摘要:

J . Chem. SOC., Faraday Trans. I , 1988, 84(2), 539-550 Thermodynamics of Fluorocarbon-Hydrocarbon Mixtures The Systems formed by 2,2,4-Trimethylpentane with Hexafluorobenzene and with Hexafluorobenzene-Benzene Javier Aracil, Ramh G. Rubio,* Mercedes Caceres and Mateo Diaz Pefia Departamento de Quimica Fisica, Facultad de Quimicas, Universidad Complutense, 28040-Madrid, Spain Juan A. R. Renuncio Catedra de Quimica General, Facultad de Quimica, Universidad de Oviedo, 33007 Oviedo, Spain The excess volume of hexafluorobenzene (C6F,)-2,2,4-trimethylpentane (2,2,4-TMP) has been measured at 298.15 K as well as the vapour pressures at 298.15, 323.15 and 348.15 K. From the latter, the excess Gibbs energies have been calculated, and the excess enthalpies have been estimated through the Gibbs-Helmholtz equation.The comparison with similar data for binary systems involving benzene (C,H,), C,F,, 2,2,4-TMP and cyclohexane (c-C,H,,) shows that c-C,H,, and 2,2,4-TMP have quite different volumetric and entropic behaviours when mixed with C,F,, whilst they are almost equivalent when mixed with C,H,. Finally, the vapour pressures have been measured and the excess Gibbs energies calculated at 298.15 and 323.15 K for the ternary system C,F6-C,H,-2,2,4-TMP. Previous work on mixtures containing alkanes has shown that correlation of molecular order plays a fundamental role in their thermodynamic properties.' When the alkanes are mixed with benzene or p-xylene, it seems that order correlations between the aromatic molecules and between the aromatic molecules and chain-like molecules have to be taken into account in order to explain the qualitative trends of the excess functions.2 C,F, presents a higher degree of orientational order than C6H6,3 therefore one should expect that breaking those correlations should play a more important role in C6F,-alkane mixtures than in the C,H6-alkane mixtures.Nevertheless, the excess properties of C,F,-n-hexadecane (nC16H34) or + n-tetradecane (n-C14H30) seem to be mainly dominated by the unfavourable hydrocarbon-fluorocarbon interaction^.^ In order to obtain further information on the importance of breaking the orientational order of pure C,F, upon mixing, we have found it interesting to study the system C6F,-2,2,4-TMP, the latest being an almost globular molecule which presents no order correlations at all.Since order correlations show a strong temperature dependence,' information about mixing functions up to near the normal boiling point of the ordered substance should be of value. Recently unusual W-shape CFam us. composition curves have been found in some alkane solutions with some halogeno- hydrocarbon^.^ Saint-Victor and Patterson6 have suggested that these effects could be related to the proximity of the mixture to a UCST, a situation which is associated with high GZ values. Perfluorocarbon-hydrocarbon systems are known to show large GE values, and frequently to present liquid-liquid eq~ilibria,~ which makes them good candidates for the study of this kind of effect. The binary system C6H6-2,2,4-TMP shows positive Gg values, while C,F,-C,H, presents an S-shaped GE us.x, curve. Therefore the ternary system C,F6-C,H,-2,2,4- TMP must have high positive GE values in some regions of the concentration triangle 539540 Thermodynamics of Fluorocarbon- Hydro carbon Mixtures and negative values in other regions. If the W-shaped CE,, curves were actually related to high G: values, data for this type of ternary system might be helpful in understanding their relationship. Experimental Excess volumes were measured using a continuous dilution dilatometer, and vapour pressures were measured by the static method. The techniques were the same as those used previ~usly,~ thus only the experimental uncertainties will be quoted here. The precision of the vapour pressure was f 8 Pa and in the excess volume was f 2 x cm3 mol-l. In both techniques the temperature was controlled to within f 5 mK, and the mole fraction was known to within & 1 x The temperature scale agrees with the IPTS-68 within f0.02 K.C,F, and C,H, were the same as used in a previous work;4 the 2,2,4-TMP was Philips- Petroleum, Research Grade, with a minimum purity of 99.9% in mole fraction. Its density at 298.15 K was 0.68769, which compares favourably with the recommended value of 0.6878.8 The refractive index of 2,2,4-TMP at 303.15 K was n, = 1.391 49, while the literature value is n, = 1.391 45.9 Results and Discussion The Binary System Table 1 shows the V z data for the C6F,-2,2,4-TMP system at 298.15 K. The excess properties of the binary system have been fitted to an (m/n) Pade approximant m Z"/X,( 1 -xl) = c A,(2x1 - l)# c Bj(2X, - 1)j (1) i - 0 ! j I o where zE is either V: or GE/RT, x, is the mole fraction of C,F,, and A, and Bj are adjustable parameters with Bo = 1.A regression method based on the maximum likelihood principle has been used to obtain the parameters of eqn ( 1).l0 These are given in table 1 for V: together with their estimated uncertainties, the standard deviations of the variables, the estimated variance of the fit and the residuals of the variables Axl and AV:. Fig. 1 shows the VE results for c,F6-2,2,4-TMP and C,H6-2,2,4-TMP at the same temperature." It can be observed that in the system with C,F, the VE curve has a maximum which is almost three times that of the system with C,H,. This is an expected result since fluorocarbon-hydrocarbon interactions are quite unfavourable,' C,F, is more ordered than C6H6,3 and both breaking correlations of molecular order and unfavourable interactions give rise to positive contributions to V;.l2 Table 2 shows the experimental pT-x, values for the C6F,-2,2,4-TMP system at 298.15,323.15 and 348.15 K.The thermodynamic consistency of the data has been tested following a version of Barker's method described previously,13 assuming that the composition dependence of G:/RT is described by eqn (1). Table 2 gives the smoothing coefficients and their uncertainties, the values of the residuals of the variables, Axl and Ap, the activity coefficients, y1 and yz, the G: values and their estimated uncertainties, AG:, calculated from the variance-covariance matrix of the parameters of eqn (1).Fig. 2 shows the three G t curves as well as the corresponding curve for the C&,- 2,2,4-TMP system at 298.15 K. One can easily understand the fact that GE for the C6F,-2,2,4-TMP system is larger than that for C6H,-2,2,4-TMP, considering the positive contribution to G: of the unfavourable fluorocarbon-hydrocarbon interactions and the high degree of enthalpic-entropic compensation of the order contribution^.'^ Similar curves have been found for the systems with n-C16H34 and with n-C14H30;4 however, it is not clear why the difference of the maxima of G: for the systems withJ. Aracil et al. 54 1 Table 1. Experimental excess volume data, their deviations from the smoothed values, and smoothing coefficients and standard deviations for system x,(C,F,)-( 1 - x,) (2,2,4-trimethyl- pentane) at 298.15 K x1 V3cm3 mol-' A V z / lo-, cm3 mol-' x, V3cm3 mol-I A V z / low3 cm3 mol-' 0.0724 0.1374 0.2023 0.2794 0.31 17 0.4082 0.4809 0.5377 0.5585 0.3386 0.6086 0.8313 1.9724 1.1402 1.2955 1.3650 1.3777 1.3716 1.4 6.5 - 0.5 -11.3 - 2.8 8.8 2.7 0.5 I .8 0.581 1 0.6375 0.6516 0.6791 0.7019 0.7 139 0.7382 0.7683 1.3661 1.3131 1.2970 1.2469 1.2074 1.1750 1.1261 1.0417 - 3.5 -2.5 -5.1 1.6 - 1.7 5.4 - 1.8 2.3 A , = 5.5004+0.0091; A, = 0.5735k0.0377; A, = 0.1502+0.0617; A , = 0.0878+0.140; o(x) c loe5; o(V3cm3 mol-') = 4.6 x lop3.2'/' / / \ \. \ 0 0.2 0.6 0.6 0.8 1 X Fig. 1. Excess volumes of the C,F,-2,2,4-TMP (---.- ) and C,H,-2,2,4-TMP (- ) systems at 298.15 K. 2,2,4-TMP is only ca. 80 J mol-', while for the corresponding systems with n-C16H34, at the same temperature, that difference is more than 500 J m01-l.~ An unrealistically large free volume contribution' would be necessary to account for such differences. The HE values have been estimated from the temperature dependence of GE.Both the Gibbs-Helmholtz equation and the procedure developed by Munsch have been used. l5542 Thermodynamics of Fluorocarbon- Hydro carbon Mixtures Table 2. Experimental and calculated variables from vapour pressure data, their deviations from smoothed values, and smoothing coefficients and standard deviations for system xl(C,F,) 41- x l ) (2,2,4-trimethylpentane) at 298.15, 323.1 5 and 358.15 K x, lo6 Ax, p/kPa Ap/Pa GZ/J mol-l AGg/J mol-' Y 1 Y 2 0 0.1114 0.1202 0.2099 0.2984 0.3816 0.4059 0.4496 0.466 1 0.4927 0.5088 0.5500 0.5606 0.603 1 0.6436 0.6887 0.731 1 0.7618 0.7962 1 .o 0 0.1114 0.1202 0.2099 0.2984 0.3816 0.4059 0.4496 0.466 1 0.4927 0.5088 0.5500 0.5606 0.603 1 0.6436 0.6887 0.73 1 1 0.7618 0.7962 1 .o 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 -1 -1 0 - 1 0 1 0 0 0 0 1 0 1 -1 -1 0 6.578 8.260 8.370 9.229 9.881 10.372 10.505 10.717 10.794 10.906 10.973 11.125 11.161 11.299 1 1.408 11.516 1 1.594 1 1.638 1 1.667 1 1.269 19.533 23.490 23.755 26.161 28.093 29.616 30.0 16 30.678 30.917 3 1.297 31.500 32.006 32.131 32.592 32.999 33.374 33.708 33.901 33.995 34.099 0 5 -5 -1 0 5 0 0 -3 -1 -3 0 1 -1 3 - 1 -1 -2 3 0 0 -4 -4 -3 7 8 5 10 7 -9 -2 -3 -6 -6 - 19 -6 - 25 -21 72 0 298.15 K" 0 200 213 327 407 457 467 48 1 484 488 489 488 487 479 465 442 41 3 387 353 0 323.15 Kb 0 153 163 257 326 372 381 394 398 402 403 403 402 395 383 364 339 316 287 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2.3530 1.8598 1.8322 1.6076 1.4553 1.3496 1.3234 1.2806 1.2657 1.2428 1.2297 1.1980 1.1903 1.1610 1.1353 1.1089 1.0860 1.0706 1.0547 1 .oooo 1.7808 1 S743 1.5607 1.4390 1.3425 1.2676 1.248 1 1.2153 1.2037 1.1856 1.1752 1.1499 1.1437 1.1201 1.0995 1.0785 1.0607 1.0490 1.037 1 1 .oooo 1 .0000 1.0133 1.0153 1.0416 1.0774 1.1200 1.1343 1.1625 1.1741 1.1939 1.2068 1.2427 1.2527 1.2969 1.3460 1.4109 1.4848 1.5484 1.6328 2.7948 1 .ow0 1.007 1 1.0083 1.0245 1.049 1 1.0805 1.0915 1.1134 1.1225 1.1382 1.1484 1.1769 1.1848 1.2197 1.2578 1.3072 1.3615 1.4067 1.4643 2.0742J.Aracil et al. 543 Table 2. (cont.) x, lo5 Ax, p/kPa Ap/Pa G:/J mol-' AGZ/J mol-' Y1 Y 2 0 0.1091 0.2077 0.2967 0.3803 0.4485 0.4583 0.4908 0.4979 0.5485 0.5599 0.6019 0.6467 0.6879 0.7305 0.7524 0.7960 1 .o 0 3 -1 -4 -2 -2 10 -3 0 -1 0 0 0 0 1 -1 -1 0 48.252 56.936 62.859 67.320 70.999 73.678 74.124 75.207 75.472 77.155 77.524 78.797 80.046 8 1.099 82.090 82.525 83.354 84.750 348.15 K" 0 0 -11 140 3 230 19 288 13 324 14 342 - 67 343 18 347 1 348 6 348 -1 347 -2 342 0 332 -2 317 - 12 297 13 284 6 255 0 0 0 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 0 1.6843 1.4609 1.3363 1.2579 1.2019 1.1646 1.1597 1.1443 1.1410 1.1191 1.1145 1.0980 1.0817 1.0676 1.0539 1.0473 1.0348 1 .oooo 1 .oooo 1.0078 1.0247 1.0457 1.0703 1.0944 1.0982 1.1 116 1.1 147 1.1387 1.1446 1.1684 1.1979 1.2299 1.2692 1.2925 1.3468 1.91 18 a A, = 0.7896+0.0003; B, = -0.0772k0.0009; B, = -0.1550+0.0019; a@) = 2Pa; a(x,) = 1 x lop6.A, = 0.5997+0.0009; B, = -0.1095+0.0038; B, = -0.0690+_0.0073; a@) = 19Pa; 18Pa; a(xl) = 3 x lop5. ~(x,) = 5 x ' A, = 0.48 12 & 0.004; B, = - 0.0902 f 0.0024; B, = - 0.1676 f 0.0043; a($) = 500 L 00 - I I E 2 300 W E u 2 oc 1 oc I I I I Fig. 2. Excess Gibbs energy of the C,F,-2,2,4-TMP system at 298.15 K (- ), 323.15K (----), 348.15 K (-*--- ) and of the C,H,-2,2,4-TMP system at 298.15 K (---------).544 Thermodynamics of Fluorocarbon-Hydrocarbon Mixtures Table 3. Maximum values excess properties for C6F6--hydocarbon systems at 298.15 K cosolvent G:/J mol-1 H:/J mo1-l TSZ/J mol-l V3cm3 mol-1 C,F,-cosolvent 2,2,4-TMP 489 1740 1252 I .37 c-C,H,,~ 776 1517 74 1 2.57 678 - 2.13 2.19 n-C16H34 624 - - - n-C14H30 C,H,-cosolvent 2,2,4-TMP * 409 990 58 1 c-C6H12 383 420 800 n-C14H30 23 I 1260 1030 n-C16H34 127 1400 1272 0.5 0.65 1.10 1.17 a At 303.15 K.Table 4. Characteristic parameters of the pure substances for the Flory-Prigogine-Patterson model at 298. I5 K substance p*/J v*/cm3 mol-' P / K P C6F6 635 87 4361 1.332 2,2,4-TMP 372 129 4728 1.287 628 69 4709 1.292 4720 1.291 c-C6H12 540 84 C6H6 From the disagreement between both methods we estimate an uncertainty of 18 % in Hg. The HE curves are symmetric around x, = 0.5, and the calculated values at that composition are 1740, 1300 and 920 J mol-1 at 298.15,323.15 and 348.15 K, respectively. Most the work done in discussing order effects in mixtures is based on the use of a globular molecule which acts as an order breaker.1*2114 Probably the most frequently used order-breakers have been c-C,H,, and 2,2,4-TMP. The existing work seems to indicate that methyl and methylene groups can be considered as equivalent in mixtures of alkanes with c-C6H12, CCl, or C,&.1'2 Since both C6Fe3 and C6H6' present some degree of orientational order, it is worth comparing the behaviour of their binary systems with C-C6H12 and 2,2,4-TMP. Table 3 shows the equimolar excess functions for these systems, and it can be observed that in the systems with C,F, they are larger than in those with C6H,.In order to discuss these values in terms of the usual energetic, free volume and order contributions,' the characteristic parameters of the pure components for the Prigogine-Flory-Patterson theory16 at 298.15 K are shown in table 4.As it can be seen, the most important differences between 2,2,4-TMP and C-C6H12 lie in their p* values. The so-called p* effect," if noticeable for these systems, would give a larger positive VE contribution for the 2,2,4-TMP system than for that with c-C6H12; however, the fact that Vg is very similar for the corresponding systems with C,H, seems to indicate that this effect is not important in this case since C6F6 and C,$6 have almost the same p* values. Moreover, the free-volume contribution (negative for VE and HE)l must be larger for the systems with C6F6 according to the reduced volume D values in table 4. The difference in interactions between the components gives rise to positive contributions to VE, 7's: and H z , in accordance with the differences between the excess functions of the systems with C6F6 and those with C6H6.Nevertheless, whilst TSE andJ . Aracil et al. 545 1.0 0 -1.0 d 5 -2.0 -3.0 -4.0 I i 0 0 2 0 4 0 6 0 8 1 X 1 0 -1.5 LL----+ 02 O L 0.6 0.8 X Fig. 3. (a) Excess number of neighbour molecules around a C,F, (or C,H,) molecule as defined in eqn (2), T = 298.15 K. C,F,-n-C,,H3, (- ) ; C,F,-n-C,,H,, (---) ; C6F,-2,2,4-TMP Bars indicate the estimated uncertainty. (b) Excess number of neighbour molecules around an alkane molecule as defined in eqn (2). Symbols as in (a). (-.-. ); C6H6-n-C1,H30 (- ); C,H,-n-C,,H,, (---); C6H,-2,2,4-TMP (-.-a- 1 HE are larger for the system C6F,-2,2,4-TMP than for C,F,-c-C,H,,, the opposite holds for Vg.We can conclude that 2,2,4-TMP and c-C,H,, show quite different volumetric and entropic behaviours when mixed with C,F,, while their behaviour is much more similar when mixed with other hydrocarbons like C,H,. However, from the energetic point of view the differences are not so important (recall that HZ for C6F,-2,2,4-TMP has an 18 % uncertainty). For the sake of completeness we have included in table 3 the maxima of GE and V: curves for the systems n-C16H34 and n-C14H3,, with C,F, or C6H6e4 Whether the differences found between the systems with 2,2,4-TMP and c-C,H,, are due to the different behaviour of methyl and methylene groups, or to the ring shape of c-C,H,, cannot be discussed with the present data. Experiments involving other octane isomers with different methyl to methylene ratios and methylcyclohexanes would be helpful in order to clarify this point.Further insight into the behaviour of these systems can be obtained from the so-called Kirkwood-Buff integrals. l8 These can be calculated from experimental data, the main contributions coming from the GE and V z ~a1ues.l~ This is interesting since these magnitudes show the most important differences in the systems discussed above. From the Kirkwood-Buff integrals one can calculate the quantity (2) N " ANj = x j v l 0 krj(r)-gjj(r)]4nr2drul P Q\ Table 5. Liquid phase compositions, xi, vapour pressures, p, vapour phase compositions, ys, activity coefficients, yi, excess Gibbs energy, G:, calculated from the PDA for the C,F6-C,H,-2,2,4-TMP system (residuals of the variables are also shown) y3 GE/J mol-' xl 105Ax1 x2 105Ax, p/kPa Ap/kPa y1 Y2 Y1 Y 2 0.6810 0.5969 0.5322 0.4810 0.4392 0.4045 0.3763 0.3472 0.0954 0.0764 0.0630 0.05 17 0.043 1 0.0360 0.0301 0.4174 0.3418 0.2878 0.2477 0.1985 0.1456 0.1042 0.0832 0.2754 0.1917 0.1421 0.1 120 0.0921 0.0762 0.0650 -1 -4 3 0.1 -4 6 ' 2 0.2 -4 -0.1 11 -0.8 -1 1 -3 2 12 16 - 0.8 4 26 28 6 20 0.2 0.3 - 16 6 12 6 0.1448 -1 0.2504 -2 0.3317 1 0.3959 -0.1 0.4485 2 0.4919 12 0.5274 1 0.5639 -0.1 0.21 14 8 0.3688 0 0.4796 11 0.5731 -0.4 0.6440 0.3 0.7025 0.3 0.7514 7 0.1061 -1 0.2680 -13 0.3838 -21 0.4695 6 0.5749 -16 0.6883 -17 0.7769 5 0.8218 0.1 0.3231 -20 0.5289 6 0.6508 -4 0.7247 1 0.7736 -0.2 0.8126 -0.7 0.8403 5 298.15 K 11.955 -0.193 12.018 -0.006 12.099 0.075 12.197 0.079 12.336 0.005 12.450 - 0.065 12.563 -0.120 12.705 -0.181 10.515 -0.172 11.827 0.069 12.608 0.034 13.120 -0.075 13.429 -0.188 13.611 -0.272 13.692 -0.316 11.317 0.057 11.829 0.015 12.192 0.145 12.478 0.272 12.871 0.332 13.228 0.283 13.365 0.177 13.386 0.096 12.572 -0.399 13.232 -0.172 13.492 0.088 13.549 -0.047 13.545 -0.036 13.524 -0.048 13.483 -0.053 0.6010 0.4546 0.3555 0.2879 0.2407 0.2078 0.1832 0.1602 0.1591 0.1 177 0.1015 0.0898 0.0805 0.07 17 0.0632 0.5253 0.3541 0,2504 0.1905 0.1354 0.0946 0.07 12 0.0606 0.2762 0.1517 0.1068 0.0862 0.0743 0.0648 0.0587 0.086 1 0.1660 0.2524 0.3355 0.4 107 0.4742 0.5264 0.5785 0.3786 0.5612 0.6328 0.6749 0.7020 0.7250 0.7486 0,1440 0.3558 0.4835 0.5624, 0.6422 0.7 160 0.7766 0.8106 0.4284 0.6039 0.68 15 0.7298 0.7640 0.7941 0.8 175 0.9034 0.7843 0.689 1 0.61 75 0.5649 0.5287 0.5012 0.4761 1.4599 1.4972 1.6546 1.8440 2.0185 2.1750 2.2973 1.2336 1.0430 0.8885 0.7948 0.7 177 0.6944 0.7319 0.778 1 1.0579 0.8571 0.8202 0.8388 0.8754 0.9191 0.9700 0.5081 0.5856 0.6899 0.7834 0.8589 0.9 138 0.9559 0.9936 1.433 1 1.3905 1.2915 1.2024 1.1409 1.0962 1.066 1 1.1302 1.1886 1.1783 1.1546 1.1171 1.0741 1.0463 1.0357 1.2695 1.1693 1.0998 1.0654 1.0467 1.0358 1.029 1 3.1076 4.5103 5.3663 5.7602 5.8591 5.7958 5.6798 5.5304 1.0262 1.0409 1.0936 1.1804 1.2794 1.3906 1.5017 1.1917 1.3544 1.5721 1.7839 2.0892 2.4436 2.6727 2.7351 1.2758 1.6470 1.9724 2.1855 2.3204 2.4005 2.4384 75 - 121 - 230 - 280 - 298 - 298 - 289 -271 322 432 484 494 476 443 40 1 456 443 440 432 408 358 296 256 47 1 477 432 38 1 337 296 264323.15 K 0.6810 - 1 0.5969 0 0.5322 -2 0.48 10 2 0.4392 0 0.4045 -0.1 0.3763 -3 0.3472 3 0.0954 2 0.0764 3 0.0630 1 0.0516 0.2 0.0431 -2 0.0360 -29 0.0301 1 0.4172 1 0.3418 -10 0.2877 -3 0.2477 -2 0.1985 2 0.1456 2 0.1042 1 0.0832 3 0.2754 3 0.1917 -6 0.1421 6 0.1120 6 0.0921 2 0.0762 -2 0.0650 -5 0.1448 0.2504 0.3317 0.3959 0.4484 0.4919 0.5274 0.5639 0.21 13 0.3688 0.4796 0.573 1 0.6441 0.7025 0.7514 0.1061 0.2679 0.3837 0.4694 0.5749 0.6883 0.7769 0.8218 0.3230 0.5288 0.6508 0.7247 0.7736 0.8126 0.8403 -1 -1 -2 2 2 1 - 5 -2 -7 -6 -2 -6 -6 2 -7 2 -2 2 -3 -2 -1 -4 6 12 -7 -4 -5 -0.1 2 0.4 34.583 0.018 34.799 - 0.122 35.020 -0.044 35.278 -0.071 35.516 0.015 35.722 0.035 35.938 0.074 29.398 0.164 33.007 0.303 35.032 0.070 36.173 - 0.027 36.3 19 - 0.250 37.03 1 - 0.434 37.41 5 - 0.477 37.596 - 0.45 1 31.249 0.266 32.576 -0.344 33.741 -0.152 34.596 - 0.03 1 35.584 0.022 36.438 0.024 36.797 0.102 36.896 0.125 32.418 0.454 34.735 0.601 36.047 0.296 36.649 0.117 36.964 -0.005 37.103 -0.048 37151 -0.064 0.72 12 0.629 1 0.5545 0.4972 0.4498 0.41 12 0.3805 0.3488 0.1556 0.1082 0.0849 0.0662 0.0525 0.0417 0.0334 0.5 157 0.3522 0.2674 0.2187 0.1699 0.1263 0.0957 0.0802 0.2737 0.1664 0.1222 0.0987 0.0839 0.0721 0.0639 0.1464 0.2705 0.3619 0.4296 0.4843 0.5284 0.5633 0.5991 0.3507 0.5257 0.6062 0.6562 0.6944 0.7299 0.7635 0.1203 0.3444 0.47 1 5 0.5486 0.6350 0.7245 0.7953 0.83 10 0.43 13 0.6 100 0.6975 0.7519 0.788 1 0.8183 0.8400 1.0556 1.0393 1.021 1 1.0070 0.991 5 0.9788 0.9688 0.9569 1.2257 1.1684 1.1497 1.1160 1.0692 1.0187 0.9733 1.0708 0.9019 0.8202 0.7833 0.7625 0.7713 0.8083 0.841 5 0.8479 0.7578 0.7585 0.7776 0.80 17 0.8288 0.8565 0.81 11 0.9104 0.9549 0.9765 0.9932 1.0042 1.0115 1.0192 1.2355 1.2396 1.1735 1.1109 1.0728 1.0504 1.0373 0.8296 1.0515 1.0738 1.064 1 1.0508 1.0396 1.0298 1.0236 1.1 127 1.0670 1.0429 1.0339 1.0284 1.0235 1.0193 1.2124 1.1267 1.0982 1.089 1 1.0890 1.0911 1.0944 1.0987 1.0730 1.0815 1.1367 1.2236 1.3090 1.3847 1.4475 1.1909 1.2649 1.3519 1.426 1 1.4982 1.5346 1.5472 1.5638 1.2732 1.457 1 1 S377 1.5613 1.5707 1.5838 1.6008 108 48 23 12 7 6 7 10 303 36 1 387 380 355 323 289 247 188 186 185 178 161 141 127 23 1 232 207 184 166 149 136548 Thermodynamics of Fluorocarbon-Hydrocarbon Mixtures Table 6.Parameters of partial differential ap- proximants for the ternary system xl(C6F6)-x2 (C6H6)-x3(2,2,4-TMP) 298.15 K 323.15 K uoo 0.4983 UlO UNl - 5.2794 - _ _ UOl 0.3214 16.190 - - 4 2 u21 u22 - PlO - 1.0464 POI - 1.0865 4 1 0.6426 dP)/kPa 0.172 104+,) 1 1044x2) 1 1 02a( T)/K 2 - 1.61 16 -3.8081 5.5081 0.8792 - 3.2822 - 3.1628 - 5.6578 12.652 18.659 - 0.241 6 4 0 where N / V is the number density of the mixture and gij(r) is the radial distribution function of the i-j pair.ANj is a measure of the difference between the distribution o f j molecules around an i molecule and around a j Fig. 3 shows ANl and AN2 at 298.15 K for the systems considered in this paper. The ANl values indicate that the aromatic molecules preferentially surround other aromatic molecules rather than alkane molecules. The AN, values indicate that the alkane molecules tend to surround other alkane molecules for x, > 0.5, while they tend to surround aromatic molecules for high alkane concentrations.The final distribution arises from the competition between both tendencies. It has been pointed out that n-alkanes show some degree of orientational correlations with C,H,, toluene or p-xylene.2 The values AN2 > 0 seem to indicate that those correlations contribute to stabilize the n-alkanes in the solution, whilst according to the values ANl < 0 in the same concentration interval, they seem to be unfavourable for the aromatic molecules. The curves corresponding to mixtures of 2,2,4-TMP with C,F, or with C,H, are very similar, the differences being due mainly to the differences in molar volumes between C,F, and C,H,.Also the behaviour of the systems with n-CI6H3* and n-C,,H,, are similar when mixed with C,F, (or C,H,), although there are some quantitative differences between the two pairs of curves corresponding to each aromatic molecule, confirming the tendency of fluorocarbons and hydrocarbons to segregate. ’ The Ternary System Table 5 shows the vapour-pressure data for the x~(C,F,)-~,(C,H,)-~~(~,~,~-TMP) system at 298.15 and 323.15 K. The data reduction has been carried out by a modified Barker’s method described previ~usly.~ The concentration dependence of GE for the ternary system has been described by where the GE(ij) are the excess Gibbs energies of the i-j binary systems, and GF,, is a ternary contribution.The GZ(iJ3 for the C,F,-C,H, system has been calculated from theJ . Aracil et al. 549 Fig. 4. (a) Concentration triangle for the ternary system including the G: curves of the three binary systems at 323.15 K. (b) GZ surface for the ternary system calculated from the PDA, eqn (4). The parameters of the ternary contributions are given in table 6. data of Gaw and Swinton,,, for C6H6-2,2,4-TMP it has been taken from the work of Funk and Prausnitz,22 and for C,F,-2,2,4-TMP the results in table 1 have been used. As in ref. (4) we have investigated the correlation abilities of several expressions for G,E,m but for the sake of brevity we will only report on the one which gave the best results : (4) i "' "* m1 mz j = O j ' = O 1 = 0 Z ' = O G,E,,/RTxlx2x3 = C C Ujj,z:zi C C Pll,z;z;.Eqn (4) is a partial differential approximant, PDA, in which z, = x, - x,, z, = x, - x, and Uijr, and P,l, are the adjustable parameters. Table 6 gives the values of the parameters550 Thermodynamics of Fluorocarbon-Hydrocarbon Mixtures of the optimal PDA, as well as the standard deviations of the variables, the activity coefficients, vapour-phase compositions and GE values. Fig. 4(a) shows the triangle of compositions for the ternary system and the GE (ij) curves for each of the three binary systems. Fig. 4(b) shows the GZ surface of the ternary system referred to the same triangle of compositions. The main feature is a minimum placed near the C6F6 corner of the composition triangle. Similar behaviour was found by Anderson et aZ.23 in their study of the C,F,-C6H6-CS, system. However, the standard deviations in vapour pressures and compositions shown in table 6 are much larger than the experimental errors.This leads to an uncertainty in the G: values of f 10 J mol-1 at the centre of the composition triangle. Since the calculation of the AN,, eqn (2), involves derivatives of G: with respect to composition, much more precise G: data than those reported in table 5 are needed for a detailed discussion of the way the molecules are distributed in the ternary solution. References 1 S. N. Bhattacharyya, M. Costas, D. Patterson and H. V . Tra, Fluid Phase Equilibria, 1985, 20, 27; A. Heintz and R. Lichtenthaler, Angew. Chem., Int. Ed. Engl., 1982, 21, 184. 2 R. G. Rubio, C. Menduiiia, M.Diaz Peiia and J. A. R. Renuncio, J. Chem SOC., Faraday Trans. 1,1984, 80, 1425; G. Tardajos, E. Aicart, M. Costas and D. Patterson, J. Chem. SOC., Faraday Trans. I , 1986, 82, 2977. 3 M. R. Battaglia, T. I. Cox and P. A. Madden, Mol. Phys., 1979, 37, 1413; P. A. Madden, M. R. Battaglia, T. I. Cox, R. K. Pierens and J. Champion, Chem. Phys. Lett., 1980, 76, 604; E. Bartsch, H. Bertagnolly, G. Schulz and P. Chieux, Ber. Bunsenges. Phys. Chem., 1985, 89, 147. 4 J. Aracil, R. G. Rubio, M. Caceres, M. Diaz Peiia and J. A. R. Renuncio, Fluid Phase Equilibria, 1986, 31, 7 1 ; J. Aracil, R. G. Rubio, J. Nuiiez, M. Diaz Peiia and J. A. R. Renuncio, J. Chem. Thermodyn., 1987, 19, 605. 5 E. Wilhelm, Thermochim. Acta, 1985, 94, 47. 6 M. E. Saint Victor and D. Patterson, Fluid Phase Equilibria, 1987, 35, 237. 7 F. L. Swinton, in Chemical Thermodynamics. A Specialist Report, ed. M. L. McGlashan (The Chemical 8 D. Rossini, API Research Project No. 44, 1954. 9 J. A. Riddick and W. B. Bunger, in Organic Solvents. Physical Properties and Methodr of Purification Society, London 1978), vol. 2. (Wiley-Interscience, New York, 1970). 10 T. F. Anderson, D. S. Abrams and E. A. Grens, AIChE J., 1978, 24,20. I I Y-P. Handa and G. C. Benson, Fluid Phase Equilibria, 1979, 3, 185. 12 M. Barbe and D. Patterson, J. Solution Chem., 1980, 9, 753. 13 R. G. Rubio, J. A. R. Renuncio and M. Diaz Peiia, Fluid Phase Equilibria, 1983, 12, 217. 14 M. Barbe and D. Patterson, J. Phys. Chem., 1987,82, 40. 15 E. Munsch, Thermochim. Acra, 1979, 32, 151. 16 P. J. Flory, J. Am. Chzm. SOC., 1965, 87, 1833. 17 H. T. Van and D. Patterson, J. Solution Chem., 1982, 11, 793. 18 J. G. Kirkwood and F. Buff, J. Chem. Phys., 1951, 19, 774; A. Ben Naim, J. Chem. Phys., 1977, 67, 4884. 19 E. Matteoli and L. Lepori, J . Chem. Phys., 1984, 80, 2856; R. G. Rubio, M. G. Prolongo, M. Cabrerizo, M. Diaz Peiia and J. A. R. Renuncio, Fluid Phase Equilibria, 1986, 26, 1 ; R. G. Rubio, M. G. Prolongo, J. A. R. Renuncio and M. Diaz Peiia, J. Phys. Chem., 1987,91, 1177. 20 E. D. Crozier, S. P. McAlister and R. Turner, J. Chem. Phys., 1974, 61, 126. 21 W. J. Gaw and F. L. Swinton, Trans. Faraday SOC., 1968, 64, 2023. 22 E. W. Funk and J. M. Prausnitz, Znd. Eng. Chem., 1970,62, 8. 23 D. Anderson, R. J. Hill and F. L. Swinton, J. Chem. Thermodyn., 1980, 12,483. Paper 7/581; Received 1st April, 1987

