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J. Chem. SOC., Faraday Trans. I , 1984,80, 2581-2597 The Structure of Ethylene Polymerisation Catalysts? Part 2.-Electron Spin Resonance Studies of y-Phase Chromium Oxide BY ALAN ELLISON School of Science, Humberside College of Higher Education, Cottingham Road, Kingston-upon-Hull HU6 7RT Received 1 1 th January, 1984 Electron spin resonance spectra have shown &type and P-type Cr3+ resonances, indicating the prevalence of clustered chromium. At calcination temperatures which produce only partial decomposition of supported Crs+, a second P-type resonance, &, has shown y-resonance characteristics with evidence for dipole-dipole broadening and exchange narrowing associated with clustered chromium. The occurrence of y-resonance is related to the extent of chromium oxide aggregation.Both alumina and silica y-resonances are complex, exchange-narrowed resonances experiencing different degrees of near-neighbour magnetic broadening. It is proposed that y-resonance arises from the surface of mixed-valency chromium oxide clusters, rejecting the usual model of magnetically isolated, crystal-field-stabilised Cr5+ species. Almost without exception the y-resonances observed for oxidised or partially reduced chromium-alumina and cited as the active polymerisation site in oxidised Philips' catalysts is attributed to Cr5+ species1 in distorted octahedral or tetrahedral crystal-field symmetry, stabilised on or in the support surface. Such analyses arise from the study of a chromium oxide-support system after quite severe heat-treatment, 500-800 "C, in which event the resonance shape does approximate to that expected for a &electron species experiencing axial distortion of C,, or & crystal-field potentials.These models inherently demand magnetic dilution, and customarily the Cr5+ species cited are assumed to be 'magnetically isolated' on the support surface. The author has previously s t ~ d i e d ~ - ~ the development of y-resonance during catalyst preparation for chromium-alumina samples and recognised that the curious magnetic properties of y-phase chromium and the properties of partially oxidised bulk, supported chromium oxide are more consistently interpreted in terms of a mixed-valency phase. Similar studies of chromium oxides on silicas have not so far been reported. In Part 1 of this series1 the prevalence of chromium oxide clusters even at low Cr loadings ( -= 1 % Cr) has beendemonstrated by FAB-SIMS (fast-atom bombardment - secondary-ion mass spectrometry) and the evidence related to e.s.r.data, speculations on the cluster-types being presented. In this paper the parameters of y- and p-resonances are studied in detail as functions of chromium loading and calcination-measurement temperatures for both silica- and alumina-supported chromium(v1) oxide. t Invited paper presented at the 184th A.C.S. National Meeting, Division of Colloid and Surface Chemistry, September 1982, Kansas City, U.S.A.2582 E.S.R. STUDIES OF CHROMIUM OXIDE EXPERIMENTAL Details of the alumina and silica supports, sample preparation and calcination, t.g./d.t.a.and FAB-SIMS studies are given in Part 1.' E.s.r. were obtained as first-derivatives at X-band (ca. 9.4 GHz). Room-temperature spectra were obtained using a Varian E-9 spectrometer at a modulation amplitude of 1.0 G and with diphenylpicryl hydrazyl (DPPH) as reference. Variable-temperature spectra were obtained at temperatures from 4.2 to 298 K using variable modulation amplitude and DPPH as reference with a Varian E 1 15 spectrometer. Samples were designated according to their chromium content (wt %), the calcination tem- perature ("C) and the nature of the support; thus sample 2-300-Si contains 2 wt % Cr on silica and was calcined at 300 "C in air. Fig. 1. E.s.r. spectra of Cr-Al,O, samples after calcination in air. Room-temperature spectra, modulation amplitude 1.0 G, field sweep 5 kG, X-band.(a) 1-25-A1, (b) l-lOO-Al, (c) 1-150-A1, (d) 1-200-A1, (e) 1-300-A1, cf) 1-400-A1, (g) 1-500-A1, (h) 1-600-A1, (i) 6-25-A1, (5) 6-100-A1, (k) 6-150-A1, ( I ) 6-200-A1, (m) 6-300-A1, (n) 6-400-A1, (0) 6-500-A1 and (p) 6-600-A1.A. ELLISON 2583 RESULTS Fig. 1 shows e.s.r. spectra measured at room temperature for 1 and 6% Cr on alumina after calcination at different temperatures in air. At 1% Cr and 25 "C, y-resonance is seen at very high signal gain, i.e. at low intensity. y-resonance appears to increase in intensity to 500 "C and, at 600 "C, occurs superimposed on a broad, low-field signal [peak-to-peak width 850 G, g (crossover) 2.851 which is not easily identified as a 6- or b-resonance of O'Reill~.~ At 6% Cr y-resonance is already more intense than at 1 % Cr and dominates the spectra up to 200 "C.Between 150 and 200 "C a broader- than-y-resonance develops, defined here as B2. From 200 to 600 "C the B2-resonance increases in intensity, dominating the still visible y-resonance. For both 25 "C Fig. 2. E.s.r. spectra of Cr-SiO, samples after calcination in air. Room-temperature spectra, modulation amplitude 1.0 G, field sweep 5 kG, X-band. (a) 1-2543, (b) 1-100-Si, (c) 1-150-Si, ( d ) 1-200-Si, (e) 1-300-Si, cf) 1-4OO-Si, (g) 1-500-Si, (h) 18-2543, (i) 18-100-Si, ( ~ 9 18-150-Si, (k) 18-200-Si, ( I ) 18-300-Si, (m) 18-400-Si and (n) 18-500-Si.2584 E.S.R. STUDIES OF CHROMIUM OXIDE Table 1. Pz-resonance parameters, Cr-Al,O, and Cr-SiO, samples, room-temperature spectra, modulation amplitude 1 .O G, X-band WIGa y/P,-amplitude P,-amplitude sample g 6-200-A1 6-300-A1 6-400-A1 6-500-A1 6-600-A1 12-200-A1 12-300-A1 12-400-A1 12-500-A1 12-600-A1 1 - 150-Si 1 -200-Si 2-200-Si 2-300-Si 2-400-Si 7- 1 00-Si 7- 1 50-Si 7-200-Si 7-300-Si 11-100-Si 1 1 - 150-Si 1 1 -200-Si 1 1 -300-Si 18- 1 50-Si 18-200-Si 18-3004 1.97 1.96 1.96 1.97 1.97 2.0 2.0 1.97 1.97 1.97 1.97 1.97 2.0 2.0 1.98 1.97 1.97 1.97 1.97 1.97 1.97 1.96 1.97 1.97 1.97 1.97 488 658 667 825 738 475 71 3 788 769 738 500 525 725 650 638 53 1 700 550 290 525 550 413 300 750 406 419 6.47 0.93 0.46 0.41 0.32 14.33 0.52 0.27 0.28 0.16 - 11.2 6.2 11.0 12.3 12.2 6.4 1.5 36.4 2.8 1.9 0.2 62.0 0.4 0.03 0.60 1.48 2.37 1.67 1.89 0.6 2.41 4.72 2.70 3.95 - 0.22 0.34 0.56 0.39 0.68 1.40 4.88 0.25 2.17 2.04 0.48 58.8 45.2 68.0 a W is the peak-to-peak width.samples, a broad resonance at low field v l ) is seen, g (crossover) in the range of 2.10-2.30. The peak-to-peak width of PI, 1050-1350 G, is remarkably constant independent of Cr loading and measurement temperature between 4.2 and 298 K. It could be inferred that, as the &-amplitude remains low and constant at 1 % Cr, the &-resonance may arise from an impurity in the alumina. However, this resonance was not observed for the pure alumina alone and for 12-150-A1 8,-resonance does significantly increase in amplitude. In addition there is slight evidence for dipole- dipole broadening as the measurement temperature is lowered. Fig. 2 shows similar room-temperature e.s.r. spectra for 1 and 18% Cr on silica.The '8-type' resonance for 1-2543 was observed for all of the samples except 18-2543, g (crossover) 1.982-1.99, peak-to-peak width generally increasing with Cr loading, 1-1 1 % Cr, from 143-202 G. As the calcination temperature is raised for 1 % Cr, y-resonance develops at 100 "C and continues to grow in an apparently smooth manner to 600 "C. Between 150 and 300 "C B2-resonance can be seen at low intensity. The 18-25% sample shows an intense and extremely narrow y-resonance, fig. 2, whose width increases with calcination temperature [see fig. 4(b) later]. Between 150 and 200 "C P2-resonance emerges abruptly and dominates the spectra until, at 400 "C, a wider signal appears, /33-resonance. &-resonance, g 1.970-1.974, is observed fromA. ELLISON 258 5 16 12 x c ." c, $ 8 E: ." 