摘要:

J. Chem. SOC., Faraday Trans. 1, 1988, 84(9), 2987-2999 X-Ray Absorption (EXAFS/XANES) Study of Supported Vanadium Oxide Catalysts Structure of Surface Vanadium Oxide Species on Silica and y-Alumina at a Low Level of Vanadium Loading Tsunehiro Tanaka,? Hiromi Yamashita,$ Risa Tsuchitani, Takuzo Funabiki and Satohiro Yoshida" Department of Hydrocarbon Chemistry and Division of Molecular Engineering, Kyoto University, Kyoto 606, Japan X-Ray absorption spectroscopy has been employed to clarify the environmental structure around vanadium atoms in silica-supported and y-alumina-supported vanadium oxide catalysts. Catalysts containing 2.8 '/o of vanadium by weight were prepared with NH,VO, and VO(acac), as impregnation agents. X.P.S. (V 2p,,,) of the catalysts showed that the vanadium atoms in these catalysts are pentavalent.E.s.r. signals from V4+ in the reduced catalysts indicated that paramagnetic VOi- and (V=O)'+ ions are generated by the reduction on silica and alumina, respectively. Although the dispersion of vanadium oxide in the catalysts prepared with VO(acac), solution was found to be higher than those prepared with NH,VO,, the XANES and EXAFS spectra do not exhibit a significant difference for the two types of the catalyst, indicating that the dominant surface species are the same at such a low level of vanadium loading. Analysis of the XANES spectra suggests that VO, tetrahedra are the dominant species on alumina and the vanadates on silica are square pyramidal ; part of the vanadium species is present as V,O, microcrystallites. EXAFS spectra of the catalysts and their Fourier-transforms show that VO, units are isolated on alumina, and that the majority of vanadates on silica are polymeric.These findings by EXAFS/XANES spectroscopy indicate that VO, on silica and VO, (or VO,) on y-alumina, as detected by e.s.r., are only a minority species on each support even at a low level of loading of vanadium. Vanadium oxide catalysts are of commercial importance for catalytic oxidation and have been studied extensively.' Although many efforts have been made to characterize the active species of supported vanadium oxide, definite conclusions on their structures have not yet been given. From e.s.r. spectra, Yoshida et al., and van Reijen and Cossee3 concluded that vanadium oxide is stabilized as a distorted square-pyramidal VO, species on alumina and as VO, tetrahedra on silica. The latter active surface oxides can easily change to a square-pyramidal structure by adsorption of polar molecules such as H,O, alcohol etc.or reducing gas such as C,H,, CO and SO,. Narayana et aL4 investigated, by electron spin-echo spectroscopy, the geometry of such surface paramagnetic species produced on silica by adsorbing water molecules and concluded that adsorption of two water molecules on a vanadium ion in a tetrahedral coordination changes the vanadium oxide cluster to a VO, octahedron. A similar change of t Present address : Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060, 1 Present address : Chemical Research Institute of Non-aqueous Solutions, Tohoku University, Sendai 980, Japan.Japan. 29872988 Supported Vanadium Oxide Catalysts coordination was also observed by Che et ~ 1 . ~ from a change of e.s.r. signals of V4+ on adsorption of 13C0 gas. These e.s.r. results strongly suggest the presence of VO, tetrahedra on the silica support. A similar conclusion about the structure of the surface species on silica and alumina was obtained by Praliaud and Mathieu' from u.v.-visible reflectance spectra, and they also proposed that VO, tetrahedra on a silica surface are the active species in the partial oxidation of propene. Furthermore, the VO, tetrahedra on silica have been proposed as the active species in photocatalysis using vanadium ~ x i d e . ~ The studies, using Raman spectroscopy, by Roozeboom et a1.' showed that more than two species are present as a mixture on the support, and they concluded from the results obtained by the combined use of the t.p.r.technique''") that at low concentrations of vanadium (V z 2.3 wt %) on alumina, surface species consisting of two-dimensional networks of distorted octahedra and isolated V04 tetrahedra, while on silica the dominant species are polymeric arrays of vanadate octahedra-like V,O, crystals with minor isolated VO, tetrahedra. In a study based on u.v.-visible reflectance spectroscopy, Hanke et al.' also pointed out that two different phases, tetrahedra and octahedra, exist together on the silica surface. Furthermore, they also arguedlO that the structure of the octahedral species is similar to that of a decavanadate ion and noted that heating the catalyst at temperatures above 640 K brought about destruction of the decavanadate- like octahedral species to give isolated tetrahedra.The presence of coordinatively unsaturated vanadium ions on alumina was found by Chan et aZ.ll using in situ Raman spectroscopy. The Raman band due to the V=O stretch, observed at a higher position than that in crystalline V205 and shifted significantly on hydration of the catalyst, was indicative of the coordination of water molecules to surface vanadium ions. As mentioned above, some of the results are mutually inconsistent. This is partly because the various spectroscopic techniques can be applied to restricted types of species and give only indirect structural information. In marked contrast to these techniques, EXAFS offers explicit structural information of the predominant species.l2 Employing EXAFS, Kozlowski et al. found that the structure of the surface vanadates on titania and alumina is very different from that of the bulk V20, cry~ta1.l~ In addition to EXAFS, XANES spectra are also sensitive to structural symmetry because XANES fundamentally originates from the transition of a core electron to an empty state.', In particular, features of vanadium K-edge XANES spectra vary significantly with geometry and valency of the vanadium present, and some attempts have been made to assign the spectra.15 Recently, a systematic study using X-ray synchrotron radiation was carried out on various vanadium compounds by Wong et a1.,16 and their results give useful information for identifying vanadium compounds.In this paper we describe the structures of the surface vanadates of silica-supported and y-alumina-supported vanadium oxide catalysts as clarified by vanadium K-edge EXAFS/XANES spectroscopy. Experimental Materials Silica and y-alumina supports were prepared by hydrolysis of silicon tetraethoxide and aluminium tri-isopropoxide, respectively, followed by calcination in a dry air stream for 5 h at 773 K. The commercial alkoxides (extra-pure grade) were distilled in vacuo more than twice prior to the hydrolysis. The supports prepared by this method have fairly large specific surface areas : 244 and 565 m2 g-' for alumina and silica, respectively, determined by the B.E.T. method using N, adsorption.Reference compounds used for EXAFS/XANES analyses were V,05, bis(2,4-pentanedionate)oxovanadium(1~) [VO- (acac),], NH,V03 and NaVO, 1 2H20. V,O, was prepared by thermal decomposition of NH,V03 in a stream of dry air. All other compounds were used as supplied.T. Tanaka et al. 2989 Catalyst Preparation The two types of catalysts were prepared by impregnating the supports with an aqueous solution of NH,VO, (M-VS and M-VA are the silica- and alumina-supported catalysts, respectively) and with a CH,Cl, solution of VO(acac), (A-VS and A-VA are the corresponding silica- and alumina-supported catalysts), and calcined as described previous1y.l' The impregnation of the supports with VO(acac), was performed under water- and oxygen-free N, atmosphere. The content of vanadium in each supported catalyst was adjusted to be 2.8 wt %.Physical Properties of the Catalysts B.E.T. specific surface areas of catalysts M-VA, A-VA, M-VS and A-VS were 210, 240, 405, 41 2 m2 g-l, respectively. X-Ray diffraction (X.r.d.) patterns from each catalyst indicated the absence of any crystalline phase on the support. The vanadium in the M-VS and M-VA catalysts was found to be pentavalent by X-ray photoelectron spectroscopy {Eb[V(2p3,,)] = 518.4 eV (M-VS), 518.1 eV (M-VA), 517.4 eV (V205)}. The dispersion of vanadium oxide (the ratio of the number of exposed V=O species to the number of V ions) on silica was determined by utilizing the isotopic oxygen hetero- exchange reaction between acetone and V=O of the catalyst, as reported previously;" the values of dispersion in the A-VS and M-VS systems were 0.92 and 0.47, respectively, indicating that the vanadates of the A-VS catalyst are present almost as a monolayer on the support.The appearance of the e.s.r. signals of V4+ of the reduced catalysts before and after water adsorption were the same as those reported previously,2 suggesting that paramagnetic VOt- and (V=O),+ ions are generated on silica and alumina, respectively, by the red~ction.~ X-Ray Absorption The X-ray absorption experiments were carried out on beam line 7-c at the Photon Factory in the National Laboratory for High Energy Physics (KEK-PF) with a ring energy of 2.5 GeV and ring current between 150 and 190 mA. The X-ray absorption spectra were recorded using the EXAFS facilities installed at the beam line in the transmission mode at room temperature with an Si( 1 1 1) two-crystal monochrometer.Energy resolution of ca. 0.5 eV can be achieved at the V K edge (5465 eV), but in practice it was ca. 0.8 eV because the monochrometer was slightly detuned to remove higher harmonics. A given sample was mixed with polyethylene powder and pressed into a disc for data sampling. The photon energy was calibrated by the characteristic peak found at the low-energy side of the edge of the absorption spectrum of V,O, (5470.0 eV). Computational analyses were performed with the FACOM M382 computer system at the Data Processing Center of Kyoto University. Results and Discussion X-Ray Absorption Near Edge Structure Fig. 1 shows XANES spectra of M-VA, A-VA, M-VS and A-VS samples together with those from reference compounds : VO(acac), and V,O, are compounds in which van- adium atoms are in square-pyramidal coordination, whereas Na,V04 and NH,VO, have vanadium atoms in tetrahedral coordination.l9 Each spectrum was normalized to the height of the edge jump after removal of the contribution from absorptions other than the K-edge absorption of the vanadium atoms. A characteristic of these XANES2990 Supported Vanadium Oxide Catalysts 1 " " I " " 5150 5500 55! I 5450 5500 55 3 photon energy/eV Fig. 1. Normalised V K-edge XANES spectra of M-VA (a), A-VA (b), NH,VO, (c), NaJO,. 12H,O (d), M-VS (e), A-VS cf), V,O, (g), VO(acac), (h). spectra is seen in the pre-edge peak? attributed to the so-called 1s-3d transition, which is mainly caused by mixing of 2p orbitals of the oxygens with the 3d71 orbitals of vanadium ions. Tullius et aL2' and Cramer and co-workers2' proposed that this d-p mixing suggests the presence of terminal 0x0 group (V=O).Our previous quantum- chemical study7(*) supported their conclusion; ab initio SCF MO calculation of a V=O(OH), cluster showed that degenerate LUMOs consist of V 3d and 0 2p atomic forming 71-like antibonding orbitals of V=O. Therefore, the intense dipole-allowed pre- edge peaks in the XANES spectra of the catalysts indicate that the catalysts possess V=O bonds. The presence of the V=O bond in silica- and alumina-supported vanadium oxide catalysts has also been confirmed by infrared spectroscopy. 22 As shown in fig. l(c) and ( d ) , the pre-edge peak is much more intense when a vanadium atom is in tetrahedral coordination.Moreover, the peak in ( d ) is sharper than that in (c). Na,VO; 12H,O is isostructural with dodecahydrates of Na,PO, and Na3As0,,lg and its XANES spectrum is almost the same as that of Pb,(V0,),C1.15 Wong et a1.16 argued that the bond lengths of four V-0 bonds in Pb,(VO,),Cl are equal judging from the linewidth of the pre-edge peak. Thus the V-0 bonds in Na,VO, are expected to be equivalent, although the lengths have not been determined to our knowledge. On the other hand, NH,VO, has two long and two short bonds (1.66 and 1.81 A).23 In the case of the XANES spectrum of vanadium in square-pyramidal coordination, the pre-edge peak is comparatively small as shown in fig. 1 ( g ) and (h). From the height of the pre-edge peak, vanadium atoms in the A-VS and M-VS systems are expected to be surrounded by five or more oxygen atoms, as with a vanadium atom in VO(acac), or 1- The pre-edge peak is partly constituted by the 1s-3d dipolar transition allowed by the mixing of the 4p orbitals of V and the 1s-3d allowed quadrupole transition."T. Tanaka et al.299 1 Table 1. Energy positions of the pre-edge peak, the edge and l s 4 p transition in V K-edge XANES spectra" relative energy positionsb/eV compounds pre-edge peak edge" l s 4 p transition v205 VOPBDd*e VOSO, * 3H20d VO(acac)2d NH,VO, CrVO, Na,VO, * 1 2H20 Pb,(VO,),C1 M-VS A-VS M-VA A-VA V in square-pyramidal coordination 0.0 (0.0) 10.8 (9.5) (- 1.5) (9.3) (- 0.8) (10.3) -0.3 11.0 -0.3 (-0.8) 12.0 (11.6) (- 1.1) (1 2.4) - 0.6 12.9 catalysts' 0.0 11.4 0.0 11.1 -0.3 12.3 -0.6 12.3 V in tetrahedral coordination (- 0.8) (12.0) 24.0 (24.5) (14.2) (1 5.4) 14.0 21.6 (21 .O) (18.6) (19.5) 17.9 17.4 17.1 19.5 19.2 " Values in parentheses are taken from ref.(16). Energy offset was taken at the pre-edge peak position of V20,. Energy resolution in the present work is 0.8 eV. " Determined from the position of the second maximum of the derivative of XANES curve. Note that formal charge of V in these compounds is 4 + . Bis( 1-phenylbutane- 1,3-dionate)oxovanadium(1v). f See text. V205 crystals. Wong et all6 correlated the integral intensity of this peak both to the average length of the V-0 bonds and the symmetry around the V atom. Unfortunately, we cannot carry out quantitative analysis on our data because the energy resolution was lower than that of the measurements carried out by Wong et al.In order to discuss the structure around V atoms, we should note the post-edge absorption as well as the pre-edge peak. Table 1 gives a summary of the features of the XANES spectra in fig. 1 together with the results of other compounds obtained by Wong et a1.16 The energy offset was taken with respect to the position of the pre-edge peak of V205. The energy positions of pre-edge peak, of the main absorption edge (the second maximum in the first derivative of the XANES curves) and of the peak due to the ls-4~ dipole-allowed transition are dependent upon the symmetry and the valence of vanadium. The XANES features of A-VA and M-VA samples suggest that V in the alumina-supported catalysts is in a tetrahedral coordination.This is consistent with the result of the EXAFS analysis reported by Kozlowski et al.', for an alumina-supported catalyst prepared from VOCl, solution. Fig. 2 shows the first-derivative spectra of normalized XANES of NH,VO,, A-VA and Na,VO, samples. The sharpness of the pre- edge peak is shown clearly by the derivative spectra. Evidently, the pre-edge peak becomes sharper in the order NH,VO,, A-VA and Na,VO,. The sharpness of the pre- edge peak can be correlated with the spread of V-0 distances." Therefore, a VO, unit in the alumina-supported catalyst has a more regular tetrahedral structure than in NH,VO,. As for the silica-supported catalysts (A-VS, M-VS), the positions of pre-edge peak and main edge agree with those of V20,, whereas the position of the peak due to the ls4p transition, the most prominent absorption above the edge, is different from those of the reference compounds (table 1).This suggests that an unknown surface vanadate is formed. Shoulders are observed at ca. 24 eV in fig. 2(e) and (f). The shoulders appear2992 Supported Vanadium Oxide Catalysts 0.4 0.2 2 2 0.0 1 -0.2 5450 5550 energy/eV 2 0.0 -0 -0.2 %:::! -0.4 5450 5550 energy/eV 0.4 2 0.0 \ x a -0 -4 -0.0 5450 5500 energ y/eV Fig. 2. The first-derivative spectra d Y/dE of NH,VO,, A-VA and Na,VO,. 12H,O obtained by differentiating the B-spline functions Y with which XANES spectra were interpolated. (a) NH,VO,, (b) A-VA, (c) Na,VO,. at a similar position to the peak assignable to a ls-4~ transition in the case of V,05.The shoulder observed in fig. 2(e) (M-VS) is clearer than that in (f) (A-VS). This may reflect the formation of V205 crystals on the silica-supported catalyst. If so, the ratio of V,O, crystals to all vanadates is larger in M-VS than in A-VS, suggesting a lower dispersion of vanadium oxide on the M-VS sample than for the A-VS system. In conclusion, XANES analysis revealed that the structure of the surface vanadium oxide species is mostly tetrahedral on alumina and square pyramidal on silica. On silica, some portion of the vanadate exists in microcrystalline V,05 forms. Extended X-Ray Absorption Fine Structure The oscillatory part, Ap(E), of absorption beyond the edge was extracted from the total absorption of the K-edge, pu,(E), by the method reported by Boland et aLZ4 [the method was found to give a good background, ps(E), for the subtraction, although oscillation on the low-energy side is slightly distorted], i.e.M E ) = rUT(E) -Pu,(E) (1) where E is the photon energy. The smoothed absorption, pu,(E), of an isolated vanadium atom? was estimated by fitting the empirical formula to ps(E) in the region between 70 and 100 eV above the edge, viz. po(E) = A/E2.75 (2) -F ,u,(E) in eqn (2) as a background for normalization of EXAFS was introduced in ref. (25). In this paper p . 7 3 was used according to the suggestion of McMaster.26T. Tanaka et al. 2993 3 2 1 220 X - 1 - 2 V - 3 1 , , , , , , , , T 4 6 8 1 0 - 4 6 8 1 0 2 2 1 1 *ri 0 0 .y - 1 - 2 - 3 - 1 4 6 8 1 0 4 6 8 1 0 k/A-’ k1A-I Fig.3. k3-weighted EXAFS spectra of A-VS (a), A-VA (b), V,O, (c), NH,VO, (d). where A is a constant to be determined by least-squares fitting. We then obtain the normalized EXAFS, x(E), as Although pu,(E) is often used for po(E), we used eqn (2) in order to avoid the unfavourable effects on the absorption curve on non-linearity of the efficiency of the ionization chamber us. X-ray energy and sample thickness. The abscissae of the EXAFS curves were converted from photon energy, E, to the wavenumber, k, according to the equation X(E) = AP(E)/Po(E)* (3) k = h-l27r[m(E- EO)]f (4) where h is Planck’s constant, m is the mass of the electron and E,, is the threshold energy for photoionization and is taken to be the energy position of the main edge listed in table 1.The normalized EXAFS oscillation is represented as a function of k by assuming single scattering2’ as N . kr: j X(k) = C L f ( k ) exp (- 2 4 k2) Sj(k) sin [2krj + dj(k)] where N j is the coordination number of scatterers at distance rj,&(k) is the back- scattering amplitude, dj(k) is the phase shift, Sj(k) is the damping factor for compensation of the loss by inelastic scattering and aj is the Debye-Waller factor, introduced to estimate the damping of the amplitude by the turbulence back-scatterers in the jth shell. Fig. 3 shows the k3-weighted EXAFS spectra of A-VS, A-VA, V,O, and NH,VO, obtained according to eqn (1)-(5). The EXAFS spectra of M-VS and M-VA are similar to those of A-VS and A-VA, respectively. Note that the EXAFS oscillation of the A-VS catalyst apparently consists of more than two contributions and resembles that of V,O,,2994 Supported Vanadium Oxide Catalysts 2 c, 6 1 0 0 2 4 6 0 2 4 6 distance /A distance/A Fig.4. Moduli of the Fourier-transforms of k 3 ~ ( k ) . (a)-(d) See captions to fig. 3 . whereas the EXAFS oscillation of the A-VA catalyst has few components of higher frequency and is reduced in amplitude at higher photoelectron momentum. This indicates that there are few atoms heavier than oxygen in the distant shells around a vanadium atom in the A-VA catalyst. Such characteristics became clcarer when a Fourier-transform was performed on the EXOAFS curves in the 3.5-1 1.0 A-l region, as shoyn in fig. 4. The peaks appearing at 1-2 A are due to V-0 bonds and the peaks at 2-3 A found in fig.4(a) (A-VS) and ( c ) (V205) show the presence of neighbouring V atoms, i.e. polymeric vanadate. The heights of the peaks due to V-V proximity are almpt the same in both (a) and (c), but the peak in (a) is seen at a distance shorter by 0.2 A than that in (c). Since tge apparently single VTV peak in (c) is the superimposition of several V-V pairs (3.08 A x 2, 3.42 A x 1, 3.56 A x 2), the coordination number and the V-V distances for sample A-VS cannot be determined from the height and the position of the peak of the Fourier-transform. However, if the peak represents average distances, it may be said that the first neighbouring V atoms are located at a smaller distance in the case of the A-VS system [fig. 4(a)] than in the case of V,05 (c). As shown with arrows in fig.4, V-V peaks are very small in (b) (catalyst A-VA) and ( d ) (NH,VO,). In the case of metavanadate chains,lg. the number of neighbouring V atoms is exactly two if the length of the chain can be regarded as infinite. The reason why the V-V peaks are very small in fig. 4 ( d ) is probably because the V-V distances are variable. Such disordering should bring about a high degree of damping of the amplitude of the EXAFS. Such a phenomenon in EXAFS spectra is observed typically with substances in the amorphous state.? Although vanadium atoms in both the A-VA catalyst and NH,VO, are expected to be surrounded by four oxygen atoms, the magnitude of the V-0 peak for the A-VA system (4.0) is much larger than that (1.5) for NH,VO,, reflecting the trend of the envelopes of the EXAFS oscillations.This difference arises mainly from the variation of the V-0 bond lengths : superposition of different sine waves causes beats,29 leading to the same effect as the Debye-Waller factor when the frequencies are close to each other. As shown in fig. 5 type 11, a VO, unit in t There are many papers dealing with disordered systems. The first report on the Fourier-transformation of EXAFS was ref. (28).T. Tanaka et al. 2995 0 O--i"\o 0 type I t y p e I1 Fig. 5. Models of two types of VO, tetrahedra. V=O represents a multiple bond of V and 0. NH,VO, has four V-0 bonds, of which two are longer (by 0.15 A) than the o t h e r ~ . ' ~ Therefore the result shows that the deviation of V-0 distances from the mean value is smaller in the case of the A-VA system than in the case of NH,VO,; the VO, unit in alumina is thought to be close to a regular tetrahedron.This supports the conclusion from XANES analysis. Estimation of V-0 Bond Distances We carried out further analysis of the EXAFS oscillations employing non-linear curve- fitting using eqn ( 5 ) against the Fourier-filtered EXAFS of V-0 shells. Fourier-filtering was performed as follows: the peaks reprqenting V-0 shells are isolated with a Hanning window in the region of 0.5-2.1 A and an inverse Fourier-transform was performed on the data. In the curve-fitting analysis, we assumed that Si is k-independent and regarded as a constant. The rational of this assumption is seen in the experimental result of Stern et a/.,' The other unknown functions, d,(k) andf,(k), were extracted from EXAFS oscillations of NH,VO, and Na,VO, as follows.We assumed the transferability of these functions and equivalence of four V-0 bonds in Na,VO,. The amplitude function, A,-,(k), of the Fourier-filtered EXAFS of Na,VO, was used, supposing that A,-,(k) is proportional tof,-,(k). AVp0 includes Svp0 and the Debye-Waller factor for Na,VO,. Then we rewrite eqn (5) for V-0 shells using A,-,(k) such as N . ri (6) k"(k) = k2XA,-, C 4 exp ( - 260; k 2 ) sin [2krj + 6 , 4 k ) ] where AajZ is the difference between the Debye-Waller factors of an unknown species and Na,VO,, and X is a constant for the scaling of the magnitude of A,-,(k). In the cgse of NH,YO,, there are two kinds of V-0 bonds, N,, N,, r, and r2 are 2, 2, 1.66 A and 1.8 1 A, re~pectively.~~ Since in the case of light atoms such as vanadium and oxygen, the phase shift is known to be almost linear with respect to k, d,-,(k) was determined by adding the linear correcting term (ak + b) to the value calculated theoretically by Teo and Lee3, as follows, (7) where d'(k) represents the theoretical phase shift.Using eqn (6) and (7), the EXAFS curve of NH,VO, was fitted with fjve variables, j.e. X , A o ~ (j = 1,2), a and h. The values of X , a and b obtained were 0.73 A2, 0.128 rad A and - 2.044 rad, respectively. In order to verify the reliability of these values, we carried out an analysis of the EXAFS of the reference compounds. The results and the crystallographic data32' 33 are summarized in table 2, showing good fits for these compounds for V-0 distances.However, the error in coordination numbers is less good. In the case of vanadium pentoxide, the total coordination number (3.3) is too small in comparison with the crystallographic data (5). This often occurs in the case of bulk metal oxides with uvequal metal-oxygen For N$,VO,, the V-0 bond length obtained was 1.7 15 A. This is close to the value of 1.721 A in the V0:- anion,35 which is stable, as a regular tetrahedron, in a basic solution. 6,-,(k) = d;(k) + ak + b2996 Supported Vanadium Oxide Catalysts Table 2. Results of curve-fitting analyses for V-0 shells of reference compounds curve-fitting results crystallographic data" compounds coordination no. bond length/A coordination no. bond length/A VO( acac) 1.1 1.579 1 1.571 4.2 1.972 4 1.968 '2'5 0.7 0.8 1.1 0.7 1.606 1.789 1.894 2.0 13 1.585 1.780 1.878 2.021 Na,VO, * 1 2H20 3.6 1.715 (4)b (1 .721)b " The data for VO(acac),, V,05 and orthovanadate ion, see ref.(32), (33) and (35), respectively. Values in parentheses are those of V0:- anion in a basic aqueous Table 3. Results of curve-fitting analyses for V-0 shells in catalysts catalyst coordination no. bond length/A A 8 / P R" 0.047 0.042 A-VA 1.3 1.67 0.0022 2.6 1.77 0.0024) M-VA 1.1 1.67 2.8 1.74 0.0020 A-VS 0.9 1.5 1.8 M-VSb 0.4 0.5 0.9 0.6 1.81 - - o-ooo2 0.0000 'I 0.046 1.61 I .98 0.0006) 1.60 0.00 14 1.76 0.0007 1.89 0.00 12 2.03 0.00 1 1 0.037 a R = ( { C , ~ o b , ( k ) - ~ c , , c ( k ) ] 2 } / ~ , ~ o b , ( k ) ] 2 ) ~ , a measure of fit. gave unacceptable Debye-Waller factors.The fitting of two or three shells This method was applied likewise to the catalysts and the results are given in table 3. The fits for the A-VA and A-VS systems are shown in fig. 6 as examples. The structural parameters of the two types of alumina-supported catalyst are similar to each other. Although unreliability in the coordination numbers can be seen in table 2, the similar results obtained from the A-VA and M-VA cases suggest that VO, tetrahedra on alumina m a j be distorted as shown in fig. 5, i.e. type I, with one short (1.67 A) and three long (1.77 A) bonds. The shorter distance corresponds to the V=O bond, the infrared absorption band of which has been found at 1016 cm-' byoIwamoto et a1.22 The difference of bond length between the two types is ca.0.1 A, consistent with the conclusion from XANES spectra and EXAFS band envelopes. In the case of silica- supported catalysts, successful fits were obtained with more than three V-0 shells: when curve-fitting was carried out with fewer V-0 shells than listed in table 3, we could obtain a good fit, but the resultant parameters were unacceptable, e.g. some relative Debye-Waller factors (Ao2) became large (ca. lo-') and some coordination numbers became much too large. The vanadates of the silica-supported catalysts are probably square-pyramidal, like the VO, unit in vanadium pentoxide as judged from the XANES analysis, with one short (1.6 A) and four long (> 1.8 A) bonds. The shorter bond is aT. Tanaka et al. 2997 ,x : 4 5 6 7 8 9 1 0 1 1 4 5 6 7 8 9 1 0 1 1 k1W-l Fig.6. The fits of Fourier-filtered EXAFS (V-0 shells). The solid curves were obtained experimentally and the broken ones are the best fits. EXAFS of A-VA (a) and A-VS (b). multiple bond (V=O) which exhibits an i.r. band at 1035 cm-1.22 The difference in the V=O distances between alumina- and silica-supported catalysts is reflected in the difference in the i.r. band positions. The lengths of the V-0 bonds in the M-VS case are similar to those in vanadium pentoxide, showing that a high proportion of the vanadate in the M-VS case is present in a crystalline V20, form. This is related to the dispersion of vanadium oxide and is consistent with the XANES results. However, the total coordination number is estimated to be only 2.4, i.e. it is smaller than that obtained in the case of V,O, (3.3).Such a low value of the total coordination number is presumably not due to disordering of the VO, unit in the dominant single phase but to mixing of several phases of vanadates. As seen in the case of the A-VS system, the values of Aa2 are lower and the total coordination number is 4.2, indicating that there is a single VO, unit dispersed uniformly. We call this an SP-phase tentatively. In the case of the M-VS system, a crystalline V20, phase is mixed with the SP-phase, resulting in a marked reduction of the apparent total coordination number. Such disordering cannot be described by a Gaussian distribution of the displacement of 0 atoms in a single phase. The structure of the SP-phase was not determined at the present stage.However, we consider that the SP-phase is a two-dimensional array of VO, species with sharing of edges and/or corners like double chains of metavanadates in KV03.H,019 or like a hexavanadate since the vanadates are presumably present as a monolayer in the A-VS sample.2998 Supported Vanadium Oxide Catalysts Surface Vanadates of the Catalyst The EXAFS and XANES analyses indicate clearly that the dominant surface vanadates are monomeric VO, tetrahedra on alumina and polymeric VO, square pyramids on silica. On silica, microcrystals of V20, are partly formed. These findings are in partial agreement with Raman and t.p.r. resultsg but in conflict with those obtained by means of e.s.r. data reported el~ewhere.~-~' 3 6 9 38 Since EXAFS/XANES offers information on the most dominant species, it is considered that VO, on silica and VO, on alumina, as detected by e.s.r., are only minor species.The presence of VO, (or VO, octahedra) on y-alumina was suggested by Roozeboom et al. on the basis of the Raman spectroscopic results.* They proposed that the species might be a two-dimensional array of polyhedral vanadates comparing the observed Raman bands with that of the decavanadate If the polyhedra detected by Raman spectroscopy are identical with the species detected by e.s.r., it is expected that the degree of polymerization of the polyhedral vanadates is not high because the hyperfine structure of the e.s.r. signal of (V=O)2+ is observed clearly. Thus, isolated VO, or VO, should be considered as the surface species on alumina.The difference in the degree of aggregation of vanadates reflects the difference in the affinity of the two supports for vanadium oxide. During impregnation of the support, vanadium ions are loaded either by physisorption of the solute or by formation of chemical bonds between the vanadium salt and the support. Very often the bonds are formed by reaction with OH groups of the support.? Vanadium ions attached in the latter way are probably bound tightly to the support. Since the surface concentration of the OH groups of y-alumina is larger than that of silica,$ the probability of formation of bonds between vanadium and the support should be higher when alumina is used as a support. This is one significant reason why the content of isolated vanadate species is lower than that of the polymeric species on silica and why most of vanadates are discrete species on alumina at a low level of loading.Since the absorption spectra were collected under the ambient conditions in the present work, the surface state may be different from that under reaction conditions. For the latter, the most likely is an increase in coordination number owing to adsorption of water molecules, as is often pr~posed.~. 4 * 6 , ''9 ''7 l7 While the information and the methods presented in this paper shed light on the surface chemistry of supported vanadium oxide catalysts, our next paper will deal with the problem of adsorption of water molecules on the surface vanadium oxide. We thank Dr Masaharu Nomura of KEK-PF for his advice in collecting X-ray absorption spectra.The X-ray absorption experiments were performed under the approval of the Photon Factory Program Advisory Committee (proposal no. 85- 101). References 1 P. J. Gellings, in Catalysis, ed. G . C. Bond and G. Webb, Specialist Periodical Report (Royal Society of Chemistry, London, 1985), vol. 7, p. 104 and references therein. 2 S. Yoshida, T. Iguchi, S. Ishida and K. Tarama, Bull. Chem. SOC. Jpn, 1972, 45, 376. 3 L. L. Van Reijen and P. Cossee, Discuss. Faraday SOC., 1966, 41, 277. 4 A. Narayana, C. Narasimhan and L. Kevan, J . Catal., 1983, 79, 237. 5 M. Che, B. Canosa and A. R. Gonzalez-Elipe, J. Phys. Chem., 1986, 90, 618. f E.g. silica dehydrated at 773 K in uacuu displays a sharp i.r. absorption band at 3750 cm-' due to isolated OH groups.A remarkable reduction in the intensity of this band is observed after loading with vanadium oxide. 1 See ref. (39). Concentrations of surface OH groups prepared by the same method in the present work were measured and reported in ref. (40).T. Tanaka et al. 2999 6 H. Praliaud and M. V. Mathieu, J. Chim. Phys., 1976, 73, 689. 7 (a) T. Tanaka, M. Ooe, T. Funabiki and S. Yoshida, J. Chem. SOC., Faraday Trans. I , 1986, 82, 35; S. Yoshida, T. Tanaka, M. Okada and T. Funabiki, J. Chem. Soc., Faraday Trans. I , 1984, 80, 119; S. Yoshida, Y. Magatani, S. Noda and T. Funabiki, J. Chem. Soc., Chem. Commun., 1982, 601; S. Yoshida, Y. Matsumura, S. Noda and T. Funabiki, J. Chem. Soc., Faraday Trans. I , 1981, 77, 2237. (b) H. Kobayashi, M. Yamaguchi, T. Tanaka and S.Yoshida, J. Chem. Soc., Faraday Trans. I , 1985, 81,1513. (c) M. Anpo, I. Tanahashi and Y. Kubokawa, J. Phys. Chem., 1980,84,3440; A. M. Gritscov, V. A. Shvets and V. B. Kazansky, Chem. Phys. Lett., 1975,35,511. ( d ) S. Kalliaguine, B. N. Shelimov and V. B. Kazansky, J. Catal., 1978,55,384; D. L. Nguyen, P. C. Roberge and S. Kalliaguine, Can. J. Chem. Eng., 1979, 57, 288. 8 (a) F. Roozeboom, M. C. Mittelmeijer-Hazeleger, J. A. Moulijn, J. Medema, V. H. J. de Beer and P. J. Gellings, J. Phys. Chem., 1980,84,2783. (b) F. Roozeboom, J. Medema and P. J. Gellings, 2. Phys. Chem. (Frankfurt), 1978, 111, 215. 9 W. Hanke, R. Bienert, H-G. Jerschkewitz, G. Lischke, G. Ohlmann and B. Parlitz, Z. Anorg. Allg. Chem., 1978, 438, 176. 10 G. Lischke, W. Hanke, H-G. Jerschkewitz and G.Ohlmann, J. Catal., 1985, 91, 54. 11 S. S. Chan, I. E. Wachs, L. L. Murrel, L. Wang and W. K. Hall, J. Phys. Chem., 1984, 88, 5831. 12 P. A. Lee, P. H. Citrin, P. Eisenberger and B. M. Kincaid, Rev. Mod. Phys., 1981, 53, 769. 13 R. Kozlowski, R. F. Pettifer and J. M. Thomas, J. Phys. Chem., 1983, 87, 5176. 14 (a) R. G. Shulman, Y. Yafet, P. Eisenberger and W. E. Blumberg, Proc. Nut1 Acad. Sci. USA, 1976,73, 15 P. E. Best, J. Chem. Phys., 1966,44,3248; E. W. White and H. A. McKinstry, Adv. X-Ray Anal., 1966, 16 J. Wong, F. W. Lytle and R. P. Messmer and D. H. Maylotte, Phys. Rev. B, 1984, 30, 5596. 17 S. Yoshida, T. Matsuzaki, T. Kashiwazaki, M. Mori and K. Tarama, Bull. Chem. SOC. Jpn, 1974, 47, 18 T. Tanaka, R. Tsuchitani, M. Ooe, T. Funabiki and S. Yoshida, J.Phys. Chem., 1986, 90, 4905. 19 A. F. Wells, Structural Inorganic Chemistry (Clarendon Press, Oxford, 5th edn, 1986), p. 568. 20 T. D. Tullius, W. 0. Gillum, R. M. K. Carlson and K. 0. Hodgson, J. Am. Chem. SOC., 1980, 102, 5670. 21 S. P. Cramer, K. 0. Hodgson, E. I. Stiefel and W. E. Newton, J. Am. Chem. SOC., 1978, 100, 2748; J. M. Berg, K. 0. Hodgson, S. P. Cramer, J. L. Corbin, A. Elsberry, N. Paryiyadath and E. I. Stiefel, J. Am. Chem. Soc., 1979, 101, 2774. 22 M. Iwamoto, H. Furukawa, K. Matsukami, T. Takenaka and S. Kagawa, J. Am. Chem. SOC., 1983, 105, 3719. 23 H. T. Evans Jr, Z. Krystallogr. Mineral., 1960, 114, 257. 24 J. J. Boland, F. G. Halaka and J. D. Baldeschwieler, Phys. Rev. B, 1983, 28, 2921. 25 F. W. Lytle, D. E. Sayers and E. A. Stern, Phys. Rev. B, 1975, 11, 4825. 26 McMaster (Report No. UCRL-50174, 1969, unpublished). 27 E. A. Stern, Phys. Rev. B, 1974, 10, 3027; C. A. Ashley and S. Doniach, Phys. Rev. B, 1975, 11, 1279; 28 E. Sayers, E. A. Stern and F. W. Lytle, Phys. Rev. Lett., 1971, 27, 1204. 29 G. Martens, P. Rabe, N. Schwentner and A. Werner, Phys. Rev. Lett., 1977, 39, 1411. 1384. (b) R. A. Bair and W. A. Goddard 111, Phys. Rev. B, 1980, 22, 2767. 9, 376; I. Salem, C. N. Chang and T. J. Nash, Phys. Rev. B, 1978, 18, 5168. 1564. P. A. Lee and J. B. Pendry, Phys. Rev. B, 1975, 11, 2795. 30 E. A. Stern, B. A. Bunker and S. M. Heald, Phys. Rev. B, 1980, 21, 5521. 31 B-K. Teo and P. A. Lee, J. Am. Chem. Soc., 1979, 101, 2815. 32 B. Morosin and K. Montgomery, Acta. Crystallogr., Sect. B, 1969, 25, 13541 33 H. G. Bachmann, F. R. Ahmed and W. H. Barnes, Z. Krystallogr. Mineral., 1961, 34 T. G. Parham and R. P. Merrill, J. Catal., 1984, 85, 295. 35 F. C. Hawthorne and R. Faggiani, Acta. Crystallogr., Sect. B, 1979, 35, 717. 36 A. D. Wadsley, Acta Crystallogr., 1955, 8, 695. 37 V. A. Shvets, M. F. Saricheu and V. B. Kazansky, J. Catal., 1968, 11, 378; V. B Shvets, M. Kon, N. Ya, V. V. Kisha and B. N. Shelimov, Proc. 5th Int. Congr. 15, 110. Kazansky, V. A. Catal., ed. J. W. Hightower (North-Holland, Amsterdam, 1973), vol. 2, p. 1423. 38 K. Tarama, S. Yoshida, S. Ishida and H. Kakioka, Bull. Chem. SOC. Jpn, 1968, 41, 2840. 39 Y. I. Yermakov, B. N. Kunznetsov and V. A. Zakharov, Catalysis by Supported Complexes (Elsevier, 40 J. Kijenski, A. Baiker, M. Glinski, P. Dollenmeier and A. Wokaun, J. Catal., 1986, 101, 1. Amsterdam 198 l), chap. 2. Paper 7/1261; Received 14th July, 1987