ISSN:0300-9599    

DOI:10.1039/F19888400539

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. 1, 1988, 84(2), 551-560 Thermodynamics of Micelle Formation of Alkali-metal Perfluorononanates in Water Comparison with Hydrocarbon Analogues Inger Johnson and Gerd Olofsson" Division of Thermochemistry, Chemical Center, University of Lund, P.O. Box 124, S-221 00 Lund, Sweden The enthalpy and heat capacity changes for micelle formation of lithium perfluorononanate in water have been determined from calorimetric measurements of differential enthalpies of dilution of concentrated surfactant solution. The final concentrations varied between 0.001 and 0.025 mol dm-3 and measurements were made at four temperatures between 15 and 43.5 "C. The enthalpy of micelle formation of sodium per- fluorononanate was determined at 30 "C from measurements of differential enthalpies of solution of the crystalline surfactant.The volume change accompanying micelle formation of sodium perfluorononanate at 30 "C was determined from density measurements. In evaluating the experimental results the concentrations of surfactant in monomer and micellar forms in solutions above the c.m.c. were computed using the thermodynamic model for the association of ionic amphiphiles proposed by Jonsson and Wennerstrom. At ambient temperatures the perfluorononanate salts give closely the same enthalpy and volume changes of micelle formation as the hydrocarbon analogues. However, the heat capacity change is larger, probably stemming from a larger partial molar heat capacity contribution of the perfluoroalkyl group in the aqueous, monomeric amphiphile. The larger size of the perfluoroalkyl group means that there will be a larger number of water molecules in the first hydration layer around a perfluoroalkyl group than around the analogous alkyl group.Thus the stronger hydrophobic character of perfluorocarbon surfactants compared to the hydrocarbon analogues may be ascribed to the difference in size between the two types of hydrophobic groups. There is considerable interest in the physicochemical properties of fluorinated surfactants, but so far little thermodynamic information is available. Perfluorocarbon surfactants behave in a way similar to hydrocarbon surfactants in the formation of micelles above the critical micelle concentration (c.m.c.). However, they are more surface-active than their hydrocarbon analogues and their c.m.c.is close to that of the analogous hydrocarbon surfactant having a 1.5 times longer carbon chain.l The Krafft point, c.m.c. and surface tension of a number of aqueous perfluorinated surfactants have been studied by Shinoda and coworkers.1.2 Phase equilibria in binary systems of water and heptadecafluorononanoic acid and a number of its salts have been investigated by Fontell and Lindman.3 From these studies we concluded that the micelle formation of lithium perfluorononanate could be studied conveniently by calorimetry over an extended temperature range and that the results would be representative for other alkali- metal salts. In this paper we report calorimetric measurements of lithium per- fluorononanate leading to values of the enthalpy of micelle formation at four temperatures between 15 and 43.5 "C.The enthalpy and volume changes for micelle formation of sodium perfluorononanate at 30 "C have also been determined. The 551552 Thermodynamics of Micelle Format ion thermodynamic quantities of micelle formation are defined as the difference between the partial molar quantity of the amphiphile in the micellar state just above the c.m.c. and the partial molar quantity of the monomer at the c.m.c. It is now well established that for ionic amphiphile systems the monomer concentration decreases with increasing amphiphile concentration above the c . ~ . c . ~ - ' It is therefore necessary to evaluate the composition of the reaction solutions in order to derive a correct value of the partial molar quantity for the micellized amphiphile.' In a previous paper,' we have shown that this can be achieved by applying the thermodynamic model for the association of ionic amphiphiles proposed by Jonsson and Wennerstrom.'O-12 Materials Experimental Lithium heptadecafluorononanate, LiPFN, and sodium heptadecafluorononanate, NaPFN, used in the calorimetric measurements were the same preparations as described in ref.(3) and were kindly provided by Dr Fontell. The solutions of NaPFN for the density measurements were prepared by neutralizing heptadecafluorononanoic acid, HPFN (Riedel-de-Haen, West Germany) with aqueous sodium hydroxide. The purity of HPFN was checked by titration with sodium hydroxide and found to be better than 99.9 wt %. Reagent-grade water produced by a Milli-Q filtration system was used to prepare solutions.The density of 20.04 wt % LiPFN solution used in the calorimetric measurements was determined using a pycnometer and was found to be 1.098 0.001 g at 25.00 "C. The density of dilute solutions of NaPFN was measured using a Paar density meter DMA60 1. Calorimetry An LKB Batch microcalorimeter modified for titration (LKB model 2 107-357) was used for titration calorimetric measurements at 25, 35 and 43.5 "C. The reaction and reference cells, made of 18-carat gold, were filled with 5.00 cm3 pure water. While the sample of 20 wt % LiPFN solution was injected into the reaction cell, the same amount of water was introduced into the reference cell. The injection volume for each titration step was 10.59 mm3.For the titration measurements at 15 "C, an LKB-8721 reaction- solution calorimeter with a 6 cm3 glass vessel was used. The sample solution was titrated into the glass vessel by means of a stainless-steel capillary tube (length 1 m, i.d. 0.27 mm), fastened by epoxy resin to a Hamilton gas-tight syringe (1710 LT). The capillary tube passes through a tube (i.d. 1 mm) mounted in a slit at the inside of the stirrer holder and ends ca. 15 mm below the surface of the calorimeter liquid. The syringe is motor-driven and samples were injected at a rate of 0.17 mm3 s-l. The calorimeter was initially filled with 5.50 cm3 pure water and 10-25 mm3 of sample solution were injected in each titration step. The performance of this small vessel was checked and found satisfactory by measuring the enthalpy of solution of propan-1-01 in water at 25 "C.13 The measurements of the differential enthalpy of solution of crystalline NaPFN were made using an LKB-8721 reaction-solution calorimeter with a 25 cm3 glass vessel.Samples of amphiphile crystals were placed in cylindrical glass ampoules (1 cm3 volume) which had thin end walls and narrow necks which were sealed under low flame and detached. The measured enthalpy changes were corrected for a small endothermal background effect that was observed when breaking empty ampoules in the filled calorimeter vessel. The effect, which was found to be 0.05 0.01 J at 30 "C, is due mainly to the introduction of the small air bubble into the calorimeter liquid, which results in some evaporation.I .Johnson and G. Oiofsson 553 *t I 20 [ LiPFN]/mmol dm-3 T -14 t Fig. 1. Comparison between calculated (full line) and experimental (bars) titration curves at 15.1 "C. Results Differential enthalpies of dilution of 20 wt % solution of LiPFN have been measured as a function of total amphiphile concentration at 15.1, 25.0, 35.0 and 43.5 "C. The experiments consisted of successive injections of small amounts of the concentrated LiPFN solution into the calorimeter vessel initially containing pure water. The concentration change in each step was ca. 1 mmol dmP3 and the titration was ended at a total concentration of ca. 25 mmol dm-3. The measured enthalpy changes varied between 1 and 70 mJ. Results of a titration series at 15.1 "C are shown in fig. 1. The measured enthalpy changes An(obs) expressed per mole of added LiPFN are plotted against total LiPFN concentration in the calorimeter vessel.The lengths of the bars indicate the change in concentration in each step. Two titration series were made at each temperature. Three different situations occur during a titration series. When the final concentration is below the c.m.c., all micelles added will break up to give monomers and the measured enthalpy changes Az(obs) will include the enthalpy of dilution of the concentrated micellar solution, AH(dil), the enthalpy of demicellization and a contribution from monomer-monomer interactions. In the c.m.c. region only a fraction a of the injected micelles will dissociate and AH(obs) will consist of AH(di1) and a fraction of the demicellization enthalpy.As the concentration increases, the degree of dissociation will decrease and at a certain concentration c(a = 0) there is no demicellization and as a consequence no change in the monomer concentration. The observed enthalpy change at this concentration equals the enthalpy of dilution AH(di1) of the concentrated LiPFN solution to the final concentration c(a = 0). In experiments with final concentration above c(a = 0), AH(obs) will contain in addition to AH(di1) a contribution from micelle formation as the monomer concentration decreases with increasing total concentration. The difference between Az(obs) measured just above and below the c.m.c. is approximately equal to the enthalpy of micelle formation AH(mic), but in order to derive a more correct value the effect of the decreasing monomer concentration above the c.m.c.must be taken into account.' The concentrations of amphiphile in the monomer and micellar states have been evaluated as a function of total concentration applying the model for the association of ionic amphiphiles proposed by Jonsson and554 Thermodynamics of Micelle Formation Table 1. Calculated concentration of LiPFN monomers as function of concentration of LiPFN in micelles at 35.0 "C c(mic) c(mon) c(mic) c(mon) /mmol dm-3 /mmol dm-3 /mmol dm-3 / m o l dm-3 0.010 0.040 0.094" 0.150 0.500 0.800 1 .ooo 1 SO0 2.000 2.500 3.000 8.774 9.109 9.399 9.498 9.800 9.877 9.900 9.9 13 9.891 9.844 9.796 4.000 5.000 6.000 8.000 10.000 12.000 16.000 20.000 24.000 30.000 9.671 9.531 9.386 9.092 8.803 8.528 8.020 7.571 7.175 6.663 a C.m.c.Wennerstrom. The processes taking place in each titration step could then be quantitatively described. The computer program used for the calculations has been described previo~sly.~ The input parameters are temperature, micelle radius, number of monomers in micelle, counterion valency and c.m.c. To be able to estimate values of the radius of the micelle and the monomer number, it is necessary to know the volume of the amphiphile molecule. Comparison bFtween densities of perfluorinated and ordinary fatty acids gives a volume of ca. 400 A3 per LiPFN molecuje. From this volume a monomer number of 20 is estimated assuming a radius of 12.4 A, which is 8 of the radius of a small, spherical micelle of sodium dodecylsulphate.The radius is thus assumed to be proportional to the number of carbon atoms in the hydrophobic chain. The same values of micelle radius and monomer number have been used at the various temperatures. Starting values of c.m.c. were read off at the breaks in the titration curves, see fig. 1. The values were adjusted slightly to get the best fit between calculated and experimental titration curves. Concentrations of LiPFN in the micellar state and the corresponding monomer concentrations calculated at 35 "C are given in table 1. There are only small changes in the relative amounts of monomers and micellized LiPFN at the other temperatures. The 20 wt YO LiPFN titrand solution was estimated to contain 99.7% in the micellar state. The linear slope of the titration curves at concentrations below the c.m.c.indicates non-ideal behaviour of the monomer solutions. The increase in AH(obs) with concentration is the same within experimental uncertainties at the various temperatures, giving a value for the monomer interaction coefficient kmon of 102 dm3 kJ mol-2. This value is very close to the slope found for SDS soluti~ns.~ At concentrations above 16 mmol dm-3 the injected micelles are diluted and in each titration step a small amount of micelles is formed from monomers in solution. The slight negative slope in this region is the sum of changes in micelle interactions as the micelle concentration increases and the decreasing monomer-monomer interactions. The slope in this region is temperature-dependent and equal to - 9 dm3 kJ mo1-2 at 15.1 "C, - 23 dm3 kJ mol-' at 25.0 "C, -47 dm3 kJ mo1-2 at 35 "C and -56 dm3 kJ mo1-2 at 43.5 "C.If it is assumed that the presence of micelles does not influence the monomer-monomer interactions, micelle interaction coefficients kmic can be calculated using the value of k,,, given above. The following values of kmic (in dm3 kJ mol-2) are calculated: -23 at 15.1 "C, -34 at 25.0 "C, -55 at 35.0 "C and -63 at 43.5 "C.I. Johnson and G. Olofsson 555 The observed enthalpy changes in each titration step can be expressed as: ninj AH(obs) = An AH(mic) + ninjA H(di1) + An[c.m.c. - c(mon)] k,,, + (ninj + An)[c(mic) - c(mic, a = O)] kmic (1) where ninj is the amount of injected LiPFN (in the micellar state), An is the change in the amount of LiPFN in the micellar state, AH(mic) is the enthalpy of micelle formation from monomers at the c.m.c.to give micelles at c(a = 0), where the micelle concentration is c(mic, tc = 0). The concentration c(a = 0) was evaluated from the results of the computations of monomer concentration as function of micelle concentration, cf. table 1, and values of AH(mic) and AH(di1) were estimated from plots of AH(obs) us. total concentration. Values of An for each titration step were calculated and titration curves were computed by eqn (1). Only small adjustments of the preliminary values of the c.m.c., AH(mic) and AH(di1) were needed to give good agreement between calculated and experimental titration curves. As can be seen in fig. 1, the agreement is within experimental uncertainties. Values of the c.m.c., AH(mic) and AH(di1) giving the best fits are shown in table 2.Note that if the c.m.c. had been chosen instead as the reference concentration for the micellar state, it would have changed AH(mic) by less than 0.05 kJ m0l-l.' Curves representing the partial molar content of LiPFN relative to infinitely dilute solution (H-H") at various temperatures are shown in fig. 2. These were calculated using values of the c.m.c. and AH(mic) evaluated from the calorimetric experiments, values of c(mon) and c(mic) computed from the theoretical model and values of the interaction coefficients k,,, and kmic as described above. The decrease of AH(mic) for LiPFN with increasing temperature is not linear, the change being larger between 15.1 and 25 "C than that between the higher temperatures.From the results in table 2, ACJmic) at 25" is estimated to - 500 30 J K-l mol-l. Measurements were made of differential enthalpies of solution of crystalline NaPFN as function of total amphiphile concentration at 30 "C. The experiments consisted of measuring the enthalpy changes when breaking a series of ampoules containing ca. 35 mg of amphiphile in the calorimeter which contained at the beginning 25 cm3 pure water. Two series of measurements were made and each series consisted of the consecutive breaking of seven ampoules. The concentration change was ca. 3 mmol dme3 in each step. The experiments are in many ways analogous to the LiPFN dilution experiments, but the amphiphile is introduced in the form of pure compound instead of concentrated micellar solution.The results were evaluated in the same way as described for LiPFN, the only difference when using eqn (1) being that ninj is replaced by the amount of NaPFN in the ampoule and AH(di1) by the enthalpy of solution of crystalline NaPFN to give micelles, A$H at c(a = 0). The values of k,,, and kmic found for LiPFN were also used for NaPFN. The following values were derived: c.m.c. = 9.0f0.3 mmol dmP3, AH(mic) = 4.0f0.3 kJ mol-1 and AZCH = 24.5 f0.5 kJ mol-'. The enthalpy of dissolution of crystalline NaPFN to give monomers in infinitely dilute solution was estimated to be 19.8f0.5 kJ mol-'. All values refer to 30.0 "C. The value of the c.m.c. is in good agreement with the value reported by Kuneida and Shinoda.2 The densities of seven solutions of NaPFN with concentrations ranging from 4.7 x mol kg-l have been measured at 30.3 "C.Apparent molar volumes of the solute were calculated using to 35.4 x L'@ = M,/d+ 1000(l/d- l/dy)/m (2) where L'@ is the apparent molar volume of the solute, d and dy are the densities of the solution and of water, M , is the molar mass of the solute and m is the molality of the solution. In the calculations the value dy = 0.995 548 g cmP3 has been used. The results of the density measurements are summarized in table 3. The three solutions with concentrations below the c.m.c. contain NaPFN in the monomer state and the556 Thermodynamics of Micelle Formation Table 2. Values of the c.m.c., the enthalpy of micelle formation, AH(mic), and the enthalpy of dilution, AH(dil), determined for LiPFN from calorimetric measurements of differential enthalpies of dilution of 20 wt YO LiPFN solution c.m.c.A H(mic) AH(di1)" t/"C /mmol dmP3 /kJ mol-' /kJ mo1-I 15.1 10.9 & 0.3b 12.6 k 0.3b 0.3 f 0.2b 25.0 9.3 f 0.3 6.8 k 0.3 0.8 f 0.2 43.5 10.3 & 0.5 - 1.4k0.3 1.8k0.2 35.0 9.4 & 0.3 2.4 _+ 0.3 1.2k0.2 Dilution to c(a = 0) which was found to be c.m.c. +2.6 mmol dm-3. Error limits indicate estimates of the overall uncertainty of the values. values. t (c) 2 - 1 0- 20 [ LiPFN]/mmol dm-3 (d) -2 - Fig. 2. Partial molar enthalpy content of LiPFN in solution relative to infinite dilution (Z-H") as function of total concentration. (a) 15.1 "C, (b) 25 "C, ( c ) 35 "C, (6) 43.5 "C. Table 3. Results of measurements of densities of sodium perfluorononanate solutions at 30.3 "C m d v* m(mic) VJmic) /mmol kg-' /g /cm3 mol-' /mmol kg-' /an3 mol-' 4.689 0.996 773 224.4 6.650 0.997 285 224.3 8.683 0.997 790 227.2 20.61 1.000 761 231.8 12.48 236.0 23.64 1.001 524 231.8 15.85 235.0 31.19 1.003 403 232.3 24.22 234.3 35.35 1.004 368 234.4 29.35 236.3 V,(mon) = 225 & 2 cm3 mol-', V,(mic) = 235 1 cm3 mol-l.I.Johnson and G. Olofsson 557 calculated V, is the apparent molar volume of monomeric NaPFN, V,(mon). Above the c.m.c. the solutions contain both monomers and micelles and the calculated V, is the sum of contributions from Vo(mon) and the apparent molar volume of NaPFN in micelles V,(mic). The composition of the post-micellar solutions was computed as described previously and the concentrations of NaPFN in micellar form (in mmol kg-') are given in table 3, as are the derived values of V,(mic).As the solutions are dilute, V,(mon) and V,(mic) are close approximations of the respective partial molar volumes at the c.m.c. and the volume change for micelle formation AV(mic) can be calculated as AV(mic) = V,(mic) - V,(mon). This gives A V(mic) = 10 f 2 cm3 mol-' (at 30.3 "C). Discussion The substitution of fluorine atoms for hydrogen atoms in alkyl carboxylic acids leads to a larger hydrophobic group and an increased acidity. Both these changes may influence the aggregation behaviour of perfluorinated carboxylates. Our aim has been to determine thermodynamic properties for micelle formation of a typical perfluorinated carboxylate so that the effect of the fluorine substitution on micelle formation could be analysed by comparison with hydrocarbon analogues.We found that sodium decanoate is the only alkyl carboxylate that has been studied calorimetrically and for which reliable values of AH(mic) and AC,(mic) have been determined.'* At 25 "C AH(mic) = 8.75 kJ mol-'. It is derived as the difference between linear regions of the partial molar enthalpy below and above the c.m.c. extrapolated to the c.m.c. Exchanging lithium for sodium as counterion is not expected to influence AH(mic) significantly. Likewise, decreasing the alkyl chain by one CH, group will probably have a minor effect on AH(mic), as for instance nonyl- and decyl-trimethylammonium bromide were found to give closely similar AH(mic) at 25 "C, 0.20 and 0.25 kJ mol-l, re~pective1y.l~ Therefore lithium nonanate can be expected to give about the same AH(mic) as sodium decanoate.The value found for lithium perfluorononanate at 25 "C is 6.8 kJ mol-l, which is of the same order of magnitude as for sodium decanoate. The c.m.c. for LiPFN is 0.0093 mol dm-3, while it is 0.21 mol kg-l for sodium nonanate at 25 OC.16 This difference in the c.m.c. corresponds to a difference of ca. - 11 kJ mol-1 in the standard Gibbs energies of micelle formation AG: if it is calculated according to the multiple equilibrium model [AG; = (1 +p) RT In X(c.m.c.)],l' assuming the extent of counterion binding p to be the same and equal to 0.5.'' The stronger hydrophobic character of the perfluorinated surfactant leading to the lower c.m.c. is not seen in the enthalpy values and therefore can be ascribed to a more positive entropy of micelle formation. We find a value of - 500 J mol-' K-' for AC,(mic) of LiPFN at 25 "C, while ACJmic) for lithium nonanate is expected to be ca.-360 J K-' mol-'. The latter value is based on ACJmic) for sodium decanoate16 equal to -430 J K-' mol-' from which - 70 J K-' mol-', the increment to ACJmic) of a CH, group, has been s~btracted.'~ The lower AC,(mic) for LiPFN can be correlated with the larger molar volume of the perfluorinated amphiphile. The molar volume V(mic) of micellized LiPFN is ca. 235 cm3 mol-', while it will be close to 148 cm3 mol-' for lithium nonanate.20p21 The cause of the volume difference is the greater van der Waals radius of fluorine relative to hydrogen.The ratio of the volumes is in accordance with the observation by Shinoda et al. that the c.m.c. of fluorinated surfactants is close to that of an ordinary surfactant whose hydrocarbon chain length is ca. 1.5 times longer than the fluorocarbon chain.' If we assume that the milieu of the alkyl group in the micelles resembles that in liquid hydrocarbon, ACJmic) can be seen as the sum of the heat capacity contribution from changes in hydrophobic hydration of the alkyl chain and head-group contributions, ACJmic) = ACJhydr) + ACJHG). Thus for the hydrophobic group, micelle formation has the reverse characteristics of dissolution in water. Generally the surface area of non-polar solutes correlates with thermodynamic properties in water such as solubility,22 entropy changes 19 FAR I558 Thermodynamics of Micelle Formation for d i s s o l ~ t i o n ~ ~ - ~ ~ and partial molar heat capacity.26* 27 From the molar volumes the surface area of the C,F1, group can be estimated to be ca.1.25 times the surface area of the CgH17 group. The larger size of the perfluorocarbon chain will primarily affect AC,(hydr) but only secondarily the heat capacity contribution of the head group. We can therefore expect the heat capacity contribution from hydration ACJhydr) to be ca. 1.25 times larger for the C8F17 group than for the hydrocarbon group. The partial molar heat capacity in water, c;,2, of the octyl group can be estimated to be 784 J K-l mol-1 at 25 "C using the group contribution scheme.,' The heat capacity of liquid octane C,(l) is 254 J K-l mol-', which gives -530 J K-' mol-' for the heat capacity of dehydration of the octyl group, AC,(hydr) = C,( 1) - C;,2.The head-group contribution ACJHG) to AC,(mic) of lithium nonanate can then be estimated to be 170 J K-l mol-1 from ACJHG) = AC,(mic) - ACJhydr). For the perfluoro-octyl group ACJhydr) then becomes -660 J K-l mol-1 (-530 x 1.25), and ACJmic) for LiPFN can be calculated to be -490 J K-l mol-l. This estimate agrees well with the experimental value and the difference between ACJmic) for the hydrocarbon and perfluorocarbon nonanates can be fully rationalized in terms of the relative sizes of the hydrophobic groups. A much larger AC,(mic) has been derived for sodium perfluoro-octanoate from c.m.c. measurements between 20 and 60 "C and a value of - 1250 J K-' mol-' is reported at 25 0C.29 In view of the present result this value does not seem realistic.Probable reasons for the overestimate of ACJmic) are magnification in the successive differentiations of errors in derived values of c.m.c. and deficiencies in the relation expressing the temperature variation of the c.m.c. The similarity in the micellization properties of the alkyl and perfluoroalkyl- carboxylates is also seen in the volume change which is closely the same. Vikingstad et al. have determined A V(mic) for a series of sodiumalkylcarboxylates from both density measurements and conductance measurements at varying pressures.2o The agreement between the two methods was good. For R8C0,Na they found AV(mic) = 9.6k0.4 cm3 mol-1 and they observed a slow increase with increasing alkyl chain length from 8.9 cm3 mol-1 for R,CO,Na to 11.2 cm3 mol-1 for RllC02Na.20 We find AV(mic) = 10+2 cm3 mol-' for C,F17C0,Na, in good agreement with these values.A higher value of AV(mic) equal to 19.4 cm3 mol-' has been derived from a high-pressure study of C7F15C02Na.30 We believe that errors propagated in the derivation of A V(mic) at 1 atm? from the conductance measurements may be larger than that estimated by the authors and the reason for the discrepancy. Shinoda et al. have determined a value of 21.5 1 cm3 mol-l for AV(mic) of C7F17C0,H at 30 "C from dilatometric measure- m e n t ~ . ~ ~ Unlike alkanoic acids, perfluorocarbon acids form micelles and liquid crystalline phases in binary systems with water. In the study of phase equilibria in aqueous systems of perfluorononanoic acid and a number of its salts, Fontell and Lindman3 found that the aggregation behaviour of HPFN (and its dimethyl- and diethyl-ammonium salts) differed significantly from that of its alkali-metal salts.They ascribe the difference to a low degree of ionization of the aggregates. The perfluorononanoic acid would act as a weak acid in aggregates, while it is a fairly strong acid as monomers in aqueous solution. The perfluoro-octanoic acid can be expected to behave in a similar way' and the volume change observed for micelle formation would include the volume contribution from protonation. This contribution can be expected to be significant, as for instance the protonation of acetic acid at infinite dilution is accompanied by a volume change of 11.5 cm3 rnol-l.,l We suggest that the major part of the difference between our value of 10 cm3 mol-1 for LiPFN and the value of 21.5 cm3 mol-1 found for C,F,,CO,H may be due to the volume change from protonation of the acid.Thus there is no need to assume any difference between hydrocarbon and fluorocarbon groups in the strength of t 1 atm = 101 325 Pa.I . Johnson and G. Olofsson 5 59 interaction with water or perturbation of solvation water. The stronger hydrophobicity of perfluorocarbon surfactants as manifested by their high surface activity compared to the hydrocarbon analogues may well arise from the size difference leading to an increased surface area of the hydrophobic group. Note added in proof. Recently results of volumetric measurements on LiPFN solutions were Their values for V&mon), V#(mic) and A V(mic) are significantly higher than the values we find for NaPFN.Therefore we have made additional measurements on LiPFN solutions at 25 "C. The sample preparation, density measurements and evaluation of V4 were made as described for NaPFN. We find V&mon) = 223 + 1 cm3 mol-l, V4(mic) = 237f 1 cm3 mol-1 and AV(mic) = 14+2 cm3 mol-l, in good agreement with our results for NaPFN. The reason for the discrepancy between our results and those reported by La Mesa and Sesta is obscure. However, we note that they report values of c.m.c. for LiPFN and NaPFN that are less than half the values we find. Our values are in good agreement with those reported in ref. (2) and (1 8).The statement by La Mesa and Sesta that according to recent n.m.r. self-diffusion experiment^^^ NaPFN is almost completely associated at concentrations close to 4 x mol dmW3 appears to be a misunderstanding. The skilful1 assistance in the calorimetric measurements of Mrs S. Bergstrom and Miss C. Wigand is gratefully acknowledged. This work has been financially supported by the Swedish Natural Science Research Council. References 1 K. Shinoda, M. Hato and T. Hayashi J. Phys. Chem., 1972, 76, 909. 2 H. Kuneida and K. Shinoda, J. Phys. Chem., 1976, 80, 2468. 3 K. Fontell and B. Lindman, J. Phys. Chem., 1983, 87, 3289. 4 T. Sasaki, M. Hattori, J. Sasaki and K. Nukina, Bull. Chem. Soc. Jpn, 1975, 48, 1397. 5 E. A. G. Ananiansson, S. N. Wall, M. Almgren, H.Hoffman, I. Kielman, W. Ulbricht, R. Zana, 6 S . G. Cutler, P. Meares and D. G. Hall, J. Chem. Soc., Faraday Trans. 1, 1978, 74, 1758. 7 E. Vikingstad, J. Colloid Interface Sci., 1979, 72, 68. 8 K. M. Kale, E. L. Cussler and D. F. Evans, J. Solution Chem., 1982, 11, 581. 9 I. Johnson, B. Jonsson and G. Olofsson, submitted. J. Lang and C. Tondre, J. Phys. Chem., 1976, 80, 905. 10 G. Gunnarsson, B. Jonsson and H. Wennerstrom, J. Phys. Chem., 1980, 84, 3114. 11 B. Jonsson and H. Wennerstrom, J. Colloid interface Sci., 1981, 80, 482. 12 B. Jonsson, G. Gunnarsson and H. Wennerstrom, in Solution Behaviour of Surfactants: Theoretical and Applied Aspects, ed. K. L. Mittal and E. J. Fendler (Plenum Press, New York, 1982), vol. 1, p. 317. 13 D. HallCn, S - 0 . Nilsson, W. Rothschild and I. Wadso, J. Chem. Thermodyn., 1986, 18, 429. 14 R. De Lisi, G. Perron and J. E. Desnoyers, Can. J. Chem., 1980, 58, 959. 15 R. De Lisi, C. Ostigny, G. Perron and J. E. Desnoyers, J. Colloid Interface Sci., 1979, 71, 147. 16 E. Vikingstad, A. Skauge and H. Hsjland, J. Colloid Interface Sci., 1978, 66, 240. 17 P. Stenius, S. Backlund and P. Ekwall, in Thermodynamics and Transport Properties of Organic Salts, ed. P. Franzosini and M. Sanensi, IUPAC Chemical Data Series No. 28 (Pergamon Press, Oxford, 1980). 18 H. Hoffmann, G. Platz, H. Rehage, K. Reizlein and W. Ulbricht, Makromol. Chem., 1981, 182, 451. 19 G. M. Musbally, G. Perron and J. E. Desnoyers, J . Colloid Interface Sci., 1974, 48, 494. 20 E. Vikingstad, A. Skauge and H. Hrajland, J. Colloid interface Sci., 1978, 66, 240. 21 F. J. Miller, Chem. Rev., 1971, 71, 147. 22 R. B. Hermann, J. Phys Chem., 1972, 76, 2754. 23 S. J. Gill and I. Wadso, Proc. Natl Acad. Sci. USA, 1976, 73, 2955. 24 S. F. Dec and S. J. Gill, J. Solution Chem., 1984, 23, 27. 25 E. Wilhelm, R. Battino and R. J. Wilcock, Chem. Rev., 1977, 77, 219. 26 N. Nichols, R. Skold, C. Spink, J. Suurkuusk and I. Wadso, J . Chem. Thermodyn., 1976, 8, 1081. 27 S. J. Gill, S . F. Dec, G. Olofsson and I. Wadso, J. Phys. Chem., 1985, 89, 3758. 19-2560 Thermodynamics of Micelle Formation 28 Landolt- Bornstein, Zahlenwerte und Funktionen, II Band, 4 Teil Kalorische Zustandgrossen (Springer 29 P. Mukerjee, K. Korematsu, M. akawauchi and G. Sugihara, J. Phys. Chem., 1985, 89, 5308. 30 G. Sugihara and P. Mukerjee, J. Phys. Chem., 1981, 85, 1612. 31 K. Shinoda and T. Soda, J. Phys. Chem., 1963, 67, 2072. 32 C. La Mesa and B. Sesta, J . Phys. Chem., 1987, 91, 1450. 33 J. Carlfors and P. Stilbs, J . Phys. Chem., 1984, 88, 4410. Verlag, Berlin, 1967). Paper 7/584; Received 1st April, 1987

