Epoxy Surface Research Articles

Influence of substrate temperature on plasma-enhanced chemical vapor deposition to improve the surface flashover performance of epoxy resin

Abstract Epoxy resin composites are widely used as insulating and supporting materials in high-voltage power systems due to their excellent mechanical and electrical properties. However, long-term operation under high-voltage direct current (HVDC) induces surface flashover. Plasma enhanced chemical vapor deposition (PECVD) has been shown to effectively improve the surface insulation properties of epoxy resin. However, the influence of substrate temperature on the film composition, stress, morphology, and surface flashover performance remains unclear. This study uses PECVD to treat epoxy resin, enhancing its surface flashover performance. Tetraethoxysilane (TEOS) is used as the precursor to deposit nano-scale SiOx films on the epoxy resin surface. The effects of different substrate temperatures on the surface flashover voltage, physicochemical properties, and mechanical properties of epoxy resin are characterized. The results show that the surface flashover voltage increases and then saturates with increasing substrate temperature, improving by 27.4% at 60°C compared to untreated samples. The surface roughness of epoxy resin decreases after plasma deposition, while highly oxidized silicon-containing functional groups are introduced. When the substrate temperature increases from 20°C to 60°C, the interfacial bonding strength improves by 25.9%. This study provides a simple, efficient, and controllable method to enhance the surface flashover performance of epoxy resin, promoting the application of this technology in engineering practice.

Mechanism exploration of ion-implanted epoxy on surface trap distribution: An approach to augment the vacuum flashover voltages

Abstract The augmentation of the epoxy (EP) resin surface to advance flashover performance has become a pivotal point of global interest. This research introduces a novel surface modification method and its mechanism for insulation materials. The research follows an electron cyclotron resonance ion implantation system to subject the surface of EP insulation to ion beams with diverse energies, i.e., 6, 10, 20, 40, 50, and 60 keV for a consistent time of 300 s at an angle of 90°. The experimental phase includes the DC flashover examination under negative polarity. Besides, the simulation phase includes the Monte Carlo model constructed using SRIM software to examine the range and distribution of bombarded ions in the targeted insulation. Results reveal that the flashover properties are affected by the surface potential, surface conductivity, trap distribution, water contact angle, and elemental composition. Likewise, based on the outcomes and theoretical point of view, it is revealed that the bombardment of energetic ions enhances the trap depth, assisting in a reduction in surface conductivity, confining the surface charge movements, and extensively suppressing the secondary electron emission yield. Also, the enhanced trap depth induces homo-charge formation near triple junctions. Synergistically, the factors contribute to high flashover voltages.

Improved Corona Resistance of Epoxy Resin for Gas‐Insulated Equipment in Nitrogen Gas by Direct Fluorination

Direct fluorination has demonstrated efficacy in modulating the surface electrical properties of epoxy insulators and preventing surface charge accumulation. Comparative corona treatments were conducted on both surface fluorinated (modified) epoxy samples and untreated (virgin/original) samples using a modified electrode setup in a nitrogen (N2) atmosphere. The purpose was to evaluate the resistance of the modified epoxy surface layer against corona discharge. The results of ATR‐IR analysis and SEM surface and cross‐sectional imaging indicate that corona treatment did not alter the chemical composition of the fluorinated sample or the thickness of the fluorinated layer. Based on assessments of potential decay and water contact angle measurements, the surface conductivity of the modified sample was decreased by corona treatment. The wettability of fluorinated sample remained unchanged after corona treatment, and no soluble degradation products were produced. Conversely, the surface conductivity of the virgin sample exhibited an increase following corona treatment, accompanied by the formation of soluble degradation products. These results confirm that direct fluorination improves the epoxy insulator's discharge resistance in N2 and provides technical support for enhancing the electrical performance of epoxy insulators in gas insulated equipment. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Comparative analysis of delamination resistance in CFRP laminates interleaved by thermoplastic nanoparticle: Evaluating toughening mechanisms in modes I and II

The study considers the delamination resistance of carbon/epoxy laminates modified with Thermoplastic Nanoparticles of Polysulfone (TNPs). A new electrospinning nanofiber technique was utilized to convert polysulfone polymer into nanoparticles and uniformly disperse them within the resin. Fracture toughness was evaluated under loading modes I and II. In mode I, the toughness (GIC) increased significantly from 170 to 328 J/m² with TNPs incorporation. However, mode II showed minimal change, with GIIC values of 955 J/m² for virgin and 950 J/m² for TNPs-modified specimens. Scanning Electron Microscopy (SEM) was employed to depict the influence of TNPs on damage characteristics and crack propagation patterns. In mode I, crack deviation enhanced toughness as TNPs bypassed the PSU, while in mode II, cracks propagated through TNPs, resulting in particle smearing on the epoxy surface. This highlights TNPs' potential to modify the fracture toughness in mode I loading, but their effect is constrained in mode II loading scenarios.

