Corrosion and wear behavior of alumina‐polyester nanocomposite coatings

The corrosion and wear behavior of powder coatings fabricated by the electrostatic method was investigated in this study. Pure polyester coating and fabricated nanocomposite powder coating with 10 and 20 mass.% alumina nanoparticles were coated with electrostatic spraying method on the surfaces of carbon steel substrate. Coatings were cured in two regimes by oven and microwave for the appropriate time. The effects of alumina nanoparticles on the corrosion resistance of coated samples were studied by immersion and electrochemical impedance spectroscopy (EIS) tests. Also, pin‐on‐disk test was applied to evaluate the wear properties and coefficient of friction (COF) of the coatings. The results of the corrosion test reveal that the samples with 10 mass.% alumina show the best corrosion resistance and cause a reduction in corrosion rates which is about 36 times to that of the pure sample. The wear rate of nanocomposite coatings is 10 times lower than that of pure ones and also the coefficient of friction of nanocomposite samples is almost half of the pure samples. Furthermore, the nanocomposite coatings cured in the microwave show better protection properties and wear resistance than that of ones cured in an oven. POLYM. ENG. SCI., 57:846–856, 2017. © 2016 Society of Plastics Engineers     

SiAlON nanoparticles effect on the corrosion and chemical resistance of epoxy coating

Effect of incorporating SiAlON nanoparticles at different loading levels (0?C12?wt%) on chemical resistance of epoxy coating was investigated by immersion in basic (Na₂CO₃, pH?=?11) and salty (NaCl 3.5?wt%) (environments at 85?°C for 60?days. Epoxy resin chemical resistant coating grade based on bisphenol A was used with polyamine hardener as a curing agent. In these testes, surface morphology changes of the samples were studied and compared owing to initiation and propagation of cracks. Results indicate an enhancement in the epoxy nanocomposite chemical resistance due to the addition of small fraction of SiAlON nanoparticles. Samples containing 3 and 5?wt% of SiAlON nanopowders were considered as optimum samples compared to all the other samples, because they showed more resistances to initiation and propagation of cracks and lower permeability in chemical environment in comparison with neat resin and other samples. Also, epoxy coatings containing SiAlON nanoparticles were successfully coated on steel substrates and corrosion electrochemical behavior of these nanocomposite coatings were characterized by electrochemical impedance spectroscopy (EIS). The electrochemical monitoring of the coated steel over 35?days of immersion in 3.5?wt% NaCl solution at room temperature suggested the positive role of nanoparticles in improving the corrosion resistance of the coated steel.     

SiAlON nanoparticles effect on the behaviour of epoxy coating

In this work, the influence of SiAlON nanoparticles loading level (0?C12?wt%) was investigated on the mechanical and chemical properties of epoxy resin-based nanocomposites coatings. The samples were characterized by fracture toughness, chemical, pull off, hardness and abrasion tests, followed by scanning electron microscopy of the fracture surfaces and sample surface after performing a chemical test. Nanoparticles were also characterized by transmission electron microscopy and linear light scattering analysis techniques. Epoxy resin coating based on bisphenol A was treated with polyamine hardener as a curing agent. Fracture toughness measurements were carried out using a single edge notched bend specimens within a three-point bending test at room temperature. Effect of SiAlON nanoparticles on the chemical resistance of epoxy resin was investigated by immersion of samples in 3.5?wt% NaCl solution at 85?°C for 60?days. Results indicated the enhancements in the mechanical properties and chemical resistance of epoxy nanocomposite due to the addition of small parts of SiAlON nanoparticles. The contents of samples with 3 and 5?wt% of SiAlON nanopowders have been considered as optimum contents compared to the other samples. They showed improvement in the crack propagation resistance in chemical solution and fracture toughness tests, both. Enhancment in abrasion resistance was found at either of 3 and 5?wt% SiAlON epoxy nanocomposite samples where they showed 59 and 34% abrasion resistance more than that of the neat resin, respectively.     

