photocatalysed reactions of benzhydrol on zinc oxide
Transcription
photocatalysed reactions of benzhydrol on zinc oxide
E. P. YESODHARAN 1. INTRODUCTION V. RAMAKRISHNAN J. C. KURIACOSE Department of Chemistry Indian Institute of Technology Madras INDIA The mechanism of the interaction of oxygen with a zinc oxide surface has aroused considerable interest in the context of the electrical and optical properties of this oxide. In order to obtain information to correlate the surface properties and the electronic structure, the effect of irradiation on the interactions on a zinc oxide surface has been studied by many authors (1-4). The nature of the adsorbed oxygen species as well as its role in the photooxidation reactions of organic substrates has been investigated in detail. The participation of 02 , present on the surface of irradiated zinc oxide has been postulated in the case of the oxidation PHOTOCATALYSED REACTIONS OF BENZHYDROL ON ZINC OXIDE REACÇÕES FOTOCATALISADAS DO BENZIDROL SOBRE ÓXIDO DE ZINCO of isopropanol as well as phenols in aqueous suspensions of the catalyst (5, 6). In the case of isopropanol, besides acetone in varying amounts, depending on the experimental conditions, a low and constant concentration of hydrogen peroxide is always found. Under similar conditions benzylalcohol yields benzaldehyde, toluene and hydrogen peroxide (7). Without the presence of oxygen no reaction is detectable, either in the dark or with irradiation. It is assumed that the reaction gets initiated by an O2 ion followed by a possible radical reaction occuring without the influence of zinc oxide. The present work is an extension of our earlier work on cheat and light induced activation of oxides», with a view to establish the nature of photocatalysed reactions of benzhydrol as well as the effect of solvent and the structure of the alcohol on the reaction. The role of adsorbed water in the photocatalysed reactions of various alcohols is also investigated. 2. EXPERIMENTAL The light source used in all the experiments is a Hanovia high are not pressure quartz mercury arc. Radiations above 3800 absorbed by zinc oxide as is revealed by its reflectance spectrum. The lamp is mounted horizontally above a mechanical shaker and provided with an aluminium foil shade to reflect the light downwards. The reaction vessel consists of a pyrex tube with an opening for introducing the solids and liquids and a small side tube A Hydrogen peroxide and benzophenone are formed in the photocatalysed reactions of benzhydrol on zinc oxide. Oxygen, either in solution or on the surface or both is essential for tfae reaction when the zinc oxide suspension is irradiated with 3650 A wavelength radiation. A small induction period in the reaction can be eliminated by the addition of small amounts of benzophenone. The reaction is faster in acetonitrile than in cyclohexane. Hydrocarbons like naphthalene and phenanthrene are found to have a strong inhibiting effect on the activity of the catalyst while benzene and fluorene are less effective as inhibitors, Adsorbed water enhances the activity of zinc oxide. It is suggested that Oz is the species responsible for the reaction. A mechanism consistent with the observations is proposed and discussed along with other relevant aspects. 164 for bubbling gases. This is provided with two outer jackets, the inner one to be used for taking external filters such as copper sulphate solution and the outer one for circulating water at the desired temperature. 0.35 gm of the catalyst and 30 ml of the liquid under investigation are taken in the reaction vessel which is then closed and clamped to the platform of the mechanical shaker and shaken throughout the experiments. Samples were removed from the reaction vessel at various intervals and analysed. Almost all types of commercially available zinc oxide samples were found equally active as photocatalysts and hence used as such. The solvent acetonitrile is purified by the well known standard method and checked by gas chromatography.The benzhydrol (reagent grade) was recrystallised from ethyl alcohol (8). The resulting white