摘要:

J. Chem. Soc., Faraday Trans. I, 1982,78, 979-989 Infrared Study of Adsorption on Oxygen-covered a-Fe,O,: Bands due to Adsorbed Oxygen and their Modification by Co-adsorbed Hydrogen or Water BY FERDOS AL-MASHTA AND NORMAN SHEPPARD* School of Chemical Sciences, University of East Anglia, Norwich NR4 7TJ AND VINCENZO LORENZELLI AND GUIDO BUSCA Laboratorio di Chimica, Facolta di Ingegneria, Universita di Genova, Genova, Italy Received 22nd May, 198 1 a-Fe,O, heated in oxygen for one hour at 400 O C exhibits two complex regions of infrared absorption between 1350 and 1250 cm-I (the type A bands at 1350, 1325, 1300 and 1270 cm-I) and between 1100 and 900 cm-l (the type B bands at 1090, 1060, 1035, 1010, 990 and 930 cm-l). Each group of absorptions is thought to characterise a particular type of species adsorbed on different cationic sites.The observed band wavenumbers lead to the tentative assignment of the type A bands to 0; species perturbed in the direction of 0,, and the type B bands to 0;- species perturbed in the direction of 0;. Evacuation at temperatures in excess of 150 O C led first to the type A and then to the type B bands becoming much reduced in intensity. These changes are correlated with previously obtained thermal desorption peaks from oxygen adsorbed on Fe,O,. The detailed appearance of the band patterns in the type A and type B regions depends on the temperature of the initial interaction of gas-phase 0, with the oxide. They are considered to reflect a frozen-in high-temperature distribution of the species over various surface sites.Redistributions of intensities within the two regions, as a result of prolonged room-temperature evacuation, are thought to reflect a relaxation to a room-temperature distribution of surface sites brought about through induced surface mobility. Similar changes are caused by the adsorption of water at room temperature or by heating in hydrogen. The type A band at 1270cm-' and the type B band at 990cm-l seem to be particularly affected by co-adsorption of water. The former band is shifted to ca. 1200 cm-I and the latter is greatly decreased in intensity. Iron oxide catalysts are widely used in industrial processes, mostly for oxidations or oxidative dehydrogenations. Halpern and Germain' and Iwamato et a1.2 have recently investigated the existence of oxygen adsorbates on the surface of a-Fe203 by means of desorption techniques.Experimental evidence was found for thermal desorption of different adsorbed species from a surface that had been heated in oxygen. Those species of 'adsorbed oxygen' were considered to be different from surface oxygen located at normal lattice positions as 02- ('lattice oxygen'). It is well known3 that a-Fe203 or haematite, which has a corundum structure, can lose lattice oxygen at high temperatures, particularly under evacuation, and be reduced to magnetite, Fe,O,. This can in turn be re-oxidised to y-Fe203 or maghemite, with an inverse spinel structure, by heating in oxygen. Maghemite transforms into the more stable haematite at temperatures above 400 0C.4 Recent studies5 have shown that even at relatively low temperatures lattice oxygen can be a reactive oxygen species in catalyst oxidations, when the redox mechanism which comprises reduction/oxidation cycles of iron oxide becomes operative.979980 I.R. STUDY OF 0, ADSORBED ON a-Fe,O, Following our previous studies,6, we have attempted to characterise the surface of a-Fe,O, by infrared spectroscopy and particularly to investigate spectral modifi- cations due to loss of adsorbed or lattice oxygens by combinations of evacuation and high-temperature treatments. Reductions with hydrogen were also investigated spectroscopically and this led to some measurements with co-adsorbed H,O and D,O. EXPERIMENTAL a-Fe,O, samples were prepared by heating discs of goethite, a-FeOOH, in U ~ C U O at 180 OC.Ca. 100 mg of a-FeOOH was pressed into a disc in a 2.5 cm diameter die at 3 ton cm-2 (2.99 x lo8 N rn-,). The disc was mounted in a silica-glass infrared cell with an electrically heated internal furnace and with KBr windows. The goethite was converted to a-Fe,O, in the infrared cell by gradually heating the disc in uucuo to 180 "C and continuing to heat at that temperature for one hour. The disc, now of a-Fe,O,, was then heated in oxygen at 400 O C for one hour in a flowing system and cooled to room temperature in oxygen before the series of spectroscopic experiments was commenced. The sample temperature was measured with a chromel-alumel thermocouple in contact with the disc. During sample heating the KBr windows were kept cool by streams of dry air from orifices in a surrounding ring of glass tubing.Cylinder oxygen was obtained from Anglia Industrial Gases and was passed through a column of molecular sieve and over P,O, for drying purposes. Bulb hydrogen of 99.99% purity was obtained from the British Oxygen Company. Infrared spectra at 4 cm-l resolution were recorded at room temperature using a Digilab FTS- 14 Fourier transform infrared interferometer. RESULTS GENERAL SPECTROSCOPIC EFFECTS OBSERVED ON HEATING 'OXYGEN-RICH' a-Fe,O, WITH EVACUATION AND ON RE-HEATING I N OXYGEN Fig. 1 (a) shows the spectrum of highly oxidised a-Fe,O, in the presence of 760 Torr of dry 0, at room temperature. Fig. 1 (b)-(e) record the spectral changes as the sample is evacuated and then heated under vacuum at progressively higher temperatures.Features common to all these spectra are a strong blackout absorption between ca. 720 and 480 cm-l and a broad weaker feature centred near 1540 cm-l. The strong feature undoubtedly corresponds to the lattice modes of the Fe,O, particles and the 1540 cm-l band is presumed to be a multi-phonon or combination band involving lower frequency lattice fundamentals. In the intervening region there are complex patterns of absorption between 1350 and ca. 1250 cm-l of relatively weak intensity compared with the lattice absorptions (the type A bands) and between ca. 1100 and 900 cm-l of moderate intensity (the type B bands). A comparison of fig. l(a) with (e) shows that both these regions of absorption have been much weakened and modified by evacuation at elevated temperatures, although the changes in between the extremes are complex in detail.In the discussion below we shall assume that the type A bands arise from essentially the same chemisorbed species, adsorbed on sites of different detailed structures. Except that a different chemisorbed species must be involved, we shall make the same basic assumption about the origin of the type B bands. Although all the bands of each type are much weakened by evacuation at high temperatures, they are not automatically restored by simply re-admitting oxygen gas at room temperature. However, fig. 2 (a)-(e) show that most of them are progressively restored on heating the sample in oxygen at increasing temperatures, although the restoration is not complete after 18 hours at 400 OC [fig.2(e)]. It is clear that an energy of activation has to be overcome in theF. AL-MASHTA, N. SHEPPARD, v. LORENZELLI AND G. BUSCA 981 t c .Y .4 rA & 2 E Y \/ -\ I I I I 1 2 000 1600 1200 800 400 wavenumber/ cm -' FIG. 1.