Submicrometer characterization of surfaces of epoxy‐based organic–inorganic nanocomposite coatings. A comparison of AFM study with currently used testing techniques

Surface properties (morphology, hardness) of transparent colorless epoxy‐based organic–inorganic nanocomposite coatings were investigated by atomic force microscopy, optical and scanning electron microscopy, nanoindentation, and the Persoz pendulum test. Friction and wear coefficients were obtained from tribological experiments. The influence of mechanical properties and the size, shape, and concentration of additives (colloidal silica particles and montmorillonite sheets) on the measured surface characteristics are discussed. It was found that the highest surface hardness (assigned by nanoindentation, pendulum test or expressed as the scratch resistance) exhibited materials with the glass‐transition temperature close to 20°C. Microcopy techniques revealed that surface morphology is influenced by both types of admixtures: on the nanometer scale by colloidal silica particles and on micrometer scale by montmorillonite platelets. Already 1 wt % of montmorillonite increased friction coefficients and wear resistance without distinctive changes of tensile properties. However, the addition of ? 20 wt. % of silica nanoparticles was necessary for the increase of wear and scratch resistances. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102:5763–5774, 2006     

Performance of corrosion protective epoxy blend-based nanocomposite coatings: a review

ABSTRACT

Epoxy is a thermosetting polymer with exceptional mechanical robustness, thermal stability, and chemical resistance. This article is devoted to updating development, processing, and physicochemical characterizations of epoxy-based anti-corrosion coatings. Incorporation of different polymers in epoxy matrix has motivated extensive research progress in the field of corrosion protection. Epoxy has been blended with polyaniline, polypyrrole, polythiophene, polyamide, polyester, polyurethane, poly(vinyl alcohol), and polydimethylsiloxane to form corrosion protective coatings. The addition of conducting polymer and nanofiller to epoxy matrix modified the nanocomposite morphology and facilitated the development of passive layer at metal/polymer interface. Consequently, nanocomposite coatings act as physical barrier to hinder the penetration of corrosive ions. Likewise, fine dispersion of nanocarbon and inorganic nanoparticles in compatible blends of epoxy/polyamide, epoxy/polyester, epoxy/polyurethane, and epoxy/poly(vinyl alcohol) has resulted in improved adhesion, wear, barrier and anticorrosion properties of the nanocomposite coatings. Design of epoxy blend-based nano-architectures may facilitate appropriate tailoring of overall performance of the resulting anti-corrosion coatings for advance technical applications including aerospace, automotive, construction, electronic devices, and biomedical relevances. New processing techniques may overcome challenges toward high performance future epoxy-based coatings.     

Tribological properties of YSZ and YSZ/Ni-YSZ nanocomposite coatings prepared by electron beam physical vapour deposition

Metal-ceramic nanocomposite coatings have been applied to many industrial applications owing to their remarkable properties such as wear, corrosion and high temperature oxidation resistance than that of metals and alloys in high temperature environments. In this study, YSZ and Ni-YSZ nanocomposite coatings deposited by electron beam physical vapour deposition (EBPVD) for high temperature environments have been investigated. Initially friction and wear behaviour of YSZ coatings deposited at various substrate temperature were studied. Then the effect on wear response of Ni-YSZ nanocomposites with different Ni content were investigated using a ball-on-disc micro tribometer. The structural and tribochemical changes that occurred in the wear tracks of YSZ and Ni-YSZ coatings were investigated using field emission scanning electron microscopy and Raman spectroscopy. The results obtained on sliding wear and friction behaviour of these nanocomposite coatings suggest that 50 wt.% of Ni in YSZ nanocomposite provides good wear resistance behaviour than that of other coatings. Such an improvement in tribomechanical and wear performance of the nanocomposite coating could be attributed to the optimum amount of Ni which promotes the formation of NiO from Ni due to the frictional heat between nanocomposite coating and the sliding counter body in wear track as confirmed by Raman analysis.     