Sulfonated polybenzimidazole membrane with graphene oxide additive for 2,3-butanediol/water separation: A molecular simulation

Membrane separation for 2,3-butanediol (2,3-BDO) recovery from fermentation broth is highly valued for sustainable and renewable processes, but it requires efficient membrane materials. This work evaluates the sulfonated polybenzimidazole (sPBI) and its graphene oxide (GO) doped composite membrane for separating 2,3-BDO and water via atomistic simulations. Density functional theory calculations are applied to identify various forms of sPBI structures and quantify their binding interactions with 2,3-BDO and water. Classical molecular dynamic simulations are used to evaluate the structural changes, diffusivity, and selectivity of 2,3-BDO and water in different sPBI models, GO surfaces, and GO-doped sPBI composite models. Our results suggest that sPBI slightly increases the crystallinity of the membrane structures, enhances the adsorption strength for both 2,3-BDO and water, and improves the water/2,3-BDO selectivity by 2–3 times. The GO surfaces display a maximum selectivity at a surface coverage of 0.1–0.15 for both hydroxyl and epoxy surface groups. The addition of GO flakes to sPBI creates new interaction sites for 2,3-BDO and water at the interface of sPBI and GO, and the water/2,3-BDO selectivity of GO-doped sPBI models is further increased up to 3 times. This work illustrates how the integrated addition of sPBI and GO flakes offers a promising approach to selective separation of 2,3-BDO and water, providing theoretical guidance for polybenzimidazole-based membranes in the potential application of 2,3-BDO recovery.

Effect of diammonium hydrogen phosphate coated with silica on flame retardancy of epoxy resin.

Epoxy resin has become one of the most widely used polymers owing to their excellent comprehensive properties. However, the inherent inflammability of epoxy resin (EP) has seriously limited its application in a range of fields with high fire safety requirements. Herein, a novel shell-core hierarchy architecture (DAP@SiO2) was prepared, composed of diammonium hydrogen phosphate (DAP) and in situ grown silica, and its structure and morphology were characterized by electron microscopy and infrared spectroscopy. The results indicated that silica particles were uniformly coated onto the surface of DAP. The modified DAP was used to reinforce the epoxy resin. The thermal stability of the EP blends was studied with the use of thermogravimetric analysis. The diammonium phosphate in DAP@SiO2 flame retardant produces pyrolysis gases such as NH3 and N2 during decomposition, diluting the concentration of oxygen and flammable volatile products around the flame. Secondly, silica migrates to the surface of epoxy resin to form a shielding layer, forming compounds containing Si-O-Si and O-Si-C structures, which can be cross-linked with other condensed phase products, greatly improving the thermal stability of the carbon layer. Fire behavior was evaluated using the limiting oxygen index (LOI), vertical burning test, and the cone calorimetry, and the flame retardancy mode of action was explained. With 12% of DAP@SiO2 involved, the EP blend passes UL-94 V-0 level, and its limiting oxygen index (LOI) reaches 33.2%. The incorporation of DAP@SiO2 in an EP matrix showed a slight reduction in the heat release and smoke production. The flame retardant mode of the EP polymer shows that its flame retardant and smoke suppression characteristics are related to the interaction of flame retardants in the gas phase and condensed phase. The mechanical properties test results illustrated that the tensile strength, elastic modulus and impact strength of EP/3%DAP@SiO2 are improved compared with pure EP. This is due to the crosslinking reaction between a large number of amino groups on the surface of DAP@SiO2 and the epoxy group on the epoxy resin, which significantly enhances the interfacial compatibility between DAP@SiO2 and epoxy resin, making the combination of DAP@SiO2 and epoxy resin closer.

