摘要:

J . Chem. Soc., Faraday Trans. I, 1982, 78, 171-183 Infrared Spectroscopic, Thermal Desorption and X-ray Photoelectron Spectroscopic Studies of NO, NO + CO and NO + 0, Adsorbed on Palladium Surfaces BY SHINICHI MORIKI, YASUNOBU INOUE,* EIZO MIYAZAKI AND IWAO YASUMORI Department of Chemistry, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152, Japan Received 2nd February, 198 1 The adsorbed state of NO on polycrystalline Pd metal surfaces, its variation with heat treatment and the effect of CO and 0, have been studied by infrared spectroscopy (silica-supported), thermal desorption (powder) and X-ray photoelectron spectroscopy (powder, foil). The i.r. spectra of NO adsorbed at 298 K showed that there exist mainly bent or bridged NO (1660-1650, 1580-1570 cm-l) for BNo < 0.5 and linear NO (1750-1730 cm-') for 8 N o > 0.6.Upon heat treatment, these i.r. bands changed in different ways. X.P.S. showed a broad N 1s peak of molecular NO (398.7 eV) at 298 K and another peak due to NO,-like surface species (404.0-404.2 eV) at 453 K. For ON, < 0.6, the t.d. spectra exhibited a main N, peak at ca. 490 K, whereas for ON, > 0.6 additional peaks of NO appeared at 373-473 K. It is proposed that in N, formation the dissociation of NO is rate-determining. Changes in the adsorbed state of NO upon heat treatment are explained by the interaction of NO with 0 atoms remaining on the surface after part of the NO is decomposed. The effect of preadsorbed oxygen supports this view. Preadsorbed CO works as a scavenger for this 0 atom and accelerates the formation of N,.The adsorption of NO on transition-metal surfaces has been extensively studied in recent years, and considerable interest has developed in comparing the adsorbed state of NO with its state in organometallic nitrosyl complexes. However, metal surfaces often differ from the case of complexes in leading to the dissociation of NO to produce surface oxygen and/or oxides which may have considerable influence on the state of adsorbed NO. Among the transition metals, palladium is potentially interesting, since its interaction with NO occurs to a relatively moderate extent' at room temperature and varies as a function of temperature. Kishi and Ikeda showed the presence of molecular NO on evaporated Pd at room temperature by the use of X .P . ~ . ~ Recently, Conrad et al. applied a combined u.P.s., LEED and t.d. technique in order to study the geometric arrangement of molecularly adsorbed NO on the Pd (1 1 1 ) surface and its decomposition at elevated temperat~res.~3 In addition, Matsumoto et al. investigated the effects of sulphur on NO adsorption and decomposition over a polycrystalline Pd surface by means of A.e.s. and u.P.s.~ However, in view of the lack of information concerning interactions between adsorbed molecules, there still remains some ambiguity in describing the multiple structures and stability of NO on Pd metal over a wide temperature range. The present study was undertaken to obtain as much information as possible on interactions in the Pd-NO system, especially by taking into account the admolecule interaction and the reactivity of adsorbed species as a function of temperature with the aid of i.r., t.d.and X.P.S. techniques. In this regard, the effects of preadsorbed chemical species such as oxygen and carbon monoxide were also investigated. In addition, a bond-energy-bond-order (BEBO) calculation6 was applied to ascertain the validity of the mechanism proposed for the desorption and surface reaction of NO. 171172 NO ADSORPTION ON Pd SURFACES EXPERIMENTAL The preparation of silica-supported palladium used for the i.r. study was carried out in a manner similar to that used by Palazov et al.' The Aerosil silica 130, from the Nihon Aerosil Co., was impregnated with a dilute hydrochloric acid solution of palladium chloride, dried at 423 K and then pressed into discs with a thickness of ca.0.2 mm. The concentration of Pd metal loaded was ca. 5 wt %. In another method of preparation, the silica was pressed into discs and dipped into the solution described above for impregnation; there was no significant difference in the NO spectra obtained. Before NO adsorption, the samples were subjected to in situ reduction with 10 Torr of hydrogen at 773 K and were evacuated at that temperature until the residual pressure fell below 2 x Torr (1 Torr = 133.3 Pa).' This pretreatment provided reproducible i.r. spectra of NO. The samples were heated by an infrared lamp (Osram 25) and the temperature was measured on a Pt-Pt/ 13 % Rh thermocouple. Infrared spectra were recorded at room temperature on a Hitachi 285 spectrometer.The absorption due to the silica support was almost compensated by inserting a Pd-free silica disc in the light path of the reference beam. For the thermal desorption study, palladium powder was prepared by reducing a dilute hydrochloric acid solution of palladium chloride with sodium borohydride. The powder was rinsed thoroughly with ion-exchanged water, dried at room temperature and then reduced in the t.d. cell with 10 Torr of H, at 773 K for 2 h. The surface area of the treated Pd was determined to be 0.9 m2 g-l by a B.E.T. measurement at 77 K using Kr gas. The t.d. spectra were obtained on a high-vacuum apparatus equipped with a Pirani gauge (Wakaida Rigaku, model PG-2) and an ion gauge (Wakaida Rigaku, model VG-51) for pressure measurements, and a quadrupole mass spectrometer (Mitsubishi Electronics, model MF-T,M) for gas analysis.The temperature of the samples was raised at constant rates of 10-20 K min-l by an electric furnace and monitored by a Pt-Pt/l3% Rh thermocouple which was brought into direct contact with the Pd samples. X-ray photoelectron spectra were recorded at room temperature on a Hewlett Packard 5950A ESCA spectrometer with monochromatized A1 Ka exciting radiation. A palladium foil of 99.99% purity, obtained from the Johnson Matthey Ltd, was used. After being etched with aqua regia and thoroughly rinsed with ion-exchanged water, the surface was cleaned in the X.P.S. preparation chamber by cycles of prolonged argon-ion bombardment and annealing at 1023 K in a similar manner to that used by Lloyd et In addition, the Pd powder described above was prepared in the form of discs and used as sample for X.P.S. after reduction in the X.P.S.chamber with a few Torr of hydrogen at 773 K. The Au 44 line, 84.0 eV, was taken as reference. Nitric oxide (99.9% purity), CO (99.5%),0, (99.8%) and H, (99.999%) were obtained from the Takachiho Shoji Co. NO was purified by prompt evacuation at 77 K and by passing through a trap cooled to 173 K. The other gases were used without further purification. RESULTS INFRARED SPECTRA The adsorption of NO on the Pd powder surface at 195 K provided 8.7 x 1014 molecule cm-2 as the saturation amount; this value was assumed to correspond to the surface coverage ON, = 1. In the i.r. experiments, the surface coverage of NO on the silica-supported Pd surface was determined according to this definition, since no adsorption occurred at room temperature on the silica support.Fig. 1 shows the i.r. absorption bands of NO adsorbed at 298 K with different values of ONo. In the region of 1350-2500 cm-l there were three characteristic peaks, i.e. a at 1750-1730 cm-l, PI at 1660-1650 cm-l and Pz at 1580-1570 cm-l. The relative intensities of these three peaks were dependent on the adsorption time as well as on ONo. As time elapsed, the intensity of the a peak was gradually attenuated, being accompanied by the enhancement of the P1 and P2 absorption bands. As soon as the spectra showed little change, the peak area of the respective absorption bands was integrated and plottedS. MORIKI, Y.INOUE, E. MIYAZAKI A N D I. YASUMORI 173 10( 9 ( aJ E Y .- E 2 c Y 8C I I I 1 IS00 1700 1600 1500 wavenumber/cm -’ FIG. 1 .-1.r. spectra of NO adsorbed at 298 K on silica-supported palladium: (1) ONO = 0.13, (2) 0.60 and (3) 0.77. as a function of ONo. As is shown in fig. 2, the values for the a, and p2 peaks increased with ON,, passed through a maximum at ON, z 0.6 and then diminished, whereas the value for the a peak enhanced monotonically with a steep rise at ON0 x 0.6. Fig. 3 shows the variation in the i.r. spectra of the adsorbed NO as the evacuation temperature was raised; the a peak drastically decreased and disappeared at 573 K, whereas the p1 peak reached a maximum at ca. 430 K with shifts towards the higher-frequency side. The p2 peak continued to grow up to 573 K, shifting to the lower-frequency side by 30 cm-l.Fig. 4 shows the effects of preadsorbed oxygen upon the adsorbed state of NO. The a peak remained nearly unchanged in peak position but became slightly asymmetric as a consequence of broadening at the higher-frequency side, whereas the /I1 peak appeared at the higher-frequency position by 20 cm-l. The p2 peak shifted by 50-60 cm-l to the lower-frequency side and was close in frequency to the p2 peak observed in spectra (3) and (4) in fig. 3. When this surface was evacuated at elevated temperatures up to 493 K, the intensities of the a and p1 peaks changed in a manner analogous to the above-mentioned behaviour of the corresponding peaks on an oxygen-free Pd surface. On the other hand, no significant variation was observed in the peak position of the p2 absorption band.The adsorption of CO on the silica-supported Pd surface gave rise to three peaks at 2105,1995 and 1820 cm-l at 298 K which were similar to those reported by Palazov et a1.’ The former two peaks shifted to 2065 and 1970 cm-l, respectively, on evacuation at 363 K. Fig. 5 shows the i.r. spectral variations as a function of evacuation174 NO ADSORPTION ON Pd SURFACES 0.2 0.4 0.6 0.8 0 NO FIG. 2.-Variations in peak areas as a function of BNO: 0, a; 0, B, and a, /I2. ' \ 1 I I I I 1800 1700 1600 1500 wavenumber/cm-' FIG. 3 . 4 . r . spectral changes with increasing temperature of evacuation (Bw0 = 0.77): (1) evacuated at 298 K (-), (2) at 428 K (--.--.), (3) at 493 K (. . .) and (4) at 573 K (---).S. MORIKI, Y.INOUE, E. MIYAZAKI A N D I. YASUMORI 175 1 80 I 1 I I I 1800 1700 1600 1500 waven urn be r/c m FIG. 4.-1.r. spectra of NO adsorbed on oxygen-preadsorbed Pd and their changes with evacuation temperature. Amount of oxygen preadsorbed = 2 x lox4 molecules cm-2; PNo = 1 Torr. (1) Evacuated at 298 K (--.--.-), (2) at 373 K (-) and (3) at 493 K (------). t I 1 I I I I I 2100 2000 1900 1800 1700 1600 1500 waven urn ber/cm-' FIG. 5 . 4 . r . spectra of NO and CO coadsorbed on Pd surface. PNo = Pco = 0.5 Torr. (1) Evacuated at 298 K (-), (2) at 403 K (----.-) and (3) at 573 K (. . . . . .). temperature after a clean Pd surface was exposed to an equimolar mixture of NO and CO. In comparison with the adsorption of single species of CO or NO, coadsorption spectra at 298 K were characterized by an appreciable enhancement of the peak relative to the & peak and by the occurrence of a specific peak at ca.1890 cm-l. By evacuation at 523 K, the CO absorption bands in the region 1900-2100 cm-l were readily removed, in contrast to their high stability in the absence of coadsorbed NO.176 NO ADSORPTION ON Pd SURFACES THERMAL DESORPTION SPECTRA Fig. 6 shows the variations in the t.d. spectra of NO adsorbed on a clean Pd surface as a function of 8NO. For 8NO < 0.4 the desorbed gas was only N,, the peak of which was recorded at 483 K with a shoulder on the high-temperature side; at ON, = 0.5 an additional peak of N,O appeared at ca. 490 K. The appearance of another broad NO peak at 373-473 K was delayed until ca.0.7 monolayer coverage was attained. The t.d. spectra from the surface saturated by the adsorption at 195 K exhibited one more broad peak of NO at ca. 333 K. No oxygen was liberated up to 773 K. The detailed quantitative relationships between ONO and the t.d. peak areas of the respective desorbing species are demonstrated in fig. 7. Fig. 8 shows the effects of preadsorbed oxygen upon the t.d. spectra of NO; a clean Pd surface was pre-covered by oxygen with different surface coverages at 273 K and then exposed to NO gas at the same temperature. As the amount of preadsorbed 300 400 500 600 temperature/K FIG. 6.-T.d. spectra of NO as a function of BNO. (a) Total pressure: (1) ONO = 0.04, (2) 0.18, (3) 0.36, (4) 0.54, (5) 0.73, (6) 0.86 and (7) 1.0. (b) Gaseous composition of spectrum (5) (ONO = 0.73).(c) Gaseous composition of spectrum (6) (ONO = 0.86).S. MORIKI, Y. INOUE, E. MIYAZAKI AND I. YASUMORI 177 oxygen increased, the desorption of N, and N,O was depressed, whereas the desorption of NO at 393 K tended to increase. Fig. 9 shows the t.d. spectra after the Pd surface was exposed to NO and then to CO. When the concentration of adsorbed NO was fixed at 3 x 1014 molecule ern-,, the amount of CO changed from 1 x 1014 to 5 x 1014 molecule ern-,; the main spectral feature was the desorption of CO, and N, as very sharp peaks at ca. 443 K, in addition to a broad peak of CO at ca. 383 and 585 K, although a small N, peak appeared at 530 K in the case of low CO coverage. When the preadsorbed NO was increased to 6 x 1014 molecule ern-,, the t.d.spectra after CO adsorption of 6 x 1014 molecule cm-, were much the same except that an extra peak for NO appeared at ca. 390 K. There was no significant change in the t.d. spectra on reversing the gas admission. 1.0 h m + .- I= -E v 0.6 4 4 m .- c W I= U .- x 2 Y w I= U .d 0.2 0 x 2 x 2 0.2 0.4 0.6 0.8 1 .o 0 NO FIG. 7.-Variations in integrated intensity of t.d. peak with ON0: a, N,; 0, N,O and 0, NO. X-RAY PHOTOELECTRON SPECTRA As is shown in fig. lO(a), the X-ray photoelectron spectra of NO adsorbed at 298 K on a Pd foil surface exhibited a broad and asymmetric N 1s peak at 398.7 eV (peak I). This characteristic structure was consistent with that observed previously.2 Evacuation at 453 K caused an additional peak at 404.0 eV (peak 11) together with little change in the position of peak I (398.5 eV) but a slight broadening towards the higher binding-energy side, On evacuation at 533 K, the position of peak I remained unchanged, whereas peak I1 appeared at 404.3 eV with an enhanced intensity.As is shown in fig. lO(b), the Pd powder surface provided almost the same N 1s photoelectron spectra at 298 K and at elevated temperatures; the binding energy of peak I in spectrum (1) was 398.7 eV, whereas those of peaks I and I1 in spectrum (2) were 398.6 and 404.2 eV, respectively. From the 0 1s region we failed to obtain useful information, since a large peak due to the Pd 3pt line interfered with the analysis of the 0 1s peak of adsorbed NO.178 NO ADSORPTION ON Pd SURFACES n e m * .I -2 2 v ?-.c ." Y e .- 'a) 300 400 500 60 0 temperature/K FIG. 8.-T.d. spectra of NO adsorbed on oxygen-preadsorbed Pd surface: (a) N,O, (b) N, and (c) NO. amount of oxygen amount of atom cm-, molecule cm-, preadsorbed/ 1014 ~0/1014 (-) 0.0 (--) 1.2 ( * * * I 0.3 (---) 2.4 (-. .-) 3.6 8.7 8.6 7.4 6.3 5.4 DISCUSSION In the chemistry of transition-metal nitrosylsgv lo there are three types of bonding between the metal and the NO molecule; they are known as the linear, bent and bridge forms. In the linear form, NO is present as nitrosonium ion and gives absorption bands above 1700 cm-l. The bent form is associated with NO- and provides characteristicS. MORIKI, Y. INOUE, E. MIYAZAKI A N D I. YASUMORI 179 400 500 600 temperature/K FIG. 9.-T.d. spectra after exposure of Pd surface to CO and then NO: (1) amount of CO adsorbed = 5 x 1014 molecule cm+, amount of NO adsorbed = 3 x 1014 molecule cm-2 (-); (2) amount of CO adsorbed = 1 x 1014 molecule cm-2, amount of NO adsorbed = 3 x 1014 molecule (---).absorption bands at 1700- 1500 cm-l. The bridged nitrosyl structure, being similar to that of carbonyls, is found in Ru(CO),,(NO), and Os(CO)l,(NO), complexesll to give rise to absorption bands at ca. 1500 cm-l. By analogy with these nitrosyl complexes one can assign the a peak to the N-0 stretching vibration due to NO in the linear form. The /I1 and #I2 peaks may not be unequivocally assigned but they are character- istic of N-0 stretching vibrations ascribable to either the bent or bridged structure. In accordance with these results, the broad but single N 1s photoelectron peak at ca.399 eV revealed that only molecularly adsorbed NO was formed at room temperature, and it is likely that its asymmetric shape involved at least two molecular states, i.e. linearly and bridge-bonded NO, as was proposed for the N 1s spectra of NO adsorbed on the Ru(OO1) plane below 200 K.12 For NO adsorption with ON, < 0.6, the i.r. spectral change with time was a decrease in the a peak and in turn an increase in the /I peaks, leaving the total amount of adsorbed NO almost unchanged. This phenomenon resembles that observed in the i.r. spectra of CO adsorbed on silica-supported Pd,' and is interpreted in terms of the delay in establishing an equilibrium among the adsorbed species ; the energetically more stable state is attained through the surface migration or hopping of NO, for which some activation energy is necessary.The fact that heating 2t 373 K can accelerate the transfer from the a to the /I state supports this view. With increasing NO coverage, the /3 peaks passed through a maximum and decreased, whereas the180 NO ADSORPTION ON Pd SURFACES ------- I I I I I I 412 408 404 400 396 3 92 binding energyleV FIG. 10.-X-ray photoelectron spectra in N 1s region: (a) Pd foil, (b) Pd powder. (1) Exposed to 1.5 Torr of NO for 8 min at 298 K and evacuated at the same temperature; (2) evacuated at 453 K ; (3) evacuated at 533 K. a peak grew markedly, suggesting that part of the former species was converted into the latter. The consolidation of the above-mentioned findings leads to the following description of stoichiometric and structural variations of adsorbed NO.For ON, < 0.6, where there exists little conformational restriction arising from repulsive interactions between the neighbouring admolecules, the adsorbed species certainly undergo interaction with the Pd metal surface; the bridged structure, bound to two surface atoms, seems to be favoured. This is substantiated by the finding that the /? species produced at an initial stage of adsorption gave rise to a lower frequency for the N-0 stretching vibration. For ON, > 0.6, a densely-packed situation will turn the adsorbed NO into a linear form which corresponds to the a state. The fact that the a species was desorbed at lower temperature than the p species, as is described later, gives support to this view.The t.d. spectra provided the three characteristic desorption peaks. From a correspondence between the temperature-dependence and dependence of amount adsorbed observed in the i.r. and t.d. spectra, the aforementioned a, PI and /?, peaks were respectively associated with the adsorbed species desorbing as NO at 273-373 K, N, (partly N,O) at 473 K and N, (partly N,O) at 530 K. A possible mechanism of N, formation is described by the following processes: k , k-1 NO(a) G N(a) + O(a) k* N(a) -+ #N,S. MORIKI, Y. INOUE, E. MIYAZAKI A N D I. YASUMORI 181 where ki is the forward rate constant for the ith step and k-i designates the reverse rate constant. The symbol (a) represents an adsorbed state. The change in surface coverage of N(a), ON, with time during thermal desorption, d6,/dt, and the rate of N, desorption, rd, are respectively given by dB, = k , 6 ~ 0 - k - , ONO0 - 2k2 6 i dt (3) in the low concentration range of NO(a) and rd = k,8& (4) where 6, denotes the surface coverage of O(a).Replacing eqn (3) in eqn (4), we obtain When ON, was changed to low coverages, no significant shift in the maximum of the N, peak was observed, indicating that the rate of desorption is first-order with respect to ON,. While this relationship is satisfied in eqn (4) for several cases, it is more plausible that k,ONo $ k-,ONOO or d6,/dt, i.e. the dissociation of NO(a) is rate-determining. Another possible pathway for N, desorption is : NO(a) + N(a) -+ N, + O(a) (6) which competes with N,O formation.Based on the BEBO calculation,6 we have tried to evaluate the activation energy, E,, for the three forward steps (I), (2) and (6). The variation in energy as a function of the bond order of the N-N and N-0 bonds is shown in fig. 11 ; the values of E, were 146, 121 and 218 kJ mol-l, respectively, for the above three steps, which indicates that step (2) is preferred to step (6) in N, formation. By assuming a pre-exponential term of 1 x 1013 s-l in the first-order desorption, the activation energy of N, desorption can be evaluated to be 134-151 kJ mol-l, which is close to the calculated value for step (1). The slow decomposition of a dimeric nitric oxide which was observed on silica-supported chromia13 might participate in the N, formation, but this possibility was probably excluded in the present case, since no evidence for the species was given in the i.r.spectra. The present t.d. spectra agreed with those obtained by Conrad et aL314 for NO adsorbed on a Pd(ll1) surface in the two peaks of NO below 370 K and in the small amounts of N,O desorbed at ca. 480 K, but they differed in exhibiting N, desorption instead of NO at ca. 480 K. Such a difference is presumably due to the specific morphology of the polycrystalline surface; judging from the structure of catalytic active sites on Pd foils for the hydrogenation of C,H, and C2H4,14 it is likely that surface imperfections and/or high-index planes facilitate the dissociation of NO at high temperatures. At elevated temperatures, 428-573 K, the i.r. spectra showed a shift of the p1 peak to the higher-frequency side and of the b2 peak to the lower-frequency side.In the X-ray photoelectron spectra, peak I1 appeared at the higher binding-energy side, in addition to the broadening of peak I. Since the resulting i.r. spectra were in substantial agreement with those of NO adsorbed on the oxygen-covered Pd surface, and since the t.d. spectra provided the decomposed species in this temperature range, it is evident that the changes in these spectra were ascribable to the effect of surface oxygen produced by NO decomposition. The effects of preadsorbed oxygen on a clean Pd surface were the depression of N,182 NO ADSORPTION ON Pd SURFACES and N,O desorption but the enhancement of NO desorption in the t.d. spectra, whereas they were the shift of the /I1 peak to higher frequency and of /3, to lower frequency in the i.r.spectra. The oxygen atoms on the Pd metal surface become electron acceptors, as is revealed by the increase in the work function upon 0, adsorption,15 and could affect the metal by lessening the back-donation to the 2n* orbital of the NO molecule. The shift in the peak (and presumably the broadening of peak I in the X-ray photoelectron spectra) can be associated with this effect. Thus, the N-0 bond is thought to be strengthened, and it follows that NO desorption is preferred to dissociation. Another effect of the preadsorbed oxygen is to reduce the number of active sites available for NO dissociation. bond order, N - 0 1.6 1.2 0.8 0.4 0 I 1 I 3 1 2 3 bond order, N - N FIG.1 1 .-Interaction energy plotted against bond orders of N-0 and N-N. (1) NO(a) -+ N(a) + O(a), (2) 2N(a) -+ N,(g), (3) NO@) + N(a) -+ N, + O(a>. The shift of the /?, peak to the opposite-frequency side can be attributed to the formation of a surface-bridged structure, i.e. \ 0 N----O I I * * through the direct interaction between the surface oxygen and nitrogen atom of the NO molecule. This assignment is reasonable, since our preliminary results for NO,S. MORIKI, Y. INOUE, E. MIYAZAKI A N D I. YASUMORI 183 adsorption on the Pd surface gave a band at ca. 1535 cm-l, and the region 1500 20 cm-l was characteristic of the N-0 stretching vibration ascribable to the NO, bridge-ligand.16 The appearance of peak I1 to higher binding energy in the X-ray photoelectron spectra also gives support to the presence of this species with the direct interaction of the nitrogen atom with surface oxygen, since a similar N 1s line was observed in NO, adsorption on Ni." Another plausible assignment is a nitrato bidentate species as proposed for Fe and Ni metals,ls but this possibility is excluded since there was no broad peak in the range 1350-1450 cm-l which is characteristic of this bidentate species.The effect of coadsorption of NO and CO on the Pd surface at room temperature was a slight shift in the PI peak to higher frequency with a considerable enhancement of its intensity, as well as a shift in the CO bands to lower frequency. These findings suggest that /I,-NO and CO on the Pd surface can interact with each other, for instance in a manner similar to that observed in the metal complex, [IrCl(NO) (CO) (P(C6H5)3)2]+, in which the CO and NO ligands form a donor-acceptor-like complex through the interaction of a lone pair on the oxygen atom of the bending NO with an empty 2n* orbital on the CO At higher temperatures the coadsorption of CO and NO resulted in the desorption of N, and CO, at almost the same temperature, 440 K.Thus the following reaction pathway can be proposed : NO@) + CO(a) + (*) -+ N(a) + O(a) + CO(a) -+ 4=N2 + CO, + 3(*) (7) where (*) denotes a vacant site. The feature of this pathway is the remarkable increase in the number of vacant sites during the course of the reaction, which was similar to the autocatalytic mechanism proposed for the decomposition of formic and acetic acids adsorbed on the Ni(ll0) surface.2o Therefore, step (7) could lead to the accelerated evolution of N, and CO,, which was well reflected by the remarkably narrow peak width in N, and CO, desorption.J. Kuppers and H. Michel, Surf. Sci., 1979, 85, L201. K. Kishi and S. Ikeda, Bull. Chem. Soc. Jpn, 1974, 47, 2532. H. Conrad, G. Ertl, J. Kuppers and E. E. Latta, Surf. Sci., 1977, 65, 235; 245. * H. Conrad, G. Ertl, J. Kiippers and E. E. Latta, Furuday Discuss. Chem. Soc., 1975, 58, 116. Y. Matsumoto, T. Onishi and K. Tamaru, J. Chem. SOC., Furuday Trans. I, 1980, 76, 1 116. E. Miyazaki, J. Cutul., 1980, 65, 84, and references herein. A. Palazov, C. C. Chang and R. J. Kokes, J. Cutal., 1975, 36, 338. P. Finn and W. L. Jolly, Znorg. Chem., 1972, 11, 893. and G. Wilkinson, J. Znorg. Nucl. Chem., 1958, 7, 38. E. Umbach, S. Kulkarni, D. Feulner and D. Menzel, Surf. Sci., 1979, 88, 65. Y. Inoue and I. Yasumori, J. Phys. Chem., 1971,75,880; I. Yasumori, T. Kabe and Y. Inoue, J. Phys. Chem., 1974, 78, 583; I. Kojima, E. Miyazaki and I. Yasumori, Appl. Surf. Sci., 1980, 6, 93. R. E. LaVittaandS. H. Bauer, J. Am.Chem.Soc., 1963,85,3597;C. C. AddisonandB. M. Gatehouse, J. Chem. Soc., 1960, 613. C. R. Brundle, J . Vuc. Sci. Technol., 1976, 13, 301. * D. R. Lloyd, C. M. Quinn and N. V. Richardson, Surf. Sci., 1977, 63, 174. l o J. Lewis, R. J. Irving and G. Wilkinson, J. Znorg. Nucl. Chem., 1958, 7, 32; W. P. Grifith, J. Lewis l 1 J. R. Norton, J. P. Collman, G. Dolcetti and W. T. Robinson, Znorg. Chem., 1972, 11, 382. l 3 E. L. Kugler, R. J. Kokes and J. W. Grydner, J. Cutal., 1975, 36, 142. l 5 P. R. Norton, Surf: Sci., 1974, 44, 624. l 8 G. Blyholder and M. C. Allen, J. Phys. Chem., 1966, 70, 352. lB D. G. Hodgson and J. A. Ibers, Znorg Chem., 1968, 7, 2345. *O J. McCarty, J. Falconer and R. J. Madix, J. Cutal., 1973, 30, 235; R. J. Madix, J. L. Falconer and A. M. Suszko, Surf: Sci., 1976, 54, 6. (PAPER 1 / 153)

