摘要:

J. Chem. SOC., Faraday Trans. I , 1988, 84(9), 3107-3112 Determination of Rate Parameters in Seeded Emulsion Polymerisation Systems A Sensitivity Analysis Ian A. Maxwell, E. David Sudol,? Donald H. Napper and Robert G. Gilbert" School of Chemistry, University of Sydney, NS W 2006, Australia It has previously been shown that rate coefficients for emulsion poly- merisation can be determined by fitting data on seeded batch reactions. Sensitivity analysis now shows that in some limiting cases this technique is not sensitive to certain rate coefficients. Consequently, some previously published values for butyl acrylate and butyl methacrylate have been amended. Improved data-analysis methods are derived. Previously we have described a meth~dologyl-~ for deducing values of rate coefficients from seeded batch emulsion polymerisation kinetic data.We present here an improved procedure which allows us to determine, via a sensitivity analysis, which of the various kinetic parameters are rate-determining, and to find accurate values for these parameters. Application of this method to previously published results shows that the technique is not sensitive to certain rate coefficients in some limiting cases, which is consistent with the proposed model for emulsion polymerisation. This re-analysis also allows us to correct some minor flaws in our earlier work. Theory Experimental studies on monodisperse seeded emulsion polymerisations, at their most propitious, give sufficient information for the unambiguous determination of the rate parameters for the following microscopic events : free-radical entry into latex particles @), free-radical exit (desorption) from particles (k), bimolecular termination (k,) and propagation (kp).In addition, one can find the value of the 'fate parameter' which expresses the relative importance of heterotermination and re-entry for desorbed free radicals in the aqueous phase. We have previously shown how to interpret data in seeded emulsion polymerisation systems, initiated by both chemical and y-radiolysis means, using an e ~ t e n d e d ~ i ~ * ~ . Smith-Ewart' mechanism which appears to be sufficiently flexible to be applicable to any heterogeneous polymerisation system. Details have been given elsewhere'. 3,4, 6,9, lo and are briefly summarised below. The time dependence of fractional conversion of monomer to polymer (x) is given by: (1) where N , is the number density of latex particles, Cm is the monomer concentration in the particles, Mo is the molecular weight of the monomer, NA is the Avogadro constant and g , is the initial mass of monomer per unit volume of reacting mixture.The average number of free radicals per latex particle, n, is found from the number of latex particles dx/dt = (Nc C, MJN, g,) k, A containing i free radicals, Ni : A = C iNi/C Ni t Present address : Emulsion Polymers Institute, Lehigh University, Bethlehem, PA 18015, U.S.A. 3107 102-23108 Seeded Emulsion Polymerisation which in turn are determined by the generalised Smith-Ewart equations : dNi/dt = p[Ni-, - Nil + k[(i+ 1) Ni+l - iNi] + c[(i+ 2)(i+ 1) Ni+2 - i(i- 1) Nil ( 3 ) where p, k and c are, respectively, the (pseudo-)first-order rate coefficients for free- radical entry, exit and termination; the last is related to k, (the second-order termination rate coefficient) by c = kt/NA V,, where V, is the swollen volume of a latex particle.The effect of aqueous-phase events arising from exit is to make p dependent on n: p = p,+akn (4) where a is the fate parameter, whose value (- 1 < a < 1) is determined by the rate coefficients for the various aqueous-phase mechanisms involving the desorbed free radicals and pA is the component of p arising from free-radical generation by initiator decomposition and thermal initiation. Eqn (1)-(4) with the infinite set of eqn (3) truncated at an appropriately large value by the ' instantaneous termination ' approximationlo are readily solved numerically.These numerical solutions yield a long- time slope and intercept of the conversion curve, which are compared to those observed experimentally. For a single x(t) curve, two rate parameters (e.g. pA and c, with fixed values of all the other rate parameters) can be deduced by fitting the observed and calculated slope and intercept. Methodology The systematic data-reduction method assumes that k and c are independent of initiator concentration and type and are constant under the experimental conditions. Two sets of kinetic data are required: x(t) for a seeded system using both chemical and y-radiolysis initiation, the latter including relaxation data [i.e. x(t) after removal of the radiation source].In summary the method3 is as follows. First, the chemically initiated data are fitted assuming sets of values of k, and a. With each k, and a, the chemically initiated data, for various initiator concentrations, are fitted in an iterative fashion. Initially, k is set equal to some reasonable value (e.g. calculated from the Nomura-Harada theory1'), and pA and c are fitted to the experimental conversion data (the value of p A depending on the initiator concentration). The mean of the c values found from the whole data set is then used to calculate pA and k by refitting the chemically initiated data. The mean value of k found is used as in the first step to calculate c, and the whole procedure is iterated until convergence is found in the values of k and c (typically such convergence can involve 3-20 iterations).In each case, the actual fitting involves finding the minimum in the hypersurface of the residual values, given by: = - (acalculated/aobserved)12 + - (bcalculated/bobserved)12 ( 5 ) where a and b are, respectively, the long-time slope and intercept of the conversion us. time curves. The second part of the procedure utilises y-radiolysis data to find the correct values of k , and a. The y-relaxation data are fitted by using the k and c obtained from the chemically initiated data with each assumed pair of values of k, and a. Only a unique pair of k, and a should be able to fit the whole set of data, and thus one obtains values of all the rate-determining parameters. These values can be shown to be ~ n i q u e .~ Note that it is essential to establish that the observed approach to steady state, and thus the long-time intercept of the conversion us. time curve, is not an artefact due to the presence of inhibitor or retardant, but is in fact governed by pA, k and c. The application of y-radiolysis initiation to solve this problem has been discussed el~ewhere.~~~I. A . Maxwell et al. 3 109 Limitations of the Fitting Technique It is important to realise the limitations of the procedure, described above, for finding rate coefficients. In general there are three situations or categories where the technique as described may break down. Category 1: k not Rate-determining Under certain circumstances (e.g. high a) the Smith-Ewart equation [eqn (3)] describing the free-radical populations in the latex particles, incorporating eqn (4), may be approximated by the ' pseudo-bulk ' equation :'* lo diildt pA-(1 -a)kn-2cnI'.(6) If a = 1, it is apparent that eqn (6) reduces to a form which is independent of k . This is because all the free radicals which undergo exit re-enter the latex particles, and thus exit becomes non-rate-determining. Therefore, if a x 1 under conditions where eqn (6) is ~alid,~~'O no reliable value of k can be found by the data-reduction procedure. Category 2 : c not Rate-determining If c 3 p, k then termination becomes non-rate-determining and eqn ( 3 ) reduces to a form independent of c : ~ where f = - 2ak and g = - 2p, - (1 - a) k. The maximum value that n can attain under these conditions is 0.5, as has been discussed in detail If, in the data treatment, some values of the steady-state n are found to be low (n 6 0.5) then care must be taken when utilising these values in calculating the value of c, because the value of c thus found may be meaningless.The inclusion of such meaningless values causes the iterative procedure to become non-convergent. Such low-n values of c must therefore be omitted from the data-reduction procedure. dE/dt = fnI'+gH+p, (7) Category 3: Varying Rate Coefficients If either or both of the values of k and c vary significantly during the kinetic measurements as a result of increased weight fraction polymer in the latex particles then unique values of these coefficients cannot be found in the first step of the data reduction.This is likely to occur in interval I11 of an emulsion polymerisation kinetic run, as the weight fraction of polymer increases significantly in this regime. In these circumstances the whole data-reduction technique cannot be used except under special conditions. Three such conditions are as follows. (i) A high-n polymerisation with a = 1 (category l), where a varying c can be fitted by assuming that c = c(p, 4), where p and 4 are two parameters to be fitted. This can be done because the number of parameters fitted may still be under-determined. (ii) A low-H (< 0.5) polymerisation (Smith-Ewart cases 1 and 2), where a varying k can be fitted by assuming that k = k(p, q), where p and q are two parameters to be fitted. The rationale for this is the same as for the high-n case described in (i) above.(iii) Any changes in k and c due solely to changes in latex particle volume during polymerisation can be trzivially incorporated into the present data-reduction technique, e.g. by setting k cc V;s and c cc V;l.l It should be noted that analytical solutions are available to solve for the rate- determining coefficients in both category l9 and category 2.l These provide a test for the numerical analysis described in this work.31 10 Seeded Emulsion Polymerisation Fig. 1. Contour diagram of residuals for butyl methacrylate fitting: (a) R(p,, k); contour values are: curve 1 : 4 x curve 3: 5 x low2; curve 4: 1 x 10-l; curve 5 : 2 x lo-'. (b) R(p,, c); contour values are: curve 1 : 5 x curve 2 : 1 x 10-l; curve 3 : 2 x 10-l; curve 4: 3 x 10-I; curve 5: 4 x 10-l; curve 6: 5 x 10-l; curve 7: 6 x 1O-I; curve 8: 7 x 10-l; curve 9: 8 x 10-l; curve 10: 9 x lo-'.curve 2: 1 x Consequences of Limitations of the Methodology and Method of Calculating Residuals Two previous studies were re-examined with due consideration to the points noted above. First, it was found previously2 that n d 0.5 for butyl methacrylate at low initiator concentrations. The residual of eqn (5) is plotted for the low initiator concentration butyl methacrylate data of ref. (2) in fig. 1, as contours R(p,, c) or R(p,, k). In fig. 1 (a) where R(pA, k) is presented, it is apparent that there is a minimum which indicates that accurate values of both pA and k can be found. However, in fig. 1 (b), where R b , , c) is plotted, there is only a very broad shallow minimum, whose position changes quite significantly with respect to c when plotted for different initiator concentration low-a kinetic runs, indicating that the 1ow-A data are quite insensitive to the value of c.This is an example of category 1 given above. In view of this, the low initiator data were used to find k but not c in recalculating the rate parameters, and the value of c obtained only from the data at higher E. The rate coefficients thus obtained are different from those published previously, as shown in table 1. The second example to which the improved method was applied was the seeded emulsion polymerisation of butyl a~rylate.~ Here, it was found, using the present sensitivity analysis, that A was large (ca. 3) even at the lowest concentration of chemical initiator and that a= 1, as was previously reported.This is an example of category 2 described above. Therefore, the value of k originally reported from the data reduction must be artefactual. This is evidenced by the plots of the residuals given in fig. 2, which show that the technique is sensitive to c [as indicated by the minima in fig. 2(b)], but insensitive to k [see fig. 2(a)]. The value of k previously reported (table 1) happens to be similar to that estimated by the Nomura-Harada mode1,ll but in view of the insensitivity of the data to k this cannot be taken as evidence supporting this model. The recalculated values obtained for the rate parameters for butyl acrylate are listed in table 1 ; these areI. A . Maxwell et al.3111 Table 1. Rate parameters deduced for butyl methacrylate and butyl acrylate recalculated from data of ref. (2) and (3), compared to the values originally reported butyl methacrylate butyl acrylate quantity original recalculated original recalculated k,/dm3 mol-' s-l 600 600 450 450 a 0.5- 1 0.5 - 1 0.5- 1 1 k/s-' 7 x 10-3 1 x 3 x 10-3 a CIS-' 3 x 10-3 2 x 5 x 10-4 5 x 10-4 k,/dm3 mol-' s-l 1 x 103 7 x 103 8 x lo2 8 x lo2 w P 0.43 0.43 0.57 0.57 -2 2.1 x 1 0 I I v) . Y 1 x 1 0 ' 1 x10-* a Data insensitive to exit. PAIS-' -3 3.1 x10-* Fig. 2. Contour diagram of residuals for butyl acrylate fitting: (a) R(p,, k); contour values are: curve 1 : 4 x curve 4: 1 x 10-l; curve 5: 2 x lo-'; curve 6 : 3 x 10-l; curve 7 : 4 x lo-'. (b) R@,, c); contour values are : curve 1 : 5 x curve 2 : 1 x lo-'; curve 3: 5 x loe2; curve 4: 1 x 10-l; curve 5: 2 x 10-l; curve 6: 3 x 10-l; curve 7: curve 2: 1 x curve 3: 5 x 4 x 10-l; curve 8 : 5 x lo-'.similar to those previously p~blished,~ except that the previous value for k is meaningless. An example of a category 3 system is not treated in this work; however, it is sufficient to say that it will be manifested by a non-steady state in interval 111. Special means of treating this case are under development. Although a complete and involved error analysis of the methodology is possible, a simple test of the uncertainty in the rate coefficients is the scatter in the converged values of k and c for different values of initiator concentrations. This is typically ca. 30% for the values of the rate coefficients found in this study.A useful check on the validity of the methodology used to calculate the rate coefficients in this work is that the converged values of k and c should show no systematic trend with respect to initiator concentration ; this is observed for the results given here.31 12 Seeded Emulsion Polymerisation Conclusion When calculating values of the rate coefficients in seeded emulsion polymerisations using the data-reduction techniques described above, it is imperative to consider three cases when these techniques must be used circumspectly. The method of calculating the residuals outlined above is a powerful tool in deducing which, if any, of the relevant rate parameters cannot be determined from such a study, and should always be applied when using the data reduction techniques.We thank the Australian Research Grants Scheme and the Australian Institute of Nuclear Science and Engineering for their financial support of these studies. E.D.S. was supported by a National Research Fellowship. I.A.M. was supported by a Common- wealth Postgraduate Research Award. References 1 R. G. Gilbert and D. H. Napper, J. Macromol. Sci. Rev. Macromol. Chem. Phys., 1983, C23, 127. 2 L. F. Halnan, D. H. Napper and R. G. Gilbert, J. Chem. SOC., Faraday Trans. I , 1984, 80, 2851. 3 I. A. Maxwell, D. H. Napper and R. G. Gilbert, J. Chem. SOC., Farday Trans. 1 , 1986, 83, 1449. 4 B. C. Y. Whang, D. H. Napper, M. J. Ballard, R. G. Gilbert and G. Lichti, J. Chem. SOC., Faraday 5 I. A. Penboss, D. H. Napper and R. G. Gilbert, J. Chem. SOC., Faraday Trans. I , 1983, 79, 1257. 6 I. A. Penboss, D. H. Napper and R. G. Gilbert, J. Chem. SOC., Faraday Trans. I , 1986,82, 2247. 7 J. Ugelstad and F. K. Hansen, Rubber Chem. Technol., 1976, 49, 536. 8 W. V. Smith and R. H. Ewart, J. Chem. Phys., 1948, 16, 592. 9 M. J. Ballard, D. H. Napper and R. G. Gilbert, J. Polym. Sci., Polym. Chem. Ed., 1984, 22, 3225. Trans. I , 1982, 78, 11 17. 10 M. J. Ballard, D. H. Napper and R. G. Gilbert, J. Polym. Sci., Polym. Letr. Ed., 1981, 19, 533. 11 M. Nomura and M. Harada, J. Appl. Polym. Sci., 1981, 26, 17. Paper 712050; Received 19th November, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403107

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chern. SOC., Furuduy Trans. I , 1988, 84(9), 31 13-31 19 Extraframework Aluminium in Steam- and SiC1,-dealuminated Y Zeolite A 27Al and 29Si Nuclear Magnetic Resonance Study Jesus Sam and Vincente FornCs" Instituto de Ciencia de Materiales, C.S.I.C. 28006 Madrid, Spain Avelino Corma Instituto de Catalisis y Petroleoquimica C.S. I.C. 28006 Madrid, Spain 29Si and 27Al m.a.s.n.m.r. techniques have been used to study the dealumination process of a Y zeolite. Dealumination by steaming or SiCI, treatment leads to the formation of silica and/or silica-alumina type phases. Extraframework aluminium shows a different type of coordination (tetra-, penta- or octa-hedral) depending on the method of dealumination. It is generally accepted that, during the dealumination of zeolite Y, octahedrally coordinated non-framework aluminium species (EFALV1) are formed and are concentrated at or near the surface of the ze01ite.l~~ However, when the framework aluminium content (FALIV) of the zeolite is determined from 29Si and 27Al n.m.r.spectra, poor agreement is obtained,,7 indicating the presence of either extraframework tetrahedral aluminium (EFALIV) or additional undetected octahedral aluminium ('invisible' EFALV1). The presence of EFALIV in ultrastable zeolite Y has been claimed recently,' while 'invisible ' EFALV1 can be 'visualized ' by treatment with acetylacetone (acac).'v7 Moreover, a new signal at ca. 30 ppm has been detected in 27Al n.m.r. spectra of ultrastable Y zeolite, and has been assigned to extraframework pentacoordinated aluminium (EFALV)8 or to extraframework aluminium in tetrahedrally distorted coordination ( EFALbv).In recent papers,lo*ll we have proposed in addition to the presence of EFALV or EFALLv, the formation of an EFALIV associated to an amorphous silica-alumina phase on dealuminated Y zeolites. In this paper, from 29Si and 27Al n.m.r. data we show further evidence for the formation of EFALIV. Moreover, the influence of the dealumination procedure on the amount and characteristics of these species is studied. Experiment a1 HYUS samples were prepared from an NH,Na-Y zeolite (SK-40, Union Carbide; with Si/Al = 2.4), by steam calcination at atmospheric pressure (100% steam) and 550-750 "C for 3-20 h. After this treatment the samples were exchanged twice with an NH; solution at 80 "C for 1 h, dried at 100 "C and finally calcinated at 550 "C for 3 h.Samples dealuminated with SiCl, (HYD samples) were prepared following the method of Beyer and Belenykaja12 at temperatures of 400, 450 and 500 "C. The structural and chemical compositions of dealuminated samples are given in table 1. The unit-cell parameters of the zeolites were determined by X-ray diffraction using Cu K, radiation and following ASTM procedure D-3942-8. The estimated standard deviation was fO.O1 A. The crystallinity of the samples was calculated by 31 1331 14 Extraframework A1 in Dealuminated Zeolite Table 1. Structural and chemical characteristics of dealuminated zeolites crystallinity B.E.T. surface zeolite Si/Ala u.c./A Si/Alb Si/Al" Alb per U.C. ("/) area/m2 g-l HYUS-8 2.8 24.42 8.1 8.3 21.1 85 804 HY US- 14 2.8 24.34 14.2 15 12.6 90 805 HYUS-141 2.3 24.24 141.0 190 1.4 60 617 HYD-400 4.0 24.31 21.2 19.6 8.6 90 740 HY D-450 10.4 24.23 - 200 ca.0 90 685 HYD-500 10.2 24.23 - ca. 0 30 420 - a From chemical analysis. From X-ray diffraction data. " 29Si n.m.r. data. 80 100 12 0 80 100 12 0 80 100 120 PPm Fig. 1. 29Si m.a.s.n.m.r. spectra of steamed Y zeolites: (a) HYUS-8, (b) HYUS-14, (c) HYUS- 141. comparing the peak height of the ( 5 , 3,3) reflection, and considering NaY SK-40 to be 100 YO crystalline. The 27Al and 29Si m.a.s.n.m.r. spectra were obtained using a Bruker MSL-400 spectrometer, working at 104.25 and 79.5 MHz, respectively, and with a spinning frequency in the range 4-4.5 kHz. All measurements were carried out at room temperature with Al(H,O):+ and TMS as standard references.Pulse lengths of 2 and 5 ps, respectively, were used for 27Al and 29Si signals; time intervals of 8 and 2 s between successive accumulations were chosen in order to avoid saturation effects. The numbers of accumulations were 100 and 400, respectively. Cross-polarization and proton decoupling were not used. The mean error in the measured isotropic chemical shifts was 0.5 ppm. Results Steam-dealuminated Samples The 29Si n.m.r. spectra of the HYUS samples are shown in fig. 1. The 29Si spectrum of the least dealuminated sample [fig. l(a)] shows the presence of four components, corresponding to Si surrounded by 4Si, 3Si lAl, 2Si 2A1 and 1Si 3A1. The Si/A1 ratio from the n.m.r. spectrum and X-ray diffraction are very similar (8.3 and 8.1,J. Sanz, V.Fornks 60 and A . Corma 60 31 15 I . . . . . 60 154 30 rll S 6 / ( d ) 0 I I . . . I . . . . 80 40 0 -40 80 40 0 -40 PPm Fig, 2. 27Al m.a.s.n.m.r. spectra of steamed Y zeolites: (a) HYUS-8, (b) HYUS-14, (c) HYUS-141, (d) HYUS- 141 impregnated with acetylacetone. respectively). With further dealumination [fig. 1 (b)] the intensity of the lines associated with Si (1, 2, 3A1) decreases and the Si/Al ratio increases. In the most dealuminated samples [fig. 1 (c)] the only component detected is that associated with Si(OAl), indicating that most of the FALIV has been removed. However, in this sample a broad component at ca. 100ppm is also detected (dashed line) that must correspond to a poorly crystallized phase formed during the dealumination process.When the 27Al spectra of these samples are analysed (fig. 2) three components are detected at 60, 30 and 0 ppm, whose relative intensities varied with the severity of the hydrothermal treatment. In the case of the least dealuminated sample [fig. 2(a)] two new components centred at 0 and 30ppm were detected besides the FALIV component, showing that a considerable part of EFAL is in octahedral coordination. Upon further dealumination [fig. 2(b)] the intensity of the component at ca. 30 ppm increased. Finally, when practically all the aluminium had been removed from the framework and the zeolite had lost ca. 40% of its crystallinity [fig. 2(c)] the 27Al31 16 Extraframework Al in Dealuminated Zeolite ( a ) ( b ) -108 . I . .. . 1 1 * 1 1 1 1 1 1 m u * k -80 -100 -12 0 -80 -100 -120 PPm Fig. 3. 29Si m.a.s.n.m.r. spectra of SiC1,-treated Y zeolites: (a) HYD-400, (b) HYD-450, (c) HYD- 500, ( d ) silica-alumina (13 % A1,0,). spectrum shows three components with large width, showing that the aluminium-rich phase is poorly crystallized. If we assume that all the A1IV is detected by 27Al n.m.r. then this sample must have ca. 3 W O % of the total aluminium in tetrahedral positions. Taking into account that from unit-cell measurements only ca. 4% of AlrV is in framework positions, it can be concluded that a considerable amount of A1IV, showing a chemical shift at ca. 60 ppm, must be in extraframework positions (EFALIV). The impregnation (short contact time) of this sample with acetylacetone' confirms the above conclusion.In fact, fig. 2(d) shows that the treatment produces a decrease in the intensity of the component at ca. 60ppm and an increase in the component at ca. 0 ppm, indicating that part of the EFALIV is transformed into EFALV'. The positions of the bands of FALIV and EFALIV are very similar, and consequently the position of the line must not be very sensitive to the environment beyond the tetrahedra.J. Sanz, V. Fornks and A . Coma 31 17 ( b ) 60 I 54 I 52 . I , , . * . . 120 60 0 120 60 0 PPm Fig. 4. 27Al m.a.s.n.m.r. spectra of SiC1,-treated Y zeolites: (a) HYD-400, (b) HYD-450, (c) HYD- 500, (d) silica-alumina (1 3 YO A120,). SiC1,-dealuminated Samples When the 29Si n.m.r. spectra of the HYD samples are analysed, it is observed that, besides the expected decrease of the intensity of the bands associated with Si( 1, 2, 3 Al) with increasing temperature of dealumination, a new broad band centred at - 108 ppm (dashed) appear, whose intensity increases appreciably with increasing dealumination [fig.3(a)-(c)]. This change in the spectra is accompanied by a marked decrease in the intensity of the narrow line at - 107 ppm associated with Si(OAl), and the appearance of new components of low intensity at - 110 and - 101 ppm that could be associated with the formation of ~i1ica.l~ Simultaneously with the formation of these phases, a considerable decrease of crystallinity and specific surface area of the samples is observed (table 1). From all these results and comparing the 29Si n.m.r. spectra of dealuminated zeolites [fig.3(a)-(c)] and that of silica-alumina (Si/A1 = 6) [fig. 3(d)], we can conclude3118 Extraframework A1 in Dealuminated Zeolite that the amorphous phase formed during dealumination of Y zeolite corresponds to a silica-alumina. l1 The important changes observed in the ,'Si n.m.r. spectra are accompanied by small changes in the n.m.r. spectra of the same samples (fig. 4). Thus, the extraction of aluminium from the zeolite framework does not produce an appreciable increase in the intensity of the EFALV1 component. The intensity of the line associated with FALrV is high, despite the fact that the unit cell size (table 1) indicates a very low level of FALIV, especially in the case of HYD-450 and HYD-500 samples. This result agrees with the conclusions concerning the steam-dealuminated samples (HYUS), in which part of the A1IV is outside the zeolite framework.Moreover, in the sample HYD-450 [fig. 4(b)] it is possible to detect two types of AlrV : one at ca. 60 ppm corresponding to FAL" and another at 54 ppm assigned to EFALIV. In the case of HYD-500 [fig. 4(c)], where the crystallinity of the zeolite decreases strongly (table l), only the EFALIV component at 54 ppm remains. The broadness of this line indicates that EFALrV occupied ill defined positions in the solid phase formed. It must be noted that in amorphous silica-alumina A1IV has also been observed at 50-56 ppm [fig. 4(d) and ref. (S)]. Discussion From the results presented here, it can be concluded that the dealumination treatment of the Y zeolite with steam or SiCl, induces very different coordination in the EFAL.In the case of steam, aluminium extracted from the framework remains in the sample, while in the SiCl, case the treatment eliminates a significant amount of this EFAL (table 1). On the other hand, in the steam-dealuminated samples it is accepted that the vacancies left by the aluminium extraction are reoccupied by silicon arising from the destroyed zeolite ; however, for SiC1,-dealuminated zeolites, the silicon needed to fill the tetrahedral vacancies comes mainly from the SiCl,. Therefore, the relative amount of silicon and aluminium available in the reaction media will be very different depending on the dealumination procedure. Consequently the composition (Si/Al ratio) of the amorphous silica-alumina formed will also be very different.At this point, it is interesting to note that during the synthesis of silica-alumina, the amount of SiO, and A1,0, used has a large influence on the coordination of the aluminium in the resulting phases.14 When the amount of SiO, is low, octahedral coordination of aluminium is favoured, while increasing the SiO,/Al,O, ratio makes the tetrahedral coordination of aluminium more likely. Consequently, in the steam-dealuminated samples, where the amount of silica removed from the framework is relatively low, the EFAL prefers the high-coordination states (namely penta- or octa-hedral). However, for SiC1,-dealuminated samples, where there is a continuous supply of silicon from SiCl,, EFAL will be present preferentially in low coordination states (tetrahedral).These results agree with the acidity measurements made by pyridine adsorption. l1 Thus, SiC1,-dealuminated samples show the presence of acidic OH groups10 (ca. 3600 cm-l, very strong), while steam- dealuminated samples show non-acidic OH bands (3700, 3670, 3615 cm-') that must correspond to AIV1-OH, AlV-0H or Si-OH groups in different positions. Conclusions From this study, we can conclude that dealumination of zeolite Y by either steam or SiCl,, leads to the formation of an amorphous phase of silica-alumina type. The aluminium of this phase can be tetra-, penta- or octa-hedrally coordinated, the relative amounts of each one depending on the dealumination method. In all cases the crystallinity of these phases is very low.J .Sanz, V. Fornks and A . Coma 31 19 This work was supported by the Cornision Asesora de Investigacion Cientifica y Tkcnica (CAICYT, Project 999/070). References 1 P. K. Maher, F. D. Hunter and U. Scherzer, Adv. Chem. Ser., 1971, 101, 266. 2 G. T. Kerr, Adv. Chem. Ser., 1973, 121, 219. 3 J. Scherzer, ACS Symp. Ser., 1984, 248, 157. 4 J. Klinowski, Prog. NMR Spectrosc., 1984, 16, 237. 5 J. Klinowski, C. A. Fyfe and G. C. Gobbi, J. Chem. SOC., Faraday Trans. 1 , 1985, 81, 3003. 6 G. J. Ray, B. L. Meyers and C. L. Marshall, Zeolites, 1987, 7 , 307. 7 P. J. Grobet, H. Geerts, J. Martens and P. A. Jacobs, J. Chem. Soc., Chem. Commun., 1987, 1688. 8 J. P. Gilson, G. C. Edwards, A. W. Peters, K. Rajagopalan, R. F. Wormsbecher, T. G. Roberie and 9 A. Samoson, E. Lippmaa, G. Engelhardt, U. Lohse and H. G. Jerschkewitz, Chem. Phys. Letf., 1987, M. P. Shatlock, J. Chem. SOC., Chem. Commun., 1987, 91. 134, 589. 10 G. GarralBn, A. Corma and V. Fornls, J. Chem. SOC., Chem. Commun., 1987, in press. 11 A. Corma, V. Fornes, A. Martinez and J. Sanz, Adv. Fluid. Catal. Crack., 1988, in press. 12 H. K. Beyer and I. Belenykaja, Catalysis by Zeolites ed. B. Imelik, C. Naccache, Y. Ben Taarit, 13 G. E. Maciel and D. W. Sindorf, J. Am. Chem. SOC., 1980, 102, 7606. 14 J. M. Thomas, J. Klinowski, P. A. Wright and R. Roy, Angew. Chem. Int. Ed. Engl., 1983, 22, J. Vedrine, G. Coudurier and H. Praliaud (Elsevier, Amsterdam, 1980), p. 203. 614. Paper 7/2057; Received 20th November, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403113

