Structural changes and dynamic behaviour of vanadium oxide-based catalysts for gas-phase selective oxidations

Selective oxidation is one of the simplest functionalization methods and essentially all monomers used in manufacturing artificial fibers and plastics are obtained by catalytic oxidation processes. Formally, oxidation is considered as an increase in the oxidation number of the carbon atoms, then reactions such as dehydrogenation, ammoxidation, cyclization or chlorination are all oxidation reactions. In this field, most of processes for the synthesis of important chemicals used vanadium oxide-based catalysts. These catalytic systems are used either in the form of multicomponent mixed oxides and oxysalts, e.g., in the oxidation of n-butane (V/P/O) and of benzene (supported V/Mo/O) to maleic anhydride, or in the form of supported metal oxide, e.g., in the manufacture of phthalic anhydride by o-xylene oxidation, of sulphuric acid by oxidation of SO2, in the reduction of NOx with ammonia and in the ammoxidation of alkyl aromatics. In addition, supported vanadia catalysts have also been investigated for the oxidative dehydrogenation of alkanes to olefins , oxidation of pentane to maleic anhydride and the selective oxidation of methanol to formaldehyde or methyl formate [1]. During my PhD I focused my work on two gas phase selective oxidation reactions. The work was done at the Department of Industrial Chemistry and Materials (University of Bologna) in collaboration with Polynt SpA. Polynt is a leader company in the development, production and marketing of catalysts for gas-phase oxidation. In particular, I studied the catalytic system for n-butane oxidation to maleic anhydride (fluid bed technology) and for o-xylene oxidation to phthalic anhydride. Both reactions are catalyzed by systems based on vanadium, but catalysts are completely different. Part A is dedicated to the study of V/P/O catalyst for n-butane selective oxidation, while in the Part B the results of an investigation on TiO2-supported V2O5, catalyst for o-xylene oxidation are showed. In Part A, a general introduction about the importance of maleic anhydride, its uses, the industrial processes and the catalytic system are reported. The reaction is the only industrial direct oxidation of paraffins to a chemical intermediate. It is produced by n-butane oxidation either using fixed bed and fluid bed technology; in both cases the catalyst is the vanadyl pyrophosphate (VPP). Notwithstanding the good performances, the yield value didn’t exceed 60% and the system is continuously studied to improve activity and selectivity. The main open problem is the understanding of the real active phase working under reaction conditions. Several articles deal with the role of different crystalline and/or amorphous vanadium/phosphorous (VPO) compounds. In all cases, bulk VPP is assumed to constitute the core of the active phase, while two different hypotheses have been formulated concerning the catalytic surface. In one case the development of surface amorphous layers that play a direct role in the reaction is described, in the second case specific planes of crystalline VPP are assumed to contribute to the reaction pattern, and the redox process occurs reversibly between VPP and VOPO4. Both hypotheses are supported also by in-situ characterization techniques, but the experiments were performed with different catalysts and probably under slightly different working conditions. Due to complexity of the system, these differences could be the cause of the contradictions present in literature. Supposing that a key role could be played by P/V ratio, I prepared, characterized and tested two samples with different P/V ratio. Transformation occurring on catalytic surfaces under different conditions of temperature and gas-phase composition were studied by means of in-situ Raman spectroscopy, trying to investigate the changes that VPP undergoes during reaction. The goal is to understand which kind of compound constituting the catalyst surface is the most active and selective for butane oxidation reaction, and also which features the catalyst should possess to ensure the development of this surface (e.g. catalyst composition). On the basis of results from this study, it could be possible to project a new catalyst more active and selective with respect to the present ones. In fact, the second topic investigated is the possibility to reproduce