ISSN:0300-9599    

DOI:10.1039/F19827800171

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1982, 78, 185-195 Thermal Conductivity of Binary Gaseous Mixtures Containing Diatomic Components BY MARC J. ASSAEL AND WILLIAM A. WAKEHAM* Department of Chemical Engineering and Chemical Technology, Imperial College, Prince Consort Road, London SW7 2BY Received 3rd February, 198 1 Absolute measurements of the thermal conductivity of binary mixtures of hydrogen +nitrogen, helium +carbon monoxide and argon +carbon monoxide are reported. The measurements were performed in a transient hot-wire instrument at a temperature of 35 OC and in the pressure range 1.8-8 MPa; the reported data have an estimated uncertainty of +0.2%. The experimental results for hydrogen +nitrogen have been interpreted with the aid of the semi-classical kinetic theory expressions of Monchick, Pereira and Mason.It has been found that the theoretical relationship is not as accurate as the experimental data although, if more accurate theory were available, rotational collision numbers for relaxation of nitrogen by hydrogen could be derived from the measurements. A recently proposed scheme for the evaluation of the effect of density on the thermal conductivity of gas mixtures provides a satisfactory description of the experimentally observed first density coefficient in the density expansion of the thermal conductivity. The modern version of the transient hot-wire technique provides a means of determining the thermal conductivity of gases with an uncertainty of &0.2%. In a number of recent publications the technique has been applied to the pure monatomic gases and some of their mi~tures,l-~ to pure polyatomic g a ~ e s ~ - ~ and to some of their binary mixtures with monatomic specie^.^? The measurements have been carried out over a range of densities and near to room temperature.In the limit of zero density the measurements upon systems containing polyatomic components are probably the more important because the kinetic theory underlying the description of the thermal conductivity is less well-developed than for the monatomic species and is essentially untested against accurate experimental data. However, at elevated densities theories for both monatomic and polyatomic species are less than complete and the new data provide one means of assessing their current status. In this paper we extend our studies to two further systems involving diatomic and monatomic components (mixtures of helium and argon with carbon monoxide) and to a system involving two diatomic molecules (mixtures of hydrogen with nitrogen).The unexpected differences which have been observed between the thermal conductivity of pure carbon monoxide and that of pure nitrogen mean that the former systems contribute to a study which is analogous to that of Fleeter et aL7 concerning mixtures of nitrogen with the monatomic gases. The latter system represents the simplest type of mixture involving two diatomic species because the very slow relaxation of the rotational energy of hydrogen implies that only two relaxation times in the mixture are significant. 185 FAR 1186 THERMAL CONDUCTIVITY OF BINARY GAS MIXTURES EXPERIMENTAL A description of the transient hot-wire instrument employed for the measurements as well as of the necessary working equations has been given e1sewhere.l' 9* lo The instrument was used without alteration for the measurements on the hydrogen + nitrogen mixtures but prior to the measurements on the mixtures containing carbon monoxide a new set of platinum wires was installed in the cells.The lengths of the new wires were 1, = 161.11 mm and 1, = 63.53 mm for the long and short wire, respectively. In order to confirm the continued correct operation of the instrument following this change, the thermal conductivities of helium and argon were remeasured. In no case did the results of these repeated measurements depart by more than +0.2% from the correlation of the original data.' The measurements reported here, on three mixtures of hydrogen with nitrogen and two mixtures each of helium and argon with carbon monoxide, were carried out at 35 OC and in the pressure range 1.8-8 MPa. The mixtures were manufactured gravimetrically from pure gases supplied by Matheson and British Oxygen Ltd; the stated purity of the gases was in no case worse than 99.995%.The density of the mixtures at the equilibrium temperature of the cells, T,, was determined directly in situ as described earlier and the small correction of this density to the reference temperat~re,~ T,, was applied with the aid of the available pVT data.ll The uncertainty in the reported density is estimated to be of the order of & 0.3 % in the worst case.TABLE 1 .-THERMAL CONDUCTIVITY OF HYDROGEN + NITROGEN MIXTURES AT T,,, = 35 OC, xH2 = 0.7338 2.23 2.82 3.41 4.00 4.65 5.38 6.25 7.27 30.49 30.48 30.48 30.46 30.47 30.50 30.44 30.46 8.03 10.09 12.35 14.26 16.40 19.06 22.01 25.36 35.18 35.09 35.02 34.94 34.89 34.87 34.75 34.63 7.91 9.95 12.17 14.05 16.17 18.80 21.70 25.02 116.1 116.3 116.4 116.7 116.9 117.2 117.4 117.7 1 16.0 116.3 116.4 116.7 116.9 117.2 117.5 117.8 (i3A/i3T)350c = 0.368 mW m-l K-2. RESULTS Tables 1-3 contain the experimental thermal conductivity data for mixtures of hydrogen and nitrogen with mole fractions xH2 = 0.7338, xH2 = 0.4865 and xHq = 0.2136, respectively. Tables 4 and 5 contain the results for mixtures of helium +carbon monoxide with xHe = 0.7403 and xHe = 0.2404, respectively, whereas tables 6 and 7 list the data for the argon+carbon monoxide mixtures with xAr = 0.7036 and xAr = 0.4080, respectively.In each case, in addition to the thermal conductivity at the reference temperature A( q, pr), we report the thermal conductivity corrected to a nominal temperature, Trio, = 35 OC. The correction to the nominal temperature has been accomplished with the aid of the equation For the purpose of this correction, it has been assumed that the derivative (8A/8T),M. J. ASSAEL AND W . A. WAKEHAM 187 TABLE 2.-THERMAL CONDUCTIVITY OF HYDROGEN + NITROGEN MIXTURES AT T,,, = 35 OC, xHZ = 0.4865 1.66 2.13 2.46 3.26 3.92 4.58 5.30 6.14 7.16 30.50 30.46 30.5 1 30.54 30.52 30.58 30.52 30.55 30.48 10.54 13.23 16.55 20.14 24.12 28.02 32.39 37.34 43.21 35.42 35.23 35.25 35.12 35.09 35.07 34.89 34.88 34.71 10.38 13.03 16.30 19.84 23.77 27.62 3 1.94 36.83 42.63 74.80 74.83 74.98 74.99 75.08 75.13 75.31 75.50 75.71 74.69 74.77 74.92 74.96 75.06 75.1 1 75.34 75.53 75.78 TABLE 3.-THERMAL CONDUCTIVITY OF HYDROGEN+NITROGEN MIXTURES AT TnOm = 35 OC, xHz = 0.2136 2.02 2.72 3.33 3.88 4.68 5.41 6.28 7.31 30.51 30.46 30.50 30.50 30.47 30.51 30.46 30.49 18.13 24.67 29.99 34.89 41.89 48.26 55.88 64.7 1 35.29 35.06 35.02 34.95 34.83 34.79 34.62 34.60 17.86 24.3 1 29.56 34.40 41.31 47.60 55.14 63.86 44.72 44.99 45.17 45.22 45.52 45.73 46.06 46.35 ~~~ ~ 44.68 44.98 45.17 45.23 45.54 45.77 46.12 46.4 1 (aA/aT)35oc = 0.150 mW m-' K-2.TABLE 4.-THERMAL CONDUCTIVITY OF HELIUM + CARBON MONOXIDE MIXTURES AT TnOm = 35 OC, x H e = 0.7403 2.20 2.86 3.48 4.17 5.00 5.69 6.50 7.41 30.34 30.33 30.33 30.33 30.30 30.28 30.24 30.19 9.12 11.52 13.96 16.72 19.97 22.51 25.43 28.85 34.82 34.69 34.64 34.56 34.47 34.42 34.3 1 34.3 1 8.99 11.36 13.76 16.49 19.71 22.21 25.10 28.47 93.51 93.82 93.89 94.04 94.38 94.74 94.86 94.24 93.56 93.90 93.99 94.16 94.52 94.90 95.05 95.42 (aA/aT),,., = 0.274 mW m-' K-2.7-2188 THERMAL CONDUCTIVITY OF BINARY GAS MIXTURES TABLE 5.-THERMAL CONDUCTIVITY OF HELIUM + CARBON MONOXIDE MIXTURES AT Tnom = 35 O C , xHe = 0.2404 2.21 2.86 3.58 4.42 5.04 5.73 6.56 7.48 30.73 30.75 30.73 30.75 30.67 30.51 30.38 30.37 19.69 25.13 31.77 38.85 44.35 50.28 57.08 65.02 34.96 34.88 34.76 34.70 34.53 34.31 34.09 34.04 19.42 25.08 31.37 38.37 43.67 49.67 56.41 64.26 40.09 40.30 40.56 40.80 40.97 41.17 41.46 41.81 40.10 40.32 40.59 40.84 41.03 41.26 41.58 41.94 (i3A/i3T)350c = 0.130 mW m-l KP2.TABLE 6.-THERMAL CONDUCTIVITY OF ARGON + CARBON MONOXIDE MIXTURES AT Tnom = 35 O C , x A r = 0.7036 2.14 2.96 3.67 4.35 5.08 5.76 6.54 7.55 30.27 31.00 30.28 43.64 30.25 54.24 30.23 64.77 30.23 74.45 30.23 85.87 30.22 97.3 1 30.22 110.6 35.30 35.08 34.90 34.74 34.61 34.56 34.40 34.35 30.50 42.97 53.44 63.84 73.41 84.68 96.01 109.1 2 1.09 21.43 21.69 21.97 22.27 22.54 22.89 23.27 2 1.08 21.43 21.69 21.98 22.29 22.56 22.92 23.30 (dA/aT)350, = 0.053 mW m-l K-2. TABLE 7.-THERMAL CONDUCTIVITY OF ARGON + CARBON MONOXIDE MIXTURES AT TnOm = 35 O C , x A r = 0.4080 1.84 2.64 3.25 3.98 4.51 5.11 5.79 6.40 7.37 30.25 30.30 30.30 30.29 30.28 30.27 30.27 30.27 30.25 24.35 35.12 42.98 52.80 59.93 68.13 77.27 87.40 98.97 36.18 35.90 35.74 35.57 35.48 35.29 35.18 35.07 34.94 23.89 34.49 42.23 51.91 58.94 67.03 76.05 86.06 97.49 23.28 23.50 23.78 24.13 24.37 24.64 24.89 25.14 25.59 23.21 23.45 23.74 24.09 24.34 24.62 24.88 25.14 25.59 (i3A/i3T)350c = 0.056 mW m-l K-2.M.J. ASSAEL A N D W. A. WAKEHAM 189 is independent of density and equal to the derivative in the limit of zero density. The derivative itself has been estimated by means of the Hirschfelder-Eucken equation12 and experimental viscosity data for the mixtures of hydrogen and nitrogen.13 In the cases of the mixtures involving carbon monoxide viscosity data are not available and the derivative has therefore been obtained from the Hirschfelder-Eucken equation with the aid of estimates for the parameters of a Lennard-Jones (12-6) potential characteristic of the unlike interaction.In any event, because the correction does not exceed 0.2%, the additional uncertainty introduced into the reported thermal conductivity is negligible. The entire set of experimental thermal conductivity data for each gas mixture at the nominal temperature has been correlated by means of an equation of the form A@) = a, -+ alp + a&. (2) TABLE 8.-cOEFFICIENTS IN THE CORRELATING POLYNOMIAL OF EQN (2) FOR THE DENSITY DEPENDENCE OF THE THERMAL CONDUCTIVITY OF THE GAS MIXTURES a,lmW allPW a2lnW std. dev., m2 kg-l K-l m5 kg-2 K-l 0 (%) mixture ,-1 K-1 H2+N2 XHn - - 0.2136 44.02 37.3 xHo = 0.4865 74.33 32.3 x H ~ - 0.7338 115.2 105.5 xHe = 0.2404 39.45 32.0 He + CO xHe = 0.7403 92.72 94 Ar + CO xAr = 0.4080 22.39 32.6 xAr = 0.7036 20.28 25.3 - k 0.09 - f 0.06 - f 0.02 101 f 0.05 - + 0.08 - - k0.15 21 f 0.08 The coefficients a,, a, and a, which secure the best representation of this kind are collected in table 8, together with the standard deviation of the fit.Fig. 1 and 2 contain plots of the deviations of the experimental results from the correlation for hydrogen + nitrogen and the systems containing carbon monoxide, respectively. In neither case do the deviations from the correlation exceed &0.25%. The experimental data have been subjected to the statistical analysis described elsewhere14 in order to determine best estimates for the zero-density thermal con- ductivity of the mixtures, A,, as well as of the first density coefficient, c,, in the (3) expansion The values thus derived are listed in table 9, together with their standard deviation and the corresponding values for the pure gases obtained earlier.6 In the cases where a quadratic representation of the data according to eqn (2) is necessary, the coefficients a, and c, of tables 8 and 9 do not quite overlap within their standard deviations.This is because only two or three points lie within the range requiring a quadratic fit so that the statistical basis for the error estimate is not reliable. A = A0+c1p+czp2+. . . .190 O 0.2 41 X tl 8 x n - --- 8 c I K 6 c i '2 -0.2 Y .M THERMAL CONDUCTIVITY OF BINARY GAS MIXTURES I 1 8 0 8 . 0 ' 8 A A 0 0.: A m 0 A A I I FIG. 1.-Deviations of the experimental thermal conductivity data from the correlation of eqn (2) for mixtures of hydrogen+nitrogen: 0, x H , = 0.2136; ., xH, = 0.4865; A, xH, = 0.7338.0.4 &? 0 X 2 0.2 3 t: x n 8 8 1 c 7 0 * 5 6 Y c .- U ?2 -0.2 -0 -0.4 0 O o 0 0 8 . 0 0 8 0 0 0 I I 25 50 density, plkg m-3 FIG. 2.-Deviations of the experimental thermal conductivity data from the correlation of eqn (2) for mixtures of helium+carbon monoxide: 0, xHe = 0.2404; ., xHe = 0.7403; and for mixtures of argon+carbon monoxide: 0, xAr = 0.4080; 0, xAr = 0.7036.M. J. ASSAEL A N D W. A. WAKEHAM 191 TABLE 9.-BEST ESTIMATES FOR THE ZERO-DENSITY THERMAL CONDUCTIVITY, &, AND THE FIRST DENSITY COEFFICIENT, c,, FOR THE PURE GASES AND MIXTURES AT T,,,, = 35 "c H2+N2 XHn - 0.0 xH2 = 0.2136 xHp - 0.7338 xHZ = 0.4865 XHZ = 1.0 He + CO XHe = 0.0 xHe = 0.2404 xHe = 0.7403 XHe 1.0 Ar + CO XAr = 0.0 xAr = 0.4080 xA,.= 0.7036 XAr = 1.0 26.45 f 0.06 44.02 & 0.04 74.33 f 0.04 1 1 5.21 k 0.03 192.2k0.1 25.68 _+ 0.03 39.34 f 0.03 92.72 & 0.08 158.4 k 0.1 25.68 +_ 0.03 22.39 +_ 0.04 20.20 k 0.02 18.18 f 0.01 37f3 37k 1 32&2 106k2 950 f 30 42_+ 1 39.3 4 0.6 94+4 256 9 42+ 1 32.6 f 0.6 28.2 k 0.3 24.0 f 0.3 DISCUSSION Z E RO-D E N S I T Y THERMAL CONDUCT I V I T Y The most accurate available theoretical formulation for the thermal conductivity of a dilute, binary gas mixture containing polyatomic components is that given by Monchick et aLl2 The thermal conductivity may be written in the form where the first term, Amix(mon), represents the contribution to the thermal conductivity of the mixture from translational energy whereas the second term is the contribution from the transport of internal energy.Together, these two terms constitute the Hirschfelder-Eucken expression for the thermal conductivity.12 The final term, AA, incorporates the explicit effects of inelastic collisions into the theory and is given by a rather cumbersome expression, derived by Monchick et u1.,12 which is omitted here in view of its length. In eqn (4) the symbol At represents the thermal conductivity of pure gas i, Ai(mon) the translational contribution to it and xi the mole fraction of that component in the mixture. The quantity Diint, is the diffusion coefficient for internal energy of component i in component j . Eqn (4) is, essentially, a first-order, semi-classical kinetic theory approximation to the thermal conductivity.It therefore fails to account for any effects arising from spin polarization or from higher-order kinetic theory approximations. At present, the most accurate calculations with eqn (4) must make use of high-quality experimental viscosity data. Therefore, we confine the discussion here to the system hydrogen + nitrogen, which is the only one for which the necessary information is available. Furthermore, because we are interested in the ability of eqn (4) to describe the composition dependence of the thermal conductivity, we identify Ai with the192 THERMAL CONDUCTIVITY OF BINARY GAS MIXTURES experimental value of the pure gas thermal conductivity obtained earlier.’? In this way it is ensured that the data at the end points of the composition range are exactly reproduced by the calculation. The translational contributions to the thermal conductivity of pure hydrogen and nitrogen, as well as the interaction thermal conductivity llij(mon), which occurs in the evaluation of Amix(mon), have been derived from viscosity measurements on the pure gases and their mixtures by means of the relation12*15 15(m, + mj) I,(mon) = 8m,rnj k V i j where qij is the interaction viscosity for i # j , k is Boltzmann’s constant and m, is the mass of a molecule.The same viscosity data have also been used to obtain the diffusion coefficients for internal energy, assuming that they are identical to the mass diffusion There is some evidence that the equality of the diffusion coefficients for internal energy and mass is not exact.ls Nevertheless, the departures from equality are usually smalls and there is no theoretical guidance towards a better assignment so that eqn (6) represents the best possible scheme for estimation at present. The quantity A& which is found in eqn (6), is a ratio of two collision integralsl5 which are functionals of the intermolecular pair potential for the species i andj.Both AS and l?;, a similar collision integral ratio which is found in Lmix(mon), implicitly contain the effects of inelastic collisions in the gas of which account cannot properly be taken at presenf.l5Js These two quantities have therefore been estimated on the basis of elastic collisions only using a Lennard-Jones (1 2-6) potential for the nitrogen + hydrogen system suggested by Kestin and Yata,13 from the potential proposed by Gengenbach et all7 for hydrogen and from the extended law of corresponding states correlation for nitrogen.The remaining quantities required for the evaluation of the thermal conductivity of the mixture occur in the inelastic term All. They are the internal heat capacities of the components and the four rotational relaxation collision numbers, Cij, which quantify the number of collisions necessary for the equilibration of the internal (rotational) energy of the molecules of species i by collision with speciesj.12 The heat capgcity of nitrogen has been taken from the tables of Hilsenrath et al.19 and that of hydrogen from the work of McCarty.20 The rotational collision numbers of nitrogen and hydrogen have been determined by extrapolation of the low-temperature experimental data obtained by Prangsma et aL2’ and Jonkman et a1,22 respectively.In the case of the unlike interactions there are no direct measurements of the collision numbers so that following Monchick et a1.12 it has been necessary to equate them with those for the corresponding pure components. The numerical values of the quantities finally employed in the calculations are collected in table 10. It should be remarked that, in the case of hydrogen, the very slow relaxation of internal energy provides a sound basis for the use of elastic values of A* and B* as well as for the identity of the mass diffusion coefficient with the diffusion coefficient for internal energy according to eqn (6).Furthermore, the large value of the collision number means that even gross errors in it make a negligible contribution to the thermal conductivity. The results of the calculations of the thermal conductivity of the mixtures of hydrogen and nitrogen are contained in table 1 1 together with the Hirschfelder-Eucken results (AA = 0) and the experimental data at zero density. First, note that the inelasticM. J. ASSAEL A N D W . A. WAKEHAM 193 TABLE IO.-DATA EMPLOYED FOR THE CALCULATION OF THE THERMAL CONDUCTIVITY OF HYDROGEN -!- NITROGEN MIXTURES AT T,,, = 35 OC A,,(mon)/mW m-l K-l 141.0 AN2(mon)/mW m-' K-' 18.93 AHlNZ(mon)/mW m-l K-l 73.70 cN2Hz 200 cN2Nz 5.7 200 5.7 4 H 2 1.102 B k H 2 1.091 TABLE 1 1 .-COMPARISON OF THE CALCULATED THERMAL CONDUCTIVITY WITH THE EXPERIMENTAL DATA FOR HYDROGEN+ NITROGEN MIXTURES AT T,,, = 35 O C ~~ hydrogen mole fraction, Hirschfelder-Eucken, full eqn (4), experimental value, Acalc/mW m-lK-l Acalc/mWm-lK-l A,,p,/mWm-lK-l 0.21 36 0.4865 0.7338 43.60 74.15 116.2 43.79 73.96 114.9 44.02 74.33 115.2 term of eqn (4) contributes as much as 1.3 % to the mixture thermal conductivity so that its inclusion in the calculation is essential.Secondly, the deviations of the calculated total thermal conductivity of the mixtures from the experimental data amount to as much as 0.7%. Although this deviation constitutes reasonable agreement, it exceeds the estimated experimental error and, furthermore, the calculation con- sistently underestimates the thermal conductivity. The latter observation is a general characteristic of first-order kinetic theory approximation^^^ and supports the earlier finding that eqn (4) is not as accurate as the best experimental data.8 It would be possible to secure improved agreement with the present experimental data by means of modest, arbitrary adjustment of some of the parameters listed in table 10.For example, numerical experimentation reveals that the calculated thermal conductivity is particularly sensitive to cN2H2, so that it would be possible to determine this quantity from the experimental data. However, the inaccuracy of eqn (4) implies that such an evaluation would be burdened with a systematic error. For this reason we postpone the calculation of the collision number until a more accurate theoretical expression for the thermal conductivity becomes available.ELEVATED DENSITIES Mason and his collaborator~~~ have devised a scheme for the calculation of the thermal conductivity of gas mixtures based upon the modified Thorne-Enskog theory. Their equations reduce to the Hirschfelder-Eucken equation in the limit ofzero-density. Consequently we prefer here to use their procedure to evaluate the coefficient c1 in the density expansion of the thermal conductivity [eqn (3)], because this avoids the systematic error in the absolute thermal conductivity which is incurred as a result of the neglect of the inelastic contributions. Because the calculation again requires the use of dilute gas viscosity data, we are once more limited to a study of the hydrogen + nitrogen system.In order to carry out the calculation in the manner described by Kestin and Wakeham,25 we have made use of the thermal conductivity of the pure gases194 THERMAL CONDUCTIVITY OF BINARY GAS MIXTURES 1000 10 0 0.25 0.50 0.75 1.0 hydrogen mole fraction, XH* FIG. 3.-First density coefficient of thermal conductivity for mixtures of hydrogen +nitrogen. 0, Experimental results; -, calculated using the theory of Mason et aLZ4 The error bars correspond to 2.5 times the standard deviation of the measured coefficient. determined earlier,6 together with the viscosity data of Kestin and Yata.13 In addition, the molecular size parameters for the three interactions in the gas have been obtained from the second virial coefficient tabulations of Dymond and Smith." The calculated first density coefficients are compared with the experimental values in fig.3. The agreement displayed is satisfactory, particularly with regard to the weak dependence of the coefficient on composition in nitrogen-rich mixtures, and confirms the usefulness of the prediction scheme. The work described in this paper has been carried out with financial support from the S.R.C. M. J. Assael, M. Dix, A. Lucas and W. A. Wakeham, J. Chem. Soc., Faraday Trans. 1 , 1981,77,439. J. Kestin, R. Paul, A. A. Clifford and W. A. Wakeham, Physica (The Hague), 1980, 100A, 349. A. A. Clifford, R. Fleeter, J. Kestin and W. A. Wakeham, Physica (The Hague), 1979, %A, 467. A. A. Clifford, J. Kestin and W. A. Wakeham, Physica (The Hague), 1979, 97A, 298.R. Fleeter, J. Kestin and W. A. Wakeham, Physica (The Hague), 1980, 103A, 521. M. J. Assael and W. A. Wakeham, J. Chem. SOC., Faraday Trans. I , 1981, 77, 697. M. J. Assael and W. A. Wakeham, Ber. Bunsenges. Phys. Chem., 1980, 84, 840. J. J. Healy, J. J. de Groot and J. Kestin, Physica (The Hague), 1976, 82C, 392. ' R. Fleeter, J. Kestin, R. Paul and W. A. Wakeham, Ber. Bunsenges. Phys. Chem., 1981, 85, 215. lo J. Kestin and W. A. Wakeham, Physica (The Hague), 1978,92A, 102. l1 J. H. Dymond and E. B. Smith, The Virial Coeficients of Pure Gases and Mixtures (Clarendon Press, l2 L. Monchick, A. N. G. Pereira and E. A. Mason, J. Chem. Phys., 1965, 42, 3241. l3 J. Kestin and J. Yata, J. Chem. Phys., 1968, 49, 4780. Oxford, 1980).M. J. ASSAEL A N D W . A. WAKEHAM 195 l4 J. J. de Groot, J. Kestin, H. Sookiazian and W. A. Wakeham, Physica (The Hague), 1978,92A, 117. l5 G. C. Maitland, M. Rigby, E. B. Smith and W. A. Wakeham, Intermolecular Forces: Their Origin and Determination (Clarendon Press, Oxford, 198 1). G. C. Maitland, V. Vesovic and W. A. Wakeham, Mol. Phys., 1981, 42, 803. J. Kestin and E. A. Mason, AZP Con$ Proc., 1973, 11, 137. J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hodge, J. F. Masi, R. L. Nutall, Y. S. Touloukian and H. W. Woolley, Natl. Bur. Stand. (U.S.) Circ. 564 (U.S. Govt. Printing Office, Washington D.C., 1955). 2o R. D. McCarty, Hydrogen Technological Survey-Thermophysical Properties, NASA 5P-3089 (US. Govt. Printing Office, Washington D.C., 1971). I1 G. J. Prangsma, L. J. M. Burstoom, H. F. P. Knaap, C. J. N. van der Meijdenberg and J. J. M. Beenakker, Physica (The Hague), 1972, 61, 527. 22 R. M. Jonkman, G. J. Prangsma, I. Ertas, H. F. P. Knaap and J. J. M. Beenakker, Physica (The Hague), 1968, 38, 441. 23 M. J. Assael, W. A. Wakeham and J. Kestin, Znt. J, Thermophys., 1980, 1, 7. 24 E. A. Mason, H. E. Khalifa, J. Kestin, R. Di Pippo and J. R. Dorfman, Physica (The Hague), 1978, l7 R. Gengenbach, C. Hahn, W. Schrader and J. P. Toennies, Theor. Chim. Acta, 1968, 34, 199. 91A, 377. J. Kestin and W. A. Wakeham, Ber. Bunsenges. Phys. Chem., 1980, 84, 762. (PAPER 1 / 164)