Durable microstructure-based superhydrophobic composite with photothermal performance for multifunctional application

Nowadays, multifunctional superhydrophobic coating has drawn widespread attention by virtue of its great water-repellent property, whereas the fragile mechanical and chemical durability of superhydrophobic coating greatly limits its practical application. Herein, a robust and multifunctional superhydrophobic composite coating (CFRE-SP@Fe3O4) with anti-corrosion, delay-icing and self-deicing performance is constructed via simple imprinting-demolding process on the carbon fiber reinforced epoxy resin (CFRE) surface and post-deposition modification with polydimethylsiloxane (PDMS) and epoxy resin modified Fe3O4 nanoparticles. The obtained CFRE-SP@Fe3O4 coating displays a superhydrophobic property with a WCA of 155° ± 1.2°. By virtue of the protection effect of the robust micro-grid structures for the inner superhydrophobic Fe3O4 nanoparticles (SP@Fe3O4), the CFRE-SP@Fe3O4 coating still maintains great superhydrophobicity after linear friction for 100 times. Additionally, compared with the carbon steel treated with CFRE, the impedance modulus at lowest frequency of CFRE-SP@Fe3O4 coating treated group further increase with a value of 107 Ω·cm2, confirming the excellent anti-corrosion performance. Owing to the air pocket captured by the micro-/nanostructure on the superhydrophobic surface, the icing time of the CFRE-SP@Fe3O4 surfaces extends from 60 s to 2130 s. Moreover, combined with the photothermal conversion performance of carbon fiber and Fe3O4 nanoparticles, the ice on the CFRE and CFRE-SP@Fe3O4 coatings surfaces begin to melt 137 s, displaying the excellent self-deicing performance.

Superhydrophobic Waterborne Epoxy Composite Coating with Good Mechanical Properties, Icing Resistance, Self-Cleaning Properties, and Corrosion Resistance.

Epoxy resins with higher corrosion resistance typically employ environmentally harmful organic solvents such as xylene, while the corrosion resistance of waterborne epoxy resins, which are relatively environmentally friendly, is not as good as that of oil-based epoxy resins. In this study, by coating the surface of waterborne epoxy resin with a superhydrophobic zinc oxide coating, the corrosion resistance of waterborne epoxy resin was enhanced. During the initial immersion, its impedance value can reach 1010 Ω·cm2. The superhydrophobic nature of the coating itself also ensures the surface's resistance to immersion, delaying the intrusion of corrosive media into the coating. Furthermore, this coating exhibits good mechanical properties, self-cleaning performance, anti-icing performance, and so on. The introduction of superhydrophobic surfaces greatly optimizes the performance of traditional waterborne epoxy resin coatings, opening up directions for the metal anticorrosion field of coatings. Meanwhile, during the EIS testing of the superhydrophobic coating, we observed the occurrence of negative impedance in the results. After studying, we speculated that this phenomenon might be related to the degree of wetting of the superhydrophobic coating. Based on this conjecture, we can evaluate the basic properties of the superhydrophobic coating through this phenomenon.

Surface degradation of epoxy resin exposed to corona discharge under bipolar square wave field: From phenomenon to the insights

The unavoidable corona discharge induced by distorted field is detrimental to the safety of power equipment, especially the equipment with high voltage magnitude and high frequency. In this paper, the degradation morphology, residual components, lifetime of endurance, partial discharge characteristics, and evolution of surface traps of epoxy insulation under bipolar square wave field is investigated. The results show that degraded zone exhibits as three layers with round pits and channel-like ravines on the surface of epoxy resin exposed to corona discharge. It is demonstrated that more oxygen element during corona discharge while more carbon element during breakdown appeared, and nano-Al2O3 fillers migrates to the discharged zone. The maximum temperature and number of emitted phonons increase with voltage amplitude and frequency in power law and exponential form, respectively, corresponding to the fitting function of endurance lifetime. The emitted light is concentrated on the near ultraviolet (UV) and infrared ray (IR) band, indicating the energy pooling and thermal effect of corona discharge, which interprets the distinct degradation behavior of samples under sinusoidal and bipolar square wave voltage. The effect of space charge and thermal conductivity should be considered simultaneously in the degradation of epoxy insulation under bipolar square wave field due to polarity reversal and high frequency, which is proved by the disparate behavior of EP/nano-Al2O3 composites resistance to corona discharge and the breakdown moment at falling edge of bipolar square wave voltage. This work may contribute to the advancement of resistance to corona discharge degradation in equipment with high power density, high voltage amplitude and high frequency.