Development of poly(vinylcarbazole)/alumina nanocomposite coatings for corrosion protection of 316L stainless steel in 3.5% NaCl medium

Poly(vinylcarbazole) (PVK) and PVK‐alumina (Al₂O₃) nanocomposite coatings were electrochemically coated on 316 L stainless steel (SS) substrates for corrosion protection of 316 L SS in 3.5 weight (wt) % NaCl medium. The formation of PVK and incorporation of nanoalumina particles in PVK‐Al₂O₃ nanocomposite coatings were confirmed from attenuated total reflectance‐infrared spectroscopy (ATR‐IR). Thermal analysis (TG) results showed enhanced thermal stability for the composites relative to PVK. Incorporation of Al₂O₃ nanoparticles enhanced the micro hardness of PVK coated 316 L SS. The dispersion of alumina nanoparticles was examined via scanning electron microscope (SEM) and tunneling electron microscopy (TEM) and revealed distinct features. The influence of nanoparticles on the barrier properties of PVK and PVK‐Al₂O₃ nanocomposites was evaluated in aqueous 3.5 wt % NaCl by potentiodynamic polarization and electrochemical impedance spectroscopy (EIS) studies. The results proved that PVK nanocomposite coatings provided better protection for 316 L SS than PVK coatings. The drastic increase in impedance values is due to the high corrosion resistance offered by the PVK nanocomposite coatings that arises due to the interaction between Al₂O₃ nanoparticles and PVK. The highest corrosion protection shown by the 2 wt % nano Al₂O₃ incorporated PVK composite coatings proved enhanced corrosion resistance compared to PVK. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44937.     

Synergistic Effects of Montmorillonite/Cerium Nitrate Additives on the Corrosion Performance of Epoxy-Clay Nanocomposite Coatings

In this work, different amounts of montmorillonite were added to cerium nitrate epoxy mixture. Nanocomposite coatings containing cerium nitrate were applied on cold rolled steel panels. The state of dispersion and incorporation were characterized by transmission electron microscopy and atomic force microscopy. To investigate anticorrosive properties of nanocomposites, electrochemical impedance spectroscopy, polarization measurement and salt spray tests were employed. Results showed that epoxy cerium nanocomposite coatings were superior to the neat epoxy in corrosion protection properties. Also, it was observed that the best corrosion protection was achieved with nanocomposite coatings containing 4 wt.% and 2 wt.% cerium nitrate.     

Aliphatic polyurethane–montmorillonite nanocomposite coatings: Preparation,characterization, and anticorrosive properties

Polyurethane (PU)–clay nanocomposite coatings were prepared by a sonication method. The stability and morphology of these coatings was characterized by turbidometry, X‐ray diffraction, and transmission electron microscopy. The anticorrosive properties of these coatings were investigated by salt‐spray and electrochemical impedance spectroscopy methods. According to the results, dispersed nanoclay layers in the matrix of the nanocomposite coating compositions led to superior anticorrosive characteristics compared to those of pure PU coatings. The best results were obtained with coatings containing about 5 wt % clay. The resistance of the coating containing 5% clay was about 9.002 GΩ after 225 days of immersion in a 3.5 wt % NaCl solution, whereas it was only 97 kΩ for the pure PU coating. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Tribological and corrosion behaviors of fluorocarbon coating reinforced with sodium iron titanate platelets and whiskers

A series of sodium iron titanate (NFTO)–fluorocarbon composite coatings have been prepared with the liquid-phase blending method. The effects of two types of NFTO, NFTO platelets, and NFTO whiskers, on the tribological and corrosion behaviors of the composite coatings, are systematically studied. The results show that the addition of NFTO can significantly enhance the friction-reducing and wear resistance performances of the fluorocarbon coating. Under dry sliding, the minimum specific wear rate is 1.67 × 10⁻⁴ mm³/Nm for the platelet-filled composite coatings and 1.15 × 10⁻⁴ mm³/Nm for the whisker-filled composite coatings, respectively, showing a decrease of 83.5 and 88.6% than that of pure coating. Under a simulated seawater environment, the minimum specific wear rate is 5.44 × 10⁻⁵ mm³/Nm for the platelet-filled composite coatings and 0.84 × 10⁻⁵ mm³/Nm for the whisker-filled composite coatings, respectively, showing a decrease of 90.5 and 98.5% than that of pure coating. The morphologies of worn surfaces, wear debris, and transfer films are analyzed, and the corresponding wear resistance mechanisms are discussed. The electrochemical impedance spectroscopy certifies a remarkably improved corrosion resistance of the composite coatings which have been immersed in 3.5 wt % NaCl solution for 30 days. The composite coating reinforced with 7.5 wt % platelets shows the highest resistance of 256.3 × 10⁶ Ω·cm², approximately two orders of magnitude higher than that of pure coating. © 2020 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020 , 137, 48936.     