ISSN:0300-9599    

DOI:10.1039/F19888402987

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Clwm So( Fctraday Trans. I, 1988, 84(9), 3001-3013 A Model for the Mass-transfer Resistance at the Surface of Zeolite Crystals Milan KoEifi?c J. Heyrovsky Institute of Physical CheFistry and Electrochemistry, Czechoslovak Academy of Sciences, Machova 7, CSSR-12138 Prague 2, Czechoslovakia Peter Struve, Klaus Fiedler and Martin Bulow* Central Institute of Physical Chemistry, Academy of Sciences of the G.D.R., Rudower Chaussee 5, DDR- I199 Berlin, German Democratic Republic A microdynamic model is proposed to describe the mass-transfer resistance localized at the surface of zeolite crystals. In addition to the intracrystalline diffusional resistance, this resistance occurs owing to the repulsion and attraction interaction between sorbing molecular species and the crystal surface.Especially for small crystals the surface resistance can exceed the intracrystalline diffusional resistance by several orders of magnitude. In particular, the model explains the non-linear behaviour of Arrhenius plots of uptake data exemplified for the sorption of n-hexane on NaMgA zeolite crystals. During the last ten years the existence of a transport resistance at the surface (within the surface region) of zeolite crystals occurring in addition to the intracrystalline diffusional resistance has been discussed in the literature [e.g. ref. (1)-( 13)]. In particular, this specific resistance has been proposed as a possible explanation of the discrepancy between uptake and n.m.r. data on intracrystalline molecular diff~sion.'~~, 7 9 8 , l1-l5 In this respect, two points of view have been formulated: (i) the peculiarity of the transport resistance at the surface of zeolite crystals was assumed to be a result of the surface energy distribution of the crystals;' (ii) the obstacles responsible for an enhanced mass- transport resistance were assumed to be localized at the surface (within the surface region) (i.e.in this case the repulsion forces play a more pronounced role than in the case of a surface which is free of obstacles).2*3*5 In this context, the supposition of an energy barrier at the micropore mouth of a molecular sieve carbon is worth menti~ning.~ It has been used for computing the potential-energy distribution in a semi-infinite slit-like pore, applying a Lennard-Jones potential for continuously distributed force centres.Analogous ideas have been considered qualitatively for zeolites. l6 With zeolites, however, the approach of a structural surface barrier seemed to be more plausible. This type of barrier may occur for various reasons [cf. ref. (4) and (5)], e.g. from deposition of impenetrable material at the outside of individual crystals (pore- mouth poisoning by coke products'O or blockage by strongly sorbed molecules of another 6, l7 by changes of the crystal structure due to chemical reactions during the processes of cation exchange and hydrothermal and by other zeolite modifications [cf. ref. (4)]. The main experimental work regarding the nature of structural surface barriers has been performed by Bulow and co-worker~~-~, *, lo, 13, 17-23 and Karger and co- Bulow and Struve compared the sorption uptake behaviour of normally activated and hydrothermally treated NaMgA2v l3 and NaCaA'8.28 zeolite crystals.In the case of hydrothermally treated zeolites they observed a marked S-shape of the uptake curves, wOrkers.3,7,8,10-12,24-27 300 13002 Mass-transfer Resistance when plotting those in the relative uptake us. square root of time mode. Such behaviour is unambiguous evidence of a so-called skin effect on the mass t r a n s p ~ r t . ~ ~ - ~ l The uptake curve shape observed after hydrothermal zeolite treatment indicates that the solid transformation follows the shrinking core model, cf ref. (32). Thus, the formation of a skin of finite thickness within the surface region of zeolite crystals must be assumed.This model suggests that the crystal transformation does not take place over the whole bulk of any crystal. Pfeifer and Karger developed n.m.r. techniques12* 33-36 that allow unequivocal identification of structural surface resistances. The application of these techniques to the mobility of various molecular species sorbed on both normally activated and hydrothermally treated NaCaA zeolites led to the conclusion that with the latter zeolites an additional mass-transport resistance arose, and this resistance is concentrated in the zeolite crystal surface layer.3. 5, 24-277 35 Although till now several physico-chemical reasons for transport resistance have been derived from appropriate experiments [e.g. ref. (4)], the development of our knowledge is still in progress.37 Besides experimental work, theoretical considerations are needed.It is the aim of this paper to give a microdynamic model for describing the mass transport through a structural surface barrier. In this way, the effect of structural changes within the first surface layer of zeolite crystals on the overall mass transport of sorbing species should be explained. The Model The model is appropriate for solid sorbents with regular intracrystalline micropore (lattice) structure, such as zeolites. Its main features are as follows. (1) The concentration of the sorbing species in the zeolite crystals is restricted to the so-called zero-pore-filling degrees and, therefore, the equilibrium sorption isotherm is given by the linear function a = Kc (1) where a is the amount sorbed per unit volume of zeolite crystals (mol ~ m - ~ ) , c is the molar concentration of sorbing species in the gaseous phase (mol ~ m - ~ ) and K is the Henry constant.(2) It is supposed that the sorption process is isothermic. The non-isothermicity of the sorption process is disregarded because it would give rise to an additional resistance at the boundary of the zeolite crystals [cf ref. (38>-(40)]. (3) It is postulated that the space distribution of the potential energy @ of a molecule of sorbing species in the force field of a zeolite crystal depends on one space coordinate x perpendicular to the interface area gas-zeolite crystal, (fig. 1). The origin of the coordinate x is situated at the position of the first local maximum which a molecule approaching the crystal encounters in the region of decreasing potential energy, before a steady periodic change of the potential energy within the crystal bulk is attained (it is assumed that the level 0 = 0 is situated far from the crystal, i.e.at x+ a). It is supposed that the first local maximum is enhanced by an energy E (cf the dashed line in fig. 1) provided a relatively immobile mass particle blocks the microporous entrances into the crystal from outside. There exists a sorption space just outside the crystal, i.e. for -d < x < 0, which is supposed to enclose a minimum of the potential energy at x = -d/2, @s = (AHo)s (2) where (-AHo), > 0 is the change in the molar enthalpy of the sorbing species with respect to its gas-phase value. This quantity represents likewise the activation energy Ed,o for the transition from the first potential minimum into the gas phase.M.KoEiiik, P . Struve, K. Fiedler and M. Biilow I 3003 I c T -(AH -(AHo) I I \ 1 'd ,1 I I I -U I I I 1 I Fig. 1. Schematic potential-energy distribution in the force field of a zeolite crystal. For x > 0 a periodic change of the potential energy occurs with the first minimum at x = d / 2 and with the potential energy mmin: CDmin z @ z AH, (3) where - 1 CD = -1 exp(-@/RT)dV 5 vfl (4) is the potential energy averaged over the intracrystalline void volume V, [cf. ref. (41)] and (- AH,) is the heat of sorption at zero pore filling. The potential energy corresponding to the maximum of the periodic potential is CDD = (AH,) + ED ( 5 ) where ED is the activation energy of intracrystalline diffusion.The quantity Ea,, indicated in fig. 1 is the activation energy of the transition from the external sorption space into the bulk of the crystal for the case of the microporous entrances into the crystals being unblocked by immobile particles. For an unblocked crystal, the quantity Ed, , represents the activation energy of the molecular transition from the position x = d / 2 to the external sorption space (x = - d / 2 ) . (4) The above potential-energy distribution allows consideration of the sorption space as consisting of three subsystems (fig. 2): (i) - d < x < 0 with the volume v0 = Sd (6) and the sorbate concentration a, averaged over the volume V,; S is the surface area perpendicular to x at x = - d / 2 (we consider plane, cylindrical and spherical surfaces, respectively); (ii) 0 < x < + d with the volume & = & (7) and the concentration a, averaged over the volume 4 ; (iii) d < x < rc - d where rc is the characteristic dimension of the crystal (radius for a sphere or cylinder; for a platelike crystal, 2rc represents the thickness).The volume of this space is < = K - S d = V , (8)3004 Mass- transfer Resistance Fig. 2. Subsystems of the sorption space of a zeolite crystal according to the potential-energy distribution. where space. Evidently, is the intracrystalline volume and a, is the sorbate concentration within this (9) a, z a where a is the total amount sorbed averaged over the volume, 6, of the crystal. following mass-balance equations can be written : ( 5 ) For the rate of accumulation of the sorbate in the respective subsystems, the (10) da dt d 2 = ka, , c - kd, a, + k:rf, a, - k:!; a,, (1 1) da dt d 1 = k::, a, - k::', a, + k",'(a, -a,) - da d a f'" dt = f'- dt = Skenff(al -a,).The meaning of the kinetic constants k:ff,, kz:fi(i = 1,2, ...) and k",' is obvious from fig. 2. These parameters have the units of mass-transfer coefficients (cm s-'). The value ka,o characterizes the transition from the gas phase into the surface layer - d < x < 0, which is assumed to proceed with zero activation energy. This constant can be expressed via the number of molecules hitting 1 cm2 of surface area per second and is given by where a is the sticking p r ~ b a b i l i t y , ~ ~ and k and rn denote the Boltzmann constant and the mass of a molecule, respectively.Note that there is an asymmetry for the molecules jumping from the point x = -d/2 to the left and to the right; although they undertake the same number of attempts to jump both to the left and to the right. However, the (1 - P) fraction of the number of molecules jumping to the intracrystalline space (cf fig. 1 and 2) is reflected and only the fraction P of these molecules experiences the potential barrier Ea,,. To account for this asymmetry, the coefficients ka, i , kd, (i 3 1) must be multiplied by a factor P < 1. Further, for i 3 2 and, therefore 'I (14) kaq = kd, = k, p f t ' , = kCff - keff J a,z t i , i - I)M . Koc'ir'ik, P. Struue, K. Fiedler and M. Biilow 3005 since the space d < x < r, is characterized by a uniform periodic potential (ki9': = P k j , , ; j = a,d, D ; i > 2; for i = 1 see below).With respect to diffusion within the latter subspace, the following simplifications are assumed. The space-separated mass-transfer resistances and capacities within d < x < r, will be substituted by a series connection of one resulting mass-transfer resistance and one resulting sorption capacity. Mathematically, this procedure is equivalent to the approximation of the exact time dependence of the sorbate accumulation curve y(t) (uptake curve) within the space by the function cf eqn (25) and (27) (later). The time constant ,uD is equal to the time constant of the exact solution of the diffusion problem within the subsystem d < x < r,. Thus, one describes the sorption kinetics within the reservoir of uniform sorbate concentration a, by a single mass-transport coefficient kgf.On the basis of the equivalence of time constants one can express k",f' using the coefficient of intracrystalline diffusion Dzff [cf. ref. ( 5 ) ] : (14) r," - r, v,(u, + 2) DEff - u, k",' PD = where u, = 1,2,3 stands for plate, cylinder and sphere, respectively. It should, furthermore, be mentioned that there is no net flow at the position x = r,, i.e. J = 0 (cf. fig. 2) (as a consequence of the symmetry of the diffusion problem.) (6) The relation of the coefficients k:ff, and k::.fl to the corresponding values of Pk,,, and Pk,, , can be found on the basis of the following consideration. Assuming a fraction of crystal entrances from outside to be partially or fully blocked by immobile particles, the activation energy (Ed,,) for the transition of a molecule through the plane x = 0 should be increased by some quantity E.This enhancement, however, cannot be expected to be uniform all over the surface. Therefore, a spectrum of additional barriers in the micropore openings of the zeolite crystal surface should be assumed. This peculiarity is expressed by the distribution function $(E) (fig. 3). The expression represents the fraction of the total number of micropore entrances with the additional barrier in the region ( E , E+ dE). The activation process for the sorbate penetration through the crystal surface should be considered as a collective effect which is realized uia kinetic energy fluctuations of both diffusing molecules and particles of the blocking material.The latter component becomes important with increasing energy E. Generally, the distribution curve $(E) is expected to exhibit two maxima (cf. fig. 3), one at Eo = 0 and another at EM. This second maximum represents the mean energy to bring about a necessary change of the blocking material to make the micropore openings effectively free (e.g. a jump of an atom of a solid particle along the surface). The constants kzff, and kzrfl can be expressed in terms of the constants Pk,,, and Pk,,, as follows: fa k$ = Pk,, , J exp (- E/RT) $(E) dE 0 kzSf, = Pk,, , JOm exp ( - E / R T ) $(E) dE. (19)3006 Mass-transfer Resistance . h 3 a E, G O 5 4 E/kJ mol-’ Fig. 3. Distribution function #(E) for the additional energetic barriers in the micropore openings of a zeolite crystal surface. If the lower part of the energy spectrum is a ‘line one’ (this may be a simplification), i.e.M E ) = o o w - 0 ) (20) and eqn (1 8) and (1 9) reduce to kEPf, = 6, Pk,,, (22) k::: = O0 Pk,, ,. (23) This is because EM % 0 and, therefore, the second group of micropore openings is effectively closed. Thus, 8, represents the fraction of open entrances in the surface. (7) The initial conditions for the kinetic problem given by eqn (10H12) are as follows : ao(t) = al(t) = a,(t) = a(t) = 0 for t = 0. (24) The function c(t) is defined as c(t) = 0 for t d 0 c(t) = c, for t > 0. Solution of the Problem The resulting mass-transfer resistance at the crystal surface can be constructed by applying the quasi-stationary approach to the problem.The sorption capacity of the two outer layers of the zeolite crystal is negligible compared with the total sorption capacity of the crystal, from which it follows that da da dt dt S d o z S d L = 0. Thus, a, can be excluded from eqn (12) using eqn (lo), (1 1) and (26). Further, the approximations suggested by relations (8) and (9) are introduced. After rearrangementsM. Koc‘ifik, P. Struve, K. Fiedler and M . Biilow 3007 and inserting expressions from eqn (16) as well as for k::; and kg:‘, from eqn (22) and (23), respectively, the resulting differential equation for the sorption uptake curve y( t) reads as: where y(t) is defined by eqn (15) and the first statistical moment of the kinetic curve px is defined via the equation +++ ‘0 “d, 1 vc(vc + 2, ,Zff where DEff = PD,.D, is defined as D, = d 2 r D where r D is the frequency of molecular jumping intracrystalline bulk to one particular neighbouring K can be expressed as: ‘a, 0 ‘a, 1 K = - - . ‘d,O ‘d.1 (29) (30) from a given position within the site. Note that the Henry constant ( 3 1 ) To call special attention to the surface resistance and to express its significance, eqn (28) can be rewritten as (32) P Z = pD(’ +c) where p,, is the first statistical moment of the uptake curve y(t), cf. eqn (1 5 ) and (16), and The parameter < becomes a key quantity in the explanation of the energetic reason for the surface resistance. The kinetic constants can be expressed in terms of jump (34) frequencies : ‘d.0 = &d,O where rd, ,, and Ta, are the jump frequencies of a molecule oscillating about the potential minimum at x = - d / 2 to jump in the direction --x and +x, respectively, and rd.1 is the jump frequency of a molecule oscillating about the potential minimum at x = d / 2 to jump into the direction -x, Using the harmonic approximation, the jump frequencies are as follows : where va and vfD are the frequencies of molecular vibration into the direction x for the potential minima of x = - d / 2 and x = (i) + nd(n = 0, 1,2,3, .. .), respectively. Thus, using eqn (30), (34)-(36) and (37)-(40), one obtains for 5:3008 Mass- transfer Resistance The quantities Ed, 1, Ea, and (- AH,)s are related to (- AH,) via the equation E d . 1 - J%, 1 + ( - AH0)S = (- AH”).In this way, the final expression for 5 reads as: The dimensionless As shown above, (43) parameters u, v , # and 6 are defined by the following formulae (44) (45) (46) (47) ( - AH,) u=- RT v = - E d 1 +- E D RT ( - AH,) d r , 6 = - (v, + 2). Discussion within the frame of the simplified model proposed, the relative importance of the mass-transport resistance localized at the zeolite crystal surface depends on three geometric parameters, O,, P and S, and on three energetic parameters, u, v and q5 [cf. eqn (44)-(46)]. The value of the geometric parameter 6 is in the range lOP2-lO5 (based on the estimate of d z lO-’cm). The parameter 0, may vary, in principle, from 0 to 1. The lower limit, however, is not allowed in the present simplified model, because the sorption capacities of the two outer layers are neglected. A rough estimate of the factor P is given by the relation P x & > 0.(48) p, is the ‘surface porosity’ of the zeolite crystal, which can be defined as the sum of the areas of free cross-sections of oxygen rings on the outer crystal surface related to the total outer crystal surface. The energetic parameters u and v relate the respective values of activation energy of the sorbate (i.e. the activation energy for escaping from the crystal and the activation energy for surmounting the barrier at x = 0) to the thermal energy of the gas. The parameter q5 is given by the ratio of ED and ( - AH,,), respectively, of the self-diffusion process within the crystal and the desorption of the sorbate. Especially for large-pore zeolites (e.g.faujasites), t$ may assume extremely low values as follows, e.g. from data for intracrystalline self-diff~sion~~ and of n-alkanes in NaX-type zeolite (cf. table 1). The effect of the energetic parameters u, v and @ on the quantity ( [eqn (43)] is shown in table 2. The examples are as follows: (1) o, = 1.0, P = 0.25, 6 = 5 x 10-3, = 0 (2) o, = 0.01, P = 0.25, 6 = 5 x 10-3, = v (3) o, = 1.0, P = 0.25, s = 5 x 10-3, v = 0. It can be concluded from table 2 that the influence of the surface resistance on the overall sorption kinetics may be greater by several orders of magnitude than that of intracrystalline diffusion. In this analysis it becomes evident that besides the influence ofM. KotifiR, P. Struve, K. Fiedler and M.Biilow 3009 Table 1. Values of E,, (-AHo) and q5 for the sorption of n- alkanes C,-C, and benzene in NaX-type zeolite EJkJ mol-l - AHo/kJ mol-' @ n-C, ca. 13.0" ca. 61.0b 0.2 1 n-C, ca. 13.5" ca. 70.0b 0.19 n-C, ca. 14.0" ca. 79.0b 0.17 benzene ca. 22c ca. 80d 0.27 " Ref. (43). Ref. (44). Ref. (45). Ref. (46). Table 2. The influence of the parameters u, u and @ on the quantity < given by eqn (43) U (1) 0.2 0.2 0.2 0.2 0.2 (1) 0.5 0.5 0.5 0.5 0.5 (2) 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 (3) 0.2 5 .O 7.0 9.0 12.0 15.0 5.0 7.0 9.0 12.0 15.0 5.0 7.0 9.0 12.0 15.0 5.0 7.0 9.0 12.0 15.0 0.34 1.69 8.37 92.28 1017.22 0.08 0.21 0.56 2.52 11.30 27.37 135.55 671.39 7400.85 81 580.84 0.07 0.34 1.68 18.46 203.44 1 oo 1 o1 1 o2 103 lo-' 1 oo lo1 10' lo2 104 105 lo-' 1 oo 10' 1 o2 intercrystalline diffusion, non-isothermicity and apparatus effects,4749 the surface resistance could be responsible for the discrepancies between the n.m.r.self-diffusion and sorption diffusion data even for large-port microporous sorbents. Another interesting problem is the non-linear behaviour of the Arrhenius plot of diffusion coefficients obtained from diffusion measurements on zeolite 22* 50 The model presented predicts such a behaviour of sorption uptake data. The explanation rsults from the analysis of the theoretical expression for pB [cf. eqn (32) and (43)] as: Evidently, the region < x 1 represents a transition between two linear branches of the Arrhenius plot (i.e. between the regions ( % 1 and r 4 1). Examples are shown in fig. 4 and 5.Fig. 4 illustrates the contribution of pz [due to the term (1 +()I to the Arrhenius dependence. In accordance with experimental sorption uptake data for n-hexane on 99 FAR 13010 Mass-transfer Resistance 1.1 1.6 1.8 2.0 2.2 2.4 2.6 2.8 1 0 3 KIT Fig. 4. Calculated Arrhenius plots of the function In{ 1/[1+ &l/T)]}. 8, = 1, P << 1, -(AH,,) = 55 kJ mol-', u = u. (1 a) ED = 19.2 kJ mol-I, 6 = 3.03 x lop4, 9 = 0.35; (1 b) ED = 25.0 kJ mol-', 6 = 3.03 x 9 = 0.45; ( 2 4 ED = 19.2 kJ mol-l, 6 = 2.30 x 9 = 0.35; (2b) ED = 25.0 kJ mol-', S = 2.30 x q5 = 0.45. 0.0 -2 -0 - c --- - -4.0 - Y C I & -6.0 -8.0 1.5 1.7 1.9 2.1 2.3 2.5 103 K I T Fig. 5. Calculated Arrhenius plots of the function In {l/[l + c(l/T)]) for a sorbed species in a zeolite of different crystal diameter; ED = 19.2 kJ mold', -AHo = 55 kJ mol-', B0 = 1, P 4 1, u = 0, 9 = 0.35 (the c-values at the curves correspond to the temperature 560 K).(a) c x r, = lo-' cm-'; (b) < cm-l. loo, T, = low3 cm-l; (c) < z lo', r, = loA4 cm-'; (d) c x lo2, rC = The dashed line marks 560 K.M. KoEiri'k, P . Struve, K. Fiedler and M. Biilow 301 1 -2.0 -4 .O - h ud + -6.0 I W --- w Y. e I W -8.0 Y. c I u - - -1o.c -12.c 4 & \ \ \ \ \ \ \ , \ \ \ \ \ \ \ \ 1.6 2.0 2.4 2.8 lo3 KIT Fig. 6. Arrhenius plots of -1nk and -In kJ(1 +{)I for the sorption of n-hexane on zeolite NaMgA with different crystal diameters: a, 33 pm; 0,43.3 pm; cf. ref. (23). The values of (1 +r) were calculated using the following parameters : 0, = 1, (- AH,,) = 55 kJ mol-', ED = 25.0 W mol-l, and 2.17 x 10-4cm, respectively; the dashed lines represent the curves from the experimental points used for calculating the ratio -In h/( 1 + l3] ; the bars at the curves are of the dimensions of -In (1 + r).= 0.45, d = lo-' cm, rc = 1.65 x NaMgA (fig. 6), two crystal radii, 1.6 x and 2.17 x low3 cm, were considered. Accordingly, using d = lo-' cm, for examples 1 and 2, therefore, gave 6 = 3.03 x and 2.3 x respectively. Two rough estimates of ED for n-hexane in NaMgA zeolite were carried out using self- diffusion data of n-alkanes in CaA ~ e o l i t e s . ~ ~ The lower limit for ED [case (a)] was taken as ED = 18.6 kJ mol-1 (experimental value for n-butane). The upper limit for ED [case (b)] was taken as ED = 25.0 kJ mol-1 based on the sum of the value ED for n-butane and the twofold increment in ED between methane and ethane.Therefore, this yields q5 = 0.35 and q5 = 0.45 for cases (a) and (b), respectively. It can be seen from fig. 4 that with increasing temperature the dependence -In (1 + <) vs. 103/T deviates from its linear course and approaches its asymptote parallel to the lo3/ T axis. It is important that this behaviour occurs within the same temperature region where the experimentally observed Arrhenius plot of sorption uptake data exhibits a remarkable deviation from the linearity (fig. 6). It is worth mentioning that for the example considered, the influence of the uncertainty of the estimation of ED on this behaviour is more pronounced than the effect of the crystal size variation. The relative insensitivity of the results shown in fig.4 to the change of rc is in accordance with experimental findings. 13* 23 Indeed, the latter show that the apparent diffusion coefficient D(aPP) 9 (50) D(aPP) = e + 2) Pz 99-23012 Mass- transfer Res is tame i.e. the quantity obtained from the uptake measurements cited, is essentially independent of the crystal size within the temperature region examined. It should be noted that the sensitivity of the expression -In (1 +Lj) to change in the crystal size r, decreases as r, increases. This behaviour is seen in fig. 5, where the dependence of -In (1 +Lj) us. 103/T is plotted for those values of model parameters used previously [i.e. ED = 18.6 kJ mol-', (-AH0)=55.0kJmol-',d= lO-'cm,v,=3,u=u,P-g l,cf:fig.4]. For measurements of pure intracrystalline diffusion data, it is important that -In (1 + <) does not change within the temperature range examined, i.e.( T E (T,, T,)) by more than a prescribed value A. The above condition is fulfilled for crystal radii exceeding a critical value r:, given by The function K( 1 / T ) can be taken from eqn (52) [cf: eqn (43)] : K( 1 / T ) = exp ( - q5u) [P exp (u) + O i l exp (u)]. (52) Fig. 6 shows the Arrhenius plot of the values l/pE [cf: eqn (SO)] observed for the system n-hexane/zeolite NaMgA (33 and 43.4 pm crystal diameter).23 Deviations from linearity occur even within the temperature region predicted by calculating the term - In (1 + 5) using the same values of energetic and geometric parameters as those for the above experiment (cf: fig.4). Such a correspondence between the Arrhenius plots, both observed experimentally and derived by means of this microdynamic model, supports the existence of an additional mass-transfer resistance localized at the zeolite crystal surface. In addition to the dependences -In pux us. 103/K, the functions -In bz/( I + <)I us. 103/K are presented in fig. 6; the latter are given as dashed curves. (1 +Lj) values were calculated via eqn (44) for 0, = 1 and P < 1 (cf: the caption of fig. 6). Comparison of the curves with the positions of experimental points -lnpu, shows that both dependences approach each other with increasing temperature. This behaviour is in accordance with the model developed. As follows from the considerations at 8, = 1, owing to the potential-energy behaviour in the vicinity of the crystal surface the mass-transfer resistance at the surface may occur even if there is no additional hindrance. This effect may become dominant especially for small zeolite crystals (r, < lom4 cm).The above analysis of experimental data suggests that it might be of interest to perform a thorough reconsideration of sorption kinetic data on the basis of the proposed model. This should be done especially for systems with small zeolite crystals, which are of large practical interest. Particularly, such an investigation would be important for the analysis of the mass-transfer resistances of pelletized zeolites, where the presence of the binder may cause additional surface resistances expressed by the factor 0, # 1. References 1 M.Bulow, Kolloidn. i., 1978, 40, 207. 2 M. Bulow, P. Struve and S. Pikus, Zeolites, 1982, 2, 267. 3 J. Karger, M. Bulow, G. R. Millward and J. M. Thomas, Zeolites, 1986, 6, 146. 4 M. Biilow, 2. Chem. (Leipzig), 1985, 25, 8 1. 5 R. M. Marutovsky and M. Biilow, Kolloidn. p., 1984, 46,43. 6 M. Guisnet, G. Bourdillon and C. Gueguen, Zeolites, 1984, 4, 308. 7 J. Karger and J. Caro, J . Chem. SOC., Furaduy Trans. I , 1977,73, 1363. 8 J. Karger, J. Caro and M. Biilow, Z . Chem. (Leipzig), 1976, 16, 331. 9 A. I. Vlasov, V. A. Bakaev, M. M. Dubinin and V. V. Serpinsky, Dokl. Akad. Nuuk SSSR, 1980,251, 912. 10 J. Karger, H. Pfeifer, J. Caro, M. Biilow, R. Mostowicz and J. Volter, Appl. Catal., 1987, 29, 21. 1 1 D. Freude, J. Karger and H. Pfeifer, Proc. Int. Symp. Zeolite Catalysis, Siofok, 1985, p.89-98. 12 J. Karger, AIChE J., 1982, 28, 417.M . KoEifik, P . Struve, K. Fiedler and M . Biilow 3013 13 M. Biilow, P. Struve, G. Finger, C. Redszus, K. Ehrhardt, W. Schirmer and J. Karger, J. Chem. SOC., 14 M. Bulow, J. Karger, M. KoEifik and A. M. VoloSEuk, Z . Chem. (Leipzig), 1981, 21, 175. 15 R. M. Barrer, in The Properties and Applications of Zeolites, ed. R. P. Townsend (The Chemical 16 G. F. Stepanez, Theor. Eks. Chim., 1967, 3, 633. 17 J. Caro, M. Biilow and J. Karger, AIChE J., 1980, 26, 1044. 18 M. Biilow, P. Struve and L. V. C. Rees, Zeolites, 1985, 5, 113. 19 W. Lutz, B. Fahlke, U. Lohse and R. Seidel, Chem. Techn. (Leipzig), 1983, 35, 250. 20 W. Lutz, B. Fahlke, U. Lohse, M. Bulow and J. Richter-Mendau, Cryst.Res. Technol., 1983, 18, 513. 21 W. Lutz, H. Fichtner-Schmittler, J. Richter-Mendau and M. Biilow, Cryst. Res. Technol., 1986, 21, 22 M. Biilow, P. Struve, C. Redszus and W. Schirmer, Proc. 5th Int. Conf. Zeolites, Naples, 1980, ed. 23 P. Struve, Thesis (Academy of Sciences of the G.D.R., Berlin, 1982). 24 J. Karger, H. Pfeifer, M. Rauscher, M. Biilow, N. N. Samulevii: and S. P. Zdanov, Z . Phys. Chem. 25 R. Richter, R. Seidel, J. Karger, W. Heink, H. Pfeifer, H. Fiirtig, W. Hose and W. Roscher, Z. Phys. 26 J. Karger, W. Heink, H. Pfeifer, M. Rauscher and J. Hoffmann, Zeolites, 1982, 2, 275. 27 J. Karger and H. Pfeifer, Zeolites, 1987, 7, 90. 28 M. Biilow, P. Struve and B. Reeck, Industr. Res. Rep., Central Institute of Physical Chemistry 29 J. Crank, The Mathematics of Diflusion (Clarendon Press, Oxford, 1964), pp.39 and 293. 30 M. Bulow, J. Karger, N. van Phat and W. Schirmer, Z . Phys. Chem. (Leipzig), 1976, 257, 1205. 31 R. M. Marutovsky and M. Biilow, Z . Chem. (Leipzig), 1984, 24, 272. 32 P. Barret, Cinetique Heterogene (Gauthier-Villars, Paris, 1973). 33 H. Pfeifer, in NMR-Basic Principles and Progress (Springer, Berlin, 1972), vol. 7, p. 53. 34 H. Pfeifer, Phys. Rep., 1976, 26, 293. 35 J. Karger, H. Pfeifer and W. Heink, Proc. 6th Int. Conf. Zeolites, Reno 1983, ed. D. H. Olson and 36 J. Karger, H. Pfeifer and W. Heink, Adv. Magn. Reson., in press. 37 B. Staudte, H. Pfeifer and H. Mix, Lecture at the 20th Annual Meeting on Catalysis, Reinhardsbrunn, 38 L. K. Lee and D. M. Ruthven, J. Chem. Soc., Faraday Trans. I , 1979, 75, 2406. 39 M. Biilow, P. Struve, W. Mietk and M. KoEiFik, J. Chem. Soc., Faraday Trans, I , 1984, 80, 813. 40 M. KoCifik, P. Struve and M. Biilow, J. Chem. SOC., Faraday Trans. I , 1984, 80, 2167. 41 D. M. Ruthven, Principles of Adsorption and Adsorption Processes (J. Wiley, Chichester, 1976), 42 V. Ponec, Z. Knor and S. Cerny, Adsorption on Solids (Butterworths, London, 1974), p. 257. 43 J. Karger, H. Pfeifer, M. Rauscher and A. Walter, J. Chem. Soc., Faraday Trans. 1, 1980, 76, 717. 44 U. Werner, M. Bulow and W. Schirmer, Proc. 2nd Conf. Phys. Adsorption, Liblice 1975 (J.-Heyrovsky Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, Prague, 1975), p. 101. Faraday Trans. I , 1980, 76, 597. Society, London 1980), p. 3. 1339. L. V. C. Rees (Heyden, London, 1980), p. 580. (Leipzig), 1981, 262, 567. Chem. (Leipzig), 1986, 267, 841; 1145. (Academy of Sciences of the G.D.R., Berlin, 1986). A. Bisio (Butterworths, Guildford, 1984), p. 184. G.D.R., May, 1987. p. 34. 45 P. Lorenz, M. Bulow and J. Karger, Izv. Akad. Nauk SSSR, Ser. Chim., 1980, 1741. 46 G. Finger and M. Biilow, Z . Phys. Chem. (Leipzig), 1981, 262, 732. 47 P. Struve, M. KoEifik, M. Biilow, A. Zikanova and A. G. Bezus, Z . Phys. Chem. (Leipzig), 1983,264, 48 M. Biilow, W. Mietk, P. Struve and A. Zikanova, Z . Phys. Chem. (Leipzig), 1983, 264, 598. 49 M. Biilow, P. Struve and W. Mietk, Z . Chem. (Leipzig), 1983, 23, 313. 50 K-P. Roethe, A. Roethe, K. Fiedler and D. Gelbin, Ber. Bunsenges. Phys. Chem., 1979, 83, 47. 51 J. Karger and D. M. Ruthven, J. Chem. Soc., Faraday Trans. I , 1981, 77, 1485. 49. Paper 711369; Received 28th July, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403001

