摘要:

7 k T h e Royal Society of Chemistry Faraday Discussions take place twice a year and are designed to cover the broad aspects of physicochemical topics, thereby encouraging scientists of different disciplines to contribute their varied viewpoints to a common theme Three recent Discussions are: - The result of a D/scussion held at the University of Nottingham September 1981 this publication covers Selective Oxidation and Hydrogenation CO H and Methanol Reactions Polymerizations and Enantiosefective Processes Newer catalyst systems to be featured will include Bimetallics Shape selective zeolites and Anchored Complexes Soft cover 431pp 0 85186 708 1 Price€30751$63 251 RSCMembersfZO 00 I arada, I>#\< ".*ill"\ c ~ t tht Chi niital \ c r Van der Waals No. 73 Molecules The oblect of thisDiscussron, held in April 1982at St Catherines College Oxford wasto increaseunderstanding of Vander Waals Molecules Topics included in this publication - a result of the above Discussion - include Spectroscopy and Photophysics of Organic Clusters Energetics and Dynamics of large Van der Waals Molecules Van der Waals Molecules and Condensed Phases Gas phase Properties and Forces in Van der Waals Molecules Dimer Spectroscopy Intermolecular Binding Soft cover431pp0851866883 Pricef25 Zit551 751 RSC Membersf16 50 l-----l This D/scussron, the result of a meeting held at the University of Southampton.September 1982, covers: Fundamental Aspects of the Chemical Kinetics of Electron and Proton Transfer Reactions in Solution with particular reference to well defined Biological Systems.Chapters include. Electron, Proton and Related Transfers; Quantum Effects on Electron-transfer processes; Fast Electron- transfer Reactions; Hydride Transfer between NAD + Analogues; Electron and Protone Transfers in Chemical and Biological Quinone Systems. Softcover 413pp 0 85186 678 6 Price CZ5.00($51.001 RSC Membersfl6.Z Faraday Symposia are usually held annually and are confined to more sperialised topics than Discussions, with particular reference to recent rapidly developing lines of research Two recent symposia: r--l Faradav Symposia No. 15 1 01 the Chromatography, :h:Y Soc'ety Kinetics Eq u i 1 i br i a and No 15in theseriesis theresultof a meeting heldat the University of Sussex in December 1980 The resulting publication covers the processes controlling separation through the underlying physical chemistn, of the subject, in addition the advantages of the chromatographic techniques for the study of the physical chemistry of surfaces.equilibria and kinetics are highlighted Softcover 191pp 0 85186 728 6 Pricef2B.W1$57.50) RSC Membersf18.25 No. 16 This publication is based on the symposium held at the Physical Chemistry Laboratory, Oxford, December 1981, and covers Liquid Vapor Interfaces. Solid-Fluid Interfaces, Interfaces formed by the Adsorption of Complex Molecules such as Polymers and Surfactants Softcover 256pp 0 85186 698 0 Price €36.25($74.25) RSC Members €23.50 ORDERING RSC Members should send their orders to: The Royal Society of Chemistry. The Membership Officer, 30 Russell Square, London WClB 5DT.Non-RSC Members The Royal Society of Chemistry, Distribution Centre, Blackhorse Road. Letchworth. Herts SG6 1HN. England.7 k T h e Royal Society of Chemistry Faraday Discussions take place twice a year and are designed to cover the broad aspects of physicochemical topics, thereby encouraging scientists of different disciplines to contribute their varied viewpoints to a common theme Three recent Discussions are: - The result of a D/scussion held at the University of Nottingham September 1981 this publication covers Selective Oxidation and Hydrogenation CO H and Methanol Reactions Polymerizations and Enantiosefective Processes Newer catalyst systems to be featured will include Bimetallics Shape selective zeolites and Anchored Complexes Soft cover 431pp 0 85186 708 1 Price€30751$63 251 RSCMembersfZO 00 I arada, I>#\< ".*ill"\ c ~ t tht Chi niital \ c r Van der Waals No.73 Molecules The oblect of thisDiscussron, held in April 1982at St Catherines College Oxford wasto increaseunderstanding of Vander Waals Molecules Topics included in this publication - a result of the above Discussion - include Spectroscopy and Photophysics of Organic Clusters Energetics and Dynamics of large Van der Waals Molecules Van der Waals Molecules and Condensed Phases Gas phase Properties and Forces in Van der Waals Molecules Dimer Spectroscopy Intermolecular Binding Soft cover431pp0851866883 Pricef25 Zit551 751 RSC Membersf16 50 l-----l This D/scussron, the result of a meeting held at the University of Southampton.September 1982, covers: Fundamental Aspects of the Chemical Kinetics of Electron and Proton Transfer Reactions in Solution with particular reference to well defined Biological Systems. Chapters include. Electron, Proton and Related Transfers; Quantum Effects on Electron-transfer processes; Fast Electron- transfer Reactions; Hydride Transfer between NAD + Analogues; Electron and Protone Transfers in Chemical and Biological Quinone Systems. Softcover 413pp 0 85186 678 6 Price CZ5.00($51.001 RSC Membersfl6.Z Faraday Symposia are usually held annually and are confined to more sperialised topics than Discussions, with particular reference to recent rapidly developing lines of research Two recent symposia: r--l Faradav Symposia No. 15 1 01 the Chromatography, :h:Y Soc'ety Kinetics Eq u i 1 i br i a and No 15in theseriesis theresultof a meeting heldat the University of Sussex in December 1980 The resulting publication covers the processes controlling separation through the underlying physical chemistn, of the subject, in addition the advantages of the chromatographic techniques for the study of the physical chemistry of surfaces. equilibria and kinetics are highlighted Softcover 191pp 0 85186 728 6 Pricef2B.W1$57.50) RSC Membersf18.25 No. 16 This publication is based on the symposium held at the Physical Chemistry Laboratory, Oxford, December 1981, and covers Liquid Vapor Interfaces. Solid-Fluid Interfaces, Interfaces formed by the Adsorption of Complex Molecules such as Polymers and Surfactants Softcover 256pp 0 85186 698 0 Price €36.25($74.25) RSC Members €23.50 ORDERING RSC Members should send their orders to: The Royal Society of Chemistry. The Membership Officer, 30 Russell Square, London WClB 5DT. Non-RSC Members The Royal Society of Chemistry, Distribution Centre, Blackhorse Road. Letchworth. Herts SG6 1HN. England.

ISSN:0300-9599    

DOI:10.1039/F198379FX001

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

xxxii Thomson, S. J., 195, 2195 Tiddy, G. J. T., 637, 975, 1901 Tokuda, T., 913,2277 Tomlinson, A. A. G., 1039 Tomlinson, E., 13 1 1 Trapane, T. L., 853 Trasatti, S., 2801 Treiner, C., 2517, 2915 Trenwith, A. B., 2755 Trevellick, P. R., 2027, 21 11 Trevethan, M. A., 637 Tsuchiya, S., 1461 Tuck, J. J., 1687 Tusk, M., 1987 Tvaruikovi, Z., 1573 TvanEkova, Z., 1591 Tyler, A. N., 1249 Ueno, A., 127 Ungarish, M., 119 Urry, D. W., 853 Valencia, E., 1833 Valera, E. de, 1061 Vanmaekelbergh, D., 1391,2813 AUTHOR INDEX Vedrine, J. C., 1921 Verhaert, I., 2821, 2835 Vesnaver, G., 699 Vickerman, J. C., 185 Vink, H., 1403, 2355, 2359 Viiiuela, J. S. Diez,, 1 191 VuEelik, D., 1633 Wacrenier, J-M., 779 Waddington, D. J., 505 Waddington, T. C., 128 1 Waernes, O., 71 1 Waghorne, W. E., 1061,2289 Wakabayashi, T., 941 Wakeham, W.A., 163 Walker, A., 689 Walls, J. R., 1073 Walsh, R., 2233 Walters, P., 1335 Wang, G-W., 1373 Ward, S., 1381, 2975 Waring, L., 975 Warner, R. W., 2639 Watling, G., 689 Vansant, E. F.; 1451,2821,2835 Watson, J. T. R., 733 Watts, H. P., 1659 Waugh, K. C., 343 Wawrzynow, A., 1523 Webb, G., 195, 2195 Webster, B. C., 1939 Weeks, I., 1471 Wells, C. F., 253, 2367, 2439 Wendt, G., 2013 White, L. R., 1701 Whittle, E., 1471 Wichterlova, B., 1585, 1591, Wood, S. W., 2597 Woolley, A., 505 Woinicka, J., 2879 Yamamoto, Y., 625 Yashonath, S., 1229 Yildiz, A., 2853 Yoshioka, M., 2277 Zagbrska, I., 2801 Zambonin, P. G., 71 1 Ziadeh, Y., 2735 Zsigrai, I. J., 2171 Zuman, P., 721 ' 1573xxxii Thomson, S. J., 195, 2195 Tiddy, G. J. T., 637, 975, 1901 Tokuda, T., 913,2277 Tomlinson, A.A. G., 1039 Tomlinson, E., 13 1 1 Trapane, T. L., 853 Trasatti, S., 2801 Treiner, C., 2517, 2915 Trenwith, A. B., 2755 Trevellick, P. R., 2027, 21 11 Trevethan, M. A., 637 Tsuchiya, S., 1461 Tuck, J. J., 1687 Tusk, M., 1987 Tvaruikovi, Z., 1573 TvanEkova, Z., 1591 Tyler, A. N., 1249 Ueno, A., 127 Ungarish, M., 119 Urry, D. W., 853 Valencia, E., 1833 Valera, E. de, 1061 Vanmaekelbergh, D., 1391,2813 AUTHOR INDEX Vedrine, J. C., 1921 Verhaert, I., 2821, 2835 Vesnaver, G., 699 Vickerman, J. C., 185 Vink, H., 1403, 2355, 2359 Viiiuela, J. S. Diez,, 1 191 VuEelik, D., 1633 Wacrenier, J-M., 779 Waddington, D. J., 505 Waddington, T. C., 128 1 Waernes, O., 71 1 Waghorne, W. E., 1061,2289 Wakabayashi, T., 941 Wakeham, W. A., 163 Walker, A., 689 Walls, J. R., 1073 Walsh, R., 2233 Walters, P., 1335 Wang, G-W., 1373 Ward, S., 1381, 2975 Waring, L., 975 Warner, R. W., 2639 Watling, G., 689 Vansant, E. F.; 1451,2821,2835 Watson, J. T. R., 733 Watts, H. P., 1659 Waugh, K. C., 343 Wawrzynow, A., 1523 Webb, G., 195, 2195 Webster, B. C., 1939 Weeks, I., 1471 Wells, C. F., 253, 2367, 2439 Wendt, G., 2013 White, L. R., 1701 Whittle, E., 1471 Wichterlova, B., 1585, 1591, Wood, S. W., 2597 Woolley, A., 505 Woinicka, J., 2879 Yamamoto, Y., 625 Yashonath, S., 1229 Yildiz, A., 2853 Yoshioka, M., 2277 Zagbrska, I., 2801 Zambonin, P. G., 71 1 Ziadeh, Y., 2735 Zsigrai, I. J., 2171 Zuman, P., 721 ' 1573

ISSN:0300-9599    

DOI:10.1039/F198379BX003

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I, 1983, 79, 15-26 Kinetics of Monticular Carbon Growth on Polycrystalline Iron BY ALAN M. EMSLEY AND MALCOLM P. HILL* Central Electricity Research Laboratories, Kelvin Avenue, Leatherhead, Surrey KT22 7SE Received 28th September, 198 1 The kinetics of carbon deposition on polycrystalline iron surfaces from methane at 750 Torrt pressure and at temperatures between 1013 and 1133 K have been studied using the change in power dissipation of an electrically heated filament caused by the increased emissivity as the surface is blackened by deposit. The carbon formed has a monticular-type structure. The growth kinetics follow a direct logarithmic rate law which is explained in terms of the availability of active sites at the surface. The total carbon uptake at maximum coverage of the monticular layer, i.e.at maximum emissivity, depends on the filament temperature and can be correlated with the amount of carbon taken up into solution during the prior induction period in accordance with the phase diagram. The activation energy has a value of 66 f 8 kJ mold'. The rate-determining step for monticular growth cannot be established, but certain possibilities, such as carbon dissolution, bulk diffusion of carbon in the metal, and surface and bulk self-diffusion of iron, can be eliminated. Various aspects of the mechanism of formation of the monticular growths are discussed. The carbon deposits formed on iron by pyrolysis of hydrocarbons have a number of characteristic morphologies, including laminar graphitic layers, mound-type (monticular) growths, columnar morphology and filamentary mate1ia1.l.~ The deposit morphology, particularly in the early stages of reaction, depends on the metallurgical state of the substrate and therefore on its previous mechanical, thermal and chemical treatment.* The monticular type deposits are formed on specimens that have received insufficient heat treatment to remove the cold-worked layer at the metal surface.They can also be formed by diffusing carbon down a thermal gradient in a well annealed metal such that precipitation occurs where the temperature falls below that of the Fe-C eutectoid (996 or 101 1 K).5 As a phase change occurs at this transition, i.e. y-(f.c.c.) Fe to a-(b.c.c.) Fe, it is possible that the monticular growths are associated with structural rearrangements of the metal surface.The surface of the mound is decorated with a polygonised ridge structure typical of the continuous laminar graphitic films formed in other transition-metal hydrocarbon systems.6'8 Two mechanisms have been proposed to explain the good graphitic order of the deposits, viz. (i) dissolution of carbon, nucleation at suitable sites, followed by precipitation, and (ii) formation and decomposition of an intermediate ~ a r b i d e . ~ Both surface and bulk diffusion mechanisms have been invoked to explain the development of particular morphologies.lO* l1 As yet there is no definite confirmation of any of these mechanisms. After the carbon dissolution stage of the reaction is complete, precipitation of carbon and/or carbide can occur both at the surface and in the bulk rneta1.l2 To simplify the kinetics it is necessary to distinguish between bulk and surface processes, and a novel method of doing so has been adopted.The localised nature of surface deposit causes areas of high emissivity to be formed on the bright metal. The early t 1 Torr = 101 325/760 Pa. 1516 GROWTH OF CARBON ON IRON stages of deposit growth can be followed by measuring changes in the electrical power dissipation of the specimen. Resistivity measurements indicate when precipitation becomes significant in the bulk metal, and the reaction can be stopped before there is any interference with the surface measurements. We have used the technique with iron foils that have a retained cold-worked layer and therefore initially form only the monticular type of deposit.The morphology present at the reaction temperatures has been confirmed by separate in situ hot-stage scanning electron microscopy (SEM)5 as well as conventional SEM examination after cooling. The formation of laminar carbon films on well annealed surfaces at temperatures above the Fe-C eutectoid is too rapid to follow by this technique. THEORY The power dissipation, W(t), from an electrically heated foil is given by Stefan’s law. For a surface with areas of differing emissivity, for example composed of bright metal with emissivity cM or carbon covered with emissivity E,: where o is Stefan’s constant, a, the geometric area of the foil, ap(t) the projected area of a carbon mound on the surface, T the reaction temperature in K, the ambient temperature in K and c a constant which corrects for conduction losses at leads and convection losses.It is assumed that the actual carbon surface area, at a time t, ac(t), bears a constant relationship to its projected area aJt), regardless of its detailed morphology, i.e. For a simple case of a solid hemispherical growth we have A = 0.5. In practice the morphology is complex and A cannot be defined. However, the assumption is valid for the early stages of growth, when the deposit is very thin. The bright metal emissivity remains constant during the experiment. In the course of an experiment the change in power dissipation is given by In the early part of the deposition reaction the rate of carbon growth is proportional to the rate of increase of the high-emissivity area da,(t)/dt, which is given by 1 (4) d a m - d[AWt)l dt dt i o(T4- T:) ( E c - - d- Heat losses by conduction and convection are constant throughout the experiment and therefore do not enter into the final expression.The value of T, is assumed to remain constant over the narrow temperature range of the experiment, and will be slightly above ambient temperature because of wall heating. The resistivity of the specimen increases during the later stages of the reaction because of localised carburisation. The power dissipation must be corrected for any such resistance increase. Eventually ‘hot spots’ will develop in these regions, but before they can influence the results the experiments are stopped.A. M. EMSLEY AND M.P. H I L L 17 EXPERIMENTAL APPARATUS A N D MATERIALS The specimen consisted of a pure iron foil (99.99% pure, ex. Johnson-Matthey) 150 mm long, 1 mm wide and 0.025 mm thick, to which were spot-welded two 0.075 mm diameter Pt-Pt/Rh thermocouples (Thermopure grade, ex. Johnson-Matthey) centrally positioned ca. 50 mm apart. The foil was spot-welded to two 3 mm diameter tungsten rods and the thermocouples to 1 mm diameter tungsten rods mounted on a standard metal vacuum feedthrough. The glass reaction vessel had an optical window for pyrometer measurements protected when not in use with a magnetically operated glass shutter. The vacuum system was capable of achieving pressures below Torr. The electrical measuring and control circuit is shown in fig. 1. The specimen foil was heated with a stabilised d.c.supply (Hewlett-Packard model 6285A). The current was determined to five significant figures from the voltage drop across a standard 0.01 CI manganin resistor using a vernier pottntiometer and a digital voltmeter. The potential drop across the central uniform temperature portion of the foil was measured using the positive thermocouple leads as potential probes, to the same accuracy as the current. To eliminate the effect of the heater voltage on the thermocouple readings a reversing switch was included so that the correct value could be determined from the averaged readings. The thermocouples gave temperatures consistently low compared with the optical pyrometer because of heat conduction through the leads. They were used only to maintain uniform temperatures.The experiments were carried out at 750 Torr pressure and a flow rate of 25 cm3 min-l. The gas supplies (grade X, B.O.C. Ltd) were purified using a platinum conversion catalyst (Engelhard M) to remove oxygen, at 723 K for methane and 298 K for hydrogen. Water and other hydrocarbon impurities were removed by passing the gas through mixed beds of 5A and 13X molecular sieves. PROCEDURE The iron foil was pretreated in hydrogen to remove dissolved nitrogen and surface oxide, as discussed previ~usly,~ except that a maximum temperature of 923 K was used so that the cold-worked layer was retained at the surface. Outgassing for CQ. 16 h was sufficient to remove the dissolved hydr~gen.~ Each run was started by raising the temperature with the methane flow set at the steady value.As the reaction proceeded, the heating current and voltage were adjusted to maintain a constant temperature, as measured with the pyrometer on either bright or dark surface areas. Runs were continued until localised carburisation made it difficult to maintain a uniform temperature. The region of possible ‘hot spot’ formation is well outside the time scale of the results presented below. If the foil was cooled during an experiment, it could not be returned to the same condition on reheating, i.e. to the same position on the power dissipation curve, possibly because of some irreversible graphite or carbide precipitation. Therefore, a run was normally completed without intermediate cooling. RESULTS The emissivity of the clean iron foil, determined from a Stefan’s-law plot, has a value of 0.32, which is in good agreement with the literature value.13 The experimental method is independent of the actual emissivity values, and E,, but the observed change in power dissipation increases with the difference in emissivities. Typical power dissipation curves for the temperature range 1013-1 133 K are shown in fig.2. The absence of experimental points near t = 0 arises because of the carbon solution induction period. The data obey a direct logarithmic law of the type observed in some oxidation reactions,l4* l5 i.e. AW= k log ( t + t o ) - k log (ti+t,) (5) where ti is the induction period, and k and to are constants.18 I gas out to pumping Line m e t a l vacuum f l o w control valve r d.c.power supply 1 to vacuum sys te locking arrangement 4k reaction vess e I thermocouple recorder C I / tunis&: rod \ th!r mo couple i r o n f o i l lmm tungsten rod ing magnet p s u l a t e d soft vacuum f eed-t hr ou g h iron r o d ur c u r r e n t me a surement I 1 iron f o i l I I I 1 s t a n d a r d manganin r e s i s t a n c e FIG. 1 .-(a) Diagram of experimental system for resistivity/power-dissipation measurements. (b) Schematic diagram of the electrical circuit (DVM = digital voltmeter).A. M. EMSLEY AND M. P. H I L L 19 0 1 2 3 4 5 6 7 8 timelh FIG. 2.4hange in power dissipation during carbon deposition from 750 Torr methane on 25 pm thick iron foils. The data in fig. 2 are plotted in accordance with eqn (5) in fig. 3. An iterative procedure has been adopted for the determination of to as follows.A plot of AW against log t is extrapolated back from high values oft to find the intercept value log I, at AW = 0. From eqn (9, when t 9 to: Il = to+ ti. (6) If a new equation is written [eqn (7)] A W+C’ = k’ log (t + 11) then when AW= 0 at t = ti C’ = k’ log (to + 24). The new intercept value on the t axis is now given by I, = t0+2ti. (9) Values of to and ti can be determined using eqn (6) and (9). The calculated and observed values of ti are shown in table 1, which also lists the values of to required to give linear plots, The agreement is regarded as good considering that induction periods of minutes are determined from reaction times of several hours.20 GROWTH OF CARBON ON IRON h c .- 1 0 1133 K J 0.5 1 5 10 t + t , FIG.3.-Direct logarithmic growth law plot for carbon deposition. TABLE 1 .-EXPERIMENTAL AND CALCULATED VALUES OF INDUCTION PERIOD (ti) AND THE CONSTANT ( t o ) IN S T / K t,(obs) ti(calc) to(calc) 1013 1980 2016 3204 1033 1872 1908 2844 1061 1000 720 2088 1078 720 720 1548 1133 180 216 1080 An overall activation energy for the early stage of deposit growth can be determined from values of the initial rate in fig. 3. By differentiation of eqn ( 5 ) and therefore a plot of log (initial rate) against l/T, using values of to from table 1 should be linear. The Arrhenius-type plot of fig. 4 gives an activation energy of 78 f 9 kJ mol-l. The total carbon uptake into the surface layer, i.e. the situation that exists when the average emissivity of the foil reaches its maximum value, is given by the maximum value of AW(t), obtained from fig.2 at longer times than shown. The observed values of AW(t)max bear a linear relationship to the reaction temperature (fig. 5). The concentration of dissolved carbon in the metal is also marked on fig. 5, the values having been determined from the y-Felcarbide phase boundary, which was shownA. M. EMSLEY AND M. P. H I L L 4.8- bo m c 0 4.6- .- - -4 4.4- v) 3 ! 4.2- P X 5 4.0- E 2 3.8- ._ 3.6- 3.4 21 1023 1073 1123 I ! ! - /' A 1 I I I I J5 0.85 0.90 0.95 1.00 1.05 1.10 1.15 -3.; - 3. h c-' a, 2 .z -3.8 - m .- .- v Do - - 3.i -3.1 I I I I I 38 90 9 2 9 4 96 9 8 lo4 KIT FIG. 4.-Activation energy determined from initial rate measurements. A€ = 78 & 9 kJ mol-I reaction temperature/K saturation concentration of carbon in iron (wt 76) FIG.5.-Relationship of surface coverage at maximum emissivity change to maximum dissolved carbon concentration (taken from the Fe-C phase diagram).TABLE 2.-x-RAY ANALYSIS OF CARBON DEPOSITS data from powder diffraction file after 14 h reaction at 1033 K after 10 h calculated reaction at 1133 K: a-Fe graphite y-Fe loose deposita substratea loose deposita (6-0696) (1 3- 148) linesb d / A I/IO d / A I/IO d / A IIIO d / A I/IO d / A I/IO d / A 3.35-3.37 2.13-2.14 2.08-2.09 2.02-2.03 1.68-1.69 1.44 1.23 1.17 1.16 1.12 1.02 0.907 100 10 10 80 40 10 40 40 20 < 5 < 5 10 3.36 2.10 - 2.030 2.025 2.017 1.680 1.430 - 1.170 - - - 0.906 33 17 - 1 00 1.7 1.5 1.7 1.2 - 1.7 - - - 1 3.37 2.1 2-2.1 3 2.08-2.09 2.05 2.02-2.03 - 1.80 1.76-1.77 1.68-1.69 1.58 1.43 1.23 1.26-1.27 1.16-1.17 1.15-1.16 1.07- 1.08 1.04 0.993 100 10 30 5 40 - - 10 10 40 20 5 10 20 20 10 < 5 5 < 5 - - - - - 2.027 - - - - - - 1.433 - - 1.170 - - 1.013 0.906 0.827 - 3.35 2.13 2.04 - - - - 1.80 1.675 1.541 - - - 1.230 - 1.154 - 1.014 0.991 0.888 - 100 50 50 - - - - 30 - - 2.08-2.10 - - - - 1.79-1.82 80 60 - - 90 90 30 80 - - 60 - 1.27-1.29 - 1.08- 1.10 1.08-1.10 0.89-0.9 1 - ~~ ~~ ~ ~ a Loose deposit examined by the Debye-Scherrer method, substrate by diffractometry ; y-Fe lines calculated for concentrations in the range 1-6 atom % carbon, respectively.A.M. EMSLEY A N D M. P. H I L L 23 to be the relevant solution limit in previous work.', The significance of this relationship will be discussed later.X-ray diffraction of the deposit (removed as a powder) and of the foil (with as much loose deposit removed as possible) has been carried out using the Debye-Scherrer and diffractometry methods, respectively. The data given in table 2 show evidence of graphite, a-Fe and y-Fe, and some weak lines that can be attributed to a carbide present in the foil, such as cementite (Fe,C). The y-Fe spacings are calculated from the unit-cell dimensions and the precise values are dependent on the concentration of carbon in so1ution.l6 The presence of y-Fe indicates that the cooling rate on switching-off power to the filament, typically 22-25 K s-l, has been sufficiently rapid to quench-in some high-temperature structure, and therefore the results provide tentative evidence for the presence of an iron carbide at temperatures above the Fe-C eutectoid.In separate high-temperature diffractometry experiments we have detected carbide lines. From X-ray measurements of the carbon interlayer spacing and using the Franklin correlation17 it is found that 8590% of the material has good graphitic order on the c-axis. Analysis of crystalline size in the a-axis has not been undertaken. DISCUSSION KINETICS The relationship in fig. 5 implies that a fixed number of reaction sites are created at each temperature, dependent on the concentration of carbon in solution. The logarithmic growth kinetics are shown below to arise directly from the loss of active sites or active area at the surface as the reaction proceeds. It is assumed that the decay of active sites follows an exponential law, i.e.N(t) = No exp - k, A W (1 1) where N(t) is the number of active sites at time t, No is the initial number of sites formed by the end of the induction period and k, is a constant. The overall rate of deposition is determined by the number of active sites available at any time t. Therefore w, = k, N(t). dt From eqn (1 1) and (12) we get exp kl(A W) d(A W) = st, No dt. Integrating between the limits 0 to AW and ti to t gives i.e. exp kl(A W) = k , k, No (15) If an arbitrary constant to is defined such that then eqn (1 5 ) can be simplified to give exp kl(A W) = k, k2 No(t + to).24 GROWTH OF CARBON ON IRON From eqn (16) and (1 7), taking logarithms, therefore Eqn (19) is identical to eqn ( 5 ) if k = l/kl.These constants give the value of the slope of the lines in fig. 3 and are independent of temperature. -3.35 -3.4c h A? 3 -3.45 c7 * c c-, v) c $ -3.x E 2 -3.55 iu u W - -3.60 -3.65 lo4 KIT 8 kJ mol-I. FIG. 6.-Temperature dependence of carbon depositing reaction rate constant, k , k,. AE = 66 The temperature dependence of k, gives the true activation energy of the deposition process. It can be derived from eqn (1 6) using the appropriate temperature-dependent values of No. From fig. 5 it can be seen that No = k,(aT+b) (20) where k,, a and b are constants, the latter two being obtained directly from the figure. From eqn (16) and (20) we have The constant k , converts AW,,, and temperature data from fig. 5 into numbers of sites, and its absolute value is not known.However, the true activation energy can be obtained by plotting log (k, k,) obtained from eqn (21) against l / T , as in fig. 6, which gives a value of 66 8 kJ mol-l. The calculation based on eqn (21) would give the same activation energy as that using eqn (10) if No were independent of temperature, which occurs only in theA. M. EMSLEY A N D M. P. H I L L - 25 eutectoid region of the Fe-C phase diagram, i.e. T = 996 or 101 1 K. The use of initial rates to derive an activation energy is only justified when there is insufficient information about the reaction mechanism. With a specimen in the form of a thin foil, the solution and initial surface deposition stages are separated in time because a homogeneous solid solution of carbon in the metal can be formed rapidly.With a thicker bulk specimen some deposition may occur at the surface before a saturated solution is formed in the centre, for example because easy diffusion paths have been blocked. In these circumstances a detailed analysis of the kinetics on the above scheme would be difficult as extra terms would be required to account for diffusion, precipitation and possible break-up of the metal structure in the surface zone. Therefore, only rate data taken at the earliest time that surface deposits were detectable could be used to make a meaningful comparison with the thin foil data. RATE-DETERMINING S T E P The kinetic analysis above does not allow the rate-determining step to be distin- guished. The activation energy of 66 kJ mol-1 is too low for carbon dissolution in y-Fe rate control, for which E = 190 kJ mo1-l.12 In the temperature range 1013-1 133 K the carbon solubility at the y-Fe (austenite) phase boundary is 3.9-4.4 atom% C , respectively.18 The activation energy for diffusion in y-Fe is a function of carbon content, and literature data19* 2o for this concentration range give values of 130-134 kJ mol-l, respectively.Enthalpies of solution for carbon in y-Fe of 40.6 kJ mol-l 21 and 44.7 kJ mol-1 22 have been reported, and therefore if either value is added to the activation energy of diffusion to obtain a calculated total energy change, then an activation energy of 170-179 kJ mol-l could have been observed. In situ SEM studies have shown that below the Fe-C eutectoid temperature (996 or 101 1 K) carbon precipitation is accompanied by reorganisation of the metal surface,23 and therefore it is probable that similar mass-transfer processes will occur above the eutectoid temperature, in which case self-diffusion of iron atoms could be rate-determining. However, surface self-diffusion and bulk self-diffusion in y-Fe have an activation energy in excess of 200 kJ mol-124 and of 280 kJ m ~ l - l , ~ ~ respectively.Therefore surface and bulk diffusion of iron atoms, as well as carbon dissolution and carbon diffusion through the bulk metal, can be eliminated as possible rate-determining steps. There are a few studies in the literature in which the kinetics of clearly identifiable single carbon morphologies have been measured. The rate of carbon filament growth on iron particles is reported to have an activation energy of 67.3 kJ mol-1 in the temperature range 925-1245 K, i.e.both below and above the eutectoid, rate control being attributed to bulk diffusion through the metal.3 This value is less than the activation energy for diffusion of carbon in a-Fe, i.e. 84-105 kJ mo1-1,20 or in y-Fe (see above). Although the same rate-controlling step may apply to both monticular and filamentary growth, there is no evidence that it is dependent on the diffusion of carbon through the bulk metal in the case of iron. An activation energy of 66.9 kJ mol-l has been reported for the growth of laminar carbon films above 653 K on nickel from butadiene and propene, and on iron from butadiene.2s The similarity of the activation energy for the development of different morphologies for a variety of gas-metal systems suggests that the same rate-controlling step may apply.This could be surface diffusion of carbon atoms or metal-carbon- hydrogen species on the metal as suggested previously,26 or mobility of catalytic metal species at the carbon-metal interface. High mobilities of metal particles on graphite surfaces have been observed in microscopic studies of graphite The correlation of the maximum island area of carbon formed at each temperature 28 2 FAR 126 G R O W T H OF CARBON ON I R O N with the amount of carbon in the saturated solution, fig. 5, implies that a fixed number of nucleation sites are created from the dissolved carbon. Dissolution of an evaporated carbon layer on nickel by high-temperature annealing followed by reprecipitation was also found to create sites for subsequent deposition from acetylene.29 The carbon that is precipitated in the monticular growths prevents further gas attack of the metal in these areas.The lateral growth of the carbon mounds ceases before the metal surface is fully covered. Subsequent reaction occurs between the mounds, a particulate type of carbon deposit being f ~ r m e d . ~ Part of this work was carried out as a Ph.D. programme (A.M.E.) with the University of Edinburgh. We thank Prof. C. Kemball for his assistance in making the arrangement, and Dr D. Taylor for helpful discussions. The work was carried out at the Central Electricity Research Laboratories and is published by permission of the Central Electricity Generating Board.A. M. Brown, A. M. Emsley and M. P. Hill, in Gas Chemistry in Nuclear Reactors and Large Industrial Plant, ed. A. Dyer (Heydon, London 1980), p. 26. S. D. Robertson, Carbon, 1970, 3, 365; 1972, 10, 221. R. T. K. Baker, P. S. Harris, R. B. Thomas and R. J. Waite, J. Catal., 1973, 30, 86. A. M. Emsley and M. P. Hill, Carbon, 1977, 15, 205. A. M. Brown and M. P. Hill, Proc. 3rd Int. Carbon Con$ (Deutschen Keramischen Gesellschaft, Baden-Baden, 1980), p. 21. G. Blau and A. E. B. Presland, 3rd Con$ on Industrial Carbon and Graphites (Society of Chemical Industry, London 1970). R. T. K. Baker, P. S. Harris, J. Henderson and R. B. Thomas, Carbon, 1975, 13, 17. F. J. Derbyshire, A. E. B. Presland and- D. L. Trimm, Carbon, 1975, 13, 189. S. M. Irving and P.L. Walker Jr, Carbon, 1967, 5, 399. lo T. Baird, Carbon, 1977, 15, 379. l 1 R. T. K. Baker, Chemistry and Physics of Carbon, ed. P. L. Walker Jr and P. A. Thrower (Marcel l 2 A. M. Emsley and M. P. Hill, J. Chem. Soc., Faraday Trans. 1 , 1983, 79, 1. l 3 Handbook of Chemistryand Physics, ed. C. R. Weast (G.R.C. Press, Cleveland, Ohio, 59th edn, 1978-9), l4 U. R. Evans, The Corrosion and Oxidation of Metals (Arnold, London, 1960). l5 K. R. Lawless, Rep. Prog. Phys., 1974, 37, 231. l 6 A. Taylor, X-ray Metallography (Wiley, New York, 1961), p. 524. l 7 R. E. Franklin, Acta Crystallogr., 1951, 4, 253. H. Goldschmidt, Interstitial Alloys (Butterworths, London, 1967). lo C. Wells, W. Baty and R. F. Mehl, Trans. AIME, 1950, 188, 553. 2o J. D. Fast, Interaction of Metals and Gases (Macmillan, London, 1971), vol. 2. *l J. A. Lob0 and G. H. Geiger, Metall. Trans., 1976, 7A, 1359. 22 J. Chipman, Trans. Metall. SOC. AIME, 1967, 239. 23 A. M. Brown and M. P. Hill, Carbon, 1981, 19, 51. 24 G. Neumann and G. M. Neumann, Surface Self-Diflusion of Metals, Diflusion Monograph Ser. No. 25 Handbook of Chemistry andPhysics, ed. C. R. Weast (C.R.C. Press, Cleveland, Ohio, 59thedn, 1978-9), 26 T. Baird, in Gas Chemistry in Nuclear Reactors and Large Industrial Plant, ed. A. Dyer (Heydon, z7 J. M. Thomas, in Chemistry and Physics of Carbon, ed. P. L. Walker Jr (Dekker, New York, 1965), 28 G. R. Hennig, in Chemistry and Physics of Carbon, ed. P. L. Walker Jr (Marcel Dekker, New York, 29 C. Bernard0 and L. S. Lobo, Carbon, 1976, 14, 287. Dekker, New York, 1978), vol. 14, p. 83. p. E364. I (Diffusion Information Centre, Solothurn, Switzerland). p. F65. London, 1980), p. 35. vol. 1, p. 121. 1966), vol. 2, p. 1. (PAPER 1 / 1 502)

