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At least 397 records · Page 22

Fast-ion confinement in LHD and W7-X (Final Technical Report)

This project was the PhD thesis project for Wataru Hayashi, who graduated in December 2025. In work performed prior to the award while Heidbrink was a Guest Professor at NIFS, we had established conditions for the study of fast-ion confinement in the Large Helical Device (LHD) with fast-ion D-alpha (FIDA) diagnostics. Subsequently, we proposed new sightlines that could augment the existing FIDA measurements with ones that were more sensitive to the highest energy ions. During the project period, the new sightlines were installed by the LHD team and showed the expected enhanced sensitivity to high-energy ions. Many LHD experiments were led by UCI scientists remotely during the pandemic and in-person afterward. One of these, which was led by one of Professor Zhihong Lin’s PhD students (Ethan Green) in collaboration with Hayashi and Heidbrink, resulted in a Nuclear Fusion article on the effect of radial electric fields on fast-ion confinement. The main output of the project, however, is two detailed experimental papers by Hayashi et al. The first of these is a study of neoclassical fast ion confinement in MHD-quiescent plasmas, a key issue in stellarator research. The second is an initial study of the effect of Alfven eigenmodes on fast-ion confinement. In addition to these studies, the project also helped partially support stellarator research with the GTC code by members of Prof. Lin’s group.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Role of Intra-Domain Heterogeneity on Ion and Polymer Dynamics in Block Polymer Electrolytes: An Approach for Spatially Resolving Dynamics and Ion Transport

The design of safe and high-performance, nanostructured, block polymer (BP) electrolytes for lithium-ion batteries requires a thorough understanding of the key parameters that govern local structure and dynamics. Yet, the interfaces between microphase separated domains can introduce complexities in this local behavior that can be challenging to quantify. Herein, the local polymer, cation (Li + ), and anion dynamics were described in salt-doped polystyrene block poly(oligo-oxyethylene methyl ether methacrylate) (PS-b-POEM) through a quantitative framework that considered the effects of polymer architecture, segmental mixing, chain stretching, and confinement on polymer mobility and ion transport. This framework was validated through nuclear magnetic resonance (NMR) spectroscopy measurements on solid (dry) polymer electrolyte samples. Notably, a mobility transition temperature (T mobility ) was identified through NMR spectroscopy that captured the local dynamics more accurately than the thermal glass transition temperature. Additionally, the approach quantitatively described the mobility gradient across a domain when segmental mixing effects were combined with chain stretching and confinement information, especially at higher segregation strengths – facilitating the assessment of local ion diffusion and conductivity. As a result, spatially averaged local ion diffusion predictions quantitatively matched NMR-measured ion diffusivities in the BP samples, while spatially summed ionic conductivity predictions across a domain qualitatively captured trends in the measured ionic conductivities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Particle-in-cell simulations of burning inertial confinement fusion capsule implosions

Anomalies observed in the neutron spectral shift of high-yield shots at the National Ignition Facility (NIF) suggest the presence of suprathermal ions [E. P. Hartouni et al., Nat. Phys. 19, 72 (2023)], implying that kinetic effects play a significant role in burning inertial confinement fusion (ICF) plasmas. Furthermore, recent measurements of reaction-in-flight (RIF) neutrons offer a direct probe of the stopping power in the burning fuel region of high-energy alpha particles and up-scattered fuel ions. We have developed the particle-in-cell code PICNIC, an exactly energy-conserving particle-in-cell Monte-Carlo collision (PIC-MCC) code to simulate the burn stage in ICF. We present results from 1D spherical simulations of NIF shot N210808, which was the first to exceed the Lawson criterion for laser fusion. We find that the suprathermal ions generated by large-angle Rutherford and nuclear elastic scattering (NES) with fusion alphas produce an alpha knock-on neutron (AKN) signal consistent with the extent and relative yield of the AKN spectrum identified in ignition experiments at the NIF. Furthermore, we also find that the inclusion of large-angle scattering physics does not explain the anomalously large spectral shift observed in the experiment.