-Infrared spectra of an oxygen-rich a-Fe,O, disc at different stages of evacuation. (a) Oxygen-rich disc prepared by heating in oxygen for 1 h at 400 OC, followed in sequence by: (b) evacuation for 2 h at room temperature, (c) evacuation for 1 h at 300 O C , (d) evacuation for 1 h at 400 O C and (e) evacuation for 12 h at 400 OC. The relative % transmission scales are as follows: (a) 100, (b) 95, (c) 95, (d) 84 and (e) 26% where the very low transmission for (e) indicates a degree of conversion of a-Fe,O, to magnetite, Fe,O,.All spectra were measured at room temperature. process of re-adsorption of oxygen, possibly associated with electron-transfer processes . The evacuation at high temperatures led, by 400 O C , to a major reduction in overall spectral transmission (fig. 1). This is to be attributed to the increasing non-stoichiometry of the Fe203 sample as its composition changes towards that of magnetite, Fe,O,. Such conversion from Fe20, to Fe30, has been previously verified by X-ray diffraction.s The loss of transmission is, as expected, fully restored by re-heating the sample in oxygen to above 300 O C . BEHAVIOUR OF INDIVIDUAL BANDS WITHIN THE TYPE A A N D TYPE B GROUPS We turn now to comments on the effects of heating and evacuation, or re-heating in oxygen, on individual absorption bands.The high-wavenumber type A band system consists of individual absorptions near 1350, 1325, 1300 and 1270 cm-l. Evacuation at room temperature causes most weakening of the ca. 1350 cm-l band (these bands vary in precise wavenumber with982 I.R. STUDY OF O2 ADSORBED ON a-Fe20, 1 i I I I I 4 2 000 1600 1200 800 400 wavenumberlcm-’ FIG. 2.-Infrared spectra of an oxygen-poor a-Fe,O, disc at different stages of re-oxidation. (a) The disc as in fig. 1 (e), followed consecutively by heating in 0,: (b) for 1 h at 100 O C , (c) for 1 h at 200 OC, ( d ) for 1 h at 300 O C and (e) for 18 h at 400 OC. The % transmission scales relative to spectrum 1 (a) are (a) 26, (b) 26, (c) 48, (d) 99 and (e) 1 1 1 %. the different treatments), less weakening of the ca.1325 cm-l band and probably less again of the ca. 1300 cm-l band. However, the ca. 1270 cm-l band is increased in intensity on room-temperature evacuation. The overall impression is that under these conditions there is primarily a redistribution of intensity between the type A bands rather than an overall weakening. It is important to note that moderate heating under vacuum, or helium, to ca. 150 O C leads gradually to a degree of redistribution of intensities back again in favour of the absorptions at 1300 cm-l and above and at the expense of the 1270 cm-l band. This is particularly clearly shown in fig. 1 of ref. (6). However, evacuation at higher temperatures, above 300 O C , [fig. 1 (c)] leads to a reduction in intensity of all type A bands, including that at ca. 1270 cm-l, to give an ‘oxygen-poor’ sample.During prolonged evacuation at 400 O C a new broader adsorption occurs at ca. 1380 cm-l. This, like the much decreased overall transmission at that temperature, probably relates to the gradual formation of bulk Fe,O,. We shall see below that adsorption of hydrogen at elevated temperatures, or water vapour at room temperature, on an ‘oxygen-rich’ surface also leads to the disappearance of the ca. 1350, 1325 and 1300 cm-l bands and to enhancement of the 1270 cm-l band. In the region of the type B bands, evacuation at room temperature also leads toF. AL-MASHTA, N. SHEPPARD, V. LORENZELLI AND G. BUSCA 983 the removal of some bands and enhancement of the intensities of others. At room temperature two bands near 1060 and 1035 cm-l are notably weakened by evacuation and additional absorption occurs near 1095 cm-l and between 960 and 800 cm-l.Again one has the overall impression of a redistribution of intensity, rather than a general weakening, of type B bands [fig. l(a) and (b)]. In fig. l(b) the absorption maxima are at 1090, 1010,990 and 930 cm-l. Some enhanced absorption also occurs between 1200 and 1100 cm-l. Evacuation at increasing temperatures [fig. 1 (c)-(e)] leads again to progressive reductions in intensities of all the type B bands, the reduction being most pronounced for the 1090 cm-l absorption and least, but still very great at 400 OC, for the 930 cm-l band, now shifted to 920 cm-l. Progressive re-heating of the a-Fe,O, samples in oxygen for 1 h each at 100, 200 and 300 O C and finally for 14 h at 400 O C [fig.2(a)-(e)] led to the gradual re-growth of the type A and type B bands, although even at the end of that process the intensities were only partially restored [fig. 2(e)]. SPECTRA FROM THE INTERACTION OF HYDROGEN WITH AN 'OXYGEN-RICH' a-Fe,O, SURFACE As a reducing agent, hydrogen should also be capable of removing oxygen from an Fe,O, surface under appropriate conditions. A series of experiments of this type proved to be instructive, particularly as the computing facility of our Digilab spectrometer was also used to ratio spectra before and after hydrogen treatments. 2000 1600 1200 800 400 wavenumberlcm-' FIG. 3.-Infrared spectra from the treatment of an oxygen-rich a-Fe,O, sample with hydrogen. (a) Spectrum of the initial oxygen-rich disc, followed consecutively by heating in 25 Torr H,: (b) for 1 h at 150 O C , (c) for 1 h at 200 OC and ( d ) for 0.5 h at 230 OC and for 0.5 h at 250 OC. The relative % transmission scales are (a) 100, (b) 100, (c) 91 and ( d ) 66%.984 I.R.STUDY OF 0, ADSORBED ON a-Fe,O, Fig. 3 (a)-(d) show the spectra obtained from an ' oxygen-rich' Fe,O, sample before hydrogen treatment and after heating in 25 Torr hydrogen for 1 h at 150 OC [fig. 3 (b)], then 1 h at 200 O C [fig. 3(c)], 30 min at 230 O C and then 30 min at 250 O C [fig. 3(d)]. The ratioed spectra (b)/(a), (c)/(a) and (d)/(a) are shown in fig. 4(a)-(c). The wavenumber/cm-' FIG. 4.