ISSN:0300-9599    

DOI:10.1039/F19837900015

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I, 1983, 79, 27-37 Structural Relationships in the Low-temperature Evolution of V,O,-MOO, Catalysts BY MIECZYSLAWA NAJBAR* AND KATARZYNA STADNICKA Institute of Chemistry, Jagiellonian University, 30-060 Cracow, Karasia 3, Poland Received 12th October, 1981 The stability of V,O,-MOO, catalysts containing up to 53 mol% MOO, has been investigated with electrical conductivity measurements and X-ray powder diffraction. The samples were obtained by the fusion of oxides and stored in an oxygen-free atmosphere. Subsequently their stability at room temperature was determined in air. It was found that in an oxygen-free atmosphere epitaxial layers of V,MoO, intermediate phase are formed on the best developed MoO,/V,O, solid solution surface (001). The orientation of the epitaxial layer with respect to (001) depends on the chemical composition of the catalyst and also determines the stability of this catalyst at room temperature in air.Vanadia-molybdena catalysts are widely used for the selective oxidation of hydrocarbons, e.g. for the oxidation of benzene to maleic anhydride. In the course of such reactions the chemical and phase composition of the catalyst may be changed by the action of reducing and oxidizing agents present in the reacting gases. Fresh V205-MOO3 catalysts, used in industry for the selective oxidation of benzene, contain mainly two phases:'* a solid solution of MOO, in V20, and an intermediate compound, V,MOO,,~ for which a well determined crystal structure is known,4 or possibly V,MO,O,,.~ In both phases segregation of the elements occurs during redox processes performed at 723 K5-' This segregation, if strong enough, is accompanied by the formation of new pha~es.~-lO Grussenmeyerll observed significant changes in the phase composition of V205-MoO3 catalysts over a 10 year storage period at room temperature. Those catalysts, however, were obtained by thermal decomposition of molybdates. The present paper concerns catalysts obtained by the fusion of oxides. Crystals of such catalysts contain less defects than those of catalysts obtained by the decomposition of molybdates.Therefore, we hoped to be able to explain the role of the grain crystal structure in the evolution of catalysts during storage. This information is important for a discussion of the behaviour of real catalysts under different usage and storage conditions.The investigations were performed by a.c. electrical resistance measurements and by X-ray powder diffraction. EXPERIMENTAL The following compositions were used: (1) V,05; (2) 10 mol% MOO, - 90 mol% V205; (3) 20 mol % MOO, - 80 mol% V205 ; (4) 30 mol % MOO, - 70 mol % V,O, ; (5) 40 mol % MOO, - 60 mol% V205; (6) 53.4 mol% MOO, - 46.6 mol% V,O,. The catalysts were prepared as in ref. (12) by the fusion of an appropriate mixture of analytically pure oxides. X-ray analysis of these pure oxides showed only the presence of V205 or MOO,, both orthorhombic phases. The mixtures were heated at 973 K for 2 h and subsequently slowly cooled (80 "C h-l). The 0.06-0.08 mm sieve fraction of the powdered samples was used for the X-ray diffraction and electrical resistance measurements.27 2-228 STRUCTURAL RELATIONSHIPS I N CATALYSTS Electrical resistance measurements were first performed on samples stored for several months in nitrogen (in order to avoid their oxidation) and then on the same samples stored additionally in air at room temperature for two years. The powdered samples were prepared in the form of pellets under 6.9 x lo9 Pa pressure, with two parallel platinum-wire electrodes inserted (3 mm apart). The measurements were carried out at 293 K in the frequency range 1 x 102-3 x lo7 Hz. An RC bridge was used in the range 1 x 102-1 x lo5 and a Tesla dissipation factor meter, type BM-27, in the range 1 x lo5-3 x lo7 Hz. To explain the changes in the electrical resistance of the samples during their storage in air it was necessary to determine the modification of the phase composition under the influence of redox processes.For X-ray powder diffraction, freshly prepared, oxidized and reduced samples containing 10 and 30 mol% MOO, were chosen. Oxidation was performed in air at 433 K for 16 h. Partial decomposition was carried out at the same temperature (in vacuum or carefully purified nitrogen) for 16 h and reduction was at 523 K in benzene vapour at a pressure of 2 x lo3 Pa for 1.5 h. A Dron-1 powder diffractometer with copper-filtered (Ni) radiation (A = 1.5418 A) was used for the freshly prepared, oxidized and reduced samples. RESULTS The electrical properties of pressed powders of semiconductors may be explained by a mode113+ l4 consisting of highly conducting grains separated by poorly conducting contacts, as shown in the upper left-hand corner of fig.1. The equivalent network is shown in the upper right-hand corner of fig. 1. C,, R, and Cb, R, denote the capacitance and resistance of the contact and the grains, respectively. Analysis of the equivalent network gives the dependence of the effective resistance, Reff, on frequency, as illustrated by the curve in fig. 1.14 As can be seen, at relatively low frequency the value of the effective resistance does not depend on frequency and is the sum of the contact and grain resistances, Reff = R, + R,. Thus, for further discussion, we consider this range of frequency. Examples of the dependence of the effective frequency FIG, 1 .-Frequency dependence of effective resistance, assuming high contact resistance and capacitance.M.NAJBAR A N D K. STADNICKA 29 B I I I I I I 1 2 3 4 5 6 7 c log v FIG. 2.-Frequency dependence of effective resistances for V,O, samples stored only in nitrogen (A) and stored in nitrogen followed by air (B). 16 Li "e 12 s Qz + V 1 v) h $ 8 ' 6 4 2 V \ 12- I I I I 1 10 20 30 40 50 mol 5% MOO, FIG. 3.-(a) Dependence of the effective resistance, Reff = R, + R,, on the composition of F and S samples (see text). (h) The ratio of the effective resistances as a function of catalyst composition.30 STRUCTURAL RELATIONSHIPS I N CATALYSTS resistance, Iteff, on the frequency for V,O, samples are shown in fig. 2. For curves (A) and (B) there is a range of frequency which gives constant values for the effective resistance.A similar dependence of Reff on frequency was observed for all the samples investigated. The effective resistance, Reff = R, + Rb, as a function of catalyst composition is given in fig. 3 (a) (where F denotes samples stored only in nitrogen and S denotes samples stored at first in nitrogen and then in air). A plot of the ratio of the effective resistances, defined as (R, + &)s/(& + Rb),, against catalyst composition is shown in fig. 3(b). The changes in the electrical conductivity of samples 4-6 are negligible compared with those in samples 1-3. It was found that sample 4, which contains a solid solution of MOO, in V,O, together with an intermediate phase (i.p.) in a ratio close to that given in published phase diagrams,159 l6 behaved quite differently from samples 2 and 3, which contain mainly the solid-solution phase. In fig.4 the X-ray diffraction pattern is shown for the freshly prepared sample 4 [fig. 4(a)] and for the same sample after storage for several months in nitrogen and then in air for two years [fig. 4(b)]. It is clear that the relative intensities of i.p. reflections in fig. 4(a) differ significantly from those in fig. 4(b). As no changes in the electrical resistance were observed after additional storage in air it seems that these differences in intensities result from some transformation in the sample during its storage in nitrogen, rather than in air. Note that the interplanar distances of the intermediate phase present in our samples agree quite well with those of the V,MoO, compound3 as well as with some of those of V9M06040.1 On the other hand, the sequence of intensities is different from that given in the literature for both VZMoO, and V,MO~O,~.For the sake of further B P U I 0 ? I l l ? I ir 19 8 FIG. 4.-X-ray powder diffraction patterns of 30 mol% MOO, - 70 mol% V,O, catalyst: (a) freshly prepared and (b) after several months storage in nitrogen and two years storage in air; 0 denotes i.p.M. NAJBAR A N D K. STADNICKA 31 discussion we shall assume the presence of V,MoO,. To determine the nature of the transformations in the V20,-MOO, catalysts X-ray powder diffraction patterns were obtained for samples 2 and 4, freshly prepared, oxidized and reduced in the way described above and also for those stored in nitrogen and in air.The most interesting results are presented in table 1. TABLE CHANGES IN THE CONTENT OF I.P. IN V205-MOO, CATALYSTS CONTAINING 10 AND 30 mol% MOO, DURING THE REDOX PROCESSES 90 mol% V,05- 70 mol% V,O,- catalyst 10 mol% MOO, 30 mol% MOO, rl = I KO0 1) V,O,l/I [(200) V205l f tr,t. ‘433 K r523 K O433 K r2 = I [(OOl) i.p.]/Z [(OOl) V,O,] f b . t . 0 4 3 3 K r433 K r523 K r3 = I [(600) i.p.J/Z [(OOl) V,05] f %.t. r433 K r523 K O433 K 4.53 (7) 12.64 (4) 4.61 (5) 6.10 (9) 2.66 (2) 0.000 0.607 (4) 0.076 (2) 0.089 (2) 0.097 (2) 0.026 (3) 0.017 (2) 0.019 (2) 0.029 (2) 0.021 (2) 4.66 (6) 1.86 (1) 1.79 (1) 2.69 (2) 0.794 (4) 1.018 (4) 1.079 (4) 0.872 (4) 0.263 (3) 0.453 (3) - - 0.517 (3) 0.328 (3) f, catalyst freshly prepared; r433K, catalyst partially decomposed in vacuum or in nitrogen at 433 K; r523K, catalyst reduced at 523 K in benzene vapour (2.1 x lo3 Pa); 0433K, catalyst heated at 433 K in air; tr.t., catalyst stored at room temperature in nitrogen for several months and then in air for two years.To exclude transformations induced by the redox treatment in pure V205, X-ray diffraction diagrams for the fresh, oxidized and reduced samples of V205 were obtained and these are shown in fig. 5. Some new reflections can be seen in each pattern. For the fresh V205 sample there are additional reflections with dhkl of 5.86, 4.30, 3.30, 2.103 and 2.065 A. In the sample stored for a few months in N, and t’len for two years in air, there are additional reflections with dhkl of 4.24,2.96 and 2.062 A.For the sample which was partially decomposed at 423 K in vacuum there are extra reflections with dhkl of 5.86, 4.01, 3.78 and 3.31 A. DISCUSSION We discuss first the possible changes occurring in powdered V205 samples during oxidation and reduction. The increase in the elect--ical resistance of the V,O, sample stored in air (fig. 3) may be explained by a decrease in the number of V4+ ions, which act as electrical current carriers, during the oxidation process. The extra reflections were observed in the fresh V,05 sample as well as in the sample stored in nitrogen and then in air and also in the sample reduced in vacuum at 433 K. The only explanation for such reflections is the formation of vanadium suboxide layers with32 STRUCTURAL RELATIONSHIPS IN CATALYSTS L L FIG.5.-X-ray powder diffraction patterns of V,O, catalyst: ((I) freshly prepared, (h) after several months storage in N, and two years storage in air and (c) after partial decomposition at 433 K in vacuum; the extra reflections are marked by circles. interplanar distances of ca. 4 A corresponding to the (001) V205 ~lanel’-~, (V,O, indices refer to those given in the powder diffraction file).20 This can be ascribed to the creation of the suboxides by a shear process in the structure of V205 along the [ 1031 22 Note that the reflections of vanadium suboxides were not observed in the samples containing MOO,. In MoO,/V,O, solid solutions, where the intermediate phase, i.p., also occurs, a good crystallographic fit can be seen between the (OOl), (010) and (100) planes of these two phases (fig.5). An estimation of lattice misfit between V20, and V2Mo0, by the method of Courtinel’+ 23 is given in table 2. This misfit is not significant and indicates, according to Ubbelohde’s the formation of ‘hybrid’ crystals without misfit dislocations. Such a concept is commonly accepted in studies of epitaxial growthz5 and extended defects in oxides.26 Because of the good crystallographic fit between (001) planes of both phases, formation of epitaxial layers of i.p. on the (001) face of Vz05 is expected. The formation of precipitates of one phase in the matrix of another could also be considered. ‘Hybrid’ crystals with a phase orientation of (100) i.p. II(O01)V,05, (010) i.p. Il(O10)V20, or (001) i.p. Il(100)V205 seem less likely because of the large lattice misfit (table 3), although their formation cannot be excluded. In discussing the mechanism of the possible phase transformations in the V205-MOO, system, the role of cation diffusion should be taken into account.The mobility of both cations is different because of their different electrical charges andTABLE 2.--LATTICE MISFIT BETWEEN v,05 AND V,MOO,, ESTIMATED ON THE ASSUMPTION THAT (lOO)V,O, /I( lOO)V,MOO,, (O10)V,05 //(OlO)V,MoO, AND (OOl)V,O,/I (001)V,MoO, - a, = 1.43 - - 16.77 ax = 122 - - 6, = 3.559 C, = 4.371 - 15.56 - b, = 3.61 C, = 4.12 - 14.87 - a, = - 5.74 y(,,,) = -4.43 V,O,( 100) V2Mo0,(0 10) a, = 3.884 - c1 = 4.12 - __ 16.00 az = -5.74 E(O,rJ, = -4.59 a, = 3.837 b, = 3.559 13.66 - - a, = 1.22 V,Mo0,(001) a, = 3.884 6 , = 3.61 __ 14.02 - - a, = 1.43 Ti(ool) = 2.64 V2Mo0,( 100) - - a, = 3.837 (3, = 4.371 v2°5(01 O) - - v2°5(00 ) a Dimensions of coordinating octahedra: a,, b,, c,, dimensions of VO, in the directions of thex,y, zaxesZo inV,O,; a,, b,, el, averagedimensions Relative lattice misfits: a, = 100(a, --uO)/uO, a, = 100(b, -b,)/b,, of MeO, (Me =V, Mo) in the directions of the x, y, z axes in V,MOO,.~ a, = 1OO(c, -co)/co, = 100(b,c, - b,c,)/b,q,, ~(,,,) = 100(a,c, -~,~,)/~,~,, Tl(,,,) = 100(a,~, - ~,~,)/~,~,.a, = 3.837 b, = 3.559 - 13.66 - - a, = 7.38 71[(O01)V20,/(100) i.p.1 = 8.86 - 14.87 - - a, = 1.43 v2°5(001 VzMoO,(lOO) U , = ~ i . ~ . = 4.12 b, = 3.61 U, = 3.837 - c,, = 4.371 - - 16.77 a, = 7.38 ~[(O10)acV20,/(O10)cai.p.] = -4.59 VzOJOl0)ac VZMoO8(010)ca U , = ci.p.= 4.12 - cI = ai.p. = 3.883 - - 16.00 a, = 11.16 - b, = 3.559 C, = 4.371 - 15.56 - a, = 1.43 ~[(lOO)VzO,/(OOl) i.p.1 = -9.90 - 6 , = 3.61 c, = ai.p. = 3.883 - 14.02 - a, = 11.16 'Z05( O0> V2M00,(001) a Crystallographic fit between (010) planes of both phases occurs as a result of the fitting of the MeO, octahedra of V20, joined in the direction of the x-axis 71[(001)V20,/( 100) i.p.1 = 100(u,b, -a,b,)/a,b,, ~[(OlO)a,V,O,/(OlO),a i.p.1 = 100(a,c, -u,c,)/a,c,, with those of i.p. joined in the direction of the z-axis. T[[( l00)V,O5/(0Ol) i.p.1 = 100(b,c, - bOcO)/bOcU.34 STRUCTURAL RELATIONSHIPS IN CATALYSTS different ionic radii. Therefore, we observe segregation of the elements as a result of the faster diffusion of The crystal structure of V,05 reveals the most possible cation diffusion paths.In the V,05 structure interstitial cavities with a diameter of ca. 2.2 A exist in the 0, i, and f, 0 1 positions. These cavities are linked by narrow windows of dimensions ca. 1.4 x 0.8 along the directions [OOI] and [OIO]. The diameter of the interstitial positions is much larger than the diameter of the Mo6+ (1.24 A) and V5+ (1.18 A) ions. If the Mo6+ or V5+ ions jump to an interstitial position, they can do so either directly through these windows or indirectly by a concerted movement through neighbouring cation positions (interstitial cation diffusion). The fact that easy cation diffusion paths are perpendicular to the most developed crystal face (001) (cleavage plane) suggests that reduction accompanied by the inward diffusion of cations as well as oxidation accompanied by the outward diffusion of cations occur mainly on the (001) face.These redox processes lead to the formation of i.p. layers with the orientation with respect to (001) plane of V,05 shown in fig. 6(a) and (6) and fig. 7. During the oxidation of partially reduced plate-like crystallites, the (100) face should develop more than the (001) and (010) faces. This should result in the crystal shape becoming less flat. On the other hand, during re- duction one expects the plates to become thinner. The shape of the crystallites gives rise to a preferred orientation in the powdered samples used for the X-ray measure- b a -- b FIG. 6.-Examples ofcrystallographic fit between (001) i.p. and (001) V,O,, (a) and (6); (100) i.p.and (100) V,O,, (c) and ( d ) ; (010) i.p. and (010) V,O,, (e) and (f).M. NAJBAR A N D K. STADNICKA a r------ 35 a - C (a 1 FIG. 7.-Crystallographic matching between (100) i.p. and (001) V,O,. ments. The ratio of the intensities of the (001) and (200) reflections of V205, rl = 1[(001)V205]/1[(200)V205], was considered suitable for the description of the texture. The ratios r2 = 1[(O01)i.p.]/1[(O01)V205] and r3 = 1[(600)i.p.]/1[(OOl)V205J were introduced as a measure of the amount of i.p. r2 corresponds to the assumption that the (001) plane of the i.p. fits the (001) plane of V205 while r3 refers to the fit of the (100) plane of the i.p. and the (001) plane of V205 [here, the intensity of the (600) reflection was the strongest]. We now discuss our experimental results from the powdered samples of V205-MOO, catalysts in the light of the above.10 mol% Moo3-90 mol% V205 The large increase in a.c. resistance for powder stored in air indicates evolution of the catalyst. The values of r1 found from the diffraction patterns for a fresh sample of pure V205 (4.76) and for a fresh sample containing 10 mol% MOO, (4.53) indicate the same shape of crystals in both cases. The increase of rl during reduction to 6.1 and its decrease during oxidation to 2.66 may be explained by the changes in the texture of the sample caused by the cation diffusion in the [00 11 and [0 101 directions, as discussed above. Lack of vanadium suboxide phases in the vanadia-molybdena samples shows that the presence of molybdenum prevents the redox processes leading to the formation of vanadium suboxides. The appearance of (001) reflections of i.p.in the samples reduced and oxidized (apart from some very weak lines observed in the fresh sample) suggests the possibility of the formation of the V2Mo08 phase with its (001) plane parallel to (001) of V205 (table 1). As can be seen from table 1, the texture does not lead to the observed increase in the value of r2 for the oxidized and reduced sample. The fact that the sample stored previously in nitrogen is easily oxidized indicates that the layer of i.p. does not prevent further cation diffusion through the large interstitial cavities joined together along the [00 11 direction, which occur also in the structure of V2Mo08. 30 mol% MOO, - 70 mol% V205 To explain the lack of changes in a.c.resistance for the sample stored in air, powder diagrams of freshly prepared, oxidized and reduced samples must be considered. The decrease in rl after redox treatments (both oxidation and reduction) may be caused by the presence in the sample of two kinds of crystals: Mo03/V20, solid solution and the intermediate phase. Crystals of the solid solution are similar to those of V205 (rl is 4.66 for the solid solution and 4.76 for V205). Crystals of i.p. are less flat than those of V205, as expected from the differences in metal-oxygen bond lengths and confirmed36 STRUCTURAL RELATIONSHIPS IN CATALYSTS by observation in a transmission electron microscope. According to ref. (6) the redox processes in the i.p. crystals are accompanied by cation segregation as in the MOO,/V,O5 solid solution.This segregation results in the formation of some additional V205 phase, either on the surface (oxidation) or inside the crystals (reduction). Therefore both oxidation and reduction are accompanied by a decrease in the texture of the V205 crystals as determined by the rl ratio. We now discuss the changes in r2 and r3 during the redox processes. As can be seen from the data given in table 1 the reduction results in an increase of both r2 and r3 ratios. Similar changes are observed after oxidation of the sample. The differences in the texture of the sample (described by rl) cannot explain the significant changes in r2 and r3 caused by redox processes. The formation of an additional V205 phase in the i.p. crystals should lead to a decrease of r2 and r3.The observed increase of these ratios indicates the formation of a new portion of i.p. ‘in the solid - solution crystals with both possible orientations in relation to the (001) plane. The lack of change in the a.c. resistance of the sample during its storage in air may be due to previous formation of the layers, which block the easy diffusion paths on the surface of crystals of both Mo0,/V205 solid solution and i.p. When layers of i.p. are formed with (100) parallel to (001) of V205 they block the diffusion paths in the solid-solution crystals. As seen in fig. 4, the electrical resistance of pure i.p. stored previously in nitrogen also does not change during additional storage in air. This suggests that the paths for easy diffusion are blocked by layers enriched in Mo formed during the reduction as a result of cation segregation.The mechanism of blocking will be discussed in detail elsewhere. CONCLUSION The cation segregation induced by redox processes in the V205-MoO3 system5+ indicates that cation diffusion plays an important role in the evolution of vanadia- molybdena catalysts. A consideration of the V205 and i.p. structures has led us to the conclusion that interstitial diffusion along channels in the [OOl] and [OlO] directions is the most probable mechanism for cation diffusion in V&-MoO, catalysts. From a comparison of the V205 and i.p. structures we found the crystallographic fit between (001) planes of both phases and between the (001) plane of V205 and the (100) plane of the i.p.to give ‘hybrid’ crystals. During reduction, a layer of i.p. forms on the crystal surface of the Mo03/V@5 solid solution with an orientation, with respect to (001) of V,05, depending on the Mo concentration. In the sample containing 10mol% MOO,, the (001) plane of i.p. is parallel to the (001) V2O5 plane and this i.p. layer does not prevent further redox processes, as the interstitial diffusion channels in the i.p. structure run in the same direction as in V205. During the reduction, layers enriched in molybdenum appear on the surface of the i.p. and block the cation diffusion. The sample with 30 mol% MOO, is composed of MoO3/V205 solid solution and i.p. The orientations of i.p. formed on the solid-solution grains during the reduction may be described by the relations: (100) i.p.Il(OO1) V205 and (001) i.p. 11(001) V205. The formation of i.p. with its (100) plane parallel to (001) of V205 in the surface layer of solid-solution crystals prevents further redox processes connected with cation diffusion. Therefore, the sample does not change during storage in air. The formation of layers blocking cation diffusion in grains during selective benzene oxidation prevents fast deterioration caused by the formation of volatile molybdenum oxides. In fact, some catalyst reduction has been observed in industrial reactors. 27 We thank Professor A. Bielanski for his comments on the manuscript.M. NAJBAR A N D K. STADNICKA 37 R. Munch and E. Pierron, J. Catal., 1964, 3, 406. M. Najbar, E. Bielanska and W.Wal, to be published. A. Magneli and B. Blomberg, Acta Chem. Scand., 1951, 5, 585. H. A. Eick and L. Kihlborg, Acta Chem. Scand., 1966, 20, 1658. A. Bielanski, J. Camra and M. Najbar, J. Catal., 1979, 57, 326. M. Najbar and S. Niziol, J. Solid State Chem., 1978, 26, 339. M. Najbar, E. Bielanska, J. Camra and S. Niziol, Proc. VI Int. Symp. Heterogeneous Catalysts, 1979, 1, 445. E. Bielanska, M. tagan and M. Najbar, Proc. 2nd Int. Conf. Applied Electron Microscopy. Zakopane, 1978, p. 2. M. Najbar and E. Bielanska, Proc. 9th In[. Symp. Solid State Reactors, Krakow, 1980, p. 465. J. Grussenmeyer, Thesis (UniversitC Claude Bernard, Lyon, 1978). 507. lo M. Najbar, E. Bielanska and S. Niziol, to be published. l 2 A. Bielanski, K. Dyrek, J. Poiniczek and E. Wenda, Bull. Acad. Pol. Sci., Ser. Sci. Chim., 1971, 19, l3 C. G. Koops, Phys. Rezi., 1951, 83, 121. l4 C. M. Huggm and A. H. Sharbaugh, J. Chem. Phys., 1963, 38, 2. l 5 T. Ekstrom and M. Nygren, Acta Chem. Scand., 1972, 26, 1827. A. Bielanski and M. Najbar, Pol. J. Chem., 1978, 52, 883. A. Vejux and P. Courtine, J . Solid State Chem., 1978, 23, 93. A. Magneli, B. Oughton, Acta Chem. Scand., 1951, 5, 581. H. G. Bachman, F. R. Ahmed and W. Barnes, Z. Crystallogr., 1961, 117, 1 10. vania) 19 103, 9-387. M. N. Colpeart, P. Claws, L. Firmans and J. Vennik, Surf. Sci., 1973, 36, 513. 20 Powder Diflraction File (Joint Committee on Powder Diffraction Standards, Philadelphia, Pennsyl- 22 R. J. D. Tilley and B. G. Hyde, J . Phys. Chem. Solids, 1970, 31, 1613. 23 J. G. Eon and P. Courtine, J. Solid State Chem., 1980, 32, 67. 24 A. R. Ubbelohde, Trans. Faraday Soc., 1937, 33, 1198. 25 K. L. Chopra, in Thin Film Phenomena (McGraw-Hill, New York, 1969), pp. 191 and 238. 26 S. Amelinckx and J. van Laduyt, in The Chemistry of Extended Defects in Non-metallic Solids, ed. 27 A. Bielanski, M. Najbar, J. Crzaszcz and W. Wal, Studies in Surface Science and Catalysis, ed. B. L. R. Eyring and M. O’Keeffe (North-Holland, Amsterdam, 1970), p. 295. Delmon and G. F. Fromet (Elsevier, Amsterdam, 1980), vol. 6, p. 127. (PAPER 1 / 1 588)