ISSN:0300-9599    

DOI:10.1039/F19888400551

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1988, 84(2), 561-574 Solvent Properties of Polyaromatic Hydrocarbons Grazyna Geblewicz Chemistry Department, University of Southampton, Southampton SO9 5NH David J. Schiffrin" Wolfson Centre for Electrochemical Science, University of Southampton, Southampton SO9 5NH The solubility of inorganic and organic salts at 150 "C in polyaromatic hydrocarbons has been studied, and the results analysed using an electrostatic model. It is shown that only significant solubilities can be obtained with quaternary ammonium salts with C, or longer carbon chains. The n* solvatochromic parameter has been calculated for the different solvents from the absorption spectra of o-nitroaniline. It has been found that the Hildebrand solubility parameter and the work of cavity formation calculated from the scaled particle theory cannot account for the large solubility differences observed in the various solvents studied. It is proposed that the Gibbs energy of solvation is determined by the local polarisability, as shown by its linear dependence on n*.It is shown that these results rationalise previous observations on the solubilisation of transition-metal ions in aromatic solvents using hydrophobic ligands. The use of organic solvents in electrochemistry has been the subject of extensive research and there has been a particular interest in finding systems suitable for electrodeposition processe~.~-~ Most of the solvents which give good solubility and conductivity of electrolytes are themselves strong ligands and can be easily incorporated in the coordination sphere of transition-metal ions, which displaces the metal reduction potentials to values where the decomposition of the solvent interferes with elec- trodeposition.It is clear, therefore, that in the choice of aprotic solvents for metal electrodeposition, there are two conflicting requirements. A high dielectric constant appears to be necessary for achieving a significant solubility and conductivity of solutions of electrolytes, but this limits the choice to solvents with a high donor number, which are precisely those that produce significant redox shifts by coordination to the transition-metal ions. One approach that can avoid this problem is to ensure that the solvent is not involved in the coordination environment around the ions by the use of solvents of very low donor number, for example, the aromatic hydrocarbons, in which solubilisation of the transition-metal ions can be achieved by the use of hydrophobic ligands, such as the aliphatic amines.* In spite of their low dielectric constants, aromatic hydrocarbons can give conducting solutions with organic electrolytes at sufficiently high temperatures, as shown recently by Campbell et aL5 For instance naphthalene, 1 -methylnaphthalene and 1 -chloronaphthalene give conducting solutions at 150 "C with quaternary ammonium salts, enabling simple electrochemical processes to be carried out.The use of some aromatic hydrocarbons for electroplating has been described in the 1iteratu1-e.~. For example, toluene has been used for electroplating aluminium on steel in a bath consisting of the complex formed between triethylaluminium and sodium fluoride and operating at 80-95 0C.6 The advantages of the aromatic solvents include their high chemical stability, the very large potential polarisation window available, their high boiling point and low cost.The 56 1562 Solvent Properties of Polyaromatic Hydrocarbons useful potential window of an aromatic solvent will be determined to a first approximation, by the difference between the energy of the lowest unoccupied and highest occupied electronic energy levels. These differences are very large and in many cases of the order of 4 eV. In agreement with this, for instance, the difference between the oxidation and reduction potentials of naphthalene and biphenyl are 3.91 and 4.28 V, respectively.' Furthermore, the very low donor properties of these solvents make them ideal as media for reactions where the control of the coordination chemistry of the metal ion without interference by the solvent is required. The purpose of the present work was to understand the conditions required to obtain good solubilities and conductivities of salts in the aromatic solvents. The solubilities measured have been analysed using electrostatic solvation models and in terms of short-range solute-solvent interactions.The nature of these interactions has been further studied by measuring the solvatochromic shifts of indicator solutes and establishing relationships between the Gibbs energy of solvation and the polarisability scales.Experimental The solvents studied and their liquid range are shown in table 1. The thermal stability and very high boiling points of some of these compounds make them suitable candidates to bridge the temperature range between non-aqueous and molten salt electrochemistry. 1 -Chloronaphthalene (Aldrich) was distilled under vacuum and then dried over CaH,. 1 -Methylnaphthalene (Lancaster Synthesis Ltd) was dried, distilled under vacuum and stored over CaH,. Fluoranthene (Aldrich) was twice recrystallised from acetone ; fluorene (BDH) was twice recrystallised from CCl, ; naphthalene (BDH) was three times recrystallised from ethanol ; m-terphenyl (Aldrich) was recrystallised from ethanol several times ; biphenyl (BDH) was twice recrystallised from ethanol. KC1 and KBr (BDH, spectroscopic grade) were recrystallised from water and dried for several hours under vacuum at 400 "C.Tetrabutylammonium tetrafluoroborate (TBABF,) (Aldrich) was recrystallised from water ; tetramethylammonium bromide (TMABr, Fluka), tetraethylammonium bromide (TEABr, Fluka), tetrapropylam- monium bromide (TPABr, Fluka) and tetrabutylammonium bromide (TBABr, Aldrich) were dissolved in hot ethanol and precipitated with ether which had been previously stored over CaH,. All these chemicals were dried at 80 "C under vacuum for several hours prior to use. Solubility measurements were made in a glass cell thermostatted in an oil bath. The mixture of molten solvent and excess salt was stirred in the cell with a PTFE-covered stirrer. The cell lid had ground joints for introducing nitrogen, for measuring the temperature and for sample removal.A dried nitrogen atmosphere was kept over the solutions throughout the experiments. After the addition of an excess quantity of the salt under study to the molten solvent, the mixture was heated and stirred for 8 - 10 h. After this, a sample was taken out by means of a heated pippete and put into a heated cell containing a fine frit. After filtering, the solution was placed in several previously weighed volumetric flasks. After cooling, the flasks were weighed again and the contents were dissolved in toluene, then mixed with triply distilled water and shaken for several hours using a mechanical shaker. The aqueous and organic phases were separated and the extraction procedure was repeated twice.The aqueous solutions were analysed using atomic adsorption spectrophotometry for potassium ions or by potentiometric titration with silver nitrate for the bromides. The conductivity of the solutions was measured using an AC Wienn bridge constructed from Sullivan components (0.05 YO accuracy). The conductometric cell had a constant of 0.727 cm-l. The measurements were carried out in the frequency range 0.5-5 kHz and in this range no significant frequency dispersion of the measured conductivity was observed.G . Geblewicz and D. J . Schiflrin 563 Table 1. Liquid range of the polyaromatic hydrocarbons studied boiling melting point/"C point/"C naphthalene 218 80.55 1 -methylnaphthalene 244.64 - 30.5 1 -chloronaphthalene 258.8" - 2.3 biphenyl 255.9 71 fluorene 293.5 116.7 fluoranthene 375 111 rn-terphenyl 365 89 At 753 mm.The high-temperature spectrophotometric measurements were carried out with a modified Pye-Unicam SP 700 spectrophotometer, and for the measurements at room temperature, a Pye-Unicam 8800 spectrophotometer was employed. o-Nitroaniline and m-nitroaniline were used as the indicator solutes to measure the shift of the absorption maximum caused by the solvent.8 Results and Discussion Solubility and Conductivity Results The solubility of KCl and KBr was studied at 150 "C. The values obtained were very low, of the order of 0.01 mmol dmV3. The results are given in table 2. An increase of temperature did not significantly affect the solubilities of inorganic salts and fig. 1 shows the temperature dependence of the solubility of KBr in naphthalene in the temperature range 100-200 "C.None of the solutions of inorganic salts showed any significant electrical conductivity. Organic electrolytes, such as tetramethyl- and tetraethyl-ammonium bromides had solubilities in the range 10-4-10-3 mol dm-3 as shown in table 3, but the conductance of these solutions at 150 "C was also very low, being less than 0.1 R-l cm-' for all of the solvents studied. The solubilities of all the organic electrolytes are compared in table 3. TBABr and TBABF, could be mixed with the solvents in all proportions. Significant conductivities were obtained for TPABr and even higher values were observed for TBABF, solutions. Fig. 2 shows the concentration dependence of the equivalent conductance of these salts in 1-chloronaphthalene at 150 "C.Analysis of Solubilities Since the solutions of salts of small ions like KCl, KBr, TMABr and TEABr were not conducting, it was reasonable to assume that extensive ion-pairing (or even the formation of higher neutral aggregates) occurred. In order to rationalise the different solubilities, a simple electrostatic association model has been used. As a first approximation, it has been considered that the solutions are totally ion-paired. This idea was verified by calculating the distances between ions forming the contact ion pairs using the Born cycle for the dissociation scheme of an ion pair, as already discussed by Denison and Ram~ey,~ and the results compared with the known ionic radii. The cycle employed is shown in fig.3. M i and X i represent the free solvated ions, (M+X-), the ion pair in the solvent, M,+ and Xi the free ions in vacuum. AGZOlv is the564 Solvent Properties of Polyaromatic Hydrocarbons Table 2. Solubilities (units loA5 mol dm-3) of inorganic salts at 150 "C ~ solvent KC1 KBr naphthalene 5.1 10.8 1 -met hy hap h t halene 3.5 2.3 1 -chloronaphthalene 7.3 3.2 biphenyl 4.2 2.5 fluorene 2.4 7.0 fluoran thene 2.6 5.2 rn-terphenyl 5.4 3.5 4 .: 4. w 0" 4 . ( - 3 .' 3.1 I 1 1 I I I 1 _I 2.2 2.3 2.4 2.5 2.6 2.7 2.8 103 KIT Fig. 1. Temperature dependence of the solubility of KBr in naphthalene. Table 3. Solubilities (mol dm-3) of organic salts at 150 "C solvent TMAB TEABr TPABr naphthalene 5.7 x 10-5 2.8 x 10-3 1.907 1 -methylnaphthalene 7.1 x 10-5 3.5 x 10-3 0.127 biphenyl 3.7 x 10-5 9.9 x 10-4 0.011 fluorene 4.3 x 10-5 4.2 x 10-3 0.047 1 -chloronaphthalene 1.6 x 6.3 x 0.89 fluoran thene 1.8 x 7.8 x 1.89 rn-terphenyl 1.82 x 4.5 x 0.295G.Geblewicz and D. J . Schifrin 0.5 0.0 < 8 d -2.0 -2.5 565 - - rd r' - - t - 1.3 1.0 0.5 0.0 log c Fig. 2. Dependence of the equivalent conductance on the concentration of solutions of tetrapropylammonium bromide (A) and tetrabutylammonium tetrafluoroborate (a) in 1-chloronaphthalene at 150 "C. A ~ o S , i p Fig. 3. Born cycle representing the solvation of an ion pair in the solvents (AG,,,) followed by dissociation into the free ions in the solvent (AGionis). AGsolv is the Gibbs energy of solvation of the free ions. Gibbs energy of solvation of the ions from the gas phase, which was calculated from Abraham's solvation mode1.l0' l1 AGYonis is the Gibbs energy of ionisation of the ion pair in the solvent calculated assuming as a first approximation a uniform dielectric constant.(1) AGYOnis is given by: where 2 is the charge of ions, e is the charge of the electron, N is Avogadro's number, AG&is = Z2e2N[4z(r1 + r,) EE,]-'566 Solvent Properties of Polyaromatic Hydrocarbons E is the dielectric constant, E, is the permittivity of free space, and rl + r2 is the interionic distance in the ion pair. In these calculations, the dielectric constants and molar volumes were calculated at 150 "C from literature data.12* l5 AGZ,ip is the Gibbs energy of formation of an ion pair in the solvent from vacuum, which is given by This Gibbs energy can be calculated also from (2) AG,",,, = AG,O,,, - AG:onis.AG;,,, = AG: - AG;. (3) AGZ is the Gibbs energy of solution of the ion pair MX from vacuum, and AG; is the Gibbs energy of sublimation from the solid lattice to free ions in vacuum. From the above equations the distance of the ions in the ion pair can be calculated from (rl + r2) = (Z2e2N/4z~~o)[AG~o,v - AG," + AGZ1-l. (4) The Gibbs energies of solution, AG,", were calculated from the solubility data, assuming that the activity coefficient of the ion pairs was equal to unity, i.e. ( 5 ) where Csat is the molar concentration of the saturated solution. The Gibbs energy of the solid salt MX was calculated from the corresponding enthalpy (AH",) and entropy (A$) of lattice formation from the free ions in vacuum :"* l7 (6) where U,, is the lattice energy.Although Uo is calculated at 0 K, this value changes very little with temperature,'* and lattice energies were used directly in the following calculations. For KCl and KBr, A% was calculated using the Sackur-Tetrode equation for the gaseous ions; the entropies of the solids and other relevant data were taken from the literature." The values of the lattice energies for KCl, KBr, TMABr and TEABr used were 704,679, 549 and 514 kJ mol-l, respectively."* 18* 2o The entropy calculations for the quaternary ammonium ions is complicated by possible rotational and vibrational contributions. The entropy data at 25 "C given by Johnson21 were used, and these values were corrected to 150 "C using the heat capacity data for the corresponding gaseous alkanes given by Benson.22 The entropy of solid TMABr has been measured at different temperatures by Chang and W e s t r ~ m ~ ~ up to 350 K; no data are available at higher temperatures.However, since the heat capacity is almost linearly dependent on temperature up to 350 K (the linear regression coefficient in the range 200-350 K was 0.9999), it was assumed that this behaviour was valid up to 423 K and was used in the calculation of the entropy at this temperature. No entropy data are available for TEABr; therefore the approximation proposed by Johnson'' was employed. This makes use of the additivity rules for the entropy of the individual elements for analogous compounds. The entropy data for TEA1 were AG: = - R T In Csat AGZ = AH", - APLT = Uo + 2RT- TAPL in this calculation, i.e.(7) where S,' and SBr' are the individual entropic contributions of these elements. These values were calculated at 423 K from Latimer's and SOTEAI was calculated from ref. (23) using the same approach as described above for correcting the entropy data to 423 K. A summary of the values used in the calculation is given in tables 4 and 5 . The calculated interionic distances of KCl, KBr, TMABr and TEABr ion pairs in several solvents obtained from eqn (4) are compared with the corresponding crystal radii in table 6. The results obtained for KC1 and KBr are reasonable for contact ion pairs.G. Geblewicz and D. J. Schifrin 567 Table 4. Thermodynamic data used in the calculations of the Gibbs energy of lattice formation" s:/ AGOL/ kJ mo1-' s:/ solute J mol-' deg-' J mol-' deg-' ~~~ ~ KCl 263.3 100.0 639.0 KBr 251.2 1 14.4 620.1 TMABr 528.2 265.5 444.9 TEABr 71 1.8 406.3 391.8 " Si and Sz are the standard entropies of the solute in the gas and in the solid phase, respectively.Table 5. Gibbs energies of solution (AG,"/kJ mol-l) and solvation (AG,",,,/kJ mol-') of the solutes in different solvents (1 50 "C) naphthalene 1 -methylnaphthalene 1 -chloronaphthalene solute AG: AG,",,, AG,O AG:ol" AG: W O I " KCl 30.9 -425.5 36.1 -435.4 33.5 -471.8 KBr 32.1 -411.8 37.5 -421.4 36.4 - 457.1 TMABr 34.3 -311.1 33.6 -317.6 30.7 - 349.5 TEABr 20.7 -295.1 19.9 -301.2 17.8 -331.9 Table 6. Comparison of the values of calculated ionic radii of ion pairs in different solvents with crystallographic ionic radii (in nm) l-chloro- 1 -methyl- crystal naphthalene naphthalene naphthalene solute radii" ( E = 3.7) ( E = 2.50) (E = 2.61) KCI 0.318 0.280 0.331 0.290 KBr 0.334 0.296 0.344 0.302 TMABr 0.454 0.584 0.595 0.537 TEABr 0.506 0.890 0.784 0.699 a Crystal radii data from ref.(1 1) and (16). In the case of TMABr and TEABr the distance of closest approach is greater than the sum of the ionic radii, probably indicating a greater interaction with the solvent. From the temperature coefficient of the solubility [d In S/d(l/T)] shown in fig. 1, a value of the enthalpy of solution (AK) of -6.2 kJ mol-' was calculated for KBr. The small value of A% is a further indication of the extensive ion-pairing and perhaps of higher aggregation which occurs in these solutions, i.e.the electrostatic interactions in solution are similar to those on the lattice, and solvation makes a minor contribution to the energy of the aggregates. It can be concluded also that one of the main factors determining the solubility is the lattice energy of the salt, which does not depend very much on temperature. Salts formed from small ions like KC1, KBr, TMABr and TEABr dissolve in polyaromatic hydrocarbons in the form of neutral ion aggregates and the very low conductivities of the solutions confirm the strong ion-ion interactions in these cases.568 Solvent Properties of Polyaromat ic Hydrocarbons Analysis of the Conductivity Data In general the dependence of the equivalent conductance on concentration of a salt in a solvent of low dielectric constant presents a minimum followed by an inflection point on the conductivity curve at higher concentrations caused by the formation of quadrupoles.25-29 The results presented in fig. 2 are indicative of the presence of triple ions and probably of higher aggregate^.^, The TBABF, data were analysed using the Fuoss-Kraus theory,28 from which the equivalent conductance is given by where g(c) is a factor taking into account interionic interaction terms, A, and A: are the limiting equivalent conductances of the fully dissociated salt and the triple ions TBA(BF,), and (TBA),BF,+, Kp and kT are the ion pair and triple ion formation constants, respectively. In this theory, the two possible triple ions are treated as species with identical properties. g(c) was found to be very close to unity, mainly due to the very low permittivity of the medium ( E = 3.7).This term departs from unity only for much more polar solvent^.^^^ 31 No conductivity data are available for the polyaromatic solvents, and the values of A. had to be estimated. Owing to the low conductivity of the solutions studied, only an approximate value of A, needs to be used in eqn (8). The contribution to A. by the cation can be estimated quite accurately from the Walden product, which is 240 and 210 C2-l cm2 equiv-l Pa s for TPA+ and TBA+, respectively, for a wide range of For the inorganic ions, the value of the Walden product is more dependent on the nature of the solvent, and unfortunately no reliable data appear to be available for BF,. For this ion, the data for I- were used in view of the similarity of the ionic radii of BF, and I-.For Br- and I-, the Walden product was estimated by averaging data for solvents of similar viscosity as 1-chloronaphthalene at 150 "C (8.4 Pa g) and a value of 360 was This is a very approximate procedure, but as discussed before, large errors in A, do not affect significantly the calculations based on eqn (8). The values of A. were 71 and 68 C2-l cm2 equiv-l for TPABr and TBABF,, respectively. Fig. 4 shows the test of the Fuoss theory for TBABF,; the correlation coefficient was 0.985. Taking A:= values of Kp = 6.3 x lo4 dm3 mol-1 and k, = 30 dm3 mol-1 were obtained. These constants are similar to those obtained for other low dielectric constant systems.28 It can be concluded that in the case of TBABF, solutions, the major proportion of the electrolyte exists as ion pairs with only a minor proportion present as triple ions, and the formation of quadrupoles is less likely owing to the larger size of the ions.In the case of the TPABr solutions, eqn (8) was not applicable. The reason for this is not clear at present, but it should be noticed that the conductance is very low and it is very likely that higher aggregates are formed. A problem with this system is that the conductivity at concentrations lower than 0.05 mol dm-3 was very difficult to measure with the bridge employed (< lo-' R-l cm-l), and therefore the concentration region of the minimum that would be expected to be observed with this electrolyte in very dilute solutions, could not be studied. The influence of the ionic size can be clearly seen from the results in fig. 2; when the size of the ion is increased by changing the hydrocarbon chain from C , to C,, and Br- for BF,, the conductivity is increased by two orders of magnitude.When comparing the conductivities and solubilities of all the alkylammonium salts, it can be seen that an increase in the length of the carbon chain results both in smaller association constants due to purely electrostatic effects, and also in larger interactions of the salt with the solvent. These two effects give rise to significant solubilities andG. Geblewicz and D. J. Schiffrin 569 Fig. 4. Fuoss-Kraus plot for TBABF, in 1-chloronaphthalene at 150 "C. conductivities. Furthermore, an increase in the ionic radii decreases the lattice energy of the salt and these two factors determine a critical condition for total miscibility between the salt and the solvent.This appears to occur for a C , chain in the quaternary ammonium cation. An important conclusion of this analysis is that in order to dissolve salts of small ions, e.g. transition-metal ions, the usually very high lattice energy of the solid can be overcome by coordination of the cation with hydrophobic ligands that display sufficiently strong dispersion interactions with the polyaromatic solvents. Therefore, the same arguments discussed before for increasing the solubility of inorganic and quaternary ammonium salts in aromatic solvents can be applied to the dissolution of transition-metal ions in solvents of low dielectric constant. These principles have been used already for the electrodeposition of nickel and cobalt from molten naphthalene.' The value of K p for TBABF, obtained corresponds to a value of the parameter b in the Fuoss-Kraus theory of 10.However, the triple ion constant k, calculated with b = 10 is 140 dm3 mol-l, nearly five times greater than the experimental result. The discrepancy between theory and results can be due to the neglect of quadrupole formation. For instance, using b = 10, a quadrupole asociation constant of 3.1 dm3 mol-1 can be ca1c~lated.l~. 34 Unfortunately, the amount of experimental data did not justify a three-parameter fit, and for the same reason, attempts to calculate quadrupole constants for TPABr were unreliable.More work is required to understand the behaviour of these strongly associated solutions. Characterisation of the Solvation Ability of the Polyaromatic Solvents It is surprising that very large differences in solubilities were observed for the different solvents studied (table 3), if it is considered that the polyaromatic solvents all have very low and similar dielectric constants. Also, many of their other properties, such as surface tension, solubility parameters etc., are very similar. The energy of solution of a solute570 Solvent Properties of Polyaromatic Hydrocarbons can be considered as resulting from the creation of a suitably sized cavity in the bulk solvent, the reorganisation energy of the solvent round the cavity and the interaction energy of the solute with the reorganised and therefore solubilities will be affected by solvent-solvent and solute-solvent interactions. The solvent-solvent interactions which determine the cavity term can be taken into account by using either the Hildebrand solubility parameter, 8H,38i 39 which represents the energy of vaporisation of the solvent per unit molar volume, or calculated from theories of liquids.40 In the case of the solubility parameter, contributions from hydrogen bonding, 6,, polar, d9, and dispersion interactions, 6d, are usually c~nsidered.~~ However, for the polyaromatic solvents (probably with the exception of 1-chloronaphthalene), the hydrogen bonding and polar interactions are expected to be relatively small.compared with the dispersion interactions, and therefore SH was calculated taking into account only the later contributions.The solubility parameter was calculated from39 37 The solvent reorganisation energy is expected to be relatively 6, = - 4 . 5 8 + 1 0 8 ~ - 1 1 9 ~ ~ + 4 5 ~ ~ (9) where x = (n2- l)/(nz + 2 ) and n is the refractive index (6, units in MPa'j2). The solubility parameters for the different solvents were compared with the energy required to create a cavity in the solvent calculated using the scaled particle theory of fluids, in which the reversible work required to form a cavity of radius r in a fluid, We, is given hv40 " J -=In(l-Y)+ wc kT where Y = 7&/6 is the reduced number density, p = N / V is the number density, V is the molar volume, a, and az are the hard-sphere diameters of the solvent and solute molecules, respectively, such that the cavity radius is (a, + a,)/2, R = a,/a,.The effective hard-sphere diameter of the solvent can be calculated from the solubility of gases4, However, in the absence of solubility data for the solvents studied, the relationship between the van der Waals volumes and a, observed by de Ligny and van der Veen4' was used. These authors found that for a large number of solvents, the relationship between a, and Vw was (1 1) where Vw is the van der Waals volume in cm3 mo1-l. Eqn (1 1) has been found to be applicable to a wide range of compounds with geometries far removed from spherical and for this reason, it has been used in the present work. Values of Vw were calculated from the corresponding group contributions given by B ~ n d i .~ ~ Since a, plays a central role in the rigid-sphere fluid model, it was desirable to ascertain the suitability of the approach of de Ligny and van der Veen by calculating these values using another method. This was done using the relationship between surface tension and o1 for a hard- sphere liquid discussed by Mayer :44 ~ X N ~ T ; = - 10+ 1.13 Vw o,RT(2+ Y) ' = 4V(1- P) where y is the surface tension. This value was calculated at 150 "C from literature data.12-15 The two sets of values are shown in table 7 and, as can be seen, there is a nearly constant difference of 0.5 nm between the two methods of calculating a,. This difference is not surprising considering that the group additivity rules given by Bondi had been calculated at 25 "C.In spite of this difficulty, it can be said that the ordering of the values obtained for the cavity term for the different solvents is correct. Values of WJRT are also given in table 7. The similarity in the values of 6, for the different solvents indicates that the energy of formation of a cavity cannot account for the different solubilities observed.G. Geblewicz and D. J. Schiffrin 57 1 Table 7. Hard-sphere diameters, work of cavity formation, solubility parameters and solvatochromic parameters for polyaromatic solvents at 150 "C solvent ui/nm ui/nm W C W 4I/ (from V,) (from 12) (from V,) MPak Z* naphthalene 0.617 0.566 9.7 19.9 0.69 1 -chloronaphthalene 0.642 0.597 10.6 20.8 0.89 1 -methylnaphthalene 0.647 0.596 10.1 19.9 0.82 biphenyl 0.662 0.621 9.7 19.9 0.54 fluorene 0.675 11.9 fiuoranthene 0.709 13.7 Furthermore, the differences observed in WJkTdo not account either for the differences in solubilities.For instance, the cavity term for fluoranthene is greater than that of biphenyl, but the solubility of TPABr is nearly 200 times greater in the former solvent. It must be concluded that the differences in solubilities are related to short-range solute-solvent interactions, where not only the average molecular polarizability is important, but also the degree of packing of the solvent round the ions is relevant. In order to test these ideas, it was desirable to have a probe for the local solvent polarizability, through which the solvation behaviour of the same family of solvents could be tested. The technique employed was based on the measurement of shifts in the absorption spectra of molecules which have significantly different dipole moments in the ground and excited states. These solvatochromic shifts have been extensively used in the past for the characterization of organic solvents.** 37 In the ground state, solvent molecules are best oriented to the indicator solute.In the excited state, the solute has a different dipole moment (usually different in magnitude but not in orientation), and during the electronic transition, solvent reorientation is ruled out by the Frank-Condon principle. To stabilize the new charge distribution in the solute, the redistribution of the charge in the environment is only possible through electronic reorganization of the solvent ;35 therefore solvatochromic shifts are very convenient for distinguishing between solvents of similar chemical structure.The shift in the adsorption maximum can be related to the local polarizability of the solvent, and hence to a variety of thermodynamic and kinetic propertie~.~~-~' This solvent polarity scale correlates solvatochromic shifts with n -+ n* and p -+ n* electronic spectral transitions and the derived solvatochromic parameter n* is defined by8T 35 where vo is the wavenumber of the absorption maximum for an indicator solute in cyclohexane for which n* is assumed to be zero (in this solvatochromic scale, n* is taken as one for dimethyl sulphoxide); v, is the absorption maximum in the solvent under study and s is a measure of the indicator solute sensitivity to interactions with the cybotactic environment.o-Nitroaniline (v, = 26550 cm-', s = 1536 cm-') was used as the indicator solute for the determination of n* (table 7) and the results for 1-chloronaphthalene were confirmed using rn-nitroaniline (v, = 28870 cm-', s = 1664 cm-'), in order to establish any possible indicator dependence of the results, The two indicators gave the same value of n* within experimental accuracy. Although the spectrophotometric measurements have been carried out at 150 "C, there is a problem in the definition of the solvatochromic scale from these data. The absorption maximum depends on the local polarizability, and therefore the spectra obtained should be temperature-dependent. This dependence was measured for572 Solvent Properties of Polyaromatic Hydrocarbons 40 r( I Z 30 E 24 O', u Q c, 20 0.4 0.5 0.6 0.7 0.8 0.9 n* Fig.5. Dependence of the Gibbs energy of solution of TMABr (m) and TEABr (0) on the solvatochromic parameter n*. naphthalene and 1-chloronaphthalene for which dv/dT are 3.0 and 1.5 cm-l K-l, respectively. No data are available for the temperature dependence of the absorption spectra of the indicator for the reference solvents used in the definition of the n* scale, and in consequence the results given in the present work are referred to a scale at 25 "C. This will not alter the conclusions regarding the comparison of the relative local polarizability of the different solvents. The relationship between the solvatochromic parameter and the local polarisability contribution to the solution energy is given by37 (14) AG," = (AG,") , + sn* + h6, where (AG,"), is a Gibbs energy of solution referred to a reference solvent and h is a constant.The calculated values of 6, and n* are compared in table 7; it is evident that solvent-solvent interactions have no significant effect on the solubilities and the differences observed result from solute-solvent interactions which are reflected in changes of the n* values, i.e. in the local polarizability of the medium. Fig. 5 shows the dependence of the free energy of solution of TMABr and TEABr calculated from the solubilities of these salts as a function of the solvatochromic parameter. The linear character of this dependency (except for fluorene) confirms that the main origin of the differences in the solubilities observed is the local polarizability of the solvent.Furthermore, the values of s calculated from the slopes dAG,/dn* are - 1.42 and - 1450 cm-l for TMABr and TEABr, respectively. These results are in excellent agreement with many other determinations of s for a wide range of solvents and obtained from the analysis of totally different properties.' This gives further support for the applicability of solvatochromic scales to the description of solution phenomena.35* 37G. Geblewicz and D. J. Schiflrin 573 In the previous discussion all the polyaromatic solvents in the molten state have been considered as homogeneous, isotropic liquids. For some of the solvents, this assumption may be quite incorrect. For example, from the measurements of the temperature coefficient of the viscosities it has been postulated that compounds like m-terphenyl associate in the melt into clusters or ‘cybotactic’ group^,^^^^^ i.e.into groups of molecules arranged side-by-side or end-to-end, giving rise to a microcrystalline structure in dynamic equilibrium with molecules in a random orientation. The high boiling point of fluorene compared with m-terphenyl, which has the same molecular weight, reflects the limited freedom of the fluorene molecules in the melt45 and indeed some of the hydrocarbons studied produce probably highly structured liquids. In consequence, the polarizability of the solvent may depend strongly on its orientation with respect to the solute. This high anisotropy in the polarizability of organic molecules may change the influence of the solvent on the electronic spectral transitions of the solute and could explain the departure of the measured value of n* for fluorene from the trend observed for the other solvents. Conclusions The polyaromatic compounds have been shown to be good solvent media at high temperatures, giving conducting solutions with hydrophobic electrolytes. The limiting requirement for solubilizing ions and obtaining conducting solutions in the case of the symmetric tetraalkylammonium salts is a C, chain. The use of C, compounds leads to total miscibility between the salt and the solvent.The conductivity measurements show the usually high degree of association of electrolyte solutions. The salts of small ions (KCl, KBr, TMABr, TEABr) are associated in neutral aggregates and their solutions are non-conducting. Increasing the size of the ions decreases the degree of association and the formation of charged aggregates occurs.This results in an increase of the equivalent conductance with concentration (fig. 2). Because there is no defined minimum on the curves but rather inflection points, it has been concluded that triple ions mainly contribute to the conductance, and quadrupole formation reduces the conductivity at high electrolyte concentration. The effect of the solvent polarizability has been found to determine the solubility of the salts in the various polyaromatic hydrocarbons studied. The Gibbs energy of solution shows a linear dependence on the z* solvatochromic parameter and does not depend on the energy of cavity formation.The most important conclusion from this work is that the solubility of organic electrolytes is mainly determined by the local polarizability of the solvent and conditions have been found to obtain good solubilities and conductivities in polyaromatic solvents. This opens the possibility of using these organic non-polar solvents as very satisfactory inert media for the electrodeposition of metals and for other electrochemical reactions due to their extremely low donor numbers and very large potential windows. The authors gratefully acknowledge the financial support and encouragement given by the Commission of the European Communities to this project, under contract RNF 024- UK of the Recycling of Non-ferrous Metals Programme. One of us (G.G.) thanks the University of Warsaw for granting leave of absence during this work.Part of the equipment used was purchased with funds from the University Grants Committee Special Award to the Electrochemistry Group at Southampton University, 1985. Helpful discussions and comments by Dr R. J. Potter are acknowledged.574 Solvent Properties of Polyaromatic Hydrocarbons References 1 A. Brenner, A h . Electrochem. Electrochem. Eng., ed. C. W. Tobias (Interscience, New York, 1967), 2 T. Takei, Electrochim. Acta, 1978, 23, 1321. 3 A. Reger, E. Peled and E. Gileadi, J. Phys. Chem., 1979, 83, 873. 4 G. Geblewicz, R. J. Potter and D. J. Schiffrin, Trans IMF, 1986, 64, 134. 5 R. H. Campbell, G. A. Heath, G. T. Hefter and R. C. S. McQueen, J. Chem. SOC., Chem.Commun., 6 R. Suckentrunk and H. Tippman, Galvanotechnik D. 7968 Saulgau, 1982, 273,2. 7 G. J. Hoijtink, Reel. Trav. Chim., 1958, 77, 555. 8 M. J. Kamlet, J. L. Abboud and R. W. Taft, J. Am. Chem. SOC., 1977,99, 6027. 9 J. T. Denison and J. B. Ramsey, J. Am. Chem. SOC., 1955, 77, 2615. vol. 5. 1983, 1123. 10 M. H. Abraham and J. Liszi, J. Chem. SOC., Faraday Trans. I , 1978, 74, 1604. 1 1 M. H. Abraham and J. Liszi, J. Inorg. Chem., 1981, 43, 143. 12 International Critical Tables of Numerical Data (McGraw-Hill, New York, 1929). 13 G. B. Arrowsmith, G. M. Jeffery and A. I. Voge, J. Chem. SOC., 1965, 2072. 14 R. N. Rampolla and C. P. Smyth, J. Am. Chem. SOC., 1958,80, 1057. 15 Beilsteins Hanbuch der Organischen Chemie, 1979, Band 513 s, 1327-2134. 16 D. A. Johnson, Some Thermodynamic Aspects of Inorganic Chemistry (Cambridge University Press, 17 A.B. D. Lever, S. M. Nelson and T. M. Shepherd, Inorg. Chem., 1965, 4, 810. 18 R. Boyd, J. Chem. Phys., 1969, 51, 1470. 19 JANAF Thermochemical Tables, ed. D. R. Stull and M. Prophel (NSRDS-NBS37 Natl. Bur. Stand. 20 C. De Visser and G. Somsen, Reel. Trav. Chim. Pays-Bas, 1971,90, 1129. 21 D. A. Johnson and J. F. Martin, J. Chem. SOC., Dalton. Trans., 1973, 1585. 22 S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haughen, H. E. ONeal, A. S. Rodgers, 23 S-S. Chang and E. Westrum, J. Chem. Phys., 1962, 36, 2420. 24 W. Latimer, J. Am. Chem. SOC., 1921, 43, 818. 25 R. Fuoss and C. Kraus, J. Am. Chem. SOC., 1933, 55, 2386. 26 R. Fuoss, Chem. Rev., 1935, 17, 27. 27 R. Fuoss and C. Kraus, J. Am. Chem. SOC., 1935,57, 1. 28 C. Kraus and R. Fuoss, J. Am. Chem. SOC., 1933, 55, 21. 29 C. Kraus and R. Vingee, J. Am. Chem. SOC., 1934, 56, 51 1. 30 H. E. Maaser, M. Delsignore, M. Newstein and S. Petrucci, J. Phys. Chem., 1984, 88, 5100. 31 M. Delsignore, H. E. Maaser and S. Petrucci, J. Phys. Chem., 1984, 88,2405. 32 B. Krumgalz, J. Chem. SOC., Faraday Trans. I , 1983, 79, 571. 33 S. Boileau and P. Hemery, Electrochim. Acta, 1976, 21, 647. 34 R. M. Fuoss and C. Kraus, J. Am. Chem. Soc.,. 1933,55, 3614. 35 M. H. Abraham, M. J. Kamlet and R. W. Taft, J. Chem. SOC., Perkin Trans. 2, 1982, 923. 36 M. J. Kamlet, T. N. Hall, J. Boykin and R. W. Taft, J. Org. Chem., 1979, 44, 2600. 37 M. J. Kamlet, J. L. M. Abboud, M. H. Abraham and R. W. Taft, J. Org. Chem., 1983,48, 2877. 38 J. H. Hildebrand and J. H. Scott, The Solubility of Nonelectrolytes (Dover Publication Inc., New York, 39 A. F. M. Burton, Chem. Rev., 1975, 75, 731. 40 R. A. Pierotti, Chem. Rev., 1976,76, 717. 41 R. A. Pierotti, J. Phys. Chem., 1965, 69,281. 42 C. L. De Ligny and H. G. Van der Veen, Chem. Engl. Sci., 1972, 27, 391. 43 A. Bondi, J. Phys. Chem., 1964, 68,441. 44 S. W. Mayer, J. Phys. Chem., 1963, 67, 2160. 45 E. McLaughlin and A. R. Ubbelohde, Trans. Faraday SOC., 1957, 53, 628. 46 J. Andrews and A. R. Ubbelohde, Proc. R. SOC. London, Ser. A, 1955, 228,435. Cambridge, 1982). U.S.A., 2nd edn, 1971). R. Shaw and R. Walsh, Chem. Rev., 1969, 69, 279. 3rd edn, 1964.). Paper 71585 ; Received 1st April, 1987