High-energy-density plasmas↗

An experimental investigation on the CO 2 storage capacity of the composite confining system

Assuring secure containment of stored CO 2 is of paramount importance—for climate change mitigation, for permitting, and for reassuring the public. Regional seals, such as those sealing petroleum accumulations, have proven to be effective for securing CO 2 . However, the goal of permanent sequestration can also be satisfied with “composite confining systems” consisting of multiple, possibly discontinuous flow barriers that, in aggregate, create a system with very high permeability anisotropy and effectively retard the vertical migration of CO 2 . This study focuses on investigating the barrier characteristics necessary for effective containment of CO 2 , using both physical flow experiments and modified invasion percolation simulations. The simulations are calibrated to the physical experiments and are used to further extend the analysis. Results show that for a composite confining system, a) even barriers with low capillary entry pressure contrast to the underlying flow unit can divert rising CO 2 ; b) curved or anticlinal barrier topography can enhance CO 2 trapping; c) fining-upward gradations make little difference to barrier effectiveness or CO 2 retention; d) longer barriers retain more CO 2 regardless of barrier topography. Finally, field-scale simulations have demonstrated the importance of barrier length for increasing CO 2 storage capacity. Furthermore, the results presented can be used to inform the development of new screening criteria for characterization and effectiveness of composite confining systems.

58 GEOSCIENCES↗

Confinement of Lewis Acid–Base Sites by Microporous Silica Layers on Titania for Enhanced Alkanol Dehydration Reactivity

Alkanol dehydration offers a pathway to upgrade biomass-derived short-chain oxygenates into alkenes, essential chemical building blocks widely used in industrial applications. Transition metal oxides with Lewis acid-base site pairs are attractive catalysts due to their high reactivity and cost-effectiveness. This work demonstrates a synthetic pathway to manipulate local environments around active Lewis acid-base pairs in anatase TiO 2 to enhance their reactivity in alkanol dehydration. Microporous SiO 2 layers with an average pore diameter of ~0.6 nm and a controlled thickness of 0.8-33 nm are deposited on anatase TiO 2 powders by using a molecular templated SiO 2 deposition method. The Lewis acid-base strength of accessible Ti-O pairs remains unchanged, as shown by temperature-programmed surface reactions of surface-bound formic acid-derived species and temperature-programmed desorption of pyridine. However, measured alkanol dehydration rates on confined Ti-O pairs are much higher (by up to 7-fold) than those on TiO 2 . The extent of rate enhancements depends on the reactant size and functional group positioning, suggesting that the rate enhancements reflect the interactions between the guest molecules (reactants and transition states) and the surrounding SiO 2 micropore environments. By providing a detailed synthetic procedure to tailor the local environments around active sites in bulk oxides, this approach offers an additional avenue for enhancing catalytic performance.

09 BIOMASS FUELS↗

Energy gap of topological surface states in proximity to a magnetic insulator

Abstract Topological surface-states can acquire an energy gap when time-reversal symmetry is broken by interfacing with a magnetic insulator. This gap has yet to be measured. Such topological-magnetic insulator heterostructures can host a quantized anomalous Hall effect and can allow the control of the magnetic state of the insulator in a spintronic device. In this work, we observe the energy gap of topological surface-states in proximity to a magnetic insulator using magnetooptical Landau level spectroscopy. We measure Pb 1-x Sn x Se–EuSe heterostructures grown by molecular beam epitaxy exhibiting a record mobility and low Fermi energy. Through temperature dependent measurements and theoretical calculations, we show this gap is likely due to quantum confinement and conclude that the magnetic proximity effect is weak in this system. This weakness is disadvantageous for the realization of the quantum anomalous Hall effect, but favorable for spintronic devices which require the preservation of spin-momentum locking at the Fermi level.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simulation of a High-Confinement Tidal Energy Array (Abstract)

When the projected area of a current turbine array occupies a substantial fraction of a tidal or river channel cross-sectional area, the confinement associated with the channel boundaries substantially increases turbine efficiency. This effect can be exploited to substantially reduce the levelized cost of energy for current turbine arrays. However, the presence of such an array will affect inflow velocity, water depth, and circulation in the surrounding area. This has implications for array performance and environmental impacts. This project combines existing numerical modeling capability from PNNL with an understanding of confined array performance from UW. The work will 1) Simulate tidal currents and water surface elevation in a regional circulation model that includes the Knik Arm site at appropriate resolution; 2) Incorporate a varying thrust coefficient into this model that reflects the outcomes of tidal hydrodynamic simulations of confined turbine arrays; 3) Use the model to determine the effects of array operation on water levels and inflow conditions as a function of different blockage ratios and control strategies; and 4) Identify the “far field” environmental implications of operating an array of this type. UW will use the outputs from this model to evaluate the implications of “feedback effects” and variable inflow conditions on levelized cost of energy estimates for a confinement exploiting array of cross-flow turbines.