‎Deposition of Ni-tungsten carbide nanocomposite coating by TIG ‎welding: Characterization and control of microstructure and wear/corrosion responses‎

In this study, the effect of the amount of tungsten carbide nanoparticles on the wear and corrosion properties of Ni-tungsten carbide nanocomposite coating which is deposited on steel St37 by Tungsten Inert Gas (TIG) welding was evaluated. For this purpose, surface alloying was firstly conducted on St37 steel by using TIG process with a current of 150 Amps using pure nickel powder and tungsten carbide reinforcement nanoparticles (in 5, 10, 15 and 20 wt%). Then, Transmission Electron Microscopy (TEM), optical microscope, Field Emission Scanning Electron Microscopy (FE-SEM), Energy Dispersive Spectroscopy (EDS), X-ray Diffraction (XRD), microhardness test by Vickers method, abrasion test by sweep method, and electrochemical tests (potentiodynamic polarization and electrochemical impedance spectroscopy) were used in order to characterize the microstructure and tribological properties of the deposited layers. Microstructural observations showed that the deposited Ni-tungsten carbide nanocomposite coating have a dendritic microstructure with a uniform distribution of tungsten carbide nanoparticles, which reduced the dendritic size by increasing the amount of tungsten carbide nanoparticles. The results of this study showed that by increasing the amount of tungsten carbide nanoparticles in the Ni- tungsten carbide nanocomposite coating, the hardness (from the coating surface to the interface of coating/substrate) and wear resistance increased sharply, but the corrosion resistance decreased. Also, the evaluation of the wear mechanism showed that by increasing the amount of tungsten carbide nanoparticles in Ni-tungsten carbide nanocomposite coatings, the wear mechanism in this coating changed from complex abrasive-sheet like to complex adhesive-oxidation.     

Synergistic effect of aluminium phosphate and tungstophosphoric acid on the physicochemical properties of sulfonated poly ether ether ketone nanocomposite membrane

This study explores the synergistic effect of aluminium phosphate (ALP) nanoparticles and tungstophosphoric acid (TPA) on the physicochemical properties of sulfonated poly ether ether ketone (SPEEK) nanocomposite membranes. SPEEK/TPA/ALP nanocomposite containing optimum TPA (10 wt %) and varying ALP content (3–10 wt %) are fabricated to investigate the effect of ALP nanoparticles on membrane properties. Experimental results reveal that nanocomposite membrane containing 3 wt % ALP nanoparticles and 10 wt % TPA exhibits 3.3 and 18.8 times higher proton conductivity compared to 10 wt % TPA filled SPEEK composite membrane and reference SPEEK membrane. ALP nanoparticles help in retaining water within the membranes and thus 59.4% reduction in water desorption rate is achieved compared to SPEEK/TPA membrane. The leaching of TPA is reduced by 34.5% which helps in retaining membrane properties. Membranes are thermally stable up to 200°C. Microstructure of the composite films is investigated by scanning electron microscope. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 42952.     

Development of epoxy/rice straw-based cellulose nanowhiskers composite smart coating immobilized with rare-earth doped aluminate: Photoluminescence and anticorrosion properties for sustainability

Novel epoxy resin (E)/CNW nanocomposite coatings were developed with different total contents of rare-earth doped aluminate nanoparticles (REA NPs). The produced epoxy-cellulose nanowhiskers-rare earth doped aluminate nanoparticles (E-CNW-REA) coatings were applied onto mild steel. The epoxy/CNW nanocomposite coatings were characterized by X-ray fluorescence analysis (XRF), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDXA), transmission electron microscope (TEM) and infrared spectra (FT-IR). Both colorimetric properties and transparency of the nanocomposite coatings were proved by exploring UV–Vis absorption spectroscopy and CIE Lab parameters. The hardness and superhydrophobic properties were also explored. The photoluminescent transparent coatings showed an excitation at 365 nm, and a bright green emission wavelength at 517 nm under UV light. The corrosion protection performance of the coated mild steel samples soaked in an aqueous solution of sodium chloride (3.5%) was investigated using electrochemical impedance spectroscopy (EIS). The coatings with CNW were found to have anti-corrosion properties. Moreover, the nanocomposite coating with CNW (1 w%) was monitored to exhibit the most pronounced long-persistent photoluminescence for 60 min in the dark. The photoluminescent coatings exhibited highly durable long-lasting phosphorescence. Thus, the current strategy can be considered as a simple promising technology for industrial production of anti-corrosive, superhydrophobic and long-persistent phosphorescent.     

