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At least 325 records · Page 18

Resistive Switching Memory Performance of Two-Dimensional Polyimide Covalent Organic Framework Films

Two-dimensional polyimide covalent organic framework (2D PI-NT COF) films were constructed on indium tin oxide-coated glass substrates to fabricate two-terminal sandwiched resistive memory devices. The 2D PI-NT COF films condensated from the reaction between 4,4',4"-triaminotriphenylamine and naphthalene-1,4,5,8-tetracarboxylic dianhydride under solvothermal conditions demonstrated high crystallinity, good orientation preference, tunable thickness, and low surface roughness. The well-aligned electron-donor (triphenylamine unit) and -acceptor (naphthalene diimide unit) arrays rendered the 2D PI-NT COF films a promising candidate for electronic applications. The memory devices based on 2D PI-NT COF films exhibited a typical write-once-read-many-time resistive switching behavior under an operating voltage of +2.30 V on the positive scan and -2.64 V on the negative scan. A high ON/OFF current ratio (>10 6 for the positive scan and 10 4 -10 6 for the negative scan) and long-term retention time indicated the high fidelity, low error, and high stability of the resistive memory devices. The memory behavior was attributed to an electric field-induced intramolecular charge transfer in an ordered donor-acceptor system, which provided the effective charge-transfer channels for injected charge carriers. Furthermore, this work represents the first example that explores the resistive memory properties of 2D PI-COF films, shedding light on the potential application of 2D COFs as information storage media.

2D covalent organic framework film↗

Grid Strength Analysis for Integrating 30 GW of Offshore Wind Generation by 2030 in the U.S. Eastern Interconnection: Preprint

Offshore wind is a key player in the transition to a decarbonized electric gird, and the United States has set ambitious goals of integrating 30 GW of offshore wind capacity by 2030 and 110 GW by 2050. To facilitate this integration, the National Renewable Energy Laboratory and the Pacific Northwest National Laboratory are conducting the Atlantic Offshore Wind Transmission Study to assess transmission solutions. To achieve the 110-GW target by 2050, meticulous planning for network expansion and resource allocation is essential; however, meeting the 2030 goals requires integrating offshore wind power with minimal system upgrades, thus necessitating a careful study of grid strength and stability. The study team developed the Grid Strength Analysis Tool (GSAT) to assess system strength under various operating conditions and contingencies, focusing on the proposed integration of 30 GW of offshore wind power by 2030. In this paper, we provide a summary of key features of the GSAT software and results of the grid strength analysis for integrating 30 GW of offshore wind generation by 2030 in the U.S. Eastern Interconnection.

Automated System-wide Strength Evaluation Tool (AS↗

Dynamics Informed Optimization for Resilient Energy Systems

Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the Western System Coordinating Council (WSCC) 9-bus test system using synthetic multi-device outage scenarios. Towards integrating our modeling framework with real threats and more realistic power systems, we explore applying hybrid dynamics to power systems. Our work is applied to basic RL circuits with the ultimate goal of using the methodology to model protective tripping schemes in the grid. Finally, we survey mitigation techniques for HEMP threats and describe a GIS application developed to create threat scenarios in a grid with geographic detail.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Grid Strength Analysis for Integrating 30 GW of Offshore Wind Generation by 2030 in the U.S. Eastern Interconnection

Offshore wind is a key player in the transition to a decarbonized electric gird, and the United States has set ambitious goals of integrating 30 GW of offshore wind capacity by 2030 and 110 GW by 2050. To facilitate this integration, the National Renewable Energy Laboratory and the Pacific Northwest National Laboratory are conducting the Atlantic Offshore Wind Transmission Study to assess transmission solutions. To achieve the 110-GW target by 2050, meticulous planning for network expansion and resource allocation is essential; however, meeting the 2030 goals requires integrating offshore wind power with minimal system upgrades, thus necessitating a careful study of grid strength and stability. The study team developed the Automated System-wide Strength Evaluation Tool (ASSET) to assess system strength under various operating conditions and contingencies, focusing on the proposed integration of 30 GW of offshore wind power by 2030. In this paper, we provide a summary of key features of the ASSET software and results of the grid strength analysis for integrating 30 GW of offshore wind generation by 2030 in the U.S. Eastern Interconnection.