crystals had a melting range 65-66 ° C. Benzophenone also was recrystallised from ethylalcohol (9) (m.p. = 47-48 °C). Naphthalene, phenanthrene and fluorene were found pure by melting point and used as received. The estimation of hydrogen peroxide was done by iodometry (10). Benzophenone is determined by gas chromatography using a carbowax column with hydrogen as the carrier gas and a column temperature of 210 °C. • 5 3. RESULTS MEDIUM : - ACETONITRILE TEMP , — 29 °C. The products of the photocatalysed reaction of benzhydrol are hydrogen peroxide and benzophenone. The product yield increases with increase in the weight of the catalyst to reach a steady value. This may be because with increase in the quantity of the catalyst, the amount of light absorbed also increases until enough zinc oxide is present to spread completely and uniformly in the reaction vessel to absorb the maximum amount of light. Further addition of zinc oxide may increase only its depth and since light does not reach the interior of the catalyst bulk, it is not effective. This is further confirmed by the observation that, the bigger the reaction vessel, the higher the limiting amount of the catalyst. The reactions were carried out in an acetonitrile medium. The effect of concentration of the alcohol on the formation of hydrogen peroxide is given in fig. 1. At higher concentrations, the peroxide 7 4 io in 3 m É xv 2 0 á C rnó t V x 00 30 60 150 120 90 Time (min) 210 180 so MEDIUM-.- ACETONITR ILE TEMP:- 29 .C. Fig. 2 4)2CHOH 40- 2C= 0 A: 0.5M Nil B. 0.1M Nil C: 70,00-2 M Nil D: 2.5x 10 2 M E: 0.1M 30— Nil 5x10 2 M F. O 1M (no Zn0) 5 x10 2 M E e e .0 20— o C n •F C o o , D 10 — i 6 8 Time (hr. ) 10 12 14 Fig. 1 Influence of concentration of benzophenone on the reaction sensitised by it in 0.1 M benzhydrol concentrations, the reaction is almost independent of it. This agrees with the observation that initially added benzophenone enhances the rate first and exerts no more influence towards the later stages of the reaction (fig. 1, curves B and E). Formation of benzpinacol has already been shown (8, 11) to proceed through the triplet of benzophenone interacting with a ground state benzhydrol molecule. Hence, if a substance which quenches this excited state is added to the reaction mixture, the observed selfacceleration of the reaction should disappear. Naphthalene, a well known quencher of the triplet state is thus initially introduced to the system. But surprisingly not only the benzophenone sensitized reaction, but the zinc oxide catalysed reaction also is suppressed considerably (fig. 3), The effect of various additives on the formation of hydrogen peroxide from benzhydrol is given in fig. 4. Phenanthrene with energy levels similar to that of naphthalene is Effect of concentration of benzhydrol and benzophenone on the formation of H2 02 goes on increasing with time and levels off later. But at lower concentration regions there is an induction period followed by a steady rise in the amount of hydrogen peroxide. Surprisingly, the amount of benzophenone was less than that of hydrogen peroxide. Since all the hydrogen required for hydrogen peroxide comes from benzhydrol by its dehydrogenation as (C6H5)2CHOH (C6H5)2C= O+H2 14 — MEDIUM.- ACETONITRILE TEMP: — 29 .C. A 12 — At io X10 e É B t1)2CHOH 4)2c °O C10H8 5x10 -2 M A 0•IM B 0.1M Nil C 0.1M Nil 8.10-4 N Nil D 0-1M Nit 4x103M E: 0.1M Nil 2:10 2 M F: 01M Nil 4x10 2 M G: 0.1M 5 x10-2 M 4x10 2 M W both the ketone and the peroxide should be formed in more or less equal amounts. This suggested that some other process involving benzophenone also is taking place simultaneously. The initial induction period also points to the fact that, the products of the reaction can accelerate it, resulting in the generation of more hydrogen peroxide. This is understandable since benzophenone itself under photochemical conditions interacts with benzhydrol forming benzpinacol and hydrogen. Considerable amount of benzpinacol is, in fact, formed in the system. When benzophenone is added initially to the system the induction period disappears (fig. 1, curve E). At lower