ISSN:0300-9599    

DOI:10.1039/F19827800185

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1982, 78, 197-211 Calculations on Ionic Solvation Part 6.-Structure-making and Structure-breaking Effects of Alkali Halide Ions from Electrostatic Entropies of Solvation. Correlation with Viscosity B-coefficients, Nuclear Magnetic Resonance B'-coefficients and Partial Molal Volumes. BY MICHAEL H. ABRAHAM* Department of Chemistry, University of Surrey, Guildford, Surrey GU2 5XH AND JANOS LISZI* AND ERZSEBET PAPP Department of Analytical Chemistry, University of Veszprem, 820 1, Veszprem, Hungary Received 9th February, 198 1 The electrostatic entropy of solvation of an ion, AS:, or the contribution to AS: from the co-ordination sphere of the ion, have been shown to be quantitative measures of the structure-making and structure-breaking effects of ions of the alkali halide series in water and in non-aqueous solvents. Both entropy criteria indicate that in water the ions Li+, Na+, Ag+ and F- are net structure-makers, the ions Rb+, Cs+, C1-, Br-, I- and C10; are structure-breakers, and K+ is a borderline case.In the non-aqueous solvents formamide, methanol, N-methylformamide, dimethylformamide, dimethylsulphoxide and aceto- nitrile, all the above ions are structure-makers with the exceptions of the weak structure-breaking ion C10; in formamide and the borderline cases of C10, in methanol and I- in formamide. It is shown that the AS: or AS: II values may be used to assign single-ion B- or B'-coefficients and that for water and several non-aqueous solvents there are good linear correlations between the entropy values and the single-ion coefficients.There are also good linear correlations between the entropy values and single-ion Vo values when the latter are based on V" (H+, aq, 1 mol dm-3) = -5.4 cm3 mol-' and when values of To in non-aqueous solvents are assigned by the correspondence method. It is further shown that the general conclusions reached do not depend on any particular choice of ionic radii, although the Goldschmidt-Pauling set is preferred, and it is suggested that the derived AS: and AS: I I values are close to 'absolute' values and hence provide an 'absolute' measure of ion-solvent interactions. In Part 3 of this series1 we deduced expressions for the electrostatic entropy of solvation of an ion surrounded by concentric layers of solvent, each with a different dielectric constant, E .In the simplest case of a one-layer model, in which the ion of radius a and dielectric constant unity is surrounded by a solvent layer of thickness b - a and E = E ~ , followed by the bulk solvent with E = E,, eqn (1) holds: For a two-layer model in which the ion is surrounded by a first layer of thickness b - a and E = E ~ , then by a second layer of thickness c- b and E = E,, followed by the bulk solvent, eqn (2) was deduced : In both of these equations, 2 denotes the charge on the ion. The advantage of eqn 197198 CALCULATIONS O N IONIC SOLVATION (1) and (2) over those we used previously2 is that the particular terms of the equations give explicitly the contributions from the layers and the bulk so1vent.l Application of eqn (1) and (2) to the solvation of univalent ions in aprotic solvents resulted in good agreement with the experimental entropie~.~ For most ions E, was quite close to the bulk dielectric constant so that there was little numerical difference between calculations using the one-layer and two-layer models; if E , = E, and hence &,/i3T = &,/aT, then eqn (2) collapses to eqn (1).In the case of hydrogen-bonded solvents, neither eqn (1) nor eqn (2) reproduced the experimental values and we concluded that for these solvents there was an additional very positive contribution to the overall AS: value, which arose from a disordered solvent region in the second layer. We therefore applied eqn (2) to solvation of ions in hydrogen-bonded solvents by calculating the contributions from the first layer and the bulk solvent and then deducing, by difference, the contribution of the second layer.3 For ions in water we briefly discussed the relationship between the entropic contribution of the first and second layers and the so-called structure-making and structure-breaking effects of ions, and in the present work we examine such relationships in more detail.Several workers 4-11 have discussed entropies of ions in terms of their structure-making and structure-breaking tendencies, and there have been attempts to correlate, for example, the standard entropies of hydration of ions with ionic viscosity B-coefficients or with partial molal volumes of ions in water. Both the B-coefficients and the partial molal volumes, especially when the latter are corrected to yield the contribution from electrostriction, es,l2? l3 have been used as probes of ion-solvent interactions, and, indeed, ionic viscosity &coefficients have been taken as a direct indication of the structure-making and structure-breaking effects of ions.l4 Friedman and Krishnanll have calculated the entropic contribution of the second layer around ions in water by estimating the bulk contribution by the Born equation; the first layer contribution was taken as - 12 cal K-l mol-l for all monatomic ions and a correction was applied for loss of translational entropy on transfer from the gas phase at 1 atm to water at unit mole fraction (-20 cal K-l mol-1 for all ions).* They concluded that the ions Li+ and F- are structure-making ions, the ion Na+ has no structure-making or -breaking effect, and the larger ions such as K+, Rb+, Cs+, NH;, Cl-, Br-, I- and C10; were structure-breaking ions.We felt that any structure-making or structure-breaking effects of ions in a given solvent should be reflected either in the electrostatic term AS: or in the entropic contribution of the first and second layers AS: I1 = ASP + We therefore, as before,2 divided the experimental ionic solvation entropy, AS:, into a neutral and electrostatic part, eqn (3), AS: = AS: + AS: (3) calculated the neutral part, AS:, again exactly as before,2 and thus obtained the electrostatic part, AS:, by difference. The electrostatic solvation entropy is then written as the sum of the contributions from the first layer, ASP, the second layer, ASIOI, and the bulk solvent, AS:, as in eqn (4), We calculate the ASP and AS: terms uia eqn (2) and then obtain the AS: term by difference.Although the numerical values of AS: depend on the standard states adopted for the gas phase and solution, the values of AS: are independent of standard * 1 cal = 4.184 J. AS: = AS: + AS:I + AS:.M. H. ABRAHAM, J. L I S Z I A N D E. P A P P 199 states because of cancellation between the AS: and AS: terms. The AS," term, eqn (3) and (4), contains not only the electrostatic effect but also the effect of any disordered layer; we shall continue to denote the overall (AS: - AS:) term as AS,", following our previous nomenclature.2 The above procedure [cf. ref. (1 l)] will yield a comparative set of entropies for a series of cations or a series of anions, but any comparison between the two series or any attempt at quantitative estimations of structure-making or structure-breaking effects will depend on the division of the AS: (M++X-) values into cationic and anionic contributions and also on the ionic radii used.We have previously2 obtained a set of AS: (M+) and AS: (X-) values that was compatible with the Goldschmidt- Pauling (GP) radii we had used,15 and was derived from Noye9 data. Most other sets of ionic radii are quite close to the GP radii except for that suggested by Adrian and Gourary" (AG). In order to examine the possible effects of different sets of ionic radii and AS: values, we have carried out calculations using both GP and AG radii and with the sets of single-ion AS: values that are compatible with these sets of radii.In all calculations, values of E,, a ~ ~ / a T ' , and the solvent radius, r, were those used l5 we took b = (a+ r ) and c = (b+ r ) = (a+ 2r), and values of cl = 2.0 and aEl/aT = - 1.6 x l5 As K-l. TABLE 1 .-SINGLE-ION VALUES OF AS:, AS:, AS: 11, B- AND B-COEFFICIENTS AND Po IN WATER AT 298 K BASED ON GOLDSCHMIDT-PAULING RADP ASSO AS: AS,qII B B P /cal K-l /cal K-l /cal K-l /dm3 /dm3 /cm3 ion a/W mol-1 mol-1 mol-l mol-1 mol-l mol-l H+ Li+ Na+ Ag+ K+ Rb+ Cs+ F- c1- Br- I- c10, - 0.90 1.05 1.13b 1.33 1.43 1.66 1.33 1.81 1.95 2.20 2.45 - 42.3 - 44.6 -36.8 - 38.6 -28.7 - 25.9 - 25.2 -37.1 - 23.3 - 19.3 - 14.3 - 13.0 - - 32.8 - 19.7 - 19.0 - 3.7 1 .o 5.1 - 12.1 8.6 14.0 21.7 25.6 - 0.096 - 30.4 0.174 - 17.4 0.1 10 - 15.7 0.115 - 1.5 0.0 17 3.1 -0.006 7.1 -0.021 - 9.9 0.072 10.6 -0.031 15.9 -0.066 23.5 -0.092 27.3 -0.089 0.09 -5.4 0.17 -6.3 0.09 -6.6 0.09 -6.1 0.02 3.6 - 0.0 1 8.7 - 0.02 15.9 0.1 1 4.2 - 0.04 23.2 - 0.07 30.1 -0.1 1 41.6 -0.1 15 49.5 Data from references in the text, except where shown.Single-ion values assigned as detailed in the text. Ref. (19). DISCUSSION RESULTS FOR WATER SOLVENT In table 1 are results based on GP radii. Both the calculated AS: and AS: values indicate that all the listed ions are net structure-breakers (AS," and AS: I I > 0) except for Li+, Na+, Ag+, K+ and F- which are net structure-makers (AS: and AS: I I < 0). In order to compare our conclusions with those based on single-ion viscosity B- coefficients, some method of assignment of these single-ion values is necessary; unfortunately there is no generally accepted method of so doing.l49 l8 We have assigned single-ion B-coefficients so that in a plot of AS: or AS: II against B points for both cations and anions lie on the same curve or line.The B-coefficients are derived from200 CALCULATIONS O N IONIC SOLVATION results collected by Nightingale14 and by Engel and Hertz.lg In the event, there are excellent linear correlations between AS: and AS: I I and the single-ion B-coefficients. In particular, all ions for which AS: and AS: II are positive have negative B-coefficients (structure-breakers) and all ions for which AS: and AS; I I are negative have positive B-coefficients (structure-makers). Engel and Hertzlg have studied structure-making and structure-breaking effects of ions through measurement of proton relaxation rates in water and also in some non-aqueous solvents. They obtain the solvent proton relaxation rate in the absence (Go) and presence (q) of electrolyte at a concentration C, and write an equation analogous to the Jones-Dole viscosity equation : (l/Tl)/(l/T;) = 1 +B’C+C‘C2 The coefficient B’ is a measure of the structure-making (B’ > 0) and structure-breaking (B’ < 0) effect of an electrolyte on the solvent.Again, B has to be separated into single-ion values; Engel and Hertzlg used the convention14 that B (K+) = B (Cl-) but we preferred to use the same procedure that we adopted for the division of B-coefficients into single-ion quantities. There is an excellent linear correlation between the single-ion B’ values in table 1 and the AS: and AS: quantities, with an exact agreement between the signs of AS: and AS: II and the signs of the B- and B’-coefficients.Structure-making and structure-breaking effects of ions should influence not only the B- and B-coefficients but also the partial molal volumes, Vo, of ions. In this case, not only must single-ion values be assigned, but it would also be useful to obtain an estimate of the electrostriction effect, Vgs, because it is this quantity that is closely related to structure-making or structure-breaking effects. We find that single-ion values of To assigned on the basis8 that To (H+, aq) = - 5.4 cm3 mol-1 need no further adjustment, and that there are again quite reasonable linear correlations between AS: or AS; II and the single-ion To values in table 1 11, 2o There have been numerous methods suggested for subtracting out from the single-ion Vo values the intrinsic molar volume of ions En so as to leave the contribution due to electrostriction.The simplest method is merely to calculate the volume of an ion, 4/3na3N, which is given by the formula 2.52a3 when a is in A and To in cm3 mol-l. Mukerjee21 applied a correction to this formula yielding 4.48a3 as the intrinsic volume, and this was later used by Surdo and Millero.22 Several other methods of calculation Kn have been put forward, but Hirata and A r a k a ~ a ~ ~ have suggested that all the various methods are more or less approximations of a more general equation for cavity formation obtainable through scaled-particle theory.For water at 298 K, Hirata and A r a k a ~ a ~ ~ deduced eqn (6) En = 2.52a3+4.310a2+2.187a+0.639 (6) where Kn is in cm3 mol-1 and a is the Pauling ionic radius in A. A much more complete analysis has recently been given by M a t t e ~ l i , ~ ~ who not only included the s.p.t. cavity calculation but also took into account non-electrostatic ion-solvent interactions. Values of Ks deduced using various formulae are in table 2, together with correlation coefficients, p, for plots of AS: I I against the KS values. Because the sets of Ks values vary so widely in numerical values, it is not easy to assess any quantitative connection between AS: or AS; II and Es. The most recently calculated values of Matte01i~~ are reasonably well-correlated with AS: or ASEI1 ( p = 0.974), however, so we feel that such a connection, if not established, is at least indicated.We thought it useful to recalculate all our results using the AG set of radii, and the various sets of values are summarised in table 3. The correlations are detailed in table 4, both for results calculated using GP radii as well as for those using the AG set.M. H. ABRAHAM, J. LISZI AND E. PAPP 20 1 TABLE 2.-vALUES OF THE ELECTROSTRICTIVE CONTRIBUTION, Cs, IN WATER CALCULATED USING VARIOUS METHODS, IN cm3 mo1-1 AT 298 K BASED ON GOLDSCHMIDT-PAULING RADII ion vo U b C d Li+ Na+ K+ Rb+ c s + F- c1- Br- 1- Ag+ c10, - 6.3 - 6.6 -6.1 3.6 8.7 15.9 4.2 23.2 30.1 41.6 49.5 0.949 0.976 -8.1 - 9.5 - 9.7 - 2.3 1.3 4.4 - 1.7 8.2 11.4 14.7 12.4 0.952 0.973 - 9.6 - 14.2 -11.8 - 17.2 - 12.6 - 18.4 - 6.9 - 13.5 - 4.4 - 11.3 - 4.6 - 11.8 - 12.2 - 12.9 - 18.4 - 10.5 -21.8 - 9.9 - 33.0 - 11.6 - 53.5 - 18.7 - 0.670 0.297 -0.710 0.322 - 28 - 24 -21 - 14.2 - 11.7 -7.1 - 14.2 - 5.2 - 4.0 -2.7 -2.1 0.974 0.962 a Es = 8O-2.52~~.Matteoli's method. cs = TO-4.48~~. cs = Po- Tion, the latter calculated via eqn (6). Correlation constant for S: I I plotted against To or V&. f Correlation constant excluding the point for Li+. Also given are values of p. A noteworthy feature is that the regression line for correlations involving B- or B'-coefficients passes quite close to the origin, hence the one-to-one correspondence between the sign of AS: or ASP, I1 and the sign of the B- or B'-coefficients.There are not very substantial differences between results based on AG radii and those based on the GP set of radii, although the former set leads to K+ as a weak structure-breaker whereas the latter set leads to K+ as a weak structure-maker. In general, the results in tables 1 and 3 are in agreement with conclusions reached by many 11, 1 4 9 l9 An exception is the infrared study of Bonner and Jumper,25 who concluded that all anions, even F, were structure-breakers and who listed structure-makers in the order Ag+ > Li+ > Cs+ > Rb+ > K+ > Na+. Jackson and Symons26 have criticised these conclusions, and our results support the latter workers views. The single-ion AS: values in table 1 correspond to so (H+, aq, 1 mol dmP3) = - 8.3 cal K-l mol-l and those based on AG radii in table 3 correspond to so (H+, aq, 1 mol dm-3) = -6.3 cal K-l mol-l.Both of these values are quite close to the generally accepted 8 l l1 absolute value of - 5 to - 6 cal K-l mol-l. Furthermore, the single-ion Vo value in table 1, Vo (H+, aq) = - 5.4 cm3 mol-l, is exactly that suggested89l1 as the absolute value for H+(aq) and the value in table 3 , Vo(H+, aq) = + 1.8 cm3 mol-', is not too far away. We therefore feel that the various single-ion values listed in table 1 (especially) and table 3 must be quite close to absolute values. If this is so, then the conventions that B(K+) = B(Cl-) and B'(K+) = B'(C1-) are not too unrealistic, although a better division would rank Cs+ and C1- as equivalent. Very recently, K r ~ m g a l z ~ ~ has reassigned single-ion partial molal volumes using the method of Conway et a1.28 This method leads to Vo(H+, aq) = -6.0 cm3 mol-l, almost identical to the value in table 1 and to the value suggested by Criss and Salomon,8 by Friedman and Krishnan'l and by Millero.20202 CALCULATIONS O N IONIC SOLVATION TABLE 3.-sINGLE-ION VALUES OF As:, As:, AS: 11, B- AND B'-COEFFICIENTS AND To IN WATER AT 298 K BASED ON ADRIAN-GOURARY RADII~ H+ Li+ Na+ K+ Rb+ cs+ F- c1- Br- I- Ag+ ClO, - - - 40.3 - 0.94 -42.6 -29.4 -27.0 1.17 -34.8 -13.9 -11.6 1.13b -36.6 -17.0 -14.7 1.49 - 26.7 1.1 3.3 1.63 - 23.9 6.1 8.2 1.86 - 23.2 9.2 11.2 1.16 -39.1 -18.5 -16.2 1.64 -25.3 4.8 6.8 1.80 -21.3 10.5 12.5 2.05 - 16.3 18.1 20.0 2.30b - 15.0 22.0 23.8 0.077 0.155 0.09 1 0.096 - 0.002 - 0.025 - 0.040 0.091 -0.012 - 0.047 - 0.073 - 0.070 0.07 1.8 0.15 0.9 0.07 0.6 0.07 1.1 0.00 10.8 -0.03 15.9 - 0.04 23.1 - 0.02 16.0 - 0.05 22.9 - 0.09 34.4 -0.095 42.3 0.13 -3.0 a Units and references as in table 1.S. Ahrland (Pure Appl. Chem., 1979,51, 2019) gives, for ionic radii based on a scale closely related to the AG scale, values of a(Ag+) = 1.12 and a(C10,) = 2.30 A. We conclude that the single-ion values in tables 1 and 3 are near to absolute values, and that the calculated AS: and AS:, II values may be taken as quantitative measures of the structure-making and structure-breaking effects of univalent ions in water. The cations Li+, Na+ and Ag+ are powerful structure-making ions, K+ is a weak structure-maker or perhaps a borderline case and Rb+ and Cs+ are structure-breaking ions.The anions are all quite strong structure-breakers except for F- which is a structure-making ion. Although values of AS: are known for a number of large polyatomic univalent ions,ll we have not carried out any detailed calculations because of the difficulty in estimating ionic radii of the ions. We confirmed, however, that CN- (a = 1.86 A) is a strong structure-breaker, being placed in order between Br- and I-. Finally, we point out that although values of AS: (tables 1 and 3) are well-correlated with B, B' and Vo values, little can be deduced from these correlations about the net structure-making and structure-breaking effects of ions. Only by separating out the AS: or ASIqI1 terms can any quantitative estimates be made. RESULTS FOR NON-AQUEOUS SOLVENTS There are not so many solvents for which sufficient AS:, B, B and To values are known to explore correlations as in the case of water.However, for methanol the required AS: values are known,2 and there are a sufficient number of B-coefficients r e p ~ r t e d ~ ~ - ~ l to enable a set of single-ion values to be constructed. Engel and Hertzlg have determined #-coefficients for several electrolytes in methanol, and Criss and Salomon8 have tabulated To values based on Vo(H+, methanol) = - 16.6 cm3 mol-l; additional To values are also available.20* 3 2 9 33 Results of calculations of AS: and AS: II based on GP radii are in table 5 . Quite unlike the case of solvent water, our calculations indicate that all these inorganic ions, with the possible exception of ClO, as a borderline case, are structure-making ions in methanol; this is in complete agreement with the conclusions of Engel and Hertz.lg After reassignment of single-ion B- and H-coefficients using the method used for aqueous solutions, there are obtained good linear correlations between AS: or ASFI1 and either of the sets ofM.H. ABRAHAM, J. LISZI A N D E. PAPP 203 TABLE 4.-REGRESSION EQUATIONS FOR PLOTS OF As: OR AS: 11 AGAINST B, B' OR To VALUES AT 298 K function plotted no.a mb CC Pd water using GP radii AS: against B 11 -204.3 2.4 0.992 ASP ,, against B 11 -200.7 4.4 0.992 AS,.' against B 11 -192.9 1.0 0.986 ASP ,, against B 11 -189.7 3.1 0.986 AS," against Vo 11 0.893 -13.8 0.950 AS: against Vo 11 0.877 - 11.4 0.949 water using AG radii AS: against B 11 -208.6 2.5 0.991 AS;,, against B 11 -206.3 4.6 0.991 AS,.' against B 11 -194.8 1.0 0.988 ASP against B 11 -192.6 3.1 0.988 AS: against To 11 1.049 - 16.3 0.936 AS: against Vo 11 1.036 -14.0 0.935 AS: against B 8 -54.5 - 1.3 0.965 AS: against B' 9 -149.0 -8.2 0.966 AS: ,, against B 9 -143.1 -3.3 0.966 AS,.' against Vo 10 0.688 -24.8 0.983 AS: ,, against V' 10 0.660 -19.2 0.983 methanol using GP radii AS:,, against B 8 -52.5 5.8 0.965 methanol using AG radii AS: against B 8 -72.0 4.5 0.962 AS;,, against B 8 -69.3 8.9 0.963 AS,.' against B 9 -145.9 -8.5 0.954 ASP I I against B 9 -140.1 -3.6 0.954 AS,.' against Vo 10 0.757 -25.4 0.958 AS;, II against To 10 0.724 -19.8 0.957 AS: against B 8 -70.4 - 1.3 0.954 ASe against B 7 -181.4 -3.1 0.947 AS; ,, against B 7 -178.8 - 1.5 0.947 AS," against Vo 8 0.614 -26.3 0.994 AS: against Vo 8 0.605 -24.3 0.994 formamide using GP radii ASi,, against B 8 -69.4 0.3 0.954 N-methylformamide using GP radii AS: against B 7 curved plot obtained ASCII against B 7 curved plot obtained ASe against B 9 -304.0 0.1 0.990 AS;, ,, against B' 9 -296.5 1.0 0.988 NN-dimethylformamide using GP radii AS: against To 8 0.627 -39.6 0.980 AS;, against Vo 8 0.604 -36.1 0.982 dimethylsulphoxide using GP radii AS: against B 9 curved plot obtained AS;,, against B 9 curved plot obtained AS: against Vo 8 0.723 -36.1 0.957 AS: ,, against Vo 8 0.714 -34.5 0.967 AS: against Vo 8 0.645 -35.5 0.954 AS: II against To 8 0.629 -32.1 0.955 acetonitrile using GP radii a Number of points; slope; intercept; correlation constant.204 CALCULATIONS ON IONIC SOLVATION TABLE 5.-sINGLE-ION VALUES OF As:, As: 11, B- AND B'-COEFFICIENTS AND Po IN METHANOL AT 298 K BASED ON GOLDSCHMIDT-PAULING R A D I I ~ ion AS: ASP,,, B B V" H+ Li+ Na+ K+ Rb+ Cs+ F- c1- Br- I- c10, - - 40.4 - 34.4 - 27.4 - 22.8 - 19.1 - 26.4 - 15.1 - 12.1 - 6.4 - 3.7 - - 34.2 -28.7 -21.7 - 17.2 - 13.8 - 20.7 - 9.9 - 7.0 - 1.5 1 .o - 0.63 0.59 0.56 0.44 0.36 __ 0.20 0.18 0.11 - - 0.25 0.14 0.1 1 0.08b 0.07b - 0.05 0.03 0.00 - 0.0 1 - 16.6 - 16.0 - 14.6 - 4.6 - 0.6 5.9 - 2.4 11.3 18.6 26.3 34.9 a Units as in table 1 ; data from references in the text except where noted.Estimated values from ref. (1 9). TABLE 6.-sINGLE-ION VALUES OF As:, As:11, B- AND B'-COEFFICIENTS AND v" IN METHANOL AT 298 K BASED ON ADRIAN-GOURARY R A D I I ~ ion AS: AS:,rI B B V" H+ Li+ Na+ K+ Rb+ cs+ F- c1- Br- I- c10, - - 38.2 -31.6 - 24.3 - 19.4 - 15.8 - 29.6 - 18.3 - 15.2 - 9.4 - 6.7 - - -32.1 0.54 -25.7 0.50 -18.8 0.47 -14.0 0.35 -10.6 0.27 -23.7 - - 12.9 0.29 -10.0 0.27 -4.4 0.20 -1.9 - - -10.6 0.23 -8.0 0.12 -8.6 0.09 1.4 0.06b 5.4 O.OSb 11.9 - 8.4 0.07 5.3 0.05 12.6 0.02 20.3 0.01 28.9 - a Units as in table 1 ; data from references in the text except where noted.Estimated values from ref. (1 9). coefficients (table 4). The regression lines pass reasonably close to the origin so that, again, there will be a correspondence between the sign of AS: or AS: I I and the sign of the coefficients. In the event, for the ions other than ClO;, both entropy quantities are always negative and the B- and B'-coefficients are positive, indicative of structure- making effects.Values of To assigned by Criss and Saloman* are in table 5; without any further adjustment, these values are linearly related to AS: or AS:,, for both cations and anions (see table 4). In order to check whether or not our general conclusions for non-aqueous solvents are affected by choice of single-ion AS! values or of ionic radii, we have repeated all the calculations for methanol using the AG set of radii (table 6). Results are very similar to those in table 5 except that C10; would now be classed as a structure-making ion instead of as a borderline case; the correlations using the GP radii are slightly better than those with AG radii. TheM. H. ABRAHAM, J. LISZI AND E. P A P P 205 single-ion B- and B'-coefficients in tables 5 and 6 are almost equivalent to a convention that sets similar values for Cs+ and Cl-; the recent division of B-coefficients into single-ion values carried out by Krumgalzls leads to appreciably different cation and anioncontributions - to those listed in tables 5 and 6.As pointed out above, the single-ion Vo values in table 5 are those suggested by Criss and Salomon8 and are equivalent to taking To (H+, methanol) = - 16.6 cm3 mol-l, whereas the division in table 6 corresponds to a value of - 10.6 cm3 mo1-l for Yo(H+, methanol). These values are quite remote from Vo(H+, methanol) = + 16.3 cm3 mol-l, a value that corresponds to the single-ion division of K r ~ m g a l z . ~ ~ TABLE 7.-sINGLE-ION VALUES OF As:, AS: B- AND E-COEFFICIENTS AND ro IN FORMAMIDE AT 298 K BASED ON GOLDSCHMIDT-PAULING RADIP Li+ Na+ K+ Rbf cs+ c1- Br- I - c10, - 29.4 - 29.4 - 22.4 - 17.8 - 14.2 - 10.1 -7.1 - 1.4 1.3 - 27.4 - 27.4 -20.5 - 16.0 - 12.5 - 8.4 - 5.4 0.2 2.8 0.353 0.465 0.239 0.217 0.19 0.125 0.083 0.053c - 4.7 0.16 -3.2 0.08 7.7 0.06 11.6 0.07 18.0 0.04 24.3 0.03 31.1b 0.005 43.1 - a Units as in table 1 ; data from references in the text except where noted.Ref. (20). Results of J. M. Notley and M. Spiro (J. Phys. Chem., 1966, 70, 1502) suggest 0.00 for B(1-) on the given single-ion division. The most interesting non-aqueous solvents studied by Engel and Hertzlg were glycerol and ethylene glycol, where it appeared that even inorganic ions could act as structure-breakers. Unfortunately, AS: values are not known for ions in these solvents, but values are available2 for formamide, a solvent that is itself so ordered that structure-breaking effects might be observable.Martinus and Vincent34 have determined B-coefficients for electrolytes in this solvent, #-values are available,lg and single-ion vo values have been assigned by Criss and Salomon;s all these values are in table 7. We have carried out calculations only in terms of GP radii, in view of the similar conclusions obtained (above) using the AG set. Our calculated AS: and AS: I I values, table 7, indicate that formamide behaves rather similarly to methanol; only for the largest ions does any structure-breaking effect appear. With the division of B- and #-values into single-ion quantities carried out as described before, the resulting ionic B- and B'-coefficients are reasonably well-correlated with AS: and AS; I I .The cationic and anionic division of B-coefficients (table 7) is very close to that given before,34 the difference being only _+ 0.04 dm3 mol-l. Our conclusions based on AS: or AS: II values are almost exactly the same as those of Martinus and Vincent,34 who found that all the alkali halide ions are structure-makers with the exception of I- which is a weak structure-breaker. The To values of Criss and Salomon (table 7) are also linearly correlated with AS: and AS& but in this case Krumgalz'~~~ division of Vo into single-ion values yields quite different results. Details of all the regression equations for formamide solvent are in table 4. Engel and Hertzlg measured B'-coefficients for a number of electrolytes in N- methylformamide, and there are excellent correlations of our calculated AS: andM. H.ABRAHAM, J. LISZI AND E. P A P P 205 single-ion B- and B'-coefficients in tables 5 and 6 are almost equivalent to a convention that sets similar values for Cs+ and Cl-; the recent division of B-coefficients into single-ion values carried out by Krumgalzls leads to appreciably different cation and anioncontributions - to those listed in tables 5 and 6. As pointed out above, the single-ion Vo values in table 5 are those suggested by Criss and Salomon8 and are equivalent to taking To (H+, methanol) = - 16.6 cm3 mol-l, whereas the division in table 6 corresponds to a value of - 10.6 cm3 mo1-l for Yo(H+, methanol). These values are quite remote from Vo(H+, methanol) = + 16.3 cm3 mol-l, a value that corresponds to the single-ion division of K r ~ m g a l z .~ ~ TABLE 7.-sINGLE-ION VALUES OF As:, AS: B- AND E-COEFFICIENTS AND ro IN FORMAMIDE AT 298 K BASED ON GOLDSCHMIDT-PAULING RADIP Li+ Na+ K+ Rbf cs+ c1- Br- I - c10, - 29.4 - 29.4 - 22.4 - 17.8 - 14.2 - 10.1 -7.1 - 1.4 1.3 - 27.4 - 27.4 -20.5 - 16.0 - 12.5 - 8.4 - 5.4 0.2 2.8 0.353 0.465 0.239 0.217 0.19 0.125 0.083 0.053c - 4.7 0.16 -3.2 0.08 7.7 0.06 11.6 0.07 18.0 0.04 24.3 0.03 31.1b 0.005 43.1 - a Units as in table 1 ; data from references in the text except where noted. Ref. (20). Results of J. M. Notley and M. Spiro (J. Phys. Chem., 1966, 70, 1502) suggest 0.00 for B(1-) on the given single-ion division. The most interesting non-aqueous solvents studied by Engel and Hertzlg were glycerol and ethylene glycol, where it appeared that even inorganic ions could act as structure-breakers. Unfortunately, AS: values are not known for ions in these solvents, but values are available2 for formamide, a solvent that is itself so ordered that structure-breaking effects might be observable.Martinus and Vincent34 have determined B-coefficients for electrolytes in this solvent, #-values are available,lg and single-ion vo values have been assigned by Criss and Salomon;s all these values are in table 7. We have carried out calculations only in terms of GP radii, in view of the similar conclusions obtained (above) using the AG set. Our calculated AS: and AS: I I values, table 7, indicate that formamide behaves rather similarly to methanol; only for the largest ions does any structure-breaking effect appear.With the division of B- and #-values into single-ion quantities carried out as described before, the resulting ionic B- and B'-coefficients are reasonably well-correlated with AS: and AS; I I . The cationic and anionic division of B-coefficients (table 7) is very close to that given before,34 the difference being only _+ 0.04 dm3 mol-l. Our conclusions based on AS: or AS: II values are almost exactly the same as those of Martinus and Vincent,34 who found that all the alkali halide ions are structure-makers with the exception of I- which is a weak structure-breaker. The To values of Criss and Salomon (table 7) are also linearly correlated with AS: and AS& but in this case Krumgalz'~~~ division of Vo into single-ion values yields quite different results.Details of all the regression equations for formamide solvent are in table 4. Engel and Hertzlg measured B'-coefficients for a number of electrolytes in N- methylformamide, and there are excellent correlations of our calculated AS: andM. H. ABRAHAM, J. LISZI AND E. P A P P 205 single-ion B- and B'-coefficients in tables 5 and 6 are almost equivalent to a convention that sets similar values for Cs+ and Cl-; the recent division of B-coefficients into single-ion values carried out by Krumgalzls leads to appreciably different cation and anioncontributions - to those listed in tables 5 and 6. As pointed out above, the single-ion Vo values in table 5 are those suggested by Criss and Salomon8 and are equivalent to taking To (H+, methanol) = - 16.6 cm3 mol-l, whereas the division in table 6 corresponds to a value of - 10.6 cm3 mo1-l for Yo(H+, methanol).These values are quite remote from Vo(H+, methanol) = + 16.3 cm3 mol-l, a value that corresponds to the single-ion division of K r ~ m g a l z . ~ ~ TABLE 7.-sINGLE-ION VALUES OF As:, AS: B- AND E-COEFFICIENTS AND ro IN FORMAMIDE AT 298 K BASED ON GOLDSCHMIDT-PAULING RADIP Li+ Na+ K+ Rbf cs+ c1- Br- I - c10, - 29.4 - 29.4 - 22.4 - 17.8 - 14.2 - 10.1 -7.1 - 1.4 1.3 - 27.4 - 27.4 -20.5 - 16.0 - 12.5 - 8.4 - 5.4 0.2 2.8 0.353 0.465 0.239 0.217 0.19 0.125 0.083 0.053c - 4.7 0.16 -3.2 0.08 7.7 0.06 11.6 0.07 18.0 0.04 24.3 0.03 31.1b 0.005 43.1 - a Units as in table 1 ; data from references in the text except where noted.Ref. (20). Results of J. M. Notley and M. Spiro (J. Phys. Chem., 1966, 70, 1502) suggest 0.00 for B(1-) on the given single-ion division. The most interesting non-aqueous solvents studied by Engel and Hertzlg were glycerol and ethylene glycol, where it appeared that even inorganic ions could act as structure-breakers. Unfortunately, AS: values are not known for ions in these solvents, but values are available2 for formamide, a solvent that is itself so ordered that structure-breaking effects might be observable. Martinus and Vincent34 have determined B-coefficients for electrolytes in this solvent, #-values are available,lg and single-ion vo values have been assigned by Criss and Salomon;s all these values are in table 7.We have carried out calculations only in terms of GP radii, in view of the similar conclusions obtained (above) using the AG set. Our calculated AS: and AS: I I values, table 7, indicate that formamide behaves rather similarly to methanol; only for the largest ions does any structure-breaking effect appear. With the division of B- and #-values into single-ion quantities carried out as described before, the resulting ionic B- and B'-coefficients are reasonably well-correlated with AS: and AS; I I . The cationic and anionic division of B-coefficients (table 7) is very close to that given before,34 the difference being only _+ 0.04 dm3 mol-l. Our conclusions based on AS: or AS: II values are almost exactly the same as those of Martinus and Vincent,34 who found that all the alkali halide ions are structure-makers with the exception of I- which is a weak structure-breaker. The To values of Criss and Salomon (table 7) are also linearly correlated with AS: and AS& but in this case Krumgalz'~~~ division of Vo into single-ion values yields quite different results.Details of all the regression equations for formamide solvent are in table 4. Engel and Hertzlg measured B'-coefficients for a number of electrolytes in N- methylformamide, and there are excellent correlations of our calculated AS: andM. H. ABRAHAM, J. LISZI AND E. P A P P 205 single-ion B- and B'-coefficients in tables 5 and 6 are almost equivalent to a convention that sets similar values for Cs+ and Cl-; the recent division of B-coefficients into single-ion values carried out by Krumgalzls leads to appreciably different cation and anioncontributions - to those listed in tables 5 and 6.As pointed out above, the single-ion Vo values in table 5 are those suggested by Criss and Salomon8 and are equivalent to taking To (H+, methanol) = - 16.6 cm3 mol-l, whereas the division in table 6 corresponds to a value of - 10.6 cm3 mo1-l for Yo(H+, methanol). These values are quite remote from Vo(H+, methanol) = + 16.3 cm3 mol-l, a value that corresponds to the single-ion division of K r ~ m g a l z . ~ ~ TABLE 7.-sINGLE-ION VALUES OF As:, AS: B- AND E-COEFFICIENTS AND ro IN FORMAMIDE AT 298 K BASED ON GOLDSCHMIDT-PAULING RADIP Li+ Na+ K+ Rbf cs+ c1- Br- I - c10, - 29.4 - 29.4 - 22.4 - 17.8 - 14.2 - 10.1 -7.1 - 1.4 1.3 - 27.4 - 27.4 -20.5 - 16.0 - 12.5 - 8.4 - 5.4 0.2 2.8 0.353 0.465 0.239 0.217 0.19 0.125 0.083 0.053c - 4.7 0.16 -3.2 0.08 7.7 0.06 11.6 0.07 18.0 0.04 24.3 0.03 31.1b 0.005 43.1 - a Units as in table 1 ; data from references in the text except where noted.Ref. (20). Results of J. M. Notley and M. Spiro (J. Phys. Chem., 1966, 70, 1502) suggest 0.00 for B(1-) on the given single-ion division. The most interesting non-aqueous solvents studied by Engel and Hertzlg were glycerol and ethylene glycol, where it appeared that even inorganic ions could act as structure-breakers. Unfortunately, AS: values are not known for ions in these solvents, but values are available2 for formamide, a solvent that is itself so ordered that structure-breaking effects might be observable.Martinus and Vincent34 have determined B-coefficients for electrolytes in this solvent, #-values are available,lg and single-ion vo values have been assigned by Criss and Salomon;s all these values are in table 7. We have carried out calculations only in terms of GP radii, in view of the similar conclusions obtained (above) using the AG set. Our calculated AS: and AS: I I values, table 7, indicate that formamide behaves rather similarly to methanol; only for the largest ions does any structure-breaking effect appear. With the division of B- and #-values into single-ion quantities carried out as described before, the resulting ionic B- and B'-coefficients are reasonably well-correlated with AS: and AS; I I . The cationic and anionic division of B-coefficients (table 7) is very close to that given before,34 the difference being only _+ 0.04 dm3 mol-l.Our conclusions based on AS: or AS: II values are almost exactly the same as those of Martinus and Vincent,34 who found that all the alkali halide ions are structure-makers with the exception of I- which is a weak structure-breaker. The To values of Criss and Salomon (table 7) are also linearly correlated with AS: and AS& but in this case Krumgalz'~~~ division of Vo into single-ion values yields quite different results. Details of all the regression equations for formamide solvent are in table 4. Engel and Hertzlg measured B'-coefficients for a number of electrolytes in N- methylformamide, and there are excellent correlations of our calculated AS: andM.H. ABRAHAM, J. LISZI AND E. PAPP 209 solvents become less polar and less ordered, so the inorganic ions become even stronger makers of structure, as shown in table 12. Not only do our AS: and AS: I I values provide a quantitative criterion of the effect of an ion on the solvent structure, they also provide a method of inter-relating quantities such as B- and #-coefficients and partial molal volumes of ions. If single-ion B- and #-coefficients are assigned so that in plots against AS: or ASZII points for cations and anions fall on the same line, the resulting single-ion B- and B’-coefficients make up a self-consistent and coherent set of data both for water and non-aqueous solvents. The plots of B or B’ against AS: or AS: I I (see fig. 1) pass almost through the origin so that on one diagram it is possible to indicate the quantitative relationship that exists between B or B’ and AS: or AS: I I in all solvents.All ions appear either in the top left-hand quadrant (AS: negative and B or B positive) as structure-makers or in the bottom right-hand quadrant (AS: positive and B negative) as structure-breakers. 1-0.2 FIG. 1 .-Plot of single-ion viscosity B-coefficients in dm3 mo1-I against single-ion values of AS:. in cal K-I mo1-I for alkali halide ions in @, water; 0, formamide and m, methanol. We have not explored possible relationships between AS: or AS[,, and the temperature variation of ionic viscosity B-coefficients, aB/a T, partly because of lack of experimental data and partly because the aB/aT values have also to be assigned to single ions. However, it seems generally to be the case for the inorganic ions studied that negative values of AS: or AS: I I (structure-making effects) correspond to positive values of B and to negative values of aB/aT, both in water and in non-aqueous solvents.Conversely, at least in water, positive values of AS: or ASFIr (structure-210 CALCULATIONS ON IONIC SOLVATION breaking effects) correspond to negative values of B and to positive values of aB/aT. Although Vo values themselves cannot be used as criteria of ion-solvent structural effects, partial molal volumes must include contributions from such effects. In the event, we find empirically that when Vo values in water are assigned to single ions so that Vo(H+, aq) = - 5.4 cm3 mol-1 and when Vo values in non-aqueous solvents are then assigned to single ions by the correspondence method,* there are excellent linear correlations between AS: or ASCII and the obtained single-ion Vo values.The correspondence method does yield single-ion To values that differ very considerably from those assigned by K r ~ m g a l z . ~ ~ All we wish to say in favour of the former method is that it does result in a set of To values that seems to be compatible with the AS:, ASIqI1, B- and B-coefficients used in the present work. Finally, we point out that our conclusions are almost unaffected by choice of a different set of ionic radii (and associated AS: values) as shown by results in tables 1, 3, 5 and 6. We prefer the GP set of radii, but conclude that our values of AS: and A S t I 1 calculated using either set of radii must be close to 'absolute' values.If this is so, then our single-ion values of B and B in tables 1, 5 , 7, 8 and 10 will also be close to an 'absolute' division. The single-ion values of B and B in cases where only a few values are available (tables 9, 10 and 11) are approximate only; more data are needed to obtain a reliable division. We thank Dr Enrico Matteoli for communicating results prior to publication and for kindly calculating values of Ves using his method. M. H. Abraham, J. Liszi and L. Meszaros, J. Chem. Phys., 1979, 70, 249. M. H. Abraham and J. Liszi, J. Chem. Soc., Faraday Trans. I, 1978, 74, 2858. M. H. Abraham and J. Liszi, J. Chem. Soc., Faraday Trans. I , 1980, 76, 1219. H. S. Frank and M. W.Evans, J. Chem. Phys., 1945, 13, 507. R. W. Gurney, Ionic Processes in Solution (McGraw-Hill, New York, 1953). E. R. Nightingale Jr, J. Phys. Chem., 1959, 63, 1381. C. M. Criss and M. Salomon, in Physical Chemistry of Organic Solvent Systems, ed. A. K. Covington and T. Dickenson (Plenum Press, London, 1973). C. M. Criss, J. Phys. Chem., 1974, 78, 1000. ' C. M. Criss, R. P. Held and E. Luksha, J. Phys. Chem., 1968, 72, 2970. lo B. G. Cox, G. R. Hedwig, A. J. Parker and D. W. Watts, Austr. J. Chem., 1974, 27, 477. l1 H. L. Friedman and C. V. Krishnan, in Water, A Comprehensive Treatise, ed. F. Franks (Plenum Press, London, 1973), vol. 3. P. Drude and W. Nernst, 2. Phys. Chem. (Leipzig), 1894, 15, 79. l3 L. G. Hepler, J. Phys. Chem., 1957, 61, 1426. I4 E. R. Nightingale Jr, in Chemical Physics of Ionic Solutions, ed. B. E. Conway and R. G. Barradas l5 M. H. Abraham and J. Liszi, J. Chem. Soc., Faraday Trans. I , 1978, 74, 1604. l6 R. M. Noyes, J. Am. Chem. Soc., 1962, 84, 513. l7 F. J. Adrian and B. S. Gourary, Solid State Phys., 1960, 10, 127. l8 B. S. Krumgalz, J. Chem. Soc., Faraday Trans. 1, 1980, 76, 1276. l9 G. Engel and H. G. Hertz, Ber. Bunsenges. Phys. Chem., 1968, 72, 808. 2o F. J. Millero, Chem. Rev., 1971, 71, 147. ** P. Mukerjee, J. Phys. Chem., 1961, 65, 740. 22 L. Surdo and F. J. Millero, J. Phys. Chem., 1980, 84, 710. 23 F. Hirata and K. Arakawa, Bull. Chem. Soc. Jpn, 1973, 46, 3367. 24 E. Matteoli, Z. Phys. Chem. (Frankfurt am Main), in press. 25 0. D. Bonner and C. F. Jumper, Infrared Phys., 1973, 13, 233. 26 S. E. Jackson and M. C. R. Symons, Chem. Phys. Lett., 1976, 37, 551. 27 B. S. Krumgalz, J. Chem. Soc., Faraday Trans. 1, 1980, 76, 1887. (Wiley, New York, 1966). B. E. Conway, R. E. Verrall and J. E. Desnoyers, Z. Phys. Chem. (Leipzig), 1965, 230, 157; Trans. Faraday SOC., 1966, 62, 2738. 29 C. M. Criss and M. J. Mastroianni, J. Phys. Chem., 1971, 75, 2532.M. H. A B R A H A M , J. L I S Z I A N D E. P A P P 21 1 D. Feakins, D. J. Freemantle and K. G. Lawrence, J . Chem. SOC., Faraday Trans. I , 1974, 70, 795. 31 R. A. Stairs, Adc. Chem. Ser., 1979, 177, part 2, 167. R2 F. Kawaizumi and R. Zana, J . Phys. Chem., 1974, 78, 627. 33 M. R. J. Dack, K. J. Bird and A. J. Parker, Aust. J . Chem., 1975, 28, 955. 34 N. Martinus and C. A. Vincent, J . Chem. SOC., Faraday Trans. 1, 1981, 77, 141. 3s B. S. Krumgalz, Russ. J. Phys. Chem., 1973, 47, 956. 36 Y.-S. Choi and C. M. Criss, Discuss. Faraday Soc., 1977, 64, 204. 37 R. T. M. Bicknell, K. G. Lawrence, and D. Feakins, J. Chem. SOC., Faraday Trans. I , 1980,76, 637. 3R N-P. Yao and D. N. Bennion, J . Phys. Chem., 1971, 75, 1727. 38 U. Sen, Indian J. Chem., 1978, 16A, 104. (PAPER 1 /208)