the surface active layer of VPP onto a support. In general, supportation is a way to improve mechanical features of the catalysts and to overcome problems such as possible development of local hot spot temperatures, which could cause a decrease of selectivity at high conversion, and high costs of catalyst. In literature it is possible to find different works dealing with the development of supported catalysts, but in general intrinsic characteristics of VPP are worsened due to the chemical interaction between active phase and support. Moreover all these works deal with the supportation of VPP; on the contrary, my work is an attempt to build-up a V/P/O active layer on the surface of a zirconia support by thermal treatment of a precursor obtained by impregnation of a V5+ salt and of H3PO4. In-situ Raman analysis during the thermal treatment, as well as reactivity tests are used to investigate the parameters that may influence the generation of the active phase. Part B is devoted to the study of o-xylene oxidation of phthalic anhydride; industrially, the reaction is carried out in gas-phase using as catalysts a supported system formed by V2O5 on TiO2. The V/Ti/O system is quite complex; different vanadium species could be present on the titania surface, as a function of the vanadium content and of the titania surface area: (i) V species which is chemically bound to the support via oxo bridges (isolated V in octahedral or tetrahedral coordination, depending on the hydration degree), (ii) a polymeric species spread over titania, and (iii) bulk vanadium oxide, either amorphous or crystalline. The different species could have different catalytic properties therefore changing the relative amount of V species can be a way to optimize the catalytic performances of the system. For this reason, samples containing increasing amount of vanadium were prepared and tested in the oxidation of o-xylene, with the aim of find a correlations between V/Ti/O catalytic activity and the amount of the different vanadium species. The second part deals with the role of a gas-phase promoter. Catalytic surface can change under working conditions; the high temperatures and a different gas-phase composition could have an effect also on the formation of different V species. Furthermore, in the industrial practice, the vanadium oxide-based catalysts need the addition of gas-phase promoters in the feed stream, that although do not have a direct role in the reaction stoichiometry, when present leads to considerable improvement of catalytic performance. Starting point of my investigation is the possibility that steam, a component always present in oxidation reactions environment, could cause changes in the nature of catalytic surface under reaction conditions. For this reason, the dynamic phenomena occurring at the surface of a 7wt% V2O5 on TiO2 catalyst in the presence of steam is investigated by means of Raman spectroscopy. Moreover a correlation between the amount of the different vanadium species and catalytic performances have been searched. Finally, the role of dopants has been studied. The industrial V/Ti/O system contains several dopants; the nature and the relative amount of promoters may vary depending on catalyst supplier and on the technology employed for the process, either a single-bed or a multi-layer catalytic fixed-bed. Promoters have a quite remarkable effect on both activity and selectivity to phthalic anhydride. Their role is crucial, and the proper control of the relative amount of each component is fundamental for the process performance. Furthermore, it can not be excluded that the same promoter may play different role depending on reaction conditions (T, composition of gas phase..). The reaction network of phthalic anhydride formation is very complex and includes several parallel and consecutive reactions; for this reason a proper understanding of the role of each dopant cannot be separated from the analysis of the reaction scheme. One of the most important promoters at industrial level, which is always present in the catalytic formulations is Cs. It is known that Cs plays an important role on selectivity to phthalic anhydride, but the reasons of this phenomenon are not really clear. Therefore the effect of Cs on the reaction scheme has been investigated at two different temperature with the aim of evidencing in which step of the reaction network this promoter plays its role.