Automated System-wide Strength Evaluation Tool (AS↗

Evaluating Grid Strength under Uncertain Renewable Generation

The increasing displacement of synchronous generators with renewable resources such as wind and solar via power electronic interfaces causes a reduction in short-circuit strength and weak grid issues. The variation and uncertainty of renewable energy increase challenges for identifying weak grid conditions. This paper proposes an efficient method to analyze the impact of uncertain renewable energy on grid strength. The proposed method uses the probabilistic collocation method (PCM) to approximate the results of grid strength assessment under uncertain renewable generation, in order to reduce computational burden without compromising result accuracy when compared with traditional Monte Carlo simulation (MCS). To improve the accuracy of the approximation results, the proposed method integrates the K-means clustering technique with PCM to select the approximation samples of input variables. The efficacy of the proposed method is demonstrated by comparison with MCS on the modified IEEE 9-bus system and modified IEEE 39-bus system with multiple renewable generators.

grid strength↗

Multi-Port Autonomous Reconfigurable Solar Power Plant

As the penetration level of power electronics increases and remote photovoltaic (PV) generation is integrated into the alternating current (ac) grid, the short-circuit ratio (SCR) at the point of interconnection of a hybrid PV–energy storage system (ESS) plant may be low. Additionally, the inertia of the alternating current (ac) grid may be low. The low SCRs and inertias can lead to reliability challenges in the power grid. These operating conditions require additional reinforcements, such as synchronous condensers, static var compensators, static synchronous compensators, and high-voltage direct current (HVdc) links/grids. HVdc links or grids may also provide the additional capability of connecting the plant to asynchronous grids and/or connecting asynchronous grids, among others. This scenario leads to discrete development of solar inverters, energy storage inverters, HVdc converters, and several transformers. Some of the problems associated with this discrete development and inverter-based generation include increased cost, lower reliability, and reduced efficiency associated with duplication of power electronics (PEs); competing controls of several individual discrete inverter-based generators due to the presence of multiple PEs, which leads to derating of the system; and transient stability problems arising from inverter-based generation, such as voltage/frequency events leading inverter shutdowns, voltage instability and control interactions in the formed weak grid, and harmonics caused by resonances of multiple inverters.

14 SOLAR ENERGY↗

Temperature-dependent dielectric function of tantalum nitride formed by atomic layer deposition for tunnel barriers in Josephson junctions

Here, we report the dielectric functions of insulating tantalum nitride (TaN) films deposited by atomic layer deposition (ALD) on 300 mm Si/SiO 2 substrates to evaluate their suitability as tunnel barriers in tantalum-based Josephson junctions (JJs) for superconducting quantum circuits. Temperature-dependent ellipsometric angles were measured for ALD TaN films with nominal thicknesses of 13 and 25 nm at an incidence angle of 70°, over photon energy ranges of 0.03–0.7 eV (80–300 K) and 0.5–6.5 eV (80–600 K). These data were used to develop a dispersion model for insulating ALD TaN that incorporates a Tauc–Lorentz oscillator with an optical bandgap of 1.5–1.8 eV to describe interband transitions. The extracted dielectric function shows insulating behavior (mid-infrared transparency) at all temperatures and for both film thicknesses tested. In particular, ALD TaN does not exhibit infrared absorption due to free carriers, even at elevated temperatures, consistent with the insulating behavior required for a JJ tunnel barrier. Results from transmission electron microscopy (including selected area electron diffraction) and x-ray diffraction are also discussed. Sputter depth-profile x-ray photoelectron spectroscopy shows an N/Ta ratio of ∼1.2 throughout the film. The lower bandgap, low roughness, and thermal stability of ALD TaN compared to AlO x suggest the possibility of fabricating JJs with thicker barriers while achieving critical current densities required for qubits, enabling improved thickness and composition control, reduced topography, and resistance to aging.