ISSN:0300-9599    

DOI:10.1039/F19827800197

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I , 1982, 78, 213-223 Apparent Molar Volumes, Temperatures of Maximum Density and Osmotic Coefficients of Dilute Aqueous Hexame t hylene te t ramine Solutions BY THELMA M. HERRINGTON* AND ELSPETH L. MOLE Department of Chemistry, The University of Reading, Whiteknights, Reading RG6 2AD Receiued 10th February, 1981 Apparent molar volumes for solutions of hexamethylenetetramine are determined over a wide range of concentrations, using both pyknometric and dilatometric techniques, at 5, 15 and 25 OC. The temperatures of maximum density of dilute aqueous solutions of hexamethylenetetramine are found. The osmotic coefficient and solute activity coefficient are determined at 25 O C for hexamethylenetetramine using the isopiestic technique. Theories of dilute solutions are applied to solute-solute and solute-solvent interactions, assuming a rigid particle model for the repulsive potential.A rigorous statistical-mechanical theory of concentrated aqueous solutions of non-electrolytes is still a distant goal, but considerable advances have been made in establishing formal connexions between the thermodynamic properties of dilute solutions and molecular behaviour.l> Determination of the partial molar volume of the solute at infinite dilution gives information on solute-solvent interaction and together with data for the osmotic coefficient of the solvent an understanding of solute-solute interaction may be attained. In order to test the theories a solute + solvent system was chosen where the solute-solvent interaction would be anticipated to be considerably larger than the solute-solute interaction. The system chosen was hexamethylenetetramine + water.Hexamethylenetetramine has four sites available for hydrogen bonding with water but no hydrogen electron donors for hydrogen bonding with another molecule of hexamethylenetetramine. There is considerable interest in the effect of hydrogen-bonding solutes on the temperature of maximum density of water. It is primarily the rate of change of the solute-solvent intermolecular forces with temperature that determines the magnitude of the depression of the temperature of maximum density. It was decided to investigate whether the behaviour of hexamethylenetetramine was consistent with the formation of four hydrogen bonds with water.This work is an extension of our earlier investigations of aqueous solutions of non-ionic solutes. EXPERIMENTAL SECTION MATERIALS The hexamethylenetetramine was recrystallized three times from an ethanol + water mixture; the purified material gave the correct percentages on C, H, N analysis. A.R. grade sodium chloride was purified three times by precipitation from a saturated solution with hydrogen chloride gas. Deionized water from a mixed-bed ion-exchange resin was used in the preparation of all solutions; any non-ionic impurities were present to less than one part in los. The conductivity water was outgassed on a water pump and then further degassed by keeping 213214 DENSITIES OF AQUEOUS SOLUTIONS at 10 O C above thermostat temperature for the volume measurements. Solutions were made up by weight to give a precision of kO.1 mg.The molar mass of N,(CH,), was taken to be 140.1876 g mol-l and water 18.0153 g mol-l. DETERMINATION OF PARTIAL MOLAR VOLUMES The densities of the concentrated solutions were determined using Ostwald-Sprengel pyknometers; from these the apparent molar volumes of dilute solutions were determined with a dilatometer, the theory and operation of which has been described previ~usly.~ Further experimental details are given in ref. (4). TEMPERATURE OF MAXIMUM DENSITY The temperature of maximum density of hexamethylenetetramine solutions was found after each dilatometric measurement at 5 O C . A six-degree Beckmann thermometer was placed in the thermostat. The thermostat temperature was lowered 0.2 O C , the dilatometer and contents allowed to come to thermal equilibrium and the level of the liquid in the capillary stem noted.This was repeated until the level of liquid had fallen and risen again by approximately the same height. The method of analysis of the measurements to determine the temperature of maximum density, Om, is described in ref. (3). ISOPIESTIC MEASUREMENTS A standard type of isopiestic apparatus was Silver dishes with close-fitting lids were fitted into copper blocks mounted in a vacuum dessicator fitted with rubber sealing rings. The evacuated dessicator was rocked gently in a water thermostat set at 25.00f0.01 O C for up to 6 days to ensure that isopiestic equilibrium had been attained. RESULTS PARTIAL MOLAR VOLUMES Densities and apparent molar volumes of hexamethylenetetramine solutions were determined at 5 , 15 and 25 OC.Density values for the concentrated solutions are given in table 1. Data for the density of water were taken from Bigg.6 Values for the apparent molar volumes 4 V of the concentrated solutions were smoothed to give the values recorded in table 1, and these smoothed values were used to calculate the apparent molar volumes of the dilute solutions, also recorded in table 1. The apparent molar volumes can be fitted to a polynomial in the molality using the equation (see later) 4V = Vp+RT (iA’rn+!B’f’ m2+. . .). (1) The coefficients are given in table 2. The results at 5, 15 and 25 OC are represented to within 0.01, 0.03 and 0.02 cm3 mol-1 in 4 V, respectively. Our results are compared with those of White’ and Creszenzi et aZ.* in fig.1. Both these sets of workers determined the densities by pyknometric methods only. The greater self-consistency of our results is undoubtedly helped by the dilatometric technique enabling the apparent molar volume to be determined in very dilute solution so that little extrapolation is required for Vp. TEMPERATURE OF MAXIMUM DENSITY The change in the temperature of maximum density of water produced by a solute, AO,, is defined by AO,/K = O,/”C - 3.980. (2) The observed values of A&, are given in table 3.TABLE 1 .-DENSITIES AND APPARENT MOLAR VOLUMES OF AQUEOUS HEXAMETHYLENETETRAMINE SOLUTIONS AT 5 , 1 5 AND 25 O C T = 278.15 K T = 288.15 K T = 298.15 K molality molality molality /mol kg-' p/g cmP3 4V/cm3 mol-l /mol kg-l p/g cm-3 4V/cm3 mol-l /mol kg-l p/g cm-3 4V/cm3 mol-' '-1 __ water 0.008 13" 0.0 15 26" 0.020 84" 0.025 38" 0.028 86" 0.069 90" 0.089 33" 0.106 42" 0.503 4 0.969 9 1.493 2 2.003 0 2.558 0 2.969 6 3.450 8 3.886 9 4.425 1 0.999 964 - - - - - - - - 1.014 98 1.027 66 1.040 70 1.052 35 1.064 04 1.072 01 1.080 67 1.087 94 1.096 42 - 108.87 108.88 108.86 108.85 108.86 108.86 108.84 108.85 108.72 108.62 108.49 108.36 108.21 108.14 108.08 108.05 107.98 water 0.004 35" 0.015 27" 0.020 70" 0.025 88" 0.031 81" 0.069 52" 0.089 36" 0.494 6 0.992 9 1.501 2 2.009 0 2.488 6 2.954 4 3.466 0 4.015 1 5.029 2 5.474 0 0.999 101 - - - - - - - 1.013 46 1.026 63 1.038 9 1 1.050 15 1.056 00 1.068 73 1.077 69 1.086 5 1 1.100 81 1.106 34 ~~ - 109.72 109.76 109.75 109.74 109.77 109.73 109.71 109.67 109.52 109.39 109.28 109.15 109.10 109.02 108.97 108.96 108.99 water 0.025 70" 0.029 85" 0.047 04" 0.088 18" 0.108 36" 0.494 5 1.005 9 1.501 6 2.022 6 2.493 0 2.940 3 3.276 8 3.286 1 3.996 6 4.078 5 4.400 1 5.551 6 0.997 047 - - - - - 1.011 01 1.024 34 1.030 60 1.047 27 1.056 56 1.064 73 1.070 60 1.070 79 1.082 03 1.083 28 1.087 82 1.102 64 - 110.58 110.59 110.57 110.52 110.51 110.46 110.29 110.20 110.08 110.02 109.98 109.92 109.90 109.85 109.84 109.85 109.84 a Dilatometric determinations.216 DENSITIES OF AQUEOUS SOLUTIONS TABLE 2.-cOEFFICIENTS OF THE POLYNOMIAL v = v$+ + RT($A’m + !jBt’mz + .. . ) A’/ 10-4 kg B+’/ 10p5 kg2 T/K V$+/cm3 mo1-l mol-l atm-l molP2 atm-l 278.15 108.87 - 0.273 288.15 109.76 - 0.263 298.15 110.58 - 0.245 0.32 0.38 0.37 TABLE 3 .-TEMPERATURE OF MAXIMUM DENSITY OF HEXAMETHYLENETETRAMINE AQUEOUS SOLUTIONS molality / 1 0-2 mol kg-l - AB,/K water 0.8 1 1.52 2.08 2.54 2.89 6.99 8.93 10.64 0.000 0.085 0.125 0.185 0.210 0.260 0.530 0.610 0.700 1 I 1 73.15 283 15 293.15 303.15 313 I! T/K FIG.1 .-Temperature dependence of the apparent molar volume at infinite dilution of hexamethylene- tetramine aqueous solutions. Values at 5, 15 and 25 O C are from e, this work; 0, ref. (6) and 0, ref. (7).T. M. HERRINGTON A N D E. L. MOLE 217 ACTIVITY AND OSMOTIC COEFFICIENTS The osmotic coefficients of aqueous solutions were determined over the range 0.5-4.5 mol kg-l at 25 *C against aqueous sodium chloride solutions as the isopiestic standard. Table 4 gives molalities of isopiestic pairs of sodium chloride and hexa- methylenetetramine solutions.The values for the osmotic coefficients of sodium chloride were taken from the compilation of Robinson and stoke^.^ The osmotic coefficients of hexamethylenetetramine are well represented by the equation 4 = 1 +0.2277 m- 1.60 x lop3 m2 (3) In y, = 0.4554 m - 2.40 x m2. (4) ( 5 ) (the mean deviation in 4 is 0.005), and hence the activity coefficient is given by Creszenzi et a1.* found that 4 is linear in molality up to 4.7 mol kg-l and given by 4 = 1 +0.220 m. TABLE 4.-ISOPIESTIC SOLUTIONS OF SODIUM CHLORIDE AND HEXAMETHYLENETETRAMINE molality molality sodium hexamethylenetetramine chloride/mol kg-l /mol kg-l 0.402 90 1.182 32 1.528 61 1.712 17 2.016 04 2.454 51 2.566 13 3.025 31 3.321 98 3.619 16 4.254 58 0.643 54 1.628 14 2.015 60 2.224 70 2.537 44 2.990 72 3.087 99 3.536 33 3.819 04 4.105 30 4.747 66 DISCUSSION Let us write for the Gibbs energy of a solution of mole ratio of solute to solvent m10 G-'/N,k T = p:/k T+ m&/k T - fii+ mlnm+ iA,,iiP + ~B2,,W' + Then for the partial molecular volume of the solvent V, = ~ ~ - k T [ ~ ( c ? A ~ ~ / t ? p ) ~ f i i ~ + ~ ( t ? B ~ ~ ~ / Q ~ ) , f i i ~ + .. .] and for the solute u, = v ~ + k T [ ( a A , 2 / i 3 p ) T ~ + ( a B 2 2 2 / i 3 p ) T l ~ 2 + . . .I. Thus the total volume, V, of the solution is given by V/ N , = V: + mvp + k T[i A,,'@, + +B2,,'m3 + . . . ] 8 . . .218 DENSITIES OF AQUEOUS SOLUTIONS where the dash represents differentiation with respect to pressure, and the apparent molar volume is given by (10) 4 % = Vp+RT(iA’m+$Bm2+.. .) where A’ = A2,’M1, B’ = B,,,/M;, etc. solvent the osmotic pressure, n, is given by According to the theory of McMillan and Mayerl for a solution of a solute in a n/kT = n+ B,*n2+ B,*,,n3+. . . . ( 1 1) (12) Hillll has shown that the coefficients A,, etc. may be related to the coefficients B,*, etc. For example where B:: = -b:,. [In relating coefficients higher than A,, (i.e. B,,, etc.) to the coefficients B**, it must be remembered that these equations are only applicable in dilute solutions when y - 1 21 In y ; in more concentrated solutions A,, V? = 2B;: - V? + byl In y = A,,m+ B t m 2 + . . . (13) B t = B,,,-4A222 etc.] (14) (15) Thus instead of eqn (10) in general we write #& = Vp+RT(+A’m+$Bt’rn2+.. .). Now byl, the solute-solvent cluster integral, is related to the partial molecular volume of solute at infinite dilution bylo byl = -up+kTu. (16) Thus values for the solute-solvent interaction can be calculated from eqn (1 6). From the experimental values for the activity coefficient values for the solute-solute interaction can be calculated from eqn (1 2), (1 3) and (1 6). SOLUTE-SOLVENT ATTRACTION Values for the solute-solvent interaction, NB:: (where B;f;O = -byl) are given in table 5. Compressibility data for water were taken from the compilation of Bradley and Pitzer.12 Now byl is given by byl = -471 [ I -exp (-co11/kT)r2dr] (17) sb; where coil is the potential of mean force between one molecule of solute and one of solvent in the pure solvent (including averaging of the force over all rotational coordinates) and Y is the distance apart of the centres of the molecules.The cluster integral byl consists of an attractive and a repulsive contribution; it can be arbitrarily split into those components in the following way. Let R be the distance of closest approach of the two molecules, then the repulsion will occur for Y < R, and attraction for Y > R, and the integral can be split into repulsive and attractive parts as follows: B;E,O = 4n [ -exp ( - d l / k T ) ] r2dr+4n [I -exp (-coll/kT)] r2dr (18) (19) s:‘ s:: = S+@* where S is the repulsive and @* the attractive contribution.T. M. HERRINGTON AND E. L. MOLE 219 If the form of the potential function mlr is known, then the integration could be performed to yield BrF. The simplest potential function regards the molecules as rigid spheres.For two hard spheres of diameters R, and R, (20) n S = - (R, + R,)3. 6 X-ray studies13 have shown the hexamethylenetetramine molecule to be almost spherical with slight protrusion of the>CH, groups; from this data and Corey-Pauling models the diameter was taken as 6.8 A. The water molecule can be considered to be a sphere of diameter 3.04 A. Then NS = 300 cm3 mol-1 and the attractive contri- bution at 25 O C is given by NOA = NB,*,o- NS = - 191 cm3 mol-l. Values at other temperatures are given in table 5; on this model the attractive contribution increases with decreasing temperature. TABLE 5.-ATTRACTIVE CONTRIBUTIONS TO THE SOLUTE-SOLVENT INTERACTION COEFFICIENT VF R TIC NB,*P NS - N<DA T/K /cm3 mol-' /cm3 mol-l /cm3 mol-l /cm3 mol-l /cm3 mol-l hexame t h ylenete tra- mine + water 278.15 108.87 1.14 107.73 300 193 hexamethylenetetra- mine + water 288.15 109.76 1.13 108.63 300 192 hexamethylenetetra- mine + water 298.15 110.58 1.11 109.47 300 191 sucrose + water 298.15 211.49 1.11 210.38 476 266 urea + water 298.15 44.2 1.11 43.10 176 143 glucose +water 298.15 112.2 1.11 11 1.10 358 246 It is interesting to compare the values of NOA for hexamethylenetetramine with those for solute-solvent interaction in aqueous solutions of urea, glucose and sucrose.In order to calculate the rigid sphere contribution to B;T,O these three solute molecules are assumed to approximate to prolate ellipsoids. For a hard sphere of radius a, and a hard prolate ellipsoid with short axis 2a, and long axis 2b2l4 +a, 1+- 1 +&)I (21) ( 1 - c 2 2& I - & 4 4 3 3 S = -nai +-naib, + 2na,b, where c2 = (b;--@)/b;.The sucrose molecule has semiaxes of 5.9 and 3.5 A using Corey- Pauling models and crystallographic data,15 the urea molecule is assumed to be an ellipsoid with semiaxes 3 and 2.4 A and glucose to have semiaxes 4.8 and 3.2 A. At 25 O C V p for sucrose is 21 1.49 cm3 m ~ l - l , ~ for urea 44.2 cm3 mol-1 l6 and for glucose 1 12.2 cm3 m ~ l - ~ . ~ ' The attractive contributions to the Solute-solvent interaction at 25 O C are given in table 5. The attraction between hexamethylenetetramine and water molecules is intermediate between that for sucrose +water and urea + water. This is in agreement with hexamethylenetetramine having four hydrogen-bond accepting sites.The interaction for glucose with probably five hydrogen-bond sites is only slightly less than that for sucrose with more sites available. The solute-water attraction is weaker for urea and rather less than might be anticipated; it is, however, in agreement with spectroscopic evidencela which shows that urea-water hydrogen-bond interactions exist but are very short-lived. 8-2220 DENSITIES OF AQUEOUS SOLUTIONS SOLUTE-SOLUTE ATTRACTION From eqn (12) and (16) 2B:: = A,,$ + 2143 - kTK (22) so that a value for B,*,O can be calculated from the partial molar volume at infinite dilution and the activity-coefficient data. Hexamethylenetetramine shows large deviations from ideal behaviour. At 4.7 mol kg-l # is 2.04 compared with 1.45 for sucrose.1g The molar volume of water at 25 O C is 18.07 cm" mo1-1.20 From eqn ( 5 ) A,, = 0.4554/M1 and hence NB:: is 338 cm3 mol-l.Now BZ: can be considered, like B::, to be composed of an attractive and a repulsive contribution from the intermolecular forces, thus B:: = S+(DA (23) where S is the repulsive and @A the attractive contribution. Isiharal* has calculated the repulsive contribution for hard ellipsoids and finds that S =f(4u2) where u, is the volume of a solute molecule and f is unit for a sphere. Taking the hard-sphere diameter of hexamethylenetetramine as 6.8 i 1 3 gives an attractive contribution N(DA of - 58 cm3 mol-l. This value of (DA is a measure of the pairwise interaction between two hexamethylenetetramine molecules in water.In table 6 it is compared with values for urea, sucrose and glucose calculated by the same method. The calculations for urea and sucrose are given in ref. (21). For glucose the osmotic-pressure data of Morse2, were used for B,*,O. The glucose molecule approximates to a prolate ellipsoid (v, = 4d:1,/3 for I, > I,) with semiaxes 3.2 and 4.8 A andffactor 1.05. TABLE 6.-ATTRACTIVE CONTRIBUTION TO THE SOLUTE-SOLUTE INTERACTION COEFFICIENT AT 25 O C NB;; NS -N@AA -N@AB /cm3 mol-l /cm3 mol-l /cm3 mol-l /cm3 mol-' - hexamethylenetetramine 338 396 58 urea 1 179 178 174 glucose 117 520 403 229 sucrose 285 783 498 557 a Our values. Kauzmann and As can be seen from table 6, the attraction between two solute molecules decreases in the series sucrose > glucose > urea > hexamethylenetetramine.This is consistent with no suitable hydrogen electron donors for hydrogen bonding in the molecule of hexamet h ylene tet ramine. have calculated values of the pairwise attraction for many non-electrolytes in aqueous solution. They used the following equation to calculate B,*,O Kauzmann and NB:; = ( V p - V,") + V,"(+ - B) where B is the coefficient in the equation for the expansion of the logarithm of the solvent activity coefficient,f,, in a power series of the mole fraction of solute, x,, thusT. M. H E R R I N G T O N A N D E. L. MOLE 22 1 Eqn (25) is shown to be equivalent to our eqn (22) in ref. (4). They then considered the repulsive contribution to be given by S = 4vF Their results are compared with ours in table 6.It can be seen from both methods that the magnitude of the attractive contribution increases with the number of groups capable of hydrogen bonding with another solute molecule. TEMPER A T U R E OF MA X I MUM D ENS1 TY-SO LU TE-SO L U TE A N D SOLUTE-SOLVENT INTERACTION There has been a great deal of interest in the effect of solutes on the temperature of maximum density of water. Whether a solute raises or lowers the temperature of maximum density depends on the nature of the solute. Despretzz4 found that many electrolytes lowered the temperature of maximum density, the effect being proportional to the solute concentration. However, it has been foundz5 that alcohols raise the temperature of maximum density. Let us write V = V,O/M,+m@V and V,O = v:" [ 1 + a,(8- 8,)2] for the temperature dependence of the molar volume of water in the neighbourhood of its temperature of maximum density.Then substituting eqn (27) into (26) and differentiating with respect to temperature gives for the solution at its temperature of maximum density The first term on the right-hand side of eqn (28) is the 'ideal dilute' contribution to the change in the temperature of maximum density caused by the addition of a solute, and the second and higher terms are the non-ideal contribution. From eqn (16) the ' ideal-dilute ' contribution involves the rate of change of solute-solvent interactions only with temperature, whereas since3 (29) the higher terms also involve the rate of change of solute-solute interactions with temperature.If we consider [a Vp/llTIom and [a( TA')/i3T],n, to be constant for small values of A@,, then (30) In table 7 the values obtained for [ and < for hexamethylenetetramine are compared with those obtained for other substances3 The value of (?Vp/3T)Qm is 9.25 x lop2 cm3 mol-l K-l. Using values of 8.0 x lop6 Kp2 and 18.02 cm3 mol-l for a, and K*", respectively,20 gives a calculated value for [ of - 5.8 K mol-1 kg, compared with the experimental value of -6.3 K mol-l kg. The sign and magnitude of [ is determined by the sign of c? Vp/c?T. For butan-2-01 and ethanol this is negative, which results in the temperature of maximum density of water being raised by these solutes. For the others it is positive and 8, is lowered. Hexamethylenetetramine has an effect intermediate between that of glycerol and sucrose as would be expected for a molecule with four sites capable of hydrogen bonding with water.A 2 , 4 = - 2bi2 + 2by1 - k TIC A$, = [m+<m2+xm3+. . . .222 DENSITIES OF AQUEOUS SOLUTIONS TABLE 7.-ANALYSIS OF THE EFFECT OF SOLUTE-SOLVENT INTERACTION ON THE TEMPERATURE OF MAXIMUM DENSITY but an-2-01 4.2 - 10.3 ethanol 1.5 - 2.0 ethylene glycol - 3.2 - 0.4 glycerol -4.1 - 1.5 hexamethylenetetramine - 6.3 25 sucrose - 18.3 20 CONCLUSION The analysis of the McMillan-Mayer interaction coefficients for the solute-solute and solute-solvent cluster integrals of aqueous solutions of hexamethylenetetramine supports our predictions. The solute-solute attractive contribution to B,*,O is consid- erably less than the solute-solvent contribution to and yet each lies in the correct sequence with respect to other hydrogen-bonded molecules. Thus, in spite of the nake model assumed for the repulsive interactions, the calculated quantities are of the anticipated order of magnitude.This gives us confidence in applying the McMillan- Mayer and Hill theoretical equations to aqueous solutions of non-electrolytes at a molecular level. It is instructive to obtain an approximate estimate of the effect of hydrogen bonding on the attractive part of BrF. It is assumed that at the surface of the hexamethylenetetramine molecule is a square-well of depth d1 and width d. Then @* = [I -exp( -coll/kT)] dx dy dz. d l is taken as 16 kJ mo1-1,26 the known order of magnitude for the enthalpy of formation of this hydrogen bond.A value of - 191 cm3 mol-1 for the integral gives d = 0.80 A which is a reasonable figure for atomic vibrations in the 0-H * - N bond. We thank the S.R.C. for the award of a Research Studentship to E.L.M. GLOSSARY OF SYMBOLS cluster integral for two molecules of solute in pure solvent cluster integral for one molecule of solute and one of solvent in pure solvent Gibbs energy Boltzmann's cons tan t molar ratio of solute to solvent (N2/N1) molality of solute molar mass of solvent in kg mol-l number density of solute Avogadro's constant number of molecules of solvent number of molecules of solute gas constantT. M. HERRINGTON AND E. L. MOLE repulsive contribution to the cluster integral absolute temperature partial molecular volume of solvent molecular volume of pure solvent partial molecular volume of solute partial molecular volume of solute at infinite dilution partial molar volume of solute at infinite dilution apparent molar volume of solute activity coefficient of solute on the molality scale osmotic pressure osmotic coefficient attractive contribution to the configuration integral density of solution isothermal compressibility of solvent temperature of maximum density of the solution 223 W.G. McMillan and J. E. Mayer, J . Chem. Phys., 1945, 13, 276. T. L. Hill, J. Am. Chem. SOC., 1957, 79, 4885. J. E. Garrod and T. M. Herrington, J. Phys. Chem., 1970, 74, 363. E. L. Mole, Thesis (Reading University, 1975). R. A. Robinson and R. H. Stokes, J . Phys. Chem., 1961, 65, 1954. P. H. Bigg, Br. J. Appl. Phys., 1967, 18, 521. 'I E. T. White, J. Chem. Eng. Data, 1967, 12, 285. V. Creszenzi, F. Quadrifoglio and V. Vitagliano, J. Phys. Chem., 1967, 71, 2313. R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworths, London, 2nd edn, 1959). T. L. Hill, J . Chem. Phys., 1959, 30, 93. D. J. Bradley and K. S. Pitzer, J . Phys. Chem., 1979, 83, 1599. l o J. E. Garrod and T. M. Herrington, J. Phys. Chem., 1969, 73, 1877. l 3 L. N. Becka and D. W. J. Cruikshank, Proc. R . SOC. London, Ser. A, 1963, 273, 435. l 4 A. Isihara, J . Chem. Phys., 1950, 18, 1446. l 5 G. A. Jeffrey and R. D. Rosenstein, Adv. Carbohydr. Chem., 1964, 19, 11. l6 R. H. Stokes, Austr. J . Chem., 1968, 20, 2087. J. B. Taylor and J. S. Rowlinson, Trans. Faraday Soc., 1955, 51, 1183. E. G. Finer, F. Franks and M. J. Tait, J . Am. Chem. Soc., 1972, 94, 4424. l 9 R. A. Robinson and R. H. Stokes, J . Phys. Chem., 1961, 65, 1954. *O G. S. Kell, J. Chem. Eng. Data, 1970, 12. 66. *l J. E. Garrod and T. M. Herrington, J. Chem. Soc., Faraduy Trans. I , 1981, 77, 2559. 2 2 H. N. Morse, Publ. Carnegie Inst. Washington, 1914, 198. 23 J. J . Kozak, W. S. Knight and W. Kauzmann, J . Chem. Phys., 1968, 48, 675. 24 M. C. Despretz, Ann. Chim. Phys., 1839, 70, 49. 25 F. Franks and B. Watson, Trans. Faraday Soc., 1967, 63, 329. 26 G . C. Pimentel and A. L. McClellan, The Hydrogen Bond (W. H. Freeman, New York, 1950). (PAPER 1 /2 19)

ISSN:0300-9599    

DOI:10.1039/F19827800213