ISSN:0300-9599    

DOI:10.1039/F19837900027

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I, 1983, 79, 39-54 Some Statements Concerning Oscillatory Phenomena BY FRANCESCA D’ALBA*Y Istituto di Ingegneria Chimica, Viale delle Scienze, 90 100 Palermo, Italy AND SERGIO Dr LORENZO Istituto Tecnico Industriale, 24030 Vercurago (Bg), Italy and Istituto Tecnico Commerciale, Piazza Lussana, 24 100 Bergamo, Italy Received 14th October, 198 1 This work attempts to provide a new theoretical model for oscillating chemical systems based on phase exchange and pulsating supersaturation. Phase exchange is of two types: one is steady exchange from the solution to the gas above it while the other is pulsating exchange between nucleations of bubbles of gas and the solution. The pulsating supersaturation allows nucleations of bubbles to form and oscillations to take place.We consider several variables, viz. temperature, bulk reaction, volume and size of the reactor, rate of stirring and pressure, and study their influence on the oscillations. The theoretical results are compared with some experimental results that can be explained by our new model. The systems considered are the oxidation of the malonic acid by bromate or iodate with cerium as catalyst and the oxidation of oxalic acid and formic acid. INTRODUCTION The cerium sulphate + malonic acid + potassium bromate + sulphuric acid system is the most useful one for studying oscillating chemical systems, as the concentrations of the following elements oscillate with time: Ce3+, Ce4+, BrO;, Br- and Br2.1-17 This system was studied theoretically by Field et ~ l ., l - ~ who proposed a model, the F.K.N. model, based on pure chemical kinetics to explain such behaviour. They supposed that the concentration of Br- determines which of the following processes occurs : process A Br- + BrO; + 2H+ -+ HBrO, + HOBr Br- + HBrO, + H+ -+ 2HOBr [Br- + HOBr + H+ -+ Br, + H,O] x 3 (1) (2) (3) [Br, + CH,(COOH), -+ BrCH(COOH), + Br-+ H’] x 3 (4) 2Br-+ BrO; + 3H+ + 3CH,(COOH), + 3BrCH(COOH), + 3H,O ( 5 ) t Present address: Via Thaon di Revel 64, 90142 Palermo, Italy. 3940 OSCILLATORY PHENOMENA process B (BrO; + HBrO, + H+ --+ 2BrO;J + H,O) x 2 (Ce3+ + BrO; + H+ --+ Ce4+ + HBrO,) x 4 (6) (7) (2Ce3+ + BrO; + 3H+ -+ 2Ce4+ + H,O + HBrO,) x 2 (8) (9) (10) (1 1) 2HBr0, -+ HOBr + BrO; + H+ Br- + HOBr + H+ --+ Br, + H,O Br, + CH,(COOH), --+ BrCH(COOH), + H+ + Br- BrO; +4Ce3+ + CH,(COOH), + 5H+ --+ 4Ce4+ + BrCH(COOH), + 3H,O. (12) In process A reaction (1) is the rate-determining step.In process B reaction (6) is the rate-determining step and reaction (9) stabilizes the concentration of HBrO, and hence controls reaction (6). Ce4+ produced by process B reacts according to reaction (13) or reaction (14), producing Br- by the latter: (13) 6Ce4+ + CH,(COOH), + 2H,O -+ 6Ce3+ + HCOOH + 2C0, + 6H+ 4Ce4+ + BrCH(COOH), + 2H,O --+ 4Ce3+ + HCOOH + 2C0, + 5H+ + Br-. (14) Summarizing, when the concentration of Br- is high, reaction (1) and process A prevail and when the concentration of Br- is below a critical value, reaction (6) and process B prevail. The concentration of Br- is then restored by reaction (14) which hinders process B, and so on.Field and Noyes3 have presented a reduced version of the F.K.N. model, the ‘Oregonator ’, summarized in the steps A + Y - + X (15) X + Y - + P (16) B+X+2X+Z (17) 2X+Q Z - f Y where A = B = BrO;, X = HBrO,, Y = Br- and Z = Ce4+ The ‘ Oregonator ’ is the opposite of the ‘ Brusselator ’ :4-6 A - X 2X+Y -+ 3 x X -+ E. We do not agree with the application of the ‘Oregonator’ or the ‘Brusselator’ to the bromate +cerium + malonic acid + sulphuric acid system, and we will present a new theoretical model based on the liquid-gas phase exchange and on the oscillating supersaturation of the solution.F. D'ALBA AND s. D I LORENZO 41 Noszticzius and Bodiss7 studied the oxidation of oxalic acid by bromate with cerium as catalyst, and, although it was not their aim, they questioned the F.K.N.model. In their work they measured the pulsating concentrations of Br, and CO, in the gas over the solution, putting an end to the controversy of whether these systems are open or closed. This work also directed its attention to Br, as a fundamental element in the production of radicals able to oxidize Ce3+ to Ce4+. They proposed the following model : Reaction (24) is the overall reaction produced by the following reactions 2H+ + 2Br0; + 5(COOH), --+ 10C0, + Br, + 6H,O. BrOH + Br, -+ Br,O, + Br' Ce3+ + Br * -+ Ce4+ + Br- (H+ + Ce3+ + BrO' --+ Ce4+ + HOBr) x 2 Br- + H+ + HOBr -+ Br, + H,O (24) (25) Br,O, -+ 2Br0' (26) (27) (28) (29) Br, 3H+ + BrOi + 3Ce3+ -+ 3Ce4+ + HOBr + H,O 2HOBr + (COOH), -+ 2C0, + 2H,O + Br,.(30) (31) Br, accelerates the oxidation of Ce3+ according to reactions (27) and (28) by reactions (25) and (26) and depletes the original BrOS concentration at the same time due to the overall reaction (30). The generation of Br, causes a transitional acceleration of the process but after the loss of BrOi, generated by a step such as reaction (6), the process decelerates. The presence of Br, inhibits the autocatalytic regeneration of HBrO, according to reaction (7) owing to reaction (25). The physical removal of Br, allows the autocatalytic production of HBrO,, because some time is necessary to regenerate HOBr by reaction (30) or (9). The physical removal of Br, is not shown as it is not known in what manner it occurs and because a steady physical removal does not lead to a steady state.Some experimental results from this work are very interesting. The system oscillates if one bubbles in a gas (HJ. Correspondingly, a flow of CO, does not alter the phenomenon, whereas a flow of Br, does. Thus they concluded that the concentration of Br, is a key element. In the work of Showalter and Noyes8 on the oxidation of formic acid there are several elements that cause us to question the F.K.N. model. They studied the oxidation of formic acid in sulphuric acid according to the reaction (32) and noticed that an initial smooth rapid evolution of CO occurs. Regular oscillations then develop and persist for up to 30 min. When the solution is oscillating regularly, bursts of gas evolution take place a few times every minute.During a burst, the solution becomes milky with many small bubbles, and foams rapidly. After this burst of foam, the solution calms down for a quiescent period during which there is very slow evolution. The behaviour of this system is critically dependent upon the stirring conditions. In unstirred solutions bursts of gas evolution are erratic. In rapidly stirred solutions, gas is evolved smoothly. A minimum pressure was found which allows oscillations and the period of oscillations decreases smoothly if there is a reduction of pressure. HCOOH -+ CO(g) + H,0(1)42 OSCILLATORY PHENOMENA Roux and Rossi9 showed the importance of a particular phase exchange in the cerium + malonic acid + bromate + sulphuric acid system. They found that a flow of oxygen can alter the range of concentration of malonic acid that allows oscillations.They refer to the following reactions to determine the factorfin reaction (19) of the ' Oregonator ' 4Ce4+ + BrCH(COOH), + 2H,O -+ Br- + 4Ce3+ + HCOOH + 2C0, + 5H+ (1 4) 4Ce4++BrCH(COOH),+HOBr+H,0 -+ 2Br-+4Ce3++3C0,+6H+ (33) Ce4+ + CH,(COOH), + Ce3+ + 'CH(COOH), + H+ 'CBr(COOH), + H,O -+ Br-+ H+ + 'COH(COOH),. (34) (36) Reactions (14) and (33) give a value 0.25 < f < 0.50, but reaction (34) is faster and can give the chain reactions (35) and (36) that lead t o f = 1 . If oxygen is present it is possible to have which interrupts the chain reactions (34)-(36) and decreases the value o f f and of the concentration of Br-. Because the concentration of Br- is a key element for the oscillations in the 'Oregonator', Roux and Rossi deduced a mechanism that can explain how a flow of oxygen puts an end to oscillations in a system which has a concentration of malonic acid inside the range that allows oscillations but near to the lower limit, and allows oscillations in a system which has a concentration outside the range but near to its upper limit.Although we do not enter into the merits of the kinetics at this point, we think that the influence of phase exchange is very important. 'CH(COOH), + CHBr(COOH), -+ CH,(COOH), + 'CBr(COOH), (35) 'CH(COOH), +O, -+ 'OOCH(COOH), (37) OSCILLATORY MODEL BY PHASE EXCHANGE We now consider a beaker containing a magnetically stirred solution (most tests of these systems have been made in electrochemical cells like a beaker).The following irreversible chemical reaction takes place inside the solution : A (sol) -+ B (sol) (38) with kinetics given by -dA/dt = K , A. (39) (B may be made with reversible kinetics by chain and/or parallel reactions of various orders without it altering the physical chemistry of the model, but altering the mathematics only.) B is a gas at the temperature and the pressure of the reaction, hence a phase exchange occurs from the solution to the gas above it (40) For such a system, the kinetics of the phase exchange is expressed by the penetration (41) B (sol) + B (8). theory as IdN/dt (p.e. 1,1)1 = K , S(B- Be) where dN/dt(p.e. 1 , l ) (mol s-l) is the molar discharge of B from the solution to the gas, S(dm2) is the interface area, (B-BB,) (mol dm-3) is the driving force, the difference between B, the concentration of B inside the solution, and Be, the concentration of B inside the solution equilibrating with the gas and K , (dm3 s-l) is the exchange coefficient expressed by K , = 2(D/nt,,)4 (42)F.D’ALBA AND s. D I LORENZO 43 where D (dm2 s-l) is the diffusion coefficient of B in the solution and tS2 is the time spent by a single liquid particle on the exchange surface and depends upon the flow dynamics of the system. If the concentration of B in the gas over the solution is 0 (the gas is renewed continuously) and the flow from the solution to the gas is negative, we have -dN/dt (p.e. 1, 1) = K , SB. (43) The physical chemical system is expressed by the following mathematical system VdB/dt (overall) = VdB/dt (chem.) + dN/dt (p.e.I , 1) (44 a) dB/dt (chem.) = - dA/dt (44 b) -dA/dt = Kl A (39) -dN/dt (p.e. 1’1) = K, SB (43) (where V is the volume of the system) I I with the boundary conditions if The solution is t = to, A = A,, and B = B,. (45) B = [B, exp (K2 St,/ V ) - Kl A , V exp ( K , St,/ V- Kl to)/ This function increases until the value of t obtained at dB/dt = 0 t = (In { Kl A, Kz S exp [(K, S - Kl V ) to/ V ] - B, K2 S exp (K, St,/ V ) / V ) that gives B(max), the maximum value of B on substituting it in eqn (46). If B (max) is lower than the value of saturation B (sat), the former is obtained and B decreases. If B(max) > B(sat) the former cannot be obtained. The concentration of B increases until it reaches B(sat). The thermodynamics would prescribe that the system creates a new phase of pure B (g) as bubbles inside the solutions.Yet there is an obstacle to their nucleation : the vapour pressure of B in the solution must be equal to the pressure inside the bubbles, given by (K,S-Kl V)]exp(-K,St/V)+K,A, Vexp(-Klt)/(K2S-Kl V ) . (46) -1n [K: A, VIW, s- Kl VI)/W2 s/ V- Kl) (47) P2 = PI + W r (48) where p 2 is the pressure inside the bubbles, p1 is the external pressure, 0 is the surface tension of the solution and Y is the radius of the bubble. Because Y is infinitesimal at nucleation,^, is very high and the solution at saturation cannot be in equilibrium with the nucleating bubbles. Hence the concentration of B exceeds B (sat) and attains a value Bb such that the probability of a fluctuation around the equilibrium conditions (homogeneous concentration of B) able to give concentrations allowing the nucleation of some bubbles is significant and thus generalized nucleation is obtained. This probability is expressed by (49) P = exp { - AS/kB} where A S is the difference between the entropy related to the homogeneous concen- tration of B in the system and the entropy related to the concentration of B allowing equilibrium with the bubbles at nucleation and kB is Boltzmann’s constant.Obviously some nucleation is possible before reaching the concentration Bb and this can occur over a range of values of time that allow generalized nucleation because44 OSCILLATORY PHENOMENA the induction time is not reproducible.lOT1l In this work we omit these anomalous nucleations because they do not alter the system substantially.At the time of generalized nucleation the system eqn (44) modifies itself because eqn (44a) becomes VdB/dt (overall) = VdB/dt (chem.)+dN/dt (p.e. 1 , l ) +dN/dt (p.e. 2) (50) where dN/dt (p.e. 2) is the negative phase exchange by nucleation of bubbles from the solution to the gas, expressed by -dN/dt (p.e. 2) = no (mol) I/ (51) where no is the specific nucleation (number of bubbles generated per unit volume) and (mol) is the number of moles going into a bubble in the time, St, of the nucleation. We may have dB/dt (overall) 2 0. If dB/dt (overall) > 0 the concentration of B increases until the probability of nucleation attains a value so great that we have a value of no able to satisfy the condition dB/dt (overall) = 0.If dB/dt (overall) < 0 the concentration of B is less than that allowing significant nucleation and we have no new nucleation. Yet the presence of the bubbles alters the system, because, although new bubbles cannot grow, the bubbles can vary their mass and volume as r is no longer infinitesimal and the solution is saturated with respect to the bubbles. The physical chemical system is expressed by the following mathematical system VdB/dt (overall) = VdB/dt (chem.) + dN/dt(p.e. 1 , l ) + dN/dt (p.e. 1,2) dB/dt (chem.) = - dA/dt -dA/dt = Kl A -dN/dt (p.e. 1 , l ) = K , SB - dN/dt (p.e. 1,2) = K3 sb n V(B- B,) B2 = P2/H - dN/dt (p.e. 1,2) = n Vd (mol)/dt = (nV/RT) (4np1 r2 + 16nro/3) dr/dt r d(mU)/dt = 4nr3[p(L)-p(G)] k / 3 + 7 do r Jsb z = J U,dt n = no - no z / h with the boundaries conditions if t = to, A = A,; if t = t,, B = B,, U = 0, z = 0, r = r, where t, is the time in which there is nucleation of the bubbles, supposed to be instantaneous.Eqn (52 a) is the overall balance of the solution : eqn (52 b) is the negative phase exchange as transport from the solution to the bubbles, in which s b is the surface of a bubble, n is the number of bubbles per unit volume, B, is the concentration of B in the solution equilibrating with that in the bubbles, and K3 is the phase exchange coefficient expressed by the penetration theory in which ts3 is the time taken by a singleF. D'ALBA AND s. D I LORENZO 45 liquid particle to glide on the surface of a bubble and is related to the rate of stirring and to the ascensional velocity of the bubbles; eqn (52 c) is Henry's law to find B,; eqn (52d) is the negative phase exchange balance from the solution to the bubbles and becomes with some suitable substitutions - dN/dt (p.e. 1,2) = [n V(4np1 r2 + 16nar/3)/RT] dr/dt; (54) eqn (52e) is Newton's second law applied to the bubbles, in which d(rnU)/dt is the time derivative of the quantity of motion of a bubble; 4nr3"p(L)-p(G)]k is the Archimedes buoyancy in which p(L) is the density of the solution, p(G) is the density of the bubbles, k is the unit vector on the z axis and rdo is the friction force due to the ascensional motion of the bubbles and to the motion of the solution because of stirring.It is a vectorial equation and hence can be resolved into three scalar equations. The components along the x and y axes influence t,, only.The component along the z axis has two parts: the former, due to the Archimedes buoyancy, is upward, the latter, due to the stirring, is alternately upward and downward; on average its value is negligible with respect to the former with regard to influence on the motion but not with regard to influence on ts,. Also we neglect the spin of the bubbles because it influences tS3 only. Eqn ( 5 2 f ) is the space covered by a bubble in the time t-rt,; eqn (52g) is the number of bubbles present in the solution at time t and is related to no, the number of bubbles nucleated per unit volume, to h, the height of the solution, and to z , the space covered at the time t - th by a bubble. With suitable substitution and coupling of eqn (52b) and eqn (54), we obtain I, V/dB/dt (overall) = K, A , V exp ( -K, t ) -K2SB-4nK,r2nV[B-(p,$ 2a/r)/H] (55a) where P, is the molecular weight of B.This system is irresolvable. A numerical integration can be performed if we consider that a constant a number of bubbles, a,, disappear per unit time; eqn (52g) then becomes n = n,-a(t-tt,) (56) and the system eqn (55) reduces to eqn (52a), (52b) and (56) only. However, this numerical integration does not give useful results, hence it is better to perform the following simplifications: (1) we cmsider the exchange surface between the solution and the bubbles as being unchanged owing to the variation of the radius of the bubbles. (2) We consider B, constant in B, = [Bb - B (sat)]/ln [B,/B (sat)]. Hence the system becomes VdBldt(overal1) = K J , exp ( - K , t ) - K , S B - K , S b V[no-a(t-th)](B-B2) (57)46 OSCILLATORY PHENOMENA with the boundary condition if t = th, B = Bh.This equation has the solution B = exp (K3 s b at2/2 - [K2 s+ K3 S b V(no + at,)] t/ v} X const. [Ki A0 exp ( - K1 t) - K3 s b aB2 t - K3 S b (no + at,) B2] X exp { - K3 S b at2/2+ [K2 S+ K3 S b v(n0 + at,)] t/ V> dt (58) 1 ( S and the integral in eqn (58) is insoluble. Yet if we consider the theorem J:flt)dt = (b-a)f(z) we have B=exp {K3Sbat2/2-[K2S+K3Sb V(no+ath)]t/V} X (COnSt.+(t-th)[K1 A0 eXp (-Klz)-K3SbaB2z-K3Sb(n0+afh)B2] x eXp(-K3Sbaz2/2+IK,S+K3Sb V(no+ath)]z/V/) (59) and obtaining the value of the constant from the boundary conditions and substituting the value (t-th)/ln (t/th) for z, we have B = Bb eXp {K3S,a(t2-t~)/2-[K2S+K3Sb V(no+ath)](t-tfh)/V} x (t-th)+(t-fh)[Ki A , exp [-Ki(t-th)]/ln (t/fh)-K3SbaBz(t-th)/ln (f/th) - K3 Sb(nO + +[& S+K3 S b v(nO+ath)](t-th)/ln (t/th) v B21 exp - K3 sb a[(t - th)/ln (t/th)12/2 +K3Sbat2/2-[K2S+K3Sb V(no+ath)] t/v}.