摘要:

Contents 4259 4269 4277 4287 4295 431 1 4321 4335 Protonation Constant of Caffeine in Aqueous Solution M. Spiro, D. M. Grandoso and W. E. Price Ionic Equilibria in Acetonitrile Solutions of 2-, 3- and 4-Picoline N-oxide Perchlorates, studied by Potentiometry and Conductometry L. Chmurzynski, A. Wawrzyn6w and Z. Pawlak Liquid-phase Adsorption of Binary Ethanol-Water Mixtures on NaZSM-5 Zeolites with Different Silicon/Aluminium Ratios W-D. Einicke, M. Heuchel, M. v.Szombathely, P. Brauer, R. Schollner and 0. Rademacher Influence of Oxidation/Reduction Pretreatment on Hydrogen Adsorption on Rh/TiO, Catalysts. An lH Nuclear Magnetic Resonance Study J. P. Belzunegui, J. M. Rojo and J. Sanz Volumetric Properties of Mixtures of Simple Molecular Fluids A. C. Colin, E. G. Lezcano, A.Compostizo, R. G. Rubio and M. D. Peiia Study of Ultramicroporous Carbons by High-pressure Sorption. Part 4.-Iso- thems and Kinetic Transport in Activated Carbons J. E. Koresh, T. H. Kim, D. R. B. Walker and W. J. Koros Kinetic and Equilibrium Studies associated with the Solubilisation of n- Pentanol in Micellar Surfactants G. Kelly, N. Takisawa, D. M. Bloor, D. G. Hall and E. Wyn-Jones The effect of Carboxylic Acids on the Dissolution of Calcite in Aqueous Solution. Part 1 .-Maleic and Fumaric Acids R. G. Compton, K. L. Pritchard, P. R. Unwin, G. Grigg, P. Silvester, M. Lees and W. A. House 130-2Contents 4259 4269 4277 4287 4295 431 1 4321 4335 Protonation Constant of Caffeine in Aqueous Solution M. Spiro, D. M. Grandoso and W. E. Price Ionic Equilibria in Acetonitrile Solutions of 2-, 3- and 4-Picoline N-oxide Perchlorates, studied by Potentiometry and Conductometry L.Chmurzynski, A. Wawrzyn6w and Z. Pawlak Liquid-phase Adsorption of Binary Ethanol-Water Mixtures on NaZSM-5 Zeolites with Different Silicon/Aluminium Ratios W-D. Einicke, M. Heuchel, M. v.Szombathely, P. Brauer, R. Schollner and 0. Rademacher Influence of Oxidation/Reduction Pretreatment on Hydrogen Adsorption on Rh/TiO, Catalysts. An lH Nuclear Magnetic Resonance Study J. P. Belzunegui, J. M. Rojo and J. Sanz Volumetric Properties of Mixtures of Simple Molecular Fluids A. C. Colin, E. G. Lezcano, A. Compostizo, R. G. Rubio and M. D. Peiia Study of Ultramicroporous Carbons by High-pressure Sorption. Part 4.-Iso- thems and Kinetic Transport in Activated Carbons J. E. Koresh, T. H. Kim, D. R. B. Walker and W. J. Koros Kinetic and Equilibrium Studies associated with the Solubilisation of n- Pentanol in Micellar Surfactants G. Kelly, N. Takisawa, D. M. Bloor, D. G. Hall and E. Wyn-Jones The effect of Carboxylic Acids on the Dissolution of Calcite in Aqueous Solution. Part 1 .-Maleic and Fumaric Acids R. G. Compton, K. L. Pritchard, P. R. Unwin, G. Grigg, P. Silvester, M. Lees and W. A. House 130-2

ISSN:0300-9599    

DOI:10.1039/F198985FX021

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY ASSOCIAZIONE ITALIANA DI CHIMICA FlSlCA DEUTSCHE BUNSEN-GESELLSCHAFT FUR PHYSIKALISCHE CHEMIE KONINKLIJKE NEDERLANDS CHEMISCHE VERElNlGlNG SOCIETE FRANGAISE DE CHIMIE, DIVISION DE CHlMlE PHYSIQUE FARADAY DIVISION GENERAL DISCUSSION No. 90 Colloidal Dispersions University of Bristol, 10-12 September 1990 Orga nising Com mitte e Professor R. H. Ottewill (Chairman) Professor P. Botherol Professor E. Ferroni Or J. W. Goodwin Professor H. Hoff mann Professor A.L. Smith Professor P. Stenius Dr Th. F. Tadros Professor A. Vrij Dr D. A. Young The joint meeting of the Societies will be directed towards examining current understanding of the behaviour of colloidal dispersions. In particular, stability and instability, short range interactions, dynamic effects, non-equilibrium interaction, concentrated dispersions and order-disorder phenomena will form topics for discussion.The preliminary programme is now availablemay be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM No. 26 Molecular Transport in Confined Regions and Membranes Oxford, 17-18 December 1990 Experimental, theoretical and simulation studies which address fundamental aspects of molecular transport will be discussed in the following main areas: a) Transport of atoms and molecules in pores, zeolite networks and other cavities; time-dependent statistical mechanics of small systems in confined geometries b) Molecular transport through synthetic membranes, biological membranes, smectic liquid crystalline phases and Langmuir Blodgett films; the dynamics of the molecules forming the membrane c) Diffusion, reorientation, conformational dynamics, viscosity and conductivity of polymer melts, to include papers dealing with bulk systems since the segments of the polymer will move in the anisotropic environment of the complete chain d) Applications of Brownian dynamics to the study of diffusion in porous media and across membranes including the transport of flexible aggregates such as microemulsions e ) The growth of crystals, colloidal aggregates and droplets on irregular surfaces and in pores Contributions for consideration by the Organising Committee are invited and abstracts of about 300 words should be sent by 31 December 1989 to: Dr D.J. Tildesley, Department of Chemistry, The University, Southampton SO9 SNH. Full papers for publication in the Symposium Volume will be required by August 1990.THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY ASSOCIAZIONE ITALIANA DI CHIMICA FlSlCA DEUTSCHE BUNSEN-GESELLSCHAFT FUR PHYSIKALISCHE CHEMIE KONINKLIJKE NEDERLANDS CHEMISCHE VERElNlGlNG SOCIETE FRANGAISE DE CHIMIE, DIVISION DE CHlMlE PHYSIQUE FARADAY DIVISION GENERAL DISCUSSION No. 90 Colloidal Dispersions University of Bristol, 10-12 September 1990 Orga nising Com mitte e Professor R. H. Ottewill (Chairman) Professor P. Botherol Professor E. Ferroni Or J. W. Goodwin Professor H. Hoff mann Professor A.L. Smith Professor P. Stenius Dr Th.F. Tadros Professor A. Vrij Dr D. A. Young The joint meeting of the Societies will be directed towards examining current understanding of the behaviour of colloidal dispersions. In particular, stability and instability, short range interactions, dynamic effects, non-equilibrium interaction, concentrated dispersions and order-disorder phenomena will form topics for discussion. The preliminary programme is now availablemay be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM No. 26 Molecular Transport in Confined Regions and Membranes Oxford, 17-18 December 1990 Experimental, theoretical and simulation studies which address fundamental aspects of molecular transport will be discussed in the following main areas: a) Transport of atoms and molecules in pores, zeolite networks and other cavities; time-dependent statistical mechanics of small systems in confined geometries b) Molecular transport through synthetic membranes, biological membranes, smectic liquid crystalline phases and Langmuir Blodgett films; the dynamics of the molecules forming the membrane c) Diffusion, reorientation, conformational dynamics, viscosity and conductivity of polymer melts, to include papers dealing with bulk systems since the segments of the polymer will move in the anisotropic environment of the complete chain d) Applications of Brownian dynamics to the study of diffusion in porous media and across membranes including the transport of flexible aggregates such as microemulsions e ) The growth of crystals, colloidal aggregates and droplets on irregular surfaces and in pores Contributions for consideration by the Organising Committee are invited and abstracts of about 300 words should be sent by 31 December 1989 to: Dr D.J. Tildesley, Department of Chemistry, The University, Southampton SO9 SNH. Full papers for publication in the Symposium Volume will be required by August 1990.

ISSN:0300-9599    

DOI:10.1039/F198985BX023

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

ISSN 0300-9599 JCFTAR 85(6) 11 99-1 509 (1 989) I199 1207 1217 1233 1245 I257 1267 1279 1294 1303 13 115 1327 1337 1351 1357 1365 1373 JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions I Physical Chemistry in Condensed Phases CONTENTS Modelling the Effect of Pressure on the Rates of Ionic and Polar Reactions B. Gavish Effect of Solvent Fluctuations in the Electron-transfer Process between two Fe+ Ions The Orthobaric Surface Tensions of the Three Binary Mixtures formed by Krypton, Ethane and Ethene B. S. Almeida, V. A. M. Soares, I. A. McLure and J. C. G. Calado Fourier-transform Infrared Studies of Copper-containing Y Zeolites. De- hydration, Reduction and the Adsorption of Ammonia J. Howard and J. M. Nicol General Phenomenological Treatment of Activation, Diffusion, and Pseudo- diffusion Control of Bimolecular Reactions in Solution J.F. Garst Translational and Rotational Molecular Motion in Solutions of Alkali-metal Halides in Dimethyl Sulphoxide A. Sacco, M. Carbonara and M. Hob Influence of Pretreatment on the Properties of Ag/a-Al,O, Catalysts containing Large (k lpm) Pure and Cs-promoted Silver Particles. Part 2 . 4 0 Oxidation Measurements G. R. Meima, M. Hasselaar, A. J. van Dillen, F. R. van Buren and J. W. Geus Spectroscopic Characterisation and Photochemical Behaviour of a Titanium Hydroxyperoxo Compound G. Munuera, A. R. Gonzilez-EIipe, A. Fernandez, P. Malet and J. P. Espinos Photocatalytic Oxidation and Adsorption of Methylene Blue on Thin Films of Near-ultraviolet-illuminated TiO, R. W. Matthews Excess Molar Enthalpies of Steam-n-Hexane and Steam-n-Heptane up to 698.2 K and 12.6 MPa N.Al-Bizreh, C. N. Colling, N. M. Lancaster and C. J. Wormald A Cubic Equation of State for Mixtures Containing Steam C. J. Wormald and N. M. Lancaster Reactivity of AIPO,-5 and the Origin of its Hydrophilic Property A. Endoh, K. Mizoe, K. Tsutsumi and T. Takaishi Interactions between Metal Cations and the Ionophore Lasalocid. Part fj.-potentiometric and Electron Spin Resonance Study of the Complexation of Gd3+ in Methanol by Lasalocid and Simpler Carboxylic Acids M. Tissier, G. Mousset and J. Juillard In situ Scanning Tunnelling Microscopy of a Platinum { 1 1 1) Surface in Aqueous Sulphuric Acid Solution S. Sugawara and K. Itaya Measurement of Activity Coefficients, Mass-transfer Coefficients and Diffusion Coefficients in Multicomponent Liquid Mixtures by Reversed-flow Gas Chromatography P.Agathonos and G. Karaiskakis The Structure of Concentrated Aqueous Ammonium Nitrate Solutions P. A. M. Walker, D. G. Lawrence, G. W. Neilson and J. Cooper Superoxide Ions Formed on MgO through the Agency of Presorbed Molecules. Part 1 .-Spectroscopic Electron Spin Resonance Features E. Giamello, P. Ugliengo and E. Garrone A. Gonzalez-Lafont, J. M. Lluch, A. Oliva and J. Bertran A1 F A R 11383 1397 1409 1425 1439 1451 1463 1469 1485 1493 1501 Con tents Thermodynamic and Vibrational Characterization of CO Adsorption on variously Pretreated Anatase V. Bolis, B. Fubini, E. Garrone and C. Morterra Infrared Spectroscopic Studies on the Aggregation of Polyoxyethylene Surfactants in Hydrocarbon Solvents W.F. Pacynko, J. Yarwood and G. J. T. Tiddy Solid-state Nuclear Magnetic Resonance Study of a Series of Phosphonic and Phosphinic Acids Activation Energies of the Reduction of Bulk and Supported Vanadium Pentoxide H. Bosch and P. J. Sinot Spectroscopic Studies of Silver(o) Centres formed Radiolytically in Water- Ethanol Solvents at 4 and 77 K A. D. Stevens and M. C. R. Symons Adsorption of Carbon Monoxide and Carbon Dioxide on Cerium Oxide studied by Fourier-transform Infrared Spectroscopy. Part 2.-Formation of Formate Species on Partially Reduced CeO, at Room Temperature C. Li, Y. Sakata, T. Arai, K. Domen, K-i. Maruya and T. Onishi Hamilton’s Principle of Least Action in Nervous Excitation trans + cis Photoisomerization of 1 -Styrylnaphthalene and its 4’-Bromo- and 4’-Chloro-derivatives. A Fluorimetric and Laser Flash Photolytic Study F. Elisei, U. Mazzucato and H. Gorner Effect of Pressure on the Properties of a Surfactant Micelle and a Lipid Membrane studied by the Spin-probe Method H. Yoshioka and T. Mitani Effects of Pressure on the Photoreduction of p-Benzoquinone in Normal and Reversed Micellar Systems K. Tamura, M. Abe and M. Terai Diffusion of Ethane in Silicalite- 1 by Frequency Response, Sorption Uptake and Nuclear Magnetic Resonance Techniques N. Van-Den-Begin, L. V. C. Rees, J. Caro, M. Biilow, M. Hunger and J. Karger R. K. Harris, L. H. Merwin and G. Hagele G. Dickel