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1988, 84(9), 3121-3128 Acidic Properties of Vanadium Oxide on Titania Hisashi Miyata," Kozo Fujii and Takehiko Ono Department of Applied Chemistry, University of Osaka Prefecture, Sakai, Osaka, 591 Japan The adsorption of pyridine on V-Ti oxide prepared by the gas-phase method (1.4-5.6 wt %) has been studied by i.r. spectroscopy. V-Ti oxide exhibits both Brarnsted- and Lewis-acid sites. The Lewis-acid sites are converted to Brarnsted sites on the introduction of water vapour. From the absorption coefficients of the 1530 cm-' band (Bramsted site) and 1440 cm-' (Lewis site), the number of both sites has been estimated. The acidic sites in two-dimensional or monolayer vanadia species are stronger Brarnsted acids than those formed from crystalline vanadia.We have recently reported the characterization of a number of vanadia/metal oxide catalysts, and have proposed that new species are formed by the reaction of vanadium oxychloride with surface OH groups on the carrier oxide.' Materials of this class are of growing interest in a wide range of practical applications. In a previous paper,2 we have also reported the oxidation properties of toluene on these catalysts. The acid-base properties of V-Ti oxide have been discussed on the basis of the results of adsorption of various basic and acidic molecules on it. The results of i.r. studies of ammonia adsorption on unsupported and supported vanadium oxides show some contradictions concerning the nature of their Previo~sly,~,~ we have described that vanadia on V-Ti oxide with low vanadium content has both Brsnsted- and Lewis-acid sites. In the present work, in order to clarify the surface acidity of V-Ti oxide, the adsorption of pyridine on it has been studied by i.r.spectroscopy and discussed quantitatively . Experimental The titania (Japan Aerosil, P25) was used to support vanadium oxide. Two preparation methods were used. The first was a gas-phase method using vanadium oxychloride (GVTi- 1.4-GVTi-5.6, 1 &5.6 wt % vanadium as V20,). The second was standard wet impregnation with ammonium metavanadate (VTi-5.0-VTi-2.0, 5.0 and 2.0 wt YO vanadium). Details of the methods of preparation of the catalysts were described previous1y.l The physical parameters of these catalysts are listed in table 1. Details of the apparatus and procedures were described in previous papers.'O.l1 A disc of sample (20 mm diameter, ca. 100 mg) was placed in the i.r. cell, the disc temperature was slowly increased from room temperature to 673 K under evacuation and kept at that temperature for several hours. Then, heating under circulation of oxygen (ca. 4 kPa) at 673 K for 2 h, followed by degassing at the same temperature for 2 h, was repeated several times. Finally, the disc was cooled to room temperature in oxygen. The Raman spectra were recorded on a JASCO NR- 1000 laser Raman spectrometer. The 514.5 nm line from an argon-ion laser was adjusted so that 200 mW was measured at the sample. The spectra of samples did not change significantly during the measurements at 200 mW. After 8 or 16 accumulations had been obtained the spectral data were transferred to a master computer (PC 9801 VX, NEC).Details of the data acquisition and analysis system were described previously.' 9 12, l3 31213122 Acidity of Vanadium Oxide Table 1. Physical properties of vanadium oxide catalysts preparation V,O, surface catalyst method" (wt YO) area/m2g-l GVTi- 1.4 GVTi-2.1 GVTi- 3.3 GVTi-4.0 GVTi-4.8 GVTi- 5.6 VTi-2.0 VTi-5.0 1.4 2.1 3.3 4.0 4.8 5.6 2.0 5.0 51 50 50 51 34 30 48 42 a Gas, gas phase preparation ; wet, wet impregnation method ; the number in parentheses shows the number of cycles of VOC1, circulation. h E c .s 3 E I I I 1 1 I I l I l I I J I I I I I I I I I I I 16 34 32 30 18 16 14 12 Fig. 1. 1.r. spectra of pyridine adsorbed on GVTi-3.3. (a) After adsorption of pyridine (1.8 molecule nm-2) at 298 K followed by 1 h evacuation; (b) followed by 1 h evacuation at 323 K; (c) 1 h evacuation at 423 K; (d) 1 h evacuation at 523 K.The dotted lines show background spectra. w avenum ber/ 1 O2 cm-'H. Miyata, K. Fujii and T. Ono 3123 n V 18 16 14 12 wavenumber/ 1 O2 cm-' Fig. 2.1.r. spectra of pyridine adsorbed on GVTi-5.6 and GVTi-4.8. After adsorption of pyridine (1.8 molecule nm-2) on GVTi-5.6 (a) and on GVTi-4.8 (c) at 298 K followed by 1 h evacuation at 323 K; followed by 1 h evacuation at 423 K (b), (4. Results and Discussion Absorption of Pyridine The use of pyridine as a selective probe molecule to characterize both qualitative and quantitative aspects of surface acidity is widespread. The assignments of the i.r.bands are in agreement with the well established correlation between the band positions and the type of interaction between pyridine and the sites on which it is adsorbed.14-16 After pyridine was adsorbed on the GVTi-3.3 sample it was evacuated at the cell temperature. As shown in fig. 1, sharp bands at 1636, 1602, 1532, 1484 and 1442 cm-' together with a weak band at 1573 cm-l were left. At desorption temperatures below 423 K the intensities of these bands did not change significantly. The results suggest that these bands are due to species strongly chemisorbed on the surface. Heating at 523 K resulted in a decrease in the intensity of the bands. From a comparison of the i.r. spectra of pyridine adsorbed on various oxides and metal oxide complexes, the bands at 1602, 1572, 1484 and 1442 cm-l are assigned to the 8a, 8b, 19a and 19b vibrational modes of Lewis-coordinated pyridine (LPy), respectively, the bands at 1636, 1578, 1482 and 1537 cm-l being assigned to the corresponding modes of the pyridinium ion (BPy), respectively. The 1537 and 1442 cm-l3124 Acidity of Vanadium Oxide 1 1 18 16 14 12 wavenumber/ 1 O2 cm-' Fig.3.1.r. spectra of pyridine adsorbed on GVTi-2.1 and GVTi- 1.4. After adsorption of pyridine (1.8 molecule nm-2) on GVTi-2.1 (a) and on GVTi- 1.4 (c) at 298 K followed by 1 h evacuation at 323 K; followed by 1 h evacuation at 423 K(b), (4. bands are characteristic of BPy and LPy, respectively. Fig. 1 also shows the OH stretching region together with the CH stretching region above 2800 cm-'. We could not obtain any information on the surface OH species.Thus we will focus on the spectra in the region below 2000 cm-l in the following results and discussion. Fig. 2 and 3 show the spectra of pyridine adsorbed on various GVTi catalysts at several evacuation temperatures. The bands due to BPy and LPy on GVTi seem to vary with the vanadium content. In addition, GVTi catalysts exhibit an intense BPy band compared with that on VTi sample.8 Fig. 4 shows the integrated intensities estimated by band-separation techniques of the spectra12.13 for GVTi-4.8, GVTi- 1.4 and VTi-5.0. The concentration of Brarnsted-acid sites increases with increasing content of vanadium oxide on GVTi, suggesting that vanadia acts as the Brarnsted-acid sites. The LPy band on low-vanadium-content catalysts is larger than that on high-vanadium-content catalysts.On VTi catalysts, the absorption due to BPy is small on VTi-5.0 and it is hardly observed on VTi-2.0. Brsnsted and Lewis Sites on V-Ti Oxide It is possible to employ i.r. spectroscopy for pyridine adsorbed on V-Ti oxide to estimate the numbers of Brarnsted- and Lewis-acid sites on samples with differing vanadium content, by using methods previously applied to silica-alumina catalysts. The number of Brarnsted sites can be increased upon addition of water vapour with a corresponding lossH . Miyata, K . Fujii and T. Ono n c, .- 3125 I - 300 400 500 2 6 1 w I I I L 100 400 500 c, .C( c, i 41 .4 T/K Fig. 4. Integrated intensity of BPy and LPy bands on GVTi-4.8, GVTi-1.4 and VTi-5.0. (a) BPy band (1540 cm-I); (b) LPy band (1440 cm-'); (a) GVTi-4.8; (0) GVTi-1.4; (A) VTi-5.0."i 8 2 5 2 x .C( c, 2 c, '1 i6!!B // I I I I I 0 1.0 2.0 amount of water absorbed/ 10" m-' Fig. 5. 1.r. spectra of successive adsorption of water vapour after pyridine adsorbed on GVTi-5.6 (A) and integrated intensity of BPy and LPy bands (B). (a) Adsorbed pyridine (1.8 nm-') after pretreatment with 0, at 753 K ; (b) (c) (4 followed by successive introduction of water vapour (0.6 molecule nm-'). of Lewis-acid sites. Thus, it is commonly conceived that any strong Lewis-acid sites react with water to form a Brransted-acid site. A small amount of water vapour (0.6 molecule nmP2) was successively introduced to the catalyst on which pyridine had already been adsorbed (1.8 molecule nm-2) [fig.5(A)], resulting in an increase of the intensity of the 19b band of BPy and a decrease of the intensity of the LPy band. From the integrated intensities [fig. 5(B)], the ratio of the absorption coefficients of the LPy band to that of3126 Acidity of Vanadium Oxide Table 2. The number of Lewis- and Br~rnsted-acid sites in vanadium/ titania catalysts acid sites/ 1017m-2 integrated catalyst Lewis Brernsted intensity" GVTi- 1.4 8.1 2.0 0.44 GVTi-2.1 8.8 4.0 1.08 GVTi- 3.3 5.3 9.2 1.40 GVTi-4.8 6.0 12.6 1.60 GVTi- 5.6 8.8 7.5 1.26 VTi-2.0 5.9 - VTi-5.0 4.7 6.6 a Ref. (I) at 980-990 cm-'. BPy was estimated to be 1.24. This value is slightly lower than that estimated by the mean value from the literature.' Thus, the numbers of Lewis- and Brarnsted-acid sites per unit surface area on various catalysts after evacuation at 298 K for 30 min are estimated and listed in table 2.Fig. 6 shows the Raman spectra of various GVTi catalysts together with VTi samples. Bands due to anatase decreased with increasing content of vanadium oxide. The band at 996 cm-', due to crystalline V205, is readily observed at vanadia loadings above 4.0 wt O/O. Bands at 1025 and 920 cm-' (broad), which are attributable to VO, octahedral p~lymer,'~ are observed on all catalysts. Crystallite phases are considerably more Raman-active than the surface phases."' l9 Therefore, although GVTi-5.6 exhibits an intense 996 cm-' band, comparison of the F.t.i.r. bands' due to V=O species leads to the conclusion that the surface in this catalyst is composed mainly of surface vanadia species.Assuming 2.4 V205 molecule nm-, as the monolayer capacity, GVTi-3.3 is covered with vanadia almost as a monolayer. This suggests that vanadium ions act as Lewis-acid sites, although the position of the 8a mode of LPy is slightly lower than that in previous reportss* for VTi oxide prepared by the impregnation method. In addition, although we could not obtain direct evidence for VOH or TiOH, the fact that Lewis-acid sites are converted to Brarnsted sites, as described above, supports this conclusion. The possibility that Ti ions act as Lewis-acid sites may not be excluded for the catalysts at vanadia loadings below 2.1 wt%. We could not distinguish between the Lewis-acid sites on titania or vanadia, because these bands are quite narrow and sharp.Recently, Haber et aL20 and Bond et aL2' have reported on the catalysts prepared by vanadium oxychloride that monodispersed VO, units are postulated on anatase (TiO,) surface from the redox properties of V-0 layers. Kuenski et a1.,22 however have proposed for the similar catalysts that two-dimensional V-0-V coordinative bonds are formed during calcination. As reported previously,' GVTi catalysts with vanadia loadings below 4.0 wt %, which are obtained by a single cycle of VOCl, circulation, exhibit a single i.r. band around 980cm-l. VO, tetrahedra would not be expected to show such a band.23 In addition, VTi catalysts also exhibit a similar band.' Thus, it may be concluded that GVTi catalysts with vanadia contents below 4.0 wt % are composed of two-dimensional vanadia species, which show both Lewis and Brarnsted acidities.For GVTi-5.6 and VTi-5.0 catalysts, crystalline V205 was observed in i.r.' and Raman spectra. As shown in table 2, the concentrations of Brarnsted sites on these catalysts are lower than those on the catalysts with vanadia loadings below 3.3 wt %. The bandH . Miyata, K. Fujii and T. Ono 3127 I I I I I 1100 1000 900 800 700 w avenum berlcm -' Fig. 6. Raman spectra of GVTi catalysts. (a) GVTi-5.6; (b) GVTi-4.8; (c) GVTi-4.0; (d) GVTi- 3.3; (e) GVTi-2.1; cf) VTi-5.0; (g) VTi-2.0. intensities, which are due to two-dimensional or surface species,l are also listed in table 2. These values at 98C990 cm-l correspond to the concentration of Brarnsted-acid sites, suggesting that the acidic sites in two-dimensional or monolayer vanadia species are stronger Brarnsted acids than those formed from higher loadings of vanadia.References 1 H. Miyata, K. Fujii, T. Ono, Y. Kubokawa, T. Ohno and F. Hatayama, J. Chem. Soc., Faraday 2 H. Miyata, T. Mukai, T. Ono, T. Ohno and F. Hatayama, J. Chem. SOC., Faraday Trans. I , 84, 3 M. Takagi, T. Kawai, M. Soma, T. Onishi and K. Tamaru, J. Catal., 1977, 50, 441. 4 Yu. Sh. Goldberg, 1. G. Iovel and M. V. Shimanskaya, React. Kinet. Catal. Lett., 1978, 8, 327. 5 Yu. V. Belokopytov, K. M. Kholyavenko and S. V. Gerei, J. Catal., 1979, 60, 1. 6 M. Takagi-Kawai, M. Soma, T. Onishi and K. Tamaru, Can. J. Chem., 1980, 58, 2132. 7 Y. Murakami, M. Inomata, A. Miyamoto and K. Mori, Proc. 7th Int. Congr. Catalysis (Kodansha, 8 H.Miyata, Y. Nakagawa, T. Ono and Y. Kubokawa, J. Chem. SOC., Faraday Trans. I , 1983, 79, 9 H. Miyata, Y. Nakagawa, T. Ono and Y. Kubokawa, Chem. Lett., 1983, 1141. Trans. I , 1987, 83, 675. 2465. Tokyo and Elsevier, Amsterdam 1981), p. 1344. 2343. 10 H. Miyata, K. Hata and Y. Kubokawa, J. Catal., 1977, 49, 8. 11 T. Nakajima, T. Sonoda, H. Miyata and Y. Kubokawa, J. Chem. Soc., Faraday Trans. 1, 1982, 78, 12 H. Miyata, K. Fujii, S. Inui and Y. Kubokawa, Appl. Spectrosc., 1986, 40, 1177. 13 H. Miyata, Y. Nakagawa, S. Miyagawa and Y. Kubokawa, J. Chem. SOC., Faraday Trans. 1, 84, 14 E. P. Parry, J. Catal., 1963, 2, 371. 555. 2 129.3128 Acidity of Vanadium Oxide 15 P. Pichat, M-V. Mathiew and B. Imelik, Bull. Soc. Chim. Fr., 1969, 8, 261 1. 16 C. H. Cline and J. Turkevich, J . Chem. Phys., 1944, 12, 300. 17 F. Roozeboom, M. C. Mittelmeijer-Harzeger, J. A. Moulijn, J. Medema, V. H. J. de Beer and P. J. 18 F. Roozeboom, J. Medema and P. J. Gellings, Z . Phys. Chem. N.F., 1978, 111, 215. 19 F. P. J. M. Kerkhof, J. A. Moulijn, R. Thomas and J. C. Oudejans, Preparation of Catalysts II 20 J. Haber, A. Kozlowska and R. Kozlowski, J . Catal., 1986, 102, 52. 21 G. C. Bond, J. P. Zurita, S . Flamerz, P. J. Gellings, H. Bosch, J. G. van Ommen and B. J. Kip, Appl. 22 J. Kuenski, A. Baiker, M. Glinski, 0. Dollenmeier and A. Wokaun, J . Catal., 1986, 101, 1. 23 K. Nakamoto, Infrared Spectra of Inorganic and Coordination Compounds (Wiley-Interscience, New Geelings, J . Phys. Chem., 1980, 84, 2783. (Elsevier, Amsterdam, 1979), p. 77. Catal., 1986, 22, 361. York, 1970). Paper 7/2121; Received 30th November, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403121