36 MATERIALS SCIENCE↗

A Semiconducting Two‐Dimensional Polymer as an Organic Electrochemical Transistor Active Layer

Abstract Organic electrochemical transistors (OECTs) are devices with broad potential in bioelectronic sensing, circuits, and neuromorphic hardware. Their unique properties arise from the use of organic mixed ionic/electronic conductors (OMIECs) as the active channel. Typical OMIECs are linear polymers, where defined and controlled microstructure/morphology, and reliable characterization of transport and charging can be elusive. Semiconducting two‐dimensional polymers (2DPs) present a new avenue in OMIEC materials development, enabling electronic transport along with precise control of well‐defined channels ideal for ion transport/intercalation. To this end, a recently reported 2DP, TIIP, is synthesized and patterned at 10 µm resolution as the channel of a transistor. The TIIP films demonstrate textured microstructure and show semiconducting properties with accessible oxidation states. Operating in an aqueous electrolyte, the 2DP‐OECT exhibits a device‐scale hole mobility of 0.05 cm 2 V –1 s –1 and a µ C * figure of merit of 1.75 F cm –1 V –1 s –1 . 2DP OMIECs thus offer new synthetic degrees of freedom to control OECT performance and may enable additional opportunities such as ion selectivity or improved stability through reduced morphological modulation during device operation.

2D-polymer↗

Recycling the Energy of Indoor Light: Highly Efficient Organic Photovoltaics via a Ternary Strategy

A ternary approach in organic photovoltaics (OPV) is simple and reliable to effectively tune the optical, electrical and morphological properties of the photoactive layer for high efficiency as well as long-term stability under 1 sun. However, there have been few papers reporting spectra and weak illumination compared to outdoor light. In this study, by using two compatible 16 structures, we demonstrate a simultaneous modulation of light absorption and molecular donor polymers (PM7 and PM7 D1) with slightly-different band gaps and similar chemical packing under ambient conditions, which resulted in efficient indoor OPVs exhibiting power conversion efficiency (PCE) over 20% under 1000 lux of warm white light-emitting diode (2900 K). From morphological analysis, we infer that PM7 serves to seed nucleation of PM7 D1 in the ternary blend, templating its crystallization and alignment along the PM7 backbone. Such templating effect leads to increased domain spacing and relative degree of crystallinity (rDoC) compared to those of each binary system. We further show that higher rDoC helps suppress both bimolecular and trap-assisted recombination of photogenerated charges in the ternary devices. As a result, the complementary absorption and synergistic molecular assembly of the two donor polymers enhance the short-circuit current density as to increase the average PCEs from 9.6 to 10.3% under 1 sun and from 18.7 to 20.0% under 1000 lux. We envision that our strategy of incorporating both a planar and a flexible donor polymer with similar chemical structures can be generally applicable to attain a high performance ternary OPV under both 1 sun and indoor light.

14 SOLAR ENERGY↗

Efficient and stable perovskite solar cells based on blade-coated CH 3 NH 3 PbI 3 thin films fabricated using “green” solvents under ambient conditions

Metal halide perovskites are considered the most promising candidates for solar cells of the decade due to their exceptional optical and electronic properties. The power conversion efficiency of metal halide perovskites, when incorporated as the active layer of solar cells, has become comparable to that observed for conventional silicon solar cells. However, the stability, scaleup, green solvent usage, and fabrication in ambient conditions of metal halide perovskites need to be solved for commercial applications. Here, in this work, we report the fabrication of blade-coated methylammonium lead iodide (MAPbI 3 ) perovskite thin films using methylamine and acetonitrile as “green” solvents under ambient conditions. Our perovskite films are initially prepared from low purity PbI2 (99%) and are blade-coated in dry air at relative humidity (RH) levels above 30%. A significant advantage of fabricating our perovskite thin films via blade-coating protocols is that there is a minimal amount of precursors (5 μL) used compared to spin-coating methods (50μL–60μL) for a 4 cm 2 substrate. With the addition of a small amount of an organic halide salt, namely, phenethylammonium chloride, the film crystallinity is improved and non-radiative recombination is suppressed, resulting in power conversion efficiencies over 20%. In addition, the device maintains more than 95% of its initial efficiency after 500 h under continuous light illumination of 1-sun at open circuit conditions, 50 °C and 60% RH. The above method leads a path towards the commercial fabrication of perovskite solar cells.