4 x c .+ Y E: ._ 2 0 2 00 400 600 0 200 400 600 Fig.3. Relative intensity of the y-resonance, arbitrary units, plotted against the calcination temperature, T/"C. Room-temperature spectra, modulation amplitude 1 .O G. (a) Cr-A1,0, samples: 0, 1 % Cr; A, 6% Cr and 0, 12% Cr. (b) Cr-SiO, samples: 0, 1 % Cr; A, 2% Cr; 0, 7% Cr; 'I, 11% Cr and +, 18% Cr. T/"C T/"C 2 to 18% Cr at high calcination temperatures, when the samples have, or are developing, a green colour. The peak-to-peak width of p3 varies widely, 438-1360 G, and in an apparently unsystematic manner, but as the calcination temperature of the sample increases the width of p3 narrows, perhaps due to exchange narrowing in the increasing Cr3+ phase. /?,-Resonance develops abruptly at a temperature which depends on the support, usually 200-300 "C for chromium-alumina and 150-200 "C for chromium-silica.For chromium-alumina, P,-resonance dominates the spectra to 600 "C for chromium loadings > 1% Cr; /?,-resonance for chomium-silica, observed from 1-18% Cr, decomposes equally abruptly at a temperature between 300 and 400 "C to give the /?,-resonance. The resonance parameters for /?,, given in table 1, are most interesting. The range of peak-to-peak width ( W ) is narrow, 290-825 G independent of sample nature and preparation. With increasing calcination temperature this width gradually increases for chromium-alumina, but for chromium-silica, as /?, (and therefore the amount of /?,-phase Cr) increases in intensity, the width first increases and then markedly decreases.Eliminating the more extreme widths from the range of /?,-widths on silica, an extremely narrow range (400-550 G) is revealed for samples calcined between 100 and 200 "C. Finally, as the Cr loading increases, overall /?,-intensity increases, and after the P,-intensity maxima the /?,-width is observed to decrease. The variation in peak width of P2 with measurement temperature shows two patterns: an increase in width from 298 to 77 K and subsequent decrease from 77 to 4.2 K; the inverse trend. &- and /?,-resonances have an intensity increasing with temperature of measurement at a rate less than that of y-resonance. In marked con-2586 E.S.R. STUDIES OF CHROMIUM OXIDE 50 0 3 . 30 200 LOO 600 0 TI" C ( b ) " 3 \ 0 2 00 LOO 600 TIo C Fig. 4.?-Resonance peak-to-peak width, WIG, plotted against the calcination temperature, T/OC. Room-temperature spectra, modulation amplitude 1 .O G. (a) Cr-A1,0, samples : 0, 1 % Cr; a, 6% Cr and 0 , 1 2 % Cr. (b) Cr-SiO, samples: 0,1% Cr; A, 2% Cr; V, 7% Cr and 0, 18% Cr. trast, the &intensity increases faster than that of y-resonance over the temperature range 298-77 K. The development of y-resonance as a function of calcination temperature is shown in fig. 3(a) for chromium-alumina samples. The amplitude values should be treated with some caution because of small changes in resonance width and shape, sample density and e.s.r.-cavity conditions. Nevertheless, after drying at 25 "C and calcination up to 250 "C, more intense y-resonance is observed at high chromium loadings.The 6 and 12% Cr samples show distinct y-amplitude maxima at 150 "C whereas for 1 % Cr, the y-amplitude increases smoothly to 400 "C. After 400°C the amounts of y-phase Cr relate to published data, Most workers concentrate almost wholly upon samples calcined at 500 "C or higher, where it is seen in fig. 3(a) that the greatest y-resonance occurs for the lowest chromium loading. Similarly, fig. 3 (b) shows the y-amplitude for chromium-silica samples as a function of calcination temperature. There is appreciable error in these amplitude data, the values of which are considerably lower in magnitude than those observed for com- parable chromium-alumina. However, at 25 "C the highest loading of chromium shows an undoubtedly high-intensity y-resonance which is absent at 1 and 2% Cr.The variation of peak-to-peak width for the chromium-alumina y-resonances is shown in fig. 4(a) as a function of calcination temperature. Irrespective of chromium loading, the y-resonance width is small at the lowest calcination temperature, the smallest value (18.75 G) occurring for the greatest chromium loading, 12% Cr. ForA. ELLISON h , 2587 1 % Cr, between 150 and 400 "C the width remains remarkably constant, and indeed between 150 and 200 "C the y-resonances have almost the same value from 1-12% Cr. At higher temperatures, 300 or 400 "C depending on chromium loading, the y-resonance width increases markedly. Similarly, fig. 4 (b) shows the y-resonance width variation with calcination temper- ature for chromium-silica samples.Extremely low-width resonances are observed for samples dried at 25 "C: 6.9 G, 7-2543; 6.3 G, 11-2543; 12.5 G, 18-25% With these exceptions, all the y-resonances have a remarkably constant width, independent of calcination temperature and chromium loading. For y-alumina samples, the use of a low value of modulation amplitude (1.0 G) only produces narrowing and changes in the overall shape of the resonances. However, for y-silica, in addition to narrowing, components of the resonances are resolved. An idealised y-resonance, fig. 5 , shows all of the parameters which were recorded to describe the resonances completely. The points ho-h5 are quoted as g-values for convenience and the half-widths, AL and A,, are the widths of the low- and high-field derivative phases, respectively, measured at half-height.The data in table 2 demonstrate that the h parameters observed for y-silica samples can indeed be classified into the groups ho-h, even though all of the h-points are not always observed. The effect of the presence of resonance components on the overall resonance shape is interesting. In fig. 6(i) for 2-100-Si, components h, and h, are observed with the high-field phase h, lower in amplitude