other factors including aggregation of nanocomponents at different densities and spatial configurations, statistical variations in the aggregates, hierarchical architectures in which they can be assembled, or local 3D configurations that result from the architectures. Over its life cycle, NEES has pursued two overarching goals: (1) to understand the scientific fundamentals of electrochemical storage from the nanoscale to the mesoscale; and (2) to create and learn from innovative, controlled, heterogeneous nanostructures, where such nanostructures can enable the first goal and serve as models for future paradigms in energy storage. Specific goals have included: Synthesize heterogeneous nanostructures comprised of multiple materials arranged in controlled fashion and characterize their behavior; Demonstrate and elucidate design principles for achieving simultaneous high power and high energy; Develop materials processes which enable precision control of thin layers and 3D structures; Investigate the impact of artificial interphases on electrode stability during ion insertion/deinsertion; Create dense arrays of nanostructures to understand how the architecture of these assemblies, along with nanostructure design, influences energy storage behavior at the mesoscale; Identify and understand the consequences of nanoconfinement and local inhomogeneities in 3D mesoscale arrays; Develop and apply computational models to stimulate, guide and interpret experiments.

25 ENERGY STORAGE↗

KENO-VI Primer: Performing Calculations using SCALE’s Criticality Safety Analysis Sequence (CSAS6) with Fulcrum

The SCALE code system developed at Oak Ridge National Laboratory is widely used and accepted around the world for criticality safety analysis. The well-known KENO-VI three-dimensional Monte Carlo criticality computer code is one of the primary criticality safety analysis tools in SCALE. The KENO-VI primer is designed to help a new user understand and use the SCALE/KENO-VI Monte Carlo code for nuclear criticality safety analysis. It assumes that the user has a college education in a technical field. There is no assumption of familiarity with Monte Carlo codes in general or with SCALE/KENO-VI in particular. The primer is designed to teach by example, with each example illustrating two or three features of SCALE/KENO-VI that are useful in criticality analysis. The primer is based on SCALE 6.2 and 6.3, which includes the Fulcrum graphical user interface. Each example uses Fulcrum to provide the framework for preparing input data and viewing output results. Starting with a Quickstart section, the primer gives an overview of the basic requirements for SCALE/KENO-VI input and allows the user to quickly run a simple criticality problem with SCALE/KENO-VI. Each following section begins with a list of basic objectives identifying the goal of the section and the individual SCALE/KENO-VI features covered in detail in the section’s sample problems. Upon completion of the primer, a new user should be comfortable using Fulcrum to set up criticality problems in SCALE/KENO-VI. The primer provides a starting point for the criticality safety analyst who uses SCALE/KENO-VI. Complete descriptions are provided in the SCALE/KENO-VI manual. Although the primer is self-contained, it is intended as a companion volume to the SCALE/KENO-VI training and documentation. The SCALE manual and training schedule are available at https://scale.ornl.gov. The primer provides specific examples of using SCALE/KENO-VI for criticality analysis; the SCALE/KENO-VI manual provides information on the use of SCALE/KENO-VI and all its modules. The primer also contains an appendix with sample input files. In addition, this primer, its errata, and sample inputs are also available at https://code.ornl.gov/scale/primers/kenovi/.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Aerosol Inlets for a Mid-Sized Uncrewed Aerial System (UAS)

The purpose of this technical report is to document the efforts to design and test two inlet systems for aerosol sampling suitable for deployment on a medium-sized fixed-wing Uncrewed Aerial System (UAS). This work, which was supported by the U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) user facility, was conducted at the Pacific Northwest National Laboratory (PNNL) for the ARM Aircraft Facility (AAF) starting in November 2017. The current work is a part of AAF efforts to instrument the ArcticShark (a mid-sized UAS owned and operated by the AAF) for atmospheric research and develop a scientific payload for deployment on a similar-sized UAS with minimal adaptation and integration. An aerosol inlet system is necessary to sample and transport ambient air sample to the scientific instrumentation with minimal distortions to the aerosols. Two isokinetic aerosol inlets were designed: the first is a simple passive system for a single instrument suitable to be installed in a wing pylon; the second is a system with active control designed to sample and distribute air among several heterogeneous instruments and to provide basic humidity control of the air sample so that the measured aerosol parameters should correspond to “dry” conditions (a common requirement). Both systems could be easily adapted for deployment on another platform and/or with a different set of instrumentation. Several conducted flight tests showed that the inlets’ performance met our design goals.

54 ENVIRONMENTAL SCIENCES↗

Aerosol Inlets for a Mid-Sized Uncrewed Aerial System (UAS)

The purpose of this technical report is to document the efforts to design and test two inlet systems for aerosol sampling suitable for deployment on a medium-sized fixed-wing Uncrewed Aerial System (UAS). This work, which was supported by the U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) user facility, was conducted at the Pacific Northwest National Laboratory (PNNL) for the ARM Aircraft Facility (AAF) starting in November 2017. The current work is a part of AAF efforts to instrument the ArcticShark (a mid-sized UAS owned and operated by the AAF) for atmospheric research and develop a scientific payload for deployment on a similar-sized UAS with minimal adaptation and integration. An aerosol inlet system is necessary to sample and transport ambient air sample to the scientific instrumentation with minimal distortions to the aerosols. Two isokinetic aerosol inlets were designed: the first is a simple passive system for a single instrument suitable to be installed in a wing pylon; the second is a system with active control designed to sample and distribute air among several heterogeneous instruments and to provide basic humidity control of the air sample so that the measured aerosol parameters should correspond to “dry” conditions (a common requirement). Both systems could be easily adapted for deployment on another platform and/or with a different set of instrumentation. Several conducted flight tests showed that the inlets’ performance met our design goals.