ISSN:0300-9599    

DOI:10.1039/F19888400561

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I, 1988, 84(2), 575-580 The Phase Response of the Explodator Matild Eszterle Department of Chemical Engineering, Institute of Physics, Technical University of Budapest, H-1521 Budapest, Hungary Zoltan Noszticziust Department of Physics, The University of Texas at Austin, Austin, Texas 78712, U.S.A. Zoltan A. Schelly" Department of Chemistry, The University of Texas at Arlington, Arlington, Texas 7601 9-0065, U. S. A. A re-examination of the 'limited Explodator' shows that with the appropriate numerical values of the parameters, this model can reproduce the experimentally observed phase response behaviour of the Belou- sov-Zhabotinskii reaction perturbed by the addition of Ag+ ion. It is shown that the phase-response method is not a crucial diagnostic test for the acceptability of a model.The response of systems to perturbation is routinely used to analyse their dynamics in many fields of sciences and engineering. In chemical kinetics, relaxation methods and flash photolysis represent well known examples. The general methodology is applicable to both linear and non-linear systems. In non-linear chemical systems such as oscillating reactions exhibiting limit cycle behaviour, the idea of examining system response is attractive since any clue obtainable in addition to usual kinetic information is greatly needed for the elucidation of the mechanism of these complex reactions. In recent papers1V2 the phase-response technique was used to test two skeleton mechanisms proposed for the Belousov-Zhabotinskii3 (BZ) oscillating reaction.The essence of the technique is the perturbation of the limit cycle system by the sudden change of the concentration of a key species and the measurement of the ensuing phase shift as compared with the unperturbed system. Periodicities of concentrations of limit- cycle systems are rather stable against perturbation in amplitude and frequency, but not in p h a ~ e . ~ Thus, in principle, comparison of the experimentally measured phase shift with that computed for a given model may be used to test the suitability of the model. In the BZ reaction, the experimental phase shift can conveniently be determined by monitoring the appearance of the next concentration maximum of the Ce4+ ion following the perturbation.2 Depending on whether the Ce4+ peak appears sooner or later than in the unperturbed system, one registers a negative or positive phase shift, respectively.The period of the unperturbed limit cycle is usually used as the unit for the phase shift and the phase of the perturbation. Ruoff compared' his experimental phase response diagrams2 (phase shift us. phase of perturbation) with those simulated for the Oregonator5 and the Explodator' models of the BZ reaction. In the experiments with which we are concerned, the perturbation of the limit cycle was achieved by the sudden addition of Ag+ ion, causing an instantaneous drop of the Br- concentration which led to the phase shift. A characteristic feature of the resulting phase response diagram is a linear portion of the curve (the 'excitable t On leave of absence from the Technical University of Budapest.575576 Phase Response of the Explodator branch ')2 with unit slope and negative phase shift. Based on the ability of the Oregonator to reproduce qualitatively the excitable branch, and the inability of the Explodator to do so with a given6 set of parameters, Ruoff concludedl that the Explodator is unable to describe essential features such as excitability'* and Ag+-induced oscillations9 of the BZ reaction. In this paper we re-examine the phase response of the Explodator and shall show that : (i) with the appropriate limiting reactions and parameters the Explodator is able to reproduce the experimentally observed excitable branch and (ii) without the knowledge of the actual rate constants it is not justified to rely on the shape of the phase-response diagram in deciding about the quality of a model, since the simulated phase response is obviously also a function of the numerical values of the parameters of the model used.Re-examination of the Limited Explodator Structural Features The Limited Explodator model6 consists of a generalized Lotka-Volterra type core (the (E 1 ) Explodator) X+Y+Z (E 2) Z + (1 +BY (B = 0.5) (E 3) y + {B} (E 4) {A}+X + (1 + a ) X (a = 1) and one or more limiting reactions, for example or 2X-,iZ+{A} {A) + X. It has two consecutive autocatalytic reactions in a serial network structure,lO in contrast to the one autocatalytic step and parallel network of the Oregonator. Noszticzius et al. (NFS) suggested6 a possible chemical identification of the Explodator variables as X 3 HBrO,, Y: Br,, Z E 3HOBr when applied to the BZ reaction.Phase Response of the Limited Explodator The dynamics of the Explodator core with the two limiting reactions (L 1 ) and ( L 2) is described by the following system of differential equations using dimensionless parameters (D) I i = F+x-xy-kx2 p = 1.5az-by-xy i = - az + xy + kx2/6. The case k = 0 corresponds to the situation where only (L 2) is considered as a limiting reaction and (L 1) is disregarded, as was done by NFS' to illustrate the limit-cycle behaviour of the model by a numerical example (not a simulation). For this purpose the following numerical parameters were chosen: a = 100, b = 1, F = 0.01, k = 0. The same parameters were also used in previous simulations of the phase response of the Explodator mode1.l The perturbation can be represented by the following 'instantaneous ' reaction Ag+ + Br, + H,O + AgBr + HOBr + H+ (1)M .Eszterle, Z . Noszticzius and Z . A . Schelly 577 that in terms of the variables of the Explodator is Ag++ Y -+ iZ. (EP) Now let us introduce the following symbols: [Ag+], for the virtual concentration of Ag+ after the perturbation, but prior to the beginning of reaction (EP) [this quantity is the same as the ‘added unreacted Ag+ ions’ in ref. (2)]; ryl-, for the Br, concentration at the instant of the perturbation but prior to the reaction with Ag+ in (EP); w]+, for the Br, concentration immediately after the ‘ instantaneous ’ reaction (EP). Since the duration of the perturbation and reaction (EP) is considered zero, clearly, the function [Y] has a discontinuity at the time t = 0 of the perturbation.[XI-,, [XI+,, [ZIP,, [Z],, and [Ag+]+, are quantities analogous to those defined above. Since X is unaffected by the perturbation, [XI-, = [XI+,. For the other concentrations, the relationship between their values prior to and after the perturbation is determined by the stoichiometry of reaction (1) and the amount of Ag+ used in the perturbation. Three qualitatively different cases are possible : (1) [YIP, > [Ag+],, i.e. small perturbation where the concentration of Br, exceeds that of the added Ag+. In this case the relationships P I + , = P I - 0 - [Ag+l, [ZI+o = P I - 0 + $[Ag+I, [Ag+l+, = 0 hold and one simply has to solve the system of differential equations (D) with the initial values of [XI+,, [v+, and [Z],, and the given parameters (a = 100, b = 1, F = 0.01, k = 0). Since Ce4+ does not appear in the model, the phase shift for component X was computed in ref.(1) and also here. (2) w]-, < [Ag+], < 2M-, + 3[Z]-,, i.e. large perturbation where the added Ag+ instantaneously reduces the Br, concentration essentially to zero (as determined by the solubiIity product of AgBr). If the size of the perturbation is in this interval, the Br, produced from Z in reaction (E3) can ultimately use up the excess Ag+. Nevertheless, so long as fy]+O E 0, the original system of differential equations with the given6.’ parameters (D’) I A? = 0.01 + x - x y j = 1502-y-xy i = -1ooz+xy must be replaced by R = 0.01 + x j = O 2 = - lOOz + (1 50/3)2 = - ~ O Z (since the 1.5 Y formed from 1 Z are instantaneously converted to Z by the Ag+).After the perturbation (2) and from this initial value [Z] decreases according to i = -502. Also, after the perturbation (3) From this intial value, the excess Ag+ concentration is used up by Y as fast as Y is formed from Z, namely [ZI+o = [Zl-o = $ M - o [Ag+l+, = [&+I, - P I - 0 . [Ag] = - 1502.578 Phase Response of the Explodator However, TY] (i.e. y)? remains zero for a period Tuntil all the Ag+ has reacted. This time is reached when [Ag+l, = [Ag+I+,+[ [Ag+ldt = 0 (4) or [Ag+]+, = JOT 150zdt. (5) Since we had z = -502 clearly, the corresponding [Z] is [zl = [a+, exp (- 502) [&+I+, = 3[Zl+,( 1 - exp ( - 50731 (6) and from eqn (5) and (6) one obtains from which Tcan be calculated since [Ag+]+, and [Z]+, are known from eqn (2) and (3).Moreover, it can be seen from the last equation that the limiting case T+ 00 is associated with the relation By substituting eqn (2) and (3) in eqn (7), one obtains the critical Ag+ perturbation as at or above which the excess Ag+ cannot be consumed within a finite time. Hence, if one adds the critical or a larger amount of Ag+ ion and k = 0, the original system of differential equations (D') will never be applicable after the perturbation. If the pertuybation is smaller than critical, the dynamics of the system are described by the equations (DP) for a period of T, until the excess Ag+ is consumed. Thereafter, the equations (D') are again applicable, and the phase shift of the next maximum in [XI can be computed.(3) [Ag+], 3 2[yl~,+3[Z]~, As we have just discussed, this is the case of critical or super-critical perturbation. Without the limiting reaction (L 1) the phase shift is +m since in the absence of Y the [XI to be monitored will autocatalytically and monotonously increase ad infiniturn. Discussion With the given parameters (a = 100, b = 1, F = 0.01, k = 0) and a perturbation' of [Ag+], = 0.1, the sum of the numerical values 2y+ 32 = 2ry]-, + 3[z]-, is smaller than the perturbation in the interval 6.2 < t < 8.4 of the phase t of the stimulation (or on the relative timescale, with the period of the unperturbed limit cycle taken as unit: 0.653 < t < 0.884). Thus, the perturbation is supercritical in this interval, where the initial phase shift should be infinitely large. If an even larger amount of Ag+ ([Ag+], = 10) is used, the perturbation is subcritical only in the interval of 0.6 < t < 1 (or on the relative scale: 0.063 < t < 0.105).Hence, infinite phase shift should be found outside this interval. Although our results are in disagreement with the previous simulations' that used a different numerical approach, nevertheless we reach the same conclusion : with this specific set of parameters the Explodator cannot reproduce the experimentally observed phase response. Now let us examine a different set of parameters, with k > 0 in eqn (D). This corresponds to the inclusion of reaction (L 1). The limiting reaction (L 1) prevents the occurrence of infinite phase shifts since it offers a route for the production of Y from X [A~+I+, = 3[z1+,.(7) [Ag+lp, wit = 3[Zl-, + 2ryl-0 -f To preserve the correspondence between the numerical values of real and dimensionless concentrations, the symbol [ ] is retained for dimensionless concentrations.M. Eszterle, Z . Noszticzius and Z . A . Schelly - I phase of perturbation I I I I I I i I I I 579 a - c 5 f c a // - / / / / - / / / / - / / - / / / 0.5 0 -0.5 Fig. 1. Simulated phase response of the Explodator with (L 1) and (L 2) limitations, a = 2, b = 0.2, F = 0.01, k = 0.001. [Ag+], = 6. Fig. 2. Simulated phase response of the limited Explodator with (L 1) and (L 2) limitations. With the parameters given in this figure the experimentally observed excitable branch* is reproduced.a = 0.2, b = 0.02, F = 0.001, k = 0.01, [Ag+], = 15 (-), [&+I, = 45 (---).580 Phase Response of the Explodator which ultimately consumes the excess Ag+, Naturally, if excessive Ag+ perturbation is used, again, a new system of differential equations different from (D) must be applied so long as the excess Ag+ is consumed. However, with k > 0 this will always ensue, and the finite initial phase shift of the next [XI maximum can be computed. Clearly, the shape of the simulated phase response diagram is a strong function of the numerical values of the parameters used. For example, with a = 2, b = 0.2, F = 0.01, k = 0.001 and [Ag+], = 6 the phase response is depicted in fig. 1. The experimentally observed excitable branch of the BZ reaction2 can be reproduced by the limited Explodator, for example, with the following set of parameters: a = 0.2, b = 0.02, F = 0.001, k = 0.01 and [Ag+], = 15 or [Ag+], = 45 (fig.2). Since the actual rate constants of some of the reactions involved in chemical oscillations are usually not known, only estimated or trial values of the parameters can be used in the simulations. Hence, phase response relationships should be used with caution for diagnostic purposes. An agreement between experimental and simulated responses is necessary but not sufficient condition for the acceptability of a model considered. Recently, for instance, Dolnik et al." found the Brusselator12 superior to the Oregonator in predicting the phase advance observed experimentally in the BZ reaction following bromide ion perturbation, even though the Brusselator had not been designed to model specifically the BZ reaction. Consequently, the phase-response method can be viewed as a useful but not a crucial diagnostic test. This work was partially sponsored by the R. A. Welch Foundation. Acknowledgement is made to the donors of the Petroleum Research Fund of the American Chemical Society for additional support. References 1 P. Ruoff, J. Chem. Phys., 1985, 83, 2000. 2 P. Ruoff, J. Phys. Chem., 1984, 88, 2851. 3 A. M. Zhabotinskii, Dokl. Akad. Nauk USSR, 1967, 157, 392. 4 Biological and Biochemical Oscillators, ed. B. Chance, E. K. Pye, A. K. Gosh and B. Hess (Academic 5 R. J. Field and R. M. Noyes, J. Chem. Phys., 1974,60, 1877. 6 Z. Noszticzious, H. Farkas and Z. A. Schelly, J. Chem. Phys., 1984, 80,6062. 7 R. J. Field and R. M. Noyes, Faraday Symp. Chem. SOC., 1974, 9, 21. 8 P. Ruoff, Chem. Phys. Lett., 1982, 90, 76; 1982,92, 239; 1983, 96, 374. 9 Z. Noszticzius, J. Am. Chem. SOC., 1979, 101, 3660. Press, New York, 1973). 10 Z. Noszticzius, H. Farkas and Z. A. Schelly, React. Kinet. Catal. Lett., 1984, 25, 305. 11 M. Dolnik, I. Schreiber and M. Marek, Physica, 1986, 21D, 78. 12 I. Prigogine and R. Lefever, J. Chem. Phys., 1968, 48, 1695. Paper 71630; Received 9th April, 1987

ISSN:0300-9599    

DOI:10.1039/F19888400575

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I, 1988, 84(2), 581-589 Absorption and Diffusion of Sulphur Dioxide into Aqueous Sodium Chloride Solutions Derek G. Leaist Department of Chemistry, University of Western Ontario, London, Ontario, Canada N6A SB7 Multicomponent diffusion equations have been used to describe the absorption of an ionizing gas into a solution that contains an insert supporting electrolyte. The example of absorption of sulphur dioxide into aqueous sodium chloride solutions has been treated in detail. In this case the electric field generated by diffusion of partially ionized sulphur dioxide (SO, + H,O = HSO; + H') produces large coupled ionic flows that re- spectively increase and decrease the interfacial concentrations of Na+ and C1- ions relative to bulk values. The added NaCl enables highly mobile H+ ions to diffuse into the bulk absorbent several times more rapidly than the sulphur-containing species.Loss of H' ions from the interfacial solution is shown to increase the interfacial solubility and the rate of absorption of sulphur dioxide by up to 60% relative to the corresponding values for absorption into pure water. Absorption of gases into aqueous salt solutions is a key step in several industrial and environmental processes. The purpose of the work reported here is to determine the effects of dissolved salt on absorption of ionizing gases such as ammonia, carbon dioxide, chlorine and oxides of nitrogen or sulphur. There are several reasons why salt effects might be important. Consider absorption of sulphur dioxide.In this example the dissolved gas hydrolyses to form bisulphite and hydrogen ions : K , (1) SO, + H,O f HSO; + H+. If the absorbent is pure water, then the H+ and HSO; ions diffuse into the liquid at the same rate, despite the exceptional diffusivity of the H+ ions. Charge separation is prevented by the diffusion-induced electric field which speeds up the HSO, ions and slows down the H+ ions. Now suppose a supporting electrolyte such as sodium chloride is dissolved in the absorbent. Because the electric field generated by diffusion of sulphur dioxide will produce a counter-current flow of Na+ ions and a co-current flow of C1- ions, the solution near the gas/liquid interface will be enriched in sodium and depleted in chloride. Moreover, the H+ ions will diffuse into the bulk liquid more rapidly than the HSO; ions, thereby lowering the pH of the interfacial solution and raising the interfacial solubility of total sulphur dioxide. These considerations prompted an analysis of absorption of sulphur dioxide into aqueous solutions of sodium chloride which includes multicomponent diffusion in the liquid phase.Theory In the following treatment the absorbent is assumed to be isothermal and free of convection. Since the rate' of hydrolysis of sulphur dioxide is very rapid compared to diffusion, the hydrolysis reaction will be at equilibrium at each point in the absorbent. 58 1582 Absorption and Diffusion of SO, in Aqueous NaCl Dissociation of bisulphite ions (HSO; = H+ + SO,, K , = 3.63 x mol rn-, at 25 OC),, which is important only at very low concentrations of sulphur dioxide (< ca.lo-, mol m-'), will be neglected. Diffusion of Sulphur Dioxide in Aqueous HCl-NaCl Solutions At first glance, diffusion of sulphur dioxide in aqueous sodium chloride solutions appears to be a ternary process with diffusional flows of the two solute components. But since there are only two restrictions (electroneutrality and local equilibrium of the hydrolysis reaction) on flows of five solute species (Na+, C1-, H+, HSO, and molecular SO,), three flows of solute components are independent. Diffusion in the solutions can be described by the quaternary transport equations3 where Ji are molar flux densities of neutral solute components in the z-direction and aCk/az are gradients in concentration of the components.Quaternary diffusion coefficient D,, measures the flow of component i produced by the gradient in component k. The components will be designated by subscripts 1 = total sulphur dioxide (hydrolysed plus unhydrolysed forms), 2 = HCl and 3 = NaCl. In this representation, the concentration of the species HSO;, H+, C1-, Na+ and molecular SO, are aC,, aC,+ C,, C,+ C,, C, and (1 -a)C,, respectively, where a denotes the extent of hydrolysis of sulphur dioxide The flux densities of the species are aJ,, uJ, + J,, J, + J,, J, and (1 -a) J,, respectively. Expressions for estimating the Dik coefficients are given in the Appendix. In fig. 1 calculated D,, values for sulphur dioxide (0 c C,/mol m-, c 100) in 100 mol rn-, aqueous sodium chloride solutions at 25 "C are shown.Coupled-diffusion effects are most pronounced at low concentrations of sulphur dioxide, where most of the dissolved gas is ionised. The large positive values of D,, indicate that diffusion of sulphur dioxide in aqueous NaCl solutions will produce a large co-current coupled flow of H+ ions. Values of D,, rise sharply as the concentration of total sulphur dioxide, C,, drops to zero. In this limit D,, equals the diffusivity of the H+ ion4 (9.32 x m2 s-l) less the diffusivity of the HSO; ion5 (1.32 x m2 s-,), and D,,, the diffusivity of the HCl component, equals the diffusivity of the H+ ion. Negative values of D,, indicate that diffusion of sulphur dioxide will generate a counter-current coupled flow of Na+ ions. Ref. (6) and (7) give detailed accounts of quaternary diffusion of acids in supporting salt solutions.a = [HSOJ/([HSOJ+[SO,]). (3) Solubility of Sulphur Dioxide in Aqueous HCl-NaCl Solutions According to Henry's law, the equilibrium concentration of molecular SO,, species is proportional to the partial pressure p of sulphur dioxide over the saturated solutions, (4) hence5 where H is a constant. The extent of hydrolysis can be evaluated from the relation p = H[SO,] = H(1 -a)C,D. G. Leaist I I I I I I 583 Cl/mol m-3 Fig. 1. Calculated quaternary diffusion coefficients for sulphur dioxide (CJ-hydrochloric acid (C, = 0)-sodium chloride (100 mol m-3)-water at 25 "C. platm Fig. 2. Equilibrium solubility of total sulphur dioxide [C,(equil.)] as a function of partial pressure of sulphur dioxide (p) at 25 "C: (-) in 0.1 mol dm-3 aqueous NaCl; (----) in pure water.584 Absorption and Diflusion of SO, in Aqueous NaCl where y + denotes the mean ionic activity coefficient.Values of y + can be estimated by using the semiempirical relation8 in which Sf = 0.0372 mi mol-i for aqueous solutions at 25 "C and Zis the ionic strength in units of mol m-3: lny, = - s ~ z ~ / [ I +(z/~ooo):I (6) I=aCl+C,+C3. (7) If HCl is removed from a region of a sulphur dioxide-sodium chloride solution, by diffusion for example, then the hydrolysis reaction will shift in favour of products. Note from eqn (4) that an increase in the extent of hydrolysis at constant sulphur dioxide pressure will in turn increase the solubility of total sulphur dioxide, C,. A reanalysis of the vapour pressure data for aqueous sulphur dioxide solutions reported by Campbell and Maass' gave the value 8.0 x atm m3 mol-lt for H at 25 "C.The recent value' of 13.9 mol m-3 for Kl at 25 "C was used in the calculations. The activity coefficient of molecular SO,. species was assumed to be unity. Fig. 2 compares the equilibrium solubilities of total sulphur dioxide in water and in 100 mol m-3 aqueous NaCl solution (without added HCl, C, = 0). Owing to lower values of yk and hence greater degrees of hydrolysis, the gas is slightly more soluble in the NaCl solution. At low partial pressures (p < ca.q.001 atm) the equilibrium solubilities of the gas are given approximately by (K,p/H)s/y+. - Absorption of Sulphur Dioxide into Aqueous NaCl Solutions Suppose the surface of a uniform, semi-infinite solution of NaCl is exposed at t = 0 to sulphur dioxide gas at a fixed partial pressure.Absorption of the gas can be described by integrating the time-dependent diffusion equations 3 aci/at = 2 a(Di,ack/az)/az k-1 subject to the initial conditions C1(Z > 0,O) = c, = 0 C,(Z > 0,O) = c, = 0 (9) (10) C,(Z > 0,O) = C3, and boundary conditions [Because HCl(2) and NaCl(3) components are relatively involatile, they do not cross the gas/liquid boundary.] Subscripts 0 and 00 designate interfacial (z = 0) and bulk (z -+ 00) values, respectively. Because the Di, coefficients vary with composition, exact solutions to eqn (8)-(14) cannot be obtained. It is an accurate approximation,s* lo however, to replace the variable coefficients with constant coefficients, Dik, which are evaluated at the mean composition (Clo + C1,)/2, C,,, C3co along the diffusion path.The diffusion equations then simplify to 3 aci/at = Dik a2ck/az2. (15) k- 1 t 1 atm = 101 325 Pa.D. G. Leaist 585 it is convenient to define In order to solve eqn (9)-(15) by standard ACi(z, t ) = Ci(z, t ) - Cia Aum(z, 1) = C Wmn AC,(z, '1. ACi(z, t ) = C Aim AUm(z, t ) (16) (17) (18) If the columns of A are constructed from the eigenvectors of D, then the expressions (19) concentration differences and their linear transforms 3 n-1 Inversion of eqn (17) gives 3 m=l where A = W-l. for AU,(z, t ) take the simple A u,(z, t ) = A urn, erfc [z/2(Dm $1 where erfc is an abbreviation for the complimentary error function, D, are eigenvalues of matrix D, and (20) AUmo = AUm(O, t)- Urn=.Values of AUmo can be obtained by transformation of the boundary conditions to m=l k = l This linear system of equations can be solved for unknowns AUmo. Back-transformation according to eqn (18) gives values of AC,, and hence 3 3 Ci(z, t ) = Ci, + c C Aim Wmk ACk,erfc(z/2(Dm t);]. m=l k = l As the first approximation, interfacial concentrations of HCl(2) and NaCl( 3) components, C,, and C,, were set equal to their bulk values, 0 and C3,, respectively, so that the extent of hydrolysis and hence the interfacial concentration of total sulphur dioxide could be estimated. Mean coefficients Dik were evaluated, then eqn (1 8) and eqn (21)-(23) were solved to obtain better estimates of the interfacial concentrations. The cycle was repeated a few times until values of Cio converged.Results The dashed curve in fig. 3 shows the concentration profile that was calculated for absorption of sulphur dioxide into pure water under a sulphur dioxide pressure of 0.002 atm. In the saturated interfacial solution, the respective concentrations of total sulphur dioxide, HSO;, H+ and un-ionised SO, species are 8.93, 6.43, 6.43 and 2.50 mol m-3 (72.0 O h hydrolysis). The solid curves in fig. 3, in contrast, show concentration profiles for absorption into 100 mol m-3 aqueous NaCl solution under the same sulphur dioxide pressure, 0.002 atm. Coupled diffusion changes the interfacial concentrations of HCl and NaCl components from the bulk values 0 and 100 mol m-3 to -6.36 and 103.3 mol mP3, respectively. The interfacial concentrations of total sulphur dioxide, HSO,, H+ and un- ionised SO, species take the respective values 14.2, 11.7, 5.33, and 2.5 mol m-3 (82.4 O h586 Absorption and Difusion of SO, in Aqueous NaCl z(2t+)-i/io-5 m s-4 Fig.3. Calculated concentration profiles for absorption of sulphur dioxide at 0.002 atm and 25 "C: (-) into 100 rnol m-, aqueous NaCl solution (Cl, = C,, = 0, C,, = 100 mol m-,); (----) into pure water (C,, = C,, = C,, = 0). (a) C,, (b) C,, (c) C,. Fig. 4. ~-) I I 1 I I 1 - m lu- W 6- I I 1 I I I 1 2 3 4 5 6 Calculated concentration profiles for absorption of sulphur dioxide at 0.05 atm and 25 into 100 mol m-, aqueous NaCl solution (Clm = C,, = 0, C,, = 100 mol rn-,); (-- - 400 z (2t))-1/10-5 m s-4 into pure water (Cl, = C,, = C,, = 0).(a) C,, (b) C,, (c) C,. "C: .--) hydrolysis). Removal of H+ ions by rapid diffusion into the interior of the absorbent increases the interfacial solubility of sulphur dioxide by 60 % relative to its solubility in pure water. For values of z/2F greater than ca. 5 x m s-5, concentrations of the HC1 component are several times larger than the concentration of the sulphur dioxide component, even though the absorbent contains no added HCl.D. G. Leaist 587 Table 1. Diffusion coefficient for absorption of sulphur dioxide into 100 mol mP3 aqueous NaCl solution at 25 OCa p = 0.002 atm p = 0.05 atm D, 1.36 D12 0.18 Dl 1.38 D,, 0.39 D, 1.49 D,, 4.59 D, 1.63 D2, 1.33 D,, 1.56 <,, 0.07 Dll 1.76 D,, 0.26 ez2 7.09 D,, -1.93 D2, 4.41 D31 -0.57 D, 7.22 D,, -0.02 D, 4.52 D13 -0.08 D,, 1.42 D,, 2.14 D,, 1.36 D32 - 1.04 a Di and D,, in units of m2 s-l.1.ot il-0 0-00 0.05 0 -10 0.15 platm Fig. 5. (a) Ratio of the interfacial concentration of sulphur dioxide during absorption into 100 mol mP3 aqueous NaCl solution to the equilibrium solubility of the gas at the same partial pressure in 100 mol m-, aqueous NaCl solution at 25 "C. (b) Ratio of the rate of absorption of sulphur dioxide into 100 mol m-, aqueous NaCl solution to the rate of absorption into pure water under the same sulphur dioxide partial pressure. Concentration profiles for absorption of sulphur dioxide at 0.05 atm into pure water and 100 mol m-3 aqueous NaCl solution are compared in fig. 4. During absorption into pure water, the interfacial concentrations of total sulphur dioxide, HSO,, H' and un- ionized SO, species are 98.0, 35.5, 35.5 and 62.5 mol mP3, respectively.During absorption into the NaCl solution, the corresponding concentrations are 1 15.9, 53.4, 31.1 and 62.5 mol IT^-^. In this case the interfacial concentrations of HC1 and NaCl components are - 22.3 and 11 1.9 mol m-3, respectively. Values of the diffusion coefficients that were used to calculate concentration profiles in the NaCl solutions are listed in table 1. In fig. 5 the interfacial concentration of total sulphur dioxide during absorption into 100 mol m-3 aqueous NaCl solution is compared to the equilibrium solubility of the gas in 100 in01 mP3 NaCl solution. The enhanced interfacial solubility during absorption is588 Absorption and Difusion of SO2 in Aqueous NaCl most pronounced at low sulphur dioxide pressures (< 0.01 atm) where hydrolysis is extensive. The enhanced interfacial solubility of sulphur dioxide during absorption into aqueous NaCl solutions might lead to an increase in the rate of absorption of the gas.To check this possibility, rates of absorption of sulphur dioxide per unit surface area, J,(O, t ) , were calculated for absorption into pure water and 100 mol m-3 NaCl solution. The rates of absorption at different sulphur dioxide pressures are compared in fig. 5. It is evident that NaCl does indeed increase the rate of absorption, by up to 60% at low sulphur dioxide pressures. In summary, during absorption of sulphur dioxide into aqueous solutions, an inert dissolved salt such as NaCl (a) allows H+ ions to diffuse into the absorbent more rapidly than the sulphur-containing species HSO; or SO,, (b) increases the interfacial solubility of the gas and (c) increases the overall rate of absorption.Similar considerations apply to absorption of other ionising gases, such as chlorine', or carbon dioxide. Because carbon dioxide is a very weak electrolyte, the effects of salt on absorption of this gas will be important only at very low concentrations of dissolved gas, such as those found in naturally occurring solutions. Appendix Quaternary diffusion coefficients for multicomponent weak electrolyte solutions can be estimated by using the identity13 D = [sT(G i GT)-l~]-l p (A 1) where lil, are Onsager transport coefficients for the solute species, pik are derivatives a & / a c k of the chemical potentials of the solute components and stoichiometric coefficients sij and 2ik denote the number of moles of constituent ion i per mole of component j and species k, respectively.At low ionic strengths it is an accurate (A 2) approximation to write13 where dik is Kronecker's delta, ci is the concentration of species i and Di is its diffusivity . If the solute species under consideration are designated : 1 = HSO,, 2 = H+, 3 = C1-, 4 = Na+ and 5 = SO,, then4*,-14 D , = 1.32 x lo-', D, = 9.32 x lo-', D, = 2.03 x lo-', D, = 1.33 x and D, = 1.77 x lo-' m2 s-l at 25 "C. Choosing constituent ions as follows: 1 = HSO;, 2 = H+, 3 = C1-, 4 = Na+ defines stoichiometric coefficients lik = 6 i k Ci Di/RT s=(; ; i) '-6 ; ; :) 1 0 0 0 1 0 0 0 1 0 Derivatives api/aCk can be evaluated by tedious implicit differentiation of eqn (5H7) and This work was supported by the Natural Sciences and Engineering Research Council.D. G. Leaist 589 References 1 M. Eigen, K. Kustin and G. Maas, 2. Phys. Chem. (Frankfurt am Main), 1961, 30, 130. 2 P. Salomaa, R. Hakala, S. Vesala and T. Aalto, Acta Chem. Scand., 1969, 23, 2116. 3 S. R. de Groot and P. Mazur, in Non-equilibrium Thermodynamics (North Holland, Amsterdam, 1962), 4 R. A. Robinson and R. H. Stokes, in Electrolyte Solutions (Academic Press, New York, 2nd edn, 1959), 5 W. B. Campbell and 0. Maass, Can. J . Res., 1930, 2, 42. 6 D. G. Leaist, J . Chem. SOC., Faraday Trans. I , 1987, 83, 829. 7 R. A. Noulty and D. G. Leaist, J . Phys. Chem., 1987, 91, 1655. 8 E. A. Guggenheim and J. G. Turgeon, Trans. Furaduy SOC., 1955, 51, 747. 9 C. Dobrogowska and L. G. Hepler, J . Solution Chem., 1983, 12, 153. p. 257. appendix 6.1. 10 D. G. Leaist and B. Wiens, Can. J . Chem., 1985, 64, 1007. 11 D. G. Leaist, J . Phys. Chem., 1983, 87, 4936. 12 D. G . Leaist, J . Solution Chem., 1986, 15, 827. 13 D. G. Leaist, J . Chem. SOC., Faraday Trans. I , 1982, 78, 3069. 14 D. G. Leaist, Chem. Eng. Data, 1983, 29, 281. Paper 71638; Received 10th April, 1987 20 FAR 1