than h,. For 2-400-Si only component h, is resolved, but now h, > h5. For 1 % Cr [fig. 6(ii)] again only resonance h, is observed from 100 to 600°C calcination temperature, but as the temperature is increased through this range the h, amplitude increases relative to h,, h, becoming sharply defined at 500 "C. This behaviour of the amplitudes of points h, and h, is general for chromium loadings between 1 and 7% Cr.Contrasting effects of measurement temperature on y-lineshape are also evident. For 2-300-Si [fig. 6(iii)] the amplitude of h, increases as the temperature is lowered from 298 to 4.2 K, but for 1 1 - 150-Si the opposite effect is seen, resonance h, merging with h, as the temperature is lowered. Spectra at 4.2 K, fig. 6(iv), show that the resolution of h, apparently improves as the calcination temperature of the sample increases, and for 18-300-Si almost complete resolution of h, and h, is achieved.2588 E.S.R. STUDIES OF CHROMIUM OXIDE Table 2. h-Parameters for y-resonance, Cr-SiO, samples 1 - 1 00-Si 1 - 150-Si 1 -200-Si 1 -300-Si 1 -400-Si 1 -500-Si 1 -600-Si 2- 1 00-Si 2-200-Si 2-300-Si 2-400-Si 2-500-Si 7-2543 7- 1 00-Si 7- 150-Si - 7-200-Si 7-300-Si 7-400-Si 7-500-Si 11-100-Si 11-150-Si 1 1 -200-Si 1 1 -300-Si 1 1 -500-Si 1 8- 1 00-Si 1 8- 1 50-Si 18-200-Si 18-400-Si 18-500-Si 1.992 1 1.9892 1.9892 1.9897 1.9916 1.9915 1.9890 1.9885 - - 1.9918 1.9885 1.9878 1.9882 1.9889 - - - - 1.9882 1.9885 1.9894 1.9918 1.9878 1.9889 - - - 1.9893 - - - - 1.9793 1.9842 - - - - - 1.9824 - - - - - - 1.9845 - - - - 1.9809 1.9762 1.9762 1.9773 - - 1.9785 1.9785 1.9779 1.978 1 1.9785 1.9785 1.9774 1.9766 1.9755 1.9779 1.9780 1.9773 1.9772 1.9769 1.9764 1.9777 1.9759 1.9786 1.9762 1.9755 1.9753 1.9769 1.9755 1.9727 1.9741 - - - - - - - - - - - 1.9730 1.9730 1.9739 1.9726 1.9734 1.9744 1.9741 1.9734 1.9744 - - - 1.9734 1.973 1 1.973 1 1.9722 1.9748 1.9734 1.9649 1.9672 1.9648 1.9687 1.9676 1.9670 1.9672 1.9691 1.9703 1.9692 1.9695 1.9683 1.9680 1.9680 1.9691 1.9693 1.9694 1.9701 1.9694 1.9686 1.9694 1.9658 1.9703 1.9680 1.9665 1.9650 1.9666 1.9666 1.9673 - - - - .9584 .9585 .9576 .9578 .9586 .9572 .9574 ,9570 1.9577 1.9590 1.9584 1.9570 1.9577 1.9566 1.9552 1.9566 1.9542 1.9576 1.9552 1.9541 1.9538 1.9524 1.9545 1.9538 1.9535 1.9504 1.9512 1.9577 - 1.9730 1.9730 1.9726 1.9730 1.9734 1.9730 1.9726 1.970 1 1.9701 1.9716 1.9730 1.9726 1.9716 1.9723 1.9719 1.9708 1.9716 1.9696 1.9736 1.9705 1.9699 1.9693 1.9702 1.9701 1.9701 1.9700 1.9704 1.9687 1.9719 The temperature dependence of the peak-to-peak width for the y-resonances is relatively small, usually < 2 G between 298 and 4.2 K.The distinguishable trends are similar to those noted for p2-resonance, but may be confused here by changes induced by the variation of modulation amplitude. The alumina y-resonance appears to be ‘broader’ than the y-resonance observed for chromium on silica.In fact the appearance of excessive ‘breadth’ in the alumina resonance is due to the greater width of each phase of the derivative and to the excessive ‘narrowness’ of the silica resonance. For alumina samples the values of half-width, AL and AR, are in general about the same as the peak-to-peak width and sometimes even greater. In contrast, for silica the y-resonance half-width AL is, with few exceptions, less than half the value of the peak-to-peak width, and often (in 18 cases out of 47) less than one-third of the peak-to-peak width.Finally, it was found to be impossible to saturate the y-resonance of, for example, 1-500-Si at room temperature. At the onset of saturation the resonance amplitude should begin to decrease and the resonance width should increase dramatically with increasing microwave power. Here, power increase from 20 to 160 mW produces an increase in y-amplitude with a simultaneous decrease in peak width to a minimum value.A. ELLISON 2589 (Y c- m c-2590 E.S.R. STUDIES OF CHROMIUM OXIDE DISCUSSION y-p2 RELATIONSHIP: NATURE OF B2 After drying at only 25 "C those samples with the higher chromium loadings produce the most intense y-phase e.s.r. signals [fig. 3 (a) and (b)]. Significantly, 6-25-A1 and 12-25-A1 were not subjected to a water wash during preparation, preventing removal of the chromium oxide that is in excess of that satisfying the adsorption capacity of the alumina.It is this excess chromium oxide, existing as heavily clumped material, which produces the intense y-phase resonance observed. For the ' thinner' chromium oxide clusters on silica2 decomposition of the Crs+ only occurs between 25 and 100 "C to give intense y-resonance. At the highest loadings on silica, for thicker clumps y-resonance occurs after drying at 25 "C. The y-resonance amplitudes become similar in value after the redistribution and sublimation processes which occur on calcination of 7-18% Cr samples. ?-Resonance has been clearly shown to be a property of the chromium oxide These data confirm that y-phase chromium develops at the surface of chromium clusters through surface reductive decomposition of Crs+ or through surface oxidation of Cr3+ 2-4 Thus a close correlation exists between the y- and B,-e.s.r.signals. For 6 and 12% Cr-alumina, y-resonance attains a maximum intensity at the same temperature at which /?,-resonance develops. Between 200 and 300 "C, as B2-resonance becomes predominant, the y-resonance peak-to-peak width increases with chromium loading and continues to increase up to 600 "C calcination temperature, presumably due to increased dipole-dipole broadening. Similarly the extremely low-width y-resonances observed for 25 "C-dried chromium-silica increase in width when the samples are calcined at 100 "C, at which temperature intense /?,-resonance appears. Indeed B2- and y-resonances have the same g-values (tables 1 and 2).The peak-to-peak width of the B,-resonance is severely limited in range, 475-800 G; the resonance width varies with calcination temperature in a systematic way for both chromium-alumina and chromium-silica, showing a maximum width before devel- oping high intensity. Further, some chromium-silica at high calcination temperatures and chromium loadings show rather low-width /?,-resonances, 290-400 G. As the /?,-phase chromium is formed by the gradual decomposition of the bulk of Cr6+ clusters, dipole-dipole broadening increases. When the P,-phase structure is realised, magnetic exchange narrows the resonance. The effect of measurement temperature on P2- and y-resonance width is complex, with two types of behaviour: an increase in width from 298 to 77 K followed by a decrease from 77 to 4.2 K and vice versa.This behaviour depends upon the calcination temperature of the sample and therefore upon the initial peak width at 298 K, reflecting the dipole4ipole broadening and exchange narrowing processes. y-Resonance intensity deviates from the Curie or Curie-Weiss laws relevant to magnetically isolated or coupled species, respectively, the intensity increasing at a faster rate than expected from these laws as the temperature is decrea~ed.