Differences in the Modification Effect in the Depth Direction on the Surface of Epoxy Resin Irradiated with Vacuum Ultraviolet Light

Differences in the Modification Effect in the Depth Direction on the Surface of Epoxy Resin Irradiated with Vacuum Ultraviolet Light

Leaf on a Film: Mesoporous Silica-Based Epoxy Composites with Superhydrophobic Biomimetic Surface Structure as Anti-Corrosion and Anti-Biofilm Coatings.

In this study, a series of amine-modified mesoporous silica (AMS)-based epoxy composites with superhydrophobic biomimetic structure surface of Xanthosoma sagittifolium leaves (XSLs) were prepared and applied as anti-corrosion and anti-biofilm coatings. Initially, the AMS was synthesized by the base-catalyzed sol-gel reaction of tetraethoxysilane (TEOS) and triethoxysilane (APTES) through a non-surfactant templating route. Subsequently, a series of AMS-based epoxy composites were prepared by performing the ring-opening polymerization of DGEBA with T-403 in the presence of AMS spheres, followed by characterization through FTIR, TEM, and CA. Furthermore, a nano-casting technique with polydimethylsiloxane (PDMS) as the soft template was utilized to transfer the surface pattern of natural XSLs to AMS-based epoxy composites, leading to the formation of AMS-based epoxy composites with biomimetic structure. From a hydrophilic CA of 69°, the surface of non-biomimetic epoxy significantly increased to 152° upon introducing XSL surface structure to the AMS-based epoxy composites. Based on the standard electrochemical anti-corrosion and anti-biofilm measurements, the superhydrophobic BEAMS3 composite was found to exhibit a remarkable anti-corrosion efficiency of ~99% and antimicrobial efficacy of 82% as compared to that of hydrophilic epoxy coatings.

Enhancing Icephobic Coatings: Exploring the Potential of Dopamine-Modified Epoxy Resin Inspired by Mussel Catechol Groups.

A nature-inspired approach was employed through the development of dopamine-modified epoxy coating for anti-icing applications. The strong affinity of dopamine's catechol groups for hydrogen bonding with water molecules at the ice/coating interface was utilized to induce an aqueous quasi-liquid layer (QLL) on the surface of the icephobic coatings, thereby reducing their ice adhesion strength. Epoxy resin modification was studied by attenuated total reflectance infrared spectroscopy (ATR-FTIR) and nuclear magnetic resonance spectroscopy (NMR). The surface and mechanical properties of the prepared coatings were studied by different characterization techniques. Low-temperature ATR-FTIR was employed to study the presence of QLL on the coating's surface. Moreover, the freezing delay time and temperature of water droplets on the coatings were evaluated along with push-off and centrifuge ice adhesion strength to evaluate their icephobic properties. The surface of dopamine-modified epoxy coating presented enhanced hydrophilicity and QLL formation, addressed as the main reason for its remarkable icephobicity. The results demonstrated the potential of dopamine-modified epoxy resin as an effective binder for icephobic coatings, offering notable ice nucleation delay time (1316 s) and temperature (-19.7 °C), reduced ice adhesion strength (less than 40 kPa), and an ice adhesion reduction factor of 7.2 compared to the unmodified coating.

The improvement mechanism of styrene grafted nano-Al2O3 on the hydrophobicity of epoxy resin composites: Based on molecular dynamics and experimental research

In the environment with high humidity, water will penetrate into the epoxy resin, resulting in the deterioration of the electrical properties and the decreasing resistance for the heat and corrosion. This study aims to utilize styrene grafted Al2O3 to improve the wettability of the epoxy resin surface and reduce the infiltration of water molecules into the epoxy resin interior. Firstly, the effects of doping PS/Al2O3 on the internal structure of epoxy resin and the diffusion process of water molecules within it are analyzed through the method of molecular dynamics (MD). Subsequently, epoxy resin samples with mass fractions of 1%, 3%, and 5% are prepared, followed by testing for hydrophobicity, water absorption, and the quality of surface condensation under different temperature differentials. The results indicate that the PS/Al2O3 and epoxy resin exhibit a strong interaction, reducing the proportion of free volume fraction of epoxy resin, which lowers the diffusion rate of water molecules. To be specific, the nanoparticles capture water molecules by forming hydrogen bonds with them, limiting the displacement of water molecules and reducing the water absorption of the epoxy resin (maximum reduction of 87%). Moreover, the addition of PS/Al2O3 decreases the adhesion energy of the material surface to water molecules, increasing the static contact angle from 103.58 ° to 125.42 °. Additionally, the total weight of condensation droplets on the material surface is reduced (maximum reduction of 26.02%). These findings serve as a reference for modifying epoxy resin materials in hygrothermal environments.