concentrations of benzophenone, the formation of hydrogen peroxide depends on its concentration (fig. 2) and at higher Nil C E E 00 2 4 6 8 10 Time (hr.) F&G 12 14 Fig. 3 Influence of naphthalene on the photocatalysed reactions and benzophenone sensitized reactions of benzhydrol on ZnO 165 MEDIUM-ACETONITRILE 14 TEMP:- 29 ° C A , 0.1M BENZHYDROL (No 0dditive) B: A+5x10 -2 M BENZENE 1 12 C: A+ 5x 10-2 M FLUORENE IQ • A+5x10 2 M NAPHTHALENE 10 E: A+ 5 x 10-2 M PHENANTHRENE x õ E 8 v a ó ã 6 4 D&E rn o v` spectral analysis showed a broad peak corresponding to adsorbed water. The photocatalysed reactions of benzhydrol, benzylalcohol and isopropanol are found to yield higher amounts of hydrogen peroxide and the carbonyl compound, on zinc oxide, when small amounts of water are initially added (fig. 6 and 7). A sample of zinc oxide dried at 400 ° C for 3 hours had a lower activity than the commercially available one. The higher yield of hydrogen peroxide compared to the aldehyde or the ketone is understandable, since water itself, when irradiated over zinc oxide gives the peroxide which does not decompose to any great extent if organic stabilizers are present. 24 • 2 A:O-iM BENZYLALCOHOL 8:0.1M BENZHVDROL C:0.2M ISOPROPANOL S 21 00 2 4 6 8 10 Time (hr.) 12 14 18 ^o DRY Zn0 1I D.0-iM BENZVLALCOHOL E:0.1M BENZHVDROL lWET Zn0 F: 0.2M 150PROPANOL E MEDIUM ACETONITRILE X TEMP.- Z9 ° C. w 15 Fig. 4 Effect of additives on the photocatalysed reactions of benzhydrol on õ E 12 ZnO T) o as effective as the latter. Fluorene and benzene are found to be less effective, the latter being very weak as a quenching agent. It looks as though there is some correlation between the triplet energy of these hydrocarbons and their efficiency for inhibition. The higher the energy, the less is the efficiency. The percentage of inhibition caused by the various hydrocarbons estimated by observing the extent of reaction after an interval of 6 hours is correlated to their triplet energies in fig. 5. When they are taken externally the photoreaction a 9 c m6 o ^ = 3 0o 24 6 Time (hr.) 8 Fig. 6 140— MEDIUM:- ACE TONITRI LE Influence of traces of water on the photocatalytic activity of ZnO — Formation of H202 TEMP:— 29 °C. 120— 1, NAPHTHALENE C o Z: 100 -3. 2. PHENANTHRENE FLUORENE 4 BENZENE C O 1 80- ¡_ 21 "o- T; 0, 60 — o 18 N A:BENZALDEHYDE B: BENZOPHENONE DRY ZnO_ C ACETONE D , BENZ ALDEHY DE E. BENZOPHENONE F: ACETONE WET ZnO á 40— É 15 - MEDIUM .- ACETONITRILE TEMP.- 29 ° C 20 o 60 a IO CH2OH - 0 -1M a E (CH 3 ) 2 CHOH-0.2M ^o 12 — 64 68 72 76 80 84 Triplet energy, k cal mole -1 88 0 9 Fig. 5 F a o Percentage inhibition caused by hydrocarbons as a function of their @ 2 CHOH-0.1M 6 E B ó U 3 triplet energies goes unaffected. Hence they are not acting as mere filters when taken internally. The photocatalysed reaction of benzylalcohol also is suppressed by naphthalene. It is observed that the reaction is faster when small quantities of water is introduced into the system when acetonitrile is the medium. Zinc oxide, the catalyst in this case, when subjected to infra red 166 00 2 4 6 Time (hr.) 8 10 Fig 7 Influence of traces of water on the photocatalytic activity of ZnO — Formation of carbonyl compounds 4. DISCUSSION According to the interpretation of several workers (12, 13) the formation of hydrogen peroxide at irradiated zinc oxide surfaces involves the reduction of molecular oxygen. ESR studies made by Sancier (14) have revealed that oxygen has indeed already trapped the conducti,n electrons of zinc oxide in the dark. But benzhydrol fails to undergo any reaction in the dark in the presence of zinc oxide showing that light must produce an excited state of oxygen and not merely an electron transfer to oxygen. Since the reactions do not take place either in the dark, or in the presence of light in the absence of oxygen, both light and oxygen are essential for the reaction. Similarly, with oxygen, but without the catalyst no photooxidation is observed. Therefore, the conditions which have to be fulfilled for the reaction are simultaneous presence of zinc oxide, oxygen and ultra-violet irradiation. Oxygen