摘要:

ISSN 0300-9599 JCFTAR 82 ( I 2 ) 3525-371 9 (1 986) JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions I Physical Chemistry in Condensed Phases 3525 3535 3553 3561 3569 3587 360 1 361 1 3625 3635 3647 3657 3667 368 1 3697 3709 3717 CONTENTS Fourier Transform Infrared Studies of the Irreversible Oxidation of Cyanide at Platinum Electrodes A. S. Hinman, R. A. Kydd and R. P. Cooney The Dielectric Properties of Zeolites in Variable Temperature and Humidity A. R. Haidar and A. K. Jonscher The Time-domain Response of Humid Zeolites A. K. Jonscher and A. R. Haidar Molecular-orbital Studies of C-H Bond Scission induced by Ionizing Radia- tion T. Tada Zeolites treated with Silicon Tetrachloride Vapour. Part 2.-Sorption Studies M. W. Anderson and J. Klinowski Studies of Propene Oxidation over Mixed Uranium-Antimony Oxides F.J. Farrell, T. G. Nevell and D. J. Hucknall Adsorption and Desorption Kinetics of Oxygen on Tin-Antimony Oxide Cat a1 y st by Quasi -cons tan t Coverage Met hods M-C. Bacchus-Montabonel and CO Adsorption at 77 K on KCl Films. An Infrared Investigation D. Scarano and A. Zecchina The Utilization of Time-resolved Dielectric Loss to probe the Role of the Surface in Heterogeneous Photochemistry C. J. Dobbin, A. R. McIntosh, J. R. Bolton, Z. D. Popovic and J. R. Harbour Polysilicate Equilibria in Concentrated Sodium Silicate Solutions I. L. Svensson, S. Sjoberg and L-0. Ohman Potentials of Ion-exchanged Synthetic Zeolite-Polymer Membranes M. Demertzis and N. P. Evmiridis Adsorption and Reduction of Nitrogen Monoxide by Potassium-doped Carbon T.Okuhara and K. Tanaka Physicochemical Properties and Isomerization Activity of Chlorinated Pt/Al,O, Catalysts A. Melchor, E. Garbowski, M-V. Mathieu and M. Primet Excess Pressures for Aqueous Solutions M. J. Blandamer, J. Burgess and A. W. Hakin Effect of Temperature on the Point of Zero Charge and Surface Dissociation Constants of Aqueous Suspensions of y-Al,O, K. Ch. Akratopulu, L. Vordonis and A. Lycourghiotis Thermal Decomposition of Solid Sodium Bicarbonate M. C. Ball, C. M. Snelling, A. N. Strachan and R. M. Strachan Reviews of Books J-P. Joly I I7ISSN 0300-9599 JCFTAR 82 ( I 2 ) 3525-371 9 (1 986) JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions I Physical Chemistry in Condensed Phases 3525 3535 3553 3561 3569 3587 360 1 361 1 3625 3635 3647 3657 3667 368 1 3697 3709 3717 CONTENTS Fourier Transform Infrared Studies of the Irreversible Oxidation of Cyanide at Platinum Electrodes A.S. Hinman, R. A. Kydd and R. P. Cooney The Dielectric Properties of Zeolites in Variable Temperature and Humidity A. R. Haidar and A. K. Jonscher The Time-domain Response of Humid Zeolites A. K. Jonscher and A. R. Haidar Molecular-orbital Studies of C-H Bond Scission induced by Ionizing Radia- tion T. Tada Zeolites treated with Silicon Tetrachloride Vapour. Part 2.-Sorption Studies M. W. Anderson and J. Klinowski Studies of Propene Oxidation over Mixed Uranium-Antimony Oxides F. J. Farrell, T. G. Nevell and D. J. Hucknall Adsorption and Desorption Kinetics of Oxygen on Tin-Antimony Oxide Cat a1 y st by Quasi -cons tan t Coverage Met hods M-C.Bacchus-Montabonel and CO Adsorption at 77 K on KCl Films. An Infrared Investigation D. Scarano and A. Zecchina The Utilization of Time-resolved Dielectric Loss to probe the Role of the Surface in Heterogeneous Photochemistry C. J. Dobbin, A. R. McIntosh, J. R. Bolton, Z. D. Popovic and J. R. Harbour Polysilicate Equilibria in Concentrated Sodium Silicate Solutions I. L. Svensson, S. Sjoberg and L-0. Ohman Potentials of Ion-exchanged Synthetic Zeolite-Polymer Membranes M. Demertzis and N. P. Evmiridis Adsorption and Reduction of Nitrogen Monoxide by Potassium-doped Carbon T. Okuhara and K. Tanaka Physicochemical Properties and Isomerization Activity of Chlorinated Pt/Al,O, Catalysts A. Melchor, E. Garbowski, M-V. Mathieu and M. Primet Excess Pressures for Aqueous Solutions M. J. Blandamer, J. Burgess and A. W. Hakin Effect of Temperature on the Point of Zero Charge and Surface Dissociation Constants of Aqueous Suspensions of y-Al,O, K. Ch. Akratopulu, L. Vordonis and A. Lycourghiotis Thermal Decomposition of Solid Sodium Bicarbonate M. C. Ball, C. M. Snelling, A. N. Strachan and R. M. Strachan Reviews of Books J-P. Joly I I7

ISSN:0300-9599    

DOI:10.1039/F198682FX039

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

FA RA DA Y 1RA N SA CTlO N S AND SYMPOSIA From the Royal Society of Chemistry FARADAY TRANSACTIONS II Molecular and Chemical Physics SPECIAL ISSUE - AUGUST 1986 Professor Alan Carrlngton delbred the 1985 Faraday lecture at the Royal lnsmutlon on 10th December, 1985. As a compliment to Professor Carrington, a group of his colleagues and Mends submitted original papers on the general theme of Molecular Dynamics and Spectroscopy. These papers are collected in the present Issue. CONTENTs: The Faraday Lecture: Spectroscopy of Molecular Ions at thelr Dissociation Limits A. Carrington The Spectroscopy, Photophysics and Photochemistry of Clusters of Metrazlne D. H. Levy Spectroscopy of Transient Species produced by Photodissociation or Photoionizatlon in a Supersonlc Free-jet Expansion T.A. Mlller Molecukr-beam Infrared Spectroscopy of the Ar-N,O van der Waals Molecule J. Hodge, G. D. Hayman, T. R. Dykeand B. J. Howard The Estimation of Vlbrational Predissociation Ufetimes M. S. Chlld The Infrared Spectrum of H; and its Isotopomers. A Challenge to Theory and Experlment J. Tennyson and B. T. Sutcliffe The Augmented Secular Equation Method for calculating Spectra of van der Waals Complexes. Application to the Infrared Spechum of Ar-HCI J. M. Hutson Quantum-mechanical Wavepacket Dynamics of the CH Group in Symmetric- top X,CH Compounds using Effecttve Hamiltonians from Hlgh-resolution Spectroscopy R. Marguardt, M. Quack, J. Stohner and f. Sutcllffe Internal Dynamics of Subunits and Bondlng Force Constants In Weakly Bound Dlmers P. Cope, D.J. Mlllerand A. C. fegon Internal Dynamics and HF Bond Lengthenlng In the Hydrogen-bonded Heterodimer CH,CN . . . HF determined from Nuclear Hyper-fine Structure in its Rotational Spectrum P. Cope, D. J. Miller, L. C. Willoughbyand A. C. fegon Pumping and Rshing. Double-resonance Measurements on Molecular Jets U. Veeken, N. Damand J. Reuss nme-resow Fluorescence of Jet-cooled Carbazoles and thelr Weak Complexes A. R. Auty, A. C. Jones and D. Philllps Prediction of the Ct(*P, J/CI(P,J Branching Ratio in the Photodissociation of HCI S. C. GIvertzand 6. C. Ballnt-Kurt/ Hlgh-resolution Laser Photofragment Spectroscopy of CH' P. J. Sam, J. M. Walmsleyand C. J. Whitham Asymmetric Uneshapes associated with Predissociating levels M. N. R. Ashfold, R. N. Dixon, J. D. Prince, B.Tutcherand C. M. Westem A Threshold-photoelectron Ruorescence-Photon Coincidence Study of Radlatlonless TransMons in the B ,iI State of BCN+ €. Castellucci, G. Dulardin and S. leach Cornpetthe Channels in the Interaction of Xe('P,) with CI,, Br, and I,. Atom Transfer, Excitation Transfer, Energy Disposal and Product Alignment K. Johnson, R. Pease, J. P. Simons, P. A. Smith and A. Kvaran Mco Non-RSC Momkn P14.30 ($27.70) RSC Momkn M.00 Payment should accompany ordon for lhlr Ihm. RSC Members should send their orders to: Membershlp Manager, The Royal Society of Chemistry, 30 Russell Square, London WC1 B SDT. Non-RSC Members should send their orders to: The Royal Socleiy of Chemistry, Distribution Centre, Blackhorse Road. Letchwotth, Herts SG6 1 HN. Faraday Discussions No.80 Physical Interactions and Energy Exchange af the Gas-Solid Interface [his publication discusses aspects of current research on the gas-solid Interface: elastic, inelastic and dlssipattve scattering of atoms and molecules from cfystal surfaces; the structure and dynamics of physisorbed species, including overlayers. Emphasis Is placed on the themes of physical interactions and energy exchange rather than on molecular beam technology or the phenomenology of phase tmnsmons in overlayen. The interplay between theory and experlment is stressed as they relate to the nature of atom and molecule-surface interaction potentials including many body effects. Faraday Discussions No. 80 (1986) Softcevor Prico 531 .OO ($60.00) RSC Mombon J66.25 ROYAL SOCIETY OF CHEMISTRY Information Services (xiii)FA RA DA Y 1RA N SA CTlO N S AND SYMPOSIA From the Royal Society of Chemistry FARADAY TRANSACTIONS II Molecular and Chemical Physics SPECIAL ISSUE - AUGUST 1986 Professor Alan Carrlngton delbred the 1985 Faraday lecture at the Royal lnsmutlon on 10th December, 1985.As a compliment to Professor Carrington, a group of his colleagues and Mends submitted original papers on the general theme of Molecular Dynamics and Spectroscopy. These papers are collected in the present Issue. CONTENTs: The Faraday Lecture: Spectroscopy of Molecular Ions at thelr Dissociation Limits A. Carrington The Spectroscopy, Photophysics and Photochemistry of Clusters of Metrazlne D. H. Levy Spectroscopy of Transient Species produced by Photodissociation or Photoionizatlon in a Supersonlc Free-jet Expansion T.A. Mlller Molecukr-beam Infrared Spectroscopy of the Ar-N,O van der Waals Molecule J. Hodge, G. D. Hayman, T. R. Dykeand B. J. Howard The Estimation of Vlbrational Predissociation Ufetimes M. S. Chlld The Infrared Spectrum of H; and its Isotopomers. A Challenge to Theory and Experlment J. Tennyson and B. T. Sutcliffe The Augmented Secular Equation Method for calculating Spectra of van der Waals Complexes. Application to the Infrared Spechum of Ar-HCI J. M. Hutson Quantum-mechanical Wavepacket Dynamics of the CH Group in Symmetric- top X,CH Compounds using Effecttve Hamiltonians from Hlgh-resolution Spectroscopy R. Marguardt, M. Quack, J. Stohner and f. Sutcllffe Internal Dynamics of Subunits and Bondlng Force Constants In Weakly Bound Dlmers P.Cope, D. J. Mlllerand A. C. fegon Internal Dynamics and HF Bond Lengthenlng In the Hydrogen-bonded Heterodimer CH,CN . . . HF determined from Nuclear Hyper-fine Structure in its Rotational Spectrum P. Cope, D. J. Miller, L. C. Willoughbyand A. C. fegon Pumping and Rshing. Double-resonance Measurements on Molecular Jets U. Veeken, N. Damand J. Reuss nme-resow Fluorescence of Jet-cooled Carbazoles and thelr Weak Complexes A. R. Auty, A. C. Jones and D. Philllps Prediction of the Ct(*P, J/CI(P,J Branching Ratio in the Photodissociation of HCI S. C. GIvertzand 6. C. Ballnt-Kurt/ Hlgh-resolution Laser Photofragment Spectroscopy of CH' P. J. Sam, J. M. Walmsleyand C. J. Whitham Asymmetric Uneshapes associated with Predissociating levels M.N. R. Ashfold, R. N. Dixon, J. D. Prince, B. Tutcherand C. M. Westem A Threshold-photoelectron Ruorescence-Photon Coincidence Study of Radlatlonless TransMons in the B ,iI State of BCN+ €. Castellucci, G. Dulardin and S. leach Cornpetthe Channels in the Interaction of Xe('P,) with CI,, Br, and I,. Atom Transfer, Excitation Transfer, Energy Disposal and Product Alignment K. Johnson, R. Pease, J. P. Simons, P. A. Smith and A. Kvaran Mco Non-RSC Momkn P14.30 ($27.70) RSC Momkn M.00 Payment should accompany ordon for lhlr Ihm. RSC Members should send their orders to: Membershlp Manager, The Royal Society of Chemistry, 30 Russell Square, London WC1 B SDT. Non-RSC Members should send their orders to: The Royal Socleiy of Chemistry, Distribution Centre, Blackhorse Road. Letchwotth, Herts SG6 1 HN. Faraday Discussions No. 80 Physical Interactions and Energy Exchange af the Gas-Solid Interface [his publication discusses aspects of current research on the gas-solid Interface: elastic, inelastic and dlssipattve scattering of atoms and molecules from cfystal surfaces; the structure and dynamics of physisorbed species, including overlayers. Emphasis Is placed on the themes of physical interactions and energy exchange rather than on molecular beam technology or the phenomenology of phase tmnsmons in overlayen. The interplay between theory and experlment is stressed as they relate to the nature of atom and molecule-surface interaction potentials including many body effects. Faraday Discussions No. 80 (1986) Softcevor Prico 531 .OO ($60.00) RSC Mombon J66.25 ROYAL SOCIETY OF CHEMISTRY Information Services (xiii)

ISSN:0300-9599    

DOI:10.1039/F198682BX041

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

ISSN 0300-9599 JCFTAR 82(11) 3289-3524 3289 3293 3307 3315 333 1 3343 3357 3367 3381 3391 340 1 3407 3415 343 1 3439 3447 3461 3475 3479 349 1 JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions I Physical Chemistry in Condensed Phases Osmosis and Reverse Osmosis. Part 1.-The Frictional Coefficients in a General Transport Equation G. Dickel Osmosis and Reverse Osmosis. Part 2.-The Separation Factor of Reverse Osmosis and its Connection with Isotonic Osmosis G. Dickel and A. Chabor Viscosity of Na,SO, and MgSO, Solutions in Ethanol-Water Mixtures at 15, 25 and 35 "C Cooperative Effects in Heterogeneous Catalysis. Part 1 .-Phenomenology of the Dynamics of Carbon Monoxide Oxidation on Palladium Embedded in a Zeolite Matrix N. I. Jaeger, K. Moller and P. J. Plath Solvent Effects on the Thermodynamics of Aquocobalamin Chloride and Model Compounds in Dioxane-Water Mixtures S.Balt and A. M. van Herk The Hydrogen Evolution Reaction under Mixed Kinetic Control A. Saraby-Reintjes The Electrical Conductance of Molten Lead@) 9,lO-Dihydroxyoctadecanoate and some Binary Mixtures with Lead(r1) Octadecanoate M. S. Akanni and P. C. Mbaneme Optical Anisotropies of Alkylcyanobicyclohexyls and Related Compounds P. Navard and P. J. Flory Optical Anisotropies of Alkylcyanobiphenyls, Alkoxycyanobiphenyls and Related Compounds P. J. Flory and P. Navard Thermal Desorption and Infrared Studies of Butylamine adsorbed on SiO,, Al,O, and CaO R. Sokoll, H. Hobert and I. Schmuck Normal Coordinate Analysis of Molecules adsorbed on Zeolite Surfaces. Part 1 .-Cyclopropane adsorbed on Sodium Faujasites and Mordenites 0.Zakharieva-Pencheva, H. Fiirster and J. Seebode An llB Nuclear Magnetic Resonance Study of the Reaction of the Tetrahydr- oxyborate Ion with Polyhydroxy Compounds J. G. Dawber and S. I. E. Green Diffusion Phenomena and Metal Complex Formation Equilibria. Part 1 .- CdII-Thiourea Systems in Aqueous and Mixed-solvent Media D. R. Crow Kinetics of the B-Hydroxy Elimination Reactions from the Protoporphyrin I~o~(III)-CHRCH,OH Complexes in Aqueous Solutions. A Pulse-radiolytic Study Y. Sorek, H. Cohen and D. Meyerstein The Relationship between Immersion Calorimetry and the Parameters of the Water Adsorption Isotherm on Active Carbons F. Kraehenbuehl, C. Quellet, B. Schmitter and H. F. Stoeckli Neutron Scattering of Supercooled Water in Silica Gels C.Poinsignon and J. D. F. Ramsay Phase Equilibria in Model Mixtures of Spherical Molecules of Different Sizes G. Jackson, J. S. Rowlinson and C. A. Leng Catalytic Ignition on PdAu Wires D. D. Eley and A. H. Klepping Electron Spin Resonance Studies of Free and Supported 12-Heteropoly Acids. Part 3.-The Stability of Unsupported H,+,(PV,Mol,~,O,,) .xH,O in Air and in a Vacuum R. Fricke, H-G. Jerschkewitz and G. Ohlmann Electron Spin Resonance Studies of Free and Supported 12-Heteropoly Acids. Part 4.-The Reduction of H,+,(PV,Mol,~,O,,) - xH,O and the Influence of Supports on their Properties R. Fricke, H-G. Jerschkewitz and G. Ohlmann C. Quintana, M. L. Llorente, M. Sdnchez and A. Vivo 109 FAR 1Con tents 3501 Hydrogen Bonding. Part 1 .-Equilibrium Constants and Enthalpies of Com- plexation for Monomeric Carboxylic Acids with N-Methylpyrrolidinone in 1,1,1-Trichloroethane M. H. Abraham, P. P. Duce, R. A. Schulz, J. J. Morris, P. J. Taylor and D. G. Barratt Electrochemistry and Stability Studies of 0x0-bridged Dinuclear Ruthenium(rI1) Complexes for Water Oxidation R. Ramaraj, A. Kira and M. Kaneko 35 15