ISSN:0300-9599    

DOI:10.1039/F198985FP073

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions II Molecular and Chemical Physics For the benefit of readers of Faruduy Transactions I, the contents list of Faruduy Transactions 11, issue 6, is reproduced below. 581 597 607 623 635 643 65 1 659 67 1 689 691 709 127 74 1 747 759 765 Secondary Relaxations and the Structure of Glass S. S. N. Murthy Infrared Multiple Photon Absorption and Decomposition of 2-Methyloxetane K. A. Holbrook, G. A. Oldershaw, C. J. Shaw and P. E. Dyer Infrared Matrix Isolation of Hydrogen-bonded Complexes between Acetone and Hydrogen Iodide. Irradiation and Temperature Effects L. Schriver Externally Driven Fluctuation of Concentration in the Second-order Chemical Reaction and the Dynamic Fluctuation Increase Viscoelastic and Ultrasonic Relaxation in Molten Mixture of Acetamide and Calcium Nitrate G.Berchiesi, G. Vitali, R. Plowiec and S. Barocci A Monte Car10 Study on Preferential Solvation of Lithium@ in Aqueous Ammonia S. Kheawsrikul, S. V. Hannongbua, S. U. Kokpol and B. M. Rode Partial Molal Absorption Spectroscopy. Application to Solvated Electrons S. Golden, T. R. Tuttle Jr and S. Obremski Low-energy Electron-impact Excitation of Methane, Silane, Tetrafluoromethane and Tetrafluorosilane M. G. Curtis and I. C. Walker Chemical Kinetics Assisted by a Microcomputer. A Study of the Pyrolysis of Acetaldehyde P. F. Knewstubb ENDOR Spectra of the Intercalated Water Molecules in V'adyl(w,v) Phosphate Pentahydrate L. Alagna, D. Attanasio, T. Prosperi and A. A. G. Tomlinson The Reaction of NO3 with Atomic Oxygen C E.Canosa-Mas, P. J Carpenter and R. P. Wayne Laboratory Studies of the Reactions of the Nitrate Radical with Chloroform, Methanol, Hydrogen Chloride and Hydrogen Bromide C. E. Canosa-Mas, S. J. Smith, S. Toby and R. P. Wayne Electrostatic Bond Dipole Moments from Dimethyl Ether, Methanol, Methane and Water C. Huiszoon Detection in the Gas Phase of Unstable Ketenimines. Photoelectronic Spectrum of N-Methylketenimine S. Lacombe and G. Pfister-Guillouzo The Collisional Quenching of Sr[5s4d ('&)I by H2 and I& over the Temperature Range 850-1000 K studied by Time-resolved Atomic Emission following Pulsed Dye-Laser Excitation D. Husain and G. Roberts An Improved Carbon-13 Nuclear Shielding Scale W. T. Raynes, R. McVay and S. J. Wright Computer Simulations of Fluids in Zeolites X and Y G.B. Woods and J. S. Rowlinson M. Katsumoto and A. Morita (1)The following papers were accepted for publication in Furuduy Transactions I during March 1989. 8/03583K 8/03943G 8/04117B 8/04168G 8/04185G 8 M 9 B 8/0483 1B 8/04837A 8/04839H 8/04883E 8/04888F Modification of Crystalline and Amorphous Phases during the Synthesis of M-ZSM-5 Zeolites (M = Li, Na, K) Nagy, J. B., Bodart, P., Collette, H., Gabelica, Z., Nastro, A. and Aiello, R. Comparison of Entropic and Enthalpic Components of the Barrier Symmetry Factor, p, for Proton Discharge at Liquid and Solid Hg in relation to the Variation of Tafel Slopes and p with Temperature Conway, B. E. and Wilkinson, D. P. Intermicellar Interactions and Micelle Size Distribution in Aqueous Solutions of Polyoxyethylene Surfactants Kato, T., Anzai, S-I., Takano, S.and Seimiya, T. Effect of Magnetic Field on Radical Yields during the Photoreduction of Xanthene Dyes in Viscous Media Klimtchuk, E. S., Irinyi, G., Khudyakov, I. V., Margulis, L. A. and Kuzmin, A. V. Ultrasonic Studies of a Rotator Phase Solid: Carbon Tetrabromide Yoon, C. S., Sherwood, J. N. and Pethrick, R. A. CO Hydrogenation using Cobalt Manganese Oxide Catalysts: Comments on the Mechanism of Carbon-Carbon Bond Formation Hutchings, G. J., van der Riet, M., and Hunter, R. Experimental Activity Coefficients in Aqueous Mixed Solutions of KCl and KF at 25 'C Compared to Monte Car10 Simulations and MSA Calculations Sorensen, T. S., Jensen, J. B. and Sloth, P. Solubilization of Some Tetramethylammonium Salts and of Ethyltrimethylammonium Bromide by their Homologues in Chloroform Czapkiewicz, J.Solubility of H2S, C& and CH4 in N-Formyl Morpholine Mather, A. E., Jou, F-Y., Deshmukh, R. D. and Otto, F. D. Thermodynamic Classification of Anions through Constituent Analysis of Transfer Enthalpies in Acetonitrile-Methanol Mixtures Kondo, Y., Fujiwara, T., Hayashi, A. and Kusubayashi, S. Study of the Ammonia-Zeolite Interaction in Modified ZSM-5 by Temperature-programmed Desorption of Ammonia Reschtilowski, W., Unger, B. and Wendlandt, K-P. Crystallization of Hydroxyapatite from Aqueous Solutions in the Presence of Cadmium Koutsoukos, P. G. and Dalas, E. Initial Cracking hperties and Physicochemical Characterization of Acid-leached Small Port and Large Port Mordenites by Pulse n-Hexane Cracking, Infrared and 27Al-MASNMR Spectroscopy Vansant, E.F., Goovaerts, F., Philippaerts, J., de Hulsters, P. and Gelan, J. Infrared Structural Vibrations of Acid-leached Mordenites: Determination of Structural Aluminium by Wavenumber and Intensity Analysis Vansant, E. F., Goovaerts, F. and de Hulsters, P. A Physicochemical Study of the Iron@)-containing Isomorph of Zeolite ZSM-5 Smith, T. D. and Handreck, G. P. High-resolution Solid-state 13C NMR Study of Dynamic Behaviour of Tetramethylammonium Ions Trapped in Zeolites Hayashi, S., Suzuki, K. and Hayamizu, K. Ultrasonic Studies of n-Eicosane Single Crystals Pethrick, R. A., Sherwood, J. N. and Yoon, C. S. (ii)8/04990D 9/00128J 9/00136K 9/00151 91002536 9/00256A 9/00258H 9/00259F 8/05056B 8/05057K 8/05060K 9/00371A 9/oo479c 9D0547A 9D0561G 9100636B 9/00709A 9/007191 9/00729F 9/00936A 9/00937J Kinetics of the Solvolysis of tram-Dichlorotetra(4-t-Butylpyridine)Cobalt(111) Ions in Water and in Water-Propan-2-01 Mixtures Wells, C. F.and Halawani, K. H. Aerosol OT Reversed Micelles as Carrier Agents Tondre, C. and Derouche, A. Amorphous Semiconductor-Electrolyte Junction. Interference Effects during the Growth of Anodic Nb205 Films under Absorbed Light Di Quarto, F., Piazza, S. and Sunseri, C. Effects of Oxidation/Reduction Treatments of WAl203 on Catalytic Activity and Selectivity for Hexane Reforming Rochester, C. H. Conductivity Study of NaI Solutions in Propanol-Butanol Mixtures at 298.15 K. The Effect of Ion Pairing on the Standard Dissolution Enthalpies of NaI Taniewska-Osinska, S., Bald, A., Piekarska, A.and Szejgis, A. A Pulse Radiolysis Study of Ion Pairing of Diphenylpolyene Radical Anions with Tetrabutylammonium and Sodium Cations in Tetrahydrofuran Yamamoto, Y., Aoyama, T. and Hayashi, K. Thermodynamics of Multilayer Adsorption of Aqueous Butanol Solution on to Printex and Graphitized Carbon Blanks Dekany, I. and Kiraly, 2. Ring-Disc Electrodes. Part 24.4uxes at a Thioninecoated Electrode Albery, W. J. and Mount, A. R. Thermodynamic Properties of Amphiphilic Drugs in Aqueous Solution Attwood, D., Mosquera, V. and Villar, V. P. Kinetic Study of the Reaction between Ferroin and Nitrous Acid by Concentration Jump/Stopped Flow Technique Bazsa, G., Lengyel, I. and Linert, W.Preferential Solvation of Ions in Mixed Solvents. Part 4.-Comparison of the Kirkwood-Buff and Quasi-lattice Quasi-chemical Approaches Marcus, Y. Protonated Carbonic Acid Egsgaard, H. and Carlsen, L. Unusual Thermodynamic Behaviour on Complexation of Cobalt(n) with Chloride, Bromide and Iodide Ions in Hexamethylphosphoric Triamide Abe, Y., Ozutsumi, K. and Ishiguro, S-I. Spectroscopic Studies of the Solvation of Amides with N-H Groups. Part 1.-The Carbonyl Group Eaton, G., Symons, M. C. R. and Rastogi, P. P. Bulk and Surface Characterization of Supported Cobalt-Copper Catalysts Active in CO Hydrocondensation Perrichon, V., Mouaddib, N. and Primet, M. Interactions between Cations and Sugars Morel, J. P. and Morel, N. A Quantitative Analysis of Calcium Carbonate Polymorphs by Infrared Spectroscopy Koutoukos, P.G. and Xyla, A. G. Numerical Interpretation of Oscillatory Glow and Ignition in a Well-stirred Flow Reactor Griffiths, John F. and Sykes, A, F. Adsorption Potential Energy of Benzene on a-Quartz Astorga Valencia, E. Topological Investigations of the State of a Salt in some Binary Mixtures of Non-electrolytes Singh, P. P. and Bhatia, M. Energetics of Molecular Interactions in Binary Mixtures of Non-electrolytes containing a Salt Singh, P. P. and Bhatia, M. Strong-stretching and Scheutjens-Fleer Descriptions of Grafted Polymer Brushes Milner, S. T. (iii)Cumulative Author Index 1989 Abe, M., 1493 Adachi, K., 1065, 1075, 1083 Agathonos, P., 1357 Aguilella, V. M., 223 Akitt, J. W., 121 Albery, W. J., 1181, 1189 Al-Bizreh, N., 1303 Albuquerque, L.M. P. C., 207 Allen, G. C., 55 Almeida, B. S., 1217 Amodeo, P., 621 Anderson, J. A., 1117, 1129 Anpo, M., 609 Apelblat, A., 373 Arai, T., 929, 1451 Archer, M. D., 1027 Asakura, K., 441 Austin, J. C., 1159 Baiker, A., 999 Bald, A., 479 Barone, G., 621 Barone, V., 621 Beckett, M. A., 727 Bellotto, M., 895 Bengtsson, L., 305, 317 Berry, F. J., 467 Bertoldi, M., 237 Bertran, J., 1207 Blandamer, M. J., 735 Bolis, V., 855, 1383 Bolton, J. R., 1027 Bond, G. C., 168 Borowko, M., 343 Bosch, H., 1425 Boss, R. D., 11 Bowker, M., 165 Brimblecome, P., 157 Bulow, M., 1501 Burgess, J., 735 Busca, G., 137, 237 Calado, J. C. G., 1217 Campbell, J. A., 843 Carbonara, M., 1257 Carlstrom, G., 1049 Caro, J., 1501 Cattania, M. G., 801 Chadwick, A.V., 166 Che, M., 609 Chen, J., 829 Chen, L-f., 33 Clegg, S. L., 157 Cohen, H., 1169 Colling, C. N., 1303 Coluccia, S., 609 Comninos, H., 633 Compton, R. G., 761, 773, 977 Conway, S. J., 71, 79 Cooper, J., 1365 Copperthwaite, R. G., 633 Cox, B. G., 187 Cristiani, C., 895 Cristinziano, P., 621 da Costa, M. A., 907 Datka, J., 47, 837 Dawber, J. G., 727 De Giglio, A., 23 Dell’Atti, A., 23 Dickel, G., 1463 Domen, K., 929, 1451 Donini, J. C., 91 Drummond, C. J., 521, 537, 551, Easteal, A. J., 1091 Eden, J., 991 Elisei, F., 1469 el Torki, F. M., 349 Endoh, A., 1327 Espinos, J. P., 1279 Falconer, J. W., 71, 79 Fernandez, A., 1279 Fernandez-Pineda, C., 1019 Finch, J. A., 91 Fletcher, P. D. I., 147 Foerch, R., 1139 Foo, C. H., 65 Forster, H., 1149 Forzatti, P., 895 Frey, H.M., 167 Fubini, B., 237, 855, 1383 Gabriel, C. J., 11 Gabrys, B., 168 Gadzekpo, V. P. Y., 1027 Garrone, E., 585, 1373, 1383 Garst, J. F., 1245 Gasser, D., 999 Gavish, B., 1199 Gervasini, A., 801 Geus, J. W., 269, 279, 293, 1267 Giamello, E., 237, 855, 1373 Gilbert, P. J., 147 Girault, H. H., 843 Gonzalez-Elipe, A. R., 1279 Gonzalez-Lafont, A., 1207 Gorner, H., 1469 Gottschalk, F., 363 Grieser, F., 521, 537, 551, 561 Guardado, P., 735 Gutierrez, C., 907 Hagele, G., 1409 Halle, B., 1049 Hampton, S., 773 Han, S., 829 56 1 Handreck, G. P., 645 Harland, R. G., 761 Harris, R. K., 1409 Hasselaar, M., 1267 Hasted, J. B., 99 Hatano, M., 199 Healy, T. W., 521, 537, 551, 561 Heatley, F., 917 Hesselink, W. H., 389 Hester, R. E., 171, 1159 Higgins, J. S., 170 Higuchi, A., 127 Hill, W., 691 Hirai, T., 969 Holmberg, B., 305, 317 Holz, M., 1257 Hong, C.T., 65 Howard, J., 1233 Howarth, 0. W., 121 Hubbard, C. D., 735 Hummel, A., 991 Hunger, M., 1501 Hunter, R., 363, 633 Hutchings, G. J., 363, 633 Ichikawa, K., 175 Ikeda, R., 111 Ikeda, Y., 1099 Imanishi, Y., 1065, 1075, 1083 Ishida, H., 111 Itaya, K., 1351 Itoh, N., 493 Iwasawa, Y., 441 Jin, T., 175 Johnson, G. R. A., 677 Johnston, C., 1111 Jonkers, G., 389 Jorgensen, N., 11 11 Juillard, J., 1337 Jutson, J. A., 55 Kaneko, K., 869 Kanno, T., 579 Karaiskakis, G., 1357 Karger, J., 1501 Katoh, T., 127 Keeler, J. H., 163 Kelebek, $., 91 Kishi, R., 655 Kiwi, J., 1043 Knijff, L. M., 269, 293 Kobayashi, M., 579 Koda, S., 957 Kosugi, N., 869 Kotaka, T., 1065, 1075, 1083 Kozlowski, Z., 479 Kuroda, H., 869 Kuwabata, S., 969Lancaster, N.M., 1303, 1315 Larramona, G., 907 Laschi, F., 601 Lawrence, D. G., 1365 Lawrence, K. G., 23 Lelj, F.,. 621 Lewis, T. J., 1009 Leyendekkers, J. V., 663 Li, C., 929, 1451 Liu, J.-Y., 1027 Lluch, J. M., 1207 Lorenzelli, V., 137 Loudon, R., 169 Lowe, B. M., 945 Lund, A., 421 Mafk, S., 223 Maignan, A., 783 Malet, P., 1279 Manzurola, E., 373 Marcus, Y., 381 Markovits, G., 373 Maruya, K., 929, 1451 Masiakowski, J. T., 421 Matsuhashi, N., 111 Matsui, H., 957 Matsumoto, T., 175 Matthews, R. W., 1291 Mazzucato, U., 1469 McAleer, J. F., 783 McLure, I. A., 1217 Meima, G. R., 269, 279, 293, Merwin, L. H., 1409 Meyerstein, D., 1169 Miessner, H., 691 Mills, A., 503 Mitani, T., 1485 Mizoe, K., 1327 Mizuno, K., 1099 Morazzoni, F., 801 Morrison, C., 1043 Morterra, C., 1383 Moseley, P.T., 783 Mosier-Boss, P. A., 1 I Mount, A. R., 1181, 1189 Mousset, G., 1337 Munuera, G., 1279 Nakagawa, T., 127 Nakamura, D., 1 1 1 Nakamura, T., 493 Natarajan, P., 813 Nazhat, N. B., 677 Neagle, W., 429, 719 Neilson, G. W., 1365 Newman, K. E., 485 Nicholas, A., 773 Levy, o., 373 1267 AUTHOR INDEX Nicol, J. M., 1233 Nomura, H., 957 Nowak, R. J., 11 Nowicka, B., 479 Nunes, M. R., 907 Ohlmann, G., 691 Ohyama, Y., 749 Okubo, T., 455, 749 Oliva, A., 1207 Oliveira Jr, 0. N., 1009 Onishi, T., 929, 1451 Orchard, S. W., 363 Osada, Y., 655 Otsuka, K., 199 Pacynko, W. F., 1397 Pandey, J. D., 331 Pellicer, J., 223 Pereira, I., 907 Piwowarska, Z., 47, 837 Pope, C. G., 945 Portwood, L., 71 1 Price, W. E., 415, 1091 Rai, R. D., 331 Ramaraj, R., 813 Ramis, G., 137 Rao, K.J., 251 Reed, W. F., 349 Rees, L. V. C., 33, 1501 Reis, J. C. R., 207 Reller, A., 855 Rhodes, C. J., 711 Rochester, C. H., 71, 79, 429, Rosen, D., 99 Rossi, C., 601 Rowlinson, J. S., 171, 172 Saadalla-Nazhat, R. A., 677 Sacco, A., 23, 1257 Said, M., 99 Sakata, Y., 929, 1451 Salvagno, S., 1009 Schmehl, R. H., 349 Schmidt, J. A., 1027 Schneider, H., 187 Schneider, I., 187 Schumann, M., 1149 Scotti, R., 801 Selvaraj, U., 251 Shido, T., 441 Shindo, Y., 1099 Shukla, R. K., 331 Sinot, P. J., 1425 Smith, G. W., 91 Smith, J. J., 11 Smith, M. R., 467 Smith, T. D., 645 Soares, V. A. M., 1217 719, 1111, 1117, 1129 Sorek, Y., 1169 Stevens, A. D., 1439 Stewart, A. A., 843 Stirling, C. J. M., 1009 Stroka, J., 187 Strumolo, D., 801 Sugawara, S., 1351 Sundar, H.G. K., 251 Sutton, H. C., 883 Symons, M. C. R., 71 1, 1439 Szejgis, A., 479 Szpak, S., 11 Takagi, T., 1099 Takagi, Y., 493 Takaishi, T., 1327 Tamura, K., 1493 Taniewska-Osinska, S., 479 Taylor, D. M., 1009 Terai, M., 1493 Thamm, H., 1 Themistocleous, T., 633 Tiddy, G. J. T., 1397 Tissier, M., 1337 Tsutsumi, K., 1327 Ugliengo, P., 585, 1373 Urch, D. S., 1139 Vaccari, A., 237 van Buren, F. R., 269, 279, 293, Van-Den-Begin, N., 1501 van Dillen, A. J., 269, 279, 293, van Leur, M. G. J., 279 van Lith, D., 991 van Rensburg, L. J., 633 van Veen, J. A. R., 389 Vazquez-Gondlez, M. I., 1019 Vink, H., 699 Vis, R. J., 269, 279 Wacker, T., 33 Walker, P. A. M., 1365 Waller, A. M., 773, 977 Warman, J. M., 991 Waugh, K. C., 163 Weale, K. E., 165 Williams, D.E., 783 Williams, G., 503 Woolf, L. A., 1091 Wormald, C. J., 1303, 1315 Yamada, Y., 609 Yarwood, J., 1397 Yeh, C-t., 65 Yoneyama, H., 969 Yoshioka, H., 1485 You, X., 829 Young, D. A., 173 Zecchina, A., 609 1267 1267THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 88 Charge Transfer in Polymeric Systems University of Oxford, 11-13 September 1989 This Discussion aims to bring together physicists and chemists interested in the mechanism of electron and ion transport in polymeric systems. The systems indude conducting polymers, redox polymers, ion exchange membranes and modified electrodes. Discussion topics will cover experimental evidence from spectroscopy, electrochemistry and new techniques such as the quartz microbalance.Theoretical models ranging from band theory through polarons to localised chemical structures will be cn'tically evaluated and compared with experiment. The following have agreed to participate in the Discussion: R. Murray W. J. Albery M. D. lngram M. B. Armand D. Bloor H. Cheradame P. G. Bruce R. Friend R. J. Latham A. J. Heeger A. R. Hillman P. V. Wright A. G. MacDiarmid M. Ratner M. E. G. Lyons S. Roth 0. Haas T. J. Lewis G. Tourillon C. Vincent P. G. Pickup G. Wegner A. Hamnett L. M. Peter K. Doblhofer The final programme and application form may be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN. DEUTSCHE BUNSEN-GESELLSCHAFT FOR PHYSIKALISCHE CHEMIE ASSOCIAZIONE ITALIANA DI CHIMICA FlSlCA THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SOCIETC FRANGAISE DE CHIMIE, DIVISION DE CHlMlE PHYSIQUE JOINT DISCUSSION MEETING 1989 Transport Processes in Fluids Mobile Phases and in Aachen, 25-27 September 1989 Organised by: H. Versmold (F.R.G.) At. Weiss (F.R.G.) M. Zeidler (F.R.G. G. R. Luckhurst (U.K.) P. Turq (France) The purpose of the meeting is to bring together scientists working on transport and related phenomena in simple and complex fluids, colloidal and micellar systems, and surface phases. Experimental techniques considered include classical methods, optical spectroscopy, light scattering, nuclear magnetic resonance, and neutron scattering. The following persons have accepted invitations to present talks: D. Evans, Canberra; B. U. Felderhof, Aachen; D. Frenkel, Amsterdam; A. Geiger, Dortmund; W. Glaser, Grenoble; H. G. Hertz, Karlsruhe; S. Hess, Berlin; J. Jonas, Urbana; R. Klein, Konstanz; K. Lucas, Duisburg; H.-D. Liidermann, Regensburg; H. Posh, Wien; P. Pusey, Malvem; J. P. Ryckaert, Brussels; W. A. Steele, Penn State; D. J. Tildesley, Southampton; H. WeingBrtner, Karisruhe. Further details may be obtained from: Professor H. Versmold, lnstitut fur Physikalische Chemie, RWTH Aachen, Templergraben 59, D-5100 Aachen, Federal Republic of Germany. (vi)

ISSN:0300-9599    

DOI:10.1039/F198985BP075