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I, 1982, 78, 225-236 Osmotic Coefficients of the Ternary System Water + Potassium Chloride + Sucrose at 0 O C BY THELMA M. HERRINGTON* AND CHRISTOPHER P. MEUNIER Department of Chemistry, University of Reading, Reading RG6 2AD Received 10th February, 198 1 The freezing points of aqueous solutions of potassium chloride have been measured in the concentration range 0.2-2.8 mol kg-'. Osmotic coefficients have been calculated and compared with the results of previous workers. The freezing points of the ternary system water + potassium chloride + sucrose have been measured for I : I mole ratio sucrose : KCl from 0.15- 1.5 mol kg-' KCl, and for a 1 : 3 mole ratio sucrose : KCl from 0.2-2.0 mol kg-' KCl. Osmotic coefficients were calculated at 0 OC and fitted to an analytic formula.The experimental results are discussed in terms of the McMillan-Mayer theory of solutions. During the last decade there has been considerable interest in the properties of ternary aqueous solutions containing non-electrolytes and electrolytes. Salting-in and salting-out effects of alkali-metal and alkaline-earth halides on alcohols, amino acids and peptides have been determined by various worker~.l-~ The objective, of gaining some understanding of solute-solute interactions in these systems, has been interpreted using several different theories - electrostatic, classical therm~dynamic,~ scaled- particle,6 and surface effects' - with little pattern emerging in the final picture. A break- through in the understanding of solutions containing a single non-electrolyte was the work of Stigters on aqueous solutions of sucrose and glucose, which he interpreted using the Hill9 and McMillan-Mayer'O theories.We have extended this approach to ternary systems using an extension of the Debye-McAulay theory for the electrostatic interactions.ll> l2 It is found in crystallizing sucrose from solutions containing other electrolytes and non-electrolytes, e.g. molasses, that the solubility of the sucrose is considerably increased. It has been suggestedl3 that 'association' of sucrose and KCl occurs on a one-to-one basis. It was decided to extend our earlier work14 on the ternary system sucrose + KCl +water to lower temperatures and investigate the effect of solute-solute interactions on the freezing point of the system.EXPERIMENTAL The equilibrium method of determining freezing-point depressions of solutions was used. At equilibrium it is necessary to determine both the temperature and the concentration of solute in the solution in equilibrium with ice. Full experimental details are given in ref. (12). APPARATUS Two identical silvered Dewars (one for solution and one for water) were each suspended from the top of a cylindrical copper can (the internal heat shield) by six springs. The two copper cans were suspended from the iid of an oval copper submarine water-tight jacket (the external heat shield) itself completely immersed in the thermostat. Each Dewar had a close-fitting polythene lid, through which passed stirrers, sampling tubes and closed glass tubes for a 225226 FREEZING POINTS OF AQUEOUS SOLUTIONS thermopile and platinum resistance thermometer. The internal arrangement in each Dewar was identical to remove any differential errors from the effect of hydrostatic pressure on the freezing points or on the gas solubility.Two electronic controllers kept the temperature of each copper heat shield the same as the contents of its Dewar; thus each Dewar was in an adiabatic environment and heat leakage was negligible. A mixture of methanol and water was used for the thermostatted bath in which the whole apparatus was immersed; its temperature was ca. 0.2 "C below the freezing point of the solution. Efficient stirring of the solutions was essential as the viscosity of concentrated solutions of sucrose increases rapidly with decreasing temperature. Both gas and mechanical stirrers were used.The mechanical stirrers were made of nylon-coated stainless steel. The gas stirrers were based on the design of Brown and Prue;15 the nitrogen gas was pre-cooled and saturated with water vapour. Initially KCl or KCl and sucrose in the required mole ratio were dissolved in cooled conductivity water in the Dewar flask and seeded with small ice particles. A glass sample tube, containing a sintered glass filter to prevent ice particles entering, enabled samples to be withdrawn for conductivity measurements, and also allowed further dilutions to be made; a small amount of solution was first sucked into a dummy cell, before the sampling cell was connected, to remove any solution in the sampling tube.After sampling, an equal volume of conductivity water was added under nitrogen pressure. A sample was taken only when the temperature drift was less than two thousandths of a degree per hour. The solutions were analysed conductometrically. The conductance cell was designed according to the recommen- dations of Jones and Bollinger.16 The cell was calibrated with solutions of known molality saturated with nitrogen. The thermopile was made of chromekonstantan and had 25 junctions. The e.m.f. was determined by a null method using a Keithley microvoltmeter (model 150B) and a Tinsley Vernier potentiometer (model 4363-E Auto). It was calibrated using the freezing-point data of Scatchard and Prentiss17 and of Harkins and Roberts.la The calibration was checked periodically.The precision obtained was & 2 x lo-* K, giving at 0.1 mol kg-l an error of 0.1 % in the freezing point. The most concentrated solution for which data are given is 1.3 mol kg-l,17 so that, for solutions more concentrated than 1 mol kg-l, a platinum resistance thermometer, calibrated to 2 x K, was used. There is a negligible error introduced between the difference in hydrostatic head between a solution and pure water. The most concentrated solution used had a density of 1.2 g ~ m - ~ , so that for a 10 cm head the difference in freezing point would be 3 x K. The effect of change in atmospheric pressure was usually negligible; an increase of 10 cm of mercury decreases the freezing point of water by lop3 K. The nitrogen gas used for stirring is not as soluble in a solution as it is in pure water at the same temperature.The freezing-point depression for nitrogen in water at 273 K is 2 x K at saturation; nitrogen is less soluble in potassium chloride solutions than in water so that the measured difference in freezing point will be too small. However, the solubility of nitrogen increases with decreasing temperature and this acts in the opposite direction to the 'salting-out' effect. It is estimated that the net effect gives an error of 3 x K for 3 mol kg-' ; if the salting-out is negligible then the temperature difference would be too large by K at 1 mol kg-l and 3 x K for 1 mol kg-' potassium chloride and 4 x K at 3 rnol kg-'. MATERIALS All solutions were prepared using once distilled, previously deionized water.The water was not used unless the conductivity was < 1 x lop6 W1 cm-l. The sucrose was supplied by the research department of Tate and Lyle Ltd; it was of 99.993% purity containing 0.002% invert sugar, 0.002% ash and 0.003% organic matter. It was stored in a desiccator before use. The potassium chloride was a B.D.H. AR reagent, recrystallized three times from conductivity water, dried at 150 "C and then stored as the sucrose. Solutions were made up by mass and buoyancy corrections applied to give a precision of & 0.1 mg. The molar mass of KC1 was taken to be 74.555 g mol-l, sucrose 342.3019 g mol-l and that of water 18.0153 g mol-l.T. M. HERRINGTON AND C. P. MEUNIER 227 RESULTS POTASSIUM CHLORIDE The osmotic coefficient at 0 "C was calculated from the formulaelg where a, is the activity of water, m3 is the molality of KCl, M , is the molar mass of water in kg mol-l, T, is the freezing point of pure water in K, 8 is the depression of freezing point, T = - 8, AH: is the heat of fusion of pure water at T,, L, is the relative partial molar enthalpy of water in the solution at T,, J , is the relative partial molar heat capacity of water in the solution at T,, ACi, is the change in heat capacity of water on fusion at T, and p is the temperature coefficient in the relation ACpl = a +pT, where ACpl is the difference between the partial molar heat capacity of water in the solution and the molar heat capacity of ice.Values for L, and J1 were taken from Randall and Rossini,20 and for AH: Giauque and Stout's value of 6007 J m o t 1 was used.21 The data of Osborne et a1.22 and O ~ b o r n e ~ ~ give AC;l as 38.1 J K-l mol-l.is a function of the composition of the solutions but in the absence of any data for our systems it was estimated from the temperature variation of the heat capacities of ice and water near 0 0C;24 the value was -0.196 J K-2 mol-l. (For 8 values < 5 "C a simpler formula could have been used to calculate 4 at 0 "C but, as the calculations were computer programmed, it was more convenient to use the exact formula throughout.) Our results are plotted in fig. 1 ; the estimated error in the osmotic coefficient at different values of the molality is shown in the figure. I 0.96 0.94 0.92 4 3 0.90 0.88 0861 1 1 I 1 1 1 0 1 .o 2 .o 3.0 m 3/m0l kg-' FIG. 1 .-Osmotic coefficient of potassium chloride plotted as a function of molality at 0 "C.The smooth curves is the least-squares fit to eqn (4); 0, our data; 0, Scatchard and Prentiss;" 0, Damkohler and Wein~ierl.~'228 FREEZING P O I N T S OF A Q U E O U S S O L U T I O N S POTASSIUM CHLORIDE+SUCROSE Two series of mixtures of fixed mole ratios were used for the measurements; the mole ratios chosen were 1 : 3 and 1 : 1 sucrose: KCl. These ratios were exact to the accuracy of weighing. TABLE 1 .-FREEZING-POINT DEPRESSIONS AND OSMOTIC COEFFICIENTS AT 0 O C FOR AQUEOUS SOLUTIONS OF 1 : 1 SUCROSE : POTASSIUM CHLORIDE AND 1 3 SUCROSE POTASSIUM CHLORIDE sucrose: KCl = 1 : 1 sucrose: KCl = 1 : 3 m,/mol 4 1 1 4 1 1 m3lmol m,/mol 4 1 3 4 1 3 kg-' 8/K (obs) (calc) kg-l kg-l 8/K (obs) (calc) 0.1505 0.1553 0.2743 0.3028 0.3776 0.3838 0.39 15 0.3919 0.4550 0.4744 0.5193 0.5304 0.5453 0.5642 0.5958 0.6012 0.6859 0.7380 0.81 17 0.8157 0.8852 0.8939 0.91 15 1.0108 1.0652 1.0756 1.0912 1.1075 1.1222 1.2188 1.3677 1.4982 0.7965 0.8194 1.4399 1.5870 1.9760 2.008 1 2.05 12 2.0520 2.3815 2.48 13 2.7137 2.7697 2.8506 2.9467 3.1089 3.1371 3.5803 3.8500 4.2360 4.2559 4.6188 4.6665 4.7573 5.2773 5.561 1 5.6166 5.6964 5.78 14 5.8605 6.3692 7.1505 7.8392 0.9489 0.9460 0.941 6 0.9402 0.939 1 0.9391 0.9403 0.9397 0.9396 0.9390 0.9384 0.9377 0.9389 0.938 1 0.9374 0.9375 0.9383 0.9380 0.9387 0.9387 0.9390 0.9393 0.9394 0.9404 0.9407 0.9410 0.9408 0.9410 0.941 5 0.9427 0.9444 0.946 1 0.948 1 0.9478 0.9421 0.941 3 0.9398 0.9397 0.9396 0.9396 0.9389 0.9388 0.9385 0.9385 0.9384 0.9383 0.9383 0.9384 0.9385 0.9387 0.9390 0.9390 0.9395 0.9396 0.9397 0.9406 0.941 1 0.9412 0.9414 0.9415 0.941 7 0.9428 0.9447 0.9463 0.2336 0.3590 0.3721 0.3837 0.3910 0.4773 0.5027 0.5185 0.5553 0.6035 0.6365 0.65 12 0.7790 0.7904 0.8728 0.9705 0.9904 1.0710 1.0839 1.1246 1.2330 1.2975 1 .3940 1.4108 1.4137 1.4358 1.4682 1.5080 1.5458 1.5668 1.6371 1.6713 1.6887 1.7024 1.7844 1.8038 1.8270 1.9608 2.0163 0.07787 0.1197 0.1240 0.1279 0.1303 0.1591 0.1676 0.1728 0.1851 0.2012 0.2122 0.2171 0.2597 0.2635 0.2909 0.3235 0.3301 0.3570 0.3613 0.3749 0.41 10 0.4325 0.4647 0.4703 0.4712 0.4786 0.4894 0.5027 0.5153 0.5223 0.5457 0.5571 0.5629 0.5675 0.5948 0.601 3 0.6090 0.6536 0.672 1 0.9323 1.4192 1.4678 1.5136 1.5407 1.8772 1.9738 2.0345 2.1724 2.3576 2.4860 2.5410 3.0261 3.0716 3.3826 3.7567 3.8284 4.1386 4.1866 4.3410 4.7484 4.9928 5.3593 5.4202 5.4309 5.5169 5.6387 5.7896 5.9295 6.0098 6.278 1 6.4009 6.4729 6.5236 6.8307 6.907 1 6.99 17 7.4920 7.7023 0.9202 0.9 120 0.9 100 0.9101 0.909 1 0.9077 0.9064 0.9059 0.9034 0.9023 0.9023 0.9016 0.8983 0.8988 0.8968 0.8964 0.8954 0.8955 0.8952 0.8950 0.8938 0.8936 0.8935 0.8932 0.8932 0.8935 0.8934 0.8935 0.8929 0.893 1 0.8935 0.8927 0.8936 0.8935 0.8932 0.8939 0.8936 0.8937 0.8941 0.9 198 0.91 17 0.91 10 0.9105 0.9101 0.9066 0.9057 0.9052 0.9040 0.9027 0.9018 0.901 5 0.8989 0.8987 0.8973 0.8960 0.8958 0.8950 0.8949 0.8945 0.8939 0.8935 0.8932 0.8932 0.8932 0.8932 0.893 1 0.8930 0.8930 0.8930 0.8930 0.893 1 0.893 1 0.893 1 0.8933 0.8934 0.8935 0.8940 0.8943T.M.HERRINGTON AND C. P. MEUNIER 229 The osmotic coefficients were calculated from the equation bij = -In a1/(m2 + 2m3) M , (3) where ij denotes the mole ratio of sucrose: KCl, and eqn (2). Values of L, and J1 for the sucrose+ KCl solution were calculated from the data for aqueous solutions of KC120 and for aqueous sucrose s01utions~~~ 26 assuming that the interactions between the two solutes were negligible. (It was estimated that this introduced an error of < 0.0001 in bij in the molality range investigated.) For sucrose solutions data for L, were taken from Gucker et al.25 and the values of Gucker and Ayres26 were used for J,. The observed osmotic coefficients are denoted by 4ij(obs) and are given in table 1. The results are plotted in fig. 2; the estimated errors in the osmotic coefficient are also shown in the figure.DISCUSSION Our results for potassium chloride are plotted in fig. 1 together with those of Scatchard and Prentiss17 and Damkohler and W e i n ~ i e r l . ~ ~ These values (except those of Damkohler and Weinzierl below 1 mol kg-l) were fitted to the Pitzer equation:28 (4) 43 - 1 = - Ad m3-f/( 1 + bm3-f) +$m3 +D1 m3 c a m s i + A , = (2n Np,); (e2/4n E kT)f/3 where e is the charge of a proton, N is Avogadro's constant, E is the rationalized permittivity and pw is the density of water (expressed in kg per unit volume); values for the relative permittivity of water were those of Malmberg and M a r y ~ t t , ~ ~ and for the density of water the values of Tilton and Taylor30 were used. At 0 O C A , = 0.3773 kgi mol-i.For b and a, Pitzer's optimized values of 1.2 and 2.0 kg-f mol-4 were used. The values obtained by a least-squares fit for the other coefficients were P/kg mol-l = 0.02661 k 0.001 05 pl/kg mol-1 = 0.17806&0.00500 C/kg mol-1 = 0.00248 0.000 37. The smooth curve for values of 4,(calc) calculated according to eqn (4) is plotted in Literature data were used to calculate the osmotic coefficients of sucrose at 0 "C. The freezing-point data of Aschaffenburg and King3, at 0.2714 mol kg-I and of Morse et a/., quoted by Timmerman~,~~ from 0.5 to 1.0 mol kg-l were used; from 1 to 7 mol kg-l the vapour-pressure data of Berkeley et al.33 gave accurate values of the osmotic coefficient. The osmotic coefficient of sucrose, b2, was fitted to the formula fig.1. where b2-1 = Pm2+Qmi Plmo1-I kg = 0.124 18 k 0.001 69 Q/mol-2 kg2 = - 0.005 13 & 0.000 29. The coefficients of the power series in eqn ( 5 ) can be used to give information on solute-solute interactions in aqueous sucrose solutions. From eqn (7 1) of Garrod and Herringtonll (6) NB;; = Vy+ V P - ~ R T K where l?:: = -b:2 (b:2 is the cluster integral for two molecules of solute in pure230 0.92 @ij 0.91 0.90 FREEZING POINTS OF AQUEOUS SOLUTIONS - - - 0'93 t 0.89 I I I ' I I I I 0 0.5 1 .o 1.5 2.0 rn ,/mol kg- ' FIG. 2.-Osmotic coefficients of aqueous solutions of (a) 1 : 1 sucrose:potassium chloride and (b) 1 : 3 sucrose: potassium chloride plotted as a function of the molality of potassium chloride at 0 O C . The smooth curves are the least-squares fit to our data, eqn (18); 0, experimental values. solvent), A,, is the linear coefficient in the expansion of In y , as a power series in the mole ratio m,, i.e.In y , = A2,m2 -t Btm; -k . . . , ( 7 ) V(: is the molar volume of pure solvent, P'P is the partial molar volume of solute at infinite dilution, K is the solvent compresibility, and m, = N , / N , ( N , and N , are the number of molecules of solute and solvent, respectively). The coefficient A,, is related to P of eqn ( 5 ) by A,, = 2P/M,, where M, is the molar mass in kg mol-l; thus, using our value for P, A,, = 13.786. For sucrose at 0 OC, V p is 206.31 cm3 mol-l l4 and, for water, RTK is 1.14 cm3 mol-1 and Vy is 18.02 cm3 m01-l.~~ These values give a value for NBZ*," of 330 cm3 mol-1 at 0 O C compared with Stigter'ss value of 305 cm3 mo1-1 at 25 OC.We can consider B:: as being composed of an attractive and a respulsive contribution from the intermolecular forces.8 Now B,*,O = 2n [I -exp ( -wo2/kT)]r2dr (8) r where coo, is the potential of average force between two molecules of solute in the pure solvent, including averaging of the force over all rotational coordinates. Let R,, be the distance of closest approach between the centres of two molecules, thenT. M. HERRINGTON AND C. P. MEUNIER 23 1 4 . 2 a3 [I - exp ( - mo2/k T)]r2 dr + 271 Bz: = 271 [ 1 - exp ( - mo2/k T)]r2 dr (9) I. I R 2 2 = S + # A where S is the repulsive and 4A the attractive contribution. I ~ i h a r a ~ ~ has evaluated B,*,O for non-interacting rigid ellipsoids: his formula is NS =f(4v2) where u, is the particle volume andfis equal to unity for a sphere, but increases when the particles become more asymmetrical.From crystallographic data35 the sucrose molecule may be approximated by a prolate ellipsoid of semiaxes 5.9 and 3.5 A. From eqn (28) of ref. (34)fis 1.07. The volume of a prolate ellipsoid is given by 4n1:1,/3 for I, > I,. These figures give a value for NS of 783 cm3 mol-1 and hence at 0 OC, the attractive contribution to Bt: is given by N4A = NB:: - NS = - 453 cm3 mol-l indicating considerable attraction (presumably via hydrogen bonding) between sucrose molecules in solution. The activity coefficients y: and y: of the non-electrolyte and electrolyte, respectively, in the ternary system may be written as In y z = In y2+ln 7 2 3 (10) and In y; = In y3+1n 732 (1 1 ) where y , and y 3 are the activity coefficients in the appropriate binary systems of molalities m, and m3, respectively, y d 3 represents the contribution of the electrolyte to the activity coefficient of the non-electrolyte in the ternary system and ~ 3 2 that of the non-electrolyte to the electrolyte activity coefficient.The theory of Debye and M ~ A u l a y ~ ~ has been extended to more concentrated so1utions,12 and the activity coefficients In 723 and In 7 3 2 can be written as power series in the molalities kT In y23 = vlm3+q2m3%+ . . . vkTln y 3 2 = a,m,fa,m,m,~+. . . where the coefficients ri, oi are functions of the ionic strength and the dielectric constant of the solution. A quantity Aij is defined in terms of experimental quantities by (14) where 4, and 43 are the osmotic coefficients of aqueous solutions of component 2 only and of 3 only, respectively, and ij is the mole ratio of m, to m3.If Aij is represented as a polynomial in the form Aij = 4ij(m2 + vm3) -m2 4 2 - vm3 4 3 Aij/m,m3= Z X,,mfmg (1 5 ) p-o,1,2. . . q=o, &l' * * then it can be shown1, by application of the Gibbs-Duhem equation that232 FREEZING POINTS OF AQUEOUS SOLUTIONS If we consider the first three terms in the above expansions, then Aii/m2m3 = Xoo+Xo~m,f+Xo,m3+ . . . In y2, = ~~~m~ + XOpz,f + ;xol m3, + . . . lny,, = . .. It was found12 that only two X,, coefficients were required to represent our data; an equally adequate fit for eqn (1 8) was obtained with a constant term plus a term in m34 or a constant term and a term in m3.The values found for the coefficients were Xo0/mol-l kg = -4.416 x (a = 8.33 x lo-,) Xo,t/mol-i kgg = - 1.716 x lo-, (a = 7.00 x lo-,) (21) and XoO/mol-l kg = -5.141 x (a = 8.33 x Xo,/mo1-2 kg2 = -9.316 x lo-, (a = 6.95 x (22) Our data extended over a relatively limited molality range, so osmotic coefficient data on other aqueous electrolyte plus non-electrolyte systems extending over a wider molality range were analysed to see whether in general the inclusion of terms in non-integral powers of the molality gave an improved fit over an integral power series. The effect of the order of adding terms, i.e. m2 or m3 first, was also investigated. In general adding m, first gave better results corresponding to the greater effect of m3 on the value of Aij/m2m3.It was found that for the systems water + sucrose + NaC13’ and water + urea+ NaC13* the best fit was obtained by using half powers of m3 and fitting the terms in m3 before those of similar order in m,. In the system of water + urea + NaCl, the seven data points for the highest concentrations, which Bower and Robinson excluded from their polynomial fit, were given a zero weighting. The polynomial of Bower and Robinson using whole powers of m3 cannot fit these data. However, our polynomial using half-powers of m, continues to give a good fit even for these points. [The reader is referred to ref. (12) for further details.] This tends to confirm the experimenters’ assertion that the extrapolations used to calculate these points should not be greatly in error, and underlines the usefulness of the Debye- McAulay theory even for these very high concentrations.The activity coefficients of sucrose and of potassium chloride in the mixture were compared with those in their single-solute solutions. For sucrose In yz = 2Pm2+3Qmi/2 and for potassium chloride The values of y2, y3, y; and y$ calculated from eqn (lo), (1 I), (21), (23) and (24) are given in table 2. The effect of sucrose on potassium chloride is to decrease the activity coefficient of the latter and similarly the addition of potassium chloride decreases the activity coefficient of sucrose. Let us consider further the coefficient Xoo. The solute-solute interactions of the electrolyte may be notionally subdivided into the purely electrostatic interactions and ‘ non-electrolyte ’ interactions.Then for the ternary system, considering non-electrolyte contributions only, eqn (25) of ref. (1 1) givesT. M. HERRINGTON A N D C. P. MEUNIER 233 TABLE 2.-ACTIVITY COEFFICIENTS OF POTASSIUM CHLORIDE AND OF SUCROSE IN THE TERNARY SYSTEM AT 0 O C . THE NUMBERS ARE yj/yf. rn,/mol kg-l m2 /mol kg-' 0 0.1 0.5 1 .o 1.5 2.0 0 1 .O/ 1 .O 0.769/ 0.641 / 0.587/ 0.559/ 0.543/ 0.1 /1.025 0.768/1.021 0.639/1.000 0.585/0.971 0.557/0.941 0.541/0.910 0.5 /1.130 0.760/1.125 0.632/1.102 0.578/1.070 0.550/1.037 0.534/1.003 1 .o /1.272 0.752p.266 0.624p.241 0.569/1.205 0.541 /1.167 0.525p.129 1.5 /1.427 0.743/1.420 0.615/1.391 0.560/ 1.351 0.532/1.309 0.516p.266 2.0 / 1.594 0.734/ 1.586 0.606/ 1.554 0.552/ 1.5 10 0.523/1.462 0.507/ 1.414 1 m, + vm, # .. - I = (iA2,m;+ A23Ei2iTi3+&A33Ei:)+. . . where m, and m, are mole ratios (m, = N , / N , and m3 = N J N , ) . From eqn ( 5 ) and (7) 4,- 1 = ;A2,m2+. . . and ~ ( 4 ~ - 1) = $A3,m3 + . . . then from eqn (14) and (18) and Aij = A,,~i,tii,+ . . . A,, = XOO/Ml. A,, gives information on the non-electrolyte-solute 2 plus non-electrolyte-solute 3 interactions in solution, as it is directly related to the McMillan-Mayer cluster integral Bz;.lo From eqn (72) of ref. (1 1) NB:: = A,, Vy+ V g + VP-RTK, (30) where B;: = -bill (b&l is the cluster integral for one molecule of solute 2 and one molecille of solute 3 in pure solvent), Vy is the molar volume of pure solvent, V g and V p are the partial molar volumes of solutes 2 and 3, respectively, at infinite dilution and K is the solvent compressibility.Using eqn (21) for Xoo and taking V p as 206.31 cm3 mol-1 at 0 OC14 and V p as 23.63 cm3 mol-l at 0 0C,39 then NB:: is 185 cm3 mol-I at 0 O C . Again, let us consider B:: as being composed of an attractive and a repulsive contribution from the intermolecular forces. Let R,, be the distance of closest approach between the centres of two molecules, then B:: = 471 [l -exp (-c;o0l1/kT)]r2dr+4n [l -exp (-c;o0l1/kT)]r2dr r3 6 = S+@ (31) where S is the repulsive and 4* the attractive contribution. The signs of the integrals can be obtained from considerations of the magnitudes of cool1. In the region 0 < r < R,,, cool1 is mostly positive and very much greater than kT, so that S is positive. For R23 < r < 00, moll is negative and comparable with kT so that q5* is negative.Thus the sign and magnitude of B:: depends on the relative magnitudes of S and #*. For a hard sphere of radius a, and a hard prolate ellipsoid with long axis234 FREEZING POINTS O F AQUEOUS SOLUTIONS 2b, and short axis 2u, 34 S = ~ n a ~ + ~ n a ~ b , + 2 n a l b , a,[(l -c2)~+sin-1s/~]+a, From the crystallogra hic data35 for sucrose b, is 5.9 A and a, is 3.5 A. An average and hence at 0 O C the attractive contribution to Bz: is N#A = - 304 cm3 mol-l. This figure can be compared with that for sucrose + water interactions in a binary system. Now according to Garrod and Herringtonll eqn (69) ionic radiusg0 of 1.57 8: was used for potassium chloride. Then NS is 489 cm3 mol-l, NB:O= VP-RTK (33) where B,*P = -byl (byl is the cluster integral for one molecule of solvent and one of solute in pure solvent).Using the above values for sucrose and assuming the water molecule to be a hard sphere of radius 1.52 A, NdA is found to be - 271 cm3 mol-1 for the attactive contribution. In table 3 these values for the interactions of different TABLE 3 .-ATTRACTIVE CONTRIBUTION TO THE PARTICLE-PARTICLE INTERACTION COEFFICIENT NB,*,O NB:; NB,*,o NS -N#A /cm3 /cm3 /cm3 /cm3 /cm3 T/K mol-' mo1-I mol-l mol-1 mo1-I hexamethylenetetraminea ureaa sucrosea sucroseb sucrose + waterb hexamethylenetetramine + sucrose + potassium chlorideb glycine + uread or-alanine + uread a-aminobutyric acid + uread glycylglycine + uread glycine +calcium chloridee 8-alanine +calcium chloride" y-aminobutyric acid +calcium E-aminocaproic acid +calcium glycylglycine + calcium waterC chloride" chloridee chloride" 298 298 29 8 273 273 29 8 273 298 298 298 298 298 298 298 298 298 - - 302 1 - - - - 3220 396 179 783 783 476 300 489 352 416 469 469 196 235 277 342 277 58 178 498 453 27 I 191 304 348 3 70 378 445 ' 521 2375 2816 3363 3497 a Ref.(41); this work; ref. (42); ref. (43); " ref. (2). molecules are compared with those for two molecules of the same species (urea, hexamethylenetetramine and s u c r o ~ e ) . ~ ~ ~ 42 The implications are that sucrose + sucrose interactions are stronger than sucrose_+ water, presumably indicating a greater degree of hydrogen bonding. The interparticle interactions in urea and hexamethylene- tetramine are weak indicating perhaps surprisingly little hydrogen bonding in the former case.Hydrogen bonding between two molecules of hexamethylenetetramine is unlikely, but hydrogen bonding between hexamethylenetetramine and water is possible and is indicated by our results. The surprising result is that the interactionT. M. HERRINGTON AND C. P. MEUNIER 235 between sucrose +potassium chloride is of comparable magnitude with that of sucrose + water; if hydration radii were used for potassium chloride in the calculations then the attraction would be even greater. The results for sucrose + KCl interactions in the ternary system can be compared with those of other workers on aqueous solutions of two non-electrolytes or electrolyte + non-electrolyte. Lilley and Scott4, have used a similar approach for aqueous solutions of amino acids and peptides.Frompsmotic coefficient data at 25 OC they calculated B& for the interaction of amino acids with urea: the values are given in table 3. The hard-sphere contributionll is 71 s = - ( R 2 + R )3 (34) 6 where R, and R, are the hard-sphere diameters. R, and R, were calculated from the partial molar volumes at infinite dilution.44 The attractive contributions, NdA, are presented in table 3. The attractive contributions of the three amino acids are very similar, but the interaction of the dipeptide glycylglycine with urea is considerably greater. However, all of these attractive values are greater than those for sucrose + KC1. Briggs et a/., used a calcium ion-exchange electrode to determine the activity coefficients of calcium chloride in aqueous solutions of various amino acids at 25 "C.They tabulate values of a parameter A , where our parameter A',, = 3 In 1 OA . We have used their data to calculate values of 82. and these are also given in table 3. The hard-sphere contribution was again calculated from an R, value based on V'p 44 and an R, value from V'? = 17.78 cm3 m01-l.~~ The striking feature is the large negative values of both NB:; and N#A. The system sucrose+KCl exhibits salting-in of the non-electrolyte by the electrolyte, whereas most non-electrolytes are salted-out by the addition of electrolyte. The data on the amino acids correspond to very extensive salting-in of the amino acids by calcium chloride. Salting-in and salting-out effects are usually expressed in terms of the Setchenov coefficient.46 Following Friedmann47 we define the Setchenov coefficient by If the solubility of the non-electrolyte is measured in a series of solutions of the electrolyte and In m, plotted against m,, then the slope of the graph at any point is - k , for the solution.Experimentally it is found that for m3 < 1 mol kg--l and m, < 0.1 mol kg-l, k , is a constant. Then if we define k , by where p: is the chemical potential of the non-electrolyte in the ternary system. From eqn (7), (10) and (19) k , = Xoo. (37) In other words the leading term in the expansion for Aij/mzm3 is the Setchenov coefficient. This coefficient is usually in the range f 0 . 7 mol-l kg.46 The system sucrose+KCl has a k , value well within these limits but it can be seen that values for amino aids+CaCl, are considerably greater - up to a factor of four.Desnoyers et a/.48 have determined k , for aqueous solutions of alcohols and alkali halides at their freezing temperatures. For t-butanol+ KCl at 0 O C . k , is 0.54 mol-l kg,236 FREEZING POINTS OF AQUEOUS SOLUTIONS and 0.19 and 0.34 mol-1 kg for methanol + NaCl and ethanol + NaC1, respectively. These figures correspond to extensive salting-out of the alcohol by the electrolyte in contrast to the salting-in of sucrose + KCl. We thank the International Sugar Research Foundation for their interest in, and support for, this work. E. E. Schrier and R. A. Robinson, J . Biol. Chem., 1971, 246, 2870. C. C. Briggs, T. H. Lilley, J. Rutherford and S. Woodhead, J .Solution Chem., 1974, 3, 649. J. E. Desnoyers, G . Perron, S. Leger, B. Y. Okamoto, T. H. Lilley and R. H. 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Kozak, W. S . Knight and W. Kauzmann, J . Chem. Phys., 1968, 48, 675. 45 L. A. Dunn, Trans. Faraduy Soc.. 1966, 62, 2348. 4 6 F. A. Long and W. F. McDevit, Chem. Ret.., 1952, 51, 119. 4 7 H. L. Friedman, J . Solution Chem., 1972, 1, 387. 4H J. E. Desnoyers, M. Billon, S. Leger, G. Perron and J. Morel, J . Sdution Chem., 1976, 5, 681. York, 1961), p. 406. edn, 1963). vol. 4. 295. (PAPER 1 /226)