ISSN:0300-9599    

DOI:10.1039/F198682FP145

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Industrial Ph ysical Chemistry Group The Physical Chemistry of Small Carbohydrates (as part of the International Symposium on Solute-Solute-Solvent Interactions) To be held at the University of Regensburg, West Germany on 10-14 August 1987 Further information from Dr F. Franks, Pafra Ltd, 150 Science Park, Milton Road, Cambridge CB4 4GG Polymer Ph ysics Group Biennial Meeting To be held at University of Reading on 9-1 1 September 1987 Further information from Dr D. Bassett, Department of Physics, University of Reading, Reading RG7 2AD Neutron Scattering Group Applications of Neutron and X-Ray Optics To be held a t the University of Oxford on 14-15 September 1987 Further information from Dr R. K. Thomas, Physical Chemistry Laboratory, South Parks Road, Oxford OX1 302 Polymer Ph ysics Group New Materials To be held at the University of Warwick on 22-25 September 1987 Further information from Dr M.J. Richardson, Division of Materials Applications, National Physical Laboratory, Queens Road, Teddington, Middlesex TWl1 OLW Division Autumn Meeting Spectroscopy of Gas-phase Molecular Ions and Clusters To be held at the University of Nottingham on 22-24 September 1987 Further information from Professor J. P. Simons, Department of Chemistry, University of Nottingham, Nottingham NG7 2RD2047 Determination of the Absolute Rate Constant for the Reaction 0 + NaO + Na + 0, by Time-resolved Atomic Chemiluminescence at A = 589 nm “a(3 2PJ) + Na (3 “4) +hv J. M. C. Plane and D. Husain 2053 A lH Nuclear Magnetic Resonance Study of the Motion of Cation in some Clathrate Hydrates of Tetramethylammonium Fluoride and Hydroxides S.Sato, R. Ikeda and D. Nakamino 2061 Reviews of Books R. W. Richard; G. Doggett; B. T. Sutcliffe; D. J. Malcolme- Lawes; R. P. Wayne The following papers were accepted for publication in J . Chem. SOC., Faraday Trans. I during August 1986. 6/55 1 Study on Conformational Equilibria between Rotational Isomers by Means of Ultrasonic Spectroscopy. Part 1 .-Isobutyl Chloride and Bromide in Hexane H. Nomura, S. Koda and K. Hamada Diffusionphoresis of a Rigid Sphere through a Viscous Electrolyte Solution R. Roman and D. C. Prieve Effusion Mass-spectrometric Determination of Thermodynamic Properties of the Gaseous Mono- and Di-hydroxides of Calcium and KCaO(g) M. Farber, R. D. Srivastava, J.W. Moyer and J. D. Leeper 6/925 Corrosion Processes in Quantized Semi-conductor Colloids studied by Pulse Radiolysis M. T. Nenadovic, J. M. Nedeljkovic and 0. I. Micic 6/ 1045 Structure of the Catalytic Site on the Silica-supported Catalyst derived from Copper(I1) Actetate M. Nomura, A. Kazusaka, N. Kakuta, Y. Ukisu and K. Miyahara 6/1190 Oxidative Coupling of Methane over Samarium Oxides using N,O as the Oxidant K. Otsuka and T. Nakajima 6/ 1235 Emulsion Polymerization of Butyl Acrylates: Kinetics of Particle Growth I. A. Maxwell, D. H. Napper and R. G. Gilbert 6/1285 Spontaneous Ignition and Thermal Runaway in Closed and Open Systems. Part 2.-Ignition and Extinction in the Adiabatic CSTR for Reactions of Order M P. Gray and J. Mullins 6/1292 Electrical and Catalytic Properties of some Oxides with the Fluorite or Pyro- chlore Structure.CO Oxidation on some Compounds derived from Gd,Zr20, S. J. Korf, H. J. A. Koopmans, B. C. Lippens Jr, A. J. Burggraaf and P. J. Gellings 6/ 408 Determination of Stability Constants using Linear-scan or Cyclic Voltammetric Data H.Gampp 6/ 458 Nature of Radical Reactivity of Organic Plasma-exposed Glass Surfaces studied by the E.S.R. Spin Trapping Technique M. Kuzuya, S. Nakai, T. Okuda, T. Kawaguchi and Y. Yanagihara 6/89 1 6/924 (ii)Cumulative Author Index 1986 Abraham, M. H., 3255, 3501 Abu-Gharib, E.-E. A., 1471 Abuladze, N. A., 2481 Adams, D. M., 1020 Adams, M., 1979 Aicart, E., 2977 Aida, M., 1619 Aika, K-i., 2269 Akanni, M. S., 3357 Al-Hakim, M., 1575 Albery, W. J., 1033 Allen, G.C., 1367 Alwis, U. de, 1265 Amiya, S., 3141 Ammann, D., 1179 Anderson, J. A., 1911 Anderson, M. W., 569, 1449, Anderson, S. L. T., 1537 Anderson, T., 767 Andrt, O., 2423 Antoniou, A. A., 483 Appleyard, I. P., 2817 Araya, P., 1351, 2473 Atherton, N. M., 3042 Attwood, D., 1903 Augustine, R. L., 3025 Avent, A. G., 1589 Aveyard, R., 125, 1031, 1755, Ayyoob, M., 1657 Balasubramanian, K., 2665 Baldwin, R. R., 89 Balk, R. W., 933 Ball, R. C., 3233 Balt, S., 3331 Barford, W., 3233 Barone, G., 2089 Barouch, E., 2801 Barratt, D. G., 3501 Bartlett, J. R., 597 Bartlett, P. N., 1033 Battisti, A. De, 2481 Baur, J., 1081 Becker, K. A., 2151 Beezer, A. E., 2863,2929 Belton, P. S., 451 Benecke, J. I., 1945 Bennett, C. O., 2155 Berei, K., 3003 Berezin, I. V., 319 Bernstein, T., 1879 Berroa de Ponce, H., 281 1 Berry, F.J., 1023 Berti, P., 2547 Bhattacharyya, S. N., 2103 285 1 295 1 Bieth, H., 1935 Binks, B. P., 125, 1031, 1755 Biswas, P. K., 1973 Blackburn, G. M., 2965 Blake, P. G., 723 Blandamer, M. J., 1022, 1471, Blesa, M. A., 2345 Bloemendal, M., 53 Bloor, D., 21 11 Blagejowski, J., 3069 B{.}Nagy, O., 1789 Boelhouwer, C., 1945,2707 Bond, G. C., 1985, 3043 Booth, B. L., 2007 Booth, C., 1865 Boucher, E. A., 1589 Bozonnet-Frenot, M-P., 2185 Brereton, I. M., 1999 Brett, C. M. A., 1071 Brigandi, P. W., 1032 Brillas, E., 495, 1781 Brown, 0. R., 3045 Bruckenstein, S., 1105 Buck, R. P., 1169 Bui, V. T., 899 Burch, R., 1985 Burgess, J., 1471, 2989 Busca, G., 3019 Cabani, S., 2547 Cameron, P., 1389 Campos, A., 2781 Canet, D., 2185 Carley, A.F., 723 Carpenter, T. A., 545 Carroll, B. J., 3205 Casal, B., 1597 Cass, A. E. G., 1033 Castro, V. Di, 723 Castronuovo, G., 2089 Celda, B., 2781 Cenens, J., 281 Cesteros, L. C., 1321 Chabor, A., 3293 Champion, J. V., 439 Chang, C. D., 1032 Chao, K-J., 2645 Chapman, D., 3048 Chiou, C. T., 243 Chitale, S. M., 663 Christensen, P. A., 3215 Christenson, H. K., 2735 Chung, J. S., 2155 Claesson, P. M., 2735 Clark, B., 1471 Clark, S., 125 2989 Clarke, R. J., 2333 Clewley, J. D., 2589 Clifford, A. A., 2235 Coates, J. H., 2123, 2333 Cochran, S. J., 1721 Cohen de Lara, E., 365 Cohen, H., 2627,3431 Coller, B. A. W., 943 Compostizo, A., 1839 Conti, G., 2547 Contreras Viguria, E., 281 1 Cooney, R. P., 597 Copperthwaite, R. G., 1007 Cortts, J., 2473 Cortes, J., 1351 Corti, H.R., 921 Costas, M., 2977 Covington, A. K., 1209, 3042 Craston, D. H., 1033 Craven, J. R., 1865 Crespo Colin, A., 1839 Crilly, J. F., 439 Crow, D. R., 3415 Crowther, N. J., 2791 Crudden, J., 2195,2207 Dalas, E., 2897 Danil de Namor, A. F., 349, 281 1, 3275 Das, M. N., 1973 Dawber, J. G., 119, 3097, 3407 de Haas, M. P., 2933 De Schrijver, F. C., 281 Dean, C. E., 89 Dearden, S. J., 1627 Del Vecchio, P., 2089 Delaney, G. M., 2195,2207 Delannay, F., 2423 Delaval, Y., 365 Delmau, J., 3053 Delmon, B., 2423 Dharmalingam, P., 359 Dias Peiia, M., 1839 Dickel, G., 3289, 3293 Domen, K., 2269 Domtnech, J., 1781 Dore, J. C., 2411 Duatti, A., 1429 Due, P. P., 1471,3501 Dupliitre, G., 2825 Eagland, D., 2008,2791 Eastland, G., 2729 Eastland, G. W., 2833 Ebeid, E-Z. M., 909 Eden, J., 2945 Edmonds, R.N., 2515 Edwards, P. P., 2515 (iii)Author Index Egawa, C., 3197 Egdell, R. G., 2003 Eid, A. E., 1643 Ekechukwu, A. D., 1965 El-Daly, S. A., 909 Elbing, The Late E., 943 Eley, D. D., 3475 Elia, V., 2089 Elworthy, P. H., 1903 Espenscheid, M. W., 1051 Espinosa-Jimhnez, M., 329 Evans, D. F., 1829 Everett, D. H., 2589, 2605, 2915 Ewen, R. J., 1127 Farnia, G., 1885 Far0 Jr, A. C., 3125 Feakins, D., 563, 2195, 2207 Fegan, S. G., 785,801 Fernandez-Prini, R., 921 Fernandez-Valverde, S. M., 2825 Findenegg, G. H., 2001, 2691 Fink, P., 1879 Fisher, D. T., 119 Flanagan, T. B., 2175, 2589 Fletcher, A. J. P., 2605 Fletcher, P. D. I., 2311, 2651 Flory, P. J., 3367, 3381 Folman, M., 2025 Forster, H., 3401 Foulds, N. C., 1259 Fraser, I. M., 607, 2747 Freiser, H., 1217 Freund, P.L., 2277 Fricke, R., 263,273, 3479, 3491 Fukuda, H., 1561 Funabiki, T., 35,707, 1771 Fyles, T. M., 617 Gaboriaud, R., 2301 Gabrys, B., 1923, 1929 Ganghi, N. S., 2367 Garbassi, F., 2043 Garbowski, E., 1893 Garden, D., 3113 Garrido, J. A., 1781 Gellan, A., 953 Geoffroy, M., 521 Gervasini, A., 1795 Ghatak-Roy, A. R., 1051 Ghoneim, M. M., 909 Ghousseini, L., 349, 3275 Gilbert, R. G., 1979,2247 Gilhooley, K., 431 Gljbolos, S., 2423 Gomez-Esthvez, J. L., 2167 Gonziilez-Caballero, F., 329 Gondlez-Elipe, A. R., 739 GonzAlez-Ferndndez, C. F., 329 Gopalakrishnan, R., 2635 Gonnally, J., 157, 2497 Gorton, L., 1245 Gosal, N., 1471 Green, M. J., 1237 Green, N. J. B., 2673 Green, S. I. E., 3407 Grieser, F., 1813, 1829 Gritmer, G., 1955 Grzybkowski, W., 1381, 1703, Guardado, P., 1471 Haddad-Fahed, O., 2301 Haggett, B.G. D., 1033 Haines, A. J., 2817 Haines, G. A. J., 2817 Hakin, A. W., 1471, 2989 Hall, D., 21 11 Halle, B., 401, 415 Hamada, K., 3141 Handn, O., 77 Harriman, A., 3215 Harris, R. K., 2817 Harrison, M. R., 2515 Havredaki, V. I., 2531 Heatley, F., 255 Heberger, K., 2621 Hedges, W. M., 179 Hegde, M. S., 1657 Hellring, S. D., 1032 Hemfrey, J. P., 1589 Hersey, A., 1271 Hewitt, E. A., 869 Hey, M. J., 1805, 2817 Heyrovski, M., 585 Hidaka, H., 2615 Higgins, J. S., 1923, 1929,2004, Higson, S., 157 Hill, C. A. S., 1127 Hill, H. A. O., 1237 Hill, T., 349 Hitchman, M. L., 1223 Hobert, H., 1527,2505, 3391 Hobson, D. B., 869 Homer, J., 533 Honeybourne, C. L., 1127 Honeyman, M. R., 89 Hooper, A., 11 17 Hoppach, D., 3053 Houghton, J.D., 1127 Howe, A. M., 2411 Howe, R. F., 2887 Hronec, M., 1405 Hsu, W. P., 851 Huang, W-S., 2385 Hubbard, C. D., 1471 Hummel, A., 2933, 2945 Humphrey, B. D., 2385 Humphreys, F. J., 1020, 2006 Hunt, D. J., 189 Hunter, W. H., 2863,2929 Hussian, S. M., 2221 Hutchings, G. J., 1007 Ige, J., 2011 Iijima, T., 3141 Iizuka, T., 1681, 61 Ikeda, H., 61 Ikeda, O., 1561 Indaratna, K., 2755,2763 Indelli, A., 1429 Inomata, S., 1733 1745 3047 HOU, X-H., 1637 (iv) Inoue, M., 2175 Inoue, T., 168 1 Ishii, T., 2615 Ishikawa, T., 2401 Issa, R. M., 909 Iwamoto, M., 1713 Jackson, G., 3461 Jackson, S. D., 189,431, 2719 Jaeger, N., 205 Jaeger, N. I., 3315 Japaridze, J. I., 2481 Japaridze, S. S., 2481 Jayasuriya, D. S., 457,473 Jensen, M., 1351 Jerschkewitz, H-G ., ,3479, Johns, A.I., 2235 Johnson, D. C., 1081 Johnson, J., 1081 Johnston, P., 1007 Jones, W., 545, 3081 Jonson, B., 767 Jose, C. I., 663,681,691 Kadhum, A. A. H., 2521 Kakuta, N., 1553 Kamat, P. V., 1031 Kaminade, T., 707 Kaneko, M., 3515 Kaneko, M. J., 1637 Kaner, R. B., 2323 Karaiskakis, G., 2897 Katime, I., 1321, 1333 Katsanos, N. A., 2897 Kavetskaya, 0. I., 319 Kawaguchi, T., 1441 Kawai, S., 527 Kawai, T., 527 Kazusaka, A., 1553 Kelly, H. C., 1271 Kelly, K. P., 3025 Kelly, R. G., 1195 Kemball, C., 3044, 3113, 3125 Kevan, L., 213 Khan, S. U. M., 2911 Khoo, K. H., 1 Kido, K., 2269 Kinoshita, N., 2269 Kira, A., 3515 Kishimoto, S., 2175 Kjellander, R., 2735 Kleine, A., 205 Klepping, A. H., 3475 Klinowski, J., 569, 1449, 2851 KodejS, Z., 1853 Komatsu, T., 1713 Komiyama, M., 1713 Kondo, S., 2401 Kondo, Y., 2141 Koreeda, A., 527 Koresh, J.E., 2057 Koster, F., 2691 Kowalak, S., 2151 Kraehenbuehl, F., 3439 Kremer, M. L., 2133 349 1 Kiss, I., 3003Author Index Krishnasamy, V., 2665 Kuji, T., 2589 Kurotaki, K., 2843 Kusabayashi, S., 2141 Kuzuya, M., 1441 Lamotte, J., 3019 Lancz, M., 883 Lang, J., 109 Langevin, D., 2001 Larkins, F. P., 1721 Larsson, R., 767 Laurie, O., 3149 Lavalley, J-C., 3019 Lawless, T. A., 1031,2951 Lawrence, K. G., 563,2195, Lawrence, M. J., 1903 Leaist, D. G., 247 Lelikre, J., 2301 Leng, C. A., 3461 Gonard, J., 899 Leyendekkers, J. V., 1663 Lilley, T. H., 2965 Lim, T.-K., 69 Lin, J-C., 2645 Lincoln, S. F., 1999, 2123,2333 Llars, S., 767 Llinares, A., 521 Llorente, M. L., 3307 Lockhart, J. C., 1161 Loewenschuss, A., 993,2873 Logan, S.R., 161 Lomen, C. E., 1265 Lorenzelli, V., 3019 Lowe, B. M., 785, 801 Lowe, C. R., 1259 Lukhcs, J., 2621 Lundin, S. T., 767 MacCallum, J. R., 607,2747 MacDiarmid, A. G., 2323,2385 Mactaggart, J. W., 1805 Mahnke, R., 1413 Malliaris, A., 109 Mandal, P. C., 2103 Manes, M., 243 Marabini, A. M., 2043 Maran, F., 1885 Marchal, J-P., 2185 Marcus, Y., 233, 993,2873,3255 Marczewski, M., 1687 Maroto, A. J. G., 2345 Marshall, W. L., 2283 Martin, C. R., 1051 Maruthamuthu, P., 359 Marx, U., 2505 Mastikhin, V. M., 1879 Matheson, R. A., 2755,2763 Mathieu, M-V., 1893 Matijevid, E., 2801 Matsuda, T., 1357 Mbaneme, P. C., 3357 McCarthy, S., 943 McQuillan, A. J., 2755, 2763 Mead, J., 125, 1031, 1755 Meiler, W., 3053 2207 Melchor, A., 1893 Meyerstein, D., 3431 Miale, J.N., 1032 Miasik, J. J., 1117 Michael, A., 3053 Michel, D., 3053 Midgley, D., 1187 Milburn, P. J., 2965 Miles, R. J., 2929 Minami, Z., 1357 Mishima, S., 1307 Mishra, S. P., 521 Miura, H., 1357 Miyake, Y., 1515 Miyamoto, A., 13 Mobbs, R. H., 1865 Mol, J. C., 1945, 2707 Moller, K., 3315 Mollett, C. C., 1589 Mollica, V., 2547 Molyneux, P., 291,635, 3287 Moore 111, R. B., 1051 Morando, P. J., 2345 Morazzoni, F., 1795 Morehouse, K., 3215 Morgan, H., 143 Mori, K., 13 Morris, J. J., 3501 Moyes, R. B., 189,2719 Mulla, S. T., 681, 691 Murakami, Y., 13 Murata, M., 2615 Muscetta, M., 2089 Nagano, S., 1357 Naito, S., 3197 Najbar, M., 1673 Nakajima, T., 1307 Nakamatsu, H., 527 Nakanishi, M., 1441 Nakano, A., 2141 Napper, D. H., 1979,2247 Narayana, M., 213 Navard, P., 3367, 3381 Neta, P., 3215 Neto, M.M. P. M., 1071 Neuburger, G. G., 1081 Nex, C. M. M., 3233 Nikitas, P., 977 Nitta, S., 2401 Nock, A., 2817 Noyes, R. M., 2999 tubkowski, J., 3069 Nyasulu, F. W. M., 1223 Oakes, J., 2079, 3149 Oesch, U., 1179 Ogino, Y., 1713 Ohlmann, G., 263, 273, 3479, Okazaki, S., 61 Okubo, T., 3163,3175,3185 Okuda, T., 1441 Oldfield, M. J., 2673 Oldham, K. B., 1099 Onai, T., 2615 Onishi, T., 2269 349 1 (v) Ooe, M., 35 OpaUo, M., 339 Orchard, S. W., 1007 Oref, I., 1289 OReilly, P. J., 2195, 2207 Ortiz, A., 495 Owen, A. E., 1195 Parbhoo, B., 1789 Park, C-N., 2589 Parry, D. E., 3051 Parsegian, V. A,, 2801 Parsons, B. J., 1575 Patterson, D., 2977 Pease, W. R., 747, 759 Peeters, G., 963 Peeters, S., 963 Penboss, 1. A., 2247 Penner, R.M., 1051 Perry, M. C., 533 Pethig, R., 143 Petropolos, J. H., 2459 Petropoulos, J. H., 2531 Pettersson, A., 2435 Pfeifer, H., 3053 Pham, H. V., 1179 Phillips, G. O., 1575 Piculell, L., 387,401,415 Piekarska, A., 513 Piekarski, H., 513 Pilarczyk, M., 1703, 1745 Pilling, M. J., 2673 Pimblott, S. M., 2673 Pinna, F., 1795 Plath, P. J., 3315 Pletcher, D., 179 Poinsignon, C., 3447 Polta, J. A., 1081 Polta, T. Z., 1081 Porter, G., 3215 Porter, S. J., 2323 Pouchl$, J., 1605 Primet, M., 1893 Puchalska, D., 1381 Puttock, S. J., 2773, 3013, 3033 Quellet, C., 3439 Quintana, C., 3307 Quintana, J. R., 1333 Radulovic, S., 1471 Rajaram, R. R., 1985 Ramakrishna Rao, D. N., 2367 Ramaraj, R., 3515 Ramdas, S., 545 Ramsay, J. D. F., 3447 Rao, D. N. R., 2833 Rashid, S., 2235 Rebenstorf, B., 767 Richards, W.G., 3047 Richardson, P. J., 869 Rideout, J., 167 Rigby, S., 431 Rizkallah, P. J., 1589 Roberts, M. W., 723 Robinson, B. H., 1271, 2311, Richoux, M-C., 3215 241 1Author Index Robinson, P. J., 869 Rochester, C. H., 953, 1805, Rockliffe, J. W., 3149 Rodriguez, R. M., 1781 Rooney, J. J., 2005 Rosenholm, J. B., 77, 2435 Rossi, P. F., 3019 Rouw, A. C., 53 Rowlinson, J. S., 3461 Rubio, R. G., 1839 Rudham, R., 2817 Ruiz-Hitzky, E., 1597 Russell, D., 2729 Ryder, P. L., 205 Sacchetto, G. A., 1853 Saez, C., 1839 Saleh, J. M., 2221 Salmon, G. A., 161, 2521 Sanchez, F., 1471 Sinchez, M., 3307 Sandona, G., 1885 Sangster, D. F., 1979 Saraby-Reintjes, A., 3343 Saris, P., 2435 Sirkany, A., 103 Saur, O., 3019 Saville, G., 3041, 3046 Sawada, K., 1733 Scharpf, O., 1923, 1929 Schiller, R.L., 2123 Schlosserova, J., 1405 Schmelzer, J., 1413, 1421 Schmitt, K. D., 1032 Schmitter, B., 3439 Schmuck, I., 3391 Schoonheydt, R. A., 281 Schulz, R. A., 3501 Scott, J. M. W., 2989 Scott, R. P., 1389 Seebode, J., 3401 Segal, M. G., 3245 Segall, R. L., 747, 759 Seloudoux, R., 365 Senij, M., 2065 Shama, S., 2497 Shibata, Y., 1357 Shigeto, M., 1515 Shindo, H., 45 Shubin, A. A., 1879 Sidahmed, I. M., 2577 Siiman, O., 851 Simmons, R. F., 1965 Simon, W., 1179 Sircar, S., 831, 843 Smallridge, M. J., 1589 Smart, R. St C., 747, 759 Smith, D. G., 2569 Smith, E. G., 3149 Smith, I., 869 Smith, J. A. S., 2004 Snowdon, S., 943 Soffer, A., 2057,2627 Sokoll, R., 1527, 2505, 3391 1911,2569,2773, 3013, 3033 Schulz-Ekloff, G., 205 Solymosi, F., 883 Somsen, G., 53, 933 Sorek, Y., 3431 Soria, J., 739 Soria, V., 2781 Soriyan, O., 2011 Spiess, B., 1935 Spiro, M., 2277, 3048 Spotswood, T.M., 1999 Stenius, P., 2735 Stephens, A., 2729 Stoeckli, H. F., 3439 Strazielle, C., 1321 Strukul, G., 1795 Strumolo, D., 1795 Sugiyama, K., 1357 Suppan, P., 509 Sutherland, I. O., 1145 Suzuki, T., 1733 Swallow, A. J., 1575 Symanski, J. S., 1105 Symons, M. C. R., 167, 2367, 2729,2833 Szentirmay, M. N., 1051 Tabony, J., 2311 Tadros, Th. F., 3045 Take, S., 3141 Tamaru, K., 3197 Tamura, H., 1561 Tamura, K., 1619 Tanaka, T., 35 Tanaka, Y., 2065 Tang, A. P-C., 1081 Taniewska-Osinska, S., 1299 Taniewska-Osinska, S., 5 13 Tardajos, G., 2977 Tatam, R. P., 439 Tawarah, K., 21 11 Taylor, P. J., 3501 Tear, S. P., 1022 Tejero, R., 2781 Tennakoon, B., 3081 Tennakoon, D.T. B., 545 Teramoto, M., 1515 Thijs, A., 963 Thomas, J. D. R., 1135 Thomas, J. M., 545, 2851, 3081 Thomson, A. J., 2009 Tiddy, G. J. T., 3043 Tilak, D., 3081 Tobias, H., 2627 Tofield, B. C., 11 17 Toprakcioglu, C., 241 1 Townsend, R. P., 1019 Trasatti, S., 2481 Tunuli, M. S., 2911 Turner, J. C. R., 3052 Turner, P. S., 747, 759 Tyler, J. W., 1367 van de Ven, T. G. M., 457,473 Van Herk, A. M., 3331 van Lith, D., 2945, 2933 Vansant, E. F., 963 Vasaros, L., 3003 Vekavakayanondha, S., 29 1, Venkatasubramanian, L., 359 Verhaert, I., 963 Veself, V., 1405 Vidhczy, T., 2621 Vijlder, M. De, 2377 Vink, H., 2353 Viswanathan, B., 2635 Vivo, A., 3307 Volkov, A. I., 815 Volpe, P. L. O., 2863, 2929 Vonk, D., 1945 Waghorne, W. E., 563, 2195, Walker, R.W., 89 Wallwork, S. C., 1589 Walton, A. J., 1023 Wang, Z-C., 375 Ward, R. J., 2915 Warhurst, P. R., 119 Warman, J. M., 2933, 2945 Warr, G. G., 1813, 1829 Watson, J. T. R., 2235 Watts, P., 1389 Weale, K. E., 1020, 2002 Weiss, E., 2025 Wells, C. F., 1643, 2577 Wells, P. B., 189, 2719 Whalley, P. D., 1209 Whan, D. A., 31 13 Whyman, R., 189,2719 Wiens, B., 247 Williams, G., 3049, 3050 Williams, R. A., 3097 Williams, W. J., 3245 Wilson, G. S., 1265 Wilson, 1. R., 943 Whjcik, D., 1381 Woinicka, J., 1299 Wren, B. W., 167 Wright, K. M., 451 Wright, P. G., 2557,2565 Wu, E. L., 1032 Wu, Q., 2423 Wuthier, U., 1179 Wyn-Jones, E., 21 11 Wysocki, S., 715 Xiaoding, X., 1945, 2707 Yamada, A., 1637 Yamashita, H., 1771, 707 Yamazaki, A., 1553 Yatsimirsky, A. K., 319 Yeates, S.G., 1865 Yeo, I-H., 1081 Yoshida, N., 2175 Yoshida, S., 35,707, 1771 Yoshikawa, M., 707, 1771 You-Sing, Y., 2887 Zakharieva-Pencheva, O., 3401 Zana, R., 109 Zanderighi, L., 1795 Ziind, R., 1179 635, 3287 2207THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM No. 22 Interaction-induced Spectra in Dense Fluids and Disordered Solids University of Cambridge, 10-1 1 December 1986 Organising Committee: Professor A. D. Buckingham (Chairman) Dr R. M. Lynden-Bell Dr P. A. Madden Professor E. W. J. Mitchell Dr J. Yarwood Dr D. A. Young Mrs Y. A. Fish Whilst interaction-induced spectra have been studied i n the gas phase for many years, their importance in the spectroscopy of condensed matter has been appreciated only relatively recently. At present a considerable number of studies of induced spectra are taking place in what are (nominally) widely separated fields of study.It is highly desirable to bring these communities together so that common issues can be identified and the progress of one field appreciated in another. The final programme and application form may 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 GENERAL DISCUSSION N o . 83 Brownian Motion University of Cambridge, 7-9 April 1987 Organising Committee: Dr M. La1 (Chairman) Dr R. Ball Dr E. Dickinson Dr J. S. Higgins Dr P. N. Pusey Dr D. A. Young Mrs Y. A. Fish The Faraday Discussion on Brownian Motion will be introduced by Professor J.M. Deutch of MIT and will include contributions from P. Mazur, P. Meakin, R. Jullien, D. A. Weitz, M. Fixman, P. N. Pusey, R. H. OttewiII, A. Vrij, J. A. McCammon, B. A. Ackerson and V. Degiorgio dealing with hydrodynamics, fractals, Brownian dynamics of aggregation processes and photon correlation spectroscopy. There will be a poster session for which contributions are invited in the form of a brief abstract to be sent by 31 January 1987 to: Dr M. Lal, Unilever Research, Port Sunlight Laboratory, Bebington, Wirral L63 3JW. The preliminary programme may be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London WIV OBN (vii)THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 84 Dynamics of Elementary Gas-phase Reactions University of Birmingham, 14-16 September 1987 Organising Committee: Professor R.Grice (Chairman) Dr M. S. Child Dr J. N. L. Connor Dr M. J. Pilling Professor I. W. M. Smith Professor J. P. Simons The Discussion will focus on the development of experimental and theoretical approaches to the detailed description of elementary gas-phase reaction dynamics. Studies of reactions at high collision energy, state-to-state kinetics, non-adiabatic processes and thermal energy reactions will be included. Emphasis will be placed on systems exhibiting kinetic and dynamical behaviour which can be related to the structure of the reaction potential- energy surface or surfaces. Further information may be obtained from: Professor R. Grice, Chemistry Department, University of Manchester, Manchester M13 9PL THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM N o .23 Molecular Vibrations University of Reading, 15-16 December 1987 Organising Committee : Professor I. M. Mills (Chairman) Dr J. E. Baggott Professor A. D. Buckingham Dr M. S. Child Dr N. C. Handy Dr B. J. Howard The Symposium will focus on recent advances in our understanding of the vibrations of polyatomic molecules. The topics to be discussed will include force field determinations by both ab initio and experimental methods, anharmonic effects in overtone spectroscopy, local modes and anharmonic resonances, intramolecular vibrational relaxation, and the frontier with molecular dynamics and reaction kinetics. Further information may be obtained from: Professor 1.M. Mills, Department of Chemistry, University of Reading, Reading RG6 2AD. (viii)THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY Marlow Medal and Prize Applications are invited for the award of the Marlow Medal for 1987 and Prize of f 100. The award will be open to any member of the Faraday Division of the Royal Society of Chemistry, who by the age of 32, had made in the judgement of the Council of the Faraday Division, the most meritorious contribution to physical chemistry or chemical physics. The award will be made on the basis of publications (not necessarily in the Transactions) on any subject normally published in J. Chem. Soc., Faraday Transactions /and /I, that carry a date of receipt for publication not later than the candidate's 32nd birthday.Candidates should be members and under 34 on 1st January 1987, the closing date for applications, which may be made either by the candidate himself or on his behalf by another member of the Society. Copies of the rules of the award and application forms may be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London WIV OBN. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 85 Solvation University of Durham, 28-30 March 1988 Organising Committee: Professor M. C. R. Symons (Chairman) Professor J. S. Rowlinson Professor A. K. Covington Dr I. R. McDonald The purpose of the Discussion is to compare solvation of ionic and non-ionic species in the gas phase and in matrices with corresponding solvation in the bulk liquid phase.The aim will be to confront theory with experiment and to consider the application of these concepts to relaxation and solvolytic processes. Contributions for consideration by the organising Committee are invited in the following areas: (a) Gas phase non-ionic clusters (b) Liquid phase non-ionic clusters (c) Gas phase ionic clusters (d) Liquid phase ionic solutions (e) Dynamic processes including solvolysis Abstracts of about 300 words should be sent by 31 May 1987 to: Professor M. C. R. Symons, Department of Chemistry, The University, Leicester LE17RH. Dr J. Yarwood Dr A. D. Pethybridge Professor W. A. P. Luck Dr D. A. YoungJOURNAL OF CHEMICAL RESEARCH Papers dealing with physical chemistrykhemical physics which have appeared recently in J.Chem. Research, The Royal Society of Chemistry's synopsis + microform journal, include the following: Crystallographic and Physicochemical Properties of 7~ - Electron Systems, Part 10. Ab initio Tadeusz Marek Krygowski Jehan A. Baban, Brian STO-3G Interpretation of Hammett Su bstituent Constants and Gunter Hafelinger (1 986, Issue 9) P. Roberts, and Alice C. H. Tsang (1986, Issue 9) E.s.r. Studies of &/-Alkyl-fl-dialkylborylaminyl Radicals in Solution A Prototype Model for Artificial Photosynthetic Membranes: Water-swollen Chelate Filter Paper with Adsorbed Tris(2,2'-bipyridine)ruthenium(2+) and Methyl Viologen Yoshimi Kurimura, Noriko Matsuo, Etsuko Kokuta, Yasuyuki Takagi and Yoshiharu Usui (1 986, Issue 7) ln situ Electrochemical Electron Spin Resonance Spectrometry: the Anodic Oxidation of Richard G.Compton, Barry A. Coles and Michael J. Day (1986, Issue 7) Racemization of Peptides. An MNDO Study of the c-(Gly-Gly) Anion Miguel Pons, Josep Triphenylmethanol M. Bofill and Ernest Giralt (1 986, Issue 7) Hydrophobic Interactions of Gaseous Hydrocarbons derived from Studies of their Solubilities Robert W. Cargill and Donald E. MacPhee (1986,lssue8) in Mixtures of Water and Ethanol FARADAY DIVISION INFORMAL AND GROUP MEETINGS Division Half-day Endowed Lecture Symposium - Chemistry at Surfaces: Metals, Oxides and Semiconductors including the Tilden Lecture by Professor J. Pritchard and the Meldola Lecture by Dr J. S. Foord To be held at the Scientific Societies Lecture Theatre, London on 4 November 1986 Further information from Mrs Y.A. Fish, The Royal Society of Chemistry, Burlington House, London WIV OBN Colloid and Interface Science Group with Macrogroup UK Polymer-Polymer interfaces To be held at the Scientific Societies Lecture Theatre, London on 15 December 1986 Further information from Dr R. Aveyard, Department of Chemistry, The University, Hull HU6 7RX Colloid and Interface Science Group with the Colloid and Surface Group of the SCI Nucleation and Growth in Colloidal Systems To be held at the Society of Chemical Industry, 14 Belgrave Square, London on 16 December 1986 Further information from Dr R. Aveyard, Department of Chemistry, The University, Hull HU6 7RX Neutron Scattering Group Neutron Crystallography To be held at Imperial College, London on 17-19 December 1986 Further information from Dr R.J. Newport, Physics Laboratory, The University, Canterbury, Kent CT2 7NR Electrochemistry Group The Photoelectrochemical Properties of Colloids To be held at the University of Southampton on 7-8 January 1987 Further information from Dr S. P. Tyefield, CEGB Berkeley Laboratories, Berkeley, Gloucestershire GL13 9PBElectrochemistry Group with the SCI and the Institute of Corrosion Science Technology Electrochemical Techniques for Corrosion Scientists To be held at St. Catherine’s College, Oxford on 7-8 January 1987 Further information from Dr S. P. Tyefield, CEGB, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire GL13 9PB Division jointly with Perkin Division Half-Day Endowed Lecture Symposium on Radical Ion and Carbon ion Chemistry including the lngold Lecture by F.G. Bordwell To be held at University College, London on 12 March 1987 Further information from Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London WIV OBN Neutron Scattering Group Neutron Scattering and Phase Transitions To be held at the University of Warwick on 30-31 March 1987 Further information from Dr D. McK. Paul, Department of Physics, University of Warwick, Coventry CV4 7AL Electrochemistry Group Spring Informal Meeting To be held at the University of Bristol on 1-3 April 1987 Further information from Dr A. R. Hillman, School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 ITS Division - Annual Congress The Chemistry and Physics of Intercalation To be held at University College, Swansea on 13-16 April 1987 Further information from Professor J.H. Purnell, Department of Chemistry, University College, Singleton Park, Swansea SA2 8PP Polymer Physics Group Fundamental Aspects of Polymer Flammability To be held at Baden Powell House, London on 14-15 April 1987 Further information from Dr G. C. Stevens, CERL, Kelvin Avenue, Leatherhead KT22 7SE Division Full-day Endowed Lecture Symposium on Intramolecular Dynamics and Chemical Reactivity including the Centenary Lecture by S. A. Rice and the Tilden Lecture by M. S. Child To be held at the Scientific Societies Lecture Theatre, London on 6 May 1987 Further information from Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London WIV OBN Polymer Ph ysics Group Electroactive Polymers To be held at the Geological Society, London on 14 May 1987 Further information from Dr G.C. Stevens, CERL, Kelvin Avenue, Leatherhead KT22 7SE Electrochemistry Group with Macro Group UK Polymer Electrolytes To be held at the University of St. Andrews on 18-19 June 1987 Further information from Dr C. A. Vincent or Dr J. R. MacCallum, Department of Chemistry, University of St. Andrews, St. Andrews KY16 9ST Division Xlth International Symposium on Molecular Beams To be held at the University of Edinburgh on 13-17 July 1987 Further information from Dr J. F. Gibson, The Royal Society of Chemistry, Burlington House, London WIV OBNIndustrial Physical Chemistry Group The Physical Chemistry of Small Carbohydrates (as part of the International Symposium on Solute-Solute-Solvent Interactions) To be held at the University of Regensburg, West Germany on 10-14August 1987 Further information from Dr F.Franks, Pafra Ltd, 150 Science Park, Milton Road, Cambridge CB4 4GG Polymer Ph ysics Group Biennial Meeting To be held at University of Reading on 9-1 1 September 1987 Further information from Dr D. Bassett, Department of Physics, University of Reading, Reading RG7 2AD Neutron Scattering Group Applications of Neutron and X-Ray Optics To be held at the University of Oxford on 14-15 September 1987 Further information from Dr R. K. Thomas, Physical Chemistry Laboratory, South Parks Road, Oxford OX1 302 Polymer Physics Group New Materials To be held at the University of Warwick on 22-25 September 1987 Further information from Dr M.J. Richardson, Division of Materials Applications, National Physical Laboratory, Queens Road, Teddington, Middlesex lW11 OLW Division Autumn Meeting Spectroscopy of Gas-phase Molecular Ions and Clusters To be held at the University of Nottingham on 22-24 September 1987 Further information from Professor J. P. Simons, Department of Chemistry, University of Nottingham, Nottingham NG7 2RD (xii)FA RA DA Y 1RA N SA CTlO N S AND SYMPOSIA From the Royal Society of Chemistry FARADAY TRANSACTIONS II Molecular and Chemical Physics SPECIAL ISSUE - AUGUST 1986 Professor Alan Carrlngton delbred the 1985 Faraday lecture at the Royal lnsmutlon on 10th December, 1985. As a compliment to Professor Carrington, a group of his colleagues and Mends submitted original papers on the general theme of Molecular Dynamics and Spectroscopy.These papers are collected in the present Issue. CONTENTs: The Faraday Lecture: Spectroscopy of Molecular Ions at thelr Dissociation Limits A. Carrington The Spectroscopy, Photophysics and Photochemistry of Clusters of Metrazlne D. H. Levy Spectroscopy of Transient Species produced by Photodissociation or Photoionizatlon in a Supersonlc Free-jet Expansion T. A. Mlller Molecukr-beam Infrared Spectroscopy of the Ar-N,O van der Waals Molecule J. Hodge, G. D. Hayman, T. R. Dykeand B. J. Howard The Estimation of Vlbrational Predissociation Ufetimes M. S. Chlld The Infrared Spectrum of H; and its Isotopomers. A Challenge to Theory and Experlment J. Tennyson and B. T. Sutcliffe The Augmented Secular Equation Method for calculating Spectra of van der Waals Complexes.Application to the Infrared Spechum of Ar-HCI J. M. Hutson Quantum-mechanical Wavepacket Dynamics of the CH Group in Symmetric- top X,CH Compounds using Effecttve Hamiltonians from Hlgh-resolution Spectroscopy R. Marguardt, M. Quack, J. Stohner and f. Sutcllffe Internal Dynamics of Subunits and Bondlng Force Constants In Weakly Bound Dlmers P. Cope, D. J. Mlllerand A. C. fegon Internal Dynamics and HF Bond Lengthenlng In the Hydrogen-bonded Heterodimer CH,CN . . . HF determined from Nuclear Hyper-fine Structure in its Rotational Spectrum P. Cope, D. J. Miller, L. C. Willoughbyand A. C. fegon Pumping and Rshing. Double-resonance Measurements on Molecular Jets U. Veeken, N.Damand J. Reuss nme-resow Fluorescence of Jet-cooled Carbazoles and thelr Weak Complexes A. R. Auty, A. C. Jones and D. Philllps Prediction of the Ct(*P, J/CI(P,J Branching Ratio in the Photodissociation of HCI S. C. GIvertzand 6. C. Ballnt-Kurt/ Hlgh-resolution Laser Photofragment Spectroscopy of CH' P. J. Sam, J. M. Walmsleyand C. J. Whitham Asymmetric Uneshapes associated with Predissociating levels M. N. R. Ashfold, R. N. Dixon, J. D. Prince, B. Tutcherand C. M. Westem A Threshold-photoelectron Ruorescence-Photon Coincidence Study of Radlatlonless TransMons in the B ,iI State of BCN+ €. Castellucci, G. Dulardin and S. leach Cornpetthe Channels in the Interaction of Xe('P,) with CI,, Br, and I,. Atom Transfer, Excitation Transfer, Energy Disposal and Product Alignment K.Johnson, R. Pease, J. P. Simons, P. A. Smith and A. Kvaran Mco Non-RSC Momkn P14.30 ($27.70) RSC Momkn M.00 Payment should accompany ordon for lhlr Ihm. RSC Members should send their orders to: Membershlp Manager, The Royal Society of Chemistry, 30 Russell Square, London WC1 B SDT. Non-RSC Members should send their orders to: The Royal Socleiy of Chemistry, Distribution Centre, Blackhorse Road. Letchwotth, Herts SG6 1 HN. Faraday Discussions No. 80 Physical Interactions and Energy Exchange af the Gas-Solid Interface [his publication discusses aspects of current research on the gas-solid Interface: elastic, inelastic and dlssipattve scattering of atoms and molecules from cfystal surfaces; the structure and dynamics of physisorbed species, including overlayers.Emphasis Is placed on the themes of physical interactions and energy exchange rather than on molecular beam technology or the phenomenology of phase tmnsmons in overlayen. The interplay between theory and experlment is stressed as they relate to the nature of atom and molecule-surface interaction potentials including many body effects. Faraday Discussions No. 80 (1986) Softcevor Prico 531 .OO ($60.00) RSC Mombon J66.25 ROYAL SOCIETY OF CHEMISTRY Information Services (xiii)FA RA DA Y 1RA N SA CTlO N S AND SYMPOSIA From the Royal Society of Chemistry FARADAY TRANSACTIONS II Molecular and Chemical Physics SPECIAL ISSUE - AUGUST 1986 Professor Alan Carrlngton delbred the 1985 Faraday lecture at the Royal lnsmutlon on 10th December, 1985. As a compliment to Professor Carrington, a group of his colleagues and Mends submitted original papers on the general theme of Molecular Dynamics and Spectroscopy. These papers are collected in the present Issue.CONTENTs: The Faraday Lecture: Spectroscopy of Molecular Ions at thelr Dissociation Limits A. Carrington The Spectroscopy, Photophysics and Photochemistry of Clusters of Metrazlne D. H. Levy Spectroscopy of Transient Species produced by Photodissociation or Photoionizatlon in a Supersonlc Free-jet Expansion T. A. Mlller Molecukr-beam Infrared Spectroscopy of the Ar-N,O van der Waals Molecule J. Hodge, G. D. Hayman, T. R. Dykeand B. J. Howard The Estimation of Vlbrational Predissociation Ufetimes M. S. Chlld The Infrared Spectrum of H; and its Isotopomers. A Challenge to Theory and Experlment J.Tennyson and B. T. Sutcliffe The Augmented Secular Equation Method for calculating Spectra of van der Waals Complexes. Application to the Infrared Spechum of Ar-HCI J. M. Hutson Quantum-mechanical Wavepacket Dynamics of the CH Group in Symmetric- top X,CH Compounds using Effecttve Hamiltonians from Hlgh-resolution Spectroscopy R. Marguardt, M. Quack, J. Stohner and f. Sutcllffe Internal Dynamics of Subunits and Bondlng Force Constants In Weakly Bound Dlmers P. Cope, D. J. Mlllerand A. C. fegon Internal Dynamics and HF Bond Lengthenlng In the Hydrogen-bonded Heterodimer CH,CN . . . HF determined from Nuclear Hyper-fine Structure in its Rotational Spectrum P. Cope, D. J. Miller, L. C. Willoughbyand A. C. fegon Pumping and Rshing. Double-resonance Measurements on Molecular Jets U. Veeken, N. Damand J. Reuss nme-resow Fluorescence of Jet-cooled Carbazoles and thelr Weak Complexes A. R. Auty, A. C. Jones and D. Philllps Prediction of the Ct(*P, J/CI(P,J Branching Ratio in the Photodissociation of HCI S. C. GIvertzand 6. C. Ballnt-Kurt/ Hlgh-resolution Laser Photofragment Spectroscopy of CH' P. J. Sam, J. M. Walmsleyand C. J. Whitham Asymmetric Uneshapes associated with Predissociating levels M. N. R. Ashfold, R. N. Dixon, J. D. Prince, B. Tutcherand C. M. Westem A Threshold-photoelectron Ruorescence-Photon Coincidence Study of Radlatlonless TransMons in the B ,iI State of BCN+ €. Castellucci, G. Dulardin and S. leach Cornpetthe Channels in the Interaction of Xe('P,) with CI,, Br, and I,. Atom Transfer, Excitation Transfer, Energy Disposal and Product Alignment K. Johnson, R. Pease, J. P. Simons, P. A. Smith and A. Kvaran Mco Non-RSC Momkn P14.30 ($27.70) RSC Momkn M.00 Payment should accompany ordon for lhlr Ihm. RSC Members should send their orders to: Membershlp Manager, The Royal Society of Chemistry, 30 Russell Square, London WC1 B SDT. Non-RSC Members should send their orders to: The Royal Socleiy of Chemistry, Distribution Centre, Blackhorse Road. Letchwotth, Herts SG6 1 HN. Faraday Discussions No. 80 Physical Interactions and Energy Exchange af the Gas-Solid Interface [his publication discusses aspects of current research on the gas-solid Interface: elastic, inelastic and dlssipattve scattering of atoms and molecules from cfystal surfaces; the structure and dynamics of physisorbed species, including overlayers. Emphasis Is placed on the themes of physical interactions and energy exchange rather than on molecular beam technology or the phenomenology of phase tmnsmons in overlayen. The interplay between theory and experlment is stressed as they relate to the nature of atom and molecule-surface interaction potentials including many body effects. Faraday Discussions No. 80 (1986) Softcevor Prico 531 .OO ($60.00) RSC Mombon J66.25 ROYAL SOCIETY OF CHEMISTRY Information Services (xiii)