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chew. Soc., Faraday Trans. I , 1989, 85(6), 1199-1206 Modelling the Effect of Pressure on the Rates of Ionic and Polar Reactions Benjamin Gavish Biochemistry Department, The Hebrew University and Hadassah Medical School, P.O. Box I 172, Jerusalem, Israel The rate k, of ionic and polar reactions in solutions is known to be sensitive to the applied pressure P. In the present work, structural and dielectric contributions to k, are expressed explicitly as functions of P. The pressure dependence of the volume and the dielectric constant of the solvent are described by the Tait equation. The model predicts the relation ln(k,/k,) = -vP/B-pln(1 + P / B ) where v, p and B are adjustable parameters. This expression fits remarkably well the kinetic data of 11 ionic and polar reactions up to 45 kbar.The resulting activation volume is AV: = AVz+(AV:-AVz)/(l +P/B) where the limiting values of A V,' at zero and infinite pressures are expressed in terms of intrinsic volume changes in the reactants and in the surrounding solvent, and by the strength of the electrostatic interaction. The results suggest that for ionic and polar reactions, the structural and the dielectric contributions to the activation volume can be separated objectively, using a single solvent. The meaning and the significance of the various parameters are discussed. High-pressure kinetics provide a powerful tool for studying the transition states of chemical reactions in the liquid state, in terms of activation volumes.1* Reactions at the transition state of which ions or dipoles are formed are of particular interest for being strikingly accelerated by pressure. The effect has been attributed by Buchanan and Hamann3 to the increase in solvation free energy of ionic charges.The dielectric constant of the solvent seems to dominate this phenomenon due to its strong pressure dependen~e.~~' On the other hand, the contribution to the activation volume of structural origin cannot be overlooked. Various expressions for the pressure dependence of reaction rates have been investigated in attempt to best-fit the kinetic data.9-13 However, the interpretation of the adjustable parameters in terms of structural and dielectric elements, and the uncertainty involved in neglecting the structural one, are still open problems to which the present paper is dedicated. Theory The effect of pressure on the kinetic coefficients k , of a chemical reaction is described (1) where AG: is the change in the free activation energy at pressure P and temperature T, and R is the gas constant.Hereby, atmospheric pressure will be taken as P = 0. This does not introduce any appreciable error in dealing with high-pressure effects. However, it does simplify considerably relevant mathematical expressions. We propose that In k,/k, = - (AG; - AG:)/RT by AG: - AG: = SU; + 6 W; 1199 (2) 41-21200 Eflect of Pressure on Reaction Rates SU:, the dielectric term, stems from the pressure dependence of the dielectric constant of the solvent. 6 W:, the structural term, corresponds to the compression work. This work is associated with volume changes of reactants and solvent molecules, that take place along the reaction pathway without any change in their ionic or polar state.For example, the formation of a bond might alter both the reactants volume and surface area. A solvent molecule, at the reactants surface, might occupy a different volume from one at the bulk. Thus, changes in the solvent volume are coupled, in this case, to the process of bond formation. In a case of a more ionic or polar transition state, a further increase in the volume difference between a solvent molecule in the bulk, and at the vicinity of the reactants, is caused by local compression which increases with increasing the electric fields.l4, l5 Structural Contribution Let us perform the following thought experiment.A cavity of volume & is generated inside a liquid under pressure P. The required energy for the process is I( P. The cavity is then filled with material (under atmospheric pressure) and becomes free to collapse under the external pressure. As the result, the pressure inside the cavity iyreases from 1 atmJf to P. The energy released curing the compression process is -1, P'd V,,.. The total free-energy change is & P+Jo P d Vp.. If the above procedure is applied separately to the transition state and the initial state of the reactants, the free-energy difference between these two processes defines the structural component as follows : 6 w; = A V; P + 1; P dP' d(A V;J/dP' (3) where AV: is the volume change in the system per mole of reactants (including the solvent).In general A V: = A VpfI + A Vps. A VpfI is the intrinsic activation volume, usually referred to as the volume change of the reacting molecules themselves. A V:s corresponds to possible variations in the packing of non-reacting solvent molecules, that follow structural rearrangements in the reactants, as explained before. The significance of this factor in interpreting activation and reaction volumes has already been pointed out by Asano and le Noble.'' It is proposed that: (i) the intrinsic volume of the reacting molecules is incompressible, i.e. d(A V,f,)/aP = 0 or, alternatively, A VpfI = A V& ; (ii) the pressure dependence of A V;ky is given by the Tait equation - d(A Vpfs)/aP = Do A V&/( 1 + P / B ) (4) where Do is the solvent compressibility at atmospheric pressure and B is a constant characteristic of the solvent and probably of the reaction.Assumptions (i) and/or (ii) are currently applied in studying ion-solvent interaction^^^-^' and activation or reaction volumes.1'* 1 3 9 21 Eqn (4) can be inserted into the integral of eqn (3) to yield 6 W: = (A V:I + A V,',) P -Do A VtS B2[P/B - In ( 1 + P/ B)]. A similar expression has been obtained by Owen and Brinkley22 using Gibson's expression for volume changes in electrolyte at the limit of infinite dilution. For P + B eqn (5) is simplified into SWpf =(AV:I+AV:s)P-/30AV:sP2/2. The second term is the elastic energy stored in the solvent. Eqn ( 5 ) and (6) are used in high-pressure kinetics5* 7, ' 9 lo and in studies of electrolyte ~olutions.'~ t 1 atm = 101 325 Pa.B.Gavish 1201 Dielectric Contribution We assume that SU: = Up- Uo, where Uo is part of the electrostatic energy that depends upon the value of the dielectric constant D, of the solvent around the reactants. We further propose that (iii) U , is proportional to I/D,. Thus, U p = Uo Do/D, and (7) For a single sphere of an effective radius r with initial charge zero and final charge Ze, U p is given by the modified Born expression NZ2e2/2rDp,3, l8 where N is the Avogadro number. Here r is taken to be pressure independent, in accordance with assumption (i). Let us consider the reaction M .+ (A + B)* in which the charge on the reactants varies. It can be shown that (8 a) Another case of interest is the occurrence of a dipole moment at the transition state.The energy required for generating a single dipole p at the centre of a spherical cavity of radius r is - (p2/r3) (D,- 1)/(2D, + l).23 Since 2(D, - 1)/(20, + 1) = 1 - (3/2)/(Dp ++), eqn (7) approximates this expression reasonably well for D, + 1/2 with Uo = 3p2/4r3D,. For M +(A+B)* we find SU: = - Uo( 1 - D,/D,). Uo = Ne2(Z2,/r, + PB/r, - ZL/rM)/2D0. uo = (3/4) N O X + P X - PL/r;)/Do; (8 b) We now assume that (iv) the pressure dependence of l/Dp follows that of pure liquids, (9) where A and B are constants characteristic of the solvent and probably of the reaction, and satisfy A / B = 8 In D,/aP at P + 0. Eqn (9) has been applied to studies of reaction kinetic^.'*^^*^^ Eqn (7) and (9) yield and is given by the Tait equation 1 - Do/D, = A In (1 + P / B ) SU; = -AU,ln(l + P I S ) .(10) Eqn (2), (5) and (10) can be combined into AG: -AG: = [AV,',+(l -a)AV,f,]P+aAV&Bln(l +P/B)-AU,ln(I +PI#) (1 1) where a = a, B. Our fifth assumption is (v) B and B' can be taken as equal without aflecting appreciably the results. This is justified by the linear relation observed between volume and l/Dp changes under pressure in pure liquids,26 and by the known insensitivity of Tait-type curves to the value of B (or B'). Under assumption (v) eqn (1 I ) is simplified into the following form: In kp/ko = - v(P/B) - p In (1 + P / B ) (12) where v and ,u are dimensionless quantities given by v = B[AV,S+(l -a)AV,f,]/RT and p = B(-AU,/B+aAV,f,)/RT. (13) Expressions bearing mathematical similarity to eqn (12) have been used by other investigators.l2.21, 27 Activation volume is defined by AV: = -RT(dln k,/aP), = (8AG;/W),. (14) AVZ = AV:+(AV,'-AVZ)/(I + P / B ) (15a) By substituting eqn (1 2) and (1 3) into (14) we obtain the following expression for A V: :1202 Effect of Pressure on Reaction Rates 8 7 6 5 h 0 % S g 4 3 2 1 I I I I I I 1 I 1 Plkbar Fig. 1. Shows a comparison between the model prediction, as expressed by eqn (12) (continuous curves), and high-pressure kinetic data. The curves' numbers correspond to the reaction numbers of table 1 and the corresponding list of parameters in table 2. 10 20 30 40 50 where AV: = AV:I+AV,',-AUo/B= RT(/i+V)/B AVZ = AV;,,+(l -a)AV& = RTv/B AV,+-AVZ =aAV,Sls-AAo/B= RTpIB. A V: and A V; are, respectively, the P -+ 0 (1 atm) and the p + co limits of A V:.Eqn (1 5 aH15 d ) show that the pressure dependence of D, contributes a volume change by the amount of -AUo/B (at I atm). This contribution vanishes gradually with increasing the pressure. The solvent component of AVZ of structural origin is an 'intrinsic volume change' (I -a) A V&. It appears that a is the compressible fraction of the solvent volume, which constitutes the term aAV& in AV: -AVZ. It should be mentioned that a similar interpretation to the pressure dependence of fluid volume was given by Asano.21 For many liquids the value of a varies in the range of 0.09-0.105, with the exception of 0.15 for water."' 28-30 Eqn (15) contains another feature of interest. It defines a limiting pressure P , ; for P 4 141 the dielectric contribution dominates the structural one.By equating the two contributions we obtain (16) If Pc is positive the activation volume changes sign at P = Pc and the reaction rate passes through a maximum. Uo can be evaluated when the dielectric term in eqn (I5d) is dominant. This is generally accepted to be the case in ionic and polar reaction^.^^ Assuming that AUo/B % alAV,f,l, and using the P -+ 0 limit of eqn (9) we obtain pC = B(AV:-AV$)/AV: = - B p / v . Uo = - Do(A Vz - A Vz)/(dD0/dP),. (17) Comparison with Experiments In order to compare eqn (12) with experimental data we shall rewrite it in the following form : Y = A0-vX1-pX2 (18)B. Gavish 1203 Table 1. Detail of analysed reactions change in number of Pm,, reaction ionic charges solvent T/"C/kbar ref. Do" (1) S , 1 solvolysis C(CH,),CI (2) S,2 solvolysis C,H,Br (3) S,2 solvolysis C,H,Br (4) S,2 solvolysis C,HJ (5) C,H5Br + NaOCH, (6) NH,'+NCO- (7) S , 1 solvolysis C,H,Cl (8) C,H5N(CH3)2 + CH,l (9) C6H5N(CH3)2 + 'ZHsBr (lo) C6H,N(CH&2 + C2H51 (1 1) S , 1 solvolysis CH,C,H,Br increase increase increase increase no change decrease increase increase increase increase increase 80% ethanol 80% ethanol methanol methanol methanol water methanol methanol methanol methanol methanol 25 15 29 27.7 55 15 29 23.0 65 15 29 26.3 65 15 29 26.3 30 15 29 30.7 60 15 29 66.6 65 31 30 26.3 25 15 31 32.6 25 15 31 32.6 25 15 31 32.6 23 45 31 33.4 a Calculated using literature data.34 where Xl = P / B and X , = In (1 + P / B ) .A , is expected to be zero. Using multilinear regression analysis eqn (1 8) has been best-fitted to kinetic data of a specific reaction for a series of B' values. The parameters A,, v, p, S.D.(the standard deviation), AVZ, AV: -AVZ and the correlation coefficient were evaluated as functions of B. S.D.(B) reaches a minimum at B = B,, giving ' the ' best-fitted curve. However, the B values in the range B, < B < B,, for which S.D.(B,) < S.D.(B) < S.D.(B,) = S.D.(B,) = (I +u) S.D.(B,) (u > 0), span a family of 'acceptable' curves that are hardly distinguishable from each other by eye. We can define an uncertainty in a best-fitted parameter Z(B,) by Z = lZ(B2)-2(BJl/2. u = 0.1 was found to be appropriate for most cases. Table 1 specifies 11 reactions for which high-pressure kinetic data have been reported, provided that seven, or more, data points were taken in a pressure range that exceeded at least 15 kbar.Table 2 shows the results of the above analysis. U was evaluated using eqn (7). The values of i3Do/i3P were taken or extrapolated from literature data. i3Do/i3P was taken as 3.6 kbar-' for water,32 2.4 kbar-l for ethano122.32 and 3.6 kbar-' for For 80% ethanol we obtain 2.6 kbar-', using the known additivity of Do in mixtures (with molar fractions). Discussion We have derived simple expressions for the pressure dependence of the reaction rate (eqn (12)] and the activation volume [eqn (15)] for ionic and polar reactions. We have assumed that the pressure dependence of the solvent volume and dielectric constant (reciprocal value), in the vicinity of the reactants, follows similar Tait equations, having the same B parameter.The predicted pressure dependence of the reaction rate fits remarkably well the data of polar and ionic reactions up to 45 kbar, with an average correlation coefficient of 0.999. Intrinsic Volume Change Analysis shows (table 2) that the intrinsic part of the activation volume (AV:) constitutes a small fraction of the activation volume at atmospheric pressure (A V,'). The observed range of A VZ (0 to - 5 cm3 mol-') overlies that found by Asano and le Nobletd 0 P Table 2. Shows the results of fitting eqn (12) to the high-pressure kinetic data of the reactions listed in table 1, using multilinear regression [eqn (1 8)] u,' AV: -AV:" B"/kbar AOb V b Pb S.D." A Vzd/cm3 mol-' /cm3 rno1-l 1.6 (0.7) 2.1 (0.5) 1.7 (1.0) 0.5 (0.1) 0.9 (1 .O) 3.2 (1.7) 1.5 (0.6) 0.5 (0.3) 0.3 (0.2) 0.6 (0.3) 1.8 (0.5) - 0.00 (0.02) -0.02 (0.01) 0.00 (0.01) 0.02 (0.04) 0.00 (0.04) 0.00 (0.02) 0.00 (0.02) 0.01 (0.05) - 0.06 (0.02) -0.01 (0.3) 0.00 (0.05) 0.01 (0.04) - 0.06 (0.03) - 0.02 (0.12) -0.01 (0.00) - 0.03 (0.01) - 0.32 (0.05) - 0.08 (0.05) - 0.09 (0.03) - 0.06 (0.03) -0.1 1 (0.04) 0.00 (0.02) - 1.46 (0.46) - 1.46 (0.28) - 1.73 (0.79) -0.71 (0.09) - 0.58 (0.38) 1.86 (0.93) - 1.75 (0.36) - 0.89 (0.22) - 0.85 (0.26) - 1.02 (0.29) -2.35 (0.33) 0.063 0.034 0.077 0.039 0.056 0.058 0.08 1 0.073 0.152 0.083 0.088 0.1 (0.9) - 0.7 (0.5) - 0.3 (1.5) - 0.7 (0.2) - 0.8 (0.6) - 2.5 (1.3) - 1.3 (0.4) -4.2 (0.6) -4.9 (0.8) -4.5 (0.8) 0.0 (0.3) - 22.4 (2.9) - 17.1 (0.9) -25.1 (3.9) -36.7 (4.5) - 15.8 (4.5) -28.8 (5.6) -43.7 (1 1) - 69.8 (29) -41.7 (1 1) 14.3 (1.1) -32.1 (4.8) 0.9991 5.8 0.9997 3.7 2 0.9990 4.4 2 0.9995 6.5 tl 0.9985 3.3 f 0.9994 5.1 0.9996 9.6 0.9984 15.3 8 0.9995 9.1 $' 0.9974 -7.7 2 0.9994 7.2 3 r?.S.D. is the standard deviation of the best-fitted curve; 2 U, uncertainty a B is the Tait parameter; is the strength of the electrostatic interaction [eqn (17)]. The uncertainty in the values of the best-fitted parameters is given in parentheses; is defined here with 5% S.D. change. A,, v and p are defined by theoretical curves [eqn (12) and (18)]; A V: and A V: are the activation volume at 1 atm and at infinite pressure, respectively [eqn (15 b) and (1 5 c)] ; R is the correlation coefficient;B. Gavish 1205 for van der Waals volume changes in pure liquids, for nearly non-polar reactions." However, what part of AV: is contributed by the intrinsic volume change of the solvent [eqn (lSc)] is still an open question.Dielectric vs. Structural Contributions Eqn (156) to (15d) show that the approximation AVZ -AVZ = -AUo/B, made in calculating the strength of the electrostatic interaction Uo, is justified if IAVZI + 1AV;l. This turns out to be the case in the studied reactions. The calculated values of Uo are found to be comparable with a typical strength of electrostatic interaction in the range of a few Angstroms. We may conclude that in ionic and polar reactions, for which [A V:l IA V:/, the dielectric and structural contributions to the activation volume can be separated. However, in order to obtain AVZ in a reasonable accuracy the kinetic measurements should be extended over a wide enough pressure range.Using eqn (16) table 2 shows that in reactions (SHlO) a few kbar are sufficient for obtaining AVZ, while for (1)-(7) tenths of kbar are required for this purpose. In reaction (1 1) A V: seems to vanish. None of these reactions has been found to satisfy the condition for maximum rate. Related Studies The above analysis suggests that under relatively low pressures the dielectric contribution dominates the reaction rate. This explains why the expression In k,/ko cc A VO+ P/( 1 + cP),'O that has been criticised for giving A V z = 0,l2 but behaves very similarly to In (1 + P/B), still fits very well high-pressure kinetic data.g Recently, Basilevsky et derived, from first principles, an expression to Ink,/k, using the Morse potential, and applied it to the same data used here.Their expression seems to fit the data very well. Unfortunately, that paper does not contain a systematic study of best-fitted parameters, and does not relate them to the possible role played by the dielectric constant. Tait Parameter Excluding reaction (6), the mean (S.D.) values of B were found to be 1.15 (0.66) kbar, which does not differ significantly from the bulk values of the solvents 0.86 (0.18) kbar. In reaction (6) the high value of B fits that of the bulk. A closer look at table 2 reveals that large deviations from the bulk values do occur. Theoretical consideration~~~ suggest that B is related to the excluded volume of a liquid. Asano and le Noble'' have shown that the excluded volume of the liquid at the reactants surface is an essential factor in the interpretation of reaction and activation volumes, for nearly non-polar reactions.We may conclude that the best-fitted value of B could be an important probe for characterising the state of the solvent in the vicinity of the reactants. However, a good estimation of B requires a relatively large pressure range. I thank the referees for their most helpful comments. References 1 M. G. Evans and M. Polyani, Trans. Faraday SOC., 1935, 31, 875. 2 S. D. Hamann, Physico-Chemical Efect of Pressure (Butterworth, London, 1957). 3 J. Buchanan and S . D. Hamann, Trans. Faraday Soc., 1953, 49, 1425. 4 E. Whalley, Adv. Phys. Org. Chem., 1964, 2, 93. 5 W. J. le Noble, Prog.Phys. Org. Chern., 1967, 5, 207. 6 G. Kohnstam, Prog. Reac. Kinet., 1970, 5, 335. 7 C . A. Eckert, Ann. Rev. Phys. Chem., 1972, 23, 239.1206 Efect of Pressure on Reaction Rates 8 S. D. Hamann, in High Pressure Physics and Chemistry, ed. R. S . Bradly (Academic Press, London, 9 M. Nakahara, Rev. Phys. Chem. Jpn, 1974, 44, 57. 1963), vol. 5, p. 131. 10 B. S. El’yanov and S. D. Hamann, Aust. J. Chem., 1975, 28, 945. 11 B. S. El’yanov and E. M. Gonikberg, J. Chem. SOC., Faraday Trans. I , 1979, 75, 172. 12 T. Asano and T. Okada, J. Phys. Chem., 1984, 88, 238. 13 M. B. Basilevsky, N. N. Weinberg and V. M. Zhulin, J. Chem. SOC., Faraday Trans. I , 1985, 85, 875. 14 J. Padova, J. Chem. Phys., 1963, 39, 1552. 15 J. E. Desnoyers, R. E. Verrall and B. E.Conway, J. Chem. Phys., 1965, 43, 243. 16 T. Asano and W. J. le Noble, Rev. Phys. Chem. Jpn, 1973, 43, 82. 17 H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolyte Solutions (Reinhold, New York, 18 J. O’M. Bockris and A. K. N. Reddy, Modern Electrochemistry (Plenum, New York, 1970), vol. 1, 19 F. Millero, G. K. Ward, F. K. Lepple and E. V. Hoff, J . Phys. Chem., 1974, 78, 1636. 20 J. V. Leyendekkers, J. Chem. SOC., Faraday Trans. I , 1981, 77, 1529. 21 T. Asano, Rev. Phys. Chem. Jpn, 1979, 49, 109. 22 B. B. Owen and S. R. Brinkley Jr, Phys. Rev., 1943, 64, 32. 23 J. G. Kirkwood, J. Chem. Phys., 1934, 2, 351. 24 H. Inoue, K. Hara and J. Osugi, Rev. Phys. Chem. Jpn, 1978, 48, 44. 25 H. Inoue, Rev. Phys. Chem. Jpn, 1978, 48, 105. 26 L. G. Schornack and C. A. Eckert, J. Phys. Chem., 1970, 74, 3014. 27 N. A. North, J. Phys. Chem., 1973, 77, 931. 28 H. Carl, Z. Phys. Chem., 1922, 101, 2338. 29 R. E. Gibson and 0. H. Loeffler, J. Phys. Chem., 1939, 43, 207. 30 R. E. Gibson and 0. H. Loeffler, Ann. N. Y. Acad. Sci., 1949, 51, 727. 31 S. D. Hamann, Rev. Phys. Chem. Jpn, 1980, 50, 147. 32 G. Beggerow, in High Pressure Properties of Matter, ed. K . Schafer [in Landott-Bornstein series, 33 R. Ginell, J. Chem. Phys., 1961, 34, 1249. 34 Y. Y. Akhadov, Dielectric Properties of Binary Solutions (Pergamon, Oxford, 1981). 35 H. G. David and S. D. Hamann, Trans. Faraday SOC., 1954, 50, 1188. 36 H. G. David, S. D. Hamann and S. J. Lake, Aust. J. Chem., 1955, 4, 285. 37 S. D. Hamann and D. R. Teplitzky, Discuss. Faraday SOC., 1956, 22, 114. 1930), p. 271. chap. 2, p. 45. ed. K. H. Hellwege (Springer, Berlin, 1980)] vol. 4, p. 263. Paper 6/00008H ; Received 2 1st November, 1986