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chern. Soc., Furaduy Trans. I, 1988, 84(9), 3015-3025 An Aluminium-27 Nuclear Magnetic Resonance Study of Ligand Exchange Kinetic and Equilibrium Properties T. Jin and K. Ichikawa" Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060, Japan 27Al Nuclear magnetic resonance measurements have been carried out between -5 and 85 "C for a methanolic aqueous Al,(SO,), solution: the 27Al longitudinal magnetization recovery (1.m.r.) was measured from the free-induction decays following the second pulse of a 1 8O0-z-90" pulse sequence. The 27Al n.m.r. spectra consisted of two resonance signals due to a first-sphere complex [Al(H,O),SO,]+( = A) and to a hexa-aquo cation [A1(H,0),J3+( = B), respectively. The equilibrium and kinetic properties of the exchange of H,O and SO:- ligands were determined by reproducing the observed 1.m.r. and lineshape with the aid of the theory developed by one of the authors (K.I.). The observed rate of 1.m.r.under the influence of ligand exchange was not equal to the energy relaxation rate R:,, or I?:,,. The lifetimes z, and z, ranged from lo-, to 5 s; the temperature dependence of both fractional populationsfA orfB was determined. These data gave a high value of AHL, and a positive ASLA and showed a dissociative reaction for the forward path; a relatively small value of AH$,, and a large negative A S i B showed an associative reaction for the backward path in the chemical exchange reaction Al"' (in B) =$ Al"' (in A). The reaction was endothermic, but the product, [Al(H,O),SO,]+, increased with increasing temperature because of the high entropy contribution.In recent years the n.m.r. technique has developed rapidly into an extremely important method for the study of inorganic and bioinorganic electrolyte solutions, and this use of the technique will undoubtedly continue.' The introduction of multivalent diamagnetic ions, as well as transition-metal ions, into an aqueous medium leads to changes in its structure. In general, an exchange between bulk water and complexed water (or any other ligand) in the inner-sphere solvation shell of the metal ions takes place in solution, and the ligand-exchange rate depends on the nature of the central cation.2* For aqueous solutions of AlIII, GaIII and In'" salts it is possible to obtain separate signals in the 'H and ''0 n.m.r.spectra of these solutions below room temperature, the lifetime of each water molecule and any other ligands coordinated around these polyvalent cations is > s. Conversely, if the lifetime is short with respect to the n.m.r. timescale, the resonance coalesces into one signal with a parameter determined by the time-averaged environment of the nuclei under investigation. The majority of dynamic studies undertaken by n.m.r. have employed the measure- ment of lineshape and its simulation with the aid of a theory concerning the effect of the ligand-exchange reaction on the phase relaxation (i.e. spin-spin ~elaxation).~-' The nuclear-spin system submitted to the radiofrequency field undergoes energy relaxation (i.e. spin-lattice relaxation), whereby the nuclear spins are correlated with the temperature of the lattice by electric quadrupole or magnetic dipole4ipole interaction, and come into thermal equilibrium with the lattice.The time evolution of the longitudinal magnetization recovery (1.m.r.) in an inversion recovery experiment for 30153016 27Al N.M.R. Study of Ligand Exchange exchanging spins is controlled not only by the energy-relaxation rate but also by the chemical-exchange rate. The energy-relaxation process of each spin in the two chemical environments A and B is perturbed by the chemical exchange between them. One (K. I.) of us demonstrated the influence of chemical exchange on 1.m.r. and derived an exact solution of the coupled expressions for the time evolution of the longitudinal magnetizations of sites A and B for the same kind of nucleis (henceforth referred to as I).The simulation of the experimental points in l.m.r., by using the equations given in I, gives the different energy relaxation rates I?:,,, the different fractional populations fa and the different lifetimes z, for sites 01 = A and B. This paper describes an examination of the temperature dependence for 27Al of R:,A,B, f,,, and z ~ , ~ of the exchanging species A and B, where A is [Al(H,O),SO,]+ and B is [A1(H20),I3+ in aqueous Al,(SO,), solution. The equilibrium and kinetic properties of the dynamic equilibrium reaction associated with ligand exchange between H 2 0 and SO:- have been determined by measuring the 27Al 1.m.r. and the 27Al n.m.r. spectrum and by reproducing the experimental results with the aid of a theory describing the effect of chemical exchange on the time evolution of the 1.m.r.and the n.m.r. lineshape. Experimental Materials For the n.m.r. measurements a methanolic aqueous Al2(SO,), solution with a composition Al,(SO,),: H20: CH,OH = 1 : 414: 60.2 and pH 3.6 was sealed under vacuum into a 10 mm tube. The amount of methanol added to the aqueous Al,(SO,), solution was measured by the depression of its freezing point. The compositions of aluminium were determined by the 8-hydroxyquinoline method, taking absorption spectra at ca. 390 nm.' N.M.R. Measurements The 27Al n.m.r. measurements were carried out between -5 and 85 "C for the methanolic Al2(SO,), solution. The 27Al resonance frequency and the time interval t, between the last 90" pulse and the start of data acquisition were ca.52.1 MHz and 30 ,us on a Varian XL-200 spectrometer or ca. 23.4 MHz and 300 ,us on a Bruker SXP4- 90 instrument, respectively. The magnetization MJz) resulted from the initial intensity of the free-induction decays measured at t, = 30 ,us using the inversion recovery (or 18O0-z-9O") method, where M,(z) was measured for ca. 10 values of z until M,(z)/M," reached ca. 0.65.l' Thus the experimental points for 1.m.r. were obtained as a function of z. Results The 27Al n.m.r. spectra of the methanolic aqueous Al,(SO,), solution at ca. 52.1 MHz are shown in fig. 1. The 27Al n.m.r. spectra contain two resonance signals arising from the hexa-aquo cation [A1(H20),I3+( = B) and a first-sphere complex [Al(H,O),SO,]+ (=A), respectively.The resonance line of the latter was 3.3 ppm to high field at room temperature. The two 27Al resonances, corresponding to the complex and the aquo cations, separated by 3.3 ppm were also observed in aqueous A12(S0,), solutions without methanol.11*12 The temperature dependence of the lineshapes in fig. 1 was similar to the data in fig. 1 of ref. (12), where the latter was measured at ca. 23.45 MHz for aqueous Al,(SO,), solution without methanol. The two peaks coalesced into one broad signal above ca. 80 "C, because the rate of the ligand-exchange reaction [Al(H20),]3+ + SO:- f [Al(H,O),(SO,)]+ + H,O (1) became larger than the resonance-frequency separation of the two lines Av ( = V, - v,).T. Jin and K. Ichikawa 3017 85 - 80 75 J 1 52.1150 52.1145 v/MHz Fig.1. 27Al spectra recorded at ca. 52.1 MHz in an aqueous Al,(SO,), solution between - 5 and 85°C. The spectra are displaced isomerically on a scale. . 59'C 75% 85'C . . . . . I I I . 1.0 20 30 r/ 10-2 0 Fig. 2. Typical data of longitudinal magnetization recovery (1.m.r.) in an aqueous Al,(SO,), solution between - 5 and 85 "C. The dashed line is a fit of the data to the theory of the effect of chemical exchange on 1.m.r. values. Typical 1.m.r. data are shown in fig. 2. The temperature dependence of the apparent rates, resulting from the slopes of plots of the logarithmic longitudinal magnetization (1.l.m.) us. z, are shown in fig. 3. We also obtained the longitudinal rates RyP! and R:!: of the individual sites A and B from the measurements of individual lines which resulted from the Fourier- transformation of the free-induction decays, obtained as a function of z between the 180 and 90" p~1ses.l~.l4 Fig. 3 also shows the temperature3018 27Al N.M.R. Study of Ligand Exchange 6o t a AA 0 tl pc A 0 0 0 0 "1 m A I I I 1 1 2.8 30 3.2 3-4 3.6 3.8 103 KIT Fig. 3. R;b: (a), RYbi (0) and R:pp (A) plotted as a function temperature, where A and B stand for [Al(H~O),SO,]+ and [AI(H,0)J3+. The experimental techniques of these rates are mentioned in this text. dependences of Robs and Robs; these correspond to the slopes in plots of 1.l.m. for A and B us. z for ,'A1 in [Al(H,O)SO,]+ and [A1(H,0)6]3+, respectively. Above 50 "C, RY;: became roughly equal to Ry!;, agreeing in magnitude with RYpp. The published data for the 1.m.r.and Rtpp above 75°C should be replaced by the data in fig. 2 and 3.14 We have found the following contradictory results for both the lineshapes and the 1.l.m. values. (i) The appreciable increase in both Rtpp and the linewidth with increasing temperature above 50°C [see fig. 1, 2(b) and 31 is not interpretable in terms of the quadrupole-relaxation process for 27Al associated with nuclear spin Z = 5/2.15 (ii) The 1.m.r. showed a single-exponential decay below 50 "C, as shown in fig. 2(a), in spite of the separate lineshapes and the different magnitudes between the 27Al quadrupole-energy relaxation rates R;".* and R& of 27Al in [Al(H,O),SO,J+ and [Al(H,0)6]3+. We must resolve the meaning of Rtpp and the cause of the paradoxes mentioned in (i) and (ii) above.We will examine the experimental results (see fig. 1-3) using the theory of the effect of chemical exchange on the 1.m.r. and lineshape. Discussion We focus on chemical exchange between the two sites A and B for the 27Al nuclei, as shown in eqn (l), in the Al,(SO,), solution. We will characterize the equilibrium and kinetic properties of ligand exchange and discuss its effect on 1.m.r. using the theory about the effect of chemical exchange on 1.m.r. in I and lineshape in ref. (16) (referred to as 11). Calculations of L.M.R. and Lineshape In the case of be simplified to n.m.r. experiments the usual ligand-exchange reaction, eqn (l), can ~ B A ~ A B Al"' {in B: [A1(H,0)6]3+} t Al"' (in A: [Al(H,O),SO,J+}. (2)T. Jin and K. Ichikawa 40°C 3019 I I 23.4517 23.4522 V 6 VA v/MHz 52.1150 V e VA 52.1145 vIMHz -5°C Fig. 4.Experimental spectra (-) and their simulation ( * * -). The dotted-dashed and dashed lines show the contribution from the two environments A and B in aqueous Al,(SO,), solution. The parameters used in their simulation are shown in fig. 5-8. The resonance-frequency dependence of the spectra at 22 "C is shown in (a).3020 27Al N.M.R. Study of Ligand Exchange h 0 *:- Under the chemical exchange between the two sites A and B the time evolutions of their longitudinal magnetizations, Mz,,(z) and M2,,(z), and the total magnetization, Mz(z), are given by Here M,Oag and Rl,,(cr,~: A or B) are expressed in terms of the energy-relaxation rate Rr,A(R:,B) of site A (site B) and the lifetime of chemical exchange ( 2 , and z,), and the fractional population (f, and f,), as shown in eqn (8)-(10) and (13)-(17) in I.For a solution which consists of the main A and B species the relation between f,,, and zA,, is expressed as ' S f A = ' A f B (6) because the predominant equilibrium reaction of eqn ( 2 ) is established in the aqueous medium. We have been able to investigate the influence of chemical exchange on the 1.m.r. for any categories of the slow, intermediate or rapid rate of exchange kAB( = zil, k,, = z,'). Hence the simulation of the experimental results of the n.m.r. spectra as well as the 1.m.r. values provides the energy-relaxation rate and the equilibrium and kinetic parameters of the chemical-exchange reaction of eqn (2). We simulated the experimental points of the 1.m.r.as shown by the dashed lines in fig. 2(a) and the typical lineshapes (solid lines) at - 5, 22 and 40 "C as shown by dotted lines in fig. 4 . The simulation of the observed lineshapes was carried out using the equations given in 11. Fig. 4 ( a ) shows the frequency dependence of the 27Al spectra, where the same parameters were used for calculation except for the separations between the resonance frequencies of sites A and B [Av (= v, - v,)] at ca. 52.1 and ca. 23.4 MHz. Fig. 5 illustrates the temperature dependence of the product parameters z,Av and RT,, z,, where Av = 171 The simulation of the observed 1.m.r. values and lineshapes above 50 "C could not be carried out without the temperature dependence of Av. The paradox resulted from the 2 MHz.T. Jin and K.Ichikawa 302 1 T/”C 0 0 P a P 4 ”3.0 3.2 3.4 3.6 3.8 103 KIT Fig. 6. & A (01, &,B (El), R:,* (0) and R;,* (a) as a function of temperature. For symbols A and B, see caption of fig. 3. contribution of the new sites of 27Al, as shown in the following scheme for the ligand- exchange reactions :12 [A1(H20),13+ G [A1(H2O)dSOhI+ B A 11 11 (7) [Al(H20),0H]2+ e [Al(H,O),SO,OH] B’ A’ The exchange reactions A e A’ and B f B’ should be very fast processes in comparison with the other reactions B e A and B’$A’, because of the forward and backward rate- constants between ca. lo5 and lo9 s-l for acidic hydrolysis and proton transfer.17 The contradictory results of (i) as shown in the Results section originate from the protolytic reactions B‘B’ and AeA’.Paradox (ii) shown in the Results section was attributed to the very small values of M z , A A and M;,,, [see eqn (1 1) in I]. Thus is nearly equal to the slow rate, Rl,B. The Rate (R,,J and Energy-relaxation Rate (RZJ of “Al”’ Fig. 6 shows the temperature dependences of R1,, and R:,, for sites A and B. From the simulation of the 1.m.r. we found that (1) RF,, = in eqn (3) and (4) below room temperature because of slow exchange between the two sites A and B; (2) Rf,a # Rl,E above room temperature because of the influence of the exchange reaction on the time evolution of the longitudinal magnetization; (3) the large value of ( >R1,B) and the3022 27A1 N.M.R. Study of Ligand Exchange difference between R1,A and Rl,B increased with increasing temperatures, since R1,* and R1.B (< R1,A) approach the values ' 1 .A = + +fB R?,A +fA Rr",B (8) and ' 1 , B = f A R?,A +fB R;",B (9) which were derived at the rapid exchange limit (R:,,t, 6 1) from eqn (SHlO) in I . We concluded that the energy-relaxation rate RT,, could not be calculated from the data of Ripp, RYP," and the 1.m.r. values without using the theory of the effect of exchange reaction on the 1.m.r. in I. The 27Al nucleus has a quadrupole moment (Q = 0.15 x esu cm2). The interaction of the nuclear electric quadrupole moment with the electric field gradients (e.f.g.) at the A1 nucleus causes quadrupole relaxation, which is usually the predominant relaxation mechani~m.~,'~ The high-field shift of site A may be consistent with the electron density from the SO:- ion being transferred to the aluminium ion.The redistribution of electron density around the A1 nucleus due to ligand exchange from a water molecule to an SO:- ion may give rise to the large e.f.g. and the larger I?;,,, compared with RT,, (see fig. 6). The temperature dependence of the electric quadrupole relaxation rate may, to a good approximation, be taken as equal to that of q/T of the well known Debye formula (q is the viscosity of the medium surrounding the species). Since the temperature dependence of R?,A below ca. 50 "C was similar to that of q/T, where q is the viscosity of an aqueous solution with 12.7 mol YO CH,OH without A12(S04), solute,ls the fluctuation of the e.f.g. at the 27Al nucleus mainly arises from rotational diffusion of the species.Kinetic and Equilibrium Properties of the Ligand-exchange Reaction According to Eigen, a chemical-exchange reaction occurs when an outer-sphere complex is converted into an inner-sphere complex as follows :19 [A1"1(H20),]3' + SO:- [A1111(H20),]3+ : SO:- g [A1111(H20)5S04]+ + H,O. (10) We have not been able to observe any signal for an outer-sphere complex [Al"1(H20),]3+: SO:-, because (1) the e.f.g. around Al"' is attributed mainly to the water molecules which are located as ligands at the nearest-neighbour distance and (2) the lifetime of the outer-sphere complex is too short to observe a separate signal. The two lifetimes zA and z,, which were determined in the calculations of the 1.m.r. and lineshape, ranged from to 5 s below 50 OC, as shown in fig.7. One assumes that both forward and backward reactions in eqn (2) can be described by first-order rate laws with rate constants k,, = l/z, and k,, = l / z B . Here, kap = WEp.shown in the modified Bloch equations for the longitudinal time-dependent magnetization [i.e. eqn (3) and (4) in I]. According to the transition-state theory of reaction rates given by2' k = K - exp (- AH'/RT) exp (ASf/R) (1 1 ) (k:) one may obtain a straight line for ln(k,,/T) [or ln(k,,/T)] us. 1/T with a slope - A H f / R and an intercept in (Ick/h) + A S f / R . The values of AH$ and ASf are shown in table 1, where, for simplicity, the transmission coefficient K was set equal to 1. The activation parameters of the forward reaction were of course different from those of the backward path, since the exchange took place between the two unequally populated sites A and B.T.Jin and K. Ichikawa 3023 TIOC Fig. 7. t 0 0 0 0 0 0 0 1 3.2 3.4 3.6 3.8 1 O3 KIT Lifetimes z, (0) and zR (0) as a function of temperature. 0 50 T/"C Fig. 8. Fractional populations f A (0) and f, (0) as a function of temperature. Fig. 8 shows the temperature dependence of fA and fB. The equilibrium constant Knmr for the chemical exchange reaction, eqn (2), is given by Knmr = fA/fB = k d k A B - AGO = - RT In Knmr (12) (13) and the differences in enthalpy and entropy AH" and AS" can be obtained by the thermodynamic relationship AH" = - Ra In Knmr/a(l/T) and AS" = -aAG"/aT. AH" = 28.7k0.5 kJ mol-' and ASo = 82.8 k 1.6 J K-l mol-l. The difference between the kinetic parameters for the forward and backward paths for the reaction of eqn (2) is attributed to their different exchange mechanisms.The high value of AHLA and the positive ASLA for the forward reaction (see table 1) may be consistent with a mechanism in which the coordination number of the ligands is decreased in the activated-state complex [A1(H,0)J3+, i.e. corresponding to a dissociative mechanism or a S, 1 mechanism.21 Conversely, the relatively small AHIB and the large The free-energy difference AGO ( = G l - G i ) between sites A and B is given by3024 27Al N.M.R. Study of Ligand Exchange Table 1. Kinetic properties of the ligand-exchange reaction eqn (2) in aqueous Al,(SO,), solution forward reaction backward reaction 75.1 _+ 1 .O 19.9k 3.3 46.1 f 1.3 - 64.8 & 4.1 CAI[ H,O), 13' c AI(H~O)~SO$+ Fig.9. Gibbs free-energy diagram for the ligand exchange reaction of eqn (2) at - 5 "C. AGip and AGO were obtained from the kinetic parameters shown in table 1 and the equilibrium parameters shown in the literature, respectively. negative Ask, for the backward reaction of eqn (2) may be consistent with a mechanism in which the coordination number of the ligands increased in the activated complex [Al(H,O), * SO, - H,O]+, i.e. an associative mechanism or an SN 2 mechanism.21 The activated complexes [A1(H20),l3+ for forward path are produced more largely with increasing temperatures because of the decrease in AGHA ; the other activated complexes [Al(H,O),SO,]+ for the backward path decrease with an increase in temperature because of the increase in AGL,.Fig. 9 illustrates the good inter-relationship between the equilibrium and kinetic parameters of the free-energy differences between the two environments the reactant of [Al(H,0),]3+ and the product of [Al(H,O),SO,]+ at -5°C. The forward reaction for eqn (2) was endothermic with a high entropy contribution. We thank Prof. Y. Sanada (Faculty of Engineering) for his hospitality during course of this work and Prof. M. Yokoi (Faculty Science, Shishu University) for his personal communication in which the temperature dependence of the 27Al n.m.r. lineshapes was shown given an aqueous Al,(SO,), solution. The n.m.r. measurements were carried out in the NMR Laboratory, Faculty of Engineering, Hokkaido University. T. J. is indebted to Dr T. Matsumoto for the use of material from his dissertation.This work wasT. Jin and K. Ichikawa 3025 supported in part by a Grant-in-Aid for Scientific Research no. 61470040 from the Japanese Ministry of Education, Science and Culture. References 1 See e.g. H. G. Herz, in Water, ed. F. Franks (Plenum Press, New York, 1972), vol. 1, p. 301; R. A. Dwek, Nuclear Magnetic Resonance in Biochemistry (Clarendon, Oxford, 1973) ; D. G. Gordian, Nuclear Magnetic Resonance and its Applications to Living Systems (Clarendon, London, 1982). 2 M. Eigen, Pure Appl. Chem., 1963, 6, 97; A. Fratiello, R. E. Lee, V. M. Nishida and R. E. Schuster, J. Chem. Phys., 1968, 48, 3705. 3 F. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions (Wiley, New York, 2nd edn, 1967). 4 J. A. Pople, W. G. Schneider and H. J. Bernstein, High Resolution Nuclear Magnetic Resonance (McGraw-Hill, New York, 1959), pp. 196 and 218. 5 A. Carrington and A. D. Maclachlan, Introduction to Magnetic Resonance (Harper and Row, New York, 1967), p. 204. 6 G. Binsh, Topics in Stereochemistry (Wiley Interscience, New York, 1968), vol. 3, p. 97. 7 M. L. Martin, G. J. Martin and J-.I. Depluech, Practical NMR Spectroscopy (Heyden, London, 1980), 8 K. Ichikawa, J. Chem. Soc., Faraday Trans. 2, 1986, 82, 1913. 9 E. B. Sandell, Colorimetric Determination of Traces of Metals (Interscience, New York, 1959), p. 291. p. 231. 10 T. Matsumoto and K. Ichikawa, J. Am. Chem. Soc., 1984, 106, 4316. 11 J. W. Akitt, N. N. Greenwood and B. L. Khandelwal, J. Chem. Soc., Dalton Trans., 1972, 1226. 12 J. W. Akitt and J. A. Farnsworth, J. Chem. Soc., Faraday Trans. I , 1985, 81, 193. 13 R. L. Vold and J. S. Waugh, J. Chem. Phys., 1968,48, 3831. 14 K. Ichikawa and T. Jin, Chem. Lett., 1987, 1179. 15 A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, London, 1961), p. 264. 16 K. Ichikawa and T. Matsumoto, J. Magn. Reson., 1985, 63, 445. 17 D. W. Fong and E. Grunwald, J. Am. Chem. Soc., 1969, 91, 2413; A. Takahashi, J. Phys. SOC. Jpn, 18 The Chemist’s Companion (Maruzen, Tokyo, 1975). 19 M. Eigen and K. Tamm, Z. Elektrochem., 1962, 66, 107. 20 S. Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941). 21 D. Fiat and R. E. Connick, J. Am. Chem. Soc., 1968, 90, 608. 1970, 28,207. Paper 711561; Received 25th August, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403015