~. The data clearly show that /?,-intensity increases at a faster rate than y-resonance intensity, showing an even more marked deviation from para- or antiferro-magnetism. The /?-resonances usually reported5 for these catalysts originate from Cr3+ ions in heavily clumped conditions, subjected to varying degrees of antiferromagnetic exchange forces. Such resonances show a rapidly increasing width with decreasing temperature as the N6el temperature is approached, and a width which varies with respect to the amount of supported chromium oxide, phenomena characteristic of supported species showing antiferromagnetism./?,-Resonance does not exhibit these characteristics, and an alternative model must be sought.A. ELLISON 259 1 /?,-Resonance occurs in heavily decomposed Cre+ samples which are black or very dark brown in colour and which contain appreciable amounts of both Cr3+ and Crs+ species. From the data it would appear that Bz-resonance arises from Cr3+ and Cr6+ ions in the bulk of chromium oxide clusters, coupled through mixed-valence, double-exchange ferromagnetism.s It is then logical to suppose that the y-resonance is a function of regions of the surface of these mixed-valence clusters. NATURE OF 7-RESONANCE It has usually been reported5 that the y-resonance peak-to-peak width remains constant irrespective of chromium loading, a property which could characterise a species in magnetic isolation but which is not unique to this situation.A discrete magnetic phase arising from heavily exchange-coupled entities would similarly show this behaviour, especially if the resonance relaxation mechanism was dominated by spin-spin rat her than spin-la t tice processes. Fig. 4(a) clearly shows that for chromium-alumina, in the region of maximum y-resonance intensity at calcination temperatures between 1 50 and 200 "C, y-resonance peak width is remarkably constant independent of chromium concentration.However, the width does depend upon chromium concentration when &phase chromium maximises in amount. Perhaps paradoxically, the low-width y-resonances found for freshly prepared samples show the lowest width for the highest chromium concen- tration, where the most reductive decomposition of Cre+ has occurred, producing magnetic chromium oxide species. For chromium-silica, fig. 4 (b), the y-resonance width remains independent of chromium loading from 100 to 500°C calcination temperature. Yet in this temperature range considerable variations occur in the compositions of the samples. The extremely low-width resonances found for freshly prepared catalysts above 5 % Cr are most unusual for transition-metal-ion powders.The natural line width for Cr3+ ions at infinite dilution in single-crystal a-Al,O, is estimated to be between 11 and 16 G.7 The linewidth for species in powders possessing less symmetric structures should be in excess of this value, yet at 7 and 11 % Cr loadings a y-resonance linewidth of only 6 G is found, suggesting that exchange narrowing is a major factor determining the width of these resonances. For both chromium-alumina and chromium-silica the minimal temperature variation of y-resonance width cannot be explained on the basis of spin-lattice relaxation alone. The spectral components observed8 for spin-lattice-relaxed Cr5+ ions in C4v or Relaxation of the y-spin system at room temperature is efficient; saturation studies at 4.2 K, although in~omplete,~ show that some differential saturation may be occurring amongst the y-resonance components for chromium-silica, but even at this temperature the minimal and complex linewidth variation shows that spin-relaxation mechanisms cannot operate via spin-lattice interactions, spin energy being transferred instead amongst the spin assembly through spin-spin exchange.1° The alumina y-resonance is essentially isotropic, in contrast to the marked anisotropic appearance of the silica y-resonance.ll9 l2 Usually the alumina y-resonance width is claimed to be greater than that of the silica y-resonance.ll Satisfactory explanations on the basis of isolated Cr5+ ions have not been forthcoming, and indeed insistence on this model for y-resonance causes inconsistencies.For example, Beck and Lunsford" find /I-phase resonance at a loading of only 0.4% Cr, confirming the clustering of supported chromium, together with a y-resonance width of 150 G, yet the authors claim that the y-spectrum demands the isolation of chromium oxide species. At 1.2% Cr y-resonance widths in excess of 100 G are observedf3 for catalysts which, in the reduced state (Cr3+), yield very broad /?-phase resonances. The envoronments are not confirmed in this study.2592 E.S.R. STUDIES OF CHROMIUM OXIDE y-resonance for a 53Cr-enriched sample shows considerable broadening, yet again it is claimed that Cr-Cr interactions are improbable at this concentration. Here the y-resonance widths for chromium-alumina and chromium-silica are found to be similar. The appearance of excessive width for the alumina y-resonance is a consequence of the half-width values AL and AR, which are comparable to the peak-to-peak width.The computed Gaussian envelope yields a reasonably close fit to an alumina y-resonance, while the equivalent Lorentzian shows considerable deviation, especially in the outer 'wings ' of the envelope. This Gaussian resonance results from dipole-dipole broadening of Lorentzian spin-exchanged components arising from chromium species at the surface of clusters on alumina which have some three-dimensional character. In contrast the peak width and half-width, AL, of the silica y-resonance are both small and seemingly independent of the number and amplitudes of the components in the envelope.For example, y-resonances for 2-200-Si, 7- 1 00-Si, 7- 150-Si and 7-200-Si show both components h, and h, and yet have small values of half-width. This behaviour would not be exhibited if the species responsible for the resonance components were unrelated and unaffected by severe magnetic-exchange interactions. The analysis of anisotropic powder resonances is usually based upon the treatment of Sands1* or of Kneubuhl15 with suitable anisotropic terms in the appropriate spin Hamiltonian. This approach may explain the observed variations in y-resonance shape with respect to h, and h, for y-species developing at different calcination temperatures and chromium loadings [fig. 6(i) and (ii)]. I.e. the different calcination conditions may produce y-species in slightly different crystal-field environments so that their e.s.r.envelopes would differ only slightly