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1988, 84(9), 3129-3139 Influence of Organic Solutes on the Self-diffusion of Water as studied by Nuclear Magnetic Resonance Spectroscopy Per-Olof Eriksson and Goran Lindblom" Department of Physical Chemistry, University of UmeG, S-90187 Umeh, Sweden E. Elliott Burnell Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, British Columbia V6T 1 Y6, Canada Gordon J. T. Tiddy Unilever Research, Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, Merseyside L63 3JW The self-diffusion coefficient of water and of the organic solute have been measured for aqueous solutions of tertiary butanol and tertiary alkyl ammonium chlorides (CnH2n+J4NCl, n = 1-4, as a function of solute concentration at 25 "C with the pulsed field gradient Fourier-transform n.m.r.technique. The decrease in the water diffusion coefficient with increasing solute concentration is interpreted with a model which includes the obstruction from the solute particles to the diffusion of water and the hydration of the solute particles. The decrease of the obstruction effect due to particle motion is accounted for by a correction which gives the model the proper limiting behaviour. Hydration numbers for the organic solutes have been calculated. The reduction of the water diffusion coefficient with increasing solute concentration can be explained by assuming that less than a monolayer of water molecules are associated with the surface. For solutions of (C,H,),NCI and (C,H,),NCI the inclusion of the obstruction effects from the solute particles is essential to explain the concentration dependence of the water diffusion coefficient.The solute diffusion coefficient at infinite dilution agrees with predictions of the Stokes-Einstein equation for the hydrated solute particle. The self-diffusion of water in a solution is reduced by the presence of obstructions in the form of solute particles and, possibly, by the association of water to the particles. Previous studies have invoked the possibility that the water near surfaces has a structure different from bulk water, and that this restructuring could affect the diffusion of water well away from the particle surface1" More recenty it has been claimed*" that the long- range attractions observed between hydrophobic mica sheets covered with a surfactant monolayer, and the attractions between aggregates present in polyoxyethylene surfactant systems above the cloud point, arise from the structuring effect of hydrocarbon groups on water.In this paper we shall test if, for a selection of small organic solutes (molecular weights ranging from 75 to 278) dissolved in water, there is a need to invoke restructuring of water in the bulk, or if the diffusion measurements can be explained by the presence of up to or less than a surface layer of associated water at the particle surface. The choice of organic solutes for this study (ionic and hydrogen-bonding solutes) was motivated by the expectation that such solutes might be expected to cause major changes in the structure of water in order to balance the hydrophobic interactions.31293130 Self-diflusion of Water studied by N.M.R. 0 2 4 6 8 gradient pulse length/ms A A A 7 6 5 4 3 2 1 0 PPm Fig. 1. Spin-echo spectra obtained with the pulsed magnetic field gradient spin-echo technique. The sample contained 0.188 mol Pr,N+ per 55.5 mol water. The spectra were obtained from a Fourier transform of the second half of the 'H spin echo. The length (6) of the magnetic field gradient pulses applied at either side of the n-pulse in a (n/2),--2--(n)y--2 spin-echo sequence was varied between 1.2, and 8.4 ms in steps of 0.3 ms. The time between the centre of the two magnetic field gradient pulses, A, was 135 ms, the gradient strength, g, was 9.2 G cm-' and z was 125 ms. The inset shows the amplitude of the HDO peak (circles) and of the methyl peak (rectangles) as a function of 6 together with the least-squares fits of the Stejskal-Tanner equation A, = A, exp [ - (ygS)2 (A - 6 / 3 ) D] to the amplitudes.Experiment a1 Materials Samples were prepared in the following way. Tetramethylammonium chloride (Me,NCl), tetraethylammonium chloride (Et,NCl), tetrapropylammonium chloride (Pr,NCl) and tetrabutylammonium chloride (Bu,NCl) were obtained from Eastman Organic Chemicals, Rochester, New York and t-butyl alcohol (ButOH) from Sigma Chemical Co., St Louis, MO. Heavy water was obtained from Ciba Geigy, Basel, Switzerland. The chemicals were used without further purification. Stock solutions of ca. 1 mol dm-3 solute concentration were made by weighing appropriate amounts of vacuum-dried material and a mixture of H,O and D,O (5/95vol/vol).The n.m.r. samples were prepared by weighing appropriate amounts of stock solutions and the water mixture in 7 mm 0.d. Duran glass tubes which were flame-sealed after mixing. The sample volume was kept constant at 100 mm3. The 5/95 mixture of H,O and D,O was used to avoid dynamic range problems associated with a water signal that is much more intense than the solute methyl signal in the 'H n.m.r. spectrum.P - 0 . Eriksson, G. Lindblom, E. E. Burnell and G. J. T. Tiddy 3131 N.M.R. Measurements The self-diffusion coefficients of HDO and the organic solute were measured with the Fourier-transform pulsed magnetic field gradient spin-echo technique7-' using a Bruker MSL-100 n.m.r. spectrometer operating at 100 MHz for 'H equipped with a 2.35 T 89 mm bore superconducting magnet.The magnetic field gradient pulses were generated with a slightly modified Bruker B-2 18 B gradient unit. A 'H diffusion probe with two oppositely wound Helmholtz coils manufactured by Bruker Analytisch Messtechnik GMBH, F.R.G. was used. The gradient unit was modified for digital setting of the gradient amplitude by a series of fixed resistances. The setting of the gradient pulse length was controlled by the pulse programmer. In the diffusion measurements the length, 6, of the two gradient pulses at either side of the (x),-pulse in the (x/2)0-z47r)0+,,-z spin-echo sequence was varied from 1 to at most 10 ms while the time between the r.f. pulses, z, the time between the centre of the two gradient pulses, A, and the gradient strength, g , were kept constant.To reduce the overlap between adjacent peaks (see fig. 1) the value of z was selected to minimize the amplitude of the methylene proton peak(s) which are affected by J-modulation. Typically z was between 100 and 130 ms. A was 10 ms longer than z and g was 9.2 or 13.2 G cm-' (c$ below on the calibration of g). A multiple of four scans with cyclops phase cycling (# = 0, 90, 180 and 270") was collected in the quadrature receiver mode with at least two dummy scans rejected at the beginning of each measurement. The waiting time between successive pulse sequences was set to between 4 and 30 s, depending on the spin-lattice relaxation time of the water protons. With two dummy scans it was found that the result of the diffusion measurement was invariable to a change in the waiting time between pulse sequences even though the waiting time was not always long enough to allow complete relaxation of the water proton magnetization.Spectra were obtained for each gradient pulse-length setting by a Fourier transform of the second half of the spin echo. Suitable baseline corrections were applied to the spectra, and the amplitudes of the water and solute peaks were recorded by the routine of the Bruker n.m.r. program. The diffusion coefficients, D, of HDO and solute were obtained from a two-parameter non-linear least-squares fit of the Stejskal-Tanner equation' A, = A , exp [ - (ygS)2 (A - 6/3) D] to the peak amplitudes as a function of the gradient pulse-length, 6, to obtain the parameters (yg)2D and A,,.D is the self-diffusion coefficient and y is the proton magnetogyric ratio. The value of A , obtained from the fit closely agreed with the measured amplitude in the absence of gradient pulses. For some samples measurements were also performed with z = 60 ms and A = 70 ms, giving identical results for the diffusion coefficients. This is what is expected, since the size of the obstructions (the distance between the solute particles) is much smaller than the root mean-square displacement during the diffusion time, given by A - 6/3. Since z was kept constant in each experiment the spin-spin relaxation and J-modulation effects were equal for all spectra within each experiment. The gradient strength, g , was determined from measurements on doubly distilled H20 for which reliable self-diffusion data exist .lo The errors in the determined relative diffusion coefficients (fig.2) were estimated from repeated measurements to be ca. f 3 %. In fig. 1 an example is shown of spectra from a diffusion measurement together with the fit of the Stejskal-Tanner equation to the signal amplitudes as a function of the gradient pulse length.3132 Self-diflusion of Water studied by N.M.R. 0 0.5 1 .o 0 0.5 1.0 0 0.5 1 .o 0 0.5 1.0 1.5 0 0.5 1 .o Fig. 2. For legend see facing page. 0 mol solute per 5 5 . 5 mol water Method of Analysis The analysis of the self-diffusion of a solvent in the presence of obstructions has been treated in the literat~re.~. 11-13 However, there exists considerable confusion with the analysis.Recently Jonsson et aZ.13 have presented a theoretical discussion of the problem, and have introduced a cell model to aid its solution. However, the theory of Jonsson et aZ.13 is not able to treat rigorously the change in the obstruction effect caused by particle diffusion. For the small particles being studied in this paper, such effects might be expected to play a significant role. We shall attempt to account for the obstruction effect of diffusing particles in an intuitive way. A further important point that has been neglected previously is the finite volume ofP-0. Eriksson, G. Lindblom, E. E. Burnell and G. J . T. Tiddy 3133 the water molecules. The diffusion equations can be thought of as describing the motion of the centre of the solvent molecules (assumed spherical), and thus the solvent can approach the particle surface up to only one solvent radius.Thus the effective radius of the (spherical) obstructing particles is increased by the radius of the solvent molecules. This increase in the size of the obstruction is quite important in extracting the hydration number from diffusion experiments. The effect of a regular array of immobile spherical obstructions on solvent diffusion is given to high solute concentration by13 where D is the measured self-diffusion coefficient of water in the mixture, Do is the diffusion coefficient of bulk water,fis the fraction of water that is bound to the particles, and $ is the volume fraction of the obstructions, including the bound water. As pointed out above, the factor q5 must also include an extra half layer of water in addition to the bound water.Eqn (1) is valid for diffusion measured during a time corresponding to a root mean- square displacement much larger than the average interparticle distance in the solution. In the n.m.r. spin-echo measurement of self-diffu~ion,~ the diffusion time is given by A -6/3, which in the present investigation is between 100 and 140 ms. This corresponds to a root mean-square displacement in the order of m, which is about three orders of magnitude larger than the average interparticle distance in the most dilute solutions in this study. Thus the observed water diffusion is a result of movements of water molecules past a large number of obstructing particles or through a large number of unit cells in terms of the cell m0de1.l~ Since the size of the obstructors is much smaller than the root mean-squares displacement during A the measured diffusion coefficient is expected to be independent of the chosen value of A,'* which was also found experimentally.A further asumption implicit in eqn (1) is that the exchange between free and bound water is fast on the timescale of A-6/3. Jonsson et d.13 have shown that arrays of obstructing particles which are not regular lead to an increase in the value of D. The current analysis will be based on regular arrays of particles, for dilute solutions this analysis is valid, but for concentrated solutions it will predict values of D that are too small. Consequently, the hydration numbers obtained from the analysis are too small owing to this assumption.In the presence of particle diffusion, the normal procedure is to add a term D,fto eqn (I), where D, is the self-diffusion constant of the particle :13 D = Do(1 - M I + $ / 2 ) (1) Fig. 2. (a)-(e) The diffusion coefficient of HDO (circles) and of the solute (rectangles) in solutions of (a) Me4NC1, (b) Et4NC1, ( c ) Pr4NC1, ( d ) Bu4BNCl and (e) t-butyl alcohol in H,O/D,O 5/95 (vol/vol) as a function of solute concentration. The diffusion coefficients are given relative to the diffusion coefficient of HDO in pure solvent (Do = 1.90 x m2 s-l). T = 25 "C. The lines drawn through the water diffusion results represent one-parameter least-squares fits of three of the four models described in the text for the effect of a solute on the water diffusion; model (2) (solid line) : eqn (2) which represents a time-average of the diffusion of free water obstructed by the solute particles and of water bound to the particles, taking the finite size of the water molecules into account [eqn (7)] ; model (3) (dotted line) : eqn (3) which accounts for obstructions, the finite size of the water molecules and also the reduction of the obstruction effects due to the diffusion of the obstructing particles (see text); model (4) (dashed line): eqn (4) which neglects the obstruction effect.The line drawn through the solute diffusion points (rectangles) represents the fit of a second-order polynomial in rn. cf) The reduction of the diffusion coefficient of water in an aqueous solution of Bu,NCI as predicted by the four different models for a hydration number of 20 water molecules per solute molecule: model (1) (dashed/dotted line), model (2) (solid line), model (3) (dotted line) and model (4) (dashed line).For explanation of the models, see the figure caption to (a)-(e) and Results section. The solute diffusion coefficient is taken as those measured for Bu,NCl.3134 Self-difusion of Water studied by N.M.R. Eqn (2) represents a time-average of the diffusion of free water obstructed by the solute particles (which are treated as immobile as far as the free water is concerned), and of water bound to the particles. It is assumed that the lifetime of bound water on the particle surface is long relative to the rotational correlation time of the particle (see further below).Eqn (2) has been used to interpret water diffusion measurements in colloidal systems and to extract hydration numbers for amphiphilic micelles. l5 Eqn (2) does not have proper limiting behaviour, and cannot be expected to be valid for cases where the particle diffusion approaches that of the water, as is the case for some of the experiments reported here. For example, considering a system where the particle and solute are of equal size and have the same diffusion coefficient, D, = Do, then eqn (2) predicts an observed diffusion coefficient which.is less than Do. For f = 0, i.e. for the case of no bound water, it predicts that D is independent of D,. In the spirit of the cell model, we shall assume that the whole cell diffuses with the particle diffusion constant, D,, and, furthermore, that the first term is reduced by the factor (Do - D,)/ Do : r D = (Do - D,) (1 -f>/( 1 + #/2) + D,.(3) By these modifications, we obtain a model which has the correct limiting behaviour. For example, if particle and solvent are of equal size and have the same self-diffusion coefficient, we obtain, as required, D = D, = Do and iff = 0 we get D = Do/(l + #PI + DpP - 1 / v + #/31 ( f = 0) which makes D dependent on the particle diffusion coefficient D, even in the absence of bound water. If the volume fraction of the obstructing particles is neglected we obtain D=Do(l-f)+Dpf ( # = O ) . (4) Eqn (4), known as Lindman's first law,' represents a model where the obstruction effect of the particles is not taken into account, and where the concentration dependence of D is due solely to an exchange between bound and free water.A further potential problem involves the rotational diffusion of the particle. If the lifetime of a water molecule at the particle surface is much greater than the rotational correlation time of the particle, then the diffusion constant of the surface water is the same as the translational self-diffusion constant of the particle D,. If, however, the water stays only a short time (compared to the rotational correlation time of the particle) at the surface, rotation of the particle will lead to an increased value of the self-diffusion constant of the bound water. It has been shown," using the Stokes-Einstein equation for translational and rotational diffusion, that if the water only stays for a short time on the particle surface, the term D, f in eqn (2) becomes 1.5DPf.The longest rotational correlation time for the solutes in this study can be estimated to be ca. 3 x s. Recent results from spin relaxation studies on colloid^'^ and ultrasound relaxation measurements on concentrated surfactant systemsls indicate that for water bound via hydrogen bonding the lifetime in the bound state is equal to or longer than this value. Because of the lack of firm data on this we shall assume that the surface water diffuses with the particle. Since we use a mixture of H,O and D,O (5/95 vol/vol) as solvent it is convenient to use expressions for $ and f in terms of the reduced (dimensionless) concentration unit m = mol solute per 55.5 mol water which for H,O has the same numerical value as the usual molality.The fraction of bound water is then given by f = mn,/55.5 ( 5 )P - 0 . Eriksson, G. Lindblom, E. E. Burnell and G. J . T. Tiddy 3135 Table 1. The hydration numbers n$ of the organic solutes as obtained from one-parameter least- squares fits of the four different models to the water diffusion coefficient as a function of solute concentration (see text and fig. 2); T = 25 "C ~~ ~ ButOH 11.8 & 0.9 5.2 f 0.9 8.2 f 0.9 18.0 & 1.9 27.0 Me," 6.4 f 1.5 0.0 f 0.9 3.6 f 1.4 13.7 f 2.8 26.9 Et,N+ 8.7 f 1.5 1.4f 1.3 4.5f 1.5 16.7f2.3 34.5 Pr,N+ 18.94 1.8 10.9 f 2.0 13.5f 1.8 27.4+ 3.0 40.6 Bu,N+ 24.0 f 2.1 15.7+_ 1.2 18.2+ 1.4 32.5 +_ 4.8 46.0 a ng) = estimate of the number of water molecules in a monolayer around the solute particle (see text).ButOH = (CH,),COH; Me,N+ = (CH,),N+; Et,N+ = (CH,CH,),N+; Pr,N+ = (CH,CH,CH,),N+ ; Bu,N+ = (CH,CH,CH,CH,),N+. where n H is the number of bound water molecules per solute particle. The effective volume fraction of the obstructing particles is taken as mu, + nH mv, mu, -k 5 5 . 5 ~ ~ # = A where v, is the molar volume of species i. The factor A in eqn (6) is the relative increase in the effective volume fraction of the obstructing particles due to the fact that the centre of the solvent molecules cannot come closer to the particle surface than one half of the radius of the solvent molecules. If both the water molecyles and the solute particles are assumed to be spherical with a radius proportional to vi then A is given by Results Self-diffusion coefficient at 25 "C of both water and solute have been measured at several concentrations for a number of systems. The experimental results are presented in fig.2. The results are in agreement with other published data on diffusion in tetra- alkylammonium salt '' The solute diffusion coefficient as a function of concentration was fitted by a second-order polynomial in m through a least-squares adjustment of the polynomial coefficients. In the analysis of the water diffusion, Dp was taken as this polynomial function. The measured reduction of the water self-diffusion coefficient, D, as a function of solute concentration was fitted by four different models with a least-squares adjustment of nH as the only adjustable parameter.In all our calculations we treat the solute molecules as being spherical. The models are as follows. (1) D as given by eqn (2), which includes the obstruction effects from the solute particles. However, the correction for the finite size of the water molecules [eqn (7)] is not taken into account, i.e. 1 = 1. ( 2 ) D as given by eqn (2), which includes the obstruction effects from the solute particles. The finite size of the water molecules is corrected for according to eqn (7). Both model (1) and model (2) treat the particles as stationary as far as the diffusion of the free water is concerned. ( 3 ) D as given by eqn (3), which includes the obstruction effects from the solute particles. The decrease in the obstruction effect due to particle motion is taken into account in a way which gives the model the correct limiting behaviour at large solute diffusion coefficients.The finite size of the water molecules is corrected for according to eqn (7). (4) D as given by eqn (4), which neglects the obstruction effects. The reduction3136 Self-diflusion of Water studied by N.M.R. of- the water diffusion coefficient is attributed solely to the exchange between free water and water bound to the solute particles. It is assumed that the chloride ions in the salt solutions do not influence the water diffusion coefficient [c.J table 1 of ref. (3)]. The molar volumes are taken as ui = Mi/pi, where Mi is the molecular weight of species i and pi is the density. For the organic solutes the density is taken as pp = 0.8 g ~ m - ~ .The calculated value of nH is not sensitive to the value chosen for p,. For example a change in pp of kO.1 gives a change in the calculated value of nH of < 0.3 water molecules for the Bu,NCl system applying model ( 3 ) . The lines drawn in fig. 2 represent the least-squares fits of the models (2) (solid line), ( 3 ) (dotted line) and (4) (dashed line). The fits of model (1) are not shown in the figures but are qualitatively as good as for models (2) and ( 3 ) . The hydration numbers, n:), which were obtained from the least-squares fits are given in table 1 . The errors in the hydration numbers are estimated as the interval within which the error squares sum is less than twice the minimum value. Discussion As seen in table 1 , the four different models give different hydration numbers. The lowest hydration numbers are obtained with model (2), which takes obstruction and the finite size of the water molecules into account but neglects the influence of the particle diffusion upon the obstruction factor.Neglect of the finite size of the water molecules (model 1) gives considerably larger hydration numbers. Model (3), which also takes the influence of particle motion on the obstruction effect into account, gives slightly higher hydration numbers than model (2). Finally, model (4), which neglects the obstruction effects, gives the largest hydration numbers. For comparison, we give in table 1 an estimate of the number of water molecules, ng), in a monolayer around a solute particle. For this purpose both the solute and the water molecules are cotlsidered as spherical with volumes u INA and vw/NA and radii R, and R,, where NA is Avogadro's number.We estimate n$ as the number of spheres of volume v,/N, which can be placed on a plane surface with the same area as the area of a sphere of radius R, + R,. It is found that ng) = 2n/3t[(Rp + Rw)/RWl2. This gives numbers for ng) that are slightly too large. For example, for spherical solute and solvent molecules of equal size, the predicted value of 14.5 is 20% larger than the value of 12 appropriate for close-packed spheres. Nevertheless, for all models used the value of nz) is much less than the value of ng) predicted by eqn (8) (see table 1). In addition, recent theoretical workz1 gives 10-15 as a reasonable estimate of the coordination number for univalent charged particles that have twice the diameter of the water molecule.It was found2' that this number does not depend strongly on charge for such particles. The radii of the solute molecules studied here are at least twice the diameter of the water molecule, and, except for Bu,NCl, the values of ng) for models 2 and 3 (table 1) are all less than 15. Thus for the solutes studied here there is no need to invoke any structuring of water extending further out than one monolayer from the (organic) particle surface. For the small molecules, Me,N+, Et,N+ and ButOH, the four models give similar fits to the experimental points [fig. 2(a), (6) and (e)]. For Pr,N+ and Bu,N+ [fig. 2(c) and (d)] it is found that inclusion of the obstruction effects (models 2 and 3 ) gives significantly better fits than if these effects are neglected (model 4; the dashed lines in fig.2); model 4 cannot reproduce the curvature of the experimental points. This demonstrates that obstruction effects are essential for the description of water diffusion in solutions of large organic solutes. To see the relative importance of the various factors that govern the decrease in theP-0. Eriksson, G. Lindblorn, E. E. Burnell and G. J. T. Tiddy 3137 Table 2. Observed and calculated solute diffusion coefficients in a mixture of H,O and D,O (5/95 vol/vol); T = 25 O C a ButOH Me,N+ Et,N+ Pr,N+ Bu,N+ E i i c k SE 93 0.33 0.60 0.90 H 8.2 n(3) up + ng) u, 24 1 0.46 0.44 DSliP SE 0.66 RP" 0%" D p 0.77 dehydrated solute 92 163 0.33 0.40 0.60 0.50 0.90 0.75 hydrated solute 157 244 3.6 4.5 0.40 0.46 0.50 0.44 0.76 0.65 measured 0.93 0.72 233 0.45 0.44 0.66 13.5 476 0.57 0.35 0.52 0.55 303 0.49 0.40 0.60 18.2 63 1 0.63 0.32 0.48 0.50 a up = molar volume of the solute (in cm3 mol-').u, = molar volume of water. ng) = hydration number of the solute particles calculated from water diffusion measurements using model 3 (see text and table 1). R: and RF = radius (in nm) of the dehydrated and the hydrated solute particles, respectively. DiFk and = solute diffusion coefficient (in units of lop9 m2 s-l) calculated from the Stokes-Einstein equation for the stick and slip boundary condition, respectively, see eqn (9a) and (9b). DB) = measured solute diffusion coefficient (in units of m3 s-') extrapolated to infinite dilution.water diffusion coefficient with increasing solute concentration, the predictions of the four different models are given in fig. 2(f) for the Bu,NCl-water system assuming 20 bound water molecules per solute molecule. Neglect of the obstruction effect [dashed line in fig. 2 0 3 or the finite size of the water molecules [dashedldotted line in fig. 2 0 1 makes the predicted water diffusion coefficient considerably larger than when both these effects are taken into account [solid line in fig. 2 01. When the effect of particle diffusion on the obstruction is taken into account [eqn (3)] the predicted water diffusion coefficient gets larger [dotted line in fig. 2 0 1 . It is clear that the upward bend in the curve for the concentration dependence of the water diffusion coefficient arises from the obstruction effects.Considering the approximations made in the models and the goodness of fit to the experimental results, model 3 is thought to provide the best estimate of the hydration of spherical solute particles. The difference between hydration numbers for models 2 and 3 in some sense gives an estimate of the reliability of the hydration numbers reported for model 3. The solute diffusion coefficient at infinite dilution can be compared with predictions from the Stokes-Einstein equation for the diffusion coefficient of a sphere in a continuum. For a sphere of radius R in a medium with viscosity v, the diffusion (9 4 coefficient is when applying the stick-boundary condition and (9 4 p i c k - SE - kB T/6nqR DgF = k, T/4nqR when applying the slip-boundary condition.22 T is the absolute temperature and k , is Boltzmann's constant, Table 2 gives the measured diffusion coefficient, D r ) , of the solute particles 103 F A R I3138 Self-diflusion of Water studied by N.M.R.extrapolated to infinite dilution, the molar volumes, v, and v, + nH v,, and molecular radii, R; and Rp”, of the dehydrated and the hydrated solute particles and the calculated diffusion coefficients, Dig“ and DiF, of the dehydrated and the hydrated particles applying the stick and the slip boundary conditions, respectively. A density of 0.8 g cm-3 is assumed for the organic solutes. For the experimental hydration number, nH, the values calculated with model (3) are chosen. The diffusion coefficients of the dehydrated and the hydrated particles are calculated with both the stick and the slip boundary conditions.The viscosity of the solvent (H,O/D,O 5/95 vol) is taken as 1.23 times the viscosity of H,O at 25 OC.l The calculated solute diffusion coefficients are all of the same magnitude as the measured diffusion coefficients (table 2). Except for Me,NCl, the calculated diffusion coefficient for the hydrated and the dehydrated particle border the measured diffusion coefficient when applying the slip boundary condition. The stick boundary condition gives too small a diffusion coefficient both when applied to the hydrated and to the dehydrated particle. It is interesting to note that if the ‘hydration’ of the particles is seen as the correspondence on a molecular level to the hydrodynamic stick- boundary condition for a dehydrated particle, then the slip-boundary condition where the surrounding fluid is not drawn along with the diffusing particle could be expected to be applicable to the diffusion of a hydrated particle.This is found for the larger solutes Pr,NCl and Bu,NCl, whereas for the smaller solutes the slip boundary condition for the dehydrated particles gives a calculated diffusion coefficient in better agreement with the measured particle diffusion coefficient. Conclusions The analysis in this paper of the water self-diffusion coefficient in the presence of low- molecular-weight organic solutes has shown that the experimental results can be explained by assuming less than a monolayer of water molecules associated with the particle surface. The effect of obstruction from the solute particles must be accounted for in order to get the correct qualitative concentration dependence of the water diffusion coefficient in solutions of Pr,N+ and Bu,N+.No ‘structure-making ’ or ‘structure- breaking’ effects of the solutes on the water far away from the solute surface have to be invoked to explain the results. Discussions with B. Jonsson and G. N. Patey are acknowledged. This work has been supported by the Swedish National Research Council. We wish to acknowledge the ‘ Knut och Alice Wallenberg’ Foundation for the generous donation of the MSL-100 spectrometer. The Estoril Sol is acknowledged for providing the ambience suitable for scientific discussions. References 1 E. v Goldammer and H. G. Hertz, J . Phys. Chem., 1970, 74, 3734. 2 M. D. Zeidler, in Water: A Comprehensive Treatise, ed. F. Franks (Plenum, New York 1973), vol. 2, p. 529. 3 M. E. Clark, E. E. Burnell and N. R. Chapman, Biophys. J., 1982, 39, 289. 4 B. W. Ninham, D. F. Evans, Furuday Discuss. Chem. Soc., 1986, 81, 1. 5 R. M. Pashley, P. M. McGuiggan, B. W. Ninham and D. F. Evans, Science, 1985, 229, 108. 6 P. M. Claesson, R. Kjellander, P. Stenius and H. K. Christensen, J. Chem. Soc., Furuday Trans. I , 7 E. 0. Stejskal and J. E. Tanner, J . Chem. Phys., 1965, 42, 288. 8 T. L. James and G. G. McDonald, J . Mugn. Reson., 1973, 11, 58. 9 P. Stilbs, Progr. Nucl. Mugn. Reson. Spectrosc., 1987, 19, 1. 1986, 82, 2735. 10 R. Mills, J . Phys. Chem., 1973, 77, 685. 11 J. H. Wang, J . Am. Chem. Soc., 1954, 76,4755.P-0. Eriksson, G. Lindblom, E. E. Burnell and G. J. T. Tiddy 3139 12 M. A. Lauffer, Biophys. J., 1961, 1, 205. 13 B. Jonsson, H. Wennerstrom, P. G. Nilsson and P. Linse, Colloid Polym. Sci., 1986, 264, 77. 14 E. 0. Stejskal, J. Chem. Phys., 1965, 43, 3597. 15 P. G. Nilsson and B. Lindman, J. Phys. Chem., 1983, 87, 4756; P. G. Nilsson, B. Lindman, R. G. Laughlin, J. Phys. Chem., 1984, 88, 6357. 16 B. Halle, personal communication. 17 L. Piculell, J. Chem. SOC., Faraday Trans. I , 1986, 82, 387; L. Piculell and B. Halle, J. Chem. SOC., Faraday Trans. I , 1986, 82, 401 ; B. Halle and L. Piculell, J. Chem. SOC., Faraday Trans. I , 1986, 86, 415. 18 G. J. T. Tiddy, M. F. Walsh and E. Wyn Jons, J. Chem. SOC., Faraday Trans. I , 1982, 78, 389. 19 H. G. Hertz, B. Lindman and V. Siepe, Ber. Bunsenges. Phys. Chem., 1969, 73, 542. 20 A. J. Easteal and L. A. Woolf, J. Solution Chem., 1986, 15, 1003. 21 P. G. Kusalik and G. N. Patsy, to be published. 22 C. R. Cantor and P. R. Schimmel, Biophysical Chemistry, Part ZZ (W. H. Freeman and Co., San Francisco, 1980). Paper 712165; Received 9th December, 1987 103-2