ISSN:0300-9599    

DOI:10.1039/F19898501199

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chern. Soc., Furaday Trans. I, 1989, 85(6), 1207-1215 Effect of Solvent Fluctuations in the Electron-transfer Process between two Fe+ Ions Angels Gonz6lez-Lafont, Jo& M. Lluch, Antonio Oliva and Juan Bertran* Dept. de Quimica, Universitat A d n o m a de Barcelona, Bellaterra (Barcelona), Spain A Monte Carlo simulation of the solvent intervention in the process Fe++Fe+ 4 Fe2++ Fe" in aqueous solution has been carried out within a classical model. The configurations whose solvation energy does not change when the electron- transfer process occurs, have been determined. The results obtained show that the effect of the outer hydration shells can be very important in order to reach these isoenergetic configurations. Furthermore, an important energy dispersion in the configurations that makes possible the electron-transfer process has been found, this being due to the great complexity of the solvent fluctuations which leads to isoenergetic con- figurations.The elucidation of the molecular mechanism which regulates the rate of electron-transfer processes is one of the most important problems in physics, chemistry and biology. The homogeneous outer-sphere electron-transfer reactions in solution are especially interesting since they occur at a rate that is noticeably slower than the diffusion rate. This peculiar behaviour has been e~plainedl-~ through a three-step mechanism : formation of a precursor complex from the separated reactants, actual electron transfer within this complex to form a successor complex and dissociation of the latter complex into separated products.The reaction rate is usually controlled by the electron-transfer step, this step being governed by the Franck-Condon prin~iple.~ According to this principle, internuclear distances and nuclear velocities do not change during an electronic transition. This principle is embodied in classical electron-transfer theories5-' using an activated-complex formalism in which the electron transfer occurs at the intersection of two potential-energy surfaces, one for the reactants and the other for the products. This implies that the second step necessarily involves the reorganization of the solvent before and after the electron transfer itself is produced. Thus it is obvious that the solvent must play an essential role in the rate of electron transfer reactions in solution.As Levich' mentioned in 1967 a consistent statistical theory of the liquid state did not exist at that time, this fact being particularly true in the case of such a complex liquid as a polar solvent. For this reason, very simple solvent models have been generally used in order to study electron-transfer processes in solution. The original applications by Levich and co-workersg~ lo included only a single solvent harmonic vibrational mode (or equivalently, many solvent modes, all with a common frequency). A two-mode model has commonly been employed in subsequent work, 1,11-13 this model including the contributions of a low-frequency solvent mode and of a high-frequency inner-shell mode associated with the symmetrical stretching.Thus these models imply a drastic reduction of the degrees of freedom of the system and in them the movement of the solvent is represented by harmonic oscillations. Moreover, the two-mode model considers the inner shell in a discrete way, the rest of the solvent molecules being taken as a continuum characterized by its longitudinal optical frequency. In recent years, statistical methods based on numerical simulations, such as the Monte Carlo m e t h ~ d ' ~ - ' ~ and molecular d y n a m i c ~ ' ~ - ~ ~ techniques, have been revealed as very powerful tools in the treatment of chemical systems in solution. Such studies of electron- 12071208 Electron Transfer between Two Fe+ Ions transfer reactions would permit one to treat explicitly many solvent molecules in a discrete representation, without the usual reduction in the number of the degrees of freedom or the common adoption of a harmonic oscillator model.These statistical methods open a very hopeful perspective for the characterization of the solvent nuclear reorganization which has to be produced before the electron transfer itself takes place. However, their actual application is limited because of the enormous number of configurations which ought to be generated in order to obtain configurations appropriate to electron transfer in the intersection region of both potential-energy surfaces. The object of the present work is to carry out a simple Monte Carlo simulation of the process Fe+ + Fe+ + Fe2+ + Feo in aqueous solution within a classical model. We have chosen this system because it takes place at a very fast rate.Thus, we expect to find some configurations which make electron transfer possible in this system in spite of the large number of degrees of freedom that are involved when a reasonable number of water molecules are explicitly considered. Method of Calculation In this paper we have studied the disproportionation process of Fe+ leading to Fe2+ and Feo which takes place in clusters of 12 and 50 water molecules ground the system composed by two Fe+ ions separated by a reasonable distance of 5 A. We have chosen a number of 12 water molecules, since in this way the first hydration shell of six water molecules around each Fe+ ion is represented. On the other hand, calculations with 50 water molecules permit us to obtain a first estimate of the effect of the next solvation shells.As discussed above since internuclear distances and nuclear velocities do not change during an electronic tran~ition,~ the actual electron transfer on the precursor complex occurs at essentially constant nuclear configuration and momentum. This requirement is incorporated into classical electron-transfer theories by postulating that the electron transfer occurs at the intersection of the reactants' (precursor complex) and products' (successor complex) potential-energy surfaces. ' 9 2 * 5-7 This intersection region is reached by a suitable fluctuation in the nuclear configurations of the reactants. To determine which fluctuations favour the electron-transfer process, we have performed the following scheme of calculations in both clusters : (1) minimum-energy structures have been obtained using the Metropolis2' Monte Car10'~-'~ method as a minimization technique.21 In each case the only minimum found represents the solvent configuration of minimum energy in the potential-energy surface of this precursor complex at 0 K.(2) Statistical simulations of clusters at 298 K have been carried out by the Monte Carlo method using the Metropolis algorithm.20 Statistical equilibration has been achieved after 3 x lo5 configurations and statistical analysis has been done over 3 x lo5 or 8 x lo5 additional configurations for the systems with 12 and 50 water molecules, respectively. (3) Pairwise additive potential functions have been used to evaluate the solvation energy of each configuration generated.The MCY 22 potential for the water-water interaction and ab initio analytical potentials generated by us for the Fe2+-water,23 F e + - ~ a t e r ~ ~ and FeO-~ater~~ interactions have been employed. (4) For each one of the solvent configurations generated around the system composed by two Fe+ ions, the solvation energy of this system, and the solvation energy of the system obtained by keeping unchanged the water molecules' coordinates but replacing the two Fe+ ions by Fe2+ and FeO, have been calculated. The difference between these two solvation energies gives the change (AE,,,,) in solvation energy between the potential-energy surface of the successor complex and the potential-energy surface of the precursor complex, for the frozen- solvent configuration.AEsolv could be obtained merely by subtracting the solute-solvent interaction energies after and before the electron transfer, given that the solvent-solvent interactions are kept constant.A . Gonzalez-Lafont et al. 1209 Fig. 1. Minimum-energy structure for the cluster containing 12 water molecules around the Fe+-Fe' system. The values of AEsolv permit us to determine which of the configurations generated are isoenergetic when the electron transfer takes place, and therefore correspond to the intersection region of both potential-energy surfaces. Note, however, that in this work only the change of the solvation energy has been taken into account to define isoenergetic configurations, the interaction between both metal atoms and the energy associated with the electron transfer in vacuum not having been considered.( 5 ) Micro- scopical information of the configurations generated has been obtained through a procedure proposed by one of us.25 In this procedure, a geometrical criterion permits one to classify the configurations into different classes in such a way that each class corresponds to a significant structure of the solvent. In this way, the most significant structures of the system can be identified. Results and Discussion We will first present the results corresponding to the minimum-energy structures at 0 K for the clusters, containing 12 or 50 water molecules, around the Fe'-Fe' system. In both cases, the configuration of the first solvation shell that we have found is very similar, six water molecules being octahedrally disposed around each Fe' ion (see fig.1). Since in this paper we intend to study the electron-transfer process Fe' + Fe' + Fez' + FeO, it is convenient to distinguish between both Fe' ions. This has been done in fig. 1 and thereafter by calling 'reductor' the Fe' ion which loses an electron and transforms into Fez+ and 'oxidant' the Fe+ ion which gains and electron and transforms into Fe". Table 1 presents for each cluster the mean distances Rred and R,, between both Fe' ions and the oxygen atoms of water molecules of the first solvation shell. As it might be expected both mean distances are identical in each cluster. On the other hand, the comparison of the results obtained for the two clusters shows that the first hydration shell is more expanded in the cluster containing 50 water molecules, this fact being due to the effect of the solvent molecules which form the other hydration shells.Following the strategy described in the method of calculation, we have calculated the energy difference, AEsolv, associated with the electron-transfer process which would take place keeping unchanged the geometry structure of the precursor complex at 0 K. The calculated values of AEsolv for the clusters with 12 and 50 water molecules are presented in the third column of table 1. It is interesting to remark that the two values are very different, AESolv being negative for the cluster containing 12 water molecules and positive for the other cluster. This different behaviour can easily be rationalized in the activated-complex formalism, in which the electron transfer occurs at the intersection region between the N-dimensional hypersurfaces of reactants and products, N being the number of independent variables which are necessary to define the nuclear configuration1210 Electron Transfer between Two Fe+ Ions Table 1.Mean Fe+-0 distances and solvation energy difference associated with the electron- transfer process at 0 K for the clusters containing 12 and 50 water molecules n Rred/A Rox/A AE,,,,/kJ mol-' 12 2.30 2.30 - 67.2 50 2.3 1 2.3 1 57.8 of the solvent. According to the relative position of the intersection region with respect to the equilibrium configurations of the precursor and of the successor complexes, the two situations shown schematically in fig. 2 can be c o n ~ i d e r e d .' ~ ~ ~ ~ In the normal-energy region [fig. 2 (a)] the crossing q* is situated between the equilibrium configurations of the precursor (4;) and of the successor (4:) complexes, and this leads to a positive value of AEsolv. On the contrary, in the abnormal or inverted energy region [fig. 2 (b)] the crossing q* is situated to the side of the equilibrium configuration of the precursor complex and ALEsolv is negative. Thus, the results obtained in this work indicate that the clusters containing 12 and 50 water molecules around the Fe+-Fe+ system provide examples of the abnormal and of the normal energy regions, respectively. This different behaviour between the two clusters studied seems to indicate that the water molecules of the first hydration shell and the rest of the water molecules act in opposite senses.To confirm this hypothesis we have decomposed the value of ALEsolv for the cluster containing 50 water molecules into two components : the one corresponding to the 12 water molecules of the first hydration shell and the one which is due to the rest of the water molecules. It is interesting that this decomposition needs only the evaluation of the interaction energy of the solvent molecules with the metal atoms, since the disposition of the water molecules is the same before and after the electron transfer. The values obtained are - 60.6 and 118.4 kJ mol-', respectively. These values show clearly that the water molecules of the first hydration shell afford an exothermic component to ALEsolv, while the rest of water molecules contribute an endothermic component.It is also interesting that the contribution of the water molecules of the first hydration shell is similar to the value of ALEsolv for the cluster containing 12 water molecules (see table 1). This similarity indicates that the presence of outer hydration shells does not essentially change the interaction of the two metal atoms with the first hydration shell. The calculated values of ALEsolv imply that the electron-transfer process between the two Fe+ ions in the clusters containing 12 and 50 water molecules is not possible at 0 K, since, according to the Franck-Condon principle, the electron-transfer process can only be produced in the intersection region between the hypersurfaces of reactants and products.We will now investigate the possibility that solvent fluctuations due to the effect of thermal agitation lead to the existence of some configurations which possess nearly the same energy before and after the electron transfer. To this aim, statistical calculations have been done at 298 K. Table 2 presents, for the clusters containing 12 and 50 water molecules, the mean value of the solvation energy over all the configurations generated at 298 K, along with the solvation energy corresponding to the minimum-energy structure at 0 K, in order to compare both values. The increase in temperature is accompanied by a decrease in the solvation energy owing to the fact that thermal agitation makes possible the existence of higher-energy configurations.To study the effect of such configurations on the electron-transfer process, we have calculated AEsOlv for each of the configurations generated of the clusters containing 12 and 50 water molecules. According to the value of ALEsolv, we have selected three kinds of configurations that we have identified as isoenergetic, highly exoenergetic andA . Gonzalez-Lafont et al. 121 1 I I I I I I I I I I I I I I 4* 4; 4s” (6) Fig. 2. Schematic representation of the normal (a) and abnormal (6) energy regions in the crossing of the potential-energy surfaces of the precursor and successor complexes. Table 2. Solvation energy of clusters containing 12 and 50 water molecules at 0 and 298 K 12 I o 50 f 0 1 298 1 298 - 1261.2 - 1163.4 - 3032.8 -2513.61212 Electron Transfer between Two Fe+ Ions Table 3. Percentage of the total number of configurations belonging to the three groups defined in the text and mean Fe+-0 distances (A) for the first solvation shell in each group n = 12 n = 50 ” Rred ” Rred isoenergetic 5.2 2.34 2.30 3.8 2.28 2.33 highly 44.5 2.26 2.33 4.1 2.28 2.36 highly 6.3 2.36 2.26 62.8 2.32 2.28 exoenergetic endoenergetic highly endoenergetic.The first are those for which IAEsolvl < 6 kJ mol-’, i.e. those for which the solvation energy hardly changes when the electron transfer is produced, the geometry of the precursor complex being kept frozen. A configuration is identified as highly exoenergetic when AEsOlv < -67.2 kJ mol-’ in the case of the cluster containing 12 water molecules or AEsol, < -28.9 kJ mol-’ in the case of the cluster containing 50 water molecules.Finally, the highly endoenergetic configurations are those for which AEsolv > 33.6 or 57.8 kJ mo1-l for the clusters with 12 or 50 water molecules, respec- tively. The choice of these boundary values is rather arbitrary; the indicated values have been selected from the values of AEsolv at 0 K (table 1). Once the configurations belonging to the three abovementioned groups have been identified, we have determined the most significant structure of each group. Table 3 presents the percentage of the total number of configurations belonging to each one of the three groups for the two clusters studied along with the two mean Fe+-0 distances between the ‘reductor’ and the ‘oxidant’ Fe+ ion and the oxygen atoms of the water molecules of the first hydration shell, these mean distances being calculated for the most significant structure of each group.The first thing to observe in table 3 is that the number of isoenergetic structures in the clusters containing 12 or 50 water molecules is not negligible. This fact indicates that the increase in temperature to 298 K strongly enhances the probability of the electron-transfer process to be produced. In each cluster, the greatest number of configurations belong to the group for which AEsolv has the same sign as the one presented at 0 K. Let us now analyse the two mean Fe+-0 distances. This analysis will permit us to understand the way in which the first hydration shell has to be varied starting from the minimum-energy structure for the system to reach an isoenergetic configuration. As has been shown previously, the cluster containing 12 water molecules corresponds to the energy-inverted region [fig.2 (b)]. In this case, the intersection region, q*, is approached when solvent fluctuations displace the minimum-energy structure of the precursor complex, qi, in the opposite direction to the one which would lead to the minimum- energy structure of the successor complex, q:. In good agreement with this prediction, table 3 shows that isoenergetic configurations are reached when the first hydration shell of the ‘reductor’ Fe+ ion is expanded and the first hydration shell of the ‘oxidant’ Fe+ ion is contracted. Obviously, expansion and contraction are more important when highly endoenergetic configurations have to be reached.On the contrary, highly exoenergetic configurations are obtained when the fluctuation of the solvent leads to a contraction and to an expansion of the first hydration shells of the ‘reductor’ and of the ‘oxidant’ Fe+ ions, respectively. On the other hand, the cluster containing 50 water molecules corresponds to the normal energy region [fig. 2 (a)], and the intersection region q* is approached when the minimum-energy structure of the precursor complex, qi, is displaced to that of the successor complex, 4:. Again, the results of table 3 confirm thisA . Gonzalez-Lafont et al. 1213 2( l! 11 % 10 % 5 -1150 -2625 - 2575 -1100 1 -2525 Esolv 1 -2475 -2 -c, L 25 Fig. 3. Histograms of the distribution (YO) of isoenergetic configurations at 298 K against their total solvation energy for the clusters containing (a) 12 and (b) 50 water molecules.prediction, since isoenergetic configurations correspond to a contraction of the first hydration shell of the ‘reductor’ Fe’ ion and to an expansion of the first hydration shell of the ‘oxidant’ Fe’ ion. When a comparison is made between the clusters, one can observe that the variation of the two mean distances from one group to another is appreciably smaller in the cluster containing 50 water molecules. This fact seems to indicate that the fluctuations of the outer hydration shells are not negligible. Any attempt to reduce the effect of solvent fluctuations in the electron-transfer process to the expansion or contraction of the first hydration shell is thus an oversimplification.1214 Electron Transfer between Two Fe+ Ions Now the geometrical aspects of the solvent fluctuations which lead to isoenergetic configurations have been analysed, let us consider the energy dispersion in this group of configurations.Fig. 3 shows two histograms in which the percentage distribution of isoenergetic configurations at 298 K is plotted against their total solvation energy for the clusters containing 12 [fig. 3(a)] or 50 [fig. 3(b)] water molecules. In each case, one can observe that the energy dispersion is very important, this fact being a direct consequence of the large number of degrees of freedom of the system. The same reason explains why the energy dispersion is much more important in the case of the cluster containing 50 water molecules.This increase in the energy dispersion when the number of water molecules is increased again confirms that the outer hydration shells play a non- negligible role for the system to reach an isoenergetic configuration. To obtain a more thorough understanding of the role played by the outer hydration shells in the electron- transfer process we have decomposed the value of AEsolv for each of the isoenergetic configurations of the cluster with 50 water molecules in the same way that we did in the case of its minimum-energy structure at 0 K, i.e. we have separated the effect of the first hydration shell from that of the other hydration shells. An analysis of this decomposition clearly shows that the existence of isoenergetic configurations is usually due to a compensation between both contributions.As an example, let us take the case of an isoenergetic configuration whose total solvation energy is - 25 15.44 kJ mol-'. The decomposition of AEsolv into the two components leads to values of - 116.98 kJ mol-' for the contribution of the first hydration shell and 116.92 kJ mol-' for the remaining hydration shells. The fact that this configuration belongs to the isoenergetic group arises from a compensation of both contributions, in such a way that the total value of AEsolv is only -0.06 kJ mol-'. Finally, some words have to be said about the limitations which are present in this work. First, the accuracy of the pairwise approximation can perhaps be questioned for transition-metal atoms in solution, where the effect of the d-orbital splitting owing to the symmetry of the environment should be considered through the use of an anisotropic pair potential.Secondly, only the solvation energy in the determination of isoenergetic configurations has been considered. However, we have to emphasize that the purpose of this paper has not been to afford quantitative results for the reaction studied, but to show that the models developed up to now, which imply a drastic reduction of the degrees of freedom of the solvent system, do not allow us to give a complete description of the nuclear reorganization of the solvent, prior to the electron transfer. In this sense, we believe that, in spite of the abovementioned limitations, the results presented here open very interesting perspectives for the treatment of electron- transfer processes in solution.Conclusions In this work we have carried out a theoretical study of the solvent intervention in the electron-transfer process between two Fe+ ions. The calculations have been done with a classical model, no quantum effects having been introduced. However, it must be emphasized that we have taken into account a factor not usually considered in this kind of study, since we have explicitly considered a large number of water molecules with all their degrees of freedom. Our statistical calculations show that the usual separation between inner and outer solvent shells does not appear. As a matter of fact, the existence of isoenergetic configurations is generally due to a compensation between solvation contributions from both shells.Any attempt to reduce the effect of solvent fluctuations to the first hydration shell thus leads to an oversimplified model. We have also shown that there exists an important energy dispersion in the configurations which makes possible the electron- transfer process, this dispersion being due to the great complexity of the solvent fluctuations which lead to isoenergetic configurations. Thus we believe that the usualA . Gonzalez-Lafont et al. 1215 treatment in which the degrees of freedom of the solvent are reduced to only two harmonic oscillations is an oversimple representation of the actual movement of the solvent. This work was supported by the Spanish ‘Comision Asesora de Investigacion Cientifica y T h i c a ’ under contract no.3344/83. References 1 B. S. Brunschwig, J. Logan, M. D. Newton and N. Sutin, J. Am. Chem. SOC., 1980, 102, 5798. 2 B. L. Tembe, H. L. Friedman and M. D. Newton, J. Chem. Phys., 1982, 76, 1490. 3 N. Sutin, in Inorganic Reactions and Methods, ed. J. J. Zuckerman (V.C.H., Deerfield Beach, Florida, 4 W. F. Libby, J. Phys. Chem., 1952, 56, 863. 5 R. A. Marcus, J. Chem. Phys., 1965, 43, 679. 6 N. S. Hush, Trans. Faraday SOC., 1961, 57, 155. 7 N. Sutin, Annu. Rev. Nucl. Sci., 1962, 12, 285. 8 V. G. Levich, in Physical Chemistry, ed. H. Eyring, D. Henderson and W. Jost (Academic Press, New 9 V. G. Levich, Adv. Electrochem. Electrochem. Eng., 1966, 4, 249. 1986), vol. 15. York, 1970), vol. 9B, p. 1004. 10 R. R. Dogonadze, A. M. Kuznetsov and V. G. Levich, Electrochim. Acta, 1968, 13, 1025. 11 N. R. Kestner, J. Logan and J. Jortner, J. Phys. Chem., 1974, 78, 2148. 12 I. Webman and N. R. Kestner, J. Chem. Phys., 1982, 77, 2387. 13 E. Buhks, M. Bixon, J. Jortner and G. Navon, J. Phys. Chem., 1981, 85, 3759. 14 J. P. Valleau and S. G. Whittington, in Statistical Mechanics, ed. B. J. Berne (Plenum Press, New York, 15 J. P. Valleau and G. M. Torrie, in Statistical Mechanics, ed. B. J. Berne (Plenum Press, New York, 16 W. W. Wood, in Physics of Simple Liquids, ed. H. N. V. Temperley, J. S. Rowlinson and 17 J. Kushick and B. J. Berne, in Modern Theoretical Chemistry: Part B, ed. B. J. Berne (Plenum Press, 18 A. Warshel, J. Phys. Chem., 1982, 86, 2218. 19 A. Warshel and J. K. Hwang, J. Chem. Phys., 1986, 84, 4938. 20 N. A. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. Teller and E. Teller, J. Chem. Phys., 1953, 21 K. S. Kim, M. Dupuis, G. C. Lie and E. Clementi, Chem. Phys. Lett., 1986, 131,451. 22 0. Matsuoka, E. Clementi and M. Yoshimine, J. Chem. Phys., 1976, 64, 1351. 23 A. Gonzalez-Lafont, J. M. Lluch, A. Oliva and J. Bertran, Znt. J. Quantum Chem., 1986, 30, 663. 24 A. Gonzalez-Lafont, J. M. Lluch, A. Oliva and J. Bertran, Znt. J. Quantum Chem., 1988, 33, 77. 25 0. Tapia and J. M. Lluch, J. Chem. Phys., 1985, 83, 3970. 26 M. D. Newton and N. Sutin, Annu. Rev. Phys. Chem., 1984, 35, 437. 1977), vol. A, chap. 4. 1977), vol. A, chap. 5. G. S. Rushbrooke (North-Holland, Amsterdam, 1968), chap. 5. New York, 1977), vol. 6. 21, 1087. Paper 7/00045F; Received 22nd June, 1987