ISSN:0300-9599    

DOI:10.1039/F198682BP147

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1986,82, 3289-3292 Osmosis and Reverse Osmosis Part 1 .-The Frictional Coefficients in a General Transport Equation Gerhard Dickel Institute of Physical Chemistry, University of Munich, 8000 Miinchen 2, Sophienstr. 11, Federal Republic of Germany Whilst according to Nernst's theory the frictional forces between the dissolved particles and the solvent are taken into account, in thermodynamics of irreversible processes frequently the interactions between the different particles themselves are considered. Searching, however, for universal coefficients, which control the electric potential as well as the osmotic transport effects, one must use a simplified model. The theory of viscosity is helpful in elucidating this. Physical equations usually consist of functional relations involving one or more constants.Often, some of these constants rather than the functional connections are the decisive quantities in physics. An example is the ideal gas law taken as a limiting case. In order to describe a real gas we have to change the form of the law but not the constant R. Surely, we could have considered the ideal gas law as a generalized law by determining individual gas constants for every gas and every state. However, the physical way of thinking does not presume the general form of a law a priori. The investigations of membranes of Donnan,l Teorell,2 Meyer and Severs3 and Schmid4 have shown that the concentration of the fixed ion cF plays the role of such a constant. To obtain quantities controlling the osmotic transport effects it is convenient to take into account the frictional coefficients, because the membrane potential is given as a function of these together with the value of c ~ .~ * ~ Therefore the classical concept of the frictional coefficients should be discussed and compared with other concepts used in thermodynamics of irreversible processes. The Model of Viscosity According to the theory of viscosity used in the simplified kinetic theory of gases,5 the streaming medium is divided into thin strips sliding by one another with different velocities. Let us consider the strips A, and A, whose velocities in the direction of the z-coordinate are v, and v, + dv,. If a particle i moves from A, to A,, the excess impulse midv, is given off to the bulk of A,.In the opposite case the bulk must deliver this impulse to the particle i. Thus, the theory of viscosity is based on an (integral) impulse exchange between a single particle and the bulk. Therefore, the frictional coefficients fiL involve the impulse exchange between a particle and the solution, but not the solvent and so a frictional coefficient between the dissolved particles i and j has only an indirect meaning. To clarify this, we keep in mind that the frictional coefficient fiL depends on the composition of the solution. Having N dissolved particles we write N 3289 109-23290 Frictional Coeflcients in a General Transport Equation where ALo is the frictional coefficient if the solution contains only particles of the type i. All other termsAj of the right-hand summation giving rise to a variation of the zero term A L o involve summarily the influence of the other dissolved particles.Flux Equations with Determined Coefficients and the System of Reference The frictional coefficients in eqn (1) were used in previous paper^^-^ to obtain the representing an extremal which furnishes Onsager’s principle of least dissipation of energy. The index i refers to a dissolved particle i. For simplicity we have written& instead offi,. ci and cL are the concentrations of the particle i and the solvent L, respectively, and Pi is the electrochemical potential. Eqn (2) represents the extended version of the Nernst-Planck equation as it results from the boundary condition using Routh’s method.*. From this it follows that a, = 1 if the solvent is the system of reference.In this case eqn (2) stands for a Galilean transformation realized if a solution exhibiting a concentration gradient flows through a tube. In his investigations Meareslot l1 has found a, = 1 to be valid as far as the flux j , of the Donnan-ion is concerned. This means that the pore solution in the membrane represents the frame of reference of the Donnan-ions. Concerning the counter-ions, it is obvious to take the matrix of the membrane as the frame of reference. In this case the theory yields a, = 4. a, can be construed as a coupling of the ion i and the flux of the solvent. Concrete values of the drag coefficients were published by Meares.l09 l1 It is true that the mean values aNa = 0.65 and a,, = 1.35, as found in the investigations, are greater than those derived from the theory of fields of extremals; the proportion ac/aD = 0.48, however, is in good agreement with the theoretical value oft.The coefficient ac = implies a restriction of motion. To understand this, let us study the matrix of a membrane, relative to which there is a flux of the pore solvent j , = cLuL, maintained with the help of a pressure difference. This way, the co-ions carried along with the solvent have an excess impulse mDuL relative to the counter-ions attached to the matrix of the membrane. For the latter ions, only the ones which stay momentarily in the pore solution are provided with an excess impulse. Assuming an equilibrium exists between these free counter-ions and those counter-ions being attached to the fixed ions, one concludes that any exchange involves the loss of the excess impulse mCvL and so a reduction of their mobility takes place.The moving pore volume can be taken as a ‘nested frame of reference ’ where the counter-ions carried along undergo intrinsic interfacial kinetics with the ‘base frame’, represented by the matrix of the membrane. Flux Equations with Undetermined Coefficients According to the thermodynamics of irreversible processes, Vink12 has produced a set-up involving the undetermined coefficients Aj as well as f i 0 coordinated to the matrix component. By calculating the sum of all forces, he stated that all frictional coefficients cancel. This is in agreement with our conclusion concerning the sum of all forces in a solution, but not in a In order to apply his statement to a membrane, Vink introduced an arbitrary force co& ‘immobilizing the matrix component’.In this way he obtained the relation grad p = co&. (3)G. Dickel 3291 Though Vink has restricted his statement to non-electrolytic solutions, there is no reason to preclude the extension of eqn (3) to ion-exchange membranes. If the matrix component involves electric forces then these forces must be included in the immobilizing force cJo. This is in agreement with Schmid’s c~nception.~ Thus eqn (3) can be compared with the relation resulting from a mechanical equilibrium for the Donnan-ions. Such an equilibrium was first postulated by Prigogine.13 In this way the sum of the frictional as well as that of the chemical forces in a membrane disappear.The disappearance of discrete forces results from the compensation of internal forces and can be conceived as a consequence of the principle of least constraint. It is an outstanding advantage of the choice of the frictional coefficientsfi, that not only the relations between j , on the one hand and/or j , and j , on the other can be obtained immediately from the extended version of the Nernst-Planck equation, but also the membrane potential’ as already found by Teorel12 and Meyer and Seven3 Moreover in isotonic solutions eqn (2) yields Goldman’s equation :14 dp = - ~ ( c F - cD) Fd# (4) as adapted by Hodgkin and Katz15 in their investigations of nervous excitation. In isotonic solutions we must regard c 6 = c: = c,. Another equation dealing with undetermined coefficients is given by de Groot and Mazur.ls Instead of eqn (2) the arrangement n-1 was used.Lij represent undetermined Onsager coefficients. As the solvent is taken as the nth particle representing the frame of reference,j, is not included in the sum. If F grad # = -x ( t i / z j ) grad pi (7) i is the so-called Hittorf transference number of component j. Assuming that near equilibrium in a large field the linear relation (6) is valid, Delmotte and Cham1’ obtained after integration a relationship which is very different from eqn (5). According to Nernst’s theory, the diffusion potential is caused by the frictional forces between the dissolved particles and the solvent. The solvent, however, is not contained in eqn (6) and (7). Considering that the collisions taking place between two particles i and j can hardly be taken as the cause of the diffusion potential and, moreover, that no method exists to determine the coefficients hi or L,, we have taken the frictional coefficients according to eqn (1) as the general constants in the theory of osmotic transport phenomena as well as of diffusion potentials.Finally, we remark that in the range from 1 - n to 6 - n solutions eqn (5) is fulfilled in the isotonic system HCl/HCl+LiCl in membranes as well as in s01utions.l~ As far3292 Frictional Coeficients in a General Transport Equation as the values of the frictional coefficients in membranes are concerned a variation of ca. 20% was found in this range. References 1 F. G. Donnan, 2. Elektrochem., 191 1, 17, 572.2 T. Teorell, Proc. Exp. Bio. Med., 1935, 33, 282. 3 K. A. Meyer and J. F. Sievers, Helv. Chim. Acta. 1936,29, 649, 665. 4 G. Schmid, 2. Elektrochem., 1950,54,424; 1951,55,229; 295; 684; 1952,56,35; 181; Ber. Bunsenges. 5 J. 0. Hirschfelder, R. B. Bird and C. R. Curtiss, Molecular Theory of Gases and Liquids (John Wiley, 6 G. Dickel and G. Backhaus, J. Chem. SOC., Faraday Trans. 2, 1978,74, 1 15. 7 G. Dickel, in Topics in Bioelectrochemistry and Bioenergetics, ed. G. Milazzo (John Wiley, New York, 8 G. Dickel and B. Pitesa, J. Chem. SOC., Faraday Trans. 2, 1981,77,441. 9 G. Dickel, Faraday Discuss. Chem. SOC., 1984,77, 157. 10 J. S. Mackie and P. Meares, Proc. R. SOC. London, Ser. A, 1955, 232,498. 11 P. Meares, J. Membr. Sci., 1981, 8, 295. 12 H. Vink, J. Chem. Soc., Faraaizy Trans. 1, 1983,79, 2355. 13 I. Prigogine, Etude Thermodynamic des PhinomPnes Irriversibles (Dunod, Paris and Desoer, Likge, 14 G. Dickel and R. Kretner, 2. Phys. Chem., 1979,118, 161. 15 A. L. Hodgkin and B. Katz, J. Physiol., 1949, 108, 37. 16 S. R. De Groot and P. Mazur, Non-equilibrium Thermodynamics, (North-Holland, Amsterdam, 1962). 17 M. Delmotte and J. Chanu, in Topics in Bioelectrochemistry and Bioenergetics, ed. G. Milazzo (John Phys. Chem., 1967, 71, 778. New York, 1954). 1981), VO~. 4, pp. 271-340. 1947). Wiley, New York, 1980), vol. 3, pp. 307-359. Paper 5/1418; Received 12th August, 1985