ISSN:0300-9599    

DOI:10.1039/F19888403129

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1988, 84(9), 3141-3158 Excess Enthalpies and Cross-term Second Virial Coefficients for Mixtures containing Water Vapour Christopher J. Wormald* and Neil M. Lancaster School of Chemistry, University of Bristol, Bristol BS8 ITS Measurements of the excess molar enthalpy for {x H,O + (1 - x) CH,Cl}(g) and {x H,O-(l + x) C,H,Cl)(g) mixtures at pressures around 60 kPa and over the temperature range 363.2-423.2 K are reported. Cross-term second virial coefficients, BIZ, have been derived from the measurements. A method of calculating third virial coefficients of mixtures containing water vapour is suggested. The method allows a more detailed analysis of HZ measurements than was previously possible when third virial terms were ignored and a small systematic error was introduced into derived B,, values.Previously reported H t values for 11 mixtures containing water have been reanalysed and better B,, values have been obtained : these agree well with values obtained from measurements of the solubility of water in compressed gases. HZ values for water-chloroalkane mixtures, together with previously reported measurements on 11 mixtures of water with non-polar fluids have been used to obtain parameters of the Stockmayer potential for water in its interaction with any substance with which it does not associate. It was found that the interaction parameter when used in the combining rule E,, = ~ ( E , , E , , ) ~ works as well for water-n- alkane mixtures as it does for alkane-alkane mixtures. Using this combining rule together with the Stockmayer parameters Elk, = 233 K, 0 = 0.312 nm and t* = 1.238 for water, B,, values can be calculated for mixtures of water with any polar or non-polar substance.For mixtures of water with carbon dioxide, ethene, propene or benzene the experimental B,, values are significantly more negative than those calculated. This is attributed to specific interactions between the water lone-pair electrons and unfilled orbitals in the n-electron system of the other component of the mixture. Although accurate (p, Vm, T ) properties of many vapour mixtures have been measured there remains a paucity of data for mixtures containing water. Steam is a component of many industrial process streams. It is used as a reactant in the water-gas shift reaction, the Fischer-Tropsch process, the Shell ethanol process and in steam reforming of petroleum. It is also used as an extraction fluid in steam distillation and enhanced oil recovery, and is a component of combustion gases.Much effort has been expended in trying to make accurate (p, Vm, T ) measurements on these mixtures, but large adsorption errors make the task almost impossible. At a time when the optimisation of process conditions is of increasing importance the need for accurate thermodynamic data on steam mixtures and for methods of calculating steam mixture properties is pressing. The second virial coefficient, B, is simply related to the pair potential, and for water dimer much theoretical work on the potential surface has been done.lP3 The surface is complicated, and no simple potential function is available.That little work has been done on pair potentials for water mixed with other components is largely due to the shortage of experimental measurements. Measurements of the solubility of water in 31413142 H: and B,, for Steam Mixtures compressed gases4v5 have yielded some cross-term second virial coefficients B12 over a narrow range of temperature. The measurements are not extensive, and the technique is limited to mixtures of water with gaseous substances. Independent verification of these B,, values by another technique is desirable if theorists are to take them seriously. An alternative to @, Vm, T) is flow calorimetric measurement of the isothermal Joule- Thomson coefficient + = (i3H/i3~)~, which in the limit of zero pressure, becomes +O = B-T(dB/dT).While flow-calorimetric measurements have the advantage that there are no adsorption errors, good calorimeter design and careful control of heat leaks are needed if the measurements are to be free from systematic error. A careful analysis of (p, Vm, T) and flow calorimetric measurements on water vapour at low densities has been made by LeFevre' whose equation for the second virial coefficient is still the best available. In 1984 Haar, Gallagher and Kel17 (HGK) published new steam tables which are accepted internationally. They devised a new equation of state for water which fits the measured properties with high accuracy. Second, third and fourth virial coefficients, B, C and D, consistent with (p, Vm, T) properties generated by the HGK equation have been calculated by Gallagher.8 The Bs are almost the same as those obtained by LeFevre, and the Cs are probably more accurate than those obtained from any other analysis.The Ds are negative at high temperatures, and are unlikely to be accurate. An encouraging feature of the D(T) curve is that it is of similar shape to D( T) curves for Lennard-Jones fluids. Gallagher's virial coefficients are listed in Appendix 1. To interpolate between the tabulated values and to calculate temperature derivatives we fitted the coefficients to seventh-order polynomials in powers of T1. The coefficients B and q5O for water can be fitted moderately well using the Stockmayer potential, although the parameters obtained depend on the temperature range chosen.Over the range 350-700 K the best fit to values of B and +O consistent with the HGK equation is obtained with the parameters &/kB = 370 K, o = 0.267 nm and t* = 1.244. Comparison with B values listed in Appendix 1 is shown in fig. 1. Below 350 K the Stockmayer potential is not a good fit to the HGK values. pm Values for Water-Non-polar Fluid Mixtures A recent technique which yields information about cross-term B,, and q512 values is vapour phase flow mixing calorimetry. A low pressure differential flow mixing calori- meter capable of accuracy between 1 and 2% has been described.' Over the last decade the calorimeter has been used to make systematic measurements of the excess molar enthalpy HE of 17 binary mixtures containing water. These include mixtures of water with hydrogen," nitrogen," argon,12 carbon monoxide,13 C, to C, n - a l k a n e ~ , ' ~ ~ ~ ~ - l ~ C, to C, alkenes,l41l5 benzene17 and cyc10hexane.l~ The measurements were made at pres- sures of ca.80 kPa at temperatures from 363.2 to 423.2 K, and were reported adjusted to the standard pressure po = 101.325 kPa. A high-pressure flow mixing calorimeter capable of 2% accuracy has also been constructed.ls It has been used to make H z measurements at temperatures from 448.2 to 698.2 K at pressures up to 15 MPa. The mixtures studied include water with hydrogen," nitrogen,', carbon monoxide,20 carbon dioxide,20 C, to C, n-alkane~~l-~~ and ethene.22 Extrapolation of the measurements to low pressures yields HE at P". It has been ~hownl~-~* that values of Ht(pO) obtained from the low- and high-pressure mixing calorimeters are consistent.For a binary vapour mixture of components 1 and 2 at low densities Zfz is given by9 H: = Xl x2 P(2+;2 - +;1- +;21 - (P2/RT) (B+" - Xl Bll +;1- x2 B22 +;2) + (P2/RT) (V - X l Vlll -x, V z 2 2 ) . (1)C. J. Wormald and N . M . Lancaster 3143 0 I I 1 I I - - k 3 \ rq - - 1 1 1 I I q5' and w are related to second and third virial coefficients B and C by the equations q5' = B - T(dB/dT) (2) = C-(T/2)(dC/dT). (3) B, q5' and in eqn (1) are properties of the mixture, and are given by B = x~B,,+2x,x,B,,+x~B,, (4) w = 4 will + 3 4 x, wl12 + 3x1 4 w12, + 4 wZz2- ( 5 ) q5' is given by an equation similar to eqn (4). The absence of information about third virial coefficients for steam the y term could not be calculated and was previously neglected. For some hydrocarbon mixtures the ty term was found to be 1 % of H:(pO). If it is the same size for steam mixtures it is no larger than the uncertainty on the measurements, but nonetheless introduces a systematic error into the calculation if it is omitted.Now that third virial coefficients for steam are available,8 a better analysis of the Ht(pO) measurements obtained using the low-pressure mixing calorimeter is possible. To make clear how the new analysis differs from that used previously it is important, first of all, to give details of the earlier method. To obtain B,, and &, from HE@) measurements, values of B and q5' for the pure components must be known. B,, and q5yl for steam were previously calculated from the LeFevre equation.s B,, and q5i2 for the non-polar substances mixed with steam were calculated from the Kihara potential with parameters obtained by fitting to class I second virial coefficient^.,^ Analysis of the H:(p) measurements on (water-argon)', mixtures showed that B,, and q5y2 for the water-non-polar fluid interaction could be calculated using the Lennard-Jones parameters E/kB = 285 K and 0 = 0.27 nm for water, the Kihara parameters for the non-polar fluid, and the combining rules3144 HE and B,, for Steam Mixtures The HZ(p) measurements on all mixtures were analysed by adjusting ( until HE@) calculated from the right-hand side of eqn (l), omitting the terms in ly, agreed with the values of Hz(p) obtained at the pressure p of the experiment.When 4: had been found, 4, and q4, were calculated, and the HE@) measurements were adjusted to po and reported as measurements at this pressure. Careful analysis of B,, values obtained from VE measurements on 15 mixtures of n- alkanes26 and from HE measurements on 20 mixtures of n - a l k a n e ~ ~ ~ ? ~ , showed that values of 4: obtained from the analysis agreed to within experimental error with values of 4: calculated from the combining rule (9) 4: = 2 ( 4 a;,); (a;;) (Z1Z2)+ (Il + I,)-, where Z is the ionisation energy. This rule was shown2s to be superior to that of Hudson and McCoubrey2’, to that of Fender and Halsey3’ and to four other similar rules. When HE measurements on mixtures of water with C,-C, n-alkanes were analysed. the values of ( were found to be given by this same combining rule.15*16 The rule works equally well for water-nitrogen and water-cyclohexane mixtures.Eqn (9) was found not to work for mixtures of water with carbon dioxide, ethene, propene or benzene. In each case experiments gave values of 4: greater than unity. For these mixtures there may be specific donor-acceptor interactions between the lone-pair electrons of the water molecule and the n-electron system of the other component. Agreement between the 4: values obtained for water-n-alkane mixtures with eqn (9) is satisfactory but a little surprising. It implies that either dipole-induced-dipole forces between water and n-alkanes are negligible, or that these forces give rise to deviations from the geometric mean rule which are adequately described by eqn (9).Calculation of the dipole-induced-dipole energy using the method described by Hirschfelder et aL31 shows that it is indeed very small compared with the dispersion energy, even for water- n-octane mixtures. The programme of work on water mixtures would not be complete without measurements on mixtures containing polar fluids. Measurements on water-methanol and water-ethanol mixtures have been made and will be reported shortly, but the results cannot be analysed without prior investigation of the interaction of water with substances which are polar but with which no hydrogen bond is formed. For such mixtures it is important to know if eqn (9) is a good combining rule for obtaining the cross-term dispersion energy, and if the dipole4ipole energy is adequately calculated from formulae which assume a point dipole situated at the centre of the molecule.With this in mind we decided to make measurements on water-chloromethane and water-chloroethane mixtures. As these measurements turn out to be important to the further analysis of the measurements on water-non-polar fluid mixtures we must describe the experiments and report the results before proceeding further. flms for Water-Polar Fluid Mixtures Measurements of HE for {xH,O + (1 - x)CH,Cl} and {xH,O + (1 - x)C,H,Cl} have been made at pressures around 60 kPa over the range 363.2423.2 K. The low-pressure differential flow mixing calorimeter was the same as that previously de~cribed.~ Steam was generated by boiling ordinary distilled water.Chloromethane or chloroethane of 99.9 mol % purity, supplied from cylinders, was drawn into the apparatus through a calibrated dry gas meter accurate to 0.1 YO. The possibility that the experiments might be spoiled by partial hydrolysis of the alkyl chloride to form the alcohol and hydrogen chloride was considered, and steam which was passed through the apparatus was condensed and analysed. The highest acidity, [H+] = 4.6 x mol dmP3, was obtainedC. J. Wormald and N. M. Lancaster 3 145 360 3 80 400 420 TIK Fig. 2. Excess molar enthalpies Hz(po) of (0.5 H,O + 0.5 CH,Cl) and (0.5 H,O + 0.5 C,H,Cl). The measurements are listed in Appendices 2 and 3, and are at po = 101.325 kPa. The solid curves were calculated as described in the text using the Stockmayer parameters ElkB = 233 K, Q = 0.312 nm and t* = 1.238 for water.The broken curves were calculated using the parameters (now shown to be wrong) E/kR = 285 K, Q = 0.27 nm and t* = 1.562. Upper solid and broken curves are for the C,H,Cl mixture, lower solid and broken curves are for the CH,Cl mixture. for runs on {xH20 + (1 - x)CH3C1} at 423.2 K. The standard enthalpy of the gas-phase hydrolysis of chloromethane to form methanol and hydrogen chloride is 30.4 kJ mol-', and the enthalpy change corresponding to the measured amount of decomposition is 0.2 J mo1-l. As the residence time of the gaseous mixture in the heated calorimeter outlet pipe was ca. 10 times larger than in the calorimeter itself the error in H: must be + 0.2 J mol-l, and can be neglected. When (xH,O + (1 - x)C,H,Cl} measurements were made at 423.2 K the acidity of the condensate was about half that obtained with the CH,Cl mixture.The results are listed in Appendix 2. The overall uncertainty on the measurements is no worse than 2%. Fig. 2 shows values of HZ(pO, x = 0.5) plotted against temperature. First Analysis of pm{xH20 + (1 - x)CH,Cl) and pm{ xH20 + (1 - x)C2H,C1) Second virial coefficients for CH3Cl and C,H,Cl listed in ref. (25) were fitted using the Stockmayer potential, and the parameters obtained are listed in table 1. For interactions between two unlike polar molecules 1 and 2 we require the additional combining rule15 where p12 is the dipole moment appropriate to the cross-term interaction. With t = 1, eqn (10) is equivalent to the rule t,*, = (t:t$ usually used with the Stockmayer potential. As before, we used the parameters &/kB = 285 K, CT = 0.27 nm and p = 1.85 D for water, the third virial coefficient term in eqn (1) was neglected, and < was adjusted until the right-hand side of eqn (1) agreed with HE@) obtained experimentally.Eqn (9) gives = 0.996 for water-chloromethane and 0.995 for water-chloroethane mixtures. The experimental values are = 0.886 and 0.885, very different from those expected. If we calculate HE@) for the two mixtures using the values of given by eqn (9) we obtain the broken curves shown in fig. 2. When this is done for mixtures of water-n-alkane the calculated curves agree with the measured H z values to within experimental error. The3146 HE and B,, for Steam Mixtures difference between the broken curves and the experimental HE values shown in fig.2 shows how much the HZ measurements would have to be in error for agreement with eqn (9) to be obtained. The difference is > 10 times the maximum uncertainty (1 J mol-') on the measurements, and is too large to be attributed to neglect of the 'y term in eqn (1). However, it is necessary at this stage to examine the third virial coefficient term and to make our best calculation of it before we can make further progress. Calculation of Third Virial Coefficients When the programme of measurements on steam mixtures was begun in 1977 reliable third virial coefficients for steam were not available, but with the advent of Gallagher'sa second, third and fourth virial coefficients for steam the situation has greatly improved.Third virial coefficients of non-polar fluids can be calculated using the corresponding- states correlations of either Chueh and P r a u s n i t ~ ~ ~ or of Orbey and Vera.33 The Chueh-Prausnitz correlation was used previously9 to calculate the 'y term of eqn (1) for mixtures of n-alkanes. We now prefer to use the Orbey-Vera correlation, as this equation uses Pitzer's acentric factor cu as a measure of departure from simple fluid behaviour. Calculation of 'ylll for water from Appendix 1 and 'y,,, for non-polar fluids is now straightforward, the problem is to obtain the cross-terms 'yl12 and 'yy,,, in eqn (5)- It was shown previously12 that the second virial coefficient water might have in the absence of hydrogen bonding is close to that for CH3F.This homomorph has the same dipole moment (1.85 D) as water, but a smaller reduced dipole t*. (ElkB = 205 K, 0 = 0.345 nm hence t* = 1.041). We now make the assumption that the critical parameters of CH3F are the same as those that 'unassociated water' might have. To obtain pseudo-critical parameters for the calculation of cross-term third virial coefficients and their temperature derivatives we used the following equations where Ztjk was calculated from z : j k = 0.291-0.08 w i j k . Subscripts i, j and k in these equations take the values either 1 or 2. Pseudo-binary interaction parameters were calculated from T9, = l ( T i Ti)' v;, = {( v;)i + ( V$}3/8 m12 = ( 0 1 + cu,)/2. (18) CH,F parameters ( Tc = 3 18 K, v" = 124 cm3 mol-' and w = 0.19) were used in place of water parameters (Tc = 647.3 K, v" = 56 cm3 mo1-l and w = 0.344) for cross-terms relating to the interaction of a non-associating pair.For example, when eqn (1 1) is used to calculate C,,,, T;, is that for water while Ti, and T i , are those calculated from eqn (16) using CH3F and component-2 parameters. The parameter in eqn (16) was calculated from eqn (9). The above procedure cannot be tested using low-pressure Hzs. In the following paper3* we report measurements of H z for water-n-pentane mixtures at high pressures. Comparison of the measurements with values calculated from second and third virialC. J . Worrnald and N. M. Lancaster 3147 coefficients shows that the v/ term calculated by the above method gives good agreement with experiment.We are now in a position to make a better analysis of the low-pressure HE values than was possible previously. This will be done in two parts. Hk values for water-non-polar fluid mixtures will be reanalysed separately from the results on water-polar fluid mixtures. Reanalysis of Water-Non-polar Fluid pm Values The I,U term in eqn (1) is biggest at the lowest temperature (363.2 K) at which measurements were made. At this temperature, and at p = 101.325 kPa, the v/ term is 1.2% of HZ for water-methane and 1.5% of HE for water-ctane. Eqn (9) was found to be the best combining rule of those tested and was therefore used to fix the values of < for each mixture. As adjustable parameters in the fitting procedure we used the parameters ElkB and 0 for water in its interaction with a non-polar component, and abandoned the values ElkB = 285 K and 0 = 0.27 nm obtained from analysis of HE measurements on a single mixture (water-argon).l2 Rather than analyse a mixture at a time we chose to reanalyse our H t measurements on all 11 water-non- polar fluid mixtures simultaneously. In eqn (l), B,, and C,,, for water, and their temperature derivatives, were calculated from polynomials fitted to the data in Appendix 1. B,, and q522 for the non-polar fluids were calculated from the Kihara potential using the parameters listed in table 1. Eqn (6t(8) were the combining rules used for the calculation of pair potential cross-terms. C:222 and tyZ2, for the non-polar fluids were calculated from the Orbe~-Vera~~ correlation, and cross-terms were calculated using eqn (1 1H18).Everything except &/kB and 0 for water in its interaction with a non-polar molecule was known. The unknown parameters were found using a grid search. A grid of values of Elk, between 200 and 400 K, and values of 0 between 0.25 and 0.35 nm, was used. For pairs of values of ElkB and IT within this range we computed the standard deviation s of HE values calculated for the 11 mixtures from the experimental HE values at x = 0.5. As HE for each mixture was measured at between 4 and 6 temperatures, the total number of HZ values from which s was calculated was 61. For each experimental HZ(p) value the calculation was done at the pressure p at which the measurements were made. This avoided the difficulties of the earlier analyses where measurements at pressures of ca.80 kPa were adjusted to the standard pressure po = 101.325 kPa and then analysed, a process which involved a tedious iterative procedure. The standard deviation s was recorded as a number on the E/kB against 0 grid. No single minimum on the grid was found. Instead points of minimum standard deviation were found to lie on a line. This line is shown as (a) in fig. 3. Any pair of points ElkB and 0 on this line fits the 61 HE measurements with a standard deviation of c 1.5%. If instead of eqn (9) we used the combining rules of Hudson and McCoubrey2' or of Fender and Halsey3' we of course obtain different lines, but the standard deviation along the bottom of the valley is ca. 1.5 times bigger than that obtained using our combining rule.That there is a range of values of elk, and o which fit the Hf measurements equally well was expected. There are no unique parameters, and valleys in ElkB against 0 standard deviation grids are always found when fitting approximate potentials to inexact experimental measurements. Reanalysis of Water-Polar Fluid pm Values We next applied the same treatment to our measurements of HE@) for water- chloromethane and water-chloroethane mixtures. We continued to use the Orbey-Vera correlation for the calculation of the v/ term even though it was not designed for polar fluids. Eqn (10) was now included in the combining rules. No attempt to take account3 148 I-3: and B,, for Steam Mixtures Table 1. Parameters for the Kihara and Stockmayer potentials H2 NZ CH4 Ar co ‘ZH6 C3H8 C4H10 C5H12 C6H14 C8H18 C6H12 CH,Cl C2H,CI co2 ‘ZH4 C3H6 C6H6 0.0000 0.01 79 0.0353 0.0000 0.0393 0.0491 0.0737 0.0939 0.1 131 0.1329 0.1526 0.1650 0.1 124 0.0000 0.0000 0.07 16 0.0475 0.0743 0.1020 0.0000 0.2930 0.33 17 0.3527 0.3763 0.3565 0.4325 0.461 1 0.47 18 0.5020 0.5458 0.5769 0.621 1 0.5578 0.3436 0.3556 0.3760 0.4075 0.4652 0.5074 0.2666 37.00 146.5 139.2 100.2 227.1 336.8 501.9 701.2 845.3 93 1.9 1057 1109 783.5 3 18.0 455.2 424.4 324.4 467.0 856.3 370.0 0.00 0.00 0.00 0.1 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.87 2.02 0.00 0.00 0.37 0.00 1.85 (e/k,)/K Fig.3. Lines of minimum standard deviation obtained by fitting steam mixture data to the Stockmayer potential. (a) was obtained by fitting the HE measurements on 11 mixtures of water-non-polar component.