may give rise to different species such as 0 -2 (ads), 0 (ads), 02 (ads), etc. when adsorbed on a solid catalyst (1, 15, 16). Other species like 02 , 0, 0 -* , 02* , 0 - , etc. may also be formed on the surface of a photocatalyst. For reasons given earlier (5), 0 cannot be the active species. Barry and Stone (17) have reported exchange of isotopic oxygen on zinc oxide at room temperature in the dark. This exchange must take place through dissociated oxygen and hence atomic oxygen as the active species can also be excluded. The species that is stable at room temperature only (18, 19) and therefore weakly fixed to the solid is 02. Hence 02 either in the ground or in the excited state could be the active species for the reaction. Calvert et al. (13) have ruled out other excited species of oxygen as possible intermediates. Taking all these factors into consideration two possible mechanisms can be proposed for the present reaction. i.e. H02 + H0 2 ---{ H2 02 + 02 The radical (C6 H5)2 COH can compete with this reaction leading to the formation of benzophenone. (C6 H5 )2 COH + H02 --i(C6 H5 ) C = O + H202 SCHEME 2 If 0 — , formed by the donation of an electron to the adsorbed oxygen from the conduction band of illuminated zinc oxide is the active species, a polar solvent should favour the reaction. In fact in a polar solvent like acetonitrile, the reaction is much faster, suggesting the intermediacy of a polar intermediate. Hence a second scheme of reaction may be proposed as : HH C^ C6Hs O I I \ C6H5 H-0 0 —i /C6H5 H02 H —O Ì Ì ® —C \ C6 H 5 Zn --- O i ® Zn --- O desorption (C6H5)2C=0 +H202+Zn0 Another possibility where, a (O6 H5 )2 COH radical interacts with a molecule of oxygen and gives rise to the observed products cannot be ruled out. ( C 6 H 5 ) 2 C` OH + 02 --+(C6H5)2C(OH)02 SCHEME 1 When the catalyst is illuminated, the Zn-O bonds are excited and loosened. As a result there is a relative shift of bond electron towards the zinc atom (2). Thus an adsorption where the cationic hydrogen bridge is formed between the alcoholic oxygen of the benzhydrol and zinc atom, now electron-enriched, can be envisaged as C6 H5 C6 H 5 (C6 H512 CHOH ZnO hv The anionic bridge is formed between the carbon atom of the benzhydrol and the electron exhausted excited oxygen of the surface. Subsequently, C6H5 (C6 H5 )2 COH can easily lose a hydrogen atom to give (C6 H5 )2 C = O. The H62 radicals can combine in the presence of a third body forming H202. C6 H5 \C / OZ H (b-) (S+) Zn ---- -0 (C6H5)2 CON (C6H5)2C(OH)02 H(C6H5)2C = O + H2 0 2 Of the two mechanisms proposed, scheme 2 is more probable in the present case because it explains the role of a polar solvent in the reaction. Once the benzophenone is formed in the reaction it gets photoexcited under the influence of the absorbed light and converts to the long lived triplet by a highly efficient intersystem crossing (11, 20). These triplet molecules can abstract hydrogen from benzhydrol in a rate determining step forming two free radical species which dimerise to give benzpinacol. (C6H5)2C=0 —h ----(C6H5)2C v = 0. (C6H5)2C= O . + (C6 H5)2 CHOH --i (C6 H5 )2 COH + (C6 H5 )2 COH 2(C6H5)26OH ---o- (C6 H5 )2 — C — C — (C6 H5 )2 H ) COH + H (C6 H5 Zn -H (C6H512C(OH)02 + (C6H51 2 CHOH— ► 1(C6H5) 2 C(OH)02H+ ó 0 ^((C6H5)2COH+ I Há 2 OH OH This will result in the disappearance of benzophenone. But hydrogen and hence hydrogen peroxide will go on accumulating. The behaviour of benzophenone can be understood from the effect of its concentration on hydrogen peroxide formation (fig. 2). At 167 lower concentrations the reaction depends on benzophenone. But in the higher concentration regions (of the order of 2 x 10 -2 M and above) it is independent of the concentration of the ketone. When a sufficient amount of benzophenone is formed from benzhydrol dehydrogenation the rate is equal to that in the case of initially added benzophenone. Moreover, the benzpinacol formed in the system will occupy the surface of the catalyst depriving the alcohol from access to the surface, thus suppressing the catalysed reaction. Naphthalene is a well known