ISSN:0300-9599    

DOI:10.1039/F19827800225

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC., Faraduy Trans. I , 1982, 78, 231-254 Nitrogen- 1 5 Nuclear Magnetic Resonance Spectroscopy of Adsorbed Molecules BY DIETER MICHEL,* ANDREAS GERMANUS AND HARRY PFEIFER N.M.R.-Labor der Sektion Physik, Karl-Marx-Universitat Leipzig, DDR-70 10 Leipzig, German Democratic Republic Received 16th February, 198 I Nitrogen-15 n.m.r. spectroscopy has been applied to the study of the interactions between solid surfaces and molecules adsorbed on them. Nitrogen- 15 spectra of ammonia, trimethylamine, pyridine and acetonitrile molecules sorbed in various zeolites were measured at 9.12 MHz by means of the conventional Fourier-transform n.m.r. technique. In all measurements carried out, substances were employed which were enriched with nitrogen-1 5 nuclei (ca. 95%). The resonance shifts depend strongly on the nature of adsorption sites which may occur in the zeolites ( e g .Na+ cations, Bronsted- and Lewis-acid sites). The results clearly reveal the advantage of nitrogen- 15 n.m.r. investigations in characterizing acidic properties in comparison with the carbon- 13 n.m.r. measurements performed until now on adsorbate- adsorbent systems and emphasize that nitrogen- 15 spectroscopy may become a powerful tool for the study of surface phenomena. 1 . INTRODUCTION Until now resonance shifts for adsorbates have been measured predominantly for carbon- 13 nuclei since for protons highly resolved spectra could be obtained only in isolated cases. It is well-known1 that the peculiarities in the n.m.r. spectra of large nuclei like carbon-13 are due to (i) the greater shielding, (ii) their smaller magnetogyric ratio and (iii) their low natural abundance giving rise to smaller line-widths because of the lack of 13C-13C couplings and a reduced magnetic interaction with paramagnetic impurities of the adsorbent.An analogous situation holds for nitrogen-] 52 but while carbon-I3 n.m.r. spectra can be observed even in adsorbed molecules having only natural abundance, the much reduced sensitivity for nitrogen-1 5 nuclei requires in general the use of nitrogen- 15-labelled compounds. This follows from a comparison of the values of the n.m.r. sensitivity and of the natural abundance of carbon-I 3 and nitrogen-] 5 nuclei.' If we take the products of both factors as a measure of the relative signal intensity, a relative reduction by a factor of ca.50 results for nitrogen-15. A study of the nitrogen-15 resonance spectra of adsorbed molecules is of special interest because the nitrogen atoms of a variety of molecules possess lone-pair electrons which may participate in the formation of hydrogen bonds, giving rise to strong nitrogen- 1 5 resonance shifts. Moreover, molecules like pyridine and acetonitrile may be protonated directly at the nitrogen atom. Consequently, the difference between the nitrogen-1 5 resonance shifts of protonated and non-protonated species may be considerably larger than the resonance shifts for the adjacent carbon-13 spins and protons in the molecule. Hence nitrogen-1 5 measurements should be more favourable for a study of the acidic sites on a surface.In addition, through a study of the nitrogen-1 5 n.m.r. the electronic state of the ammonia molecule can be investigated in more detail than with proton resonance because the proton resonance shifts are small and often less than the line-widths, which prevents their accurate measurement. 237238 15N N.M.R. OF ADSORBED MOLECULES A brief description of the experimental conditions and of the zeolites used as adsorbents is given in section 2. In section 3 a procedure is developed to derive values for the resonance shifts of molecules bound in surface complexes and for the number of sites involved from the resonance shifts measured as a function of the total number of adsorbed molecules. The results for ammonia, pyridine and acetonitrile molecules adsorbed in various zeolite specimens are presented in section 4.2. EXPERIMENTAL Nitrogen-15 n.m.r. spectra were measured at 9.12 MHz by means of the Bruker Fourier- transform n.m.r. spectrometers WH 90 DS and HX 90 R. The repetition time varied between 0.2 and 0.8 s for the different samples. The pulse widths varied between 16 and 20 ps for ca. 40' pulses. In most cases spectra were taken with proton broad-band decoupling. Only for ammoniamolecules were the coupling constants measured. The number of transients was lo2-1 05. Resonance shifts were indirectly referred to liquid nitromethane. Positive shifts are to lower magnetic field. The correction of resonance shifts due to the adsorbent susceptibility was calculated to be < 0.6 ppm (for Nay, NaX and NaA) on the basis of bulk susceptibility data given in ref.(3) and hence were omitted for the other adsorbents. The deuterated lock substances ([2H6]DMS0, [2H6]acetone) were filled in 10 mm 0.d. glass tubes in which 8 mm 0.d. sealed tubes containing the adsorbate-adsorbent systems were inserted. For adsorbents we used zeolites of type NaX (ratio of the number of silicon to aluminium atoms Si/A1 = 1.3), NaY (Si/Al = 2.6), NaA and Na-mordenite (all substances supplied by VEB Chemiekombinat Bitterfeld, G.D.R.) and different decationated zeolites. Non-stabilized decationated Y-type zeolites, for which 88% of the total number of Na+ ions were replaced by NH: ions and which were then decomposed in ULICUO, are denoted by 88 HY. The stabilization process for the stabilized forms was carried out under self-steaming conditions. Zeolites of type 70 HY-St 840 supplied by Bosaeek were prepared from decationated zeolites of type 70 HY by controlled heating at a rate of 4 K min-l up to 840 K in the presence of ca.2.13 x lo3 Pa (16 Torr) of water vapour [cf. ref. (4) and ( 5 ) ] . The sample US-Ex represents a stabilized zeolite containing only a small amount of aluminium which was prepared by Lohse from NaY zeolite using a treatment described in ref. (6). The composition of the unit cell corresponds to Na,., o,, (AlO,), (SiO,),,,.,,,. Before adsorption by distillation in uucuo the adsorbents were activated at temperatures of 670 K (20 h, p = Pa) except for types 88 HY (620 K) and some samples with stabilized zeolites 70 HY-St 1040 (870 K). All adsorbates were labelled with 15N-nuclei [NH,, 99.9%; CH3CN, 95.2%; C,H,N, 96%, (CH,),NH, 94.4%; (CH,),N, 95.7%) The methylamines were prepared by decomposition of methylamine hydrochloride using concentrated solutions of NaOH.The amines were dried over freshly regenerated 3 A zeolite immediately before the preparation of the samples. 3. THEORY The most important problem to be solved in the interpretation of the resonance shifts, measured here as a function of the number of adsorbed molecules, is the determination of the resonance shifts for those molecules which are bound in complexes. In most cases this information cannot be drawn directly from experiment because the experimental resonance shifts extrapolated to zero pore-filling factors are not necessarily identical with the resonance shift for the molecules bound in complexes.One way to solve the problem is to consider the equilibrium between the physisorbed molecules (M), free adsorption sites (A) and the complexes formed (MA) and to derive the number of sites (NA) and the equilibrium constant k from the fit of the experimental resonance shifts as a function of the total number ( N ) of adsorbed molecule^.^D. MICHEL, A. GERMANUS AND H. PFEIFER 239 We consider here only one type of adsorption site. It is then possible to describe M+A$MA (1) (2) this equilibrium by the equation k from which the relation NC k = ( N - N C ) ( N A - N C ) can be derived. Nc denotes the number of molecules bound in complexes and NA the number of adsorption sites, i.e. the number of centres multiplied by the number of molecules which can be adsorbed on one centre.Hence, N - N , is the number of physisorbed molecules which are not bound in complexes and NA - N , is the number of free sites. Furthermore, we denote by 6 the observed resonance shift with respect to the physisorbed state (i.e. aM = 0 for physisorbed molecules) and by 6, the respective shift for a molecule bound in a complex; the latter has to be derived from the experimental data. If the condition for rapid exchange is fulfilled the two shifts are related by the equation d=6,-. NC N By the combination of eqn (2) and (3) a quadratic equation results: with I+kN+kNA NA N kN +-=o x 2 - x 6 X=-. 6, (3) (4) A suitable form of eqn (4) with respect to an analysis of experimental data is given 1 l + k N A N - + -(1 -x).X kNA NA From this equation it follows that in the general case of an arbitrary strength of complexes, i.e. for an arbitrary value of the quantity kN, a plot of l/x against N( 1 -x) should give a straight line with a slope 1 INA if the value for 6, has been chosen correctly. Hence, in order to analyse the experimental shift 6 as a function of the number N of adsorbed molecules the quantity 6, has to be chosen, by means of a trial-and-error procedure, in such a way that a straight line results. If we cannot exclude the possibility that very low ratios x 6 1 also occur, the problem is to find the smallest possible value for 6, by this trial-and-error procedure because for x < 1 a linear dependence always results. We should also consider the two special cases of a strong and a weak complex.A complex is said to be strong if the condition k N $ l (6) is fulfilled. Then it follows from eqn (4) that (NA/N)6, if N A < N 6, if N A b N . (7) This is the well-known result for the fast exchange if, due to the strong interaction,240 15N N.M.R. OF ADSORBED MOLECULES all molecules are adsorbed at adsorption sites, as long as their number, NA, is still higher than the total number, N , of molecules involved (cf. fig. 1). For a weak complex, i.e. if the condition is fulfilled, we obtain Since the number of sites, NA, is reasonably less than, or at least of a comparable magnitude to, the total number of molecules, N , we also have kNA Q 1. Thus the observed resonance shift, 6, is less than the shift, &, for the complex.A further characteristic feature is that the quantity 6 does not depend in this case on the total number, N , of molecules adsorbed (cf. fig. 1). k N + 1 (8) (9) 6 = [kNA/( 1 +kNA)] 6,. N A N FIG. 1 .-Schematic plot of resonance shifts, 6, observed as a function of the total number, N , of molecules in the case of (a) a weak and (b) a strong adsorption complex. 4. RESULTS AND DISCUSSION 4.1. SORPTION OF AMMONIA ON VARIOUS ZEOLITES NH, I N Nay, NaX, NaA, NA-MORDENITE AND DEALUMINATED Y-TYPE ZEOLITE The nitrogen-1 5 resonance shift for the adsorbed ammonia molecules referred to gaseous ammonia was measured as a function of the pore-filling factor and at different temperatures, viz. NH,/NaY (240-360 K), NH,/NaX and NHJNaA (240-300 K).Since for the resonance shifts in gaseous ammonia different values are reported in the literature, we also investigated gaseous samples both with and without proton decoupling. The results of our measurements are as follows: (i) The nitrogen-15 resonance shift for ammoniamolecules adsorbed in Nay, NaX, NaA and Na-mordenite type zeolites depends strongly on the pore-filling factor. The plot (cf. fig. 2) is characterized by the approach of the resonance shift for adsorbed ammonia molecules to values characteristic of liquid ammonia (1 8 ppma) if we have nearly complete pore filling (6 = 1) and gaseous ammonia (0 ppm) if we extrapolate to zero coverage (6 = 0). (ii) The resonance shifts for these adsorbate-adsorbent systems are of the sameD. MICHEL, A. GERMANUS AND H.PFEIFER 24 1 order of magnitude and remain constant within the temperature intervals chosen. (iii) For the dealuminated Y-type zeolite, the nitrogen- 15 resonance shift does not change as a function of the pore-filling factor (between B = 0.2 and 0.72, measurements at 300 K, fig. 2). Its value is about the same (16 ppm) as that reported for liquid - 0 - -0 0.5 e 1.0 FIG. 2.-Nitrogen-1 5 n.m.r. shifts, 6, of ammonia in various zeolites (in ppm referred to gaseous NH,) as a function of the pore-filling factor 0 at 300 K : 0, Nay; x , NaX; +, NaA; A, Na-mordenite; 0, US-Ex. [6 (liquid) = -382i-0.2 ppm, 6 (gas) = 399.9kO.l ppm on the CH,NO, These experimental data allow the unambiguous conclusion that at higher pore-filling factors the ammonia molecules are packed so closely that their resonance shifts become liquid-like.In the case of dealuminated samples (US-Ex) even for small pore-filling factors (3.8 molecules per large cavity) a strong association of ammonia molecules occurs leading to liquid-like resonance shifts and to the observed constancy of resonance frequencies over a wide range of coverage. Further proof of the strong resemblance between ammonia adsorbed at higher pore-filling factors in zeolites and liquid ammonia was found during a study of samples in which different portions of water were added to zeolites already containing a certain amount of ammonia. With an increasing number of adsorbed water molecules the nitrogen-1 5 resonance lines are shifted to lower fields in a manner similar to that observed for aqueous solutions of ammonia where this phenomenon was explained by hydrogen-bonding interaction^.^242 15N N.M.R.OF ADSORBED MOLECULES US-Ex-type zeolites and the Na-forms of X and Y zeolites have the same topology and their different behaviour is mainly due to the very small number of Na+ ions in the US-EX.~ Hence it is reasonable to attribute the linear change in resonance shifts with the number of adsorbed molecules for the sodium forms of X, Y, A and mordenite type zeolites (in contrast to the dealuminated zeolites) to an interaction with Na+ ions. Such an interaction is well-known from measurements of the heat of adsorption.1°-12 However, the nitrogen-I 5 resonance shifts reveal that even in the limit of zero pore filling, where the greatest adsorption effects are l1 only a small deviation of the resonance shift from the gas-phase value occurs.Moreover, for various zeolites (Nay, NaX, NaA, Na-mordenite) having different kinds and numbers of Na+ ions approximately the same plot of shifts against pore-filling factors is observed. Obviously the variation of the resonance shifts with decreasing coverage between the values measured for the liquid and the gas can simply be explained by the fact that the association of the ammonia molecules is increasingly prevented due to the interaction with the Na+ ions, which itself leads, however, to an almost negligible influence on the electron density at the nitrogen atom. Litchman and co-workersg* l4 showed that the nitrogen- 15 resonance shifts for various ammonia solutions and for the pure liquid can be explained satisfactorily by a superposition of different mechanisms which were determined empirically by comparing the behaviour of ammonia and of trimethylamine in various solutions.The contributions include hydrogen-bonding interactions between the nitrogen lone-pair electrons and the hydrogen atoms of neighbouring molecules as well as interactions of the hydrogen atoms of ammonia molecules with oxygen and nitrogen atoms in their surroundings. In the present study, the strong resemblance of the resonance shifts measured for high pore-filling factors with the values for the pure liquid clearly indicates the presence of hydrogen-bonding interactions between adsorbed ammonia molecules. This finding is in contrast to conclusions drawn by Basler et a1.12 On the basis of measurements of the apparent molar heat of adsorption of ammonia in the pores of zeolites NaX and NaY they concluded that at all coverages no considerable number of hydrogen bonds exists.The question now arises as to whether the remaining small shift with respect to the gaseous state at very low pore-filling factors (3-5 ppm to lower field for the different ammonia samples) is also due to a superposition of several contributions2 (such as the interaction between the lone-pair electrons and Na+ ions and a hydrogen-bonding interaction between the hydrogen atoms of ammonia and the oxygen atoms of the zeolite skeleton) which may compensate each other. For this purpose we measured the nitrogen-I5 shift for trimethylamine as a function of the pore-filling factor at 380 K.The difference between the shifts for zero and high pore-filling factors is of the same order of magnitude as the value for the liquid-phase shift referred to the gaseous state.13 As in the case of ammonia, for zero pore-filling only a small deviation (ca. 1-2 ppm) in the resonance shift for the gas results. In the case of trimethylamine, however, the resonance shift only reflects the interaction between the lone-pair electrons of the molecule and active sites in the zeolite because a contribution to the nitrogen- I 5 n.m.r. shift of the trimethylamine molecule arising from hydrogen-bonding interactions between the methyl protons and the oxygen atoms of the zeolite skeleton should be negligible. This conclusion is suggested by investigations of nitrogen-1 5 resonance shifts in various solution^.^^ l4 The similar behaviour for both ammonia and trimethylamine molecules therefore suggests that the explanation of the small resonance shift as a consequence of the superposition of several contributions including hydrogen-bonding interactions is not very probable.A more probable interpretation would be one given in terms of a specific adsorptionD. MICHEL, A. GERMANUS AND H. PFEIFER 243 but with a comparable electronic state relative to the gas phase. Moreover, the same value for the indirect spin-spin coupling constant (62 & 5 Hz) was measured at low pore-filling factors as that obtained for ammonia in the gas or liquid phase (61.6 Hz). Because it is well-known15 that the coupling constant of the ammonia molecule depends on the bonding angle, this fact also emphasizes that the geometrical structure of the ammonia molecule has not been changed in the course of adsorption in Na-forms.At higher pore-filling factors in NaY zeolites (0 2 0.3) the multiplet splitting disappears; this is probably due to an increasing proton exchange rate. For the NaX-type samples a multiplet splitting was not observed. In the case of NaA zeolites the splitting appeared up to the highest filling factor studied (0 x 0.8).13 An analysis of exchange phenomena was not undertaken due to a lack of relevant experimental data such as the line-shape function of the multiplet for various temperatures and pore-filling factors and the transverse spin-relaxation time [cf.the IH spin resonance study in ref. (16)J. NH, I N 88 HY TYPE ZEOLITE In contrast to the Na forms, where resonance shifts of the ammonia molecules were strongly influenced by molecule-molecule interactions, the nitrogen- 1 5 resonance shifts in the following systems clearly reflect the interactions with acidic sites. We first discuss the results obtained for ammonia molecules in decationated zeolites of type 88 HY. At room temperature spectra could only be taken if more than ca. 9 molecules were adsorbed per large cavity. For the samples with only 1.9-4.4 molecules per large cavity, measurements could be performed at temperatures above ca. 380 K where the line-widths are sufficiently small. From the values for the line-widths given in table 1, we can conclude that for HY-type zeolites the molecular mobility is reduced in comparison with the Na forms but still high enough at 380 K to enable the application of conventional Fourier-transform n.m.r.spectroscopy to the liquids. However, as mentioned above, a more detailed characterization of the thermal mobility will not be undertaken here because of the lack of relaxation data. TABLE 1 .--NITROGEN- 15 N.M.R. SHIFTS, 6, AND LINE-WIDTHS, Av;, OF AMMONIA MOLECULES ADSORBED IN 88 HY-TYPE ZEOLITES AS A FUNCTION OF THE NUMBER, N , OF MOLECULES PER 6 in ppm referred to liquid nitromethane, Av; in Hz. The line-widths for NaY at 300 K are ca. 20 Hz. LARGE CAVITY 20.5 - 369 265 300 17.1 - 364 195 300 14.6 - 364 125 300 9.0 - 362 42 300 4.4 -361 33 380 2.3 - 361 33 380 1.9 - 361 39 380 Typical spectra are shown in fig.3 and some results summarized in table 1 . With respect to the Na forms, the nitrogen-15 resonance lines for ammonia molecules adsorbed in 88 HY-type zeolites are shifted appreciably to lower fields. At low coverages (4 molecules per large cavity) the resonance shift remains constant at a value of - 360 ppm referred to liquid nitromethane, which is typical for NH,+ solutions not244 15N N.M.R. OF ADSORBED MOLECULES 15NH4N03- inaqueous solution - NH3 gas -350 -360 -370 -380 -390 - 400 -410 6 (PPm) FIG. 3.-Nitrogen-l5 n.m.r. spectra of adsorbed ammonia molecules in 88 HY [ N = 9 molecules per large cavity; number of transients N, = 500; temperature T = 380 K (a), T = 300 K (b)] and in Nay-type zeolites [(N = 3.4; T = 300 K (c)].All shifts are referred to liquid CH,NO, [a (NH, gas) = -399.9kO.l ppm,B d(NH:) = -359.55k0.17 ppm* in 12.3 rnol drn+ solution of NH,NO, in water]. containing C1- ions. From this result we can conclude that all molecules are converted into ammonium ions as a consequence of their interaction with structural hydroxyl groups in the HY-type zeolites. As discussed recently in more detail for pyridine molecules sorbed in the same zeolites,17 the interaction with structural hydroxyl groups leads to a large reduction in the molecular mobility. This fact may explain why the nitrogen-1 5 resonance lines are broadened and disappear if the number of molecules is equal to or less than the number of accessible hydroxyl groups. At elevated temperatures for medium pore-filling factors also the resonance shifts approach a value characteristic of pure ammonium ions.The change in the resonance shift as a function of temperature is reversible. This temperature dependence is probably due to a decrease in the relative amount of non-protonated molecules because these species are more mobile and will be desorbed at higher temperatures. This suggestion is supported by a decrease in the signal intensity which is stronger than would be expected according to the Curie law if the temperature increases. In conclusion, the formation of ammonium ions in HY-type zeolites (well-known also from i.r. spectroscopic investigations'** 19) can be quantitatively studied by means of nitrogen- 15 n.m.r.D. MICHEL, A. GERMANUS A N D H. PFEIFER 245 NH, IN STABILIZED ZEOLITES The extremely high sensitivity of the nitrogen- 15 resonance shifts to an interaction with acidic sites will also be demonstrated by the following results obtained for stabilized decationated zeolites.For these samples the spectra could only be measured at temperatures of 340 K and higher because of the strong line broadening. This is the reason why all systems discussed here were investigated at 380 K. In fig. 4 the 10 I 15 N 20 N FIG. Q.-Nitrogen-15 n.m.r. shift, 6, of ammonia in 70 HY-St 840 type zeolites (in ppm referred to gaseous NH,) as a function of the number, N , of molecules (for dC and NA see the text). 5 NA = 12.5 resonance shifts for ammonia molecules in stabilized zeolites are plotted as a function of the pore-filling factor.In spite of the high enrichment with nitrogen-15 nuclei, the signal-to-noise ratio was not sufficiently high to study samples with < ca. 2 molecules per large cavity. However, the small change in the shifts below a pore-filling factor of 6 molecules per large cavity justifies an extrapolation of the values to zero coverage. The resonance shift thus obtained (1 16 ppm to lower field as referred to the gas) is considerably larger than the values reported in the literature20 for ammonium ions in different media and thus cannot be interpreted in terms of a dominant interaction of ammonia molecules with residual hydroxyl groups acting as Bronsted-acid sites. This conclusion is supported by analogous measurements using acetonitrile (see below). Moreover, BosaEek et aL21 showed recently that the Bronsted acidity of the (residual) OH groups of these stabilized forms is less than for the corresponding non-stabilized zeolites.Stabilized samples contain, besides the structural OH groups already mentioned, sites of the Lewis-acid type due to defects generated during the stabilization process. In order to derive the number of Lewis-acid sites which are involved in the interactions with adsorbed ammonia molecules we analyse the plot of the nitrogen-15 resonance shifts by means of eqn (5). The best fit results if 6, = 116 ppm is chosen, which can also be derived directly by means of a simple extrapolation of the experimental shifts to zero pore-filling factor (fig. 4). This finding is experimental proof of the existence of a strong adsorption complex.The number of sites obtained from the slope is NA = 12.5 per large cavity. In order to compare this value with the results of adsorption measurementsz1 we note that NA is given by the coordination number of the centres multiplied by their total number.246 15N N.M.R. OF ADSORBED MOLECULES For the following discussion we need an upper limit for the coordination number in order to determine a lower limit for the number of centres. It seems reasonable to take a coordination number of 4-6 in analogy with the arrangement of ammonia molecules in the vicinity of metal cations in solution. However, since the centres are located in front of the solid surfaces, the coordination number will be less than its value in solution. Thus the number of centres should be ca.2 per large cavity. In a recent paper by BosaEek et al.,l the number of irreversibly sorbed pyridine molecules was determined by sorption measurements to be ca. 0.17 mmol g-l or 0.25 pyridine molecules per large cavity for the same type of stabilized decationated zeolite. This value was taken in ref. (21) as a measure of the total number of acidic centres in the zeolite. However, this value is appreciably less than the number of Lewis-acid centres derived from the nitrogen-1 5 n.m.r. shifts for ammonia molecules. The discrepancy between both values goes beyond the uncertainties due to the choice of coordination number for the ammonia molecules. Clearly this comparison reveals the limitation of this method of determining the number of acidic centres.It may at least qualitatively account for the occurrence of certain sites but is not suitable for a more detailed characterization of their nature and order of magnitude. 4.2. SORPTION OF PYRIDINE I N NaY AND 88 HY TYPE ZEOLITES Since the lifetime of pyridinium ions (z = 5 x s at 313 K17) in 88 HY zeolites is milch smaller than the inverse value of the difference in Larmor frequencies of adsorbed pyridine molecules and pyridinium ions (u-l = 2 x s according to a resonance shift of 89 ppm, see below), the condition of a fast exchange is fulfilled. Moreover, in analogy to the interpretation of carbon- 13 resonance shifts,,, the pyridinium ion can be considered as a strong adsorption complex (see section 3). Hence, as long as the total number of molecules adsorbed is less than the number of Bronsted-acid sites the resonance shift, 6, observed is identical with the resonance shift, 6,, of the pyridinium ion [C = I, cf.eqn (7)) For higher pore-filling factors a mean resonance shift (10) is observed where 6, denotes the resonance shift for the adsorbed pyridine molecules andp, is the relative amount of pyridinium ions [cf. eqn (7) where 6, = 0 was chosen]. To analyse the plot of resonance shifts against the number, N , of molecules per large cavity in fig. 5 on the basis of eqn (1 l), the values for dM and 6, must be determined. It is reasonable to take for the quantity 6, the resonance shift (-90 ppm) observed in NaY zeolites because in NaY only non-protonated molecules occur, the resonance shifts of which do not depend on the pore-filling factor.Furthermore it was checked experimentally that the different numbers of Na+ ions in the sodium and decationated forms do not play a decisive role because resonance shifts of pyridine molecules on SiO, surfaces are of a comparable order of magnitude (cf. table 2). For the resonance shift 6, the value found for pyridinium ions in aqueous is taken (6, = 179.6 ppm). This assumption is supported by the following result: If the total number of adsorbed pyridine molecules ( N = 2.1 per large cavity) is only slightly in excess of the number of accessible OH groups [NOH x 2 per large cavity, cf. ref. (22)] then the observed resonance shift is about the same as that measured for the pyridinium ions in aqueous solution (cf. fig. 5 ) .Obviously at this pore-filling level almost all molecules are protonated. At a lower pore-filling level ( N = 1.7 per large cavity) no nitrogen-15 n.m.r. signal can be observed. An analogous situation occurred in the case of carbon-1 3 n.m.r. measurements. The disappearance of the spectra has been attributed here to the appreciable reduction in thermal mobility of the pyridinium ions which was = (l -PI) 6M +PI dlD. MICHEL, A. GERMANUS AND H. PFEIFER 247 FIG. 5.-Nitrogen- a function of the - 140 1 2 3 4 N .15 n.m.r. shift, 6, of pyridine in 88 HY-type zeolites (in ppm referred to CH,NO,) as number, N , of molecules ( T = 380 K). For pyridinium ions in solution (4.3 mol% C,H,NH+ in H,O) a value dI = - 179.6kO.l ppm was found.,, TABLE 2.-NITROGEN-15 RESONANCE SHIFTS 6 (IN ppm REFERRED TO NITROMETHANE) OF PYRIDINE MOLECULES ADSORBED ON SILICA GEL24 AND IN NaY TYPE ZEOLITES The coverage is given as number, N, of molecules per large cavity (Nay) or multiples, 0, of a statistical monolayer.adsorbent coverage 6 NaY N = 2.4 - 90.7 5.6 - 89.2 SiO, e = 0.08 -89.3 0.16 -89.9 0.79 -85.7 1.35 -78.9 studied independently by means of proton spin-re1axation.l’ Inserting the values for 6, and dI into eqn (1 l), the relative amount of pyridinium ions could be determined from a plot of nitrogen-15 resonance shifts. As can be seen from table 3 the number of pyridinium ions thus evaluated is about the same as that determined in ref. (22). In general the accuracy of the data derived from nitrogen-15 n.m.r. measurements should be higher because the differences between carbon- 13 resonance shifts for pyridine molecules and pyridinium ions in solution are much less (e.g.12.2 ppm for carbon C4) than the respective value for the nitrogen n.m.r. spectra (1 16 ppm, cf. fig. 6).248 lSN N.M.R. OF ADSORBED MOLECULES TABLE 3.-RELATIVE NUMBER, PI, OF PYRIDINIUM IONS IN 88 HY ZEOLITES CALCULATED WITH THE AID OF EQN (11) Values from analogous carbon- 13 n.m.r. investigations22 are given in parentheses (6 in ppm referred to liquid nitromethane). no. of pyridinium ions per large N 6 PI cavity 2.1 (2.6) -171.2 0.9 12 1.9 (1.9) 3.0 (3.0) - 165.4 0.847 2.5 (2.2) 4.6 (3.6) - 147.9 0.650 3.0 (2.5) I 1 1 I I I -50 -60 -70 -80 -90 -100 -110 -120 -no -uo -150 -m -170 -a -190 6 (PPm) FIG. 6.-Nitrogen- 15 n.m.r.spectra of pyridine molecules sorbed in NaY [(a) T = 300 K, N = 2.4 per large cavity; (6) T = 300 K, N = 5.6; (c) T = 380 K, N = 5.61 and in 88 HY-type zeolites [(d) T = 380 K, N = 4.61. 6 in ppm referred to CH,NO,, 6 = - 57.6 f 1.8 ppm for gaseous pyridine, 6 = - 63.9 f 0.1 ppm for liquid pyridine and 6 = - 179.6 f 0.1 ppm for pyridinium ions in solution (cf. legend to fig. 5). 4.3. SORPTION OF ACETONITRILE Nitrogen- 15 resonance shifts were measured for acetonitrile adsorbed in various zeolites and on SiO, surfaces. Except for CH,CN molecules adsorbed in the stabilized forms 70 HY-St, the line-widths are sufficiently small (ca. 20 Hz at 300 K for aceto- nitrile in Nay, NaX, US-Ex and on SO,, ca. 60-90 Hz for acetonitrile in HY zeolites) that the nitrogen-1 5 n.m.r.spectra could be measured at ambient temperature.D . MICHEL, A. GERMANUS A N D H. PFEIFER 249 , I I 10 -135 ' I ' ' ' ' 5 N FIG. 7.-Nitrogen-1 5 n.m.r. shifts, 6, of acetonitrile (in ppm referred to liquid CH,NO,) adsorbed in NaY (a), US-Ex (b), and 88 HY-type zeolites ( c ) at 300 K. For the shifts see also table 4. TABLE 4.-NITROGEN-15 N.M.R. SHIFTS, 6, OF ACETONITRILE MOLECULES IN DIFFERENT STATES 6 in ppm referred to liquid nitromethane. state/adsorbate 6 ref. zeolite 70 HY-St 840 (670 K, N = 7.8) (870 K, N = 8.1) 70 HY-St 1040 gas liquid protonated form (superacid medium) - - 109f3 -108+33 - - 126.5 25 - 1 3 6 . 4 25 - 239 20 9 FAR 1250 I5N N.M.R. OF ADSORBED MOLECULES For the system CH3CN/70 HY-St temperatures of ca. 400 K are necessary to obtain sufficiently small lines (ca.250 Hz). The resonance lines of the adsorbed acetonitrile molecules are in general shifted to higher fields relative to both the gaseous and liquid phases (cf. fig. 7). Only the resonance lines of acetonitrile molecules adsorbed in the stabilized forms are shifted to lower fields (cf. table 4). CH3CH I N NaX, Nay, US-EX TYPE ZEOLITES A N D ON sio, SURFACES As is shown in fig. 7 ( a ) the resonance shifts remain constant (- 156 ppm referred to liquid nitromethane) for CH,CN in NaY zeolites as long as the number of adsorbed molecules is less than ca. 5 per large cavity. This behaviour suggests that acetonitrile molecules interact with a relatively large number of adsorption sites. From the whole plot of 6 as a function of N , by means of eqn (5) a value for the number of active sites per large cavity (6k0.5) and a value for the shift of the complexed molecules (6, = - 156 ppm) can be calculated in agreement with the simple interpretation of the plateau (infinitely strong adsorption complex).For the physisorbed molecules a resonance shift of - 136.4 ppm (as in the liquid state) was taken. This assumption is supported by the following results: In order to check whether sodium ions can act as adsorption sites, similar measurements were performed using dealuminated zeolites of type US-Ex and silica gel. The different behaviour of acetonitrile molecules due to an appreciable reduction in the number of sodium ions can be clearly inferred from fig. 7(b). At nearly complete pore filling of the US-Ex-type zeolite the resonance lines appear in an interval which is typical of the liquid state of acetonitrile.Thus, in contrast to the pure Na forms the influence of molecule-molecule interactions is directly reflected by the measured resonance shifts at high pore-filling factors. The influence of an interaction with remaining adsorption sites clearly appears at lower pore-filling factors where the resonance lines are more and more shifted toward the value which is typical of the pure sodium Y-type zeolites. Obviously the number of sites is very small because a plateau cannot be observed within the limits of I t FIG. 8.-Nitrogen-15 n.m.r. shifts, 6, of acetonitrile (in ppm referred to liquid CH,NO,) adsorbed on silica gel. Value for 0 in monolayers, (-) fitted curve (see text), (0) experimental values.D.MICHEL, A. GERMANUS AND H. PFEIFER 25 1 a I I I I I I I \ \ \ 0 \ \ CH3CN, gas liquid / ,CH3CN adsorbed \ 0 5 10 N FIG. 9.-(a) Nitrogen-15 n.m.r. shifts, 6, of acetonitrile adsorbed in NaX type zeolites at 300 K (in ppm referred to liquid CH,NO,). (6) Nitrogen-15 n.m.r. spectrum of acetonitrile adsorbed in NaX type zeolite for a coverage of 0 = 1.2 (complete pore filling, 0 = 1, corresponds to ca. 10 molecules per large cavity). experimental error. This is reasonable, too, since the number of sodium ions in the US-Ex-types is very Clearly these deviations from the system CH,CN/NaY zeolite underline the role of Na+ ions as adsorption sites for acetonitrile in the Na form of Y-type zeolites. However, it cannot be ruled out that adsorption sites other than Na+ may also be of importance for the shifts occurring at low pore-filling factors in US-Ex, since it was not possible to fit the experimental plot of the resonance shifts against pore-filling factor by means of eqn (5).This fact can be understood if the observed nitrogen-15 n.m.r. shift at low pore-filling factors is a result of a fast exchange in which more than one kind of active site is involved, e.g. residual Na+ ions and residual OH groups. To estimate the possible influence of the weakly acidic OH groups in US-Ex zeolites on the nitrogen-15 n.m.r. shift we investigated additionally the resonance shift of acetonitrile molecules adsorbed on silica gel. As is well-known, the surface OH groups of silica gel are only weakly acidic sites.Using eqn ( 5 ) we obtain from the plot in fig. 8 the value of 2.15 OH groups per nm2, which is in good agreement 9-2252 15N N.M.R. OF ADSORBED MOLECULES with the results of other methods (uiz. 2.2 per nm2 at a pretreatment temperature of 670 K26). The resonance shift, 6,, of the acetonitrile-OH-group complex is - 146 ppm (referred to liquid nitromethane) which is even smaller than the value for the acetonitrile-Na+ complex (- 156 ppm, see above). In conclusion, for the system CH,CN/US-Ex a fast exchange of the CH,CN molecules between the small number of OH groups and Na+ ions can be responsible for the experimental shifts observed at low pore-filling factors. Since in Nay-type zeolites the number of OH groups is much less than the number of Na+ ions these measurements confirm the result that sodium ions in the NaY zeolites are responsible for the resonance shifts of adsorbed acetonitrile molecules. The number of active sites (6 _+ 0.5, see above) is equal to about twice the number of accessible Na+ ions (ca.3.3 Na+ ions at S,, sites2’) so that the coordination number of the Na+ ions for CH,CN molecules in NaY zeolites is ca. 2. Measurements were also performed using NaX-type zeolites (cf. fig. 9). For higher pore-filling factors the nitrogen-15 resonance shifts are nearly the same as those measured for the Nay-type zeolites : they decrease monotonically with increasing pore-filling factors as long as the total number of molecules is larger than ca. 6.5 0.5 per large cavity and are independent of the number, N , of molecules for 4.0 6 N 6 6.5.In contrast to the NaY zeolites, for N < 4.0, an additional shift to still higher fields occurs. Presumably the CH,CN molecules adsorbed at low pore-filling factors interact preferentially with Na+ ions at S,,, sites (ca. 4 per large cavity2’) which practically does not occur in NaY zeolites. Only at higher pore-filling factors (4.0 < N < 6.5) can the influence of sodium ions at S,,-type sites be inferred from the resonance shift. The total number of interacting acetonitrile molecules derived from this plot of the resonance shifts is again ca. 6-7 per large cavity. However, for the NaX zeolites this number is less than the total number of sodium ions per large cavity. Obviously the fraction of the acetonitrile molecules which can interact simultaneously with the Na+ ions occurring in the large cavities is limited here for sterical reasons.At still higher numbers of adsorbed acetonitrile molecules (N > 10, i.e. pore-filling factors 8 > 1) the resonance shift for the molecules within the large zeolite cavities remains constant. In addition a resonance line appears at a frequency which is typical of liquid acetonitrile [cf. fig. 9(b)]. Obviously under these conditions a slow exchange occurs between species adsorbed in the zeolitic holes and a liquid-like phase at the outer surface of the crystallites. ACETONITRILE I N DECATIONATED ZEOLITES The nitrogen-1 5 n.m.r. shifts of acetonitrile molecules in a decationated 88 HY-type zeolite are plotted as a function of the number, N , of molecules per large cavity in fig.7(c). In contrast to the adsorption of ammonia and pyridine molecules in 88 HY-type zeolites, where the formation of the protonated forms can be followed in the spectra, the resonance shifts [ - 161 to - 147 ppm, fig. 7(c)] are of a comparable order of magnitude to those for unprotonated acetonitrile molecules adsorbed on silica-gel surfaces (- 146 to - 141 ppm, fig. 8). At higher pore-filling factors the resonance shifts [ - 147 ppm, fig. 7(c)] are about the same as the values measured for the pure sodium forms [ - 149 ppm in fig. 7(a), - 148 ppm in fig. 91. Furthermore, if we eliminate the influence of molecule-molecule interactions, i.e. if we take to a first approximation as reference the resonance frequencies measured for the liquid and the gaseous phases at complete and zero pore filling, respectively, or a weighted average value between both values at medium number N , then we obtain for the resonance shift 6, = - 180 ppm.This value differs appreciably from the value for protonated acetonitrile species in superacid solutions (- 239 ppm referred to liquid CH,N02).20 The number of sites (NA = 3.0f0.5 per large cavity), however, is of the sameD. MICHEL, A . GERMANUS A N D H. PFEIFER 253 magnitude as obtained from the nitrogen-1 5 n.m.r. shifts of pyridine molecules adsorbed in the same zeolites. This result reveals that even in decationated zeolites the CH,CN molecules are not protonated but interact with the structural OH groups via hydrogen bonds.Finally, measurements using stabilized decationated zeolites are discussed. With respect to the gas phase, the nitrogen- 15 resonance line is shifted here by ca. 17 ppm to lower fields. This result is of special interest because the resonance frequency is substantially different from both systems containing Bronsted-acid sites of various strengths (SiO,, 88 HY) and those having sodium ions. Clearly, protonation of acetonitrile cannot account for this shift. Also other weak interactions already described cannot be responsible for the shift because for all of them the nitrogen-15 resonance line appears at higher fields. Because the resonance shift to lower fields (relative to the gas phase) only occurs when a stabilized zeolite is investigated we attribute it to an interaction with Lewis-acid sites created during the stabilization process.This interpretation is supported by analogous experiments using ammonia, as described above. 5 . CONCLUSIONS (1) The first detailed nitrogen-1 5 n.m.r. study, presented here, has revealed that this method is a powerful tool for the study of surface phenomena. The resonance shifts depend very strongly on the nature of the adsorption sites, and the changes in the spectra are often much larger than in the case of analogous carbon-13 n.m.r. measurements (cf. e.g. section 4.2). (2) To derive the resonance shifts for the surface complexes, and hence to eliminate the influence of exchange processes on the nitrogen-15 n.m.r. shifts observed, the equilibrium of the reaction with surface sites is considered (section 3).This method could be checked directly in the case of adsorbate-adsorbent systems characterized by strong adsorption complexes (e.g. CH,CN adsorbed in Nay, pyridine adsorbed in 88 HY). (3) A very surprising result is that the nitrogen-15 resonance shifts for ammonia molecules adsorbed in the sodium forms of various zeolites (types A, X, Y and mordenite) are mainly due to molecule-molecule interactions although a strong influence of the Na+ ions can be clearly inferred from results of adsorption-heat measurements.10311 In the case of decationated zeolites (88 HY) the spectra reveal unambiguously, as expected, the formation of NH,' ions (strong shift to lower fields relative to the gaseous phase). Lewis-acid sites in stabilized decationated forms give rise to a still larger resonance shift to lower fields (section 4.1).(4) The formation of pyridinium ions in decationated zeolites can be clearly followed in the nitrogen- 15 n.m.r. spectra. From the resonance shifts the number of interacting OH groups is derived. Nitrogen-1 5 n.m.r. spectroscopy seems to be better suited to this analysis than analogous carbon-1 3 n.m.r measurements published recently22 (section 4.2). (5) Nitrogen-1 5 n.m.r. resonance shifts of acetonitrile molecules can be favourably used in the characterization of interactions with the exchangeable cations of the zeolite ( e g . Na+) and with Lewis-acid sites (section 4.3). In summary, suitable use of the adsorbate in nitrogen-1 5 n.m.r. measurements should enable a selective study of the different active sites present in an adsorbent.254 15N N.M.R. OF ADSORBED MOLECULES H.Pfeifer, Phys. Rep. C., 1976, 26, 293; D. Michel, Surf. Sci., 1974, 42, 453. D. Michel, A. Germanus, D. Scheller and B. Thomas, Z . Phys. Chem. (Leipzig), 1981, 262, 113. D. Michel, W. Meiler, A. Gutsze and A. Wronkowski, 2. Phys. Chem. (Leipzig), 1980, 261, 953. Z. Tvarbikova, V. Patzelova and V. BosaEek, React. Kinet. Catal. Lett., 1977, 6, 433. V. Patzelova, J . Chromatogr., 1980, 191, 175. U. Lohse, E. Alsdorf, and H. Stach, 2. Anorg. Allg. Chem., 1978, 447, 64. T. Bernstein, P. Fink, D. Michel and H. Pfeifer, J . Colloid Interface Sci., in press; V. 1. Borovkov, G. M. Zhidomirov and V. B. Kazanski, Zh. Struct. Chim., 1975, 16, 308. M. Witanowski, L. Stefaniak, S. Szymanski and H. Januszewski, J . Magn. Reson., 1977, 28, 217. W. M. Litchman, M. Alei Jr and A. E. Florin, J. Am. Chem. Soc., 1969, 91, 6574. lo R. M. Barrer and R. M. Gibbons, Trans. Faraday Soc., 1963, 59, 2569. l1 A. V. Kiselev, in Proc. 5th Int. Conf. on Zeolites, Naples, 1980, ed. L. V. C. Rees (Heyden & Sons, l2 W. Basler, D. Clausnitzer and H. Lechert, Ber. Bunsenges. Phys. Chem., 1975, 79, 527. l3 A. Germanus, Diplomarbeit (Karl-Marx-Universitat, Leipzig, 1980). l4 M. Alei Jr, A. E. Florin and W. M. Litchman, J . Am. Chem. SOC., 1970,92,4828. l5 R. E. Wasylishen and T. Schaefer, Can. J . Chem., 1973, 51, 3087. l6 E. B. Whipple, P. J. Green, M. Ruta and R. L. Bujalski, J . Phys. Chem., 1976, 80, 1350. H. J. Rauscher, D. Michel and H. Pfeifer, J . Mol. Catal., in press. A. V. Kiselev and V. I. Lygin, IR Spectra of Surface Compounds (in Russian) (Nauka, Moscow, 1973), p. 366ff. London, 1980), p. 400. l9 L. H. Little, IR Spectra of Adsorbed Species (Academic Press, New York, 1966), p. 365. 2o G. A. Webb and M. Witanowski, Nitrogen-NMR (Plenum Press, London, 1973), p. 204. 21 V. Bosakk, V. Patzelova, Z. Tvarbikova, U. Lohse, W. Schirmer and H. Stach, Proc. Workshop, AdForption of Hydrocarbons in Zeolites (Academy of Sciences, ZIPC, Berlin, 1979), vol. 1, p. 157. 22 H. J. Rauscher, D. Michel, D. Deininger and D. Geschke, J . Mol. Catal., 1980, 9, 369. 23 R. 0. Duthaler and J. D. Roberts, J . Am. Chem. SOC., 1978, 100, 4969. 24 L. E. Kitaev, T. Bernstein, P. Fink, D. Michel and H. Pfeifer, J. Chem. Soc., Faraday Trans. I , 25 M. Alei Jr, A. E. Florin, W. M. Litchman and J. F. O’Brien, J . Phys. Chem., 1971, 75, 932. 26 A. V. Kiselev and V. I. Lygin, IR Spectra of Surface Compounds (in Russian) (Nauka, Moscow, 1973), 27 W. J. Mortier, H. J. Bosmans and J. B. Uytterhoeven, J. Phys. Chem., 1972, 76, 650. in press. p. 99. (PAPER 1 /253)