(60) Obviously this solution is not exact but it is a sufficient approximation to calculate the value of B. Eqn (60) may have two ranges of validity. One is t h < t < ti (61) where ti is the time of disappearance of the last bubble from the solution calculable no - a(ti - th) = 0 (62 a> by ti = no/a + t h (62 b) and the other is t, d d t h + l (63) where th+l is the value o f t higher than t h that, substituted in eqn (60), gives B = Bh. The ranges of validity are related to two different phenomena.In the former case because the bubbles are leaving the solution dBldt(overal1) is negative, but it is increasing. It is possible that it is negative until the last bubble leaves, but also it is possible it becomes positive because dN/dt (p.e. 1,2) is too small to maintain dB/dt(overall) negative. In both cases after the minimum the concentration of B increases and the phenomenon is repeated and the physical chemical system is governed by the systems (4:) --+ (50) + (57). (64) In the latter case dB/dt (overall) again becomes positive while many bubbles are in the solution and it is able to renew B, before the bubbles leave; and hence we have another nucleation before the last bubble leaves the solution and by turns the physical chemical system is governed by the system (44) + (50) + (57).uF. D’ALBA AND s. DI LORENZO 47 In this case eqn (50) changes to eqn (66) and eqn (57) changes to eqn (67) VdB/dt (overall) = VdB/dt (chem.) + dN/dt (p.e. 1 , l ) + dN/dt (p.e. 1,3) + dN/dt (p.e. 2) (66) VdB/dt (overall) = VdB/dt (chem.) + dN/dt (p.e. I , 1) + dN/dt (p.e. 1,3) (67) where dN/dt (p.e. 1’3) = K3 s b nV(B- B,) and n = X[noj-a(t-ti)] (t-nOj/a) < tj < th. (68) If we have kinetics as in eqn (39)’ the latter case must be followed by the former, because dB/dt (overall) is decreasing. Note that in the case of eqn (64) we have two cusps in a cycle, the former at the nucleation of the bubbles because the derivative of B is different on the left and on the right [the former is the derivative of eqn (46), the latter of eqn (60), if we suppose instantaneous nucleation], the latter at the disappearance of the bubbles because the derivative with respect to time is on the left the derivative of eqn (60) and on the right the derivative of eqn (46) [we suppose that the function n = n(t) is continuous].In the case of eqn (66) we can say nothing about the cusp because the phenomena overlap. In the case of eqn (64) we can unite eqn (44a) and (57) VdB/dt (overall) = Kl A , V exp ( - Kl t) - K , SB -{[nO-a(t-th)1/2 InO-a(t-fh)l+ 1/2) X K3 S b V[no-a(t-th)] (B-B,). (69) In fact the term (70) has two values only: 1 if the numerator is positive and there are bubbles; 0 if the numerator is negative and there are no bubbles. A useful change of variable is to (71) assume hence eqn (69) becomes [no - a(t - th)]/2 In, - a(t - th)l+ 1 /2 9 = t - t h VdB/d9 (overall) = VK, Ah exp (- Kl 9) - K, SB - [(no - a9)/2 In, - a91 + 1 /2] (no - a$) VK3 Sb(B- B,) (72) where Ah are the concentrations of A at the different times th at which there are nucleations of the bubbles and eqn (72) is a function of B against 9 in a single cycle.The boundary conditions are that if 9 = 0 , A=Ah, B = B b (73) where A = Ah identifies the cycle and B = Bb allows us to calculate the constant of integration. Proceeding as in eqn (57), because eqn (70) is a constant and assuming 9,, = (9 - O)/ln (9/0) z 9/ln ( lo6$) B = Bb exp ({ - K , S / V - [(no - a9)/2 In, - a91 + 1 /2] we have x K3 S,(n, - cc9/2)) 9) + &[(no - a9)/2 In, - d l + 1 /2] ~K~S,B,[n,-a$ln-~ (1o6$)]+K1Ah exp [ - K 1 9 1n-l (1069)]} x exp ( ( K , S[ln-l ( I 069) - I]/ V + [(no - a9)/2 In, - a91 + 1 /2] x K3 S,(n,[ln-l ( lo6$) - 13 - [ln-, ( lo6$) - I] a9/2} 9).(74)48 OSCILLATORY PHENOMENA EXPERIMENTAL RESULTS AND THEIR CORRELATION WITH THE MODEL In this section we present some experimental results obtained by us and by others and correlate them with the model. We studied the cerium + malonic acid + sulphuric acid+bromate system and also made some tests with the malonic acid+iodate+ hydrogen peroxide + manganese sulphate + sulphuric acid system. These systems differ from the proposed model because bubbles of CO, are starting in them continuously, but this has the effect of increasing the exchange surface in eqn (43) only. It could be important that bromine and iodine are not normally gases.However, they take part in the phase exchange, since they have high vapour pressures. If they do not come off as bubbles of gas, bromine coming off as liquid bubbles and iodine as solid crystals, this is negligible. > 41 --. 0.90 0.80 5 10 r/min ~ ~~ 15 20 FIG. 1.-Voltage against time plot (potential referred to the normal hydrogen electrode) for (in mol drn-,): KIO,, 7.02 x lo-*; malonic acid, 5.23 x 10P; H202, 1 ; H,SO,, 3.8 x lo-*; MnSO,, 3.47 x lo-,. Stirring is stopped at point A and solid iodine is generated at point B. The presence of bromine in the gas phase was confirmed by us during the oxidation of malonic acid and was studied by Noszticzius and Bodiss' during the oxidation of oxalic acid. Until now the oscillating supersaturation of bromine inside the solution has not been proved, but it is evident that the generation or flow of bromine is the rate-determining step.In fact during the oxidation of malonic acid we have an induction time, if we use cerium as catalyst, which is removed when we add bromide to the solution by the reaction BrO; + 5Br- + 6H+ -+ 3Br2 + 3H,O (75) increasing dB/dt (chem.). The oxidation of oxalic acid is discussed in the introduction. During the oxidation of malonic acid with iodate and hydrogen peroxide we noticed the production of solid iodine when we stopped stirring (fig. I ) and in the following systems without stopping the stirring (all in mol dm-3): malonic acid, 2.6 x 1 O-2; iodate, 7.02 x loe2; H,02, 1 ; MnSO,, 3.47 x lo-"; with (a) sulphuric acid, 2 x (fig.2) and (b) sulphuric acid, 3.8 x low2 (fig 3). During the oxidation of formic acid, supersaturation was considered to occur by Morgan12 and Growij,13 whilst the continuous presence of bubbles, which does not allow supersaturation according to Showalter and Noyes,s is compatible with our model if the bubbles are generated by secondary reactions, as in the generation of CO, and bromine in the oxidation of malonic acid. In fact, if we have supersaturationF. D'ALBA AND s. DI LORENZO 49 1.00- 0.95 0.90 > h 1 0.85 0.80 of CO, which allows the nucleation of its bubbles it is not necessary to have supersaturation of Br, also. Noszticzius and Bodiss' showed that phase exchange of bromine is pulsating and is not steady. - - - - I I I I 1 I I I I I I I I FIG.2.-Voltage against time plot (potential referred to the normal hydrogen electrode) for (in mol dmP3): KIO,, 7.02 x malonic acid, 2.61 x loP2; H,O,, 1 ; H,SO,, 2 x lo-,; MnSO,, 3.47 x loP3. Solid iodine is generated at point A. 0.85 0.80 J A I I 1 I I 1 I I I I I 1 1 2 3 4 5 6 7 8 9 10 11 tlmin FIG. 3.-Voltage against time plot (potential referred to the normal hydrogen electrode) for (in mol drn-,): KIO,, 7.02 x malonic acid, 2.61 x lop2; H,O,, 1 ; H,SO,, 3.8 x low2; MnSO,, 3.47 x lo-,. Solid iodine is generated at point A.50 1.40 OSCILLATORY PHENOMENA - > 4 A -. 1.20 1.10- FIG. 4.-Voltage against time plot (potential referred to the normal hydrogen electrode) for (in mol dmP3): KBrO,, 0.165; malonic acid, 0.075; H,SO,, 0.45; Ce(SO,),, 13.99 x lo-, g-ion dme3.Rate of stirring (in rev. min-I): A-C, 150; C-D, < 150; D-E, > 150; E-F, 0; F-G, < 150. B C D E F t - 1 I I 1 1 1.50- 1.10 - FIG. %-Voltage against time plot (potential referred to the normal hydrogen electrode) for (in mol dm-3): KBrO,, 0.165; malonic acid, 0.075; H,SO,, 0.45; Ce(SO,),, 13.99 x lo-, g-ion dm-3. Rate of stirring < 150 rev. min-I. 1.20 1.1 0 INFLUENCE OF THE RATE OF STIRRING The influence of the rate of stirring has been noted by several authors.*. 1 4 9 l5 During the oxidation of malonic acid with cerium as catalyst we observed a maximum rate of stirring below which oscillations begin after having stopped naturally or above which oscillations stopped even though they do not stop naturally (fig. 4). Fig. 5 is similar to fig.4 but with a rate of stirring lower than 150 rev. min-l. We also observed a minimum value of the rate of stirring below which oscillations stopped but this phenomenon is more clear if we use ferroin as Botrk et all5 observed (fig. 6). - - 1 1 1 1 IF. D’ALBA AND s. DI LORENZO 51 A 0 C D E F FIG. 6.-Voltage against time plot (potential referred to the normal hydrogen electrode) for (in mol dm-9: KBrO,, 0.33; malonic acid, 0.15; H,SO,, 0.45; ferroin, 14.15 x g-ion dm-3. A-B and C-D, with stirring; B-C and D-E, without stirring; E-F, at low pressure. Showalter and Noyes,8 working with formic acid, were obliged to change the rate of stirring twice and they obtained a rate constant for CO formation that seems to be independent of the rate of stirring above the threshold for smooth decomposition only.These effects cannot correlate with an exchange of oxygen as proposed by Roux and Rossi (see Introduction) because De Kepper et aZ.16 showed similar phenomena without exchange. They can, however, be explained by our model. If other variables are constant, the sign and modulus of dB/dt (overall) depend upon t,,. This increases if the rate of stirring decreases and vice versa; hence K , increases if the rate of stirring increases and vice versa. If the rate of stirring has a value allowing perfect homogeneity and hence correct tests, we may have the following cases. THE RATE OF STIRRING IS VERY HIGH Phase exchange has a value so great that the value B(max) obtained by eqn (46) is lower than B(sat) and the system cannot oscillate.Decreasing the rate of stirring, it is possible to obtain a value of B (max) higher than B (sat) and the system oscillates. This explains why there is a maximum in the range of values of stirring that allow oscillations. This range is steady if the rate of reaction is constant, yet because it is not constant the maximum is variable as it must meet the condition (74) and this explains why we must decrease the rate of stirring in some cases in order to have oscillations after they have stopped naturally. VdB/dt (chern.) + dN/dt (p.e. 1 , l ) > 0 THE RATE OF STIRRING IS INADEQUATE Phase exchange has such a small value that dB/dt(overall) cannot be negative in eqn (50) and hence the concentration of B does not decrease because nucleation of bubbles below that allows a generalized nucleation of bubbles.This explains why systems which do not oscillate can do so on an increase in the rate of stirring. The minimum rate of stirring which allows oscillations decreases with time in a first-order reaction because dB/dt(chem.) is decreasing. Yet it is also possible that a minimum does not exist, i.e. a system could oscillate by phase exchange due to diffusion only52 OSCILLATORY PHENOMENA in stagnant solution if dB/dt(overall) is negative in YdB/dt (overall) = VdB/dt (chem.) +dN/dt (p.e. 3) + dN/dt (p.e. 2) (77) where dN/dt (p.e. 3) is a negative phase exchange of B from the stagnant solution to the gas above it. This model explains why a pseudo rate constant of reaction independent of the rate of stirring has been obtained when oscillations have ceased.In fact, this is not a rate constant but an aggregate coefficient correlating dB/dt(overall) with the concentration of B. Obviously it depends upon K, and upon the rate of stirring during oscillations. It is independent for a steady state. In fact either a steady state is obtained by continuous nucleation of bubbles and dN/dt (p.e. 1 , l ) is negligible with respect to dN/dt(p.e. 2) or a steady state is obtained because the concentration of B does not reach the value B, allowing nucleation of bubbles; chemical reaction is then the rate-determining step and variations in phase exchange are negligible. The rate of stirring influences either the induction time of the oscillations or their frequency. An increase in the rate of stirring increases the modulus of dN/dt(p.e.1, 1) and decreases dB/dt (overall), hence the system takes more time to reach the concentration allowing nucleation if other variables are constant. This leads to an increase in the induction time to the first oscillation and in the period to the others. A decrease in the rate of stirring has the opposite effect. INFLUENCE OF TEMPERATURE The influence of temperature was shown by Botre et al.15 in the case of malonic acid and by Ropp17 in the case of formic acid. The tests for malonic acid show that an increase of temperature gives rise to an increase of frequency until a temperature above which oscillations stop. Ropp showed an increase of induction time when T decreases. The temperature influences several parameters of these systems : viscosity, density, the value of H in eqn (52c), diffusivity of B in eqn (42), etc.These influences are negligible with respect to the influence on Kl and hence on dB/dt(chem.). A decrease of 7‘ causes a decrease of dB/dt(chem.) and hence, if other variables are constant, a decrease of dBldt(overal1) and vice versa. It follows that a decrease of T increases the induction time and the period and vice versa. If the other parameters are constant, a range of temperature allowing oscillations exists, at least theoretically. The maximum observed by Botre et all5 is a temperature that, because dB/dt (chem.) is increased, does not allow dB/dt (overall) to be negative in eqn (50). The minimum observed by Bray18 during oxidation of malonic acid by iodate corresponds to a steady state with the concentration of B that does not allow a nucleation of bubbles caused by the small value of dB/dt(chem.).INFLUENCE OF PRESSURE We noticed that a reduction of pressure allows a regularization of the oscillations, if the rate of stirring does not allow it (fig. 4). Botrk et all5 noticed that a reduction of the partial pressure of CO, increases the size of the oscillations and lowers the rate of stirring necessary to stop oscillations, The influence of pressure on the oxidation of formic acid is discussed in the Introduction. These effects are explained by our model. A decrease of pressure in the gas decreases the value of Be in eqn (41) increasing the driving force and dN/dt (p.e. 1 , l ) and decreasing dB/dt (overall).In particular we can have a smooth decomposition during a decrease of pressure. In fact we can have an increase of dN/dt (p.e. 1 , l ) to a value able to give dB/dt (overall) < 0 during a transition between two values of p because of stripping. Afterp reaches the minimum value, it is possible that there are conditions which allow oscillations or oscillations are stopped. Although it was not observed,F. D ’ A L B A AND s. D I LORENZO 53 there is a maximum of partial pressure of the exchanged element which stops oscillations and it gives a value of Be so great that it does not allow dBldt(overal1) to become negative in eqn (50). The effects of a decrease in the partial pressure of CO, are analogous. It increases the phase exchange of CO, that occurs as bubbles and leads to an increase in dN/dt (p.e. 1 , l ) because it increases S (the exchange surface, which, when there are bubbles, is constituted by the surface of the bubbles and by the surface of the solution).Increases in dN/dt (p.e. 1 , l ) due to a decrease of pressure counterbalance decreases due to a decrease of the rate of stirring. Hence it is obvious that a decrease of partial pressure of CO, causes a decrease in the minimum rate of stirring allowing oscillations. The influence of the addition of an inert gas has been noticed by several authors (see Introduction). These effects are explained by our model. The addition of an inert gas increases the exchange surface and hence increases dN/dt (p.e. 1,l). If it has a value which is too low to allow oscillations, as in the oxidation of oxalic acid by Noszticzius and Bodiss, this addition is necessary for oscillations.If there are oscillations a flow of inert gas can stop them if dN/dt (p.e. 1 , l ) takes a value so great that it does not allow the condition dB/dt (chem.) + dN/dt (p.e. 1 , l ) > 0. Note that addition can be substituted by the generation of bubbles by a secondary chemical reaction, which explains why some chemicals generating a gas stop oscillations in Cl- and Na,S0,.7 I N F L U E N C E O F THE B U L K O N T H E REACTION The influence of the bulk has been noticed by several authors, but with no attempt to explain it because a purely chemical model cannot acknowledge that the bulk has any influence if the concentrations are constant. Noszticzius and Bodiss’ showed that the regularity of the oscillations increases due to an increase of the bulk of the reaction.This is explained by our model. A change of bulk, when the rate of stirring is steady, influences t S z . An increase of bulk decreases the turbulence of the system and increases t,, and vice versa. Practically it is equivalent to a reverse change in the rate of stirring. The volume of the reactor has two different effects. Changing the form of the reactor, the ratio S / V changes. When it decreases the value of dB/dt(chem.) + dN/dt(p.e. 1, 1) increases because dB/dt(chem.) depends upon V and is constant, whilst dN/dt(p.e. 1 , l ) decreases because S decreases and vice versa. A change of the form influences the turbulence [in fact it changes the characteristic dimension in N(Re)] and hence influences z,,.The influence of the stirrer is correlated to the turbulence it produces with a steady number of revolutions per minute. I N F L U E N C E OF T H E RATE OF REACTION The influence of the rate of reaction is very difficult to analyse because these systems are very complicated and we can see only the overall reaction. It is not possible to discuss the influence of the concentrations, since the exact mechanism of the reaction is not clear because the purely kinetic model proposed by Field et al. cannot be thought valid. An increase of dB/dt(chem.) produces a decrease in the induction time and in the period of oscillations. It is not clear why we have a decrease in the number of oscillations on increasing the concentration of the catalyst during the oxidation of malonic acid.Two explanations are possible. The rate of reaction is increasing and the system oscillates according to eqn (73) uncil it reaches a steady state by continuous nucleation of bubbles. The catalyst increases the rate of reaction and allows it to reach the steady state more quickly. The reaction has a higher average rate in a whole cycle. The time necessary to renew the concentration Bb after the last bubble leaves decreases and hence the frequency increases. However, if dB/dt (chem.), without catalyst, has54 OSCILLATORY PHENOMENA such a small value then it limits the absorption by the bubbles, and when there is a catalyst which increases dB/dt (chem.), the bubbles absorb more because B has a higher value in the driving force ( B - B2). This influences the time the bubbles remain in the solution and the period of the oscillations. Yet, because more B is produced, more reagents are destroyed in a cycle and hence less cycles are necessary to reach the lowest concentration allowing oscillations. R. J. Field, E. Koros and R. M. Noyes, J. Am. Chem. SOC., 1972, 94, 1394. * R. J. Field, E. Koros and R. M. Noyes, J. Am. Chem. Soc., 1972, 94, 8649. R. J. Field and R. M. Noyes, J. Chem. Phys., 1974, 60, 1877. P. Glandsdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley Interscience, New York, 1971). G. Nicolis, Adu. Chem. Phys., 1971, 19, 209. J. J. Tysson, J. Chem. Phys., 1973, 58, 3919. Z .Noszticzius and J. Bodiss., J. Am. Chem. Soc., 1979, 101, 3177. * K. Showalter and R. M. Noyes, J. Am. Chem. SOC., 1978, 100, 1042. * J. C. Roux and A. Rossi, C. R. Acad. Sci., Ser. C, 1978, 287, 15 I . lo F. D’Alba and G. Serravalle, J. Chim. Phys., 1981, 78, 131. S. Barkin, M. Bixon, R. M. Noyes and K. Bar-eli, Int. J. Chem. Kinet., 1977, XI, 841. J. S. Morgan, J. Chem. Soc., 1916, 109 and 274. l 3 P. G. Bowers and G. Rawji, J. Phys. Chem., 1977, 81, 1549. l4 G. J. Kasperek and T. C. Bruice, Inorg. Chem., 1971, 10, 382. C. Botre, P. Giacomello and A. Memoli. Bioelectrochem. Bioener., 1975, 2, 314. la P. De Kepper, A. Rossi and A. Pacault, C.R. Acad. Sci., Ser. C, 1976, 283, 371. l7 A. Ropp, J. Am. Chem. Soc., 1960, 82, 842. W. C. Bray, J. Am. Chem. Soc., 1921, 43, 1262. (PAPER 1 / 1602)