in the amplitudes and separation of the resonances parallel and perpendicular to the applied magnetic field. In this scenario point h, corresponds to a gradient inflexion in the region between the two maxima of the resonance absorptions, the value of this gradient depending simply upon their field separations and amplitudes. However, such changes in y-resonance shape observed when the sample temperature is varied, fig. 6(iii) and (iv), require rejection of this model. Lowering of sample temperature cannot realistically cause such alterations in the crystal-field symmetry of the y-species, especially when the spectra show two contrasting behavioural types.Further, a surprising resolution of components h, and h, occurs for 18-200-Si at 4.2 K [fig. 6(iv)]. Here, P,-resonance is at a maximum, so that dipole-dipole broadening at this temperature should have prevented this clear resolution unless exchange-narrowing predominates. A detailed analysis of the y-resonances, fig. 7, produced by silica-supported chromium dried at only 25°C confirms that the y-resonance shape cannot be explained in terms of two axial-symmetry-related crystal-field components. The y-resonance for 11-25-Si at 298 K is extremely narrow (peak-to-peak width 3.95 G) and symmetric, consisting predominantly of one resonance component, rl. The apparently minor component, r,, predominates in the spectrum of 7-2543 at 25 "C in which is also revealed components r3 and r4.For 18-25-Si7 rl and Y , are clearly distinguishable. The crossover g values, referred to previously as h, of these resonances are within a narrow range but are clearly affected by the presence or absence of the components ~ 1 - - ~ 4 . The unusual observed temperature dependence of the y-resonance shape is in fact a function of the amplitudes of these components modified by low-temperature broadening of the resonances. Thus the superposition of the resonances of 7-25-Si at 298, 77 and 4.2 K [fig. 8(a)] clearly shows that the low-field phase of the derivative becomes dominated by components r2 and r3 with decreasing temperature. ResonanceA. ELLISON 2593 !i Fig. 7. Components of the y-resonances observed for Cr-SiO, samples dried at 25 “C.Room-temperature spectra, modulation amplitude 4.0 G, X-band, field sweep 200 G. (- - - -) 7-25-si, (.-.-.- ) 11-25-Si and (-) 18-25-Si. component rl is now located in the high-field derivative phase as the intensity maximum, and hence crossover g-value h, of the envelope shifts to lower field. As the temperature decreases, the amplitude of r2 decreases while the r4 amplitude increases. Similarly fig. 8(b) shows the superposition of the resonances for 11-25-Si at 298, 77 and 4.2 K. Although dipole-dipole-broadened /?-phase resonances distort the y-envelopes, arguments analagous to those for 7-25-Si again explain y-shape variation with temperature. For 18-253 [fig. 8 (c)] the y-resonance components are so profoundly affected by temperature that at 4.2 K an almost-symmetric resonance results, clearly a Gaussian, dipole-dipole-broadened superposition of the predominant components r3 and r4.The initial width and temperature dependence of width and of amplitude of the components r1-r4 cannot be explained through the simple crystal- or ligand-field model for single, magnetically isolated Cr5+ species normally adopted. The single-temperature studies of severely calcined materials produce well defined y-resonances which do appear to approximate closely to the powder-resonance envelope of gll and g , components from axially distorted &electron species. However, the envelope distortion introduced through over large values of modulation amplitude has pre- vented the resolution of resonance components observed here.In fact even these ‘regular’ or ‘normal’ y-resonances can be analysed in terms of the components r1-r4, In fig. 9(a) for 2-200-Si the low-field derivative phase shows the presence of r3 at 298 and 4.2 K. The turning-point labelled r2, and that corresponding to the crossover g , are functions of components r2 and rl, while r4 is clearly responsible2594 E.S.R. STUDIES OF CHROMIUM OXIDE Fig. 8. For legend see opposite.A. ELLISON 2595 Fig. 8. Effect of components r1-r4 on the variation in y-resonance shape with measurement temperature. Modulation amplitude 4.0 G, X-band, field sweep 200 G. (Q) 7-2549: (- - - -) 298, (*--.-----) 77 and (-) 4.2 K. (b) 11-25-Si: (----) 298, ( * - * - a - --) 77 and (-) 4.2K [7-25-si; ( - - - - - -) 298 K].(c) 18-2543: (- - - -) 298, (.-.-.-. ) 77 and (-) 4.2 K. for the resonance usually assigned to gl. A similar analysis is relevant to the 298 K spectrum for 11-100-Si [fig. 9(b)], but at 4.2 K the low-field phase is dominated by component r3. The temperature modification at r2 and rl alters the slope of the resonance absorptions in this region, so that the measured point in the derivative, previously referred to as h,, can no longer be distinguished. In conclusion, the properties of the y-resonances revealed here strongly suggest that the species responsible suffer magnetic exchange and dipole-dipole broadening interactions, spin transitions occurring within a manifold of spin-coupled states whose population is temperature dependent. The chromium clusters required by this new model have indeed been shown to occur on these supports at even the lowest chromium oxide loadings ~tudied.~ It is also clear that for both alumina- and silica-supported chromium(1v) oxide, y-phase chromium arises from regions of the surface of Zener double-exchange-coupled clustered species of the type -Cr3+-02-, Crs+-02-, the bulk structure of the clusters producing p2-resonance.(Theoretical and experimental studies of the exact nature of the y-species are now in progress in collaboration with Dr F. E. Mabbs of Manchester University.) Finally, reduction of this mixed-valence phase either by ethene during the induction period prior to catalytic reaction or by hydrogen or carbon monoxide catalyst- pretreatment may produce a mixed-valence phasela -Cr2+-02--Cr3+- at the surface of Cr3+ clusters, as indeed has been proposed by Groenveld et aZ.” and Wittgen et aZ.18 This oxidative addition of olefin is claimed to produce the active Cr-C b ~ n d , l ~ - ~ l cus-Cr2+ sites being responsible for reaction propagation.Both y- and Cr2+ species gain stability from the mixed-valence interactions yet are available and active at the catalyst surface during the polymerisation reaction.2596 E.S.R. STUDIES OF CHROMIUM OXIDE 5 Fig. 9. Relationship between the y-resonance envelope of calcined chromium-silica samples and resonance components rl-r4. Modulation amplitude 4.0 G, X-band, field sweep 200 G. (a) 2-200-Si: (-) 298 and (- - - -) 4.2 K. [7-25-Si: (--.-.-. ) 298 K]. (b) 11-100-Si: (-) 298 and (----) 4.2 K [7-25-Si: (.