Catalytic liquid- and gas-phase oxidations for the synthesis of intermediates and specialty chemicals: some examples of industrial relevance

Nowadays, it is clear that the target of creating a sustainable future for the next generations requires to re-think the industrial application of chemistry. It is also evident that more sustainable chemical processes may be economically convenient, in comparison with the conventional ones, because fewer by-products means lower costs for raw materials, for separation and for disposal treatments; but also it implies an increase of productivity and, as a consequence, smaller reactors can be used. In addition, an indirect gain could derive from the better public image of the company, marketing sustainable products or processes. In this context, oxidation reactions play a major role, being the tool for the production of huge quantities of chemical intermediates and specialties. Potentially, the impact of these productions on the environment could have been much worse than it is, if a continuous efforts hadn’t been spent to improve the technologies employed. Substantial technological innovations have driven the development of new catalytic systems, the improvement of reactions and process technologies, contributing to move the chemical industry in the direction of a more sustainable and ecological approach. The roadmap for the application of these concepts includes new synthetic strategies, alternative reactants, catalysts heterogenisation and innovative reactor configurations and process design. Actually, in order to implement all these ideas into real projects, the development of more efficient reactions is one primary target. Yield, selectivity and space-time yield are the right metrics for evaluating the reaction efficiency. In the case of catalytic selective oxidation, the control of selectivity has always been the principal issue, because the formation of total oxidation products (carbon oxides) is thermodynamically more favoured than the formation of the desired, partially oxidized compound. As a matter of fact, only in few oxidation reactions a total, or close to total, conversion is achieved, and usually the selectivity is limited by the formation of by-products or co-products, that often implies unfavourable process economics; moreover, sometimes the cost of the oxidant further penalizes the process. During my PhD work, I have investigated four reactions that are emblematic of the new approaches used in the chemical industry. In the Part A of my thesis, a new process aimed at a more sustainable production of menadione (vitamin K3) is described. The “greener” approach includes the use of hydrogen peroxide in place of chromate (from a stoichiometric oxidation to a catalytic oxidation), also avoiding the production of dangerous waste. Moreover, I have studied the possibility of using an heterogeneous catalytic system, able to efficiently activate hydrogen peroxide. Indeed, the overall process would be carried out in two different steps: the first is the methylation of 1-naphthol with methanol to yield 2-methyl-1-naphthol, the second one is the oxidation of the latter compound to menadione. The catalyst for this latter step, the reaction object of my investigation, consists of Nb2O5-SiO2 prepared with the sol-gel technique. The catalytic tests were first carried out under conditions that simulate the in-situ generation of hydrogen peroxide, that means using a low concentration of the oxidant. Then, experiments were carried out using higher hydrogen peroxide concentration. The study of the reaction mechanism was fundamental to get indications about the best operative conditions, and improve the selectivity to menadione. In the Part B, I explored the direct oxidation of benzene to phenol with hydrogen peroxide. The industrial process for phenol is the oxidation of cumene with oxygen, that also co-produces acetone. This can be considered a case of how economics could drive the sustainability issue; in fact, the new process allowing to obtain directly phenol, besides avoiding the co-production of acetone (a burden for phenol, because the market requirements for the two products are quite different), might be economically convenient with respect to the conventional process, if a high selectivity to phenol were obtained. Titanium silicalite-1 (TS-1) is the catalyst chosen for this reaction. Comparing the reactivity results obtained with some TS-1 samples having different chemical-physical properties, and analyzing in detail the effect of the more important reaction parameters, we could formulate some hypothesis concerning the reaction network and mechanism. Part C of my thesis deals with the hydroxylation of phenol to hydroquinone and catechol. This reaction is already industrially applied but, for economical reason, an improvement of the selectivity to the para di-hydroxilated compound and a decrease of the selectivity to the ortho isomer would be desirable. Also in this case, the catalyst used was the TS-1. The aim of my research was to find out a method to control the selectivity ratio between the two isomers, and finally to make the industrial process more flexible, in order to adapt the process performance in function of fluctuations of the market requirements. The reaction was carried out in both a batch stirred reactor and in a re-circulating fixed-bed reactor. In the first system, the effect of various reaction parameters on catalytic behaviour was investigated: type of solvent or co-solvent, and particle size. With the second reactor type, I investigated the possibility to use a continuous system, and the catalyst shaped in extrudates (instead of powder), in order to avoid the catalyst filtration step. Finally, part D deals with the study of a new process for the valorisation of glycerol, by means of transformation into valuable chemicals. This molecule is nowadays produced in big amount, being a co-product in biodiesel synthesis; therefore, it is considered a raw material from renewable resources (a bio-platform molecule). Initially, we tested the oxidation of glycerol in the liquid-phase, with hydrogen peroxide and TS-1. However, results achieved were not satisfactory. Then we investigated the gas-phase transformation of glycerol into acrylic acid, with the intermediate formation of acrolein; the latter can be obtained by dehydration of glycerol, and then can be oxidized into acrylic acid. Actually, the oxidation step from acrolein to acrylic acid is already optimized at an industrial level; therefore, we decided to investigate in depth the first step of the process. I studied the reactivity of heterogeneous acid catalysts based on sulphated zirconia. Tests were carried out both in aerobic and anaerobic conditions, in order to investigate the effect of oxygen on the catalyst deactivation rate (one main problem usually met in glycerol dehydration). Finally, I studied the reactivity of bifunctional systems, made of Keggin-type polyoxometalates, either alone or supported over sulphated zirconia, in this way combining the acid functionality (necessary for the dehydrative step) with the redox one (necessary for the oxidative step). In conclusion, during my PhD work I investigated reactions that apply the “green chemistry” rules and strategies; in particular, I studied new greener approaches for the synthesis of chemicals (Part A and Part B), the optimisation of reaction parameters to make the oxidation process more flexible (Part C), and the use of a bioplatform molecule for the synthesis of a chemical intermediate (Part D).