ISSN:0300-9599    

DOI:10.1039/F19827800237

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1982, 78, 255-271 Water Oxygen- 17 Magnetic Relaxation in Polyelectrolyte Solutions BY BERTIL HALLE* AND LENNART PICULELL Division of Physical Chemistry 1, Chemical Center, S-220 07 Lund 7, Sweden Received 16th February, 198 1 Water oxygen- 17 longitudinal and transverse relaxation rates have been measured at two frequencies for aqueous solutions of poly(acry1ic acid) and poly(methacry1ic acid) under conditions of variable temperature. concentration and degree of dissociation. The proton-exchange broadening of the ''0 resonance from these polyacid solutions has also been investigated. The data show that the residence time for water molecules interacting with the polyacid is of the order of s, during which time they reorient anisotropically, an order of magnitude slower than bulk water, and engage in rapid proton transfer with acidic groups.The motional perturbation of associated water is to a large extent electrostatically induced. A new method for determining an upper limit for the lifetime of 'bound' water from the proton-exchange broadening is employed and the necessary equations are derived. The perturbing effect of macromolecules in aqueous solution on the structure and dynamics of water, commonly referred to by the imprecise term ' hydration', has been intensely studied in recent years.l Before the ultimate goal of a full understanding of the interaction of water with complex biological structures can be accomplished, it will be necessary to study a wide variety of simpler model systems.One class of systems, which shares important features with many biological macromolecules, is aqueous solutions of synthetic linear polyelectrolytes. Of the various manifestations of the water-macromolecule interaction, effects on the rate and anisotropy of water reorientation, as well as the average residence time of a water molecule in the perturbed region, are probably most directly studied through the magnetic relaxation of solvent nuclei. In the present investigation of aqueous solutions of poly(acry1ic acid) (PAA) and poly(methacry1ic acid) (PMA) we have studied the magnetic relaxation of water oxygen-I7 nuclei. This nucleus is preferable to the other two accessible solvent nuclei, the proton and the deuteron, for several reasons. The 1 7 0 nucleus relaxes through the interaction of its electric quadrupole moment with the field gradient generated by the charge distribution of the water molecule.The virtual absence of intermolecular contributions2* l6 greatly simplifies the molecular interpretation of experimental relaxation rates. The large magnitude of the quadrupolar interaction leads to observable relaxation enhancements at comparatively low polyelectrolyte concentra- tions and makes the 170 relaxation rates much less sensitive to paramagnetic impurities, particularly in comparison with proton relaxation. Furthermore, it has been shown that, in aqueous solutions of PAA and PMA, the deuteron relaxation is determined by the rapidly exchanging acidic deuterons on the polyacids and thus cannot yield information on the state of water in these ~ y s t e r n s .~ ? ~ 255256 1 7 0 N.M.R. I N POLYELECTROLYTE SOLUTIONS EXPERIMENTAL CHEMICALS Aqueous solutions of poly(acry1ic acid) (25 %) and poly(methacry1ic acid) (20 %) were obtained from B.D.H. Chemicals. The degree of polymerization for the PAA preparation is ca. 3200 according to the manufacturer. Since no such information was available for the PMA preparation, we determined the intrinsic viscosity at 3O.O0C and pH 2.7. The value thus obtained, [q] = 5.8 cm3 g-l, corresponds5 to a degree of polymerization of ca. 90. Polyacid solutions were made by dilution with doubly distilled water (quartz apparatus) and titrated to complete dissociation (a = 1) with NaOH prior to relaxation measurements. The sodium-ion concentration was thus, at all degrees of dissociation, equal to or in slight excess of the monomer concentration.Polyacid concentrations are given as mol monomer per kg H,O (m), throughout this paper. Samples of ca, 4 g polyacid solution, enriched to ca. 1 % in 1 7 0 , were prepared in n.m.r. tubes with 12 mm outer diameter. H,O enriched to 10 atom% in 1 7 0 was obtained from Biogenzia Lemania, Lausanne. Propionic acid and isobutyric acid were from B.D.H. Chemicals and Th. Schuchardt Gmbh, respectively. TITRATIONS A N D pH MEASUREMENTS pH was varied by adding small volumes of concentrated HCI solutions to the n.m.r. samples. Relaxation rates from the titration experiments (fig. 3) were corrected for dilution assuming proportionality between excess rates and monomer molality.This correction, which is largest at a = 0, never exceeds 8%. pH was measured in the n.m.r. tubes at room temperature with Radiometer PHM 52 or PHM 64 pH meters, equipped with Radiometer GK2322C combination electrodes. Corrections for the sodium error were made according to a nomogram supplied by the manufacturer. The degree of dissociation, a, of the polyacids as a function of pH was determined through a separate potentiometric titration at each polyacid concentration. From the pH of the solution [H,O+] or [OH-] was calculated using operational activity coefficients (determined in the absence of polyacid). The fraction of charged monomers then follows from stoichiometric considerations. RELAXATION MEASUREMENTS Oxygen-17 magnetic relaxation rates were measured at 13.56 MHz on a modified Varian XL-100-15 Fourier-transform spectrometer and at 34.56 MHz on a home-built Fourier- transform spectrometer equipped with a 6 T wide-bore magnet from the Oxford Instrument co.Longitudinal relaxation rates ( R , ) were measured with the inversion recovery method (n-r-n/2 pulse sequences). Each R , value is the result of a least-squares fit of the magnetization plotted against delay time for ten different z values. Transverse relaxation rates ( R , ) were obtained from the linewidth (Avob,) at half amplitude of the absorption spectra according to R,. nhs = nAvohs. Reported R, values are averages of 2-4 spectra. The precision was better than & 2 s-l. The excess relaxation rates, defined by eqn (8), were calculated as Ri, ex = ' i , obs- R i , ref (i = 7 2).Ri, obs is the relaxation rate (or half-width times n) observed for a polyacid solution and Ri, rc,f is the same quantity for a sealed sample of H,O at pH 2.7, measured at the same temperature. Although R , = R , for pure water, Rz,ref > R l , r e f due to a contribution (ca. 3 s-l) to the linewidth from magnetic-field inhomogeneity. In the calcuation of Ri, ex this contribution cancels. From a large number of measurements we have found the true 1 7 0 relaxation rate in pure water [RF in eqn (8)] at 28.0 OC to be 127.3 & 2 s-l. The experiments were carried out at probe temperatures ranging from 27.4 to 28.5 OC and the data were subsequently normalized, using the temperature-dependence data in fig. 1, to 28.0 O C , unless otherwise stated.These corrections never exceeded 2 %. During each experiment the probe temperature was kept constant to within & 0.2 OC by the passage of dry thermostated air or nitrogen. The overall accuracy of the corrected and normalized excess data is estimated to be better than &3 s-l.B. H A L L E A N D L. P I C U L E L L 257 THEORETICAL BACKGROUND For a nucleus like oxygen-17, with spin I = $, the macroscopic magnetization decays, in general, as a weighted sum of three exponentiak6 No general analytical expressions exist for the three amplitudes or for the corresponding relaxation rates in terms of the spectral densities characterizing the molecular motion; rather the eigenvalues and eigenvectors of the relaxation matrix must be obtained numerically for each set of values for the spectral densities.However, in the systems under study the comparatively rapid motion of the ‘bound’ water and the large fraction of rapidly reorienting bulk water result in an effective spectral density that is only weakly frequency dependent in the experimental frequency range. The relaxation then becomes nearly exponential and approximate analytical expressions for the longitudinal and transverse rates can be deri~ed.~9 * For the present data, these expressions are accurate to better than 1 %. Since no 1 7 0 quadrupolar splittings were observed for the polyacid solutions, the molecular motion must average the quadrupolar interaction to zero on a time-scale of the order of 1 /x, where x is the quadrupole coupling constant. The relaxation rates can then be expressed as6 3n2 Rl = -x2 625 ( I +;) [~J((w,) + 8J(20,)] where coo is the resonance frequency and the reduced spectral density is Here it has been assumed that the molecular motion is isotropic, so that the correlation function for the field gradient decays exponentially with a correlation time 7,.(This assumption will be partly removed in the subsequent treatment.) For the H2170 quadrupole coupling constant we use the recent2f l6 estimate x = 6.67 MHz, while the asymmetry parameter is taken to be the same as in ice,9 q = 0.925. If the 1 7 0 nuclei exchange rapidly between two environments or states with different intrinsic relaxation rates but negligible chemical shift difference, then the total rates may be decomposed according tolo.l1 Ri = PFR,+PBRiB ( i = 1,2) (3) where PB = nm/55.5 is the fraction of nuclei in the B state and PF = 1 -PB. m is the monomer molality and n is the number of motionally perturbed water molecules per monomer. Eqn (3) corresponds to a two-state model with ‘free’ (F) and ‘bound’ (B) water. For ‘free’ water RIF = RZF = R,. ‘Rapid exchange’ here means that the average ‘lifetime’ z~~ of a water molecule in the B state is short compared with the intrinsic relaxation times in that state, i.e. that rlB 4 l/RiB. Due to the scalar spin-spin coupling between the 1 7 0 nucleus and the two protons, the water 1 7 0 resonance consists, in the absence of proton exchange, of a triplet12 with spin-spin coupling constant13 JOH = 90 Hz. At normal temperatures, however, the proton exchange rate Y > 2nJoH, making the 170 resonance nearly Lorentzian with a linewidth determined by Y, JOH and the transverse relaxation rate, R,, in the absence of exchange.In practice, R, is obtained from the linewidth at pH values where258 1 7 0 N.M.R. I N POLYELECTROLYTE SOLUTIONS Y 9 271JOH, from the proton decoupled linewidth, or from the longitudinal relaxation rate (provided that extreme narrowing conditions obtain). Starting from the extended Bloch equations,12 it is straightforward to derive an expression for the 1 7 0 lineshape as a function of Y, broadening of the linewidth due to proton exchange, Avexch AvObs- R2/71, can be obtained numerically. However, for the data simple expression, which is derived in Appendix approximation JOH and R,, from which the presented here, the following A, is valid to an excellent The rate of proton exchange in pure water may be YF = $k,[H3O+] + k,[OH- written as1, 1 ( 5 ) where k , and k , are the second-order rate constants for the acid- and base-catalysed transfer processes, respectively.With pH = - log(y'[H30+]), y' being an operational activity coefficient, and K, the ionic product of water eqn (5) becomes rF = ik;lO-pH +k;lK,IOPH (6) where k; = k,/y' and k;l = y'k,. In an aqueous polyacid solution additional mechanisms for water proton exchange may exist. Let rR be the rate of proton exchange for the fraction Pg of the water molecules which are engaged in proton transfer with prototropic groups on the polymer. [Note that Pg is not necessarily equal to the fraction P, appearing in eqn (3)].The proton-exchange kinetics is thus described by a six-state model with three spin states for each of the F and B states. However, provided that Pg < 1, the system can be treated as if there were proton exchange between only three (spin) states, with an effective rate where z g is the average lifetime in the B state for the fraction Pg of the water molecules. This result is derived in Appendix B. RESULTS In order to determine whether the fast exchange limit is applicable to the water 1 7 0 relaxation in our polyacid solutions, i.e. if eqn (3) is valid, we measured the linewidth as a function of temperature in the range 5-93 "C for solutions of PMA at two degrees of dissociation (fig. 1). Under very general conditions, an Eyring plot of ln(R,, ex/ T ) against 1 /Tyields a line of positive slope in the fast exchange limit.14 This is evidently the case for water interacting with either the coiled (a = 0.08) or the extended (a = 0.54) conformations (see below) of PMA.According to eqn (3) the excess relaxation rates may be written as Ri, ex G Ri - R , = P,(Ri, - RF). (8) The evaluation of Ri,ex as described in the Experimental section is equivalent to setting R, equal to the relaxation rate of pure water (127.3 s-l at 28.0 "C). The excess rates thus include a small contribution ( 5 3 s-l) from sodium and chloride ions (cf Discussion). Fig. 2 shows that the transverse excess relaxation rate is, within theB. HALLE AND L. PICULELL 259 0 0 2 7 2 9 3 1 3.3 3 5 37 lo3 KIT FIG. 1 .-Temperature dependence of the I7O transverse excess relaxation rate at 13.56 MHz for 0.55 rn PMA at a = 0.08 (0) and for 0.57 m PMA at o! = 0.54 (m).Error bars correspond to a 3 s-' uncertainty in 4, ex. experimental accuracy, proportional to the monomer molality, except for PMA at a = 0. Measurements on PMA at 0.19 and 0.59 m as a function of a (table 1) show that this non-linear behaviour becomes less pronounced as the charge density increases, but it persists up to at least a N 0.2. In the absence of polymer-polymer interaction, the intrinsic relaxation rates Ri, should be concentration independent, whereas P, and thus, according to eqn (8), Ri, ex should be proportional to the monomer molality. These findings therefore demonstrate the presence of polymer-polymer interaction in PMA solutions at low a in the investigated concentration range.Note that a linear concentration dependence, as was obtained for PAA and for PMA at a = 1 , is a necessary, although not sufficient, criterion for absence of polymer- polymer interactions. Indeed, our results show that the I7O relaxation rates in the concentration range < 0.6 m are unaffected by inter-polymer electrostatic repulsion. Since the non-linearity for PMA becomes more pronounced with decreasing charge density, it cannot have an electrostatic origin. As an explanation we suggest polymer-polymer association. That this occurs for PMA, but not for PAA (cf. also table 2), may be due to stronger van der Waals forces between the PMA chains with their additional methyl groups. A change in the degree of dissociation of the polyacid may influence the water 1 7 0 relaxation directly through the altered charge density or indirectly via conformational transitions or changes in counter-ion association.Indeed, fig. 3 reve$s a not-trivial a-dependence. For PAA we found that extreme narrowing conditions [J(w) = J(0) and thus, according to eqn ( I ) , R, = R,] obtain over the entire a range, whereas for PMA at low a values we observed considerable differences between longitudinal and260 1 7 0 N.M.R. I N POLYELECTROLYTE SOLUTIONS 40 - 30 - I 0 02 94 06 [monomer] /m FIG. 2.-Concentration dependence of the 1 7 0 transverse excess relaxation rate at 34.56 MHz and 27.7 OC for aqueous solutions of PAA and PMA at a = 0 (A) and a = 1 (0). Solid lines from least-squares fits.TABLE 1 .-RATIO OF NORMALIZED (TO r?.i = 1 ) TRANSVERSE EXCESS RELAXATION RATES AT 13.56 MHZ FOR TWO PMA CONCENTRATIONS AT DIFFERENT DEGREES OF DISSOClATlON a 0.19 R2, ,,(0.59 rn) 0,59 R2, ex(O. 19 rn) 1 .ooo 1.05 0.222 1.23 0.086 1.39 0.005 1.45 0.000 I .96 Data from the pH range of significant proton-exchange broadening, corresponding to 0.3 < a < 1 .O for 0.19 rn PMA, are not included.B. HALLE AND L. PICULELL 26 1 100 80 - 60 vl \ ?2 e 40 20 0 . .O O.0 Q o 0 m . 0 0 A & A A k 1 1 1 , , , , , , 1 , 0 0.5 1 .o a FIG. 3.--"0 excess relaxation rates at 28.0 O C plotted against degree of dissociation for 0.59 m PAA (A), 0.59 m PMA at 13.56 MHz (0, O), and 0.57 m PMA at 34.56 MHz (a, 0). Open symbols refer to longitudinal, filled symbols to transverse rates.At a values where only filled symbols are shown, measured R,. ex and R2, ex overlap. No data from the region of significant proton-exchange broadening are included. TABLE 2.-EXCESS RELAXATION RATES AT 0.59 rn AND 28.0 OC FOR MONOMERS AND POLYMERS monomer Rexa/s-l polymer R,,"s b / s - l CH,CH,COOH 10.5 PAA a = 0 11.3' (CH,),CHCOOH 14.4 PMAa=O (CH,),CHCOO- 30.4' PMA a = 1 56.7d CH,CH,COO- 23.6' PAA CI = 1 41.2d a The uncertainty in Re, is estimated to be 2 ssl. In all cases R, = R,. ' From the slopes ' The contribution of 3 s-l from 0.59 rn NaCl or Na+ (C1- makes a negligible A contribution of 1 s-l, corresponding to 'free' Na+ in fig. 2. contribution) has been subtracted. (see Discussion), has been subtracted. Frequency-dependent relaxation rates.transverse relaxation rates as well as a frequency dependence. This behaviour indicates that there are rapidly exchanging water molecules with motional components on a timescale of nanoseconds. Common to both polyacids is a nearly linear increase in relaxation rates with increasing charge density above a 5 0.5. In order to facilitate the interpretation of the 1 7 0 relaxation data for PAA and PMA, we studied the corresponding monomers, propionic acid and isobutyric acid, respectively. The results are shown in table 2 together with some polyacid data from fig. 2. The effect of the monomers is more than doubled upon dissociation of the carboxylic group. In the fully protonated state (a = 0) PAA produces the same effect as an equivalent concentration of monomers.This is not so for PMA, for which, as noted above, the relaxation rates are frequency-dependent and much larger than for the corresponding monomer solution. In the fully dissociated state (a = 1) we observe significantly larger effects from both of the polymers, as compared with the dissociated262 1 7 0 N.M.R. I N POLYELECTROLYTE SOLUTIONS monomers. Finally, we note that the difference between PAA and PMA at a = 1 is larger than the difference between the anionic monomers. The broadening of the 1 7 0 absorption curve around neutral pH, due to slow water-proton exchange, is drastically reduced on addition of even small amounts of PAA or PMA (fig. 4). This effect is evidence of additional catalytic mechanisms that are much more effective than those operating in bulk water around neutral pH.The shift of the linewidth maximum towards higher pH indicates that dissociation reduces thecatalyticefficiency of the polyacid. Furthermore, a reduction of the proton-exchange broadening to the level of the two intermediate, almost coincident, curves requires a 7-fold higher concentration of PMA as compared with PAA. PAA is thus a considerably more powerful proton-exchange catalyst than PMA. 80 60 ; d \ f 40 20 0 I I I I I I \ I f J 0 f’ / I I i 0 \. 6 7 8 9 PH FIG. 4.-Proton-exchange broadening of the 1 7 0 resonance plotted against pH at 28.4 *C for H,O (a), 1 . 5 0 ~ mPAA(.,dashedcurve), 10.2 x mPMA(A)and0.585 mPMA(A).Thecurvesare based on least-squares fits to theoretical expressions as explained in the text. DISCUSSION GENERAL CONSIDERATIONS The simplest picture consistent with the temperature and concentration dependences of the water 1 7 0 relaxation rate is a fast exchange of water molecules between two states: ‘free’ (F) and ‘bound’ (B) water. In attempting a more detailed interpretation one must, even within this relatively simple model, consider several dynamic processes : (1) reorientation of free water molecules, (2) chemical exchange between free and bound states, (3) reorientation (possibly anisotropic) and translation of bound water molecules, and (4) reorientation (possibly anisotropic) of entire polymer molecules (or aggregates) and segments thereof.Furthermore, all these processes may be influenced by the presence of counterions. To begin with, assume that water molecules in the B state are rigidly bound to theB.H A L L E AND L. P I C I J L E L L 263 polyelectrolyte, i.e. that processes of type 3 can be disregarded. Furthermore, assume that processes of types 2 and 4 can be described by a single effective correlation time zCH [cf. eqn (lo)]. With relaxation rates from fig. 3 for PMA at cc = 0 and with T , , ~ = 2.35 ps [from eqn (1) and (2) with R, = 127.3 s-l], eqn (I), (2) and (8) yield T ( , ~ = 3.3 10 monomer units. We regard this as an unreasonably low value for the number of interacting water molecules, even for a relatively compact polymer conformation. (A monolayer coverage of a compact sphere consisting of 90 monomers corresponds to ca. 3 water molecules per monomer.) These considerations led us to refine the model by allowing the bound water molecules some reorientational freedom, while still taking into account the inherent anisotropy of the water-polymer interaction. The local anisotropic reorientation will only partially average the quadrupolar interaction,lj the remaining part being averaged out by a slower motion, presumably chemical exchange and/or polymer reorientation.Since this extended two-state model involves more parameters than justified by our data, we will introduce several simplifying assumptions: (1) the local and the overall motions occur independently and on different timescales, (2) there is local axial symmetry and (3) the anisotropy is small. The spectral density for the B state may then be decomposed into components associated with the fast (0 and the slow (s) motionsl5? I 6 1.3 ns, corresponding to one bound water molecule for every 41 Zince the fast motion is in the extreme narrowing limit (see below), eqn (2) yields JRf = 2&.The residual anisotropy A , the magnitude of which is confined to the range [0, 11, is determined by the asymmetry parameter q and by the orientational probability distribution for the ‘bound’ water molecules with respect to the polymer chain.16 If the ‘ boznd ’ _water molecules were to reorient completely isotropically, then A = 0 giving J R = JRf, i.e. only the fast motion would contribute to the relaxation. From eqn (9), which is valid only for A2 6 1, it is seen that for the slow motion to contribute significantly to the relaxation rate, it must be of the order of a factor 1 / A 2 slower than the fast motion.On the basis of water 170 data [ref. (2) and unpublished data] from similar systems, we expect IAl to lie in the range 0.01-0.2. In the following, we will interpret the direct effect of carboxylic-group dissociation (indirect effects on polymer conformation and counter-ion association will be considered explicitly) on the ‘hydration’, as measured by the 170 relaxation rate, in terms of variations in reorientational rate and/or anisotropy for a fixed number of water molecules, rather than in terms of a changing ‘hydration number’. In view of the short-range character of the water-polyelectrolyte interaction (its most long-ranged component, the average charge-dipole potential, falls off as r4 to first order), we feel that this interpretation is physically reasonable and conceptually preferable.The other view may be more natural in connection with hydration studies through measurement of the water self-diffusion coefficient17 or of absorption and desorption isotherms.1s The results from such studies are, however, not simply related to the properties determining water magnetic relaxation rates. LOW a RANGE It has been documented with a variety of experimental t e ~ h n i q u e P ~ ~ that PMA, and to a much lesser extent also PAA, in aqueous solution undergoes a conformational transition from an extended form at high a to a more or less compact random coil264 1 7 0 N.M.R. I N POLYELECTROLYTE SOLUTIONS at lower a. This transition is undoubtedly the origin of the large 170 relaxation rates for PMA at low a values. The non-linear concentration dependence for PMA (fig.2 and table 1) implies that, in the investigated concentration range, association occurs also between chain segments situated in different polymer molecules. At a = 0, PAA has the same effect on the 1 7 0 relaxation as an equivalent concentration of monomers (table 2). This indicates that the local water reorientation is similar in these two systems and that more extensive motions do not contribute significantly at a = 0. For PMA, on the other hand, slow motions must be invoked to explain the much larger effect compared with the monomer solution (table 2), the inequality of R, and R,, and the frequency dependence (fig. 3). Since the rate and anisotropy of the local water reorientation should be similar for PMA and PAA at a = 0, the difference between PMA and its monomer must lie mainly in the slow correlation time z:~.This correlation time can be estimated if we assume that the local water reorientation is the same for PMA as for the monomer, as was found for PAA at a = 0. From the data in fig. 3 and table 2 we then find, using eqn (l), (2), (8) and (9), for PMA at a = 0: z S , ~ = 6 If: 2 ns and nA2 = 0.023. ‘Coordination numbers’ n in the range 2-10 thus correspond to anisotropies IAl in the range 0.1 1-0.05. The maximum in relaxation rates for PMA in the low a range can be understood as the result of two opposing factors. First, deprotonation of carboxylic groups should, through the charge-dipole interaction, increase the anisotropy of the local water reorientation.The factor A2 in eqn (9) is thereby increased and the slow motion is more heavily weighted, resulting in enhanced relaxation rates with increasing a. Secondly, as the polymer chain gradually unfolds with increasing charge density, the correlation time z S , ~ , which is at least partially (see below) determined by extensive polymer motions, decreases. This is seen from the decreasing ratio R2, ex/R1, ex with increasing a in the range 0.1-0.5 (fig. 3). The conformational transition thus has the effect of decreasing the slow motional contribution to the relaxation rates with increasing a. HIGH a RANGE Small-angle neutron and X-ray scattering studies of aqueous solutions of PMAZ5 and PAA,26 respectively, in the concentration range 0.1-0.4 rn and in the a range 0.4- 1 .O have revealed a peak in the plot of scattered intensity against scattering vector.This was taken as evidence for an electrostatically induced lattice-like structure with parallel extended polyelectrolyte chains. Since this ordering was found to persist down to the lowest investigated concentration (ca. 0.1 rn) and degree of dissociation (0.4 and 0.6), the linear dependence of the 1 7 0 relaxation rate on concentration at a = 1 (fig. 2) and on a above a N 0.5 (fig. 3) is not surprising. Thus, although the ordered structure is a direct result of electrostatic polymer- polymer interaction, this interaction is not expected to affect the water motion as long as the polymer segments remain extended and sufficiently separated.The monomer data in table 2 clearly demonstrate that the perturbation of the water reorientation, to a large extent, is electrostatically induced. The increase in relaxation rate with increasing a above a N 0.5 (fig. 3), where the polyacids exist in an extended conformation,19 26, 28 is thus readily accepted. The same situation, with charged residues (carboxylates in particular) contributing more than uncharged ones to the 1 7 0 relaxation rate, is found in aqueous protein solutions.2 In sharp contrast to our results, deuteron relaxation in PMA has been taken as evidence for a decreasing ‘hydration’ with increasing charge density. Later work3’ has, however, cast serious doubts on this interpretation. Our results clearly reinforce these doubts. The larger effect on the water 1 7 0 relaxation rate of charged groups is not a consequence of an increased electric field gradient at the oxygen nucleus.The waterB. HALLE A N D L. PICULELL 265 1 7 0 field gradient is, to an excellent approximation, of intramolecular origin. Indeed, recent quantum chemical calculations2* l6 have shown that the perturbation induced by a nearby charge is negligible. It remains for us to explain the substantially larger effect on the 170 relaxation rate of the fully dissociated polyacids as compared with the monomers (table 2). One difference between a polyelectrolyte and its separated monomers is that a fraction of the counter-ions associate with the polyelectrolyte, thereby reducing its effective charge density. This phenomenon can often be adequately described in terms of an ‘ion condensation’ m ~ d e l : ~ ~ t ~ ~ there exists a critical charge density or degree of dissociation, a,, below which all counter-ions are ‘free’ and above which all additional counterions become ‘bound’ to the polyion.For PAA and PMA a, = 0.35, according to this model. 0.5, the polymer (segmental) motions were sufficiently rapid for their contribution to the relaxation rate to be negligible [cf. eqn (9)], then one would expect ‘condensed’ counter-ions to produce roughly the same effect on the 1 7 0 relaxation rate as ‘ free’ counter-ions. We therefore conclude that the much larger effect of the polyacids in the high a range, relative to the monomers, is due to a contribution from slow motions. Consequently, the effect of carboxylic group dissociation on the 170 relaxation rate in the high a range can be viewed as the resultant of three electrostatic contributions.First, the charge-dipole interaction lowers the rate of local water reorientation, i.e. increases zfcB. This is the sole effect for the monomers. Secondly, the charge-dipole interaction enhances the anisotropy in the local water reorientation. As noted above, for PAA at a = 0 the anisotropy IAl is so small that the slow motion does not influence the relaxation significantly. For charged groups, on the other hand, the anisotropy is sufficiently large for the slow motion to contribute substantially according to eqn (9). Thirdly, association of counter-ions increases the number of water molecules associated with the polyelectro- lyte and thus ‘feeling’ the slow motion.(It has been that sodium ions retain their primary hydration sheath upon binding to carboxylate groups.) Finally, it is possible that the aforementioned electrostatic interactions are enhanced in the polyacid solutions because the adjacent hydrocarbon core of the polymer chain reduces the effective local dielectric permittivity through a ‘ dielectric shielding’ effect.34 Table 2 shows that there is a larger difference (15.5 s-l) between PMA and PAA at a = 1 than between the anionic monomers (6.8 s-l). In view of the previously discussed lattice-like structure in this a range, it is unlikely that this difference should be caused by the disparity in the degree of polymerization of our polyacid preparations (see Experimental section).As a check, we investigated the molar mass dependence of the 170 linewidth for 0.6 m solutions of PAA at a = 0 and at a = 1. No difference was found between degrees of polymerization 30, 90 and 3200. This leaves us with the conclusion that the additional methyl groups in PMA have a greater effect on the 1 7 0 relaxation rate than they have in the monomers. This would be the case if these methyl groups interfere with segmental chain motions, thereby increasing zEB, or if they, by adding to the bulk of the hydrocarbon core, promote the ‘dielectric shielding’ effect. Concluding the discussion of relaxation rates, it may be of interest to give an order-of-magnitude estimate of the rate of local water reorientation, i.e. of the correlation time zfc+ From the monomer data in table 2 we estimate the contribution from a carboxylate group to be ca.17 s-l. Using eqn (l), (2) and (8) we can then calculate the quantity n(zfcB-z,,), where zCF = 2.35 ps (see above). In this way we find that ‘coordination numbers’ n in the range 2-10 correspond to zfcB/zCF ratios in If, in the range a266 1 7 0 N.M.R. I N POLYELECTROLYTE SOLUTIONS the range 7-2. The rate of 'bound' water reorientation is thus less than an order of magnitude slower than in pure water. The same order of magnitude should apply for water associated with the polyacids. In fact, even if we disregard the contribution from slow motions at a = 1, we arrive at similar rates. Thus, for PAA at a = 1 we find that n values of 2-10 correspond to ztH/zCF ratios of 16-4.PROTON EXCHANGE In fig 4 is included the result of a redetermination of the rate constants k; and k; appearing in eqn (6). The upper curve, which resulted from a least-squares fit to the complete theoretical expression derived from the extended Bloch equations [the approximate eqn (4) yields identical results], corresponds to k ; = 13.1 k0.3 dm3 mol-1 ns-l and k; = 4.06 f 0.1 dm3 mol-l ns-l at 28.4 "C. To obtain these values, we have used JOH = 90 Hz,13 R, = 126 s-l and pK, = 13.88.35 Using Arrhenius activation energies36 of 10.9 kJ mol-1 ( k ; ) and 20.1 kJ mol-1 (k;), our results can be converted to 25.0 OC: k ; = 12.5 f 0.3 dm3 mol-1 ns-l and ki = 3.70f0.1 dm3 mo1-l ns-l, in close agreement with Meiboom's original results12 of 10.6f4 and 3.8 Studying the effect of acetic acid and sodium acetate on the kinetics of proton exchange in aqueous solution by means of the broadening of the proton resonance, Luz and Meiboom3' concluded that the dominant mechanism involves a hydrogen- bonded complex consisting of one undissociated acetic acid molecule and two water molecules.If this mechanism prevails also for the polyacids, an increased polyacid concentration should not only lower the exchange-broadening curve but also shift its maximum towards higher pH. This behaviour is confirmed by our experiments (fig. On the basis of these observations and the finding (table 2) that the COOH-water interaction is similar in monomer and polymer solutions, we assume that I'E in eqn (7) can be calculated as 2(1 -a)rn/55.5, corresponding to two water molecules per undissociated carboxylic group.[In contrast to PB in eqn (3) and (8), we have included a in the definition of PE.1 The three lower curves in fig. 4 were calculated from least-squares fits to the model defined by eqn (4), (6) and (7). We used cx values from separate potentiometric titration experiments and the values given above for J O H , K,, k ; and k ; . Thus we neglect the influence of counter-ions and added chloride ions on the rate of proton exchange in the F state. According to our studies of the salt effect on the rate of water proton exchange (unpublished data), this influence is completely negligible, at least for the two lower polyacid concentrations. From these data we obtain (1 /rH + zyB) = 5.6 f 0.6 ns for PAA and 3 1 5 ns for PMA.(The less accurate result from the higher PMA concentration is 40 12 ns.) Previous proton n.m.r. studies at 25 "C have resulted in values of 21 ns for acetic and 14-90 ns for PMA.4 The higher catalytic efficiency of PAA, as compared with acetic acid, suggests that another mechanism, presumably involving a chain of one or more water molecules linking a protonated with a deprotonated carboxylate group, contributes to the proton exchange in PAA solutions. This mechanism is expected to be less important for PMA, which was found to be less potent than acetic acid, since the methyl group has a stiffening effect on the polymer chain, as deduced from molecular models. Although the effect of solutes on the water proton exchange rate has been studied in a variety of systems [e.g.ref. (4) and (37)], no attempt has been made to extract information about the rate of water exchange from the experimental data. However, as shown by the analysis in Appendix B, the experiments yield the composite quantity (I/rH+~yH), which constitutes an upper limit for the average residence time zyB for those water molecules that exchange protons with the solute. 1.5 dm3 mol-1 ns-l, respectively. 4).B. HALLE A N D L. PICULELL 267 If the liO relaxation rate contains a contribution from slow motions, it may be possible to determine the slow correlation time zzB. If both polymer reorientation (correlation time zrB) and chemical exchange (average lifetime z,,) contribute to the slow motion, then this may be characterized by an effective correlation timell 1 1 1 - --+-.- - z:B zrB zlB This result is strictly valid only in the absence of orientational correlation between successive water-polymer encounters. For PMA at a = 0 we found (see above) zER = 6 f 2 ns. According to eqn (lo), this is a lower limit for the water lifetime in state B. Since the effect of PMA on the proton exchange broadening is due mainly, or entirely, to undissociated carboxylic groups, this value may be compared with the upper limit for z g obtained from the proton-exchange broadening. We can therefore conclude that water molecules associated with COOH groups in PMA at a = 0 have an average lifetime in the range of 4-36 ns. SUMMARY The present study shows that water 170 magnetic relaxation is a valuable tool for the understanding of dynamic processes in aqueous polyelectrolyte solutions.Water molecules associated with the polyelectrolyte are not rigidly bound; rather they reorient anisotropically with a rate that is merely an order of magnitude slower than in bulk water. This perturbation of the water reorientation is, to a large extent, electrostatically induced. Water molecules directly hydrogen-bonded to acidic groups are engaged in rapid proton transfer and have average residence times of the order of s. In addition, water li0 relaxation rates contain information about polymer dynamics which can be related to results obtained by other techniques. We are grateful to Maj-Lis Fontell for helping us with the potentiometric titrations and the viscosity measurements and to Hans Gustavsson and Torbjorn Drakenberg for experimental advice and helpful discussions. Grants from Stiftelsen Bengt Lundqvists Minne and from Kungl Fysiografiska Sallskapet i Lund are gratefully acknowledged .APPENDIX A: EFFECT O F RAPID PROTON TRANSFER ON THE 1 7 0 LINEWIDTH The observed 170 linewidth for pure water at 28 O C is strongly pH dependent with a maximum of ca. 115 Hz at pH 7.2 (fig. 4)’ whereas the ‘natural’ linewidth (due to quadrupolar relaxation) is merely ca. 40 Hz. Despite the considerable magnitude of this proton-exchange broadening, the lineshape remains Lorentzian, or very nearly so. This fact indicates that the proton-exchange broadening can be described, to high accuracy, by an equation which is simpler than the complete lineshape expression.Various limiting forms can be derived by introducing suitable approximations in the exact solution of the extended Bloch equations. Since this involves rather heavy algebra, we will choose a more elegant approach due to Wennerstrom.ll The essence of Wennerstrom’s treatment of chemical exchange is to write the spin Hamiltonian as (A 1) where the sum extends over all states (‘sites’). The random functionsf;(t) have the property of being unity if the nucleus considered is in state i at time t and zero otherwise. The ensemble average ( f i ( t ) ) , which we will denote by l$(t), is simply the fraction of nuclei in state i at time t . At equilibrium ( f i ( t ) ) , , = pi. H = C f i ( t ) H i 2268 1 7 0 N.M.R. I N POLYELECTROLYTE SOLUTIONS If the ‘natural’ linewidth is the same in all states, which, in the present case, must be true since the 1 7 0 field gradient is unaffected by the proton spin state, then it can be shown1’ that the exchange broadening is Av,,,.~ = - d7ZZ Cf,(O&(f+T)),,j Awi AWj (A 2 ) 2n - x i j where A o i == oOi - Ci pi woi, mOi being the resonance frequency in state i.Eqn (A 2) is valid only if the exchange rate is large compared with the relaxation rate and if the lineshape is Lorentzian. Furthermore, it is assumed that the exchange is slow compared with those motions (water reorientation in the present case) that are responsible for the ‘natural’ linewidth. The time correlation function in eqn (A 2) may be written6 as the product of the probability pi and the conditional probability pji(7) that the nucleus is in statej at time t + z , given that t .Thus (A 3) l X 2n --J. AvexCh = - dr Z p i p j i ( 7 ) A o i Awj. the exchange of 1 7 0 nuclei between different proton spin states is it was in state i at time The kinetic scheme for where Y is the proton exchange rate, i.e. the inverse of the average lifetime of a water molecule with a given pair ofprotons. The numerical factors follow from simple probability considerations and the principle of detailed balancing.I2 Furthermore, we have p 1 - 4 - 1 Aw, = -2nJ0, p 2 = $ and Aw, = O P 3 = a A o 3 = 2nJOH. The rate laws for the system (A 4) may be written in matrix notation as d -F(r) = -rF(t) dt where F(r) is the column vector with elements &(t) and 1 -1 0 -1 - 1 2 The formal solution to eqn (A 6) is F(t) = S exp( - A[) S-’ F(0) where S is the transformation that diagonalizes r according to A = S-I r S.After a little algebra we find 1 0 0 0 0 0 and The conditional probabilitypji(7) can now be obtained from the solution (A 8) as 4(7), subject to the initial condition &(O) = 6 k i . ThusB. HALLE AND L. PICULELL 269 Upon substitution of the elements of r7. and S (and its inverse) we find p , ,(7) = p3,(7) = f (e+ + 2e-r/r1/2 + 1 ) (A 13) pl,(7) = p3,(7) = (e-rlrl - 2e-rl*l12 + 1) where we have introduced absolute values in the exponentials to ensure that the correlation function becomes invariant with respect to time reversal. Conditional probabilities involving state 2 are not needed since Aw, = 0. It now remains only to substitute eqn (A 5) and (A 13) into eqn (A 3) and to carry out the integrations.The result is In order to assess quantitatively the accuracy of the approximate eqn (A 14), we have compared it with the exact numerical solution of the extended Bloch equations." For given values of r , R, and JOH we calculated the exact Av,,,,,, which was then inserted into eqn (A 14) to yield an approximate value of r . We used R, = 127.3 s-l and JOH = 90 Hz; however, the result is insensitive to the value of R,. Fig. 5 shows that eqn (A 14) is accurate to better than 1 % for the polyacid data in fig. 4. Avexch /Hz 90 80 70 60 50 40 30 20 1.10 , r . . . . . 1 r* 7 1.05 1.00 30 3.5 4.0 log ( r / s - l ) FIG. 5.-Ratio of proton exchange rate, r*, as calculated by eqn (A 14), to the exact rate r , plotted against log r and exchange broadening Av,,,~.The ranges of interest for pure water at 28 O C and for the polyacid data in fig. 4 are indicated. APPENDIX B : EFFECT OF TWO-STATE WATER EXCHANGE ON THE PROTON SPIN-STATE KINETICS Consider a system in which water molecules can reside in either of two states, defined by their respective proton exchange rates rF and r,. At equilibrium, the fraction of water molecules in each state is P, and P,, respectively. If the water molecules can exchange between the two states, with rates equal to the inverse of the respective lifetimes tF and t,, then kinetic scheme for the exchange of 1 7 0 nuclei between different proton spin F, Z$ F, % F, is r F I 2 r F l 2 rF/4 rF/4 states (indicated by a subscript) 1 _ _ 7F270 1 7 0 N.M.R.I N POLYELECTROLYTE SOLUTIONS Assume now that the equilibrium fraction of water molecules in the B state is very small, i.e. that P, < 1. (For the experimental data to be considered, i.e. the two intermediate curves in figure 4, P, < 2.5 x lop4.) In the absence of water exchange, the effect of the B state on the observed proton-exchange broadening would then be completely negligible. For non-zero water exchange rates, however, the B state can, despite its low population, affect the observed broadening. This is so because a transition between, for example, spin states F, and F, can occur not only by a proton exchange in the F state, but also via two water-exchange events and an intervening proton exchange in the B state. For this latter, indirect, route to contribute significantly to the observed proton spin-state kinetics, the water exchange as well as the proton exchange in the B state must be fast compared with the proton exchange in the F state, i.e.1 /tn. % rF and rB $- r?. It is thus clear that, in the limit P, Q 1 , the only effect of the B states on the proton spin-state kinetics is to increase the effective rate of transitions among the F states. Consequently, the scheme (B 1) reduces to rlz r / z F, $ F, + F,. r/J r/4 It remains to derive an expression for the effective proton-exchange rate r in terms of PB, z,, rB and rF. The principle of detailed balancing requires that, at equilibrium, where the 4 and Bi denote fractional populations. Furthermore, from the rate laws pertaining to scheme (B 1) we find that, at equilibrium Combination of eqn (B 3)-(B 5 ) leads to Consider now the return from an infinitesimal displacement of the equilibrium population of the species F,.According to the scheme (B 1) Since the actual populations are assumed to differ only infinitesimally from their equilibrium values, we may substitute B, from eqn (B 6) into eqn (B 7 ) to obtain According to the equivalent scheme (B 2) which, on comparison with eqn (B 8), yields the desired result Eqn ( 7 ) in the main text differs slightly in notation.B. HALLE AND L. P I C U L E L L 27 1 For an introduction to the vast literature, see Water-A Comprehensive Treatise, ed. F. Franks (Plenum Press, New York, 1975), vol. 4 and 5. B. Halle, T. Anderson, S. Forsen and B. Lindman, J. Am.Chem. Soc., 1981, 103, 500. J. J. van der Klink, J. Schriever and J. Leyte, Ber. Bunsenges. Phys. Chem., 1974. 78, 369. J. Schriever and J. C. Leyte, Chem. Phys., 1977, 21, 265. A. Katchalsky and H. Eisenberg, J. Polym. Sci., 1951, 6, 145. A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961). B. Halle and H. Wennerstrom, J. Magn. Reson., 1981, in press. A. D. McLachlan, Proc. R. SOC. London, Ser. A, 1964, 280, 271. D. T. Edmonds and A. Zussman, Phys. Lett. A, 1972, 41, 167. lo J. R. Zimmerman and W. E. Brittin, J. Phys. Chem., 1957, 61, 1328. H. Wennerstrom, Mol. Phys., 1972, 24, 69. l 2 S. Meiboom, J . Chem. Phys., 1961, 34, 375. l 3 L. J. Burnett and A. H. Zeltmann, J, Chem. Phys., 1974, 60, 4636. l4 B. Lindman and S. Forsen, Chlorine, Bromine and Iodine NMR; Physico-chemical and Biological Applications (Springer-Verlag, Heidelberg, 1976). l5 H. Wennerstrom, G . Lindblom and B. Lindman, Chem. Scr., 1974, 6, 97. B. Halle and H. Wennerstrom, J . Chem. Phys., 1981, 75, in press. l 7 Gy. Inzelt and P. Grof, Acta Chim. Acad. Sci. Hung., 1977, 93, 117. K . Hiraoka and T. Yokoyama, Polym. Bull., 1980, 2, 183. R. Arnold and J. Th. G. Overbeek, Rec. Trail. Chim. Pays-Bas, 1950, 69, 192. J. C. Leyte and M. Mandel, J. Polym. Sci., Part A2, 1964, 1879. 2o A. Silberberg, J. Eliassaf and A. Katchalsky, J. Polym. Sci., 1957, 23, 259. 22 M. Mandel, J. C. Leyte and M. G. Stadhouder, J. Phys. Chem., 1967, 71, 603. 23 0. Schafer and H. Schonert, Ber. Bunsenges. Phys. Chem., 1969, 73, 94. z4 A. Ikegami, Biopolymers, 1968, 6, 431. 25 M. Moan, J. Appl. Crystallogr., 1978, 11, 519. 2fi N. Ise, T. Okubo, Y . Hiragi, H. Kawai, T. Hashimoto, M. Fujimura, A. Nakajima and H. Hayashi, *’ J. J. v.d. Klink, L. H. Zuiderweg and J. C. Leyte, J. Chem. Phys., 1974, 60, 2391. 2H H. Gustavsson, B. Lindman, and B. Tornell, Chem. Scr., 1976, 10, 136. 29 H. Gustavsson, B. Lindman and T. Bull, J . Am. Chem. Soc., 1978, 100, 4655. 30 J. A. Glasel, J . Am. Chem. Soc., 1970, 92, 375. 31 F. Oosawa, Polyelectrolytes (Marcel Dekker. New York, 1971). 32 G . S. Manning, Ace. Chem. Res., 1979, 12, 443. 33 H. Gustavsson and B. Lindman, J. Am. Chem. Soc., 1978, 100, 4647. 3 3 J. D. Jackson, Classical Electrodynamics (Wiley, New York, 2nd edn 1975), sect. 4.4. 35 H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions (Reinhold, New York, 36 A. Loewenstein and A. Szoke, J. Am. Chem. Soc., 1962, 84, 1151. N Z . Luz and S. Meiboom, J. Am. Chem. Soc., 1963, 85, 3923. J . Am. Chem. Soc., 1979, 101, 5836. 3rd edn, 1958), chap. 15. (PAPER 1 /255)