ISSN:0300-9599    

DOI:10.1039/F19868203289

出版商:RSC    

年代:1986

数据来源: RSC

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J. Chem. Soc., Faraday Trans. I, 1986,82, 3293-3305 Osmosis and Reverse Osmosis Part 2.-The Separation Factor of Reverse Osmosis and its Connection with Isotonic Osmosis Gerhard Dickel” and Abdeslam Chabor Institute of Physical Chemistry, University of Munich, 8000 Miinchen 2, Sophienstr. 1 I , Federal Republic of Germany Two variational principles control isotonic osmosis and reverse osmosis : the principle of least dissipation of energy referring to a definite time integral and the principle of least constraint referring to the stationary (extremum) value of a volume integral. An extended form of the Nernst-Planck equation resulting from the time variation has been taken as the basis of our investigations. A theorem of Gyarmati dealing with the minimum conditions of local variation in the presence of constraints yields a lemma concerning the force equilibrium in reverse osmosis.According to Weierstrass’s excess function we have obtained linear relations between the potential gradients (forces). Whilst in isotonic osmosis there is an electro-osmotic equilibrium, an electrochemical equilib- rium takes place in reverse osmosis. The latter controls the separation effect. An inversion takes place if c,, = cF. Experiments have demonstrated that at this point the demineralization effect turns over into a concentration effect. The mathematical correlations between osmosis and reverse osmosis manifest that reverse osmosis represents the inverse of the transcendental function of osmosis. If one considers the flux of water connected with the flux of ions through a permeable membrane as osmosis then the reverse effect, the flux of the dissolved particles resulting from a flux of the solution, can be conceived as reverse osmosis.The advent of Onsager’s relations gave rise to the supposition that osmosis and reverse osmosis could be connected to each other by reciprocal relations. This conception coming on in the fifties, however, has fallen short of expectations. So, Sourirajan’ says on the first page of his monograph Reverse Osmosis: ‘It must be understood that the mechanism of both “ osmosis ” and “ reverse osmosis ” is still an open question, and the distinction between the two terms is entirely one of arbitrary convention and popular usage.’ The importance of reverse osmosis is based on the fact that it represents a thermo- dynamical separation effect.Therefore we have to consider the thermodynamic separa- tion methods rather than theories of the reciprocal effects. A general theory concerning such an operation (the thermal diffusion separation) as developed by Onsager’s school2 and later generalized to membrane separation effects by Cohen3 will be the basis of the following treatment. Onsager’s theory is remarkable in this context because it deals with an important and well clarified reciprocal effect : the diffusion thermoeffect, generally called the Dufour effect. This fact, however, was not taken into account in Onsager’s theory, as the Dufour effect neither exerts an influence on the separation effect, or is of any relevance in this context.Keeping in mind Sourirajan’s statement, even more attention must be paid to this fact as no reciprocal relations could be proved between osmosis and reverse osmosis. Over 32933294 The Separation Factor of Reverse Osmosis VL “t/‘, = source S,, 0 = sink St Fig. 1. Schematic representation of a separation device. and above that we have to deal with the admissibility of this principle. In this context we must take into account the following theorem of Gyarmati:4 ‘If homogeneous linear relationships exist between the fluxes as well as between the forces, Onsager’s reciprocal relations are not necessarily fulfilled ’. An example should explain this : Diffusion in the presence of a temperature gradient is controlled by two independent forces: the concentration gradient giving rise to the familiar diffusion and the temperature gradient giving rise to the thermal diffusion. Concerning the reciprocal effect, along with the familiar heat conduction an additional effect of heat conduction arises from the concentration gradient. In both cases the gradients of concentration and temperature are the common variables of the fluxes of diffusion and heat.In osmosis and reverse osmosis the corresponding forces are given by the chemical potentials of the ions and the solvent. According to the Gibbs-Duhem equation these forces are linearly dependent on each other, and Gyarmati’s theorem must be considered. In this case the electric potential offers itself as a second variable. However, since in osmosis and reverse osmosis the electric potential is a ~onstraint,~ but not an independent variable, such a procedure will not be correct.It was Gyarmati who showed that in this case the application of the extremum principles leads to the goal. Already de Groot and Mazur5 have demonstrated how to treat problems where diffusion potentials as well as outside electric potentials are applied to a system. Theories of the Separation Effects General Remarks Onsager’s as well as Cohen’s theories are based on the application of the condition of continuity to the flux equations. So the master-quantity of a separation theory is not the flux, but the transport z resulting therefrom. To understand this, let us examine a thermal diffusion tube. In the stationary state where the transport vanishes, the fluxes of diffusion and thermal diffusion continue.In this case the separation effect reaches a maximum value which decreases with increasing values of transport. So the dependence of the separation effect on the transport must be taken into account in order to obtain quantitative results. The outstanding result of Cohen’s theory was the finding of a ‘value function’ representing the value of energy expended in order to enrich a gas from any given concentration to a concentration under consideration. This is a potential function which controls all separation effects if an individual coefficient is taken into account. We have showns that Cohen’s value function is identical with Hamilton’s eiconal resulting fromG. Dickel and A. Chabor 3295 the principle of the variation of the endpoint.We note this because Hamilton's method will play a dominant role in the following treatment. Condition of Continuity d the Transport Equation Let us consider a separation device bordered by the reservoirs vb and V, at both ends (fig. 1). If a solution of a particle i of the concentration C&b) enters at the point zb with a velocity uL, in a stationary state the unchanged solution comes out at point zt if neither sources nor sinks of particles are present in the separation device. As shown in fig. 1, it is suitable to imagine a plane source sb instead of the reservoir vb, and a plane sink S, instead of V,. Both must be situated at the inside boundaries of the separation device at z = zb and z = z,. Thus, the separation device consists of the real separative element, e.g.the membrane, bounded by a source and a sink with surface divergence r&) and - r,(z,). According to the relations and 4 divji(zb) = q divji(z,) = -ri(zt) the divergence depends on the flux densitiesj,(zb) andj,(z,), where q is the cross-section of the separation element. According to the principle of continuity, the relation divj,(x,y, z) = 0, where zb < z < z,, (i = 1,2,. . ., N) (3) is valid at any point inside the separation device in the stationary state. As concerns the points z = zb and z = z,, however, eqn (1) and (2) are valid. By integrating eqn (3) over the total volume from zb to zt we get, restricting to the stationary state, for any component i: Transforming the volume integral with the help of Gauss's theorem into a surface integral, we obtain considering eqn (1) and (2): ~~~' divji dxdydz = j i ( x , y, 2,) dxdy - j i ( x , y, 2, ) dxdy + zi(z,) - &) = 0.( 5 ) It was taken into account that fluxes enter or leave the separation device only at z = zb and z = zt in the direction of the abscissa. After integration over the cross-section q we obtain, considering dxdy = dq: ss" 1s" qjkzt) - qjdzb ) = - 1. (6) In the absence of sources and sinks we havej,(z,) =ji(zb) as stated at the beginning. Because r, represents the number of moles i leaving or entering the reservoirs vb and vt in unit time, it is called the transport. In order to express rc(Zb) in terms of the fluxes, we integrate eqn (4) from z = zb to an arbitrary position z inside the separation device (zb < z < z,).Instead of eqn (6) we get (because the sink S, is excluded from the integration) : j,(z) represents the flux moving at any arbitrary position z under the influence of the separation effect through the membrane and ji(q,) the flux superimposed on it. Replacing (7) ) = qjdZ) - qjdZb 1. in eqn (6) by eqn (7) we obtain: Q(Zt 1 = qjdz) - qjdz, 1. (8)3296 The Separation Factor of Reverse Osmosis Concerning the boundary conditions, the flux j i is subjected to the ‘separation force’ at all points z > zb and z < z,, but not at the points zb and zt. At these points we have a break of the forces, but not of the fluxes. According to the condition of continuity we have where J?(z,) and J?(z,) represent the fluxes at the solution-membrane boundaries. Concerning the velocities of the particles entering or leaving the separation device we have stating that in a solution, in the absence of discrimination, solvent and dissolved particles have the same velocity.The fluxes necessary for the calculation will be discussed in the next section. J%) = J?(zn), (n = b, t) (9) v,(z) = vL(z) in (2, > z > 2,) (10) Flux Equations and the Canonical Representation of Reverse Osmosis The base of our investigations of osmosis7 is Onsager’s principle of least dissipation of energy represented by the variation of the double integral rAt rAz 6,6,E= StdZ J, J dLdt = 0. 0 dL is the Lagrangian in the volume element qdz given according to the model of viscosity by N ri, represents the number of moles of dissolved particles of type i passing the volume element qdz in unit time and iiL the corresponding numbers of moles of the solvent.N is the number of the different types of dissolved particles,f,, are the frictional coefficients as defined in the preceding paper, ci and cL the concentrations of the dissolved particles i and the solvent L, respectively, and q is the cross-sectional area. As the relations furnish the extremum value of the condition (1 1). In this case j , represent the observable fluxes, p is the chemical potential and 4 the membrane potental. F is the Faraday constant and z, the valence including the charge sign. Instead off,, we have writtenf,. Eqn (1 3) can be conceived as an extended form of the Nernst-Planck equation. Already in our first paper’ we found the drag coefficient a = 1 for Donnan-ions, and a = ?j for counter-ions.As discussed in the preceding paper, investigations of Mearesg, lo have confirmed this. In order to understand how a separation effect comes about, let us take generally a = 1. Thus eqn (13) entails a Galilean transformation of the Nernst-Planck equation as represented by the flux of a solution, exhibiting a concentration gradient, through a tube or the pores of a membrane. This transformation is realized only in the absence of constraints resulting from specific interactions between the walls of the pores and the penetrating solution. In this case the solution penetrates the membrane unchanged as postulated by a Galilean transformation. Conversely, these considerations demonstrate that specific interactions (constraints) are necessary in order to bring about a separation effect.Phenomenological theories can point out such effects. As shown by G~armati,~ the application of the variational principles to the thermodynamics of irreversible processes yields a method to treat effects resulting from constraints. Concerning variational principles, relation (1 1) represents the general form of Onsager’s principle of least dissipation of energy because it involves the time as well as the local variation. The time variation yields Prigogine’s principle of least production of entropy, whilst the local variation deals with the constraints.G. Dickel and A. Chabor 3297 The following theorem of Gyarmati4 will be helpful in solving the local problem under consideration : ‘ In any thermodynamic system in the case of given thermodynamical free forces and in the case of given local constraint conditions, the only irreversible processes which take place are such that the “constraint” C is minimum for them.’ Concerning the constraint controlling the fluxes of the cations and anions in reverse osmosis, we have to concede that the drag force of the flux of water must be taken as the driving force of the ions.Whilst in isotonic osmosis, where dp, = 0, the membrane potential is the driving force of the Donnan-ions,ll in reverse osmosis dp, represents a free force. Therefore, according to Gyarmati’s theorem, dp, furnishes the minimum constraint C = 0 if we postulate Whilst grad p, gives rise to an irreversible diffusion process, when the conditionj,.= j , is applied to eqn (1 3), the intrinsic membrane potential dpD+ZDFd(b = 0. (14) Fdd = - (CC ~ P C / ~ C -cD ~ P D / ~ D )/(CC/~C + CD/.D 1 follows. In order to evade the constraint resulting from the membrane potential, the Donnan-ions give rise to a concentration gradient compensating it. The same result can be obtained from Hamilton’s method. According to Hamilton, a potential representation can be obtained, if a transport process is controlled by an extremum principle. In the case of the permeation of a solution through a membrane it is natural to take the principle of least constraint as such a principle. In order to understand the influence of this constraint on the transport process we consider the stationary-state situation, where a pressure gradient is applied to the solution bordering a membrane.Having a fixed electrochemical potential jib = F,(z,) of the Donnan-ion at the solution-membrane boundary, the value P,(Z, + dz) = jib + dji, at the opposed membrane-solution boundary represents a free boundary condition. In this representation dji, is called the variation of the end-point. The idea of free (natural) boundary conditions is the basis of Hamilton’s method of the variation of the end-point. To understand this method, let us consider the electrochemical potential &.at the boundary point zo of the membrane and determine the change of the value of pD(z) in any volume element along the path z in order to furnish the principle of least constraint. The answer can be found easily: if pD evades the constraint along the path z, surely the principle of least constraint is fulfilled.This means the vanishing of the variation along the path z, which is given by 6BD = 0. (144 Indeed, this is in accordance with eqn (14), called the canonical representation of reverse osmosis. Concerning the Donnan-ion, from eqn (13) and (14a) eqn (16) follows immediately j~ = (CD/CL)~L (16) a relation demonstrating a Galilean transformation. The Separation Factor Substituting eqn (1 5) into the canonical representation (14), we obtain regarding dp, = (dpD/dc,)dc, and dc, = dc, the differential equation of the separation effect3298 The Separation Factor of Reverse Osmosis The slope dc,/dz can be interpreted as the simple process factor within the membrane element dz. Extending eqn (14) to an arbitrary number of ions we can obtain instead of eqn (1 7) a relation involving multicomponent systems.In the point cF = c,, dc,/dz vanishes and the effect changes from a demineralization effect to a concentrating effect. This is a consequence of the factor a, = 4 concerning the counter-ions. Arbitrarily setting a, = 1 in eqn (13) we obtain the extended version of the Nernst-Planck equation which was discussed by Schlogl12 in order to explain anomalous osmosis. In this case we get C, instead of 8 (c, - c,) in eqn (14) and (1 7) and therefore no inversion occurs. If dc, @ C, we can replace dc,/dz by the difference quotient AcD/Az. Taking into account that the difference Acs of the solutions adjoining the membrane is the unique measurable quantity, we replace C, by 8 with the help of the Donnan-equilibrium as follows.Considering p = RT In c and the relation of the Donnan concentration as well as its differential, we get the equation of the separation effect where Instead of j , we can represent the separation effect as a function of the pressure. This will become necessary in the following investigations. For this sake we start from the relation:" l3 N N Z (ci/cL X j L - X aihji = - CL grad (& + V L PI. (21) Relation (21) furnishes the extremum value of the condition (1 1) with respect to j,. Considering eqn (16) we obtain This equation is the reciprocal counterpart of the relation (23) resulting from a transposition of eqn (13). It must be emphasized that the summation in eqn (22) involves the counter-ion C only.By neglecting j i and setting p: = 0 in eqn (22), we conclude that the permeation is nearly inversely proportional to the frictional coefficientf, of the counter-ions. An influence of the matrix or the membrane is not included in this concept, explicitly. The latter, however, is contained in the frictional coefficients f, representing the only measurable quantities. Measurements never can discern between the frictional action of the fixed ions and their counter-ions. fa lit - S ( c i / c ~ ) j L 1 = - ci grad (pi + zi F4) Experimental The Compensating Method The separation factor given by eqn (19) is derived under the condition of a stationary state and the vanishing of the transport z. As the familiar osmotic cells are composed of two reservoirs separated by the membrane, the following procedure will be in accordance with these conditions.Having filled at the beginning of the operation the reservoir V, (see fig. 1) with the original solution, the reservoir V, was filled up with a solution exhibiting the presumed end-concentration. If this condition is fulfilled, theG. Dickel and A . Chabor I capillary 3299 t I I Fig. 2. Schematic representation of the osmotic cell. M = ion-exchange membrane, V, = reservoir of the initial solution, V, = reservoir of the separated solution. concentration in the reservoir remains unchanged in the course of the separation process and so the condition z = 0 is fulfilled. Otherwise an increase or decrease of the original solution in the reservoir takes place until the stationary state is reached.With the help of interpolation we can find out quickly the point of compensation where the concentration remains unchanged. This method avoids the concentration fluctuations occurring in the case of the outflow method, and so it can be applied successfully to the small effects in the neighbourhood of the point of inversion. Apparatus The osmotic cell used in our investigations is represented in fig. 2. The membrane M of type Nepton C 61 AZL 183 was a cation-exchange membrane of condensed phenolsulphonic acid reinforced with an inert support. In order to resist high pressure differences a perforated disc of Plexiglas was placed between the two cell halves as a mechanical support. The operating pressure was 6 bar. The original solution enters the reservoir Vb at the taps E and leaves simultaneously at tap 0 in order to avoid a decrease in the concentration due to diffusion through the membrane. The solution, having penetrated the membrane, passes along the capillary, and so the flux j, can be determined.On average the fluid in the capillary moves 10 cm h-l, corresponding to 0.8 cm3 per day. After a run of ca. 12 h, the solution in the reservoir V, was analysed and subsequently a solution, exhibiting the concentration found in the preceding run, was filled into V, using tap A. This operation was repeated until no change of the concentration could be found. Finally V, was filled with a solution of concentration exceeding that necessary for producing the separation effect in order to check whether equilibrium was really attained.A decrease of the concentration was found in this case. In the first phase of our investigations, relaxation effects resulting from a change of the concentration of the solutions bordering the membrane were found. So no point of inversion but a concentration interval, depending on the preliminary treatment of the membrane, could be determined. However, having applied the compensating method and approaching from both sides to the point z = 0, satisfactory results could be obtained.3300 The Separation Factor of Reverse Osmosis Table 1. General specifications of the membrane Az 5.00 x cm fU 27.50 x lo8 J s mol-1 [ref. (2)] fK 13.50 x lo8 J s mol-1 [ref. (2)] j,(Li) 0.28 x mol cm-8 s-l jL(K) 0.50 x mol cm-2 s-l cF(Li) 1.22 mol dm-3 [ref.(2)l Table 2. Values of the flux of solvent (in 108cm s-1) as a function of the normalized concentration of the solution 0.16 0.40 0.82 0.94 1.25 1.40 1.43 1.65 1.68 1.89 2.04 0.25 0.26 0.28 0.28 0.28 0.28 0.26 0.26 0.49 0.50 0.49 ReSults In table 1 the values necessary to evaluate eqn (19) are quoted. Whilst the value of j , in table 1 corresponds to the point of inversion of an LiCl solution, a number of values of j , concerning additional points and those of a KC1 solution are represented in table 2. The curve in fig. 3 represents the separation factor according to eqn (19) with cs/c, taken as the abscissa. Note that the values in table 1 yield fLi A.z/RTcL = 1.00 x log. Along with the theoretical curve we find in fig. 3 the measured values of LiCl marked by + and those of KCl marked by *.Each point represents a mean value of more than ten runs performed using the compensating method. Whilst in the point of inversion there is a good agreement between the values found experimentally and the theoretical ones, the other values deviate from the latter. This is not surprising, because on the one hand relaxation effects falsify the results and on the other hand our model is an idealized one and so neither inhomogeneities nor activity coefficients have been taken into account. Considering that the degree of accuracy of the measurements of the flux of the solution is much higher than that of the concentration, the fact thatj, exhibits a maximum value in the point of inversion (see table 2) can be taken as a consequence of the fact that no diffusion film bordering the membrane is present if the solution passes unchanged through the membrane.A diffusion film reduces the fluxes in all cases.G. Dickel and A . Chabor 3301 \ * * 2 . 0 \ Fig. 3. Dependence of the separation effect on the concentration of the solution. Graphical representation of the normalized separation effect A8/c, as a function of the normalized concentration 8 / c , of the solution in the reservoir V,. +, LEI; *, KC1. Frictional Coefficients According to the preceding paper our frictional model contains only the frictional coefficients between the particle i and the solution. Considering that according to Nernst only these coefficients give rise to the diffusion potential, it is possible to determine these with the help of electric measurements. A representative example is the determination of the frictional coefficientf,, in isotonic osmosis.14 Since the only driving force of j,, is the membrane potential, it is easy to determine fcl with the help of measurements of the flux j,, and the membrane potential.Concerning the cations, the influence of the chemical potential must additionally be taken into account. The values quoted in table 1 are determined in this way. The application of Nernst’s frictional coefficients assures a consistent theory. According to eqn (22), j , is inversely dependent on the frictional coefficients of the counter-ions if j , and can be neglected. Replacing Li* by K in the membrane and consideringf,:f, = 27.5: 13.5,14 the theoretical ratiojK:jLi = 2.04 should be obtained.However, we have found the value 1.80 in the point of inversion, being approximately in accordance with our frictional model. It is possible that this deviation results from the influence of the matrix. However, a proof will not be possible. We prefer to conceive the matrix of the membrane as the container of an electrolytic solution. As was demonstrated by measurements, the narrow interspace between the discrete sections of the matrix strongly reduces the mobility of the ions. Thus the frictional coefficient of the chloride ion increases from the value f3c1 = 1.22 x los (J s cm-2 mol-l) in a solution tofg = 16.0 x lo8 in a membrane.14 The ratio between the mobility of cations and anions, however, was found to be nearly equal in both phases.Concluding Remarks Constraints Let us compare our concept with the theory based on the application of the Onsager relations to a suitable flux scheme. This can be obtained by splitting off the flux of the solution into a flux of the solventj, and a flux of the dissolved particlesj, and choosing two suitable forces. The following dilemma results therefrom : if no constraint arises from the membrane, the solution permeates unchanged and a discrimination between j , andj, is irrelevant. As the fixed ratioj,/j, of the solution reduces both the equations to a single one, an Onsager relation is not realizable. If constraints resulting from the membrane are controlling the permeation through the membrane, these can give rise to3302 The Separation Factor of Reverse Osmosis a breakdown of the Onsager relations, as stated by G~armati.~ This statement calls for an experimental decision. The introduction of the reflection coefficient Q by Stavermanls controlling osmosis as well as reverse osmosis will be helpful.As shown by SchlOgl,l7 Q = 1 means a semipermeable membrane where the theoretical osmotic pressure occurs; concerning reverse osmosis, the solute is held back totally in this case. If Q = 0, the solution passes unchanged through the membrane and simultaneously the apparent osmotic pressure should vanish in osmosis. From an imaginary experiment we conclude that the general validity of the latter relation is realized only in a trivial case. Taking a paper membrane, in reverse osmosis the solution flows unchanged through the paper over the whole concentration range; simultaneously no osmotic pressure occurs if concentration differences are applied to this membrane.However, replacing the paper by an ion-exchange membrane, the solution passes unchanged through the membrane only if cD = cF. At this point, Q changes from a positive to a negative value. Concerning the osmotic pressure, however, at this point no inversion of the apparent osmotic pressure could be found in investigations dealing with univalent electrolytes.l*~ l9 This is a consequence of the influence of the constraints as stated in the dilemma. However, considering the electro-osmotic pressure in isotonic osmosis, ‘negative’ osmosis takes place, if cD > cF. Inverse Functions of Transcendentals In order to understand the connection between osmosis and reverse osmosis, let us consider the mathematical correlations between both effects.Concerning osmosis this phenomenon is defined by the boundary conditions of the adjacent solutions. This becomes clear by considering in a simple example that the free energy F is dependent on the concentrations c, and c, ~ ~ ( c o , ce ) = df[~(c)l. (24) co Turning to reverse osmosis and taking c, as the concentration of the original solution, the end concentration c, is an unknown variable in this case. Therefore we have to replace the limit of integration ce by a variable c. Solving eqn (24) for c we obtain c = Y(F) representing the inverse of the transcendental function (24). Men of mathematics succeeded in solving such problems in cases of transcendental functions.Excellent examples are the elliptic integrals and their inverse functions, the elliptic transcendentals. More than a hundred years were necessary to solve and understand this problem to its full extent. However, such general methods cannot be applied in physics. Variation of the End-point Fortunately a simplifed method appropriate for dealing with physical problems exists. Instead of solving the integral (24) for the integration variable c, Hamilton showed that the variation of the end-point leads to the goal if an extremum principle (in our case the principle of least constraint) controls the path through the membrane. Pressing a solution through a membrane and keeping in mind that the drag coefficient of the Donnan-ion is found to be Q = 1, no constraint (the total minimum) is acting on this i6n.Therefore the variation of the end-point represented by eqn (14a) vanishes along the path through the membrane. Concerning the counter-ions, the restricted dragging, resulting from a = &, gives rise to an increased electric field [see eqn (1 5)] in order to fulfilG, Dickel and A . Chabor 3303 the condition j , = j D . With increasing concentration of the Donnan-ion an increasingly concentrated solution passes the membrane and finally the desalination turns over into a concentration. We note that Hamilton’s method plays a dominant role in any separation theory, especially in the multistage separation theory, because the concentration is the unknown variable in any separation device.The minimum value of the energy consumption of a separation cascade follows from Hamilton’s eiconal. This yields Cohen’s value function3, V = Y [sin(F), cos (F), Ac] representing a rational function of the transcendentals sin(F) and cos(F). Theory of Fields of Extremals The difficulties arising from the restrictions of the application of the Onsager relation to osmosis and reverse osmosis and the unconvincing experimental results concerning the osmotic phenomena have suggested a complete reversal by taking Hamilton’s theory in the modern form of the theory of the fields of extremals as basis of our investigations. As shown in a preceding paper,* this way we went over to a potential representation. According to Weierstrass all terms of higher order of a Taylor series vanish and linear sets of forces satisfying the relation F(7tl, x,,.. . , 7tL) = 0 (26) can be obtained. In eqn (26) nB denote potential gradient^.^ An example is the Gibbs-Duhem relation. It must be emphasized that such relations exist only if extremals are controlling the process. This follows from Hamilton’s theory as well as from Hilbert’s independence theorem. Only in such cases Onsager’s principle of least dissipation of energy is applicable. The investigations concerning this concept were the object of our first publications in the field of membrane transport. Because the strong coupling of the solvent and the dissolved particles gave rise to difficulties, we have taken 7tL = 0 in eqn (26) by restricting to isotonic states. The results of our first paper20 can be summarized as follows: (a) the flux of water is nearly linear dependent on the pressure; (b) in the range of low concentrations of the Donnan-ions cD, the electro-osmotic pressure depends on the concentration of the fixed ions according to 4 c,; (c) because the electro-osmotic pressure decreases with increasing cD, the Donnan-ion must be conceived as a parameter of the electro-osmotic pressure. In order to cover the full concentration range, the isotonic system HCl/(HCl-LiCl) was used.The result is represented in fig. 4.,l In a further paper7 we showed that the inversion results from the application of an electromechanical equilibrium to eqn (13). In this way we could demonstrate that linear relations between potential forces exist in isotonic osmosis.22 Eqn (14) is a further example.This, however, cannot be postulated in non-isotonic osmosis. To understand this, let us consider fig. 4. Starting from point PI on the left-hand side of an ion-exchange membrane, where a 1.5 mol dm-3 solution of HCl adjoins the membrane, the path Pl-Pi leads to an isotonic LiCl-HCl mixture of mole fraction y = 0.8 on the other boundary. Because the path P1-P; is taken along an extremal of the variational problem (1 l), the principle of least dissipation is fulfilled. Going over to non-isotonic conditions and regarding instead of Pi the point P,, where a,, > a,, the point P, is inaccessible along an extremal and so the principle of least dissipation of energy is not fulfilled along the path PI-P,. Moreover, in the neighbourhood of any extremal there is an arbitrary manifold of points being inaccessible from any point along an extremal. Nevertheless, any arbitrary point is attainable by using Weierstrass’s excess function representing the remainder of a Taylor series if we accept an increased dissipation of3304 The Separation Factor of Reverse Osmosis t 1 .o -41 -+\ Fig.4. System of fluxes of water in the isotonic system HCl/(HCl-LiC1). Concentration of the HCl solution and/or the activity of water of the adjoining HCl and HCl-LiCl solutions us. ratio of LiC1:HCl of the solutions adjoining the membrane. Isotones would be presented by lines parallel to the ordinate. energy. An example of this important theorem of the theory of fields of extremals should demonstrate this.The orbit of a space shuttle represents an extremal, because no dissipation of energy takes place along this path. Any other point in the neighbourhood of this orbit, however, is inaccessible along any extremal. So the return path to the earth leads to the total dissipation of the potential energy. No extremal exists in this case. This, however, does not mean that a calculation of a path involving essential dissipation effects cannot be performed, rather it means that in such cases linear relations between potential forces do not exist. Nevertheless, we could calculate the flux ratio jL/j6 = Add) in non-isotonic osmosis from the mechanical equilibri~m~~ represented by a relation between a potential force and a frictional force. Only forces resulting from extremals according to Hamilton’s theory are potential forces. It was not disappointing that no extremal involving non-isotonic osmosis could be found.There is no extremal connecting the different orbits of an electron in an atom. Any change of an electron to a deeper orbit is connected with a total dissipation (radiation) of energy. Concerning a permeable ion-exchange membrane, ca. 95-97 % of the osmotic energyl8, lB will be dissipated in non-isotonic cases. Reciprocal Relations Whilst no comparison between isotonic and non-isotonic osmosis is possible, a comparison between isotonic osmosis and the electrokinetic effects is. The latter point out how to get the electro-osmotic pressure dP/d& and its reciprocal effect d#/dP, the streaming potential, from a linear set.Taking into account that in isotonic osmosis the electrochemical potential brings about the electro-osmotic pressure, we have to regard dP/dji instead of dP/d&; analogously, in reverse osmosis, the pressure brings about the ‘electrochemical’ effect dji/dP. Keeping in mind that ji is a transcendental function, noG. Dickel and A . Chabor 3305 linear correlation must exist between osmosis and reverse osmosis. From this we conclude : reverse osmosis represents the transcendental inverse function of osmosis. The intensive investigations of mathematicians lead us to assume that in the case of transcendental functions reciprocal relations can be found in another way. To find such relations let us consider eqn (13), from which it follows immediately that in reverse osmosis the action of the flux of solvent on the counter-ions equals half the action on the co-ions.Regarding the relation cF + cD = cc, the equation of electro-osmotic pressure’ can be written It follows that in osmosis the action of the counter-ions on the electro-osmotic pressure equals half the action of the co-ions. dp = - (+ CC - c,) Fd4. (27) The experimental investigations were performed in the years 1977-79, financially supported by the Deutschen Forschungsgemeinschaft. The inversion of reverse osmosis was found in the first months, but an explanation of this effect could not be given before Professor Meares9,10 had given a proof of the ‘anomalous’ behaviour of the drag coefficient of the counter-ions. We should like to express our thanks. References 1 S. Sourirajan, Reverse Osmosis (Logos, London, 1970). 2 W. H. Furry, R. C. Jones and L. Onsager, Phys. Rev., 1939,55, 1003. 3 K. Cohen, The Theory of Isotope Separation (McGraw-Hill, New York, 1951). 4 I. Gyarmati, Non-equilibrium Thermodynamics (Springer-Verlag, Berlin, 1970). 5 S. R. De Groot and P. Mazur, Non-equilibrium Thermodynamics (North-Holland, Amsterdam, 1962). 6 G. Dickel and E. Triitsch, Isotopenpraxis, 1966,2,429. 7 G. Dickel and G. Backhaus, J. Chem. Soc., Faraday Trans. 2, 1978,74, 115. 8 G. Dickel, 2. Phys. Chem. (Munich), 1985,144, 33. 9 P. Meares, J. Membrane Sci., 1981,8, 295. 10 P. Meares, Faraday Discuss. Chem. SOC., 1984,77, 217. 11 R. Kretner and G. Dickel, 2. Phys. Chem. (Frankfurt am Main), 1977,105, 221. 12 R. Schliigl, Farahy Disms. Chem. SOC., 1956, 21, 46. 13 G. Dickel, in Topics in Bioelectrochemistry and Bioenergetics, ed. G. Milazzo (John Wiley, New York, 14 G. Dickel and R. Kretner, 2. Phys. Chem., 1979,118, 161. 15 G. Dickel and R. Kretner, J. Chem. SOC., Farahy Trans. 2, 1978,74, 2225, 16 A. I. Staverman, Red. Trav. Chim. Pays-Bas, 1951,70, 344; 1952,71,623. 17 R. Schlogl, Stoftransport durch Membranen (Steinkopf-Verlag, Darmstadt, 1964). 18 H. Kramer, Dipl. Arbeit (University of Giittingen, 1963). 19 U. Balz, Dissertation (University of Munich, 1972). 20 G. Dickel and W. Franke, 2. Phys. Chem. (Frankfurt am Main), 1972,80, 190. 21 H. Honig, Z . Phys. Chem. (Frankfurt am Main), 1973, 87, 278; Dissertation (University of Munich, 22 R. Kretner, H. Honig and G. Dickel, 2. Phys. Chem. (Frankfurt am Main), 1977, 106, 330. 23 G. Dickel, U. Balz and B. Pitesa, J. Chem. Soc., Faraday Trans. 2, 1981, 77, 451. 1981), V O ~ . 4, pp. 271-340. 1973). Paper 61696; Received 9th April, 1986