16 TIDAL AND WAVE POWER↗

Three-dimensional reconstruction of inertial confinement fusion hot-spot plasma from x-ray and nuclear diagnostics on OMEGA

Multidimensional effects degrade the neutron yield and the compressed areal density of laser-direct-drive inertial confinement fusion implosions of layered deuterium–tritium cryogenic targets on the OMEGA Laser System with respect to 1D radiation-hydrodynamic simulation predictions. A comprehensive physics-informed 3D reconstruction effort is under way to infer hot-spot and shell conditions at stagnation from four x-ray and seven neutron detectors distributed around the OMEGA target chamber. Neutron diagnostics, providing measurements of the neutron yield, hot-spot flow velocity, and apparent ion-temperature distribution, are used to infer the mode-1 perturbation at stagnation. The x-ray imagers record the shape of the hot-spot plasma to diagnose mode-1 and mode-2 perturbations. A deep-learning convolutional neural network trained on an extensive set of 3D radiation-hydrodynamic simulations is used to interpret the x-ray and nuclear measurements to infer the 3D profiles of the hot-spot plasma conditions and the amount of laser energy coupled to the hot-spot plasma. A 3D simulation database shows that larger mode-1 asymmetries are correlated with higher hot-spot flow velocities and reduced laser-energy coupling and neutron yield. Three-dimensional hot-spot reconstructions from x-ray measurements indicate that higher amounts of residual kinetic energy are correlated with higher measured hot-spot flow velocities, consistent with 3D simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Towards fully predictive gyrokinetic full- f simulations: validation and triangularity studies in TCV

Designing economical magnetic confinement fusion power plants motivates computational tools that can estimate plasma behavior from engineering parameters without direct reliance on experimental measurement of the plasma profiles. In this work, we present full-f global long-wavelength gyrokinetic simulations of edge and scrape-off layer turbulence in tokamaks that use only magnetic geometry, heating power, and particle inventory as inputs. Unlike many modeling approaches that employ free parameters fitted to experimental data, raising uncertainties when extrapolating to reactor scales. This approach directly simulates turbulence and resulting profiles through gyrokinetics without such empirical adjustments. This is achieved via an adaptive sourcing algorithm in Gkeyll that strictly controls energy injection and emulates particle sourcing due to neutral recycling. We show that the simulated kinetic profiles compare reasonably well with Thomson scattering and Langmuir probe data for Tokamak á Configuration Variable (TCV) discharge #65125, and that the simulations reproduce characteristic features such as blob transport and self-organized electric fields. Applying the same framework to study triangularity effects suggests mechanisms contributing to the improved confinement reported for negative triangularity (NT). Simulations of TCV discharges #65125 and #65130 indicate that NT increases the E x B flow shear (by about 20% in these cases), which correlates with reduced turbulent losses and a modest change in the distribution of power exhaust to the vessel wall. While the physical models contain approximations that can be refined in future work, the predictive capability demonstrated here, evolving multiple profile relaxation times with kinetic electron and ion models in hundreds of GPU hours, indicates the feasibility of using Gkeyll to support design studies of fusion devices.

Hoffmann, Antoine Cyril David [Princeton Plasma Ph↗

Anion Exchange Ionomers: Impact of Chemistry on Thin-Film Properties

Ionomer thin-films (i.e., 20–100 nm) on supports serve as model systems to understand ionomer-catalyst interfacial behavior as well as the confinement-driven deviation in properties from bulk membranes. While ionomer thin-films have been examined for proton exchange ionomers, the thin-film properties of anion exchange ionomers (AEIs) remain largely unexplored. More importantly, delineating the convoluted impact of chemistry and confinement on thin-film morphology and hydration is of interest to advancing the field on functional ionic interfaces. In this work, these aspects are studied by using AEIs of different backbones (perfluorinated, aliphatic, and aromatic) and side chains (various lengths, and single versus dual functional groups). Quartz-crystal microbalance and spectroscopic ellipsometry are used to analyze density and coupled with calculated free volume fraction of thin-films to provide insights on their gas transport properties. AEI side-chain's chemical character plays a key role in how confinement modulates hydration (in thin-film versus bulk). Overall, the results elucidate the effects of backbone, side-chain chemistry versus anion/cation type in the confinement-driven changes in thin-film morphology and swelling. This study also provides new insights for tuning AEI transport functionalities at interfaces via chemistry, which can benefit the design and development of electrode-ionomers for alkaline membrane-based energy systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of cross-beam energy transfer on target-offset asymmetry in direct-drive inertial confinement fusion implosions