(b) was obtained by fitting the HE measurements on two mixtures of water-alkyl chloride. The point of intersection at ElkB = 233 K and 0 = 0.312 is the only pair of potential parameters which fits the measurements on all mixtures. of dipole-induced-dipole interactions was made, it was assumed that the energies were negligible compared with other terms. Again a valley on the ElkB us. 0 standard deviation grid was found and a line was drawn through points of minimum s. This is shown as (b) in fig. 3. Because of the additional combining rule (10) the valley runs in a different direction to curve (a). The standard deviation at the minimum of the valley is 2.5%. At the intersection of curves (a) and (b) the parameters are ElkB = 233 K and c = 0.312, which yield t* = 1.238.These are the only Stockmayer parameters which fit the measurements on both water-non-polar and water-polar mixtures. The uncertaintyC. J . Wormald and N . M. Lancaster 3149 on the parameters clearly depends on the accuracy of the HZ measurements, but it also depends on the choice of potential parameters for chloromethane and chloroethane. Virial coefficients for these substances are less accurate than those for n-alkanes, and there are no isothermal Joule-Thomson coefficients. Values of B calculated from ElkB = 233 K, (T = 0.312 nm and t* = 1.278 are plotted in fig. 1. These are second virial coefficients that water might have in the absence of hydrogen bonding. Also plotted in the figure are B values for CH,F.That B for CH,F is smaller than that obtained for unassociated water is due to the smaller reduced dipole t* = 1.041. The curves are close, and suggest that CH,F is not an unreasonable choice of homomorph for water in the calculation of the term in eqn (1). The collision diameter o = 0.312 nm is bigger than that for water dimer (a = 0.286 nm). As the potential energy of interaction ElkB = 233 K is smaller than that obtained by fitting the Stockmayer potential to water (ElkB = 370 K), this is to be expected. Redetermination of Values of 6 In the above analysis we excluded the H: measurements on mixtures of water with carbon dioxide, ethene, propene or benzene as our earlier treatment showed that there are specific forces between the unlike molecules. The reanalysis of the HE measurements for these mixtures will be done by returning to the procedure originally adopted, using 5 as an adjustable parameter. To see the results of the analysis of these HE values in context the HZ values for all 19 mixtures will be reanalysed this way.B,, and C,,, for water, and their temperature derivatives were calculated from Appendix 1. Kihara or Stockmayer potential parameters were used to calculate B,, and &, for the other component. Third virial coefficients and temperature derivatives were calculated as described above. We adopted the parameters E/kB = 233 K and (T = 0.312 nm for water in its interaction with a component with which it does not hydrogen bond, and we again adopted the combining rules given by eqn (6)--(8) and (10). As before, was adjusted until HZ calculated from eqn (1) agreed with experiment. For each mixture this was done for the measurements at each temperature, at the experimental pressure, and for x = 0.5.The above procedure yielded values of B,, and #y2 which are ca. 5% more negative than those reported earlier, but because third virial coefficients have now been included, are free from the systematic error that neglect of this term previously caused. Results of the recalculation are listed in Appendix 3. Here p is the pressure at which the measurements were made, HE@) is the excess enthalpy at pressure p and x = 0.5, HE($) is the excess enthalpy at p" and x = 0.5. The standard deviation s is on HE(p") and was obtained from the 10 or so measurements made over a range of x from which HE@) was calculated.The value of s allowed the uncertainties dB,, on B,, and d& on #:, to be obtained. Finally, the values of 5 obtained at each temperature are listed. The values of scatter randomly about the mean for each mixture, no temperature dependence is evident. The solid curves drawn in fig. 2 were calculated as described above. Fig. 4 shows our B,, values for water<, to C, n-alkane mixtures compared with those obtained from measurements of the solubility of water in compressed gases. Agreement between the two sets of measurements is good, well within the limits of the combined experimental error. Solid curves in the figure were calculated using values of < given by eqn (9)- Mean values of 5 from Appendix 3, denoted 5" to indicate that they were obtained from experiments, are listed in table 2, where they are compared with values of r" calculated from eqn (9).As eqn (9) was built into the procedure by which the parameters ElkB = 233 K and a = 0.312 nm for water were obtained, the ratio e/r" should be unity for all but the last four mixtures listed. The mean value of the ratio is actually 1.01. For the last four mixtures the ratio is between 1.22 and 1.40. For water-carbon monoxide mixtures Ce/r = 1.1 1 and for water-nitrogen mixtures3150 Hz and B,, for Steam Mixtures i - 50 I - z ,E 1 I: -100 Q -1 50 300 320 340 360 380 400 420 T/K Fig. 4. Cross-term second virial coefficients for mixtures of (H20+C,H,,+,) for n = 1 to 8. The figure shows the agreement between B,, values derived from H: values, and B,, values derived from measurements of the solubility of water in compressed gases.+ , x , B,, values from solubility mea~urernents.~~~ All other B,, values are listed in Appendix 3. 0, H20-CH4, H2GC,H6, H2@C3H8, H2@C4H,0; A, H2w5H,2 ; v7 H2@C6H14 ; 0, H2@C7H16; 0, H2@C8H18' Table 2. Interaction parameters, 5, for use with the combining rule E,, = < ( E , , E ~ ~ ) ~ ' H2 N2 CH4 Ar co C2H6 C3H8 C4H10 CP12 C6H14 C7H16 GH12 co2 CH3Cl C,H5Cl C2H4 'ZH6 C6H6 0.99 0.98 0.99 0.44 0.99 1.05 1.06 0.15 0.99 1.09 1.10 0.16 0.99 1.09 1.11 0.14 0.99 1.02 1.02 0.10 0.96 0.95 0.99 0.06 0.94 0.92 0.97 0.05 0.93 0.94 1.01 0.05 0.92 0.91 0.99 0.05 0.89 0.87 0.98 0.06 0.87 0.88 1.02 0.07 0.84 0.83 1.00 0.09 0.88 0.88 1.00 0.06 1.00 1.00 1.01 0.01 0.99 0.99 0.99 0.01 0.99 1.33 1.35 0.05 0.99 1.21 1.25 0.06 0.93 1.14 1.22 0.04 0.90 1.27 1.40 0.03 93 185 180 153 230 280 342 404 444 466 496 508 428 293 338 314 275 3 30 447 -1 11 18 16 5 -3 -8 2 -3 - 10 7 -1 0 2 -3 109 67 67 162 41 28 29 21 23 18 18 19 22 28 37 46 24 3 3 15 16 13 13 0.0 0.4 0.6 0.8 0.2 - 0.2 - 0.4 0.1 -0.1 - 0.4 0.2 0.0 0.0 0.7 - 1.0 7.3 4.2 5.2 12.5 ~ a Values of tc were calculated from eqn (9), and values of 5" were obtained from an analysis of HE measurements.Ste is the uncertainty on 5" calculated assuming a 2 YO uncertainty on HE. Other quantities are explained in the text.C. J . Wormald and N . M . Lancaster 3151 it is 1.10. To decide if these deviations from unity are significant it is important to estimate the uncertainty on 5". It was therefore assumed that the uncertainty on all HZ measurements was 2%, and an uncertainty St" was calculated as the difference between 5" fitted to the HE measurements and re fitted to values of 1.02H:.As the uncertainty on many of the measurements is < 2 % St" is nearer to being the maximum uncertainty rather than the probable uncertainty. Values of See listed in column 4 of table 2 vary considerably. St" for water-hydrogen mixture is large (0.44) because qb;, for this mixture is unusually small and contributes only ca. 5 % to HE. For water-n-alkane mixtures the contribution of q5:, to HE depends on the ratio 2&2/(q5;1 + q5i2). This results in Sre being minimum for water-propane and water-butane mixtures rather than for water-octane mixtures, for which &, is relatively small because &, for octane is so large.Inspection of the 5" and St" values listed in columns 2 and 4 shows that for the first 15 mixtures re is always smaller than (cc + St"), while for the last four mixtures 5" is clearly greater than (e"+S<'). According to this criterion the values re/<" = 1.10 for water-nitrogen and 1.11 for water-carbon monoxide are not significant. If the uncertainty on the HE measurements is 1 O/O, rather than 2 O/O, Sl" is halved, and for both mixtures c" > (c"+Sce). As N, and CO are isoelectronic, and both molecules possess large quadrupole moments, it could be that the values of c"/c" of around 1.1 reflect quadrupole-quadrupole and quadrupole-dipole coupling with water. There is no evidence for a specific interaction between water and carbon monoxide as there is for water and carbon dioxide.The increase Ac12 in potential energy due to specific interactions is given by1' A&,,/k, = (re - c") ( E ~ E,);. AEl,/kB is listed in column 6. The uncertainty SE12/k, is given by 6&12/kB = 6ce(&1&2)'. (20) In column 8 we list the ratio Ahe,,/Se,,. Only when AcI2 >&,, can any significance be attached to the calculated increase in potential energy due to specific interaction. The only significant values of A&,,/k, occur for mixtures of water with ethene, propene, carbon dioxide or benzene. Our B,, values for water-carbon dioxide confirm those obtained by Coan and King5 from solubility measurements. Coan and King showed that the strength of the interaction between water and carbon dioxide molecules could not be accounted for by adding dipole-induced-dipole or dipole-quadrupole terms to the pair potential, and suggested that a weak charge transfer, or donor-acceptor interaction is present.We suggest that an interaction of this kind will always occur when electron donor molecules such as water, ethers, ketones or alcohols interact with systems containing n electrons where there are unfilled orbitals. The interaction between water and benzene is particularly strong. Table 2 shows that A&,,/kB for water-benzene is 1.5 times larger than that for waterxarbon dioxide, and 2.5 times larger than that for water-ethene or water-propene. Conclusion Prior to this work no satisfactory method for the calculation of cross-term second virial coefficients for mixtures containing steam was available.The method proposed is very simple. Lennard-Jones, Kihara or Stockmayer potentials are fitted to second virial coefficients of the fluid mixed with steam. The parameters &/kB = 233 K, 0 = 0.312 nm and t* = 1.238 of the Stockmayer potential are used for water. Cross-term parameters are calculated using the usual combining rules, eqn (6)-(8), together with values of calculated from eqn (9). The method works for mixtures in which there are no specific interactions with water.3152 HZ and B,, for Steam Mixtures A method for calculating third virial coefficients of mixtures containing water is also proposed. Although the method is unproven at this stage it will be shown that it allows thermodynamic properties of mixtures containing steam to be calculated with good accuracy up to pressures around 5 MPa.Appendix 1 Second, third and fourth virial coefficients for steam consistent with ref. (7). The fourth virial coefficients are unlikely to be correct, but are useful for the calculation of thermodynamic properties at moderate densities from the virial equation of state. The coefficients were computed by J. S. Gallagher and are published with permission. ~~ ~~ T / K B/cm3 mol-' C/cm6 molP2 D/cmg m ~ l - ~ 273.15 298.15 323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 623.15 673.15 723.15 773.15 873.15 973.15 1073.15 1173.15 1273.15 1373.15 1473.15 - 1788 - 1153 - 802 - 590 - 453 - 359 - 292 - 242 - 204 - 174 - 150 - 131 -115 - 90.6 - 72.6 - 59.2 -48.7 -33.8 -23.7 - 16.6 -11.2 - 7.07 - 3.8 - 1.1 -4.024 x 10' - 1.992 x 10' - 1.026 x 10' -5.460 x lo5 -2.980 x lo5 - 1.660 x lo5 - 9.402 x lo4 -3.125 x lo4 - 1.074 x lo4 -6.361 x lo3 - 5.394 x 104 - 1 x 104 - 3797 - 1395 - 552 - 195 - 32 259 487 68 1 844 94 1 973 1006 6.137 x lo8 3.031 x lo8 1.562 x 10' 8.353 x lo7 4.612 x lo7 2.625 x lo7 1.539 x lo7 9.320 x 10' 5.835 x 10' 3.800 x 10' 2.584 x lo6 1.830 x 10' 1.356 x 10' 8.361 x lo5 5.671 x lo5 4 .0 3 4 ~ lo5 2.865 x lo5 1.169 x lo5 0 -7.601 x lo4 - 1.637 x lo5 - 1.812 x lo5 - 1.286 x 105 - I .929 x 105C. J . Worrnald and N. M. Lancaster 3153 Appendix 2 Experimental excess molar enthalpies HE of {xH,O + (1 - x)CH,Cl)(g) and (xH,O + (1 -x)C,H,Cl)(g). HE(p) was measured at pressure p.H:(po, 0.5) was calculated at p" = 101.325 kPa and x = 0.5 using eqn (1) as described in the text. B,, and $y2 values, derived from the measurements, are listed in Appendix 3. P HZ(p) H:(p", 0.5) P HZ(p) H:(P", 0.5) x /kPa /J mol-' /J mol-' x /kPa /Jmol-' /Jmol-' 0.469 0.504 0.506 0.510 0.524 0.459 0.462 0.483 0.496 0.534 0.475 0.490 0.509 0.514 0.534 0.470 0.475 0.49 1 0.415 0.450 0.488 0.493 0.515 0.472 0.479 0.496 0.525 0.530 0.449 0.493 0.526 0.550 0.564 0.493 0.495 0.503 T = 363.2 K 62.8 30.8 62.6 29.9 62.8 30.2 63.2 29.2 63.2 30.2 63.7 23.3 63.7 21.7 63.7 23.3 63.7 21.9 63.8 23.1 64.0 17.7 64.0 18.2 61.8 18.0 61.7 17.0 61.7 17.2 62.1 14.1 61.7 14.1 61.6 13.4 T = 383.2 K T = 403.2 K T = 423.2 K T = 363.2 K 54.2 28.3 54.0 29.3 54.1 30.2 58.2 33.2 58.3 32.6 63.7 26.7 63.7 27.2 63.7 26.6 63.7 26.7 63.6 27.3 63.9 19.6 63.6 20.7 63.5 21.5 63.6 21.1 63.6 21.3 62.1 17.4 62.1 15.9 62.1 15.7 T = 383.2 K T = 403.2 K T = 423.2 K {xH,O + (1 - x)CH,Cl) 51.6 49.9 50.4 48.3 50.2 38.3 35.7 38.0 35.7 37.9 28.6 29.4 30.2 28.5 28.9 23.5 23.5 22.3 0.469 0.472 0.498 0.499 0.522 0.457 0.478 0.484 0.523 0.531 0.488 0.497 0.509 0.5 15 0.532 0.519 0.539 {xH,O + (1 - x)C,H,Cl) T = 373.2 K 63.9 25.5 63.7 26.5 63.9 26.2 63.7 26.6 63.9 26.7 60.5 18.3 60.0 19.3 60.4 18.8 60.0 19.3 60.4 18.8 63.5 15.9 63.2 16.3 63.2 16.6 63.3 16.0 63.1 15.7 61.6 13.7 61.5 14.3 T = 393.2 K T = 413.2 K T = 423.2 K 56.4 57.6 58.6 59.7 58.6 43.5 44.4 43.3 43.5 44.7 32.0 33.6 34.9 34.6 35.2 28.7 26.3 26.0 0.447 0.500 0.5 18 0.527 0.537 0.437 0.468 0.473 0.494 0.546 0.490 0.491 0.505 0.512 0.524 0.514 0.538 T = 373.2 K 55.1 26.6 54.9 26.2 54.8 27.3 54.9 26.4 54.9 25.9 66.0 24.5 65.2 25.4 65.2 24.7 65.9 25.0 64.3 22.5 61.0 18.9 61.1 18.0 61.1 19.1 61.1 19.3 61 .O 19.4 62.1 17.2 62.1 17.0 T = 393.2 K T = 413.2 K T = 423.2 K 41.7 43.4 42.7' 43.5 43.7 31.6 33.4 32.4 33.6 32.5 25.9 26.6 27.1 26.0 25.7 23.0 24.1 51.0 50.0 52.1 50.4 49.7 38.9 40.3 39.2 39.1 36.6 31.9 30.3 32.2 32.5 32.8 28.5 28.3w ul Appendix 3 + Excess molar enthalpies of mixtures containing water.The experimental excess enthalpy HZ@) was measured at pressure p and is the mean of 10 or so measurements made over a range of composition and interpolated to x = 0.5. H:(po) at po = 101.325 kPa was calculated from H:(p). s is the uncertainty on Hz(p”). PO+” = x, x2(2+,, - - $22) and allows easy recalculation of B12.373.2 378.2 383.2 393.2 403.2 413.2 423.2 373.2 383.2 393.2 403.2 413.2 423.2 373.2 380.2 390.2 400.2 410.2 423.2 363.5 375.2 393.2 403.2 75 75 75 75 75 75 75 101 101 101 101 101 101 77 101 101 101 101 101 46 63 80 80 54.6 51.7 49.3 44.0 39.0 35.8 32.2 53.7 47.5 41.5 37.5 33.7 30.7 53.5 48.4 42.9 38.0 34.9 30.6 59.5 51.2 41.7 36.5 55.2 52.2 49.7 44.3 39.3 36.0 32.4 53.7 47.5 41.5 37.5 33.7 30.7 54.0 48.4 42.9 38.0 34.9 30.6 61.1 52.0 42.0 36.7 (0.5 H20+0.5 H,} (g) 51.6 0.6 - 35 49.1 1 .o - 25 47.0 0.9 -11 42.2 0.7 -8 37.5 0.9 - 16 34.6 0.4 -2 31.3 0.8 -7 (0.5 H20+0.5 Ar}(g) 50.2 1.6 - 93 44.8 0.6 - 83 39.4 1.2 -91 35.8 0.6 - 77 32.4 1.3 - 72 29.6 1 .o - 63 (0.5 H 2 0 + 0.5 N2}(g) 50.5 0.6 - 80 45.5 0.5 - 96 40.6 0.7 - 88 36.2 0.7 - 87 33.5 1 .o - 65 29.5 1.2 - 59 (0.5 H20+0.5 CO}(g) 56.5 0.7 - 100 48.7 2.0 - 96 39.8 0.9 - 79 35.0 1.2 - 89 12 19 17 13 18 8 15 30 12 20 14 28 16 12 12 15 14 20 24 16 24 16 22 -3 1 7 8 5 11 9 - 24 - 20 - 24 - 18 - 16 - 12 - 17 - 24 - 20 - 20 - 10 -8 - 25 - 23 - 16 - 20 6 10 8 6 9 4 7 7 3 5 4 7 4 3 3 3 3 4 4 7 9 7 8 1.3 12 1.149 0.893 0.855 1.041 0.757 0.884 1.080 1.039 1.122 1.045 1.037 0.990 1.039 1.169 1.144 1.164 1.023 1.008 1.093 1.100 1.034 1.136(0.5 H20+0.5 CH,j(g) 49.5 0.7 - 134 44.8 0.5 - 108 39.7 1 .o - 109 36.0 0.5 - 97 32.1 1 .o - 100 29.5 0.7 - 88 (0.5 H,O + 0.5 C,H,)(g) 60.4 1.3 - 202 52.9 1.9 - 198 46.9 1.1 - 198 42.5 1.1 - 177 (0.5 H 2 0 + 0.5 C,H,)(g) 66.8 1.3 - 286 59.4 1.4 - 266 54.7 0.9 - 230 48.7 1.2 -231 (0.5 H20+0.5 C,H,,j(g) 81.3 1.2 - 340 72.2 1.5 - 334 64.4 0.4 -331 58.6 0.9 -310 (0.5 H,O+0.5 C,H,,j(g) 105.1 2.6 - 390 93.3 2.1 - 396 84.9 2.4 - 368 77.2 2.7 - 353 60.3 1.1 - 298 (0.5 H 2 0 + 0.5 C,H,,)(g) 136.9 3 .O -446 124.4 2.4 - 408 111.8 1.6 -414 103.2 1.3 - 370 81.1 1.5 -314 373.2 75 383.2 75 393.2 75 403.2 75 41 3.2 75 423.2 75 52.4 47.1 41.5 37.4 33.2 30.4 53.0 47.5 41.8 37.7 33.4 30.6 14 10 22 11 20 14 - 39 - 28, - 28 - 23 - 25 - 20 7 5 11 6 9 8 1.092 0.991 1.021 0.982 1.027 0.976 363.2 60 373.6 65 383.2 71 393.3 74 37.3 35.3 34.1 32.2 64.9 56.3 49.5 44.6 26 36 21 22 -61 - 59 - 59 - 50 10 15 9 9 0.935 0.948 0.974 0.937 0.948 0.935 0.910 0.920 0.956 0.946 9 4 0.883 3 5 % 0.936 R 3 is 363.2 61 373.6 61 383.2 74 393.3 73 41.8 37.0 41.4 36.2 71.3 62.8 57.4 50.8 25 27 17 23 - 90 - 82 - 67 - 68 10 11 7 9 363.2 61 373.2 72 383.3 71 393.3 72 50.7 53.2 46.6 42.8 86.2 76.1 67.4 60.9 24 29 8 17 - 107 - 105 - 104 - 96 9 11 3 7 - 121 - 123 -113 - 107 - 86 19 15 17 19 8 0.892 0.924 0.913 0.915 0.899 363.2 63 373.2 76 383.2 67 393.2 65 423.2 101 110.5 97.9 88.4 80.0 62.1 111.8 98.6 89.1 80.5 62.1 50 36 46 52 21 363.2 51 373.2 76 383.2 76 393.2 70 423.2 101 145.6 132.4 118.1 108.3 84.2 148.2 133.4 118.8 109.0 84.2 57 45 30 25 29 - 135 - 121 - 123 - 107 - 86 21 17 11 9 11 0.874 0.858 0.887 0.858 0.846 w wl wl 1Appendix 3 (cont.) ~ (P> H%P) H3P0) PO$" s( HE) $12 W12) 4 2 W12) X T/K /kPa /J mol-1 /J mol-' /J mol-' /J mol-' /cm3 mol-' /cm3 mol-' /cm3 mol-' /cm3 mol-' J m 363.2 373.2 383.2 393.2 423.2 363.2 373.2 383.2 393.2 423.2 363.2 373.2 382.8 393.3 363.2 373.2 383.2 393.2 403.2 413.2 423.2 51 75 68 69 101 30 34 55 67 101 60 64 65 65 63 64 64 60 63 63 62 205.2 185.8 163.4 151.3 116.0 290.1 259.5 233.2 212.0 160.1 73.7 71.9 65.7 59.6 30.1 26.4 22.8 18.9 17.7 16.0 14.0 210.8 188.0 165.4 152.7 116.0 308.7 272.0 239.7 215.6 160.1 129.2 117.1 104.8 94.8 50.1 43 .O 37.1 32.7 29.1 26.3 23.3 (0.5 H20 + 0.5 C,H,,}(g) 187.3 3.2 - 525 169.7 3.6 - 487 151.1 3.3 - 520 141.2 1.9 - 426 109.8 1.8 - 371 (0.5 H20 + 0.5 C,H,,}(g) 257.1 3.4 - 520 232.4 2.4 - 495 209.0 1.9 -513 191.3 1.8 - 477 147.3 1.4 -447 118.4 0.8 - 459 108.6 0.9 -41 1 98.1 1.3 -413 89.5 1.8 - 393 46.0 1.2 - 706 39.9 0.8 - 660 34.7 1.3 -621 30.8 0.8 - 577 27.7 0.7 - 536 25.1 0.6 - 496 22.3 0.6 - 472 (0.5 H20 + 0.5 C,H12}(g) (0.5 H20 + 0.5 CH,Cl}(g) 60 66 62 36 34 63 45 35 34 27 16 17 24 34 22 15 25 16 13 11 13 - 158 - 144 - 156 - 122 - 101 - 150 - 141 - 147 - 134 - 123 - 143 - 125 - 126 -118 - 202 - 190 - 180 - 168 - 157 - 146 - 139 21 24 22 13 13 22 16 13 12 10 6 7 9 13 6 4 7 4 4 3 4 2 0.883 Q.0.873 0.927 0.859 0.860 0.807 W N 0.808 % 0.845 g 0.836 5 0.870 2 0.886 0.856 0.88 1 0.88 1 1.002 1.005 1.009 1.007 1.004 0.999 1.003363.2 373.2 383.2 393.2 403.2 413.2 423.2 363.4 375.2 383.2 392.6 363.2 373.6 383.2 393.3 363.2 373.2 383.2 393.2 363.2 373.2 383.2 393.2 56 31.1 55 26.6 64 27.1 65 24.4 64 21.1 61 19.0 62 16.6 45 54.0 55 46.5 80 42.5 83 37.5 61 33.7 65 32.5 75 32.7 73 27.8 59 36.0 69 37.2 71 33.7 69 29.5 60 58.3 64 55.7 62 48.7 61 42.6 58.2 50.6 43.9 38.8 34.1 32.0 27.6 55.6 47.4 43.0 37.7 57.8 51.5 44.9 39.2 63.8 55.8 48.9 44.0 101.6 90.5 81.5 72.4 (0.5 H,O + 0.5 C,H,Cl)(g) 53.9 1.2 - 762 47.3 1 .o - 829 41.3 0.6 - 779 36.8 1.4 - 722 32.5 1.3 - 682 30.7 1 .o - 609 26.6 1.3 - 596 (0.5 H,O + 0.5 CO,}(g) 51.3 3.4 -317 44.3 1.6 - 287 40.3 1.6 - 270 35.7 2.0 - 262 (0.5 H,O + 0.5 C,H,}(g) 53.4 1.1 - 295 48.2 0.7 - 247 42.3 0.9 - 247 37.1 0.7 - 243 (0.5 H,O + 0.5 C,H,)(g) 59.5 1.1 - 387 52.4 1.1 - 368 46.4 1 .o - 355 42.0 0.8 - 328 (0.5 H,O 4- 0.5 C,H,}(g) 94.2 1.3 - 855 84.6 1 .o - 802 76.8 1.8 - 747 68.6 1.1 - 726 24 18 12 26 25 19 25 66 31 30 39 21 13 18 14 21 22 18 15 22 18 32 19 -221 - 234 - 222 - 208 - 198 - 178 - 175 - 105 - 95 - 88 - 86 - 99 -81 -81 - 79 - 127 - 120 -115 - 105 - 285 - 267 - 249 - 242 6 5 3 7 7 5 7 22 10 10 13 8 5 7 5 8 8 7 6 7 6 11 7 0.988 0.988 0.992 0.99 1 0.996 0.978 0.994 1.359 1.329 1.313 1.325 1.263 1.171 1.202 1.222 1.139 1.139 1.147 1.125 1.273 1.267 1.256 1.2713158 HE and B,, for Steam Mixtures References 1 Z.Slanina, Int. J. Thermophys., 1987, 8, 387. 2 P. A. Kollman, J. Am. Chem. Soc., 1977, 99, 4875. 3 H. Hideaki and K. Morokuma, J. Am. Chem. SOC., 1977. 99, 1316. 4 M. Rigby and J. M. Prausnitz, J. Phys. Chem., 1968,72, 330. 5 C. R. Coan and A. D. King, J. Am. Chem. SOC., 1971,93, 1857. 6 E. J. LeFevre, M. R. Nightingale and J. Rose, J. Mech. Eng. Sci., 1975, 17, 243. 7 L. Haar, J. S. Gallagher and G. S. Kell, NBSINRC Steam Tables (Hemisphere Publishing Corp., New 8 J. S. Gallagher, personal communication. 9 C. J. Wormald, J. Chem. Thermodyn., 1977, 9, 901. York, 1984). 10 G. R. Smith, A. J. Sellars, T. K. Yerlett and C. J. Wormald, J. Chem. Thermodyn., 1983, 15, 29. 11 P. Richards, C. J. Wormald and T. K. Yerlett, J. Chem. Thermodyn., 1981, 13, 623. 12 P. Richards and C. J. Wormald, 2. Phys. Chem. N.F., 1981, 128, 35. 13 G. R. Smith and C. J. Wormald, J. Chem. Thermodyn., 1984, 16, 543. 14 N. M. Lancaster and C. J. Wormald, J. Chem. Thermodyn., 1985, 17, 295. 15 N. M. Lancaster and C. J. Wormald, J. Chem. Thermodyn., 1986, 18, 545. 16 G. R. Smith, M. J. Fahy and C. J. Wormald, J. Chem. Thermodyn., 1984, 16, 825. 17 C. J. Wormald and N. M. Lancaster, J. Chem. Thermodyn., 1985, 17, 903. 18 C. J. Wormald and C. N. Colling, J. Chem. Thermodyn., 1983, 15, 725. 19 C. J. Wormald and C. N. Colling, J. Chem. Thermodyn., 1985, 17, 437. 20 C. J. Wormald, N. M. Lancaster and A. J. Sellars, J. Chem. Thermodyn., 1986, 18, 135. 21 C. J. Wormald, AIChE J., 1984, 30, 386. 22 N. M. Lancaster and C. J. Wormald, J. Chem. Thermodyn., 1987, 19, 89. 23 N. M. Lancaster and C. J. Wormald J. Chem. Thermodyn., 1987, 19, 1001. 24 C. J. Wormald, C. N. Colling, N. M. Lancaster and A. J. Sellars, Gas Processors Association Research 25 J. H. Dymond and E. B. Smith, The Virial Coeficients of Pure Gases and Mixtures (Clarendon Press, 26 E. M. Dantzler, C. M. Knobler and M. L. Windsor, J. Phys. Chem., 1968, 72, 676. 27 D. J. Hutchings, E. J. Lewis and C. J. Wormald, J. Chem. Thermodyn., 1978, 10, 559. 28 C. J. Wormald, E. J. Lewis and D. J. Hutchings, .I. Chem. Thermodyn., 1979, 11, 1. 29 G. H. Hudson and J. C. McCoubrey, Trans. Faraday Soc., 1960, 56, 761. 30 B. E. F. Fender and G. D. Halsey, J. Chem. Phys., 1962, 36, 1881. 31 J. D. Hirschfelder, C. F. Curtis and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New 32 P. L. Chueh and J. M. Prausnitz, AIChE J., 1967, 13, 896. 33 H. Orbey and J. H. Vera, AIChE J., 1983, 29, 107. 34 C. J. Wormald, N. M. Lancaster and N. Colling, J. Chem. Soc., Faraday Trans. 1, 1988, 84, in Paper 7/2218; Receiued 18th December, 1987 Report 68, Tulsa, Oklahoma, 1983. Oxford, 1980). York, 1964). press.