ISSN:0300-9599    

DOI:10.1039/F19868203293

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1986,82, 3307-3314 Viscosity of Na,SO, and MgSO, Solutions in Ethanol-Water Mixtures at 15, 25 and 35 "C Concepci6n Quintana, M. L. Llorente, Manuela Sinchez and And& Vivo* Department of Physical Chemistry, University of La Laguna, Canary Islands, Spain The viscosities of the associated electrolytes Na,SO, and MgSO, have been measured in the following water-rich mixtures of ethanol and water: 0, 5, 10, 15,20,25 and 30 wt % ethanol at 15,25 and 35 "C, and the Jones-Dole equation has been found to be in good agreement with experiments in the concentration range studied: < c/mol dm-3 < 5 x loe2. From conduc- tance measurements the association constants in these systems at 25 "C were calculated, and the degrees of association and the Bion and coefficients were obtained.The viscosity decreases through ion-pair forma- tion in the Na,SO, solutions and it is a constant factor in the MgSO, solutions. The ion-solvent interaction increases in the MgSO, and decreases in Na,SO, as the permittivity of the medium decreases. The BMrlg3+ coefficients suggest that these ions are controlling the viscosity of the solutions to a greater degree than was expected. Previous papers1 concerning 1:l electrolytes that do not show ionic association in ethanol-water mixed solvents have pointed out the applicability of the Jones-Dole equation as a quantitative formulation of the ion-ion and ion-solvent interactions. In order to obtain more information on alcoholic media as solvents for a wide range of electrolytes, we undertook a study of the relative viscosities of sodium and magnesium sulphate solutions in ethanol-water mixtures.Ionic association is appreciable in MgSO, solutions,2 although it is weaker in Na,SO, solutions. We can restate the Jones-Dole equation, introducing the degree of association, B, Bion.pair coefficients for the ion pair and Bion coefficients for the dissociated fraction :3 where A is the Falkenhagen coefficient, which can be theoretically calculated, and the other two terms are a manifestation of solute-solvent interactions. Experiment a1 The viscometric techniques and apparatus have been described previously.1 Relative viscosities of all solutions were reproducible within f 0.003 % . Densities of the mixed solvents, or pure water, and of the solutions were determined using an A.Paar model DMA-60 densimeter. The DMA-602 cell was calibrated periodically with dry air and conductivity water. The accuracy of the data was & 5 x g J ~ m - ~ . All the density and viscosity measurements were carried out at 15, 25 and 35f0.005 "C in water ultrathermostats. Merck Suprapur Na,SO, was recrystallized in conductivity water and dried at 150 "C under vacuum for two days. Merck MgS0,.7H20 of analytical reagent grade was melted at 700°C and then dried for several days at 200°C. Merck (p.a. quality) absolute ethanol was analysed for its water content, the necessary corrections to the solvent composition of the mixtures being carried out. The weighings were accurate up to f 5 x g (salts) and kO.01 g (solvents) and were corrected to vacuum conditions.The conductivity water used was of Milli-Q4 quality and had an average 33073308 Table 1. Density p( & 5 x Viscosities of Na,SO, and MgSO, in Aqueous Ethanol for Na,SO, at c( f 5 x lo-' mol dm-3) in ethanol-water mixtures (% EtOH) g ~ m - ~ ) and relative viscosity q,( f 3 x low5) at temperature T("C) 15 "C 25 "C 35 "C 103c P 11, 103c P qr 103c P G'r 0 1.168 0 5.383 9 10.468 19.956 49.774 0 1.474 6 4.904 9 9.811 3 19.728 0.999 101 1 0.999 259 1.000 94 0.999 818 1.003 00 1.000 489 1.005 29 1.001 733 1.009 29 1.005 606 1.021 27 0.983 044 1 0.983 250 1.001 06 0.983 707 1.002 64 0.984 350 1.004 72 0.985 646 1.008 61 0% 0 0.997 047 0.996 40 0.997 178 4.978 4 0.997 693 9.959 7 0.998 339 19.933 9 0.999 621 49.758 1.003 414 0 0.980 4251 1.446 4 0.980 619 4.895 6 0.981 065 10.025 0.981 722 19.574 0.982 945 10% 1 1.000 85 1.002 97 1.005 33 1.009 79 1.022 43 1 1.001 11 1.002 84 1.005 17 1.009 26 0 1.214 5 4.068 1 7.754 4 12.689 53.229 0 1.271 4 3.151 1 6.344 3 10.596 0.994035 1 0.994 202 1.001 02 0.994 587 1.002 63 0.995 071 1.004 50 0.995 692 1.006 87 1 .OOO 795 ' 1.025 00 0.977 113 1 0.977 126 1.001 04 0.977 342 1.002 07 0.977 765 1.003 61 0.978 300 1.005 66 49.256 0.989 439 1.019 63 49.125 0.986 695 1.021 30 44.767 0.982 579 0 0.970674 1 0 0.966385 1 0 0.961 414 1.143 7 0.970 854 1.000 85 1.447 6 0.966 582 1.001 08 4.333 4 0.961 992 4.849 0 0.971 333 1.002 47 5.294 4 0.967 066 1.003 04 7.992 7 0.962 419 9.653 2 0.971 970 1.004 18 11.566 0.967 843 1.005 65 1 1.033 0.962 803 19.392 0.973 171 1.007 66 19.432 0.968 832 1.008 45 23.970 0.964 386 48.499 0.976 798 1.017 03 48.116 0.972 381 1.019 85 46.676 0.967 165 20% 25 'X 0 1.443 0 4.831 2 9.525 6 19.436 48.265 0 1.176 3 4.780 0 10.846 18.980 47.859 0.964240 1 0.964 461 1.000 94 0.964 888 1.002 28 0.965 461 1.003 88 0.966 683 1.007 06 0.970 233 1.015 59 0.956854 1 0.957 026 1 .OOO 7 1 0.957 470 1.002 10 0.958 168 1.003 86 0.959 174 1.006 23 0.962 558 1,013 81 0 1.148 9 4.778 8 1 1.459 19.134 47.801 0 1.213 4 4.962 3 11.685 18.961 47.537 .020 94 .002 69 .004 47 .005 92 .011 73 .021 58 0.958558 1 0.959 099 1.000 90 0.959 560 1.002 59 0.960 384 1.005 35 0.961 335 1.008 34 0.964 802 1.018 95 0.950645 1 0.950 831 1 .OOO 90 0.951 277 1.002 61 0.952 087 1.005 30 0.952 950 1.008 03 0.956 327 1.018 16 30% 0 0.953 382 1 1.5144 0.953 548 1.001 18 2.905 6 0.953 702 1.001 92 7.462 3 0.954 295 1.004 16 9.499 0 0.954 538 1.005 03 48.835 0.959 348 1.022 04 0 0.944456 1 2.788 7 0.944 591 1.001 78 6.522 9 0.945 042 1.003 57 10.200 0.945 541 1.005 24 21.228 0.946 807 1.010 01 48.402 0.950 001 1.021 22 specific conductance of ca.5 x lo-' S cm-l. Five different concentrations of each salt were used, for each solvent and temperature, within the range 0.001-0.05 mol dm-3. Results and Discussion Na,SO, Table 1 contains the densities and relative viscosities at three temperatures together with the systematic errors involved. Plots of (qr- 1)/& vs. ci are linear; this type of plot is clearly not sensitive enough to reveal the presence of ion association, especially if B does not differ too greatly from zero and Bion NN Bion-pair. Table 2 presents these A and BC.Quintana, M. L. Llorente, M. Shnchez and A . Vivo 3309 Table 2. Values of A and B coefficients for Na,SO, and MgSO, solutions in ethanol-water mixtures at 15, 25 and 35 "C, considering no association Na,S04 MgSO4 A f 0.001 B f 0.004 A fO.OO1 B f 0.004 T "C /(dm3 mol-l)$ 102AA /dm3 mol-l /(dm3 mol-1)i 102AA /dm3 mo1-1 15 25 35 15 25 35 15 25 25 15 25 35 15 25 35 15 25 35 15 25 35 - 0.02 - - - - 0.04 - - - - 0.07 - 0.02 0.05 0% EtOH 0.400 5% EtOH - - - 10% EtOH 0.338 { 0.365 0.401 15% EtOH - - - 20% EtOH 25% EtOH 0.255 30% EtOH 0.221 0.022, 0.023, 0.023, 1 1 1 1 1 0.022, 0.023, 0.023, 0.02 1, 0.023, 0.023, 0.022, 0.023, 0.023, 0.022, 0.023, 0.023, 0.022, 0.023, 0.023, 0.022, 0.022, 0.023, 0.600 0.02 [ 0.593 0.588 0.601 0.01 { 0.606 0.600 - 0.02 0.602 0.603 0.02 { 0.607 0.602 -0.01 0.603 0.616 0.01 { 0.600 0.606 0.604 0.01 { 0.608 0.605 coefficients obtained graphically.It is significant that there are small differences, AA, between the theoretical values and the graphical ones for the A coefficients. Let us now consider the effects of association. This ternary electrolyte dissociates in two stages: Na,SO, = Na+ + NaSO, NaSO; s Na+ + SO:- where the association constant is The degree of association, 8, can be determined by successive approximations once the association constant is established; in the present case this can be obtained at 25 "C only from conductance measurements. The mixture rule4 is applied to the equivalent conductance of a solution made up of two salts : (Na+ + NaSO;) and (2Na+ + SO:-) A = -$PAl+(l -P)A2 (1)33 10 Viscosities of Na,SO, and MgSO, in Aqueous Ethanol in conjunction with the conductance equation of Davies et al. :5 i = 1 for the uni-univalent salt (Na+, NaSO,) and A: = A",++0.6Ag0,2-, considering that AgaSOa x 0.6Ag0,2-; i = 2 for the unsymmetrical ion pair (2Na+, SO:-), with A; = A&,+ + Ago;-, the ionic strength being Z = c(3 - 2m.Since d values (or the association distance required to obtain the best set of conductance parameters) frequently refer to b or Bjerrum's critical distance a result also in accord with observations of Justice,s we have used b instead of d to calculate the activity coefficients using the Debye-Huckel approximation. The use of d values smaller than Bjerrum's b values would be also in poor agreement with approxi- mations made in deriving the activity coefficient expressions : The values of A&,+ and Ago;- and data for c and A in ethanol-water mixtures at 25 "C are from a previous paper.' Table 3 shows the association constants calculated by eqn (11), and the B, (BNa++BNaSOT) and B, (2BN,++Bs0;-) coefficients obtained from plots of Y vs.x, where q,-l-A[(l-j?)~]b Y = B,j?+B,(l -p) = C x=p. These plots gave good straight lines with slopes (B,-B,) and an intercept at p = 0 of B,, while at j? = 1 the intercept is B,. The deviations are those obtained as an average of the two limiting straight lines drawn considering the greatest errors in the points Y and 8. The A-coefficients used are taken from table 2, since the adequacy of the term A[(1 to represent ion-ion interactions may be doubtful at these concentrations (a problem considered by Davies and Malpass3); if we use the theoretical A-coefficients from Falkenhagen, or those calculated by the mixture rule of Onsager and Fuoss in their treatment of the viscosity of mixed electrolytes,* then these graphical A-coefficients are almost identical to the theoretical ones.In this kind of electrolyte, which is almost completely dissociated, the effect of ion-pairing on the viscosity is small, but it clearly causes a reduction in viscosity. The B, and B2 values in each mixture are very similar, and use of the Jones-Dole plots without considering ion-pairing does not introduce any serious error. At 25 "C both B, and B, decrease as the concentration of ethanol is increased.The values of dB/dT (table 2) are crediblyg positive and increase with increasing concentration of ethanol, but they must be interpreted with some caution as they are based on mean B values; however, the effects are large. MgS0* The plots of (q,- I)/& vs. ci are also linear in these solutions, and the fact that this salt is an associated electrolyte in ionic pairs seems to indicate also that Bion = Bion.pair. Table 4 contains densities and relative viscosities of this salt in the ethanol-waterC. Quintana, M. L. Llorente, M. Sanchez and A . Vivo 331 1 Table 3. Association constants and B coefficients of the Na,SO, and MgSO, solutions in ethanol-water mixtures at 25 "C Na,S04 0 10 20 25 30 12.1 k0.9 0.404 f 0.028 0.392 f 0.0 10 13.0f2 0.385 f0.017 0.375 2 0.01 1 14.5f 1 .1 0.370 f 0.018 0.357 f 0.006 19.2 f 0.7 0.352 f 0.021 0.341 f0.011 25.6 f 1 .O 0.339 f0.016 0.325 2 0.010 0 5 10 15 20 25 30 210f6 0.659 f 0.016 0.610 k 0.01 5 268 k 7 0.668+0.017 0.61 8 f 0.01 3 356f3 0.686 f 0.019 0.620 f 0.012 476 f 9 0.708 f 0.01 5 0.618f0.009 624 f 7 0.754 f 0.0 19 0.616f0.009 908 f 13 0.798 f 0.020 0.615 k 0.008 1310 f 21 0.835 k 0.018 0.612 f 0.008 mixtures. The errors are considered as previously. Table 2 shows these A and B coefficients graphically calculated at the three temperatures. Let us now consider the ion-pairing Mg2+ + SO:- + [MgSO,]O Conductivity results are again available to calculate Ka. We can choose among various conductance equations in order to calculate the association constant, since MgSO, is a symmetrical salt.As before, we must also use an equation which is consistent with the H values used in obtaining the activity coefficients. The value of Ka at 25 "C calculated previously2 from eqn (11) are suitable. (table 3). With Ka and H values from the Fuoss conductance equation,1° d being the closest distance of approach of ions in solution, we reached the same results, which confirms that it is necessary to specify also the H or b parameters together with the association constants or these would be meaningless.ll The partition of the B-coefficients into the corresponding ionic components can be carried out using the extra-experimental criterion given by Gurney12 (Bcl- = BK+ = iBKcl), and developed by Kaminskyg at several temperatures in aqueous solution.In the EtOH mixtures this splitting method is likely to be particularly reliable, since the limiting equivalent conductances of the K+ and C1- ions are equal in the vicinity of the 8 wt% EtOH mixture at 25 OC.13 Other criteria for separating B-coefficients in aqueous solutions of water and protic organic solvents have been published,14 reaching essentially the same results as the Gurney method. We must use the Bion(BMG2++BSO;-) values instead of B, although with these last values we obtained the ionic B coefficients closer to the values given in the literature in aqueous solutions (table 5). Using the B, (2BNa+ + Bso;-), Bion(BMg2+ + Bso;-) and B(Na+) coefficients, the new Bso;- and BMg2+ coefficients were calculated (table 6). These new values increase rapidly with the EtOH content in the medium.In aqueous solution The plots of Y us. X gave satisfactory straight lines with intercepts Bion and3312 Table 4. Density p( f 5 x lob8 g Viscosities of Na,SO, and MgSO, in Aqueous Ethanol for MgSO, at c( f 5 x lo-' mol dm-3) in ethanol-water mixtures (% EtOH) and relative viscosity q,( f 3 x at temperature T("C) 103c P Vr 103~ P r r 103c P tlr 0% 0 0.999 101 1 0 0.997047 1 0 0.994035 1 1.399 5 0.999 278 1.001 68 1.438 8 0.997 228 1.001 70 0.992 0 0.994 159 1.001 31 4.974 4 0.999 732 1.004 60 4.945 3 0.997 667 1.004 57 2.962 5 0.994 405 1.003 01 9.956 8 1.000 355 1.008 23 9.925 0 0.998 284 1.008 20 6.926 0 0.994 895 1.006 02 19.784 1.001 580 1.015 05 19.748 0.999 502 1.014 97 9.891 6 0.995 257 1.008 17 49.612 1.005 270 1.034 86 49.150 1.003 071 1.034 30 49.300 1.000 059 1.034 38 5% 0 0.990 309 1 0 0.988 146 1 0 0.985019 1 1.030 7 0.990 449 1.001 26 1.211 0 0.988 311 1.001 52 0.979 3 0.985 122 1.001 32 4.887 7 0.990 941 1.004 51 4.901 2 0.988 769 1.004 53 4.890 7 0.985 617 1.004 53 10.238 0.991 607 1.008 37 9.801 0 0.989 373 1.008 12 13.976 0.986 738 1.011 09 19.701 0.992 782 1.014 55 19.611 0.990 582 1.014 93 19.622 0.987 416 1.014 97 49.122 0.996 405 1.034 72 48.958 0.994 146 1.034 36 48.330 0.990 922 1.034 16 10 % 0 0.983052 1 0 0.980421 1 0 0.976856 1 1.289 6 0.983 218 1.001 56 1.148 5 0.980 585 1.001 47 0.973 5 0.977 002 1.001 31 4.800 0 0.983 665 1.004 45 4.887 0 0.981 036 1.004 53 4.850 6 0.977 485 1.004 51 9.730 1 0.984 278 1.008 08 9.736 8 0.981 639 1.008 09 9.763 5 0.978 088 1.008 13 19.532 0.985 495 1.014 93 19.489 0.982 837 1.014 88 19.398 0.979 243 1.014 82 48.763 0.989 080 1.034 43 48.455 0.986 356 1.034 14 48.491 0.982 761 1.034 19 15% 0 0.976723 1 0 0.973 350 1 0 0.969 139 1 1.291 8 0.976 916 1.001 59 1.269 0 0.973 523 1.001 57 0.969 2 0.969 252 1.001 31 4.891 9 0.977 374 1.004 46 4.791 0 0.973 961 1.004 46 4.820 0 0.969 733 1.004 51 9.545 8 0.977 924 1.007 94 9.574 0 0.974 539 1.007 99 9.652 1 0.970 335 1.008 10 22.354 0.979 498 1.016 93 19.426 0.975 735 1.014 86 19.303 0.971 482 1.014 86 48.646 0.982 713 1,034 27 48.595 0.979 224 1.034 21 48.217 0.974 975 1.034 19 20% 0 0.970697 1 0 0.966383 1 0 0.961 322 1 1.345 5 0.970 892 1.001 66 1.358 7 0.966 577 1.001 68 1.246 2 0.961 533 1.001 58 4.784 3 0.971 319 1.004 48 4.808 3 0.967 006 1.004 51 5.072 9 0.961 968 1.004 73 9.612 8 0.971.897 1.008 07 10.523 0.967 685 1.008 75 9.569 1 0.962 514 1.008 07 20.258 0.973 202 1.015 58 21.498 0.969 003 1.016 38 19.052 0.963 664 1.014 76 48.219 0.976 575 1.035 96 48.016 0.972 148 1.034 09 48.381 0.967 146 1.034 43 25 % 0.964 256 1 0 0.958 931 1 0 0.953032 1 0 1.129 6 0.964 417 1.001 42 1.101 5 0.959 115 1.001 43 1.422 7 0.953 223 1.001 75 4.656 0 0.964 837 1.004 34 4.722 3 0.959 562 1.004 45 4.726 4 0.953 635 1.004 51 9.488 6 0.965 426 1.007 92 9.563 0 0.960 101 1.008 06 9.486 6 0.954 204 1.008 08 19.202 0.966 579 1.014 71 20.459 0,961 381 1.015 67 18.893 0.955 339 1.014 73 48.044 0.969 983 1.034 00 47.534 0.964 565 1.033 75 47.339 0.958 642 1.033 97 30 % 0 0.956889 1 0 0.950671 1 0 0.943990 1 1.086 4 0.957 022 1.001 39 1.260 5 0.950 823 1.001 55 1.259 8 0.944 220 1.001 61 4.649 8 0.957 454 1.004 36 4.736 9 0.951 233 1.004 40 4.610 9 0.944 634 1.004 20 9.483 2 0.957 989 1.007 96 9.588 3 0.951 811 1.007 98 9.339 6 0.945 166 1.007 95 21.687 0.959 402 1.016 50 18.970 0.952 894 1.014 51 18.786 0.946 229 1.014 61 47.174 0.962 335 1.033 55 46.946 0.956 080 1.033 14 47.015 0.949 659 1.035 50C.Quintana, M. L. Llorente, M. Sanchez and A . Vivo 3313 Table 5. Bion values for Na+, SO:- (BNa2S04-2BNa+) and Mg2+ (B,,,,; B,,q-) ions in ethanol- water mixtures at 15, 25 and 35 "C EtOH (% 1 T/"C B(Na+)l f 0.006 B(SOi-) f 0.016 B(Mg2+) f 0.020 0 0 0 10 10 10 20 20 20 25 25 25 30 30 30 15 25 35 15 25 35 15 25 35 15 25 35 15 25 35 0.086 0.088 0.088 0.069 0.08 1 0.089 0.055 0.077 0.088 0.047 0.080 0.085 0.046 0.08 1 0.082 0.189 0.205 0.23 1 0.191 0.204 0.222 0.173 0.189 0.2 17 0.161 0.168 0.213 0.126 0.151 0.21 1 0.408 0.388 0.360 0.414 0.394 0.377 0.43 1 0.41 1 0.386 0.443 0.433 0.392 0.479 0.449 0.395 Table 6.B,,, values for SO:- and Mg2+ ions, considering the ion pair [MgSO,]" in ethanol-water mixtures at 25 "C 0 0.216 f 0.022 0.443 & 0.038 10 0.2 13 f 0.023 0.473 f 0.042 20 0.203 ItO.018 0.551 & 0.037 25 0.18 1 f 0.023 0.617 & 0.043 30 0.163 f 0.022 0.672 & 0.040 and in the first percentages of EtOH: B(Mg2+) E BMg2+, and B(SOi-) = Bso;- within experimental error, but the BMgz+ coefficients increase rather more rapidly with increasing EtOH concentration than the uncorrected B(Mg2+) values. This is also true for the corrected Bion values (BMgz+ + Bso;-) compared with the uncorrected B values, and demonstrates the importance of the analysis. We thank one of the referees for valuable suggestions. References 1 A. Vivo, C. D. Silgo and A. Arkvalo, An. Quim., 1980,76, 240; 1981, 77, 31. 2 A. Vivo, M. A. Esteso, M. L. Llorente and B. Dominguez, An. Quim., 1981, 77, 209. 3 C. W. Davies and V. E. Malpass, Trans. Faraday Soc., 1964, 60, 2075. 4 I. L. Jenkins and C. B. Monk, J. Am. Chem. SOC., 1950,72,2695. 5 W. G. Davies, R. J. Otter and J. E. Prue, Discuss. Faraday Soc., 1957, 24, 103. 6 P. Beronins, Acta Chem. Scand., Ser. A., 1975, 29, 289; M. C. Justice and J. C. Justice, J. Solution 7 A. Vivo, M. A. Esteso and M. L. Llorente, An. Quim., 1981, 77, 204. 8 L. Onsager and R. M. Fuoss, J. Phys. Chem., 1932,36, 2689. 9 M. Kaminsky, Discuss. Faraday SOC., 1957,24, 171. Chem., 1977, 12, 819.33 14 Viscosities of Na,SO, and MgSO, in Aqueous Ethanol 10 R. M. Fuoss, L. Onsager and J. F. Skinner, J. Phys. Chem., 1965, 69,2581. 11 E. M. Hanna, A. D. Pethybridge and J. E. Prue, J. Phys. Chem., 1971,75,291. 12 R. W. Gurney, Ionic Processes in Solution (McGraw Hill, New York, 1953). 13 A. Arevalo, A. Vivo, M. A. Esteso and M. A. Cabrera, An. Quim., 1971, 73, 15. 14 A. Sacco, A. de Giglio, A. Dell’Atti and M. Petrella, J. Chem. Soc., Faraduy Trans. I , 1981, 77, 2693. Paper 511829; Received 21st October, 1985