quencher for the first excited triplet of benzophenone (21, 22) and hence to its photoreduction to benzpinacol. The activity of zinc oxide is found to be suppressed to a great extent by naphthalene. This is further confirmed by the inhibition of the reactions of benzylalcohol under similar conditions. The mechanism by which naphthalene quenches the photoreduction of benzophenone is well established (22) as a. H2O + O s= - -► OHS + OH S b. dissociative chemisorption of water accompanied by annihilation of preexisting surface anion vacancies LI (0 2- 1. (C6H5)2 C= 0 --i (C6 H 5)2 C = 0 • (singlet) (C6H5 )2 C = exciplex formation should be the cause of inhibition. The possibility of naphthalene getting adsorbed on the catalyst resulting in the nonavailability of sites for dehydrogenation is unlikely since the different hydrocarbons show different inhibiting efficiency. Yet another possibility of the hydrocarbon scavenging the active species of oxygen and causing the suppression of the photoreaction cannot be ruled out. All these processes could contribute to the quenching effect by the hydrocarbon. The presence of water on zinc oxide was found to enhance the activity. In the case of TiO 2 many authors have shown (23, 24) that the surface has weakly and strongly bound molecular water and hydroxyl groups created by the dissociative chemisorption of water. This can take place in different ways (25). O (triplet) (C6 H51 2 C = O (triplet) + C 10 H8--iC10H8 (triplet) + ^(C6H5)2C = O i.e. H2 O +O producing surface OH and bulk 0HE. The hydroxyl groups may be responsible for the enhancement of the rate. The mechanism can be postulated as h — e (exciton) --•- h + e. ZnO This is possible since the triplet energy of naphthalene is 60 k cats mole -1 whereas that for benzophenone is 70 k cal mole -1 . The quenching through singlet-singlet energy transfer can be ruled out since the excited singlet of naphthalene lies at a higher energy level than that of benzophenone. Oxygen also is reported (22) to be a quencher for the reaction. But from the observations we have made it is seen that naphthalene is more efficient as a quencher than oxygen. The solutions used in the reactions were not deaerated and hence oxygen is present both in the dissolved form and the adsorbed state. Still there was a considerable inhibition by naphthalene. The superiority of naphthalene may be due to the fact that oxygen slowly reacts with the benzophenone-benzhydrol system while naphthalene is chemically inert. The inhibition to the activity of zinc oxide caused by naphthalene can also be explained in a similar manner. One of the major phofoeffects on zinc oxide is the transfer of an electron from the valence band to the conduction band which requires about 3.5 eV of .energy. The alcohol gets adsorbed by donation of an electron to the valence band. It is possible that zinc oxide in its excited triplet state transfers its energy to naphthalene and becomes deactivated. The suppressing effect decreases es the singlet-triplet gap of the hydrocarbon increases. Thus the quenching effect is in the order naphthalene phenanthrene > fluorene. Anthracene could not be The singlet levels of used in these studies since it absorbs 3650 all these hydrocarbons lie at much higher levels compared to that of zinc oxide. Hence singlet-singlet energy transfer is precluded. The observation that phenanthrene, with a triplet energy similar to that of naphthalene is equally effective as a quencher while fluorene is less efficient and that benzene whose triplet energy is 84 k cal mole -1 which is more than the band gap of zinc oxide is very weak as an inhibitor supports the energy transfer mechanisms. It is also possible to envisage the formation of an exciplex between excited zinc oxide and ground state naphthalene which again is inefficient as a photocatalyst. It is not clear whether excited zinc oxide is in the singlet state or in the triplet state. If this is a triplet, formation of e3 ZnO • — hydrocarbon» exciplex must be considered. On the other hand if it is a singlet, « 1 Zn0 • — hydrocarbon» + ❑ x(0 2 )--► OHS +OHL The