ISSN:0300-9599    

DOI:10.1039/F19888403141

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1988, 84(9), 3159-3168 Excess Molar Enthalpies of {xH,O + (1 - x)C,H,,}(g) up to 698.2 K and 14.0 MPa Neil M. Lancaster and Christopher J. Wormald* School of Chemistry, University of Bristol, Bristol BS8 ITS Excess molar enthalpies, HZ, of (xH,O + (1 - x)C,H,,} have been measured at temperatures from 448.2 to 698.2 K and at pressures up to 14.0 MPa. HZ is defined as the residual enthalpy of the mixture minus the mole-fraction- weighted mean of the pure component residual enthalpies. The residual enthalpy HZ of n-pentane was calculated from virial coefficients B and C, and H: of water was calculated using coefficients B, C and D, which are consistent with the NBS/NRC steam tables. H: for the mixture was calculated from cross-term B,, values obtained by combining Stockmayer parameters, ElkB = 233 K, CT = 0.312 nm and t* = 1.238 for water with Kihara parameters for n-pentane, and cross-terms C,,, and C,,, obtained from the Orbey-Vera third virial coefficient corresponding states correlation using fluoromethane parameters in place of those for water in non- associative interactions.HZ values calculated from the virial equation of state are in good agreement with experiment. In the previous paper1 low-pressure measurements of the excess molar enthalpy HE of 17 binary mixtures containing water which had been reported in the literature were reanalysed. When the measurements were made there was no way of calculating the contribution to HE values from third virial coefficients, and this term was neglected, introducing a small but systematic error into derived cross-term second virial coefficients B12.Since 1975, when work on steam mixtures was begun, there have been two advances which make possible an improved analysis. In 1983 Orbey and Vera2 published a corresponding-states correlation for third virial coefficients of non-polar and weakly polar fluids which uses T", p" and Pitzer's acentric factor o as parameters. In 1984 Haar et aL3 published new steam tables, based on a multiproperty analysis of steam, and a new equation of state. Gallagher4 computed second, third and fourth virial coefficients B, C and D for steam which are consistent with the low-density volumetric and thermal properties published in the tables. The B values are of high accuracy and the C coefficients are probably the best available, The D values are unlikely to be correct, but nevertheless have value as parameters which, as they are consistent with the B and C values, can be used to generate accurate low-density steam properties from the virial equation of state.In the previous paper1 we suggested combining rules for use with the Orbey-Vera correlation which would allow the calculation of mixture properties. We also suggested that cross-term C values for mixtures containing water can be obtained using the critical parameters of CH,F in place of water parameters in the calculation of water-non-polar fluid interaction terms. New measurements of HE for {xH,O + (1 - x)CH,Cl}(g) and {xH,O + (1 - x) x C,H,Cl)(g) mixtures at pressures ca. 60 kPa and at temperatures between 363.2 and 423.2 K were reported previous1y.l Measurements on these polar fluid mixtures were combined with measurements on 1 1 water-non-polar fluid mixtures5-10 in a simultaneous analysis.It was found that B12 values for water in its interaction with polar and non- polar fluids could be calculated using Stockmayer, Lennard- Jones or Kihara parameters 31593160 H: for Water-n- Pentane Mixtures Table 1. Excess molar enthalpies HZ of (0.5H20 + OSC,H,,)(g) measured over a range of temperatures and pressures PI H 3 P I H2I PI HlY MPa J mol-' MPa J mol-' MPa J mol-' T = 448.2 K 0.49 287 0.62 382 0.75 468 T = 473.2 K 0.49 237 0.77 385 1.03 557 1.05 555 1.17 655 T = 498.2 K 0.83 346 1.50 700 2.03 1046 T = 523.2 K 0.76 272 1.44 547 2.22 923 2.81 1316 3.67 1915 T = 548.2 K 2.41 876 3.22 1223 3.79 1550 5.01 2327 5.44 2686 T = 573.2 K 0.66 176 0.88 238 2.13 629 2.76 832 2.96 915 3.64 1216 4.87 1738 4.88 1758 5.01 1844 5.64 2171 5.95 2321 6.72 2690 7.05 2847 8.01 3366 8.02 3407 T = 598.2 K 3.29 875 3.36 950 4.12 1214 4.15 1078 4.76 1443 5.04 1420 5.50 1665 6.31 1995 6.55 2095 7.22 2400 8.10 2727 8.72 2916 9.48 3187 10.0 3355 10.6 3528 T = 648.2 K 0.81 155 1.89 371 2.35 482 3.76 805 4.58 982 5.01 1104 5.53 1202 6.26 1367 6.97 1562 7.07 1645 7.76 1772 7.94 1774 8.93 2034 10.4 2322 11.2 2466 T = 698.2 K 3.11 510 5.01 868 5.49 949 5.74 979 6.38 1136 6.86 1205 7.52 1303 7.89 1389 8.35 1507 8.83 1551 9.93 1731 11.1 1903 11.8 1936 12.1 2107 14.0 2258 for the polar or non-polar substance, the Stockmayer parameters c / k B = 233 K, 0 = 0.312 nm and t* = 1.238 for water, and the combining rules where It has been shown'' that for hydrocarbon mixtures, eqn (1) and (2) give B,, values in agreement with experiment.It has also been shown7 that B,, values calculated using Stockmayer parameters for CH,F in place of those for water agree reasonably well with those for water-non-polar fluid mixtures obtained experimentally. When we reanalysedl our low-pressure HE values we produced no evidence to support our choice of combining rules for the calculation of cross-term C values using CH,F as a homomorph for water in non-associative interactions. As the contribution of third virials to HE values measured at pressures close to atmospheric is ca. 1 YO theseN . M . Lancaster and C.J. Wormald 3161 0.5 0 0 8 12 p / W a X 1 Fig. 1. (a) Excess molar enthalpies HZ of (0.5H20 + O.SC,H,,)(g) plotted against pressure. (b) HZ of {xH,O + (1 - x)C,H,,}(g) at pressures around 4.5 MPa plotted against mole fraction, x. 0, Tables 1 and 2; (-) calculated as described in the text.3162 H f for Water-n-Pentane Mixtures Table 2. Excess molar enthalpies H: (in J mol-l) of {xH,O+(l -x)C,H,,}(g) measured at four temperatures at pressures around 4.5 MPa T = 573.2 K T = 598.2 K T = 698.2 K T = 548.2 K p = 4.46 MPa p = 4.50 MPa p = 4.40 MPa p = 4.46 MPa 0.270 1311 0.408 1240 0.273 642 0.252 1609 0.390 1877 0.397 1506 0.458 1265 0.388 717 0.498 1877 0.497 1538 0.602 1190 0.496 751 0.600 1476 0.699 1029 0.602 705 0.611 1809 0.719 1535 0.685 1304 0.798 757 0.689 627 measurements provide no test of proposed calculation methods; C terms become significant only at high pressure.Several binary mixtures containing water have been studied at temperatures up to 698.2 K and pressures up to 15 MPa. These include water with hydrogen, l2 nitrogen, l3 carbon monoxide,14 carbon dioxide,'* C, to C, n-alkanes15-18 or ethene.16 Most of the measurements are accurate to 2%. The measurements were fitted by empirical equations which were consistent with what was known about second virial coefficients. In the absence of third virials this was the best that could be done. The choice of mixture to test our suggested method for the calculation of third virial contributions to Ht needs to be made with care. Clearly water+arbon dioxide and water-ethene mixtures, in which there are specific interactions between the unlike molecules, are unsuitable.In water-methane and water-ethane mixtures C for water is much larger than the other third virial terms, and these mixtures are not the best choice. Our calculations suggest that water-n-heptane or water-n-octane mixtures would not be a good choice, as C for the hydrocarbon is likely to swamp the other terms. A mixture for which the C terms for the pure components are comparable is water-n-pentane, and we will show that H z values for this system provide a good test of the proposed method for obtaining cross-term third virials. Experimental The apparatus was the same as previously described.13 The n-pentane was at least 99.5 mol YO n-C5H12, i-C,H,, being the main impurity.Steam was generated from ordinary distilled water. The measurements were made at nine temperatures between 448.2 and 698.2 K at pressures up to 14.0 MPa. Most of the measurements were made at x = 0.5, but the composition dependence of HE was investigated under four selected conditions. Results of the measurements at x = 0.5 are listed in table 1 and plotted in fig. 1 (a). Measurements made over a range of composition are listed in table 2 and are plotted in fig. 1 (b). The overall accuracy is ca. 2 YO. Calculation of HE from the Virial Equation of State HE was previously related to B and C and their temperature derivatives by an equation in powers of the pre~sure,~ but when the equation is extended to include higher coefficients a cumbersome form is obtained.When HE is expressed as a series in powers of the density, the equation is more compact. The residual enthalpy P ( V , T) of a pure fluid can be written H*(V, T) = JI [T(%))-p]dV+pV-RT (3)N. M. Lancaster and C. J. Wormald 3163 Table 3. Coefficients of eqn (14) fitted to Gallagher's virial coefficients B, C and D for steam,4 with exponents of the coefficient in parentheses 2.7522 (1) -4.3051 (4) -9.5677 (1) -2.3180 (5) -9.5393 (1) -9.2759 (4) - 3.7940 (3) -2.4401 (0) -4.8033 (2) -3.3858 (1) 1.5853 (5) 2.6460 (1) 1.8416 (5) 7.4819 (- 1) 2.9713 (4) 6.9959 (- 1) 4.4306 (5) - 1.6063 (6) 5.7364 (5) - 1.0675 (6) 3.0574 (5) 1.1700 (6) 4.6556 (4) 1.1075 (5) Using the virial equation of state truncated after the fourth term we obtain H* 1 ( dB) 1 ( TdC) 1 ( TdD) RT V dT V 2 2 d T V3 3 dT ' -=- BAT-+- C---+- D - - - (4) For a binary mixture of components 1 and 2 we define HZ by H t = H*( V, T, X) - X, H:( 5, T) - X, e( G, T) (6) and 4 are molar volumes of the mixture and pure components at pressure (7) dB dT where V, p.We define the quantities #O=B-T- TdC 2 dT v/ = c--- TdD = D - - - 3 dT' Substitution into eqn (6) gives (9) Here #O, w and A are properties of the mixture given by #O = 4 Kl+ 2x1 x2 &2 + 4 &2 v = 4 vlll + 3x?x2 vl12 + 3x1 xi vlz2 + 4 vZz2 2 = xi A,,,, + 4x: x2 A,,,, + 6x: xi iz,,,, + 4x1 x A2221 + xi A,,,,. (1 1) (12) (13) Similar equations were used to calculate the coefficients B, C and D of the mixture. In a previous publication1 we listed Gallagher's second, third and fourth virial coefficients for steam.These coefficients are fitted by the equation 7 A,/(cm3 mol-')fl-' = a,,i( 1000/T)t i-0 where A, is the virial coefficient and n = 2, 3 or 4. Coefficients a,,t are listed in table 3. Differentiation of eqn (14) yielded the derivatives # O , w and A.3164 HE for Water-n-Pentane Mixtures Calculation of Cross-term Third Virial Coefficients Pure-component and cross-term second virial coefficients were calculated as described previously. Hydrocarbon third virials and cross-terms were obtained from the corresponding states correlation proposed by Orbey and Vera2 where T = (T/Tc) and As the correlation uses Pitzer's acentric factor w it can be applied more widely than the correlation of Chueh and Prausnitz," for which the parameter d must be obtained by fitting to known third virial coefficients.Cross-term third virial coefficients C,, are difficult to predict. Studies by Strogryn2' show that no simple approximation is entirely satisfactory, even for simple non-polar molecules. Orentlicher and Prausnitz21 suggested a useful approximation, which in its simplest form can be written C ( T ) = 0.01407 + 0.02432TF2.' -0.003 13T~".~ C ( T,) = - 0.026 76 + 0.017 7 0 T ~ ' * ~ + 0.040T,3.0 - 0.003 - 0.002 28 TK10e5. C i j k = (cij Cik cjk)'. (16) Orbey and Vera2 followed the same approach. As there are obvious problems when any one of the terms in parentheses becomes negative we will not consider this equation further. In the absence of information about cross-term third virials an approximation that might be used is (17) This equation is similar to the Lewis and Randall rule for cross-term second virial coefficients.We suggest that cross-term third virials can be obtained from the Orbey-Vera correlation using pseudo-critical parameters calculated using the equations c112 = $Cl,l+ 5 c 2 2 2 ; c 1 2 2 = 5Clll + g c 2 2 2 - T:jk = (TFj T:k)i (18) Vtjk = [( VFj)i + ( Vj"k); + ( V:k)4]3/27 (19) cjk = ZFjk RT&/ (20) where Subscripts i, j and k in these equations take the values either 1 or 2. Eqn (22) is due to Pitzer et aZ.,23 and was obtained by plotting the critical compressibility factor Z" for a number of hydrocarbons and slightly polar substances against w. Pseudo-binary interaction parameters were calculated from the equations a 1 2 = (a1 +02)/2' (25) ( was calculated from eqn (2). Cross-term third virials for water-pentane mixtures calculated using the above equations are too big, as are cross-terms B,, coefficients for all mixtures containing water calculated using any corresponding-states correlation for second virial coefficients.It was shown previously' that the second virial coefficient that water might have in the absence of hydrogen bonding is close to that for CH3F. This homomorph has the sameN. M. Lancaster and C. J. Wormald 3165 dipole moment (1.85 D) as water, but a smaller reduced dipole. We now make the assumption that when water interacts with a second molecule with which it does not associate, the interaction is assumed to be that expected between CH3F and the second molecule, calculated on a corresponding-states basis.The critical parameters of CH,F are assumed to be those that unassociated water might have, and we use these parameters (T" = 318 K, pc = 5.87 MPa, V" = 124 cm3 mol-', cu = 0.19) in place of those for ordinary water (T" = 647.3 K, pc = 22.05 MPa, Y c = 55.5 cm3 mol-l, cu = 0.344). When CH3F parameters are combined with those for n-pentane, or for any non- polar substance, and used in second virial coefficient corresponding-states correlations, good values of B,, are obtained. It will be shown that the critical parameters for CH3F are a good choice of pseudo-critical parameters for steam, but they are not unique, nor are they necessarily the best. The steam pseudo-critical parameters were used for the calculation of the cross-terms relating to the interaction of a non-associating pair of molecules.For example when eqn (23)-(25) were used to calculate C,,,, which corresponds to the interaction of two water molecules and one pentane molecule, T;, was that for water, while T;, and T i , were calculated by combining n-pentane and CH3F parameters. Comparison with Experiment We will compare our results with eqn (10) in such a way as to show the effect of making different approximations in the third virial coefficient mixture terms. To obtain the best values of the residual enthalpy of steam and n-pentane we will calculate the q5' and y terms for both these fluids and include them in eqn (10). For the moment we will ignore what little is known about the D and A terms and set these equal to zero. We shall approximate the C and y mixture cross-terms firstly by setting them to zero, secondly by eqn (17) and lastly by the Orbey-Vera correlation as described above.To facilitate comparison with experiment we will focus on the two isotherms at 598.2 and 698.2 K, as these extend to higher pressures than isotherms at lower temperatures. The isotherms are plotted in fig. 2(a) and again in fig. 2(b) in the form of graphs of (HZ/p) against p . It has been shown13 that the intercepts of these graphs are related to values of #' by the equation and this provides a straightforward test of the q5' terms. B,, and for steam were calculated from eqn (14). B,, and &, for n-pentane were calculated from- the Kihara potential with the parameters &/kB = 845 K, a = 0.1 13 1 nm and Q = 0.5030 nm which fit class second virial coefficients. Cross-terms B,, and y:, values were obtained by combining Kihara parameters for n-pentane with the Stockmayer parameters &/kB = 233 K, Q = 0.312 nm and t* = 1.238 for water' using eqn (1) and (2) together with the usual arithmetic mean rules for a12 and o,,.C,,, and ylll for steam were again calculated from the polynomial equations fitted to Gallagher's4 coefficients, while C,,, and y,,, for n-pentane were calculated from the Orbey-Vera correlation. Values of HZ/p calculated by setting Cl12, C12,, yl12 and y12, to zero are shown by the long-dashed curves in fig. 2(a). Although the curves fail to fit the experimental results the intercepts are clearly consistent with values that might be obtained by extrapolating the (HE/p) points to zero pressure, indicating that all terms in eqn (1 1) are right.The short dashed curves in fig. 2(a) were calculated from eqn (17). This approximation is clearly better than neglecting the cross-terms altogether, but for steam-n-pentane mixtures gives cross-terms which are too big. Mixtures containing steam are, however, not the best test of eqn (17). Finally we calculated cross- term third virials and their temperature derivatives from the Orbey-Vera correlation together with the combining rules suggested above and with CH,F parameters in place of those for steam in non-associative interactions. The solid curves shown in fig. 2(a) were calculated using this procedure. At 698.2 K the solid curve (26) lim (P + 0) ( H 3 P ) = x, x, ( 2 K 2 - &1- &,I3166 H t for Water-n- Pentane Mixtures 400 * & 300 2 200 5 698.2 r - -1 1001 J 0 4 8 12 plMPa 4 00- _ _ _ - - - .001 1 I s 5 $ 2 0 1001 J 0 4 8 12 plMPa Fig. 2. (HZ/p) of (0.5H20 + O.SC,H,,)(g) plotted against pressure. Intercepts are given by eqn (26). (---) Calculated with C,,, = C,,, = 0; (- - -) calculated with C,,, and C,,, given by eqn (17); (-) calculated with C,,, and C,,, given by eqn (15) and (18)-(25) using CH,F parameters for water; 0, table 1 . (a) With H: for water calculated using B and C only. (b) With HZ for water calculated using B, C and D terms. is a good fit to experiment, deviating from the experimental points only above 10 MPa. At 598.2 K the solid curve fits the measurements up to 8 MPa but then diverges.This divergence is due to the limitations of the virial equation of state when truncated at the third term; a good fit at high pressures was not expected. Fig. 2(a) shows that below 8 MPa our suggested procedure for steam mixture third virial coefficients gives HE values which agree well with experiment, While we have no way of obtaining the fourth virial cross-terms in eqn (18), it is interesting to examine the effect of including Gallagher's approximate fourth virials for steam in the calculation of H:. In fig. 2(b) we have repeated the calculation of the curves shown in fig. 2(a) putting 1,,,, for steam into eqn (10) and (1 3). Because of the x: term in eqn (1 3) the contribution of 1,,,, to the enthalpy of the mixture is small, and reduces HZ by only ca. 1 % at 598.2 K and 10 MPa.However, putting 11111 into eqn (10) greatly improves the fit to the residual enthalpy of steam at high pressures, and this changes the shape of the curves shown in fig. 2(a) to those shown in fig. 2(b). The solid curves shown in fig. 2(b) now fit the H z measurements to within experimental error. This agreement suggests that the remaining terms in eqn (1 3) are either small or that they are of opposite sign and partially cancel.N. M . Lancaster and C. J. Wormald 3167 1 I 1 I I I I 0 4 8 12 I p/Wa Fig. 3. (H:/p) of (0.5H20 + 0.5C,HI2)(g) plotted against pressure. (-) Calculated with C,,, and C,,, given by eqn (15) and (18H25) using CH,F parameters for water. H: for n-pentane was calculated using B and C terms, flm for water was calculated using B, C and D terms.The fit is to within experimental error at all temperatures. As the residual enthalpy of steam is the biggest term in eqn ( l o ) , and as we have fourth virials for steam which, though approximate, yield the correct residual enthalpy at pressures up to 15 MPa, we believe it is better to include this term in our H t calculations rather than omit it. The solid curves drawn in fig. l ( a ) and (b) were all obtained by including steam fourth virials in the calculation. In fig. 3 we show all our measurements plotted on an H E / p against p diagram. The solid curves were calculated as described above. At all temperatures agreement with experiment is to within the uncertainty on the measurements. References 1 C. J. Wormald and N. M.Lancaster, J. Chem. SOC., Faraday Trans. I , 1988, 84, 3141. 2 H. Orbey and J. H. Vera, AIChE J., 1983, 29, 107. 3 L. Haar, J. S. Gallagher and G. S. Kell, NBSINRC Steam Tables (Hemisphere Publishing Corp., New 4 J. S. Gallagher, personal communication. 5 G. R. Smith, A. J. Sellars, T. K. Yerlett and C. J. Wormald, J. Chem. Thermodyn., 1983, 15, 29. 6 P. Richards, C. J. Wormald and T. K. Yerlett, J. Chem. Thermodyn., 1981, 13, 623. 7 P. Richards and C. J. Wormald, 2. Phys. Chem. N.F., 1981, 128, 35. 8 N. M. Lancaster and C. J. Wormald, J. Chem. Thermodyn., 1985, 17, 295. 9 N. M. Lancaster and C. J. Wormald, J. Chem. Thermodyn., 1986, 18, 545. York, 1984). 10 G. R. Smith, M. J. Fahy and C. J. Wormald, J. Chem. Thermodyn., 1984, 16, 825. 11 C. J. Wormald, E. J. Lewis and D. J. Hutchings, J. Chem. Thermodyn., 1979, 11, 1. 12 C. J. Wormald and C. N. Colling, J. Chem. Thermodyn., 1985, 17, 437. 13 C. J. Wormald and C. N. Colling, J. Chem. Thermodyn., 1983, 15, 725. 14 C. J. Wormald, N. M. Lancaster and A. J. Sellars, J. Chem. Thermodyn., 1986, 18, 135. 15 C. J. Wormald, AIChE J., 1984, 30, 386. 16 N. M. Lancaster and C. J. Wormald, J. Chem. Thermodyn., 1987, 19, 89.HZ for Water-n- Pentane Mixtures 17 N. M. Lancaster and C. J. Wormald, J. Chem. Thermodyn., 1987, 19, 1001. 18 C. J. Wormald, C. N. Colling, N. M. Lancaster and A. J. Sellars, Gas Processors Association Research 19 P. L. Chueh and J. M. Prausnitz, AZChE J., 1967, 13, 896. 20 D. E. Strogryn, J. Chem. Phys., 1968, 48, 4474; 1969, 50, 4667; 1970, 52, 3671. 21 M. Orentlicher and J. M. Prausnitz, Can. J. Chem., 1967, 45, 373. 22 J. H. Dymond and E. B. Smith, The Virial Coeficients of Pure Gases and Mixtures (Clarendon Press, Oxford, 1980). 23 K. S. Pitzer, D. Z. Lippmann, R. F. Curl, C. M. Huggins and D. E. Petersen, J. Am. Chem. Soc., 1955, 77. 3433. Report 68. Tulsa, Oklahoma 1983. Paper 712219; Received 18th December, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403159