ISSN:0300-9599    

DOI:10.1039/F19837900039

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1983, 79, 55-64 Photoinduced Electron Transfer in the Paraquat-Thiourea Molecular Complex BY ARTHUR T. POULOS* AND CHARLES K. KELLEY Department of Chemistry, Rutgers University, Newark, New Jersey 07102, U.S.A. Received 27th October, 198 1 The bipyridinium ion paraquat forms a 1 : 1 association complex with thiourea in aqueous solution. Excitation in the region 360-440 nm with a high-intensity pulse causes transient changes in the visible absorption spectrum which are completely reversible within 10 s. A study of the time evolution of the absorption spectrum indicates that the primary photoproducts are the paraquat radical cation and the thiourea radical cation. Subsequent dimerization of thiourea radicals produces formamidine disulphide, which, along with thiourea radicals, reacts with paraquat radicals to regenerate the association complex.We report here that association complexes formed between thioureas and pyridinium ions undergo electron transfer and emission upon excitation into the charge transfer (c. t.) electronic absorption band where Pn+ represents the pyridinium ion and TU represents thiourea. This behaviour is of interest because paraquat, a pyridinium ion, is a common electron acceptor in reactions of excited states, including the triplet state of Ru(bipy)i+ and its derivatives.' Our previous findings for the paraquat-p-phenylenediamine complex2 suggest that ground-state interactions should not be ignored in interpreting electron-transfer behaviour. This type of reaction is also relevant to the problem of solar-energy conversion, since electron transfer is reversible and one pathway for back electron transfer occurs with a relatively low rate constant.Finally, the system is unusual in that emission is observed in liquid water, a very polar solvent. The normal behaviour for exciplexes formed between electron-donor and electron-acceptor molecules is electron transfer in polar solvents and emission in solvents of low dielectric ~ o n s t a n t . ~ EXPERIMENTAL REAGENTS Paraquat dichloride was purchased from Aldrich Chemical Co and recrystallized from a mixture of ethanol and water. Paraquat tetrafluoroborate was synthesized by addition of O(CH,),BF, to a solution of 4,4'-dipyridyl in acetone, followed by standing overnight; the salt was precipitated with diethyl ether and recrystallized several times from a mixture of ethanol and water.Reagent grade thioureas (ICN Pharmaceuticals and Eastman Kodak Co) were recrystallized from acetonitrile. SPECTROSCOPY Ultraviolet-visible absorption spectra were recorded on a Beckman Acta CIII spectrophoto- meter. Infrared spectra were obtained in KBr pellets using a Beckman IR 4240 spectrophoto- meter. Emission spectra were recorded on the Spex Fluorolog; operation in the ratio mode 5556 PHOTOINDUCED ELECTRON TRANSFER yielded corrected excitation spectra. Transient absorption in the oxidation of thiourea by cupric ion was detected using a Durrum model D- 1 10 stopped-flow spectrophotometer. FLASH EXCITATION The microsecond flash-photolysis apparatus was described ear lie^.^ Nanosecond flash excitation with a xenon fluoride eximer laser was performed at the Regional Laser Laboratory at the University of Pennsylvania.RESULTS AND DISCUSSION GROUND-STATE PROPERTIES OF THE PARAQUAT-THIOUREA COMPLEX Most of the photochemical observations described here are for solutions containing thiourea and paraquat. Consequently, it was desirable to study their ground-state interaction. This was done by examining the ultraviolet-visible spectrum in solution and the infrared spectrum of a solid mixture. When aqueous solutions of paraquat (PQ2+) and thiourea (TU) are mixed, a new absorption shoulder appears which is red-shifted from the component spectra and extends from 450 to 305 nm. Long-wavelength absorption was reported for complexes of pyridinium ions with other donor molecules, such as i ~ d i d e , ~ ferrocyanide6 and hydr~quinone.~ With 2 x mol dm-3 PQ2+ and 2 x mol dm-3 TU, the absorp- tion change occurs within the time of mixing on the stopped-flow spectrophotometer ( 5 ms), indicating a rate constant > lo5 dm3 mol-1 s-l.This is consistent with weak c.t. bonding since no activation energy would be required for bond-breaking processes. The absorption change is reversible, as shown by the fact that a 100-fold dilution of this sample gives an absorption spectrum which matches the sum of the component spectra. Variation of the absorbance at 360 nm with mole fraction of the components at constant total concentration (method of continuous variations8) indicates that one mole of TU combines with one mole of PQ2+.Further confirmation of a 1 : l stoichiometry in solution comes from being able to fit to eqn (2) the change in absor- bance at 360 nm upon successive dilution of a solution of TU and PQ+2: - v = KA, E mA m,/vA - KA, m, where v is the solution volume, m is the molar mass of A or D, 2 is the absorbance, KAD is the equilibrium constant for the AD complex and E is the extinction coefficient for the complex at the monitored wavelength. Eqn (2) is valid for 1 : I complexes under conditions where one component (D) is in large exce~s.~ For 360 nm, a plot of v against (l/vA) is linear and the slope and intercept yield the values KAD = 0.4 dm3 mol-l and E = 2.0 x lo2 dm3 mol-1 cm-l. This low equilibrium constant is of the order of magnitude expected for a c.t.complex. The specific geometry with which TU and PQ2+ interact is an important consideration because the excited singlet state (which may be the photoactive one) achieved immediately upon excitation into the c.t. band will have the same geometry as the ground state, according to the Franck-Condon principle. The work of White7 on other paraquat complexes suggests that PQ2+ accepts electron density into its ;n antibonding orbitals. With TU as the electron donor, one can imagine three idealized bonding modes: donation from a sulphur lone-pair electron, from the S-C-N n system or from a nitrogen lone-pair electron. Since the infrared spectrum of metal complexes has found use as a structural probe,1° we decided to study the infrared spectrum of the paraquat-thiourea complex.Infrared spectra in KBr pellets were taken of TU, PQ2+'2C1- and the yellow solid formed on evaporation of an aqueous 1 : 1 molar mixture of the two. The mixture appears to be a sum of the components, with several significant differences. First, theA. T. POULOS AND C . K. KELLEY 57 N-H stretching bands of TU are reduced from 3360, 3250 and 3150 cm-l to 3310, 3245 and 3 120 crn-l. This is consistent with nitrogen acting as electron donor since a shift to lower frequency occurs on binding of amines to metal cati0ns.l' Also, such frequency shifts have been used as a diagnostic for the mode of binding in metal complexes of ureas and thioureas.1° Secondly, the infrared frequencies of TU which contain C = S stretching character are slightly increased in the complex, from 1072 to 1078 cm-l and from 721 to 723 cm-l.This also supports donation from nitrogen since decreased contribution from polar resonance structure (I) will increase the C-S bond order. Finally, there are several substantial increases in the frequency of PQ2+ bands on complexing, 458-468, 807-813 and 1630-1638 cm-l. If the 807 cm-l band is due to aromatic C-H bending, the shift suggests that bonding by thiourea creates crowding of the ring hydrogens. The shift of the double-bond stretch at 1630 cm-l to higher frequency is puzzling since electron donation to an aromatic system should decrease the C=C and C=N bond orders. FLASH EXCITATION: CHEMICAL INTERMEDIATES AND THEIR KINETICS OF DECAY To determine whether electron transfer from thiourea to paraquat occurs upon light absorption into the c.t. band, the complex was flash photolysed (A > 320 nm, 100 ps 0.3( 0.21 a) C .fl s: 2 0.N I I I 4 50 550 650 h/nm FIG.1 .-Absorption spectrum of transient species existing 100 ps after flash excitation of 2.5 x lo-' mol dmP3 TU + 2.5 x lo-' mo! dmP3 PQz+. 3 FAR 158 PHOTOINDUCED ELECTRON TRANSFER pulse) under a nitrogen atmosphere and changes in absorption monitored in the visible region, where the paraquat radical absorbs. A transient absorption was indeed observed and the spectrum, fig. 1, matches that of the paraquat radical (PQ'+).12 This transient event is completely reversible. In the region 390-650 nm, the transmittance returns completely within 10 s to that prior to the pulse. Also, the near u.v.-visible absorption spectrum recorded using a double-beam spectrophotometer shows no changes after 100 flash-lamp pulses.The magnitude of transient absorption does not change with repeated flashing, another indication that there is no irreversible reaction. The decay kinetics, monitored at 395 or 605 nm, are complex (fig. 2). Attempts to fit data to a differential equation of the form - kJn, n = 0, 0.5, 1, 1.5, 2 d a dt -- - where 2 is the absorbance, were unsuccessful. The shape of the decay c_urve suggests at least two pathways for reaction of the paraquat radical. A plot of l / A against time is linear in the slow time regime, 0.4 to 6 s. I 1.0 I 900 2000 6000 r/ms FIG. 2.-Absorption at 605 nm after flash excitation of 2 x loF2 mol dmW3 TU+2 x mol dm-3 PQ2+.A mechanism which accommodates these results is: hv PQ2+*--TU -+ PQ'++TU'+ PQ'++TU'+ 4 PQ2++TU (3) (4) 2 TU'+ 4 FDS2+ ( 5 ) FDS2+ + PQ'+ + PQ2+ + FDS'+ (6) FDS'++PQ'+ 4 PQ2++2TU (7) where FDS2+ represents formamidine disulphide, H,NCSSCNHE+, a stable compound which can be prepared by oxidation of thiourea with H,O, l 3 or Cu2+,I4 and FDS'+A. T. POULOS AND C. K. KELLEY 59 represents the product from one-electron reduction of FDS2+. According to reactions (4)-(7), the rate of disappearance of paraquat radical should follow the rate law If FDS'+ is a steady-state intermediate, this reduces to d[PQ'+l - [PQ'+](k,[TU'+]+2k6[FDS2+]). dt If k , B k, the initial rate law will be and the slope of a plot of 1/A" against time at early times will be k , / d .For 1 = 15 cm, E~~~~~ = 1.06 x lo4 dm3 mol-1 cm-l,ll k, is calculated to be 8.1 x lo8 dm3 mol-1 s-l. When all TU'+ has been consumed by reactions (4) and (9, [PQ'+] = 2[FDS2+] and the rate law will be -~ d[PQ'+l = k,[PQ'+]2. dt The slope at long times yields k6 = 1.92 x lo5 dm3 mo1-l s-'. Additional support for FDS2+ as a reaction intermediate is found in the effect of authentic FDS2+ on the transient decay rate. At [FDS+2] = 2.4 x mol dm-3 the decay profile is exponential and the pseudo-first-order rate constant divided by 2 x [FDS2+]is 1.5 x lo5 dm3 mol-l s-l. Thisc_ompares favourably with the second-order rate constant obtained from the 1/A against time plot at long times, 1.92 x lo5 dm3 mol-1 s-l. The effects of light intensity on the radical yield and decay kinetics are also consistent with the proposed mechanism.During microsecond flash excitation, the intensity was varied by changing the voltage on the storage capacitor. Transient absorption 100 p s after lamp firing was linearly dependent on voltage (fig. 3). If one assumes that the spectral profile of the lamp is independent of voltage, the intensity will be proportional to the voltage squared because the energy stored in a capacitor is $ CV2. Thus, the paraquat radical yield at 100 ,us varies with the square root of light intensity. In contrast, absorption 30 ms after lamp firing, the time regime during which FDS2+ is proposed to predominate over TU'+, is found to vary with V 2 to a better linear fit than V(R, the5orrelation co$icient, = 0.9983 as against 0.9946).Also of significance is the fact that A(t = 30 ms)/A (t = 100 ps) increases linearly with V(data taken from fig. 3). All of these results are consistent with PQ'+ achieving a steady-state concentration while the lamp is emitting. Then d[PQ'+l = 0 I,/V-k,[PQ'+],,[TU'+],, x 0 dt where I, is the absorbed intensity, ss denotes steady-state, @ is the quantum yield for electron transfer and Vis the volume. If [TU'+],, cc [PQ' +Iss, then [PQ' +Iss cc 2/Ia and the transient absorbance immediately after the pulse (a first approximation to [PQ'+],,) will vary with V. The initial concentration of FDS2+ after the pulse, however, should vary linearly with I, ( V 2 ) since = K,[TU'+12-2k6[PQ'+] [FDS2+] x K4[TU'+l2 d[FDS2+] dt 3-260 PHOTOINDUCED ELECTRON TRANSFER t = loops Y t = 3 0 m s I 1 I I I 2 4 6 8 10 V/k V FIG.3.-Effect of capacitor voltage on transient absorption (595 nm) from flash excitation of 4.9 x 10+ mol dm-3 TU+4.3 x lop2 mol dm-3 PQ2+. when t 6 30 ms. Then -1oops [TU'+12 dt = k, [TU'+]& =constant x la dt. As mentioned above, the transient absorbance at t = 30 ms reflects [FDS2+] while the absorbance at t = 100 p s reflects [TU'+]. The ratio of the two absorbances should then be proportional to z/la. The non-zero intercepts in fig. 3 are probably a condition of the discharge characteristics of the lamp. In fact, the existence of a threshold voltage for substantial intensity has been observed before.l59 l6 Another contributing factor may be destruction of PQ'+ by very low concentrations of impurities. The effect of pulse duration on the yield of PQ'+ was also studied.Transient absorption observed 20 ns after a 353 nm eximer laser pulse varied linearly with pulse energy (intensity) in the range 1.7-4.0 mJ. This can be explained by the same mechanism. Within 20ns very little PQ'+ will have decayed by reaction (4) and consequently -- d[PQ' +I - a la/ F/. dt That is, the concentration of PQ'+ 20 ns after laser firing will be proportional to the number of absorbed photons.A. T. POULOS AND C. K. KELLEY 61 To explore the generality of reaction (l), we studied the behaviour on flash excitation of these complexes : 4-carbomethoxy- 1 -methylpyridinium cation-thiourea, paraquat- "'-diethylthiourea, paraquat-"'-di-isopropylthiourea and paraquat-tetramethyl- thiourea.In these four cases, the transient spectrum indicates the formation of paraquat radical. The kinetics were complex, again implicating disulphides as intermediates. The paraquat-tetramethylthiourea complex behaved differently from the others. After decay of PQ.+ absorption, transient bleaching was observed in the region 390-475 nm, with the effect being greatest at 430 nm. Complete recoxery of trans- mittance to that prior to the flash occurred after 30 s, and a plot of l / A against time was linear ( R = 0.9982). 1 x mol dm-, HC10, completely quenches the bleaching process, increases the PQ'+ absorption by ca. 20%, and slows down the rate of decay of PQ'+ by a factor of 9.4. In contrast, for c.t. complexes of the other four thioureas H+ has no significant effect on the yield of PQ'+ or decay kinetics between pH 5.6 and 1.7 For the 4-carbomethoxy- 1 -methylpyridinium cation-thiourea complex, the transient absorption spectrum matched that reported by Itoh and Nagakura" for the pyridinyl radical, except for a shoulder at 400 nm.To determine whether this additional band represents TU'+, we attempted to generate and record the absorption spectrum of TU'+ by two different reactions. First, the oxidation of thiourea by Cu" in CH,CN, reaction (8), was monitored by stopped-flow spectrophotometry. An absorbing transient inter- mediate was detected and it has the absorption spectrum shown in fig. 4. From the analytical concentration of Cult under conditions of an excess of thiourea the extinction coefficient at 405 nm was estimated as 1.1 x lo3 dm3 mol-1 cm-l.Com- parison of this value with E for PQ'+ (2.8 x lo4 dm3 mol-l cm-l at 395 nm) and for the Cu(CH,CN)"," + TU -+ Cu(CH,CN)$ + iFDS2+ (8) 350 L 50 h/nm 5 50 FIG. 4.-Absorption spectrum of the transient produced by stopped-flow mixing of Cu(CIO,), and thiourea in acetonitrile.62 PHOTOINDUCED ELECTRON TRANSFER 4-carbomethoxy-I-methylpyridinyl radical (3.1 x lo3 dm3 mol-1 cm-l at 395 nm)17 explains why TU'+ is only detected in the presence of the latter radical. An attempt was also made to generate TU'+ by flash photolysis of F D S 2 with U.V. light. Reaction (9) seemed feasible because the S-S bond is probably the weakest one in FDS2+ and because other workers1* have reported the breaking of S-S bonds by U.V. excitation: (9) FDS2+ + 2 TU'+.Flash excitation of 5 x lop2 mol dm-3 FDS2+*2C1- in water in a quartz cell gave 5 transient optical density change at 398 nm, the absorption maximum. A plot of l / A against time was linear with slope ( k / d ) = 0.056 s-l. Linearity is consistent with bimolecular recombination, probably via reaction (5). With the value E = 1 x lo3 dm3 mo1-l cm-l obtained by stopped-flow methods, 8 x lo8 dm3 mol-1 s-l is calculated for the rate constant of reaction (5). This high value adds credence to the mechanism of reactions (4)-(7), because k , and k , must be of the same order of magnitude for FDS2+ to accumulate during the photostationary state. hv PHOTOPHYSICS The wavelength dependence of reaction (l), where Pn+ represents paraquat, was studied to determine whether there is participation by the light-absorbing c.t. state. Excitation of 8.4 x rnol dmP3 TU with a 353 nm eximer laser pulse produced within less than 20 ns a transient absorbance at 395 nm. The decay fits second-order kinetics, with a rate constant which was nearly the same* as that of the fast decay seen after microsecond flash excitation. The occurrence of electron transfer caused by 353 nm excitation is significant because neither uncomplexed PQ2+ nor Tu absorb at that wavelength. Further support for c.t. state participation mol dm-3 PQ2+ and 9.3 x [ I s (aqueous, pH 5) in a quartz cell with a nitrogen atmosphere and monitored at 395 nm. FIG. 5.-Decay of the paraquat radical cation produced on flash excitation of 2 x mol dm-3 PQ2+ * The radical decay observed on a nanosecond time-scale was slightly faster (k = 1.2 x lo8 dm3 mol-l s-l) than that observed in the microsecond time region by conventional flash photolysis.This is probably due to the total absence in the former case of a contribution by reaction (6) to the decay process.A. T. POULOS AND C . K. KELLEY 63 comes from microsecond flash excitation experiments in which an 0-52 Corning filter is inserted between the sample cell and the flash lamp to prevent excitation of the uncomplexed species. Under this condition, the transient absorbance increased with increasing TU concentration when [PQ2+] is constant and also increased with increasing PQ2+ concentration when [TU] is held constant. The rate of change of absorbance with analytical concentration of reactant is the same for both TU and PQ2+, as would be expected if a 1 : 1 complex were photoactive.If PQ2+'2C1- or PQ2+'2BF4- is excited in the absence of TU in a quartz cell with no 0-52 filter, the paraquat radical forms and decays in a complex fashion (fig. 5 ) . Addition of 4.8 x mol dm-3 NaCl does not increase the radical yield, indicating that the counterion is not the electron donor. Participation of OH- is likely because the paraquat radical is not generated when the pH of the solution lowered to 2.2 by HClO,. In this case, the paraquat triplet state may be responsible for electron transfer. The multiplicity of the photoreactive state for reaction (1) was investigated by exciting a PQ2+/TU solution in the presence of 3,3'-diethylcarbocyanine iodide, a water-soluble triplet quencher (ET = 39.2 kcal mol-l).A 7-54 Corning filter was inserted between the sample cell and the flash lamp to prevent excitation of the dye singlet state. If the photoactive state is of triplet multiplicity and higher in energy than 39.2 kcal mol-l, energy transfer should occur, causing a decrease in the yield of PQ*+ and promoting the appearance of the triplet-triplet absorption of the dye.* With 1 x mol dm-3 dye, no change in the yield of PQ'+ nor formation of dye triplets was observed. I I I I 125 475 525 575 625 X/nm FIG. 6.-Emission spectrum obtained from exciting 2 x rnol dmP3 PQz+ at 385 nm in nitrogen- or air-saturated water. The narrow band at 440 nm is the Raman-shifted excitation beam. mol dm-3 TU + 2 x Neither PQ2+ nor TU emit light when irradiated in aqueous solution at room temperature.However, the c.t. complex when irradiated at 385 nm exhibits a broad, featureless emission centred at 525 nm (fig. 6). The emission intensity is of the same order of magnitude as Raman scattering by water. The corrected excitation spectrum (fig. 7) is interesting because the fall-off in emission yield below 395 nm might be due to a change in the mechanism of the decay of the c.t. excited state. For example, * The triplet-triplet absorption spectrum of the dye has a maximum at 630-650 nm.1964 PHOTOINDUCED ELECTRON TRANSFER X/nm FIG. 7.-Corrected excitation spectrum for the 525 nm emission by 2 x lo-* mol dmV3 TU + 2 x mol dm-3 PQ*+. low-energy c.t. states may emit but higher-energy states undergo electron transfer. A detailed study of the dependence of radical yield on excitation wavelength is in progress.We thank the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work and the Rutgers University Research Council and Allied Corporation for support. Certain components of the flash-photolysis system were on loan from the Department of Chemistry, University of California at Santa Cruz. We also thank the Regional Laser Laboratory at the University of Pennsylvania for use of the nanosecond laser photolysis system. 1 2 3 4 5 6 7 x 9 l o 11 12 1 3 14 15 16 17 18 19 I. Okura and K-T. Nguyen, J. Chem. Soc., Faraday Trans. I , 1981, 77, 141 1 . A. T. Poulos, C. K. Kelley and R. Simone, J . Phys. Chem., 1981, 85, 823. (a) A. Weller and H. Leonhardt, 2. Phys. Chem. (Frankfurt am Main), 1961, 29, 277; (6) A. Weller and H. Leonhardt, Ber. Bunsenges. Phys. Chem., 1963, 63, 791 ; (c) A. Weller, H. Knibbe, K. Rollig and F. P. Schafer, J. Chem. Phys., 1964, 47, 1 184. R. P. Asbury, G. S. Hammond, P. H. P. Lee and A. T. Poulos, Znorg. Chem., 1980, 19, 3461. E. M. Kosower, J. Am. Chem. Soc., 1958, 80, 3253. A. Nakahara and J. H. Wang, J. Phys. Chem., 1963, 67, 496. B. G. White, Trans. Faraday Soc., 1969, 65, 200. P. Job, C.R. Acad. Sci., 1925, 180, 938. G. Cilento and D. L. Sanioto, Z. Phys. Chem. (Leipzig), 1963, 223, 33. (a) R. B. Penland, S. Mizushima, C. Curran and J. U. Quagliano, J. Am. Chem. Soc., 1957, 79, 1575; (b) A. Yamaguchi, R. B. Penland, S. Mizushima, T. J. Lane, C. Curran and J. V. Quagliano, J . Am. Chem. Soc., 1958, 80, 527; ( c ) T. J . Lane, A. Yamaguchi, J. V. Quagliano, J. A. Ryan and S. Mizushima, J. Am. Chem. Soc., 1959,81, 3824. G. F. Svatos, C. Curran and J. V. Quagliano, J. Am. Chem. Soc., 1955, 77, 6159. E. M. Kosower and J. L. Cotter, J. Am. Chem. Soc., 1964, 86, 5524. P. W. Preisler and L. Berger, J. Am Them. Soc., 1947, 69, 322. D. A. Zatko and B. Kratochvil, Anal. Chem., 1968, 40, 2120. S. Claesson and L. Lindqvist, Ark. Kemi, 1958, 12, 1 . T. Efthymiopoulos and B. K. Garside, Appl. Opt., 1977, 16, 70, M. Itoh and S. Nagakura, J. Am. Chem. Soc., 1967,89, 3959. For a short discussion see The Analytical Chemistry of Sulphur and its Compounds, ed. J. H. Karchmer (J. Wiley, New York, 1972), part 11, pp. 131-133. V. Kuzmin, personal communication. (PAPER 1/1671)