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I, 1988, 84(9), 3027-3041 Catalytic Decomposition of Mercaptans on Metal Films of Iron, Nickel, Palladium, Aluminium and Copper Yousif Kadim Al-Haidary and Jalal Mohammed Saleh" Department of Chemistry, College of Science, University of Baghdad, Baghdad, Jadiriya, Republic of Iraq Adsorption and decomposition of methanethiol, ethanethiol and n- propanethiol on clean and oxidized films of Fe, Pd, Ni, A1 and Cu have been studied in the temperature range 193-500 K. Mainly molecular chemi- sorption of the mercaptans occurred on the films at 193 K. All the mercaptans were chemisorbed dissociatively on all surfaces above 300 K by the rupture of S-H, C-S, C-H and C-C bonds. The proposed dominant pathway involved decomposition of the mercaptan to form a thiolate (-SR) on a surface site and a hydrogen adatom on the adjacent site.In another less important pathway, sulphhydryl (-SH) and alkyl groups are formed. Surface recombination reactions of the bound species took place at temperatures > 300 K yielding hydrogen, hydrocarbons together with some alkyl sulphide. The gaseous products subsequent to the decomposition of the mercaptans on the oxidized metal films also involved other gases, including CO, H,O and olefins. The pattern of the products formed and their relative concentrations at temperatures 300-500 K indicated that the extent of mercaptan dissociation decreased in the order S-H, C-S > C-H > C-C. The rate of mercaptan adsorption directly depended on its pressure and the kinetic data revealed the operation of a compensation effect throughout the interaction of the mercaptan with various films.The transition-metal films showed greater activity than A1 and Cu, and among the former metals Fe exhibited the greatest activity for mercaptan adsorption. Considerable attention has always been given to the adsorption and catalytic decomposition of alcohols and other organic compounds containing C-0 bonds. 1-7 An understanding of the simple adsorption and decomposition properties of such compounds has been of value in understanding their corresponding reactions in heterogeneous catalysis. Compounds containing C-S bonds, on the other hand, did not attract similar attention despite the importance of such compounds in many respects, and very little is so far known about the adsorption and surface dissociation behaviour of organic sulphur compounds ; the literature regarding the adsorption and decompo- sition of mercaptans on metal films is even smaller.8-12 In previous papers the adsorption and decomposition of hydrogen sulphide on a number of rnetals,l3-l6 and of methyl mercaptan on nickel and tungsten films,17 have been investigated.The object of the present work has been to extend the previous work by examining the catalytic decomposition of three mercaptans, methane-, ethane- and n- propane-thiols, on five metal films (Fe, Pd, Ni, A1 and Cu). Thus processes involving the cleavage of C-S, C-H, S-H and also C-C bonds in such compounds could be investigated. A further extension of the work was made by studying the effect of preadsorbed oxygen on the metals on the adsorption and subsequent decomposition of the mercaptans. No such work has been reported previously although few investigations on the adsorption, dissociation and exchange reactions of the mercaptans on some sulphide and oxide catalysts have previously been published.''3 l9 30273028 Catalytic Decomposition of Me rcap tans Experimental The ultra-high vacuum system used in this investigation has thoroughly been described el~ewhere,~. 20-22 as have the general techniques utilized in the outgassing of the apparatus, and the preparation and sintering of the metal film~.~9”0-~~ The metal films were prepared from Johnson Matthey spectroscopically standardized wires (0.5 mm in diameter) which were first degassed at as a high temperature as possible for a minimum of 8 h.Each film was prepared at 78 K and sintered for 30 min at 350 K. During the deposition and sintering of films the reaction vessel was pumped and the pressure was always < N mP2. The reaction vessel was connected through a leak device to a Quadruvac 200 mass-spectrometer partial-pressure gauge (Leybold-Heraus) ; the details of the construction, operation and analysis have been given previ~usly.~. 20-22 Mercaptans, obtained from B.D.H. and Fluka, were purified from higher boiling impurities by repeated distillation under nitrogen atmosphere. The product collected was analysed mass-spectrometrically and was shown to be more than 99.5 % pure. The mercaptan was degassed by successively melting and freezing in vacuo; it was then passed through a trap maintained at 193 K and stored.Since the vapour pressure of the mercaptan at 78 K is ca. loP4 N mP2, it was removed from the uncondensable impurities by cooling a ‘finger’ in liquid nitrogen; any uncondensable gases could be pumped out before introducing the mercaptan doses into the reaction system. The extent (8) of mercaptan adsorption on the film was expressed as where VKr represents the volume of krypton monolayer on the film surface at 78 K and I/R is the volume of mercaptan (RSH) adsorbed subsequent to area determination; the volumes were measured in units of mm3 at s.t.p. In a series of experiments the metal film was first saturated with oxygen gas at 300 K and a pressure of 2.0 N m-2. The oxygen pressure was then reduced to N m-2 and the area of the oxidized film was redetermined prior to mercaptan addition.The extent of metal oxidation ( X ) and of subsequent RSH adsorption (0) on oxidized films were determined from the relations : and where Vo, is the volume of oxygen adsorbed at 300 K and vKr the volume of the krypton monolayer on the oxidized film. Results Adsorption at 193 K Fast adsorption of the mercaptans (RSH) occurred on all films at 193 K until the value of 0 was ca. 1.0 in the case of methanethiol (MeSH), ca. 0.9 for ethanethiol (EtSH) and ca. 0.8 with n-propanethiol (PrSH) under a gas pressure of 2.0 N m-2. The adsorption at this stage became slow and proceeded at a rate of ca. 10” molecule cm-2 s-l, corresponding to ca. 0.1 YO of the monolayer per second.Adsorption on Fe, Pd and Ni at this temperature was accompanied by the evolution of small amounts of hydrogen and alkanes, which corresponded to 10-15% of adsorbed RSH; the alkanes were CH, in the case of MeSH, C2H, with EtSH and C3H, for PrSH. Some (ca. 10%) of the adsorbed mercaptan on A1 and Cu films at 193 K was reversible; such a fraction of the adsorbed mercaptan could be removed from the films on pumping down to N m-2 or on warming the films to 300 K. Table 1 gives the volume of the krypton monolayerY . K. Al-Haidary and J . M. Saleh 3029 Table 1. Adsorption of methane-, ethane- and n- propane-thiols on metal films of Fe, Pd, Ni, A1 and Cu at 193 K. Fe Pd Ni A1 c u Fe Pd Ni A1 c u Fe Pd Ni A1 MeSH 70.50 62.00 31.81 27.00 23.50 EtSH 74.85 54.82 39.42 19.50 13.20 PrSH 80.83 71.30 30.35 18.47 0.989 1.015 1.100 1.129 0.936 0.875 0.899 0.921 1.021 1.030 0.835 0.820 0.840 0.894 a Volumes of krypton are expressed in mm3 at s.t.p.Table 2. Adsorption of methane-, ethane- and n- propane-thiols on oxidized films of Fe, Pd, Ni, A1 and Cu at 193 K film Fe Pd Ni A1 c u Fe Pd Ni A1 c u Fe Pd Ni A1 78.50 68.50 44.00 25.30 22.60 80.50 73.80 42.00 18.30 14.00 73.80 70.32 42.76 17.05 X MeSH 1.058 1.034 0.921 1.072 0.796 1.249 1.008 0.952 1.387 0.928 1.069 1.056 1.102 1.3 19 EtSH PrSH 56.18 44.88 37.64 32.50 26.50 63.4 1 55.01 35.00 23.20 15.50 68.92 50.51 34.47 20.13 e 0.805 0.880 0.890 0.729 0.754 0.820 0.869 0.888 1.043 1.535 0.805 0.794 0.820 0.852 (VKr) on the film at 78 K and the corresponding values of 8 under RSH pressure of 2.0 N mP2.Adsorption of RSH on the oxidized films at 193 K took place in a similar manner, although the final values of 8 were slightly lower than on the clean films (table 2). No3030 Catalytic Decomposition of Mercaptans Table 3. Analysis of the gas phase, given as percentage of each gas, throughout the decomposition of mercaptans on various films film T/K H, CH, C,H, C,H, C,H, Me,S Et,S RSH Fe 443 45.2 30.5 Pd 448 36.1 31.6 Ni 448 36.8 13.3 A1 448 61.4 17.1 Cu 448 30.5 39.9 Fe 443 67.2 0.8 Pd 483 45.8 1.5 Ni 443 65.2 1.4 A1 493 63.5 1.4 Cu 493 55.9 1.4 Fe 453 80.3 - Ni 453 79.3 - Pd 453 80.2 - A1 493 67.4 - MeSH 18.3 - 12.7 - 7.9 - 5.1 - EtSH 8.2 13.9 28.7 15.7 8.4 9.2 15.9 6.9 14.4 5.3 PrSH - - 3.8 - 2.2 12.1 - 7.5 35.6 - 16.3 13.6 6.4 - 18.1 - - - - - - - 2.3 7.6 8.2 15.8 1.4 17.7 1.70 21.3 - - - - - - - - - - - - 7.4 - - 12.3 12.6 - - 7.2 9.3 - - 11.4 8.1 - - 24.5 gaseous products were detected subsequent to the interaction of the mercaptans with the oxidized surfaces at 193 K.Dissociative Chemisorption Dissociative chemisorption of RSH occurred on all films at temperatures > 300 K and the adsorption at these temperatures was accompanied by the evolution of hydrogen and certain hydrocarbons. The latter involved CH, and C,H6 in the case of MeSH, C2H6, C2H4 and considerably small amounts of CH, with EtSH and only C,H, with regard to PrSH. Hydrogen was always the major gaseous product on all surfaces with all mercaptans and its amount increased generally with the rise of temperature. Methane evolution subsequent to the dissociative chemisorption of MeSH on the films above 300 K was substantial particularly on Fe and Cu films and the extent increased with increasing temperature.Ethane liberation with the adsorption of this mercaptan was far less than that of methane and its amount did not alter significantly with the increase in temperature; no C,H6 was detected on the Ni film at any temperature < 500 K. Dissociative adsorption of EtSH on the films at temperatures > 300 K was followed by the liberation of H2, C,H, and C2H4 together with negligible amounts of CH,. The amounts of C,H, and C,H, were appreciable on the Pd film. The decomposition of PrSH on the film at temperatures > 300 K was accompanied by the evolution of hydrogen and C,H, gases; no CH,, C2H6 or C2H4 gases were observed throughout adsorption of this mercaptan at any temperature < 500 K.Dimethyl sulphide, Me2S was also identified among the gaseous products subsequent to the decomposition of MeSH on Fe, Pd, Ni and Cu films at temperatures 3 340 K. Very small amounts of diethyl sulphide, Et,S, were detected during the adsorption of EtSH on Fe, Cu and A1 films above 400 K. Table 3 gives the composition of the gas phase at one temperature > 300 K; the analysis was made only when the rate of RSH adsorption had become lo1, molecule cm-, s-l. Fig. 1 shows the interaction of the mercaptans with metal films above 400 K.Y. K. Al-Haidary and J . M. Saleh 4 N E z Q ---. 2 I 1 I I 10 20 30 r x 303 1 ( C ) 1 I I I 10 20 30 10 20 30 t/min Fig. 1. Interaction of mercaptans with metal films.(a) MeSH on Ni at 448 K ; (6) EtSH on Fe at 443 K ; (c) PrSH on Pd at 453 K. 0, H,; A, CH,; x , C,H,; 0, C2H4; A, Me,S; W, Et,S; V, C,H, and 0, RSH. Table 4. Analysis of the gas phase, given as percentage of each gas, throughout the decomposition of mercaptans on oxidized films film T/K H, CH, C,H, C,H, C,H, C,H, CO H,O Me,S Et,S RSH Fe 485 40.8 31.6 5.8 - Ni 443 30.3 34.0 6.1 - Pd 443 32.1 33.5 6.2 - A1 493 64.4 14.4 3.7 - CU 483 31.0 38.3 6.3 - Fe 493 38.9 2.7 7.9 30.7 Pd 438 51.2 2.4 8.2 20.8 Ni 483 39.2 1.1 10.7 28.0 A1 500 45.2 2.0 7.0 22.0 Cu 500 45.3 1.3 5.4 14.6 Fe 453 48.6 - - - Pd 453 40.9 2.5 3.0 - Ni 493 35.8 5.0 6.2 - A1 500 45.6 2.8 3.2 - MeSH EtSH PrSH 13.9 8.1 15.6 12.2 20.1 15.3 12.8 13.4 3.3 3.0 6.8 - 8.6 3.5 5.2 7.1 - 12.4 2.1 3.0 15.6 - 8.9 3.9 3.4 - - 10.2 3.8 6.2 8.2 - 6.2 5.4 5.2 - 2.4 6.8 9.4 15.0 - 6.1 - 1.5 14.0 4.0 7.5 - 1.8 20.1 - 1.9 6.1 - 6.1 - - - 1.4 4.0 - - 24.0 - 19.0 2.0 4.8 - 2.3 3.3 - - 12.0 1.0 2.5 - - 18.7 Hydrogen remained the major gaseous product throughout the mercaptans’ decomposition on the oxidized films above 300 K.Mainly CH,, together with small amounts of C,H6, accompanied MeSH decomposition on the oxidized films. The hydrocarbons resulting from the dissociative chemisorption of EtSH on the oxidized surface above 300 K involved C,H, and small amounts of C,H,, and a considerably smaller amount of CH,. In the case of PrSH decomposition on the oxidized films the hydrocarbons formed were C3H6 and C3H, gases, together with small amounts of3032 Catalytic Decomposition of Mercaptans 6 4 N E z 4 1 2 10 20 30 10 20 30 10 20 30 Fig. 2.Interaction of mercaptans with oxidized metal films. (a) MeSH on oxidized Ni at 443 K; (b) EtSH on oxidized Fe at 438 K; PrSH on oxidized Pd at 453 K. 0, CO; 6, H,O and 7, C,H,; other symbols as in fig. 1 . tlmin CH, and C,H, gases on the oxidized films of Pd, Ni and Al. Methyl sulphide, Me$, in the case of MeSH decomposition on oxidized Fe, Pd, Ni and Cu, and ethyl sulphide, Et,S, throughout the dissociation of EtSH on oxidized Fe, A1 and Cu, were also detected among the gaseous products. Small amounts of CO and H,O were also identified in the gas phase with the decomposition of all mercaptans above 340 K. Table 4 gives the composition of the gas phase at one temperature subsequent to the dissociative chemisorption of the mercaptans on the oxidized films.Fig. 2 shows the interaction of the mercaptans with oxidized films as typical results at certain temperatures. Careful analysis of the gas phase did not identify any amount of alcohol, aldehyde, CO,, CS,, H,S or any other substance, excluding those referred to in tables 3 and 4. Mercaptan adsorption at 193 K did not displace preadsorbed hydrogen on the films. In a typical experiment 43 mm3 of EtSH could be adsorbed at 193 K on an iron film ( VKr = 75.6 mm3) which had adsorbed at 300 K ca. 74 mm3 of pure hydrogen gas. The displaced hydrogen was ca. 5% of the total hydrogen adsorption. The overall surface coverage as expressed by the sum of Y+8 values on this film was ca.1.55, where Y represents VH,/ VKr. Extensive oxygen adsorption at 193 K occurred on films which had been saturated with mercaptan at this temperature. In a typical experiment on an iron film (VKr = 85.8 mm3) which had adsorbed at 193 K a maximum amount of 70.1 mm3 of EtSH (8 = 0.817), the same film could also take up 78.6 mm3 of pure oxygen gas at 193 K ( X = VOp/VKr = 0.916), the total surface coverage thus amounting to X+8 = 0.916+ 0.817 = 1.733. Similar behaviour was observed with other mercaptans on Fe and Ni films with respect to pre-adsorbed hydrogen or to subsequent oxygen uptake. Surface F%ase The structure of the surface phase on each film at a given temperature and value of 8 was expressed as C,H,S,, where n, m and 1, respectively, denote the number of carbon, hydrogen and sulphur atoms remaining in the surface phase per adsorbed mercaptan molecule.Values of n, m and 1 have been estimated from the volumes of mercaptanY. K. Al-Haidary and .I. M. Saleh 3033 - (?---, I I I I 200 300 400 500 x-- - - - -x - x-x-x-x *------ I 1 I I 200 300 400 500 T/K 1 I 1 I 200 300 400 500 Fig. 3. Composition of the surface phase as a function of temperature for (a) MeSH, (b) EtSH and (c) PrSH decomposition on clean metal films. 0, N ; A, M ; x , R. O--- - --- x - - - - x-x-xlx 1X.X xsc I------ 200 300 400 500 200 300 400 500 T/K e- I I I I 200 300 400 500 Fig. 4. Composition of the surface phase as a function of temperature for the decomposition of mercaptans on the oxidized films. Symbols as in fig. 3. adsorbed and of gaseous products formed, taking into consideration the number of carbon, hydrogen and sulphur atoms in the adsorbed mercaptan molecule and in each of the resulting gaseous products; the procedure of the estimation is similar to that presented previously.5* 2o The composition of the adsorbed phase was then expressed by the following ratios : N and M, the number of adsorbed carbon and hydrogen atoms to sulphur adatoms, and R, the ratio of hydrogen to carbon atoms in the surface phase; values of N, M and R may thus be represented, respectively, as n / l , m/Z and m/n.3034 Catalytic Decomposition of Mercaptans Table 5.Activation energies (Ea/kJ mol-l), pre-exponential factors (A/molecule cm-2 s-l) and entropies of activation (AS/J mol-l K-l) for the adsorption of the mercaptans on various surfaces film T/K e 'a A A S Fe Pd Ni A1 c u oxid.Fe oxid. Pd oxid. Ni oxid. A1 oxid. Cu Fe Pd Ni A1 c u oxid. Fe oxid. Pd oxid. Ni oxid. A1 oxid. Cu Fe Pd Ni A1 oxid. Fe oxid. Pd oxid. Ni oxid. A1 301-443 301-453 301-448 348-493 301-458 301-448 301-448 348-493 383-523 388-528 301-448 301-448 348-503 348-583 383-583 301-448 348-448 348-483 383-573 383-583 301-453 301-453 348-5 13 393-573 353-5 13 353-51 3 393-573 348-5 1 3 MeSH 0.98-3.13 41.2 f 2.0 1 .O 1 -3.46 53.0 f 2.2 1.10-3.18 45.9 f 2.3 1.13-1.30 62.5 f 2.5 0.93-1.96 67.3 f 2.3 0.80-1.83 51.9 f 2.0 0.88-1.78 57.4 f 3.5 0.89-1.08 61.2 f2.9 0.73-0.91 70.7 f 2.6 0.75-2.1 1 74.1 f 2.9 EtSH 0.8 7-2.0 1 48.7 f 2.1 0.89-1.85 55.3 f 3.3 0.98-2.05 61.2 f 3.1 1.02-1.26 75.3 f 2.9 1.03-1.69 85.1 f 3.3 0.82-1.80 54.7 f 1.2 0.86-2.02 62.9 f 3.6 0.88-2.08 67.7 f 2.0 1.04-1.52 78.5 f 1.9 1.53-1.91 88.6 f4.3 PrSH 0.83-1.12 57.1 f 3.3 0.82-1.33 67.4 f 1.4 0.84-0.85 70.2 f 2.8 0.89-1.90 76.2 f 1 .O 0.8 1-1.16 60.8 f 1.3 0.79-1.13 71.7f2.3 0.82-0.94 75.7 f 2.1 0.85-1.73 82.9 f 1.9 2.10 x 10l8 7.62 x 10l8 1.64 x lozo 3.75 x lozo 3.30 x 1019 4.47 x 1019 7.82 x 1019 1.82 x 1020 1.44 x 1021 1.58 x lo2' 1.52 x 1019 4.15 x 1019 1.19 x 1020 8.24 x 1020 3.60 x 1021 4.20 x 1019 6.40 x 1019 2.24 x lozo 1.41 x 1021 4.21 x loz1 7.67 x 1019 2.47 x 1020 9.38 f 1020 1.01 x lo2' 8.83 x 1020 1.76 x 1021 7.34 x lo2' 8.35 x 1019 -463f 1.9 - 434 f 3.7 -454f3.2 -421 f4.4 -410f 3.5 -444 f 2.0 -420f3.0 -416 f 2.8 -403 f 3.6 -389f 3.8 -44of 1.1 -428 f 3.3 -41 1 f 1.7 -394f4.3 - 373 2.4 -431 f3.6 -413 f2.5 -403f2.4 - 376 f 4.0 - 363 f 2.2 -413 f 2.8 -390f 1.9 -383 f 3.1 -371 f2.3 -400f 1.7 -381 f 1.8 - 370 f 2.9 358 f 3.0 Fig. 3 and 4 show plots of N, M and R against temperature for the three mercaptans on various clean and oxidized films.The points on each plot represent various films regardless of the variations in the values of 8, provided that the sequence of temperature treatments of the films are the same. Values of N, M and R were slightly (ca. 10 YO) lower for Ni, and higher for Cu, than those for the remaining metals with respect to all the three mercaptans; such values are not shown in the plots. Fig. 3 and 4 reveal the following. (1) Values of N, the ratio of carbon to sulphur adatoms, generally decreased with a rise in temperature in the range 193-500 K.If the influence of temperature on the value of N is considered with respect to each carbon atom of the mercaptan molecule (N per number of C atoms in the mercaptan), it is seen that the extent of the decrease in N is greatest for MeSH and smallest for PrSH; these were estimated to have, respectively, values of 2 x lod3, 1 x lod3 and 0.75 x per carbon atom of the mercaptan molecule per degree for MeSH, EtSH and PrSH. A similar trend exists for the behaviour of the mercaptans on the oxidized surfaces, although the values at any temperature were ca. 5-10% greater than the corresponding values on the clean films.Y. K. Al-Haidary and J. M. Saleh 3035 22 n 7 21 N E 3 20 - 2 E p: \ W M - 19 3 60 80 I 1 60 80 E, JkJ mol-' 60 80 Fig.5. Plot of logA us. E, for (a) MeSH, (6) EtSH and (c) PrSH. 0, Fe; A, Ni; 0, Pd; 0, A1 and V, Cu. Filled symbols for the oxidized films. (2) The values of R, the ratio of hydrogen to carbon adatoms, never fell below 3.0 in the case of MeSH, even when the temperature was raised to 500 K. This applies to both clean and oxidized surfaces, as seen in fig. 3 and 4. With EtSH, R also decreased with temperature, attaining values at 500 K of 2.4 and 2.2 on clean and oxidized films, respectively. Values of R in the case of PrSH behaved in a similar manner, attaining at 500 K a value of ca. 2.0 on clean and oxidized films. (3) The variation of M, the ratio of hydrogen to sulphur adatoms, with temperature was almost linear on the clean films (fig. 3) but occurred in two distinct stages on the oxidized surfaces (fig.4); the latter involved an initial stage taking place at temperatures 193-330 K, while the second stage, which was rather more intense followed the first stage at temperatures > 300 K. (4) The value of I, the number of sulphur atoms per adsorbed RSH molecule, did not alter significantly from unity even when the temperature was raised to 500 K owing to the removal of small amounts of sulphur, as Me,S and Et,S, from the surface phase. The variation of I with temperature was therefore not considered independently, but is indicated indirectly in the variation of N and M with temperature. Kinetics of Adsorption The variation of the rate of mercaptan adsorption at a given temperature and RSH pressure was determined by measuring the velocity rl of RSH uptake at an initial pressure Pl; The pressure was then rapidly changed to a different constant pressure P2 at the same surface coverage (8) and the new velocity r, measured.The rates thus obtained are assumed to depend on Ps; consequently the pressure dependence S may be (4) estimated from the relation5, 2o The values of S obtained for all the three mercaptans were close to unity. A check of the pressure dependence was the linear relationships obtained by plotting log P at a constant temperature as a function of time for the different mercaptans and films. w 2 = (pl/p2)s.3036 Catalytic Decomposition of Mercap t ans From the rates of RSH adsorption at two different temperatures, but virtually the same mercaptan pressure and value of 8, the activation energy of adsorption (E,) was determined, and the results are indicated in table 5; the value of Ea for each mercaptan did not alter with temperature or with the extent of adsorption (8).Values of Ea could also be obtained from Arrhenius plots, provided the rates at different temperatures are derived under constant RSH pressure. From the appropriate value of EB and the rate at given temperature, the value of the pre-exponential factor (A) in the rate equation rate = A exp (- E,/RT) was also calculated. Plots of Ea against logA on clean and oxidized films are shown in fig. 5. Discussion Clean Films The evidence indicates that mainly molecular adsorption of the mercaptans occurred on the films at 193 K. This agrees with the fact that only very small amounts of hydrocarbon have been detected subsequent to mercaptan adsorption on the films at this temperature. Values of 8 close to unity at 193 K on various surfaces probably indicate surface saturation with the adsorbed mercaptan on the basis of two-site coverage for each of the adsorbed krypton atom and mercaptan molecule.The extensive RSH adsorption at 193 K on films which had been saturated with hydrogen corresponded to Y+8 values of ca. 1.55. Such extents of RSH and H, adsorption on the same surface require considerably more surface sites than those present on the metal surface. This may suggest that RSH adsorption occurs on metal sites and partly on the adsorbed hydrogen layer. Hydrided Pd films adsorbed H,S at 188 K, and adsorption on hydrogen-covered Pd films caused the displacement of only a small proportion of the surface hydrogen, the remainder being displaced into the subsurface region.23 A similar phenomenon20 was indicated subsequent to CH,Cl adsorption on Fe, Pd and Ni films which had been saturated with hydrogen. Dissociative chemisorption of the mercaptan became the main feature of the interaction with the films only at temperatures > 300 K. The surface decomposition of the adsorbed mercaptan molecule may take place as RSH(g) - RSH(a) ' \ (b)' R(a) + SH(a) where (8) and (a) refer to the gaseous and adsorbed species, respectively. The pathway (a) in reaction (9, which involves the cleavage of the S-H bond, is similar to those suggested for the dissociative adsorption of MeSH on Ni and W films'' and of MeOH and EtOH adsorption on a number of metal films' under similar experimental conditions.The pathway (b), on the other hand, involves the breakage of the C-S bond in RSH, leaving an adsorbed alkyl group (-R) together with a sulphhydryl group (-SH) on the adjacent surface site. The latter pathway (b) is a possibility based on methanol decomposition on Ti0,8* 24.25 on a number of other surfaces.26* 27 The large H, evolution on all surfaces after adsorption of the mercaptan at temperatures >, 300 K gives evidence that decomposition occurs primarily via pathway (a) of reaction (5).Y. K. Al-Haidary and J . M. Saleh 3037 The formation of RH gas, liberating CH, with MeSH, C2H6 in the case of EtSH and C,H, with PrSH, may proceed through the reactions R(a) + H(a) -b RH(g) (6 4 and RS(a) + H(a) + RH(g) + S(a) (6 b) where the sulphur atom resulting from reaction (6b) is adsorbed on the surface and ultimately incorporated into the metal lattice.Thermochemical calculations from bond dissociation energies of the metal-adsorbate bond, the gas-phase enthalpies of formation and the tabulated bond dissociation energies2l9 28-30 indicated that reaction (6 b) is considerably more exothermic than reaction (6a); on Fe the values of AH for reactions (6a) and (6b) are, respectively, -96 and - 143 kJ mol-'. The production of C2H6 gas from MeSH decomposition may occur by the recombination of the adsorbed Me or MeS radicals. Calculation of the enthalpy changes associated with the formation of C2H6 by such reaction as: MeS(a) + MeS(a) -+ C2H6(g) + 2S(a) (7) indicated to be more exothermic (AH = -430 kJ mol-l) than by the recombination of Me(a) with MeS(a) (AH = - 48 kJ mol-') or of Me(a) with Me(a) (AH = - 344 kJ mol-l).Formation of R2S gas subsequent to the surface reactions may occur as RS(a) + RS(a) -+ R2S(g) + S(a) (8) on the basis of thermochemical calculations and disregarding the associated entropy changes, reaction (8) is found to be thermodynamically more feasible than through recombination of R(a) with RS(a) radicals. Reaction (8) resembles those forwarded previously" for the formation of R2S from MeSH, and for the production of Me20 and Et20 from methanol and ethanol decomposition on metal films.' No H2S gas was detected at any stage of RSH dissociation on various surfaces, suggesting no tendency for the recombination of the surface H(a) and HS(a) species, probably because of the relatively strong attachment of the SH radicals to the surface sites.This also supports the fact that pathway (b) of reaction ( 5 ) constitutes only a minor part compared with the predominant decomposition pathway (a). metal sites as: The formation of ethylene from EtSH decomposition H I probably requires sulphided in a similar manner to the production of ethylene throughout the decomposition of ethanol on the oxidized metal films.' Thus reaction (9) is accompanied by the simultaneous breakage of the C-S and C-H bonds in EtSH. Formation of CH, from EtSH requires the existence of CH, groups on the surface. These may be formed through such steps as CH,CH,S(a) -H(s! CH,CHS(a) 2 CH,CS(a) --+ CH,(a) + CS(a) in a similar procedure to the formation of CH, from EtOH decomposition on metal fi1ms.l Such a number of steps involved in the formation of CH,(a) species combined3038 Catalytic Decomposition of Mercaptans with the energies associated with the breakdown of two C-H bonds probably restrict the extent of reaction (1 0) to a small fraction of the adsorbed EtSH and this may account for the limited extent of CH, formation from EtSH decomposition.Oxidized Films The main process occurring on the oxidized surfaces at 193 K was the molecular adsorption of the mercaptans. The molecular species were either bound through hydrogen bonding to oxygen sites of the surface or coordinated to the surface metal sites (M) through the lone pair of electrons on sulphur in a similar manner to the adsorption of MeSH on oxides.a Lavalley and co-workers'2 studied the adsorption of MeSH on alumina, using i.r.techniques finding that MeSH is molecularly adsorbed in these two modes, with hydrogen bonding preferred by a ratio of 5:3. They also suggested that MeSH can be molecularly bound through hydrogen bonding to a surface hydroxyl group. Either of the two configurations for the adsorbed MeSH molecule on oxidized films can act as a precursor state leading to dissociation at temperatures 2 300 K. Because mercaptans are relatively acidic, the S-H bond is cleaved, leaving a thiolate (-SR) group bound on an acid site (metal site) and a proton bound to an adsorbed oxygen site [type (a) cleavage].Breakage of the S-C bond leaving an adsorbed alkyl group on adsorbed oxygen and a sulphhydryl (-SH) group on the metal site [type (b) cleavage] is also a possibility based on the decomposition of methanol on a number of s~rfaces.~~-~' The two types of adsorbed species resulting from the dissociation are illustrated as: R H S H S R -M-0 -M-0- I I I t I I type (a) type (b) Type (a) is expected to be the predominant decomposition pathway, for which preference has been demonstrated in adsorption studies on a number of surfaces, including modified tungsten, alumina and anatase.a* 12* 31 Comparison with methanol and ethanol decomposition1 suggests that formation of type (a) species can lead to a number of gaseous products by the reassociation of the adjacent species or through their reactions with the adjacent adsorbed alkyl groups in similar steps to those of The formation of H,O may take place by the recombination of the surface OH radicals. The type (b) species on the oxidized surfaces decompose mainly to CO in similar steps to those forwarded for the production of CO throughout the decomposition of methanol on oxidized films;' oxidized surfaces are better able to stabilize the alkyl group (-OR) than the sulphided surface (-SR).The production of some CO gas with all the three mercaptans on oxidized films suggests that some dissociation of the mercaptan via type (b) intermediates does take place. With PrSH, adsorbed methyl or ethyl groups are probably produced through the rupture of the C-C bond, resulting in the formation of methoxide and ethoxide radicals in the surface phase; such species are likely to contribute to the formation of CO gas throughout the decomposition of this mercaptan on oxidized surfaces.H, adsorption from type (b) decomposition species (-OR) is probably not important, since relatively little CH, and CO accompanies H, evolution in all cases on the oxidized films (table 4). The formation of only small amounts of CH, and CO gases with EtSH and PrSH reflects the very low extents of rupture of the C-C bond which occur in these two mercaptans at temperatures < 500 K. Oxidized metal films probably act as betterY. K. Al-Haidary and J. M. Saleh 3039 catalysts than sulphided metals for extracting sulphur atoms from EtSH and PrSH. This is reflected in the production of C,H, gas from PrSH only on the oxidized films, and also in the liberation of relatively larger amounts of C2H4 gas from EtSH on the oxidized surfaces than on the clean metals.The formation of C2H4 and C,H, gases subsequent to the decomposition of EtSH and PrSH on oxidized surfaces may take place as H * ,S+H+C,H, I I I I M O and H Surface Phase The value of R throughout the decomposition of MeSH on both clean and oxidized films did not fall below 3 (fig. 3 and 4) even at 500 K. This suggests that C-H bonds are not readily broken and that methyl groups (or -SMe) may exist on the surface without further dissociation in the temperature range 300-500 K. This suggestion is in agreement with the types of products observed through the interaction of MeSH with the films (table 3); it also agrees with the previous results of MeSH interaction with Ni and W films.17 The behaviour is also in line with the results of CH, adsorption on Ni films, which indicated slow liberation of hydrogen from the adsorbed phase, even above 400 K.Values of R of 2.4 and 2.2 (fig. 3 and 4) with EtSH in the range 300-500 K suggest the existence of C,H, and C2H4 adsorbed species, which probably account for the liberation of C2H, and C2H4 gases through the interaction of this mercaptan with the films. The lowest value of R in the case of PrSH was 2.0, reflecting a more extensive C-H bond dissociation in this mercaptan as compared with EtSH. This also implies the presence of such surface species (C,H6 and C,H,) which may give rise to the formation of C,H, and C,H, gases through the dissociation of PrSH films.The structure of the surface phase with MeSH at 500 K may be represented as H,&,S and Hle,Co.,S or as (CH3.2)o.5S and (CH,),.,S on clean or oxidized films, respectively, indicating the existence of CH, groups in the surface phase in the ratio of 0.5 per adsorbed sulphur atom. With EtSH the surface phase at 500 K could be represented as H3.84C1.6S and H,.,,C,.,S or as (C2H4J0$3 and (C2H4.4)o.6S on clean or oxidized films, respectively. This is likely to imply the presence of ethyl and ethylenic species in the surface phase; the decomposition is thus shown from the surface structures to be more extensive on the oxidized films than on the clean metals. If C-C bond breakage is considered with this mercaptan at temperatures close to 500 K, the surface phase may also involve such structures as (CH2.4)1.6S and (CH2.2)l.2S, suggesting the presence of CH, and CH, species on the surface although to a small extent; these may take part in the production of C2H4 and C2H6 gases throughout the decomposition of this mercaptan.3040 Catalytic Decomposition of Mercaptans With PrSH the surface composition may be represented at 500K as H,C,.,S and H,C,S or as (C3H6)o.83S and (C3H6)o.6,S on the clean or oxidized films, respectively. Such surface species may account for the production of C,H, and C3H8 gases in the decomposition of this mercaptan.Further dissociation of such structures, although to a small extent, into (C2H4)l.25S and (C,H,)S on the clean and oxidized film, respectively, is also a possibility on the assumption of C-C bond cleavage of this mercaptan.Such a composition probably accounts for the liberation of C2H6 gas subsequent to hydrogenation of the C2H4(a) species. Kinetic Data The direct dependence of the adsorption rate on RSH pressure together with the values of S = 1.0 [eqn (4)] suggest that the rate-determining step is the adsorption of RSH which is, thereafter, followed by the rupture of the S-H and C-S bonds. The adsorption of the mercaptan and its subsequent decomposition at temperatures above 300 K occurred with appreciable rates on various surfaces despite the variation of E, and A values as indicated in table 5. This suggests the operation of a compensation probably arising from the relationship between the heat and entropy of adsorption34 which leads to a connection between activation energy and entropy of activation (and hence the pre-exponential factor).Fig. 5 shows linear relationships existing between E, and log A. The kinetic data reveal the following. (1) The slopes and intercepts of the various log A us. Ea plots in fig. 5 are almost the same for the three mercaptans, indicating the operation of compensation effect of the same nature on various surfaces regardless the type of the mercaptan used as adsorbate. (2) The sequence of activity among the films toward MeSH uptake as derived from fig. 5 was: Fe > Ni > Pd > A1 > Cu and toward EtSH and PrSH adsorption as: Fe > Pd > Ni > A1 > Cu. The activities of the oxidized films for the adsorption of the mercaptans follow a sequence similar to that given for EtSH and PrSH.(3) It would also be possible to conclude from the results of fig. 5 that tendencies of the mercaptans for adsorption on the clean and oxidized film lie in the order MeSH > EtSH > PrSH. The ease of the decomposition of the mercaptans as judged from the values of N, M and R (fig. 3 and 4) lies in the reverse order to that of adsorption. The results also indicate that transition-metal films have higher tendencies for reaction with mercaptans than A1 and Cu films; this result agrees with those obtained earlier20 for the interaction of methyl chloride with a number of metal films. References 1 D. Al-Mawlawi and J. M. Saleh, J. Chem. SOC., Faraday Trans. I , 1981, 77, 2965; 1981, 77, 2977.2 J. Yasumori, T. Nakomura and E. Miyazaki, Bull. Chem. SOC. Jpn, 1967, 40, 1372; 3967, 40, 4012. 3 D. W. Mekee, Trans. Faraday SOC., 1968, 64, 2200. 4 N. Takezawa, C. Hanamaki and H. Kobayashi, J. Caral., 1975, 38, 101. 5 J. M. Saleh and S. M. Hussian. J. Chem. SOC., Faraday Trans. I , 1986, 82, 2221. 6 M. Y. Ekerdt and G. John, J. Catal., 1984, 90, 17. 7 W. Mokwa, D. Kohl and G. Heilend, Surf Sci., 1982, 117, 659. 8 D. D. Beck, J. M. White and C. T. Ratcliffe, J. Phys. Chem., 1986, 90, 3137. 9 L. D. Neff and S. C. Kitching, J. Phys. Chem., 1974, 78, 1648. 10 H. Blyholder and D. 0. Bowen, J. Phys. Chem., 1962, 66, 1288. 11 K. Klosterman and H. Hobert, J. Catal., 1980, 63, 355. 12 0. Saur, T. Chevreau, J. Lamotte, J. Travert and J. C. Lavalley, J . Chem. SOC., Furaday Trans. I , 1981, 77. 427.Y. K . AI-Haidary and J . M. SaIeh 304 1 13 J. M. Saleh, C. Kemball and M. W. Roberts, Trans. Faraday SOC., 1961, 57, 1771. 14 J. M. Saleh, Trans. Faraday SOC., 1970, 66, 242. 15 J. M. Saleh, J. Chem. SOC., Faraday Trans. I , 1972, 68, 1520. 16 Y. M. Dadiza and J. M. Saleh, J. Chem. SOC., Faraday Trans. 1 , 1973, 69, 1678. 17 J. M. Saleh, M. W. Roberts and C. Kemball, Trans. Faraday SOC., 1962, 58, 1642. 18 R. L. Wilson and C. Kemball, J. Catal., 1964, 3, 426. 19 P. Kieran and C. Kemball, J. Catal., 1965, 4, 380. 20 A. K. Mohammed, J. M. Saleh and N. A. Hikmat, J. Chem. SOC., Faraday Trans. 1, 1987, 83, 2391. 21 K. K. Al-Shammari and J. M. Saleh, J. Phys. Chem., 1986, 90, 2906. 22 Y. K. Al-Haydari, J. M. Saleh and M. M. Matloob, J. Phys. Chem., 1985, 89, 3286. 23 M. W. Roberts and I. R. H. Ross, Reactivity of Soloids (Wiley, New York, 1969), p. 411. 24 I. Carrizosa, G. Munuera and S. Castanar, J. Catal., 1977, 49, 265. 25 I. Carrizosa and G. Munuera, J. Catul., 1977, 49, 174; 189. 26 T. Matsushima and J. M. White, J. Catal., 1976, 44, 103. 27 D. C. Foyt and J. M. White, J. Catal., 1977, 47, 260. 28 M. Grunze, Surf. Sci., 1979, 81, 603. 29 L. Pauling, Nature of the Chemical Bond (Cornell University Press, 1960). 30 C. T. Mortimer, Reaction Heats and Bond Strengths (Pergamon, Oxford, 1962). 31 H. Saussey, 0. Saur and J. C. Lavalley, J. Chim. Phys.-Phys. Chim. Biol., 1984, 81, 261. 32 P. G. Wright, P. G. Ashmore and C. Kemball, Trans. Faraday SOC., 1958, 54, 1692. 33 E. Cremer, Advances in Catalysis (Academic Press, New York, I955), vol. 7, p. 72. 34 C. Kemball, Proc. R. SOC. London, Ser. A , 1953, 217, 376. Paper 7/ I563 ; Received 25th August, 1987 100 FAR 1