presence of adsorbed oxygen in the dark can cause a space charge to develop at the surface which under illumination favours the movement of photoholes to the surface. Here they become trapped at surface states which in the present case is OH ions. e., h + 0H --- -OH. Now the photoelectron is free to participate in the adsorption of oxygen resulting in 02. Thus the presence of water assists in the generation of the active species. These studies particularly those on the inhibition caused by naphthalene may be of relevance in the electronic theory of photocatalysis. The importance of electronic energy levels cannot be overemphasized when dealing with semiconductors. The energy levels of surface states with respect to the energy bands of the solid will determine whether an adsorbed species will become charged or not and in large part determine the electron exchange (26). Because of the dominant role played by surface state energy levels in the electron exchange process, these levels can be controlling factors in chemical processes such as adsorption and catalysis. ACKNOWLEDGEMENT A. 168 We are grateful to the National Science Foundation (U.S.A.) for financial support. It is a pleasure to record our thanks to Prof. M. C. Markham for all the stimulating discussions. REFERENCES 1. J. H. LUNSFORD, Catal, Revs., 8, 135 119731. 2. F. STEINBACH, «Heterogeneous Photocatalysis», Topics in Current Chemistry, 25, 1 1 7 119721. 3. J. HABER, K. KOSINSKY and M. RUSIEKA, «Photoeffects in adsorbed species», Disc. Farad. Chem. Soc., B-11 11974). 4. TH. WOLKENSTEIN, Adv. in Catalysis, 23, 157 (1973). 5. J. C. KURIACOSE and M. C. MARKHAM, J. Catalysis, 1, 498 (1962). 6. M. C. MAR KHAM and K. J. LAIDLER, J. Phys. Chem., 57, 363 (1953). 7. E. P. YESODHARAN, V. RAMAKRISHNAN and J. C. KURIACOSE (in press). 8. W. M. MOORE and M. D. KETCHUM, J. Phys. Chem., 68, 214 (1964). 9. J. N. PITTS JR., R. L. LETSINGER, R. P. TAYLOR, J. M. PATTERSON, G. RECKTENWALD and R. B. MARTIN, J. Amer. Chem. Soc., 81, 1068 (1959). 10. C. N. CHARI and M. QUERESHI, J. Indian Chem. Soc., 21, 97 (19441. 11. W. M. MOORE, G. S. HAMMOND and R. P. FOSS, J. Amer. Chem. Soc., 83, 2789 (1961). 12. J. C. KURIACOSE and M. C. MAR KHAM, J. Phys. Chem., 65, 2232 (1961). 13. J. G. CALVERT, K. THEURER, G. T. RANKIN and W. M. McNEVIN, J. Amer. Chem. Soc., 76, 2575 (1954). 14. K. M. SANCIER, J. Catalysis, 5, 314 (1966). 15. E. R. S. WINTER, Adv. in Catalysis, 10, 196 (1958). 16. G. C. A. SCHUNT, Chim. Ind., 12, 1307 (1969). 17. T. I. BARRY and F. S. STONE, Proc. Roy. Soc. (London), 335 A, 124 (1960). 18. V. L. RAPPORPORT, Dokl. Akad. Nauk. SSSR., 153, 371 (1963). 19. Y. FUJITA. and T. KWAN, J. Res. Inst. Catalysis, Hokkaido Univ., 7, 224 (1959). • 20. H. J. BACKSTROM and K. SANDROS, J. Chem. Phys., 23, 2197 (1955). 21. G. S. HAMMOND and J. LEERMAKERS, J, Phys. Chem., 66, 1148 (1962). 22. W. M. MOORE and M. KETCHUM, J. Amer. Chem. Soc., 84, 1368 (1962). 23. R. I. BICKLEY, G. MUNUERA and F. S. STONE, J. Catalysis, 31, 389 (1973). 24. G. MUNUERA, J. Catalysis, 18, 19 (1970). 25. G. MUNUERA and F. S. STONE, Disc. Farad. Chem. Soc., 52, 205 (19711. 26. S. R. MORISON, Surface Science, 13, 85 (19691. RESUMO As reacções fotocatalisadas do benzidrol sobre óxido de zinco dão origem a peróxido de hidrogénio e benzofenona. O oxigénio, quer em solução ou à superfície, ou sob ambas as formas, é essencial para a reacção, quando a suspensão de óxido de zinco é submetida a uma radiação com o comprimento de onda de 3650 A. Há um pequeno período de indução na reacção que pode ser eliminado pela adição de pequenas quantidades de benzofenona. A reacção procma•se a maior velocidade em acetonitrilo do que em ciclo-hexano. Verificou-se que hidrocarbonetos tais como o naftaleno e o fenantreno têm um efeito fortemente inibidor sobre a actividade do catalisador, enquanto o benzeno e o fluoreno são menos efectivos como inibidores. A água adsorvida aumenta a actividade do óxido de zinco. Sugere-se que o 02 é a espécie responsável pela reacção. Propõe-se e discute-se um mecanismo consistente com os resultados experimentais e com outros aspectos relevantes. 169