ISSN:0300-9599    

DOI:10.1039/F19868203307

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1986,82, 3315-3330 Cooperative Effects in Heterogeneous Catalysis Part 1 .-Phenomenology of the Dynamics of Carbon Monoxide Oxidation on Palladium Embedded in a Zeolite Matrix Nils I. Jaeger,* Karin Mollert and Peter J. Plath Institut f u r Angewandte und Physikalische Chemie, FB 2, Universitat Bremen, 0-2800 Bremen 33, Federal Republic of Germany Hysteresis behaviour, simple and complex oscillations showing a fractal pattern, long-term changes of the oscillations as well as periodic multistability have been uncovered during the oxidation of CO. Pd zeolites with different amounts of Pd particles per unit volume were used as a catalyst in order to study the synchronization process during the reaction. Zeolites with the highest Pd content showed the largest capability to oscillate, with amplitudes up to 95% of the conversion.Examination of the catalyst before and after the reaction leads to the assumption of a cyclic oxidation-reduction mechanism. Coupling of the individual particles is suggested by a concen- tration wave travelling across the surface. The analysis of complex temporal behaviour in heterogeneous catalytic reactions has led to new insights into the basic mechanism of catalysed reactions. The oxidation of carbon monoxide on Pt foils and wires and on Pd and Pt supported catalysts has been studied intensely in this context,l-ls beginning with the observations presented by Hugo and Jakubithl and Wicke and coworkers.2 Early models put forward to account for the observed reaction rate oscillations propose phase transitions regarding structure and reactivity of adsorbate layers of reacting molecule^,^^ l 1 9 l2 a point of view which has recently been supported by in-situ infrared spectroscopy on Pd supported catalysts.16 Direct observations of phase tran- sitions travelling across single-crystal surfaces of Pt were reported by Cox et al." under vacuum conditions.The idea of phase transitions involving the catalyst had been proposed by Wagner.18 A mathematical model of ideal storagelg involving a phase transition of the bulk of catalytically active crystallites has been developed that shows the essential dynamic properties observed in experimental systems. In this article we describe the phenomenology of heterogeneously catalysed CO oxidation and propose a reaction mechanism.In a subsequent paper (Part 2) we will use techniques developed in connection with chaos theory to create and study attractors from the computer-stored reaction data. Suggestions will then be made for a chemical interpretation of the observed results. Models often suggest that the bulk of a supported catalyst acts in synchrony with the dynamics of a single active centre undergoing phase transitions. Synchronized behaviour of all parts of the catalyst surface cannot be expected, as was demonstrated recently by highly resolved infrared thermography20 supported by i.r. spectroscopy.14 The coupling mechanism required for the cooperation of large numbers of active centres therefore must be specified. Coupling can be achieved by simple diffusive processes, e.g. heat transfer and/or diffusion of molecules participating in the reaction. Local temperature peaks have to be taken into account, especially in the case of exothermic oxidation reactions, and t Present address : Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, Delaware 197 16, USA.33153316 Cooperative Efects in Heterogeneous Catalysis models should not be based on overall isothermal conditions established as a questionable constraint on the reaction. In the present work the phenomenology of the non-isothermal CO oxidation on a highly dispersed palladium phase supported within a zeolite matrix will be presented. The faujasite-type zeolite was chosen for three reasons. (i) It is a suitable carrier for the growth of a Pd phase with a narrow particle size distribution within the channels and cages of the matrix.21 (ii) It allows the preparation of catalysts with varying amounts of metal loading, adjustable by the ion-exchange process. (iii) Different metal particle sizes can be generated within the framework by applying well studied reduction routes.22 With this catalyst system it was possible to study the reaction not only in terms of its dependence on the temperature and the CO concentration in the feed, but also in terms of the number of Pd crystallites per unit volume and different metal particle sizes.The experimental results will be interpreted by phase transitions of the Pd crystallites, and a mechanism for their coupling will be suggested which will be evaluated in Part 2.Experiment a1 Preparation of the Catalyst The sodium form of zeolite X (faujasite) was prepared by hydrothermal synthesis, yielding an Si/Al ratio of 1 : 2 and a crystallite size of 10-20 pm. The sodium cations of the zeolite with the overall formula [(A102)86(Si02)l,,6] - nH20 were exchanged with an aqueous [Pd(NH3),]C12 solution ranging from 0.003 to 0.025 mol dm-3 at room temperature under shaking for 24 h. After washing the sample chloride-free it was dried and the Pd content was determined by atomic absorption spectroscopy (degree of exchange 7-43%, corresponding to 2.4-14.7 wt %). The metal phase was then prepared by an autoreduction process during the decomposition of the ammine complex, heating a sample in a fluidized-bed reactor up to 623 K (5 K min-l) for 16 h.According to the desired metal particle size either argon or oxygen was used, with a flow rate of 1.4 cm3 s-l at 1 x lo5 Pa. Details regarding the reduction mechanism have been Characterization of the Catalyst The Pd-loaded zeolite was characterized by X-ray diffraction using a Debye-Scherrer camera and electron diffraction, in addition to transmission electron microscopy prior to and following the catalytic reaction. Both the crystallinity of the zeolite and the reduction of the Pd cations to the metal were detected with these methods. The pore volume of the zeolites was checked in addition by measuring the nitrogen physisorption capacity of the sample, while the accessibility of the metal surface towards the reacting molecules such as CO was examined by the oxygen chemisorption capacity of the metal surface, assuming that both molecules would cover about the same surface area with respect to their cleft fractal The geometrical metal surface was estimated from transmission electron micrographs.The micrographs were taken from cuts of the zeolites embedded in epoxy resin. The metal phase with a narrow particle size distribution was located exclusively within the zeolite matrix even though the size of the Pd single crystals was found to exceed greatly the largest cages of the host lattice. The catalysts with a high Pd loading showed local damage to the zeolite framework after the reaction, which was confirmed by physisorption measurements. Details of the results obtained by transmission electron microscopy and Xps, and a discussion of the growth of large metal single crystals within the channels and cages of the zeolite matrix are given in ref.(21), (25) and (26). Depending on the gas atmosphere used in the autoreduction procedure a narrow palladium crystallite size distribution around 10 nm (in argon) or 4 nm (in oxygen) could be obtained. Plate 1 shows the catalysts A-C treated under argon, always with anJ. Chem. Soc., Faraday Trans. 1, Vol. 82, part I I Plate 1 Plate 1. Electron micrographs of (a) catalyst A with 14.7 wt % Pd, (b) catalyst B with 4.4 wt % Pd, (c) catalyst C with 2.4 wt % Pd and ( d ) catalyst D with 14.7 wt % Pd. The scale bar indicates 50 nm. N. I. Jaeger, K. Moller and P. J. Plath (Facingp.3316)N. I. Jaeger, K. Moller and P. J. Plath 3317 Table 1. Catalysts used in the experiments Pd crystallites average size number/ l0ls catalyst Pd (wt %) support /nm per g catalyst A 14.7 zeolite X 10 B 4.4 zeolite X 10 C 2.4 zeolite X 10 D 14.7 zeolite X 4 E 0.5 Al,O,/SiO, 2 (amorphous) 2.34 0.71 0.38 36.5 9.8 -r gas inlet 7- thermocouple connected with a t silver sieve preheating El! Fig. 1. Differential flow reactor. average Pd size of 10 nm but with a decreasing amount of Pd particles per unit volume. Catalyst D is a highly loaded sample treated under oxygen to give an average size of 4 nm. The catalysts used in the experiments are listed in table 1. Catalytic Measurements The Pd-loaded zeolite was pressed and ground up again. Pellets between 0.06 and 0.1 mm in diameter were used in the experiments.The reaction was carried out in a differential flow reactor under shallow-bed conditions. The catalyst rested either on a silver sieve or on a ceramic support (fig. 1). The temperature of the silver sieve is representative of the average temperature of the catalyst bed under reaction conditions and was measured3318 Cooperative Efects in Heterogeneous Catalysis 1 .o 2.0 co (vol %) Fig. 2. Influence of the reaction temperature on the hysteresis effect for catalyst C (50mg) at reaction temperatures T, = @, 423 ; + ,433 and 0 , 4 4 3 K. by a thermocouple connected to the silver support. The temperature of the feed was varied between 403 and 523K and controlled by a second thermocouple. Most experiments were carried out with either 20 or 50 mg of the catalyst.The carefully dried gas mixture containing between 0.2 and 5.0 vol% CO were prepared from a CO-N, test gas mixture (1 5 % CO) and synthetic air [Messer Griesheim, impurities < 0.1 vpm (volumes per million)]. A linear flow rate of 2.5 cm ~ ~ ~ ( 2 . 5 cm3 s-l) was used in most of the experiments (1 x lo5 Pa, residence time 5 s). The CO, and CO concentrations on the outlet of the reactor were continuously monitored by i.r. spectrometers (URAS 2T and URAS 3G, Hartmann und Braun, F.R.G.). Concentration changes with time could be resolved to within 1 s. The reaction data were digitized and stored on floppy discs with a PDPl 1 computer (DEC) for further analysis. For dehydration prior to the catalytic measurements the catalyst was heated to 600 K ( 5 K min-l) within the flow reactor and left at this temperature in streaming dry synthetic air (1 x lo6 Pa) for 16 h.Any appreciable activity of the carrier or the silver sieve in the parameter region where oscillations occur was ruled out by running blank measurements.N . I. Jaeger, K. Moller and P . J. Plath 3319 2oi / 15 i 7 7 /i + + 1.0 2.0 co (vol %) I Fig. 3. Influence of the number of Pd crystallites per g of catalyst on the hysteresis loop at T, =423 K for catalysts A (O), B (0) and C (+) (50 mg). Results Hysteresis of the CO Oxidation The Pd-zeolite system shows hysteretic behaviour during CO oxidation, similar to results from other authors using Pt catalysts for this rea~tion.~ Depending on the CO concentration in the feed a threshold value is found to exist for oscillating CO, production.Beyond this value the reaction rate drops to a low stationary state which does not change, even after 20 h. The high-activity branch can only be recovered by considerably reducing the concentration of the carbon monoxide or by increasing the temperature of the catalyst. Resulting hysteresis loops are depicted for different system temperatures in fig. 2 and for three of the catalysts which have the same Pd particle size of 10 nm but differ in the amount of Pd in fig. 3. The difference, AT, of the average temperature of the supporting silver sieve and the reactor temperature, which is proportional to the reaction rate, is plotted as a function of the CO concentration. Hysteresis behaviour can be observed for system temperatures in the range 403-443 K.The threshold and ignition points are found to rise to higher CO concentrations with increasing system temperature (fig. 2) and for increasing numbers of Pd crystallites per g catalyst (table 1 and fig. 3) under 110 FAR 13320 Cooperative Eflects in Heterogeneous Catalysis Table 2. Threshold value for the extinction of the high-activity branch of the reaction at 423 K as a function of the metal loading of the catalyst threshold value of turnover number Pd surface co (vol %) CO/Pd surface atom per s area catalyst /m2 per g catalyst (4 (4 (4 (4 A 7.38 1.20 1.60 0.15 0.21 B 2.22 0.78 1.20 0.33 0.50 C 1.18 0.78 0.57 otherwise constant conditions. Similar behaviour is found for repeated hysteresis loops at a given temperature, indicating a memory effect of the catalyst.The calculation of turnover numbers at the extinction points leads to the surprising result that the oxidation of a smaller number of CO molecules per Pd surface atom per second is needed to suppress oxidation on catalysts with a larger Pd surface area. These results are summarized in table 2, including the threshold values for succeeding hysteresis loops. The Pd surface area and the number of Pd surface atoms were estimated for Pd spheres with the experimentally observed average diameter of 10 nm by using the specific weight of bulk Pd (12 g cm-9. Running the system below temperatures of 433 K may result in spontaneous quenching of the reaction below the threshold value, which recovers without any parameter manipulation.The catalyst changes autonomously between 95,50 and 30 % conversion, and the different states are maintained unpredictably for between 30 min and several hours. The periodic instabilities are observed in the region of hysteresis behaviour between 403 and 433 K. A stepwise quenching is also found in this region.' Oscillation of the CO Oxidation Temperature oscillations and corresponding concentration oscillations occur along the high-activity branch of the hysteresis. At temperatures > 443 K no threshold value is observed, but stable oscillations persist up to 525 K with a level of > 95% conversion. The CO, oscillations represent depressions in the reaction rate, matching the temperature pattern. Both are inverse to the CO oscillations in the effluent gas.As a characteristic feature of the reaction, a fractal structure2' of the product oscillations could be observed. Fig. 4 depicts results representative of all the catalysts, here shown for catalyst B, at T, = 453 K as a function of the amount of catalyst. The oscillations show self-similarity, which means that the global pattern will repeat inside itself with a similar structure, but always on a smaller scale. A prerequisite for the unfolding of pronounced oscillations, and specifically of their fractal character, is the use of small amounts of catalyst. The oscillations obtained for charges in the ranges 7-20 mg and 50-100 mg are compared in fig. 4. A well developed fractal pattern can only be observed in the case of small charges of catalyst (7-20 mg).Here the increase in the oscillatory capacity is obvious: on using 100 mg of catalyst the conversion drops by 8 % at 0.40 % CO compared to a decrease of 50 % when using only 20 mg. Going to a slightly higher CO concentration with a small amount of catalyst may even result in a decrease of conversion by 95%. Total quenching was observed at concentrations around 1 % CO. The heights of the amplitudes during the reaction can be used as a relative measure of the system's capability to oscillate and gives an indication of the number of Pd crystallites that are synchronized at the same moment. The amplitudes themselvesN . I. Jaeger, K. Moller and P . J. Plath 0.401 3321 I 30 rnin Fig. 4. Influence of the amount of catalyst on the oscillation patterns of catalyst B at T, = 453 K and 0.40 vol % CO: (a) 7, (b) 20 and (c) 100 mg.I t represent a loss of activity with respect to the reference point of almost total conversion ( > 95 % ). In fig. 5 the maxima of the depression of CO conversion during the oscillations are shown for different catalysts as a function of CO concentration. Following curve A of the catalyst with the highest Pd content indicates that at low CO concentrations, e.g. 0.37 v o l x , only very small amplitudes for the CO, oscillations are visible, and with increasing time these are no longer resolvable by temperature measurements. With increasing CO concentration in the educt stream the amplitudes grow and the fractal structure builds up more clearly. Both the fractal structure of the oscillations and the amplitudes are most pronounced for medium CO partial pressures.For higher CO concentrations the amplitudes decrease again and the visual appearance of the observed pattern seems to be of a chaotic nature. At around 5 vol % CO a steady state of the reaction is established. The patterns stabilize within several minutes following an alteration of the experimental conditions. A characteristic long-term change in the catalyst properties did not interfere with the experiments using 50 mg of catalyst, and a similar succession of patterns could be established in the reverse order by decreasing the CO concentration again. If the different catalysts are now compared, distinguished by their increasing amounts of Pd crystallites per unit volume going from catalyst C to catalyst A (table l), an increase in the amplitudes and the evolution of the fractal structure can be observed.For comparison the data of the amorphous catalyst E are added, which contains even more Pd particles per unit volume, whereby the crystals are also of a smaller size (2 nm) (see table I), resulting in amplitudes of 75 % of the yield even at low CO concentrations. The reproducibility of the curves is within f 3 % conversion for different samples of the same amounts of the chosen catalysts. 110-23322 40- - 20 - - Cooperatbe Eflects in Heterogeneous Catalysis 100- 80- - n 8 60- c .r( h > - s 0 \ E 0-0 l l I ~ I l I I ~ l l l 1 1.0 2.0 co (vol %) Fig. 5. Maximum decrease in conversion during the oscillations as a function of the CO concentration and the number of Pd crystallites per g of catalyst (catalysts A, B, C and E, see table 1) at T, = 453 K (50 mg).The dependence of the largest amplitudes on the CO concentration for catalyst A is plotted for several temperatures in fig. 6. The amplitudes increase with decreasing temperature. Below 453 K hysteresis behaviour is found, and below 433 K the reaction is characterized by the appearance of multistable, aperiodic behaviour. The influence of the amount of the catalyst can again clearly be seen in fig. 7. The maximum depression of the CO conversion during the oscillations is compared between a 50 mg and a 20 mg charge of catalyst A. The formation of large-amplitude oscillations is much more pronounced for the small charges. Fig. 8 summarizes the experimental observations in the temperature-CO-concentration phase plane for 50 mg charges of catalyst A.If the experimental conditions were chosen such that large amplitudes could be expected by using a catalyst with a high Pd particle density and the temperature was near the region where hysteresis occurs, a decrease of the amount of catalyst to 20 mg led to an evolution of the oscillation pattern on a large timescale. Representative results obtained for catalyst A (20 mg, = 453 K, 0.37 vol % CO), left under constant conditions for more than 100 h, are depicted in fig. 9. The different patterns represent situations which remain stable for several hours. The fractal structure is established within 15 min and evolved during the first 20 h. The evolution can be characterized by an increase in the length of the largest amplitudes as well as by an increase of the period.After 20 h the maximum amplitude disappeared abruptly and the system was found to'4 \ y 3 / . 1 .O 2 .o co (vol%) Fig. 6. Maximum decrease in conversion during the oscillations for catalyst A for various reaction temperatures between 453 and 523 K. 100- 90- 80- - - - - I 473 '0 i \ a '@ 493 0 0 I \ 1 1 ' " ' ' ~ ~ " " ' ' 1.0 2.0 3.0 co (vol %) Fig, 7. Influence of the reaction temperature T, and the CO concentration in the feed on the mafima of the depression of CO conversion during the oscillations for different amounts of catalyst A: 0, 20 mg; 0, 50 mg. w w td w3324 0.35- 0.25- 0.15- Cooperative Efects in Heterogeneous Catalysis 250 - 240 230 220 210 u 200- iG 190 180 170 160 150- 140 130 - - no conversion Fig.8. Summary of the dynamic behaviour of catalyst A in the temperature-CO-concentration phase plane. I 1 30 min t 25 0.35 n * 3 0.25 6 0 . 3 5 " I 0.25 65 O.2SJ 98 I . I 1 18 min 6 min t Fig. 9. Long-term changes of the oscillation pattern of catalyst A by using 20 mg of the catalyst at T, = 453 K and 0.37 vol % CO. Total time on stream given in h.N. I. Jaeger, K. Moller and P . J. Plath 3325 50. 4 I I 60 min t I I I 60 min t '"1 + I 60 min I i" ( d ) t I 60 min I t Fig. 10. Multiplicity of states as a function of the CO concentration in the feed. 20 mg of catalyst D, T, = 453 K. (a) 0.85 (b) 1.10 and (c) 1.33 vol % CO; ( d ) quenching after concentration change of CO in the feed (arrow).3326 Cooperative Efects in Heterogeneous Catalysis approach a state of apparently chaotic oscillations which could be maintained for several days.The different sections of the time series represent trajectories of the system which remain stable for several hours. The initial pattern and a similar sequence of structure changes could be repeated by subjecting the same catalyst to the standard pretreatment conditions in dry air (600 K, 16 h). Performing the experiments under the same conditions but choosing catalyst D, which has a smaller particle size of 4 nm and a larger number of Pd crystallites per unit volume (see table 1) prevents the system from undergoing these changes on the long timescale. In this case different behaviour with periodic multistability is found at higher CO concentrations (fig.10). Again the formation of self-similar oscillations takes place, which is now interrupted by sharp, long-lasting quenchings of the conversion level starting at a concentration of 0.85 vol % CO [see fig. lO(a)]. Larger amounts of CO in the feed result in broadening of the low conversion level, and at 1.33 vol % CO an autonomous change in the conversion between 98, 50-60 and 10% is obtained [see fig. lO(c)]. The different states are maintained between 30min and several hours, increasing with the CO concentration. A decrease in the conversion to 10% is always found after concentration changes in the feed [see arrow in fig. lO(d)]. Catalyst E, also with a high Pd loading and small particle size, showed similar results between 453 and 407 K at 0.37 vol % CO.With the exception of reaction states with periodic multistability all observed oscillations were found to be stable against small perturbations in the experimental parameters (flow rate, CO concentration and temperature of the reactor). However, the patterns undergo quantitative changes following a mechanical rearrangement of the catalyst bed. Characterization of the Catalyst by X-Ray Diffraction The studied reaction was carried out in an excess of oxygen, and the pretreatment of the zeolite was made under flowing synthetic air at a temperature of 600 K in order to drive the water out of the zeolite cavities. Under these conditions it can be assumed that the metal phase may undergo oxidation to PdO, as was observed by several a ~ t h o r s .~ ~ - ~ ~ To confirm this, small amounts of catalyst A were collected at different steps of the pretreatment procedure in order to perform X-ray studies (fig. 11). The reference (pattern tl) shows the strong (lll), (200) and (220) reflections of the Pd phase, in addition to the zeolite pattern. After 2.5 h at 600 K the PdO phase started to appear (pattern tJ and was found to dominate the Pd intensities after 22 h (pattern t3), with the PdO reflections (1 0 1 ), (1 lo), (1 12), (103) and (202). The catalytic measurements were therefore started with a catalyst containing both a Pd and a PdO phase. From the line-broadening of the reflections in the X-ray diffraction patterns the size of the particles could be estimated, and were in agreement with the results obtained by transmission electron microscopy (table 1).X-Ray diffraction patterns obtained for samples of the catalyst taken in the course of the catalytic reaction, on the other hand, showed either the reflections of the metal and the metal oxide simultaneously (although with varying relative intensities) or in several cases the Pd metal phase alone. The latter observation points towards the reducibility of the PdO phase under reaction condition, because decomposition of PdO does not take place below at least 1073 K.31732 The PdO phase can be almost completely reduced by switching from synthetic air in the reaction gas mixture to N, as a carrier. The reduction of PdO starts at relatively low temperatures (370 K), as could be demonstrated by temperature-programmed reduction of the samples.3327 I .. . . 1 . . . , l l l , , r . . . , 1 , , , , 1 , , , I I , . . , I . . , 0 10 20 30 01" Fig. 11. X-Ray diffraction pattern of catalyst A after treatment in synthetic air. (tJ Sample taken during the temperature programme (5 K min-l) at 473 K; (tz) sample taken after 2.5 h at the final temperature (600 K); (t3) sample taken after 22 h at 600 K. x , Pd; 0, PdO. Discussion The first discussions of CO oxidation oscillations mainly concerned kinetic aspects of the adsorbates. Ideas such as the transformation of an inactive linear bonded CO to the reactive bridge-bonded C0,l a switch between the Langmuir-Hinshelwood and Eley- Rideal mechanisms33 or the key role of a slowly desorbing intermediate34 stimulated further investigations.In-situ studies performed with F. tir., u.h.v. measurements on single crystals or i.r. thermography now indicate that the catalyst itself undergoes changes during the oscillations. Adsorbate-induced transitions found on Pd and Pt catalysts,ls* l7 which may spread non-uniformly over the surface,l49 2o have to be taken into account. In the present work we found evidence of an alternating oxidation and reduction of the Pd metal in the zeolite during the reaction. The starting material, consisting of a mixture of Pd and mainly PdO, turned in some cases into a catalyst with only the Pd phase, as examined after the reaction. Both the formation of PdO and its transformation into Pd were shown to be possible under the reaction conditions. This confirmed the in-situ diffraction measurements of Bergeret et al., who observed the complete oxidation3328 Cooperative Eflects in Heterogeneous Catalysis of 2-2.5 nm Pd crystallites supported in a zeolite matrix in the temperature range 450-500 K.35 The experimental results, however, allow no correlation of the timescales of the redox reaction involving the Pd phase with the timescale of the observed oscillations.It is well known that a Pd crystal shows different types of surface transformation, being either covered only with oxygen or at the same time with C0,36 and an enhanced reduction of PdO was in fact observed in the presence of 0,.37 As a result, the redox cycle during the oscillation may proceed much faster than expected from the reduction and oxidation experiments with the coadsorption of both components, CO and 0 on the surface, yielding a higher surface partial pressure.The transmission electron micrographs taken after the reaction support this assumption in another way : only the catalyst that reacted under large oscillations showed blurred images of the metal phase and local distortions of the zeolite. This might be caused by the cyclic change of volume of ca. 60% from Pd to PdO. These observations form the basis of our interpretation of the observed oscillations, where a phase transition (and its reversal) is proposed between a catalytically active Pd metal phase and an inactive PdO phase. Models of cyclic oxidation and reduction have been proposed in order to explain the oscillating oxidation of H, on Pd wires and Ni f0ils,~~,3~ and for the CO oxidation on Pd In the case of Pd-loaded zeolites the bulk of the metal phase can be transformed into stoichiometric PdO in the course of the reaction.No sintering or redispersion of the mixed metal-metal-oxide phase can be observed in the electron micrographs taken from the catalyst after reaction. This is supported by the same line-broadening in the observed X-ray patterns for both the Pd and PdO phases. The possibility of oxidizing highly dispersed Pd to PdO at relatively low temperatures during prolonged pretreatment of the catalyst in air, and the fact that the activity of the catalyst is established under oxidizing conditions, allow the conclusion that the active phase of the catalyst consists of an oxide phase, at least on the surface of the Pd crystallite.The catalyst surface, as well as in our case the bulk of Pd crystallites, can be regarded as a store for oxygen. At a certain threshold value a new phase is formed with little activity for CO conversion. From the experiments and from the literature data43 the surface of the bulk PdO appears to be the inactive phase, because no further adsorption of oxygen is possible on the surface. Our proposed scheme suggests the diffusion of adsorbed oxygen into a Pd crystallite in the course of the strongly exothermic reaction between the dissociatively adsorbed 0, and the molecularly adsorbed CO. The oxidation of Pd is favoured in the state of high catalyst activity when the local overheating of a metal crystallite supported on a matrix of low heat conductivity can be considerable, according to Ruckenstein and Petty.44 Following the phase transition to PdO, i.e.the transition to a state of low activity, the local temperature drops, the adsorption of CO is favoured and the reduction of the oxide by CO is the only reaction route until the original state of high activity is re-established. This reaction cycle is summarized in the following reaction equations. Overall reaction: CO +to, + CO,. (1) Active phase of a Pd crystallite (adsorption of reactants and reaction): Pd + CO + Pd/CO Pd+$O, + Pd/O Pd/O + Pd/CO + 2Pd + CO,. (2) Oxidation of Pd and transition to an inactive palladium oxide phase: Pd/O + PdO, 0 < x < 1 PdO,+(l-x)O+PdO.N. I. Jaeger, K. Moiler and P. J. Plath 3329 (3) Reduction of the inactive palladium oxide phase and transition back to the active phase of a Pd crystallite: PdO + CO + PdO/CO PdO/CO + Pd + CO,.The outlined model describes a cyclic reaction mechanism for a single catalyst particle. The average number of Pd crystals in the catalysts is ca. 1015, which would yield an apparent steady-state conversion when acting in a totally uncorrelated way, averaging all small-scale oscillations. Almost no discussion can be found in the literature concerning the synchronization of a large number of catalytically active centres. Our results indicate that an internal geometrical factor of the catalyst is responsible for the coordination of events. The application of zeolites as a support has made it possible to vary the amount of Pd particles per unit volume by keeping the particle size constant.In this way the distance between neighbouring crystallites could be decreased, making heat transfer or the diffusion of reactants easier. As a result the observed amplitudes of the oscillations increased, indicating a synchronization of more particles (see fig. 5). The process itself may be pictured as a concentration wave travelling across the catalyst surface : the trigger for the oscillations can be assumed to be one particle or a group of particles being oxidized earlier than others owing to a statistically higher coverage of reactants, a slightly smaller particle size or for other reasons. Their oxidized surface is no longer able to convert the succeeding molecules, since the crystallites are too hot to adsorb CO and are unable to adsorb further oxygen.The resulting local excess of feed molecules begins to diffuse to the still active neighbouring particles, driven by a small-scale concentration gradient. These crystallites can consequently increase their reaction rate until they undergo the same transition to PdO, thus becoming in phase with the timing particle. Depending upon the distance between the particles, more or less time will be taken before the concentration wave becomes diluted by diffusion in space. In the meantime the starting particle is cooled, covered with CO and reduced again, shortly followed by its neighbours. This same mechanism provides an explanation for the observed quenching phenomena, where the catalyst with the highest number of Pd particles per unit volume was quenched by a smaller number of CO molecules per Pd surface atom.The stronger coupling in this case overwhelms the factor of a much higher Pd surface area. The most pronounced decrease in conversion during the oscillations was found with catalyst E (see fig. 5), which contains the largest number of Pd particles among the compared samples. This result may be influenced by (in addition to the short distances between neighbouring particles) the small size of the metal particles, which are much more easily oxidized and reduced. Synchronization of the catalytic activity across the catalyst charge via heat transfer through the supporting disc seems to be less important in this reaction, since the replacement of the highly conducting silver sieve by a ceramic plate did not influence the oscillation patterns.Even a division of the catalyst charge into spatially separated parts showed no effect. The proposed reaction cycle leaves unexplained the long-term changes in the state of the experimental system and the possibility of restoring the original pattern by repeating the pretreatment of the aged catalyst in dry air. The ageing of the catalyst apparently involves no irreversible loss of activity. As a possible mechanism the deposition of carbon species on the surface of the Pd crystallites via the Boudouard reaction (2CO + C+CO,) at local overheated sites may be suggested. Precursors for coke deposition due to residual hydrogen in the carbon monoxide may also be taken into account.3330 Cooperative Eflects in Heterogeneous Catalysis A model involving transitions between phases of different catalytic activity yields oscillations in the case of a single oscillating system.This has been demonstrated by the mathematical and numerical analysis of a model of ideal ~t0rage.l~ The model involves transitions in the catalytic activity of an independently reacting crystallite as a function of the amount of chemical species stored. This simple model does not account for the complex structure of the observed oscillations. A numerical analysis of the experimental data, as the basis for the development of a suitable model which accounts for the synergetic behaviour of large numbers of a catalytically active crystallite or ensembles of crystallites, will be presented in Part 2 following proposals by Dress et al.45 We are grateful for financial support from the Stiftung Volkswagenwerk (AZ 1/38 880). References 1 P.Hugo and M. Jakubith, Chem. Ins. Tech. 1972,44, 383. 2 H. Beusch, P. Fieguth and E. Wicke, Chem. Ins. Tech., 1972,44,445. 3 M. Sheintuch and R. A. Schmitz, Catal. Rev.-Sci. Eng., 1977, 15, 107. 4 W. Keil and E. Wicke, Ber. Bunsenges. Phys. Chem. 1980,84, 377. 5 E. Wicke, Chem. Ing. Tech., 1974, 46, 365. 6 J. Rathousky, J. Puszynski and V. Hlavacek, Z . Naturforsch., Teil A , 1980,35, 1238. 7 N. I. Jaeger, K. Moller and P. J. Plath, 2. Naturforsch., Teil A, 1981, 36, 1012. 8 W. Adlhoch, H. G. Lintz and T. Weisker, Surf. Sci., 1981, 103, 576. 9 D. Barkowski, R. Haul and U. Kretschmer, Surf. Sci., 1981, 107, L329.10 P. C. Liao, E. E. Wolf, Chem. Eng. Commun., 1982, 13, 315. 11 G. Ertl, P. R. Norton and J. Rustig, J. Phys. Rev. Lett., 1982, 49, 177. 12 M. P. Cox, G. Ertl, R. Imbihl and J. Riistig, Surf. Sci., 1983, 134, L517. 13 J. Puszynski and V. Hlavacek, Chem. Eng. Sci., 1984,39,681. 14 D. J. Kaul and E. E. Wolf, J. Catal., 1985, 91, 216; 93, 321. 15 N. I. Jaeger, K. Moller and P. J. Plath in Springer Series in Synergetics, Vol. 29, Temporal Order, ed. L. Rensing and N. I. Jaeger, p. 96. (Springer, Berlin, 1985). 16 D. Bocker and E. Wicke, ref. (15), p. 75. 17 M. P. Cox, G. Ertl and R. Imbihl, Phys. Reu. Lett., 1985,54, 1725. 18 C. Wagner, Bet. Bunsenges. Phys. Chem., 1970,74,401. 19 A. Dress, N. I. Jaeger and P. J. Plath, Theor. Chim. Acta, 1982, 61, 437. 20 J. R. Brown, G. A. DNetto and R. A. Schmitz, ref. (15), p. 86. 21 D. Exner, N. I. Jaeger, K. Moller, R. Nowak, H. Schriibbers, G. Schulz-Ekloff and P. Ryder, Stud. 22 D. Exner, N. I. Jaeger and G. Schulz-Ekloff, Chem. Ing. Tech., 1980,52, 734. 23 D. Exner, N. I. Jaeger, K. Moller and G. Schulz-Ekloff, J. Chem. SOC., Faraday Trans. I , 1982,78,3537. 24 P. Pfeifer and D. Avnir, J. Chem. Phys., 1983,79, 3558. 25 G. Schulz-Ekloff, D. Wright and M. Grunze, Zeolites, 1982, 2, 70. 26 D. Exner, N. I. Jaeger, G. Schulz-Ekloff and P. Ryder, Proc. 6th Int. Zeolite Conf. 1983, ed. A. Bisio 27 B. B. Mandelbrot, The Fractal Geometry ofNature (Freeman, New York, 1983). 28 J. M. Guiot, J. Appl. Phys., 1968, 39, 3509. 29 E. Ruckenstein and J. J. Chen, J. Catal., 1981, 70, 233. 30 T. W. Orent and S. D. Bader, Surf. Sci, 1982, 115, 323. 31 S. I. Ginzberg, Analytical Chemistry of Platinum Metals (Keter, Jerusalem, 1975). 32 ci. Bayer and H. G. Wiedemann, Thermochim. Acta, 1975,11, 79. 33 R. Dagonnier and J. J. Nuyts, J. Chem. Phys., 1976, 65, 2061. 34 G. Eigenberger, Chem. Eng. Sci., 1978,33, 1263. 35 G. Bergeret, P. Gallezot and B. Imelik, J. Phys. Chem., 1981,85, 411. 36 T. Engel and G. Ertl, Ado. Catal., 1979, 28, 2. 37 P. V. McKinney, J. Am. Chem. SOC., 1932,54,4498. 38 Z . Kurtanjek, M. Sheintuch and D. Luss, J. Catal., 1980, 66, 11. 39 K. Rajagopalan, M. Sheintuch and D. Luss, Chem. Eng. Commun., 1980, 7, 335. 40 J. E. Turner, B. C. Sales and M. B. Maple, Surf. Sci., 1981, 109, 591. 41 J. E. Turner, B. C. Sales and M. B. Maple, Surf. Sci., 1981, 103, 54. 42 B. C. Sales, J. E. Turner and M. B. Maple, Surf. Sci., 1982, 114, 381. 43 P. V. McKinney, J. Am. Chem. SOC., 1933, 55, 3626. 44 E. Ruckenstein and C. A. Petty, Chem. Eng. Sci., 1972, 27, 937. 45 A. Dress, M. Gerhardt, N. I. Jaeger, P. J. Plath and H. Schuster, ref. (15), p. 67. Surf. Sci. Catal., 1982, 12, 205. and D. H. Olson (Butterworths, Guildford 1984), p. 387. Paper 511840; Received 22nd October, 1985