42 ENGINEERING↗

Graph-Directed Approach for Downselecting Toxins for Experimental Structure Determination

Conotoxins are short, cysteine-rich peptides of great interest as novel therapeutic leads and of great concern as lethal biological agents due to their high affinity and specificity for various receptors involved in neuromuscular transmission. Currently, of the approximately 6000 known conotoxin sequences, only about 3% have associated structural characterization, which leads to a bottleneck in rapid high-throughput screening (HTS) for identification of potential leads or threats. In this work, we combine a graph-based approach with homology modeling to expand the library of conotoxin structures and to identify those conotoxin sequences that are of the greatest value for experimental structural characterization. The latter would allow for the rapid expansion of the known structural space for generating high quality template-based models. Our approach generalizes to other evolutionarily-related, short, cysteine-rich venoms of interest. Overall, we present and validate an approach for venom structure modeling and experimental guidance and employ it to produce a 290%-larger library of approximate conotoxin structures for HTS. We also provide a set of ranked conotoxin sequences for experimental structure determination to further expand this library.

59 BASIC BIOLOGICAL SCIENCES↗

Semantic Property Graph for Scalable Knowledge Graph Analytics

Graphs are a natural and fundamental representation to describe entities, relationships, activities, and evolution of complex systems. Many domains such as communication, citation, procurement, biology, social media, and transportation can be modeled as a set of entities and their relationships. Resource Description Framework (RDF) and Labeled Property Graph (LPG) are two of the most used data models to encode information in a graph. Both models are similar in terms of using basic graph elements such as nodes and edges but differ in terms of the modeling approach, expressibility, serialization, and target applications. RDF is a flexible data exchange model for expressing information about entities but it tends to a have high memory footprint and inefficient storage, which does not make it a natural choice to perform scalable graph analytics. In contrast, LPG has gained traction as a reliable model to perform scalable graph analytic tasks such as sub-graph matching, network alignment, and real-time knowledge graph query. It provides efficient storage, fast traversal, and flexibility to model various real-world domains. At the same time, the LPG lacks the support of a formal knowledge representation such as an ontology to provide automated knowledge inference. We propose Semantic Property Graph (SPG) as a logical projection of reified RDF into the LPG model. SPG continues to use RDF ontology to define the type hierarchy of the projected graph and validate it against a given ontology. We present a framework to convert reified RDF graphs into SPG using two different computing environments. We also present cloud-based graph migration capabilities using Amazon Web Services.

Purohit, Sumit↗

FuncQEE CT Scans - Set 11

A collection of x-ray computed tomography scans of specimens from the Museum of Southwestern Biology.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Contaminant Investigation and Pre‐Processing Opportunities for Textile‐To‐Textile Recycling

Millions of metric tons of textiles are landfilled or incinerated each year in the United States, with less than 1% of textiles recycled into new clothing or fabrics. To counter this trend, a growing number of companies and researchers are exploring how a circular economy can be applied to support textile‐to‐textile recycling. A significant barrier they face comes down to quickly and efficiently extracting pure feedstock material from post‐consumer garments that feature a mix of natural and synthetic fibers. Textile recyclers prefer pure feedstocks, as working with mixed sources typically means lower throughput, higher risk of equipment failure, and diminished business margins. To facilitate a circular economy for textiles, methods, and technologies are needed that can efficiently separate out materials and contaminants from end‐of‐life textiles to increase the flow of pure feedstocks to recyclers. This paper summarizes findings from interviews with a cross section of textile recyclers and from a review of literature to define basic feedstock requirements. In addition to our qualitative research, we deconstruct a bale of post‐consumer textiles and analyze them using computer‐vision imaging, Fourier transform infrared spectroscopy (FTIR), and machine learning. The resulting data are used to set system‐level design inputs for an automated contaminant removal system to process post‐consumer clothing into appropriate feedstocks for recycling. To set the system's levels for automated real‐time near‐infrared analysis, we identify the minimum percentage of primary material that any single garment in a load of used clothing must contain for the average of the full output stream to meet the target purity levels of recyclers. Here, the envisioned automated system can also address undesirable trace materials that might contaminate the processed stream by using imaging cameras coupled with artificial intelligence to identify sections of clothing for de‐trimming. Proof‐of‐concept machine learning algorithms are evaluated to locate and identify trims or garment areas with hidden contaminant materials. Integrating these methods into automated textile cutting systems can provide a cost‐effective means for increasing feedstock purity from used clothing, which can advance circularity for textiles by helping recyclers to reach production volumes and quality targets that were not possible solely with manual dismantling operations.

Parsons, Ryan [Rochester Institute of Technology, ↗

First Principles Simulations of Electrified Interfaces in Electrochemistry

This chapter discusses some of the recent advances made in the first principles modeling of electrochemical catalysts. It also discusses the key development, namely the ability to explicitly treat the effects of surface electrification due to electrochemical processes and applied voltages in a computationally efficient manner. The chapter introduces the thermodynamics and statistical mechanics of electrified metal-solution interfaces. It then discusses the structure of the electrode-electrolyte interface and the effects of applied voltages, followed by an overview of the first-principles model and a motivating example. The chapter also provides a brief summary of classical thermodynamics and describes the basics of thermodynamic detour. It considers the thermodynamics of macroscopic systems and introduces several useful fundamental relations. Here, the chapter also considers a system to exist in a certain macrostate, which is a particular thermodynamic state specified by a set of fixed properties such as constant particle number, constant volume, and constant temperature.

36 MATERIALS SCIENCE↗