ISSN:0300-9599    

DOI:10.1039/F19837900055

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1983, 79, 65-74 Particle Adhesion and Removal in Model Systems Part 6.-Kinetics of Deposition of Haematite Particles on Steel BY NIKOLA K A L L A Y , ~ JOHN D. NELLIGAN AND EGON MATIJEVIC* Institute of Colloid and Surface Science and Department of Chemistry, Clarkson College of Technology, Potsdam, New York 13676, U.S.A. Receiiied 28th October, 198 1 The kinetics of adhesion of uniform colloidal spherical particles of haematite on steel was studied as a function of pH, ionic strength and particle size. It was shown that deposition occurs when the collector and the particles have charges of opposite sign and that the rate of adhesion can be greatly affected by the extent of surface coverage by the adhered particles. The deposition of solids of the same charge as the substrate can be induced if a sufficient amount of an indifferent electrolyte is added.Data were interpreted in terms of existing theories of diffusional deposition; the model of Ruckenstein and of Pfeffer and Happel explained the adhesion of small particles (0.15 pm in diameter). The effect of the electrolyte was considered by using the interaction-force boundary-layer concept combined with the double-layer and dispersion terms. Several techniques have been used to study the kinetics of deposition of colloidal particles on solid surfaces. Among these methods the rotating disc1 has received considerable attention, because the Levich theory5 has made it possible to interpret the data quantitatively. Other approaches include the deposition of particles in channels of different geometries6, or the adsorption of small dispersed particles on larger ones,8 lo which can be treated as a special case of heterocoag~lation.~~ lo The packed-bed technique used in this work has the advantage that the results obtained are directly applicable to certain practical situations.11-16 Treatment of data is possible by considering the theories of particle transport toward a single col- lector,5> l 7 l 9 and by taking into consideration the flow characteristics of the colloidal dispersion through a multiparticle collector system.20 24 The deposition of the particles may involve three different mechanisms: sedimen- tation, interception and d i f f ~ s i o n .~ ~ The experimental evidence has clearly shown that the rate of deposition of sufficiently small particles, which have a charge opposite to that of the substrate, is governed by diffusion and that it can be enhanced by attraction forces (dispersion and electrostatic).When the particles and the substrate are of the same sign of charge the deposition is expected to be considerably slower than in the absence of electrostatic repulsion. The latter effect can be eliminated by the addition of electrolytes. It is found in some cases that the rate of deposition varies with the quantity of adhered particles due to a consequent change of the charge of the substrate.26 2R To eliminate the need for considering this effect, the initial rates were normally used in the interpretation of data. This paper reports a study of the rate of deposition of colloidal spherical haematite particles on steel as a function of the change in the surface coverage of the substrate by adhered solids.The design of the experimental set-up allowed for the investigation of the attachment of the particles as singlets even at electrolyte concentrations which t On leave of absence from Faculty of Science, University of Zagreb, Zagreb, Yugoslavia. 6566 KINETICS OF PARTICLE ADHESION led to coagulation of the same haematite sol in the bulk. Thus, the results could be interpreted in terms of the theories of Ruckenstein20*21 and of Pfeffer and HappelZ4 with special consideration of the effects of dispersion and electrostatic forces. EXPERIMENTAL MATERIALS The stainless-steel 316 LSS beads used for packing the column were purified as described earlier.29 Two different samples of spherical haematite particles of narrow size distribution having modal diameters of 0.15 k 0.02 and 0.5 0.1 pm, respectively, were prepared by hydrothermal ageing of FeCl, solutions and purified as described earlier.30 All dispersions, whose pH was adjusted to 4, were agitated in an ultrasonic bath before use.METHOD The packed column assembly was essentially the same as used before,16 except that the flow of the suspension was carefully controlled by a peristaltic pump. The cross-sectional area of the column was 0.64 cm2 and the experimentally determined void volume fraction was 0.40. The mass of stainless-steel beads (density, p = 8.3 g cm-,) was either 3 or 5 g. The temperature was kept constant at 25 OC in all experiments. To eliminate the effect of CO, all measurements were carried out in an argon atmosphere.When the effects of electrolytes were studied, the salt solutions were introduced by means of a peristaltic pump at the top of the column into the flowing haematite suspension. To secure proper mixing of the sol and the electrolyte solution, the tube carrying the latter was continuously moved above the bed by an eccentric motion. The flow rate of the two liquids was adjusted to prevent upward movement of the electrolyte. Coagulation of the sols was minimized by the described procedure since the duration of the experiment after the mixing of the sol with the electrolyte was -= 1 min. Assuming fast coagulation, a dispersion containing 2 x lo1* particles rn-, would still contain > 90% singlets when leaving the column.The relative particle number concentration was determined by light scattering at an angle of 45O using an incident beam of 436 nm. The absolute value was obtained from the mass content, density and the particle size. THEORETICAL BACKGROUND The deposition of colloidal particles in a packed bed could be described in terms of the mass-transfer coefficient, K , defined by dC A , -=--KC dt V where Cis the particle number concentration in the bulk of the dispersion, t is the time, A , the total surface area of the collector and V the volume of the dispersion that is in contact with the collector. (2) Integrating yields A In (Cin/Cout) = 2 Kt, V in which Cin and Cout are the particle number concentrations in the influent and effluent dispersion which passes through the column and t , is time required for a volume element to flow through the collector bed.This time depends on the size of the column as well as on the flow rate, v: 1, = v/v. (3)N. K A L L A Y , J. D. NELLIGAN AND E. MATIJEVIC 67 The available area of the spherical collector beads can be calculated from their mass, m,, density, p, and radius, rs. Combination with eqn (1)-(3) yields the expression 3m In (Cin/Cout) = 2 K Pr, v (4) which allows the determination of the value of K . At constant flow rate a constant mass-transfer coefficient should give a constant ratio of Cin to Gout. 0 20 40 60 1 r/m-2 N E 4: . L 0 25 5 0 75 100 125 t / c m 3 FIG. 1 .-Adhesion of haematite on steel at pH 7.0, ionic strength mol dmP3, 25 O C .Diameter of steel beads, d, = 69 pm; mass of steel, m, = 5.0 g; diameter of haematite particles, dh = 0.15 pm; initial concentration, Ci, = 3.3 x 1014 m-3; flow rate, = 0.82 cm3 min-'. Lower part: particle surface density (r) as a function of the volume of haematite dispersion which passed through the column. Upper part: plot of log K as a function of the particle surface density. RESULTS The influence of the amount of the adhered haematite particles on steel on the deposition rate was examined over the pH range 4-8. The pH of the colloid suspension, which was initially acidified with HNO, (final concentration lob4 mol drn-,), was adjusted with NaOH. Thus, the ionic strength was maintained constant (lob4 mol dmd3). Fig.I (lower) shows the increase in the surface density of particles, r (= number of adhered particles divided by the surface area df steei kads), as a function of the68 -6.6 h 7 , -6.8 s E 1 Oll 2 -7.0- -7.2 KINETICS OF PARTICLE ADHESION 9 - I I I I - \ \ \ --**--* ......, ....,. '3 - J l - \ HAEMATITE ,2 I- \ 4 10- h N I E --. k 2 5 - M ; 2 c1 .. 5 6 PH 7 8 4 5 6 7 8 PH FIG. 3.-Upper: electrophoretic mobility (p) of haematite and stainless steel as a function of pH. Lower: plot of K values extrapolated to zero coverage and of the slope of log K against r as a function of pH for the system illustrated in fig. 1 .N. KALLAY, J. D. NELLIGAN AND E. MATIJEVIC 69 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 FIG. 4.-Plot of the ratio of the particle number concentrations of the influent and effluent dispersions as a function of the dispersion flow rate (circles).Solid lines were calculated from the theory of Ruckenstein and of Pfeffer and Happel for the haematite-steel system at pH 3.2, 25 OC, [NaNO,] = 1.0 mol dmP3, d, = 108 pm, m, = 3 g, dh = 0.15 pm, Ci, = 3.6 x 1014 mP3. log ( t / c m 3 min-1) - 5 L / / - I r, I : I I I I I t- I I $ . I I -3 -2 -1 0 log ([NaNO, I /mol dm-,) FIG. 5.-Plot of log K as a function of the concentration of NaNO, for the haematite-steel system at pH 3.3, d, = 94 pm, m, = 3 g, = 3.2 cm3 min-’ and spherical haematite particles of dh = 0.15 pm (0) and dh = 0.5 pm (0). The right-hand side ordinate gives the corresponding W values. volume of the haematite dispersion that passed through the column at pH 7.0.The upper part of this figure gives the same data in terms of a plot of log K against r. In the latter case a linear relationship is evident with a correlation coefficient of 0.995. From data in the lower part of fig. 1 it would seem that the rate of adhesion is constant at least for the first half of the volume passed through the column. However, a constant70 KINETICS OF PARTICLE ADHESION deposition rate would require K to be invariable, which is obviously not the case. It is apparent that the change in the rate of deposition is more readily evaluated from the plot of log K against r than from the change in the shape of the plot of the particle surface density as a function of time (or volume). Fig. 2 gives a plot of log K against r for the same system at pH 5.2.Except for the point at the lowest value of the adhered amount of haematite, the data show a reasonable linear dependence (correlation coefficient 0.98), although the slope is higher and the value of the intercept lower than at pH 7.0. The results obtained over the entire pH range studied are summarized in fig. 3 (lower part), which gives the values of K extrapolated to zero coverage and of the slopes of log K against r as a function of pH. In the upper part are shown the corresponding electrokinetic mobilities of haematite particles and of stee1.16 The influence of the flow rate on the deposition of haematite on steel is illustrated in fig. 4 for a system at pH 3.2 in the presence of 1.0 mol dm-, NaNO,. Varying the concentration of the electrolyte (NaNO,) affects values of K as shown in fig.5 for spherical haematite particles of two different sizes. DISCUSSION The studied system lends itself well to a quantitative analy,sis of particle deposition processes. The charges of the haematite and of the steel can be readily altered by changing the pH. The adhering particles are spherical and uniform and non-reacting electrolytes can be used to control the ionic strength. Also, the technique employed made it possible to determine the adhesion of single particles under conditions that would normally lead to coagulation. Finally, from a practical point of view, the system can serve as a good model for phenomena related to the corrosion of metals, pigment application, filtration, etc. The deposition of sufficiently small particles (ca. 1 ~ 1 1 1 ) ~ ~ may be considered in terms of convection diffusion because the contribution of interception and sedimentation phenomena is negligible.In the absence of interaction forces between the substrate and the particles the mass-transfer coefficient, Kd, can be calculated from the following expression, which is valid for spherical collector beads :31 Kd = 0.624 Dbr,"(/3~);. ( 5 ) The diffusion coefficient, D, is given for spherical particles by where k is the Boltzmann constant, T the absolute temperature, q the dynamic viscosity of the medium and rh the radius of the spherical colloidal particles. The superficial velocity, v, of the influent dispersion can be calculated from the flow rate and the cross-sectional areas of the column according to v = v/s.(7) The correction parameter /3 [in eqn (5)] accounts for the specificity of the packed column relative to the simple case in which the dispersion flows towards a single collector bead. According to Ruckenstein and Pfeffer and Happel, /3 can be calculated for a column filled with such a collector from the e x p r e s s i ~ n ~ ~ - ~ ~ D = [2(1- y5)1/(2 - 3 y + 375 - 279 (8)N. KALLAY, J. D. NELLIGAN AND E. MATIJEVIC 71 where y is related to the void volume fraction of the packed bed (b by 73 = 1-4. (9) For the column used in this work the experimentally determined (b = 0.4, which gives Combination of eqn (5)-(7) and insertion of the above value for p allows the calculation of the mass-transfer coefficient, Kd, for the case when the interaction forces between the collector and the adsorbing particles have little effect on the convection diffusion, from the relationship p = 38.In the presence of a repulsion energy barrier the rate of deposition is diminished. The actual value of K is related to Kd through the stability factor W, i.e. W = KJK. (1 1) Fig. 1 and 2 show that K decreases with increasing particle coverage of the steel surface. No removal of the adhered particles could be detected under the conditions of the described experiments.16*29 Thus, at constant flow rate, V, and void volume fraction, #, a decrease in K is caused by an increase in W, which signifies a rise in the potential barrier. The latter may be interpreted in terms of the change in the charge of the steel beads caused by deposition of the oppositely charged particles. In examples given in fig.1 and 2 the adhesion of haematite recharges the steel surface to positive; thus, the substrate and the particles are of the same sign of charge resulting in mutual repulsion and, consequently, in a decrease in the deposition rate. The deviation of the log K value at low r from the straight line (fig. 2) reflects the transition from prevailing attraction to repulsion due to particle adhesion. Similar trends were observed in all experiments at pH < 6.5. The described effect of the magnitude of particle charge on deposition rate is also supported by the slopes of the plots in fig. 1 and 2, which are larger the more strongly charged the haematite particles. In the case discussed here the latter would not seem applicable in view of the low particle surface population and the strong dependence of adhesion on pH.The values of K extrapolated to zero coverage, which are not necessarily the same as those that could be obtained from the lowest measured adhesion densities as exemplified in fig. 2, are plotted as a function of pH in fig. 3. The particle deposition takes place over a narrow pH range near the isoelectric point of haematite particles. One would expect adhesion over the entire range of pH where the particles and the substrate have charges of opposite sign. However, at pH < ca. 6 steel is readily recharged causing a decrease in the deposition rate. The maximum of K corresponds to a W value of ca. 1, which indicates that in this case the interactions between the collector surface and the particles do not affect the deposition rate.In order to test the mass-transfer theory of Ruckensteinz09 21 and of Pfefferz31 24 and Happelz2 it is necessary to produce the condition at which only the short-range attraction force prevails; thus, diffusion should not be affected over the major portion of the boundary layer. This condition is most readily accomplished by either adding an indifferent electrolyte or a solute that can neutralize the particle charge. In either case coagulation takes place, which caw -s a change in particle size and morphology. Alternatively surfactants or polyelectrolytes could be added,2g 25 but the system is then altered due to restructuring of the solid/solution interfacial layers. In order to interpret the data, the radius of the adhering particles must be known [eqn (lo)]; hence, in coagulating systems it is necessary to account for particle An alternate explanation could be based on the surface saturation72 KINETICS OF PARTICLE ADHESION aggregation.In principle, one may ascertain the change in the particle size distribution from Smoluchowski’s theory, although the reliability of such results is questionable. The experimental procedure employed in this work minimized the coagulation effects when the simple electrolyte (NaNO,), added to achieve high ionic strengths, was in excess of the critical coagulation concentration. Thus, the conditions implied in eqn (10) were fulfilled, making it possible to test its applicability to the studied system.Fig. 4 gives the relationship between the ratio Cin/Cout and the flow rate as calculated from the theory of Ruckenstein and of Pfeffer and Happel by using eqn (4) and (10). The line drawn through the experimental points has the theoretically predicted slope of - and agrees with the Ruckenstein, Pfeffer and Happel expression providing W is chosen to be 1.5. This value is higher than expected (W = 1 ) and the small deviation could mean that the actual experiments may not have fully met the assumptions introduced in the model. These results do confirm the applicability of the Ruckenstein, Pfeffer and Happel treatment to the studied system, which indicates that the adhesion of the small haematite particles on steel is primarily governed by diffusion. Although data for systems at high electrolyte concentration (fig.4) and at pH 7 at low electrolyte concentration (fig. 3) correspond to a value of W = 1 , there is a difference in the conditions. At pH 7 the particles and the substrate are of opposite charge resulting in interaction forces, the magnitudes of which change with the particle deposition. Thus, only at the initial stage does the attraction prevail (corresponding to the value of K extrapolated to zero coverage). In contrast, the addition of neutral electrolyte to a system of particles and substrate of like charge reduces the repulsion barrier between the two surfaces. In the latter case the rate of deposition should be independent of the surface coverage by particles, as indeed found experimentally. At low pH, where the particles and the substrate are positively charged, the rate of deposition is diminished as the concentration of neutral electrolyte is lowered below a critical value (fig.5). The maximum rate of deposition for small haematite particles (dh = 0.15 pm) occurs at W = 1 in good agreement with the data in fig. 4. The faster deposition (w < 1) of larger particles (dh = 0.5 pm) indicates that eqn (10) underestimates the effect of the particle size on deposition rate. It would appear that the gravity and interception mechanisms are felt by particles smaller than predicted by the simple 25 mol dm -13 NaNO,, arrow in fig. 5) is quite close to the critical coagulation concentration for the same electrolyte as determined with a haematite sol.3z Fig. 5 also shows that the slope of the plotted function in the slow deposition region is steeper for smaller particles.The critical electrolyte concentration for deposition (1.6 x THEORETICAL EVALUATION OF w A N D ‘ K The dependence of the deposition rate on the repulsion barrier, which exists between the particle and the collector, can be evaluated theoretically using different When the diffusion boundary layer is thick compared with the interaction-force approaches.1,2,17,18.33 boundary layer, the mass-transfer coefficient, K, is given by1’> 31 K = (l/Kf+ 1/Kd)-I where Kequals Kd in the absence of interaction forces and Kf is related to the repulsion barrier through the expression Kf = D(o/27rkT)$ exp (- V,,,/kT) in which V,,, is the maximum value of the interaction potential and co = - d2 V/dh2,N.K A L L A Y , J . D. NELLIGAN AND E. M A T I J E V I C 73 where h is the distance of separation. The total interaction energy, I/, can be calculated from the dispersion and double-layer contributions. The former is available for the sphere/plate case from the known expression^.^^ The double-layer interaction energy can be estimated using the models derived by Hogg, Healy and Fuerstenau (HHF),35 based on the solution of the linearized Poisson-Boltzmann equation for the one-dimensional sphere-sphere model. Alternat- ively, it can be obtained by employing the Poisson-Boltzmann equation in its two-dimensional form (BMRF).36 The values from the latter theory were evaluated using a variable number of terms in the Taylor series and extrapolating to a limiting value.37 TABLE 1 .-COMPA~ON OF THE EXPERIMENTAL AND CALCULATED VALUES OF THE STABILITY CONSTANT w FOR DEPOSITION OF HAEMATITE ON STEEL 2.5 x lop3 1.06 10.2 40 5.0 x 10-3 0.76 5.3 31 1.0 x 0.27 0 0.01 1.5 x lo-* 0 0 0 2.5 x 0 0 0 In calculating the double-layer energies the values of the potentials were substituted by zeta potentials as obtained from electrokinetic mobilities.38 In this work the experimentally determined stability coefficient is compared with the calculated values using both the HHF and BMRF models. Values of W were calculated using A = 1.4 x J, the value giving the best fit to the data for the kinetics of the removal of haematite from The results are summarized in table 1, which compares the experimental stability constants with those computed using the BMRF and HHF expressions.At concentrations of NaNO, 2 1.5 x mol dm-3 both expressions yield log W = 0 in agreement with the experimental findings. At lower ionic strengths, at which the energy barrier is still present, the calculated values of Ware considerably higher than expected, particularly when the HHF model is employed. The discrepancy may be due to not considering the effect of the liquid flow on the particles crossing the energy barrier.” However, it is significant that the critical concentration of deposition can be predicted from the theory. Furthermore, calculations with different values of the Hamaker constant showed no effect of the latter on the electrolyte concentration which causes rapid particle deposition. This work was supported by the National Science Foundation Grant CPE-8 1 1 161 2.We thank the referees for their constructive criticisms. ’ J . K. Marshall and J. A. Kitchener, J . Colloid Interface Sci., 1966, 22, 342. ‘ M. Hull and J. A. Kitchener, Trans. Faraday SOC., 1969, 65, 3093. G. E. Clint, J. H. Clint, J. M. Corkill and T. Walker, J . Colloid Interface Sci., 1973, 44, 121. P. H. Tewari and A. B. Campbell, in Recent Developments in Separation Science, ed. N. N. Li (CRC Press, Cleveland, Ohio, 1978), vol. IV, p. 83. V. G. Levich, Physicochemical Hydrodjwamics (Prentice Hall, Englewood Cliffs, New Jersey, 1962), p. 69.74 K I N E T I C S OF P A R T I C L E ADHESION H. P. Hermansson, Chem. Scr., 1977, 12, 102. B. D. Bowen and N. Epstein, J . Colloid Interface Sci., 1979, 72, 8 1.B. Alince, J. Colloid Interface Sci., 1979, 69, 367. A. Bleier and E . Matijevid, J . Chem. Soc., Faraday Trans. I , 1978, 74, 1346. l o F. K: Hansen and E . Matijevid, J . Chem. SOC., Faraday Trans. I , 1980, 76, 1240. l 1 E. J . Clayfield and A. L. Smith, Environ. Sci. Technol., 1970, 4, 413. l 2 L. A. Spielman and S . L. Goren, Enuiron. Sci. Technol., 1970, 4, 135. l 3 J. Th. Cookson Jr, Environ. Sci. Technol., 1970, 4, 128. l4 J. E. Kolakowski and E. Matijevid, J . Chem. Soc., Faraday Trans. I , 1979, 75, 65. l6 R. J. Kuo and E . Matijevid, J . Colloid Interface Sci., 1980, 78, 407. l i E. Ruckenstein and D. C. Prieve, J. Chem. Soc., Faraday Trans. 2, 1973, 69, 1522. lU L. A. Spielman and S. K. Friedlander, J . Colloid Interface Sci., 1974, 46, 22.l9 K. A. Nielsen, J . Colloid Interface Sci.. 1978, 64, 13 1. 2o E. Ruckenstein and F. Westfried, C.R. Acad. Sci., 1960, 251, 2467. 21 E. Ruckenstein, Chem. Eng. Sci., 1964, 19, 131. 22 J . Happel, AIChE J., 1958, 4, 197. 23 R. Pfeffer, Ind. Eng. Chem., Fundam.. 1964, 3, 380. 24 R. Pfeffer and J. Happel, AKhE J., 1964, 10, 605. 2s K. M. Yao, M. T. Habibian and R. O’Melia, Enuiron. Sci. Technol., 1971, 5, 1105. 26 W. J. Wnek, D. Gidaspow and D. T. Wasan, Chem. Eng. Sci., 1975, 30, 1035. 2 i W. J. Wnek, D. Gidaspow and D. T. Wasan, J . Colloid Interface Sci., 1977, 59, 1. 2u J. Gregory and J . Wishart, Colloids Surf., 1980, 1, 313. 29 N. Kallay and E. Matijevid, J . Colloid Interface Sci., 1981, 83, 289. 30 E. Matijevid and P. Scheiner, J . Colloid Interface Sci., 1978, 63, 509. 31 E. Ruckenstein and D. C. Prieve, in Testing and Characterization of Powders and Fine Particles, ed. J . K . Beddow and T. P. Meloy (Heydon, London, 1980), p. 10’lff. 32 E. Matijevid, R. J. Kuo and H. Kolny, J . Colloid Interface Sci., 1981, 80, 94. 33 R. Rajagopalan and J. S . Kim, J . Colloid Interface Sci., 1981, 83, 428. 34 J. Visser, in Surface and Colloid Science, ed. E. Matijevid (Wiley-Interscience, New York, 1976), 3s R. Hogg, T. W. Healy and D. W. Fuerstenau, Trans. Faraday Soc., 1966, 62, 1638. 36 E. Barouch, E. Matijevic, T. A. Ring and M. Finlan, J . Colloid Inferface Sci., 1978, 67, 1; 1979, 70, 37 J. D. Nelligan, N. Kallay and E. Matijevic, J . Colloid Interface Sci., 1982, 89, 9. 38 A. L. Smith, in Dispersions of Powders in Liquids, ed. G. D. Parfitt (Elsevier, New York, 1969), R. J. Kuo and E. Matijevid, J. Chem. SOC., Faraday Trans. I , 1979, 75, 2014. vol. 8, p. 3ff. 400. p. 129ff. (PAPER 1 / 1680)