Temperature-Controlled Molecular Bonding Hysteresis: Interphase Dynamics of a Nanoparticle-Modified Polymer Network.

This study demonstrates the existence of temperature-induced molecular bonding hysteresis at nanoparticle-polymer interfaces in a highly cross-linked epoxy-based polymer, modified with core-shell rubber nanoparticles. This thermally induced bond hysteresis manifests itself in a hysteresis-like change of the strength of the electrical bond polarization between epoxy molecules and surface molecules of the core-shell nanoparticles. This kind of dynamic bond behavior can be controllably switched from one bond state to the other by a sufficient temperature change. The related optical remanence is evidenced by a refractive index hysteresis independent of the temperature change using the new experimental technique of temperature-modulated optical refractometry (TMOR). From the investigation of quasi-static and dynamic thermal expansion separately, TMOR allows for the conclusion that the observed hysteresis is caused by the specific refractivity and not the dipole number density.

Solid-like slippery surface for anti-icing and efficient fog collection

Ice accumulation on the surface of aerospace and transportation equipment under extreme weather seriously endangers the safety and efficiency of equipment operation. In recent years, metal corrosion, especially in the marine engineering industry, has become a global concern. The slippery liquid infused porous surface (SLIPS) is a new bionic surface which has caused extensive research in recent years, and has great potential in anti-corrosion and anti-icing. In this study, a multifunctional solid-like lubricated slippery surface (SL-SLIPS) was developed by superhydrophobic modification of the base of copper hydroxide nanoneedles and injection of solid-like lubricant synthesized by embedding oil-stored mesoporous silica nanoparticles on the surface of epoxy resin. At −30 °C, the delayed icing time on the surface of the SL-SLIPS sample was 22.6 times that of the original copper substrate. The ice adhesion was tested on the surface of the sample, and the results showed that the adhesion of the icicle on the SL-SLIPS surface was the smallest, which decreased by 89% compared with the original copper substrate. In addition, SL-SLIPS have excellent corrosion resistance and rapid droplet trapping, nucleation and drop. It has good practical application prospects in corrosion resistance of marine equipment and icing resistance of aerospace and transportation equipment. This study provides new ideas for the design of new slippery surfaces and their application in practical fields, such as anti-corrosion of offshore equipment, anti-icing of equipment in aviation and fog collection engineering in industry.

Investigation on surface metallization of epoxy resin and its electromagnetic interference shielding performance

In this study, aluminum and aluminum/nickel metal layers with varying thicknesses were deposited on the surface of epoxy resin using electron beam evaporation technology. The research aimed to explore and compare the impact of the thickness and material of the metal layer on electromagnetic interference shielding efficiency. The study revealed that the metal layer on the pre-treated surface of the epoxy resin displays a more complete morphology with uniform coverage and a distinctive stratification in the aluminum/nickel (Al/Ni) metal layer. The application of aluminum and aluminum/nickel metal layers onto the surface of epoxy resin demonstrates effective electromagnetic interference shielding. The investigation reveals that electromagnetic interference shielding efficiency escalates with the thickness of the metal layer within the test frequency range of 4 GHz to 15 GHz. Notably, it attains 70 dB when the aluminum/nickel metal layer achieves a thickness of 1 μm. These findings signify that the aluminum/nickel metal layer displays outstanding electromagnetic interference shielding performance, making it suitable for widespread application in the domain of electromagnetic interference shielding for polymer composites.