The unintentional mispositioning of inertial confinement fusion (ICF) capsules from the center of laser beam convergence has long been shown in simulations to generate large ℓ = 1 asymmetry and significantly degrade implosion symmetry and fusion yields. Experimental yields on the OMEGA Laser System, however, have shown much less sensitivity to this initial target offset. This paper presents simulations of offset ICF implosions improved by including a physics model of cross-beam energy transfer (CBET), a mechanism of laser energy scattering from one beam to another. Room-temperature OMEGA implosion experiments with prescribed target offsets are simulated with and without CBET, illustrating that CBET mitigates the ℓ = 1 implosion asymmetry from target offset. Here, comparison of simulations to multiple complementary experimental observables indicates the addition of CBET physics in offset simulations is necessary to match experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of cross-beam energy transfer on target-offset asymmetry in direct-drive inertial confinement fusion implosions

The unintentional mispositioning of inertial confinement fusion (ICF) capsules from the center of laser beam convergence has long been shown in simulations to generate large ℓ = 1 asymmetry and significantly degrade implosion symmetry and fusion yields. Experimental yields on the OMEGA Laser System, however, have shown much less sensitivity to this initial target offset. This paper presents simulations of offset ICF implosions improved by including a physics model of cross-beam energy transfer (CBET), a mechanism of laser energy scattering from one beam to another. Room-temperature OMEGA implosion experiments with prescribed target offsets are simulated with and without CBET, illustrating that CBET mitigates the ℓ = 1 implosion asymmetry from target offset. Comparison of simulations to multiple complementary experimental observables indicates the addition of CBET physics in offset simulations is necessary to match experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Role of sheared E × B flow in self-organized, improved confinement states in magnetized plasmas

A great scientific success story of magnetic fusion research in the past several decades is the theoretical development and experimental testing of the process of turbulence decorrelation and stabilization by sheared E×B flow which shows that E×B shear effects are ubiquitous in magnetized plasmas. This concept of turbulence decorrelation and stabilization has the universality needed to explain the H-mode edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines; the broader edge transport barrier seen in VHmode plasmas; and the core transport barriers formed in tokamaks. Similar effects are seen in linear devices. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to reduce transport when an additional source of free energy is applied to it. The transport decrease associated with E×B velocity shear is also of great practical benefit to fusion research, since it contributed to substantially increased fusion yield in all DT magnetic fusion experiments conducted to date. The fundamental physics involved in transport reduction is the effect of E×B shear on the growth, radial extent, and phase correlation of turbulent eddies in the plasma. The same basic transport reduction process can be operational in various portions of the plasma because there are a number of ways to change the radial electric field Er. An important secondary theme in this area is the synergistic effect of E×B velocity shear and magnetic shear. Although the E×B velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of E×B velocity shear and facilitate turbulence stabilization. Our present understanding in this area is the result of a multi-decade, intertwined effort in theory, modeling and diagnostic development combined with continuing experimental investigations. These experiments have clearly demonstrated that increased E×B shear causes reductions in turbulence and transport. Finally, the experimental findings are generally consistent with the basic theoretical models although considerable work remains to be done before we have a fully predictive theory of transport in magnetized plasmas including E×B shear effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Doppler effect in rotating systems and Mössbauer rotor experiments

We address once more the problem of the physical interpretation of the Mössbauer effect in a rotating system in the view of the recently discovered extra energy shift (EES) between emitted and absorbed resonant radiation, which emerges in addition to the usual second order Doppler shift for an orbiting absorber. We highlight that both fractional components of the total energy shift have the same sign and correspond to the blueshift of the resonant radiation propagating from the rotational axis to the rotor rim. We indicate a possible way of understanding the origin of the EES in terms of combining metric effects in rotating systems with the quantum mechanical description of resonant nuclei confined in crystal cells by taking into account the recoil-free essence of the Mössbauer effect, where no energy is transmitted to the source (absorber) during the emission (absorption) of resonant radiation.