14 SOLAR ENERGY↗

Solid-state prealkylation of electrode architectures to tune solid electrolyte interphase composition

Efficient electrochemical cycling of certain Si anodes is limited by irreversible Li consumption to form and continually reform the solid electrolyte interface (SEI) due to Si expansion/contraction and fracture. Prelithiation can compensate for these losses; however, the starting open circuit potential (VOC) becomes highly reducing and, therefore, the electrolyte reduction chemistry that influences the SEI composition can change. Herein, we compare SEI formation for electrodes prelithiated using Solid State Prealkylation of Electrode Architectures (SPEAR) versus traditional electrochemically lithiated architectures (ECLAR), focusing on SEI compositional changes as a function of stoichiometry (0.28 ≤ x ≤ 1.38 in LixSi). Increasing SPEAR prelithiation decreased the initial VOC of Si anodes vs. Li/Li+ from ∼3 V (Li0.28Si) to < 0.5 V for Li1.38Si, enabling simultaneous competitive reduction of EC, EMC, and LiPF6 at low potentials. Ex situ7Li and 29Si cross-polarization NMR and XPS reveal that SPEAR drives thicker SEI formation with substantially increased P/F contributions and a predominantly inorganic insoluble SEI (71.4% inorganic for Li1.38Si), consistent with accelerated LiPF6-derived POx/LiPFx/LiF formation relative to ECLAR analogs which exhibit carbonate-rich organic SEI compositions. Symmetric-cell EIS further indicates SPEAR-specific impedance features consistent with pore reduction (filling) during LixSi formation. In full cells, SPEAR prelithiation increases the initial coulombic efficiency (ICE) and accelerates SEI formation and stabilization with Li1.38Si reaching 99.4% coulombic efficiency (CE) by cycle 2.

Musgrove, Amanda [ORNL] (ORCID:0009000220910389)↗

Solid Electrolyte Interphase Formation at the Ionic Liquid Electrolyte—Lithium-Metal Interface Using an Ab Initio Molecular Dynamics Approach

An interfacial study is performed using ab initio molecular dynamics (AIMD) simulations to elucidate the electrochemical interfacial stability of an ionic liquid (IL) as component of an electrolyte in contact with a Li-metal anode when an additive, vinylene carbonate (VC), is added to the electrolyte. The IL electrolyte is composed of 1-butyl-1-methylpyrrolidinium bis(fluoro-sulfonyl)-imide (PYR14 + FSI − ) with lithium bis(trifluoromethane-sulfonyl)imide salt (Li + TFSI − ) in a 8:2 concentration ratio. Reactions observed at the interface electrolyte/Li-metal during the AIMD simulations are verified by electronic structure calculations using density functional theory calculations considering a continuum solvent model. We found that the addition of VC to the IL prevents further reduction of the counter-ion TFSI − and retards reduction of FSI − in comparison to the case when the additive VC is absent. The PYR14 + reduction is never observed with or without the additive. The 1st, 2nd, and 3rd electron affinities of the PYR14 + are −0.08, −0.36 and −3.65 eV, indicating little to large repulsive behavior against electrons. The opposite is observed for the two negative ions, FSI − and TFSI − , which yield 1st electron affinities of 1.73 and 1.83 eV, respectively. Reactions obtained under open circuit conditions. Dissociation mechanisms are presented for all IL components reduced at the IL/Li-metal interface.

Electrochemistry↗

Challenges and Gaps in the Development of Pulsed Power for Fusion Applications: A Preroadmapping Perspective From Industry, Academia, and National Laboratory Experts

Fusion energy meets the twenty-first century World Grand Challenge of sustainable, ubiquitous, and safer energy sources. However, harnessing the promise of fusion energy has proven elusive. The competing approaches to fusion power plant design include inertial confinement fusion, National Ignition Facility (ICF-NIF, Z machine, etc.,) magnetic confinement fusion (MCF-Tokamak, stellarators, etc.), and other approaches that show promise in small- (flow stabilized Z pinches) or large-scale applications. These approaches are being accelerated with private and public funding and seek to demonstrate the feasibility of different approaches to fusion-based power plants. Yet, how can the necessary pulsed power technologies for these disruptive technology bases be accelerated with no clear “Dominant Design?” Roadmapping holds the promise to identify and develop common critical pulsed power components for laboratory, prototype, and commercial fusion, and can accelerate the commercialization of fusion reactor designs. A preroadmapping Workshop on Pulsed Power for Fusion was held at the IEEE International Pulsed Power Conference in San Antonio, TX, USA, in June 2023. The workshop had 177 attendees. Here, the common elements for many of the ICF technologies vying for dominant design were identified. The advancement of these technologies through roadmapping will enhance commercial expectations that require their rapid and innovative development in the next five years, as well as the next five to ten years. The key technologies identified that underpin and limit the advancement of fusion power include pulsed power technologies such as energy storage, high-voltage switching, additive manufacturing, and modular pulsed power circuit topologies. In conclusion, they are the focus of our effort in the following roadmap scenario, which will delineate potential paths to technology development.