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1988, 84(9), 3169-3174 Nature of the P-Phase of Bismuth Molybdate Mouhiedine M. El Jamal," Michel Forissier and Aline Auroux Institut de Recherches sur la Catalyse, CNRS, 2 avenue A . Einstein, 69626 Villeurbanne, France Infrared and Raman spectroscopies, X-ray diffraction and d.s.c. analysis have confirmed that the /?-phase (B mixture) is different from an equimolar mixture of the a- and y-phases (A mixture) of bismuth molybdate. A comparison of the catalytic properties between A and B mixtures in the partial oxidation of propene and the dehydrogenation-dehydration of isopropanol also confirms this difference. The @-phase is a defined phase of the bismuth molybdate system and is metastable at room temperature, but is stable enough to be used in catalytic tests.The enthalpy of transformation of mixture A to mixture B at 560 "C was found to be 6330 J mol-'. The kinetics and mechanism of propene oxidation over bismuth molybdate catalysts have been studied in considerable detail and are the subject of several extensive reviews. 1-4 The three phases showing simultaneously high activity and selectivity for the partial oxidation of hydrocarbons are Bi,MoO, (y-phase), Bi,Mo,O, @-phase) and Bi,Mo,O,, (a-phase). Some researchers5. thought that the Q-phase was only a mixture of the a- and y-phases and not a distinct phase, while others7. believed that the Q-phase was unstable at the high temperatures required for propene oxidation. Thermal decomposition or reduction by butene of the Q-phase decomposed it into the y-phase and Mo029910 or into the a- and y-phases." Monnier has verified that the Q-phase is a pure phase of the bismuth molybdate system and is stable at the temperatures required for an in-depth study of the kinetics of propene oxidation.l2 Grasselli et aL5 thought that the best catalyst among these bismuth molybdates is Bi,Mo,O,. The structure of the P-phase was controversial because of its thermal instability. Van den Elzen and Riek13 published a structure for the Q-phase based on X- ray powder data. Sleight and Chen14 obtained a suitable single crystal of the Q-phase and an accurate structure was reported. X-Ray, i.r. and Raman spectra of the Q-phase have been reported in many articles.12* 1 5 3 l6 Thermal methods and catalytic studies are often used to characterize the properties of solid materials, such as heterogeneous catalysts.Thermal analysis gives an idea about the stability of the catalyst and its chemical evolution. By microcalorimetric studies we can determine not only the temperature of the typical d.s.c transformation, but also the corresponding heat evolved. Catalytic properties which depend strongly on the surface compositions give an idea about the nature of catalytic sites. We have investigated this system in order to confirm the difference between the b- phase and the equimolar mixture of a- and y-phases and to obtain an insight into the stability of the /?-phase under catalytic and laboratory conditions. Experimental Catalyst Preparation The Q-phase catalyst used in this study was prepared by calcination in air at 560 "C of a hand-ground equimolar mixture of a- and y-phases (A mixture) for 2 days.The a- and 104 3169 FAR I3170 B-Phase of Bismuth Molybdate y-phases were prepared according to the method of Batist." Details regarding their purity have been discussed previously.18 D.s.c. studies were carried out with a differential scanning calorimeter (DSC 11 1) from Setaram. The high sensitivity of this heat-flow microcalorimeter allows a heating rate up to 30 "C min-l and the use of a very small amount of solid. The experimental study was carried out from room temperature to 700 "C. 1.r. and Raman spectra were recorded using a Perkin-Elmer 580 spectrophotometer with KBr discs and a DILOR, OMARS 89 spectrograph, respectively. X-Ray powder spectra were recorded using Cu K, radiation.We studied two catalytic reactions : partial oxidation of propene in comparison with the published results, and dehydration-dehydrogenation of isopropanol to estimate the acid-base properties. 1 9 3 2o The microreactor which was used to measure the catalytic activity consisted essentially of a single-pass flow system, and has been described previously.21 The tests were carried out in the temperature range 300-400 "C under atmospheric pressure. The total gas flow was 1 cm3 s-l. Propene oxidation was studied with the ratio C,H,: O,:N, = 100: 100: 560. The conversion level was less than 4% in order to maintain a homogeneous temperature in the catalytic bed. Samples were also characterized for isopropanol reaction in the air flow at temperatures ranging between 100 and 250 "C with C,H,OH : 0, : N, = 10 : 150 : 600.The total gas flow was 0.32 cm3 s-l. The products were either propene (dehydration reaction due to acidic sites) or acetone (dehydrogenation due to redox or basic sites). Results and Discussion D.S.C. The d.s.c. curve of the y-phase shows two endothermic peaks. The smaller peak at 607 "C (AH = 282 J mol-I), corresponds to the transition of y- to y"-phase,22 and the second, more intense one at 658 "C (AH = 10065 Jmol-l) is attributed to the transition of y"- to y'-phase,22 while the d.s.c. curve of the a-phase does not show any peak between 0 and 650 "C. The metastability of the 7"-phase, and the low value of the enthalpy of the transition of y- to 7"-phase explain the controversy about the existence of this 23 The d.s.c.curve of a hand-ground mixture of the a- and y-phases (A mixture) shows an endothermic peak at 560 "C (AH = 6330 J mol-l). This peak corresponds to the chemical reaction of the a- and y-phases to give the B-phase according to the reaction Bi,Mo3012 + Bi2Mo06 -+ 2Bi2Mo,0,. The endothermic value of the peak shows the evolution of the system to a more organized one. This reaction was evidenced by the following spectroscopic studies. Spectroscopic Studies The i.r. and Raman bands of bismuth molybdates are situated below 1000 cm-'. Characteristic Mo-0 stretching vibrations can be seen in the 950-800 cm-' range, and the Bi-0-Mo and/or Bi-0 stretching vibrations in the 750-550 cm-l range. Finally, the bands in 400-200 cm-l range are assigned to Mo-0 and Bi-0 bending vibrations.It is therefore doubtful whether evidence from i.r. and Raman spectroscopy can be used to make a distinction between an 'octahedral' or 'tetrahedral' environment of the molybdenum in this case. The i.r. spectrum of the A mixture before calcination shows only the a and y bands (fig. 1). There are three bands between 950 and 900 cm-l characteristic of the a-phase,M . M. El Jamal, M. Forissier and A . Auroux 3171 1000 800 600 LOO 200 wavenumber/cm-' Fig. 1. 1.r. spectra of equimolar mixture of a- and y-phases before (a) and after (b) calcination at 560 "C for 2 days in air. Table 1. X-Ray diffraction peaks observed for different bismuth molybdate samples a Y mixture A mixture B d I r d Ir d Ir d I r ~~ - - 8.10 8.5 - - 6.94 20 4.87 23 3.18 100 - - 3.15 100 3.05 67 2.86 28 - - 2.74 15 - - 1.94 19 - - 1.65 17 - - - - - - - - 8.10 10 6.94 17 4.87 22 3.18 100 3.15 100 3.05 60 2.86 33 2.74 20 1.94 14 1.65 18 - - 5.94 12 4.9 16 3.20 100 3.1 14 2.8 29 2.69 17 1.68 18 1.64 16 - - Mixture A: a hand-ground equimolar mixture of a- and y-phases.Mixture B: B-phase. I,, relative intensity defined by lO0I/Imax; d, inter-reticular distance defined by the Bragg equation: nA = 2d sin 8, with d in A. 104-23172 /3-Phase of Bismuth Molybdate x l 4 A I I 1 I 1 1 I I 1000 800 600 4 00 wavenum ber/cm-' Fig. 2. Raman spectra of an equimolar mixture of a- and y-phases before ( a ) and after (b) calcination at 560 "C for 2 days in air. and a band at 360 cm-l which corresponds to the y-phase.15* l7 There is no enhanced intensity or new band. After calcination of mixture A at 560 "C (mixture B), the i.r.spectra show an important change (fig. I): the a and y bands disappear. There is an intense band at 740 cm-l which corresponds to the p-phase.15* l7 Detailed study of this spectrum leads us to conclude that the a- and y-phases are transformed to the p-phase and that the B mixture corresponds only to the Q-phase. This conclusion was confirmed by the X-ray data. The A mixture corresponds to an equimolar mixture of well crystallized a- and y- phases (table 1),15-17 but when the A mixture is calcined above 560 O C , the X-ray spectrum is found to cqrrespond to the p-phase, characterized by the presence of two peaks at 3.20 and 2.80 A15-17 (table 1).The Raman spectra of mixtures A and B are shown in fig. 2. The Raman spectrum of mixture A shows three bands at 955,925 and 900 cm-l, which correspond to the a-phase and a band at 842cm-l, corresponding to the 7-pha~e.l~ The B mixture shows the presence of a strong band at 885 cm-l, characteristic of the p-phase.17 1.r. and Raman spectroscopies and X-ray diffraction and d.s.c. analysis show that the b-phase is different from an equimolar mixture of a- and y-phases. The /?-phase is a defined pure phase of the bismuth molybdate system. The B mixture @-phase) remains stable under catalytic conditions, as shown by i.r. and X-ray spectra of the solids used in propene oxidation and in isopropanol reactions. However, the i.r. and X-ray spectra of the p-phase which had been aged over 2 years under laboratory conditions (pressure = lo5 Pa, temperature = 23 "C) show the pre- sence of traces of a- and y-phases.This implies that the p-phase is a metastable phase which involves decomposition with time into a mixture of a- and y-phases. Catalytic Study The results for selectivity for the two catalytic reactions studied are given in table 2. The selectivity of propene to acrolein was found to follow the order: mixture A > mixtureM. M. El Jamal, M. Forissier and A. Auroux 3173 Table 2. Selectivity in propene oxidation and in dehydration-dehydrogenation of isopropanol propene isopropanol selectivity (YO) selectivity (YO) - S(B.E.T.) acrolein CO, acetone propene /m2 g-' mixture A 95 3 88 12 4.7 mixture B 90 6 12 28 0.3 Mixture A: Hand-ground equimolar mixture of a- and y-phases.Mixture B: Bi,Mo,O, (B-phase). Catalytic conditions for the partial oxidation of propene: mass = 0.1 g, T = 380 "C. Catalytic conditions for isopropanol dehydration-dehydrogenation: mass = 0.1 g, T = 190 "C. B (B-phase). The A mixture is more selective than the /?-phase in the partial oxidation of propene. This result is in agreement with the work of Carson et al., and the effect is explained by a synergetic effect.16. l8 The selectivity for the dehydration of isopropanol was found to follow the order mixture B @-phase) > mixture A. This suggests that the /?-phase shows a stronger superficial acidity than the A mixture. Comparison of catalytic properties confirms that the /?-phase is significantly different from an equimolar mixture of a- and y-phases.Conclusions D.s.c. analysis and spectroscopic studies have shown that a chemical reaction occurs between the a- and y-phases to give rise to the /?-phase. The i.r., Raman and X-ray spectra of the P-phase are very different from those of an equimolar mixture of a- and y-phases, confirming that the P-phase is a well defined phase of the bismuth molybdate system. After a long time the /?-phase begins to decompose at room temperature into the a- and y-phases. The 8-phase can also be differentiated from an equimolar mixture of a- and y-phases of bismuth molybdate by the selective oxidation of propene and the dehydration of isopropanol to propene. We thank Prof. G. Ollier for his help with the Raman spectra. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 H.H. Voge and C. R. Adams, Adv. Catal., 1967, 17, 151. W. M. Sachtler, Catal. Rev., 1970, 4, 26. L. Ya. Margolis, Catal. Rev., 1973, 8, 24. G. W. Keulks, L. D. Krenzke and T. M. Notermann, Adv. Catal., 1978, 27, 183. R. K. Grasselli, J. D. Burrington and J. F. Brazdil, Faraday Discuss. Chem. SOC., 1982, 72, 203. Ph. A. Batist, A. H. W. M. DerKinderen, Y. Leeuwenburgh, F. A. M. G. Metz and G. C. A. Schuit, J . Catal., 1968, 12, 45. R. Kohlmuller and J. P. Baduad, Bull. Chem. SOC. Jpn., 1969, 10, 3434. L. Ya. Erman and E. L. Gal'perin, Russ. J . Inorg. Chem., 1968, 13, 487. L. Ya. Erman and E. L. Gal'perin, Russ. J . Znorg. Chem., 1970, 15, 441. M. F. Portela, Proc. 8th Iberamer. Symp. Catal., ed. Malquisa, Huelva, Spain, (1982), p. 315. J. M. Herrmann, M. J. Pires and M. F. Portela, J. Chem. SOC., Faraday Trans. I , 1985, 81, 2107. J. R. Monnier, Ph.D. Thesis (University of Wisconsin, Milwaukee, 1978). A. F. Van den Elzen and G. D. Riek, Mater. Res. Bull., 1975, 10, 1 163. H. Y. Chen and A. W. Slight, J . Solid State Chem., 1986, 63, 70. D. Carson, G. Coudurier, M. Forissier, J. C. Vedrine, A. Laarif and F. Theobald, J. Chem. Soc., Faraday Trans. I , 1983, 79, 1921. Ph. A Batist, J. Chem. Tech. Biotechnol., 1979, 29, 451.3174 P-Phase of Bismuth Molybdate 17 1. Matsuura, R. Shuit and K. Hirakawa, J. Catal., 1980, 63, 152. 18 M. El Jamal, M. Forissier, G. Coudurier and J. C. Vedrine, Proc. 9th Znt. Congr. Catal., ed. M. J. 19 M. Ai, Bull. Chem. SOC. Jpn, 1977, 49, 1328. 20 K. Tanabe, Solid Acids and Bases (Academic Press, New York, 1970). 21 M. Forissier, L. de Mourgues and J. L. Portefaix, Rev. Phys. Appl., 1976, 11, 639. 22 P. Gaucher, V. Ernest and P. Courtine, J . Solid State Chem., 1983, 47, 47. 23 A. Watanabe and H. Kodama, J. Solid State Chem., 1980, 35, 240; 1985, 56, 225. Phillips and M. Dernan, Calgary (1988), vol. 4, p. 1617. Paper 7/2220; Received 14th December, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403169