Caratterizzazione di membrane metalliche e ionomeriche per applicazioni energetiche

The work of this thesis has been focused on the characterization of metallic membranes for the hydrogen purification from steam reforming process and also of perfluorosulphonic acid ionomeric (PFSI) membranes suitable as electrolytes in fuel cell applications. The experimental study of metallic membranes was divided in three sections: synthesis of palladium and silver palladium coatings on porous ceramic support via electroless deposition (ELD), solubility and diffusivity analysis of hydrogen in palladium based alloys (temperature range between 200 and 400 °C up to 12 bar of pressure) and permeation experiments of pure hydrogen and mixtures containing, besides hydrogen, also nitrogen and methane at high temperatures (up to 600 °C) and pressures (up to 10 bar). Sequential deposition of palladium and silver on to porous alumina tubes by ELD technique was carried out using two different procedures: a stirred batch and a continuous flux method. Pure palladium as well as Pd-Ag membranes were produced: the Pd-Ag membranes’ composition is calculated to be close to 77% Pd and 23% Ag by weight which was the target value that correspond to the best performance of the palladium-based alloys. One of the membranes produced showed an infinite selectivity through hydrogen and relatively high permeability value and is suitable for the potential use as a hydrogen separator. The hydrogen sorption in silver palladium alloys was carried out in a gravimetric system on films produced by ELD technique. In the temperature range inspected, up to 400°C, there is still a lack in literature. The experimental data were analyzed with rigorous equations allowing to calculate the enthalpy and entropy values of the Sieverts’ constant; the results were in very good agreement with the extrapolation made with literature data obtained a lower temperature (up to 150 °C). The information obtained in this study would be directly usable in the modeling of hydrogen permeation in Pd-based systems. Pure and mixed gas permeation tests were performed on Pd-based hydrogen selective membranes at operative conditions close to steam-reforming ones. Two membranes (one produced in this work and another produced by NGK Insulators Japan) showed a virtually infinite selectivity and good permeability. Mixture data revealed the existence of non negligible resistances to hydrogen transport in the gas phase. Even if the decrease of the driving force due to polarization concentration phenomena occurs, in principle, in all membrane-based separation systems endowed with high perm-selectivity, an extensive experimental analysis lack, at the moment, in the palladium-based membrane process in literature. Moreover a new procedure has been introduced for the proper comparison of the mass transport resistance in the gas phase and in the membrane. Another object of study was the water vapor sorption and permeation in PFSI membranes with short and long side chains was also studied; moreover the permeation of gases (i.e. He, N2 and O2) in dry and humid conditions was considered. The water vapor sorption showed strong interactions between the hydrophilic groups and the water as revealed from the hysteresis in the sorption-desorption isotherms and thermo gravimetric analysis. The data obtained were used in the modeling of water vapor permeation, that was described as diffusion-reaction of water molecules, and in the humid gases permeation experiments. In the dry gas experiments the permeability and diffusivity was found to increase with temperature and with the equivalent weight (EW) of the membrane. A linear correlation was drawn between the dry gas permeability and the opposite of the equivalent weight of PFSI membranes, based on which the permeability of pure PTFE is retrieved in the limit of high EW. In the other hand O2 ,N2 and He permeability values was found to increase significantly, and in a similar fashion, with water activity. A model that considers the PFSI membrane as a composite matrix with a hydrophilic and a hydrophobic phase was considered allowing to estimate the variation of gas permeability with relative humidity on the basis of the permeability in the dry PFSI membrane and in pure liquid water.

Food Safety and Mineral Oil Contaminated Paperboard Packaging: an Analytical Challenge and a Migration Study