Curry, Randy D. [I-Pulse Group, Albuquerque, NM (U↗

Design and performance of an in-vacuum, magnetic field mapping system for the Muon g-2 experiment

The Muon g - 2 experiment at Fermilab (E989) aims to measure the anomalous magnetic moment, a μ , of the muon with a precision of 140 parts-per-billion. This requires a precise measurement of both the anomalous spin precession frequency, ω α , of muons stored in a magnetic field of 1.45 T, and a precise measurement of that magnetic field in terms of the shielded proton Larmor frequency, ω' ρ . The measurement of ω' ρ with a total systematic uncertainty of 70 parts-perbillion involves a combination of various nuclear magnetic resonance (NMR) probes. There are 378 probes mounted in fixed locations that constantly monitor field drifts. A water-based, cylindrical calibration probe provides the calibration in terms of the shielded proton Larmor frequency. A crucial element for the multi-step measurement of ω' ρ is the regular mapping of the magnetic field over the muon storage region. The former experiment at Brookhaven National Laboratory (BNL) employed an in-vacuum field mapping system equipped with 17 NMR probes, which was developed by the University of Heidelberg. We have refurbished and upgraded this system with new probes and electronics. The upgrades include the addition of 16-bit, 1 MSPS digitization of the NMR signals, which replaced the hardware-implemented zero-crossing counting of the system at Brookhaven. The digitized signals offer new capabilities in the NMR frequency analysis and its related systematic uncertainties. To sustain the higher data rates, a new communication scheme with time-division multiplexing was implemented to separate the important NMR reference clock from the data communication in order to reach the specifications for the accuracy and stability of the reference clock. A new barcode reader provides more precise azimuthal position determination during the measurement and calibration. While the mechanical systems that move the field mapper inside the storage ring have been mostly refurbished from BNL, the motion control system was completely replaced with a custom-built electronics centered around a commercial Galil motion controller. Both the field mapping NMR system and its motion control were successfully commissioned at Fermilab and have been in reliable operation during the first three data taking periods of the experiment at Fermilab. Finally, this article will provide the details of the upgrades of the field mapper and its performance.

47 OTHER INSTRUMENTATION↗

Perovskite superlattices with efficient carrier dynamics

Compared with their three-dimensional (3D) counterparts, low-dimensional metal halide perovskites (2D and quasi-2D; B 2 A n-1 M n X 3n+1 , such as B = R-NH 3 + , A = HC(NH 2 ) 2 + , Cs + ; M = Pb 2+ , Sn 2+ ; X = Cl - , Br - , I - ) with periodic inorganic-organic structures have shown promising stability and hysteresis-free electrical performance. However, their unique multiple-quantum-well structure limits the device efficiencies because of the grain boundaries and randomly oriented quantum wells in polycrystals. In single crystals, the carrier transport through the thickness direction is hindered by the layered insulating organic spacers. Furthermore, the strong quantum confinement from the organic spacers limits the generation and transport of free carriers. Also, lead-free metal halide perovskites have been developed but their device performance is limited by their low crystallinity and structural instability 11 . Here, in this paper, we report a low-dimensional metal halide perovskite BA 2 MA n-1 Sn n I 3n+1 (BA, butylammonium; MA, methylammonium; n = 1, 3, 5) superlattice by chemical epitaxy. The inorganic slabs are aligned vertical to the substrate and interconnected in a criss-cross 2D network parallel to the substrate, leading to efficient carrier transport in three dimensions. A lattice-mismatched substrate compresses the organic spacers, which weakens the quantum confinement. The performance of a superlattice solar cell has been certified under the quasi-steady state, showing a stable 12.36% photoelectric conversion efficiency. Moreover, an intraband exciton relaxation process may have yielded an unusually high open-circuit voltage (V OC ).