-.---. ) 298 K]. I thank the Royal Society, B.P. Chemicals Ltd, Croda Chemicals Ltd and the Humberside College of Higher Education for financial help and Drs F. E. Mabbs (Manchester University) and K. A. K. Lott (Brunel University) for providing the e.s.r. spectra. My thanks also go to A. K. Coverdale and M. Cawley for help and encouragement and to Dr R. B. Moyes (Hull University) for valuable discussions.A. ELLISON 2597 A. Ellison, J. Chem. Soc., Faraday Trans. I , 1984,80, 2567. A. Ellison, J. 0. V. Oubridge and K. S. W. Sing, Trans. Faraday Soc., 1970,66, 1004. A. Ellison and K. S.W. Sing, .I. Chem. Soc., Faraday Trans. I , 1978,74, 2017. A. Ellison and K. S. W. Sing, J. Chem. Soc., Faraday Trans. 1, 1978, 74, 2807. D. E. O’Reilly and D. S. MacIver, J. Phys. Chem., 1962, 66, 276. C. Zener, Phys. Rev., 1951,82,403. R. S . de Biasi and D. C. S. Rodrigues, J. Muter. Sci., 1981, 61, 968. L. L. van Reijen and P. Cossee, Discuss. Faraday SOC., 1966,41, 277. F. E. Mabbs and A. Ellison, unpublished work. lo C. P. Poole and H. A. Farach, Relaxation in Magnetic Resonance (Academic Press, New York, 1971). l 1 D. D. Beck and J. H. Lunsford, J. Catal., 1981, 68, 121. l2 V. B. Kazansky, A. N. Pershin and B. N. Shelimov, Proc. In?. Congr. Catal. (Elsevier, Amsterdam, l3 J. R. Pearce, D. E. Sherwood, M. B. Hall and J. H. Lunsford, J. Phys. Chem., 1980,84, 3215. l4 R. H. Sands, Phys. Rev., 1955,99, 1222. l5 F. K. Kneubuhl, J. Chem. Phys., 1960,33, 1074. l7 C. Groenveld, P. P. M. M. Wittgen, A. M. van Kersbergen, P. L. M. Mestrom, C. E. Nuijten and l8 P. P. M. M. Wittgen, C. Groenveld, J. H. G. J. Janssens, M. L. J. A. Wetzels and G. C. A. Schuit, 1980). M. B. Robin and P. Day, Adv. Inorg. Chem. Radiochem., 1967, 10, 247. G. C. A. Schuit, J. Catal., 1979, 59, 153. J. Catal., 1979, 59, 168. V. A. Zakharov, V. N. Druzhkov and Y. I. Ermakov, Kinet. Katal., 1973, 14,998. 2o Y. I. Ermakov and V. A. Zakharov, Adv. Catal., 1975, 24, 173. 21 K. G. Miesserov, J. Polym. Sci., Part A, 1966, 1, 3047. (PAPER 4/054)

ISSN:0300-9599    

DOI:10.1039/F19848002581

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I, 1984,80, 2599-2607 Phase Separation in Model Colloidal Dispersions BY JOHN EDWARDS, DOUGLAS H.. EVERETT,* TIMOTHY O’SULLIVAN, IRENE PANGALOU AND BRIAN VINCENT School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 ITS Received 7th February, 1984 Dispersions in n-alkanes of silica particles coated with grafted-C,, chains (silica-g-stearyl) exhibit both upper (UFT) and lower (LFT) flocculation temperatures. The dependence of the UFT and LFT on particle volume fraction (#), particle diameter ( d ) and the nature of the alkane (pentane to heptane) has been studied. The equilibrium phase diagram (T against 4) has been constructed for one system. Comparison with the UFT against 4 curve suggests that the latter is the spinodal curve.A preliminary theory is given for the low-concentration behaviour of these systems. A close analogy exists between the weak, reversible flocculation exhibited by certain types of colloidal dispersion and the phase behaviour of molecular systems, as exemplified by the order-disorder transition observed with charge-stabilised, monodisperse particles at very low electrolyte concentrations where the long-range double-layer repulsion results in a high ‘ effective ’ volume The present work is concerned with a second example in which a dilute (‘dispersed’) phase and a more concentrated (‘floc’) phase coexist in systems in which there is a net attraction between the particles. Such systems have upper and lower flocculation temperatures which depend on the volume fraction of the particles (4).Sterically stabilised dispersions are one class of system which may show this behaviour. In a good solvent environment for the stabilising, attached polymer species the interparticle pair potential may be considered as a hard-sphere repulsion plus a van der Waals attraction, giving rise to a shallow minimum rather akin to that occurring in corresponding intermolecular pair potentials. Weak, reversible flocculation may be observed in systems of this kind on heating and/or cooling, as demonstrated, for example, in the work of Everett and stage man*^^ for non-aqueous dispersions of poly(acrylonitri1e) and poly(methy1 methacrylate) particles stabilised by anchored poly(dimethylsi1oxane) chains, and of Cowell and Vincents for aqueous dispersions of (uncharged) poly(styrene) particles stabilised by anchored poly(ethy1ene oxide) chains.With conventional sterically stabilised systems, in which the particle cores are surrounded by an extended polymer-plus-solvent sheath, both the van der Waals attraction and the steric interaction are dependent on temperature. It is often supposed that their stability behaviour is controlled only by the change in sign of the steric interaction from a hard-sphere repulsion to an attraction in the vicinity of the &temperature of the attached polymer, and a correlation between the flocculation temperature and the @-temperature has been extensively studied by N a ~ p e r . ~ However, some of the results obtained by Everett and Stageman and by Cowell and Vincent indicate that flocculation often occurs in better-than-8 solvents, showing that in these cases the phenomena probably arise from a combination of both factors.The problem may be simplified by studying systems in which the hard-sphere part 25992600 PHASE SEPARATION IN COLLOIDAL DISPERSIONS Fig. 1. Schematic representations of (a) conventional sterically stabilised particles consisting of a (hard) core plus a (soft) polymer-plus-solvent sheath and (b) hard-sphere particles of the type prepared by Vrij and coworkers** where the sheath is a grafted layer of C,, chains. A,, A , and A , are the Hamaker constants in the various regions. of the potential is essentially independent of temperature. This criterion is met by dispersions of silica particles carrying a close-packed layer of terminally grafted n-C,, (stearyl) chains in non-polar solvents, as prepared and studied by Vrij and coworkers.6* These silica-g-stearyl dispersions are stable at ambient temperatures for the same reason as the more conventional sterically stabilised dispersions : that is, the increase in free energy (AGhs) associated with the loss of configurational entropy (AShs) of the hard spheres on flocculation outweighs the decrease in free energy (AGi) associated with the pair contacts which are formed.6 In the case of conventional, sterically stabilised systems [fig.1 (a)] this minimum is shallow because 6, the thickness of the sheath, is relatively large and the effective Hamaker coefficient of the sheath (A2) is comparable to that of the medium (A,), even though A , of the particle may be much larger than A,.For the silica-g-stearyl particles [fig. 1 (b)] 6 is small (ca. 2 nm) but both A , and A , are comparable to A , at ambient temperatures. However, it may be expected that this Hamaker coefficient ‘match’ will break down on changing the temperature, since A , is more strongly temperature-dependent than either A , or A,. The objective of this work was to examine the temperature dependence of the stability of silica dispersions of this kind. Not only do they show both upper and lower flocculation temperatures, but the resulting T against 4 plots resemble those found for molecular systems showing upper and/or lower critical solution temperatures. EXPERIMENTAL Five silica-g-stearyl dispersions (A-E) were prepared in cyclohexane, using the method of van Helden et a/.