ISSN:0300-9599    

DOI:10.1039/F19827800255

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1982, 78, 273-28 I Calorimetric Study of the Adsorption of Carbon Monoxide, at 296 K, on Supported Nickel and Nickel-Copper Catalysts BY JEREMIA J. PRINSLOO~ AND PIERRE C. GRAVELLE* Institut de Recherches sur la Catalyse, CNRS, 69626 Villeurbanne, France Received 23rd February, 198 1 A calorimetric study of the adsorption of carbon monoxide, at 296 K, on a series of silica-supported nickel and nickel-copper catalysts was carried out. The experimental results were compared with previously published i.r. spectroscopic and magnetic data for the same systems. In agreement with the Chatt-Dewar model for CO chemisorption on metals, changes of the heat of formation of metal-CO bonds can always be associated with shifts of the frequency of the C-0 stretching vibration.The heat of the metalLC0 bond formation appears to be related to the position of the Fermi level at the metal surface. Formation of both linear and bridged adspecies, in definite proportions on each alloy, would obey a concerted mechanism, controlled by the electronic properties of the surface nickel atoms. Data on the heats of chemisorption of carbon monoxide on nickel surfaces are abundant: in their recent review,' Toyoshima and Somorjai cite nine determinations on polycrystalline samples and eleven on single-crystal surfaces. Therefore, the present study was not carried out with the aim to add one more set of values to the list. The purpose of the present study was to characterize calorimetrically the changes in the surface reactivity with respect to carbon monoxide which occur when nickel is alloyed with progressively larger amounts of copper and, by comparing these calorimetric results with those of previous volumetric,2 magnetic and infrared (i.r.) spectroscopic studies3 carried out with the same samples, to look for possible correlations between adsorptive and other properties of nickel surfaces.Correlations between the magnetic and electronic properties of nickel surfaces and their reactivity with respect to hydrogen have been recently pr~posed.~ EXPERIMENTAL The catalysts were prepared by adding the support (silica, 220 m2 g-') to aqueous solutions of ammonia containing nickel and copper nitrates in different proportion^.^ The solid was then filtered, washed and dried at 400 K for 24 h in order to decompose the metal complexes and evacuate ammonia.All the samples used in the present work come from the batches of catalysts which were prepared for previous studies on the nickekopper ~ y s t e m . ~ - ~ , Before each calorimetric experiment, a sample of catalyst (0.1-0.2 g) was reduced at 920 K in flowing hydrogen (4 dm3 h-l) for cu. 15 h, rapidly cooled to room temperature and transferred, in uucuo, into the calorimeter. This procedure, identical to that adopted in the preceding studies with these catalysts,2 was moreover carried out by means of the same vacuum line. In order to test the constancy of behaviour of successive samples, most calorimetric experiments were duplicated (column 5, table 1). t On sabbatical leave from the Chemistry Department of the Rand Afrikaans University, Johannesburg, South Africa.273TABLE I.-VOLUMETRIC AND CALORIMETRIC DATA FOR THE ADSORPTION OF CARBON MONOXIDE, AT 296 K, ON SILICA-SUPPORTED NICKEL AND NICKEL-COPPER CATALYSTS - amount of irreversibly heat of adsorption adsorbed from i.r. bond number average carbon average calculated spectroscopic metal diameter monoxide for per surface data3 composition of metal /(pmol CO) initial" e = 0.2 nickel atom /(atom surface Ni) catalyst [atom % (Cu)] particles/nm (m2 metal)-' /kJ mo1-l /kJ mol-l /kJ (atom Ni)-l (molec. adsorbed CO)-l Ni 0 6.7 4.8 _+ 0.2 142 (3) 141 86 1.65 Ni 98 Cu 2 1.52 5.8 6.1 kO.1 139 (2) 139 87 1.59 Ni 91 Cu 9 8.48 6.2 9.25 f. 0.15 133 (2) 133 92 1.45 Ni 88 Cu 12 11.8 6.1 6.95 +O. 15 125 (1) 124 89 1.40 Ni 80 Cu 20 20.2 6.0 6.25 & 0.15 123 (2) 120 95 1.30 Ni 73 Cu 27 26.7 5.6 4.95 & 0.15 120 (1) 112 97 1.24 Ni 54 Cu 46 46.2 13.3 - 111 (2) 94 100 1.11 " Figures in parentheses indicate the number of separate experiments from which the calorimetric data were obtained.J.J. PRINSLOO AND P. C. GRAVELLE 275 The composition of the samples and the average diameter of the metal particles determined from magnetic data6 are listed in table 1. Evidence has been presented elsewhere6 which demonstrates that the metal phase in all samples is completely reduced and that the surface composition of the alloy particles is very similar to that in the bulk. The heat-flow microcalorimeter, the ancillary volumetric line and the calibration procedures have already been described.' Throughout this work the calorimeter was maintained at 296 K.At this temperature carbon monoxide readily adsorbs on nickel surfaces but its dispropor- tionation to carbon dioxide and carbon does not occur.8 RESULTS The adsorption of carbon monoxide was carried out by introducing successive doses of adsorptive onto the catalyst sample, located in the calorimeter cell. The heat evolved, the quantity of gas adsorbed and the equilibrium pressure were measured at the end of the interaction of each dose, i.e. when the calorimeter had returned to thermal equilibrium. Introduction of doses was repeated until the equilibrium pressure reached ca. 200 Pa. Adsorption isotherms are, for all samples, similar to that reported in fig. 1 of ref. (2), in the case of the pure nickel sample.After the adsorption of the first doses the residual pressure is very low and the adsorbate is irreversibly held on the surface at 296 K. After the adsorption of further doses a measurable equilibrium pressure builds up, evacuation of which brings the desorption of the reversible fraction of the adsorbate. The amounts of irreversibly-held carbon monoxide are given in column 4 of table 1. Mass-spectrometric analyses of the gas phase in equilibrium with the sample have not revealed the presence of impurities at significant level. 2 4 6 Ni91 Cu9 8 k 10 adsorbed CO/pmol (m2 metal)-' FIG. 1.-Differential heats of adsorption of carbon monoxide as a function of the coverage of the silica-supported nickekopper catalyst (Ni 9 1 Cu 9). The calorimetric results are illustrated on fig.1, which reports the variation of the heats of adsorption as a function of the coverage of the metal surface by successive doses of carbon monoxide, in the case of two separate experiments with the Ni 91 Cu 9 sample. Heats recorded during the adsorption of the first doses are constant, within experimental uncertainty ( f 4 kJ mol-I). However, they progressively decrease when the coverage exceeds 3.5-4 pmol (m2 metal)-l, in the case of the Ni 9 1 Cu 9 sample (fig. 1). Constant heats of adsorption for low coverages have been also observed for276 ADSORPTION OF CO ON Ni AND Ni-Cu the other samples of nickekopper catalysts, at least when the copper content does not exceed 20-25 atom %. This observation is more quantitatively presented in columns 5 and 6 of table 1 where values of the initial (extrapolated) heat of adsorption and of the average heat of adsorption for a coverage of 0.2 are given.[In order to determine the quantity of adsorbed carbon monoxide which covers 20% of nickel atoms at the surface of each alloy, the following assumptions were made: (i) bulk and surface compositions are identical,6 (ii) the area covered by each adsorbed carbon monoxide molecule is defined by the bond-number deduced from either i.r. spectra (table 1 , column 8) or volumetric and magnetic data,2 (iii) carbon monoxide adsorbs irreversibly on copper atoms exposed at the alloy surface as it does on pure copper, i.e. 0.5 (pmol CO) (m2 metal)-']. Adsorption of carbon monoxide on copper being ten times smaller than on nickel (table 1 , column 4), the results presented in columns 5 and 6 of table 1 essentially characterize the adsorption of carbon monoxide on nickel atoms exposed at the surface of the alloy particles, at least when the copper concentration is small [< 20 atom % (Cu)].The difference which appears between initial and average heats of adsorption when the copper concentration exceeds 20% is probably explained by the adsorption of part of the adsorbate on exposed copper atoms : experiments with samples of silica-supported copper have indeed shown that the initial heat of adsorption of carbon monoxide on copper only amounts to 77 kJ mol-1 and that the differential heats steadily decrease with increasing coverage. DISCUSSION The observed stability of the differential heats of adsorption of carbon monoxide with increasing (low) coverage is a notable feature of this system.This result indicates that carbon monoxide chemisorption is not sensitive to surface heterogeneity which exists on supported metal particles and this confirms previous experimentalg and theoreticallo studies showing that, with this adsorption system, the role of surface orientation is only of minor importance [with, perhaps, the exception of the (1 11) plane]. Magnetic methods and i.r. spectroscopy have shown that upon adsorption at 296 K two distinct surface species, namely the linear and bridged forms of adsorbed carbon monoxide, are formed in the same proportion for all surface coverages3 The constancy of the adsorption heats (0 < 0.2) is in agreement with these previous results.The present calorimetric data also demonstrate that the adsorption of carbon monoxide, at least for OGO.2, does not modify the surface reactivity for the adsorption of further amounts of carbon monoxide. This result is in contrast with those obtained in the case of the adsorption of hydrogen on the same samples:4 preadsorbed hydrogen does create an induced heterogeneity and, as a result, the differential heats of adsorption of hydrogen regularly decrease with coverage. As previously di~cussed,~ the heat of adsorption of hydrogen always follows the changes in surface saturation magnetization and thus appears to be related, as is ferromagnetism for surface nickel atoms, to the density of electronic states near the Fermi level. Adsorption of carbon monoxide also decreases the saturation magnetization of the sample (fig.2), and it has been demonstrated2 that it is indeed this feature of carbon monoxide adsorption that explains the decrease in the nickel surface reactivity with respect to hydrogen after preadsorption of carbon monoxide. Therefore the constancy of the differential heats of adsorption for 0 < 0.2 shows that a relation between the adsorption energetics and the density of electronic states near the Fermi level is unlikely in the case of the adsorption of carbon monoxide.J. J. PRINSLOO AND P. C . GRAVELLE 277 adsorbed CO/cm3 (n.t.p.) (g metal)-’ FIG. 2.-Differential heats of adsorption, frequency of the stretching vibration of the linear adspecies and decrease of saturation magnetization3 as a function of the surface coverage of the Ni 98 Cu2 copper-nickel catalyst by adsorbed carbon monoxide.Chemisorption of carbon monoxide on nickel causes a nett electron transfer from the metal to the adspecies as shown by the observed increase in work function by ca. 1.5 eV at complete c~verage.~’ l2 Alloying nickel with copper, which produces the filling of holes in the d band of nickel by copper s electrons, as demonstrated by the resulting decrease in the nickel magnetic moment, should therefore increase the binding energy of carbon monoxide with the alloy surface. The shift in frequency of the C-0 stretching vibration in the adsorbed state towards lower values, observed in the i.r. spectra of carbon monoxide adsorbed on nickel alloyed with increasing amounts of copper (from e.g.2058 cm-1 for pure nickel to 2005 cm-l for Ni 28 Cu 72),3 is in agreement with this analysislO since it indicates that electron transfer from adsorbent to adsorbate becomes easier as the copper concentration increases. Therefore, the large decrease in the adsorption heats experimentally observed when carbon monoxide is adsorbed on samples of nickel alloyed with an increasing proportion of copper (table 1 , columns 5 and 6) is surprising and cannot be directly related to the frequency shifts in the i.r. spectra of carbon monoxide adsorbed on the same sample^.^ The most obvious feature of the i.r. spectra is not the frequency shifts but the evolution of the intensity of bands A and B, respectively corresponding to linear and bridged ad specie^.^ The bond numbers, listed in column 8 of table 1, quantitatively represent this evolution.Therefore, it is tempting to relate the variation in the adsorption heats to changes in the respective populations of linear and bridged species on different alloys. In fig. 3 the initial heats of adsorption of carbon monoxide are plotted as a function of the proportion of linear species at the surface of different nickekopper alloys. The linear correlation which is observed indicates that the heat of adsorption of carbon monoxide on any nickel-copper alloy may be satisfactorily explained by the respective proportions of linear and bridged species on its surface, the heat of formation of each adspecies being constant, within experimental uncertainty.From the linear correlation in fig. 3, values of 108 and 160 kJ mol-1 have been278 ADSORPTION OF C o ON Ni A N D Ni-Cu 1 n I N i54Cu46 Ni73Cu27 80 N i80 Cu20 m a 401 0 XgNru2 I 1 1 1 201 1;o 130 150 heat of adsorption/kJ mol-' FIG. 3.-Initial heats of adsorption of carbon monoxide on different nickel and nickekopper catalysts as a function of the proportion of linear species in the adsorbate, calculated from the i.r. ~pectra.~ computed for the heat of adsorption of carbon monoxide as, respectively, linear and bridged species. The difference between the two heats of formation (52 kJ mol-l) is larger than the value previously reported for the separation between the two states (21 kJ m ~ l - l ) . ~ When the surface coverage by carbon monoxide exceeds 0.2, the differential heats of adsorption decrease (fig.1 and 2). As discussed earlier, carbon monoxide adsorption on nickel is not very sensitive to surface structure: the decrease is not related to a pre-existing surface heterogeneity. Furthermore, it does not result from a modification in the respective proportions of linear and bridged species since the saturation magnetization of the sample decreases linearly for any increasing coverage (6' < 0.5) by adsorbed carbon monoxide (fig. 2). Similarly, throughout the adsorption experiment the ratio of intensities of the two i.r. adsorption bands A and B remains c o n ~ t a n t . ~ Therefore, the decrease in the adsorption heats for coverages > 0.2 is related to some induced heterogeneity. The changes in the adsorbate properties with increasing surface coverage, and particularly the positive shift in the frequency of the stretching vibration, have received several interpretations, invoking such phenomena as dipole-dipole interaction~l~ or collective vibrational modes.14 It seems, however, that the decrease in adsorption heats which has been observed for all samples (fig.1 and 2) is too large to be accounted for by direct or indirect dipolar-coupling effects. The changes in the metal-adsorbate bond strength as a function of coverage are probably due to a modification of the electronic structure of the metal atoms and consequently some delocalization ofthe adsorbate-adsorbent bond must be considered. The fact that the decrease in the adsorption heats appears, for all alloys with < 20% (Cu), at a constant coverage of exposed nickel atoms (0 = 0.2) may give a clue to the extent of delocalization. Induced effects develop when the number of bonds between carbon monoxide molecules and nickel exceeds one bond per five surface nickel atoms.Thus it appears that the electronic perturbation caused by adsorption extends on average to the four nearest neighbours of the nickel atom directly involved in the chemisorption process. A linear CO species would thus sit on an ensemble of five nickel atoms (and correspondingly a bridged CO species would require an ensemble of ten surface atoms). When the surface coverage by carbon monoxide exceeds 0.2, some adspecies are brought in close proximity so that the surface ensembles they need for adsorbing overlap and induced heterogeneity develops.This description is valid for all samples, at least when the copper concentration does not exceed 20-25%. Thus induced heterogeneity is characteristic of the properties of the chemisorptive bond andJ. J. PRINSLOO A N D P. C. GRAVELLE 279 it is not related, but may be indirectly, to the electronic properties of free surface nickel atoms since introduction of copper modifies the electron population and distribution at the nickel sites. As discussed earlier, the calorimetric results for samples containing 27% (Cu) and more integrate various contributions of the less-energetic adsorption of carbon monoxide on exposed copper atoms. It is therefore not possible to extend the preceding discussion to the case of copper-rich surfaces.As the surface coverage by adsorbed carbon monoxide increases, there is a shift of the stretching vibrations characteristic of both linear and bridged adspecies towards higher values. For instance, the shift attains 75 cm-1 in the case of band B, corresponding to bridged species, on the Ni 92 Cu 8 ample.^ In the case of the Ni 98 Cu 2 sample (fig. 2), the total shift for band A (linear species) is smaller. Although the i.r. spectroscopic data in fig. 2 are rather sketchy, they suffice to show that there exists a parallelism between the evolution with coverage of the differential heats and of the frequency of the stretching vibration. This in turn suggests that the Chatt-Dewar modeP5 for the chemisorption of carbon monoxide does apply. If, in agreement with thismodel, the adsorptionenergy is related to the back-donation of electrons from the metal to the 27c* orbital, then there should be a relation between the experimental heats of adsorption on the different copper-nickel alloys and the filling of the dstates of nickel by copper electrons. Since no values of the work-function for the homogeneous alloys have been reported to our knowledge, it is once more necessary to consider the previously published i.r.-spectroscopic data for the same ~amples.~ As discussed earlier, the calorimetric data collected in columns 5 and 6 of table 1 are in opposition to the observed negative shift of the i.r.bands maxima. However, these calorimetric data are expressed per mole of adsorbed carbon monoxide, and therefore from sample to sample they concern a variable number of surface nickel atoms, as shown by the bond numbers listed in column 8 of table 1.If a correlation is to be sought between the electron density at the metal site and the adsorption energy, then all calorimetric data should be referred to a single metal site. The initial heats of adsorption, recalculated per surface nickel atom involved in the chemisorptive bond, are given in column 7 of table 1 . As expected from the i.r.-spectroscopic data, the adsorption energy of carbon monoxide per nickel atom increases when copper is alloyed to nickel. Furthermore, fig. 4 shows that there exists, within experimental uncertainty, a correlation between calorimetric and i.r.- spectroscopic data. Note that the straight line in fig.4 indicates that a frequency close to 2000 cm-l should correspond to 108 kJ (atom Ni)-l, value previously calculated from the correlation presented in fig. 3 for the formation of the linear adspecies, and that the same frequency is also obtained by extrapolating the plot of v-CO frequencies for the A band against copper content towards copper-rich samples on which carbon monoxide adsorbs almost exclusively as a linear specie^.^ Fig. 4 indicates that, in agreement with the Chatt-Dewar model for the chemisorption of carbon monoxide on transition metals, there is a parallelism between the adsorption energy of carbon monoxide, expressed per nickel atom, and the intensity of the back-donation from the metal d states into the molecule 27c antibonding orbital, measured by the frequency of the C-0 stretching vibration.Therefore, the heat of formation of the Ni-CO bond appears to be related to the energetic position of the highest filled chemisorption level with respect to the highest occupied d state in the metal, i.e. with respect to the position of the Fermi level at the nickel-metal surface. However, the changes in adsorption energy resulting from the modifications of the electron density at the metal sites caused by alloying cannot simply be accommodated by the chemisorptive bond, since the correlation, presented in fig. 3, has indicated that either linear or bridged adspecies are formed on all nickekopper alloys with the280 ADSORPTION OF CO ON Ni AND Ni-Cu --. .? d E 2ol / Ni 2060 I 1 1 - 80 90 100 110 heat of adsorption/kJ (atom Ni)-' FIG.4.-Initial heats of adsorption of carbon monoxide, expressed per nickel atom involved in the chemisorptive bond, as a function of the frequency of the stretching vibration of the monodendate species at the surface of different nickel and nickel-copper catalysts. release of constant energy. Inspection of columns 5, 7 and 8 in table 1 reveals that it is only through a modification of the respective proportions of linear and bridged species (i.e. of the bond number) that chemisorption of carbon monoxide complies with the changes brought to the electronic structure of surface nickel atoms by the addition of copper. The formation of linear and bridged species, in definite proportion on any alloy, appears to be concerted and directly related to the electronic properties of the surface nickel atoms.The picture which emerges is that of a surface coordination complex including both linear and bridged carbonyl ligands in defined proportions for any Ni-Cu alloy and retaining its stoichiometry for all surface coverages. This description of the chemisorption of carbon monoxide is in agreement with (i) the linear decrease of saturation magnetization with increasing CO coverage and (ii) the existence of two adsorbed states at all surface coverages, demonstrated by i.r. spectroscopy in the case of the present samples and also by EELS (electron energy loss spectroscopy) on nickel single-crystal surfaces.ll CONCLUSIONS The comparison of the calorimetric data of the present study with data previously obtained with the same samples by magnetic methods and i.r.spectroscopy3 allows us to propose the following main conclusions, which complement the description of the adsorption of carbon monoxide on the surface of nickel or nickel-copper alloys at 296 K presented in the first article of this series.2 (i) The heats of formation of linear and bridged adspecies differ (108 and 160 kJ mol-', respectively) but they remain constant on all nickel-copper alloys. (ii) Linear and bridged adspecies are not separate states, independently adsorbed on distinct sites or patches at the nickel surface. The proportion of the two adspecies varies with the copper content of the alloy, so that the average energy of theJ. J. PRINSLOO AND P. C. GRAVELLE 28 1 metal-carbon-monoxide bond formation follows the same trend as the back-donation of electrons from the metal d states into the 2n antibonding orbital of the carbon monoxide molecule.The energy of adsorption of carbon monoxide, expressed per metal atom, thus appears to be related to the position of the Fermi level at the metal surface. (iii) The electronic perturbation caused by the chemisorptive bond extends on average to five surface nickel atoms. When the surface coverage by adsorbed carbon monoxide exceeds 0.2, i.e. when some ensembles of five nickel atoms start to overlap, induced heterogeneity develops and the heat of adsorption of further quantities of carbon monoxide decreases. (iv) Chemisorption of carbon monoxide is also associated with other electronic perturbations, such as the transformation of ferromagnetic nickel atoms (so.6 dS.*) into non-magnetic ones (so 8 O ) , demonstrated by magnetic measurement^.^ Carbon monoxide adsorption is not influenced by modifications of the electron density of states near the Fermi level as hydrogen adsorption Therefore, preadsorption of carbon monoxide (0 < 0.2) creates an induced heterogeneity for the subsequent adsorption of hydrogen, although the free surface still appears energetically homo- geneous to adsorbing carbon monoxide molecules. The authors thank J.A. Dalmon for the gift of the nickel and nickel-copper samples, P. Moral for the pretreatment of these samples, and G. A. Martin and M. Primet for many helpful discussions. I. Toyoshima and G. A. Somorjai, Cataf. Rev. Sci. Eng., 1979, 19, 105. J. J. Prinsloo and P. C. Gravelle, J. Chem. SOC., Faraday Trans. I , 1980, 76, 512. J. A. Dalmon, M. Primet, G. A. Martin and B. Imelik, Surf. Sci., 1975, 50, 95. J. J. Prinsloo and P. C. Gravelle, J. Chem. SOC., Faraday Trans. I , 1980, 76, 2221. G. A. Martin, B. Imelik and M. Prettre, J. Chim. Phys., Phys. Chim. Biol., 1969, 66, 1682. J. A. Dalmon, J. Catal., 1979, 60, 325. ’ P. C. Gravelle, Ado. Cataf., 1974, 22, 191. * G. A. Martin, M. Primet and J. A. Dalmon, J. Catal., 1978, 53, 321. T. N. Taylor and R. J. Estrup, J. Vac. Sci. Technof., 1973, 10, 26. lo G. Doyen and G. Ertl, Surf. Sci., 1974, 43, 197. l 1 J. C. Bertolini and B. Tardy, Surf. Sci., 1981, 102, 131. l 3 M. Moskovits and J. E. Hulse, Surf. Sci., 1978, 78, 397; M. Scheffler, Surf. Sci., 1979, 81, 562. l4 G. D. Mahan and A. A. Lucas, J. Chem. Phys., 1978,68, 1344. l5 J. Chatt, J. Chem. Soc., 1953, 1, 2939. H. H. Madden, J. Kuppers and G. Ertl, J. Chem. Phys., 1973, 57, 3401. (PAPER 1 /3 12) 10

ISSN:0300-9599    

DOI:10.1039/F19827800273

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. Soc., Faraduy Trans. I, 1982, 78, 283-287 Enthalpies of Mixing of Simple Electrolyte Solutions with Sodium Carboxymethylcellulose BY PHILIP W. HALES AND GEOFFREY PASS* Department of Chemistry and Applied Chemistry, University of Salford, Salford M5 4WT Received 26th February, I98 1 The enthalpies of mixing have been determined for the reaction between aqueous solutions of two samples of sodium carboxymethylcellulose with different degrees of substitution and aqueous solutions of lithium chloride, sodium chloride, and potassium chloride. The effect of temperature on the enthalpy of mixing has also been investigated. The results are compared with the predictions of the line-charge theory. Mixing solutions containing lithium and sodium ions gives an additional endothermic contribution to the reaction, while mixing solutions containing potassium and sodium ions gives an additional exothermic contribution to the reaction. The enthalpy change occurring when solutions containing a polyelectrolyte and a simple electrolyte containing the same cation are mixed does not obey a simple additivity rule.Although the enthalpies of dilution of the polyelectrolyte and the simple electrolyte are negative, corresponding to an exothermic process, the enthalpy of mixing of the two solutions is found to be p0sitive.l Good agreement was found between experimental values and values calculated from an expression derived from the line-charge theory.2 More recent measurements have shown a dependence of the enthalpy of mixing on the nature of the ~ a t i o n .~ The line-charge theory assumes that as the charge on a polyelectrolyte is increased a critical value is reached, above which counter-ions are condensed on to the polyelectrolyte and limit the increase in effective charge. The results so far reported for the enthalpies of mixing of polyelectrolytes refer to polystyrenesulphonates, in which a considerable proportion of the counter-ions is taken to be condensed on to the polyanion. Measurement of the enthalpy of mixing of a polyelectrolyte with low linear charge would not only extend the range of polyelectrolyte charge over which the expression might apply but comparison with a similar polyelectrolyte with a linear charge above the critical value may help to establish the validity of the assumption regarding c~ndensation.~-~ The enthalpies of mixing of two samples of sodium carboxymethylcellulose, with different degrees of substitutions above and below the critical value, have been measured.The influence of the cation has been investigated by using solutions containing like cations and solutions containing unlike cations. The influence of temperature was also investigated. EX P E R I M E N T A I, Two samples of sodium carboxymethylcellulose, (4M6F) and (7L2P) were supplied by the Hercules Co. The samples were dialysed for 48 h against distilled water before use. Lithium chloride, sodium chloride and potassium chloride were dried at 105 O C for 48 h before use. A stock solution of each chloride was prepared containing 16 x lop2 mol dm-3. Aliquots of these solutions were diluted as required.Since the enthalpies of mixing were found to depend on the 283 10-2284 ENTHALPIES OF MIXING OF SIMPLE ELECTROLYTES initial concentration of the p~lyelectrolyte,~ all the enthalpies of mixing in the present work were determined by mixing equal volumes of polyelectrolyte solutions of constant concentration (1 x mol dm-3). Enthalpies of dilution of the salt solutions were also determined. Calorimetric measurements were made using a flow calorimeter (LKB Produkter, Bromma, Sweden, model 2107) and the procedure previously described.' mol dm-3) and salt solutions with a range of concentrations (16 x 1OP2-1 x RESULTS AND DISCUSSION A theoretical model2 has been developed to explain the behaviour of polyelectrolytes in aqueous solution in terms of a linear charge parameter, <, defined for monovalent charged groups and counter-ions as e2 ' = 4m,DkTb where e is the charge on the proton, D is the bulk dielectric constant of water, b is the average distance between charged groups, k is Boltzmann's constant and T is the thermodynamic temperature.An expression for the enthalpy change when a polyelectrolyte is mixed with a salt solution containing the same counter-ion has been derivedl from the line-charge model : (1) where in addition to the terms defined above n = 1 when 5 < 1 and n = - 1 when < > 1 , mE, is the final polyelectrolyte concentration, ma is the initial polyelectrolyte concentration, mi is the final salt concentration, a = 1 when < < 1 and a = < when 5 > 1.According to the charge model, when < > 1 a sufficient proportion of counter-ions will condense on to the polyelectrolyte to give an effective linear charge -2.303RTr"( 1 +-- TdD) log,, m; + 2am; 2 D d T mT, AHmi, = FIG. 1.-Enthalpy of mixing of NaCMC with alkali metal chlorides at 25 OC: 0, LiCI+NaCMC 4M; x , LiClfNaCMC 7L; a, NaCl+NaCMC 4M; ., NaCl+NaCMC 7L; 0, KCl+NaCMC 4M; A, KCI + NaCMC 7L. Broken line shows calculated values.P. W. HALES AND G. PASS 285 parameter of unity. Condensation results in a smaller fraction of the counter-ions, c-l, having Debye-Huckel interactions with the polyion. Two samples of sodium carboxymethylcellulose (NaCMC) were selected with different degrees of substitution (d.s.). One sample, NaCMC 4M6F, had d.s. = 0.45. The second sample, NaCMC 7L2P, had d.s.= 0.83. Taking the lengths of an anhydroglucose unit in the poly- electrolyte as 0.5 15 nm, eqn (1) gives values of 5 = 0.64 and 5 = 1.15 for NaCMC 4M6F and NaCMC 7L2P, respectively. The enthalpy changes occurring when aqueous solutions of the two samples of NaCMC were mixed with solutions of simple electrolyte at 25 "C have been measured and the results are plotted in fig. 1. The experimental values are corrected for the enthalpy of dilution of the simple electrolyte. In order to compare the results for the two samples of NaCMC different ordinate scales are used; these are suitably selected so that the theoretical values calculated from eqn (1) for the two values of 4: fit the same straight line. When plotted in this way the enthalpies of mixing of the different NaCMC samples with the same simple electrolyte give overlapping plots.Since one of the samples of NaCMC has a value of 5 > I , when condensation of a proportion of counter-ions is assumed to occur and is allowed for in eqn (l), the good agreement with the other sample where 5 < 1 and no condensation occurs appears to confirm the predictions of theory with regard to condensation and the dependence of the enthalpy of mixing on the linear charge parameter. The results in fig. 1 suggest that even when simple electrolyte and polyelectrolyte containing the same cation are mixed interactions occur which are not covered by the theoretical assumptions. The effects become more pronounced when simple electrolyte and polyelectrolyte containing different cations are mixed, as shown by the results of mixing lithium chloride and potassium chloride with the two samples of NaCMC.The different effects produced by the three cations are shown in fig. 2 where the additional molar enthalpy change of added cation is plotted against the amount of added cation. If the mixing behaviour was fully interpreted by eqn (1) all the FIG. 2.-Excess enthalpy of mixing of NaCMC with alkali metal chlorides at 25 OC: 0, LiCl+NaCMC 4M; x , LiCl+NaCMC 7L; 0 , NaCl+NaCMC 4M; W, NaCl+NaCMC 7L; 0, KClfNaCMC 4M; A, KCl+NaCMC 7L.286 ENTHALPIES OF M I X I N G OF SIMPLE ELECTROLYTES experimental points should lie on the abscissa. Mixing of sodium chloride with NaCMC shows an exothermic shift from the theoretical value which has only a small dependence on the amount of added sodium chloride.The effect is slightly increased when the linear charge parameter is increased. In the case of lithium chloride mixed with NaCMC, where an endothermic effect is observed, and potassium chloride mixed with NaCMC, where an exothermic effect is observed, there is a greater dependence of the additional enthalpy change on the concentration of the simple salt, and the influence of the linear charge parameter also increases at the lower concentration of simple salt. The enthalpies of mixing simple electrolyte with NaCMC 4M6F were also determined at 40 O C and the results are plotted in fig. 3. The enthalpy of mixing of sodium chloride with NaCMC gives greatly improved agreement with the theoretical values compared with fig.I . The results obtained from mixing potassium chloride with NaCMC a t the higher temperature are also shifted towards the theoretical line but the results obtained with lithium chloride and NaCMC at the higher temperature show greater divergence from the theoretical values. log,, [(mi i- 2CX/?Z~)/t??b ] FIG. 3.-Enthalpy of mixing of NaCMC 4M with alkali metal chlorides at 40 OC: 0, LiCl; x , NaC1; 0, KCl. Broken line shows calculated values. The results for the mixing of sodium chloride with the samples of NaCMC are similar to the results recently reported for the mixing of sodium chloride with sodium poly(styrene sulphonate), which also show an exothermic shift from the calculated value^.^ Investigation of the volume changes occurring in the interaction between counter-ions and polyions has led to the conclusion that only counter-ions which are condensed onto the polyanion undergo a change in hydration.9+ The enthalpy changes observed when solutions of simple electrolytes are mixed have been interpretedP.W. HALES AND G. P A S S 287 in terms of a contribution to the overall enthalpy change from changes in the water structure associated with the different ions.ll Thus for the mixing of sodium chloride with NaCMC 4M6F, where 5 = 0.64 and there is no counter-ion condensation, a change in the overall water structure when the cations move from bulk solution into the ion atmosphere of the polyanion is a possible cause of the additional enthalpy effect. In this respect it is significant that additional enthalpy effects have the opposite sign for dilution of the ion atmosphere of the polyion.12 The greatly improved agreement between experimental and calculated values for the mixing of sodium chloride with NaCMC 4M6F at 40 "C is consistent with a decreased contribution from water-structure effects at the higher temperature.When polyelectrolyte and simple salt containing unlike cations are mixed a contribution from changes in water structure is again to be expected. There is also the further possibility of a mixing or exchange reaction between the sodium ions in the ion atmosphere of the polyanion and lithium or potassium ions in the bulk solution. An exchange reaction of this type might be responsible for the cmcentration dependence of the additional enthalpy effects shown in fig.2. The molar enthalpy contribution of added cation showing a marked decrease as equilibrium is established between mixed cations in the ion atmosphere of the polyanion and mixed cations in the bulk solution. The results in fig. 3 are also consistent with such a reaction scheme. Thus the extent of the endothermic reaction involving lithium chloride is increased and the extent of the exothermic reaction involving potassium chloride is decreased as the reaction temperature is increased. As the concentration of added cation is increased the molar enthalpy change decreases and approaches the values obtained for mixing of simple salts with unlike cations.ll G. E. Boyd, D. P. Wilson and G. S. Manning, J . Phys. Chem., 1976, 80, 808. J. Skerjanc, A. Regent and L. B. Kocijan, J . Phys. Chem., 1980, 84, 2584. G. S. Manning, J. Phys. Chem., 1978, 82, 2349. C. Tondre, K. M. Kale and R. Zana, Eur. Polym. J . , 1978, 14, 139. P. W. Hales and G. Pass, J . Chem. Soc., Faraday Trans. I , 1980, 76, 2080. K. J. Palmer and M. B. Hartzog, J . Am. Chem. Soc., 1945, 67, 1865. U. P. Strauss and Y. P. Lueng, J . Am. Chem. SOC., 1965, 87, 1476. * G. S. Manning, J . Chem. Phys., 1969, 51, 934. -I D. Stigter, J . Phys. Chem., 1978, 82, 1603. l o R. Zana, C. Tondre, M. Rinaudo and M. Milas, J. Chim. Phys., Phys. Chim. Biol., 1971, 68, 1258. l 1 Y. C. Wu, M. B. Smith and T. F. Young, J. Phys. Chem., 1965, 69, 1868. l 2 P. W. Hales and G. Pass, in Solution Properties of Polysaccharides, ed. D. A. Brant (ACS Symp. Ser. No. 150, Washington, 1981), chap. 24. (PAPER 1 /333)

ISSN:0300-9599    

DOI:10.1039/F19827800283

出版商:RSC    

年代:1982

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1982, 78, 289-293 Proton Chemical Shift of the Aqua-aluminium Ion Al( H 20); + BY J. W. AKITT? Physicochimie des Solutions, ENSCP, Universite Pierre et Marie Curie, 1 1 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France Received 4th March, 1981 The variation of the proton chemical shift of the aqua-aluminium complex Al(H,O):+ has been measured for solutions of AI(CIO,), in a series of acetone+ water mixtures of different compositions from - 80 to + 32 OC. The variation of chemical shift with temperature depends strongly upon the acetone/water ratio and appears to be small in pure water. Evidence is obtained for ion pairing in the second sphere in the acetone-rich solutions and this is believed to account for the temperature effects observed.There is general agreement that the study of solvent proton chemical shifts, particularly for aqueous solutions, is likely to give information about the solvation of ions. It is now well-established that anions and cations affect the n.m.r. parameters quite different1y;l for example, low-temperature spectra of concentrated aqueous MII1 and some MI1 solutions show two resonances at low temperatures, one due to the water coordinated by the cation and one due to all the remaining water, including that interacting with the anion. Such spectra are used to obtain solvation numbers which are in this case the same as the coordination numbers., At temperatures above 0 OC only one water resonance is observed and the presence of the electrolyte reduces the temperature dependence of its chemical shift, which effect may also be used to estimate cationic hydration number^.^^ The calculation used assumes that the chemical shift of the water complexed to the cation is independent of temperature, an assumption which so far has been only partially tested in pure water though it is not correct for Mg(H,O)E+ in a~etone.~' The chemical shift of the water in those cationic complexes which can be measured is well-correlated with the calculated shift to be expected from the electric field of the However, the shift for Al(H,O);+ in MeCN differs from that obtained in water so that it appears that some medium effect is likely.s We report here measurements of the behaviour of the complex A1(H20),3+ in aqueous acetone over a range of compositions in an endeavour to clarify its behaviour.EXPERIMENTAL Proton n.m.r. spectra were obtained at 100 MHz on a Varian XL 100 12 WG in the C.W. mode. Probe temperatures were measured using a thermocouple placed in a sample tube for each temperature used. Samples were made up by weight using distilled water, hexadeuteroacetone from Spectrometrie Spin et Techniques and Al(C10,), .8H,O from Fluka (purum cryst.) as received. Initially DSS was used as internal reference but this formed a complex with the AIL" in those solutions which contained much acetone and had to be replaced by TMS. The shifts t On sabbatical leave from the School of Chemistry, University of Leeds, Leeds LS2 9JT, where all correspondence should be addressed. 289290 were corrected for the small difference between the two references and then to the ethane gas reference normally used in this type of work3* * using the relationshiplo.l 1 PROTON CHEMICAL SHIFT OF A1(H20)iS 6 = 6,,, - 0.88. Concentrated HC10, was added to the highly aqueous solutions to reduce the rate of proton exchange12 so as to increase the range over which the resonance of the bound water could be seen without perturbation of its position by exchange. RESULTS In those solutions which contained predominantly acetone, the bound-water resonance moved downfield with decreasing temperature at a maximum rate of 0.0056 ppm O C - l . Below ca. - 10 O C the resonance split into a poorly resolved doublet whose two components then moved in parallel but changed in relative intensity as the temperature decreased, the high-field component being the most intense at high temperatures and the low-field one becoming most intense by - 60 O C , fig.1. A sample containing an excess of perchlorate (as NaClO,) behaved similarly except that the high-field component now dominated the doublet at all temperatures. The chemical shift of the high-field component is plotted in fig. 2 where it can be compared with the results for the singlets obtained in the more moist solutions. The proportion of free water in the acetone was measured from the spectra and it was found that this did not vary with temperature and agreed with the assumption that all the A1 was present as A1(H20)i+. The composition of the solutions is summarised in table 1. Proton exchange between acetone and water takes place slowly in the acetone-rich solutions.n I I 1 FIG. I.-lH n.m.r. spectra at 100 MHz of the bound water in aqueous acetone solutions of AI(CIO,), at two temperatures, - 58 OC (upper) and - 38 OC (lower). The shift markers are at 10 ppm from TMS for each spectrum and the peak separation is 0.08 ppm. The left-hand spectra are for Al(ClO,), in a mixture with X = 0.95, the central ones for AI(ClO,), in a mixture with X = 0.86 and the right-hand ones for Al(CIO,), plus NaClO, with X = 0.95. Xis the mole fraction of acetone, based on the quantity of Eon-bound water in solution.J. W. AKITT 8.0 29 1 - + I 1 I t TABLE 1 .-COMPOSITION OF THE SOLUTIONS MEASURED mole fraction acetone, X , [H,O] free [All relative to free water /[A13+] /mol kg-I notes 0.95 0.95 0.86 0.48 0.17 0 0 0.15 - 4 4 0.18 NaClO, addeda 8 0.31 - 24 0.42 acid added 35 0.90 acid added 52 1.01 acid added 11.5 2.36 acid added a The ratio [C10;]/[A13+] is 3.0 in all cases except where NaC10, was added, where it had the value 7.5.292 PROTON CHEMICAL SHIFT OF Al(H,O);+ As the water content of the samples increased, the temperature dependence of the chemical shift decreased and became too small to measure below a mole fraction, X , of acetone equal to 0.2.The certainty with which the slope of the plots can be measured decreases as the acetone content is reduced, since the range over which chemical shifts can be measured is decreased. Exchange sets in at lower temperatures on the one hand and the solutions freeze at progressively higher temperatures.The trends are nevertheless unmistakeable in fig. 2. The chemical shift at a given temperature moves steadily upfield as Xis decreased until X = 0.2 when the rate of change increases. The chemical shift in pure water as solvent is close to that found previo~sly.~ DISCUSSION It is obvious from these results that the behaviour of Al(H,O);+ in pure water cannot be inferred from its behaviour in aqueous acetone.13 It appears reasonable to accept for this aqua-cation at least that the proton shift is temperature-independent in pure water and has a value of ca. 8.8 ppm downfield of gaseous ethane. It will, however, prove difficult to obtain equivalent data for other cations where either proton exchange is too fast or the hydrolysis reactions are such that acid addition does not seem to slow the exchange, although the existing data are now more happily based in the light of the present results.BEHAVIOUR IN PREDOMINANTLY ACETONE SOLUTION This differs so much from that in pure water that the interactions and the species present must be of quite different types. The chemical shift is a linear function of temperature between 0 and - 80 OC provided the mole fraction of acetone is high and of the order of 0.95. Two resonances with the same sensitivity to temperature are observed for bound water but whose relative areas change with temperature, while the low-field component is almost entirely suppressed by the addition of excess C10, as NaClO,, an indication that we are observing an anion-cation interaction. However, the proportion of bound water is in accordance with the existence at all times of only Al(H,O);+, a conclusion which is reinforced by the small changes which occur in the spectra for an increase in water content from X = 0.95 to X = 0.86.Thus we must be observing the formation of second-sphere ion pairs such as have recently been reported in DMSO + benzene.', The numbers of water molecules and ClO; ions are similar in these solutions and we can expect the second sphere to contain some water, some acetone and some anions, the exact proportions depending upon any specific preferences for the molecule concerned. An ion pair formed in such a mixture will have a strong dipolar electric reaction field which will cause the proton chemical shift of the first-sphere water to move downfield: that nearest to the anion because its field will have the predominant effect, that furthest away from the anion due to the reaction field.We note that the low-field component is favoured ( a ) by low temperatures and so high dielectric constant, &,15 and (b) by addition of small quantities of water, but is suppressed by the addition of NaClO,. This points to its being the I : I complex. The high-field line must then arise from a complex involving more anions, disposed in such a way that the resulting multipole reaction field is a little weaker than that of the dipolar field. The chemical shifts of both components move in parallel and sensibly linearly with temperature. The dielectric constant of acetone also changes almost linearly with temperature, from 21.4 at 20 OC to 31.0 at - 80 OC15 and, if we assume that aqueous acetone with X = 0.95 behaves similarly, then the shifts correlate strongly with E , as is to be expected for a reaction-field effect.J.W. A K I T T 293 On the other hand, when the full range of compositions is considered we see that the chemical shifts move upfield with increasing E . In this case we must be observing a decrease in the extent of ion pairing as more water is added. I thank Madame M. J. Pouet of Madame Simonnin’s laboratory for obtaining the spectra and wish to record my warm appreciation of the interest and hospitality shown by Prof. R. Schaal. See, for example, Faraday Discuss. Chem. SOC., 1978, 64. A. Fratiello, R. E. Lee, V. M. Nishida and R. E. Schuster, Znorg. Chem., 1971, 10, 2552. E. R. Malinowski, P. S. Knapp and B. Feuer, J . Chem. Phys., 1966, 45, 4274. J. W. Akitt, Faraday Discuss. Chem. SOC., 1978, 64, 102. F. Toma, M. Villeman and J. M. Thiery, J . Phys. Chem., 1973, 77, 1294. G. W. Stockton and G. S . Martin, J . Am. Chem. Soc., 1972, 94, 6291. J. W. Akitt, J . Chem. SOC., Dalton Trans., 1973, 42. Y. Reuben and J. Reuben, J . Phys. Chem., 1976,80, 2394. J. W. Emsley, J. Feeney and L. M. Sutcliffe, High Resolution NMR Spectroscopy (Pergamon Press, London, 1965), vol. 2, pp. 669 and 673. j M. C. R. Symons, Faraday Discuss. Chem. SOC., 1978, 64, 127. lo W. G. Schneider, M. J. Bernstein and J. A. Pople, J . Chem. Phys., 1958, 28, 601. l 2 J. W. Akitt, J. Chem. SOC., Dalton Trans., 1973, 1177. l3 J. W. Akitt, Faraday Discuss. Chem. SOC., 1978, 64, 130. l4 W. Libius, W. Graybkowska and R. Pastewski, J . Chem. SOC., Faraday Trans. I , 1981, 77, 147. l 5 International Critical Tables, ed. E. W. Washburn (McGraw-Hill, New York, 1929), vol. 6. (PAPER 1 /369)

ISSN:0300-9599    

DOI:10.1039/F19827800289

出版商:RSC    

年代:1982

数据来源: RSC