-Ratioed infrared spectra at different stages of treatment of oxygen-rich a-Fe,O, with hydrogen as in fig.3. (a) 3(b)/3(a), (b) 3(c)/3(a) and (c) 3(d)/3(a). 'zero' lines can be drawn reliably with the help of the flat ratio-background above 1400 cm-l. Of course it is not possible to make precise evaluations of positive and negative intensity changes and this is obviously so where these regions greatly overlap. Fig. 3 (b) shows that heating with hydrogen at 150 O C causes changes in the spectra, both for the type A and type B bands, closely similar to those reported in fig. 1 (a) and (b) for prolonged evacuation at room temperature. The ratio-mode spectrum, fig. 4(a), is particularly interesting. It shows clearly the removal of the bands near 1350, 1325 and 1300 cm-l as discussed earlier. Also the absorption enhancement near 1270 cm-1 is evident, but seen in the ratio spectrum as being more accurately centred near 1250 cm-l.Again, in the 1100-900 cm-l region the previously-found labile bands at 1060 and 1035 cm-l are seen to weaken substantially, together with another one that is more weakly reduced near 995 cm-l. The ratioed spectrum emphasises more clearly the increased absorptions between 1150 and 11 10 cm-l and near 900 and 840 cm-l, that were discerned less accurately in the previous section. An additional weak SHpH absorption at 1620 cm-l and associated vOH bands near 3400 cm-l show that the interaction with hydrogen has led to the production of some adsorbed waterF. AL-MASHTA, N. SHEPPARD, V. LORENZELLI AND G. BUSCA 985 which may also (see below) be contributing additional absorption in the 950-800 cm-1 region.The spectra shown in fig. 3(d) and 4(c) show the presence of enhanced amounts of water and also enhanced removal of type A bands at 1350, 1335 and 1300 cm-I and of type B bands at 1060, 1040 and now particularly at 995 cm-l. The spectral changes are now different from those observed in fig. 1 as a result of high-temperature evacuation. In particular in fig. 3(d) the ca. 1270 cm-l band has now moved to give absorption between 1240 and 1 180 cm-l and a more clear-cut absorption maximum occurs near 1120 cm-’. These changes also show up in the ratioed spectrum, fig. 4(c). Further heating in H, for 30 min at 265 OC led to a particularly extreme removal of the band near 990 cm-l. SPECTRA FROM THE ROOM-TEMPERATURE ADSORPTION OF WATER ON ‘ OXY GE N-R I c H’ a-Fe,O, It seemed probable that some of the spectral changes shown in fig.3 and 4 might be related to the adsorption of the water that was the product of the H,/surface-oxygen reaction. Therefore several spectra were obtained of H,O and D,O adsorbed on ‘oxygen-rich’ a-Fe,O, at room temperature. These spectra are shown in fig. 5. The adsorption of a small amount of water [fig. 5(b)] led to spectral changes involving intensity redistributions amongst the type A and type B bands, closely c 2000 1600 1200 800 4 00 wavenumberlcm-’ FIG. 5.-Infrared spectra from the treatment of an oxygen-rich a-Fe,O, sample with water vapour at room temperature. (a) The spectrum of the initial oxygen-rich disc, followed consecutively by: (b) a first stage of water adsorption and (c) a second stage of water adsorption.*An absorption from adsorbed water occurs between 1640 and 1620 cm-’. Relative % transmission scales (a) 100, (b) 88 and (c) 68%.986 I.R. S T U D Y OF 0, ADSORBED ON a-Fe,O, similar to those seen in fig. 3 (c) due to the interaction of hydrogen with a similar sample at 200 OC. Adsorption of a greater amount of water, fig. 5(c), shows more extreme changes resulting in a spectral similarity with fig. 3 ( d ) after interaction with hydrogen at 250 OC. In particular, in fig. 5 (c) the ca. 1270 cm-l has again shifted to ca. 1200 cm-l and there is additional general absorption in the 950-800 cm-l region. Evacuation of the excess water restored the 1270 cm-l band and in general returned the spectrum to an appearance similar to fig. 3 ( c ) but not to fig.3(b). Interaction of ‘oxygen-rich’ Fe,O, with D,O shows, in addition to the expected shift of the &OH band at ca. 1630 to 1200 cm-l for BDOD, the ca. 1270 cm-l band shifted, presumably to coincide with the JD0, band, and considerably reduced absorption in the 950-800 cm-l region. The absorption in this latter region from adsorbed H,O is probably from a librational mode of the latter which for the D,O case is shifted into the lattice blackout region. We conclude that indeed many of the spectral changes recorded in fig. 3 and 4 as a result of heating in hydrogen can be associated with the effects of the resulting adsorbed water. DISCUSSION As the initial ‘ oxygen-rich’ sample was pre-treated with oxygen and its spectrum taken in the presence of the gas, it is possible that 0, species occur on the surface.Molecules or ions of this formula are known to absorb at 1552 cm-l (O,), ca. 1140 cm-l (OF) and at ca. 850 cm-l (Oi-).8* 9 1 lo These wavenumbers relate to formal bond orders of 2, 1; and 1, respectively, but intermediate situations are possible.ll It seems probable that such species perturbed by the strong electrical forces of the quasi-ionic solid would give bands of higher wavenumbers than the above values, due to partial electron withdrawal from anti-bonding orbitals by the polarising power of the cations. A number of previous infrared studies have led to seemingly satisfactory assignments of adsorbed 0;- species (x = 0, 1 or 2) on oxide surfaces obtained either through the use of ls0/l8O mixed isotopes to check the presence of two oxygen atoms in the surface species, or by parallel paramagnetic resonance experiments used to identify the presence of the odd-electron species 0;.The 0, species, possibly in the lA electronic state on adsorption, has been assigned to a band at ca. 1550 cm-1 adsorbed on NiO at low temperatures.l2? l3 0; species have been assigned to bands between 1180 and 1060 cm-l adsorbed on TiO, in the form of rutile14 and 0;- species have been assigned to bands between 1024 and 980 cm-l on Cr,O,.l5 Also in a few cases l60/l8O studies have identified surface species containing only one oxygen atom, on NiO at ca. 1000 cm-l l2 and on Cr,O, at 890 cm-l.15 The latter bands, at notably higher wavenumbers than the lattice modes of the oxides in question, probably involve vibrations of the particularly strongly held outer layers of formal 0,- ions.These may alternatively be approximately described as M=O bonds (M = metal) or as surface- located and polarised Mn+02- ion-pairs. Because of the high wavenumbers of the type A bands there seems to