Food packaging protects food, but it can sometimes become a source of undesired contaminants. Paper based materials, despite being perceived as “natural” and safe, can contain volatile contaminants (especially if made from recycled paper) able to migrate to food, as mineral oil, phthalates and photoinitiators. Mineral oil is a petroleum product used as printing ink solvent for newspapers, magazines and packaging. From paperboard printing and from recycled fibers (if present), mineral oil migrates into food, even if dry, through the gas phase. Its toxicity is not fully evaluated, but a temporary Acceptable Daily Intake (ADI) of 0.6 mg kg-1 has been established for saturated mineral oil hydrocarbons (MOSH), while aromatic hydrocarbons (MOAH) are more toxic. Extraction and analysis of MOSH and MOAH is difficult due to the thousands of molecules present. Extraction methods for packaging and food have been optimized, then applied for a “shopping trolley survey” on over 100 Italian and Swiss market products. Instrumental analyses were performed with online LC-GC/FID. Average concentration of MOSH in paperboards was 626 mg kg-1. Many had the potential of contaminating foods exceeding temporary ADI tens of times. A long term migration study was then designed to better understand migration kinetics. Egg pasta and müesli were chosen as representative (high surface/weight ratio). They were stored at different temperatures (4, 20, 30, 40 and 60°C) and conditions (free, shelved or boxed packs) for 1 year. MOSH and MOAH kinetic curves show that migration is a fast process, mostly influenced by temperature: in egg pasta (food in direct contact with paperboard), half of MOSH is transferred to food in a week at 40°C and in 8 months at 20°C. The internal plastic bag present in müesli slowed down the startup of migration, creating a “lag time” in the curves.

Investigation of heterogeneous catalysts for the synthesis of fine chemicals

In order to match the more stringent environmental regulations, heterogenization of traditional homogeneous processes is one of the main challenges of the modern chemical industry. Great results have been achieved in the fields of petrochemicals and base chemicals, whereas in fine chemical industry most of the synthetic procedures are based on multistep processes catalyzed by homogeneous catalysts mainly used in stoichiometric amounts. In the fine chemicals manufacture not so much efforts have been devoted to the investigation of suitable solid catalysts for the development of greener processes, then this sector represent a very attractive field of research. In this context, the present work deals with the extensive investigation of the possibility to heterogenize existing processes, in particular two different classes of reactions have been studied: alkylation of aromatic and heteroaromatic compounds and selective oxidation of aromatic alcohols. Traditional solid acid catalysts, such as zeolites, clays and alumina have been tested in the gas phase alkylation of 1,2-methylendioxybenzene, core building block of many drugs, pesticides and fragrances. The observed reactivity were clarified through a deep FTIR investigation complemented by ab initio calculation. The same catalysts were tested in the gas phase isopropylation of thiophene with the aim of clearly attribute the role of the reaction parameters in the reaction proceeding and verify the possibility to enhance the selectivity of one of the two possible isomers. Finally various Au/CeO2 catalysts were tested in the synthesis of benzaldehyde and piperonal, two aldehydes largely employed in the manufacture of fine chemical products, through liquid phase oxidation of the corresponding alcohols in very mild conditions.

Development of innovative catalysts for the hydrodechlorination to fluoroethers

In this work the hydrodechlorination of CF3OCFClCF2Cl to produce unsaturated CF3OCF=CF2 was studied over a series of supported metal catalysts. Currently this molecule is produced from the precursor CF3OCFClCF2Cl by dechlorination with zinc powder. An important cost on the economic and environmental balance is represents by the large amount of ZnCl2 produced and to be disposed of. A new approach, based on gas-phase hydrodechlorination over supported catalysts can lead to a new sustainable process. During the feasibility step of this project, substantially two kind of materials were studied: metals supported over activated carbon and Pd/Cu species supported over MCM-41 mesoporous silica. Observed catalytic performances were strongly dependent on the metal and support used. All carbon-supported Ru, Pd, and bimetallic catalysts are fairly active and yielded the target product CF3OCF=CF2, the higher selectivity being obtained with ruthenium- and palladium-based materials. Nevertheless, Ru-based catalysts showed poor stability and this deactivation may be attributed to the deposition of chlorinated organic species blocking the active sites. On the other hand, palladium-containing catalysts showed high stability. Ru/Pd and Pd/Cu bimetallic catalysts exhibited long-term selectivity and stability, highlighting the possibility for these materials to be employed in the CF3OCF=CF2 production process. During the second part of this thesis, a series of bimetallic meso-structured Pd/Cu MCM-41 catalysts were studies to overcome possible mass transfer limitations. The materials were obtained by different synthesis methods. The incorporation of Pd and Cu during MCM-41 synthesis, did not destroy the typical hexagonal array and ordered pore system of MCM-41. However, the calcination for the removal of the template provoked significant segregation of oxides. The impregnation leads to pore-occlusion and formation of Cu particles and large bimetallic PdCu species. Larger metal particles leads to lower CF3OCFClCF2Cl conversion, while the monometallic particles can decrease the selectivity to CF3OCF=CF2, fostering the dehalogenation to CF3OCH=CF2.