ISSN:0300-9599    

DOI:10.1039/F19888400581

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chem. SOC., Faraduy Trans. I, 1988, 84(2), 591-599 Enthalpic Pair Interaction Coefficients of NaI-Non- electrolyte in DMF Solution at 25 OC A Comparison of Electrolyte-non-electrolyte Interactions in DMF and in Aqueous Solutions Henry k Pie karski University of t d d i , Institute of Chemistry, ul. Nowotki 18, 91-416 t o d i , Poland Dissolution enthalpies of NaI in dilute solutions of N-methylformamide, dimethyl sulphoxide, tetrahydrofuran, acetonitrile, acetone and isobutanol in N,N-dimethylformamide have been measured. From these data, the enthalpic pair interaction coefficients h,,[(Na+ + I-)-non-electrolyte] have been determined. The h,, values for all investigated systems containing NaI are positive, in contrast to aqueous solutions, where they are both positive and negative.A comparison of appropriate data concerning the h,, (electrolyte-non-electrolyte) values in water and in DMF solution indicates that in the former systems the unusual properties of water influence the analysed h,, values to a great extent, while in the latter, the h,, values mainly reflect the replacement of the solvent molecule by cosolvent molecules in the solvation region of the ions. The enthalpic pair interaction coefficients, h,, derived from McMillan-Mayer theory are regarded as a measure of the enthalpic effect of interactions between two solute molecules in dilute solution.'V2 Many studies have been devoted to this subject in recent years: most have concerned the interactions that occur in aqueous solutions of non- electrolytes. The interactions between an electrolyte and a non-electrolyte in water have also been examined, but to a looser extent [e.g.ref. (3)-( 1 l)]. Systematic investigations of the latter have shown that the enthalpic pair interaction coefficients of an electrolyte (NaI or NaCl) with different non-electrolytes are correlated with the molecular polarizability (a) of the non-electrolyte, with its Kosower acidity parameter (2) as well as with the heat capacity of transfer of the non-electrolyte molecule from gas phase to a high dilution in water.8.'0,11 Moreover, the h,, coefficients in these systems appear to be a sum of group contributions.l0vl' From the point of view of enthalpic pair interaction coefficients, the differences between electrolyte-non-electrolyte and urea-non-electrolyte appear to be predominantly qualitative.12 It was of interest to determine whether the observed correlations occur only in aqueous solutions or whether they also apply in the case of solutions in non-aqueous media.With this aim N,N- dimethylformamide was selected as a solvent, since it is much less structured in its liquid state than water. Moreover, it contains some of the main elements of the inner parts of globular proteins, such as amidic and hydrophobic methyl groups, and hence it may be an appropriate model compound for the interior of l4 Recently the enthalpic pair interaction coefficients h,, (water-non-electrolyte) in DMF have been analysed. 153 l6 This work attempts an examination of a system containing an electrolyte as solute instead of water.As in other studies performed in our laboratory,*-" the electrolyte selected was NaI because of its relatively good solubility in the mixtures under study. The choice of this electrolyte makes possible a comparison of the results obtained in this investigation with appropriate literature data concerning interactions in aqueous solution. The values of the enthalpic pair interaction coefficients were calculated from 59 1 20-2592 Enthalpic Pair Interaction Coeficients experimentally determined values of the enthalpy of solution of NaI in mixtures of DMF with several non-electrolytes, namely N-methylformamide, dimethyl sulphoxide, tetra- hydrofuran, acetonitrile, acetone and isobutanol, all in low concentrations, at 298.15 K. Experimental Sodium iodide, analytically pure (I.T. Baker Chemicals B.V.) was purified and dried using the procedure described in an earlier paper. N,N-Dimethylformamide (Fluka) and dimethyl sulphoxide (Fluka) were dried with 4A molecular sieves and fractionally distilled under reduced pressure. Acetonitrile (Fluka), N-methylformamide (Fluka), acetone (Merck), tetrahydrofuran (Merck) and isobutanol (P. 0. Ch. Gliwice Poland) were purified and dried by methods described in the literat~re."~'~ The water content of the solvents determined by the Fisher method did not exceed 0.02 %. The mixtures were prepared by weight in a dry box, using freshly distilled DMF. Measurements of dissolution enthalpies were performed in the calorimetric system described in an earlier report." The range of electrolyte concentrations was 0.002-0.0 12 mol kg-' of solvent.The uncertainties in the measured enthalpies did not exceed & 0.5 YO of the measured value. Results and Discussion Solution Enthalpy The measured enthalpies of solution, AH,, of NaI in the mixtures of DMF with acetonitrile (ACN), dimethyl sulphoxide (DMSO), tetrahydrofuran (THF), N-methyl- formamide (NMF), acetone (ACT) and isobutanol (Bu'OH) listed in table 1 were extrapolated to infinite dilutions as a function of the square root of electrolyte concentration. The slope of the function AHs =Am:) in all the mixtures investigated was close to that calculated theoretically for pure DMF (7820 J kgi m~l-~)." and relatively narrow range of composition of the investigated mixtures, the correction for ionic association was neglected.The molar solution enthalpies of NaI at infinite dilution, A%, in all mixtures under study are collected in table 2. The value of AX of NaI in DMF, determined in this work (- 56.40 kJ mol-l) agrees reasonably well with literature data (e.g. - 55.0 & 0.3 kJ mo1-1,21 - 56.82 kJ mo1-1).22 Owing to the relatively low association constant of NaI in pure DMF (< Enthalpic Pair Interaction Coefficients Enthalpic pair interaction coefficients, h,., for NaI-non-electrolyte pairs in DMF were estimated on the basis of the dissolution enthalpy of NaI in mixtures of the above non- electrolytes with DMF measured in this work. In order to calculate the h,, coefficients, the method described in detail in previous papers was employed.'O*ll The values of h,.obtained in this way are presented in table 3. Owing to simplifications in the deter- mination of AX, the uncertainties in the h,, values are estimated to be ca. & 10 %. The same table also gives the h,, data for other non-electrolytes, not investigated in this work. These values were taken from the literature23 or calculated on the basis of appropriate literature 25 For the sake of comparison, the analogous data referring to aqueous solution are also presented in table 3. Note that the h,. coefficients constitute, in each case, the 'mean ionic ' pair interaction coefficients; more precisely, in the case of 1-1 electrolytes they correspond to half of the enthalpic effect of the interaction between the molecule of a given non-electrolyte, Y, and the cation C+ and (1) anion A-: h,, = !j[h(C' + A-) - y3 = a[h(C' - Y) + h(A- - Y)].Table 1.Enthalpies of solution of NaI in mixtures of DMF with the non-electrolytes at 25 "C ACN DMSO THF rnlmol kg-' AHJkJ mol-' rnlmol kg-' AHs/kJ mol-' rnlmol kg-' AH,/kJ mol-' - 0.002 384 0.003 775 0.006 168 0.008 747 0.012 360 0.001 960 0.003 785 0.006 745 0.009 362 0.012 420 0.001 748 0.002 897 0.005 350 0.007 895 0.01 1 840 0.003 310 0.003 570 0.005 843 0.007 383 0.012 750 - 55.77 - 55.70 - 55.55 - 55.45 -55.30 -55.50 - 55.35 - 55.25 - 55.10 - 55.00 - 54.90 - 54.85 - 54.70 - 54.55 - 54.45 - 53.48 - 53.45 - 53.35 - 53.27 - 53.08 ACT rn/mol kg-' AHJkJ mol-' 0 , a = 0.025 0.002 704 - 55.85 0.004 881 - 55.70 0.007 624 - 55.60 0.009 871 - 55.45 0, = 0.05 0.001 309 - 55.80 0.004 438 - 55.60 0.007 060 - 55.46 0.009 663 - 55.38 0, = 0.10 0.003 045 - 55.30 0.005 542 -55.16 0.009 665 - 55.01 0.012 745 - 54.90 0, = 0.20 0.001 646 - 54.68 0.003 705 - 54.44 0.006 390 - 54.18 0.009 123 - 53.95 0.001 734 0.004 264 0.007 449 0.01 1 507 0.002 573 0.005 533 0.007 550 0.010 308 0.001 794 0.003 273 0.004 726 0.006 086 0.003 296 0.005 861 0.008 375 0.009 936 - 55.75 - 55.56 - 55.40 - 55.25 - 55.30 - 55.10 - 55.02 - 54.90 - 54.65 - 54.50 - 54.40 - 54.36 - 53.03 - 52.85 - 52.68 - 52.57 Bu'OH NMF rnlmol kg-l AH,/kJ mol-' rnlmol kg-' AHJkJ mol-' 0.002 486 0.003 871 0.005 364 0.007 886 0.001 980 0.003 133 0.006 045 0.008 172 0.002 120 0.004 455 0.006 432 0.009 378 0.002 336 0.003 775 0.005 460 0.008 812 - 55.70 - 55.60 - 55.52 - 55.40 - 55.38 - 55.30 -55.15 - 55.05 - 54.75 - 54.55 - 54.45 - 54.30 - 53.30 - 53.20 - 53.08 - 52.90 O,a = 0.025 0.002 735 - 55.35 0.003 160 - 55.30 0.006 342 -55.15 0.008 717 - 55.00 0, = 0.05 0.002 340 - 54.72 0.002 875 - 54.65 0.004 933 - 54.50 0.007 767 - 54.37 0, = 0.10 0.002 750 - 53.27 0.004 81 1 -53.15 0.005 253 -53.10 0.009 084 - 52.95 0, = 0.20 0.002 213 - 50.68 0.003 781 - 50.55 0.006 467 - 50.38 0.008 749 - 50.25 0.001 986 0.002 735 0.005 466 0.008 738 0.001 736 0.003 467 0.005 351 0.008 490 0.002 398 0.004 635 0.007 396 0.009 193 0.002 134 0.003 532 0.004 788 0.006 875 - 55.46 - 55.40 - 55.25 -55.10 - 54.85 - 54.75 - 54.65 - 54.50 - 53.52 - 53.40 - 53.26 - 53.22 -51.27 -51.20 -51.15 -51.05 a Mass fraction of the non-electrolyte.594 Enthalpic Pair Interaction Coeficients Table 2.Molar enthalpies of solution of NaI at infinitely dilute solution in mixtures of non- electrolytes with N,N-dimethylformamide at 25 "C QJ,a ACN DMSO THF ACT Bu'OH NMF 0.000 - 56.40 - 56.40 - 56.40 - 56.40 - 56.40 - 56.40 0.025 - 56.13 - 56.22 - 56.05 -56.06 - 55.73 - 55.78 0.05 -55.82 -56.05 -55.70 -55.72 -55.05 -55.15 0.10 - 55.22 - 55.70 - 55.00 - 55.10 - 53.70 - 53.85 0.20 -53.90 -54.97 -53.60 -53.73 -51.10 -51.55 a Mass fraction of the non-electrolyte. Estimated uncertainty is & 70 J mol-'.Table 3. Enthalpic pair interaction coefficients h,,(J kg mol-2) and 'linear' h,*, and 'specific' h;rc contributions to h,, for NaI-non-electrolyte interactions in DMF and in water at 25 "C and ion-alkyl group interaction parameters, hion.alkyl, calculated from functional-group parametedo non-electrolyte methanol pro panol isopropanol isobutanol NMF DMSO ACT THF ACN water methanol ethanol propanol isopropanol isobutanol DMSO ACT THF ACN DMF solvent: DMP 230" 447 430b 573 480b 520 500 516 380 400 135 150 210 224 250 - 120 504 780 890 solvent : water 157" -110 298" - 77 395" - 78 509" - 92 600" - 92 -208" -182 -46" -164 202" - - 247" - 95 -175" -220 -217 - 143 - 40 - 16 - 20 - 15 - 14 - - 384 -110 267 375 473 60 1 692 118 - 26 - - 152 45 217 362 507 507 652 435 - - 435 a Ref.(23) Calculated from ref (24). " Ref. (10). The results presented in table 3 show that the h,, coefficients for (Na++I-)-non- electrolyte interactions in DMF solution are positive for all the systems examined, while in aqueous solution these coefficients are both positive and negative.'-'O For an explanation of this behaviour it seemed advisable to examine which property of the system gives the largest contribution to pair interaction coefficients in DMF.It is well known that the interactions between solute molecules are solvent-mediated. An analysis of the interactions in water showed that the enthalpic pair interaction coefficients h,, for pairs of NaI (X) with several non-electrolytes (Y) are linearly dependent on the molar heat capacity of transfer of the non-electrolyte (Y) from the gas phase to high dilution in water (the heat capacity of solvation, given byH. Piekarski 600 N - 0 E COO- 3 3 h 1 -E: 200 595 - - 01 I I I I I 20 40 60 6CJJ K-’ mol-’ 80 Fig. 1. Enthalpic pair interaction coefficients hzv[(Na+ + I-)-non-electrolyte] as a function of the molar heat capacity of transfer of the non-electrolyte from the gas phase to high dilution in DMF (dC, = Cp”,z-C%p,m): (1) water, (2) methanol, (3) propanol, (4) isopropanol, ( 5 ) isobutanol, (6) acetonitrile, (7) N-methylformamide, (8) dimethyl sulphoxide, (9) acetone and (10) tetra- hydro furan.SC, = Cr, - Cp,m).8, lo The same observations were also made for (Na+Cl-Fnon- electrolyte interactions, as well as for DMF-non-electrolyte and urea-non-electrolyte pairs in water.12 The observed dependences suggest that in aqueous solution, for a given X the effect of hydration of the non-electrolyte Y is more important than the direct interaction between X and Y. Therefore, changes in water structure around the dissolved species make the main contribution to h,, values.Fig. 1 shows the dependence of h,, for (Na+ + I-)-non-electrolyte pairs on SC, of the non-electrolyte in DMF. The molar heat capacities of transfer of the non-electrolyte molecule from the gas phase to high dilution in DMF had been determined in previous papers16’ 26 or were calculated from literature Only the enthalpic pair interaction coefficients for NaI with the alkanols and with N-methylformamide are linearly correlated with SC,. Note that the picture presented above is very similar to that observed earlier for water-non-electrolyte interactions in DMF.“ These findings indicate that the energetic effect of changes in the solvent structure in the vicinity of the dissolved particles leads to a variation in h,, values in DMF, to a lesser extent than occurs in water as solvent, since DMF is less structured than water in its liquid state.Therefore, a direct interaction between electrolyte and non-electrolyte, leading to the replacement of DMF molecules by non-electrolyte molecules in the solvation region of the ions, seems to play a very. important or even dominant role in the systems under study. These electrolyte-non-electrolyte interactions should be connected, to some extent, with the donor-acceptor properties of the non-electrolyte molecule. In fig. 2 the values of h,, in DMF solution are plotted as a function of the ‘acceptor number’ (Na) of the non-electrolyte. As can be seen, the non-electrolytes examined are divided into two groups, just as in the previously discussed correlation.However, here we have two straight-line segments, one of which refers to alkanols and N-methylformamide while the other represents the non-electrolytes that are aprotic in character (acetonitrile, DMSO, THF and acetone). The h,, value corresponding to the interaction of NaI with water is not located on either of the two straight lines. The absence of an electron- acceptor group in ACN, DMSO, THF or ACT should make interactions between the iodide anion and molecules of these substances in DMF solution relatively weak.596 Enthalpic Pair Interaction Coeficients I I I I I I0 20 30 40 50 N* Fig. 2. The dependence of h,,[(Na+ + I-)-non-electrolyte] in DMF solution on ‘ acceptor number ’ (N,) of the non-electrolyte : (1) water, (2) methanol, (3) propanol, (4) isopropanol, (5) isobutanol, (6) acetonitrile, (7) N-methylformamide, (8) dimethyl sulphoxide, (9) acetone and (10) tetra- hydrofuran.Therefore, the small slope of the left-hand line in fig. 2 may indicate that in these systems the interaction between the aprotic non-electrolytes and the sodium cation is relatively similar. The interactions between NaI and aliphatic alcohols (the right-hand line in fig. 2) are more sensitive to the properties of the non-electrolyte. However, in those systems both ions can give comparable contributions to h,, owing to the amphiprotic character of the molecules in question. The dependences presented above do not allow us to say which of the mentioned interactions dominate within a given system. To throw some light on this problem, the alternative analysis of h,, coefficients given below appears to be useful.It has been found in many studies that the enthalpy of solution of electrolytes in some binary mixtures changes virtually proportionally to the mole fraction of each 31 This so-called ‘ linear behaviour ’ is considered to indicate the absence of specific solvation effects31 or of radical changes in the mixed-solvent In that case the solvation shell of the solute particle should gradually change from a shell typical of one pure component of the mixed solvent to one typical of the other. Therefore, the enthalpic pair interaction coefficients for the solute-cosolvent pairs, which are related to very dilute solution with respect to both the solute and the cosolvent, will illustrate in such a system the effect of replacement of solvent molecules by cosolvent molecules in the immediate vicinity of the ions. Let AX(X in S + Y) denote the enthalpy of solution of a solute X in a mixture of solvent S and cosolvent Y.AG(X in S) and AX(X in Y) denote the enthalpy of solution of X in pure S and pure Y, respectively, whereas x, and x, are the mole fraction of S and Y in the mixed solvent. Then for a system that exhibits ‘linear behaviour ’ we obtain : (2) (3) (4) ( 5 ) AX@ in S + Y) = x, AK(X in S) + x, AK(X in Y) AK(X in S + Y) = (1 - x,) AK(X in S) + x, AK(X in Y) AK(X in S + Y) = AK(X in S) + x,[AK(X in Y) - AK(X in S)]. AKr(S + S + Y) = X, AKr(S -+ Y). or and Hence In a more general case, when specific interactions are present, this equation takes the (6) following form : Aer(S S + Y) = X, AKr(S + Y) + &xu)H.Piekarski 597 where d(x,) is a function (unknown in most cases) describing deviations from linearity due to specific effects. Since the molar enthalpy of transfer of a solute X from a pure solvent S to a mixture of S with cosolvent Y is related to the enthalpic pair interaction coefficients h, , : lo 9 l1 (7) a 1 - [AKr(S + S + Y)],y+o = 2vh,, - ax, Ms where v is the number of ions and Ms is the molecular mass of the solvent S (in kg mol-l), we can calculate h,, by differentiation of eqn (6) with respect to the mole fraction of the cosolvent x,: and (9) The first term on the right-hand side of the above equation, derived on the basis of the assumption about linearity of AG(X in S + Y) [eqn (5)] illustrates the contribution to h,, connected with the gradual changes in the solute solvation-shell structure : MS -AKr(S + Y) = h:,.2v (12) spec -- The second term gives the contribution to h,, arising from the specific interactions in the system examined. Using literature data for the molar enthalpy of NaI solution in appropriate pure solvents8.11,25,32,33 the h:, coefficients were calculated. The h z y values were next estimated from the relation The results obtained, given in table 3 indicate that the values of h,*, in DMF for the pairs of (Na' + I-) with NMF, ACT, DMSO, Pr'OH and Bu'OH are very close to hzy, which means that hzrc x 0 (within the error limits). Therefore, the observed positive h,, (Na+ + I-)-non-electrolyte values probably reflect the replacement of DMF molecules by the cosolvent in the solvation region of the electrolyte in these systems.In the other systems under study (the lower alkanols, water and acetonitrile) the calculated h:, coefficients are higher than the observed pair interaction coefficients, which results in a relatively large negative specific contribution (table 3). These negative values of hire could arise from an electrostatic interaction between the iodide anion and the non-electrolytes of the above group or from selective solvation in the investigated system. To check which of these suppositions is true it would be necessary to divide the h,, coefficients into ionic contributions. This is not possible at present because the data are insufficient. The results of analogous calculations in aqueous solution are also presented in table 3.In this case, the hiye values are negligibly small only for the pairs (Na+ + I-)-DMSO and (Na++I-)-DMF, which may indicate that in these systems the enthalpic pair interaction coefficients are an effect of the replacement of water molecules by DMSO or DMF, respectively, in the solvation region of the ion. For most of the other discussed Ms a [~(x,)l,y4 = h,, 2v ax, h z y = h,,-h:,. (13)598 Enthalpic Pair Interaction Coeficients pairs in water, a significant contribution from specific interactions to h,, is observed. The positive values of for (Na++I-Falkanol and (Na++I-)-acetone pairs seem to reflect interactions between the ions and the hydrophobically hydrated alkyl group in the non-electrolyte molecule, leading to the partial destruction of the hydration region.If this conclusion is true, it should be possible to calculate the above effect using the so- called ' functional group interaction parameters ' hiu."q 34 The enthalpic pair interaction coefficients h,, for electrolyte-non-electrolyte pairs in water can also be presented as a sum of group contributions.lOT1l For NaI as an electrolyte, three types of interaction were distinguished : i[(Na+ + I-)-CH,], i[(Na+ + I-)-OH] and i[(Na+ + 19-01 and group contributions were calculated (145 & 1 1, -48 & 36 and - 394 & 34 J kg rnol-,, respectively).1° Assuming following other authors, e.g. ref. (34) that the CH, group corresponds to 1.5 CH, groups while the CH group corresponds to 0.5 CH, groups, the contributions arising from the ion-hydrocarbon group interactions to h,, in water were estimated (table 3).A comparison of these data with h : r for (Na++I-balkanols seem to confirm the opinion presented earlier concerning the origin of the positive specific contribution to h,, in water.? The same kind of interaction is probably responsible for the positive h i r coefficients in the systems (Na+ + I-)-acetone and to some extent (Na+ + I-)-DMF, although the h ; r values are lower than the appropriate ion-alkyl group interactions (table 3). The hydration cosphere around the non-polar groups in the latter non-electrolytes is not typically hydrophobic, owing to the possibility of a strong influence of the highly polar carbonyl group in acetone and the amide group in N,N-dimethylformamide. Unfortunately the small number of enthalpic pair interaction coefficients for (Na+ + I-)-non-electrolyte pairs in DMF makes it impossible to determine the functional group interactions as in aqueous solution.However, a comparison of the h,. values for (Na+ + I-)-alkanol pairs allows us to conclude that the electrolyte-CH, interaction in DMF in the group-additivity system is positive, just as occurs in water. Nevertheless, it should be assumed that the origins of these positive values in both solvents are different. Conclusions (1) Enthalpic pair interaction coefficients for NaI-non-electrolyte pairs in DMF are positive in all investigated systems, unlike the case in aqueous solutions, where they are both positive and negative.(2) Energetic effects connected with changes in solvent structure in the vicinity of the dissolved particles exert a smaller influence on the h, values in DMF than in water. (3) Direct interaction between ions and the non- electrolyte, leading to the replacement of DMF molecules by the non-electrolyte in the ionic solvation shell, has an affect on h,, values in DMF that is comparable with structural effects (sometimes even predominant). References I W. G. McMillan Jr and J. E. Mayer, J. Chem. Phys., 1945, 13, 276. 2 H. L. Friedman and C. V. Krishnan, J. Solution Chem., 1973, 2, 119. 3 R. B. Cassel and R. H. Wood, J. Phys. Chem., 1974, 78, 2460. 4 C. de Visser, G. Perron and J. E. Desnoyers, J. Am. Chern. SOC., 1977,99, 5894. 5 G. Perron, D. Joly, J.E. Desnoyers, L. Avedikian and J-P. Morel, Can. J. Chem., 1978, 56, 552. 6 C. de Visser, W. J. M. Heuvelsland and G. Somsen, J. Solution Chem., 1978, 7 , 193. 7 W. J. M. Heuvelsland, C. de Visser and G. Somsen, J. Chem. SOC., Faraday Trans. I , 1981, 77, t Relatively large difference between both series of the data for Pr'OH comes from the simplification of the model used in additive group parameters calculation, that does not distinguish primary from secondary carbon atoms in a molecule. 1191.H. Piekarski 599 8 H. Piekarski, Can. J . Chem., 1983, 61, 2203. 9 H. Piekarski, A. Piekarska and S. Taniewska-Osinska, Can. J. Chem., 1984, 62, 856. 10 H. Piekarski, Can. J . Chem., 1986, 64, 2127. 11 H. Piekarski and M. Tkaczyk, Thermochim. Acta, in press. 12 H. Piekarski and G.Somsen, Can. J. Chem., 1986, 64, 1721. 13 0. D. Bonner, J. M. Bednarek and R. Arisman, J . Am. Chem. SOC., 1977,99, 2898. 14 H. E. Kent, T. H. Lilley, P. D. Milburn, M. Bloemendal and G. Somsen, J . Solution Chem., 1985, 14, 15 M. Bloemendal, A. Rouw and G. Somsen, J . Chem. SOC., Faraday Trans. 1 , 1986, 82, 53. 16 H. Piekarski and G. Somsen, J . Chem. SOC., Faraday Trans. I , in press. 17 J. F. Coetzee, G. P. Cunningham, D. K. McGuire and G. R. Padmanabhan, Anal. Chem., 1962, 34, 18 A. Weissberger, E. S. Proskauer, J. A. Riddick and E. E. Toops Jr, Organic Solvents (Interscience, New 19 R. P. Held and C. M. Criss, J . Phys. Chem., 1965, 69, 261 1. 20 G. J. Janz and R. P. T. Tomkins, Nonaqueous Electrolyte Handbook (Academic Press, New York, 1973). 21 L. Weeda and G. Somsen, Red. Trav. Chim., 1967, 86, 893. 22 G. A. Krestov and V. A. Zverev, Zzv. V. U.Z., Khim. Khim. Tekhnol., 1971, 14, 528. 23 A. Piekarska, H. Piekarski and S. Taniewska-Osinska J. Chem. SOC., Faraday Trans. I , 1986, 82, 24 N. A. Solomatina, S. N. Solovl’ev and A. F. Vorob’ev, Proc. IX All-Soviet Conference on Calorimetry 25 S. Taniewska-Osinska and A. Piekarska, Bull. Acad. Pol. Sci., Ser. Sci. Chim., 1978, 26, 612. 26 H. Piekarski, Can. J . Chem., in press. 27 H. C. Zegers and G. Somsen, J . Chem. Thermodyn., 1984, 16, 225. 28 C. de Visser and G. Somsen, J . Solution Chem., 1979, 8, 593. 29 S. Cabani, P. Gianni, V. Molica and L. Lepori, J . Solution Chem., 1981, 10, 563. 30 A. Piekarska, J . Chem. Thermodyn., 1987, 19, 925 (and references therein). 31 A. Rouw and G. Somsen, J . Solution Chem., 1981, 10, 533. 32 E. M. Arnett and D. R. McKelvey, J. Am. Chem. SOC., 1986, 88, 2598. 33 V. V. Sokolov and K. P. Mischchenko, Zh. Strukt. Khim., 1964, 5, 819. 34 J. J. Savage and R. H. Wood, J . Solution Chem., 1976, 5, 733. 101. 1139. York, 1955). 513. and Chemical Thermodynamics, Tbilisi, Sept. 1982. Paper 71740; Received 23rd April, 1987