ISSN:0300-9599    

DOI:10.1039/F19888403027

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1988, 84(9), 3043-3057 Adsorption and Catalytic Decomposition of Dimethyl Sulphide and Dimethyl Disulphide on Metal Films of Iron, Palladium, Nickel, Aluminium and Copper Yousif Kadim Al-Haidary and Jalal Mohammed Saleh* Department of Chemistry, College of Science, University of Baghdad, Baghdad, Jadiriya, Republic of Iraq The interaction of dimethyl sulphide (Me,S) and dimethyl disulphide (Me,S,) has been studied with metal films of Fe, Pd, Ni, A1 and Cu over the temperature ranges 193-500 K with Me,S and 223-600 K in the case of Me,S,. At 193 K mainly molecular chemisorption of Me,S occurred on the films. With Me,S,, multilayer adsorption, involving both chemisorption and van der Waals adsorption, took place on the films at 223 K. Dissociative chemisorption of Me,S or Me,S, began above 300 K and was accompanied by the evolution of gaseous products.The latter involved H,, CH, and C,H, gases with Me,S and H,, CH,, C,H,, MeSH and Me,S subsequent to the dissociation of Me,S,. Additional gaseous products throughout the decomposition on the oxidized films were CO, H,O and C,H,. The rate of Me,S or Me,S, chemisorption depended on the pressure of the reacting gas, and the kinetic data indicated the operation of a compensation effect throughout the interaction of Me,S or Me,S, with the films. On the basis of kinetic data it was possible to arrange the metal films in the order of decreasing activity toward Me,S or Me,S, adsorption. The transition-metal films showed greater activity than A1 and Cu, and among the former films Fe showed the greatest activity, for chemisorption of Me,S and Me,S,.All the metals have higher tendencies for Me,S adsorption than for Me,S,. Methyl sulphide and dimethyl disulphide are discharged during industrial processes into the atmosphere and are listed as substances having an offensive odour in many countries. Both substances are highly corrosive1 under various conditions and can also act as corrosion inhibitors when used in small amounts under certain circumstances.l, Poisoning of catalytic surfaces by compounds containing unshielded sulphur atoms, including dimethyl sulphide and dimethyl disulphide, is of widespread interest. The poisoning effects of such compounds on a number of catalysts are well known.4 This investigation contributes to a series of studies on the adsorption of sulphur- containing gases on various ~olids.~-l~ In the present work the adsorption and the decomposition of dimethyl sulphide and dimethyl disulphide was investigated on a number of clean and oxidized metal films over a wide range of temperatures (193-600 K).The product phase was analysed mass-spectrometrically and the kinetics of adsorption were followed at each stage. Although there have been some studiesl1-l4 of the adsorption of dimethyl sulphide and dimethyl disulphide, very few have dealt with such fundamental aspects. 15-17 Experimental The apparatus and general techniques utilized in the outgassing, preparation and sintering of the films have been described elsewhere.1s-21 The metal films were prepared from Johnson Matthey spectroscopically standardized wires (0.5 mm in diameter) which were first degassed at as high a temperature as possible (ca.1300 K) for a 3043 100-23044 Interaction of Me,S and Me,S, on Metal Films minimum of 8 h. Each film was prepared at 78 K and sintered for 30 min at 350 K. During the deposition and sintering of the films the reaction vessel was pumped and the pressure was always < The reaction vessel was connected through a leak device to a Quadruvac 200 mass- spectrometer partial-pressure gauge (Leybold-Heraus) ; details of the construction and operation have been given elsewhere. Dimethyl sulphide (Me,S) and dimethyl disulphide (Me,S,) with purity > 98 YO were obtained from Rideal Dehan. Each substance was purified by vacuum distillation twice at room temperature into a receiver at 78 K followed by cold pumping.Only middle fractions of the distillate were used, and mass-spectrometric analysis showed these to be > 99.6% pure. The stored samples were further outgassed, purified and then analysed prior to use. All the materials used in the cracking-pattern determination were obtained from Matheson and B.D.H. and had stated purities exceeding 99.5%. Each substance was subjected to the same purification treatment as for Me,S and Me,S,. The surface area of each film was determined from the krypton adsorption isotherm at 78 K before the admission of Me,S or Me,S, doses. The extent (0) of dimethyl sulphide or disulphide adsorption on the film was expressed as N mP2. where VKr represents the volume of the krypton monolayer on the surface at 78 K and 5 is the volume of Me,S or Me,S, adsorbed subsequent to the determination of the area.In a series of experiments, each film was first saturated with oxygen gas at 300 K and a pressure of 2.0 N m-,. The oxygen pressure was then reduced to lop4 N rn-, and the area of the oxidized film was redetermined prior to the addition of Me,S or Me,S, to the surface. The extent ( X ) of metal oxidation was estimated from the relation The extent (0) of the subsequent Me,S or Me,S adsorption was calculated from eqn (1) using the volume of the krypton monolayer (vKr) on the oxidized surface instead of VKr; all the volumes were measured in units of mm3 at s.t.p. Results Adsorption of Me,S Fast adsorption of Me$ occurred on all films at 193 K, the pressure falling to N in < 1 min.Further adsorption took place in a similar manner until the rate of uptake decreased rapidly to lo1, molecule cm-, s-l, corresponding to 1 % of the monolayer per second at values of 8 ranging from 0.57 to 0.881 for the transition-metal films Pd, Ni and Fe and from 1.14 to 1.34 on A1 and Cu. Table 1 gives the volumes of the krypton monolayer (VKr) on the films, the subsequent maximum Me,S adsorption (5) at 193 K and the corresponding values of 8. Ca. 15 O/O of the adsorption on A1 and Cu films at 193 K was reversible. Some CH, and H, gases, amounting to ca. 5 YO of adsorbed Me,& was desorbed at 193 K. Slow Me$ uptake continued on all surfaces in the temperature range 250-340 K without liberation of significant amounts of product gases; the values of 8 increased by ca.15 YO over a period of 1 h of the reaction at such temperatures. Adsorption of Me,S on the films above 340 K was accompanied by the evolution of gaseous products; these involved H,, CH, and C,H, gases on Fe, Pd, A1 and Cu and only CH, and C,H, on Ni. Hydrogen evolution was appreciable only on Fe and A1 films forming the dominant gaseous product of Me,S decomposition on these metals. The extent of CH, liberation at any temperature was generally greater on Fe, Pd, Ni and CuY, K. Al-Haidary and J . M . Saleh 3045 Table 1. Adsorption of dimethyl sulphide (Me,S) on clean and oxidized films of Fe, Pd, Ni, A1 and Cu at 193 K film X 8 Fe 101.0 - - - 89.0 0.881 Pd 79.5 - - - 46.0 0.578 - - 25.2 0.700 A1 17.5 - - - 20.1 1.148 cu 8.4 - - - 11.3 1.345 oxidized Fe 80.0 79.3 0.991 70.5 58.1 0.824 oxidized Pd 76.5 84.2 1.100 60.8 37.5 0.616 oxidized Ni 50.0 57.2 1.144 39.9 26.4 0.663 oxidized A1 18.0 24.3 1.350 21.7 19.1 0.880 oxidized Cu 15.4 18.0 1.168 22.0 22.2 1.009 Ni 36.0 - a The volumes of the gases were expressed in mm3 at s.t.p.Table 2. Analysis of the gas phase, given as percentage of each gas, throughout the decomposition of dimethyl sulphide (Me2S) on various films film T/K H, CH, C,H, H,O CO Me,S Fe 30 1 338 498 Pd 338 383 498 Ni 383 498 A1 383 448 cu 573 oxidized Fe 383 498 oxidized Pd 453 498 oxidized Ni 448 498 oxidized A1 383 498 oxidized Cu 573 21.24 31.26 32.69 8.19 - - 29.21 35.77 7.87 29.41 43.64 9.04 27.98 11.10 17.77 33.81 33.37 12.79 6.03 21.72 38.77 17.59 58.37 72.06 40.31 55.77 7.18 10.33 39.28 16.98 21.1 1 46.69 45.63 20.05 50.17 6.04 12.01 3 1.55 11.21 10.00 10.87 9.41 10.82 10.94 23.04 25.28 18.90 19.38 11.90 - - 61.52 - 37.02 - - 17.67 - 61.26 - - - - 30.81 - 17.00 _- - 36.65 - 18.95 - - - 44.71 - 34.52 - - - 40.95 - 3.95 2.81 1.23 4.76 3.46 2.28 4.70 1.50 3.13 5.11 2.17 3.03 2.32 1.07 6.29 2.23 1.88 6.66 3.34 3.95 4.06 3.20 4.53 4.83 1.38 1.75 3.15 45.62 24.75 34.94 16.08 59.27 21.29 48.80 42.06 49.38 films than of C,H,.On Al, the percentage of ethane in the gas phase exceeded that of CH,. Table 2 gives the composition of the gas phase on the films at two or three temperatures. Fig. 1 (a) shows the interaction of Me,S with Fe film at 383 K. Adsorption of Me,S on oxidized films at 193 K occurred also rapidly to the extent (0) which are indicated in table 1 at which the rate of adsorption decreased to < loll molecule cmP2 s-' (< 0.1 '/o monolayer s-').Some 10 % of the adsorption at 193 K on all films was reversible. No gaseous products were identified subsequent to Me,S adsorption on oxidized surfaces at this temperature. Further slow Me,S adsorption3046 Interaction of Me,S and Me,S, on Metal Films 10 20 30 10 20 30 tlmin Fig. 1. Interaction of Me,S with Fe film at 383 K (a), and of Me,S, with Pd film at 448 K (b). 0, H,; A, CH,; x , C,H,; 0, MeSH; A, Me,S and A, Me,S,. Table 3. Adsorption of dimethyl disulphide (Me,S,) on clean and oxidized films of Fe, Pd, Ni, A1 and Cu at 223 K film 'Kr '0, 'Kr % ' Fe Pd Ni A1 c u oxidized Fe oxidized Pd oxidized Ni oxidized A1 oxidized Cu 73.10 65.81 54.00 15.56 11.31 80.8 71.7 57.2 16.9 12.5 - 110.0 - 124.9 - 104.4 50.70 35.7 82.1 1.096 70.5 144.0 78.5 1.094 67.3 140.1 63.1 1.103 48.7 114.5 21.8 1.289 20.2 63.0 19.7 1.576 15.1 48.8 - - - - - - - - - - - - 1 SO4 1.807 1.933 3.258 3.156 2.042 2.08 1 2.35 1 3.1 18 3.23 1 occurred at temperatures < 340 K.Dissociative chemisorption of Me,S was the main feature of the interaction above 340 K resulting in the formation of gaseous products (table 2). The composition of the gas phase consisted (table 2) of H, and CH, gases, together with small amounts of C,H,, H,O and CO. The dominant product was H, on oxidized Fe and A1 films and CH, on oxidized Pd, Ni and Cu (table 2). Fig. 2(a) shows the interaction of Me$ with oxidized Fe film at 383 K.Adsorption of Me,S, Rapid Me,S, uptake occurred on films at 223 K until 8 became 1.5-1.9 on Fe, Pd and Ni and 3.15-3.25 on Cu and Al. The rate of uptake at this stage decreased to lo', molecule cm-' s-l under an Me,S, pressure of 8.0 N m-,. Table 3 gives the values of VKr, 5 and the corresponding maximum values of 8 on the films at this temperature. No gaseous products were observed subsequent to the adsorption of Me$, on the films at 223 K. On warming the films to 273 K desorption of Me$, took place, lowering the values of 8 to ca. 1.0. Adsorption of Me,S, on all films above 340 K was accompanied by the evolution of H,, CH,, C,H,, MeSH and Me,S gases. The rate of adsorption and dissociation increased with the rise of temperature above 340 K.The major gaseous products on Fe and Ni films at any temperature in the range 340-600 K was Me,S, while H, was theY. K. Al-Haidary and J . M. Saleh 3047 F Table 4. Analysis of the gas phase, given as percentage of each gas, throughout the decomposition of dimethyl disulphide (Me,S,) on various films film T/K H, CH, C,H, Mesh Me,S H,O CO Me,S, Fe Pd Ni A1 c u oxidized Pe oxidized Pd oxidized Ni oxidized A1 oxidized Cu 394 443 493 448 498 433 483 523 383 443 513 343 433 573 343 453 493 383 498 348 498 383 513 348 498 6.47 - - 48.87 49.26 14.37 21.54 23.70 4.39 18.54 28.64 5.88 20.29 38.40 20.67 - - 20.15 19.53 15.90 11.45 24.15 11.92 10.70 - 17.82 21.22 25.67 9.14 10.83 13.03 20.24 21.21 7.21 14.94 16.26 4.83 7.27 15.77 9.48 41.82 40.2 1 32.65 28.56 11.73 32.82 4.17 10.19 11.58 20.66 11.37 23.01 23.07 22.08 22.45 19.23 20.53 21.15 13.03 12.23 12.39 26.26 27.8 29.95 8.17 8.48 10.44 7.17 8.69 12.42 13.67 16.56 18.34 10.34 12.9 1 4.18 9.26 5.18 35.93 7.55 40.45 2.89 3.40 7.69 4.30 6.73 12.33 7.65 27.33 6.66 26.95 8.31 4.48 13.02 10.08 15.48 23.65 5.02 3.55 5.29 5.62 15.94 5.91 15.46 6.28 20.97 15.78 11.87 5.65 21.10 10.37 18.61 13.32 25.48 18.16 17.90 13.84 18.10 14.93 13.00 21.45 18.08 23.83 4.2 - 4 P) E z 1 Q 2 10 20 30 - - - - - - - - - - - - - - 2.37 4.10 4.89 3.20 4.80 2.50 2.60 2.30 3.31 5.89 4.04 50.90 14.66 3.26 13.62 5.47 33.93 2.7 1 0.33 62.58 31.19 3.58 58.83 36.03 4.97 37.46 22.05 5.65 19.3 1 3.60 25.52 3.86 33.78 8.09 25.82 8.05 10 20 30 t/min Fig.2. Interaction of Me,S with oxidized Fe at 383 K (a) and of Me,S, with oxidized Pd at 498 K (b).0, CO and 0, H,O. Other symbols as in fig. 1. main product on Pd, A1 and Cu films at similar temperatures. The extent of MeSH formation on all films was very small, even when the temperature was raised to 600 K. Table 4 shows the percentages of the gaseous products throughout the interaction of Me$, with the films at various temperatures. Fig. l ( b ) shows the interaction of Me,S, with a Pd film at 448 K. Adsorption of Me$, on oxidized films at 223 K was also rapid, and the extent of3048 6 4 cl: a m E 2- 2 Interaction of Me,S and Me,S, on Metal Films 200 4 00 600 1 I I 200 400 6 00 T/K Fig. 3. Values of 0, N; 0, M and A, R plotted as a function of temperature for Me,S adsorption on clean (a) and oxidized (b) films.adsorption on oxidized Fe, Pd, and Ni films was greater than on the corresponding clean metals (table 3). Ca. 50 O/O of the adsorption on oxidized Fe, Pd and Ni and ca. 68 O/O on oxidized A1 and Cu at 223 K were reversible. Above 340 K dissociative chemisorption of Me,S, occurred on the oxidized surfaces, and the adsorption was followed by the liberation of such gases as H,, CH,, C,H,, MeSH and Me,S, together with small amounts of H,O and CO. Methane and methanethiol were the main products on oxidized Fe, Pd and Ni films, while CH, and Me,S were the dominant products on oxidized Cu. H, evolution on oxidized Fe and Ni films occurred at 343 K but discontinued at higher temperatures. A summary of the results at various temperatures is presented in table 4, and fig.2(b) describes the behaviour of Me,S, on an oxidized Pd film at 498 K. Surface Composition The composition of the surface phase on each film is expressed as C, H, S,, where It, m and I represent, respectively, the number of carbon, hydrogen and sulphur atoms re- maining in the surface phase per adsorbed Me,S or Me,S, molecule. Values of n, m and 1 have been obtained from the volumes of the resulting gases for a given volume of adsorbed Me,S or Me$,, taking into consideration the number of carbon, hydrogen and sulphur atoms in each gas; the procedure of estimating these parameters is similar to that presented These data were then used to calculate the values of N and M, indicating, respectively, the number of carbon and hydrogen atoms to sulphur adatoms, and R, the number of hydrogen to carbon adatoms.Thus N , M and R correspond, respectively, to the ratios n/l, m / l and m/n. The value of 1 remained equal to unity throughout Me,S decomposition on both clean and oxidized films, as none of the gaseous products contained sulphur atoms at any temperature < 600 K; this makes n = N and m = A4 with respect to the surface composition of the adsorbed Me,S. Fig. 3 shows the values N , M and R for Me,S plotted as a function of temperature on both clean and oxidized films over the temperature range 195-600 K; the points on each plot represent a general trend for the temperature dependence of the respective parameter. Values of these parameters are shown in fig. 3 to decrease considerably with the rise in temperature, but the extent is slightly greaterY. K.Al-Haidary and J . M. Saleh 3049 on the oxidized films than on clean surfaces. Some specific values of the three parameters for Me,S at four temperatures which are involved in fig. 3 may be arranged as follows, where c and o refer, respectively, to the clean and oxidized films. N A4 R _ _ _ ~ _____ T / K c 0 C O C O 193 2.0 2.00 6.0 6.00 3.00 3.00 400 1.6 1.70 4.2 4.40 2.62 2.59 500 1.4 1.35 3.5 3.25 2.50 2.40 600 1.2 1.10 2.5 2.00 2.10 1.80 Values of N and M are thus shown to be higher at 400 K, but lower at 500 and 600 K, on oxidized surfaces than on clean films. Values of R decreased steadily with increasing temperature, attaining values of 2.1 and 1.8 on clean and oxidized films, respectively. Decomposition of Me,S,, as indicated in fig.4 and 5, was less dependent on temperature on A1 and Cu films than on Fe, Ni and Pd. Moreover, the variation of n, m and 1 (fig. 4) with temperature was greater on clean A1 and Cu than on the oxidized surfaces of these films; the reverse of this trend existed with respect to Fe, Pd and Ni (fig. 4). Some specific values for n, m and 1 on Fe, Pd, and Ni may be arranged as follows : n m I ~______ T / K c 0 C o c o 223 2.0 2.0 6.0 6.0 2.0 2.0 400 1.8 1.4 4.5 4.8 1.9 1.9 500 1.2 0.7 2.0 1.8 1.8 1.7 600 0.5 0.3 0.7 0.5 1.2 1.2 Thus the change in the values of n, m and 1 is substantial, particularly over the temperature range 500-600 K. On A1 and Cu the values of these parameters are considerably higher than those on Fe, Ni and Pd. Values of I in the case of Me$, also decreased with increasing temperature as a consequence of the removal of adsorbed sulphur-containing species (MeSH and Me,S) from the surface.Owing to the temperature dependence of I, another plot was necessary to represent the ratios n/l, m / l and m/n as expressed in terms of N , M and R us. temperature as in fig. 5. The drop in N values to below unity with increasing temperature reflects the fact that more carbon is removed from the surface phase than sulphur. There is a sharp fall in the values of M (fig. 5 ) over the temperature range 500-600 K, attaining at the latter temperature a value as low as ca. 0.5. The variation of R on clean films of Fe, Ni and Pd became less temperature-dependent over the temperature range 500-600 K as compared with the range 400-500 K; on oxidized surfaces of these films a steady temperature dependence continued at all temperatures > 400 K. Kinetics of Adsorption The rate of Me,S and Me,S, adsorption on each surface was determined at various surface coverages (8) and temperatures.At a given temperature and Me,S or Me,S, pressure the velocity (rl) of uptake was measured at an initial pressure p l ; the pressure3050 Interaction of Me$ and Me$, on Metal Films 6- 4 - - a T E e 2 - r - - 1 I I I I 1 Fig. 4. Composition of the surface phase plotted against temperature for Me$, adsorption on clean (a) and oxidized (b) films. 0, n ; 0, m and A, 1 for Fe, Pd and Ni and D, n; @, m and A, 1 for A1 and Cu. -\ I r I I 200 400 600 TIK 200 400 600 Fig. 5. Values of N, A4 and R plotted as a function of temperature for Me,S,.adsorption on clean (a) and oxidized (b) films.Symbols as in fig. 2 for Fe, Ni and Pd and a similar filled symbol for A1 and Cu.Y, K. Al-Haidary and J . M . Saleh 305 1 Table 5. Activation energies (Ea/kJ mol-l), pre-exponential factors (A/molecule cm-, s-l) and entropies of activation (AS*/J mol-' K-l) for the adsorption of dimethyl sulphide (Me$) on various films film T/K e 'a A AS* Fe Pd Ni A1 c u oxidized Fe oxidized Pd oxidized Ni oxidized A1 oxidized Cu 301-498 301-498 338-498 338-498 443-533 338-498 383-498 383-498 338-498 383-55 3 0.881-1.525 0.578-1.452 0.70Cb1.941 1.148-2.119 1.345-2.414 0.824-1.195 0.616-0.853 0.663-0.930 0.880-2.055 1.009-2.089 50.228 f 2.9 56.678 f 2.1 53.28 1 1.8 65.756 f 3.3 78.268 f 4.2 58.382f 3.5 68.593 f 2.7 72.419 & 2.2 79.392 f 3.1 83.992f 3.5 2.891 x l0l8 4.686 x 1Ol8 3.697 x 10" 1.560 x 10'' 4.808 x lo1' 4.882 x l0l8 1.625 x 1019 2.517 x lo1' 8 .9 1 4 ~ 10'' 4.01 x 1019 - 460.94 -457.97 - 459.46 -451.41 - 442.94 -453.28 -448.61 -445.18 - 441.40 - 434.85 Table 6. Activation energies (Ea/kJ mol-I), pre-exponential factors (A/molecule cm-, s-l) and entropies of activation (AS*/J mol-1 K-l) for the adsorption of dimethyl sulphide (Me$,) on various films film T/K e 'a A AS* ~ Fe Pd Ni A1 c u oxidized Fe oxidized Pd oxidized Ni oxidized A1 oxidized Cu _ _ _ _ ~ ~ 343-493 343-498 343-523 348-493 348-493 348-498 348-498 348-493 348-573 39 3-5 8 3 1.504-3.906 1.897-3.467 1.933-3.503 3.255-5.396 3.156-6.151 2.042-4.5 59 2.08 14.05 1 2.35 1-5.167 2.351-5.167 3.1 18-6.871 43.503 f 2.1 49.138+_ 1.7 58.395 f 1.4 61.690f 1.9 72.510k2.3 47.692 f 2.6 55.839 f 2.9 63.633 f 1.6 68.799 f 1.7 80.478 +_ 2.5 3.890 x 1017 7.687 x 1017 1.493 x loL8 2.517 x 10l8 6.622 x 10l8 4.886 x 1017 1.119 x 10I8 2.328 x 10I8 4.204 f 10" 1.005 x 1019 -473.79 -472.10 - 466.2 1 -465.18 -457.28 -473.81 -467.83 -463.78 - 460.08 -452.16 was then rapidly changed to a different constant pressure p2 at the same surface coverage (O), and the new velocity r2 measured.These data were then used to estimate the pressure dependence, S, from the relation : I s , l9 The values of S obtained for both sulphur compounds were close to unity. Moreover, the plots of logp for each adsorbate at a constant temperature against time were found to be adequately linear.From the rates of adsorption of each sulphur compound at two different temperatures, but essentially the same adsorbate pressure and value of 8, the activation energy of adsorption (E,) was determined, and the results are given in tables 5 and 6. The value of E, for each adsorbate did not vary with temperature or with the extent of adsorption (0). Values of Ea could also be estimated from Arrhenius plots, provided the rates at different temperatures are derived under similar adsorbate pressures. The extent (0) of adsorption did not influence the values of E and A , as these values remained constant over an increase of 8 to ca. 3.0 in the case of Me2S and to ca. 6.0 for Me2S2 (tables 5 and 6). The kinetics of Me2S and Me,S, adsorption are thus shown to be independent of the nature and amount of adsorbed species remaining on the surface over the experimental values of 8 that are given in tables 5 and 6.3052 Interaction of Me,S and Me,S, on Metal Films I I I 50 70 90 I I 1 50 70 90 EJkJ mol-' Fig.6. log A us. E, for Me,S (a) and Me$, (b) adsorption on clean and oxidized films. 0, Fe; 0, Pd, A, Ni, 0, Al; V, Cu, and similar filled symbols for the oxidized films. The rate of adsorption ( r ) and the appropriate value of E, were then used to calculate the pre-exponential factor ( A ) in the rate equation: r = A exp ( - E,/RT). (4) The entropy of activation (AS:) for Me,S and Me,S, was then calculated from the value of A using relationship A = (kT/h) Cg C, exp(ASf/R) ( 5 ) where Cg and C, are, respectively, the concentrations of the sulphur compounds per unit volume (cm3) and the surface sites per unit area (cm2).Plots of Ea values against log A are shown in fig. 6. Discussion Me,S The results indicated that mainly molecular adsorption of Me,S occurred on all surfaces at 193 K, as only very small amounts of CH,, alone or together with H,, appeared in the gas phase at this temperature. Magnetization measurement~'~ on supported nickel catalysts have shown that Me,S is associatively chemisorbed at room temperature with the formation of two bonds with two nickel atoms of the surface. Molecular adsorption of Me2S on the surface may also occur via coordination to a single metal site through a lone pair of electrons on sulphur in a similar manner to those reported ear1ier10.'3.22 for the adsorption of mercaptans and alkyl sulphides on a number of surfaces; the relatively large size of the adsorbed Me,S molecule may then cause the blockage of an additional (adjacent) site.The formation of very small amounts of CH, and H, on certain films at 193 K shows that some dissociative chemisorption is also possible through the rupture of both C-S and C-H bonds. The dissociative chemisorption which began above 350 K may take place as Me,S(g) -+ Me,S(a) -+ MeS(a) + Me(a) ( 6 ) involving the rupture of the C-S bond of the methyl sulphide. This is similar to the adsorption behaviour of alkyl sulphides on silica-supported nickel13, 23 and of mercaptans on a number of surface^.^^'^*^^ The formation of appreciable amounts of hydrogen and alkanes as a result of chemisorption of methyl sulphide above 350 K requires at leastY.K. Al-Haidary and J . M. Saleh 3053 partial dissociation of C-H bonds of the chemisorbed Me(a) and MeS(a) residues in addition to the dissociation of C-S bonds. The dissociation of methyl sulphide on supported-nickel catalysts was reported to be highly temperature-dependent. l5 At ca. 400 K extensive dissociation of Me,S occurred through the cleavage of both C-S and C-H bonds, and magnetization experiments indicated15 the formation of 8-10 bonds at this temperature for each Me,S molecule adsorbed, depending on the nature of the products formed in the surface phase. Surface recombination reactions between chemisorbed methyl (or thiolate) groups and between these residues and atomically chemisorbed hydrogen lead to the formation of hydrogen, methane and ethane as AH/kJ mol-1 Me(a) -+ CH,(a) + H(a) - 98.0 (7 a) (8) H(a) + H(a) + H2k) Me(a)+Me(a) + MeMe(g) 334.0 238.0 Me(a) + H(a) + MeH(a) The Me(a) species in reactions (7a), (9a) and (loa) may be replaced by MeS(a) species to give such reactions as AH/kJ mol-' MeS(a) -, CH,S(a) + H(a) - 187.0 (7 b) Me(a) + MeS(a) +MeMe(g) + S(a) -48.0 (9 b) MeS(a) + MeS(a) +MeMe(g) + 2S(a) - 450.0 (9 4 MeS(a) + H(a) +MeH(a) + H(a) - 143.0 ( 1 0 4 An attempt was made to calculate the enthalpy changes [AH(a) associated with these and previous reactions from the heats of adsorption, enthalpies of formation and the bond dissociation energies, using the procedure already adopted in previous pub- l i c a t i o n ~ , ~ ' .~ ~ the resulting data for Fe film are indicated in reactions (7H10). A similar trend operates among the AHa values of reactions (7)-( 10) on other metals. The results generally show that reaction (7h) is more exothermic than reaction (7a), and that reactions (9a) and (10a) are endothermic while the corresponding reactions (9b), (9c) and (lob) are exothermic. If the enthalpy changes were roughly treated as equivalent to the changes in the free energies of the corresponding reactions, through ignoring the accompanying changes in entropy, the calculated values of AHa should reflect the thermodynamic feasibilities of the various proposed reactions. Dissociation of C-Cl and C-H bonds has been foundlg to occur throughout the chemisorption of CH,C1 on a number of clean and oxidized films above 300 K; the formation of hydrocarbons and hydrogen on such surfaces proceeded through reaction steps similar to those of reactions (7)-(10).Methyl sulphide was also shown to be chemisorbed dissociatively 2 300 K on silica-supported nickel'? by the rupture of C-S and C-H bonds, and surface recombination reactions as followed by thermodesorption and i.r. transmission measurements gave rise to hydrogen and hydrocarbons. The extensive production of H, subsequent to the dissociative adsorption of Me,S on Fe and A1 films indicates the significance of reaction (7) on these films. The predominance of CH, over C,H, on most surfaces may be attributed to an abundant supply of atomic hydrogen at or near the surface which can migrate on or through the lattice and hydrogenate the bound MeS or Me groups.A significant amount of atomic hydrogen has been found to be incorporated in a number of metals during adsorption of H2S2, and MeSH.24*27 Diffusion to the surface of hydrogen atoms contained in the lattice is p r o p o ~ e d ~ ~ , ~ ~ to be the probable source of the broad intense H, desorption peak on rutile throughout H,S and CH,SH adsorption at 600 K.3054 Interaction of Me,S and Me$, on Metal Films Dissociative chemisorption of Me,S on oxidized surfaces above 300 K may take place Me,S(g) + O(a) -+ MeS(a) + MeO(a) (1 1) as where the thiolate group (-SMe) bound on a metal site and the methyl group (-Me) attached to preadsorbed oxygen site, the latter probably forming a methoxide radical on the surface.The chemisorption of Me,S on silica was enhanced by high-temperature pre- treatment of the oxide; the adsorbed species consisted of methyl groups attached to oxide sites and thiolate groups on silicon atoms.13 Reaction (1 1) resembles in some respects the adsorption behaviour of methanethiol on Ti0,28 and on a number of and oxidized films." The formation of CO subsequent to the decomposition of Me,S on oxidized films suggests that dissociation of Me,S via reaction (1 1) does occur. The production of ethane and methane gases from the decomposition of Me,S on oxidized films above 300 K may proceed through reactions similar to those of (9 b), (9 c) and (10 b). Methl groups bound to oxide sites are less susceptible to such recombination reactions than those attached to sulphur owing to the fact that the C-0 bond is relatively stronger than C-S.Thermochemical calculations indicated that the recombination reactions (9b), (9c) and (lob) are more exothermic than the corresponding reactions involving MeO. The methoxide radicals OMe(a) resulting from the dissociative adsorption of Me,S on the oxidized films decompose mainly to CO in similar steps to those suggested for the production of this gas from methanol decomposition on oxidized metals.,' Values of R (fig. 3) dropped to below 3.0 at 400 K and decreased further to ca. 2.0 when the temperature of the film was raised to 600 K. This is an indication of sub- stantial cleavage in the C-H bonds of Me,S subsequent to chemisorption on the films at such temperatures. This also reflects the extent of the contribution of surface species to production of hydrogen atoms in the surface phase.Comparatively lower values of N and M were attained on oxidized surfaces than on clean films as a result of the additional reactions which take place entirely on the oxidized films. The drop in R (fig. 3) to values in the range 2-3 in the temperature range 400-600 K may suggest the existence of CH, and CH, radicals in the surface phase. In the presence of sufficient hydrogen adatoms, any C,H,(a) species that may be formed should rapidly be hydrogenated into C,H, gas. This is one likely explanation for the fact that no C,H, gas was detected over such temperatures. Me*% Multilayer adsorption of Me,S, took place on all films at 223 K, as the values of 6 were considerably higher than unity, and a substantial fraction of the adsorption at this temperature was reversible.Dissociative chemisorption and subsequent evolution of gaseous products began only at temperatures 2 350 K. The chemisorbed Me,S, molecule can act as a precursor state leading to dissociation via either or both of the following paths: MeS(a) + MeS(a) (12) MeS,(a) + Me(a) Me2S2(g) - Me,S,(a) Reaction 12(a) is expected to be the predominant decomposition pathway, as the MeS-SMe bond dissociation energy (306.6 kJ mol-l) is lower than that of Me-SSMe (327.6 kJ mol-I). Calculation of the enthalpies of adsorption in the manner described in previous papers2l3 25 indicated that the dissociation of the adsorbed Me,S, via pathwayY .K. Al-Haidary and J . M. Saleh 3055 (a) is more exothermic than according to the pathway (b); the values of AHa on films of Fe, Pd and Ni according to paths (a) and (b) are, respectively, - 450 and - 380 kJ mol-l. These AHa values may reflect the different tendencies of the dissociation pathways to proceed if entropies associated with such steps could be ignored. Further dissociation of MeS,(a) to MeS(a) and S(a) is also possible, as the enthalpy change involved in such dissociation is also exothermic on all surfaces by ca. 5&70 kJ mol-l. On oxidizing films, the MeS,(a) and MeS(a) species resulting from reaction (12) are likely to be attached to the metal sites, while Me(a) is being bound to the oxide site. Cleavage of the C-S bond leaving an adsorbed methyl group on lattice oxygen forming a methoxide radical was a possibility in methanethiol decomposition on a number of surfaces.,, The formation of hydrocarbons as a result of Me,S, chemisorption on the films at temperatures > 350 K requires at least partial dissociation of the C-H bonds of the chemisorbed methyl or thiolate groups, in addition to the dissociation of the C-S bonds.Surface recombination reactions between chemisorbed methyl or thiolate species, and between these species and atomically adsorbed hydrogen, leading to the formation of the various products, proceed in parallel with the dissociation of S-S, C-S and C-H bonds. Considering the most abundant surface species to involve H, Me and MeS, then reactions similar to those described by eqn (7H10) can occur throughout Me,S, decomposition on various surfaces.Additional reactions are possible in the case of Me,S,, probably because of the presence of MeS,(a) species on the surface. These may include MeS,(a) + H(a) + MeSH(g) + S(a) MeS,(a) + Me(a) -+ Me,S(g) + S(a) (13) (14) MeS,(a) + MeS(a) + Me,S + 2S(a). The formation of MeSH from the reaction of MeS(a) and H(a) has been disregarded, as no such reaction occurred throughout Me,S decomposition on the same metals where similar species were suggested to exist in the surface phase. The reaction of MeS(a) with adjacent Me(a) or MeS(a) species to produce Me,S has been ignored, as Me,S decomposition on the same metals was found to be entirely irreversible. On the basis of thermochemical calculations, reactions (1 3H15) were found to be all exothermic.Decomposition of Me,S, on the oxidized films may also take place in similar steps to those of reaction (1 2), the resulting MeS, and MeS species covering the metal sites and Me radicals binding to preadsorbed oxygen atoms. The methoxide radicals resulting from the interaction of Me and O(a) species, probably enter into a series of decomposition reactions similar to those mentioned before to produce CO, H, and H,O gases. MeS(a) and MeS,(a) species, on the other hand, may take part in reactions similar to (7H10) and (13)-(15) to liberate such gases as H,, CH,, C,H,, MeSH and Me,S. The decomposition of Me,S, on silica-supported nickel at 300 K have been found” to produce similar gaseous products. Surface structure (fig.4) indicated a steady decrease in the parameters n and rn to very low values at 600 K, while I attained a value of 1.2 at the same temperature; the latter reflects the possibility of sulphur adsorption and also possibly incorporation in the metal lattice. The surface sites initially form terminal or bridged bonds to sulphur lone pairs, and at higher temperatures the loss of H,, CH, and CH, species occurs, leaving sulphur anions which may then be incorporated into the lattice. Values of R (fig. 5), reflecting the ratio of H to C, decreased to below 3 above 400 K, indicating the presence of CH, and CH,’species in the surface phase. Lower N , M and R values (fig. 5 ) on the transition-metal films (Fe, Pd and Ni) than on A1 and Cu may reflect the higher heats of the surface species on the latter films than the former.3056 Interaction of Me,S and Me,S, on Metal Films Kinetics of Adsorption It is concluded from the value of S = 1.0 [eqn (3)] and the direct dependence of the adsorption rate on Me,S or Me,S, pressure that the rate-controlling step in each case is the adsorption of the sulphide or the disulphide on the surface, which is then followed by the rupture of S-S, C-S and C-H bonds in these adsorbates. The relationships existing between log A and E, (fig.6) suggest the operation of a compensation effect31 throughout the adsorption of the sulphur compounds on the films. The compensation phenomenon is likely to arise from a relationship between the heat and the entropy of adsorption,31* 32 which leads to a connection between the activation energy and entropy of activation (and hence the pre-exponential factor).The kinetic results presented in fig. 6 indicate that the activities of various surfaces towards Me,S adsorption follow the following sequence : Fe > Ni > Pd > oxidized Fe > A1 > oxidized Pd > oxidized Ni > oxidized A1 = Cu > oxidized Cu (a) while the activities of Me,S, adsorption on the same surfaces may be arranged as: Fe > oxidized Fe > Pd > oxidized Pd > Ni > oxidized Ni = A1 > oxidized A1 > Cu > oxidized Cu. (b) Thus the most active metals toward both sulphur compounds are the transition-metal films, among which Fe occupies the highest rank. On the other hand, A1 and Cu were the least active metals among the five covered in this investigation, Cu being less active than Al.The sequence of activity among the oxidized films towards both sulphur compounds was as follows: oxidized Fe > oxidized Pd > oxidized Ni > oxidized A1 > oxidized Cu. (c) Comparing sequences (a) and (b) it is shown that Ni is far less active than Pd towards Me,S,, while the reverse of this trend holds with respect to Me,S. A further point is that the oxidized Fe film shows a higher activity for Me,S, chemisorption than do the clean metals Pd, Ni, A1 and Cu. References 1 Corrosion ; Metaf/Environment Reactions, ed. L. L. Shreir (Butterworths, Boston, MA, 1976), 2 B. G. Ateya, B. E. El-Anadeuli and F. M. A. El-Nizamy, Buff. Chem. SOC. Jpn, 1981, 54, 3157. 3 E. B. Maxted, Advances in Catalysis (Academic Press, New York, 1951), vol.3, p. 129. 4 E. B. Maxted and M. Josephs, J. Chem. Soc., 1956, 2635. 5 J. M. Saleh, C. Kemball and M. W. Roberts, Trans. Faraday Soc., 1961, 57, 1771. 6 J. M. Saleh, Trans. Faraday Soc., 1970, 66, 242. 7 J. M. Saleh, J. Chem. Soc., Faraday Trans. 1, 1972, 68, 1520. 8 Y. M. Dadiza and J. M. Saleh, J. Chem. SOC. Faraday Trans. I, 1973, 69, 1678. 9 J. M. Saleh, M. W. Roberts and C. Kemball, Trans. Faraday Soc., 1962, 58, 1642. 10 Y. K. Al-Haideri and J. M. Saleh, J. Chem. SOC., Faraday Trans. I, 1988, 84, 3027. 11 S. Tanada, K. Baki and K. Matsumots, Chem. Pharm., 1978, 26, 1527. 12 R. W. Glass and R. A. Ross, J . Phys. Chem., 1973, 77, 2571. 13 C. H. Rochester and R. J. Terrell, J . Chem. SOC., Faraday Trans. I, 1976, 72, 596. 14 W. J. Jones and R. A. Ross, J. Chem. Soc., 1968, 1787. 15 E. Den Bosten and P. W. Selwood, J . Catal., 1962, I, 93. 16 0. Saur, T. Chevreau, J. Lamstte, J. Travert and J. C. Lavollay, J . Chem. SOC., Faraday Trans. 1, 1981, 17 K. Klostermann and H. Hobert, J. Cataf., 1980, 63, 355. 18 J. M. Saleh and S. M. Hussian, J . Chem. SOC., Faraday Trans. 1 , 1986, 82, 2221. p. 352. 77, 427.Y. K. Al-Haidary and J . M. Saleh 3057 19 A. K. Mohammed, J. M. Saleh and N. A. Hikmat, J. Chem. Soc., Faraday Trans. I , 1987, 83, 2391. 20 Y. K. Al-Haideri, J. M. Saleh and M. H. Matloob, J. Phys. Chem., 1985, 89, 3286. 21 K. K. Al-Shamari and J. M. Saleh, J. Phys. Chem., 1986, 90, 2906. 22 M. H. Dilke, E. B. Maxted and D. D. Eley, Nature (London), 1948, 161, 804. 23 G. Blyholder and D. 0. Browen, J. Phys. Chem., 1968, 66, 1288. 24 D. D. Beck, J. M. White and C. T. Ratcliffe, J. Phys. Chem., 1986, 90, 3137. 25 M. Grunze, Surf. Sci., 1979, 81, 603. 26 M. W. Roberts and J. P. H. Ross, Reactivity of Sofids (Wiley, New York, 1969), p. 41 1. 27 J. B. Bates, J. C. Wang and R. A. Perkins, Phys. Rev. B, 1979, 19, 4130. 28 I. Carrizosa, G. Munuera and S. Castanar, J. Cataf., 1977 49, 265. 29 I. Carrizosa and G. Munuera, J. Cataf., 1977, 49, 167; 189. 30 D. Al-Mawlawi and J. M. Saleh, J. Chem. SOC., Faraday Trans. I , 1981, 77, 2965. 31 E. Cremer, Advances in Catalysis (Academic Press, New York, 1955), vol. 7, p. 75. 32 C. Kemball, Proc. R. Soc. London, Ser. A , 1953, 217, 376. Paper 711672; Received 18th September, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403043