ISSN:0300-9599    

DOI:10.1039/F19837900065

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I, 1983, 79, 75-80 Reactions for Chemical Systems far from Equilibrium BY GEOFFREY A. M. KING Physics and Engineering Laboratory, DSIR, Lower Hutt, New Zealand Received 25th January, 1982 Reactions formulated for systems operating far from equilibrium may generate misleading conclusions if they contain an implied assumption of steady state. This assumption is introduced most commonly by eliminating an intermediate product from a pair of elementary, reactions, condensing them into a single summary reaction. The consequences of using such inadequate reactions are illustrated through two well known model systems, the Lotka oscillator and the Brusselator. The Brusselator includes a termolecular reaction which could be generated by summarizing any of several sets of elementary reactions.When an elementary set is used in place of the termolecular reaction, the revised Brusselator fails to show its characteristic limit cycle. Both the Brusselator and the Lotka scheme have reactions in which the same substance appears both as reactant and as product, formed by eliminating some intermediate in a catalytic cycle. Including even short-lived intermediates alters the stability shown by the Lotka scheme, so that behaviour in the phase plane changes from a conservative cycle into an expanding spiral. Since Lotkal introduced his well known theoretical oscillator (S+) Y 3 E (1 4 (where constant reagents S will be given unit concentration in later kinetic analysis) the most exciting development has been the scheme of Prigogine and Lefever, (S+) X 2 E.( 2 4 The special termolecular reaction (2 c) was invoked to make it possible for the system’s steady state to become unstable. It is unstable if (3) (4) XS = kl/k4, 5 = k2k4/klk3 k, > k, X: + k4 and in this regime the system exhibits a ‘limit-cycle’ oscillation in the X , Y phase plane, see fig. 1 (a), curve A. Although Prigogine and Lefever pointed out that reaction (2c) is not a chemically realistic reaction, the passage of time has allowed their caution 7576 CHEMICAL SYSTEMS FAR FROM EQUILIBRIUM to be forgotten. Many of the hundreds of papers [see ref. (3) for references] discussing scheme (2) draw parallels between its limit-cycle oscillation and the oscillations observed in the chemical laboratory and in b i ~ l o g y .~ However, the shortcomings of reaction (2c) [(a) it is termolecular and (h) the same substance, X, appears both as reactant and as product] are quite critical. Our present purpose is to emphasise the care needed in formulating reactions for the kinetic analysis of systems operating far from equilibrium. We use schemes (1) and (2) to illustrate the artefacts that unrealistic reactions may produce. The feature common to both shortcomings of reaction (2c) is the use of a summary equation for kinetic analysis instead of a set of elementary reactions. When the elementary reactions are condensed into the summary equation, intermediate products are eliminated by the assumption that they are in steady state. If a system operates far from equilibrium, like scheme (2) when showing limit-cycle behaviour, this assumption is not warranted.In the case of shortcoming (b) above, when a reaction has the same substance both as reactant and as product, the arguments against it are rather subtle, so we shall deal with it last. It is easiest to start with an example of a summary equation familiar to all experimental chemists. Copper dissolves in dilute nitric acid with the following stoichiometry 3Cu + 8NH0, -+ 3Cu(NO,), + 4H,O + 2NO. ( 5 ) As Evans5 remarked, ‘No-one really pictures a collision between eleven molecules’. He then elucidated the elementary reactions, showing that the system is autocatalytic in nitrogen dioxide. Now, the production of nitrogen dioxide is balanced by destruction so it does not appear in the summary reaction (5).(This particular system is heterogeneous and oscillatory. The balance is achieved only over complete cycles of the oscillation.) Likewise with HNO,. However, if the conditions are changed to well-stirred concentrated acid the main gaseous product becomes nitrogen dioxide and NO is balanced out in the resulting stoichiometric equation Cu+ 4HNO,3 Cu(NO,), + 2H,O+ 2N0,. ( 6 ) The elementary reactions are the same but their relative throughputs have altered making it appropriate to assume different materials in steady state. Although the simultaneous collision of eleven molecules is incredible, many chemists accept the validity of three-body collisions, even after Bodenstein’s6 analysis and refutation of the putative termolecular reaction 2NO+0, -+ 2N0,.(7) Theoretically we expect three reactants to interact by consecutive bimolecular steps since a termolecular reaction would have to compete with its bimolecular components and it has a much lower occurrence. It is significant that there is no unique way of resolving any particular termolecular reaction into component bimolecular steps. For example X + Y + Z (8 4 x + z - + 3 x (8 b) approximates to reaction (2c) for values of X , Y and 2 selected so that Z is in steady state. However, when reaction (8) is substituted for reaction (2c) in scheme (2) the system does not oscillate but rather goes directly to an overall steady state different from that for the original scheme (2). On the other hand, when x+x+z (9 4 Y+Z+3X (9 b)G. A. M. KING 77 substituted for reaction (2c) there is no finite steady state for Y and Z, Y going 1 infinity while 2 goes to zero.One special resolution of reaction ( 2 ~ ) ’ B, x + x e z (104 a 1s to has achieved popularity in the literature because it is thought still to allow the limit-cycle oscillation. It is easy, though, to give an example indicating the contrary. The dashed line B in fig. 1 ( a ) shows the effect of replacing reaction (2c) with scheme (10): k,, k , 8 6 1’ L 2 timc 1.0 2- % 0.9 0 2 L <Y 6 FIG. 1.-(a) Curve A, limit cycle generated by scheme (2), k , = 0.01, k , = 0.04, k , = 0.01, k , = 0.01. Curve B, the result of replacing reaction ( 2 c ) by scheme (lo), a = 0.05, p, = 0.05, p, = 0.01. (b) Variation of X 2 / Z with time for the conditions of curve B, showing departures from equilibrium between X and Z.and k , as before, PI = a = 0.05, /?, = 0.01 yielding equivalent k , = P1p2/a so that the inequality (4) is satisfied, and 2, = 2.25 ensuring equilibrium between X and Z at the starting point, X , = & = 1.5. The steady state for X and Y remains the same but, instead of following a limit cycle, the system spirals in to the steady state. Fig. l(b) shows how X 2 / Z varies with time. It starts with unity corresponding to steady state for reaction (10a) above, rapidly departs from this value and then converges on equilibrium through a damped oscillation as the whole system moves to the overall steady state. Finally, let us consider reactions where the same substance appears both as reactant and as product, e.g. reactions (2c), (1 a), (1 b), (8b) and (lob).We use scheme (1) for illustration. Its reactions ( 1 a) and (1 6) were suggested* by the reproductive growth of living things and, in their ecological setting, they certainly act as summaries for numerous chemical reactions. Lotka was careful to point out that they are simplistic.78 CHEMICAL SYSTEMS FAR FROM EQUILIBRIUM The problem is that whereas one reactant, S in reaction (1 a), suffers consumption and transformation, the other, X, suffers at most a change in physical properties like momentum. Possibly, any other physical encounter would equally transform S, such as a collision between two molecules of S. In order to make collision with X unique, it seems necessary to postulate an intermediate compound between S and X so that the structure of X can influence the isomerization (or dissociation) of S.Although the lifetime of this intermediate compound may be very brief and its concentration therefore much less than that of X, it still affects the kind of stability shown by the steady state of a scheme like scheme (1). The steady state for scheme (1) is X , = h,/h,, Y , = hl/h2. (1 1) When departures from this steady state are small, the product term, AXAY, can be omitted from the differential equations describing scheme (1) so that they become linear. Analysis then yields two eigenvalues 1 = k i d h l h 3 (12) corresponding to an undamped oscillation about the steady state, which is thus a centre. We now include intermediate compounds in reactions (1 a) and (1 b) : (S+) x 3 u (134 (S+) Y 5 E.The steady state is (134 X , = h3/h2, Y, = hl/h,, us = hlh,/h,a,, V , = h1h,/h2~2 (14) which for X and Y are the same as eqn (1 1). Stability analysis about the steady state yields four eigenvalues L1 = 1, = 0, 1, = - (2h1 + a1), A4 = - (2h3 + a2). (1 5 ) The last two eigenvalues represent modes of decay while the first two correspond to neutral stability, a characteristic different from that indicated by eqn (12) for scheme The linearized analysis applies only in the neighbourhood of the steady state, while ‘interesting’ behaviour is distant from it. For this reason, the qualitative differences between schemes (1) and (1 3) are not immediately obvious from their different kinds of stability about the steady state. However, it is well known from Volterra’s workg that scheme (1) has an associated constant of motion (16) describing a closed trajectory in the phase plane about the centre X,, Y,.A larger G corresponds to a trajectory spaced at all points further from X,, K . On the other hand, scheme (1 3) appears not to have any constant of motion associated with it, leading us to expect that its trajectories about X,, K are not closed. (1). G = W/XS - In ( ~ I ~ s ) l I h + [ Y / r, - In ( y / Y,)llh,G. A. M. KING 79 Numerical analysis confirms this expectation. In fig. 2, the closed curve A was generated from scheme (1) and it shows the conservative ' predator-prey ' oscillation about the steady state X,, Y,. The dashed curve B was generated from scheme (13) and it spirals outwards, showing no conservative motion.Reagents, S, are supplied at constant concentrations and, because of time delays in passing material through U and V, the autocatalytic growth of X is not completely offset by the autocatalytic consumption of Y. This is so even when the relative concentrations of U and V are small. Mean values of X per cycle thus increase and mean values of Y increase along with them. The rate of expansion in the phase plane is controlled by terms containing ( U - U,)/(X-X,) and (V- K)/( Y - G), and therefore varies inversely with a, and a,. 0 2 L 6 8 10 X FIG. 2.-Curve A, conservative trajectory generated by scheme ( l ) , h, = 0.015, h, = 0.01, h, = 0.02. Curve B, the result of adding intermediates to make scheme (13), a, = 0.05, a, = 0.05. Clearly, the conservative oscillation (curve A) of scheme (1) depends on the use of the special reactions (1 a) and (1 b) in which the same substances appear both as reactants and as products. Any chemically realistic system would have intermediate products, like U and V in scheme (1 3), causing time delays which allow the oscillations to grow until limited by factors outside the scheme considered.It has been a-gued [ref. (3), p. 1631 that the conservative oscillations of scheme (1) count against its use as a model chemical oscillator. Because scheme (1 3) portrays the growth of oscillations from small, almost sinusoidal, waves to large distorted waves, as may be observed in laboratory systems, it deserves more serious consideration as a model. To sum up, reactions for kinetic analysis far from equilibrium should avoid the implied assumption of steady state. This implies that the following kinds of reactions should not be used: (a) reactions with molecularity greater than two and (b) reactions in which the same substance appears both as reactant and as product. A. J. Lotka, J . Am. Chem. Soc., 1920, 42, 1595. I. Prigogine and R. Lefever, J . Chem. Phys., 1968, 48, 1695. G. Nicolis and I. Prigogine, Self-organization in Nonequilibrium Systems (Wiley, New York, 1977).80 CHEMICAL SYSTEMS FAR FROM EQUILIBRIUM Faraday Symp. Chem. SOC., 1975, 9. U. R. Evans, Trans. Faraday SOC., 1944, 40, 120. M. Bodenstein, Z . Phys. Chem., 1922, 100, 68. J. J. Tyson, J . Chem. Phys., 1973, 58, 3919. A. J. Lotka, J . Phys. Chem., 1910, 14, 271. N. S. Goel, S. C. Maitra and E. W. Montroll, Rev. Mod. Phys., 1971, 43, 231. (PAPER 2/148)