ISSN:0300-9599    

DOI:10.1039/F19888400591

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1988, 84(2), 601-608 Activation and Chain-carrying CH, Species in Terminal A1 kene Me tat hesis on Mol ybdena-Titania Catalysts Katsumi Tanaka" Research Institute for Catalysis, Hokkaido University, Kita-Ku, Sapporo 060, Japan Ken-ichi Tanaka The Institute for Solid State Physics, The University of Tokyo, 7-22-1 Roppongi, Kinato-Ku Tokyo 106, Japan The metathesis reaction of terminal alkenes other than isobutene took place on Moo,-JTiO,, whereas that of isobutene proceeded in the presence of ethylene and following treatment of the catalyst with SnMe, at room temperature. These results infer that chain-carrying CH, species are generated to only a small extent by the adsorption of isobutene on MOO,-,/ TiO,, although they are formed by the adsorption of alk-1-enes and SnMe,.The metathesis-inactive material, fully oxidized MoOJTiO,, was changed to a metathesis-active catalyst by treating it with SnMe,. This suggests that MoO,/TiO, has no ability to yield CH, species with terminal alkenes but that these species can be supplied with SnMe,. An analysis by X-ray photolectron spectroscopy infers that SnMe, adsorbed on MoO,/TiO, releases methyl groups concomitant with the oxidation of Sn. At the present time, a mechanism proceeding via metal-alkylidene and metalla- cyclobutane intermediates is accepted as an approved route for catalytic alkene metathesis reactions.' In fact, some non-Fischer-type metal-alkylidene complexes2 have been found to promote metathesis-like reactions, and metallacyclobutane derivatives of Ti3 and W4 undergo metathesis-like reactions with alkenes.It has also been shown by means of n.m.r. spectroscopy that the neopentylidene ligand in a tungsten complex is replaced by ethylidene and propylidene ligands on reaction with ~ent-2-ene.~ Homogeneous catalysts for alkene metathesis sometimes require a cocatalyst, such as the addition of EtAlCI, to WCl,,, and the role of Lewis acids or hard ligands in the cocatalysts is interpreted in terms of electronic effects due to the central Unlike the electronic effect produced by electron-deficient molecules, the activation of WCl, by ZnMe, may be caused by the formation of W=CH, species in the reaction with ZnMe,.8 Similar phenomena have been found using Cp,TaMe326 and C ~ T i c l , ~ treated with AlCl,.On the other hand, alkene metathesis on heterogeneous catalysts proceeds in general by contact with the alkenes. This fact implies that the key intermediates for alkene metathesis, metal alkylidenes, are produced automatically in the initial stages of the reaction by contact with the alkenes. If this is the case, whether or not a solid surface is active for alkene metathesis should be determined by the ability for the alkylidene formation process to take place. In this paper we will demonstrate that alkylidene formation is a significant step in heterogeneous alkene metathesis. Experimental Catalyst Preparation Molybdena-titania catalysts were prepared by immersing p-titanic acid, TiO, * H20, into an aqueous solution of ammonium paramolybdate, (NH,),Mo,O,, * 4H20.The solid was then dried at 120 "C in air for 12 h, and its MOO, content was found to be 6.7 wt '10. Details of the preparation of /?-titanic acid have been described previously." 60 1602 Alkene Metathesis on Molybdena-Titania Catalysts Freshly prepared catalyst was oxidized with 0, (ca. 200 Torr, 1 Torr = 101 325/760 Pa) at 500 "C for 1 h, which rzsulted in the fully oxidized MoO,TiO, catalyst. Partially reduced MOO,-,/TiO, (0.1 < x < 0.7) was prepared by reoxidizing a MoO,/TiO, catalyst (reduced with H,; 100-200 Torr, 500 "C, 1 h) with a 1 : 1 mixture of N,O and H, at ca. 300 Torr and 200 "C for 1 h.l0 Prior to the catalytic reaction or treatment with SnMe,, the catalyst was evacuated at 500 "C for 1 h. Reactions and Product Analysis Pretreatment of the catalyst and the reaction were performed in a closed glass circulation system with a volume of ca. 260 cm3.0.5 g of catalyst was treated with diluted SnMe, ( 5 Torr of SnMe, in ca. 60 Torr of He) for 30 min at room temperature, and this was followed by evacuation at the same temperature for 30 min." Metathesis was carried out at room temperature with an alkene pressure between 4 and 65 Torr. Analysis of ethylene, propene, but- 1 -ene, isobutene, but-2-ene, hex-3-ene and 2,3-dimethylbut-2-ene was performed using a gas-chromatograph with a 13 m length column comprising Sebaconitrile (25 %) on Uniport C (60-80 mesh), while for methane, ethane and ethylene the column comprised 2 m of Gaskuropack 54 (a copolymer of polystyrene and divinylbenzene, commercially available from Gasukuro Kogyo Co.). Deuterium atom distributions in the alkene products were calculated by mass-spectrometric analysis with an ionization voltage of 10-15 eV.[,H,]Ethylene, [2H,]propene (Merck Sharp & Dohme) and [l3C2]ethylene (Amersham International, 92 % 13C) were used without further purification. [,H,]But- 1 -ene was prepared by deuteration of commercially available E2H4]butadiene on ZnO at room temperature. [2H,]Isobutene was obtained by reacting isobutene with deuterium gas at room temperature on Mg (OH), evacuated at 450 "C. The prepared samples of [,H,]but- 1-ene and [2H,]isobutene were purified using gas- chromatographic separation. X.P.S. Analysis X-Ray photoelectron spectra of the catalyst were measured with a VG-ESCA 3 spectrometer.MoO,/TiO, powder was compressed into a disc and was mounted on a Ni holder with an internal standard Au wire. The catalyst was treated in the preparation chamber using the same procedure as performed in the circulation system. However, the adsorption of tetramethyl tin on the MoO,/TiO, disc was performed at liquid-nitrogen temperature (ca. - 190 "C). Binding energy (Eb) values were referenced to the 0 1s peak at 530 eV, and 2p,,, for Ti4+ was found to be at 458.7 eV, in good agreement with the value reported for Ti4+ on Ti0,.12 Results and Discussion Alkene Metathesis on Moo,-,/TiO, and Moo,-,/TiO,-SnMe, Table 1 summarises turnover frequencies for the metatheses of ethylene, propene, but- 1-ene and isobutene on Moo,-,/TiO, and MOO,-,/TiO,-SnMe, at room tempera- ture.The turnover frequencies are evaluated by assuming that all the Mo cations on TiO, participate in metathesis. Therefore the true turnover frequencies should be larger than those in table 1. It is of interest that ethylene, propene and but- 1 -ene undergo metath- esis, whereas for isobutene, metathesis was entirely prohibited and the polymerization of isobutene occurred on Moo,-,/TiO,. This polymerization may be cationic, via the tertiary butyl cation, or it may be an addition polymerization of a-alkenes via a Ziegler-Natta mechanism on reduced TiO,. Despite the fact that the metathesis of isobutene does not proceed on MoO,-,/TiO,, when a 1 : l : l mixture of isobutene,K . Tanaka and K-i. Tanaka 603 Table 1. Turnover frequencies of metathesis reactions of ethylene, propene, but- 1-ene and isobutene on MoO,-,/TiO, and Moo,-,/TiO,-SnMe, at room temperature metathesis reaction Mo03-,/Ti0, M00,-,~/Ti0,-SnMe, CH,=CH, + CD,=CD, - 2 CH,=CD, 3.2 x 10-5 1.9 x 10--3 2c=c-c - c=c + c-c=c-c 2.0 x 10-7" 5.4 x lo-J" 2c=c-c-c - c=c + c-c-c=c-c-c 7.9 x 2.0 x lo-" /c c, /c 'C c/ ' c 2c=c - c=c + c=c 0 3.3 x 10-3 a Ref.(1 1). Turnover frequencies (ethylene molecules per Molybdenum ration per second) were obtained by assuming that all Mo cations participate in metathesis. [l2C2]ethylene and [13C,]ethylene was added on Moo,-,/TiO, at room temperature, ['3C,]ethylene and [13C,]isobutene were formed by the following metathesis reaction (see fig. 1 ) : / c + C=13C ( l a ) '3c=c\c + 13C='3C /c 'C c=c C / C c\ / 2c=c - c=c + c=c 'C C ' 'c [13C,]ethylene is produced by the reactions (1 a ) and (1 b), and reaction (1 a ) yields equal amounts of [13C,]isobutene and [13Cc,] ethylene.Accordingly, reaction ( 1 b) is ca. 10 times faster than reaction (1 a). 2,3-Dimethyl but-2-ene was formed distinctly [reaction (1 c)] in the co-metathesis of isobutene and ethylene on Mo03-,/Ti0,; however, its rate was extremely slow. From these results it is concluded that the metathesis of isobutene proceeds on MoO,_,/TiO, in the presence of ethylene. Such a phenomenon can be interpreted as follows. Any metal alkylidene species required for alkene metathesis are not produced on MoO,-,/TiO, by the adsorption of isobutene ; however, the adsorption of ethylene gives a metal alkylidene species on the surface. As a result, the metathesis of isobutene can proceed in the presence of ethylene via the alkylidene species furnished from ethylene in the initiation steps. The fact that polymerization of isobutene is suppressed in the presence of ethylene while simultaneously metal alkylidene is supplied from ethylene under such conditions suggests that the metal alkylidene formation might proceed through a metal alkyl species formed by a reaction between ethylene and hydrogen species which yields the tertiary carbonium cation on the MoO,_,/TiO, catalyst .When MoO,_,/TiO, was treated with SnMe, at room temperature, it changed to a super-active alkene metathesis catalyst. The turnover frequency for the metathesis of propene was enhanced more than three orders of magnitude, and those of ethylene and but-1-ene were increased by factors of ca.10, and 3, respectively. Note that the604 Alkene Metathesis on Molybdena- Titania Catalysts > I 240 I 300 3( 0 t/min Fig. 1. Metathesis of a 1 : l : 1 mixture of isobutene, ethylene and [13C,]ethylene on MOO,-,/ TiO, at room temperature: 0, [l3C1]ethylene [reaction (1 a)]; 0, [13Cl]isobutene, x 10 [reactions (1 b) and (1 c)]: total pressure, 48 Torr; catalyst 0.5 g. metathesis of isobutene proceeded on MoO,-,/TiO,-SnMe,. This result clearly indicates that chain-carrying metal alkylidene species are formed on the Moo,-,/TiO, surface by the adsorption of SnMe,. When a 1 : 1 mixture of [,H,]- and [,H,]-ethylene, [,H,]- and [2H6]-propene or [,H,]- and [,H,]-but- 1 -ene was added on Moo,-,/TiO, at room temperature, neither the hydrogen- scrambling nor the double-bond shift reactions occurred during metathesis.In contrast, when a 1 : 1 mixture of [,H,]- and [2H,]isobutene was reacted on Moo,-,/TiO, at room temperature, hydrogen scrambling proceeded rapidly, concurrent with polymerization. This result may be due to a rapid equilibration between isobutene and the butyl carbonium cation, in which three equivalent methyl groups can participate in hydrogen exchange. When a 1 : 1 mixture of [,H,]- and [2H,]-isobutene was reacted on MOO,-, Ti0,-SnMe, at room temperature, metathesis occurred with little hydrogen mixing ; i.e. the productive metathesis of isobutene [reaction (2 a)] yielded ethylene composed of [,H,], ['H,] and ['H,] isomers and 2,3-dimethylbut-2-ene composed of [,H,] [,H6] and [2H12] isomers, and the degenerate metathesis [reaction (2 b)] gave [,H,]- and [2H6]isobutene : r 1 ethylene I 2,3-dimethylbut-2-ene + /CH3 CH,=C + 'CH, ,.D3 CD,=C \ CD, / \K.Tanaka and K-i. Tanaka 605 Table 2. Initial formation rates of methane, and ratios of ethane to methane formed in the early stages of the reaction of SnMe, (5 Torr) on molybdena-titanias (0.5 g of each) at room temperature CH, formation rate /(molecules Mo)-' s-I initial C,H,/CH, ratio catalyst MoO,/TiO, 6.3 x lo-, Moo,-,/TiO, 4.0 x M 00, /Ti0 2.5 x 10-5 4.0 0.5 0.0, From this result it is deduced that the activation of MOO,-,/TiO, with SnMe, is responsible for the introduction of chain-carrying CH, species on the surface and that the adsorption of SnMe, inhibits the formation of t-butyl carbonium ions on acidic sites.Note that the treatment of inactive MoO,/TiO, with SnMe, results in the formation of an active catalyst for the metathesis of isobutene, as well as of ethylene, propene and but-1 -ene at room temperature. In addition, productive and degenerate metathesis oc- curred selectively on the catalyst in a 1 : 1 mixture of [,H,]- and [2H,]-isobutene. Reaction of SnMe, on Molybdene Titania As discussed above, the role of SnMe, in activating molybdena-titania is undoubtedly to graft the CH, chain-carrying species required for alkene metathesis. When SnMe, was contacted with a molybdena-titania surface at room temperature, small amounts of methane, ethane and ethylene were evolved. Table 2 shows the rate of methane formation and the ratio of C,H, to CH, obtained in the initial stage of the reaction with SnMe, on MoO,/TiO,, Moo,-,/TiO, and MoOJTiO,.Not such a big difference is seen in the rate of methane formation on these catalysts, but the initial C,H,/CH, ratios strongly depend on the extent reduction of molybdenum oxide, i.e. ethane formation selectively proceeds on MoO,/TiO,. The turnover frequency of propene metathesis was 9.3 x on MoO,/TiO,-SnMe,. Consequently, CH, species may be produced on the MoO,/TiO, surface by the reaction of 2CH3+CH, + CH,. A reductive coupling of CH, giving ethane, 2CH,-+C2H6, may occur also on the MoO,/TiO, surface. So far, five different modes of alkyl metal cleavage have been proposed :lo (i) D-elimination, (ii) reductive coupling, (iii) a-elimination, (iv) hydrogen and alkyl transfer and (v) electrophilic attack.13 Cases (ii), (iii) and (iv) are relevant to the reaction of SnMe, on molybdenum oxides on TiO,.If the reductive coupling occurs on MoO,/TiO, in the reaction with SnMe,, the valence states of Sn and Mo should be of considerable interest. The X-ray photoelectron spectra of the Sn 3d region are shown in fig. 2. When MoOJTiO, was exposed to SnMe, with 60 [l L (1 langmuir) = 1 x lo-, Torr s] at liquid-nitrogen temperature, the peaks indicated as species I were observed at ca. 483 and 492 eV; these correspond to a 3d5/2 and 3d3,, doublet [fig. 2(a)] and were accompanied by weak peaks at ca. 486 and 495 eV indicated as species 11. The peaks were little influenced by continuing X-irradiation for 30 min [fig.2(b)]. However, if the MoO,/TiO,-SnMe, sample was left in vacuu overnight to reach room temperature, species I1 remained with the same intensity as in fig. 2(a) [see fig. 2(c)]. Species I corresponds to Sno;l4 however, the weak species I1 may be assigned to Sn2+ or Sn4+ because of their close binding energies.14* l5 These results imply that monolayer adsorption of SnMe, results in the oxidation of the Sn species, giving ethane and leaving the SnMe, overlayer in the Sno+ state. The oxidation of Sn may compensate the reduction of Mo6+ in MoO,/TiO,. The X.P.S. band for Mo 3d did not appreciably change on adsorption of SnMe,, perhaps because of the606 Alkene Metathesis on Molybdena-Titania Catalysts I I I t II I I I I I I I I I 1 I 480 484 488 492 496 EbIeV Fig.2. (-Ray photoelectron spectra of the Sn 3d region following addition of SnMe, to Lao,/ TiO,: (a) 60 L of SnMe, at ca. - 190 "C; (b) under X-irradiation for 30 min; (c) at room temperature following (b). Table 3. ,H distribution of methane, ethane and ethylene formed after 30 min of the reaction of SnMe, (10 Torr) on an MOO,/ TiO, catalyst (1 .O g) at room temperature" amount amount formed 2H distribution formed per total product /mol Mo ,H,, 2H, ,H, methane 1.16 x 2.5 x lo-, 81.5 18.5 0 ethane 2.78 x 6.0 x 100.0 0 0 ethylene 0.20 x 0.4 x 96.2 3.8 0 "The H atoms on the surface were replaced by ,H atoms. Amount of Mo in 1 g catalyst 4.66 x lov4 mol. amount of reduced Mo species. In the case of Re20,/y-A1203, reduction of the Re species by SnR, (where R = methyl, ethyl or butyl) is detected by e.s.r. spectroscopy.ls Note that the reduction of the MoO,/TiO, surface by SnMe, is not indispensable for activation: partially reduced MOO,-,/TiO, is not so active for metathesis but is changed into a superactive catalyst by treatment with SnMe, as shown in table 1.To clarify the role of SnMe,, surface hydrogen on MoO,/TiO, was exchanged with deuterium to 97 YO, and was subjected to reaction with SnMe,. The amount of methane, ethane and ethylene and their ratios to the total amount of Mo cation are listed in table 3. The amount of methane is ca. 0.25% of that of the total amount of Mo cations. Methane involves 18.7 YO CH,D, but there is no deuterium present in ethane. 85 % of the [,Holmethane in table 3 should be formed by an a-hydrogen abstraction between two CH, groups supplied from SnMe,, and [,H,]methane is formed by the reaction of the CH, group with deuterium atoms on on the surface: 2CH, -+ C,H, (reductive coupling) 2CH, + CH, + CH, CH, + OD + CH,D + [O] (a-hydrogen abstraction) (hydrogen and methyl transfer).K.Tanaka and K-i. Tanaka 607 The abstraction of hydrogen from the CH, group results in a grafting of CH, species onto the surface. A similar phenomenon was reported in the homogeneous metathesis system, WC1,-ZnMe,, in which methane formation is noted in the activation of WC1, by ZnMe,.8 The formation of ethylene shown in table 3 may reflect the formation of CH, species during the activation process, because ethylene is formed either by coupling of two CH, species or by the insertion of CH, into M-CH, (M=Mo and/or Sn). The fact that the amount of [2H,]ethylene (3.8%) is far lower than that of [,H,]methane (18.5 %) in fig.3 seems to support the following processes: CH, + CH, + C,H, (CH, coupling) M-CH, + CH, + M-CH, + CH, + M-H + C,H, (CH, insertion; @-hydrogen abstraction). In conclusion, the formation of highly active metathesis catalysts by treatment with SnMe, may be explained by the introduction of chain-carrying CH, species on their surfaces. Here a ligand effect of SnMe, is not excluded, because the activity in homogenous catalysis is known to be enhanced by the ligand effect, but the remarkable enhancement of metathesis activity observed here is interpreted by the grafting of chain- carrying CH, species onto the catalysts.This conclusion is quite feasible in the case of isobutene metathesis observed on Moo,-,/TiO, : Alk- 1 -enes can furnish alkylidene species by being adsorbed on Moo,-,/TiO,, but isobutene cannot furnish such a key species on the surface. (This may eventually aid the alkylidene formation process on solid metathesis catalysts, so that metathesis of isobutene is not catalysed by MOO,-,/ TiO,). However, if chain-carrying CH, species are supplied from alk-1-ene or from SnMe,, the propagation process via CH, species proceeds. According to this mechanism, hydrogen mixing in alkenes is a side reaction, and the metathesis of a 1 : 1 mixture of [,H,]- and [2H,]-isobutene also proceeds with no hydrogen mixing on MOO,-,/ Ti0,-SnMe, : initiation: M + propagation: on MoO,-,/TiO, /c \C c=c SnMe, c \ /c c’ ‘c c=c M o d ‘C / c ‘C c=c / c \C C608 References Alkene Metathesis on Molybdena-Titania Catalysts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 I J.J. Rooney and A. Stewart, in Catalysis, ed. C. Kemball (Specialist Periodical Report. The Chemical Society, London, 1977), vol. 1, p. 277; (b) R. L. Banks, in Catalysis, ed. C. Kemball (Specialist Periodical Report, The Chemical Society, London, 1981), vol. 4, p. 100; (c) R. H. Grubbs, in Comprehensiue Organometallic Chemistry, ed. G. Wilkinson, (Pergamon Press, London, 1982), vol. 8, chap. 54; (4) K. J. Ivin, OlZefin Metathesis (Academic Press, London, 1983). (a) C. P. Casey and T. J. Burkhardt, J. Am. Chem. Soc., 1973, 95, 5833; 1974, 96, 7808; C. P. Casey, Reactive Intermediates, 1981, 2, 135; (b) R.R. Schrock, Acc. Chem. Res., 1974, 12, 98; Science 1983, 219, 13. J. B. Lee, K. C. Ott and R. H. Grubbs, J. Am. Chem. SOC., 1982, 104, 7491. C. J. Schaverien, J. C. Dewan and R. R. Schrock, J. Am. Chem. SOC., 1986, 108, 2771. J. Kress, M. Wesolek and J. A. Osborn, J. Chem. Soc., Chem. Commun., 1982, 514. R. Walovsky and X. Nir, J. Chem. SOC., Chem. Commun., 1975, 302; N. Calderon, H. Y. Chen and K. W. Scott, Tetrahedron Lett., 1967, 34, 3327; N. Calderon, E. A. Ofstead, J. P. Ward, W. A. Judy and K. W. Scott, J. Am. Chem. SOC., 1968,90,4133; H. Haecker and F. R. Jones, Makromol. Chem., 1972,161,251 ; E. Wasserman, D. A. Ben-Efrais and R. Walovsky, J. Am. Chem. SOC., 1968,90,3286; R. Walovsky, J. Am. Chem. SOC., 1970,92,2132; L. Bencze and L. Marko, J. Organomet. Chem., 1971, 28, 271. G. Doyle, J. Catal., 1973., 30, 118; J. M. Basset, G. Coudurier, R. Mutin, H. Praliaud and Y. Trambouze, J. Catal., 1974, 34, 196; J. H. Webgrovius, R. R. Schrock, M. R. Churchill, J. R. Missert and W. J. Youngs, J. Am. Chem. Soc., 1980., 102, 4515. E. L. Muetterties and M. A. Busch, J. Chem. SOC., Chem. Commun., 1974, 754. F. N. Tebbe, G. W. Parshall and G. S. Reddy, J. Am. Chem. SOC., 1978,100,361 1 ; F. N. Tebbe, G. W. Parshall and D. W. Ovenall, J. Am. Chem. SOC., 1979, 101, 5074. K. Tanaka, K. Tanaka and K. Miyahara, J. Chem. SOC., Chem. Commun., 1979, 314; K. Tanaka, K. Miyahara and K. Tanaka, J. Mol. Catal., 1982, 15, 133. K. Tanaka and K. Tanaka, J . Chem. SOC., Chem. Commun., 1984, 748. M. Schrocco, Chem. Phys. Lett., 1979,61,453; C. C. Kao, S . C. Tsai and Y. W. Chung, J. Catal., 1982, 73, 136; B. H. Chen and J. M. White, J. Phys. Chem., 1982, 86, 3534; S. C. Fung, J. Catal., 1982, 76, 225; J. A. Schreifels, D. N. Belton, J. M. White and R. L. Hance, Chem. Phys. Lett., 1982, 90, 261; K. Tanaka, K. Miyahara and I. Toyoshima, J. Phys. Chem., 1984, 88, 3504. J. K. Kochi, Organometallic Mechanisms and Catalysis (Academic Press, New York, 1978), chap. 12. C. D. Wagner, W. M. Riggs, L. E. Davis, J. F. Moulder and G. E. Muilenberg, Handbook of X-ray Photoelectron Spectroscopy (Perkin-Elmer C o p , New York, 1979), p. 118. A. W. C. Lin, N. R. Armstrong and T. Kuwana, Anal. Chem., 1977,49, 1228. Xu. Xiaoding, A. Andreini and J. C. Mol. J. Mol. Catal., 1985, 28, 133. Paper 71797; Received 5th May, 1987

ISSN:0300-9599    

DOI:10.1039/F19888400601

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1988, 84(2), 609-616 Radical Cations of Nitroso Derivatives A Radiation-chemical and Electron Spin Resonance Study Harish Chandra, David J. Keeble and Martyn C. R. Symons" Department of Chemistry, The University, Leicester LEI 7RH Exposure of dilute solutions containing nitrosobenzene in trichloro- fluoromethane to 6oCo y-rays at 77 K gave the corresponding radical cation, characterised by e.s.r. spectroscopy. The results confirm the interpretation of liquid-phase data assigned to this cation, which showed that loss is from an in-plane a-orbital localised on nitrogen and oxygen, rather than from the aromatic n-system. However, solutions containing the t-butyl derivative in equilibrium with its dimer,(Me,CNO),, gave primarily the dimer cation, (Me,CNO):, with possible traces of the monomer cation.The e.s.r. data for the latter resemble those for the nitrosobenzene cation, whereas results for the dimer cation suggest that loss is from a n-type orbital with very low spin density on the two cquivalent nitrogen atoms. Some years ago Cauquis et al.' studied liquid-phase e.s.r. spectra assigned to nitrosobenzene cations and various derivatives thereof, and suggested that the SOMO lies in the plane of the benzene ring as in (I), rather than being a n-SOMO as is found R ,-. ,/ '2 8 . 1 (11) 'c=i?\, R for the corresponding radical anions.2 Thus the SOMO closely resembles those of 'NO, and of the iminoxy radicals (II).,T~ No solid-state spectra for this interesting class of radical has been reported to our knowledge, and we therefore thought it of interest to use the new ' freon' solution method for preparing these cations unambigu~usly.~ This technique involves exposing very dilute solutions of the substrate in solvents such as CFCl, to ionizing radiation at low temperatures.The solid-state reactions involved are summarised in reactions (1)-(4), which are self-explanatory, X being any substrate with an ionization potential less than that for the solvent (ca. 11.8 eV in this case): (1) (2) ( 3 ) (4) We also attempted to prepare an alkyl derivative, and selected (CH,),C-NO as being the most likely candidate. The problem with nitrosoalkanes is that they readily dimerise, even in dilute solution. For Me,C-NO, dimerisation is sterically inhibited, but, even so, at low temperatures we have found it impossible to avoid some dimer formation.Hence, perforce, we have also studied the radical cation of (Me,CNO),, the e.s.r. results making an interesting contrast with those for the monomer cations. CFCl, -+ CFClj+ + e- e- + CFC1, -+ (CFC1,)'- -+ CFCl, + C1- CFCli+ + CFCl, --+ CFC1, + CFCli+ CFClj+ + X + CFC1, + X'+ 609610 Radical Cations of Nitroso Derivatives Experiment a1 Nitrosobenzene (Aldrich) and 2,2’-dimethyl-2-nitrosopropane (Me,CNO, Aldrich) were dissolved in purified, degassed CFCl, (Fluka) and frozen as small beads in liquid nitrogen. A range of concentrations in the region of 0.01 mole fraction were used, and the Me,CNO beads were blue, indicating the presence of a considerable proportion of the monomer at 77 K.Samples were exposed to ‘OCO y-rays at 77 K in a Vickrad source with doses up to ca. 2 Mrad. E.s.r. spectra were measured using an X-band Varian E-109 spectrometer at 77 K. Samples were annealed by decanting the coolant and monitoring the e.s.r. spectra as the sample temperature increased. Samples were recooled to 77 K when significant spectral changes occurred. Q-Band spectra were measured using a Bruker ER-200 spectrometer with a specially adapted gas-flow cryostat which enabled us to obtain spectra at ca. 90K without annealing the irradiated samples above this temperature during transfer. Results and Discussion Nitrosobenzene The Q-band spectrum (fig. 1) was far better defined than that at X-band, although there was reasonable agreement in the extracted data.It is not obvious why this should be the case, but it may be connected with the lack of symmetry of the cation, such that the g and (14N) A tensors only share one common axis. This may be responsible for the unusual strength of the features marked + l(x) and - l ( x , y ) in fig. 1. The 14N isotropic coupling extracted from these spectra (ca. 34 G) is close to the liquid-phase value (37 G), but significantly reduced, and we were not able to fit the spectra using 37 G. It seems probable that Aiso is temperature dependent, reflecting a small increase in the average C-N-0 angle on cooling. However, it is clear from the results that structure (I) is correct, the SOMO being in the benzene plane with relatively high 2s-character on nitrogen. 2,2’-Dimethyl-2-nitrosopropane Dimers Although the very dilute solutions used contained largely monomer units at room temperature and, judging from the colour, also in the frozen state, nevertheless the major cation formed was always the dimer, (Me,CNO);I+.This can be judged from fig. 2(a) and (b), which show that coupling to 14N is very small, in marked contrast with the results for PhNO+, and that there are two equivalent nitrogen atoms, giving rise to the quintet splitting of the x feature. This preference reflects the smaller ionisation potential for the dimer, as revealed by photoelectron spectroscopy of the methyl derivative [MeNO, 9.68 eV; (MeNO),, 8.63 ev]. We expect the t-butyl derivative to follow the same trend. In unpublished work we have established that when two substrates are present, that with lower ionisation potential preferentially forms the cation under our conditions, even when it is the minor constituent.However, these studies also suggest that the other cation should be present in low, but detectable concentration. We therefore increased the gain in the regions in which the M,(I4N) = f 1 features were expected, and invariably obtained features identical with those shown in fig. 2(c). Exposure to visible light decreased the concentration of the dimer cation, but with little significant gain in the outer features. The resulting data (table 1) are sufficiently close to those for PhNO+ cations that we have some confidence therein.H. Chandra, D. J. Keeble and M. C. R. Symons 12152 G M 61 1 Fig. 1. First-derivative Q-band e.s.r.spectrum for nitrosobenzene in CFCl, after exposure to 'OCo prays at 77 K, showing features assigned to the radical cation, PhNO', Aspects of Structure If the results assigned to Me3CNO+ radicals are correct, there is a clear shift of spin density from nitrogen, presumably,to oxygen. This may reflect the change in carbon orbital hybridisation (ca. sp2 for PhNO+ and ca. sp3 for Me3C-NO+). This will alter the effective energy of the nitrogen 2p(n) orbital, and, given that the SOMO has antibonding character, the shift in spin density should be as observed. In fact, the form of the HOMO suggested by Kuhn et al. for MeNO has the required antibonding character.6 The SOMO for the dimer cation is clearly quite different. The structure of the methyl analogue (trans-azomethanedioxide, (MeNO),] has been discussed by Kuhn et as we'll as by Frost et a1.' It is suggested that the HOMO is as shown in (111), which indicates the upper lobes of the 2p(n) orbitals involved.Clearly, the major spin density is on oxygen, but there is real n-spin density on nitrogen as well. Our results are in good accord for a SOMO of this form for the dimer cation. The estimated spin density on each nitrogen is ca. lo%, leaving 40% on each oxygen, in good accord with structure (111). The very low 2s-character on nitrogen establishes the n-character of this orbital. Since612 Radical Cations of Nitroso Derivatives 121225 9 x 1 , 1% , ,H Fig. 2(a) and (b). For legend see facing page.H . Chandra, D . J . Keeble and M. C. R. Symons 613 1 32055 Fig.2. First-derivative e.s.r. spectra for Me,NO+ (Me,NO), in CFCI, after exposure to 6oCo y-rays at 77 K (a) at X-band at 77 K, showing features assigned to the dimer cation, (Me,CNO);+, (b) at Q-band showing increased resolution for the spectrum assigned to (Me,CNO);+ cations and (c) at X-band at high gain, after.partia1 photolysis, showing features tentatively assigned to the cation Me,CNO+. The central region contains dimer features. it is bonding between the two nitrogen atoms, the weak N-N bond of the parent should be strengthened in the cation, which shows no tendency to decompose on annealing to These results show that an orbital switch must occur as dimerisation proceeds, since the SOMO of the parent cation is potentially part of the N-N a-bond: For sufficiently long N-N bonds the a-structure is presumably the more stable. A similar structural dilemma was considered for the dimer cation of 'NO,, i.e.N20;+.8,9 In this case some evidence for the a-structure was obtained from irradiated N,O, crystals,' but irradiation of N,O, in CFCI, gave a rearranged species best represented as (IV).' Furthermore, in the case of MeNOg+ the first-formed species was not the expected cation with major spin density on oxygen, but was the a-cation (V).'' This readily rearranged to (VI) on annealing above 77 K. The e.s.r. parameters for the cations (IV) and (VI) closely resembled those for 'NO, itself, as expected for these structures.b Table 1. E.s.r. parameters for radical cations derived from nitroso compounds a @ g values 14N hyperfine coupling constantsb E 2 radical matrix (T/K) g, g, g, A , A, A, Aiso 2B U;(YO) a:(%) p / s (s+p)(%) ref.g. z - - - b % temperature) 3 “L Me,CNO’+ CFCl, (77) 2.004 2.002 2.002 24 44 24 30.7 13.3 5.6 42 7.5 49.5 : , d 5 1.7 3.3 0.3 (2N) 10 (2N) 33 20 b , f 2 e. - ;. 37 - 6.7 PhNO’+ MeNO, (room 2.007 (average) - - - Y PhNO*+ CFCl, (77) 2.0033 2.002 2.002 25 54 22 34 20 6.1 62 10.1 68.1 gas 2.0062 1.9910 2.002 46.13 44.8 66.76 52.6 15.4 9.6 45.4 4.75 55 e b NO2 (Me,CNO);+ CFCl, (77) 2.0021 2.0058 2.0113 5.0 0 0 a 1 G = T. Ref. (I). This work. Tentative assignment. Ref. (14). The major species formed from (Me,CNO), dimers. 2H. Chandra, D. J . Keeble and M. C . R. Symons 61 5 1 3285G +3m*, 0 , , , , , MI (14Nl+l 0 -1 Fig. 3. As for fig. 2, after annealing to ca.150 K, showing isotropic features assigned to spin- trapped CFCl, radicals. CFCl, \ 7 - N o Clearly, the preferred structures for these species vary widely, but there can be no doubt that for (RNO);+ dimer cations the basic structure of the parent is retained, the SOMO being the weakly bonding n-orbital (111). n We also draw attention to the similarity between the R,C-NO+ cations and R,N-NO cations derived from N-nitrosodialkylamines. l 1 I l2 The isotropic hyperfine coupling to the (NO) nitrogen of ca. 45 G is significantly increased, suggesting a smaller N-N-0 bond angle than the C-N-0 angles for the carbon derivatives. This is expected on simple electronegativity arguments on going from carbon to nitrogen sub~tituents.'~ However, the situation is complicated by the possibility of conjugative II- delocalisatipn onto the secpnd nitrogen. Nevertheless, the trend in AiS,(l4N) on going from R,CNO+ to R,N-NO+ and 'NO, (ca.31 to 45 to 52.6 G) nicely follows the increase in electronegativity of the variable ligand. Spin Trapping The monomer, Me,C-NO, is important as a spin trap in radical chemistry, pince it will add a wide range of radicals, X', to give nitroxide radicals, (X) (Me,C)NO, having characteristic e.s.r spectra. For example, 'CCl, radicals add to give (CCl,) (Me,C)NO, having Aiso (14N) = 12.7 G and Aiso (35Cl) = 2.46 G.13 We would not expect (CFC1,)'-616 Radical Cations of Nitroso Derivatives radicals or (RNO);+ radicals to be able to add in this manner, but CFCl, radicals formed from the parent solvent anions should add readily.This indeed occurred on annealing, with good isotropic spectra appearing just below the softening point of the solids (ca. 160 K), as can be seen in fig. 3. The data A(14N) = 12.2 G and A(35Cl) = 2.2 G (2C1) accord well with those for the - CCl, adduct, and clearly establish the presence of two equivalent chlorine atoms. Thus dissociative electron capture must occur at some stage in this system. References 1 G. Cauquis, M. Genies, H. Lemaire, A. Rassat and J. P. Ravet, J. Chem. Phys., 1967, 47, 4642. 2 D. H. Levy and M. J. Myers, J. Chem. Phys., 1965,42,3731; E. J. Gals, R. Konaka and G. A. Russell, 3 B. C. Gilbert and R. 0. C. Norman, J. Chem. SOC. B, 1966, 86. 4 W. M. Fox and M. C. R. Symons, J. Chem. SOC. A , 1966, 1503. 5 M. C. R. Symons, Chem. SOC. Rev., 1984, 363. 6 J. Kuhn, W. Hug, R. Geiger and G. Wagniere, Helv. Chim. Acta, 1971, 54, 2260. 7 D. C. Frost, W. M. Lau, C. A. McDowell and N. P. C. Westwood, J. Phys. Chem., 1982, 86, 3577. 8 D. R. Brown and M. C. R. Symons, J. Chem. SOC., Dalton Trans., 1977, 1389. 9 D. N. R. Rao and M. C. R. Symons, J. Chem. SOC., Dalton Trans., 1983, 2533. 10 D. N. R. Rao and M. C. R. Symons, J. Chem. SOC., Faraday Trans. I , 1985, 81, 565. 11 S. P. Mishra and M. C. R. Symons, J. Chem. SOC., Perkin Trans. 2, 1977, 1449. 12 M. Masui, K. Nose, H. Ohmori and H. Sayo, J. Chem. SOC., Chem. Commun., 1982, 879. 13 M. C. R. Symons, E. Albano, T. F. Slater and A. Tomasi, J. Chem. Soc., Furaday Trans. I , 1982, 78, 14 R. M. Rees, J. Chem. Phys., 1966, 45, 2037. J. Chem. SOC., Chem. Commun., 1965, 13. 2205. Paper 7/798; Received 5th May, 1987