* The mean particle diameters ( d ) determined by electron microscopy, were A, 305+20nm; B, 276+15nm; C, 110flOnm; D, 60f10nm; E, 50f5nm. The larger particles showed improved sphericity compared with the smaller ones. Dispersions in other hydrocarbons were prepared by evaporating the cyclohexane dispersion to dryness and redispersing in the new medium.Flocculation was observed visually on heating and cooling the dispersions in sealed tubes in a variable-temperature bath. It was only practicable to make observations over the range of volume fractions from 0.005 to 0.06 since the flocculation was difficult to detect at lower concentrations, while at higher volume fractions the dispersion became too opaque.Consequently it was not possible to follow with any precision the behaviour in very dilute suspensions. InJ . Chem. SOC., Faraday Trans. 1, Vol. 80, part 9 Plate 1 Plate 1. Photographs of phase-separation volumes as a function of temperature, for sample B in n-hexane. (a) 60, (b) 70 and (c) 80 "C. Note increase in volume of the lower phase and decrease in concentration of the upper phase as the temperature is raised. J. EDWARDS et al. (Facing p . 2601)150 140 J. EDWARDS et al. 260 1 0.01 0.02 0.03 4 Fig. 2. Upper (open symbols) and lower (filled symbols) flocculation temperature of sample C (1 10 mm diameter) as a function of particle volume fraction in n-pentane (O), n-hexane (A) and n-heptane (0). some cases turbidity (z) against wavelength (A) scans were made using a Unicam SP 1800 visible-range spectrometer with thermostatted cell housing.The temperature at which the gradient (n) of the log z against log A plot changed sharply was taken as indicating the onset of aggregation.1° In addition, for one system, the equilibrium-phase volume fractions and particleconcentrations were determined at a series of temperatures by placing the dispersions in sealed tubes with a capillary attachment at the bottom end (see plate 1) immersed in a thermostat. After equilibration the volume of the concentrated phase was determined with the aid of a cathetometer and the particle concentration in the dilute phase found by solvent evaporation and weighing. RESULTS Except for dispersion A, all the dispersions could be redispersed in n-hexane and n-heptane, while all except A and B redispersed in n-pentane.None gave a stable dispersion in liquid n-butane at room temperature. Dispersion A was stable in cyclohexane but in no other alkane. Fig. 2 shows the upper and lower flocculation temperatures (UFT and LFT,2602 PHASE SEPARATION IN COLLOIDAL DISPERSIONS 180 160 120 u k 8 0 40 0 0 0.02 0.04 0.06 0.0 8 d Fig. 3. Upper (open symbols) and lower (filled symbols) flocculation temperatures of samples B (A) and D (0) as a function of particle volume fraction in n-hexane. Dashed curves: calculated using eqn (2). respectively) of sample C as a function of particle volume fraction in n-pentane, n-hexane and n-heptane. In contrast to the behaviour of the UFT of the poly(dimethylsi1oxane)-stabilised polymer latices studied by Everett and Stageman, where the UFT was not far from the bulk critical temperature of the dispersion medium, the UFT observed with the silica dispersions are ca.100 K below the corre- sponding critical temperature (see fig. 9). Similarly, the LFT for the latex dispersions were in the range from - 80 to - 100 OC, while in the present instances they fall in the range from +0.5 to - 11 "C. As shown in fig. 3 and 4 the UFT is strongly dependent on particle size, the LFT much less so. This again contrasts with the polymer latices, where the particle-size effect was only barely detectable." The dependence of the UFT, at a volume fraction of 0.01, on particle size is shown in fig. 5 . In all cases two coexisting fluid phases were formed.This again contrasts with the behaviour of the latices, where the 'floc' phase was solid-like, i.e. it appeared as a shower of irregular 'curd'-like aggregates. It was observed, however, that the lower concentrated phase exhibited, on standing undisturbed, marked iridescence, indicating an ordered phase, even though slight disturbance showed that it retained its fluidity. The volumes of the coexisting phases above the UFT vary with temperature, (plate 1): as the temperature increases the volume of the lower phase increases. There is a gradual decrease in the particle concentration in the upper phase and aJ. EDWARDS et al. 2603 130 120 110 100 V 90 fi 80 70 0 -10 0 0.01 0.02 0.03 0.04 0.05 4 Fig. 4. Upper (open symbols) and lower (filled symbols) flocculation temperatures of samples C (1 10 mm diameter, A) and E (50 mm diameter, 0) as a function of particle volume fraction in n-pentane.200 150 V 100 50 0 ‘6 i I I 100 200 300 dlnm Fig. 5. Variation of UFT with particle size in n-heptane (a), n-hexane (0) and n-pentane (A).2604 PHASE SEPARATION IN COLLOIDAL DISPERSIONS 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 dJ Fig. 6. 4 against Tphase diagram for the UFT of sample B in n-hexane. Dashed curve is the rectilinear diameter leading to a critical point at 4 = 0.15 kO.02 and T = 16 "C. 100 80 u 70 2 60 50 0 0.004 0.008 0.012 4) Fig. 7. Comparison of the low-volume-fraction region of the phase diagram for sample B in n-hexane (open symbols) with the visually observed UFT (filled symbols), suggesting that the UFT lie on the spinodal curve.Also shown are two points (0) corresponding to the onset of cluster formation as detected from turbidity against wavelength plots.J. EDWARDS et al. 2605 corresponding increase in that of the lower phase. The phase diagram showing the equilibrium particle volume fractions as a function of temperature for sample B in n-hexane is presented in fig. 6. The phase diagram appears to show a lower critical point at 4 = 0.15+0.02 and at a temperature of ca. 16 "C. On comparing the equilibrium dilute phase compositions with the observed UFT, there is evidence (fig. 7) that, on the basis of the limited data so far available, the observed UFT for a