ISSN:0300-9599    

DOI:10.1039/F19868203315

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I, 1986,82, 3331-3341 Solvent Effects on the Thermodynamics of Aquocobalamin Chloride and Model Compounds in Dioxane-Water Mixtures1 Sijbe Balt* and Alexander M. van Herk Department of Chemistry, Free University, de Boelelaan 1083, 1081 HV Amsterdam, The Netherlands The solubilities of aquocobalamin chloride and eight other cobalt(n1) complexes have been measured in dioxane-water mixtures. For aquocobala- min chloride, aquanitrocobaloxime and aquamethylcobaloxime solubilities have also been measured as a function of temperature. The transfer thermodynamic functions a,Go, a,H" and a m p have been calculated. The results may be accounted for in terms of the cavity energy and specific interactions. A difference has been found between the transfer functions of the aquocobalamin cation in dioxane-water mixtures and those in acetonitrile-water mixtures.In a series of investigations1 into the reactivity of aquocobalamin and model compounds we have attempted to obtain insight into the factors that determine the solvent dependence of the kinetic parameters by separating the solvent effects in initial-state and transition-state contributions. The transfer Gibbs energies of the reacting compounds in mixed solvents, necessary for this approach and calculated from measured solubilities, in themselves provide interesting information on the solute-solvent interactions and the factors that control the kinetics. In this study we present the solubilities in dioxane- water mixtures of the following complexes : aquocobalamin chloride ([Bl,-H,O]Cl), trans-bis(diaminoethane)diazidocobalt(m) perchlorate ([Co(N,),(en),]ClO,}, aqua- chlorocobaloxime (ClCo(DH),H,O}, aquamethylcobaloxime (CH,Co(DH),H,O}, aquani t roc0 baloxime perc hlor a te ([pyCo(DH),H,O]ClO,}, benzimidazolechlorocobaloxime (bimCo(DH),Cl), aqua-N- methylbenzimidazolecobaloxime perchlorate ([mbimCo(DH,)H,O]ClO,), aqua-N-meth- ylbenzimidazole -2 - butanone - 3,3'[ 1,3 -propanediyldinitrilo]bisdioximatocobalt (111) per- chlorate ([mbimCo(DO)(DOH),,H20](C10,),}.t These are compared with published data for aquocobalamin chloride and hexa-amminecobalt(II1) chloride in acetonitrile- water mixtures.lb, For aquocobalamin chloride, CH,Co(DH),H,O and NO,Co(DH),H,O the temperature dependence of the solubility in the mixtures is also presented. These values are discussed in terms of cavity formation energy and specific interactions.(NO ,Co( D H) , H ,O} , aqua p yr idineco baloxime Experimental Materials The following cobalt complexes were prepared by established procedures. 16.1 % Co (calc. 16.25%), analysis for the ClO, ion gave 27.3% (calc. 27.42%). [Co(N,),(en),]ClO, was prepared according to Staples., Elementary analysis was Abbreviations: en = diaminoethane, bim = benzimidazole, mbim = N-methylbenzimidazole, py = pyridine, DH = dimethylglyoximato group, (DO)(DOH), = 2-butanone-3,3'( 1,3-propanediyldinitnlo)- bisdioximato group, [B1,-H,O]Cl = aquocobalamin chloride. 33313332 ClCo(DH),(DH),H,O was prepared according to B a b k ~ . ~ Elementary analysis was 17.0% Co (calc.17.3%). CH,Co(DH),H,O was prepared according to Schra~zer.~ Elementary analysis was 18.0% Co (calc. 18.29%), 33.64% C (calc. 33.55%), 6.00% H (calc. 5.94%), 17.47% N (calc. 17.39% ), 24.68 % 0 (calc. 24.83 % ). NO,Co(DH),H,O was prepared according to Tschugaeff.s Elementary analysis was 16.5% Co(ca1c. 16.69), 27.05% C(ca1c. 27.20%),4.49% H (calc. 4.57%), 19.78% N(ca1c. 19.83%), 31.95% 0 (calc. 31.71%). [pyCo(DH),H,O]ClO, was prepared from pyCo(DH),C15 by reaction with an equi- molar amount of AgC10, in 50% ethanol-water v/v (20 cm3 of the mixture per gram cobaloxime) at 70 "C for 1 h. The solution was filtered and cooled. The resulting brown needles were collected and recrystallised from 50 % ethanol-water v/v (yield 70 % ). Elementary analysis was 12.26 % Co (calc.12.13 % ). bimCo(DH),Cl was prepared from H[Co(DH),C1,I7 by reacting with equimolar amounts of KOH and bim. To a solution of 5 g (0.0126 mol) H[Co(DH),Cl,] - 2H,O and 0.71 g KOH (0.0126 mol) in 250 cm3 ethanol, a solution of 0.84 g (0.0123 mol) bim in 100 cm3 ethanol was slowly added (1.5 h). After 1 h the solution was filtered and the brown crystals were washed with water, ethanol and ether (yield 76%). Elementary analysis was 13.3% Co (calc. 13.31%). [mbimCo(DH),)H,O]C10, - 2H,O was prepared from mbimCo(DH),Br [prepared in a similar way as bimCo(DH),Cl] by addition of AgClO, as described for the synthesis of [pyCo(DH),H,O]ClO, (yield 74%). Elementary analysis was 10.1 % Co (calc. 10.25%), analysis for H,O gave 5% (calc. 6.26%). [mbimCo(D0)(D0H),,H20](C10,), was prepared from CO(DH)(DOH)~,B~,;* 250 mg was dissolved in 25 cm3 50% acetone-water v/v at 40 "C.To this solution a solution of 72mgmbim in 2cm3 acetone was added. After 5 min a solution of 2 equivalents AgClO, in 2 cm3 water was added. After 10 min the solution was filtered. The filtrate was left standing for 24 h. The resulting brown crystals were filtered and washed with water. The compound was purified by extracting impurities from the solid with chloroform (yield 50%). Elementary analysis was 9.10% Co (calc. 9.10%), 35.64% C (calc. 35.25%), 4.76% H (calc. 4.52%), 13.07% N (calc. 12.99%), 27.09% 0 (calc. 27.19%), analysis for the ClO, anion gave 30.0% (calc. 30.7%). Chemicals of analytical-reagent grade were used throughout this study. Acetonitrile (Baker) was used without purification and dioxane (Baker) was purified as described before.la Solubilities of Aquocobalamin Chloride in Dioxane- Water Apparatus and Procedures The solubilities of all compounds were measured as previously describedlC in a specially designed solubility tube; equilibration for 2 h [bimCo(DH),Cl within 10 min].The temperature accuracy was always better than 0.1 "C. The temperature region for the measured solubilities was 20-35 "C for aquocobalamin chloride, 15-45 "C for NO,Co(DH),H,O and 15-35 "C for CH,Co(DH),H,O. The lH n.m.r. and 59C0 n.m.r. spectra were recorded on a Bruker WM-250 spectrom- eter. The 59C0 n.m.r. spectra were measured at a frequency of 59.73 MHz. U.v.-visible spectra were recorded on a Beckman Acta MIV spectrophotometer.Hydrolysis reactions of the cobalt complexes were followed on a Zeis M4QIII photometer. Infrared spectra were measured with a Perkin-Elmer 580 B spectrophotometer ; the compounds were suspended in paraffin oil and measured between NaCl discs. Results All compounds show the expected lH n.m.r. spectra. For the compound [mbimCo(DO)(DOH),,H,olo, two types of crystals were isolated. The cobaltS. Balt and A . M. van Herk 3333 Table 1. Extinction coefficients of the compounds used in the solubility measurements and diameters used in the calculations compound A/nm &/mol-l dm3 cm-la D / A [Co(N3)2(en) &lo4 bYCo(DH),H,OIC104 ClCo(DH),€€,O [rnbimC0(DH)~H~O]C10, 2H20 bimCo(DH),Cl NO,Co(DH),H,O CH,Co(DH),H,O aquocobalamin chloride [mbimCo(DO)(DOH),,H,0](C104), 562 300 300 340 300 375 441 350 300 3.37 x 4.80 x 103 4.78 x 103c 2.08 x 103 3.89 x 103c 1.47 x 103 2.62 x 104d 4.07 x 103 1.53 x 10, 7.5 9.43 8.59 9.90 9.83 8.72 8.63 14.4e 9.63 a In water at ca.22 "C. From W. J. Jackson and C. M. Begbie, Inorg. Chim. Acta, 1982,60, 115. CIn 50% ethanol-water v/v. dFrom J. M. Pratt and R. G. Thorp, J . Chern. SOC. A , 1966, 187. eThere are no values available for the partial molar volume of the chloride ion in the mixtures, so we used the value of aquocobalamin chloride instead of the aquocobalamin cation. analysis and u.v.-visible spectra are identical but the infrared spectra in the solid state show differences. The first fraction is brown and consists of [mbimCo(DO)(DOH),,H20](C10,),. The second fraction of crystals is more red-brown, and in the infrared spectrum shows indications of perchlorate coordination.It probably consists of [mbimCo(DO)(DOH)pnC104]C104 - H,O. In aqueous solution evidence of perchlorate coordination was also found in the 'H n.m.r. spectra. Two sets of peaks were found, of which the ratio of the integrals shows concentration dependence. The ratio also changes on addition of sodium perchlorate. From the ratio [mbimCo(DO)(DOH)pnH20](C104)2 : [mbimCo(DO)(DOH)p,C104]C104 as a function of sodium perchlorate concentration, an equilibrium constant of 3 dm3 mol-1 was estimated. lH n.m.r. in D20 (relative to (CH,),SiC,H,SO,Na} : [mbimCo(DO)- (DOH),,H,0](C104), 2.33 (m, 2H), 2.62 (s, 6H), 2.73 (s, 6H), 4.06 (s, 3H), 4.13 (t, 4H), 7.4-7.8 (m, 4H), 8.96 (s, 1H); [mbimCo(DO)(DOH)pnC104]C104: 2.24 (m, 2H), 2.57 (s, 6H), 2.73 (s, 6H), 3.76 (s, 3H), 4.33 (t, 4H), 7.42 (m, 4H).For CH,Co(DH),H,O and NO,Co(DH),H,O, lH n.m.r. and u.v.-visible spectra exclude coordination of dioxane in the solvent mixtures used. In 98 % dioxane-water v/v the methyl peak of CH,Co(DH),H,O shows a shoulder, probably caused by coordination of dioxane or dimeri~ation.~ During the course of the solubility measurements no appreciable hydrolysis of the compounds occurs. Usually the solubility determinations were reproducible to within 5 % . The concentrations of the saturated solutions were measured photometrically after dilution with water or 50 % ethanol-water v/v (table 1). The wavelengths and extinction coefficients used are given in table 1. The solubilities are given in table 2.The solubilities of aquocobalamin chloride in dioxane-water mixtures at 298.15 K were measured previouslylb by us with a different method. The solubilities were found to be equal within experimental error for the two methods. For the calculation of the transfer Gibbs energies in dioxane-water mixtures the contributions of the perchlorate or chloride ion1* (after conversion to the molarity scale) were subtracted. The transfer Gibbs energies (a,G",,,) were calculated with the following formula i3mGzx, = - RT In Pm/Pw (1) where Pw is the solubility or the solubility product in water and Pm that in the mixture (molarity scale). In fig. 1 the transfer parameters are shown for the dioxane-water3334 Solubilities of Aquocobalamin Chloride in Dioxane- Water Table 2.Solubilities (units mol dm-3) as a function of solvent composition and temperature [BI2-H20]Cl ( x lo-') dioxane(vol%) 20°C 25°C 30°C 35°C 0 7.73 8.04 8.56 8.95 10 10.3 10.7 11.2 12.0 20 10-7 11.4 12.6 13.9 30 9.5 10.1 11.6 13.2 40 8.1 8.6 10.0 11.6 60 3.0 3.5 4.3 5.5 80 2.2 2.2 2.7 3.2 NO,Co(DH),H,O ( x lop3) dioxane(vol%) 15 "C 25 "C 35 "C 45 "C 0 10 20 30 40 50 60 70 80 9.4 12.6 17.0 28.0 41 .O 46.0 49.0 53.0 44.0 10.2 15.4 21.6 31.8 46.6 58.0 65.4 70.2 55.4 12.8 13.8 17.0 20.4 26.0 31.8 41.0 48.0 56.6 68.0 76.6 92.0 91.4 114 90.4 116 70.8 84.0 CH,Co(DH),H,O ( x dioxane(vol%) 15°C 20°C 25°C 30°C 35°C 0 10 20 30 40 50 60 70 80 90 95 2.4 3.1 3.9 5.2 6.9 9.2 11.9 11.2 9.8 6.3 3.3 2.5 3.1 4.2 5.9 7.7 10.0 13.0 14.4 12.7 8.2 4.4 2.6 3.4 4.2 5.9 7.9 10.2 13.3 15.1 15.2 9.0 5.3 2.5 3.2 4.2 6.3 7.0 11.1 13.7 14.7 15.4 10.9 5.8 2.3 3.2 3.5 6.2 8.3 11.1 14.9 16.6 15.4 12.3 7.4 [Co(N,),(en),]ClO, [pyCo(DH),H,O]Cl C1Co(DH),H20 dioxane(vol% ) 25 "C 25 "C 25 "C 0 1.5 x 4.2 x 1.2 x 10-2 20 2.0 x 10-2 5.2 x lov2 2.6 x lop2 45 2.9 x 1.0 x 10-1 5.3 x 70 2.0 x 10- 1.4 x 10-l 7.3 x [rnbimCo(DH),]ClO, bimCo(DH),Cl [mbimCo(D0)(D0H),,H20](C10,), dioxane(vol% ) 25 "C 25 "C 25 "C 0 9.5 x 10-3 0.77 x 10-4 1.2 x 20 2.8 x 4.8 x 10-4 2.9 x 45 1.1 x 10-1 4.0 x 10-3 8.7 x 70 3 .0 ~ 10-1 2.1 x 10- 2.1 x 10-1S . Balt and A . M . van Herk 3335 10 0 " 13 I g -10 c, Y --. a 0 3 u E -20 VJ - 30 -40 I I 1 I I 1 I I I 1 I 20 40 60 80 100 dioxane (~01%) Fig. 1. Transfer Gibbs energies in dioxane-water mixtures at 298.15 K of: ., [Co(N,),(en),]+; a, CpyCo(DH),H,O]+ ; A, ClCo(DH),H,O; +, [ ~ ~ ~ ~ C O ( D O ) ( D O H ) ~ ~ H , O ] ~ + ; A, aquocobal- amin+; x , bimCo(DH,)Cl; + , [mbimCo(DH,)H,O]+; 0, NO,Co(DH),H,O and CH,Co(DH),H,O.Estimated standard deviation (e.s.d.) 0.4 kJ mo1-l. - 51 1 I I 1 0 20 40 60 80 100 acetonitrile (~01%) Fig. 2. Transfer Gibbs energies in acetonitrile-water mixtures at 298.15 K of: 0, [Co(NH,)J3+ and A, aquocobalamin+. E.s.d. 0.5 kJ mol-I. mixtures and in fig. 2 for the acetonitrile-water mixtures.1b,2 The values for the Co(NH,)3,+ ion were calculated from the solubilities of the chloride salt given by Brisset,, together with the transfer Gibbs energies for the chloride ion in acetonitrile-water mixtures given by Kundu et aLl1 From the temperature dependence of the solubilities of NO,Co(DH),H,O, CH,Co(DH),H,O and aquocobalamin chloride in the mixtures, the transfer enthalpy and transfer entropy values were calculated according to (2) 8,G" = 8,H" - mmS0.3336 Solubilities of Aquocobalamin Chloride in Dioxane- Water 4oi 30 CI - 1 P O a 0' 10 0 cg I 20 40 60 80 cosolvent (~01%) Fig. 3.Transfer enthalpy (a) and transfer entropy (b) for: A, aquocobalamin+ in dioxane-water mixtures; A, aquocobalamin+ in acetonitrile-water mixtures; 0, CH,Co(DH),H,O in dioxane- water mixtures and 0, NO,Co(DH),H,O in dioxane-water mixtures. E.s.d. aquocobalamin+ : a,N" 5 kJ mol-l, a m p 16 J K-l mol-l (both mixtures); CH,Co(DH),H,O: 3,W 2.5 kJ mol-l, I a m p 8 J K-l mol-I; NO,Co(DH),H,O:a,W 2 kJ mol-l, a m p 5 J K-l mol-l. The transfer enthalpy values for the chloride ion in dioxane-water mixtures, necessary to calculate the transfer enthalpy values for the aquocobalamin cation, were calculated from values of Bhatnagar;', the transfer entropy values were calculated with these and the transfer Gibbs energies.The results are shown in fig. 3, where for comparison the previously publishedlb transfer values for the aquocobalamin cation in acetonitrile-water mixtures are included. Calculations and Discussion The transfer Gibbs energy curves (fig. 1) all decrease at first on addition of dioxane to water. The more hydrophobic complexes are more strongly stabilized on addition of dioxane. The complexes ClCo(DH),H,O, CH,Co(DH),H,O, [Co(N,),(en),]+ and the aquocobalamin cation show a minimum in transfer Gibbs energy, which is more pronounced for the latter two compounds.The transfer Gibbs energy can be considered as the sum of three tenns:13q14 (a) the cavity term, the energy needed to create a cavity in the solvent of suitable size to accommodate the solute molecule; (b) the coulomb interaction, the Born-type interaction between the charge of the solute and the solvent; (c) the specific interaction, including dispersion interactions and hydrogen bonding : (3) arnGOexp = ~XnG:," + %nG:oul+ aInG&e,. For the metal complexes used here the coulomb term is small [Co(NH,)t+ excepted].S. Balt and A . M. van Herk 3337 The cavity term can be calculated with the scaled particle theory (SPT).l39 l5 G,,, = G, + RT In (RT/ V ) (4) where Y, = (nN/6V) (xlan +x2bn) (n = 1-3) v = (x, M, + x,M,)/do.(7) x, and x, are the mole fractions and M, and M, the molecular weights of the two solvents, do is the density of the solvent mixture, N is Avogadro’s number, a and b are the diameters of the two solvent molecules, D is the diameter of the solute molecule and P is the pressure. The SPT has been successful in predicting transfer Gibbs energies, enthalpies and entropies of large organic solutes and apolar gases.l49 16* l7 Recently this theory was also applied to metal complexes; the partition coefficients of some acetylacetonatometal complexes for the partition between water and an organic phase were successfully calculated.18 Also, solubilities of tris(acetylacetonato)chromium(m) in aqueous alcohol mixtures were calculated with the SPT.19 It has been argued that the SPT cannot be applied to solutes that have strong and directional interactions with the solvent molecules.In that case the additivity of the cavity term and the specific interaction term is questioned.,O In our case the metal complexes do have these specific interactions. We fully recognise the limited applicability of the SPT in this case, but we only want to establish the order of magnitude of the cavity term and not a quantitative agreement between experiment and theory. The following constants were used in the calculation of the cavity term; for the densities of the dioxane-water mixtures those of Griffithsz1 and for the acetonitrile-water mixtures those of Maslan et aL2, The diameters of the cavities that water, dioxane and acetonitrile occupy were taken as 2.76,17 5.2423 and 4.12&17 respectively. The diameters of the cobaloximes could be estimated from the partial molar volume of NO,CO(DH),H,O~~ and the principle of group additivity.25* 26 The same principle was used for [Co(N,),(en),]+, where the crystal structure parameters of [Co(NO,),(en),]+ 27 were taken to estimate the diameter of the complex. The electrostriction was estimated from the relation found by van Eldik28 for cobaltammine complexes. The diameters are given in table 1. These values may not be very accurate, and are only used here for comparison. The cavity energy is not very sensitive to variations in the diameter of the solute, but is very sensitive to .variations in the diameter of the solvent. The partial molar volumes of NO,Co(DH),H,O and aquocobalamin chloride were measured in dioxane-water mixtures and were found to vary by no more than 5 and 2 % , re~pectively.~~ The partial molar volumes of aquocobalamin chloride were also measured in acetonitrile-water mixtures ; in these mixtures a dramatic increase in partial molar volume of 20% was found.24 The cavity term was calculated for this system, using both a constant diameter for aquocobalamin chloride (14.4 A) and a variable diameter, calculated from the partial molar volume in the mixtures.The transfer Gibbs energies of cavity formation were calculated. As expected, there is not much difference for the cobaloximes in the magnitude of the cavity term, the difference between water and 80% dioxane-water v/v being ca.10 kJ mol-l. Aquocobal- amin chloride shows the largest stabilisation caused by the decrease of the cavity term, the difference between water and 80% dioxane-water v/v being 30 kJ mol-l. From the difference between amGZxpm and aGZ,, we find the specific interaction transfer Gibbs energy (amG&,,), which is shown in fig. 4. The amGip,, curve for the small cobaloximes remains almost constant up to 50% dioxane-water v/v, after which3338 30 20 L 10 2 00 i 5 rs E O u) - 10 -20 Solubilities of Aquocobalamin Chloride in Diuxane- Water 20 40 60 80 100 dioxane (~01%) Fig. 4. Transfer Gibbs energies of specific interactions (spec) [calculated with eqn (3) and (4)]. Symbols as used in fig. 1. a destabilisation sets in, probably caused by the loss of hydrogen bonds as a consequence of the replacement of water by dioxane in the second coordination sphere.From the shape of the a,Gip,, curve it can be concluded that the small cobaloximes NO,Co(DH),H,O, CH,Co(DH),H,O and ClCo(DH),H,O are preferentially solvated by water. Aquocobalamin chloride also shows preferential solvation up to 40% dioxane-water v/v, as concluded before.lb An independent indication of the preferential solvation of these complexes can be obtained from 59C0 n.m.r. spectra in the solvent mixtures. The 59C0 n.m.r. chemical shifts are known to be very sensitive to changes in the chemical 30 A decrease in the donor properties of the solvent results in a decrease in electron density at the cobalt ion causing an upfield shift.2s We were able to measure the 59C0 n.m.r.spectra in the mixtures for CH,Co(DH),H,O, for which compound the solubilities are large enough over the whole composition range. The spectra were measured of almost saturated solutions. The linewidth was ca. 6000 Hz. In fig. 5 the chemical shift relative to an external reference of a solution of [Co(NH,),]Cl, in water is shown as a function of solvent composition. In pure dioxane the linewidth of the 59c~ n.m.r. peak almost doubled, indicating a chemical change in the complex, which could be substantiated from the 'H n.m.r. spectra. We were not able to find 59C0 n.m.r. signals for aquocobalamin chloride, NO,Co(DH),H,O and [pyCo(DH),H,O]ClO,. If the amG:pe, term is plotted against the 5BC0 n.m.r. shift for the different mixtures, a straight line is obtained with a correlation coefficient of 0.97 (R).It is clear that both parameters, a,G:pe, and the 59C0 n.m.r. shift, reflect the same changes in the composition of the second coordination sphere. The shape of the i3mG:p,, curves is determined by a balance between hydrophobic and hydrophilic interactions. Aquocobalamin and [Co(N,),(en),]+ show the largestS. Balt and A . M. van Herk 39501 3900 - n E a W GO 3850- 3800- 3339 0 I T 1 I I Fig. 5. sBCo n.m.r. chemical shifts (ppm) of CH,Co(DH),H,O in dioxane-water mixtures at 294.75 K {external reference [Co(NH,),]Cl, in water). 10 0 -10 r( -20 ' -30 2 0 5 -40 - 50 -60 - 70 I - \ u E (0 20 40 60 80 100 acetonitrile (vol k) Fig. 6. Transfer Gibbs energies of cavity formation for aquocobalamin+ in acetonitrile-water mixtures calculated with eqn (4); A, variable diameter for the solute; 0, constant diameter for the solute.destabilisation in the dioxane-rich mixtures, whereas the cobaloximes with large hydrophobic ligands [mbim Co(DH),H,O]+, [mbim CO(DO)(DOH),,H,O]~+, bimCo(DH),Cl and [pyCo(DH),H,O]+, show a stabilisation upon addition of dioxane, up to ca. 50% dioxane-water v/v. Apparently at that composition the gain of hydrophobic interaction energy with dioxane is compensated by the loss of hydrogen-bond energy. The position of the minimum reflects the balance between hydrophobic and hydrophilic groups in the molecule. From this, vitamin B,, can be characterized as a mainly3340 Solubilities of Aquocobalamin Chloride in Dioxane- Water hydrophilic molecule, as reflected also by its general solubility behaviour in several The order of increasing ratio hydrophilic/hydrophobic character as concluded from the amGip,, curves is [rnbimC0(DO)(D0H)~~H,0]~+ > [mbimCo(DH),H,O]+ > bimCo(DH),Cl > [Co(N,),(en),]+ x aquocobalamin+ x [pyCo(DH),H,O]+ > NO,Co(DH),H,O x ClCo(DH),H,O x CH,Co(DH),H,O. The transfer Gibbs energy of the aquocobalamin cation in acetonitrile-water mixtures shows a maximum in the water-rich mixtures (fig.2). This maximum has previously been ascribed to an increase in solvent structure at low acetonitrile contents.,, A roughly similar shape of the transfer Gibbs energy curve in these mixtures is found for [Co(NH3),l3+ (fig. 2). The transfer Gibbs energies of cavity formation for aquocobalamin chloride calculated with either a constant or a variable diameter (calculated from the partial molar volumes) are shown in fig.6. In the latter case a maximum is observed at a higher percentage of acetonitrile than observed for amGzXp. It is not clear whether the partial molar volume changes in the acetonitrile-water mixtures for aquocobalamin chloride are completely caused by the changes in the size of the solute molecule or that other factors are inv01ved.~~~~~ A full discussion of the partial molar volumes of aquocobalamin chloride and NO,Co(DH),H,O will be published ~eparately.,~ We verified that the conclusions are not affected by the choice of the scale for the transfer parameters (i.e. molarity or mole fraction scale). It is not possible to calculate cavity formation contributions to the transfer enthalpy and entropy values in the two mixtures, because the available thermal expansibilities do not cover the entire composition range necessary for these calculations. The a,H" and a m p curves show the familiar compensation effect1s+34 (fig.3). Although the amGZxp values for CH,Co(DH),H,O and NO,Co(DH),H,O are very similar (fig. l), the amH" and amp values differ considerably in the dioxane-rich mixtures. Values for CH,Co(DH),H,O increase in the dioxane-rich mixtures, whereas the values for NO,Co(DH),H,O decrease. The amW and a,So curves for aquocobalamin show a maximum at 60 % dioxane-water v/v. The aquocobalamin cation behaves similarly in the two solvent systems. In the acetonitrile-water mixtures a maximum is present at 10 vol% ,just as in the amGz,, values (fig.2). After 70 vol% organic cosolvent differences occur: values for a,H" and a m p for the aquocobalamin cation decrease more in the dioxane-water mixtures. The solvent dependence of the partial molar volumes of aquocobalamin chloride is totally different in the two solvent systems.24 Therefore it might be interesting to compare the temperature and pressure dependence of the kinetics of axial ligand substitution reactions in the two solvent systems. Maxima and minima in i3,W profiles are generally attributed to changes in solvent structure and solvation/desolvation of the solutes. The nature of the dioxane-water interactions in the water-rich region is still controversial as to whether dioxane enhances or breaks the water s t r u ~ t u r e .~ ~ - ~ ~ When we compare the results for aquocobalamin in dioxane-water and acetonitrile- water mixtures and attribute the maximum at 10 vol% in the amGo values to structure enhancement in acetonitrile-water, then dioxane is effectively a structure breaker when added to water. Both for dioxane and acetonitrile mixtures eventually the structure of water is broken down. The differences in the a,H" and a,S' profiles for the studied compounds between the two solvent systems might be partially attributed to a difference in solvation after 70 vol% cosolvent. We thank Dr E. G. van der Velde, Mr R. J. van de Nesse and Mr I. de Herder for performing some of the measurements and Dr M. W. G. de Bolster for stimulating discussions.S. Balt and A .M. van Herk 3341 References 1 This is Part 5 of the series ‘Effects of Solvent and Ionic Medium on the Kinetics of Axial Ligand Substitution in Vitamin B,,.’ Parts 1-4 are as follows: (a) S. Balt and A. M. van Herk, Trans. Met. Chem., 1982, 8, 152; (b) S. Balt, A. M. van Herk and W. E. Koolhaas, Znorg. Chim. Acta, 1984, 92, 67; (c) S. Balt, M. W. G. de Bolster, C. J. van Garderen, A. M. van Herk, K. R. Lammers and E. G. van der Velde, Znorg. Chim. Acta, 1985,106,43; ( d ) S . Balt, M. W. G. de Bolster and A. M. van Herk, Znorg. Chim. Acta, 1985, 107, 13. 2 J. L. Brisset, J. Chem. Eng. Data, 1982, 27, 153. 3 P. J. Staples and M. L. Tobe, J. Chem. SOC., 1960,4812. 4 A. K. Babko and M. V. Korotun, J. Gen. Chem. U.S.S.R., 1954, 24, 597. 5 G. N. Schrauzer, Znorg. Synth., 1968, 11, 61.6 L. Tschugaeff, J. Russ. Chem. Soc., 1909, 41, 1355. 7 A. V. Ablov and N. M. Samus, Russ. J. Znorg. Chem., 1960,5,410. 8 G. Costa, G. Mestroni and E. de Savorgnani, Znorg. Chim. Acta, 1969, 3, 323. 9 L. M. Ludwick and T. L. Brown, J. Am. Chem. SOC., 1969,91, 5188. 10 C. F. Wells, J. Chem. SOC., Faraday Trans. I , 1978,74, 1569. 1 1 K. K. Kundu and A. J. Parker, J. Solution Chem., 1981,10, 847. 12 0. N. Bhatnagar, Can. J. Chem., 1976,54,3487. 13 R. A. Pierotti, Chem. Rev., 1976,76,717. 14 C. Treiner, P. Tzias, M. Chemla and G. M. Poltoratskii, J. Chem. SOC., Faraday Trans. I , 1976,72,2007. 15 H. Reiss and D. M. Tully-Smith, J. Chem. Phys., 1971, 55, 1674. 16 M. Lucas and A. Feillolay, Bull. SOC. Chim. Fr., 1970, 4, 1268. 17 M. H. Abraham and A. Nasehzadeh, Can. J. Chem., 1979,57,71. 18 H. Watarai, H. Oshima and N. Suzuki, Quant. Struct.-Act. Relat., 1984, 3, 17. 19 M. Yamamoto, Bull. Chem. SOC. Jpn, 1985,58, 1505. 20 N. Morel-Desnoyers and J. Morel, Can. J. Chem., 1981, 59, 1. 21 J. Griffiths, J. Chem. SOC., 1952, 1326. 22 F. D. Maslan and E. A. Stoddard Jr, J. Phys. Chem., 1956,60, 1146. 23 D. Bax, C. L. de Ligny and A. G. Remijnse, Recl. Trav. Chim. Pays-Bas, 1973,92, 374. 24 S. Balt and A. M. van Herk, Znorg. Chim. Acta, 1986, 125, 27. 25 A. Bondi, J. Phys. Chem., 1964,68,441. 26 J. T. Edward and P. G. Farrell, Can. J. Chem., 1975, 53, 2965. 27 0. Bortin, Acta Chem. Scand., 1969,23, 3273. 28 Y. Kitamura and R. van Eldik, Ber. Bunsenges. Phys. Chem., 1984,88,418. 29 G. Gonzalez, U. Mayer and V. Gutmann, Znorg. Nucl. Chem. Lett., 1979, 15, 155. 30 P. Laszlo and A. Stockis, J. Am. Chem. SOC., 1980, 102, 7818. 31 J. M. Pratt, Inorganic Chemistry of Vitamin B,, (Academic Press, New York, 1972). 32 D. A. Armitage, M. J. Blandamer, M. J. Foster, N. J. Hidden, K. W. Morcom, M. C. R. Symons and 33 M. R. J. Dack, Aust. J. Chem., 1976, 29, 779. 34 H. P. Bennett0 and E. F. Caldin, J. Chem. SOC. A , 1971, 2191. 35 C. J. Clemett, J. Chem. SOC. A , 1969, 455. 36 C. J. Clemett, J. Chem. SOC. A , 1969, 761. 37 K. Remerie, Thesis (Groningen, 1984) and references therein. M. J. Wootten, Trans. Faraday SOC., 1968, 64, 1193. Paper 512082; Received 27th November, 1985