ISSN:0300-9599    

DOI:10.1039/F19888400609

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1988, 84(2), 617-629 Electron Energy-loss Spectroscopy and the Crystal Chemistry of Rhodizite Part 1 .-Instrumentation and Chemical Analysis W. Engel, H. Sauer and E. Zeitler Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 0-1000 Berlin 33, Federal Republic of Germany R. Brydson and B. G. Williams? Department of Physical Chemistry, University of Cambridge, Lensjield Road, Cambridge CB2 1EP J. M. Thomas* Davy-Faraday Laboratories, The Royal Institution, 21 Albermarle Street, London W1X 4BS An electron microscope fitted with a magnetic prism spectrometer and a parallel recording system has been used to measure the electron energy-loss spectrum of rhodizite, a naturally occurring mineral containing a number of light elements which are difficult to detect with energy-dispersive X-ray emission analysis (X.r.e.).We consider in detail the use of electron energy- loss spectroscopy (EELS) as an analytical probe and the quantitative chemical analysis for beryllium, boron and aluminium, measured with respect to oxygen, is in good agreement with the analysis obtained using wet chemical and crystallographic methods. The presence of potassium and caesium is confirmed, but for these elements the quantitative analysis is less reliable. X.r.e. measurements are also given for comparison. The potential as well as the limitations associated with the use of parallel recording arrays for chemical analysis based on EELS, is discussed. Electron energy-loss spectroscopy (EELS) carried out in a transmission or scanning transmission electron microscope (TEM or STEM) constitutes a versatile probe of the solid state.Using the facilities provided by the microscope it is possible to observe images and diffraction patterns from which structural information may be derived,' and by using a spectrometer to measure the energy-loss spectrum of the electrons which are scattered within the sample, further information concerning the elemental composition and the electronic structure may be obtained. There are several processes which give rise to distinct features in EEL spectra. The excitation of plasmons and interband transitions at energy losses from ca. 5 to 30 eV contains information concerning the valence and conduction electrons. When the energy transfer is equal to or greater than the binding energy of a particular inner-shell electron, core-edges are observed. From the energy of these edges it is possible to identify the elements which are present in the sample and, by measuring their intensities, t o quantify the analysis.The core-edges observed in experiments on free atoms are either featureless steps or broad peaks, but with solid samples detailed structure is observed close to the edge. The structure within ca. 20 eV of the edge is usually referred to as the electron energy-loss near-edge structure (ELNES), which is directly analogous to the X-ray t Present address: International Centre for Insect Physiology and Ecology (ICIPE), P.O. Box 30772, Nairobi, Kenya. 61761 8 EELS Study of Rhodizite absorption near-edge structure (XANES), and the structure extending up to a few hundred electronvolts beyond the edge is referred to as the extended electron energy-loss fine structure (EXELFS), which is analogous to the extended X-ray absorption fine structure (EXAFS).These features of the spectrum reflect the density of unoccupied states above the Fermi level and are also sensitive to the arrangement of the neighbouring atoms and therefore the nearest-neighbour distances and coordination, the oxidation and the hybridisation state of the atoms and the charge transfer between neighbouring atoms. (A number of review articles are available covering various aspects of and attention is drawn, in particular, to the book by Egert~n.~) There are a number of difficulties which must be overcome if sufficiently good data are to be obtained using EELS.The dynamic range spans eight orders of magnitude from the top of the zero-loss line to edges at an energy loss of 2 keV, and it is necessary to record the count rates at both extremes to an accuracy ca. 0.1 %. In order to reveal the details of the fine structure associated with an edge the resolution should be of the order of 0.5 eV or better at an incident energy of 60 keV or more. Furthermore, the power of EELS experiments in \he microscope stems precisely from the fact that the samples may be as small as 10-100 A in their linear dimensions, and the necessary concomitant of this is that beam damage to the sample is the ultimate limiting factor. To minimise the effects of beam damage the scattered electrons must be collected as efficiently as possible.Until recently, most EELS microscopes employed serial detection systems in which the spectrum is scanned over a slit, one channel at a time. With parallel detection, in which the entire spectrum is recorded simultaneously, the collection efficiency may be increased by up to 1000 times, and a number of such systems based either on SIT (silicon-intensified target) vidicon detectors'. ' or on photodiode arrays8-lo have been developed. The advent of effective parallel detection now promises to transform EELS from an interesting, but perhaps marginal, technique to one which will play a central role in helping to understand and to probe the chemistry of the solid state. In this paper we report on measurements of the various edges in rhodizite both to confirm the structure and properties of rhodizite and to investigate the potential, as well as the limitations, of EELS as a probe of the solid state.Rhodizite was chosen as the subject of this study for several reasons. Next to diamond it is one of the hardest solids known, and it is extremely insoluble in most solvents, making wet chemical analysis difficult. X-ray fluorescence analysis is inherently unreliable in view of the very light elements (oxygen, lithium, beryllium, boron, aluminium and sodium) which are present. It is a naturally occurring but rare mineral, containing, in addition to the light elements, varying amounts of potassium, rubidium and caesium. It has recently been the subject of a detailed X-ray diffraction and high-resolution (real-space) electron microscopic study by Pring et all1 who also used magic-angle spinning nuclear magnetic resonance, electron diffraction and wet chemistry to characterise the material. Nevertheless, further confirmation of the structure is still desirable. The present study divides naturally into two parts.In Part 1 we use EELS to determine the elemental composition of the samples andX.r.e. to provide acomparison and an independent analysis. Part 2isconcerned with the analysis of the near-edge structures which we have used to investigate the coordination of the aluminium atoms and the site occupancy of the oxygen atoms. Instrumentation and Experiment In these experiments a scanning transmission electron microscope with a spectrometer which allows parallel recording of the electron energy-loss spectra has been used.This instrument was designed and built in the electron microscopy department of the Fritz- Haber Institute. It operates with a field emission gun at 60 keV, and its probe-forming lens, which has a relatively long focaldlength of 50 mm, restricts the lower limit of the attainable probe diameter to ca. 15 A. The spectrometer unit consists of a transferW. Engel et al. 619 lens, a sector field spectrometer and two projector lenses which allow rotation-free magnification of the spectra onto a fluorescent screen. A P20 powder screen is used to convert the electrons to photons, and an optical fibre bundle is used to transfer the photons to the SIT detector of a commercial optical multi-channel analyser (OMA I1 system from EG & G).In order to improve the detector stability, its target temperature was stabilised using a device described by Rust.12 The SIT detector has 512 channels with a 25 pm spacing and a spatial resolution of ca. 3 channels f.w.h.m. (full width at half-maximum). By suitable excitation of the projector lenses the dispersion in the plane of the fluorescent screen can be varied from 1.5 eV per channel to 30 meV per channel. This feature makes it possible to trade resolution against range and to measure either small regions of the energy-loss spectrum with high resolution or larger regions of the spectrum at a correspondingly lower resolution. With the projector lenses turned off, a range of 1690 eV is accessible at a resolution of 10 eV.The spectrometer is designed to correct for second-order spherical aberrations. Provided the spectrometer acceptance angle is < 10 mrad, the resolution is determined solely by the energy spread of the primary beam, which increases with increasing beam current from 0.25 to 0.5 eV. For recording of the near-edge fine structures, for example, high beam currents are needed, so that in these experiments a resolution of ca. 0.5 eV is used. A precise high-voltage divider and a differential voltmeter is used to measure the incident beam voltage, which can be changed continuously thus making it possible to record different regions of the spectrum. With this facility calibration of the energy on an absolute scale is easily performed, and energies may be determined with an accuracy of kO.2 eV, which is desirable for the measurement of chemical shifts.An important feature of the instrument is the parallel detection, which gives a collec- tion efficiency 500 times higher than serial detection. To underline the importance of this, a 5 min experiment with parallel detection would require 1.8 days with serial detection in order to obtain data of the same quality provided the noise performance of both detectors is the same. Uncertainties arising from the counting statistics determine the detectability limits and the accuracy of the chemical analysis, and for a given recording time an uncertainty of, say, 10% with serial detection is reduced to 0.4% with parallel detection. When beam damage is the limiting factor a parallel detection system would provide data froF an area of 50 A on a side when a serial detection system would require an area of 1100 A on a side to obtain data of the same quality.An ideal parallel detection system for EELS, in which each channel acts as a perfect electron counter, is not available at present. All systems which have been developed up to now accumulate an amplified analogue signal which is digitised and then stored in the memory of a multichannel analyser. The amplification results from a chain of quantum conversion steps beginning with the electron-to-photon conversion in the fluorescent screen which is followed by a photon-to-photoelectron conversion at the cathode of the SIT detector. The photoelectrons are then accelerated onto the target and produce electron-hole pairs which in turn cause positive charging of the elements in proportion to the number of electrons which were originally absorbed in the corresponding areas of the fluorescent screen.After an exposure of typically 30 ms, readout, amplification, digitisation and storage in the memory of the multichannel analyser take place. This procedure is then repeated the desired number of times. The action of the intensifier chain for a channel n may be expressed in terms of the average gain g , and its variance V(g,), which results from the statistical fluctuations associated with the various conversions in the chain13 and provides a figure for the noise which is introduced by these fluctuations. Fluctuations of the dark signal, ambient noise in the ground line and other noise sources which are not correlated with the signal increase the noise in the output signal.These noise sources are of minor importance for the system in use, and they are negligible in most experimental situations contributing < 1.5 counts (r.m.s.) per channel for a 30 ms exposure and one readout. The gain is620 EELS Study of Rhodizite between 1 and 10 and can be altered by changing the accelerating voltage in the SIT detector. A gain of ca. 4 counts per electron is optimal because it is the highest gain which preserves the intrinsic range of the SIT detector of 4000 : 1. To a first approximation the detective quantum efficiency, Qd, is The gain statistic is determined by the initial conversion stages and is dominated by the statistics of the electron-to-photon conversion in the fluorescent screen.In the case of a P20 powder screen, the number of photons generated follows an exponential distribution1** l5 which gives a Qd value of 0.5. Recent measurements on a system which is almost identical to the one used in this instrument gave a value of 0.4.16 The average gain g, varies from channel to channel, giving rise to the so-called fixed pattern noise. In principle this can be removed, but deviations from a linear response, instabilities and other effects prevent an exact correction. Several procedures for the removal of fixed- pattern noise have been described." The dependence of the gain on the channel number was measured with homogeneous electron illumination of the fluorescent screen.The remaining fixed pattern noise leads to a further reduction of Qd to between 0.1 and 0.2, based on previous measurements. The detector is not ideal, and further improvements should be possible. Nevertheless, with a Qd value of 0.2 it is still superior to a perfect serial counting system, as the dose needed to produce a given signal is reduced by a factor of 100. In the spectra discussed below an effective signal, Seff, is given which we define as where Si and So are the input and output signals, respectively, and g is the gain of the detector averaged over all the channels. It can be shown that the variance of Seff is equal to Seff, since the input signal obeys Poisson statistics. Thus the noise can simply be judged the square root of Seff (the numbers of counts given in the spectra).The Qd can then be regarded as a factor describing the devaluation of the input signal and, compared to an ideal detector, l/Qd times more electrons are needed in order to obtain the same signal-to-noise ratio at the output. To obtain Seff we note that Qd/g is equal to So/V(So), where V(So) is the variance of So and &/g is independent of So provided that So is well above the dark-current noise as is the case in our experiments. A region of the spectrum showing no apparent structure was fitted to a low-order polynomial, and the variance of the residuals was used to estimate V(So), The advantages of performing EELS in an electron microscope have been documented previo~sly,~-~ but we would like to stress two points in the context of the sample investigated in this work.The stoichiometry and structure of natural minerals often vary over microscopic distances, and the ability to analyse small areas provides an opportunity to inve$igate such variations. Furthermore, in EELS the samples should be less than ca. 1000 A thick in order to minimise problems associated with multipl? ~cattering,~ but with the aid of an electron microscope very thin areas a few hundred A across can usually be found in samples which have simply been ground with a mortar and pestle and dispersed on a holey carbon film even when it is not possible to prepare a large sample area which is sufficiently thin. In order to quantify the elemental analysis obtained using EELS it is necessary to measure the entire spectrum, extending from the zero-loss line to the last edge of interest. Since the useful dynamic range of the detector system is only three orders of magnitude, while the dynamic range of the entire spectrum is eight orders of magnitude, separate spectra were measured over sevezal overlapping energy ranges.In order to minimise specimen damage, an area of 400 A on a side was scanned during the acquisition of each spectrum. Where a complete set of overlapping spectra spanning the range 0 to 1800 eV was measured, the scanned area was shifted between the recording of each spectrumW. Engel et al. 62 1 in order to ensure that an undamaged area was analyseg in each case. The total area was then ca. pm2, and the thickness was ca. 600 A. Thus a volume of roughly 6 x g, was used to record a complete spectrum from which the cheqical analysis has been derived.The dose varied from <a. 5 x C cm-2 (3 electron AP2) at the boron K-edge to ca. 0.5 C cm-2 (300 electron AP2) at the aluminium K-edge. For each spectrum the recording time was 5 min, except in the case of the aluminium K-edge, where a 10 min measurement was made. To ensure that the sample did not suffer significant beam damage the spectra were collected at 1 min intervals and these were then added if no significant changes were observed. Three sets of data were acquired. The first set was measured at an energy resolution of 0.5 eV (0.15 eV per channel), and no attempt was made to match the spectra one to another. The second set was measured at an energy resolution of 3 eV (1 eV per channel) and the third set at an energy resolution of 10 eV (3.3 eV per channel), both of these covering the entire energy range from - 50 to 1800 eV, with significant overlaps between spectra so that the individual measurements could be matched up.To investigate the effect of the collection semi-angle the first two sets of data were acquired with a semi-angle of 5 mrad, while the third set was acquired with a semi-angle of 10 mrad. In these experiments carbon contamination proved to be quite severe. This was reduced considerably by first baking the sample at 250 "C for 3 h in a vacuum at lo-' Torr. pm, corresponding to a mass of 2 x Results and Discussion From their study of rhodizite, Pring et al." deduce a compositional formula which is and they conclude that the mineral is cubic (a = 7.318f0.01 A) with space group ~ 4 3 m .Fig. 1 shows the spectra recorded at 0.5 eV resolution. The beam current was increased by several orders of magnitude going from (a) to (f), so that this series of spectra does not reflect the strong decrease of the inelastic cross-section with increasing energy loss. With the exception of spectrum (f), Seff was always of the order of lo5 counts per channel. In the series of spectra which were measured at 3 eV resolution and then matched, the full dynamic range can be determined and the count rates at the peaks of the K-edges of beryllium, boron, oxygen and aluminium were 4.1 x 4.4 x lop5 and 3.0 x times the count rate at the peak of the zero-loss line, respectively. Small significant features associated with the various edges and the noise are largely hidden in fig.1 and the spectra will be shown in greater detail in Part 2, where the fine structure associated with each edge is discussed. The low loss spectrum [fig. 1 (a)], which is due mainly to the excitation of plasmons and interband transitions, is dominated by the broad plasmon peak. Immediately beyond this [fig. l(b) and (c)] the edge signals are superimposed on a very high background, which gives the dominant contribution to the noise. The signal-to-background ratio improves significantly for the edges at high energy losses [fig. l(d)-(f)J. The quantitative analysis was carried out using the second set of data (3 eV resolution). After the individual spectra had been matched the entire spectrum was deconvoluted using the ' Fourier-log ' method'* with a thickness parameter (thickness divided by the plasmon mean free path), derived from the data, of 0.64.The intensity under each edge was calculated after subtracting an appropriate background. The dependence of the background on the energy loss, AE, was assumed to obey the power law AAE-'. The exponent Y and the constant A were derived from a fit to the pre-edge region. In some cases a region far beyond the edge was used to determine the exponent 1.2 x 21 F A R 1622 EELS Study I " ' ' I " " " " ' " ' " I " ' " " ' I I ' '"I of Rhodizite l , l , l t l , l , l , I , I , l , I , 80 I00 I20 I20 I10 I 200 2 20 240 1560 1580 1600 energy/eV Fig. 1. Rhodizite EELS spectra before background subtraction, measured with a resolution of 0.5 eV.(a) The low loss, (b) the aluminium L,,,-edge, (c) the beryllium K-edge, ( d ) the boron K-edge, (e) the oxygen K-edge, (f) the aluminium K-edge. The collection semi-angle was 5 mrad for (a)-(e) and 10 mrad for 0. The incident beam energy was 60 keV. The counts give Serf (see text for explanation). r. The cross-sections for exciting the various core electrons were calculated using Egerton's SIGMA programs,5* l9 including a correction for the convergence of the incident beam. The oxygen edge at 532 eV, which is strong and well separated from the other edges, provides a useful reference edge with respect to which the others have been measured. The results are given in table 1. The presence in the sample of beryllium, boron, aluminium, oxygen, potassium and caesium is immediately confirmed, and the quantitative estimates are in good agreement with the values obtained by Pring et uLl1 However, the analysis reveals a number of difficulties which are associated with the quantification of EELS data.In the low-resolution spectrum it was difficult to extract the aluminium Ledge, and the amount of aluminium was estimated with respect to beryllium using the high- resolution spectrum, which was not deconvoluted. This spectrum (which is shown in Part 2) reveals detailed structure in the tail of the aluminium Ledge which starts atW. Engel et al. 623 Table 1. The elemental composition of rhodizite as determined by EELS and X.r.e. compared to the results of Pring et al." (Crystallography)" EELS X crystallography E,IeV O K Li K Be K B K A1 L A1 K Na K K K K L Rb L c s L cs M 28 4.9 f 0.5 11.2f0.5 4.2 f 0.4b 5.9 f 0.3' 4.1 f0.2d - - 0.37 f0.05 - 0.24 28 28 - 0.02 - 4.55 - 11.35 - 3.99 13.5 3.99 - 6.3 - e 6.6 - 0.02 0.46 0.46 0.06 0.36 0.36 532 55 111 188 73 1560 1071 3608 294 1830 5012 727 ~~ a The EELS and X.r.e.measurements were normalised with respect to the amount of oxygen, which was set to 28 atoms. * Calculated assuming 4.55 Be atoms per unit cell. ' Measured with a 5 mrad collection aperture. Eb gives the XPS binding energies to indicate the energies of the edges. The EELS edge energies are discussed in Part 2. Measured with a 10 mrad collection aperture. Detected but not quantified. 79 eV and runs into the beryllium K-edge at 118 eV. It also contains a weak contribution from the caesium N-edge at ca.80 eV, although this is entirely submerged in the structure associated with the aluminium Ledge. Using an approximate cross-section, based on the energy loss and the number of N-shell electrons which are excited, together with the amount of caesium determined from the caesium M,,,-edge, the contribution of the caesium N4, ,-edge to the integrated intensity under the aluminium L2, ,-edge was estimated to be 15%. An aluminium-to-beryllium ratio of 1.08 was then obtained assuming that the contribution of the aluminium and caesium signals to the integrated intensity under the beryllium K-edge is negligible. Using the deconvoluted, low- resolution data the beryllium content was found to be 4.9f0.5 atoms per unit cell (normalised to 28 oxygen atoms).Because of the overlap of these signals and the uncertainties in fitting the background we estimate that the amounts of beryllium and aluminium (derived from the L2, ,-edge) given in table 1 are reliable to within & 10 %. The boron K-edge at 188 eV is both intense and well separated from the other edges, and the amount of boron deduced from the EELS data is 1 1.2 & 0.5 atoms, which agrees well with the value of 11.35 obtained by Pring et u1.l1 The quantification of the weak Ledge of potassium at 298 eV, which Pring et a1.l1 estimate to constitute 0.9 atom%, also caused difficulties. The spectrum recorded at 3 eV resolution and the background which was obtained by smoothing the tail of the boron K-edge are shown in fig.2. The EXELFS oscillations from the boron K-edge are clearly seen, and extend into the potassium Ledge. Knowing the general form of the EXELFS oscillations, their contribution to the integrated intensity under the potassium edge was estimated to be 10 %. Further complications arise from the possible presence of carbon contamination, as the carbon K-edge occurs at 289eV. After extended irradiation of the sample the signal from the carbon K-edge increased to 4 times the signal from the potassium Ledge. Using this spectrum as a guide we were able to estimate the contribution of the carbon to the spectrum used for the analysis. This was found to be between 5 and 10% of the area under the potassium Ledge, and corresponds to one carbon monolayer, assuming that the sample was 100 unit cells thick 21-2624 EELS Study of Rhodizite 6 m 4 0 0 -2 1 3 2 , 2 2 50 300 350 400 energy/eV Fig.2. Rhodizite EELS spectrum of the potassium L2, ,-edge after subtraction of the background (solid line). The background is indicated by the dashed line. The resolution is 3 eV and the counts give S,,, (see text for explanation). (700 A) and that 10 carbon atoms on a unit cell face form a monolayer. The amount of potassium given in table 1 is then reliable to within 15%. lines at 734.0 and 747.6 eV [fig. 3(a)] show up very clearly in the EELS spectrum, although EXAFS oscillations from the oxygen K-edge also run through this edge. Their amplitude is much smaller than in the case of the potassium L,,,-edge, and to a first approximation they can be neglected in the calculation of the caesium M4, intensity.Unfortunately, the cross-sections for scattering from M-shell electrons are not available, so that the L-shell cross-section for iron at 710 eV, scaled according to the number of electrons, was used instead. The dominant factors which determine the cross-section of a given shell are the number of electrons in that shell and the corresponding energy-loss, so that this should provide a rough estimate of the M-shell cross-section. The amount of caesium is then 30% less than that obtained by Pring et a/.'' It should be borne in mind, however, that the alkali-metal content of rhodizite is quite variable, and is partly dependent on the electron dose, so that the low figure may also reflect the differences between one crystal and another as well as the con- ditions under which they were examined.In fig. 3(b) the caesium M4,,-edge measured at a resolution of 10 eV is also given in order to illustrate the importance of high resolution in detecting low concentrations of particular elements. In the 10 eV data the resolution blurs out the sharp features, which both reveal and serve to identify the edge. Of course, the degradation caused by the low resolution will be less severe in edges which have less fine structure. The analysis of the aluminium K-edge at ca. 1565 eV reveals problems which are associated with the limited collection aperture of the spectrometer. The analysis based on the data measured at 3 eV resolution gives an aluminium-to-oxygen ratio which is 50% greater than that given by Pring el al." We believe that this may be attributed to the effect of multiple Bragg-edge scattering.20 In these experiments the first Bragg spot is at 6.8 mrad, while the spectrometer collection semi-angle is 5 mrad.The characteristic angle (equal to AE/2E0 where AE is the energy loss and Eo is the incident energy), which determines the angular spread of the inelastically scattered electrons, is 13.0 mrad for the aluminium K-shell excitations, so that an electron which is scattered into a (100) Bragg beam has a high probability of being scattered back into the collection aperture. On the The caesiumW. Engel et al. 625 1.0 0 700 750 800 energ y/eV Fig. 3. Rhodizite EELS spectra of the caesium M4, ,-edge after background subtraction, measured with a resolution of: (a) 3 eV and (b) 10 eV.The counts give SePP (see text for explanation). The background decreases from 1.5 x lo5 counts to 8 x lo4 counts across the energy range shown in the figure. other hand the characteristic angle for the excitation of an oxygen K-shell electron is only 4.4 mrad, so that the probability of scattering into the (100) direction and then back into the aperture is significantly less. The effect of this will be to enhance the intensity in the aluminium K-edge as compared to the oxygen K-edge, and from results calculated in a previous paper for the silicon K- and L-shells2' this correction should be of the order of 20-30Y0, which would bring the aluminium value close to the value given by Pring et al.ll This explanation was confirmed by the analysis of deconvoluted spectra recorded with a 10 mrad collection aperture and resolution of 10 eV.This gave a figure of 4.05 aluminium atoms per unit cell, uncertainties in the A1 K-edge background indicating errors of & 5 %, and this is close to the value obtained by Pring et al.," indicating that once the collection aperture is large enough to include the first strong set of Bragg spots, the effect of elastic-inelastic scattering is relatively small. With the exception of the aluminium Ledge, all of the elemental quantification was performed on deconvoluted spectra, and the effect of this is illustrated in fig. 4, which shows the oxygen edge from the data measured at 3 eV resolution before and after deconvolution. The effect of deconvolution is to increase the calculated boron to oxygen ratio by 31 YO and to decrease the aluminium to oxygen ratio (derived from the aluminium K-edge) by 16 YO.Sodium and lithium, which are only 0.04 atom YO in the sample, were not detected. The sodium Ledge at 31 eV and the lithium K-edge at 55 eV are superimposed on626 EELS Study of Rhodizite 500 600 energy/eV 700 Fig. 4. Rhodizite EELS spectra of the oxygen K-edge after background subtraction and measured with a resolution of 3 eV. The dashed line is before and the solid line is after deconvolution. The deconvoluted data are normalised to give the same area under the edge. the very intense tail of the plasmon peak and become submerged in the statistical fluctuations of the strong plasmon signal even though the cross-sections are large.We were unable to detect the sodium K-edge or any of the core-edges of rubidium, which constitutes 0.1 atom % of the sample.'' X-Ray Emission Analysis X.r.e. spectra were also measured for rhodizite using a JEOL 200 CX microscope fitted with a windowless, lithium-drifted silicon detector, and the results are given in table 1. The presence of oxygen, aluminium, potassium, caesium and a small amount of rubidium was confirmed. With such a detector it is possible to identify elements as light as carbon or nitrogen, but it is difficult to quantify the analysis. Two complicating factors are the adosorption of the characteristic X-rays, even for samples which are only a few hundred A thick, and the fluorescent enhancement which arises when the X-rays emitted from more tightly bound electrons excite fluorescence from the less tightly bound electrons.21 The values given in table 1 were obtained without correcting for fluorescent enhancement or absorption.As the X.r.e. and the EELS measurements were carried out on different crystallites in different microscopes it was not possible to use the EELS to determine the sample thickness for the XRE measurements. However, if one calculates the sample thickness, assuming an approximate elemental composition and an absorption term proportional to exp(-pt), where p is the mass absorption coefficient and t is the thickness which reproduces the oxygen-to-aluminium ratio given by Pring et aZ.,ll the thickness was found to be 1600 A assuming that the fluorescence yields of the oxygen and aluminium K, lines are approximately equal.If this thickness is then used to calculate an absorption correction for the potassium K,-to-aluminium K, ratio, allowing for the fluorescence yields of the two K-shells, a value for the potassium-to-aluminium ratio is obtained which is within 10 YO of the value given by Pring et a2." This procedure was also applied to the caesium-to-aluminium ratio, but in this case it gave a value 40% too high.W. Engel et al. 627 Statistical Accuracy and Detection Limits The discussion in this section is based on the high-resolution data (0.5 eV), although the chemical analysis was performed using the data measured at lower resolution. The intention is to demonstrate the statistical quality of the high-resolution data which can be achieved using parallel detection.The statistical errors affect the accuracy with which the intensity under an edge can be measured in two ways. If, in a given energy window, the background is B and the signal is S, the standard error in the estimated value of S is (S+B)t. For the data shown in fig. 1 (b) the number of counts in the aluminium edge can be estimated with an accuracy of 0.15 Yo. In addition, statistical fluctuations in the data affect the accuracy of the background fit, and since the background must be extrapolated over a large range, small variations in the fit may lead to large variations in the background subtraction. To ascertain the importance of this, a confidence band for the whole of the fitted line was determined and the upper and lower bounds of this confidence band were used to estimate the uncertainty associated with the fit.The uncertainty deduced in this way was 0.17 Yo so that the two sources of error combine to give an overall figure of 0.23 '/O or 0.5 Yo for a 95 Yo confidence interval. Using these data it is therefore possible to estimate the intensity under the aluminium edge with an accuracy of A second, related parameter is the detection limit for a given element.22 In endeavouring to detect very small amounts of any element it is important to use the best possible resolution, as this avoids smearing out the structure which reveals the presence of an edge. If the entire background could be reduced to a single point and the same could be done for the signal, the detection limit for aluminium in rhodizite would be 0.5% of the amount which is actually present.In practice, an edge must be measured over a range of channels, the edge must be apparent and only then can one proceed as above. To determine a realistic figure for the detection limit, the observed edge has been divided by 10, added to the fitted background, and normally distributed random numbers have been added to this pseudo-signal with variance equal to the number of counts at each point. By fitting and then subtracting a background and smoothing by convoluting with a Gaussian of f.w.h.m. = 0.3 eV, the edge shown in fig. 5 is obtained. Estimating the number of counts under the edge gives a value of (1.02 _+ 0.02) x lo6. The original value divided by 10 is 0.96 x lo6, which is 3 standard deviations from the estimated value.In other words, with data of this quality, the amount of aluminium in the sample could be estimated with an accuracy of f0.5 YO, the detection limit is ca. 5 to 10% of the amount which is actually present (0.5-1 atom YO), and this amount of aluminium could be measured to an accuracy of ca. 5 YO. It is important to remember that it is not possible at the present time to calculate the cross-sections and to allow for systematic errors in the measurements with anything like this precision. In practice, on the other hand, it is sometimes possible to prepare standard samples, from which accurate calibration cross-sections can be obtained. Alternatively, in experiments to determine variations in composition within one sample, the high accuracy would be invaluable.The same approach has been applied to the other edges with the following results. The intensity under the beryllium edge can be measured to an accuracy of 0.2 YO and the detectability limit is ca. 5 YO of the amount present (0.5 atom %). For boron the intensity under the edge can be measured with an accuracy of +0.03%, the detectability limit is 0.5 YO of the amount which is present (0.1 atom YO), and this amount of boron could be measured to an accuracy of +6%. The intensity under the oxygen edge can be measured to an accuracy of rt 0.02 O/O ; the detectability limit is 1 O/O of the amount present (0.6 atom "lo), and this could be measured to an accuracy of ca. f 10 YO. For comparison with the EELS detectability limits, we estimated the X.r.e.detectability limits for the oxygen K3, and aluminium K, peaks. An element may be 0.5 YO.628 EELS Study of Rhodizite r 1 1 1 1 1 1 1 1 I l I I I I I I I I I I l I 1 I I 1 1 1 1 1 1 1 1 1 60 80 100 I20 energy/eV Fig. 5. The aluminium L-edge in rhodizite reconstructed to represent a sample containing 10 % of the amount of aluminium actually present. The spectrum consists of the fitted background plus the observed edge divided by ten to which has been added normally distributed random numbers to simulate the counting statistics. This reconstructed spectrum has then been smoothed with a Gaussian of f.w.h.m. = 0.3 eV and a background has been fitted and subtracted. The edge at 118 eV is the beryllium K-edge. regarded as present if the number of counts in the peak exceeds three times the standard deviation of the counts in the background.2' Applying this to the peaks used for the X.r.e.analysis in table 1 gives the detection limit for oxygen K, as 2 YO (1 atom YO) and for aluminium 6% (0.5 atom %). Conclusions From the spectra of rhodizite, which is a complex and rather beam-sensitive mineral, it is clear that the use of parallel detection to record EELS spectra makes it possible to obtain data which are significantly better than those obtained using serial detection. The most important disadvantage associated with parallel detection systems currently available arises from the limited dynamic range, so that if a complete spectrum is needed in order to quantify the analysis, it is necessary to measure several spectra over small energy ranges and then to match them up.It is also necessary to correct for the effects of the fixed pattern noise. For well separated edges their areas can be determined to better than 1 O h , even in a material as complex as rhodizite, and the accuracy of the quantitative elemental analysis is limited by the systematic errors in the theoretical cross-sections and the power-law fit for the background, For edges which are widely separated in energy, Bragg-edge multiple scattering events may also introduce a significant error unless the spectrometer collection aperture is sufficiently large to include at least the lowest order Bragg beams, as is seen in the analysis using the aluminium K-edge. For the light elements considered in this paper EELS is significantly better than X.r.e.and provides elemental ratios for beryllium, boron and aluminium, calculated with respect to the oxygen, which are in good agreement with the analysis given Pring et d.ll using wet chemistry and crystallographic techniques. The detection limits for these light elements are estimated to be between 0.1 and 1 atom %. Using X.r.e. we were unable to detect either beryllium or boron, and the analysis of the aluminium and potassium were both significantly in error because of the difficulties associated with the effects of X-ray absorption andW. Engel et al. 629 fluorescent enhancement. Of course, for heavier elements beyond the second row of the periodic table X.r.e. analysis using the K-shell X-rays is superior to that which can be obtained from EELS.Even with the high resolution obtainable using EELS as compared to X.r.e. the extended nature of the signals can lead to problems when two edges are close together, and this is seen in the difficulty of separating the aluminium Ledge from the beryllium K-edge, the pottasium Ledge from the boron K-edge, and even more so in the problem of separating the carbon K-edge from the potassium Ledge. It is clear that with the benefit of parallel detection, EELS provides a powerful analytical tool for the analysis of light elements in microscopic volumes, and it is to be expected that the use of EELS in this way will become much more widespread in the future. We thank Dr D. A. Jefferson for his invaluable advice and help in this work.We also thank the Fritz-Haber Institute for financial support, the S.E.R.C. for a studentship (to R.B.) and the Royal Society for a Senior Research Fellowship (to B.G.W.). The rhodizite used for the EELS measurements was from Ambatofinandrahana in the Ankaratara mountains, Malagasy Republic (British Museum reference BM 1984,495). We thank the Keeper of Mineralogy, British Museum for Natural History for providing the samples. References 1 P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley and M. J. Whelan, Electron Microscopy of 2 C. Colliex, in Advances in Optical and Electron Microscopy, ed. R. Barer and V. E. Cosslett (Academic 3 R. D. Leapman, Ultramicroscopy, 1979, 3, 413. 4 A. P. Somlyo and H. Shuman, Ultramicroscopy, 1982, 8, 219. 5 R. F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope (Plenum Press, London, 6 H. Schuman, Ultramicroscopy, 1981, 6, 163. 7 Th. Lindner, H. Sauer, W. Engel and K. Kambe, Phys. Rev. B, 1986, 33, 22. 8 R. F. Egerton and S. C. Cheng, J. Microscopy, 1982, 127, RP3. 9 A. J. Bourdillon, W. M. Stobbs, K. Page, R. Home, C. Wilson, Am Ambrose, L. J. Turner and G. P. Thin Crystals (Butterworths, London, 1965). Press, London, 1984), vol. 9. 1986). Tebby, Znst. Phys. Con$ Ser., 1985, 78, 161. 10 0. L. Krivanek, C. C. Ahn and A. B. Keekey, Ultramicroscopy, 1987, 22, 103. 11 A. Pring, V. K. Din, D. A. Jefferson and J. M. Thomas, Mineral. Mag., 1986, 50, 163. 12 H. P. Rust, D. Krahl and K. H. Herrmann, J . Phys. E, 1984, 17, 539. 13 K. H. Herrmann and D. Krahl, in Advances in Optical and Electron Microscopy, ed. R. Barer and V. E. Cosslett (Academic Press, London and New York, 1984), vol. 1. 14 H. P. Rust, Entwicklung eines elektronischen Bildregistriersystems fur die Elektronenmikroskopie und dessen Untersuchung und Erprobung, Dissertation (Technische Universitat Berlin, D83, 1982). 15 W. Kerzendorf, Entwicklung und Erprobung eines hochauflosenden Flachenzehlers f u r 100 k V Elektronen zur Bildregistrierung am Durchstrallungsmikroskop, Dissertation (Technische Universitat Miinchen, 1978). 16 W. Kunath and K. Weiss, personal communication. 17 H. Shuman and P. Kruit, Rev. Sci. Znstr., 1985, 56, 231. 18 R. F. Egerton, B. G. Williams and T. G. Sparrow, Proc. R. SOC. London, Ser. A., 1985, 398, 395. 19 R. F. Egerton, Ultramicroscopy, 1979, 4, 169. 20 R. D. Brydson, J. M. Thomas and B. G. Williams, J . Chem. SOC., Faraday Trans. 2, 1987, 83, 747. 21 S. J. B. Reed, Electron Microprobe Analysis (Cambridge University Press, 1976). 22 M. S. Isaacson and D. Johnson, Ultramicroscopy, 1975, 1, 33. Paper 7/821; Received 11th May, 1987