given volume fraction of particles lies significantly above the equilibrium phase composition curve. This suggests strongly that the observed UFT lies on the spinodal rather than the binodal curve.If so, this would be the first direct evidence for spinodal decomposition in a liquid-like system. Fig. 7 also includes two points corresponding to the location of the break in the slope of the log z against log ;1 plots as a function of temperature. These points lie far below the temperatures at which flocculation is detected visually, and this may be evidence that embryo clusters form in the disperse phase prior to bulk phase separation. In the case of the LFT, several observers confirmed that on approaching the LFT there is visual evidence for some kind of premonitionary change before flocculation occurs. This could not be checked by turbidity measurements since there are difficulties in thermostatting the cell at sub-zero temperatures and of avoiding condensation on the windows.DISCUSSION We attribute the UFT phenomenon to the increase in the van der Waals attraction between the particles, assumed to behave as hard attracting spheres, as the density of the intervening liquid decreases. The magnitude of these forces and their screening by the intervening medium depend on the dielectric properties of the particles and of the medium, which are reflected in their respective refractive indices (n). Before seeking a more complete theory, it is therefore of interest to seek an empirical correlation between the UFT and the refractive indices of the media in comparison with that of the silica particles. In fig. 8 the UFT at a volume fraction 0.01 is shown as a function of the difference between the values of [(n2- l)/(n2+2)]2 at 25 "C for medium and silica, taking n for the latter as the mean (1.445) of the values given by van Helden et aL9 If the linear relation which this graph suggests is valid then, on extrapolation, one would not expect the silicas used in this work to be stable in liquid butane at room temperature.Smaller particles, of, say, ca. 30 nm diameter might possibly form a stable dispersion. Nor would one expect dispersions in cyclohexane to show a UFT below its critical temperature. The failure of sample B to disperse in n-pentane is also compatible with this empirical representation of the results. One may attempt a more quantitative, though still approximate, calculation of the spinodal at very low concentrations using the arguments of de Hek and Vrij.12 If the interparticle potential V(h) is known as a function of h, the separation of the particle centres, then the second virial (osmotic) coefficient (B) can be calculated. For hard spheres, V(h) = 00 for h < o [where here, fig.1 (b), 0 = r +6] while for h > 0, V(h) may be calculated using Vold's extension13 of the Hamaker expression for the van der Waals interaction between composite (i.e. core + sheath) particles, leading to B , B = - = 4+- jm{l-exp[- V(h)/kT]}2nh2dh (1) u0 uo 0 where uo is the volume of the particle. In a dilute dispersion the osmotic pressure, n, becomes a quadratic in d, and the condition dn/d# = 0 may be used to locate the2606 PHASE SEPARATION IN COLLOIDAL DISPERSIONS + V ‘iz c6 ‘7 c8 c9 CH I I I I L 1 -0.025 -0.020 -0.015 -0.010 - 0.005 Fig.8. Empirical correlation of the UFT with the difference n2+2 at 25 “C: (u) 60, (6) 110 and (c) 276 nm. Also shown are the critical temperatures of the media (+I. critical particle volume fraction (4c) corresponding to spinodal decomposition at a given temperature : 4c = - 1/[2B’(T)]. (2) For the present systems A , and A , were assumed to be independent of temperature and were ascribed the following values derived from data in ref. (14) and (15): A , = 6.4 x J. The temperature dependence of A , was calculated from the density variation of the liquid n-alkane concerned, using the equation given by Gregory.ls The thickness of the grafted stearyl layer, 6, was taken as 2 nm.The calculated upper boundary curves are indicated by the dotted lines in fig. 3 for dispersions B and D in n-hexane. The correct trends are predicted and a closer fit could have been obtained by a different choice of parameters. It is important to emphasize that a phase diagram of this kind can only arise from a strongly temperature-dependent V(h); V(h) independent of temperature leads only to LFT. However, the existence of the LFT in the present systems is not easily accounted for on this basis, unless the properties of the grafted chains become temperature- dependent at sub-zero temperatures. Since these are far below the freezing point of the parent hydrocarbon, n-hexadecane, such effects cannot be ruled out. It is, however, too soon to reach any firm conclusion as to the origin of the LFT. To extend the theory of the upper flocculation temperature to higher concentrations one needs to adapt theories of hard-sphere liquids to the present problem, or to employ computer simulation methods.It is interesting that the volume fraction at the critical J and A , = 5.0 xJ. EDWARDS et al. 2607 point (0.15 0.02) is close to that predicted for a system of hard spheres (0. 1287).17 In addition it is necessary to develop more precise procedures for calculating Hamaker coefficients as a function of temperature and for estimating the interparticle pair potential. Further work along these lines is in hand. J.E. and T.O'S. thank S.E.R.C. for financial support. ' P. A. Hiltner and I. M. Krieger, J. Phys. Chem., 1969, 73, 2386. S. Hachisu, Y. Kobayashi and A. Kose, J. Colloid Interface Sci., 1973, 42, 342. R. H. Ottewill, J. Colloid Interface Sci., 1977, 58, 357. D. H. Everett and J. F. Stageman, Colloid Polym. Sci., 1977, 255, 293. D. H. Everett and J. F. Stageman, Faraday Discuss. Chem. SOC., 1978, 65, 230. C. Cowell and B. Vincent, J. Colloid Interface Sci., 1982, 87, 518. jr D. H. Napper, J. Colloid Interface Sci., 1977, 58, 390. * H. De Hek and A. Vrij, J. Colloid Interface Sci., 1981, 79, 289. A. K. Van Helden, J. W. Jansen and A. Vrij, J. Colloid Interface Sci., 1981, 81, 354. lo J. A. Long, D. W. J. Osmond and B. Vincent, J. Colloid Interface Sci., 1973, 42, 545. l1 D. H. Everett, Science and Technology of Polymer Colloicis (NATO AS1 Series, no. 68, Plenum Press, l2 H. De Hek and A. Vrij, J. Colloid Interface Sci., 1981, 84, 409. l 3 M. J. Vold, J. Colloid Interface Sci., 1961, 16, 1 . l4 C. Pathmamanoharan and M. M. Kops-Werkhoven, Chem. Phys. Lett., 1982, 93, 396. l5 D. B. Hough and L. White, Adv. Colloid Interface Sci., 1980, 14, 3. l6 J. Gregory, Adv. Colloid Interface Sci., 1969, 2, 396. l7 M. Grimson, J. Chem. SOC., Faraday Trans. 2, 1983, 79, 817. New York, 1983), vol. 2, p. 353. (PAPER 4/217)

ISSN:0300-9599    

DOI:10.1039/F19848002599

出版商:RSC    

年代:1984

数据来源: RSC