be little alternative to assigning these absorptions between 1350 and 1250 cm-l to species containing two oxygen atoms that are intermediate between the extremes of 0, and 0;. We shall refer schematically to these as perturbed 0; species. The type B bands between 1100 and 900 cm-l could, on wavenumber grounds, be in principle assigned to species intermediate between 0; and 0:-, or to Fe=O surface bonds. In view of the fact that all the type B absorptions are substantially weakened on heating the oxide at high temperatures in vacuum, we prefer the assignment of the bands to 0;- species which we shall schematically refer to as perturbed 0:-.Fe=O bands of the surfaceF. AL-MASHTA, N. SHEPPARD, v. LORENZELLI AND G. BUSCA 987 might have been expected to remain, or to be shifted in wavenumbers, on evacuation. We plan to confirm the Ot- assignment by future 1sO/180 isotope experiments. The use of electron paramagnetic resonance spectroscopy to identify 0; species on the surface is likely to be very difficult because of the paramagnetic nature even of stoichiometric a-Fe203. A number of previous publications have been concerned with infrared spectra of Fe20, or oxygen-treated Fe,O, surfaces.1sy22 It is clear that different methods of preparation and pre-treatments of the Fe203 surfaces give different results.In some cases particular combinations of oxygen treatment and high-temperature evacuations have led to spectra with no absorption bands, except for the ca. 1540 cm-l combination band, above the lattice cut-off between 700 and 800 cm-1.20v 22 This adds support to our assumption that both type A and type B bands relate to adsorbed species. In two cases the strongest additional absorptions occurred just above 900 cm-l,ls, 22 reminiscent of our spectrum, fig. 1 (e), obtained after evacuation at 400 O C . In other cases bands have been observed similar to our type A bands between 1350 and Interpretations of the previous spectra of a-Fe203 also differ. Griffiths et all7 assigned type A bands at 1350 and 1270 cm-l to 0, and 0; species.We agree with this except that we suspect that such close-lying bands will not differ in charge by as much as a whole electronic unit. We assign all the type A bands to perturbed 0, species adsorbed on different sites. On heating Fe,O, in oxygen Davydov et aZ.22 observed two strongish bands at 965 and 918 cm-l in the type B region and assigned them, together with weaker bands at 890,835 and 797 cm-l, to ‘the vibrations of bonds between the surface cation and oxygen, produced as a result of dissociative adsorption of oxygen’ (i.e. to what we have described as Fe==O or Fe3+02- species) on cation sites of different coordination. However, in the same paper they gave the same assignments to bands from Cr,O, in the type B region,22 which later, as a result of their own 180/1s0 experiments, they re-assigned to 0,-containing species,15 possibly 0;-.It seems probable that, as we have proposed for our more extensive series of type B bands on a-Fe,O,, the 965 and 918 cm-l absorptions should also be assigned to negatively charged 0, species. The additional weaker bands observed by Davydov et al. below 900 cm-l 22 can plausibly be assigned to Fe=O groups as for analogous bands of Cr,O3.l5 As described above, interesting redistributions of intensities occur within the individual sets of type A and type B bands as a result of either prolonged evacuation at room temperature or the adsorption of water at the same temperature. This behaviour is simpler within the type A bands. It should be recalled that the original pattern of absorptions for the ‘oxygen-rich’ surface is formed by heating in oxygen at 400 “C for long periods, followed by cooling to room temperature in oxygen.Most of the complex changes in the type A spectra with evacuation and with changes of temperature seem to be accountable on the following hypothetical model. (i) The oxygen-rich pattern of 1350-1270 cm-l bands reflects the distribution of the species between incompletely covered sites at or near the high temperature, ca. 400 O C , where the adsorption was brought about under a pressure of oxygen. (ii) On cooling in oxygen to room temperature this equilibrium becomes frozen-in because of a lack of surface mobility for the adsorbed species. (iii) On evacuation at room temperature most of the adsorbed species in question remain strongly adsorbed, but a few mobility-enhancing sites are freed which allow a re-distribution to a low-temperature equilibrium between the available sites.The more stable site giving the lower-wavenumber adsorption at 1270 cm-l now becomes the strongest. 1250 cm-1.16, 17, 18988 (iv) Heating to 150 O C , either in vacuum or in helium, still gives little desorption of these species but allows the resumption of an intermediate-temperature thermo- dynamic equilibrium between sites. Some regrowth of the higher-wavenumber bands therefore occurs at the expense of that near 1270 cm-l. (v) Heating to higher temperatures in vacuum now leads to desorption with an overall weakening of the set of type A bands but, fig.1 (d), with increased relative intensity of the ca. 1350 cm-l band. (vi) Adsorption of water at room temperature also displaces the adsorbed species from the less stable Lewis-acid sites because of the higher basicity of the new adsorbate. These species however do not desorb but are given sufficient mobility to again find vacant more stable sites (1270 cm-l band) where they cannot be displaced by water. The same basic model can only partially account for the intensity redistributions etc. within the type B bands at higher temperatures of evacuation. In this case, unlike with the type A bands, there is no simple relationship between the band wavenumbers and the stability of the different adsorption sites. The intensity redistribution on room-temperature evacuation, or on water adsorption, is from the bands at 1060,1035 or 990 cm-l to others at higher (1090 cm-l) or lower (930 cm-l) wavenumbers. Also, when desorption sets in strongly, cf.fig. 1 ( d ) and (e), it is the highest-wavenumber band at 1090 cm-l that is weakened to the greatest extent and the lowest-wavenumber band that persists. This would be explicable if redistribution between the various sites is difficult compared with the desorption from the less stable ones. It is of interest to compare the removal of the type A and type B infrared absorptions as a function of temperature with measurements of temperature-programmed desorptions of oxygen from