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chern. SOC., Furuduy Trans. I, 1988, 84(9), 3059-3070 The Construction and Characteristics of Drug-selective Electrodes Applications for the determination of Complexation Constants of Inclusion Complexes with a- and fi-Cyclodextrins including a Kinetic Study Norboru Takisawa,? Denver G. Hall, Evan Wyn- Jones* and (in part) Philip Brown Department of Chemistry and Applied Chemistry, University of Salford, Salford M.5 4WT Ion-selective membrane electrodes selective to the drugs chlorpromazine, dicyclomine, imipramine, desipramine and propranolol hydrochlorides have been constructed using a modified poly(viny1 chloride) membrane which has ionic end-groups as ion-exchange sites and which was cast using a solid polymeric plasticiser. These drug electrodes show excellent Nernstian responses in the concentration range 10-2-10-7 mol dmP3 and their selectivity coefficients with respect to each other, as well as their workable pH range have been investigated.The electrodes have also been used to determine the complexation constants of chlorpromazine and dicyclomine hydrochlorides with both a- and B-cyclodextrins. In all cases a 1 : 1 complex was observed. The kinetics associated with the formation of the complex involving a-cyclodextrin and dicyclomine hydrochloride have also been investigated using the ultrasonic technique. Ion-selective membrane electrodes which are selective to a variety of ionic drugs have attracted much interest because of their potential use in pharmaceutical analysis. Recently, two types of drug-selective membrane electrodes have been reported.The membranes used in these electrodes were made from liquid4” and liquid-plasticized poly(viny1 chloride) (PVC)5 and are based on a water-insoluble ion-pair complex acting as an ion-exchanger. Although these electrodes showed acceptable characteristics in pharmaceutical analysis, especially in the simple way they can be constructed and in which they show a fairly rapid response, some problems have been encountered with the membranes, e.g. the requirement of extensive pre-conditioning treatment, care in storage, sensitivity to some hydrophobic counter-ions and a relative short lifetime. In connection with a study of surfactant-selective electrodes some of the above disadvantages encountered with the above PVC membrane have been overcome by the use of a modified PVC which has ionic end-groups as ion-exchange sites6-* and a solid polymeric plasticiser to cast the membrane.8 The former inhibits the dissolution of the ion-exchanger and the latter method yields membranes which have longer lifetimes.Following these works the electrode design was modified and significantly impr~ved,~ resulting in a more robust device. In the present work, several drug-selective electrodes were constructed by the improved polymeric plasticized PVC method described above and have been characterised in the sense that e.m.f. values have been measured over a range of drug concentrations in the region 10-2-10-7 mol dmP3 and the resulting data analysed using the Nernst equation. In addition to these experiments the selectivity coefficients of these 7 Permanent address : Department of Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan.30593060 Drug-selective Electrodes Table 1. Drugs investigated drug structure therapeutic supplier m.wt category chlorpropmazine hydrochloride dicyclomine hydrochloride imipramine hydrochloride desipramine hydrochloride propranolol hydrochloride CH,CH2CH,N(CH3)2 I n COOCH2CH2 N(C2 H5)2 3 HCI CH2CH2CH2N(CH,)z a HCI @ OH HCI Sigma Vick International R and D Labs Geigy Pharmaceuticals Geigy Pharmaceuticals Sigma 355.3 346.0 316.9 302.9 295.8 antiemetic antipsychotic anticholinergic antidepressant antidepressant cardiac depressant adrenergic blocker drug electrodes relative to the other drugs and the workable pH range of the electrodes were also determined.Apart from their potential application in pharmaceutical analysis these electrodes could also be used to investigate the interaction of drugs with other solute species such as biopolymers and receptors." To demonstrate this we describe binding studies (to a- and j3-cyclodextrins) of two of the drugs used. The reasons for the use of cyclodextrin in these experiments were two-fold. First, these compounds are known to inhibit the side-effect of the drug'' and secondly, as cyclodextrins have been used as neutral carriers12 in membrane electrodes, data on complexation coefficients may give clues on how to improve the selectivity of these devices. Finally, the kinetics associated with the formation of the inclusion compound involving a-cyclodextrin and dicyclomine hydrochloride were also investigated using the ultrasonic technique. Experimental Materials All the drugs used in this work were of the highest purity available.Table 1 lists the drugs used, their structure and their suppliers. The PVC was made by Montefibre and kindly donated by Professor P. Meares. It contains 24.3 pequiv. per gram of SO,H+ end- groups. The plasticiser Elvaloy 742 was a Dupont product. Tetrahydrofuran (THF), BDH, was fractionally distilled each time before use. The a- and j3-cyclodextrins were carefully recrystallised commercial products (Aldrich). All the solutions were prepared in doubly distilled deionised water and stored in the dark to prevent photochemical oxidation of the drug.13N . Takisawa et al.306 1 drug electrode test solution containing lop2 mol dm-3 sodium chloride electrode reversible to sodium ion. Preparation of the PVC Membrane The polymeric plasticised PVC membranes used in this work were prepared in a similar way to the recipe described by Davidson.8 Initially the commercial PVC product is conditioned for use with the respective drug. Basically this procedure involves exchanging the hydrogen ion of the SO;H+ end charge groups with the drug cation. The method used to carry out this ion-exchange step was to dissolve 0.5 g of the powdered PVC in 30cm3THF and add the respective drug to this solution. Any insoluble gel components of the PVC and undissolved drug were removed from the solution by filtering through a 10 pm millipore filter, the filtrate being poured into 200 cm3 of water and stirred continually.This results in the precipitation of the conditioned PVC in a fibre form which was then filtered and washed thoroughly with water and dried in a vacuum desiccator for 48 h. 0.12 g of this PVCdrug complex and the polymeric plasticiser (0.18 g) were then dissolved in 30 cm3 THF and filtered through a 10 pm millipore filter into a flat-bottomed beaker (diameter 55 mm). This solution was left for 3 days for the THF to evaporate. The resulting PVC membrane was dried in a vacuum desiccator, peeled off, and punched out so that it could be attached to the electrode tip with a small amount of THF. E.M.F . Measurements The potentiometric measurements were made using a digital pH/millivolt meter (Corning ion analyser 150).In all the experiments the temperature was controlled to within f 0.1 "C by circulating thermostatted water through the double glass cell and the sample solution was continuously stirred using a magnetic air stirrer. During the e.m.f. measurements the concentration of the test sample solutions was changed successively by adding a known amount of solution to the initial sample (30 cm3) using an Aglar microcylinder system. The response of the drug electrodes was tested in the concentration range 10-7-10-2 mol dm-3 at 25 "C. The binding of chlorpromazine and dicyclomine hydrochlorides to both a- and 8-cyclodextrins was measured in the3062 Drug-selective Electrodes Table 2. Response characteristics of the drug membrane electrodes slope/mV linear response drug electrode per decade intercept/mVa range/mol dmP3 chlorpromazine 57.7k0.2 -28.7f0.7 1 x 10-5-1 x dicyclomine 56.1 k0.5 -28.9+ 1.2 2 x 10-5-2 x imipramine 59.0k0.5 -28.2k0.5 1 x 10-6-2 x propranolol 58.8k 1.0 -27.2k 1.5 1 x lO+-l x desipramine 58.8k0.3 -29.4k0.5 1 x 10-6-1 x a Intercept is the e.m.f.measured when the inner and the outer solution have the same drug concentration. drug concentration range 10-6-10-3 mol dm-3 and 10 mmol dmP3 a-cyclodextrin and 2.0 mmol dm-3 P-cyclodextrin at 25 "C. All the test solutions contained a constant amount (0.01 mol dmP3) of NaCl in order to ensure that the Na+ concentration was constant during the experiments. Kinetic Measurements The kinetic measurements were carried out using the ultrasonic-relaxation technique in which measurements of ultrasonic absorption and velocity were made in solutions thermostatted at 25 "C.The Eggers resonance technique,14a for which the frequency range has recently been extended'** from 2 to 0.2 MHz, was used in the range 0.2-20 MHz, and a standard pulse technique was used for frequencies up to 95 MHz. Results and Discussion Electrode Responses The response characteristics of the drug-selective membrane electrodes constructed in this work are summarized in table 2. In all cases these membrane electrodes showed stable e.m.f. values over 30 min. and the response time was always < 3 min. With the exception of the chlorpromazine and dicyclomine electrodes, the present electrodes showed excellent Nernstian behaviour in the sense that a plot of e.m.f.against log concentration was reproducible and linear over a wide concentration range with a slope of 59 mV (very close to the theoretical value expected from the Nernst equation). In addition, the intercept of this plot was always constant within the range - 28.5 0.8 mV. Typical e.m.f. data are shown in fig. 1. The slopes of the e.m.f. plots for chlorpromazine and dicyclomine electrodes were 57.7 and 56.1 mV, respectively (values which are slightly smaller than those predicted from the Nernst equation), but in all cases the data were found to be reproducible. The cause of this slight deviation is not known but could be due to a small amount of self-aggregation of the drug molecule or an impurity in the sample. Deviations from linear 'Nernstian' behaviour are found both at high and low drug concentrations (fig.1). The former deviations are due to aggregation of the drug, the latter at concentrations of the order 10-6mol dm-3 or less, are presumably due to the transport number of the drug in the membrane falling below unity. In these respects the drug electrodes behave in much the same way as surfactant electrodes, but the concentration range over which linear ' Nernstian ' behaviour occurs is sometimes significantly greater for drugs than for surfactants.C - 5c > E 4 1 - 10( -15( N . Takisawa et al. 1 I I 1 / 0 /, I 1 I -6 -5 -4 -3 log (C/mol dm-3) 3063 Fig. 1. E.m.f. response of chlorpromazine hydrochloride electrode. Table 3. Selectivity coefficients for drug membrane electrodes KDJ interferent, J, drug chlorpromazine dicyclomine imipramine desipramine chlorpromazine 1 .o 2.3 5.7 7.0 imipramine 0.17 0.41 1 .o 1.3 propranolol 0.05 0.08 0.25 0.27 dicylomine 0.52 1 .o 2.7 3.4 desipramine 0.16 0.36 0.99 1 .o Selectivity Coefficient Relative to Interferent Drugs The selectivity coefficient K,,, of a drug (D) membrane electrode towards another drug as an interferent ion (J) is defined by the equation: (1) RT nF E = - In [CD + KDJ C,] + constant.The selectivity coefficients of the drug electrode were measured relative to the other drug as follows : a solution was prepared containing a known amount of the interferent drug (J) and the e.m.f. of the solution was measured with the drug (D)-membrane electrode. To this solution was then added small amounts of drug (D) ion.From the resulting e.m.f. measurements the selectivity coefficient KDJ was evaluated for each drug concentration and the values averaged out. The KDj values are listed in table 3. The selectivity of the drug electrode increased in the order chlorpromazine > dicyclomine > imipramine > desipramine and propranolol, i.e. in the same trend as the molecular weights. We could not find any correlations between the selectivity and the lower limit of the linear response of the electrodes.3064 Drug-selective Electrodes Fig. 2. Effect of pH on e.m.f. response of drug electrodes. 0, Chlorpromazine; 0, dicyclomine; A, desipramine ; A, imipramine ; 0, propranolol. Table 4. Working pH ranges of drug-selective electrodes drug pH range chlorpromazine 2 4 .5 dic yclomine 2-6.5 desipramine 2 6 . 5 imipramine 2.5-7.5 propranolol 2.5-8.5 The e.m.f. of the drug electrodes used in this work were measured relative to an electrode which was reversible to sodium ion used as a reference. It was found that the performance of the electrode was unaffected by altering the concentration of the reference electrolyte by a factor of 100. In addition to this, these electrodes did not respond significantly to hydrophobic counter-ions; the e.m.f. changed less than 10 mV by addition of dodecyl sulphate ions in the concentration range 1 x 10-6-5 x lo-* mol dm-3. The Effect of pH on the Response of the Drug Electrodes The effect of pH on the e.m.f. response of the drug electrodes was studied by recording e.m.f. values at various pHs.The cell used was the type Ag I AgClI5 x mol dm-3 drug hydrochloride-10-2 mol dm-3 NaCl (inner solution) I membrane I test-drug solution in In the acidic region the e.m.f. values of all five drug electrodes are unaffected by mol dm-3 NaCl (outer solution) 11 calomel electrode.I?. Takisawa et al. 3065 changes in pH even at pH = 2 as shown in fig. 2. On the other hand, the e.m.f. values decreased at the higher pH values because the concentration of unprotonated drugs is increased. In addition, all drugs except propranolol hydrochloride precipitate in the outer solutions at higher pH. The working pH range of these drug electrodes is listed in table 4 and is essentially determined by the basicity and solubility product of the respective drugs. The propranolol hydrochloride electrode shows widest working pH range, pH 2-8.5, and that of chlorpromazine hydrochloride, pH 2-6.5, is almost the same as that of the liquid and liquid-plasticized membrane electrodes described in the literat~re.~.In principle it is possible to estimate the pKa values of the drugs from the data presented in fig. 2; the pKa being equal to the pH where the initial concentration of protonated drug is halved. In the present case it was possible to use this method only for propranolol hydrochloride, which gave a value of 9.3. For the other drugs studied, precipitation of the unprotonated drug occurs which prevents an estimation of pKa being obtained. 46 Lifetime and Maintenance of Electrodes The electrodes constructed in this work can be used continuously for at least 1 month before any damage to the membrane occurs.The membranes do not require any pre- conditioning before measurements or storage in the respective drug solutions before use. They were washed thoroughly with water after each run and kept in a desiccator under atmospheric conditions. Overall, these PVC membranes are easy to handle and use and appear to have a distinct advantage over the corresponding liquid-plasticised membranes. Complexation Constant of Drug Binding to 01- and p-Cyclodextrins Inclusion compounds in which the host can admit a guest compound into its cavity without any covalent compounds being formed have been used extensively in fundamental studies and have also found a wide variety of application~.~~-~’ The cyclodextrins are known to form several inclusion compounds with substrates and, indeed, are also known to inhibit side-effects in drugs.ll In general, a drug which is in solution with cyclodextrin is expected to form an inclusion compound of the type: drug + cyclodextrin inclusion compound.(2) The purpose of this exercise was to demonstrate how the complexation constant associated with the formation of the inclusion compound can be evaluated using the drug electrodes. The measurements were carried out using the following procedure. First the e.m.f. of the drug electrode relative to the sodium reference electrode was measured as a function of monomer drug concentration up to the high-concentration limit of the electrode, when self-aggregation of the drug begins. The experiment was then repeated by measuring the relative e.m.f.of the drug electrode in the presence of a constant amount of cyclodextrin, again ensuring that measurements were taken in the concentration range where the drug exists as a monomer only. These measurements on the drug/cyclodextrin formulations were performed in such a way that the reversibility of the above equilibrium was confirmed. Once the e.m.f. measurements on the drug/cyclodextrin formulations were finished the e.m.f. of the drug electrode was rechecked against monomer drug to ensure consistency. All the measurements were made in solutions containing 0.01 mol dm-3 NaCl, and typical data are shown in fig. 3. From these data it is possible to evaluate the drug monomer concentration, m,, at each total concentration of drug, C, for which the3066 Drug-selective Electrodes Fig.3. log (C/mol dm-3) E.m.f. response of chlorpromazine hydrochloride electrode with and without dmP3 /?-cyclodextrin. 0, Calibration : a, with B-cyclodextrin. 2 x 10-3 mo1 measurements were taken. The data were analysed by first assuming that equilibrium (2) between the drug and cyclodextrin involves a 1 : 1 complex, in which case the equilibrium complexation constant, K, for each solution can be evaluated from the e.m.f. data as using the classical Scatchard equation in the form: V -- - K-KV m1 (3) where : v = concentration of drug complexed with cyclodextrin/ total concentration of cyclodextrin. (4) The plots of v/m, us. v for the data involving the drugs chlorpromazine and dicyclomine hydrochlorides binding to P-cyclodextrin are shown in fig.4. In the case of both drugs binding to a-cyclodextrin the binding constants are lower by a factor of CQ. 100 than that of /3-cyclodextrin, and in these circumstances the Benesi-Hildebrand plot in the form l/v plotted against l/ml [eqn (5)] were used. These are shown in fig. 5. l/v = (l/Kml)+ 1. ( 5 ) The linearity and intercepts of these plots confirm the 1 : 1 stoichiometry of the complex and the equilibrium constants, listed in table 5, were obtained. The large difference in K between chlorpromazine and dicyclomine hydrochlorides suggests the possibility of constructing drug membranes which are more selective to dicyclomine hydrochloride than chlorpromazine hydrochloride by using modified /3-cyclodextrin as a neutral carrier in the membrane.12N.Takisawa et al. 3067 V Fig. 4. Scatchard plot for the binding of drugs to /3-cyclodextrin in 0.01 mol dm-3 NaCl at 25 "C. 0, Chlorpromazine ; , dicyclomine. mi'/& mm~r' Fig. 5. Benesi-Hildebrand plot for the binding of drugs to a-cyclodextrin in 0.01 mol dm-3 NaCl at 25 "C. 0, Chlorpromazine; 0, dicyclomine. Kinetic Studies Recently there has been some attention directed towards investigating the kinetics associated with the inclusion compounds of dyes20 and related molecules2' with cyclodextrins. In the present work a 1 : 1 complex was observed for all the drugs studied and it was therefore decided to determine whether the ultrasonic relaxation method3068 Drug-selective Electrodes Table 5. Binding constants (mole' dm3) of chlor- promazine and dicyclomine hydrochlorides to a- and P-cyclodextrins in 10 mmol dmP3 NaCl at 25 "C drug a-cyclodextrin P-cyclodextrin chlorpromazine (1.2k0.1) x lo2 (1.1 kO.1) x lo4 dicyclomine (2.8 0.3) x lo2 (9.5 +_ 0.9) x lo4 Table 6.Ultrasonic relaxation parameters for mixtures of dicylomine hydrochloride and a-cyclodextrin single relaxation [a-CD]/mol dm-3 [DCH]/mol dm-3 A / 10-15 s2 m-l f,/ 1 O6 Hz B/ s2 m-' 0.05 0.05 0.07 0.04 614 509 0.69 0.65 double relaxation 51 50 A,/10-15 s2 m-' jJ106 Hz A2/10-15 s2 m-I f,/lO-'j Hz B/10-15 s2 m-' 0.05 0.07 506 0.76 77 6.9 32 0.05 0.04 488 0.62 47 12.5 26 could be used to investigate the kinetics associated with the formation of these inclusion compounds. For the purpose of the present exercise the most suitable drug to use is dicyclomine hydrochloride (DCH) since it is known from previous studies22 in this laboratory that the relaxation of the monomer/aggregate equilibrium associated with the self-aggregztion of this drug at concentrations exceeding the c.m.c.(50 mmol dm-3) occurs in the ultrasonic frequency range. We have chosen a-cyclodextrin (a-CD) as the host molecule since the excess ultrasonic absorption associated with pure aqueous solution of this compound is only marginally in excess of that of 24 As a result, ultrasonic measurements have been carried out on two solutions containing a-CD and DCH. The initial concentrations of both a-CD and DCH used together with their equilibrium concentrations evaluated from the complexation constant derived using the e.m.f.data are listed in table 6. The relaxation data for these solutions are presented in fig. 6 in which the quantity a / f 2, where a is the sound adsorption coefficient at frequency f, is plotted against frequency. Also included in this figure are the ultrasonic measurements calculated for a 50 mmol dm-3 solution of a-CD from the relaxation data reported by Kato et al.24 in a previous publication. Some selected measurements carried out in the present work were consistent with these calculated values. We did not observe any excess adsorption in solutions of DCH in water at concentrations below the c.m.c. (50 mmol dm-3). The substantial decrease in a / f with increasing frequency clearly demonstrates that a strong relaxation occurs in both solutions containing a-CD and DCH.This relaxation occurs only when these two components are mixed together and therefore must be associated with interaction between them which we attribute to the perturbation of equilibrium (2) involving the formation of the 1 : 1 inclusion complex. It is also clear from the data presented in fig. 6 that this new relaxation is orders of magnitude stronger than any excess absorption due to 50 mmol dmw3 a-CD. To a first approximation we haveN . Takisawa et al. 3069 600 500 - 400 E % v) 300 2 % 5 200 -.- N n 100 ( 1 ~ I 0.3 0.6 1.6 4.0 10.0 25.1 63.1 fIMHz Fig. 6. Ultrasonic relaxation data for dicyclomine hydrochloride complexing with a-cyclodextrin. 0, 40 mmol dm-' DCH + 50 mmol dmP3 aCD; a, 70 mmol dm-' DCH + 50 mmol dm-3 aCD ; (-) 50 mmol dmP3 a-CD.neglected the weak contribution from a-CD and attempted to analyse the data using the relaxation equation : = c(1 +$.,),)tB where Ai are the relaxation amplitudes, f,$ are the relaxation frequencies and B is frequency-independent excess absorption term. The relaxation parameters for a single relaxation (i = 1) are given in table 6; the fits to the experimental data were excellent in the low-frequency range 0.2-5 MHz and deteriorated at higher frequency. It is therefore clear that the relaxation data at the higher frequencies cannot be described in terms of a single relaxation. As a result we reanalysed the data using eqn (6) with i = 2 and obtained excellent fits over the whole frequency range (table 6). An examination of the relaxation data associated with the formation of the 1 : 1 complex shows that, as expected, the relaxation frequency increases as the drug concentration is increased.The following values were calculated : forward rate constant k, = 1.5 x 10' dm3 mol-1 s-l backward rate constant k-, = 5.2 x lo5 s-l. For the purpose of the present exercise it is the order of magnitude of the rate constant that is of importance, especially when compared with those found in recent studies20, 21 involving the 1 : 1 complexation of a-CD with alcohol, and also for 2: 1 complexes with dyes. From the amplitude analysis the value of IAVJ the volume change associated with equilibrium (2) was estimated to be 6.3 f 5.0 x The second relaxation of very weak amplitude observed at the higher frequencies certainly deserves further investigation and is more likely to be associated with the a-CD molecule itself.We are presently turning our attention to this problem. m3 mol-'.3070 Drug-selec t ive Electrodes We thank the S.E.R.C. for a research grant and a CASE award (P. B.) and the University of Salford for a CAMPUS Fellowship (N. T.). We also thank Dr Derek Bloor for several useful discussions. References 1 V. V. Cosofret, Membrane Electrodes in Drug Substances Analysis (Pergamon Press, Oxford, 1982). 2 V. V. Cosofret and R. P. Buck, Ion-selective Electrode Rev., 1984, 6, 59. 3 R. P. Buck and V. V. Cosofret, ACS Symp. Ser., 1986, 309, 363. 4 (a) A. Mitsana-Papazoglou, T. K. Christopoulos, E. P. Diamandis and T. P. Hadjiioannou, Analyst (London), 1985, 110, 1091 ; (b) T.K. Christopoulos, A. M. Papuzoglou and E. P. Diamandis, Analyst (London), 1985, 110, 1497. 5 V. V. Cosofret and R. P. Buck, Analyst (London), 1984, 109, 1321. 6 S. G. Cutler, Ph.D. Thesis (University of Aberdeen, 1975). 7 S. G. Cutler, D. G. Hall and P. Meares, J. Electroanal. Chem., 1977, 85, 145. 8 C. J. Davidson, Ph.D. Thesis (University of Aberdeen, 1983). 9 N. C. Blomley, Unilever Internal Report, 1984. 10 D. Attwood, Aggregation Processes in Solution, ed. E. Wyn-Jones and J. Gormally (Elsevier, 11 T. Irie, M. Otagiri, K. Uekama, Y. Okano and T. Miyata, J. Inclusion Phenom., 1984, 2, 631. 12 K. Shirahama, K. Takashima and N. Takisawa, Bull. Chem. Soc. Jpn, 1987, 60, 43. 13 The Pharmaceutcial Codex (Pharmaceutical Press, London, 1 1 th edn, 1979). 14 (a) F. Eggers, Acoustica, 1968, 19, 323; (b) F. Eggers, Th. Funck and K. H. Richmann, Rev. Sci. 15 W. Saenger, Angew. Chem., Int. Ed. Engl., 1980, 19, 344. 16 D. W. Griffiths and M. L. Bender, Adv. Catal., 1973, 23, 209. 17 F. Crames, W. Saenger and H. Ch. Spatz, J. Am. Chem. Soc., 1967, 89, 14. 18 E. A. Lewis and L. H. Hansen, J. Chem. Soc., Perkins Trans. 2, 1973, 2081. 19 S. F. Lincoln, A. M. Hounslow, J. H. Coates and B. G. Doddridge, J. Chem. Soc., Faraday Trans. I , 20 R. P. Villani, S. F. Lincoln and J. H. Coates, J. Chem. Soc., Faraday Trans. I , 1987, 83, 2751 and 21 D. Hall, D. Bloor, K. Tawareh and E. Wyn-Jones, J. Chem. Soc., Faraday Trans. 1, 1986, 82, 2111. 22 D. Causon, J. Getting, J. Gormally, R. Greenwood, N. Natarajan and E. Wyn-Jones, J. Chem. Soc., 23 S. Rauth and W. Knoche, J. Chem. Soc., Faraday Trans. I, 1985, 81, 2651. 24 S. Kato, H. Nomura and Y. Miyahara, J. Phys. Chem., 1985, 89, 5417. 25 J. E. Rassing and H. Lassen, Acta. Chem. Scand., 1969, 23, 1007. Amsterdam, 1983), pp. 211. Instrum., 1976, 47, 361. 1987, 83, 2697. references therein. Faraday Trans. 2, 1981, 77, 143. Paper 711809; Received 9th October, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403059