ISSN:0300-9599    

DOI:10.1039/F19888400617

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1988, 84(2), 631-646 Electron Energy-loss Spectroscopy and the Crystal Chemistry of Rhodizite Part 2.-Near-edge Structure R. Brydson and B. G. Williams? Department of Physical Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EP W. Engel, Th. Lindner, M. Muhler, R. Schlogl and E. Zeitler Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 0-1000 Berlin 33, Federal Republic of Germany J. M. Thomas Davy-Faraday Laboratories, The Royal Institution, 21 Albermarle Street, London WlX 4BS An electron microscope fitted with a magnetic prism spectrometer and a parallel recording system has been used to measure the electron energy-loss spectrum of the mineral rhodizite at an energy resolution of 0.5 eV. The near-edge structures associated with the oxygen and aluminium edges have been analysed using both well established and novel techniques.We are able to confirm the presence of aluminium in octahedral sites and to determine the relative site occupancies of the oxygen in three chemically inequivalent sites. These occupancies are in agreement with those derived from X-ray diffraction, high-resolution electron microscopy and nuclear magnetic resonance data. Measured chemical shifts are consistent with the predictions of a simple charge potential model. X-ray photoemission and Auger spectra were also measured, and the conclusions drawn from them are in agreement with our interpretation of the structure of the oxygen K-edge based on the electron energy-loss spectra. Electron energy-loss spectroscopy (EELS) provides a sensitive probe of the solid state, yielding information concerning the elemental composition of the sample, the coordination and oxidation states of particular atoms, nearest-neighbour distances and bond lengths.’ The power of this technique has been greatly enhanced by the development of effective parallel detection systems, and in Part l 2 we described in some detail a dedicated EELS microscope fitted with a parallel detection system, designed and built in the Fritz-Haber Institute.In order to explore the potential of EELS as an analytical tool we carried out an elemental analysis of the mineral rhodizite, and in Part 1 we compared the results with X.r.e. (X-ray emission analysis) measurements and with the results obtained using wet chemical and crystallographic methods.The crystal chemistry of rhodizite has been the subject of a detailed study by Pring et aL3 using data from high-resolution electron microscopy (HREM), magic-angle spinning nuclear magnetic resonance (MASNMR), single-crystal X-ray diffraction and a new chemical analysis. Their analysis yields a compositional formula (K0.46 “0.36 Rb0.06 Na0.02)Z0.90 “3.99 (B11.35 Be0.55 Li0.02) ‘28 t Present address : International Centre for Insect Physiology and Ecology (ICIPE), P.O. Box 30772, Nairobi, Kenya. 63 1632 EELS Study of Rhodizite and they conclude that the mineral is cubic (a = 7.3 18 k 0.01 A) with space group P43m. The alkali-metal atoms are randomly distributed on appropriate sites. The beryllium and boron atoms are located in chemically equivalent sites with 4 beryllium atoms occupying a special 4e position while the remaining 0.5 are randomly distributed with the 11.35 boron atoms over the 12h sites.The aluminium atoms are all in equivalent 4e sites while the oxygen atoms occupy three sites, their nearest-neighbour coordination and symmetry being: A1 B B A1 B B O(1): Be-O( 4e O(2): Al-O< 12i O(3): Be-O< 12i. Rhodizite is an ideal test sample for EELS as it contains a number of light elements. In this paper we examine in detail the structure associated with each core-loss edge. This so-called electron energy-loss near-edge structure (ELNES) depends on a variety of factor^.^ When the energy transfer is greater than the binding energy of a particular electron, the ejected electron will undergo a transition into one of the lower unoccupied states above the Fermi level of the sample.The near-edge structure will therefore depend on the unoccupied density of states. In addition, at low scattering angles, and therefore momentum transfers, the allowed transitions are those which obey the dipole selection rule AZ = 1, so that the observed structure reflects the angular momentum projected density of states. Further complications arise from the influence of the core-hole which remains when an electron is ejected from its ground state. Another way to model the near-edge structure is based on multiple scattering cluster calculation^.^. For MgO it has been shown' that in a large enough cluster the XANES (X-ray absorption near-edge structure) calculations reproduce the density of states derived from a band-structure calculation.However, the cluster approach permits the core-hole effect to be included, and it has been demonstrated that this is important for K-edges.' The XANES code has also been successfully applied to the ELNES of Be,C, and it was found that charge- transfer effects also contribute significantly to the near-edge structure.' Earlier work in this field has concentrated on binary systems such as transition-metal and little work has been done on more complicated systems of interest to chemists, so that rhodizite constitutes an ideal sample with which to explore the potential of EELS in the study of such materials. Edge Structures The most exciting prospect for EELS lies in the possibility of using the near-edge structure to obtain information about the electronic state and the local environment of particular atoms.The energies of the various edges and lines present at each core-loss are given in table 1. (The data before subtraction of the background are given in Part l.,) The energies of the most prominent peaks were determined by measuring the shift in the beam voltage which was required to move the peak of the zero-loss line to the channel of the peak under consideration. The error in the determination of the voltage was less than k times the voltage shift. The determination of the positions of the peaks is also affected by the counting statistics, and we estimate that the energies reported below are accurate to kO.2 eV. Aluminium The aluminium Ledge at ca.79 eV is shown in fig. 1(A) after subtraction of the background. The L-edge shows a great deal of detailed structure, and in particular there is a sharp peak (a) at 79.1 eV and a rather broader peak (b) at 85.2 eV. To confirm theR. Brydson et al. 633 Table 1. Energies of the significant features in the EELS of rhodizite relative to the X.P.S. binding energies (Eh), in eV A1 L Be K B K O K A1 K line ( a ) line (b) line (c) line ( d ) line (e) 74.7" 114.2" 4.0 4.2 19.9 - 4.4 (1.1) 4.9 (2.0) 10.5 (2.3) 10.4 (5.4) 24.3 (7) 20.7 (2) - - 192.0' 5.8 21.2 6.6 (2.0) 11.7kO.5 22.4 (2.4) 27.5 2.4 ( 1 .O) 53 1 .8h 1559.60' 4.8 5.2 6.7 (4.0)" 13.7 (4.0)d - 19.0 10.1 (4.0)d 9.4 - - 36.7 k 0.5 - -2.0 (1.0) - -7.2 (1.0) For A120,27 and for Be0.2H ' This work for rhodizite.For A120,.32 Edges a correspond to the point of Derived using the mathematical analysis described in the text. The inflection at the beginning of the edge. accuracy is k0.2 eV unless otherwise stated. Numbers in brackets give the f.w.h.m. accuracy of the energy scale the position of peak (a) was measured using data recorded from a different region of the sample and this also gave 79.1 eV. It is important to confirm that the structure is not a consequence of multiple inelastic scattering. A plasmon event followed by an edge excitation would produce the same structure convoluted with the single plasmon spectrum, so that it would be shifted by ca. 25 eV and then broadened. Without a measurement of the zero-loss and plasmon region of the spectrum for the same area of the specimen it is not possible to deconvolute the data using the standard methods,12 and for this reason a serial deconvolution which progresses from the left-hand side to the right-hand side of the spectrum was applied to the data in a way which makes it possible to evaluate the deconvoluted spectrum at each point from a knowledge of the deconvoluted spectrum to the left of that point only.13 Deconvoluting the aluminium edge in this way with a zero-loss spectrum based on the fit obtained in the low-loss region of the spectrum lowers the intensity in the region beyond the edge but does not alter the structure significantly.Increasing the scattering parameter to simulate a thicker sample lowers the edge further, but still does not affect the structure at the edge.From the chemical analysis given in Part l 2 we were led to conclude that only 15 % of the area between 80 and 100 eV is due to the caesium N-edge, and its seems reasonable to associate the major features with the aluminium edge. Colliex et a1.14 have published an EELS spectrum for a-A1203, and the structure of the aluminium edge in their measurement is similar to that in fig. 1(A). This provides strong confirmation for the conclusion reached by Pring et ~ 1 . ~ that the aluminium in rhodizite is octahedrally coordinated to oxygen. In order to confirm the coordination, the structure in the aluminium Ledge was calculated using the XANES program of Vvedensky et d5 with the aluminium atom octahedrally and tetrahedrally coordinated to a single shell of oxygen atoms as shown in fig.1(B). The phase shifts used were obtained using Hartree-Fock free-atom wavefun~tionsl~ and a muffin-tin potential; the bond lengths were those given by Pring et ~ 1 . ~ Transitions to excited states with angular momentum 1 = 2 and m = - 2, - 1, 0, 1, 2 were included in the calculation, as well as those with 1 = 0 and m = 0. The total spectrum was taken to be the sum of the spectra calculated for each transition separately so that interference between the possible excitations was not included. (Schaichl' has shown that in a cubic environment the cross-interference terms may be omitted.) The zero of the energy scale in the calculations depends on the muffin-tin potential and the634 EELS Study of Rhodizite 80 I00 I20 I , I I I , I , I 80 100 I20 energy/eV Fig.1, (A) The aluminium Ledge in rhodizite after subtraction of the background. The edge at 118 eV is the start of the beryllium K-edge. The energies of the labelled peaks and edges are given in table 1. (B) The results of the XANES calculation for aluminium octahedrally (a) and tetrahedrally (b) coordinated to a single shell of oxygen atoms. spectra were therefore shifted in order to align the first strong peak with the corresponding peak in the measurement. The calculated spectrum for the octahedral coordination shown in fig. 1(B) is much closer to the observed spectrum than is the calculated spectrum assuming tetrahedral coordination. In particular, the sharp line at the edge [(a) in fig. 1 (A)], which arises entirely from the 1 = 0 final state, is present in the calculation for octahedral coordination but is completely absent in the calculation based on tetrahedral coordination. The energy spacings of the various peaks in the calculated spectrum [fig. 1 (B)] do not agree precisely with those in the observed spectrum, but the qualitative agreement is good.Since rhodizite has a large unit cell which contains a number of different types of atoms, there is relatively little middle-range order, and this may help to explain the success of the calculation which includes only a single shell of neighbours. The K-edge in aluminium [fig. 2(A)], on the other hand, is relatively featureless beyond the edge 01 which occurs at 1564.8 eV, 5.2 eV beyond the X.P.S. (X-ray photoemission spectroscopy) binding energy.The peak (a) is at 1569.0 eV. Taftnr and Zhu" have published spectra for aluminium and magnesium K-edges tetrahedrally and octahedrally coordinated to oxygen. They show that in the case of octahedral coordination a strong line is observed at the edge, while in tetrahedral coordination this is absent. Using the XANES program5 to calculate the structure at the aluminium K-edge,R. Brydson et al. 63 5 e, U E Ei E c .r( .r( Y t l I I I l ~ l ~ l ~ l I I I ~ I l r l 1 I ~ I I ~ ~ ~ ~ ~ L L 1 1 ~ I I 1 1 ~ 1 f i ~ I 1560 1580 energy/eV Fig. 2. (A) The aluminium K-edge in rhodizite after subtraction of the background. The energies of the labelled peaks and edges are given in table 1. (B) The results of the XANES calculation for aluminium octahedrally (a) and tetrahedrally (b) coordinated to a single shell of oxygen atoms.again including only a single shell of oxygen atoms, gives the results shown in fig.(B). The aluminium K-edge in rhodizite is again closer to the calculation assuming octahedral co-ordination. Beryllium Immediately beyond the aluminium Ledge is the beryllium K-edge. Fitting a background to this edge is problematical because the aluminium edge extends right up to, and presumably into, the beryllium edge. For this reason the background was pinned to the average value of the data between 113.3 and 115.6 eV, and a power-law was used to describe the background with the exponent chosen to match the power-law dependence of the data beyond the edge, where it is relatively featureless.The data for this edge are shown in fig. 3. Once again there is a significant structure near the edge a which occurs at 118.4 eV with a sharp peak (a) at 119.1 eV and a rather broader peak (b) at 124.6 eV. The structure observed 20 eV beyond the aluminium Ledge is not observed in this edge, or indeed in the boron, oxygen or aluminium K-edges. Since the beryllium and boron atoms are tetrahedrally coordinated to oxygen the relative lack of structure may be symptomatic of the tetrahedral coordination. Future calculations using636 EELS Study of Rhodizite 5 --. * E 8 0 I -. - I I I I I I I I 1 I 1 1 1 1 I l l 1 1 1 1 1 1 I I I l I l I I I I I I I I I I I I 2 0 I40 160 energy/eV Fig. 3. The beryllium K-edge in rhodizite after subtraction of the background. The energies of the labelled peaks and edges are given in table 1.the XANES program are planned to see if these edges can be modelled in the same way as for the aluminium L- and K-edges as described above. In the structure proposed for rhodizite by Pring et aL3 there are 4.55 beryllium atoms per unit cell and 11.35 boron atoms per unit cell. Having assigned 4 of the beryllium atoms to a particular crystallographic site the remaining 0.55 are assumed to occupy 12h sites, otherwise occupied by boron, to make up for the deficit of boron atoms. If the beryllium atoms occupied two different chemical environments, the presence of two distinct chemical shifts should be apparent at the edge, but the two sites are very similar, the only difference being in the oxygen bond distances, and the EELS data do not indicate any splitting in the lines.Boron The boron edge a in fig. 4(A) is at 197.8 eV and the spectrum shows a strong peak very close to the edge at 198.6 eV and a strong shoulder, probably produced by a peak at ca. 204 eV. In addition there is a peak before the edge at 194.4 eV. The pre-edge peak, shown in fig. 4(B), is probably due to an excitonic effect in the band gap, and similar peaks have been observed in MgO.' If this feature were due to an excitonic transition the binding energy of the exciton would be 2.8 eV. The relative intensity of this peak depended on whether the beam was scanned over an area or focussed to a spot. In the latter case significant beam damage occurred and this peak disappeared. Beyond the initial structure, the boron edge displays two weak peaks which are shown in fig.4(C), one at 214.4 eV and the other at 219.5 eV. These two peaks must be associated with the boron edge, being a weaker version of the structure which is observed in the Al Ledge, since there are no other K- or Ledges close to this energy. Oxygen The oxygen K-edge is shown in fig. 5 (A) after subtraction of the background. The signal- to-background ratio is favourable, being > 3, and the edge structure is quite different from any of those discussed above. Fig. 5(B) shows the pre-edge region of the spectrum on an expanded scale revealing two further, very weak, peaks at 524.6 and 529.8 eV. As in the case of the boron K-edge these pre-edge peaks are symmetrical, a fact which some authors believe to be indicative of excitons.18 If we assume that these two peaks are the first two in an excitonic series, the energies varying as 1 /n2, with n = 1, 2, .. . we obtainR. Brydson et al. 637 50 0 2 8 ---- c) S 3 0 i- I I r ll w I I 200 220 240 I2 10 8 192 194 196 210 220 230 energy/eV Fig. 4. (A) The boron K-edge in rhodizite after subtraction of the background. (B) Pre-edge region of (A) shown on an expanded scale. (C) Near edge region of (A) shown on an expanded scale. The energies of the labelled peaks and edges are given in table 1. a value for the ionization edge of 531.6 eV which corresponds to the initial rise at a at the 0 K-edge shown in fig. 5 (A). However, the transition strengths for an excitonic series vary as l/n3, so that the second peak should be of the size of the first, which is clearly not the case.Consequently we must assume that these two excitons are due to the presence of oxygen in more than one chemical environment and, as we discuss below, we believe this to be the case. Once again there is a strong peak at the edge, but this time it is very broad. It is well known from X.P.S. measurements that core-level binding energies may change by several eV depending on the chemical environment or 'effective charge' on the atom in question. Assuming therefore that this indicates the presence of oxygen in several inequivalent crystallographic sites, the nain peak was fitted to a set of Gaussians in order to extract the number of inequivalent sites and their occupancies. To complicate matters further, it is clear that in addition to the peak there is an edge in the spectrum and the precise position of the edge is also not known.To minimise the effect of the edge the fit has been done to the derivative of the data, which is shown in fig. 6(A). The quality of the data is shown by the low level of statistical noise in the derivative spectrum. The derivative of a Gaussian is a 'wave' with a peak followed by a trough, and it is immediately clear from the flat section in the middle of the derivative spectrum that at least two peaks are present. Furthermore, the slope at the point of inflection on the main peak and the main trough determines the width of the Gaussians to be fitted. Attempts to fit two Gaussians to the data were only moderately successful, the main difficulty being that in638 EELS Study of Rhodizite 100 L w 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 520 540 560 580 52 50 48 46 525 530 550 555 energy/eV Fig.5. (A) The oxygen K-edge in rhodizite after subtraction of the background. (B) Pre-edge region of (A) shown on an expanded scale. (C) Near-edge region of (A) shown on an expanded scale. The energies of the labelled peaks and edges are given in table 1. order to reproduce the flat section in the middle the Gaussians must have almost equal areas, and the ratio of the main peak to the main trough is then ca. 1, which is clearly not so in the data. The presence of a further small trough at ca. 546 eV indicates the need for a third Gaussian which reduces the amplitude of the main trough and also introduces this second trough.This gives a seven-parameter fit : three positions, three amplitudes and one width. The fit indicated by the line in fig. 6(A) is now reasonably convincing, but a significant departure remains at ca. 534 eV. Attempts to account for this by introducing yet another peak were not successful, and this is therefore attributed to the edge which will produce a single peak in the derivative spectrum. The fitted derivative curve can now be integrated, and this is shown in fig. 6(B). Subtracting the fitted curve from the experimental data leaves the edge shown in fig. 6(C) and this looks quite satisfactory. The final fit therefore consists of three Gaussians, each with a standard deviation of 1.7 eV (f.w.h.m. = 4.0 eV), their means being 538.5,541.9 and 545.5 eV and their relative intensities being 1.0: 1.0:0.33.With such a non-linear fit one should be cautious about assigning error limits to the fitted values, but by varying the parameters one at a time, each energy appears to be accurate to ca. 0.2 eV and each intensity to ca. 10 %. The fit to the data therefore suggests that oxygen occurs in three inequivalent sites in rhodizite, with occupancies in the ratio 3 : 3 : 1, and this supports and confirms the conclusion reached by Pring et aZ.,3 who place the oxygen atoms in a 12i site coordinated to beryllium and boron, in a second 12i site coordinated to boron and aluminium and in a 4e site coordinated to beryllium and aluminium. The success of the fit suggests trying to relate the EELS chemical shifts to the effectiveR.Bryhon et al. 639 530 540 550 0 I00 0 530 540 550 n 530 540 5 50 energy/eV Fig. 6. (A) The derivative spectrum (first difference) of the oxygen K-edge spectrum shown in fig. 5. The dots are the experimental points, the line gives the best fit using three Gaussians as described in the text. (B) Gives (a) the original spectrum and (b) the integral of the fitted curve shown in (A). (C) Gives the original spectrum before and after subtracting the fitted curve shown in (B). charges on the different oxygen atoms, as has been done by Isaacson for carbon atoms in the nucleic acid bases adenine, thymine and ura~i1.l~ Taking the electronegativities to be 1.76 for beryllium, 1.5 for aluminium, 2.04 for boron and 3.41 for oxygen, and using Pauling’s method, as discussed by GhoshZ0 to calculate the net charges on each oxygen atom arising from each of the three possible neighbours, the following results are obtained: Be -+ 0, 0.494e-; B --+ 0, 0.375e-; A1 --+ 0, 0.598e-.Using a charge potential model in which the atoms may be approximated by hollow non-overlapping electrostatic spheres, the core binding energy depends on the potential at the core due to the charge transferred to the valence electrons on a particular atom as well as on the charge transferred to the neighbouring atoms. The potential energy, Ei, experienced by a core electron on an atom i may then be written Ei = ke(q,/r, + Cq,/r,) + V640 EELS Study of Rhodizite 1 a 530 I I 1 1 I 0 10 20 30 effective core potential/eV Fig.7. The energies of the three fitted peaks at the oxygen K-edge plotted against the effective core potential arising from the charge transferred between each oxygen atom and its nearest neighbours. Details are given in the text. where qi is the charge transferred to atom i, ri is the radius of the valence shell of atom i, qi is the charge transferred to atom j and rii is the distance of atom j from atom i. The sum is over all nearest neighbours, e is the electron charge, and k and Vare constants. The factor k allows for the difference in the effects of the charge transfer on the initial and final states and V represents a reference binding energy, which will depend on the band gap and relaxation of the core hole. For oxygen the average value of l / r for the 2p valence shell may be calculated using the hydrogenic expression Z/a,n2, where a, is the Bohr radius and Z is the effective nuclear charge estimated using Slater atomic shielding constants.21 The bond lengths were taken from the data of Pring et al.' The peak positions derived from the Gaussian fit are plotted against this effective core potential in fig.7. As is evident, the relationship is linear, and from the fitted line we get k = 0.49f0.01 and V = 531.6f0.3 eV. The value of V corresponds to the binding energy of an oxygen 1s level in rhodizite for an oxygen atom with zero charge. The band gap in rhodizite [ca. 10.3 eV measured from the low loss shown in fig. 1 (A) in Part 13 should shift the edge to higher energy losses by approximately half the band gap, or 5 eV.However, electronic relaxation around the core hole shifts the binding energy to lower energy loss. In the carbon K-edge of graphite Mele and Ritsko estimate this relaxation to be ca. 2.5 eV,22 and this effect would be larger in the oxygen so that a final figure of 532 eV is reasonable. This simple charge potential model thus provides further support for the Gaussian derivative fitting procedure and the assignment of the peaks to three inequivalent sites. As can be seen from fig. 7, it correctly places the O( 1) site coordinated to two aluminium atoms and one beryllium atom, which has a relative occupancy of 1 and for which the effective core potential is most positive, at the highest energy loss. With an energy resolution of ca. 0.5 eV, the f.w.h.m. of the strongest lines at the beryllium, boron and aluminium K-edges are all close to 1.5 eV.However, the width of each Gaussian fitted to the oxygen K-edge is significantly broader (ca. 4 eV). This broadening may be due to the fact that each oxygen atom possesses two different nearest neighbours, and the broadening could also be due to the different back-scattering phase- shifts. The lifetime of the excited state is also important here, and in the near-edge region this is sensitive to the band structure of the unoccupied states. As a rough approximation the final state width increases as (E- E,)", where 1 < c < 2, E is the energy of the final state and Ef is the Fermi en erg^.^ Since the band gap in rhodizite is rather large the final state width will be larger than in insulators with smaller band gaps.Indeed, preliminary investigations on the mineral w~llastonite~~ in which there are also inequivalent oxygenR. Brydson et al. 64 1 sites, seem to confirm both the applicability of the fitting procedure and the above argument. The band gap in wollastonite is considerably smaller than in rhodizite, and the widths of the Gaussians fitted to the oxygen K-edge are correspondingly narrower, so that the separate peaks are clearly resolved. An alternative explanation for the presence of three peaks at the oxygen K-edge could involve the presence of three different nearest neighbours. In EELS spectra taken from molecules in the gas phase, a correlation between the energy of a continuum resonance, referred to as the shape resonance, and the bond length has been reported.A linear relation between the resonance energy above the X.P.S. binding energy and the bond length holds for molecules in which the sum of the atomic numbers of the atoms constituting the bond is constant.24 In our case the prominent peaks above the edges could also be looked upon as quasi-bound states or scattering resonances. The energy position of these would, according to the picture developed for the gas-phase data, shift in the continuum if the absorber were surrounded by the same type of atom at different distances or by atoms with different atomic numbers, since each atom could produce a distinct resonance. In order to distinguish between this picture and the charge-transfer interpretation of the structure of the oxygen 1s K-level, X.P.S.and Auger spectra were also measured for rhodizite. X.P. and Auger Spectra The photoemission data were obtained from a spectrometer working with an ultra-high vacuum which was free of pumping oil at a base pressure of 5 x lo-'* mbar. The system was equipped with a hemispherical analyser (VSW HA loo), a twin X-ray gun operating with Mg K , radiation (10 kV, 12 mA), sputtering facilities (2 x mbar, Ar', 3 kV, 16 mA) and a sample lock suitable for fine powdered materials. The analyser was operated in the constant-pass energy mode with instrumental resolution of 1.6 eV (f.w.h.m. Au 4f7'2), which yielded typical intensities of lo4 counts. The sweep rate was 0.03 eV s-l. The spectrometer was calibrated against the Au 4fline, taking 84.0 eV for the reference binding energy.The samples were thin deposits of finely ground powder on a gold substrate. The reference samples of sodium hydroxide and sodium borate were deposited as aqueous solutions on a gold substrate. Care was taken to deposit suitable amounts in order to obtain a homogeneous thin film of the sample without significant charging. The reference compounds, boron oxide and aluminium oxide, were analytical- grade commercial products. Results Photoemission from non-conducting materials is severely hampered by the ill-defined common binding energy scale. This renders evaluation of both binding energies and linewidths more difficult than with metallic samples, the energy scale of which can be related to the Fermi edge. A set of reference compounds were therefore studied in addition to the sample of rhodizite using both the oxygen 1s X.P.S.core-level emission and the oxygen KLL Auger transition. The results are given in fig. 8 and 9 and summarised in table 2. The resolution of the oxygen Is X.P.S. spectra is usually not very good for different oxides, as the span of chemical shifts in different metal oxides is small. This holds in particular for the oxides of the main-group elements. An additional problem arises from the presence of structural water or OH groups on the surface.25 The chemical shift for water and any other oxide is much larger than the difference in shift between two metal oxides. This is illustrated by the difference between sodium hydroxide (529.8 eV) and sodium oxide (532.9 eV) of 3.1 eV on the one hand26 and the difference between sodium oxide and aluminium oxide (531.8 eV), for which the difference in shifts is only 1.1 eV, on the other.The curves labelled (a) in fig. 8 and 9 represent typical rhodizite spectra. They are not642 EELS Study of Rhodizite 538 536 534 532 530 528 526 1 1 1 1 1 1 1 1 1 1 1 1 1 4,IeV Fig. 8. The X.p. spectra (0 1s) for (a) rhodizite, (b) boron oxide, (c) sodium borate, ( d ) aluminium oxide and (e) sodium hydroxide. influenced by any surface contamination. The spectra were studied as a function of excessive sputtering for 3 h, and no detectable change was found once the initial atmospheric contaminants had been removed. There is no evidence for the presence of significant amounts of adsorbed water. Any OH still present is a component of the mineral and does not arise as an artefact of the surface sensitivity of photoemission.The oxygen 1s spectrum of rhodizite exhibits a binding energy significantly higher than in sodium oxide (fig. 8). This binding energy is typical of boron oxide [curve (b)] and aluminium oxide [curve (41, which are in a sense intrinsic binary ingredients of rhodizite. We conclude that the mean charge density at the oxygen ions in rhodizite isR. Brydson et al. 643 I L86 492 500 508 516 524 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 EkIeV Fig. 9. The Auger spectra (OKLL) for (a) rhodizite, (b) boron oxide, (c) sodium borate, ( d ) aluminium oxide and (e) sodium hydroxide. Table 2. Photoemission and Auger data for rhodizite and some reference compoundsa compound 0 1s EJeV f.w. h.m. /eV EIKIeV rhodizite boron oxide sodium borate aluminium oxide sodium hydroxide 531.8 3.3 508.3 531.8 3.3 508.3 531.8 2.9 508.8 531.8 2.9 507.0 532.4 2.2 508.0 ~~ ~~ a Eb is the binding energy of the oxygen Is level and Ek the energy of the oxygen Auger KLL transition. significantly different from the formal charge of - 2. Using the binding energy difference between sodium oxide (charge - 2) and sodium hydroxide (charge - 1) as references and assuming a linear relation between charge and binding energy difference, we obtain a mean charge of - 1.6 for the oxygen sites in rhodizite. In the charge-transfer model discussed above, the mean charge transferred to the oxygen atoms is - 1.5, so that the X.P.S. data provide further confirmation for the charge-transfer model.The oxygen 1s signal (table 2) is broader than is usual for a single emission line. This can be seen from a comparison of curves (a) and (e) in fig. 8, the latter being for pure sodium hydroxide. The width is at least as large as in any of the reference compounds. We therefore conclude that the broad spectrum indicates the presence of oxygen in more than one site, as is suggested by the EELS data, and the estimation of the formal charge is an average over these three sites with slight variations for the different oxygen environments. By comparison with sodium oxide (fig. 8) it is clear that none of the oxygen sites in rhodizite carries a formal charge of -2. It is important for this argument that a common energy scale is used for all the spectra.To ascertain this crucial condition the following procedure was adopted. The spectrum of rhodizite was corrected for charging up by comparing the measured value of the binding energy for caesium 3d5,, with the literature value2’ of 724.1 eV (for CsOH). We used this core level for calibration since caesium shows only a negligible644 EELS Study of Rhodizite range of chemical shifts and the shift is essentially independent of the chemical environment. This correction also yields a value for the binding energy of boron 1s electrons in rhodizite of 192.0 eV (approximately half the band-gap) below the edge energy measured from the EELS spectra (table 1). The X.P.S. value for beryllium oxide is 114.2 eV, which is also 5 eV below the edge energy measured from the EELS spectrum.28 The control sample of sodium borate prepared as an uncharged thin film on gold gave the same value for the boron 1s core level, confirming the correction for the rhodizite spectrum, Boron oxide and aluminium oxide are important binary constituents of rhodizite.As can be seen from fig. 8 [curves (b) and (d)] and table 2, it is not possible to distinguish between these two oxides from their oxygen 1s binding energies. This conclusion holds under the assumption that the aluminium 2p binding energy of 74.9eV, which we obtained and which is also quoted in the literat~re,~' is correct. The compound boron oxide is very hygroscopic and tends to incorporate structural water as OH groups. We therefore measured 'pure' boron oxide [curve (b) in fig.81 and sodium borate without water [curve (c)]. The two spectra are almost identical. This and the large linewidth as compared with the sodium hydroxide spectrum indicates that both compounds contain significant amounts of OH. These conclusions are supported by the analysis of the oxygen KLL Auger spectra shown in fig. 9. The rhodizite spectrum [curve (a)] is very similar to the spectrum of boron oxide [curve (b)]. The other ingredient, aluminium oxide, gives rise to a spectrum as shown in curve (d). Despite the clear shift relative to the spectrum of boron oxide, this spectrum may well be a minority contribution to the rhodizite spectrum. The spectrum of sodium hydroxide [curve (e)] is different in shape from all the other oxide spectra and is typical of hydroxo oxygen.This is due to the different bonding character in the oxides and in the OH group, which allows a clearer distinction to be made between the transition in the oxygen 2p final states in the latter case. Comparison with the rhodizite spectrum indicates that the OH group makes no significant contribution to the spectrum. The Auger spectrum for rhodizite (fig. 9) is again wider than that of all of the reference spectra which also indicates the presence of a variety of oxygen sites. The shape and position of the rhodizite spectrum allow us to exclude the presence of purely ionic oxide species. The spectrum of sodium oxide is a single narrow line at the position indicated in fig. 9. As in the oxygen 1s spectra the Auger transition exhibits no intensity at the pure oxide position.This and the overall shape support the view that oxygen in rhodizite is not purely ionic 02-. A significant covalent contribution to the bonding is inferred from these photoemission data. Note that the binding energies determined by X.P.S. are referred to the Fermi level, whereas EELS data give the energy for a transition of a core electron to the lowest unoccupied state which is allowed by the dipole selection rule. This should lead to a difference between the X.P.S. binding energy and the corresponding edge energy determined with EELS of half the band gap. However, this still ignores significant differences between the two experiment^.^' In EELS the excited core electron stays close to the core hole, and the perturbation of the remaining electrons is small.This is not the case in X.P.S. because the excited electron leaves the solid and the remaining electrons see a totally unscreened hole. Relaxation is therefore much stronger in X.P.S., which should reduce the difference between the X.P.S. binding energy and the corresponding edge energy found in EELS. The strong effect of relaxation can be seen from the data in table 2, where the Auger transition involving the oxygen 1s core-level and the oxygen 2p valence states is found at an energy ca. 21 eV lower than the oxygen 1s binding energy. This difference is, at least in part, due to relaxation effects. The fluctuation of this energy difference forR. Brydson et al. 645 different compounds is due to chemical shifts of the core level and/or the valence states, which are rather localised in the oxides studied here, giving distinct peaks of ca.3 eV width at a binding energy of ca. 5.5 eV in the X.p. spectra. Conclusion This study reveals the wealth of information that can be obtained from the near-edge structures of core-loss edges in complex materials. In order to extract such details the importance of high resolution and parallel detection cannot be over emphasised. We have shown that EELS is sensitive to the local atomic environment, and with an energy resolution of ca. 0.5 eV and an absolute energy calibration it is possible to measure chemical shifts and peak positions with an accuracy of 0.2 eV. We are able to confirm the octahedral coordination of aluminium in rhodizite by comparison with theoretical multiple-scattering calculations and the results of other workers on related compounds.We hope to extend the use of the XANES calculations to other systems in the near future. The most exciting results stem from an examination of the oxygen K-edge. Using a relatively novel approach in the field of EELS we are able to extract both the number and relative occupancies of oxygen atoms in inequivalent environments. The results agree well with the predictions of a simple charge potential model, and this suggests that, with data of this quality, it should be possible to use EELS as a ' fingerprinting' technique to determine the number and type of inequivalent atomic sites, as can be done using magic-angle spinning n.m.r.30,31 Although the X.p.and Auger spectra are less well resolved than the EEL spectra they provide strong supporting evidence for our interpretation of the EELS of the oxygen K- edge in terms of the transfer of charge, and they serve to emphasize the power and sensitivity of EELS as a probe of the solid state. EELS is still a relatively unexplored technique, and there is a need for extensive systematic studies to establish a sound methodology for the analysis of EELS data. These measurements on rhodizite demonstrate the potential of parallel detection EELS in solid-state science. We thank Dr D. A. Jefferson for his invaluable advice and help in this work and Dr D. D. Vvedensky for providing us with his XANES program and advice on how to run it. The rhodizite used for the EELS measurements was from Ambatofinandrahana in the Ankaratara mountains, Malagasy Republic (British Museum reference BM 1984,495).The specimen used for the X.P.S. measurements was from Manjaka, Malagasy Republic (British Museum reference BM 1912,418). We thank the Keeper of Mineralogy, British Museum for Natural History for providing the samples. We also thank the Fritz-Haber- Institute, Dr M. Stobbs (B.G.W.) and the S.E.R.C. (R.B.) for financial support and the Royal Society for a Senior Research Fellowship (B.G.W.). References 1 R. F. Egerton, Electron Energy-loss Spectroscopy in the Electron Microscope (Plenum Press, London 2 W. Engel, H. Sauer, E. Zeitler, R. Brydson, B. G. Williams, and J. M Thomas, J . Chem. SOC., Furuduy 3 A. Pring, V. K. Din, D. A. Jefferson and J.M. Thomas, Mineral. Mag., 1986, 50, 163. 4 J. M. Thomas, B. G. Williams and T. G . Sparrow, k c . Chem. Res., 1985, 18, 324. 5 D. D. Vvedensky, D. K. Saldin and J. B. Pendry, Comput. Phys. Cornmun., 1986, 40,421. 6 Th. Lindner, H. Sauer, W. Engel and K. Kambe, Phys. Rev. B, 1986, 33, 22. 7 M. M. Disko, J. H. Spence, 0. F. Sankey and D. Saldin, Phys. Rev. B, 1986, 33, 5642. 8 R. D. Leapman, L. A. Grunes and P. L. Fejes, Phys. Rev. B, 1982, 26, 614. 9 L. A. Grunes, R. D. Leapman, C . N. Wilker, R. Hoffman and A. B. Kunz, Phys. Rev. B, 1982, 25, and New York, 1986). Trans. 1, 1988, 84, 617. 7157.646 EELS Study of Rhodizite I0 C. N. R. Rao, T. G. Sparrow, B. G. Williams and J. M. Thomas, J. Chem. Soc., Chem. Commun., 11 J. M. Thomas, C. N. R. Rao, B. G. Williams and T. G. Sparrow, J. Phys. Chem., 1984,88, 5770. 12 R. F. Egerton, B. G. Williams and T. G. Sparrow, Proc. R. Soc. London, Ser. A, 1985, 398, 395. 13 W. A. Rachinger, J. Sci. Instr., 1984, 25, 254. 14 C. Colliex, T. Manoubi, M. Gasgnier and L. M. Brown, Scanning Electron Microscopy, 1985, 2, 489. 15 E. Clementi and C. Roetti, Atomic Data and Nuclear Data Tables, 1974, 14, 177. 16 W. L. Schaich, Phys. Rev. B, 1984, 29, 6513. 17 J. Tafts and J. Zhu, Ultramicroscopy, 1982, 9, 349. 18 M. Brown, R. E. Peierls and E. A. Stern, Phys. Rev. B, 1977, 15, 738. 19 M. Isaacson, J. Chem. Phys., 1972, 56, 1813. 20 P. K. Ghosh, Introduction to Photoelectron Spectroscopy (Wiley Interscience, New York, 1983). 21 J. C. Slater, Phys. Rev., 1930, 36, 57. 22 E. J. Mele and J. J. Ritsko, Phys. Rev. LRtt., 1979, 43, 68. 23 R. Brydson, B. G. Williams, H. Sauer and W. Engel, unpublished work. 24 F. Settle, J. Stohr and A. P. Hitchcock, J. Chem. Phys., 1984, 110, 577. 25 C. T. Au, M. W. Roberts and A. F. Carley, Znt. Rev. Phys. Chem., 1986, 5, 57. 26 A. Barrie and F. J. Street, J. Electron Spectrosc., 1975, 7, 1. 27 C. D. Wagner, W. M. Eggs, L. E. Davis, J. F. Moulder and G. E. Muilenberg, Handbook of X-Ray Photo-electron Spectroscopy (Perkin-Elmer, London 1979). 28 D. J. Vaughan and J. A. Tossell, Am. Mineral., 1973, 58, 765. 29 G. van der Laan, J. Zaanen and G. A. Sawatzky, Phys. Rev. B, 1986, 33,4235. 30 S. Schramm and E. Oldfield, J. Am. Chem. Soc., 1984, 106, 2052. 31 J. M. Thomas and J. Klinowski, A h . Catal., 1985, 33, 199. 32 S. Hagstrom and S-E. Karlsson, Arkiu. Fys., 1964, 26, 451. 1984, 1238. Paper 71822; Received 1 lth May, 1987

ISSN:0300-9599    

DOI:10.1039/F19888400631

出版商:RSC    

年代:1988

数据来源: RSC