Preparation of epoxy resin/CaCO3 nanocomposites and performance of resultant powder coatings

Epoxy resin/CaCO₃ nanocomposites were prepared by the methods of extruding, solution blending, and in situ and inclusion polymerization, respectively. The contents of nanoparticles in the nanocomposites were varied from 5 wt % to 15 wt %. Powder coatings with different content of nanoparticles were made from the nanocomposites. The results showed that the cupping property and impact resistance decreased with the increase of coating film thickness. The dispersion of nanoparticles in epoxy matrix affected the impact resistance and cupping property of the obtained coating films greatly. The coating films made from the nanocomposite prepared by in situ and inclusion polymerization showed that the best impact resistance and the maximum cupping property was achieved when nano‐CaCO₃ content was 5 wt %. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2656–2660, 2006     

Anti-corrosive properties of Poly(aniline-co-2,3-xylidine)/ZnO nanocomposite coating on low-carbon steel

A copolymer nanocomposite Poly(aniline-co-2,3-xylidine)/ZnO [Poly(AN-co-XY)/ZnO], pure copolymer and its homopolymers namely, Poly(aniline-co-2,3-xylidine) [Poly(AN-co-XY)], Polyaniline (PANi) and Poly (2,3-xylidine) were synthesized by chemical oxidative polymerization using ammonium persulfate as an oxidant in hydrochloric acid medium. The synthesized compounds were characterized by FTIR, XRD, SEM, and TEM techniques. Saturated solutions of the synthesized compounds were made in N-methyl-2-pyrrolidone and casted on low-carbon steel specimens using 10% epoxy resin as a binder. The anticorrosion behavior of polymeric coatings was studied in 3.5 wt% NaCl solution at a temperature of 30 °C by electrochemical techniques, which include: open-circuit potential, potentiodynamic polarization and electrochemical impedance spectroscopy. Protective properties of nanocomposite coating were also evaluated at different immersion times for an extended period of 60 days. Anticorrosion properties of nanocomposite coating were compared with parent copolymer and individual homoplymers. SEM photomicrographs of the coated surface showed that Poly(AN-co-XY)/ZnO nanocomposite coating is crack free, uniform, and compact, whereas, copolymer and homopolymer coatings have surface defects. The performance of the polymer coatings followed the order: Poly(AN-co-XY)/ZnO > Poly(AN-co-XY) > PANi > Poly(2,3-xylidine). The presence of ZnO nanoparticles in copolymer resulted in significant improvement in corrosion resistance and provided better barrier properties.     

Tribological and mechanical properties of amorphous and semi-crystalline PEEK/SiO2 nanocomposite coatings deposited on the plain carbon steel by electrostatic powder spray technique

One of the main practical limitations of polymer coatings is dependency of their mechanical and physical properties on the crystallinity of polymer matrix. In this research, the effect of the presence of silica nanoparticles on microhardness, interfacial adhesion strength and tribological behavior of amorphous and semi-crystalline polyether–ether–ketone (PEEK) coatings were examined. The coatings were prepared by a combination of ball milling and electrostatic powder spraying methods. The results showed that the semi-crystalline pure PEEK coating had higher hardness, lower adhesion strength, coefficient of friction (COF) and wear rate than the amorphous one. However, the incorporating of PEEK with surface modified silica nanoparticles led to an increase in the coatings microhardness and interfacial adherence. The wear rates of both the semi-crystalline and amorphous nanocomposite coatings were lower than the pure ones but their COF were slightly higher. It was also found that, compared with the pure coatings, the sensitivity of the mechanical and tribological properties of the nanocomposite coatings to the crystalline structure of the PEEK matrix are less pronounced.     