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1988, 84(9), 3071-3077 Thermal Decomposition of Pyrite Kinetic Analysis of Thermogravimetric Data by Predictor-Corrector Numerical Methods Ian C. Hoare,* Harry J. Hurst and William I. Stuart CSIRO Division of Fuel Technology, Lucas Heights Research Laboratories, Private Mail Bag 7, Menai, NSW 2234, Australia Australian Nuclear Science and Technology Organisation, Lucas Heights Research Laboratories, Private Mail Bag I , Menai, NS W 2234, Australia Tim J. White . The thermal decomposition of pyrite has been studied by combining thermogravimetric (t.g.) and microscopic techniques. Predictor-corrector methods, coupled with screen graphics, were used to solve the differential equations representing kinetic models of t.g. data. Kinetic conclusions from t.g.data are in good agreement with microscopic observations. De- composition occurs in two stages. The first and major stage of mass loss proceeds by formation of a porous layer of pyrrhotite around each particle with the reaction interface advancing inwards in three dimensions. A contracting-volume kinetic model with chemical rate control gives an excellent fit to experimental t.g. data for first-stage decomposition. The second stage is further decomposition to lower members of the pyrrhotite series, and this is described well by a kinetic model based on solid-state diffusion of species from the reaction interface. The virtues and deficiencies of non-isothermal kinetics have been debated for more than two decades. In that time, much effort has been directed to methods for extracting kinetic parameters from non-isothermal data and especially from thermogravimetric (t.g.) and thermometric however, the work has been circumscribed by mathematical and computational problems.Consider the ostensibly simple case where thermal decomposition of a solid is determined throughout by a single mechanism, so that the isothermal rate is given by where $ is the fraction of unreacted solid and g(q5) is some function appropriate to the reaction mechanism. For a solid heated at a constant rate dT/dt = p, it is common practice to combine the isothermal equation with the Arrhenius expression k = A exp ( - E / R T ) and the linear heating rate j? to give the non-isothermal kinetic -d$/dt = kg($) (1) - d$/dT = (A/B) A$> exp ( - W R T ) equation which on integration gives (3) There are difficulties in applying eqn (1) and (2) to kinetic modelling, even when referring to a simple system with a single rate-controlling mechanism.First, there is no analytical solution to the Arrhenius integral, although various approximations have been ~uggested.~-~ Secondly, the choice of g($) has been confined to expressions that give an analytical evaluation of the reaction integral G(4). This restriction excludes, inter uliu, 307 13072 Pyrite Decomposition Kinetics the more complex systems where the solid-state reaction occurs through several pathways. However, recent work in our laboratories showed that predictor-corrector numerical (PCN) methods can be combined with screen-graphical techniques to overcome the difficulties that in the past have restricted the interpretation of non- isothermal kinetic data.Application of these methods to the,pyrolysis of oil shale8’ and the dehydration of crystalline hydrates1* has confirmed their usefulness for kinetic analysis of complex multistage reactions as well as single-stage decompositions. This paper describes further application of PCN methods to the thermal de- composition of pyrite. This reaction, which has been studied by a number of has the advantage that the kinetic conclusions obtained from analysing t.g. data can be compared with the geometric features that have been obtained by microscopy. Experimental T.g. and d.t.g. data were obtained using the two thermogravimetric systems: (i) a Stanton-Redcroft TG76 1 thermobalance interfaced to an IBM PC/XT computer for which each data point was the mean of 100 measurements and the standard deviation about the mean was 0.1 O h for both temperature and mass (this yielded high-quality t.g.and d.t.g. plots from single particles of pyrite in the mass range 0.5-10 mg); (ii) a Cahn RG thermobalance interfaced to a DEC PDP11/23 computer which yielded t.g. data from larger particles (50-200 mg). A nitrogen flow of 35 cm3 min-l was maintained through the Stanton-Redcroft balance and 200cm3min-l through the Cahn balance. The nitrogen supply was reticulated from a bulk liquid-nitrogen tank. Oxygen and moisture impurity levels were each less than 10 ppm. Single particles of pyrite were used for all experiments and each particle was freshly cleaved from a massive agglomerate. Specimens were stored under nitrogen in a drybox.An IBM 4381 mainframe computer was used for kinetic analysis of t.g. and d.t.g. data. Software packages were devised to provide the following facilities : (i) direct solution of non-isothermal rate equations using the Gear method1* for solving systems of stiff ordinary differential equations of the form y’ = f ( x , y ) ; (ii) high-speed screen graphical display for comparing experimental t.g. and d.t.g. curves with those calculated by the Gear method essential for assessing the various kinetic models and then obtaining a first estimate of the kinetic parameters; (iii) iterative refinements of kinetic parameters by non-linear regression. Results and Discussion In fig.1 there are two sets of experimental t.g. and d.t.g. curves describing the thermal decomposition of a single pyrite particle heated at 3 K min-l in nitrogen. It can be seen that particle size affects decomposition kinetics; the main d.t.g. peak for the larger (228 mg) particle is 70 K above that of the smaller (0.58 mg) particle. Another feature shown in fig. 1 is that there are two processes of thermal decomposition, so the complete t.g. and d.t.g. curves cannot be modelled on the single mechanism, implicit in eqn (2) and (3). Thermal decomposition of pyrite is given by (1 - x) FeS, = Fe,,-,, S + (0.5 - x) S, which allows for the non-stoichiometry of the resulting pyrrhotite. Dark-field optical microscopy clearly shows the development and geometry of the decomposition.The series of micrographs in plate 1 depicts the progress of the reaction in single particles of pyrite. During the first decomposition stage a layer of product grows around a core of unreacted pyrite, with the reaction interface advancing inwards in three dimensions. X-ray diffraction (X.r.d.) analysis of such partially decomposed particles indicates that only three well defined crystalline phases are present at this stage.J . Chem. SOC., Faraday Trans. 1 , Vol. 84, part 9 Plate 1 .. C 0 Ccl 0 h cf Y I. C. Hoare, H. J. Hurst, W. I . Stuart and T. J. White n u Y (Facing p . 3072)J . Chem. SOC., Faraday Trans. 1 , Vol. 84, part 9 Plate 2 Plate 2. Scanning electron micrograph of a partly decomposed pyrite particle, taken when 4 = 0.8 1, of (a) pyrite/pyrrhotite interface and (b) pyrrhotite.I. C.Hoare et al. 3073 1.2 1.0 0.8 U c, 0.6 5 .5 0.4 Y a & 0.2 0.0 -0.2 0 - 5 0.0 - 0.5 - I M 1 a c, 2 -1.0 c .r( c, 8 -1.5 -2.0 -2.5 700 800 900 1000 1100 1200 700 800 900 1000 1100 1200 T/K T/K Fig. 1. T.g. (a) and d.t.g. (b) curves for single particles of pyrite. 1, 58 mg; 2, 228 mg. (-) Calculated, (---) experimental. These are pyrite (FeS,) and two pyrrhotites ('Fe,S,'). Although the pyrrhotite has a composition centred on Fe,S,, selected-area electron diffraction (s.a.d.) of the decomposition product showed that during quenching it had adopted complex structural intergrowths of several Fe,,-,, S, superstructures. Secondary electron scanning micro- scopy showed a high degree of open porosity in the decomposition product (plate 2).The radial elongation of the pores suggests that they would provide very rapid transport paths for gaseous sulphur during the reaction. At the completion of the first stage no unreacted pyrite remains [plate l ( d ) ] , and it can be deduced from t.g. data that the principal product at this point has the composition Fe,S,. The X.r.d. of this material resembles the pattern of a natural pyrrhotite of this composition, 17-200 in the Powder Diffraction File. It follows that the second stage of decomposition is thermal reduction of Fe,S, to lower members of the pyrrhotite system. Having observed the broad chemical and geometric features of the first stage, we now consider the rate-controlling mechanism. There are two possibilities. (i) If the rate of product formation is determined by the rate of chemical reaction at the advancing interface and, as observed for pyrite decomposition, the interface advances in three dimensions, then the non-isothermal rate is3 -d$/dT= (A/flg($J exp(-WRT) (4) where &l) = $i* ( 5 ) (ii) If the overall rate is determined by diffusion of species across an increasing barrier of product, then the rate15 is given by: where g($,) = %i($-L 1)-1 or alternativelyls by : g($,) = %$-i- l)-l.The merits of these models were first assessed visually, using screen graphical displays. That is, the Gear method was used in conjunction with the graphics software to 101 FAR 13074 Pyrite Decomposition Kinetics 1.2 1 .o 0.8 z c 0.6 c .- 0.4 & c d 0.2 0.0 -0.2 0.5 0.0 - -0.5 M \ c $ -1.0 0 (d .r( c -1.5 -2.0 -2.5 700 800 900 1000 1100 1200 700 800 900 1000 1100 1200 T/K T/K Fig.2. Comparison between calculated (-) and experimental (---) t.g. and d.t.g. curves, where the first stage is modelled on the Jander equation. construct and display two series of calculated t.g. and d.t.g. curves based on the respective kinetic models, using various values of the parameters A and E. This initial assessment readily showed that the model based on diffusion control cannot fit the experimental data for the first stage of decomposition under any circumstances. This is illustrated in fig. 2. Other kinetic functions, listed by Brown et aZ.,3 were found to be even less appropriate. By contrast, the model based on chemical contrgl at the reaction interface was shown to fit the experimental t.g.and d.t.g. data for the first stage of decomposition. This model is consistent with the microscopic observation of radial open porosity, with the implication that the product layer does not present a rate-controlling diffusion barrier to the sulphur species. The converse is true for the second stage of decomposition. The experimental data of the second stage are described very well by the Jander equation15 or the Ginstling-Brounshtein equation,16 implying rate control by diffusion of species from the reaction interface. Therefore, a good description of the complete d.t.g. curve for a thermal decomposition of a single pyrite particle is given by where s(A) = $5 d$/dT = (4/PM$l) exp(-E,/RT)+(A,/B)g(~,) exp(-E,/RT) and g($& = &5:(+-;- l)-l.As can be seen in fig. 1, calculated t.g. and d.t.g. curves derived from eqn (4) are in excellent agreement with the experimental curves. At this point it should be noted that we examined other kinetic models as well as the two described above, using the various forms of g($) listed by Brown et aZ.,3 but none could be fitted to the experimental data. We now consider the relation between particle size and kinetic parameters. The contracting volume with chemical control as applied to the first stage implies that the parameter El should be independent of particle size, whereas the pre-exponential factor A, should decrease with increasing particle size. This is indeed the case. Since each t.g. experiment refers to a single particle, the initial sample mass is a measure of particle size.So in fig. 3 the kinetic parameters for the first and second stages are each plotted againstI. C. Hoare et al. 3075 c .r( c.) > 0 .* U 240 3 0.1 1 10 100 1000 masslmg 2 . 4 4 7 0.1 1 10 100 1000 240 (..-..,I...-..( 3 .,-I U m c c a 4, 140 0.1 1 10 100 1000 mass/mg I ' """" ' """" - ."'"'I ' '"""I mass/mg masslmg Fig. 3. Plot of kinetic parameters vs. particle mass. (a) First stage of decomposition. (b) Second stage of decomposition. The solid line is a least-squares fit for the pre-exponentials. Table 1. Kinetic parameters for pyrite particles of different mass mass/mg A,/s-' EJkJ mol-1 A,/s-l E,/kJ mol-I 0.58 2.1 x 1014 287 2.7 x lo6 190 1.10 2 . 0 ~ 1014 289 2.3 x lo* 192 1.90 1.1 x 1014 289 1.3 x los 191 5.10 3.6 x 1013 288 1.2 x lo6 196 9.10 2 .4 ~ 1013 285 7.5 x 105 192 58.50 1.1 x 1013 280 1.8 x 105 188 228.40 1.0 x 1013 285 1.7 x 105 183 initial sample mass. For a mass range 0.6-230 mg El remains constant around a mean of 286 kJ mol-l, which is within the range of isothermal values of 291 f25, 270+ 14, 280 f 21 kJ mo1-1 determined by three different methods from earlier work." The value of A, decreases from 2.1 x 1014 s-' for a 0.6 mg particle to 1.0 x 1013 s-l for a 228 mg particle. An exact relationship between A, and particle size is difficult to establish. 101-23076 Pyrite Decomposition Kinetics Applying the kinetic model to a cubic or spherical particle or a particle with fourfold and threefold symmetrx gives A , = A; f(m,), where m, is the initial particly mass.For a cube f(m,) = 2(rn,/d0)-5 and for a spherical particle, f(m,) = l.61(mo/do)-5. As shown in fig. 3, the plot of A , us. particle mass deviates considerably from the idealised cube-root representation, and is more closely fitted by an rn-'.' relation. Better agreement is obtained for masses over 5 mg. The reaction rate in the second stage is controlled by diffusion from the reaction interface but, unlike the first stage, it is not so clearly defined. At the end of the first stage, the pyrrhotite formed has a lower density than pyrite and a larger particle size, with an open porous structure of apparently uniform composition when viewed by optical microscopy. If the original particles were considered to be loose aggregates of identically similar small particles, then the activation energy would be expected to be independent of the initial mass.The experimental parameters given in table 1 and fig. 3, show that the value of E, is essentially constant at 190 kJ mol-1 over the range of particle size, and that the A , values range from 2 . 7 ~ 10's-l for the 0.58 mg particle to 1.7 x lo5 s-l for the 228 mg particle, and are fitted by an m-0*5 relation. Use of the Ginstling-Brounshtein equation resulted in very similar results for A , and E2. The marked mass dependence suggests that the rate-controlling step may be solid-state diffusion of sulphur at the pore walls. Conclusions This work has continued the application of predictor-corrector numerical methods to the analysis of non-isothermal thermogravimetric data in order to determine the nature of the solid-state reactions.It has shown that the thermal decomposition of pyrite in nitrogen is best fitted by a contracting core model and a three-dimensional diffusion model for the further loss of sulphur from pyrrhotite. The models are supported by optical and electron microscopy results. Furthermore, the mass dependences observed for the pre-exponential constants of the processes suggest that more advanced models could be used to investigate the effect of particle size in irregularly shaped and multiparticulate systems. This work was partially funded by a CSIRO/University Collaborative Research Fund and by a CSIRO Collaborative Research Contract with the Exxon Corporation. We thank Mr J. H. Levy of the CSIRO Division of Energy Chemistry and Prof.S. St J. Warne of the University of Newcastle for their helpful discussions. References 1 J. H. Flynn and L. A. Wall, J. Res. Natl Bur. Stand., Sect. A, 1966, 70, 487. 2 J. Sestak, V. Satava and W. W. Wendlandt, Thermochim. Acta, 1973, 7 , 333. 3 W. E. Brown, D. Dollimore and A. K. Galwey, Comprehensive Chemical Kinetics (Elsevier, 4 H. Horowitz and G. Metzgar, Anal. Chem., 1963, 35, 1464. 5 A. W. Coats and J. P. Redfern, Nature (London), 1964, 201, 68. 6 A. Briodo and F. A. Williams, Thermochim. Acta, 1973, 6, 245. 7 G. I. Senum and R. T. Yang, J. Therm. Anal., 1977, 11,455. 8 I. C. Hoare and W. I. Stuart, Thermochim. Acta, 1987, 113, 53. 9 W. I. Stuart and J. H. Levy, Proc. 14th Conf. of the North American Thermal Analysis Society, San 10 I. C. Hoare and W. I. Stuart, Proc. 15th Conf. of the North American Thermal Analysis Society, 11 A. W. Coats and N. F. H. Bright, Can. J. Chem., 1966, 44, 1191. 12 G. Kullerud and H. S. Yoder, Econ. Geol., 1959, 54, 533. 13 M. S. Jagadeesh and M. S. Seehra, J . Phys. D, 1981, 14, 2153. Amsterdam, 1980), vol. 22. Francisco, September 15-18, 1985. Cincinnati, September 21-24, 1986.I. C. Hoare et al. 3077 14 C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, 15 W. Jander, Z. Anorg. Allg. Chem., 1927, 163, 1. 16 A. M. Ginstling and B. I. Brounshtein, Zh. Prikl. Khim. (Leningrad), 1950, 23, 1249. Englewood Cliffs, NJ, 197 1). Paper 7/1835; Received 12th October, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403071

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. Sac., Faraday Trans. I, 1988, 84(9), 3079-3091 Double-layer Interaction between Spheres with Unequal Surface Potentials J. Theodoor G. Overbeek Van ’t Hoff Laboratory, University of Utrecht, Padualaan 8, 3584 CH Utrecht, The Netherlands After a qualitative and quantitative comparison of various methods for calculating double-layer interaction the results of Hogg, Healy and Fuerstenau and those of Barouch, MatijeviC and coworkers on the energy of interaction between unequal spheres are dealt with. These results show unexpectedly large differences. The cause of these differences is found and after application of a necessary correction to the results of Barouch and MatijeviC the remaining differences are small, even for moderately large surface potentials. In 1966 Hogg, Healy and Fuerstenau’ (HHF) published a paper in which a theory for the double-layer interaction between spheres of unequal size and unequal surface potential is given, using the linear approximation of the Poisson-Boltzmann equation (PB equation), valid for small potentials, smaller than 25 mV.They derived a fairly simple equation for the free energy of interaction, which appeared to give quite reasonable results, even at potentials much higher than 25 mV. In 1978 Barouch, Matijevid, Ring and Finlan2 (BMRF) analysed the same problem, now using the full PB equation, and found results which differed rather markedly from those of HHF. This paper was challenged by Chan and White3 (CW), who suggested that the main cause of the difference between HHF and BMRF was due to an inappropriate truncation of a series expansion used by BMRF.Chan and Chan4 (CC) obtained a few exact numerical solutions of the full PB equation, compared these with the HHF and BMRF results and concluded ‘that any disagreement between . . . HHF and BMRF must be due to errors in the BMRF result ...’. Then in 1985 Barouch and Matijevid published three papers, one with Wright as coauthor (BM, I,5 BMW, 11,‘ BM, III’) in which they gave a new analysis of the expression for the double-layer interaction energy already derived by BMRF2 and found large deviations from the HHF results, in particular at separations between the spheres smaller than one Debye length ( l / ~ ) . They reject the criticism by CW3 and CC4 explicitly. Very recently Barouch, Matijevid and Parsegian’ (BMP) described their earlier results as ‘an exact solution for the force between spheres... ’ and mention ‘at intermediate separations . . . where force and energy go through extrema . . . a qualitative difference’ is found with HHF. This is a very unsatisfactory situation. On the one hand there is the critique by Chan and coauthors and the general feeling that HHF is correct at low potentials and still quite a good approximation at potentials of ca. 50 mV. On the other hand, the results of the elaborate and intricate calculations of Barouch, Matijevid and coauthors show in quite a number of cases ‘a qualitative difference’ with HHF. I therefore decided to check the problem again and try to understand where the difference between BM and HHF came from.However, before considering the papers by BM and HHF in detail, a few general remarks are in order about some aspects of the problem, that evidently are not always fully recognized. 30793080 Double- layer Interaction Fundamental Difficulty of the Problem For two spheres in proximity no analytical solutions of the PB equation are known, not even for the linearized case, let alone for the full equation. Only approximate analytical or numerical solutions can be used. Moreover, for two particles with surface potentials of the same sign but different magnitude, the double-layer interaction changes from repulsive at large separations to attractive at short distances, owing to the fact that the proximity of the surface of high potential causes the charge of the low potential surface to change sign.Remarkably enough the problem was already very fully treated by Derjaguing in 1954 but, unfortunately, this paper has not received as much attention as it deserved, possibly because in the words of HHF ' the solutions are extremely unwieldy '. Methods for Calculating Interaction The force on a particle can be seen as the sum of the Maxwell stress of the electric field and the hydrostatic pressure due to the increased concentration of ions (see Verwey and Overbeek, VO'O'). Derjaguing described the force for parallel flat surfaces and for convex surfaces with large radii of curvature, using the full PB equation, but also giving simplified equations valid for low surface potentials. The free energy of interaction can be found by integrating the force from infinite separation to the actual distance between the particles (VOIOb), but also as the difference between the free energies of the double-layer system at the actual and at infinite distance.The force is completely determined by the electric potential field, independent of the boundary conditions (constant surface potential, constant surface charge or other), but the change of the force with distance does depend on these boundary conditions. The free energy depends on the choice of its zero and on the boundary conditions. The free energy of the double layer contains four contributions. These are: the chemical free energy (due to adsorption or desorption) of the surface charge, the electrical energy of the surface charge, the electrical energy of the space charge in the solution and the entropy contribution due to the uneven distribution of ions in the solution.The free energy is most easily found by the use of an imaginary charging process, thus limiting the calculation to the surface charge or to the bulk charge, but including all the other contributions automatically. If the particle charge, Q, is constant, the chemical term may be dropped and the free energy is simply J v/,(Q) dQ, yo being the surface potential (see Overbeek, Oila). For low surface potentials Q is proportional to yo and the free energy becomes +;Qv/,. At constant surface potential, where the surface charge changes with the configuration, the chemical term has to be added, and the double-layer free energy, F, becomes ~ ~ l i n a l Q Qfinal ryodQ+-Ap(surface-bulk) = [yodQ-y0Q = -s Qdv, (1) F = Jo e 0 where e is the elementary charge, Ap is the difference in chemical potential of the ions responsible for the surface charge and, since equilibrium is supposed to occur at wo, Ap = - ely, (see 01' b).For low surface potentials F becomes - ;Qv/,. The equality of the absolute values of the linearized double-layer free energies at constant charge and at constant potential has in some cases led to confusion. For surface charge adjustment with a limited number of adsorption or desorption sites, equations become slightly more complicated because then Ap is not constant. We shall not consider this case here. HHFl used F = -;Qv/,, and since Q = capacity x yo, F = -(geometrical factor) x E, E, v/i, where E, is the relative dielectric constant of the solution and E, is the permittivity of free space.J .Th. G. Overbeek 308 1 Table 1. Double-layer free energies per unit area divided by E , E , K ( ~ T / ~ ) ~ for a single flat double layer according to three different approaches. z = ey/,/kT 0.5 1 .o 2.0 4.0 linear approximation, - iz2 - 0.125 -0.5 - 2.0 - 8.0 (used by HHF) (exact equation) (equivalent to BMRF) -JQdy/,+-4(~0sh~/2- 1) -0.125 65 -0.510 50 -2.172 3 -11.048 8 -iJ y/,adA = -iQlyo+-z sinhz/2 -0.126 31 -0.521 10 -2.350 4 - 14.507 4 BMRF2 state in their eqn (2.3) that the ‘electrostatic energy’, E = +aJ yo adA (at constant ly, equivalent to ily, Q), where a is the surface charge density and A is the area of the surface. Then they replace CT by - E, E, ay/an, where awlan is the normal derivative [their eqn (2.4)] and they set leading to their eqn (2.6): This equation should have contained a choice of sign, f , since the normal derivative in eqn (2.4) is the change of ly when going from the surface to the solution (not to the interior of the particle), and obviously this change may be either positive or negative just as a may be either negative or positive.The omission of the f sign in eqn (2.6) together with the later limitation to positive surface potentials then leads to the replacement of E = +tS ly, adA by E = the equivalent of --iJ yo adA (see also CW3), which is then used in all further calculations (BMRF,2 BM5-’). They calculate the potential gradient at the surface (proportional to a) using the full PB equation.At low potentials their results should be nearly identical to those of HHF, whereas at high potentials a difference should show up, but then - tJ +Y, adA (= -~Qly,) is not necessarily closer to -J Qdly, than the formula of HHF. As a simple illustration we calculated the double-layer free energy for a single flat double layer, where exact equations are available, with the three different approaches (table 1). The correct values lie nearly halfway betwen the HHF and the BM approximations, but slightly closer to HHF. Potential us. Distance for Various Separations In this section we shall mainly discuss the case of two parallel flat double layers. When two double layers with equal surface potentials overlap, the potential has a minimum halfway between the plates.When the two surface potentials have the same sign, but a different magnitude, and the distance between the surfaces is not too small a similar minimum occurs, not half way, but closer to the surface with the smaller potential. This is illustrated in fig. l(a). The figures have been drawn using eqn (2) of HHF, but the numbers would not be greatly different if the full PB equation had been used : lyol sinh K(H- x) + lyo2 sinh sinh KH w =3082 -0.5 /OXx I I I I I h * 0.223 -1 0 M x - 1 2 0 XX-1.0 1.317 - 0.5 - ,u 0.5 OW 0.693 0 Fig. 1. Dimensionless potential, ety/kT, vs. dimensionless distance, KX, for two parallel flat surfaces at dimensionless surface potentials 1 and 2, respectively. Four typical cases are presented. (a) Fairly large separation; minimum in the potential between the surfaces; both surfaces carry positive charge; repulsion.(b) Shorter separation; minimum in the potential has just reached the low potential surface; no charge on surface 1 ; maximum repulsive force. (c) Separation so small that the extrapolated potential goes asymptotically to zero at KX + - co ; negative charge on surface 1 ; force between surfaces zero. (d) Separation still smaller; extrapolated potential goes to - co at finite negative FCX; strong negative charge on surface 1; free energy of interaction goes through zero. Table 2. Values of KH for which various quantities change sign (a) based on eqn (2), the linear approximation 1+6 1.5 2.0 3 .O 5.0 general W02/ W O l charge on surface 1 (26); 0.962 1.3 17 1.763 2.292 arccosh ( V / ~ ~ / V / ~ ~ ) force is zero 6 0.405 0.693 1.099 1.609 In (tyo2/tyOl) is zero free energy of d2/2 0.080 0.223 0.511 0.9556 In interaction is zero (b) comparison of results obtained with the linear approximation and with the full PB equation eWOi/kT= z, z1 = 1 ; z2 = 2 Z, = 0.6; 2, = 3 linear approx.full PB linear approx. full PB charge on surface 1 is zero force is zero 1.317 1.179 2.292 2.086 0.693 0.635 1.609 1.45 1J . Th. G. Overbeek 3083 where t+v is the potential at a distance x from the surface with potential vOl and H i s the distance between the two surfaces with potentials vol and vO2, respectively. K is the inverse Debye length where F is the Faraday constant, R is the gas constant and c, is the molar concentration of the electrolyte, which is assumed to be symmetrical and monovalent.When the distance between the surfaces is made smaller, a point is reached [see fig. 1 (b)], where the minimum in the potential falls on the swface with potential vol. Then its surface charge is zero, but the surfaces still repel one another. In this situation the repulsive force even reaches its maximum, since v,, is the maximum value that can be reached by the potential in the minimum and the repulsive force per unit area, p , is given by Langmuir,12 VOrob as p = 2c, RT[cosh (etymin/kT) - 11 = E, E, K~ (“a)’ - (cosh u - 1) = [for the case of fig. 1 (b)] E, E, K~ reT)’ - [cosh (ev,,/kT) - 11 (4) where vmin is the potential in the minimum and u = evmin/kT. In Derjaguin’s paper’ this maximum in the repulsive force is nicely shown in the figures, and also that its value depends only on the lower surface potential, since there ymin = wol.At smaller distances than those in fig. l(b), the surface charge on the first surface is reversed in sign, but the potential us. distance curve can be extended to negative values of x, and as long as a minimum potential occurs in the prolonged curve, this vmin may be used in eqn (4) to find the repulsive force between the surfaces. At the separation shown in fig. 1 (c), where the minimum has shifted to x + - 00 and tymin = 0, the repulsive force is zero and a maximum occurs in the interaction free energy. At distances shorter than that in fig. 1 ( c ) there is no minimum in the potential any more, the force becomes attractive and at the separation shown in fig.1 ( d ) the free energy of interaction goes through zero to end up at minus infinity at zero separation. Table 2 illustrates how the separations at which the various sign reversals occur depend on the values of the two surface potentials. The separations at which the reversals occur increase with the ratio vO2/vol. At ey/,,/kT = 2 or 3 the linear approximation gives reversal separations which are ca. 10 YO too high. With two spherical particles, only the regions close to the axis of symmetry may show these reversals, whereas the parts of the surfaces farther away from the axis will be separated by larger distances and thus show no reversal. The net effect will be that the force and the free energy will change sign only at considerably smaller distances between the spherical surfaces than were found for parallel flat surfaces.The Free Energy of Interaction Parallel Flat Surfaces, High Surface Potentials, Large Distances From the potential distribution given in eqn (2) HHF derive an expression for the free energy of interaction per unit area of two parallel flat double layers, exact in the linear approximation and given by 1 - wtr + vt2 exp ( 2v01 v02 1 - exp (-2rcH) K H F = 2% Eo w o r v 0 2 exp (- KH) = 2 ~ , E, KW,, yo2 exp ( -KH) (for large KH).3084 Double-layer Interaction For high potentials expressions for the free energy of interaction become cumbersome and contain elliptic integrals (VO1OC), but for high surface potentials and small interaction, interesting comparisons can be made.For large separations correct values for the potential around the minimum are obtained by superimposing the potential distributions of the two separate double layers, each stretching out to infinity, on one another. The following expressions are exact in the limit, KH+ co. Henceforth we shall use yi = e y i / k T ; zi = eyoi/kT; yi = tanh(zJ4) and i = 1 or 2: tanh (y,/4) = tanh (z1/4) exp (- K X ) and For small interactions we thus find tanh ( y2/4) = tanh (Z2/4) exp [ - K ( H - x)]. (6) which has a minimum ymin = u when y , = y 2 and consequently ~ X P ( - Kxmin) = ( ~ ~ 7 1 ) ; ~ X P ( - K H / ~ ) and thus u = ~ ( y , y2)+ exp ( - KH/~). Combining this expression with eqn (4) for the repulsive force per unit area and integrating the force from H = co to H = H, we find for the free energy of interaction per unit area (10) This differs from VHHF by the replacement of yo? yo2 by 16(kT/e)2 y1 y 2 .h a ~ e ~ ? ~ for the energy of interaction per unit area of two parallel surfaces Kv = 2.5, E , Ic(kT/e)2 (1 6 ~ 1 y 2 ) exp (- K H ) . An analogous equation for BM conditions is obtained as follows. They would EBM = -(+l VOl+h2 V / 0 2 ) + [ & 1 ( H j V/Ol+$2(H+ V/021 (1 1) where oi is the charge per unit area of surface i. With 0 1 = -~r~o(d~/l/dx)z-o, *2 = +Er ~o(dy/2ldx)z==, and where the minus sign is good for x = 0 and the plus sign for x = H, we find easily EBM = $ E ~ E ~ Ic(kT/e) (tyO1(2 sinh (z,/2) - 2 sinh (z1/2) [l - sinh2 (u/2)/sinh2 (z1/2)];] + tpO2(2 sinh (z2/2) - 2 sinh (z2/2) [ 1 - sinh2 (u/2)/sinh2 (z2/2)]i}) (dy/dx),-,,,-, = T (kT/e) 4 2 cosh zi - 2 cosh u)i (12) z $cr E, K(kT/e)2 ( sinh;il/2) + sinh '2 (z2/2) ) 4 (for small u, large K H ) .(13) With u as found in eqn (9) we have (14) z1/4 + (sinh (z,/2) sinh (z2/2) EBM = ~ E , E ~ K ( ~ T / ~ ) ~ differs from Kv by the factor with [zi/4 sinh(zi/2)]. In table 3 results are given for a few typical cases and we also give general expressions for the ratio of the various free energies of interaction. Again the correct expression based on -J Q dty, is cu. half way between the linear approximation (HHF) and the BM results, but now HHF leads to the largest repulsion and BM to the smallest.Table 3. Free energy of interaction per unit area of two parallel flat double layers divided by ~ E , . E , Ic(kT/e)2 exp ( -KH) for large separation approximate ratio to 167, y 2 Z l Z2a + 48 240 240(z; + 2:) 16Y, Yzb 1 + 48 z , = 1 ; z 2 = 2 2 1.811 1.639 % Z, = 0.6; z2 = 3 1.8 1.513 1.278 ?? z, = 5; z 2 = 5 25 11.513 4.757 n ~ , = 8 ; z 2 = 8 64 14.870 2.179 a HHF.This paper. BM.3086 Double-layer Interaction Fig. 2. The Derjaguin method for finding the interaction between spheres; see text, especially eqn (15). Parallel Flat Surfaces, Small Distances The HHF solution for the free energy of interaction, eqn (9, remains valid and is exact within the limitations of the linear approximation. In the BM approach based on -+y/, the interaction of flat surfaces is implicit in their treatment of the interaction of sphere^.^.^'^ Unfortunately, a solution, other than numerical, based on - J CT d y/, is not available, since it requires the integration of eqn (1 2) for CT with respect to zi, and u is a complicated function of z, and z,.The best way to solve the problem appears to be the use of the charging process of the ions in the solution, rather than on the surface, as was used by VO'Od for the symmetric case; however, since this involves a great deal of calculation we will not do this now, but switch to spherical particles. Interaction between Spherical Particles In the absence of a closed solution of the PB equation for spheres, HHF used the method proposed by Derjaguin13 in 1934 for deriving the interaction between spheres from that between flat surfaces. In this method the interaction (force or energy) of spheres is supposed to be built up from the interaction of pairs of rings with radius h, thickness dh, at a distance H, the rings interacting as if they were parallel flat surfaces with the same area and distance as illustrated in fig.2 and in the equation h-large 2nh V(flat) dh where VR is the interaction between two spheres, V(flat) is the interaction per unit area of parallel surfaces and the upper limit of integration is so large that at the corresponding distance H interaction is negligible. The two conditions, viz. the field lines are virtually parallel and the maximum H is much smaller than the radius, limit the applicability of the Derjaguin method to large values of Ica (say Ica is 10 or more) and to Ho 4 a,,a,. To a reasonable approximation (i+-!-)hdh = d H and thus eqn (15) can be transformed intoJ.Th. G. Overbeek 3087 With this equation and VHHF(H) from eqn ( 5 ) the free energy of interaction of two spheres becomes This equation contains all the essentials of interaction and is exact for sufficiently large rca, and Ica,. The free energy goes through zero at much lower distances Ho than for flat surfaces. For vO2 = 2yOl the reversal distance is 0.001 9 7 3 / ~ as compared to 0.223/~ for flat surfaces. If Ica, and/or Ica, are not very large, eqn (16) can be slightly improved to hdh[(aT-h2)-i+(ai-h2)-i] = dH or approximately to where a, is the radius of the smaller sphere, and it is taken into account that most of the interaction takes place at K2h2 < 2 ~ a , . Thus, apart from the influence of the actual curvature of the field lines, the classical Derjaguin result, eqn (17), and thus VR,HHF, eqn (18), are too large by a factor of the order of (1 + l/Kal).Ohshima, Chan, Healy and White14 (OCHW) took the curvature of the field lines into account and calculated a correction on VR,HHF still smaller than, but of the same sign as that found above. Barouch, MatijeviC and coworkers2* 5 , 6 tackled the interaction of spheres in a rather different way, but Chan and White3 showed that their method is in the first approximation, i.e. neglecting 1 /Ica corrections, equivalent to the Derjaguin method. BMRF2 neglect the curvature of the field lines, calculate the potential gradient at the surface (proportional to the surface charge densities a, and a,) for each h (see fig. 2, and note that BM and coworkers call r what we call h here) and then find the interaction ER, BM as where the factors (1 - h2/at)-i take into account that the surfaces of the spheres are not exactly perpendicular to the axis of symmetry.I have written to bring out the parallel with the treatment for flat surfaces in eqn (1 1) and (1 2). The integration constant #(H) is equal to cosh u when the potential has a minimum between or at the low potential side of the surfaces, but #(H) < 1 and may even be negative when the # us. x curve [see fig. 1 (d)] drops to - GO. The use of the sign for o is tricky. If both surface potentials are positive, a2 is always positive (lyo21 > [~,J), but a, is positive when a minimum potential exists between the surfaces, otherwise a, is negative, as should be clear from fig.1. For negative surface potentials the signs of a are just reversed. The relation between H and q5 is found from in cases in which the potential increases monotonically with x [fig. 1 (6)-(d)], but when3088 Double-layer Interaction there is a potential minimum between the surfaces [fig. 1 (a)] eqn (22) has to be modified to dY 22 dY xmin H dx + = 10 Jzmin dx = - 1: 4 2 cosh y - 2 cosh u(H)]!+ Ju 1c[2 cosh y - 2 cosh u(H)]! (23) For the integration of eqn (20) and (21) a relation between H and h is required, for where q5 has been interpreted as coshu. which Barouch, MatijeviC and coworkers use the integrated form of eqn (16): In eqn (20) it has been taken into account that the surfaces of the sphere rings are slightly larger than 27rhdh.Similarly in eqn (21) it should have been taken into account that o is proportional to the potential gradient normal to the equipotential surface and therefore larger by a factor (1 - h2/at)-a than the value given in eqn (21). The omission of this factor makes ER,SM slightly lower than it should have been. In BM5 and BMW' the integrations of eqn (20)-(23) are carried out in detail, transforming the integrals in eqn (22) and (23) to standard elliptic integrals and switching from h to # as the independent variable in eqn (20) and (21). Two sets of final equations are generated, one for the case with a minimum potential between the surfaces for all values of h. This one is straightforward, and the results are correct, apart from the use of - f J yo adA instead of -J Qdy,, and for the distances involved and low potentials the results are not too far from those of HHF.The very large deviations found for high potentials (fig. 8 in BM') are in line with our discussion in the section Parallel Flat Surfaces, High Surface Potential, Large Distances and table 3. The other group of cases (no potential minimum between the surfaces at least for small h) is complicated. The integral for the energy [eqn (20)] has to be split into two integrals from 0 to h, and from h, to higher h, where h, is the radius of the ring where the surface charge on surface 1 changes sign [fig. 1 (b)] and therefore q5, = coshz,. The relation between q5 and H is found from eqn (22), which can be converted into standard elliptic integrals, but the exact transformation is different for different ranges of q5 (see BMW').Taking all this into account, the actual integration of eqn (20) and (21) after switching from h to q5 as the integration variable is straightforward, but it has to be carried out numerically, as dealt with in detail in BMW.' Unfortunately, BM5 and BMW' did not change the sign of o at h < h, in accordance with their omission of the & sign in eqn (2.6), thus making their interaction energy too low by twice the absolute value of the terms involved at all separations Ho < h,. It is just at these short distances that the striking differences with HHF were found. To make the point more explicit, we give the relevant equations from Barouch and Matijevid5 and indicate the changes of sign that have to be made.The BM equations have been recast using the symbols used in this paper. Their eqn (5.3) reads [cash z1 - $(H)]! - (cosh z , - I)! [(Ica,)2 - ( ~ h ) ~ ] f ER,BM ='%EOE)Yn\/2C-alz, l1 ( [cosh 2, - #(H)]+ - (cosh 2, - 1); [ ( ~ c a , ) ~ - ( K / Z ) ~ ] ! x (Ich) d(Ich) -a2 z2 They integrate eqn (5.3) by parts to obtain their eqn (5.7). However, before this is doneJ. T. G. Overbeek 3089 1000 5 00 k 4 i 0 -500 ..$.- :I I 1 I I I L 0 0.2 0.4 0.6 0.8 1 .o K H O Fig. 3. Free energy of interaction of two spheres, lyol = 25 mV, lyo2 = 50 mV; KU, = 10, K U ~ = 20 us. dimensionless shortest distance uHO ( K = lo7 rn-l). Figure redrawn from Barouch and MatijeviL7 HHF according to eqn (18), PB equation linearized. BM as given in ref. (7) using the BM eqn (5.13).BM corrected according to eqn (27) and (28). See text. (---), HHF, (-) BM, ( * * - ) BM corrected. the first integral should have been split at h = h, and the sign of [cosh z1 - #(H)]' should have been changed to - [cosh z, - #(H)]i, leading to 1 (cash z1 - 1)i + [cosh z1 - 9(H)]i ER, .,(corrected) = E, E, - (~ch)~]f x (Ich) d(ich) (cosh z1 - 1); - [cosh z1 - '(H)l') (Ich) d(rch) - ( ~ h ) ~ ] : ' -2-2J, [(~ca,)~ - ( ~ c h ) ~ ] ; Integration by parts then gives eqn (27), which should replace BM eqn (5.13) and BMW eqn (2). W # ( H , ) - 11 ER,.,(corrected) = E , E , (cosh z, - 1); [cosh z1 - #(Ho)]i3090 Double-layer In terac t ion Ultimately this error in sign causes ER,BM as used in the BM papers to be too low by an amount [cf. eqn (25) and (26)] AER,BM In order to give at least an impression of the quantitative effect of this correction, I roughly calculated it for the case yo, = 25 mV, vO2 = 50 mV, lea, = 10 and k-a, = 20, as drawn in the BM I11 fig.1, in the following way. Using tables of elliptic integrals I calculated the relation between #, varying from - 135 to + 1.5 1 16 and KH, varying from 0.0587 to 1.185 at ca. 15 points, using eqn (22). Using ca. 10 of these values of KH for K H ~ I calculated h2 corresponding to H - Ho using eqn (24). Then I plotted the integrand of eqn (28) against ( K h ) , and carried out the integration graphically. The final results expressed as AER, .,/kT are plotted in fig. 3 as additions to the line copied from the BM paper,' and the corrected ER, BM values come quite close to the VHHF values plotted in the same figure.Conclusions It is stressed that the free energy of a double-layer system under conditions of constant surface potential (i.e. the ions carrying the surface charge are in equilibrium with an excess of similar ions in the solution) is given by -J Q dv, [eqn (l)]. The remarkable success of the linearized Poisson-Boltzmann equation in the treatment of the free energy of the double layer and of double-layer interaction even at dimensionless surface potentials of 2 (ca. 50 mV) is due to the fact that the first correction factor is (1 & z2/48). The expressions, derived from the equivalent of -;Jawo dA (= -@v0 if vo is constant) as proposed by Barouch, Matijevid and coworkers deviate in the first approximation from the correct expressions derived from -JQdyO by a factor (1 T z2/48), and are thus in this respect neither better nor worse than the linear approxi- mation, but the deviations have the opposite sign.The BM results published in ref. (5)-(8) are marred by an error of calculation which invalidates their results at separations below critical separation [see fig. 1 (b) and eqn (26)], and in particular invalidates their suggestion that the true interaction shows a qualitative difference with the results of Hogg et aZ.,' who applied the linearized PB equation. There is no profit in continuing calculations on double-layer interaction based on -@p0 at high surface potentials. The method is much more complicated than that based on the linearized PB equation, and the results are not essentially closer to the true value.Further progress in this field for moderate and high potentials will require solution of the integral - J Q dvo or, equivalently, application of an imaginary charging process for the ions in solution, or integrating the force from infinity to the distance under consideration. As long as rca is large enough (rca % 10) the Derjaguin method is excellent for transforming the interaction of flat surfaces to that between curved surfaces. For small Ica and high potentials no analytical solutions or suitable series expansions are available. The only known way out at this moment is a computer solution of the :full PB equation for the relevant geometry, and after that carrying out -$ Q dty0 or one of its equivalents or (this would be a new method) calculating the field energy, the entropy of the uneven distribution of the ions and of the adsorption or dissociation free energy.J. Th. G. Overbeek 309 1 I thank my friend Prof. J. J. Hermans, who drew my attention to these problems. I thank Mrs Marina Uit de Bulten for preparing the typescript and Mr The0 Schroote for preparing the drawings. References 1 R. Hogg, T. W. Healy and D. W. Fuerstenau, Trans. Faraday Soc., 1966, 62, 1638. 2 E. Barouch, E. Matijevid, T. A. Ring and J. M. Finlan, J. Colloid Interface Sci., 1978, 67, 1 ; 1979, 70, 3 D. Y. C. Chan and L. R. White, J. Colloid Interface Sci., 1980, 74, 303. 4 B. K. C. Chan and D. Y. C. Chan, J. Colloid Interface Sci., 1983, 92, 281. 5 E. Barouch and E. Matijevid, J. Chem. Soc., Faraday Trans. I , 1985, 81, 1797. 6 E. Barouch, E. MatijeviC and T. H. Wright, J. Chem. SOC., Faraday Trans. I, 1985, 81, 1819. 7 E. Barouch and E. Matijevid, J. Colloid Interface Sci., 1985, 105, 552. 8 E. Barouch, E. Matijevid and V. A. Parsegian, J. Chem. Soc., Faraday Trans. 1, 1986, 82, 2801. 9 B. V. Derjaguin, Discuss. Faraday Soc., 1954, 18, 85. 400. 10 E. J. W. Verwey and J. Th. G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, 11 J . Th. G. Overbeek, Colloid Science, ed. H . R. Kruyt (Elsevier, Amsterdam, 1952), vol. 1 ; (a) p . 247; 12 I. Langmuir, J. Chem. Phys., 1938, 6, 893. 13 B. V. Derjaguin, Kolloid Z., 1934, 69, 155; Acta Physicochim. URSS, 1939, 10, 333. 14 H. Oshima, D. Y. C. Chan, T. W. Healy and L. R. White, J. Colloid Interface Sci., 1983, 92, 232. Amsterdam, 1948); (a) p. 92; (b) p . 95 ff.; (c) p. 77; ( d ) p. 78 ff. (b) p. 142. Paper 71 188 1 ; Received 20th October, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403079