出版商:RSC    

年代:1988

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J. Chem. SOC., Faraday Trans. 1, 1988, 84(9), 3175-3185 Interactions between Metal Cations and the Ionophore Lasalocid Part 5.-A Potentiometric, Polarographic and Electron Spin Resonance Study of Copper(I1kLasalocid Equilibria in Methanol Philippe Laubry, Guy Mousset, Pierre Martinet, Madeleine Tissier, Claude Tissier and Jean Juillard" Laboratoire d'Etude des Interactions Solute's-Solvants and Laboratoire d'Electrochimie Organique, UA 434 au CNRS, Universite' Blaise Pascal (Clermont II), BP 45, 63170 Aubiire, France The complexation of Cu2+ by lasalocid and the model compound salicylic acid, AH, has been studied in methanol. The stability constants of species ACu+ and A,Cu were obtained from potentiometric measurements using a pH glass electrode and a copper-selective electrode, and by polarographic determinations.The stability of these copper(I1) complexes was shown to be higher than that of the analogous complexes of the other transition-metal cations of the first row and very similar for lasalocid and salicylic acid. The e.s.r. spectra suggest that the structures of the species formed with the two ligands differ; the oxygen of the backbone probably participates in complexation with lasalocid. In addition, other complexes possibly involving the methoxide ion, formed in more basic media, were charac- terised. Recently' we have studied the interaction of some first-row transition-metal cations with the ionophore lasalocid (fig. 1). We report here data on copper-lasalocid interactions. Cu2+ is of biological importance, and it can be used as a structural probe by virtue of its paramagnetic and spectroscopic properties. Lasalocid has been proved to mediate the transport of Cu2+ across weakly polar phases such as chloroform.2 In deuterated chloroform, a conformation and structure for the 2 : 1 neutral complex of lasalocid anion with copper(r1) has been proposed from the observed effects of Cu2+ on the 13C relaxation of the lasalocid anion.3 The formation of lasalocid complexes of the copper(I1) ion in methanol has been studied here using potentiometry, polarography and e.s.r., with a view to assessing the relative suitability and scope of each method and obtaining more specific information.In order to discern the role played by the salicylate moiety in the complexing power of lasalocid with regard to copper, measurements were also made with salicylic acid and 3-methylsalicylic acid.Experimental Materials The specification of methanol and the preparation of tetrabutylammonium methoxide solutions were as previously described.' Solutions of (ClO,), Cu - 6H,O were prepared in methanol. The Cu2+ concentration of these stock solutions being estimated in the usual way using EDTA. The methanol solutions used contained between 0.05 and 0.1 YO water. 31753176 Copper( 11) - Lasalocid Equilibria Fig. 1. The structure of lasalocid. Potentiometric Measurements Methanolic solutions of the ligand (lasalocid or a simpler carboxylic acid) were titrated against a solution of tetrabutylammonium methoxide in the presence of copper(rr) perchlorate. In order to monitor the activities of hydrogen and Cur' ions during titration, three electrodes were immersed in the solution, which was maintained at 25.0"C: a glass pH electrode (Tacussel type TB lO/HA), a Cu2+ crystal membrane electrode (Orion model 94-29) and a calomel electrode laboratory modified for methanolic solution, as described previously.' The electrodes (the two indicative ones were used alternately by means of an appropriate interface) were connected to a Tacussel Aries 10 000 digital millivoltmeter, and pH standardization was carried out using De Ligny buffer^.^ The copper-selective electrode was standardized using copper(rr) perchlorate solutions of various con- centrations in methanol.Polarographic Measurements Polarographic measurements were performed using a Tacussel apparatus consisting of a 'TIPOL' polarographic unit and an EPL 2B recording device connected to the three electrodes in the electrolytic cell.The working electrode was a dropping-mercury electrode with an out-flow velocity of 1.49 mg s-l for a mercury column of 62.5 cm. The drop time was set at 2 s. The auxiliary electrode consisted of a platinum wire, and the reference electrode was analogous to that used for the potentiometry. A glass pH electrode was also placed in the cell to record the pH simultaneously. All the polarograms were obtained at a rate of potential scanning of 2 mV s-l, the movement of the recording paper having been tested beforehand. Before each run the solution was deaerated with an argon stream. Tetraethylammonium perchlorate and tetrabutylammonium tetrafluoroborate were found to be adsorbed on the mercury drop; lithium perchlorate was accordingly selected as a supporting electrolyte.There was some complexation of lithium by la~alocid,~ but this was fortunately very weak compared with complexation of copper(r1) so it could be neglected. All the measurements were made in a 5 x mol dm-3 solution of LiClO, in methanol. Triton x 100 was used as a maximum suppressor. Its optimal concentration was found to be 0.002%. E.S.R. Measurements E.s.r. spectra were recorded using a Bruker model ER 200 D spectrometer at X band (v = 9.21 GHz). 100 kHz frequency modulation was used with a phase of 90". All the spectra were obtained at a room temperature (ca. 20 "C). g factors were determined by comparison with the e.s.r.signal of a,a-diphenyl-P-picryl hydrazil crystal (g = 2.0038).P. Laubry et al. 3177 15 t 1 2 3 4 Cb*/Ci;l Fig. 2. Titration of copper(r1) and lasalocid or salicylic acid solutions in methanol with a tetrabutylammonium methoxide solution. 1, 2.5 x rnol dm-3 lasalocid; 3, 3', 2.5 x mol dmT3 Cu(ClO,), + 5 x mol dmP3 salicylic acid. Curves 1-4, pH from H' glass electrode. Curves 3' and 4', pCu' = -log ccu2+ from Cu2+-selective electrode indications as functions of the number of base equivalents (ratio of analytical concentration of base added c,* to analytical concentration of copper c:J. mol dm-3 Cu(ClO,),; 2, 5 x mol dm-3 Cu(ClO,),+ 5 x lop3 mol dma3 lasalocid; 4, 4', 2.5 x Results Potentiometry Ti trations of lasalocid-Cu" ion solutions in methanol were conducted for various ratios of their initial concentrations.As regards the pH curves, trends observed here were rather different from those found for the other first-row transition-metal cations' and for the alkaline-earth-metal cations.6 Taking, for example, the ratio 2: 1 as shown in fig. 2, there was for the other divalent cations a potential jump after addition of two equivalents of base [see fig. 2 of ref. (l)]; this was shown to correspond to the successive formation of 1 : 1 and 2: 1 complexes AM+ and A,M of lasalocid AH with the cation M2+. No potential jump was observed here for two equivalents, but a jump occurred for three equivalents of base. Therefore there must be formation of another species with an overall stability close to that of A,M resulting either from the ionization of the phenol function or from some interaction of the methoxide ion with the Cul* ion or a copper-lasalocid complex.3178 Copper( 11) - Lasalocid Equilibria Table 1.Stability constants of 1 : 1 (PI,) and 2 : 1 (pz0) complexes of lasalocid anion, salicylate and 3-methylsalicylate with CU" ion in methanol at 25.0 "C from potentiometric measurements (molar scale of concentrations) B L 1:l 1:l 2: 1 2: 1 3: 1 3: 1 2: 1 2: 1 lasalocid - 6.29 6.23 - 6.16 10.12 6.15 10.24 6.1 1 9.95 6.0 1 10.03 ' best values ' salicylic acid 5.68 5.69 9.65 6.4 6.1 6.5 6.5 6.4 6.3 6.5 6.0 - 10.7 10.8 10.5 10.6 10.7 10.2 3-methylsalicylic acid 6.2 10.4 9.9 1 B 2: 1 5.87 L 2: 1 5.90 a B, H+ glass electrode data alone, processed using Bjerrum formation function.L, H+ glass electrode and Cu2+ solid-state selective electrode measurements, processed using Leden formation function. Y is the initial analytical ratio of ionophore to Cu" ion: cEA/c&2+. Apparent constants under the conditions of the experiments : c&2+ = 2.5 x mol dm-3. Standard formation constants. A study of the formation of the copper methoxides in methanol was attempted. Variation of the pH of the Cu2+ solution on titration with tetrabutylammonium methoxide is shown in fig. 2 [curve (l)]. The shape of this curve is anomalous between the first and second equivalents of base. No precipitation was apparent, but the shape suggests that the (CH,O),Cu complex is somewhat unstable in solution. A study of the electronic spectra in the visible region indicated that the true solubility at equilibrium of CH,OCu+ClO; is high (> mol drn-,), but that of (CH,O),Cu is very low, of the order of mol dm-3.Therefore, the stability constants of CuI' methoxides can be determined only by using the first part of curve (1). This was done from both pH and pCu' data using Leden functions as described later. The results obtained are only qualitative and, as regards formation of (CH,O),Cu, very arguable ; nevertheless they demonstrate that putative formation of (CH,O)Cu+ after ACu+ and A,Cu in the course of the titration of lasalocid-CuII ion mixtures does not fit the various experimental titration curves, e.g. ( 3 ) and (3') in fig. 2. It can also be seen that titration curves corresponding to salicylic acid-Cu" ion mixtures (4) and ( 4 ) are rather different from (3) and (3').As previously reported for Co2+, Ni2+ and Zn2+,l between the second and third equivalents of base, a precipitate appeared, which was green in this instance. The precipitate was isolated and characterized by elemental analysis as being a complex of type OC,H,CO,Cu, resulting from the ionization of the phenol function. No such precipitation occurred with lasalocid and, as the shape of the curve was very different, the formation of such a species could not be postulated for the ionophore. The most reasonable assumption seems then to be the formation of a bidentate cupric complex involving lasalocid and methoxide anion, CuAMeO. The following species would then be formed successively : ACu+, A,Cu, A(CH,O)Cu and Cu(CH,O),, which is unstable in solution since it is sparingly soluble.P. Laubry et al.3179 Table 2. Formation constants for the complexes of lasalocid (A-) and methoxide (MeO-) anions with the Cu" ion in methanol at 25 "C po tentiometry polarograph y Z = 5 x lo-' Z = 5 x lop2 z = 0" (C104Li)b (C104Li)b A- + Cu2+ ACu+ log B,o 6.5 5.5 5.7 2A- + Cu2+ f A,Cu log B Z O 10.7 9.2 9.5 MeO- + Cu2+ MeOCu+ log B O l 10 9 2Me0- + Cu2+ f (MeO),Cu logPo, (18) (17) A- + H+ +AH PK, 8.29 7.95" A- + MeO- + Cu2+ e AMeOCu logp,, 16.1 14.7 15.1 Estimated accuracy: f 1 on the last figure. a Optimized mean values from table 1. constants (concentration ratios). Apparent In 5 x lo-, mol dm-3 ClO,NEt,. Attention was centred on the formation of ACu+ and A,Cu, for lasalocid and for the model acid, as methoxide complexes have little biological interest.The stability constants of ACu' and A,Cu were obtained by two methods. pH data were processed using the Bjerrum formation function as previously described.6 Values thus obtained are designated B in table 1. Both pH and pCu' data (pCu' = log ccu2+) were also treated using Leden formation functions according to the principles previously used for the processing of Mn2+ combined with pH and e.s.r. data.' Values obtained in this manner are designated L in table 1. For both kinds of processing, good fits were obtained only for the first part of the titration curves, progressive deviations being observed as other species, (CH,O)ACu for lasalocid or OC6H,C02CU for salicylic acid, began to form.Stability constants pl0 and pzO corresponding to the reactions A- + Cu2+ + ACu' 2A- + Cu2+ f A,Cu (1) (2) calculated from titration curves corresponding to the various initial stoichiometric ratios 1 : 1 , 2 : 1 and 3 : 1 of ligand to copper are collected in table 1. Good agreement is observed between these data and the two different methods of processing the results. In order to obtain data in the conditions used for the polarographic study, pl0 and /?20, were also determined for lasalocid in a 5 x lo-, mol dm-3 solution of lithium perchlorate in methanol using the same methods. In order to avoid any artificial decrease caused by interactions between lasalocid anion and lithium, the value used here for the pK, of lasalocid was measured in a 5 x lo-, mol dm-3 solution of tetraethylammonium perchlorate.The results are given in table 2. The stability of the lasalocid-methoxide mixed complex was also determined in the two media using pH and pCu' titration curves corresponding to 1 : 1 initial stoichiometry, for which formation of A,Cu is negligible. The stability constant Bll for reaction (3) is also given in table 2 along with formation constants of methoxide pol and Po, [reactions (4) and (5)], the values of which have to be considered unreliable, as explained above : (3) (4) ( 5 ) CH,O- + A- + Cu2+ f (CH,O)ACu CH,O- + Cu2+ + CH,OCu+ 2CH,O- + Cu2+ f (CH,O),Cu.3180 Copper(i1) - Lasalocid EquiIibria Polarograph y Measurements were made on lasalocidxupric perchlorate solutions in a 3 : 1 ratio progressively neutralised by tetrabutylammonium methoxide.The polarogram showed only one bielectronic wave corresponding to reduction of CU" to Cuo whether the CuI' was free (i.e. solvated by methanol) or complexed with lasalocid anion. The intensity of the limiting current corresponding to the complexed Cu2+ was a little lower than that corresponding to the 'free' Cu2+ and the half-wave potential was shifted to more negative values as the concentration of the added base increased. The limiting diffusion current was shown to vary linearly with both the Cu" concentration and the square root of the pressure-corrected height of the mercury column, the corresponding straight lines both passing through the origin. The electrochemical process thus does seem to be a diffusion-controlled reduction of the Cur' species.Plots of log [i/(i,-i)] as a function of E were straight lines (i is the intensity of the current for potential E, i, the intensity of the diffusion-limiting current), but the slopes varied from 35 mV for the reduction of Cu2+ alone to 64-69 mV for the reduction of Cu2+ in the presence of lasalocid anion A-. The electrochemical process was thus reversible for Cu" ion alone, but only quasi-reversible for Cu" ion involved in complexes with lasalocid. A procedure of extrapolation to zero current intensity was then employed to obtain the corresponding reversible half-wave potential. Such a procedure, derived from Gellings' work,8 had been previously used by Gaur et aI.' and Tamamushi and Tanaka. lo The reversible half-wave potentials were obtained using the formula E';:; = limi+o ( E+-- RT ln- ).2F iL)-i The stability constants of the complexes formed between lasalocid and Cu" ions could then be determined. For this purpose, only solutions corresponding to one to two equivalents of added base were found useful since in less basic solutions not all the copper was complexed and a 'free' Cu2+ reduction wave also appeared on the polarograms, and in more basic solutions formation of Cu" methoxide would be favoured. Results concerning the shift of the reversible half-wave potential as a function of the ligand concentration were processed using the method of De Ford and Hume," an application to polarography of the Leden calculation method. The formula used here was : AEheV(s) - AErV(c) i,(s) C,*U +In- = In- RT/2F i,(c) [Cu"] In& = (7) where s and c stand for simple and complexed Cul* ion, c& is the total analytical concentration of copper and [Cu"] is the actual concentration.Considering, as previously, formation of CuA+, CuA, and CuA(CH,O), corresponding to reactions (l), (2) and (3) with the respective apparent equilibrium constants, pio, Pio and pi1, the Leden function is: [Cu"] + [CuA+] + [CuA,] + [CuAOMe] [CU"] F , = where the square brackets denote concentrations. From the chemical equilibria, the mass balance and the electroneutrality of the system : (4 - l)/[A-] = pio +pio [A-] +pi1 [MeO-] = 8. (9)P. Laubry et al. 3181 Extrapolation to [A-] = 0 and then [MeO-] = 0 yields a value of Pio: lim[*-,+O 4 = P i o . Defining then yields both extrapolations, starting with and pi1 from the variation of 4 with [MeO-]/[A-].As [A-] was not known exactly, the calculations were made through successive [AH] z cf - C: - [H+] (12) where c: and c: are the analytical concentrations of the ionophore and the added base. Experimental data were consistent with values thus obtained, suggesting that assumptions made about the nature of the species formed are correct. The values obtained are given in the last column of table 2. They are consistent with potentiometric data in the same medium (column 2 of table 2). In addition, it must be mentioned that the value obtained here for the reversible half- wave potential of copper (0.178 V with respect to the saturated calomel electrode in methanol) is in good agreement with the value given by Desmarquest et aZ.12 of the standard potential Cu"/Cu0 : 0.18 0.0 1 V referred to the same reference electrode in methanol. The diffusion coefficient calculated using the Ilkovic equation (6.54 x lop6 cm2 s-l) is for a solution of copper perchlorate alone and varies for mixed lasalocid complex solutions between 4.2 x and 4.6 x cm2 s-l.E.S.R. Spectra All the measurements were made with the purpose of monitoring e.s.r. spectra along with the progressive formation of the various copper complexes during the titration of mixtures of the ligand and copper(r1) perchlorate in methanol against a solution of methoxide. The experimental conditions, analogous to those of the corresponding potentiometric titrations, provide the pH and the composition of the solutions analysed.Two experimental procedures were used; first, for the lasalocid-copper ratio 2 : 1, independent measurements of samples corresponding to the various steps of the neutralisation process, then continuous measurements for 1 : 1 and 5 : 1 lasalocid- copper and 1 : 1 and 2 : 1 salicylic acid-copper. The latter procedure, using a circulation device, allows successive addition of base to the solution without any change of the cell orientation in the magnetic field ; such changes sometimes made successive measurements using the first procedure difficult to compare reliably. The e.s.r. first-derivative spectrum of solvated copper(r1) ion in methanol is shown in fig. 3. The spectrum contains only a single broad line with a width of ca. 120 G centred at g = 2.185.As for the formation of mono- and di-hydroxides in aqueous so1ution,13 the formation of the methoxides corresponds to the disappearance of the signal; the decrease in the intensity of the e.s.r. signal is roughly proportional to the decrease in the concentration of the 'free' Cu'' ion, as calculated from the results of the potentiometric study. Unlike the case for water,13 there was no solubilization of the CuI' dimethoxide complex in concentrated methoxide solution and therefore no signal corresponding to the formation of a basic complex (CH,0),Cu2- analogous to (OH),Cu2- in concentrated hydroxide solution. Going from acid to basic solutions in methanol, e.s.r. spectra of copper show noticeable changes corresponding to the formation of various complexes with salicylate or lasalocid anion.An example of this is given in fig. 4. The trends observed are different3182 Copper(I1) - Lasalocid Equilibria 200 G Fig. 3. Experimental or recalculated first-derivative e.s.r. spectra of various Cu” species formed with lasalocid LasH and salicylic acid SalH (normalized to same concentration) at room temperature. (a) Cu2+, (b) LasCu+, (c) SalCu’, ( d ) Las,Cu, (e) Sal,Cu, cf) Las(CH,O)Cu and (g) (OC,H,C0,),Cu2-. D denotes the point used for the calculation of the g factor. for the two ligands. If some sort of additivity of the contributions of the spectra of the various species to the resulting experimental spectra is accepted, it is possible, using previously determined stability constants, to break down, step by step, the experimental spectra and thereby isolate the spectra of the various species involved. This was done here and the internal consistency of the calculations was found to be very satisfactory.The resulting normalized spectra of the pure species in methanol at room temperature are given in fig. 3. For salicylic acid (SalHNopper interactions, the following species show an e.s.r. signal: SalCu+ with a first-derivative spectrum analogous to that observed for Cu2+ [a single broad line, but shifted upfield (g = 2.160) and slightly deformed] and Sa1,Cu with a four-line signal with well resolved hyperfine structure ( g = 2.143, a = 59 G), analogous to that reported for the same species in dirnethylformamide.l4 Obviously, no signal was observed for the complex OC,H,CO,Cu which precipitated, but beyond pH 9 progressive redissolution of this complex occurred and a new four-line signal was observed (g = 2.116, a = 76 G) corresponding to an as yet unidentified complex which could be (OC,H,C0,),Cu2-.For lasalocid (LasHNopper interactions, the spectrum of LasCu+ was also analogousP. Laubry et al. 3183 . 200 G . Fig. 4. First-derivative e.s.r. spectra for 2: 1 mixtures of salicylic acid and copper perchlorate solutions (5 x and 2.5 x low3 mol dmP3) in methanol with various amounts of tetra- butylammonium methoxide, from pH 3.5 to pH 14.2 at room temperature. p denotes the beginning of the precipitation, s denotes the beginning of solubilisation of the precipitate. to that of the solvated Cu2+, but shifted upfield ( g = 2.151) and more asymmetric.The signal corresponding to Las2Cu was broader and slightly shifted (g = 2.139). A good spectrum corresponding to this species could be obtained only from a solution with a lasalocid<opper ratio 5 : 1, which is more favourable to the formation of this species. After pH 6 another signal was detected; this was a signal with an ill resolved hyperfine3184 Copper(rr) - Lasalocid Equilibria structure; only three lines (the first, the third and the fourth) were visible; the estimated e.s.r. parameters are g = 2.142, a = 51 G. This might correspond to the species Las(CH,O)Cu. The variation of the intensity of the fourth and largest line with the pH of the solution agrees well with the concentration changes of this species as calculated from the potentiometric data.Discussion Nature of the Complexes Formed As stated above, the processing of both potentiometric and polarographic data in methanol is satisfactory assuming the formation with the two ligands AH, lasalocid or salicylic acid, of the successive complexes ACu+ and A2Cu. Given the noteworthy stability of these complex salts, charged complexes of the type AHCu2+ or (AH),Cu2+ need not be considered; they could be formed only in very acidic media, if they are formed at all. The formation of AM+ and A2M between lasalocid or salicylic acid or, more generally, carboxylic acids and divalent cations has been previously shown to occur in the same solvent with alkaline-earth-metal cations6 and other transition-metal cations.' The Cur' ion thus follows the common rule; the stability of the species formed is even stronger for this cation than for the others.However, the affinity of the Cur' cation for the methoxide anion, somewhat analogous to its well known affinity for the hydroxide anion, give rise here to competition between lasalocid and methoxide anions for the ligation of the cation, which was not encountered to any such extent with the other divalent cations. This results, for lasalocid in methanol, in quasi-concurrent formation of both A2Cu and A(CH,O)Cu, which accordingly hinders the determination of the thermodynamic parameter pertaining to the formation of A2Cu. Although mixed methoxide complexes themselves have no biological importance, the occurrence of such species suggests that mixed hydroxide complexes could form, under appropriate conditions. These of course could well be biologically interesting.In basic media, the behaviour of salicylic acid differs strongly from that of lasalocid. As with Co2+, Ni2+ and Zn2+, a complex involving the salicylate dianion, resulting from the ionization of both the carboxyl and the phenol groups, precipitates. Here it was observed to redissolve in more basic medium; the resulting species could be either a mixed complex with one or two methoxide anions or more probably a charged complex ion involving two salicylate dianions. The e.s.r. spectra (fig. 3), which showed a well resolved four-line spectrum, might thus correspond to some sort of square-planar coordination of the Cu" ion in a complex of the type (OC6H,C02),Cu2-, well known in water.15 Stability and Structure of the Complexes Discussion will here be restricted to the species ACu+ and A,Cu. For both ligands, the values of the stability constants found here, for the 1 : 1 and for the 2: 1 complexes, are markedly higher (by lo2 to lo3) than those previously reported' for the other first-row transition-metal cations.However, most of the differences are ascribable to the first step, the formation of the 1 : 1 complex, the energy of the second step being only a little greater than with the other cations. The most striking fact as regards stability constants, is the closeness of the values obtained for lasalocid and salicylic acid anions, these values being only a little lower for the latter. The constants are even closer for 3-methylsalicylate and the lasalocid anion.This would suggest that the salicylate moiety might play the main, and maybe the sole, role in the complexation of the Cu" ion by the lasalocid anion. However, as shown for the alkaline-earth-metal cations," analogous values of AG do not imply structuralP. Laubry et al. 3185 identity. Values of AH and therefore of AS could well strongly differ. Determination of the enthalpies of complexation of the first-row transition-metal cations by the lasalocid anion and salicylate in methanol is in progress in our laboratory, but full data are not yet available. Nevertheless, from the e.s.r. spectra obtained here and shown in fig. 3, it can be asserted that CuII ion complexes of salicylate and lasalocid anion are appreciably different, for ACu+, and radically different for A,Cu.Oxygen sites other than those of the salicylate group certainly participate in the complexation of copper both in the 1 : 1 and in the 2: 1 complexes. From the study of effects of Cu2' on the relaxation of the carbons of lasalocid in the A,Cu salt in CDC1,3 a structure for this complex in this solvent is suggested as follows: the two lasalocid anion molecules participate in the complexation by the salicylate part for the first, by the oxygens of the backbone O,, 0,, 0, and 0, for the second, the two molecules rapidly interchanging their role. This could also be representative of the structure of A,Cu in methanol. Further information is awaited from an ongoing systematic study of the successive steps of copper complex formation monitored using n.m.r. techniques. References 1 P. Laubry, C. Tissier, G. Mousset and J. Juillard, J. Chem. SOC., Faraday Trans. I , 1988, 84, 2 H. Tsukube, K. Takagi, T. Higashiyama, T. Iwachido and N. Hayama, J. Chem. SOC., Chem. Commun., 3 J. Y. Lallemand, R. Rau and T. Prange, Nouv. J. Chim., 1980, 4, 315. 4 C. L. De Ligny, P. F. M. Luikx, M. Rebach and A. A. Vienecke, Reel. Trav. Chim. Pays-Bas, 1960,79, 5 Y. Pointud and J. Juillard, J. Chem. SOC., Faraday Trans. I , 1988, 84, 959. 6 J. Juillard, C. Tissier and G. Jeminet, J. Chem. SOC., Furaday Trans. 1 , 1988, 84, 951. 7 C. Tissier, J. Juillard, M. Dupin and G. Jeminet, J. Chim. Phys., 1979, 76, 611. 8 P. J. Gellings, Z. Electrochem., 1962, 66, 477; 481; 7999; Ber. Bunsenges. Phys. Chem., 1963, 67, 9 J. N. Gaur, D. S. Jain and M. M. Palrecha, J. Chem. SOC. A, 1968, 2201. 969. 1986, 448. 699. 1967. 10 R. Tamamushi and N. Tanaka, Phy. Chem. (Frankfurt), 1963, 39, 117. 11 D. de Ford and D. N. Hume, J . Am. Chem. SOC., 1951, 73, 5321. 12 J. P. Desmarquest, C. Trinh-Dinh and 0. Bloch, Electroanal. Chem., 1970, 27, 101. 13 Y. Y. H. Chao and D. R. Kearns, J. Phys. Chem., 1977, 81, 685. 14 W. G. K. M. Pisipati, N. V. S. Rao, S. Padmaja, Y. Anjaneyuu and R. Prabhakara Rao, Magn. Reson. 15 See for example, P. F. Brun and K. H. Schrerder, J. Electroanul. Chem., 1975, 66, 9. 16 Y. Pointud, E. Passelaigue and J. Juillard, J. Chem. SOC., Faraday Trans. I , 1988, 84, 1713. Chem., 1986, 24, 954. Paper 7/2232; Received 21st December, 1987

ISSN:0300-9599    

DOI:10.1039/F19888403175

出版商:RSC    

年代:1988

数据来源: RSC