Formulation and study of corrosion prevention behavior of epoxy cerium nitrate–montmorillonite nanocomposite coated carbon steel

Nanocomposite coatings which were applied on carbon steel panels based on epoxy cerium nitrate–montmorillonite (MMT) were synthesized and formulated. Nanoparticles were incorporated into epoxy resin by mechanical and sonication processes. The state of dispersion, dissolution, and incorporation were characterized by optical microscopy, sedimentation tests, X-ray diffraction, and transmission electron microscopy. To investigate anticorrosive properties of nanocomposite coatings, electrochemical impedance spectroscopy and salt spray tests were employed. The experimental results showed that epoxy cerium nitrate–MMT nanocomposite coatings were superior to the neat epoxy in corrosion protection effects. In addition, it was observed that the corrosion protection of nanocomposite coatings was improved as the clay loading was increased up to 4–2 wt% cerium nitrate.     

PANI-chitosan-TiO2 ternary nanocomposite and its effectiveness on antibacterial and antistatic behavior of epoxy coating

A straightforward approach has been developed for fabricating antibacterial and antistatic epoxy coatings by using polyaniline-chitosan modified TiO₂ ternary nanocomposite. This nanocomposite was synthesized through the following steps. First, chitosan was grafted onto the TiO₂ nanoparticles and then final nanocomposite was prepared via solution polymerization of aniline. Electrical conductivity measurement revealed that nanocomposite with 7.5 wt % of the modified TiO₂ nanoparticles has noticeably higher conductivity compared to polyaniline. Evaluating the coatings' antibacterial property indicated epoxy coatings with the content of ternary nanocomposite show significant bactericidal activity against Gram-positive bacteria and have acceptable antibacterial action against Gram-negative ones. Also, obtained results showed that the ternary nanocomposite would greatly decrease coatings' surface resistivity and when nanocomposite content is about 2 wt % surface resistivity is about 3 × 10⁷ Ω sq⁻¹. On the contrary, the coating with nanocomposite loading exhibits improved thermal and mechanical performance compared to the coating made of neat epoxy. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47629.     

Investigation of the corrosion protection behavior of natural montmorillonite clay/bitumen nanocomposite coatings

The influence of clay particles on the corrosion properties of bituminous coating was studied. Different percentages of natural montmorillonite clay (Cloisite Na⁺) were added to emulsified bitumen in water to make 2 wt.%, 3 wt.% and 4 wt.% of clay/bitumen nanocomposite coatings. The coatings were applied on steel 37. Optical microscopy and transmission electron microscopy (TEM) were employed to study the structure of nanocomposite. To investigate the anti-corrosion properties of the coated panels, electrochemical impedance spectroscopy (EIS) was used. The findings indicated that the addition of clay nanolayers improved corrosion resistance of the coatings. Moreover, increasing clay loading up to 4 wt.%, increased the corrosion resistance.     

Self-healing and anticorrosive properties of Ce(III)/Ce(IV) in nanoclay–epoxy coatings

The self-healing and anticorrosion effects of cerium nitrate in epoxy–clay nanocomposite coatings systems were studied. Different amounts of cerium (III) were added to epoxy–montmorillonite clay composites and the nanocomposite coatings were prepared and applied on cold rolled steel panels. Ultrasonication was applied to disperse the nanoclay into the epoxy cerium nitrate composition. Electrochemical impedance spectroscopy (EIS) was used to study the self-healing and anticorrosion behaviors of the coatings. The structure of the dry coating and the protective mechanism of the pigments in the coating were investigated by scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX) analysis and field emission electron microscopy (FESEM). Transmission electron microscopy (TEM) illustrated the separation of clay layers which interacted with the epoxy resin. Electrochemical impedance data indicated that the epoxy cerium (III)–montmorillonite nanocomposite coatings were superior to the epoxy coatings in corrosion protection properties. The self-healing behavior of such coatings was due to the presence of cerium nitrate that could be released at the defects within the coating and hindered the corrosion reactions at the defective sites. It was shown that the best corrosion protection was achieved with nanocomposite coatings containing 4 wt% clay and 2 wt% cerium nitrate.