Fe,03 that have been made earlier by Halpern et a1.l and more recently by Iwamoto et aL2 Both laboratories find several well-defined desorption maxima on raising the temperature, one at rather low temperatures (ca.601 or 50-200 "C2), one at moderate temperature (ca. 270' or 360 O C 2 ) and additional desorptions above 450 OC. The strengths and positions of the low-temperature desorption peaks were found to be particularly sensitive to the pretreatment procedure used in adsorbing oxygen. Allowing for the different timescales of the spectroscopic measurements it is tempting to relate the type A infrared absorptions, which desorb above 150 O C , to the low-temperature desorption species and the type B peaks, which mainly weaken above 300 OC, to the moderate-temperature desorption species. When the infrared spectra show very marked losses of transmission on prolonged evacuation above 400 *C this, like higher-temperature desorption peaks, probably denotes the onset of the removal of lattice oxygen from 0,- sites together with the commencement of the conversion of a-Fe,O, to magnetite, Fe30,.In electrostatic terms it is plausible that more negatively charged 0, species will be more difficult to desorb from cationic metal sites, so that the ease of desorption might increase in the order 0;- < 0; < 0,. Adsorbed 0, species seem only to have been reliably identified on oxides below room temperaturel29 l3 and our assignment of the type A and type B absorptions to perturbed 0; and perturbed 0;- species, respectively, fits in with this pattern. On this simple model 0- species should also desorb as 0, at a lower temperature than the lattice-oxygen 0,- ions.However, O--Fe3+ vibrations of such surface species, if present, may well not be observable in these experiments because of overlap with the blackout absorption region of the bulk lattice modes. Two additional points concern the special effects of water adsorption on the infrared spectra of 'oxygen-rich' a-Fe,O,. First, the shift of the type A band at ca. 1270 cm-l to near 1200 cm-l as a result of larger amounts of water adsorptian suggest that at I.R. STUDY OF 0, ADSORBED ON a-Fe203F. AL-MASHTA, N. SHEPPARD, v. LORENZELLI AND G . BUSCA 989 high coverages the latter molecules adsorb on closely adjacent sites. Secondly, the 990 cm-l absorption within the type B band system seems to be much more readily removed by hydrogen at elevated temperatures [fig.3 (d)] or by water adsorption than by heating under vacuum at high temperatures. This band may therefore have a different chemical origin from the other type B bands. We acknowledge assistance in this research programme from the Foundation for Scientific Research (Petroleum Centre), Iraq (Scholarship to F. A-M.), the British Council (V. L.) and the S.R.C. (Senior Fellowship and equipment to N. S.). B. Halpern and J. E. Germain, J. Catal., 1975, 37, 44. M. Iwamoto, Y. Yoda, N. Yamazoe and T. Seiyama, Bull. Chem. SOC. Jpn, 1978, 51, 2765. P. N. Shive and J. F. Diehl, J. Geomagn. Geolectr., 1977, 29, 345. M. S. Ridge, B. Molony and G. R. Boell, J. Chem. SOC. A , 1967, 594. K. Sakata, F. Ueda, M. Misono and Y. Yoneda, Bull. Chem. SOC. Jpn, 1980, 53, 324. V. Lorenzelli, G. Busca and N. Sheppard, J. Catal., 1980, 66, 28. V. Lorenzelli and G. Busca, J. Catal., 1980, 66, 155. K. Nakamoto, Infrared and Raman Spectra of Inorganic and Coordination Compounds (Wiley- Interscience, New York, 3rd edn, 1978). lo N. Sheppard, in Vibration Properties of Adsorbates, ed. R. F. Willis (Springer-Verlag, Berlin, 1980). l1 A. B. P. Lever, G. A. Ozin and H. B. Gray, Inorg. Chem., 1980, 19, 1823. l2 A. A. Tsyganenko, T. A. Rodionova and V. N. Filimonov, React. Kinet. Catal. Lett., 1979,11, 113. l3 A. A. Tsyganenko and V. N. Filimonov, Spectrosc. Lett., 1980, 13, 583. l4 A. A. Davydov, M. P. Komarova, V. F. Anufrienko and N. G. Maksimov, Kinet. Catal. (Engl. l5 A. A. Davydov, Yu. M. Shchekochikhin and N. P. Keier, Kinet. Catal. (Engl. Transl.), 1972,13,980. l6 G. Blyholder and E. A. Richardson, J. Phys. Chem., 1962, 66, 2597; 1964, 68, 3882. * J. Shamir, J. Binenboym and H. H. Claassen, J. Am. Chem. SOC., 1968, 90, 6223. Transl.), 1973, 14, 1342. D. W. L. Griffiths, H. E. Hallam and W. J. Thomas, J. Catal., 1970, 17, 18. V. A. Knappwost and L. Ivens, Ber. Bunsenges. Phys. Chem., 1971, 75, 1063. l9 A. A. Davydov and Yu. M. Shchekochikhin, Kinet. Catal. (Engl. Transl.), 1971, 12, 723. 2o C. H. Rochester and S. A. Topham, J. Chem. SOC., Faraday Trans. 1, 1979, 75, 1673. 22 A. A. Davydov, Yu. M. Shchekochikhin, N. P. Keier and A. P. Zeif, Kinet. Catal. (Engl. Transl.), G. Busca and V. Lorenzelli, Muter. Chem., 1980, 5, 213. 1969, 10, 919. (PAPER 1 /826)

ISSN:0300-9599    

DOI:10.1039/F19827800979

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I, 1982, 78, 991-1000 Tracer Diffusion of Organic Solutes in n-Hexane at Pressures up to 400 MPa BY JOHN H. DYMOND* Department of Chemistry, The University, Glasgow G12 8QQ AND LAWRIE A. WOOLF Diffusion Research Unit, Research School of Physical Sciences, Australian National University, Canberra ACT 2600, Australia Received 27th May, 198 1 Tracer diffusion coefficient measurements in n-hexane have been made using a high-pressure diaphragm cell for [14C]benzene, [14C]toluene, [G - 3H]benzo[u]pyrene, [‘*C]carbon disulphide and [14C]acetonitrile at 298.2 K and at pressures up to 400 MPa. The results, which have an estimated accuracy of f 2 % up to 240 MPa and 5 4% at the higher pressures, have been satisfactorily interpreted on the basis of the rough hard-sphere model.The van der Waals picture of a dense fluid, which is equivalent to the hard-sphere model for transport properties, has proved a very satisfactory basis for the interpretation of transport coefficient data of single-component systems of atoms,l* pseudo-spherical m01ecules~~~~~ and even non-spherical molecule^,^^^ providing that account is taken of the possibility of changes in angular momentum as well as in linear momentum on c~llision.