ISSN:0300-9599    

DOI:10.1039/F19898501207

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I , 1989, 85(6), 1217-1231 The Orthobaric Surface Tensions of the Three Binary Mixtures formed by Krypton, Ethane and Ethene Benilde S. Almeida,* Virgilio A. M. Soares, Ian A. McLuret and J. C. G. Calado Centro de Quirnica Estrutural, Complex0 I, Instituto Superior Tecnico, Avenida Rovisco Pais, 1096 Lisbon Codex, Portugal The surface tensions of krypton-thane and krypton-ethene mixtures have been determined as a function of composition from 116.0 to 124.0 K and for ethene-ethane mixtures from 117.0 to 135.0 K. In each case the deviations from mole-fraction linearity are negative, although least so for the mixture of hydrocarbons. The results have been analysed in terms of a number of theories that take no explicit account of the quadrupole nature of the hydrocarbons.Agreement with simple theories could be achieved by some empirical corrections of the Berthelot and Lorentz combining rules. However, the values of these differ significantly from those obtained with similar treatments applied to the bulk properties of these mixtures. Despite the importance of a knowledge of the surface tensions of simple liquid mixtures for testing both molecular theories and computer simulations of liquid-vapour interfaces, reports of experiments furnishing such results are rare. Essentially the entire stock rests upon the measurements of Fuks and Bellemans' on krypton-methane mixtures, of Sprow and Prausnitz2 on nitrogen-argon, nitrogen-carbon monoxide, nitrogen-methane, argon-methane and methane-carbon monoxide mixtures and our own measurements on methane-tetrafluoromethane mixture^.^ In addition, measure- ments on the mixture argon-krypton have recently been completed at Cornell Uni~ersity.~ With this background and paying heed to the limited number of available mixtures of truly simple substances, we have determined the surface tensions of the three binary mixtures containing krypton, ethane and ethene over a range of temperature using the method of differential capillary rise. The hydrocarbons have quadrupole moments of opposite sign, 3.54 x e.s.u.cm-3 for ethene and -0.80 x e.s.u. cmP3 for ethane; thus the results ought to afford a good test of theories of surface tension that take these factors properly into account, although this is a task that so far we have not undertaken.Experimental Apparatus The three-capillary appartus and the results of our measurements of the surface tensions of pure methane, krypton, tetrafluoromethane, ethane, ethene and dimethylether have already been r e p ~ r t e d . ~ Detailed accounts of the equipment and the experimental procedure are also a ~ a i l a b l e . ~ Materials The pure substances were obtained from the following sources with the indicated purities given by the manufacturers : krypton (Matheson, 99.997 YO), ethane (Air Liquide, i Permanent address: Department of Chemistry, The University, Sheffield S3 7HF. 12171218 Mixture Surface Tensions at Low Temperatures Table 1. Surface tensions, y, and excess surface tensions, yE, as a function of mole fraction, x,, at temperatures, T ~~ x, y/mNm-’ y”/mNrn-’ x, y/mNm-’ y”/mNm-’ 0 0.151 0.249 0.346 0.448 0 0.140 0.233 0.332 0.433 0 0.129 0.2 18 0.3 I3 0.414 0 0.21 1 0.306 0.454 0 0.202 0.295 0.441 0 0.191 0.282 0.425 0 0.149 0.298 0.400 0.499 0 0.149 0.298 0.399 0.498 25.91 21.53 20.70 19.50 18.79 24.96 20.38 19.50 18.38 17.72 24.20 19.22 18.29 17.25 16.66 27.36 23.70 22.00 20.33 26.69 22.52 20.93 19.27 26.07 21.34 19.87 18.22 27.35 26.85 26.50 26.24 26.08 25.69 25.29 24.90 24.65 24.46 krypton( 1 bthene(2) T = 116.0 K 0 0.553 -2.77 0.653 - 2.70 0.885 - 2.47 1 -2.72 T = 120.0 K 0 0.539 - 3.25 0.641 - 3.25 0.880 - 3.43 1 -3.13 T = 124.0 K 0 0.521 - 3.75 0.675 - 3.28 0.873 - 3.95 1 - 3.58 krypton( 1 )-ethane(2) T = 116.0 K 0 0.559 - 1.33 0.71 1 - 1.98 0.886 - 2.07 1 T = 120.0 K 0 0.546 - 1.90 0.700 - 2.45 0.88 1 - 2.47 1 T = 124.0 K 0 0.530 -2.50 0.685 - 2.93 0.874 - 2.96 1 ethene( 1 ethane(2) 0 0.600 - 0.093 0.700 -0.201 0.849 - 0.282 1 -0.287 T = 116.0 K T = 126.0 K 0 0.600 -0.118 0.699 - 0.236 0.849 - 0.294 1 - 0.298 18.42 -2.11 17.43 - 1.66 16.34 -0.87 16.33 0 17.22 -2.63 16.63 - 2.25 15.43 -1.18 15.48 0 16.0 1 - 3.20 15.34 - 2.87 14.32 - 1.52 14.46 0 19.44 18.17 16.95 16.33 18.36 17.04 15.90 15.48 17.27 15.91 14.85 14.62 25.93 25.93 25.68 25.53 24.30 24.16 23.98 23.82 - 1.75 - 1.35 - 0.64 0 -2.21 - 1.80 -0.91 0 - 2.7 I - 2.30 - 1.21 0 - 0.265 -0.196 -0.102 0 - 0.27 1 - 0.222 -0.127 0B.S. Alrneida, V. A . M. Soares, I. A . McLure and J . C. G. Calado 1219 Table 1. (cont.) x, y/mN m-' y"/mN m-' x, y/mNm-' y"/mN m-I T = 135.0 K 0 24.18 0 0.598 22.67 - 0.280 0.148 23.73 -0.146 0.698 22.49 - 0.249 0.296 23.30 - 0.274 0.848 22.28 -0.155 0.397 23.05 - 0.309 1 22.12 0 0.496 22.85 -0.310 Table 2.Parameters of Redlich-Kister equations A , B and C and standard deviations o for krypton-thane and ethene-ethane at various temperatures T T/K A/mN m-I B/mN m-' C/mN m-' a/mN m-' ~ ~~ ~~ krypton( lethane(2) 116.0 -7.742 1.821 0.4091 0.19 120.0 -9.503 3.077 - 2.439 0.12 124.0 - 11.34 4.498 - 5.496 0.06 ethene( 1 )-ethane(2) 117.0 - 1.135 -0.01037 0.7898 0.016 126.0 -1.186 0.006 87 0.4709 0.0 12 135.0 - 1.245 0.035 64 0.1200 0.016 99.9 YO) and ethene (Matheson, 99.98 YO). The purities quoted are considered satisfactory for the work carried out and so, save for deaeration according to techniques described by Calado,' no further purification was undertaken.Results The fluid sample is partitioned between a volume entirely within the cryostat that contains the two-phase system, and therefore the interfaces of interest, and a volume, larger by a factor of at least ten at essentially room temperature, that contains vapour only. The actual composition of the liquid in the capillaries was calculated from the total amounts of substance in the system, obtained by gas volumetry, and the known vapour-liquid equilibria results for these mixtures.' The composition of the liquid phase thus becomes a function of temperature. Since in practice it was difficult to reproduce precisely equal sets of temperatures for each different mixture, the final results listed for a given temperature were obtained by linear interpolation of the experimental quantities.The densities of the liquid mixtures were calculated from the known densities of the components : krypton,s ethane9 and ethene'O and from the excess volumes,' presumed temperature-independent. The method for calculating the correct liquid composition and the surface tension at any given temperature is described el~ewhere.~,'' A detailed statistical analysis of the likely sources of error leads to an expected error of 0.01 mN m-l in the determination of the surface tension and 0.001 in the mole fraction. The results are listed in table 1. The excess surface tensions yE were obtained from the expression Y E = y-xx,y,*-xx,y,*1220 Mixture Surface Tensions at Low Temperatures 0 XKr 0.5 1 0 - 1 w -3 -4 0 XKr 0.5 1 0 - 1 -3 XCIHJ 0 0.5 1 0 -0.1 - IE % -0.2 \ w x -0.3 -0.4 Fig.1. Excess surface tension,y", as a function of mole fraction, x, for (A) krypton-thene mixtures at (a) 116, (b) 120 and (c) 124 K; (B) krypton-ethane mixtures at (a) 116, (6) 120 and (c) 124 K ; and (C) ethene-ethane mixtures at (a) 117, (b) 126 and (c) 135 K. where y, 7;' and y t are the surface tensions of the mixture, component 1 and component 2, respectively, and x , and x, are the mole fractions in the liquid state of components 1 and 2, respectively. The definition implies the acceptance henceforward on grounds of convenience of an ideal surface tension linearly dependent on mole fraction rather than a more fundamentally based concept of surface ideality.B. S. Alrneida, V. A.M . Soures, I. A . McLure and J. C. G. Caludo 1221 Table 3. Excess Gibbs functions, GE, excess enthalpies, H E , and excess surface tensions, yE, for equimolar mixtures of krypton-ethene, krypton-ethane and ethenexthane mixture GF/J mol-I H E J/mol-' yE/mN m-' ~ _ _ kryp ton-e thene 240.4 3 15.0 - 2.42 krypton- t hane 79.8 49.1 - 1.94 et hene-e thane 98.9 192.7 -0.31 (115.8K) (117.7K) (116.0K) (1 15.8 K) ( 1 17.0 K) (1 16.0 K) (161.4 K) (161.4 K) (135.0 K) For krypton-ethane and ethane-ethene mixtures the excess surface tensions are well represented at different temperatures by Redlich-Kister expressions yE = x1 x2[A + B(x1 - x,) + C(X, - x,),] (2) with the least-squares-fitted coefficients and standard deviations 0 that are listed in table 2. The high asymmetry of the surface tension for krypton-ethene mixtures made it impossible to fit the results in the same way, and the fitting equation of Myers and Scott" devised specifically for the representation of highly skewed excess quantities was no more successful.Fig. 1 illustrates the excess surface tensions as a function of mole fraction at a series of convenient temperatures. Discussion Common features of the surface tensions of the three mixtures are the uniformly negative sign of the deviations from ideality and the far from linear dependence on mole fraction. The former is predicted by the quasi-crystalline regular solution theory of Guggenheim, which associates a negative deviation of the surface tension with positive values of the exchange energy. Values of this energy can be obtained from the positive sign of the excess Gibbs function GE and the excess enthalpy H E determined in our laboratories.' The non-linearity is very different from the near-linearity of the surface tensions of argon-krypton mixtures at temperatures far from the critical point of argon that is found both from experiment4 and from computer ~ i m u l a t i o n .' ~ ' ~ ~ It suggests that these mixtures cannot be treated as comprising simple spherical molecules, a point to which we later return. In table 3 we compare G", H E and yE for the equimolar mixtures at temperatures that, except for ethene-ethane, are close enough for purposes of comparison. For that mixture the results that are available for the bulk properties refer to temperatures well above the range of the surface-tension measurements.However, faute de mieux, they serve as a qualitative guide to the behaviour of the mixture at similar temperatures. The table shows that the signs of the excess surface tensions [eqn (l)] mirror those of the bulk excess properties in the normal way, i.e. they are opposite. The most non-ideal mixture, krypton-ethene, does exhibit the largest excess surface tension. The surface behaviour of the two other mixtures is less regular. Krypton-ethane has the higher excess surface tension but the lower excess Gibbs function, even after estimating from the excess enthalpy the effect of the difference in temperatures for ethene-ethane. The irregularity in behaviour with mixtures of such simple molecules is a reminder of the importance of the structure of the interface on the surface-tension behaviour of mixtures. Several statistical theories have been used in the study of interfaces, and the1222 Mixture Surface Tensions at Low Temperatures 0 XKr 0.5 1 0 - -1 IE " ! -2 $ -3 XKr 0.5 0 - I E -1 3 x -2 0 -0.1 - 'E -Oa2 x -0.3 -0.4 -0.5 1 0 1 Fig.2. Excess surface tension, y e , as a function of mole fraction, x, according to the lattice the'ory for (A) krypton-ethene at 116 K (B) krypton-ethane at 116 K and (C) ethene-ethane at 135 K. experimental values of the surface tension may be interpreted in terms of the models used in the theories. From the various treatments, the lattice theory of Guggenheim, the regular solution approach of Sprow and Prausnitz, the corresponding-states treatment and Flory's theory have been the most frequently applied.Quasi-crystalline Theories The lattice theory of homogeneous liquid solutions was applied by Schuchowitsky, l5 Belton and Evans1' and Guggenheiml' to the study of interfaces. The followingB. S. Almeida, V. A. M. Soares, I . A . McLure and J . C. G. Calado 1223 Table 4. W values for krytpon-ethene, krypton-ethane and ethene-thane Wopti rn i z ed / W from H E / W from G"/ mixture J mol-' J mol-I J mol-' krypton-thene 1500 1260 962 kryp ton- thane 400 196 3 19 et heneeet hane 450 77 1 396 equations were devised for the surface tension of binary mixtures in the case of regular solutions : y = y A + (RT/s)/ln (x",xk) + ( W / s ) [(x:)~ - (~3~1 - Wm(x;)'/s (3) y = yB + (RT/s)/ln (x;/xb) + ( W1/s) [(xi)2 - - W ~ ( X ; > ~ / S (4) where yi is the surface tension of pure liquid i, xs and xi are the mole fractions of component i at the surface and in the bulk, respectively, s is the molar surface area obtained from the molar volume V and Avogadro's number NA through the expression s = V2/3Ni'3 ; 1 and rn are geometrical parameters which take the values 1 /2 and 1 /4 for a close-packed lattice, W is the energy of mixing, related to the exchange energy w and the coordination number z by W = NAwz.The description of the interface with only the surface monolayer different in composition from the bulk of the liquid is inherently inconsistent with the Gibbs adsorption equation ; however, it gives sufficiently precise results for the surface tension. The calculated curves for the excess surface tension us.composition for the mixtures krypton-ethene and krypton-ethane at 116.0 K and ethene+thane at 135.0 K obtained through eqn (3) and (4) are presented in fig. 2 together with the experimental points. The dotted lines refer to the value of Wcalculated from H E and the full line to those with empirically optimised values of W. These two sets of values are presented in table 4 along with those obtained from GE. The agreement between the optimised values of W and the values from G" for krypton+thane and ethene-ethane is good. On the contrary, the optimised W for krypton-ethene is closer to the value obtained from H E . Overall, we may conclude that Guggenheim's lattice treatment yields, despite its simplicity, a reasonable empirical description of the surface behaviour for the mixtures studied.Regular-solution Theory The regular-solution approach of Sprow and Prausnitzl' considers the surface region as a regular solution in the Scatchard-Hildebrand sense. The regular-solution theory equations provide reasonable estimates of both surface and bulk properties for solutions of non-polar components. In fact Sprow and Prausnitz compared the calculated and experimental values for the surface tension of a series of binary mixtures involving argon, nitrogen, carbon monoxide and methane and found good agreement. According to this treatment the surface tension is given by where sy is the molar surface area and si the partial molar surface area of component i, fP and are the surface and bulk activity coefficients of i, respectively, and the other symbols enjoy their usual meanings.The data needed for the determination off,' were1224 28 26 24 22 - 'E z 20 E 'h 18 16 14 0 Mixture Surface Tensions at Low Temperatures 26 I I 24 22 20 E k 18 3 16 14 0 0.5 XKr 1 0.5 -YKr 1 26 - 'E 5 'h 24 22 Fig. 3. Surface tension, y, as a function of mole fraction, x, according to the regular-solution theory approach for (A) krypton-thene at (a) 116, (b) 120 and (c) 124 K; (B) krypton-ethane at (a) 116, (6) 120 and (c) 124 K ; and (C) ethene-thane at (a) 117, (b) 126 and (c) 135 K.B. S. Almeida, V. A. M. Soares, I. A . McLure and J . C. G. Calado 1225 taken from ref. (6). The following equation has been used to calculate the surface activity coefficients. where RTlnfl = SP 0; [(6; - d;), + 216; 41 s, = x;S;/x x;q (6) i and 6; is the surface solubility parameter defined as the square root of the surface cohesive energy density cii.The cross-energy density cii is the geometric mean of cii and cii for the pure components, connected through the empirical factor 1 ci. = (1 - r) (c.. c. )1'2. 22 3i (7) Unlike Sprow and Prausnitz, who found that the geometric-mean rule gave a good description of their systems, we had to use the corrected combination rule (7) with 1 taking random, temperature-dependent values. Comparison between theory and experiment for the three systems under discussion is shown in fig. 3. The value 1 = 0.02 12 obtained for the ethene-ethane mixture agrees well with the parameter k,, = 0.016 (correcting the Berthelot combining rule) calculated' through the fitting of experimental G" values to the Frisch-Longuet-Higgins-Widom equation of state. However, for the two other systems there is no correlation between the two sets of values.This is unsurprising since the values of the surface solubility parameter used to get they; are inconsistent with the observed behaviour. The calculation of 6: = c:i was made through the following expression for the cohesive energy density : where AH:ap represents the enthalpy of vaporization of component i, (Htd - Hyat) is the correction for the real gas enthalpy relative to the saturation conditions at which pp and up are the vapour pressure and molar volume, respectively, of component i. The term ( y i - Tdy,/dT) represents the change in energy on forming the surface from the pure liquid.The outcome of the calculations suggests a greater difference between the solubility parameters of krypton and ethane than between krypton and ethene, which implies a greater deviation from ideality (measured by parameter 1) for the former system, in contradiction of the experimental evidence. The main reason for the failure of this treatment when applied to mixtures involving spherical and bicentric molecules has almost certainly to do with the relatively empirical definition of the surface cohesive energy density and the neglect of the shape effects associated with the presence of the quadrupole moment of ethene and ethane. Corresponding-states Treatments More modern approaches to the prediction of the surface tensions of pure liquids and their mixtures are based on the principle of corresponding states (CSP).We discuss el~ewhere~.'~ the applicability of the CSP to the surface tensions of krypton, ethane and ethene and some other liquids confirming that a three-parameter CSP, in particular that suggested by Brock and Bird,20 leads to a fairly good description of the surface tensions of such relatively simple fluids. The generalisation of the CSP to mixtures requires the introduction of mixing rules for the CSP parameters, in this case the critical temperature T, and pressure p , as well as Pitzer's acentric factor cu. Since for simple molecules p r cc &lo3, where E and o are the characteristic energy and size, respectively, associated with the molecular pairwise energy of interaction, and T, cc E, the average values ( p c ) and (T,) for the mixture may be obtained from the average molecular parameters ( E ) and (a).For estimating surface1226 Mixture Surface Tensions at Low Temperatures tensions it seemed appropriate to consider the two-dimensional van der Waals mixing rules (&a2) = x; E l , a;, + 2x1 x , E l , a;, + x f E,, Of2 ( 0 2 ) = Xf O;, + 2x1 x , a;, + X f Of, (9) where E~~ and oij are the energy and the size parameters corresponding to interactions between the pair of unlike molecules i and j. The cross- term parameters are given by the following relations : 0 1 2 = (1 +A,) (011 + O2,>/2 (12) where k,, and j12 are empirical factors connecting the Berthelot and Lorentz combining rules. The main problem is how to relate the value of o for the mixture with the ~o values for the components. In the absence of a well founded relation we took the easiest assumption : Lo = x , Lo, + x , Lo,.Other authors2, have used an alternative approach defining a pseudo-critical volume for one of the components in order to assure conformality with the other component. The reduced surface tension for the mixtures obtained through the expression of Brock and Bird is a dynamic value corresponding to a freshly formed surface. The calculation of the equilibrium value which accounts for the selective adsorption at the surface, the static surface tension, depends on the statistical model of the interface. We chose the monolayer model developed by Prigogine and Defay,,, which correlates ydynamic with ystatic as follows : Ystat = Ydyn - x : (dYdyn/dxl)2/2RT (14) where xi is the bulk mole fraction and s is the molar surface area already defined as V2/3 N,1/3 where V represents now the average molar volume of both components and N , is Avogadro’s number.The results of the application of this treatment to our systems are presented graphically in fig: 4. The full lines denote the composition dependence of the excess surface tension obtained by optimising the fitting to the experimental points through the introduction of arbitrary values for k,, andj,,. The dotted lines were obtained at the lowest temperature using the bulk values for k,, andj,, taken from ref. (23) and (24). Both sets of values are presented in table 5 for each system at a given temperature.The effect of parameter k,, on surface tension is much more important than that of j,,.. The same dependence was found by Soares and McLure in relation to other mixtures. 25 The agreement between the experimental points and the calculated curves shown in fig. 4 is poor even with optimized values fork,, andj,,. In fact these adjusting parameters take up all the shortcomings of the model, in particular its inability to deal with shape factors. The van der Waals mixing rules may constitute a source of error. In addition the surface composition is not considered explicitly in this model, although in the definition of the surface tension it is implicitly taken into account. Conformal Solution Theory embodying Shape Factors An alternative approach to the corresponding-states treatment of surface tension was presented by Murad.26 The theoretical basis of this treatment is well established for conformal fluids.The generalisation to non-conformal fluids is possible through the introduction of empirical shape factors, which depend on the critical constants andB. S. Almeida, V. A . M . Soares, I. A. McLure and J . C. G. Calado 1227 0 -1 1 x - 3 -4 0 -1 -3 0 -0.1 - 'E 5 -0.2 \ W x -0.3 Fig. 4. Excess surface tension, .'.Kr 0 0.5 1 0 XKr 0.5 1 0 xC? HJ 0.5 1 I I I I I I I I I yE, as a function of mole fraction, x, using the corresponding-states theory for (A) krypton-thene mixtures at (a) 116, (b) 120 and (c) 124 K ; (B) krypton+thane mixtures at (a) 116, (b) 120 and (c) 124 K; and (C) ethene-thane mixtures at 117 K.1228 Mixture Surface Tensions at Low Temperatures Table 5.Bulk and surface values for the parameters k,, andj,, bulk values surface values system k,, J,, k12 j , , krypton-ethene at 116.0 K” 0.063 0.00434 0.11 0.012 krypton-ethane at 1 16.0 K1* 0.038 0.0066 0.08 0.005 ethenexthane at 135.0 K18 0.016 0 0.016 0 acentric factors of each substance. The surface tension y,(T) of a fluid a at temperature T is related to the corresponding value yo of a reference fluid by the expression: (15) where T;, V; and T,“, V,“ refer to fluid a and the reference fluid, respectively, and flz,o and $ a , o are state-dependent shape factors which can be obtained using the empirical method described by Hanley et al.27 Eqn (1 5 ) may also be applied to the calculation of the surface tension of mixtures considering fluid a as a substance equivalent to the mixture with critical constants obtained from the values for the pure components by the method described for the CSP treatment.The outcome of the application of Murad’s approach to pure components19 is encouraging and justifies its generalisation to mixtures. The results obtained for the mixtures krypton-ethene, krypton-ethane and ethene-ethane are presented in fig. 5. The agreement between the theoretical and experimental points is good for ethene-ethane mixtures but apparently poor for the mixtures involving krypton, perhaps because the change in the surface composition is not taken into account. Y,(T) = ( f l a , o TYT,“) (V,“/4,,o V,“)”I”Y~(TT~/B,.~ T,“) The Flory-Patterson Treatment A formal correlation of our results was obtained by combining Flory’s theory of mixtures with the corresponding-states principle formulated by Patterson and Rastogi.28 Lam and BensonZ9 among 0 t h e r s ~ ~ 3 ~ ~ obtained values for the surface tension of pure fluids and then mixtures using Patterson’s equation for the reduced surface tension yR: yR( VR) = MV;15/3 - [( V;l3 - I)/ V;] In [( Vk’I” - 0.5)/( V;/I” - l)] where M is the fractional reduction in the number of nearest neighbours for a cell on the surface relative to one in the bulk of the liquid, and VR is the reduced volume. The reduced surface tension is defined as where k , is Boltzmann’s constant and p* and T* are the characteristic reduction factors for pressure and temperature, respectively.They depend on the thermal expansion coefficient a and the isothermal compressibility, K .The reduced volume in Flory’s theory is given by the following expression: VR = [(I +4aT/3)/(1 +aT)I3. The treatment maybe generalised to mixtures by replacing the pure-component characteristic values with appropriate averages dependent upon the adjustable parameters s12, the ratio of molecular surface area of contact per segment for each species, and X12, a cross-interaction parameter. We applied this theory to the calculation of the surface tensions of pure krypton andB. S. Almeida, V. A. M . Soares, I. A. McLure and J. C. G . Calado 1229 0 0.5 1 XKr 0 0.5 -4- K r 1 0 0.5 -vC. HJ 1 Fig. 5. Surface tension, y, as a function of mole fraction, x, using Murad’s approach for (A) krypton-thene at 116 K, (B) krypton-ethane at 116 K and (C) ethene-thane at 117 K.42 FAR I1230 Mixture Surface Tensions at Low Temperatures Table 6. Experimental and calculated values (Flory's theory) for the excess surface tension yE of krypton( lethene(2) at 1 16.0 K 0.148 - 2.77 -0.388 0.241 - 2.70 -0.383 0.337 - 2.97 - 0.380 0.437 -2.72 - 0.377 0.541 -2.11 -0.369 0.642 - 1.66 - 0.369 0.879 - 0.87 -0.342 ethene and their mixtures. The predictions for the pure substances are poor, as the comparison between the experimental values at T = 116.0 K for the surface tension of krypton y = 16.33 mN m-l and ethane y = 25.72 mN m-' with the calculated values 14.17 and 2 1.60 mN m-', respectively, confirms. The calculated excess surface tensions for the krypton-ethene mixtures at 116.0 K are compared in table 6 with the experimental results.Again the success of the treatment is limited since although the negative sign of yE is correctly predicted its order of magnitude is not. These discrepancies are not unexpected, since even the bulk properties of this system are at best only qualitatively described by Flory's Furthermore, the treatment ignores adsorption which may explain the low values obtained for yE. The mediocre description of the experimental results, despite heavy parameterisation, leaves this theory relatively unappealing. Conclusion Although this review of the success of the different theories in describing our results is not exhaustive, it is clear that no treatment adequately describes the surface tensions of binary mixtures of nearly simple substances whose molecules are but slightly non- spherical and whose polarity is restricted to relatively small quadrupole moments, albeit in one mixture of opposite signs.Only the non-realistic lattice approach gave a reasonably quantitative account of our results without recourse to correcting parameters of unknown physical significance. The accurate prediction of the bulk properties of mixtures of polar liquids is possible only by taking specific account of multipole moments and p~larisabilities.~~~ 33 These effects are equally important at the interfaces of mixtures of polar liquids, and we intend to pursue the study of such mixtures both from the experimental point of view arid through the interpretation of the results using modern theories of interfaces, for example those based on perturbation that incorporate the influence of polarity on interfacial structure.We gratefully acknowledge receipt of the NATO research grant no. 194.80 in support of this work. References 1 S. Fuks and A. Bellemans, Physica, 1966, 32, 594. 2 F. B. Sprow and J. M. Prausnitz, Trans. Faraday SOC., 1966, 62, 1097. 3 V. A. M. Soares, B J. V. S. Almeida, I. A. McLure and R. A. Higgins, Fluid Phase Equilibria, 1986, 32, 9.B. S. Almeida, V. A. M. Soares, I. A . McLure and J . C. G. Calado 1231 4 K. C. Nadler, J. A. Zollweg, W. B. Streett and I. A. McLure, J. Colloid Interface Sci., 1988, 122, 530. 5 V. A. M. Soares, B. J. V. S. Almeida, I. A. McLure, R. A. Higgins and J. C. G. Calado. Cryogenics, 6 J.C. G. Calado, D.Phi1. Thesis (University of Oxford, 1972). 7 J. C. G. Calado, E. J. S. G. Azevedo and V. A. M. Soares, Chem. Eng. Commun., 1980, 5, 149. 8 G. M. N. Albuquerque, J. C. G. Calado, M. L. Nunes da Ponte and L. A. K. Staveley, Cryogenics, 9 W. M. Haynes and M. J. Hiza, J. Chem. Thermodyn., 1977, 9, 179. 1987, 27, 263. 1980, 20, 416. 10 F. Menes, T. Dorfmuller and T. Bigeleisen, J. Chem. Phys., 1970, 53, 2869. 11 B. J. V. S. Almeida, Ph.D. Thesis (Instituto Superior Tecnico, Lisbon, 1986). 12 D. B. Myers and R. L. Scott, Ind. Eng. Chem., 1963, 55, 43. 13 G. A. Chapela, G. Saville, S. M. Thompson and J. S. Rowlinson, J. Chem. SOC., Faraday Trans. 2, 14 D. J. Lee, M. M. Telo da Gama and K. E. Gubbins, Mol. Phys., 1984, 53, 11 13. 15 A. Schuchowitsky, Acta Physicochimica U.R.S.S., 1944, 19, 176; 508. 16 J. W. Belton and M. G. Evans, Trans. Faraday SOC., 1944, 41, 1. 17 E. A. Guggenheim, Trans. Faraday Soc., 1945, 41, 150; Mixtures (Clarendon Press, Oxford, 1952), 18 F. B. Sprow and J. M. Prausnitz, Trans. Faraday SOC., 1966, 6, 1105. 19 B. J. V. S. Almeida, V. A. M. Soares, I. A. McLure and J. C. G. Calado, Rev. Port. Quim., submitted 20 J. A. Brock and R. B. Bird, Am. Inst. Chem. Eng. J., 1955, I, 174. 21 R. A. Higgins, MSc. Thesis (University of Sheffield, 1985). 22 R. Defay, J. Prigogine and D. H. Everett, Surface Tension and Adsorption (Longmans, London, 1966). 23 V. A. M. Soares, Ph.D. Thesis (Instituto Superior Tecnico, Lisbon, 1976). 24 E. J. S. G. Azevedo, Ph.D. Thesis (Instituto Superior Tecnico, Lisbon, 1979). 25 I. A. McClure and V. A. M. Soares, J. Phys. Chem., 1980, 84, 680. 26 S. Murad, Chem. Eng. Commun., 1983, 24, 353. 27 J. F. Ely and H. J. M. Hanley, Ind. Eng. Chem. (Fundam.), 1981, 20, 325. 28 D. Patterson and A. K. Rastogi, J. Phys. Chern., 1970, 74, 1067. 29 V. T. Lam and G. C. Benson, Can. J. Chem., 1970, 48, 3773. 30 A. K. Adya and P. P. Singh, Z. Phys. Chem. Leipzig, 1973, 257, 651. 31 R. L. Mishra and J. D. Pandey, Chem. Scr., 1977, 11, 117. 32 J. G. C. Calado, E. J. S. G. Azevedo, P. Clancy and K. E. Gubbins, J. Chem. SOC., Faraday Trans.1, 33 L. Q. Lobo, L. A. K. Staveley, P. Clancy, K. E. Gubbins and J. R. S. Machado, J. Chem. Soc., 34 S. M. Thompson and K. E. Gubbins, J. Chem. Phys., 1981, 74, 6467. 1977, 73, 1133. chap IX. for publication. 1983, 79, 2657. Faraday Trans. 2, 79, 1399. Paper 7/00068E; Received 8th December, 1987 42- I