36 MATERIALS SCIENCE↗

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Polarity-dependence of the nonlinear dielectric response in interfacial water

Molecular dynamics simulations are used to study the nonlinear dielectric responses of a confined aqueous film in a planar nanopore under perpendicular electric fields at varied voltages between confining graphene sheets. Dielectric saturation reminiscent of the bulk phase behavior is prevalent at very strong fields, whereas we observe a nonmonotonic permittivity dependence on the electric field at intermediate strengths where field-alignment and spontaneous polarization of interfacial water are of comparable magnitude. The coupling between the two effects results in distinct dielectric responses at opposite confinement walls. The normal component of both the differential dielectric constant and dielectric difference constant tensors averaged over the region closer to the wall under an incoming electric field (field pointing from the liquid to the solid phase) initially increases with the strength of the imposed field. The differential permittivity peaks at a field strength previously shown to offset the surface-induced orientation bias of hydration molecules at this wall. Further strengthening of the field results in a conventional saturation behavior. At the opposite wall (subject to outgoing field) and in the central region of the water slab, the nonlinear dielectric response resembles bulklike saturation. The conditions at the permittivity extremum coincide with the window of accelerated reorientation rates of interfacial water molecules under an incoming field we uncovered in earlier molecular dynamics analyses.

Chemistry↗

Nucleation and Growth of Blue Phase 3D Cubic Structure Under Continuously Changing Curved Boundary Conditions

The blue phase of liquid crystals (BPLCs) with a cubic lattice of disclination lines and 3D nanostructure enables the modulation of photonic bandgap thus casting them in the category of photonic crystals. Its unique nature promises applications in display technologies, electro‐optics, and sensors. To integrate these ordered materials into wearable devices a fundamental understanding of curvature, and spatial confinement is necessary. Although continuous confinement in flat geometries have been studied, confining curvature has shown to induce strong destabilization effects on the cubic structure and formation of topological defects, thereby deteriorating their optical performance. Moreover, limitations in controlling the curvature of droplets further hinder studies of nucleation and growth of BPLCs. Here, to address these challenges, micro‐scale patterned surfaces of concentric cylinders are exploited to systematically control curvatures. The impact of curvature on the confined BPLCs is revealed in terms of phase transition temperature, nucleation and growth, morphology, as well as phase transformation. This research offers valuable insights into the stability, and structural characteristics of BPLCs in adaptive photonic devices, paving the way for future advancements in flexible displays, sensors, and other technologies leveraging liquid crystal (LC) materials.

3D Cubic Structure↗

Probing the meta-stability of oxide core/shell nanoparticle systems at atomic resolution

Hybrid nanoparticles allow exploiting the interplay of confinement, proximity between different materials and interfacial effects. However, to harness their properties an in-depth understanding of their (meta)stability and interfacial characteristics is crucial. This is especially the case of nanosystems based on functional oxides working under reducing conditions, which may severely impact their properties. Here, the in-situ electron-induced selective reduction of Mn 3 O 4 to MnO is studied in magnetic Fe 3 O 4 /Mn 3 O 4 and Mn 3 O 4 /Fe 3 O 4 core/shell nanoparticles by means of high-resolution scanning transmission electron microscopy combined with electron energy-loss spectroscopy. Such in-situ transformation allows mimicking the actual processes in operando environments. A multi-stage image analysis using geometric phase analysis combined with particle image velocity enables direct monitoring of the relationship between structure, chemical composition and strain relaxation during the Mn 3 O 4 reduction. In the case of Fe 3 O 4 /Mn 3 O 4 core/shell the transformation occurs smoothly without the formation of defects. However, for the inverse Mn 3 O 4 /Fe 3 O 4 core/shell configuration the electron beam-induced transformation occurs in different stages that include redox reactions and void formation followed by strain field relaxation via formation of defects. This study highlights the relevance of understanding the local dynamics responsible for changes in the particle composition in order to control stability and, ultimately, macroscopic functionality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