~ One serious disadvantage of this model is that it predicts a phase transition at a density significantly less than the density at which a real liquid solidifies at any given temperature, and this limits the applicability of the model to a fraction of the normal liquidrange. However, it has been shown8 that the predictions of this model provide a basis for the successful correlation of experimental transport coefficient data over the whole liquid range.It is therefore of interest to determine whether transport coefficient data for mixtures can also be satisfactorily interpreted on the basis of the rough hard-sphere model. A previous applicationg of this model to mutual diffusion in binary liquid mixtures showed that for nearly ideal solutions the calculated diffusion coefficient was in excellent agreement with experiment. However, the calculations were based on the assumption that the mass and size ratios were equal to unity and only data at atmospheric pressure were considered. In order to make a rigorous test of the theory it is necessary to have accurate experimental data over a wide range of experimental conditions.In this paper we report measurements on the tracer diffusion coefficient for different organic solutes diffusing in n-hexane at 298.2 K and at pressures up to 400 MPa using a high-pressure diaphragm cell. Details of the experimental method have been given earlierlO and the only modifications were to the pressure vessel to enable the pressure range to be extended above 240 MPa and to the cell, where a new top dome section was made to accommodate.the greater changes in volume. The experimental results are used to estimate the activation volume and to examine the Stokes-Einstein relationship. For a comparison with the predictions of the rough hard-sphere theory, the data are reduced in terms of the self-diffusion coefficient data of the solvent at the same density obtained by the n.m.r.spin-echo technique.ll 99 1992 DIFFUSION OF ORGANIC SOLUTES I N n-HEXANE EXPERIMENTAL DIFFUSION MEASUREMENTS The high-pressure diaphragm cells, the experimental procedures for their use and the method of calculation of the diffusion coefficient have been described previously.10v12 The only modification necessary to extend the pressure range from the maximum of 240 to 400 MPa was the replacement of the pressure vessel closure by a new closure with a higher tensile strength manufactured from a martensitic chrome-nickel steel, Bohler Antinit AS 17N4, conforming to AISI 17-4PH. The diffusion experiments were made using [14C]labelled benzene, [14C]labelled toluene, [G - 3H]benzo[a]pyrene, [14C]labelled carbon disulphide and [14C]labelled acetonitrile from the Radiochemical Centre, Amersham. All experiments were carried out using the solvent-filled diaphragm technique13 with the tracer material added to the top compartment of the diffusion cell.Corrections were made to the measured concentrations for the bulk-flow which occurs at the end of each pressure experiment.1° The compressibility data needed to calculate the cell compartment volumes and bulk-flow corrections were obtained from densities given in the 1iterat~re.l~ MATERIALS AND COUNTING PROCEDURE Spectroscopic grade n-hexane was supplied by Merck. Measured diffusion coefficients, in a glass diaphragm cell at atmospheric pressure for a trace of benzene in n-hexane which had been carefully dried, fractionally distilled and the middle fraction taken, agreed to within the estimated uncertainty with measured coefficients obtained using the undistilled solvent.Counting procedures and equipment have been fully described e1~ewhere.l~ For n-hexane, the scintillator solution consisted of 4 g dm-3 PPO and 0.4 g dm-3 POPOP in toluene and a ratio of 1 part of active liquid to 10 parts of scintillator solution was used. RESULTS AND DISCUSSION The tracer diffusion results obtained with the diaphragm cell are given in table 1, together with densities, calculated from the secant bulk which have an estimated accuracy of 0.2 %. The errors inherent in the diffusion coefficient measurement have been extensively discussed and it is estimated that the results have an accuracy of 4% at higher pressures. The atmospheric pressure diffusion coefficients for benzene in n-hexane agree to within 1 % with the all-glass diaphragm cell meas~rementl~ of 4.747 x m2 s-l and are in good agreement with limiting mutual diffusion coefficient values of 4.758 x The measured tracer diffusion coefficient for toluene in n-hexane at atmospheric pressure agrees closely with the all-glass diaphragm cell valuels of 4.335 x m2 s-l.Tracer diffusion coefficients in n-hexane for benzo[a]pyrene, carbon disulphide and acetonitrile measured in the high-pressurecell agreed to within 1.5 % with measurements in an all-glass cell. The effect of increased pressure on the tracer diffusion coefficients is illustrated in fig. 1. It is clear that the variation of log D with pressure is not linear.Although there is both theoretical evidencelg and experimental evidence20 to show that the activation model is not valid, the dependence of diffusion-coefficient data on pressure is frequently represented in terms of an activation volume AV,, defined by 2% at pressures up to 240 MPa and m2 s-l l6 and 4.723 x m2 s-l,17 obtained using a diffusiometer. AVD=-RT(-) aln D . aP TJ. H. DYMOND A N D L. A. WOOLF 993 TABLE 1.-TRACER DIFFUSION COEFFICIENTS OF ORGANIC SOLUTES IN n-HEXANE AT 298.2 K solute PlMPa [ 14C]toluene [G - 3H]benzo[a]pyrene [14C]carbon disulphide [14C]acetonitrile 0.101 18.7 44.6 88.1 124.3 160.3 198.0 217.5 282.4 292.1 369.3 0.101 41.1 78.1 124.1 191.6 244.9 294.2 375.0 0.101 78.2 129.3 217.3 291.1 369.8 0.101 0.101 40.0 102.6 163.4 221.6 261.1 301.2 324.7 384.0 0.101 39.1 85.9 102.2 146.0 218.8 385.6 p(n-hexane)/kg m-, D/10-9 m2 s-l 655.0 671.4 691.7 712.9 732.7 746.4 757.2 765.2 783.0 784.4 803.4 655.0 688.8 710.8 732.7 757.0 772.9 786.3 805.7 655.0 710.8 735.1 765.0 785.4 803.5 655.0 655.0 687.8 723.4 748.0 767.6 779.3 789.4 795.0 807.4 655.0 686.4 715.3 723.2 741.4 766.8 807.6 4.71, 4.76, 4.12, 2.8 1 , 1.83, 1.38, 3.43, 2.20, 1.54, 1.10, 1.07, 0.75, 4.37, 3.26, 2.63, 2.03, 1.49, 1.10, 0.93, 0.70, 2.68,, 2.64,a 1.56, 1.19, 0.80, 0.57, 0.41, 5.84,, 5.92, 5.96,, 5.9Osa 4.36, 3.23, 2.43, 1.91, 1.66, 1.33, 1.30, 1.06, 6.10, 6.13a 4.50, 3.80, 3.11, 2.70, 1.08, 2.07, a Glass diaphragm cell measurements.994 DIFFUSION OF ORGANIC SOLUTES I N n-HEXANE I I I I 1 I I I 100 200 30 0 408 PlMPa FIG.1.-Effect of elevated pressure on tracer diffusion coefficients at 298.2 K. Key to tracers: 0, [14C]benzene; A, ["Cltoluene; ., [G- 3H]benzo[a]pyrene; e, [14C]acetonitrile; 0, [14C]carbon disulphide. Activation volumes are given to within 0.4 x lo-' m3 mol-1 for the aromatic hydro- carbons diffusing in n-hexane by the equation (2) (3) 1 0' A V D = 1 7.4 - 0 . 0 4 ~ + 0.000 04p2 1 0' A V D = 1 6.3 - 0 . 