ISSN:0300-9599    

DOI:10.1039/F19898501217

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans I, 1989, 85(6), 1233-1244 Fourier-Transform Infrared Studies of Copper-containing Y Zeolites Dehydration, Reduction and the Adsorption of Ammonia Joseph Howard I.C.I. p.l.c., Wilton Materials Research Centre, Wilton, Middlesbrough, Cleveland TS6 8JE Jacqueline M. Nicolt Department of Chemistry, University of Durham, South Road, Durham DHI 3LE The reduction of Cur' to Cur ions in partially Cu'*-exchanged zeolite Y by CO plus co-adsorbed NH, has been studied (298-673 K) using Fourier- transform infrared spectroscopy. While the data are complex the formation of a variety of species including [Cu(NH,)I2+, [CuCO(NH,),]+, NH: and hydrogen-bonded NH, have been identified. The data indicate that at low temperature reduction by NH, is dominant while at elevated temperature CO is a more important reducing agent.Introduction Although standard ion-exchange techniques are used to prepare partially exchanged Cur' Y zeolite [CuI'Na-Y], difficulties arise in the preparation of Cu'Na-Y due to the instability of CuI ions in aqueous solution. Direct ion-exchange of Cu' ions is only accomplished in the absence of oxygen with Cu" in liquid NH, solution. The preferred route is via the reduction of CuI'Na-Y zeolite, using C0,2 H2,, NH3,4-6 olefins6V7 etc. as reducing agents. The most frequently used reduction method is CO in the presence of NH,, described by Huang.2.8 The adsorption of NH, results in the relocation of the mobile Cu" ions in sites in or near the supercages, where they are more readily reduced by CO. By this method reduction is accomplished in 1 h at 673 K, while without NH, reduction times of ca.30 h are required. For reduction by hydrogen lower temperatures are required, but the Cu' ions so formed are found to be susceptible to further reduction to Cuo if the temperature exceeds 473 K3 Reduction by NH, or butadiene has also been shown to occur at 373 K.6 An additional mechanism by which Cu' ions are introduced into Cu"Na-Y zeolites is by autoreduction during dehydration at temperatures exceeding 623 K.', lo In this paper we report our detailed infrared studies of the dehydration of CuI'Na-Y, the adsorption of NH, on dehydrated Cu"Na-Y and of the reduction of Cu" ions in Y zeolite by CO and co-adsorbed NH, at a variety of temperatures. Copper-Ammine Complexes The formation of copper-ammine complexes in Y zeolites has been studied by a number of techniques, e.g.adsorption measurements,2. l1 X-ray diffraction,12 e . ~ . r . ~ * 13* l4 and i.r.13 spectroscopy. Adsorption of NH, by dehydrated Cu"Na-Y was shown by both e.s.r. s p e c t r ~ s c o p y ~ ~ ' ~ and X-ray diffraction12 to cause the migration of Cu" ions from sites t Current address : Reactor Radiation Division, National Bureau of Standards, Gaithersburg, MD 20899, USA.1234 + 4 4 I Cu'Na-Y reduction at 362 K for 13 h reduction at 673 K for 1 h evacuation for 3 h at 673 K F. T.I.R. Studies of Copper-containing Y Zeolites Table 1. A summary of the treatments applied to Cu'INa-Y within the small cavities, to sites in the supercages, where copper-ammine complexes were formed.From the observed e . ~ . r . ~ parameters the Cu"-ammine complex was concluded to be square planar at room temperature. On partial desorption of the NH, at 373 K, the symmetry of the complex changed to a distorted tetrahedron, the complex being formed by the coordination of Cu" to three lattice oxygens and one NH,. Upon increasing the desorption temperature (473-573 K) the original signal due to the Cu" ions in the small cavities was again observed. Adsorption isotherms of ammonia adsorbed on 13, 48 and 75% exchanged Cu"Na-Y zeolites were measured by Huang and Vasant. '' These measurements indicated complex formation to be complete at pressures of less than 20 Torrt. From the NH, uptakes, in agreement with e.s.r. result^,^ complexes of [Cu(NH,)J2+ stoichiometry were identified. For samples with a high copper content it was concluded that not all the Cu" ions were formed in complex formation.In Cu'Na-Y zeolites ammonia adsorption, as with Cu"Na-Y zeolites, results in the migration of Cu' ions into sites within the supercages. Ammine complexes of [Cu(NH,),]+ stoichiometry were identified.2 Infrared measurements have previously only been p~blished'~ for NH, adsorbed onto Cu"Na-Y. By comparison with the infrared spectrum of Cu(NH,), SO,15 a band at 1275 cm-' in the spectrum of Cu"Na-Y +NH, was assigned to the [Cu(NH,),I2+ complex. Quantitative intensity measurements of the 1275 cm-' band with increasing NH, adsorption confirmed this stoichiometry. On desorption of NH, the 1275 cm-' band shifted to 1260 cm-l, which led the authors to assign this band to the tetrahedral complex described earlier from e.s.r.results. t 1 Torr z 133.322 Pa.J . Howard and J . M . Nicol 1235 n A B 1800 1700 1600 1500 1400 1300 I w avenumberkm- ' wavenumber/cm- ' Fig. 1. The dehydration of CuI'Na-Y under vacuum at various temperatures (y-axis offset, note y-scale expansion in B is twice that of A). Sample heating at: (a) 323 K; (6) 437 K; (c) 528 K; ( d ) 618 K; ( e ) 698 K for 15 h; (f) sample cooled to ambient temperature. Experimental For our studies of the adsorption of NH, and Cu" reduction we have used 'sample I ' of our previous paper." This sample of Cu,o~,Na,,.l-Y contains a number of Cu' ions introduced by autoreduction during the initial dehydration of the sample. We will refer to it hereafter as Cu"/Cu'Na-Y.The treatments applied in the present work are summarised, for clarity, in table 1. Carbon monoxide (99%, British Oxygen Company) was passed through a liquid- nitrogen trap before use. Ammonia gas (99.9%, British Oxygen Company), was dried over sodium metal and purified by the freeze-pumpthaw technique. The purity of both gases was checked by infrared spectroscopy. Infrared spectra were measured, in transmission mode, using a Nicolet 60SX Fourier-transform spectrometer. The zeolite sample consisted of a thin self-supporting disc (ca. 7 mg) 15 mm in diameter. All sample treatments (dehydration, adsorption, etc.) were carried out in situ in an all-metal cell fitted with KRS-5 windows (4 cm path length), attached to an all-metal pumping and gas-handling system.Results and Discussion The results will be presented in five stages (see table 1) : (1) the dehydration of Cu"Na-Y; (2) the adsorption of NH, on Cu"/Cu'Na-Y; (3) Cu'karbonyl complexes in the presence of NH,; (4) the reduction of Cu"/Cu'Na-Y; ( 5 ) adsorption of CO on Cu'Na-Y. The Dehydration of Cu"Na-Y Spectra of Cu"Na-Y in the region above 1200 cm-' during dehydration are depicted in fig. 1. Although the data are complex, owing to the possible presence of a range of species, a number of bands can be assigned'' using literature data (table 2). In previous studies of the dehydration of CuI'Na-Y, bands in the 365C3500 cm-l region were assigned to Cu(OH)+."~ l8 These bands disappeared on heating samples above 573 K. In the present investigation vibrations observed at 3640 and 3550 cm-' were not lost on dehydration above 573 K [fig.1 (ct(e)]. Thus it is unlikely that they are due1236 F. T.I.R. Studies of Copper-containing Y Zeolites Table 2. Summary of bands observed during the dehydration of CuI'Na-Y and their assignments wavenum ber / cm- assignment 3 740 v(0H) of Si-OHI6 3700 -+ 3000" (broad) 3640 3550 3444" 3345" (3360)"~' 1640" I 600- 1200 v(0H) of adsorbed, hydrogen-bonding, H,O 3680" v(OH) of A1-OH16 } v(0H) of framework hydroxyl groups v(0H) of copper hydroxides d(H,O) of absorbed, hydrogen-bonding H,O framework vibrations" or carbonates formed during ion exchange (3318) " Lost on dehydration. ' below 450 K the 3345cm-' band consists of two components as indicated. " Overtone or combination bands.to copper hydroxyl species, which would have decomposed at these temperatures. We assign these bands to structural hydroxyl groups, similar to those found in decationated zeolites." The remaining bands at ca. 3444 and 3345 cm-' were not previously observed during the dehydration of CU"N~-Y.'~~ l8 B y comparing the v(0H) adsorption frequencies of copper hydroxide corn pound^'^-^' with these bands, they appear to be due to copper hydroxyl complexes that were probably formed during ion exchange. At elevated temperatures these species are observed to disappear, with the probable formation of non-linear coupled copper pairs (CU-O-CU)~+, which have previously been detected by e.s.r. spectroscopy.22 A summary of all band assignments in the 4000-1200 cm-' region is given in table 2.The Region Below 1200 cm-' Additional evidence for the presence of copper hydroxides should be found in the 1000-670 cm-' region, where the d(0H) vibration of these species has been reported.ls3 21 In fact in fig. 2(a) all the bands, except that at 900 cm-', may be assigned to vibrations of the internal and external tetrahedral linkages of the zeolite framework as described by F l a ~ ~ i g e n . ~ ~ The intensity of the 900 cm-' band gradually decreased with increasing dehydration temperature and is lost above 523 K. This behaviour correlates well with that of the features at 3444 and 3360 cm-' and we therefore assign the band to 6(OH) of a copper hydroxide species. From the available evidence, however, we are unable to determine whether these species are bridging or linear.During dehydration the external linkage band at 970 cm-' is observed to shift to 950 cm-' and more structure appears in the 700-600cm-' region. These changes reflect the migration of the mobile copper cations into the sodalite cage sites, as well as the formation of non-linear coupled copper pairs. 22 During dehydration of CuI'Na-Y we have shown previously'' that a number of Cu' centres are introduced into our samples by the autoreduction mechanism.' In the following section the sample is described as Cu"/Cu'Na-Y to reflect the Cu"/Cu' content.J. Howard and J. M. Nicol 1237 wavenumber/cm- ' Fig. 2. Transmission infrared spectra in the 120WOO cm-' region of CuI'Na-Y during dehydration under vacuum (y-axis offset). Sample heating as in fig.1. wavenumber/cm- ' wavenumber/cm- ' Fig. 3. The adsorption of ammonia on Cu"/CurNa-Y. (y-axis offset). ( a ) Zeolite background; (6) adsorption of 1.2 Torr of NH,; (c) spectrum (b) after 30 min; ( d ) evacuation of (c) for 15 minutes. The Adsorption of NH, on Cu'*/Cu'Na-Y As part of our studies of the reduction of Cu"Na-Y zeolite by NH, plus CO, separate studies of the adsorption of CO and NH, were performed. Details of the CO adsorption experiments are given elsewhere. lo Here we summarise our findings of ammonia adsorption and compare them to the previous i.r. study of Flentge et a1.131238 F. T.I.R. Studies of Copper-containing Y Zeolites Table 3. Assignment of bands in the 3800-1200cm-1 region due to NH3 adsorbed on Cu"/Cu'Na-Y ~~~ ~ band/cm-l assignment 3700-3500 (broad) 3400 (broad sh) 3374 (sh) 3319 3269 3216 3181 1627 (sh) 1610 (sh) 1580 1475 1420 1273 1 hydrogen-bonding hydroxyl groups hydrogen- bonding y(NH) v(NH) of NH,f or hydrogen bonded NH, v(NH) of [CU(NH,),]~+ [ref.(15), (25)] coordinately bound NH, zeolite framework deformations of NH; dd(NH3) of [CU(NH 3)4)4I " d,(NH,) of [Cu(NH,),I2+ [ref. (1 3)] The spectrum of ammonia adsorbed (1.2 Torr) on dehydrated Cu"/Cu'Na-Y is shown in fig. 3. Intense bands are observed in the 3800-3000cm-' [v(NH)] and 1700-1200 cm-' [G(HNH)] regions due to the formation of [Cu(NH,),I2+ complexes within the zeolite cages. After 30 min contact time the features due to adsorbed NH, were observed to increase in intensity. These intense features remain even after evacuation for 15 min.The spectral features can be assigned by comparison with published data on gaseous NH3,24 Cu(NH,) S0,15725 and the previous study of NH, adsorbed on Cur1Na-Y.13 A summary of these assignments is given in table 3. The 1700-1200 cm-' Region A band at 1273 cm-l in the spectrum of CuI'Na-Y has been assigned to the symmetric deformation of [Cu(NH,),I2+ com~lexes.~~ On evacuation of gaseous NH, for 15 min at room temperature [fig. 3(d)] we observe the intensity of this band to increase slightly. This infers that the number of [Cu(NH,),I2+ complexes initially increased on evacuation. In contrast, it was observed previously that the presence of excess NH, had no effect on the intensity of the 1273 cm-l band.l3 However, it was noted that in highly exchanged samples not all the CU" ions were participating in complex formation, and that sample pretreatment affected the availability of cations 'for complex formation. 11, l3 A possible explanation for the behaviour of the 1273 cm-l band in the present work is that, on removal of excess NH, from the cages, additional CU" ions enter the supercages to form ammine complexes from sites that are probably located just inside the sodalite cages at sites SII.The 3800-3100 cm-' Region In this region bands due to v(NH) and structural hydroxyl groups are observed (fig. 3; table 3). A difference spectrum of the data before and after NH, adsorption [fig. 3(b) minus fig. 3(a) show that on adsorption of NH, the hydroxyl bands observed at ca. 3740, 3640 and 3550 cm-l in the background spectrum are considerably reduced in intensity.This reduction is commensurate with their (a) hydrogen bonding to an NH, molecule (as indicated by the broad band at ca. 3700-3500 cm-l), and (b) having formed NH,+ species. Evidence for NH; is provided by the existence of the deformation modes of these species, which are observed at ca. 1475 and 1420 cm-l. On evacuation, furtherJ. Howard and J. M . Nicol 1239 2200 2000 w avenumber /cm- ' Fig. 4. The adsorption of CO onto autoreduced Cu"/Cu'Na-Y with preadsorbed NH,. (a) Zeolite background : evacuation of NH, for 15 min [spectrum 3 (d)]. (b) sample (a) + 0.5 Torr of CO; (c) sample (a)+8.0 Torr of CO; ( d ) evacuation. difference spectra show that hydroxyl bands reappear as the coordinating NH, molecules are removed from the zeolite cavities.Bands observed below 3400 cm-l are due to v(NH). These may arise from several possible species, e.g. copper-ammine complexes, NH, hydrogen-bonding to framework hydroxyl groups and NH;. No unique assignment may be made from the data available but the most probable assignments are summarized in table 3. The bands at 3269, 3216 and 3181 cm-l are best assigned to [Cu(NH,)J2+ ions by comparison with similar ammine complexes,15, 25 whereas the assignment of the 33 19 cm-l band remains unclear. This latter feature could be associated with any of the species listed earlier. The shoulder at ca. 3374 cm-' and the general broad band beneath the sharper features in the 3400-3000 cm-l region are, from their width, assigned by hydrogen-bonding NH, and to NH; species. Cu'-Carbonyl Complexes in the Presence of NH, After the removal of gaseous NH, from the sample, by evacuation for 15 min, CO was adsorbed (fig.4) onto the zeolite. Although no direct evidence for Cu'(NH,), complexes was obtained from the i.r. data, published adsorption measurements2 have shown NH, to initiate the migration of the CuI ions towards the supercages, where cuprous-ammine complexes are formed. Previously, Huang8 observed the v(C0) vibration of Cu'CO(NH,). complexes in the presence of NH, (10 Torr) at 2080 cm-l. The u(C0) band was observed to almost disappear on evacuating the sample for 5 min. After partial1240 F. T.I.R. Studies of Copper-containing Y Zeolites I 1 3800 3500 3200 2900 2600 2300 2000 1700 1400 wavenumber/cm- ' Fig.5. Adsorption of NH, and CO onto Cu"/Cu1Na-Y (y-axis offset). (a) Background [spectrum 4(d)]; (b) sample (a)+ 10.7 Torr of NH,; (c) sample (b) + 146 Torr of CO. desorption of the NH, (evacuation for 2 h at 298 K) a band was observed at 2125 cm-l &th CI P h n l l l A e r at %IQh rm-1 nn rearlm;ccinn nf C'n Fiirthpr pvariiatinn ('7 h a t 191 K \ followed by CO adsorption at room temperature resulted in a band at 2150 cm-l with a shoulder at 2135 cm-l; this band was, however, not now removed on evacuation. In the present work, the adsorption of CO (0.1 Torr) onto Cu'I/CuINa-Y with preadsorbed NH, resulted in the observation of one weak band at 2111 cm-l. Raising the CO pressure to 8 Torr caused the intensity of the 2111 cm-l band to increase significantly and a second band to appear at 2069 cm-l.Both hands were removed by evacuation for 5 min at beam temperature. Since it has previously been shown that only CU' ions adsorb CO," these two bands must reflect CuI ions in either different sites or complexed to different numbers of NH, molecules. We have previously correlated the different v(C0) vibrational frequencies found for CO adsorbed on Cu'-containing Y zeolites with CuI-carbonyl complexes located in S, or S;, S;, and S,, sites.1° The lower frequency band was only observed with a significant overpressure of CO. The large wavenumber shift in this band, compared with those previously observed in Cul- containing Y zeolites, reflects an increased amount of n-bonding between the CO ligand and the CuI ion.Such a complex is expected to be located in the supercages, where CO n-bonding has been predicted to be most effective.g Coordination of NH, ligands to the Cul ion, will, by donating electron density, increase the amount of n back-bonding possible between CU' and the coordinating CO molecule. This will result in a greater shift in the CO vibration frequency compared with the gas phase. The observation of this band only at high CO pressures, may indicate that a significant pressure of CO is needed to allow coordination to a Cu' ion surrounded by the NH, ligands. In the case of the higher-frequency band at 2111 cm-', less n-bonding is envisaged in the species responsible for this complex. It is possibly associated with Cu' ions that are coordinating to both framework oxygens and NH, ligands in or near the six-rings between the supercages and sodalite cages.In this location n-bonding will be less effective owing to the influence of the framework oxygens and the reduced number of coordinating NH, ligands. Of the bands due to adsorbed NH,, only the band at 1273 cm-' is observed to be significantly perturbed by the adsorption of CO as, on adsorption, its intensity decreases. This suggests that displacement of the [Cu(NH,),I2+ complexes occurs onJ . Howard and J . M . Nicol 1241 2400 2200 2000 1800 1600 1400 1200 w avenumber/cm- ' Fig. 6. The reduction of Cu"Na-Y by CO in the presence of NH,. (y-axis offset) (a) Zeolite+ 10.7 Torr NH,+ 146 Torr of CO. Sample heated at: (b) 358 K; (c) 358 K for 13 h ; (d) 473 K; (e) 673 K.Cul-carbonyl formation. This observation was also made when adsorbing NH, and CO prior to the reduction of CU" discussed in the next section. The Reduction of Cu"Na-Y The reduction of Cu" ions in Y-zeolite with CO in the presence of NH, has been shown to occur within 1 h at 673 K2,' The reduction of our sample by this method is discussed here. For reduction, NH, at 10.7 Torr and CO at 146 Torr were introduced at room temperature. The infrared spectra of the zeolite after addition of NH, and CO are shown in fig. 5. Bands assignable to Cu-ammine and Cu'CO(NH,), complexes discussed in the previous sections are clearly visible. The position of the intense v(C0) band of the carbonyl complex at 2060 cm-l is shifted slightly with respect to that noted earlier. This is presumably due to a slight increase in n-bonding within the Cu'CO(NH,),complexes. Bands displaying fine structure within ca.2220-2100 cm-l are due to gaseous CO present in the sample cell. During reduction, spectra were measured at various stages as depicted in fig. 6 and 7. After heating at 673 K for 1 h, a noticeable drop in the transmission of the sample was observed, although the relative intensities of the bands remained unchanged. On removal of the zeolite disc from the cell its pink-brown colour indicated that some1242 F.T.I.R. Studies of Copper-containing Y Zeolites r Fig. 7. The reduction of Cu"Na-Y at 673 K (y-axis offset). (a) Sample heated at 673 K for 1 h; (b) evacuation of gas phase at 673 K; (c) evacuation for 3 h ; ( d ) sample cooled to ambient temperature.Cuo clusters had been formed, reducing the transmittance of the sample. This is observed to have no effect on the CO-Cu' complexes formed (section 5). The spectra in fig. 6 and 7 show a number of aspects of interest: (1) The bands at ca. 1444 cm-l and 1484 cm-l are due to NH,+ ions formed as a result of H+ production during reduction by NH,. These species reach their maximum intensity at 473 K [fig. 6(d)]. Above this temperature the decomposition of NH; occurs leaving H+ in the zeolite framework. This observation indicates that at low temperatures NH, is the preferred reducing agent. (2) Bands observed in the 2160-2060 cm-l region (2060,2120 and 2160 cm-l) are due to Cu'-Co complexes. The shift to higher wavenumber with increasing temperature indicates a migration of the Cu' ions into the sodalite cavity sites where z-bonding is less effective.The intensities of the bands are much reduced above 358 K, showing a reduction in the stability of the complexes. This temperature corresponds well with that observed previously for the desorption of CO from Cu'karbonyls in Y zeolites.1° (3) On heating at 358 K for 13 h [fig. 6(c)] a new band is observed at ca. 2230 cm-l. At the same time a band reappears in the region of 1275 cm-l. On heating to higher temperatures both of these bands disappear. The agreement in the wavenumber of these new bands with the v(NN), and v(NO), vibrations of gaseous N,O, which are observed at 2224 and 1285 cm-', re~pectively,~~ leads us to tentatively assign them to N,O.The N,O is a product of the reduction of Cu" by NH,. This is in agreement with the formation of NH; ions and indicates that at low temperatures NH, and not CO is the preferred reducing agent. (4) Bands which appear above 473 K in the 2400-2300 cm-l region are due to gaseous CO,, a product of the reduction of the Cu" ions by CO. The observation of CO, indicates that above 358 K reduction is occurring via the CO reduction mechanism. ( 5 ) On heating above 573 K a shoulder develops at 1320 cm-l, which is not lost on subsequent evacuation and cooling of the sample. This band may possibly be due to the symmetric deformation of the Cu'-(NH,), complexes. (6) After evacuation and cooling the residual structure in the spectrum is due to ammine carbonyl complexes, NH; and OH- species.These points show that a variety of species are formed during the reduction of Cu"J. Howard and J. M . Nicol 1243 2200 2170 2140 2110 2080 2200 2170 2140 2110 2080 wavenumber/cm-' Fig. 8. The adsorption and desorption of CO on Cu'Na-Y: (a) zeolite background after reduction ; (6) sample (a) + 0.2 Torr CO ; (c) sample (a) + 2.1 Torr CO; ( d ) sample (a) + 9.4 Torr CO; (e) evacuation of gas phase; (f) evacuation for 10 min. by CO in the presence of NH,. The data are complicated by the fact that NH, on its own may reduce Cu" ions. At low temperatures the appearance of NH; species as well as the identification of N,O, indicates that this is indeed the preferred mechanism. Only at temperatures above 473 K is CO, observed, indicating that reduction by CO is the preferred route.The Adsorption of CO on Cu'Na-Y The spectra obtained where CO is adsorbed onto CuINa-Y are shown in figure 8. Bands due to Cul-carbonyl complexes are observed at ca. 2156 and 2143 cm-l. The intensity pattern of these bands is similar to those obtained previously for CO adsorbed on autoreduced Cu"Na-Y zeolite.1° This indicates that the majority of the Cu' ions are located in SII, sites (2143 cm-l) within the zeolite framework, while a smaller number occupy S, sites (21 56 cm-l). The band at 21 78 cm-l is associated with the Lewis-acid sites in the zeolite framework, and has been discussed elsewhere.'O The similarity in CO adsorption spectra in Cu'Na-Y zeolites prepared by either CO/NH, reduction or autoreduction shows that the distribution of Cu' ions in the framework must be similar.Conclusions Infrared spectra of CuI'Na-Y during dehydration revealed the presence of copper hydroxyl species formed during ion exchange of the zeolite. These species were found to dissociate on heating the sample above 530 K, possibly to (cu-0-C~)~' and H,O. In the presence of ammonia the formation of copper-ammine complexes has been observed, as well as the interaction of ammonia with the structural hydroxyl groups. The latter interactions were only revealed in difference spectra. The formation of NH,+ species was shown by the presence of bands at ca. 1450 cm-l. In addition, a band at 1273 cm-l, characteristic of the d(NH,), vibration of the [Cu(NH,)J2+ complex, was shown to increase in intensity on the evacuation of NH,, and to decrease in intensity in the presence of CO.This behaviour has not been reported by other authors who have studied the same systems. We have associated the behaviour of the 1273 cm-l bands with (a) the removal of excess NH, from the cages on evacuation which allows additional1244 F. T.I.R. Studies of Copper-containing Y Zeolites [Cu(NH3),l2+ complexes to form and (b) the formation of Cu'CO(NH,), complexes in the presence of CO which either disassociate some of the [Cu(NH3),l2+ and/or perturb the d(NH,), mode to move to a lower wavenumber. Spectra of the reduction of Cu'INa-Y with CO and co-adsorbed NH, indicate that at low temperatures reduction by NH, was preferred, whereas at higher temperatures reduction by CO dominates the reduction mechanism.The adsorption of CO by Cu'Na-Y showed the CU' cations to be located in the same sites as those observed previously in autoreduced CuI'Na-Y. We would like to thank the S.E.R.C. for the provision of a quota studentship to one of us (J.M.N.) and Durham University for the provision of research facilities. References 1 U. K. Kruerke, US. Patent No. 3476 462, February 24, 1970. 2 Y. Y. Huang, J. Catal., 1973, 30, 187. 3 R. G, Herman, J. H. Lunsford, H. Bayer, P. A. Jacobs and J. B. Uytterhoeven, J. Phys. Chem., 1975, 4 W. B. Williamson, D. R. Flentge and J. H. Lunsford, J. Catal., 1975, 37, 258. 5 E. F. Vansant and J. H. Lunsford, J. Phys. Chem., 1972, 76, 2860. 6 I. E. Maxwell and E. Drent, J. Catal., 1976, 41, 412. 7 I. E. Maxwell, R. S. Downing and S. A. J. Van Langen, Acta Phys. Chem., 1978, 24, 215. 8 Y. Y. Huang, J. Am. Chem. SOC., 1973,95, 6036. 9 P. A. Jacobs, W. de Wilde, R. A. Schoonheydt and J. B. Uytterhoeven, J. Chem. SOC., Faraday Trans. 79, 2388 1, 1976, 72, 1221. 10 J. Howard and J. M. Nicol, Zeolites, 1988, 8, 142 11 Y. Y. Huang and E. F. Vansant, J. Phys. Chem., 1973, 77, 663. 12 P. Gallezot, Y. Ben Taarit and B. Imelik, J. Catal., 1972, 26, 295. 13 D. R. Flentge, J. H. Lunsford, P. A. Jacobs and J. B. Uytterhoeven, J. Phys. Chem., 1975, 79, 354. 14 C. Naccache and Y. Ben Taarit, Chem. Phys. Lett., 1971, 11, 11. 15 I. Nakagawa and T. Shimanouch, Spectrochim. Acta, 1966, 22, 759. 16 J. Ward, A.C.S. Monograph 171, 1976, p. 1 18. 17 J. Ward, Trans. Faraday SOC., 1971, 67, 1489. 18 Y. Ben Taarit, J. Primet and C. Naccache, Compt. Rend., 1970, 67, 1434. 19 P. Tarte, Spectrochim. Acta, 1958, 13, 107. 20 W. B. McWhinnie, J. Znorg. Nucl. Chem., 1965, 27, 1063. 21 J. R. Ferraro and W. R. Walker, Znorg. Chem., 1965, 4, 1362. 22 C. Chao and J. H. Lunsford, J. Chem. Phys., 1977, 57, 2890. 23 E. M. Flanigen, A.C.S. Monograph 171, 1976, p. 80. 24 T. Shimanouchi, Tables of Molecular Vibrational Frequencies, Consolidated Volume I (NSRDS-NBS 39, 25 K. H. Schmidt and A. Muller, J . Mol. Struct. 1974, 22, 343. 1972). Paper 7/00084G ; Received 2 1st December, 1987