Surface modification strategies of 304 austenitic stainless steel plate with different micromorphology and composition for improved mechanical interlocking and chemical bonding in metal–epoxy joints

304 austenitic stainless-steel (SS) strip-based carbon fiber metal laminates (CFMLs) have raised significant concerns, in terms of their mechanical performance. On top of that, the hybrid laminates’ interlamination performance is vital in regulating their failure patterns. Along these lines, in this work, SS strips with regulatable micromorphology and composition were obtained by using physical and chemical surface modification strategies, including polishing, acid etching, anodization, and thermal treatment. The shear strength of the treated-SS/epoxy single lap joints (two treated-SS strips bonded by the epoxy resin via hot curing process) was systematically explored, and the origins of the enhancement mechanism were attributed to the resulting surface microstructure, as well as the possible chemical reactions between the treated surface and the curing agent. The etching-anodizing-thermally treated-SS (EAT-SS)/epoxy joint exhibited the maximum shear strength (16.04 MPa) and work of fracture (5.85 kJ·m−2) due to the substantial cohesive failure pattern of the epoxy. The encouraging enhancement was mainly attributed to the synergistic effect of the micro-annular pit and the nanoporous array structure of the EAT-SS surface. These effects induced a significant mechanical interlock and a plausible chemical reaction at the interface, which led to improved bonding strength between the epoxy and treated-SS surface. Overall, in this work, it was demonstrated that the combination of the anodization and thermal treatment can effectively improve the interlamination bonding properties between the SS strip and the epoxy resin due to the combination effect of mechanical interlocking and chemical bonding.

Solid Product Analysis on the Epoxy Resin Surface After Flashovers in C4F7N-Based Gas Mixtures Under Negative DC Voltage

Solid Product Analysis on the Epoxy Resin Surface After Flashovers in C₄F₇N-Based Gas Mixtures Under Negative DC Voltage

Comparative study between micro- and nano-carbon with epoxy for gamma shielding applications

In the current study, the epoxy material was mixed with 10%, and 30% weight percent carbon material as filler in different thicknesses (1 cm, 1.5 cm, and 2 cm). Transmission electron microscope (TEM) measurements showed the average size of the nano-carbon was 20 nm with a standard deviation of 5 nm. The morphology of samples was examined using scanning electron microscopy (SEM), which showed the flatness of the epoxy surface, and when the content of carbon increases, the connection between the epoxy array and carbon increases. The compression test indicates the effect of nano-size on enhancing the mechanical properties of the studied samples. To survey the shielding properties of the epoxy/carbon composites using gamma-rays emitted from Am-241, Ba-133, Cs-137, Co-60, and Eu-152 sources, which covered a wide range of energies from 0.059 up to 1.408 MeV, the gamma intensity was measured using the NaI (Tl) detector. The linear and mass attenuation coefficients were calculated by obtaining the area under each peak of the energy spectrum observed from Genie 2000 software in the presence and absence of the sample. The experimental results obtained were compared theoretically with XCOM software. The comparison examined the validity of experimental results where the relative division rate ranged between 0.02 and 2%. Also, the measurement of the relative division rate between linear attenuation coefficients of micro- and nano-composites was found to range from 0.9 to 21% The other shielding parameters are calculated at the same range of energy, such as a half-value layer (HVL), mean free path (MFP), tenth-value layer (TVL), effective atomic number (Zeff), and the buildup factors (EBF and EABF). The data revealed a consistent reduction in the particle size of the shielding material across various weight percentages, resulting in enhanced radiation shielding capabilities. The sample that contains 30% nano-carbon has the lowest values of TVL (29.4 cm) and HVL (8.85 cm); moreover, it has the highest value of the linear attenuation coefficient (LAC), which makes it the best in its ability to attenuate radiation.

Extending Copper Interconnects and Epoxy Dielectrics to Multi-GHz Frequencies.

Future multichip packages require Die-to-Die (D2D) interconnects operating at frequencies above 10 GHz; however, the extension of copper interconnects and epoxy dielectrics presents a trade-off between performance and reliability. This paper explores insertion losses and adhesion as a function of interface roughness at frequencies up to 18 GHz. We probe epoxy surface chemistry as a function of curing time and use wet etching to modulate surface roughness. The morphology is quantified by atomic force microscopy (AFM) and two-dimensional fast Fourier transform (2D FFT). Peel test and vector network analysis are used to examine the impacts of both type and level of roughness. The trade-offs between power efficiency and reliability are presented and discussed.