0 4 ~ + 0.000 04p2 and for carbon disulphide and acetonitrile diffusing in n-hexane by the equation where p is in MPa. This difference in the activation volumes for these two groups of tracers arises from the smaller sizes of acetonitrile and carbon disulphide. In general, the magnitude of tracer diffusion coefficients depends upon the relative molecular masses, the relative sizes and shapes, and the strengths of the molecular interactions.Fig. 2 shows that the pressure dependence of the present tracer diffusion-coefficient data is practically identical for the different aromatic hydrocarbons diffusing in n-hexane and is in very close agreement with the pressure dependence of the self-diffusion coefficient of n-hexane at 298.2 K determined from n.m.r. spin-echo measurements.l' This is an interesting and unexpected result since the tracer molecules vary significantly in mass, size and shape from benzene and n-hexane to the five fused-ring molecule of benzo[a]pyrene, and their molecular interactions with n-hexane will differ also. The tracer diffusion coefficient for carbon disulphide in n-hexane shows the same pressure dependence as that for acetonitrile in n-hexane, but the pressure dependence is significantly lower than for trace hydrocarbons in n-hexane.The difference increases to 17% at 400 MPa. These differences can be interpreted on a molecular basis by consideration of the7 5 a 9 6 3 J. H. DYMOND AND L. A. WOOLF 1 -4 + * 995 0 100 2 00 3 00 400 P F I P a FIG. 2.-Effect of elevated pressure on the ratio of the tracer diffusion coefficients at atmospheric pressure and at pressure p , compared with the corresponding ratio of the self-diffusion coefficient of n-hexane at 298.2 K, 0. Key: 0, [14C]benzene; 0, [14C]toluene; A, [G-3H]benzo[u]pyrene; A, [14C]carbon disulphide, ., [14C]acetonitrile. results obtained from molecular-dynamics studies on the effects of varying molecular parameters separately on tracer diffusion coefficients. Such calculations have been carried out at different densities for hard-sphere systems2' where the single test particle has a mass and size less than that of the solvent.On the basis of the rough hard-sphere model, the binary diffusion coefficient for a dense fluid mixture is given by where n is the total number density, a,, = (a, + a,)/2 for spheres of diameter a, m,, m, are the molecular masses and (D/DE)Mn is the computed correction2, to the Enskog value. A,, is the translation-rotation coupling constant and g,,(a) is the unlike radial distribution function at contact which is given in terms of the like radial distribution functions byz2 where gii (a) is given by ( 5 ) g12W = [a,g,,(a) + 6 2 sll(a)l/2~,2 g&) = -+A+- 1 3Y.YS 1 - x 2(1-x)2 2(1-x)3 x = x,+x,, with xi equal to nn,ai3/6, and yi = (aixj+ajx,)/aj.996 DIFFUSION OF ORGANIC SOLUTES I N n-HEXANE When component 2 is present in trace concentration the expression reduces to This expression differs significantly from the approximate result of L e b o w i t ~ ~ ~ which is seriously in error at densities approaching the normal liquid densities as shown by a comparison with molecular dynamics results. The Thorne equation24 for g12 (a) gives values significantly lower than computed values even at densities corresponding to critical densities. Computed corrections to Enskog theory for different solute-solvent mass and size ratios are given21725 at V/Vo values of 3.0, 1.6 and 1.5, where Vo = Na3/2/2.For comparison, V / Vo for n-hexane at atmospheric pressure is ca. 1.7. Core sizes required for calculation of binary diffusion coefficients were derived from self-diffusion- coefficient data using the expression given earlier26 for a hard-sphere system but modified for rough hard spheres: 2.527A RT 1 0 9 ~ = ( ~ y ( V - 1.384 Vo) Vf! where A is the translation-rotation coupling constant for the single-component system. Values of A, Vo and a for n-hexane, benzene, carbon disulphide and acetonitrile derived using eqn (8) from self-diffusion-coefficient data1” 2 7 9 28 at 298 K are given in table 2. For acetonitrile, A is significantly smaller than the lower limit calculated for rough hard but this is not unexpected for a real molecule which is non-spherical and has an asymmetric mass distribution.TABLE 2.-vALUES OF A , AND 0 FROM SELF-DIFFUSION-COEFFICIENT DATA AT 298.2 K liquid A V,/ m3 mol-l o/nm 77.3 0.566 n-hexane 0.72 benzene 0.67 56.8 0.51 1 carbon disulphide 0.67 33.4 0.428 acetoni trile 0.55 29.1 0.409 These parameters can be used in eqn (4) for direct calculation of the limiting intradiffusion coefficients Di since most theories agree that these are identical to limiting mutual diffusion coefficients DZ for x, + 1 . However, for a comparison of the pressure dependence of the tracer diffusion coefficients predicted on the basis of the hard-sphere theory with the experimental results, it is convenient to reduce the data in terms of the self-diffusion coefficient of the pure solvent Dl(l) at the same density.This reduces the uncertainties associated with the extrapolation of the computer corrections to Enskog theory to infinite particle systems. The variation of the ratio D i / D l ( l ) with mass ratio and size ratio is given for rough hard spheres by the equation with g12(a) given by eqn (5).3 n c. W . 62 O N 9 1 J. H. D Y M O N D A N D L. A. WOOLF I 1 1 I I I 0.4 0.5 0.6 vo/ v 997 FIG. 3.--Comparison of experimental ratio of the limiting tracer diffusion coefficient to the self-diffusion coefficient of the solvent at different reduced volumes with calculated values for the rough hard-sphere model for different tracer :solvent size ratios, mass ratios as given. Key as for fig. 2. The variation of Di/Dl( 1) with &/ V is illustrated in fig.3 on the assumption that A,, = All, at fixed rn,/rn, and a2/al values for Vo/ V > 0.3. The shape of the curves in this region has been determined from curves which include the low-density intercepts. For binary mixtures where the size ratio is approximately one, the ratio of tracer diffusion coefficient to self-diffusion coefficient of the solvent is predicted to be pressure independent for densities above twice the critical density. Where the solute molecule is appreciably smaller than the solvent molecule, the pressure dependence of Di/Dl( 1) becomes more marked, the ratio increasing on going to higher pressures. At present there are no published computer data for diffusion coefficients of hard-sphere systems where the solute is larger than the solvent.However, it is expected that Di/Dl( 1) will show little pressure dependence until a2/al becomes much greater than one, when a decrease in Di/D,(l) with increasing pressure