ISSN:0300-9599    

DOI:10.1039/F19898501233

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chew. SOC., Faraday Trans. I , 1989, 85(6), 1245-1255 General Phenomenological Treatment Diffusion, and Pseudodiffusion Control Reactions in Solution of Activation, of Bimolecular John F. Garst Department of Chemistry, School of Chemical Sciences, The Uniuersity of Georgia, Athens, Georgia 30602, USA A simple but rigorous and general phenomenological treatment of the bimolecular association A + B C in solution gives the fundamental relationship k = k,k,/(k,+bk,), where k , k,, k , are the observable, diffusion control, and activation control rate constants, respectively, for the forward reaction, and b is the ratio of the geminate recombination probability i~ to the non-geminate combination probablity a. The pro- babilities ii and a can differ. The criterion for diffusion control is a -+ 1, while the criterion for activation control is (1 -a) -, 1.Thus, the criteria for diffusion and activation control involve different parameters. The para- meter b can be greater than unity. When b is greater than unity and k , is large, k reaches a limiting value of k,/b, corresponding to pseudodiffusion control, rate constant kvD. When b is viscosity- and temperature-independent k,, and k, vary in parallel with viscosity and temperature. To estimate the extent of pseudodiffusion control by simulation would require simulations of both a and a, as well as values of k , and k,. Bimolecular associations such as radical-radical or enzyme-substrate combination often occur at or near the diffusion control limit (reaction at every colli~ion).~-~ However, some slower reactions respond to variations in viscosity and temperature as if they were diffusion contr~lled.l-~ They are ' pseudodiffusion controlled '.' The equation is often given as the relationship among second-order rate constants k (observable), k , (diffusion control) and k, (activation control).3* 4 t lo However, eqn (1) is not correct in '9 l2 Its limits do not include pseudodiffusion control; when k, % k,, k = k,, and when k, + k,, k = k,.Eqn (1) fails, for example, for fast radical-radical reactions that have rate constants k,/4 because three-quarters of AB collisions are electronic triplets that cannot collapse to singlet C. Orientational, conformational and other factors can have similar effects in reducing k, when k, is large, from k, to a pseudodiffusion control value k,,.1-3 In the tradition phenomenological treatment, eqn (1) is derived from the scheme : 4 9 lo Neither this scheme nor certain modified versions of it are logically s ~ u n d .~ ~ ~ A simple but rigorous alternative phenomenological treatment is given below. l3 The equation k = k,k,/(k,+bk,); b 2 1 (2) results, where b is the ratio of the probability a of geminate recombination to the probability a of non-geminate combination. ' Geminate recombination ' and ' non- 12451246 Bimolecular Reactions in Solution geminate combination’ are reactions of the associated AB pairs that result when C molecules cleave to geminate AB pairs or when previously uncorrelated A and B molecules collide for the first time giving non-geminate associated AB pairs. For eqn (2), the limiting values of k are k, (k, % bk,) and k,/b (k, < bk,). In the latter limit, k = k,, = k,/b if b > 1.(The possibility that b can be less than unity, which is unlikely, is not considered further here.) When b is viscosity and temperature independent, k,, and k, vary in a parallel fashion with variations in viscosity and temperature. For radical-radical reactions, b can be 4, since a can be ii/4, giving k,, = k,/4. The new treatment applies in a unified way to all cases, no matter how complex, including those in which the associated-pair states change significantly during their effective lifetimes. Terminology Owing to solvent caging, AB collisions occur in sets, or ‘encounters’.’ An encounter begins when diffusion brings a previously uncorrelated A and B together (initial collision) and lasts until diffusion separates them (at least temporarily) or reaction occurs.Encounters also occur in sets, that is, an AB pair that separates from an encounter has a significant probability of undergoing another encounter.’ ‘ Engagement ’ denotes the entire set of encounters (and therefore collisions) of a particular non-geminate AB pair.14 An engagement begins with the first collision of a previously uncorrelated, non- geminate A and B. It ends with the last collison of that particular pair. The only possible consequences of an engagement are reaction and permanent separation. An engagement of small inert molecules in solvents of low viscosity lasts no longer than ca. lo-’ s, after which the probability that that particular pair will ever collide again is vanishingly small.’ An engagement of reactive molecules may be terminated earlier by reaction.In sufficiently dilute solutions, the probability that a third A or B will collide with a member of an engaged pair during its effective lifetime is negligible. Consequently engaged pairs behave as if they were isolated. Definition of k , For dilute solutions, it can be shown (see later, for example) that the engagement rate is second order in A and B. DeJnition :’ k , = (engagement rate)/[A] [B]. (3) Local and Global Rates Noyes and Berg have pointed out that there is more than one valid way to express the forward and backward rates of a bimolecular association.'^ l5 Berg’s local and global rates are used here.15 The distinction between local and global reactions focuses on geminate recombination.In the local forward reaction, all reaction events in which A and B react to give C, including geminate recombination, are included. Thus, the local forward rate is the sum of the rates of non-geminate combination and geminate recombination. Similarly, all bond cleavages of C are part of the local backward reaction, whether or not they are followed by geminate recombination. In contrast, geminate recombination does not contribute to the global forward reaction. Only those bond cleavages of C that are not followed by geminate recombination contribute to the global backward reaction.John F. Garst 1247 The equations global forward rate = local forward rate - ii(loca1 backward rate) (4) (5) global backward rate = (1 -a) (local backward rate) give the relationships between local and global rates.Global rates have an important practical advantage over local rates. If the system is at equilibrium in degrees of freedom other than the extent of reaction, then the same global rate constants k and k describe the forward and backward reactions, whether or not the extent of reaction is at equilibrium. For local rates, the rate constants vary with the deviation from equilibrium, since the relative proportions of non-geminate combination and geminate recombination vary. Global rates are measured in most (but not all) experiments. Unless otherwise stated, rates referred to here are global rates. Definition of k, When A and B have equilibrium distributions in space, the local forward rate is k, [A] [B].l-’- l 5 This applies, in particular, when A + B + C is at equilibrium. Dejinition : k, = (local forward rate at equilibrium)/[A] [B].( 6 ) Traditional Phenomenological Treatment By definition of k,, the local forward rate at equilibrium, is k,[A][B]. The pseudo- steady-state approximation for AB in scheme (I) leads to the equation At equilibrium, [AB] = (k,/k,) [A] [B] and the local reaction rate is (k, k,/k,) [A] [B], so that k, = k, k,/k,. With this identification, eqn (7) can be rewritten as eqn (1). k = k , k,/(k, + k2). (7) Flaws in the Traditional Phenomenological Treatment Scheme (I) implies that engaged and geminate AB pairs are equivalent, but they are not, except in special cases.For free radicals, A and B, engaged pairs are initially 25% singlet, but geminate pairs are 100% singlet. Thus, scheme (I) violates the principle of microscopic reversibility ; the forward process that it represents is not the microscopic reverse of the backward process. The obvious ways of correcting the traditional phenomenological treatment are not acceptable. Eqn (2) results if k, of scheme (I) is replaced by k,/b, but then AB cannot include all engaged pairs, so how is AB defined? A precise definition may be impossible. In a typical attempt AB is described as ‘the diffusion complex with reactants A and B properly positioned for subsequent transformation into products ’.3 Fowever, not all of the ‘properly positioned’ AB pairs react, and some of those that are not ‘properly positioned ’ initially can gain ‘proper positioning’ during their lifetimes.‘Proper positioning’ is not clearly defined, and consequently it is not clear how b can be determined. In addition, reaction and dissociation of associated pairs are not governed by first- order rate laws with constant coefficients, as specified in scheme (I). According to diffusion and random-walk treatments of associated molecular pairs,** the probability of repction between times t and t + dt is proportional (after a very brief initial period) to t-5, not to the first-order factor exp (- ct), where c is a constant rate coefficient. Rate laws for associated-pair processes can be described as first-order in form with time- dependent, but concentration- independen t, rate coefficients.Thus, the ‘ corrected ’ traditional phenomenological treatments considered above invoke ill defined intermediates and incorrect rate laws for their disappearance.1248 Bimolecular Reactions in Solution Kinetics of (AB) Disappearance It is easy to alter scheme (I) to avoid the improper treatment of AB disappearance. In the pseudo-steady-state analysis of scheme (I), the probabilities a [ = k2/(El + k,)] and (1 - a ) [ = k l / ( k l + k,)] of reaction and escape from AB are calculated using constant first-order rate coefficients. These probabilities exist whether or not they can be reckoned by first-order kinetics. Therefore the assumption of constant first-order rate coefficients for the disappearance of AB can be abandoned, as in scheme (11), kD a 1 -a f'4 - C - (M) ---- A+B----- which is otherwise equivalent to scheme (I). (The dashed arrows denote reactions of intermediates to which the pseudo-steady-state approximation is applicable.The parameters associated with the dashed arrows are probabilities of transmission or reflection, not rate constants.) Eqn ( 7 ) reduces to k = k , k2/kl = k , when the second step of scheme (I) is rate- determining. Since the same step must be rate-determining for both the forward and backward reactions, the cleavage of C to AB is rate-determining, under activation control, for the backward reaction. Accordingly, the rate constant for the cleavage of C in scheme (11) is denoted by k,. Scheme (11) leads to the equations k = ak, (8) k= (I -.)FA (9) but thermodynamics requires that It then follows that K = k / k .k = (I -a)kA K The local (non-geminate combination plus geminate recombination) forward rate is expressed as local forward rate = ak, [A] [B] + akA [C]. (13) At equilibrium [C] = K[A] [B]. Substituting for [C] and ak, [eqn (12)] converts eqn (13) into local forward rate at equilibrium = [( 1 - a) k, K + ak, K ] [A] [B] = k A K[A] [B]. Using this equation and the definition of k,, k, is identified as thus allowing eqn (1 1) to be rewritten in the form k = (1-a)kA. Eqn (1) results when a is eliminated from eqn (8) and (16).John F. Garst 1249 Labelling by Origins The useful device of labelling intermediate associated pairs according to their origins is illustrated by its application to scheme (11). Let engaged pairs be denoted by g and geminate pairs by g.Lower-case letters are used for g and g to distinguish their status as species from that of A, B, and C. While A, B, and C are ordinary chemical species whose definitions do not refer to their origins, g and g are defined by the events that create them, i.e. engagement and bond cleavage, respectively. In this notation, scheme (11) becomes scheme (111). \ l - a \ \ C Labelling by origins separates global C formation events [upper branch of scheme (III)] from global C dissociation events (lower branch). The one-way reaction arrows of scheme (111) are entirely the result of labelling, that is, of the definitions of g and g. They do not imply any violation of microscopic reversibility that is not already present in scheme (11), since scheme (111) is equivalent, precisely, to scheme (11).In scheme (111), g and g are equivalent, except for labelling, to AB of scheme (11). In the general case, however, g and g are not equivalent. Free-radical coupling provides a simple example of inequivalent g and g. New Phenomenological Treatment The scheme A+B is the basis for a general and rigorous phenomenological treatment. It differs from scheme (1.11) in assigning possibly different values to the probabilities a and a, in recognition that engaged pairs g and geminate pairs g can differ. While the same components, A and B, make up both engaged and geminate pairs g and g, the latter may initially be distributed differently among electronic spin states, relative rotational orientations, conformations, etc.If g and g had infinite lifetimes, then both would relax to the same distributions. However, relaxation times may be comparable to or longer than associated-pair lifetimes, in which case reaction and permanent diffusive separation may occur while g and g differ, so that a and amay differ.1250 Bimolecular Reactions in Solution elimination of a and ii from eqn (8) and the equations The kinetic analysis of scheme (IV) is parallel to eqn (8)-(16). Eqn (2) follows by the E = (1 - i i ) E , [cf. eqn (9)] k = (1 -a)kA [Cf. eqn (16)] Definition : b = a/a. Magnitudes of b For a class of special cases of scheme (IV) that may be encountered frequently in solution, it follows from general arguments that b must be greater than or equal to unity (a 2 a). The class is defined as follows: Associated pairs g and g are composites of various subspecies Qi that have no memories, that is, their behaviour is classical, independent of their histories.Only the Qi can convert directly to C and, by microscopic reversibility, cleavage of C leads only to Qi. Associated pairs g and g may have memories by virtue of different, age-dependent distributions among the Qi. A particular example is analysed in detail later. Criteria for Activation, Diffusion, and Pseudodiffusion Control Eqn (1 7) and (1 8) show that the criterion for activation control is that (1 - ii) 3 1. On the other hand, the criterion for diffusion control, given by eqn (8), is a + 1. Thus, the criteria for activation and diffusion control involve different parameters. This is especially significant.An Q value near unity implies diffusion control and an avalue much less than unity implies activation control, but a small a value does not imply activation control nor does a large a value imply diffusion control. When b > 1 and bk, >> k,, eqn (2) reduces to k = k,, = k,/b. An equivalent statement of the criteria for pseudodiffusion control is that b > 1 and ii + 1. The equivalence can be shown by eliminating k from eqn ( 2 ) and (16) and solving for ii, giving (17) (18) (19) ii = bk,/(k, -k bk,). (20) When bk, 4 k,, ii+ 1. When b > 1, near-pseudodiffusion control arises if bk, is comparable to k, or ii is comparable to, but less than, unity. Critique of the General Phenomenological Treatment At equilibrium, and as infinite dilution and infinite K are approached, the general phenomenological treatment becomes exact.For non-equilibrium situations, dilute solutions (< mol dm-3), and moderate K (> lo2), the consequences of approxi- mations are well within ordinary experimental error. Associated pairs are treated as being isolated. The isolated-pair approximation becomes exact in the infinite-dilution limit. The approximation is excellent for solutions of A and B with concentrations up to ca. Associated-pair concentrations are neglected (pseudo-steady-state approximation). Concentrations of g and g are steady at equilibrium. Steady-state ratios [g]/[A] and [g]/[B] approach 0 in the limit of infinite dilution, while [g]/[C] approaches 0 in the limit of infinite K. When [A] = [B] = mol dm-3, the ratio [g]/[A] is no more than ca.lop2. Similar maximum possible values of [g]/[C] are ca. l/K or ca. when K = lo2; typically, K is much larger for fast bimolecular associations.? For certain initial conditions, the treatment applies only after a brief initial period (ca. s) during which there is a relaxation to 'long-time' behaviour. When there is no transient, or after relaxation, the long-time global rate constants k and k can be used to describe the reaction kinetics whether the reaction is far from equilibrium, at equilibrium [see eqn (13)], or in between, as discussed earlier and as demonstrated by Noyes and mol dm-3.9 t These estimates assume k, to be 10" dm3 mo1-ls-l and assign effective first-order rate constants of 10" SC' to permanent diffusive separation of g and g.John F.Garst 1251 Equilibrium is governed by K = [C]/[A] [B] and the rate of bond cleavage in C by a first-order rate law, rate = k, [C]. These are the usual assignments of equilibrium and rate laws for such reactions. The second-order engagement rate constant k , is taken to be concentration- independent. Eqn (21) follows for a possibly variable k, from eqn (8), (15) and (18). For isolated pairs, all of the parameters on the right-hand side of the equation k , = (1 -a)kA K/a (21) are independent of concentration, thus k , is also. These considerations establish eqn (2) as the correct general relationship among k , k , and k , in the limits stated above. Any other treatment, no matter how sophisticated or complex, must conform or be suspect.A Particular Case of Scheme (IV) with Classical Memory-free Intermediates For the additional insight that it provides, scheme (V), a particular case of scheme (IV) with classical intermediates Q, and Q,, is analysed below. A+B In scheme (V), Q1 and Q, have no memories, that is, their behaviours are independent of whether they are formed from A + B or from C . However, Q, and Q, may differ in properties such as spin state, relative orientation, and conformation. Consequently they may have different probabilities x, and x, of combination to give C . Q, and Q, interconvert with probabilities w,, and wzl, and they separate permanently with probabilities z, and z,. They are formed with probabilitiesf, and& from A + B and with probabilities dl and d, from C .The scheme A+ shows the relationship of scheme (IV) to scheme (V).1252 Bimolecular Reactions in Solution Scheme (VI) is a particular example of scheme (IV). The latter is derived from the former by labelling Q1 and Q, by their origins; Q1-Q, and Q1-Q, pairs (in boxes) constitute g and g of scheme (IV). A kinetic analysis of schemes (V) and (VI) must give results in accordance with those for scheme (IV). Let P, be the probability that a Q,, once formed, collapses to C (with any number of intervening Q1-Q2 interconversions) instead of suffering permanent separation to A+B. While x1 is the probability that a Q1 goes to C directly, P, is the probability that it goes to C (rather than to A+B) ultimately. Let P, be the similar probability for Q,.The equations P, = x, + w,, P2 P, = x,+ w,, P, (22) (23) follow from these definitions and those of xi and wii. For example, eqn (22) states that P, is the probability x, that a Q1 goes directly to C plus the probability w,, P, that it goes instead directly to Q2, which then goes ultimately to C. Solving eqn (22) and (23) simultaneously for P, and P, gives the equations (24) Pl = (x,+ w12 x2)/(1 - w,, w21) Later, we will use the fact that the sign of (Pl-P2) is the same as that of [(x, + w12 x,) - (x, + w,, x,)], since the denominator of the equation must be positive. 4 - P2 = Kx,+ w,, x,) - (x, + w,, x1)1/(1 - w12 %,I (26) In terms of the parameters of schemes (V) and (VI), the probabilities a and a are given by the equations a =f,P,+(l -f,)P, (27) a= d,P,+(l-d,)P,.(28) The sign of the difference (a- a) is determined by the signs of two factors, (d, - f,) and (P, - p,): a- a = (d, - f,) (P, - P,). Schemes (V) and (VI) include cycles within which detailed balance must be enforced. Consider the cycle (A + B) -+ Q1 -+ C -+ Q, -+ (A + €3). For a system at equilibrium, let R, denote the rate of formation of A+B (in all reactions giving A + B), R, the similar rate of formation of Q,, etc. Also, let R,, be the rate of direct conversion of A to Q,. R,, the similar rate of conversion to Q1 to C, etc. Then the following equations apply : R,, = f i R, R,, = Xi R, R,, = d2 R, R2, = Z, R, (3 OH3 3) R,, = f, RA R,, = x, R, R,, = d, R, R,, = Z, R,. (34)-(37) Since detailed balance requires R,, = R,, etc. the product of the left-hand sides of eqn (30)-(33) is equal to the product of the left-hand sides of eqn (34)-(37).Therefore the product of the right-hand sides of eqn (31)-(34) must be equal to the product of the right-hand sides of eqn (34)-(37). R,, R,, R, and R, all cancel from the equation of right- hand products, leaving the equation f l x1 d2z2 = f 2 x, dl z1 (38) as a requirement of detailed balance. For reaction probabilities, instead of rate constants, this states the familiar rule that the clockwise and anticlockwise productsJohn F. Garst 1253 must be equal. Using f, +f2 = d, + d2 = x, + w12 + z , = x2w2, + z2 = 1, eqn (38) can be recast as (39) If d, = f l or if Pl = P2, then a = a, but if neither condition holds, then a and ii can differ [eqn (29)]. Let dl >fl; then the left-hand side of eqn (39) is greater than unity, as is the right-hand side: (40) (dllfl) E( 1 - f M 1 - dl11 = (x,/x,> [( 1 - w,, - x&/( 1 - w,, - x,)].(XlIX2) [(I - w,, -x2)/(1- w,, - x1)l > 1 * Eqn (40) rearranges to x,+w12x2 >x2+w21x, which implies [eqn (26)] that (Pl - P2) > 0. Therefore ii > a, since both factors on the right-hand side of eqn (29) are greater than zero. If d, <fl then similar algebra shows that both factors on the right-hand side of eqn (29) are less than zero, so that ii> a in this case also. Thus, for schemes (V) and (VI) a and a are not necessarily equal, and if they are not equal then ii > a ; b 2 1. This shows that the intermediates g and g of scheme (IV) are not necessarily equivalent (they can ‘remember’ their origins), even when they consist of mixtures of the same memory-free species Q1 and Qz as in schemes (V) and (VI); g and g are inequivalent because they are formed as different distributions between Q1 and Q2.Schemes (V) and (VI) are not equivalent to scheme (IV). Scheme (IV) is more general. Schemes (V) and (VI) represent only one of many classical (and non-classical) schemes that are represented by scheme (IV). The division of associated pairs into only two categories, Q1 and Q2 [schemes (V) and (VI)], may sometimes be a poor approximation. In a better representation, Q1 and Q2 would be replaced by a spectrum of N associated pairs with various reaction possibilities. By using analogies with electrical circuits, it can be shown that ii 2 a for any number N of interconverting memory-free inter- mediates Q,.l6 Scheme (IV) is a much better representation of the general case because it refers to well defined events and species while hiding difficult details that must be specified in classical schemes. It should be noted that the intermediate associated pairs g and g of scheme (IV) need not be made up of memory-free subspecies such as Q1 and Q2; they could instead be made up of subspecies with memories. Ratio k / k , Eqn (18) gives k / k , as 1 -a, but Noyes obtained 1-p’ instead.’ Since /?’ is the ‘probability [that] two molecules [A and B] separating from an encounter will subsequently react with each other’’ while a is the probability of geminate recombination following bond cleavage of C , which can produce an A and B that are adjacent in solution, these are not equivalent.The discrepancy disappears when errors in Noyes’ original treatment are corrected. 1 7 7 l8 Pseudodiffusion Control The term ‘pseudodiffusion control’ was coined recently by Burshtein et a2.l To handle the case of pseudodiffusion control, some authors simply redefine ‘diffusion control’ as the limit in which reaction occurs at every collision in which A and B are ‘properly positioned ’ for rea~tion.~. ’ For reasons given above, the original definition (reaction occurs at every collision) is better. It is appropriate to use ‘pseudodiffusion control’ for cases in which the rate constant approaches k , / b (b > I), instead of k,, as k, becomes large compared to k,. This definition of pseudodiffusion control is broader than that of Burshtein et al.For example, they treat spin effects separately, instead of including them as contributors to pseudodiffusion control. The present treatment is unified. All factors that make b > 11254 Birnolecular Reactions in Solution are included here as contributors to pseudodiffusion or near-pseudodiffusion control. This certainly includes spin effects. It also includes the rotational and orientational effects that are the main concern of Burshtein et al., and includes conformational factors, which may have the largest effects of all. Eqn (5.2) of ref. (l), which is similar but not equivalent to eqn (2) here, contains a hypothetical and ill defined reference rate constant k:. Neither Burshtein et al. nor the references they cite provide a general proof of either their eqn (5.2) or eqn (2).The present treatment provides a proof of the fundamental relationship [eqn (2)] and avoids ill defined parameters by enforcing the requirements of thermodynamics ; k, appears naturally to fill the role played by k:. Conformational Contributions to Pseudodiffusion Control Very large effects can originate from conformational factors. Consider a case in which the residue of A in C is forced to adopt a conformation A’ that is not preferred for free A. When C cleaves, a geminate pair A’B results, where A’ has a high-energy conformation. If the conformational relaxation time of A is much longer than the effective lifetimes (ca. lO-’s) of associated pairs, but shorter than the mean lifetimes of free A molecules, then conformational equilibrium will be nearly established in the free A population.Under those conditions, only collisions of A’ with B can lead to C. If a fractionfof the free A population exists as A’, then a (but not a) is reduced by a factor f, providing a contribution to b of 1 /A which could be many orders of magnitude greater than unity. Such reactions could be slow even on an ordinary laboratory timescale. Short Associated-pair Relaxation Times If spins, rotational attitudes, conformations, and other fators that can contribute to pseudodiffusion control have relaxation times that are very short compared with associated-pair lifetimes, pseudodiffusion control is not possible. Consider the limit in which relaxation is instantaneous. Then relaxation makes g and g equivalent at all times.Accordingly, a and ii are equal. Thus, eqn (2) reduces to eqn (1). If the reaction is not diffusion-controlled, then its rate constant is influenced by k,. In order to prevent pseudodiffusion control, geminate-pair relaxation must not only compete effectively with diffusive separation but also with geminate recombination. For very reactive geminate pairs, this could require relaxation times as short as or 10-l2 s or less. Consequently, geminate-pair relaxation has little chance of occurring, and pseudodiffusion control is virtually guaranteed, for cases of the most reactive geminate pairs, provided that other requirements for pseudodiffusion control are met. Factors Making Engaged and Geminate Pairs Inequivalent Pseudodiffusion control cannot occur when engaged and geminate pairs are equivalent. ‘ Slow ’ associated pair relaxation is not sufficient to produce pseudodiffusion control when there are no inherent differences between engaged and geminate pairs that relaxation might eliminate.Spin, orientational and conformational states are the most obvious possible differences. If A and B are spin-free spheres, then there are no such differences, b = 1, and there can be no pseudodiffusion control. This is the case that is treated explicitly in the Collins-Kimball analysis and implicitly in the traditional phenomenological treatment, both of which lead to eqn (1).l0 Thus, both treatments lack generality for the same reason.John F. Garst 1255 Viscosity and Temperature Effects Both a and a will be viscosity- and temperature-dependent in general.However, their ratio b may be sensibly independent of these variables, over some range, because the effects on a and a may be parallel. In such cases k,, will parallel k , in response to viscosity and temperature variations. When k z k,,, a -+ 1, so a must be independent of viscosity and temperature if k / k , is constant. Examples of this behaviour are given by Burshtein et al.’ Simulations Perhaps a and a can be estimated from simulations. Recently McCammon et al. reviewed their work in estimating k by ~imulation.~ Estimates of k and k, provide an estimate of a [eqn (S)]. Since this is not sufficient to specify all of the parameters of eqn (2), it is not sufficient to establish pseudodiffusion control. Values of ii and k , are still needed. Simulations of reverse reactions might provide the necessary information. Acknowledgment is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for support of this research. The author is grateful to Professor D. W. Smith and Dr Brian L. Swift for helpful discussions. References 1 A. I. Burshtein, I. V. Khudyakov and B. I. Yakobson, Prog. React. Kinet., 1984, 13, 221. 2 0. G. Berg, P. H. von Hippel, Annu. Rev. Biophys. Biophys. Chem., 1985, 14, 131. 3 J. A. McCammon, S. H. Northrupt and S . A. Allison, J . Phys. Chem., 1986, 90, 3901. 4 S . A. Rice, ‘Diffusion-limited Reactions’, in ‘Comprehensive Chemical Kinetics’, ed. C. H. Bamford, 5 J. Keizer, Acc. Chem. Res., 1985, 18, 235. 6 U. M. Gosele, Prog. React. Kinet., 1984, 13, 63. 7 D. F. Calef and J. M. Deutch, Annu. Rev. Phys. Chem., 1983, 34, 493. 8 R. M. Noyes, Prog. React. Kinet., 1961, 1, 129. 9 R. M. Noyes, J . Chem. Phys., 1954, 22, 1349. 10 D. G. Truhlar, J. Chem. Educ., 1985, 62, 104. 11 J. M. Schurr and K. S . Schmitz, J. Phys. Chem., 1976, 80, 1934. 12 S. Hess and L. Monchick, J . Chem. Phys., 1986, 84, 1385. 13 J. F . Garst, J . Chem. Soc., Chem. Commun., 1987, 589. 14 J. F. Garst, F. E. Barton I1 and J. I. Morris, J. Am. Chem. Soc., 1971, 93, 4310, footnote 5. 15 0. G. Berg, Chem. Phys., 1978, 31, 47. 16 J. F. Garst, D. W. Smith and B. L. Swift, presented at the American Conference on Theoretical 17 J. F . Garst, J . Chem. Soc., Chem. Commun., 1987, 1440. 18 J. F. Garst, unpublished results. C. H. Tipper and R. G. Compton (Elsevier, Amsterdam, 1985), vol. 25. Chemistry, Brainerd, Minnesota, USA, July 2 6 3 1, 1987. Paper 7/00172J ; Received 9th November, 1987