36 MATERIALS SCIENCE↗

Investigation of flow regimes in arc plasma–gas interactions using a two-temperature arc in crossflow model

The perpendicular impingement of a gas stream on an electric arc, a configuration known as the arc in crossflow, is of primary relevance in the study of plasma-gas interactions, as well as in industrial applications such as circuit breakers and wire-arc spraying. The flow dynamics in the arc in crossflow are the result of coupled fluid-thermal-electromagnetic phenomena accompanied by large property gradients, which can produce significant deviations from Local Thermodynamic Equilibrium (LTE) among electrons and gas species. These characteristics can lead to the establishment of distinct flow regimes depending on the relative values of the controlling parameters of the system, such as inflow velocity, arc current, and inter-electrode spacing. A two-temperature non-LTE (NLTE) model is used to investigate the arc dynamics and the establishment of flow regimes in the arc in crossflow. The plasma flow model is implemented within a nonlinear Variational Multiscale (VMS) numerical discretization approach that is less dissipative, and hence better suited to capture unstable behavior, than traditional VMS methods commonly used in computational fluid dynamics simulations. The Reynolds and the Enthalpy dimensionless numbers, characterizing the relative flow strength and arc strength, respectively, are chosen as the controlling parameters of the system. Simulation results reveal the onset of dynamic behavior and the establishment of steady, periodic, quasi-periodic, and chaotic or potentially turbulent, regimes, as identified by distinct spatiotemporal fluctuations. The computational findings reveal the role of increasing the relative arc strength on enhancing flow stability by delaying the growth of fluctuating and unstable flow behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Stable electrospray signal on a microfabricated glass chip with three-dimensional open edge and tiered depth geometries

This paper presents the microfabrication and performance of a three-dimensional electrospray ionization (ESI) emitter tip made from glass, which achieves stable current signals important for chemical analysis. Our novel microfabrication process and custom-built signal conditioning hardware provides the advantage of providing accurate features and steady signals. The fabrication process relies on standard microfabrication techniques (i.e., deposition, photolithography, and wet etching). This fabrication method involves the novel application of two layers of positive and negative photoresists in addition to Parafilm® wax tape. Open edge and tiered depth details were successfully created from a multilayer planar mask. This is a benefit for integrated miniaturized and microfluidic systems that often require micro features for their functionality but relatively large millimeter size features for their physical periphery. We demonstrate the fundamental performance of electrospray with this microfluidic chip. The emitter tip was fixed on a linear axis stage with high resolution (10 μm) to finely control the tip distance from a metal counter electrode plate. Further, a custom printed circuit board system was built to safely control four voltages applied to the microchip ports from a single high voltage power supply. To readily form the electrospray, non-aqueous solvents were used for their low viscosity and a constant voltage of +2.7 kV was applied to the sheath electrospray microchannel. The liquid being sprayed was 80/20 (v/v) methanol/acetonitrile with 0.1% acetic acid in the sheath microchannel and with ammonium acetate (10–40 mM) in its remaining microchannels. The electrospray signal was measured in response to varying the distance (1.4 to 1.6mm) between the electrospray emitter tip and a metal counter electrode plate in addition to the varying concentration of the background electrolyte, ammonium acetate. Stable and repeatable electrospray signal showed linear relationships with emitter tip distance and concentration (r 2 ≥ 0.95).

42 ENGINEERING↗

Predicting the recovery and grade of a rougher flotation circuit from liberation data

A flotation model has been validated against the survey data obtained from a copper rougher flotation circuit with a circulating load. Here, the model was developed using the hydrophobic force as a kinetic parameter, which made it possible to use the contact angles of the free and composite particles as input parameters so that the model can predict both recoveries and grades. The model also recognizes the role of bubble coarsening in determining the froth phase recoveries and grades. The model predictions are in good agreement with the survey data. The size-by-size recovery curve as predicted from the model shows an optimum particle size range that is consistent with most of the operating data reported in the literature. The model suggests that the upper particle size limit may be determined by the instability of the froth phase rather than the turbulence in the pulp phase of a flotation cell.

36 MATERIALS SCIENCE↗