is predicted. For a given size ratio, the change in solute: solvent mass ratio from 1 to 0.1 leads to an increase in Di/Dl(l) of 35% at a,/al = 1, increasing to ca. 55% at a2/cl = 0.5. Values of D;/D,(l) calculated from the present measurements are included in fig. 3. Although these molecules are not spherical in shape it is remarkable how closely these results agree with the hard-sphere predictions. The ratio for the aromatic hydrocarbons diffusing in n-hexane shows no pressure dependence. Di/Dl( 1) with benzene as tracer is higher than that for toluene tracer as expected from con- sideration of the relative values of tracer:solvent mass and size ratios given in table 3.As a2/a, < 1, Di/Dl(l) is predicted by the model to be a few percent greater than one, in agreement withexperiment. For benzo[a]pyrene theestimated size is significantly greater than that of n-hexane. Extrapolation of the values of Di/Dl( 1) for a mass ratio of unity at size ratios of 0.5, 0.75 and 1.0 gives Di/Dl(l) between 0.7 and 0.8 at998 DIFFUSION OF ORGANIC SOLUTES I N n-HEXANE TABLE 3.-TRACER : n-HEXANE MASS AND SIZE RATIOS AT 298.2 K [ l*C]benzene 0.93 0.905 [14C] toluene 1.09 (0.94)" [14C]ace tonitrile 0.50 0.723 [14C]carbon disulphide 0.93 0.756 [G - 3H]benzo[a]pyrene 2.92 (1.23)" a Estimated. Vo/ V > 0.6 for this estimated size ratio. The predicted ratio will be further reduced for a much heavier trace molecule, in close agreement with the experimental result.The experimental D:/Dl( 1) ratios for carbon disulphide lie a few percent below the line for o,/a, = 0.75 and a mass ratio of unity as expected since 02/ol for this system is marginally greater than 0.75. Acetonitrile has half the molecular mass of n-hexane and q2/o, < 0.75, and yet the experimental points lie close to those of carbon disulphide. This suggests that whereas the assumption that A,, = A,, is valid for the other systems, for acetonitrile + n-hexane the unlike translation-rotation coupling constant A,, is ca. 20% less than A,,. The conclusion is in accord with the values derived for A,, and listed in table 2, which differ by only a few percent for benzene, carbon disulphide and n-hexane but are on average ca. 25% greater than the value for acetonitrile.These results can form the basis of an accurate predictive method for tracer diffusion coefficients under elevated pressure. If the self-diffusion coefficient of the solvent is accurately known over the pressure range it is only necessary to measure the tracer diffusion coefficient at atmospheric pressure. From the value of D:/Dl(l) and approximate knowledge of the ratios 02/01 and m,/m,, the density dependence of D:/D,(l) can be drawn and D: calculated for elevated pressures. The molecules considered here are neither hard nor spherical and the inference is that non-spherical shape and realistic forms of the intermolecular potential-energy function will affect the calculated Dl( 1) and D: coefficients to approximately the same extent, so that the general picture produced in fig.3 of the effects of differences in molecular mass and size ratios on D:/Dl( 1) is essentially unchanged. Confirmation of this must await the results of computer calculations at different densities and temperatures for molecules with different forms of intermolecular potential-energy function. Results that have been obtained30 for atoms interacting with a Lennard-Jones (12-6) potential-energy function at a reduced temperature of one confirm that variations in the size ratio at a constant mass ratio produce a significantly greater change in Di/Dl( 1) than corresponding changes in mass ratio for a constant size ratio. Although the computed results are given for a finite (108) particle system, for atoms of equal size Di/D,( 1) has the value of 1.14 for m,/m, = 0.5 and 0.83 for m,/m, = 2.0 in close agreement with the hard-sphere predictions.For atoms of equal mass with a,/ol = 0.5, D;/D,(l) is 1.79, which at the equivalent V0/V value of 0.55 is lower than the hard-sphere results. Further computations are necessary and experimental measurements should be made for systems where the tracer and solvent have widely different sizes. For neon or acetonitrile in octamethylcyclotetrasiloxane at 323 K for example the ratio of tracer diffusion coefficient to self-diffusion coefficient of the liquid solvent should be greater than three and this ratio can be expected to increase rapidlyJ. H. DYMOND AND L.A. WOOLF 999 with increase in pressure. Such measurements would provide a critical test of the assumption of the equivalence of A,, and A12. A final point concerning the present measurements is that they can be used in conjunction with recent accurate mea~urernents~~ of the viscosity coefficient of n-hexane at 298.2 K to test the validity of the Stokes-Einstein equation where Di is the limiting diffusion coefficient at zero concentration of spheres of radius r moving in a hydrodynamic continuum of viscosity coefficient q. a is a constant and k is Boltzmann's constant. At the same temperature it follows that where subscripts a or p denote the value of the limiting tracer diffusion coefficient or solvent viscosity at atmospheric pressure or elevated pressure. This relationship is tested in fig.4. The ratios are identical only at very low pressures. A similar result has been found for benzene and cyclohexane from self-diffusion-coefficient data. However, a comparison of fig. 4 and 2 indicates that DJD, + qp/qa as the size of the solute particle increases. This is in general agreement with the conclusion of a recent re-examination of Stokes' Law.2B 7 - 5 s 1 0 100 2 00 300 400 PlMPa FIG. 4.-Test of the Stokes-Einstein relationship. The shaded region indicates the possible range of values for the ratios of viscosity coefficients of n-hexane and tracer diffusion coefficients for the hydrocarbons in n-hexane at 298.2 K.1000 DIFFUSION OF ORGANIC SOLUTES IN n-HEXANE CONCLUSION Tracer diffusion-coefficient measurements for [14C]beilzene, [14C]toluene, [G - 3H]benzo[a]pyrene, [l*C]carbon disulphide, and [14C]acetonitrile in n-hexane at 298.2 K at pressures up to 400 MPa have been interpreted very satisfactorily on the basis of the rough hard-sphere model.J.H.D. is grateful to the Australian National University for a Visiting Research Fellowship during the tenure of which most of the experimental results reported here were obtained. 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ISSN:0300-9599    

DOI:10.1039/F19827800991

出版商:RSC    

年代:1982

数据来源: RSC