ISSN:0300-9599    

DOI:10.1039/F19898501245

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. SOC., Furuday Trans I, 1989, 85(6), 1257-1265 Translational and Rotational Molecular Motion in Solutions of Alkali-metal Halides in Dimethyl Sulphoxide Antonio Sacco* and Marilisa Carbonara Dipartimento di Chimica, Universita degli Studi, Bari Via Amendola 173, I-70126 Bari, Italy Manfred Holz* Institut f u r Physikalische Chemie und Elektrochemie der Universitat Karlsruhe, Kaiserstrasse 12, D- 7500 Karlsruhe, Federal Republic of Germany The relative proton relaxation rates 1 / and the translational diffusion coefficients of dimethyl sulphoxide (DMSO) in solutions of NaBr, KBr, NaI, KI, RbI and CsI have been measured at 25 "C. The n.m.r. B' coefficients and the self-diffusion B, coefficients have been determined for all the salts. For a given salt the B and B, values are equal within the experimental error limits.A comparison of these data with literature values for the viscosity B coefficients of the same systems revealed that in DMSO (and in other organic liquids) the viscosity B coefficients always have higher values than the corresponding B' and B, coefficients. Thus, the viscosity is more strongly influenced by the presence of the ions than the reorientational and translational molecular motion of the solvent. The n.m.r. B' coefficients have been split into intra- and inter-molecular contributions (Bintra and Bin,,,) and into single-ion values. Thus the ratio 7:/7: of the reorient- ational correlation time in the first solvation sphere of the ions to the reorientational correlation time in the bulk could be determined. These values reflect the relatively strong ion-solvent interaction ; however, the Na+-DMSO interaction turns out to be weaker than expected.The equality of Bin,,, and B, found for all systems leads to the conclusion that in the aprotic solvent DMSO strong coupling exists between translational and rotational molecular motion. In 1967 Hertz and co-workers1 published fundamental work about the study of microdynamics of aqueous electrolyte solutions using nuclear magnetic relaxation and translational diffusion data. They introduced, in analogy to the viscosity B coefficients the n.m.r. B coefficients and showed that these coefficients contain information about the reorientational behaviour of solvent molecules in the first coordination sphere of the ions. The translational diffusion data were used in a similar way to study the influence of the dissolved ions on the translational behaviour of the water molecules.Engel und Hertz' extended the application of the &-coefficient method t o electrolyte solutions of a number of organic solvents. In the meantime, only a few papers appeared in the literature where B coefficients were dete~rnined.~'~ On the other hand, Abraham et al.5 showed that B and B' coefficients may be very valuable in the interpretation of thermodynamic data of electrolyte solutions, since they established good linear correlations between the entropy of solvation and these coefficients. However, as the authors pointed out, there is a lack of reliable and systematic B and B' data which are needed for further investigations. Beside this fact, there is a second reason why B'- coefficient measurements are desirable.This second reason is connected with the application of nuclear quadrupole relaxation of ionic nuclei t o the study of electrolyte solutions,6, ' where the knowledge of the reorientational correlation time of the solvent 12571258 Molecular Motion in Solutions of Alkali-metal Halides - u n -k W I . , , , , > 0.5 1.0 1.5 elm Fig. 1. The salt concentration dependence of the proton relaxation rates of DMSO in solutions of different alkali halogenides relative to the relaxation rate in pure DMSO. c is given in the aquamolality scale m. T = 25 "C (a) NaBr; (b) KBr; (c) NaI; ( d ) KI; (e) RBI; (f) CsI. molecule in the ion's first coordination sphere is required.Thus we decided to resume systematic %-coefficient measurements in organic solvents and to combine them for the first time with translational diffusion measurements on these systems. In this paper we report 'H relaxation rates, l/T,, and translational diffusion coefficients, D, of dimethyl sulphoxide (DMSO) as a function of concentration of the following salts: NaBr, KBr, NaI, KI, RbI and CsI. We have the following three aims: (i) the comparison of B' coefficients with the corresponding viscosity B coefficients; (ii) the determination of translational diffusion B, coefficients in order to compare the influence of the ions on translational and rotational molecular motion by the separation of the B' coefficients into Bintra and Binter coefficients; and (iii) the determination of the reorientational correlation time of DMSO in the first solvation shell of the ions under consideration.Experimental The 'H spin-lattice relaxation time measurements by the inversion-recovery method were performed at 20 MHz, using an automated n.m.r. process analyser (BRUKER Minispec pc 120). The instrument was equipped with a pulsed magnetic field gradient (PMFG) accessory unit, which allowed automated measurement of self-diffusion coefficients relative to water (DIIz0 = 2.30 x lo-' m2 s-l at 25 OC*). We chose for the salt concentration the aquamolality scale FZ (moles of salt per 55.5 mol of solvent, 1 m 2 0.2306 mol kg-' in DMSO). DMSO (Aldrich, HPLC gradeTable 1. Translational diffusion coefficients D of DMSO in solutions of different alkali-metal halides at 25 OCa NaBr KBr NaI KI RbI CSI C D C D C D N C D N C D C D 0.086 0.234 0.298 0.356 0.509 0.752 0.915 1.08 1.27 0.71 0.70 0.69 0.68 0.66 0.64 0.60 0.59 0.57 0.137 0.239 0.283 0.354 0.400 0.492 0.500 0.671 0.786 0.9 13 1.02 1.20 1.43 1.63 0.71 0.69 0.69 0.68 0.66 0.65 0.65 0.63 0.62 0.62 0.59 0.58 0.55 0.53 0.15 0.71 0.30 0.68 0.45 0.66 0.60 0.65 0.75 0.64 0.90 0.62 - - 0.509 0.506 0.505 0.504 0.504 0.503 - 0.15 0.30 0.45 0.60 0.75 0.7 1 0.68 0.67 0.66 0.64 0.506 0.506 0.505 0.504 0.503 0.2 0.71 0.4 0.67 0.6 0.67 0.8 0.64 1.0 0.62 1.2 0.60 - - 0.2 0.4 0.6 0.8 1 .o - 0.70 0.68 0.66 0.64 0.62 - is h d n 2i Q "The salt concentration c is given in the aquamolality scale; D is given in lo-' m2 s-'.(The experimental error for all diffusion coefficients is +O.Ol.) As examples for two systems, the number densities N in loz9 spins mW3 are also listed.The number density in pure DMSO is: Ncm0 = 0.507 x lo2' spins m-3.1260 Molecular Motion in Solutions of Alkali-metal Halides Table 2. B coefficients and AB" in DMSO at 25 "C salt B (salt)" A B k b + 0.001 - 0.001 + 0.025 + 0.023 A B + (Na+-K') A S - ( Br--I-) I NaBr 0.178 ( f 0.003) NaBr-KBr KBr 0.177 ( k 0.002) NaI 0.153 (k0.002) Nal-K1 RbI 0.140 (+0.005) CsI 0.132 ( 0.003) KBr-K1 KI 0.154 ( f 0.002) N ~ B ~ - N ~ I ~. a Values in parantheses are standard errors.b AB" = difference of B of two salts with one common ion. purity > 99.9 YO) was used without further purification. All salts used were of ' suprapur ' grade and supplied by Merck, Darmstadt.All the samples for the measurements were freed from oxygen by the ' freeze-pumpthaw ' technique. The sample temperature was 25kO.l "C. The estimated experimental error in & measurements was* 1 Yo. In the diffusion measurements a maximum deviation from the average values of kO.01 occurred corresponding to an experimental error of ca. k 1.5 Yo. Results We can compare our experimental values for salt-free DMSO with literature data. The proton relaxation rate in pure DMSO of 1/T, = 0.322 s-l is in excellent agreement with the value of 0.323 s-l by Engel and Hertz2 and in good agreement with other literature values of 0.316' and 0.343 s-'.l0 Our results for the self-diffusion coefficient in pure DMSO (D = 0.72 kO.01 x lo-' m2 s-l) is 1 I YO lower than two older literature value^,^,^^ whereas it is in a fair agreement with a third literature value of Claessens et a1.l' of 0.70 x lo-' m2 s-l (corrected for DHZo = 2.3 x lo-' m2 s-l).The salt concentration dependence of the proton relaxation rate is given in fig. 1. The relative relaxation rate (1/Qre, = (l/&)/(l/&)c=o shows for all salts in the concentration range 0 < c/m < 1 a clear linear dependence upon c. The translational diffusion coefficients of DMSO in the different alkali-metal halide solutions are given in table 1. These data reveal also a linear salt concentration dependence for c < 1 m. Results and Discussion The B' coefficients In analogy to the Jones-Dole equation12 for the relative viscosity of electrolyte solutions, yl/v0= l+Bc+CC2+ ...(1) Hertz and co-workers' introduced the following equation for the relative relaxation rate of solvent nuclei: (l/q)/(l/&)c=o = 1 +B'C+C'C2+ ... where in both equations the term in cf is neglected. The n.m.r. B' coefficients thus defined are used, as are the viscosity B coefficients, for the characterization of the properties of electrolyte solutions. Positive B' values, for example, correspond to a 'structure-making' influence of the salt on the solvent. For a more detailed discussion of the meaning of the B' coefficients we refer to the literature. ' 7 2 , The evaluation of the data in fig. 1 by means of the least-squares method provided theA . Sacco, M . Carbonara and M . Holz 1261 Table 3. The BIB’ ratios of alkali-metal halides in different solvents (25 oC)a salt H20b formamide‘ NM F“ CH,OHC DMSOd 0.77 0.833 -- = 1.18 0.0443 NaBr ~ 0.04 0.40 0.46 0.36 0.705 0.74 0.843 0.58 - 0.049 0.322 KBr -=0.98 - - 0.05 0.24 0.43 0.32 0.701 0.806 0.5 18 0.54 0.70 NaI -- o‘018 - -0.90 - = 1.48 - = 1.26 - 1.33 - 0.02 0.35 0.43 0.32 0.606 0.67 0.818 -- = 1.34 - 0.0755 0.292 0.56 -0.08 0.19 0.39 0.25 0.610 0.55 0.795 - 0.099 0.278 -0.11 0.16 0.18 0.554 -0.114 0.243 0.60 0.47 0.764 -0.12 0.13 0.33 0.16 0.523 0.548 0.56 = 1.11 -= 1.37 -= 1.22 - 2.14 - -- = 1.34 - - - 1.35 - 2.31 -= 1.20 -=2.19 -- KI ~ = 0.94 - = 1.54 - = 1.44 - 2.68 - - = 1.44 -- = 1.74 - 3.06e - RbI ~ = 0.90 - CSI ~ = 0.95 - = 1.87 - = 1.82 - = 2.94e - = 1.46 a The B and B’ values are given in units of dm3 mol-’.B and B values are taken from ref.1 ; B values are taken from ref. 13; B values are taken from ref. 2, B values as listed in ref. 5; estimated values as in ref. 5. B’ coefficients given in table 2. The values for KI and NaI can be compared with literature data by Engel and Hertz,2 B’(Na1) = 0.18 and B’(K1) = 0.15, and we establish excellent agreement for KI but not such good agreement for NaI. The positive B’ values for all salts investigated show that the alkali-metal and halide ions are powerful structure makers in the aprotic solvent DMSO, and this finding is in full agreement with experience from other data.5 Surprisingly we found that B’(Na1) = B’(K1) and B’(NaBr) z B’(KBr). (We first measured the iodide systems and, in order to confirm this unexpected result, we also measured the bromide solutions.) Since the B’ coefficient of a salt is the sum of a cationic (B’+) and an anionic (B’-) contribution, the difference AB’ of two salts with a common anion gives the differ- ence of the cationic B’+ coefficients, which we call AB’+.We see from table 2 that AB’+(Na’-K+) is very small, which means that within the experimental error limits B’+(Na+) = B’+(K+) is valid in DMSO. This result is surprising since the B+ and B’+ coefficients for the alkali-metal ions normally decrease as the ionic radius increases and therefore B’+(Na+) > B’+(K+) is expected. However, we point out that our result confirms B coefficient measurements in DMSO by Feakins and co-w~rkers,’~ where even a slightly higher B+(K+) compared with Bf(Na+) has been found (see table 5, later).We also emphasize that DMSO is not the first solvent, where the relative positions of Na+ and K+ are changed, this fact has also been observed for the corresponding B coefficients in N-methylformamide (NMF).l4, l5 A further interesting point is the fact that in all non-aqueous solvents previously investigated (methanol, formamide, glycol and glycerol)2 the value of AB’-(Br--I-) is ca. 0.02. As can be seen from table 2, our average value for DMSO, AB’-(Br--I-) = 0.024, also fits this rule. We come now to the comparison of B and B’ values. In table 3 we tabulate the BIB’ ratio for the salts investigated in DMSO together with the corresponding quantities in other solvents. This table reveals an extremely interesting fact, which up to now obviously did not find attention in the literature. We recognize that the viscosity B coefficients and the n.m.r.B’ coefficients are almost identical in water, but differ 43 FAR 11262 Molecular Motion in Solutions of Alkali-metal Halides markedly in the non-aqueous solvents. There is an increase of the BIB' ratio in the sequence DMSO < NMF < formamide < methanol and for a given non-aqueous solvent BIB' increases with the ionic radii. The data in table 3 show that in non-aqueous solvents the viscosity reflects more strongly the presence of the ions than the reorientational and translational molecular motion of the solvent. The BIB' ratios in table 3 cannot be correlated, e.g. to the dielectric constant or the dielectric relaxation time 2, of the solvents; however, we point out that the Walden product lo q of the alkali- metal and halide ions (Ao is the limiting molar conductance) decreases in the same solvent sequence as BIB' increases.23 The increase of BIB' in a given solvent with the ionic radii might be an indication that the diameters of the solvation complexes play a role in determining the BIB' ratio.The BIB' ratios given in table 3 may also serve for a rough estimate of B' coefficients in those cases where the B coefficients are known, but the B coefficients have not yet been measured. The B,, Kmter and Ern** Coefficients The n.m.r. B coefficients for a given salt are defined in eqn (2) with respect to the total relaxation rate for a given solvent. If the solvent nuclei relax by the dipolar interaction, as the DMSO protons in our case, the total relaxation rate (l/TJ has both intra- and inter- molecular contributions'? l6 ('/T,)total = (1IT)intr-a + ('/T,)inter.(3) The correlation time for the intramolecular contribution is the reorientational correlation time of the vector connecting the interacting protons in the solvent molecule, whereas the correlation time for the intermolecular contribution is proportional to D-l, the inverse translational diffusion coefficient of the solvent is connected with the rotational motion and (l/K)inter with the translational motion of the solvent molecules. If we are able to separate 1 / q in the two above contributions we can define in analogy to eqn (2) new coefficients by: l6 Thus (1 ( ' / ~ ) i n t r a / ( ' / q ) i n t r a , c = o = I +BIntrac+ * * .(4 a) and These coefficients, Blntra and Binter, reflect the influence of the dissolved salt on the rotational and translational motion of the solvent, respectively. Introducing the quantity p, as the ratio of intra- and inter-molecular relaxation rate in the salt-free solvent: from eqn (2)-(4b) it follows that ('l~)interl(ll~)inter, c = o = 1 + Blnter C+ * * * * (4 b) P = ('/T)intra, c=O/(l/K)inter, c = o B' = '/(I +P> %ter + p / ( l +P)B!ntra. ( 5 ) There is another measurable quantity, namely the translational diffusion coefficient of the solvent molecule, which allows the definition of B, coefficients of the reciprocal translational diffusion coefficients by :* (I/D)/(l/Dc=O) = 1 +BDc+ * . * . (6) We see that these B, coefficients unambiguously characterize the influence of the salt (ions) on the translational motion of the solvent.The B, coefficients obtained by a least-squares fit of the data in table I are listed in table 4. We recognize that the two sets of data, namely the B' coefficients in table 2 and the B, coefficients in table 4, derived from completely different measuring quantities, areA . Sacco, M. Carbonara and M. Holz Table 4. B, and BIntra coefficients in DMSO at 25 "C salt NaBr 0.178 ( & 0.006) 0.178 f 0.009 KBr 0.174 ( f 0.003) 0.180 & 0.005 NaI 0.156 ( 0.003) 0.150 & 0.005 KI 0.153 ( f 0.003) 0.155 0.005 RbI 0.140 (k0.004) 0.140&0.009 CSI 0.134 (& 0.005) 0.130 & 0.008 1263 a Values in parantheses are standard errors. Calculated from eqn (5) using the B and B, values in tables 2 and 4, respectively.practically identical since they agree within the experimental error limits. The consequences of this experimental finding will be discussed in the following. The intermolecular relaxation rate can be written in the following form:',16 where K is a constant, N is the number of interacting spins per unit volume and a is the closest distance of approach between the interacting nuclear dipoles on different solvent molecules. Consequently Binter could theoretically also reflect a possible influence of the salt on the quantities a and N . On the other hand, at low concentrations where the B coefficients are measured we can assume that the quantity a does not change appreciably. Under this assumption the intermolecular relaxation contribution can be determined at low salt concentrations by : The number density N as a function of c is obtained from density data.However, as can be seen from examples in table 1, in DMSO in the concentration range of interest N / N , = , does not differ from unity by more than 0.8 %. Thus, in the systems under investigation, the concentration dependence of (1 / 7Jinter is only given by D,=,/D and consequently Binter = B, holds. Since within the experimental error limits we found B, = B , it follows that B' and Blnter are also equal. From eqn ( 5 ) we can immediately see that in this case, within the experimental error limits for all six salts in DMSO, B = Blnter = Bintra must be valid. (Taking the actual values for B' and B,, we obtain from eqn ( 5 ) the absolute Blntra values given in table 4).This result means that the rotational and translational motions of the solvent DMSO are affected to the same extent by addition of a salt. This may be regarded as experimental proof that, as in water,17 in the aprotic and consequently less structured solvent DMSO a strong interrelation exists between the rotational and translational motion of the molecules. Reorientational Correlation Times in the Ionic Solvation Sphere So far we have been concerned with B and B coefficients for salts, which are the sum of contributions from the cationic and anionic species in solution. Information about ion-solvent interaction can be derived if the B' values can be divided into the single-ion contributions. For basic reasons the splitting of the B (and B') coefficients requires assumptions and therefore different separation methods can yield different results.For DMSO in recent years, two splitting procedures were proposed.13* l8 In the present stage it is hardly possible to judge which one of the two assumptions delivers the more reliable 43-21264 Molecular Motion in Solutions of Alkali-metal Halides Table 5. Ionic B' and Bin,,, coefficients together with ratio z'/z: of. the reorientational correlation times in the solvation spheres and in pure DMSO for two solvation numbers n: (25 "C) Ion B" Na+ K+ Rb' CS' Br- I- Na+ K+ Rb+ cs+ Br- I- 0.1 18 0.1 19 0.105 0.097 0.060 0.035 0.088 0.089 0.075 0.067 0.090 0.065 0.120 0.122 0.1 10 0.100 0.058 0.030 0.092 0.094 0.082 0.072 0.086 0.058 n:=4 n $ = 6 2.7 2.1 ~- splitting on the basis of 1.5 2.7 2.5 2.4 1.8 1.4 1.3 2.3 1.9 ) splitting on the basis of 1.8 2.3 2.1 2.0 2.2 1.8 1.5 ) a TF M 6.5 ps (see text). results and thus we will give two sets of B" values, based on the two different procedures.Since B;n4'a(RbI)/B;ntra(CsI) = 1.077 and B(RbI)/B(CsI) = 1.041 l3 has been found, we multiplied the B+(Rb+)/Bt(Cs+) ratios obtained in ref. (1 3) and (1 8) by the factorf = 1.077/ 1.041 = 1.035, and we used this corrected ratio for our Bintra values, namely BI,'t,,(Rb+)/B!,',,,(Cs+) = 1.100 and 1.139, respectively. Having the ratio of two single-ion coefficients B&, we could calculate the B;Zra coefficients as given in table 5. (The B * values in table 5 were obtained in an analogous way.) The B' coefficients in DMSO are somewhat higher than the corresponding values in NMF,2 indicating a comparatively stronger ion-solvent interaction.A plot of the B' or B" coefficients against the ionic radius, as proposed by Engel and Hertz,2 shows that the data lie on a fitting curve, with the exception of Na+. Thus we conclude that the equality of B+ and B + for K+ and Na' reflects a somewhat weaker interaction of Na+ with DMSO than expected, whereas K+ shows the 'normal ' behaviour. Using the B&., values we can determine the correlation time ratio z'/z: by applying the following equation : l ~ where z' is the reorientational correlation time of DMSO in the solvation sphere, 7: is the reorientational correlation time in pure DMSO and n: is the solvation number. (The number 55.5 in eqn (9) comes from the fact that we use the aquamolality scale.) In table 5 we list the z'/z: values obtained for n, = 4 and 6.In the following we will give an estimate for the reorientational correlation time of the overall molecular motion, 7:. In this connection we should keep in mind that our B coefficients were obtained from measurements of the CH, protons in DMSO. Consequently, we are concerned with reorientational correlation times of the H-H vector in the methyl group. For pure DMSO two research groups determined a reorientational correlation time of the H-H vector to be ca. 3.3 ps,9710919 If there were fast internal rotation of the methyl group, the true correlation time for the overall molecular motion could be up to a factor of four longer than 3.3 ps." On the other hand, there are strong hints that the internal motion in DMSO is only slightly faster than the overall motion2' and therefore we can assume that we have to correct only by a factorA .Sacco, M. Carbonara and M. Holz 1265 of ca. two.21 This is supported by the value of the dielectric relaxation time for DMSO, z, = 19.6 PS.~' Since z: = f z, is a good approximation if the Kirkwood g factor is near unity as in DMSO, we conclude that for the calculation of absolute z' values for table 5, as a well founded estimate, 7: z 6.5 ps can be used. Owing to the assumptions inherent in the splitting procedures of the B coefficients and in eqn (9), it is clear that the results given in table 5 have a higher degree of uncertainity relative to the other data given in this paper.The authors thank the National Research Council of Italy (CNR, Internat. contract no. 85.1459) for financial support. References 1 L. Endom, H. G. Hertz, B. Thul and M. D. Zeidler, Ber. Bunsenges. Phys. Chem., 1976, 71, 1008. 2 G. Engel and H. G. Hertz, Ber. Bunsenges. Phys. Chem., 1968, 72, 808. 3 M. S. Ansari and H. G. Hertz, J. Solution Chem., 1984, 13, 877. 4 see e.g. H. G. Hertz, in The Chemical Physics of Solvation, ed. R. R. Dogonadze, E. Kalman, A. A. 5 M. H. Abraham, J. Liszi and E. Papp, J. Chem. Soc., Faraday Trans. 1, 1982, 78, 197. 6 see e.g. M. Holz, Progr. NMR Spectrosc., 1986, 18, 327. 7 M. Holz and A. Sacco, Mol Phys., 1985, 54, 149. 8 H. Weingartner, 2. Phys. Chem. N.F., 1982, 132, 129. 9 K. J. Packer and D. J . Tomlinson, Trans. Faraday SOC., 1971, 67, 1302. Kornyshev and J. Ulstrup (Elsevier, Amsterdam, 1986), part B, p. 31 1. 10 M. D. Zeidler, Ber. Bunsenges. Phys. Chem., 1965, 69, 659. 11 M. Claessens, P. Fiasse, 0. Fabre, D. Zimmermann, and J. Reisse, Nouv. J . Chim., 1984, 8, 357. 12 J. Jones and M. Dole, J . Am. Chem. SOC., 1929, 51, 2950. 13 R. T. M. Bicknell, K. G. Lawrence and D. Feakins, J . Chem. SOC., Faraday Trans. I , 1980, 76, 637. 14 D. Feakins and K. G. Lawrence, J. Chem. SOC. A, 1966, 212. 15 C. Finter and H. G. Hertz, J. Chem. SOC., Faraday Trans. I , 84, 2735. 16 see e.g. H. G. Hertz, in Water, A Comprehensive Treatise, ed. F. Franks (Plenum Press, New York, 1973), vol. 3, p. 301. 17 see e.g. M. N. Buslaeva and 0. Ya. Samoilov, in The Chemical Physics of Solvation, ed. R. R. Dogonadze, E. Kalman, A. A. Kornyshev and J. Ulstrup (Elsevier, Amsterdam, 1986), part B, p. 391. 18 K. G. Lawrence and A. Sacco, J. Chem. SOC., Faraday Trans. I , 1983, 79, 615. 19 E. v. Goldammer and M. D. Zeidler, Ber. Bunsenges. Phys. Chem., 1969, 73, 4. 20 R. E. London, M. P. Eastman and N. A. Matwiyoff, J . Phys. Chem., 1977, 81, 884. 21 D. E. Woessner, J. Chem. Phys., 1965, 42, 1855. 22 J. Barthel, H. Behret and F. Schmithals, Ber. Bunsenges. Phys. Chem., 1971, 75, 305. 23 see e.g. R. L. Kay, in Water, A Comprehensive Treatise, ed. F. Franks (Plenum Press, New York, 1973), vol. 3, p. 173. Paper 8/00497H ; Received 23rd September, 1988

ISSN:0300-9599    

DOI:10.1039/F19898501257

出版商:RSC    

年代:1989

数据来源: RSC