Study of molecules of astrochemical, astrophysical and atmospheric interest by means of High - Resolution Infrared Spectroscopy

The spectroscopic investigation of the gas-phase molecules relevant for the chemistry of the atmosphere and of the interstellar medium has been performed. Two types of molecules have been studied, linear and symmetric top. Several experimental high-resolution techniques have been adopted, exploiting the spectrometers available in Bologna, Venezia, Brussels and Wuppertal: Fourier-Transform-Infrared Spectroscopy, Cavity-Ring-Down Spectroscopy, Cavity-Enhanced-Absorption Spectroscopy, Tunable-Diode-Laser Spectroscopy. Concerning linear molecules, the spectra of a number of isotopologues of acetylene, 12C2D2, H12C13CD, H13C12CD, 13C12CD2, of DCCF and monodeuterodiacetylene DC4H, have been studied, from 320 to 6800 cm-1. This interval covers bending, stretching, overtone and combination bands, the focus on specific ranges depending on the molecule. In particular, the analysis of the bending modes has been performed for 12C2D2 (450-2200 cm-1), 13C12CD2 (450-1700 cm-1), DCCF (320-850cm-1) and DC4H (450-1100 cm-1), of the stretching-bending system for 12C2D2 (450-5500 cm-1) and of the 2nu1 and combination bands up to four quanta of excitation for H12C13CD, H13C12CD and 13C12CD2 (6130-6800 cm-1). In case of symmetric top molecules, CH3CCH has been investigated in the 2nu1 region (6200-6700 cm-1), which is particularly congested due to the huge network of states affected by Coriolis and anharmonic interactions. The bending fundamentals of 15ND3 (450-2700 cm-1) have been studied for the first time, characterizing completely the bending states, v2 = 1 and v4 = 1, whereas the analysis of the stretching modes, which evidenced the presence of several perturbations, has been started. Finally, the fundamental band nu4 of CF3Br in the 1190-1220 cm-1 region has been investigated. Transitions belonging to the CF379Br and CF381Br molecules have been identified since the spectra were recorded using a sample containing the two isotopologues in natural abundance. This allowed the characterization of the v4 = 1 state for both isotopologues and the evaluation of the bromine isotopic splitting.

Aerobic biodegradation of chlorinated solvents and plastics in batch and continuous-flow bioreactors: process development, and identification of suitable chemical pre-Treatments

The purpose of the first part of the research activity was to develop an aerobic cometabolic process in packed bed reactors (PBR) to treat real groundwater contaminated by trichloroethylene (TCE) and 1,1,2,2-tetrachloroethane (TeCA). In an initial screening conducted in batch bioreactors, different groundwater samples from 5 wells of the contaminated site were fed with 5 growth substrates. The work led to the selection of butane as the best growth substrate, and to the development and characterization from the site’s indigenous biomass of a suspended-cell consortium capable to degrade TCE with a 90 % mineralization of the organic chlorine. A kinetic study conducted in batch and continuous flow PBRs and led to the identification of the best carrier. A kinetic study of butane and TCE biodegradation indicated that the attached-cell consortium is characterized by a lower TCE specific degredation rates and by a lower level of mutual butane-TCE inhibition. A 31 L bioreactor was designed and set up for upscaling the experiment. The second part of the research focused on the biodegradation of 4 polymers, with and with-out chemical pre-treatments: linear low density polyethylene (LLDPE), polyethylene (PP), polystyrene (PS) and polyvinyl chloride (PVC). Initially, the 4 polymers were subjected to different chemical pre-treatments: ozonation and UV/ozonation, in gaseous and aqueous phase. It was found that, for LLDPE and PP, the coupling UV and ozone in gas phase is the most effective way to oxidize the polymers and to generate carbonyl groups on the polymer surface. In further tests, the effect of chemical pretreatment on polyner biodegrability was studied. Gas-phase ozonated and virgin polymers were incubated aerobically with: (a) a pure strain, (b) a mixed culture of bacteria; and (c) a fungal culture, together with saccharose as a co-substrate.