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Furaday Trans. I, 1988, 84(9), 3093-3095 Double-layer Interaction between Spheres with Unequal Surface Potential Response to the Critique Eytan Barouch Department of Mathematics and Computer Science, Clarkson University, Potsdam, New York 13676, U.S.A. It is shown that the criticism by Overbeek is not applicable. The expression for the interaction energy as used is shown to be equivalent to Derjaguin’s definition published in 1939. Genuine differences still exist for energies at short separaiions between our results and those calculated using the expression of Hogg, Healy and Fuerstenau. In view of the importance of composite systems in numerous applications, much effort has been devoted to obtaining expressions describing the interactions between spheres of unequal potential and size.Since associated problems are rather involved, certain simplifying assumptions have commonly been introduced. The basic premise in all treatments is that the Poisson-Boltzmann equation (PB) is valid in an electrolyte in which finite-sized particles may be suspended. In a series of papers summarized in ref. (l), Derjaguin was the first to introduce the concept of the energy of interaction at constant potential in terms of the solution of the PB equation and standard formulae of electricity and magnetism. The first system considered was that of parallel plates bearing potentials smaller than 50 mV, which allow the Maxwell stress tensor to be expressed in terms of the excess osmotic pressure. In this case the PB expression is reduced to an ordinary differential equation, and the linearization associated with the Debye-Huckel theory yields extremely simple formulae.In his classic paper2 Derjaguin introduced an approximate method to deal with the curved surfaces which has been the basic tool in obtaining the interaction energies. Hogg, Healy and Fuerstenau (HHF)3 employed Derjaguin’s approach and derived an approximate equation for systems of unlike spheres. This expression is greatly appealing because of its simplicity and, as such, it has been widely employed. However, several experimental systems4. yielded much lower interaction energies than those calculated by the HHF expression, which raised some doubts about the applicability of this approximation. To resolve the apparent differences between the experimental and theoretical results the validity of the underlying basic assumptions has been Accepting Derjaguin’s argument that the interaction energy must be expressed in terms of the potential alone, the solution of the PB equation was obtained.Furthermore, the geometry of the system requires that a two-dimensional scheme should be employed since there is only one axis of symmetry for two spheres. In the preceding paper OverbeeklO claims that there is a sign error in our computations. This is not so. The definition employed of the interaction energy is based upon Derjaguin’s classical paper, ‘7 and it coincides with Overbeek’s definition for repulsive systems. Certain integrals have opposite sign depending upon the definition used. Furthermore, the results obtained seem to be in much closer agreement with a variety of experiments dealing with heterocoagulation and particle adhesion phenomena.The 30933094 Double-layer Interaction discrepancies in the calculated interaction energies using the same set of parameters by Overbeek and by our procedure is the consequence of different definitions of the free energy of interactions. In essence one deals here with two different models [see eqn (711. Fundamental Principles Owing to the cylindrical symmetry, the geometry of two spheres is in principle a two- dimensional problem with non-constant coefficients. Furthermore, the PB equation is not representing elementary electrostatics ; in particular, the two basic invariant laws of electrostatics (scale and zero potential) are violated. This issue was addressed by Eigen and Wicke," who state that the success of the Debye-Huckel theory is partially due to the recovery of the scale-invariant law as a consequence of the linearization process.Because of the latter, it is clear that interactions due to the statistical potential obtained from the PB equation must be expressed in terms of the potential, ly, as well as the geometry at hand. It is essential to recognize that the physical variables so defined can be uniformly obtained regardless of the boundary conditions and previous interactions. Furthermore, it is the only consistent way to express interaction energies of a particle of a given geometry with a potential field, regardless of its statistical nature. This fact has been recognized and discussed by Derjaguin,' who expresses thermodynamic observables, including the Gibbs-Helmholtz interaction energy as where D is the dielectric constant.Furthermore, tc2ry was used instead of Ary. In this equation the volume integral is related to the particle geometry, while ry is determined from the PB equation. Note that eqn (1) is totally independent of the boundary conditions invoked to obtain ry. It is also understood that if the particle participates in the creation of the field, the self-energy must be subtracted. The free energy F is uniformly valid for any sign of the components of grad ry since it is dependent on its absolute value squared. A direct application of the second form of Green's theorem transforms the volume integral into a surface integral given explicitly12 by JJJ[yV'ry+(VW)P]dv = ff ry-dA.z Thus the energy is expressed (in terms of units used by Derjaguin) as (3) where aly/an is the normal derivative of the potential, orthogonal to the surface enclosed by the volume of Derjaguin's formula.' The integrals on the right-hand side of eqn (2) and (3) encompass a specific closed surface given by (in general) (4) where g(x,y,z) is a reasonably smooth function. Thus, the integrand can be written as ( 5 ) where represents a scalar product. The case of constant potentials on the surfaces is obtained by imposing the condition : (6) g(x, y , z ) = const. ry aly/an = ly(grad g) (grad ly)/lgrad 81 ry(x, y , z ) = ly, = const.E. Barouch Thus, for this case only, we modelled (for > 0) w awlan = wclgrad wl.(7) It should be emphasized here that Derjaguin's formulae (1) and (3) are equally valid for any set of boundary conditions. The latter includes constant potentials, constant surface charges, one particle with prescribed charge distribution and the other with assigned potential etc. However, expression (7) is valid only for constant potentials, since eqn (6) is used in its derivation. It is the expression (7) that has been used in the definition of the interaction energy, which is invariant under a change of the sign of the gradient. This invariance is consistent throughout the analysis. However, when a change of integration variables takes place, the correct shape and slopes must be taken into account. Overbeek in his manuscript overlooked this invariant property, thus claiming that there is an error in the sign of the integral between zero and the critical separation. The entire argument of the criticism is based on this change in sign, which is inconsistent with the definition of the free energy as employed in the model.Conclusions The major comments by Overbeek as summarized in his Conclusions are answered as follows. The expression -SQdw is a one-dimensional integral asserting that Q is an explicit function of ly, which may or may not be the case. The model is the PB equation; thus, the energy has to be expressed in terms of the model only, and not of its applied derivatives. In other words, Derjaguin's definition [eqn (l)] or, equivalently, eqn (3) must be used. As stated above, the major claim of the sign error is rejected; there is no error in our expression.Significant difference in calculated interaction energies using the expression given in this work and approximate equations reported before justify the more cumbersome computations involved in our case. This is important since the largest differences are encountered at short separations, which are of greatest interest in the interpretation of particle interactions. Note that v/ can be computed to any desired accura~y.'~ In the analysis by HHF the partial attraction at small separations is not considered. By reversing the sign in the first integral Overbeek nullified the effect of the partial attraction as well. Consequently, the results are expected to be similar to those obtained by HHF. This work was supported by NSF grant CBT-8420786. References 1 B. V. Derjaguin, Trans. Faraday SOC., 1939, 36, 203. 2 B. V. Derjaguin, Kolloid Z., 1934, 69, 155. 3 R. Hogg, T. W. Healy and D. W. Fuerstenau, Trans. Faraday SOC., 1966, 62, 1638. 4 J. K. Marshall and J. A. Kitchener, J . Colloid Interface Sci., 1966, 22, 342. 5 F. K. Hansen and E. Matijevid, J. Chem. SOC., Faraday Trans. I , 1980, 76, 1240. 6 E. Barouch and E. Matijevid, J . Chem. SOC., Faraday Trans. I , 1985, 81, 1797. 7 E. Barouch, E. Matijevid and T. H. Wright, J. Chem. SOC., Faraday Trans. I , 1985, 81, 1819. 8 E. Barouch and E. Matijevid, J . Colloid Interface Sci., 1985, 105, 552. 9 E. Barouch, E. MatijeviC and V. A. Parsegian, J . Chem. SOC., Faraday Trans. 1, 1986, 82, 2801. 10 J. Th. G. Overbeek, J. Chem. SOC., Faraday Trans. I , 1988, 84, 3079. 1 1 M. Eigen and E. Wicke, J. Phys. Chem., 1954, 58, 702 and references cited therein. 12 F. B. Hildebrand, Advanced Calculus for Applications (Prentice-Hall, Englewood Cliffs, NJ, 2nd edn, 13 E. Barouch and S. Kulkarni, J. Colloid Interface Sci., 1986, 112, 396. 1976), pp. 301. Paper 8/00191J; Received 15th January, 1988

ISSN:0300-9599    

DOI:10.1039/F19888403093

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1988, 84(9), 3097-3106 Excess Enthalpies and Excess Volumes of [xCO,+(l -x)N20] in the Liquid and Supercritical Regions Christopher J. Wormald* and Julian M. Eyears School of Chemistry, The University, Bristol BS8 ITS Measurements of the excess molar enthalpy, HZ, and excess molar volume, VE, of [ K O , + (1 - x ) N,O] are described. The measurements are in both the liquid and supercritical regions and cover the range 262.4-324.7 K at pressures up to 12.08 MPa. The excess functions at 262.4 K are small, but in the critical region very large HE and VE were measured. The uncertainty of the H: values is +2.5% and that of the V: is +4%. The Patel-Teja equation of state reproduces all the main features of HE($ and V:(x), and has been used to generate H:(p,x) and V g ( p , x ) surfaces at 312.5 K.The carbon dioxide and nitrous oxide molecules are isoelectronic and have the same molar mass. N,O has a higher static polarisibility (2.92 x cm3) than CO, (2.59 x cm3) and therefore stronger dispersion forces. N,O has a dipole moment of 0.166 D,t while CO, has none, yet the melting temperature of CO, is 216.55 K, while that of N,O is 182.3 K. This probably reflects the fact that CO, has a quadrupole moment 1.5 times bigger than that of N,O. Pitzer’s acentric factor w for CO, is 0.225, while that for N,O is 0.160, and again this may reflect the stronger quadrupole forces in CO,. For CO, T, is 304.2 K and p, is 7.38 MPa, while for N,O T, is 309.6 K and p , is 7.24 MPa. The critical compressibility factor 2, is 0.274 for both fluids.Cook’ measured dew and bubble pressures for five mixtures of [XCO, + (1 - x) N,O] from 293.15 K up to the critical point of the mixture. He also measured, the vapour pressure and orthobaric densities of the pure substances and determined the pure- component critical parameters. Isothermal liquid-vapour equilibrium loops at 293.15, 298.15 and 303.15 K constructed from the measurements showed the mixture to be almost ideal, with small positive deviations from Raoult’s law and no sign of an azeotrope. Interest in the mixture was stimulated by the development of conformal solution t h e ~ r y , ~ and Cook found that the liquid-vapour equilibrium loops could be interpreted satisfactorily in terms of this theory. Cook’s examination of earlier measurements by Caubert4 showed these data to be wrong, probably due to the presence of impurities. Cook’s measurements have been used5 for the calculation of liquid-vapour equilibria in ternary mixtures of (CO,-N,O-C,H,) and no inconsistencies were found.This simple mixture of similar three-centre linear molecules should be ideal for machine simulation and for developing perturbation theory. Prior to this work no measurements of heats or volumes of mixing have been made. This may well be due to the experimental difficulties associated with handling substances with such high vapour pressures. To do mixing experiments at say 273.15 K a pressure of at least 3.5 MPa is required to keep the CO, in the liquid state. Even at the triple point (216.6 K) of CO, the vapour pressure is 0.518 MPa, so that pressurised apparatus is always needed.The advent of modern flow calorimeters makes it possible to perform mixing experiments at high pressures with no vapour space in the calorimeter. i 1 D = 3.33564 x C m. 30973098 HE and V: of [xCO, + (1 - x) N,O] 12 c ' T j 0 T I I I I 1 1 J 260 2 80 300 320 TIK Fig. 1. The phase diagram of carbon dioxide-nitrous oxide in the critical region. The upper curve is the vapour pressure of carbon dioxide and the lower curve is that of nitrous oxide. The curves terminate at the critical points and are linked by the ( p , T ) projection of the critical locus of the mixture. Broken lines indicate the range of pressure over which we made a series of HZ and V': measurements at x = 0.506. Circles indicate conditions under which HE and V: measurements were made over a range of mole fraction.The phase diagram for (C0,-N,O) is shown in fig. 1. The critical locus was drawn through the five points measured by Cook.' Circles indicate the temperature and pressure conditions at which we have made measurements of the excess molar enthalpy, HE, and excess molar volume, VE, over a range of composition x. Vertical broken lines indicate the two temperatures and the range of pressure over which we have made HE and VZ measurements at x = 0.5. We were particularly interested in the supercritical region, but experimental problems made it difficult for us to work too close to the critical temperature (309.6 K) of N,O. The apparatus worked satisfactorily at 312.5 K, however.Experimental The apparatus was the same as that used previously to make measurements on [KO, + (1 - x) C,H,CH,I6 and [KO, + (1 - x) C,H,].'. The flow mixing calorimeter was fitted with a calibration heater and a Peltier cooling device to allow both endo- and exo- thermic heats to be measured. Mixtures leaving the calorimeter passed through a vibrating tube densimeter. The pure components were stored as liquids in cylindrical vessels maintained at 253.2k0.1 K. The liquids were displaced from the vessels by mercury pumped from similar cylinders, and this in turn was displaced by water from metering pumps. The molar flow rate and composition of the mixture were calculated from the flow rate of water entering the pumps, the density of the liquified gases at 253.2 K and the pressure chosen for the experiment. Densities of CO, were taken from the IUPAC table^.^ Cook2 fitted his N,O densities measured over the range 293-307 K using a simple equation in powers of (T, - T), but the equation does not give the correct density (1.226 g at the normal boiling temperature Tb( 184.6 K).We refitted his measurements including this point and obtained the eguation (1) The equation fits the saturated liquid densities from Tb to T, within the uncertainty on the measurements. Densities at pressures greater than saturation were calculated using the compressibility of CO, at the same reduced temperature and pressure. As the two fluids are so similar this is not an unreasonable procedure and is better than using a cubic , - p/(g = 0.452 + 0.001 205( T, - T) + 0.1242( T, - T)i.Table 1. Excess molar enthalpies, HE, and excess molar volumes, VE, of [xCO, + (1 - x) N,O] measured over a range of x T = 262.4 K; p = 3.48 MPa 164 507 76 174 577 70 177 649 62 T = 262.4 K; p = 10.04 MPa 122 505 69 136 648 68 143 719 60 57 1 604 96 658 654 93 739 703 84 749 752 81 T=298.8K;p= 11.03MPa 273 504 68 305 604 71 327 653 66 35 1 703 58 T = 298.8 K; p = 7.0 MPa 290 363 435 148 143 134 720 789 860 49 41 31 114 97 - 72 146 219 26 47 61 92 125 141 70 77 78 72 145 218 18 38 53 45 75 101 289 362 434 61 66 68 145 106 105 788 859 930 48 37 19 91 64 36 586 504 422 355 151 204 254 305 42 57 64 79 267 358 433 510 356 456 504 554 85 93 97 99 744 723 684 604 804 853 900 920 65 53 42 33 254 305 356 456 59 62 67 75 349 296 285 261 809 85 1 900 91 49 39 28 9 208 159 118 64 51 102 153 204 8 20 33 48 81 136 188 233 T = 312.6 K; p = 7.78 MPa 102 344 78 305 578 145 504 527 132 705 365 86 204 533 123 404 578 140 606 465 110 804 252 58 102 60 - 12 303 556 87 504 783 141 705 594 111 204 296 33 406 759 139 604 725 133 804 419 T = 312.6 K; p = 8.08 MPa 76 w s \o3100 HE and VE of [XCO, + (1 - X) N,O] equation of state.Several measurements of the density of N,O made at pressures up to 10 MPa confirmed the adequacy of the procedure. A computer controlling the apparatus allowed HZ and V; to be measured either as a function of composition at constant pressure or as a function of pressure at constant composition. Mole fraction scans were begun by passing pure CO, through the apparatus and were completed by passing pure N,O through.Runs on the pure components were used to calibrate the densimeter at the chosen temperature and pressure. When measurements were made over a range of pressure at x = 0.5 it was necessary to repeat the pressure scan using pure CO, and then pure N,O to calibrate the densimeter fully. Pressure scans were always begun at the high-pressure end. Results The carbon dioxide used was 99.99 mol % CO,. The nitrous oxide used was 99.6 mol % pure N,O, the chief impurity being nitrogen. When N,O had been condensed into the cylindrical vessel at 253.2 K the vapour phase was pumped away and traces of uncondensible gas were removed. The uncertainty on the mole fraction x is no more than 1 YO, and the overall uncertainty on the HE measurements is between 2 and 3 YO.As the uncertainty on the VE measurements depends on the accuracy with which the densities of the mixture and the pure components were measured, it is greater than that on the HE measurements and is between 3 and 5 YO. The results of measurements made over a range of x are listed in table 1 and plotted in fig. 2. Results of measurements at x = 0.506 are listed in table 2 and plotted in fig. 3. In planning the experiments we chose to make measurements of H: and VE in the liquid region at a temperature as low as we could conveniently manage and at a temperature just below the critical. It was expected that HE and V: at 262.4 K would be small, and this proved to be the case. At 3.48 MPa H:(x = 0.5) is 78 J mol-' and VE(x = 0.5) is 0.17 cm3 mol-', while at 10.04 MPa these figures are reduced to 70 J mol-' and 0.15 cm3 mol-'.At 298.8 K, 5.4 K below TJCO,), HE(x = 0.5) at 7.00 MPa is 98 J mol-' and V:(x = 0.5) is 0.75 cm3 mol-l. Increasing the pressure to 11.03 MPa reduces H:(x = 0.5) to 73 J mol-1 and VE(x = 0.5) to 0.34 cm3 mo1-'. The measurements of HE(x) and V:(x) at 312.5 K, at 7.78 MPa shown in fig. 2(e), and 8.08 MPa shown in fig. 2 ( f ) , initially surprised us for two reasons. First, we did not expect that such a small change of pressure would change the shape of the V;(x) curves so much. Secondly, in contrast to the behaviour at subcritical temperatures, the measurements show an increase of both HE and V: with increasing pressure. At 7.78 MPa HE(x = 0.5) is 600 J mol-' and at 8.08 MPa it is 780 J mol-', while V i ( x = 0.5) is 13.3 and 14.5 cm3 mol-' at the same pressures. These findings motivated us to do a pressure scan at 312.5 K and x = 0.5.(When we calculated our results we found that x was actually 0.506.) Results of the scan are shown in fig. 3(a) and (b). The maximum measured HE was 803 J mol-' at 7.98 MPa and the maximum VE was 16.5 cm3 mol-1 at the same pressure. Had the incremental changes of pressure been smaller in this region it is likely that slightly bigger HE and V: values would have been measured, and the maximum HE would have been at a different pressure to the maximum VE. The pressure scan showed that the HE(x) and V:(x) measurements at 7.78 MPa shown in fig. 2(e) were made about midway up steeply rising parts of the HE@) and VE(p) curves, while the measurements at 8.08 MPa shown in fig.2(f) were made just beyond the peak at 7.98 MPa. Results of a pressure scan at x(C0,) = 0.506 and 324.7 K are shown in fig. 3. HE and VE are now smaller and the maxima are at 9.5 MPa rather than 8.0 MPa. This shift of the maxima to higher pressures was expected, even the van der Waals equation predicts it."C. J . Wormald and J, M. Eyears 0.8 0.4 8ool(e1 / / ' _ _ ' \ \ ' ' I2O X I I 1 I 80- ( b ) 40 0 I I I 1 ( d ) 80 40 c i 10 1 1 1 I 1 I 0 0.2 0.4 0 . 6 0.8 1 X 3101 0.8 0.4 0 Fig. 2. Measurements of H:(x) and V:(x) of [ K O , + (1 - x ) N,O]. Measurements at 262.4 K are shown in (a) and (b); and at 298.8 K in (c) and (d); at 312.5 K in (e) and (A. 0, H: measurements, table 1. A, V z measurements, table 1.(---) H z calculated from the Patel-Teja equation of state, (---) V z calculated from the Patel-Teja equation of state, (-) drawn with a flexicurve. (a) 3.48, (b) 10.04, (c) 7.00, ( d ) 11.03, (e) 7.78, cf) 8.08 MPa. Comparison with the Patel-Teja Equation of State It was shown previously7-* that the Patel-Teja (PT) equation of state'' fits the HZ and VZ measurements for [ K O , + (1 - x) C,H,] reasonably well and that it reproduces all the main features of the measured functions of mixing. It is informative to see how well the PT equation fits our measurements on [xCO,+(l -x)NzO]. Equations for the calculation of the residual enthalpy were given previously. l2 Pure-component parametersw 0 h, 1 Table 2. Excess molar enthalpies, HZ, and excess molar volumes, V z , of (0.506 CO, + 0.494 N,O) measured over a range of pressures V; v: v: v: z p / MPa /Jmol-' mol-' p/MPa /J mol-' mol-' p/MPa /J mol-l mol-' p/MPa /J mol-' mol-' a m HE /10-'cm3 HZ /10-lcm3 H ; /10-1cm3 HZ /10-'cm3 T = 312.5 K; x = 0.506 8 3.49 20 - 15 7.41 184 60 8.18 593 101 8.79 - 50 - 29 c 5.02 38 -3 7.63 324 78 8.38 230 8 9.00 14 -11 % 6.55 70 17 7.78 55 1 126 8.40 153 - 46 1 1 .oo 59 41 x 7.21 126 42 7.98 803 165 8.59 - 27 -40 T = 324.7 K; x = 0.506 6.01 3 21 8.80 144 46 9.84 259 39 10.82 103 4 7.00 18 16 9.00 183 48 10.04 229 32 11.02 90 6 7.97 65 33 9.2 1 214 52 10.06 219 28 11.24 74 2 1 8.18 84 33 9.42 252 55 10.24 197 21 1 1.46 73 4 W 8.38 101 36 9.52 255 53 10.40 165 15 11.86 66 3 Z 8.58 125 41 9.64 262 49 10.61 126 10 12.08 62 3 a m n 0 + n CI XC.J. Wormald and J. M. Eyears 3103 800 400 . . 1 1 4 6 8 10 ; " - I E *1 8 \ WE L 6 4 2 0 PIMPa Fig. 3. Measurements of HE and V z of (0.506 CO, + 0.494 N,O) made over a range of pressure. Measurements at 312.5 K are shown in (a) and (b); at 324.7 K in (c) and (d). 0, H: measurements, table 2. A, V z measurements, table 2. (---) H: calculated from the Patel-Teja equation of state, (---) VE calculated from the Patel-Teja equation of state, (-) drawn with a flexicurve. x , H;(x = 0.506) interpolated from the measurements made over a range of x shown in fig. 2(e) and (f). a, b and c were calculated from criticality conditions. Mixture parameter b was calculated from b = xb,+(l - ~ ) b , and mixture parameter c was calculated from a similar expression.A quadratic expression was used to obtain mixture parameter a, and a12 was given by As the mixture is not far from ideal it was expected that the adjustable parameter k,, would be small. We adjusted k,, to give the best fit to the HE(p) and V z ( p ) scans shown in fig. 3; the choice k,, = 0.006 fits these measurements quite well. In all figures the curves of long dashes are HE values calculated using this value of k12, and curves of short dashes are calculated V z values. We prefer to make comparison with experiment using a single value of k12 rather than by adjusting it to obtain the best fit at each temperature. Fig. 3(a) shows that the calculated HE peak is bigger than the largestw 0 P c, 16 8 i E - 4 m E . wE ?r c 3 M % ( i ) ' ' - .. ( j ) ' ' ' ' : /-\ -- ->b ---\ / # .*--/ * - -> . -. \--- ' * * - - - _ - - * * - - . - - - - *---I '* . 0 0.2 0.4 0.6 0.8 1 Fig. 4. H:(x) and Y:(x) of [xCO,+(l -x)N,O] at 312.5 K and over the pressure range 7.0-8.8 MPa calculated using the Patel-Teja equation of state with k,, = 0.006. (---) H z ( x ) , (---) V z ( x ) . The curves cover the range of pressure at which the peaks shown in fig. 3(a) and (b) were observed. (a) 7.0, (b) 7.2, (c) 7.4, ( d ) 7.6,'(e) 7.8, df) 8.0, (g) 8.2, (h) 8.4, (i) 8.6, (j) 8.8 MPa. I . , , I . & , X 16 n 8 0 8 + h c, I x W 0 - 4C. J . Wormald and J. M . Eyears 3 105 0. 0 1000 I - I 2 2 500 w f % 0 .99 PIMPa Fig. 5. The H z ( x , p ) surface of [xCO,+(l -x) N,O] calculated from the Patel-Teja equation of state using k,, = 0.006 at 312.5 K.measurement, and fig. 3 (b) shows that the calculated VE peak is smaller than the largest measurement. The calculated peaks are, however, almost coincident with those from experiment. Fig. 2(a) shows that the experimental VE values at 262.4 K and 3.48 MPa are fitted almost within the uncertainty on the measurements, and fig. 2(b) shows that the HE values at 10.04 MPa are fitted almost exactly. This good fit of the HE values is also found at 298.8 K, as shown in fig. 2(c) and ( d ) , although the calculated V z values at this temperature are only ca. half those observed. As with [KO, + (1 - x) C,H,]’. the PT equation cannot be adjusted to fit HE and V: measurements simultaneously. It is particularly interesting to examine the composition dependence of HZ and V t in the neighbourhood of the peaks at 312.5 K and at pressures around 8 MPa.Calculated HZ and VE values for the supercritical fluid mixture are shown in fig. 2(e) and (f). At 7.78 MPa the calculated VE(x) curve agrees with the measurements within experimental error. However, at 8.08 MPa, on the high-pressure side of the peaks shown in fig. 3(a) and (b), the V;(x) measurements lie on an S-shaped curve which the PT equation does not reproduce. This initially led us to believe that our measurements were wrong, but an examination of the way HE(x) and VE(x) curves calculated from the PT equation change with pressure showed that S-shapes are to be expected. The way the calculated HZ(x) and VE(x) curves at 312.5 K change with pressure is shown in fig. 4, where curves are calculated at 0.2 MPa intervals between 7.0 and 8.8 MPa.The S-shaped HZ(x) curve observed experimentally at 8.08 MPa is actually generated by the PT equation at 8.2 MPa. At 8.6 MPa both excess functions are S-shaped curves. Fig. 4 gives the impression that both HE(x) and VE(x) will become negative at higher pressures. That this is not so can be seen from an examination of the whole HE(p,x) and V z ( p , x ) surfaces at 312.5 K. The H Z ( p , x ) surface at 312.5 K calculated using k,, = 0.006 is shown in fig. 5, and the V;(p, x) surface is shown in fig. 6. The peak maxima on the V z ( p , x ) surface are at pressures between 0.1 and 0.2 MPa lower than those on the HE(p,x) surface. The minima on the VE(p,x) surface are deeper than those on the H Z ( p , x ) surface and the peaks are a little sharper.Both surfaces show that HE and V z are positive at high pressures. The surfaces are quite different from those reported previously’. for [KO, + (1 - x) C,H,] where double maxima were found. Even at x = 0.01 the HZ and V: peaks are quite pronounced. The surfaces are not symmetric about x = 0.5, the peaks at the N,O-rich end being sharper. The PT equation fits the HE and V: values of [xCO, + (1 - x)N,O], for which the T, I02 FAR I3106 HZ and VE of [xCO, + (1 - x) N,O] r3 I 3 0 E m 5 WE a 20 lo[ O4 0. 0 .99 PIMPa Fig. 6. The VE(x,p) surface of [xCO, + (1 - x) N,O] calculated from the Patel-Teja equation of state using k,, = 0.006 at 312.5 K. values are separated by 5.4 K, almost as well as those of [KO, + (1 - x) C,H& for which the T, values are separated by 1.12 K.For mixtures where the To values are close together the PT equation fails to fit the pure-component and residual properties by similar amounts. These errors largely cancel when the excess functions are calculated, and agreement with experiment is better than it otherwise might be. The maxima seen in the critical region originate from the way residual functions for the pure components combine with that of the mixture to generate the excess functions. This was explained previously7 in more detail. In general the shape of the H:(p, x ) and VE(p, x) surfaces depends on the relative position of the critical points on the phase diagram, and the amplitude depends on their separation. Although the T, values for C0,-N,O are 4.3 K further apart than those for C0,--C,H,, the p" values are separated by only 0.14 MPa, whereas p , values for C0,-N,O are separated by 2.51 MPa. The excess functions for C0,-N,O in the critical region are therefore smaller than those for C0,-C,H,. References 1 D. Cook, Proc. R. SOC. London, Ser. A , 1953, 219, 245. 2 D. Cook, Trans. Faraday SOC., 1953, 49, 716. 3 D. Cook and H. C. Longuet-Higgins, Proc. R. SOC. London, Ser. A , 1951, 209, 28. 4 F. Caubert, Z . Phys. Chem., 1904, 49, 101. 5 J. S. Rowlinson, J. R. Sutton and J. F. Watson, Joint Conf. Thermodynamic and Transport Properties 6 C. J. Wormald and J. M. Eyears, J. Chem. Thermodyn., 1987, 19, 845. 7 C. J. Wormald and J. M. Eyears, J. Chem. SOC., Faraday Trans. I , 1988, 84, in press. 8 C. J. Wormald and J. M. Eyears, J. Chem. Thermodyn., 1988, 20, in press. 9 IUPAC Thermodynamic Tables of the Fluid State: Carbon Dioxide (Pergamon Press, Oxford, 1976). of Fluids (Institute of Mechanical Engineers, London, 1957). 10 C. J. Wormald, Fluid Phase Equilibria, 1986, 28, 137. 1 1 N. C. Pate1 and A. S. Teja, Chem. Eng. Sci., 1982, 37, 463. 12 T. K. Yerlett and C. J. Wormald, J. Chem. Thermodyn., 1986, 18, 371. Paper 711991 ; Received 9th November, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403097

出版商:RSC    

年代:1988

数据来源: RSC