ISSN:0300-9599    

DOI:10.1039/F19868203331

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1986,82,3343-3355 The Hydrogen Evolution Reaction under Mixed Kinetic Control A. Saraby-Reintjes Applied Electrostatics Research Group, Department of Electrical Engineering, The University, Southampton SO9 5NH A theoretical description of steady-state current-potential curves for the hydrogen evolution reaction has been given in which the rates of all forward and reverse steps have been taken into account. In addition to the limiting ranges of quasi-equilibrium and coupled reactions, the treatment includes the intermediate interval in which the Tafel relationship is not linear, and the reaction order with respect to H+ ions can have fractional values which vary with the potential. The derivation of volcano curves according to Parsons and Gerischer has been extended to the case of mixed control by the kinetics of the first and second steps.By combining the assumptions underlying the theory of volcano curves with the derivation of polarisation curves, it is possible to deduce the dependence of these polarisation curves on the nature of the metal. It appears that Tafel slopes are determined primarily by the potential range in which hydrogen evolution is studied, but are in addition dependent on the free energy of adsorption of hydrogen; these predictions are supported by experimental data. The theory further confirms that the customary volcano curve only indicates the catalytic activity at the standard potential, but that at more negative potential the highest rate of hydrogen evolution is found on a metal with a low positive free energy of adsorption of hydrogen.It is generally accepted that the first step in the hydrogen evolution reaction (HER) is the Volmer (discharge) reaction which involves the formation of adsorbed hydrogen (H), and that it is followed by either the Heyrovsky (ion+atom) reaction, or the Tafel (recombination) reaction : k+l H+ +e- (H) k-1 k+3 2 (H) H,. (3) k-3 It is usually assumed that the forward rate of one of these reactions is rate-determining in the overall reaction mechanism. This approach has the advantage that the kinetics of the HER can be described by linear Tafel relationships and constant reaction orders. Such conditions apply over wide potential ranges and kinetic parameters thus predicted often represent experimental data for the HER well.However, there is a potential interval connecting the range of quasi-equilibrium for reaction (1) on the one hand, and of coupled first and second steps on the other, in which the overall rate of the HER is 33433344 Hydrogen Evolution Kinetics under mixed control by the kinetics of the first and second steps. Here the Tafel relationship is not linear, and reaction orders have fractional values which vary with the potential. It is the aim of this paper to give a theoretical description of the HER by the Volmer-Heyrovsky (V-H) and the Volmer-Tafel (V-T) reaction mechanisms under steady-state conditions, in which the kinetics of all forward and reverse steps are taken into account. Since the various rate constants are related to the free energy of adsorption of hydrogen, it is possible to indicate the dependence of polarisation curves for the HER on the nature of the metal.A description of volcano curves under mixed kinetic control will also be given. It will be assumed for the sake of simplicity that (H) is the only adsorbed species, that all adsorption sites are energetically equivalent and that the hydrogen coverage OH follows a Langmuir isotherm. Double-layer effects and mass-transfer restrictions will be neglected. It will moreover be assumed that reactions (2) and (3) do not occur simultaneously in competition with each other. Current-Potential Curves The Volmer-Heyrovsky Reaction Mechanism The kinetic treatment developed for the anodic dissolution of the iron-group metals, can be applied to the V-H mechanism with minor modifications.The steady-state condition deH/dt = 0 is given by Here E is the electrode potential referred to the standard H2/H+ potential (V), the quantities k are the rate constants in eqn (1)-(3) at the reference potential (mol cm-2 s-l), pH2 is the hydrogen gas pressure (atm),* [H+] the activity of H,O+ ions in the solution, and F, R and T have their usual meanings. It will be assumed that the symmetry factors a, and a, for reactions (1) and (2) are both 0.50. The number of potential-dependent terms in the expression for OH is reduced to two if one introduces two new potential- dependent parameters : Hence (7) This quantity varies from k+,/k+, at low E, where P 6 1 and Q 4 1, to k-2PH2/k-1 at high E, where P 9 1 and Q 9 1. The overall (cathodic) current density iH is given by iH -UFE F - = (1 - Q) k+,[H+] (1 - 0,) exp ( F ) + (1 - P) k+,[H+]OH exp * 1 atm = 101 325 Pa.A .Saraby- Reintjes 3345 With the aid of eqn (7) this becomes: -aF k+,[H+I exp (r? i~ - 2(1-pQ) F- (P+1) (9) If H, is absent from the system and newly formed H, is continually removed from the electrode surface, e.g. by the action of an inert gas, the parameter Q approaches zero. 2 - aFE The equation 1H - - (P+l) -- k+, (P + 1) k+2 1+ F describes the polarisation curve for the HER in the absence of H, in an extended potential range. Kinetic parameters such as the Tafel slope b, = (6E/S logi,) and the reaction order with respect to H+ ions v,+ = (6 log iH/6 log [H+])E are obtained by differentiation of eqn (10): 2.303 61niH F P - _---- - b, 6E RT It has been pointed out by Parsons that the overall logi, vs.E curve for the V-H mechanism contains two linear sections., At the positive side one finds the quasi- equilibrium range with b, = -40 mV per decade and v,+ = 2; this corresponds to [P/(P+ 1)](1- 8,) + 1. This range is found when P % (1 +k+,/k+,).* At sufficiently negative potentials the term [P/(P+ l)] (1 - 8,) 0; this condition corresponds to P 4 (1 +k+,/k+,). In this potential range reactions (1) and (2) are coupled, and the kinetic parameters are b, = - 120 mV per decade and v,+ = 1 ; the coverage 1 9 ~ approaches a limiting value, the magnitude of which depends on the ratio k+,/k+, only and is independent of the pH.,, The transition range in which the kinetic parameters have intermediate values, i.e.- 120 < b, < -40 mV per decade and 1 < vH+ < 2, is charac- terised by say 0.1(1 +k+l/k+2) < P < lO(1 +k+,/k+,) and extends in this case over 120 mV and two decades of current. The exact shape of the complete iH-E curve as predicted by eqn (10) and its dependence on the nature of the metal will be discussed at a later point in this paper. The Volmer-Tafel Reaction Mechanism If desorption of (H) occurs by recombination and it is assumed that surface diffusion of (H) is not a rate-determining factor, the steady-state condition (68,/62) = 0 is given by For given values of rate constants, this quadratic equation can be solved for &. The cathodic current density is: Strictly speaking, the condition of quasi-equilibrium for reaction (1) is given by P B 1, but Tafel slopes of -40 mV per decade require the additional condition that (P+ 1) B k+,/k+,.3346 I A Hydrogen Evolution Kinetics eH 0.8 :I 02 200 100 0 -100 -200 EImV c 1 I 2 00 Id0 0 -100 -200 Fig.1. A. The coverage 8, as a function of the potential E for the Volmer-Tafel reaction mechanism in the absence of H,, calculated using eqn (13) for [H+] = 1, k+,/k-, = 1 and the following values for the ratio k+3/k+l: (a) 0.1, (b) 1, (c) 10, ( d ) lo2, (e) los, cf) lo4 and (g) lo5. B. The current-potential curves for the HER by the Volmer-Tafel mechanism calculated using eqn (1 5 ) with use of the ratios k+,/k+, and the coverages of fig. 1 A. E/ mV If H, is absent from the system, and newly formed H, is continually removed from the electrode surface, e.g.by the action of an inert gas, the term k-,pHz( 1 - eH), approaches zero. The steady-state current density is then also given by = k+,ek. F Hydrogen coverages and iH-E curves calculated for various values of k+, are shown in fig. 1. All iH-E curves are in principle characterised by Tafel slopes ranging from -30 mV per decade at high E, where the Volmer reaction is in quasi-equilibrium, toA . Saraby - Reintjes 3347 -a mV per decade at low E. The current becomes independent of E and pH when 8, + 1. There is in this case also a transition range with non-hear Tafel relationships; this range becomes wider as k+, increases. At sufficiently high values of k,, part of the i H - E curve in the transition range approaches a Tafel line with a slope of - 120 mV per decade.In this case iH is effectively given by the first term in eqn (14), 8, is low and Tafel slopes of - 120 mV per decade in combination with v,+ = 1 can thus occur with both the VIH and the V-T reaction mechanisms. There are, however, some characteristic differences in 8,: (a) in the V-H mechanism 8, is constant and can have any value between 0 and 1. Limiting coverages in the range 0.1 < 8, -c 0.9 are possible if k+, and k,, differ by less than one order of magnitude; this may be the case for the HER on Cu and Ag.4 (b) In the V-T mechanism 8, is low and varies with the potential at the rate (6 log8,/6E) = - 1/240 mV-l. v,+=+l. Volcano Curves It has been recognised for many years that there is a direct correlation between the exchange current density on a metal M and the strength of the M-H bond, expressed as the free energy of adsorption AGads.5-15 It is customary to associate AG,,, = 0 with an equilibrium coverage of 0.50 under standard conditions ([H+] = 1, pH2 = 1 atm, E = 0) The subscript eq denotes equilibrium values. Volcano curves which express the relationship between the exchange rates of the individual reactions (l)-(3) at equilibrium and AGads have been derived in ref.(lo)-( 15). Appleby predicts volcano curves for various combinations of rate-determining s t e p P The treatment by Parsons and Gerischer will be extended in this paper to include mixed control by the kinetics of the first and second steps. If in a diagram of potential energy vs. the reaction coordinate the curve associated with (H) moves up by AG,,, from its original position at AG,,, = 0 without loss of shape,6 then the relations between the various rate constants and AGads are given by Here the superscript O denotes rate constants for a metal with AG,,, = 0 and p,, p, and 2p3 indicate by what fraction of AG,,, the heights of the activation energy barriers for reactions (1)--(3) have been increased.The symmetry factors p1 and /3, are essentially equal to a, and (1 - a,). The value of p is predicted to range from 1 at high positive AG,,, to 0 at high negative AG,,,, and to equal ca. 0.5 when AG,,, = 0.11-15 In the present discussion it will be assumed for the sake of simplicity that p1 = p2 = p3 = /? = 0.50. The equilibrium condition for the V-H mechanism is [according to eqn (9)] given by Peq Qe, = 1 ; this yields the Nernst equation for the equilibrium potential.The dependence3348 Hydrogen Evolution Kinetics AG,&/kcal mol" , -3: -2.0 -I? 7 I? 2 0 3,O 0 - -5 - n O i r( 5 .... W M c( -10 - -1 5 -120 -80 -40 0 40 80 120 AG,&/kJ mol" Fig. 2. Volcano curves for the Volmer-Tafel and Volmer-Heyrovsky reaction mechanisms, calculated using eqn (30) and (23), respectively. (a) Volmer-Tafel mechanism. Volmer-Heyrovsky reaction mechanism for the following ratios k;,/k",: (b) (a) 1 and (c) lo3. AGads has been given in kJ mol-1 as well as in kcal mol-l. of the standard exchange current density io on AG,,, is obtained by combining eqn (9) and (17) to (20), and taking [H+] = 1, pH2 = 1 atm, E = 0 and Qeq = l/Peq: Eqn (23) represents the volcano curve for the V-H mechanism; Peq is independent of AG,,, if p1 = B2.The dependence of i, on AG,,, is obtained by differentiating eqn (23) and can be written 1 1 -- - -- +-9,. 6 In i, a&,,, 2RT RT The maximum of this volcano curve is characterised by OH = 0.50 and AGads = 0; i, at the maximum equals Fig. 2 shows volcano curves for the V-H mechanism calculated for the ratios k"+l/I~:~ = 1 and lo3. The exchange current density for the overall V-H reaction mechanism can be expressed in terms of the exchange current densities (i,)l and (i0)2 of the individual steps (1) and (2):A . Saraby-Reintjes 3349 Since Peg = (iO)J(iO),, this can also be written The exchange c.d. approaches 2F(i0)l if (i0)2 density i; (io)l, and 2F(i0)2 if (io)l b (iO),.The equilibrium for the V-T mechanism is characterised by an exchange current in which The standard exchange c.d. io is derived with the aid of eqn (17), (18), (21) and (22); it can be written which is equal to (io)l. The exchange rate of the V-T mechanism at equilibrium is therefore entirely controlled by the Volmer reaction and is independent of the rate of the Tafel reaction. The maximum of this volcano curve is characterised by 8, = Q.50, AG,,, = 0 and io = iFkTl. The position of the volcano curve for the V-T mechanism relative to that for the V-H mechanism is illustrated in fig. 2. Before drawing conclusions regarding the rate of the HER in the cathodic range from the position and the shape of the volcano curves, one must examine to what extent the rate of a two-step electrocatalytic reaction is defined by its exchange c.d.and its Tafel slope. The points to be considered are: (a) whether the volcano curve at E # 0 differs from that at E = 0 as a result of the potential dependence of Tafel slopes and (b) whether reaction rates at equilibrium under standard conditions are representative of steady-state conditions in the cathodic range and specifically whether the cathodic current is independent of pH2. Parsons has extended the calculation of volcano curves to the cathodic range and has found that in the case of variable a and B the maximum shifts to positive AGads.15 A similar procedure will be followed in the next section for mixed kinetic control with a and /3 equal to 0.50 and a similar result will be obtained.Appleby also predicts potential dependence for the maxima of his volcano curves.lS Let us first consider steady-state and equilibrium conditions for the V-H mechanism. According to eqn (7) and (9), the dependence of OH and iH on pHa is contained in the parameter Q in the denominator. It is likely that Qeq under standard conditions equals ca. 10-3.17 If Q 6 1 at E < 0 when pH2 = 1 atm as well as when pH2 + 0, 8, and iH can be considered independent of pH2, provided pH2 does not become very high. The partial cathodic current for pH2 = 1 atm is thus practically identicai with the cathodic current in the absence of H,. The use of volcano curves for the V-H mechanism as a basis for describing the HER in the cathodic range is therefore justified. The situation is considerably more complicated in the case of the V-T mechanism.In the presence of 1 atm H, the Volmer reaction is rate-determining at E = 0, but at E # 0, 8, is under mixed control by the kinetics of reactions (1) and (3) and so is the steady-state current. The extra adsorption term k3pH2( 1 - causes OH to be higher in the presence of H, than in its absence; H, thus decreases the partial cathodic current and increases the partial anodic current. For instance, for a metal with AG,,, = 0 and3350 Hydrogen Evolution Kinetics a ratio kT3/kTl = a, immersed in a solution of [H+] = 1, one can calculate that OH at E = 0 in the absence of H, amounts to 0.49, 0.41, 0.23 and 0.09 for a = 0.1, 1, 10 and 100, respectively, while O, under standard conditions equals 0.50 for any value of a.If a is high, 8, in the vicinity of the equilibrium potential is chiefly controlled by reaction (3) and is practically constant; the value of OH exhibits a marked dependence on pH2. If a is low, say a < 0.1, the variation in OH due to changes in pH2 is negligible, but the quasi-equilibrium condition for reaction (1) would result in a net current at either side of the equilibrium potential which is practically zero. Since the rate of the HER by the V-T mechanism is under mixed kinetic control under non-equilibrium conditions and since the pressure of molecular hydrogen can affect and iH, the conclusion must be drawn that the volcano curve for the Volmer-Tafel mechanism is only of limited use in the prediction of the rate of hydrogen evolution under non-equilibrium conditions.The Dependence of Polarisation Curves on AGads It is possible to express the simultaneous dependence of iH on E, pH and AG,,, by substituting the values of the rate constants in eqn (17)-(22) into the equations for OH and iH for either reaction mechanism. If reasonable estimates can be made for the rate constants on a metal with known AG,,, (preferably AG,,, = o), then it is in principle possible to calculate iH-E curves for all other values of AGads. The HER by the V-H mechanism in the absence of H, will be considered in more detail. By combining eqn (lo), (17) and (19) one obtains for the steady-state current density 2 -BAG,,, exp - aFE iH (P+l) k:~[Hilexp( RT ) ( RT ) _ - F - Likely estimates for P and for the ratio of rate constants are P = lo3 at E = 0 and k:Jk:, = 103.109 l7 The polarisation curves which can thus be calculated for various AG,,, are shown in fig.3. These iH-E curves resemble each other in shape; each consists of two linear sections with Tafel slopes of -40 and - 120 mV per decade and an intermediate part with a non-linear Tafel relationship. The height and location of the iH-E curves is related to AGads. It will be shown in the discussion that it is possible to formulate general predictions regarding the dependence of experimental Tafel slopes on the nature of the metal on the basis of the polarisation curves in fig. 3. Since iH at E = 0 is practically equal to i,, additional information on i, can be obtained. The volcano curve for the V-H mechanism can be recognised in the values of iH at E = 0 in fig.3. The standard potential is situated in the range in which P + (1 +k+,/k+,) and where b, = -40 mV per decade on metals with high positive AG,,,, in the range in which P 6 (1 + k+Jk+,) and where b, = - 120 mV per decade on metals with high negative AG,,, and in the transition range when AG,,, has low positive or negative values. As a result the volcano curve at E # 0 will differ from that at E = 0. Plots of logiH vs. AG,,, at E # 0, derived from fig. 3, are shown in fig. 4. They form a family of volcano curves in which the maximum shifts to higher AG,,, as E becomes more negative. By differentiating eqn (31) one obtains for the dependence of iH on AGads :A . Saraby-Reintjes 3351 P EImV Fig. 3. Polarisation curves for the HER according to the Volmer-Heyrovsky mechanism as a function of the free energy of adsorption of hydrogen, calculated using eqn (31) for the data k:l/k:2 = lo3, [H+] = 1, P = lo3 at E = 0 and various values of AG,,, which are marked in the figure (kJ mol-l).AG,d$kJ mol-' Fig. 4. Volcano curves for equilibrium and non-equilibrium conditions. Values of log i, derived from fig. 3 at constant potential are plotted us. AG,,, (kJmol-l). The potentials are, on the hydrogen scale: (a) 360, (b) 240, (c) 120, ( d ) 0, (e) - 120, df) -240 and (g) - 360 mV. Points with coverage OH = 0.50 have been connected by a dotted line. 111 FAR 13352 Hydrogen Evolution Kinetics Since p has been assumed equal to 0.50, it follows that the maximum for each volcano curve is found at 8, = 0.50.The value of AG,,, at the maximum follows from At low E, when P 4 1, AG,,, at the maximum becomes independent of E ; for the assumed value k:l/k:2 = lo3, AGads then attains the value of 17.1 kJ mol-l. Discussion The variety of kinetic parameters for the HER has given rise to the belief that a characteristic mechanism exists for the HER on different groups of metals. Thus it is generally believed that the Volmer reaction is rate-determining on metals with high AG,,, (low 8,) such as Hg, Pb, Sn and T1. The second step of the HER is considered rate-determining on most other metals, whereby the Volmer reaction is either assumed to be in quasi-equilibrium, or so fast that OH + 1. These conclusions are to a large extent based on experimental Tafel slopes. The application of a Temkin isotherm has been recommended for Tafel slopes of -60 mV per decade.The assumption of mixed kinetic control allows a more unified interpretation of iH-E relations. Let us for the moment assume that the HER occurs through the V-H mechanism on all metals. Metals can then be divided roughly into four groups on the basis of the factors which determine their Tafel slopes. In three of these b, = - 120 mV per decade; according to eqn (1 1) this means that either P 4 1 or OH + 1. The predictions for each group agree well with experimental data. Base Metals If P x lo3 at E = 0 under standard conditions, the condition of e.g. P < is obeyed when E -= - 300 mV. Since the HER can only be studied at the negative side of the corrosion potential, Tafel slopes of -12OmV per decade are therefore to be expected in the first place on base metals, and have indeed been observed on such metals as Zn, Fe, Cd and T1.Metals with High Positive AG,, The HER on metals with high AG,,, and low i, is usually studied at high overpotential where again E < - 300 mV. Tafel slopes of - 120 mV per decade have been observed on Hg, Pb and Sn. However, lower values of -b, have been reported for the HER on Hgl89l9 and Pb,20 when the range of measurements was extended towards lower overpoten tials. Metals with High Negative AGads The condition OH + 1 indicates low AG,,,. It can be seen in fig. 3 that the potential range of b, = - 120 mV per decade is considerably extended towards positive potentials when A(?,,, has a high negative value.Tafel slopes of - 120 mV per decade are therefore predicted for the HER on such metals as Ta, Ti and Mo and have been reported for Cr and Ti. Lower values of -be may, however, be encountered at more positive potentials where 8, < 1. Non-base Metals with Intermediate AG,, It follows from the above that values of -b, below 120 mV per decade are most likely to be found on non-base metals with low positive or negative AG,,,. Examples of metalsA . Sa raby - Re in tjes 3353 in this group, in order of increasing nobility, are Co < Ni < Cu < Te < Rh < Ag < Pd < Pt c Ir < Au and W. AG,,, probably decreases in the order Au > Ag > Cu > Fe > Co, Ni > Pt, Pd, Rh, Ir. For the HER on many of these metals a range of Tafel slopes is possible. Thus, while - b, is still close to 120 mV per decade for Ni and C0,21-35 data reported for Cu range from 53 to 120 mV per decade,26’ 36-40 for W from 60 to 116 mV per decade,,l9 41-45 for Te from 44 to 115 mV per 46 for Ag from 58 to 120 mV per decade,4* 26y 4 2 9 4 3 9 47-50 for Au from 30 to 120 mV per decade26* 369 51-59 and for the noble metals Re, Rh, Pd, Pt and Ir from 27 to 120 mV per decade.,,, 26v 36* 41-43v 5 7 9 60-76 Many investigators have observed that there is no simple linear Tafel relationship for these metals; data have often been represented as two straight lines.The agreement between predicted behaviour and experimental data lends support to the conclusion that the Tafel slope is determined in the first place by the potential range in which the HER is studied and in the second place by the free energy of adsorption of hydrogen. The discussion for the V-T mechanism follows in principle along the same lines and yields similar conclusions.The analysis of steady-state iH-E curves can provide an estimate of those rate constants which play a role in the overall rate of the HER. Data thus obtained on the basis of the simplifying assumption that all symmetry factors equal 0.50 must then be compared with and supplemented by information from non-steady-state methods. It is well known that extrapolation of linear sections of the log iH us. E curves to E = 0 can yield k+, or k,, for the V-H mechanism and k+, or k+, for the V-T mechanism. In the case of the V-H mechanism it is in principle possible to obtain estimates for k-l/k+2 and k+,/k+, from the intersection of Tafel lines with b, = -40 and - 120 mV per decade.It can be derived from eqn (10) that at the potential of intersection P = (1 +k+,/k+,). If the potential at which P = 1 is found first with the aid of a metal with very low k+,/k+,, then the ratio k+,/k+, for other metals follows from the positive potential shift of the potential of intersection: AE = - RT In ( 1 + 2). F (34) P is the same for all metals if p1 = B2 and is a measure for the ratio k-,/k+,. The rate of the HER on metals with very low k+,/k+, is completely defined by k,, and P; the ratio k+,/k+, cannot, therefore, be extracted from their steady-state iH-E curves. Unfortunately, the entire iH-E curve is not often accessible to measurement.In the case of iH-E curves containing part of the transition range, one may still be able to make use of the prediction by the theory that 6 , = - 60 mV per decade at the potential at which P = (1 + k+,/k+,), though the accuracy is naturally lower. If only Tafel lines with 6, = - 120 mV per decade are available, one may have to resort to measuring steady-state iH--E curves under conditions of continuous surface renewal.,’ If k+, 9 k+,, extrapolation of the Tafel line on the unscoured electrode to E = 0 will yield k+,, and on the scoured electrode at sufficiently high scouring rates k+,. Conclusion The description of the HER based on mixed control by the kinetics of the first and second steps is capable of interpreting many aspects of this reaction, even under the simplifying assumptions made at the outset.There is no need to restrict the description of the HER to limiting conditions only, since a complete treatment of steady-state current-potential curves for the V-H and V-T mechanisms can be given, which covers an extended potential range and, moreover, takes the free energy of adsorption of the intermediate into account. 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ISSN:0300-9599    

DOI:10.1039/F19868203343

出版商:RSC    

年代:1986

数据来源: RSC