ISSN:0300-9599    

DOI:10.1039/F19837900075

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1983, 79, 81-92 Alternative Boundary Conditions for a Drop Hanging from a Circular Tube BY M. AMARAL FORTES* AND ROSA M. MIRANDA Departamento de Metalurgia, Instituto Superior TCcnico, CEMUL-Centro de Mecinica e Materiais da Universidade Tkcnica de Lisboa, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal Receive,d 9th February, 1982 The stability of pendent liquid drops with axial symmetry is usually discussed for a specific type of boundary condition, ignoring the possibility of transitions between one type and another. The alternative configurations are denoted by 6, ri and re, according to whether the drop contacts the base of the tube or its inner (Ti) or outer edge (re). Transitions between these configurations are predicted from the appropriate thermodynamic functions for both volume- and pressure-controlled drops.The main conclusion is that in volume-controlled drops the r configurations are unstable relative to the 6 configuration when the actual contact angle is reached, but in pressure-controlled drops the reverse may be true. The behaviour of drops in pressure-controlled conditions depends on the geometry of the system in which the drop is formed. The limiting stable configurations of drops are discussed, taking into account the transitions between different boundary conditions. In various instances, particularly in the drop-weight1? and related methods of determining the surface tension of a l i q ~ i d , ~ a pendent drop is formed at the end of a vertical cylindrical tube, the liquid being fed into the drop through the interior of the tube.There are essentially two methods by which the shape of the drop may be altered. These methods will be termed volume ( V ) and pressure ( p ) controlled. Using the first (see fig. 8 later), which is the situation pertinent to the drop-weight method, the liquid is forced into the drop by means of a syringe or an equivalent device, so that the volume of the drop is directly controlled. In pressure-controlled drops, it is a pressure difference, for example pl-po in fig. 9, that is changed, producing alterations in the drop configuration. This case includes situations where liquid is added from the outside to the tube or to a reservoir above the tube. Pressure-controlled drops are formed and measured in a method4 for measuring the surface tension of a liquid, and, more generally, when a drop is formed with a pipette.In both V- and p-controlled drops various types of equilibrium configurations may be considered with respect to the boundary condition at the line of contact between the drop and the tube end. This line will be referred to as the base line of the drop. There are three distinct possibilities, as shown in fig. 1 : the ri configuration, the re configuration, and the 8 configuration. In the first two the radius of the base line has a fixed value, ri or re, respectively the inner and outer radii of the tube. The possibility of r configurations is due to the property that sharp edges have of pinning the line of c o n t a ~ t . ~ ' ~ This property is directly related to the high radius of curvature of the solid surface at the edge.' In the 8 configurations the radius r of the base line is between ri and rp, and the boundary condition is the contact angle 8, which will be regarded as characteristic of the three interfaces that meet at the base line.The contact angle 8182 BOUNDARY CONDITIONS FOR A PENDENT DROP / i ‘C 0 FIG. 1.-The three types of boundary conditions: Ti, re and 0. The angle 9 in the r configurations is in general distinct from the contact angle 8. is related to the interfacial tensions ysL (tube-liquid-drop), ys (tube-surrounding-fluid) and y (of the fluid interface) by Young’s equation Y 0 configurations cannot occur when the value of 5 in eqn (1) is outside the interval The purpose of this paper is to investigate which of the three configurations actually occurs in each case, as I/ or p is changed. This may be regarded as a generalization of the problem of stability of pendent liquid drops, which is generally treated for only one type of boundary c0ndition,~9 8* ignoring the possibility of transitions to configurations of a different type.Such transitions have been brkfly discussed by Boucher et aL8 for one or two particular cases of I/-controlled drops, but without attempting a sound thermodynamic analysis. Such an analysis will be undertaken in this paper and leads to a general method for studying the stability of fluid interfaces when bifurcation in a sequence of equilibrium shapes occurs. This rnzthod has been applied to liquid bridges between parallel identical plateslo and to rotating fluid masses.ll [- 1, + 11.THERMODYNAMIC BASIS For given values of the imposed parameters (i.e. drop volume or pressure difference; tube radii; contact angle) the drop may in general assume equilibrium configurations of each of the three types defined above. To decide which is the actual configuration we calculate the appropriate thermodynamic function (Helmholtz or Gibbs energy) of a closed system comprising the drop and the surrounding fluid in each of the three configurations. As will be shown, the stable configuration is always the one with smallest energy. More precisely, continuous transitions between different configurations will occur whenever the energy decreases. VOLUME-CONTROLLED DROPS For comparing Helmholtz energies of configurations at constant volume and temperature it is sufficient12 to calculate @ai yi + potential energy) where Ri is the area of the interface i with interfacial tension yi.We separate the term (Qy + potential energy) where 0 is the fluid interface area and denote this term by A,, the Helmholtz energy of the drop.M. A. FORTES A N D R. M. MIRANDA 83 In Appendix 1 it is shown [eqn (16)] that for any configuration with base-line radius r, the Helmholtz energy A , can be calculated from A, = w 2 y + s," (Ap), d V is the pressure difference, at constant r , between points B and B at the level of the base line, respectively located in the drop and in the surrounding fluid (fig. 8); b is the radius of curvature at the drop apex, z the height of the drop, p(p > 0) is the density difference between the two fluids and g is the acceleration due to gravity.The integral in eqn (2) can be calculated numerically from curves of (AP)~ as a function of V for constant r. Such curves were prepared from the tables of Padday13 for axially symmetric menisci. Each table refers to a value of b/a where a = ('r (4) is the capillary constant, and includes the coordinates of the drop profile and the value of the angle # with an horizontal plane at any point (fig. 1). Eqn (2) avoids the determination of the centre-of-mass of the drop, which is not included in the tables. Fig. 2 shows examples of Helmholtz-energy curves with A,/ya2 plotted as a function of V/a3 for constant r/a. Values of # can be assigned to each point and curves for constant # can also be drawn.Alternatively, such curves can be obtained directly from eqn (17). We shall now illustrate how stability can be assessed from such curves. Consider drops with fixed r and fixed V. The configurations in the upper branch of the corresponding energy curve are unstable. To see this, we take a drop configuration in the upper branch with a volume just below the maximum; its energy will decrease when it changes to the neighbouring configuration with the same volume in the lower branch. The first configuration is therefore unstable relative to the second. The stability of the configuration in the lower branch, relative to perturbations at constant r, is expected, because otherwise there would be two maxima of A and no minimum. The stable configurations are therefore those in the lower branch of the energy curve.The same argument can be applied to V-controlled 8 configurations. In both cases the conclusions drawn coincide with those reached by Pittss in a more elaborate analysis of the stability of V-controlled pendent drops. The stable configurations are indicated in a different way in fig. 3, with r/a plotted as a function of V/a3 for various values of #. The dashed curve is the envelope of the various curves and gives the maximum possible value of V/a3 for a given r/a. It indicates the stability limit of r drops. For r/a up to ca. 0.56 the maximum volume is reached when # = 90". Volume-controlled 8 configurations are stable up to the maximum volume for each 8;9 the dotted curve indicates the limiting configurations.Curves of this type were previously published by Boucher et aZ.14 For # 5 48' the complete curves are closed loops, but for smaller values ,Iiey are spiralled,14 as shown schematically in the insert of fig. 3. For any configuration with base-line radius r, the total energy A (including the interfacial energies at the tube end) is A = A, + n(rg - r2) ys + n(r2 - r t ) ysL.84 BOUNDARY CONDITIONS FOR A PENDENT DROP t c 8 N F 6 1 0 'g: 4 2 1 0 2 4 6 Vla FIG. 2.-Helmholtz energy of drops as a function of volume for various values of r / a : (a) 1.0, (6) 0.5, (c) 0.1. The upper branches are not shown complete. The circles indicate stable 8 configurations with 4 = 8 = 90'. If we subtract the constant n(rE ys - r: ysL) and divide by ya2 we obtain the quantity [cf.eqn (113 A r2 A* = 2 - n - cos 8. (6) ya2 a2 This equation is applicable, with cos 8 replaced by < [eqn (l)], even if If transitions between r and 8 configurations are allowed, stability will be decided by comparing the values of A* for both types of configurations. When two configurations, infinitesimally different, are possible for a given volume, it will be the one with smaller A* that is stable. This is a generalization of the argument exemplified above for drops with fixed r. With the curves of A,/ya2, such as those in fig. 2, plotted for various values of r / a and 8, the comparison of A* values can be made by superimposing the relevant curves with the appropriate translation n(r2/a2) cos 8 [cf. eqn (6)] along the energy axis.Clearly only the stable branch of such curves has to be considered. > 1.M. A. FORTES A N D R . M. M I R A N D A 85 FIG. 3.-Volume as a function of base line radius for different values of 4: (a) 30°, (b) 45', ( c ) 60°, ( d ) 90°, (e) 135'. The envelope of the loops is the dashed line. The dotted line gives the maximum volume for each 4. In the main figure only the stable portions of the curves are drawn. The complete curves are schematically shown in the inserts. PRESSURE-CONTROLLED D R O P S The stability of the various configurations is in this case determined by comparing the Gibbs energies for a given pressure difference. The Gibbs energy of the system, Go, excluding the interfacial energies at the tube end, is calculated in Appendix 2 leading to the equation (7) k' 2 Go = A,-(Ap+k) V+- V2 where k and k' are constants that depend on the geometry of the system and on the contact angles of the two fluids with their reservoirs [eqn (23) and (25)]; the other symbols have the same meaning as before. The applied pressure difference pl-po is related to Ap by p1 -po = Ap +pb gHb -pt gH, + constant (8) provided the radii of the reservoirs are constant in the region of contact with the fluid interface (see Appendix 2); Hb and Ht denote the heights of the contact lines relative to the base line (fig.9). If the reservoirs are large enough so that the level of the fluid is constant in the reservoirs, k and k' in eqn (7) can be taken equal to zero and eqn (8) gives p1--p0 = Ap+constant. Fig. 4 shows curves of G,/ya2 (with Go = A,-ApV) as a86 BOUNDARY CONDITIONS FOR A PENDENT DROP 2 N P 1 0 u 1 FIG.4.-Gibbs energy, Go, of drops as a function of Ap for various values of r / a : (a) 1.0, (b) 0.75, (c) 0.5. The upper branches are not shown complete. Values of the angle 4 are indicated in each curve: x , 30'; 0, 4 5 O ; 0, 60'; 0, 90°. For r / a = 0.75 and 1 , the angle 90' is not reached. function of Ap for various constant values of r / a . Values of 4 are marked on the curves. The inatability of the configurations (for fixed r/a) in the upper branch of the curves can be concluded from fig. 4 using the same argument as above. The stability of the other shapes up to ( A P ) ~ ~ ~ has been directly demonstrated by P i t t ~ . ~ Fig. 5 shows curves of Ap as a function of r / a for constant 4.The envelope of the curves (dashed) coincides with the 8 = 90' curve for values of r / a up to ca. 0.56 and gives the limiting stable r configurations. No stable configurations occur for 2.4.9 The complete curves are again of two types, which are shown schematically in the inserts of fig. 5 . The stability of p-controlled 8 configurations was not studied by P i t t ~ . ~ However, comparison of the values of Go shows that, for each 6, stable configurations occur up to the minimum in Ap. The dotted line in fig. 5 indicates such limiting configurations. . r / a The total Gibbs energy, G, for a configuration with base radius r is G = Go + n(r2, - r2) ys + n(r2 - rt) ysL. (9) Using the same procedure as before [eqn (5) and (6)] we define The stability is assessed from the value of G*, for fixedp, -po; the stable configuration is the one of lower G*.Translation of the Go/ya2 curves (such as those in fig. 4) according to eqn (10) provides a simple means of comparing the G* values for the various configurations. As eqn (7) and (8) show, the stability and therefore the transitions between different configurations depend on geometry.M. A. FORTES A N D R . M. M I R A N D A 87 I r FIG. 5.-Pressure difference Ap as a function of r / a for different values of the angle 4: (a) lo', (b) 135', ( c ) 45', ( d ) 90'. The complete curves are schematically shown in the inserts. The dashed line is the envelope of the minimum Ap for each 4. The dotted curve is the locus of the minimum Ap for each 4. The curves for 4 and 180'-$ almost coincide in the low r / a region.RESULTS AND DISCUSSION Using the energy curves such as those in fig. 2 and 4, it is possible to predict the transitions that occur between r and 0 configurations as the volume or pressure difference is changed. The criterion is always that between two neighbouring (i.e. infinitesimally different) configurations the drop will assume the configuration of lower energy; the other configuration is unstable. For configurations with a fixed boundary condition this argument leads to the same conclusions with regard to stability as do more elaborate treatmentss that consider, for any equilibrium shape, the change in energy that results from a perturbation in the shape at fixed boundary conditions. The treatment presented assumes that a unique equilibrium contact angle, satisfying Young's equation, can be defined between the liquid and the tube end.Contact-angle hysteresis is ignored ; its inclusion would require considering a rough or heterogeneous tube end.15 Situations of complete wetting of the tube end by one of the fluids are included in the treatment presented. Young's equation is not applicable in such cases and cos 0 should be replaced by the actual value of 5 [cf. eqn (l)] in the equations for the energy. The previous analysis and the following conclusions are of course independent of the value of the capillary constant, a, and in particular also hold in the limit pg = 0 (spherical drops). VOLUME-CONTROLLED D R O P S In this case it is always the 0 configuration that has a smaller Helmholtz energy when both the 0 and an infinitesimally close Y configuration are geometrically possible.88 BOUNDARY CONDITIONS FOR A PENDENT DROP / / / /C I / / / / k’ 1 ; I .,// / / / d / / / ‘i re / r . re FIG. 6.-Examples of transitions in V-controlled drops as the volume increases from zero in the rj configuration. The loop is for the appropriate contact angle 8. The dashed curve is the envelope of the various loops (see fig. 3). p1 is the value of r / a at maximum volume and p2 the maximum r / a for that 8. An example is shown in fig. 2 for 8 = 90°, in which case the total energy A* = A,/ya2 [eqn (6)]. The ri configuration has lower A* than the re configuration when V -+ 0. The transitions between ri, re and 8 configurations, as the volume increases or decreases starting in a particular configuration, are conveniently discussed from plots of V/a3 against r / a for constant 8, such as those in fig.3. Various possibilities are shown in fig. 6 for drops starting in the ri configuration and with the volume increasing from zero. The maximum volume can be reached in any of the three types of configuration. In the more complicated case [fig. 6(f)] the drop changes from ri -+ 8 + re + 8 + ri. All paths shown can be traversed in the reverse direction. .Note that the Oconfigurations in the loop regions to the left of the maximum volume are always unstable. For a given value of 8 it is possible to define two critical reduced radii p1 and pz,M. A. FORTES A N D R. M. MIRANDA 89 Of" FIG. 7.-Critical reduced radii pI and p2 as a function of contact angle 0 for V-controlled drops.respectively at the maximum volume and maximum radius for that 8. The drop breaks in the re configuration if r,/a < pl. The drop breaks in the 8 configuration if r , / a < pl. In the other cases it breaks in the ri configuration. Fig. 7 shows the variation of p1 and p2 with 8. Note that all stable configurations indicated in fig. 3 and 6 can be produced. The actual path for a drop depends on the initial configuration and on the way V is changed, and can always be determined from these figures. An interesting situation is that of an r drop, the volume of which is decreased reaching the contact-angle curve in the region of instability [fig. 6(a), path indicated on the left-hand side]. The drop will then be unstable relative to fluctuations at constant 8 and will break.Finally, if the ratio ( = (ys-ysr,)/y in the second term of eqn (1) is outside the interval [ - 1,1] no 8 configurations can occur. For ( > 1 the configuration with lower energy is re and for ( < - 1 it is ri. No continuous transitions occur in this case. PRESSURE-CONTROLLED DROPS For p-controlled drops the stability of the various configurations may depend on the type of system used to form the drop. The discussion will be confined to the cases where the levels of the drop liquid and surrounding fluid are constant. In this case, if a 0 configuration and a r configuration (infinitesimally different and with the same Ap) are both geometrically possible, it is always the r configuration that has lower Gibbs energy and is therefore stable.As Ap -+ 0 the ri configuration has lower energy (for < 1) than the re configuration. As Ap increases from zero ( V increases from zero) the drop remains in the ri configuration until it breaks, even if the contact-angle is reached. As in V-controlled drops, all stable 8 configurations represented in fig. 5 can be obtained, but not by increasing the pressure difference from zero starting from a r configuration. The sequence of configurations can be discussed from curves of Ap against r / a for constant 8, such as those in fig. 5. For < > 1 the ri configuration has lower energy at low Ap, but for large Ap the situation is reversed. For < < - 1 the re configuration is always the one of lower Gibbs energy.4 FAR 190 BOUNDARY CONDITIONS FOR A PENDENT DROP When the system constants k , k’ in eqn (7) are not equal t o zero, the behaviour ofp-controlled drops may be different, and transitions from r t o 8 configurations may occur. For example, if the tube radius rt -+ 0, then k , k’ -+ f. CD [eqn (23) and (25)]. A given applied pressure is then equivalent to a fixed volume of the d r o p [cf. eqn (24)]. This situation is therefore equivalent to that of V-controlled drops and r + 8 transitions will occur whenever A * decreases. APPENDIX 1 HELMHOLTZ ENERGY OF DROPS To avoid calculating the potential energy of the drop we determine ‘indirectly’ its Helmholtz energy A , from eqn (2), the derivation of which will be given in this Appendix. A , includes the interfacial energy of the drop and the potential energies of the drop and surrounding fluid.The zero of the potential energy will be taken at the level of the tube end. r---- I I i I .f ! 6’ -0- - 1 I I I FIG. 8.-Volume-controlled drop: the shape of the drop is changed by displacement of the piston. Consider the closed system shown in fig. 8, with a drop of volume V and constant base radius r, connected to liquid in a tube with a piston. The system also includes a given volume of the surrounding fluid. To avoid unnecessary complications we assume that the fluids have a 90° angle of contact with the tube wall, so that the interfacial energy of the tube wall is independent of the position of the piston. The system is in equilibrium with an externally applied pressure p1 in the piston, the value of which is PI = AP-Pgh (11) where p is the density difference, h the height of liquid in the tube and (12) 2Y Ap = - - PgZ b is the pressure difference between points B and B‘; b is the radius of curvature at the apex and 2 the height of the drop (fig.8). Note that p1 is not the pressure in the surrounding fluid. The work of p 1 for a volume change d V of the drop at constant r , under isothermic reversible conditions, equals the change in the total Helmholtz energy: pldV= dA,+dA, (13) where dA, is the change in potential energy of the fluids in the tube dA, = -pgh d V.M. A. FORTES A N D R. M. MIRANDA Combining eqn (ll), (13) and (14) we obtain dA, = Ap d V. Integrating at constant base radius between V = 0 and another volume V we find A , = nr2y + jov (Ap), d V 91 (15) since, for V = 0, the potential energy is zero and the surface area is m2.[(Ap), indicates that Ap is taken at constant r.] For drops with a constant 8, an extra term d( - nr2y cos 8) appears in the right-hand side of eqn (13), which is related to the interfacial energies at the tube end. The final expression for the Helmholtz energy is then A , = nr2y cos 8 + j,' (A& d V since for V = 0 it is r = 0. (AP)~ is the pressure difference at constant 8. APPENDIX 2 GIBBS ENERGY OF DROPS Consider the closed system shown in fig. 9, comprising fixed volumes of the two fluids: the drop liquid, t, and the surrounding fluid, b. There may be a third fluid or pistons that allow the pressure difference p1 -pa to be changed.It will be assumed that the levels of the two fluids b and t are always in a region of constant radius, rb and rt, of the respective containers. The contact angles of the fluids with their containers are, respectively, 8b, 8; and Ot. The heights of the apex of the meniscus of each fluid in relation to the tube end are Hb and H,, respectively, for fluids b and t. Finally, the pressure differences across the menisci at their apexes are denoted by Apb and Apt, respectively. When the volume of the drop changes by dV, the change in the height of the fluid levels is given by - nrt dH, = nrg dH, = d V. We separate in the Helmholtz energy the contributions of the drop, A,, and those of the fluids (18) I I 4 'b FIG. 9.-Pressure-~ontrolled drop: the shape of the drop is changed by varying the pressure differencep, -po between two fixed levels in the surrounding fluid.4-292 BOUNDARY CONDITIONS FOR A PENDENT DROP in their containers A , and A,. For a reversible change in the drop volume, at constant temperature and with constant base line radius, we have where the pressure difference can be written as PI-PO = ‘P-‘Pb +PbgHb -k ‘Pt- Pt gHt. (20) Ap = pB-pB’ is the pressure difference between points B and B’ in the two fluids, at the level of the tube end. Under the hypothesis made above Ap, and Apt are constants. dA, = (-2nyr, cos 8,+nr,2gpt H,)dH, For the changes dA, and dA, we have (21) where re is the outer radius of the tube. A , can be calculated from eqn (16) derived in Appendix 1. I dA, = [ - 2ny(r, COS t?, -k re COS 8;) + gpb Hb] dHb Combining eqn (18)-(21) we obtain dA, -ApdV-k d V = 0 (22) where (23) For constant p , -pl we have d(Ap) + k’d V = 0 where Therefore, the equilibrium condition, eqn (19), is equivalent to the stationary point of k‘ 2 GO = A,-(Ap+k) V+- V2 which we term the Gibbs energy of the system (at constant base line radius). A similar equation can be written for 8 configurations. If the radii r, and rb are very large (r,, rb +a) we have Apb = Apt = 0 and k = 0, k’ = 0. The equilibrium is then discussed in terms of Go = A,-ApV (27) for constant Ap (since H , and Ht are then constants). W. D. Harkins and F. E. Brown, J . Am. Chem. SOC., 1919, 41, 499. M. C. Wilkinson, J . Colloid Interface Sci., 1972, 40, 14. J. G. Padday, Pure Appl. Chem., 1976,48,485. P. F. Levin, E. Pitts and G. C. Terry, J . Chem. Soc., Faraday Trans. I , 1976, 72, 1519. J. F. Oliver, C. Huh and S. G. Mason, J. Colloid Interface Sci., 1977, 59, 568. E. Bayramli and S. G. Mason, J . Colloid Interface Sci., 1978, 66, 200. published. E. Pitts, J . Fluid Mech., 1974, 63, 487. M. A. Fortes, J. Colloid Interface Sci., 1982, 88, 338. I’ M. A. Fortes, Can. J. Phys., 1981, 59, 109. R. E. Johnson Jr and R. H. Dettre, Adv. Chem. Ser., 1964, 43, 112. l 3 J. F. Padday, Philos. Trans. R. SOC. London, Ser. A , 1971, 269, 265. l4 E. A. Boucher, M. J. B. Evans and H. J. Kent, Proc. R. SOC. London, Ser. A, 1976, 349, 81. l5 R. E. Johnson Jr, R. H. Dettre and D. A. B. Brandreth, J . Colloid Interface Sci., 1977, 62, 205. ’ M. A. Fortes, Wettability of Polymer Surfaces, Am. Chem. SOC. Meeting, New York, 1981, to be * E. A. Boucher and H. J. Kent, J . Colloid Interface Sci., 1978, 67, 10. (PAPER 2/245)

ISSN:0300-9599    

DOI:10.1039/F19837900081

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1983, 79, 93-97 Electron Spin Resonance Spectra of Tetrafluoroethylene Radical Cation? BY AKINORI HASEGAWA~ A N D MARTYN C. R. SYMONS* Department of Chemistry, The University, Leicester LE 1 7RH Received 8th February, 1982 Exposure of a solid solution of FCCl, containing C,F, to prays at 77 K gave a species whose e.s.r. spectrum comprised an anisotropic quintet attributed to hyperfine coupling to the four equivalent fluorines of the C,F, radical cation. An extra, small doublet splitting is assigned tentatively to the fluorine of a matrix molecule interacting with the radical cation. INDO calculations show that the radical cation has a planar structure with the unpaired electron in the bonding orbital, the estimated I9F coupling constants being in good agreement with the experimental data.Considerable interest has been aroused in the e.s.r. spectra and structure of the tetrafluoroethylene radical anion, C,F;, since Williams and coworkers detected the anion in y-irradiated solid solutions of C,F, in [2H12]tetramethy1~ilane and in methyltetrahydrofuran.' They considered, from the magnitude of 19F and 13C hyperfine coupling constants, that the radical has a planar structure with the unpaired electron in the o* rather than the n* molecular orbital which was predicted by ab initio calculations of the parent molecule. In a subsequent paper with Morton and Prestoq2 however, they concluded that there is insufficient evidence to decide in favour of either a o* or a n* configuration for the planar structure of the radical anion.On the other hand, one of the present authors has pointed out that these planar structures seem to be incompatible with the experimental data, but that the chemically more reasonable pyramidal (chair) configuration is quite compatible and hence is the most probable structure .3 The C2F, anion is formed preferentially in these solvents because the cationic centres formed from solvent molecules are rapidly converted into trapped radicals, whereas the liberated electrons are forced to migrate and react with solute molecules such as CzF,., The electron-capture species are formed preferentially in these matrices. In contrast, solvents such as CCl,, FCC1, and PF, capture electrons with high efficiency so that solute anions are not formed. However, the electron-loss centres do not undergo further chemical reactions and hence the positive ' hole' can migrate via electron transfer to solute molecules, and those with ionization potentials less than that of the solvent loose electrons to give radical c a t i o n ~ .~ ~ ~ - * The aim of the present study was to detect the e.s.r. spectrum for the C2F,+ cation, using these matrices, and to compare its electronic structure as deduced therefrom with that predicted by simple theory. It was hoped that the results would make an interesting contrast with those for the radical anion. t Taken as Unstable intermediates, Part 203. 1 Present address : Department of Chemistry, Faculty of Science, Hiroshima University, Hiroshima 730, Japan. 9394 E.S.R. SPECTRA OF TETRAFLUOROETHYLENE EXPERIMENTAL Tetrafluoroethylene containing [2H]limonene as a polymerization inhibitor was supplied by Fluorochem Ltd.Solid solutions containing up to 5 mol% C,F, in fluorotrichloromethane (supplied by Fluorochem Ltd.) were prepared by a method similar to that used in the e.s.r. study on C,F, and containing a process for purification of C,F, from [2H]limonene.1 Samples were exposed in a Vickrad V o y-ray source at 77 K for 2 h at a dose rate of ca. 1.0 Mrad h-l. E.s.r. spectra were measured at 77 K or above on Varian E3 or El09 spectrometers. E.s.r. spectra of irradiated pure FCCI, were also measured. 35296 ( 9 4 4 3 M H t ) FIG. 1.-First-derivative X-band e.s.r. spectrum for a solid solution of 5 mol % C,F, in FCCl, measured at 77 K on a Varian E3 spectrometer after exposure to 6oCo y-rays at 77 K, showing parallel features assigned to the C,F: radical cation interacting with the fluorine in a FCCl, matrix molecule.The positions of the calculated lines were adjusted for the slightly non-linear magnetic sweep of the spectrometer. RESULTS AND DISCUSSION The e.s.r. spectrum of an irradiated solid solution of C,F, in FCCl, showed the presence of several parallel features comprising doublets which have small coupling constants of 13.9 G, as seen in fig. 1. No substantial change was brought about in the spectrum by the rotation of the sample tube in the cavity. Since the central part of the spectrum is complicated by the signals of radicals produced from FCCl,, the e.s.r. spectrum of an irradiated pure solid of FCCl, was also measured.By comparison of the expanded central parts of these two spectra, it was confirmed that there is one intense doublet with a coupling constant of ca. 13.9 G in the central part of the spectrum of fig. 1 . The observed doublet appears at the exact position expected for the central doublet of a quintet of parallel features. Since there are no other intense signals corresponding to the perpendicular components of the double quintet, it was assumed that the central intense doublet is, at the same time, the perpendicular components of the double quintet with a coupling constant of ca. 0 G for the quintetA. HASEGAWA A N D M. C. R. SYMONS 95 and a coupling constant of up to 13.9 G for the doublet. The small value for the perpendicular splitting was indirectly supported by the fact that the separations of the parallel features of the quintet are exactly equal to one another, each being 146.3 k0.2 G, no second-order splitting being observed.The quintet can be attributed to hyperfine coupling to four equivalent fluorine nuclei ( I = i). Since it has been established that the cation radical of a solute molecule forms in an irradiated FCCl, matrix as a result of the migration of positive holes produced in the rnatrix,,9' this quintet spectrum is assigned to the C,F,+ radical cation. The extra doublet splitting may originate from the fluorine nucleus in a FCC1, matrix molecule which is close to the C,F,+ radical cation. Possibly a charge-transfer complex between C,F,+and FCCl, is involved. Unfortunately, no C,FZ radical cations formed in either of the solid matrices of CCl, and SF, which normally also stabilize cation radicals.,T E.s.r.parameters derived from the spectrum observed at 77 K are listed in table 1, together with approximate orbital populations estimated from atomic parameters in the normal way.9 On annealing, the e.s.r. spectrum decayed before it became iso- tropic, so no direct measurement of Aiso was possible. TABLE ~.-E.s.R. PARAMETERS' AND SPIN DENSITIES OF THE C,Ff RADICAL CATION FORMED IN FCC1, MATRIX g values h.f. couplings/Gb spin densities" gll g1 nuclei A 4 P s PPZ 1.9905 1.9903 19F(4)d 146, cv 0.003 0.090 1 9 ~ ( 1 ) e 13.9 G(13.9) a These parameters were determined from the e.s.r. spectrum measured on a Varian El09 spectrometer; 1G = T; the values of spin densities were obtained by use of the usual atomic hyperfine coupling constants;8 four equivalent fluorine nuclei of the C,Ff radical cation; one fluorine nucleus from the FCCl, interacting with the C,F,+ radical cation; f this value might have an error of & 10 G if some lines in the central part of the observed spectrum are involved in the signals of C,Fz.For comparison with these experimental results, INDO calculations were performed for the C,F,+ radical cation which is isolated and has no interaction with matrix molecules. The optimized geometry was obtained for the planar structure with the parameters listed in table 2, and it was also ascertained that both the possibilities of the chair and boat configurations were ruled out for the C,F,+ radical cation.Comparison of the structural parameters of the radical cation and the parent molecule, shown in tables 2 and 3, indicates that the C-C bond length is increased, as expected for loss of a bonding n-electron, the L FCC bond angle remaining almost unchanged. The C-F bond length is reduced compared with the calculated value for the parent molecule. This reflects the expected increase in C-F n-bonding. Spin densities in the atomic orbitals of the C,F,+ radical cation in the optimized geometry are shown in table 2. The spin density in the p z orbital of each fluorine is 0.1017, in good agreement with the observed value of 0.090 (table I). The spin density in the 2s orbital of each fluorine was calculated to be 0.0019, which is smaller than the observed value of 0.003.This calculated 2s spin density, however, yields a calculated isotropic hyperfine coupling constant of 85.2 G, since the value is generally given as a product of the calculated 2s spin density and the proportionality constant96 E.S.R. S P E C T R A OF TETRAFLUOROETHYLENE TABLE 2.-OPTIMIZED GEOMETRY AND SPIN DENSITY DISTRfRUTION OF THE C,FT RADICAL CATION CALCULATED BY THE INDO METHOD structural parametersa nuclei orbitalsb spin densities r c c / A = 1.40, C(2) S 0.0096 rcF/A = 1.31, PY P S 0.0035 P Z 0.2965 - 0.0005 L FCC/O = 124., F(4) S 0.0019 P X - 0.0058 - 0.0025 PY Pt 0.1017 a Planar structure; the z axis is perpendicular to the molecular plane and the y axis is collinear to the C-C bond. TABLE 3 .--CALCULATED AND EXPERIMENTAL GEOMETRIES OF THE PARENT C,F, MOLECULE parametersa calculatedb experimentalC r C C / A I .33 1.33 1.34 1.30 L FCC/O 125.5 123.0 a Planar structure; by INDO method, ref.(9); ref. (10). of 44829 G determined empirically for a fluorine nucleus.12 Thus the isotropic coupling constant of the fluorine calculated by INDO method is larger than that observed, i.e. 49 G. These are structurally unimportant differences. The important result is that the difference between observed and calculated spin densities is small. We concluded that INDO calculations explain satisfactorily the observed results for the C,Fi radical cation formed in the FCCl, matrix. INDO calculations and the results show that, as expected, the unpaired electron occupies the n-bonding orbital composed largely of the p z orbitals, perpendicular to the molecular plane, of carbon and fluorine atoms.According to the results of the INDO calculations, the isotropic coupling constant of the 13C nucleus of the C,Fi radical cation is 7.9 G, in accord with a planar n structure. This value is much smaller than that of 48.7 G which was observed for each 13C nucleus in the C,F; radical ani0n.l Also the anisotropy in the 19F hyperfine coupling constants for the radical cation is much larger than that observed for the radical anion. This comparison shows that the planar n* structure for the C,F; radical anion is highly improbable. The effect of the positive charge is brought out by comparing the results for C,F,+ with those of neutral R,cF radicals. (RcF, radicals are thought to be pyramidal at the carbon centre and hence are not so suitable for comparison as planar R$F radicals.) Typical results for such radicaisl, give an anisotropy (2B) of ca.140 G, giving a 2p(n) orbital population of ca. 12.9%. This compares with 9% on each fluorine for the cation. Multiplying by two to take account of delocalization onto the two -CF, groups gives 18%. This large increase reflects the increased electron donation for fluorine induced by the positive charge.A. HASEGAWA AND M. C . R. SYMONS 97 We conclude that the C,FZ cation has the planar n structure expected, there being nothing unusual about its structure. This underlines the problem for the anion, whose e.s.r. properties, in our view, rule out a simple planar IT* structure. R. I. McNeil, M. Shiotani, F. Williams and M. B. Yim, Chem. Phys. Lett., 1977, 51, 433. J. R. Morton, K. F. Preston, J. T. Wang and F. Williams, Chem. Phys. Lett., 1979, 64, 71. M. C. R. Symons, J. Chem. Res., S, 1981, 286. M. C. R. Symons, Pure Appl. Chem., 1981, 53, 223. A. Hasegawa, M. Shiotani and F. Williams, Faraday Discuss. Chem. SOC., 1977, 63, 157. M. C. R. Symons and I. G. Smith, J. Chem. Res., S, 1979, 382. ’ T. Shida, Y. Egawa, J. Kubota and T. Kato, J. Chem. Phys.. 1980,73,5963, and papers cited therein. * K. Toriyama, K. Nunome and M. Iwasaki, J. Phys. Chem., 1981,85, 2149. M. C. R. Symons, Chemical and Biochemical Aspects of Electron Spin Resonance Spectroscopy (Van Nostrand Reinhold, London, 1978), p. 176. J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital Theory (McGraw-Hill, New York, 1970), p. 106. T. T. Brown and R. L. Livingstone, J. Am. Chem. Soc., 1952, 74, 6084. J. A. Pole and D. L. Beveridge, Approximate Molecular Orbital Theory (McGraw-Hill, New York, 1970), p. 131. K. Toriyama and M. Iwasaki, J. Phys. Chem., 1969, 73, 2919. (PAPER 2/234)

ISSN:0300-9599    

DOI:10.1039/F19837900093

出版商:RSC    

年代:1983

数据来源: RSC