摘要:

Gas Kinetics Group and Division de Chimie-Physique de la Societe Francaise de Chimie 9th International Symposium on Gas Kinetics To be held in Bordeaux, France on 20-25 July 1986 Further information from Dr R. Lasclaux, Lab. Photophys. Photochim. MolBculaire, Universite de Bordeaux I, 33405 Talence Cedex, France Poiymer Physics Group Biologically Engineered Polymers To be held at Churchill College, Cambridge on 21-23 July 1986 Further information from Dr M. J. Miles, AFRC,Food Research Institute, Colney Lane, Norwich NR4 7UA Polymer Physics Group with the British Rheological Society Deformation in Solid Polymers To be held at the University of Leeds on 9-1 1 September 1986 Further information from Dr J. V. Champion, Department of Physics, City of London Polytechnic, 31 Jewry Street, London EC3N 2EY ~~_____________ ~~~~ Carbon Group Carbon Fibres- P ro pe rt i es and A p p I i cat i o ns To be held at the University of Salford on 1 5 1 7 September 1986 Further information from The Meetings Officer, The Institute of Physics, 47 Belgrave Square, London SW1 X 8QX ~ ~~~~~~~~ ~ Division with the Surface Reactivity and Catalysis Group-Autumn Meeting Promotion in Heterogeneous Catalysis To be held at the University of Bath on 23-25 September 1986 Further information from: Professor F.S. Stone, School of Chemistry, University of Bath, Bath BA2 7AY (viii)Gas Kinetics Group and Division de Chimie-Physique de la Societe Francaise de Chimie 9th International Symposium on Gas Kinetics To be held in Bordeaux, France on 20-25 July 1986 Further information from Dr R.Lasclaux, Lab. Photophys. Photochim. MolBculaire, Universite de Bordeaux I, 33405 Talence Cedex, France Poiymer Physics Group Biologically Engineered Polymers To be held at Churchill College, Cambridge on 21-23 July 1986 Further information from Dr M. J. Miles, AFRC,Food Research Institute, Colney Lane, Norwich NR4 7UA Polymer Physics Group with the British Rheological Society Deformation in Solid Polymers To be held at the University of Leeds on 9-1 1 September 1986 Further information from Dr J. V. Champion, Department of Physics, City of London Polytechnic, 31 Jewry Street, London EC3N 2EY ~~_____________ ~~~~ Carbon Group Carbon Fibres- P ro pe rt i es and A p p I i cat i o ns To be held at the University of Salford on 1 5 1 7 September 1986 Further information from The Meetings Officer, The Institute of Physics, 47 Belgrave Square, London SW1 X 8QX ~ ~~~~~~~~ ~ Division with the Surface Reactivity and Catalysis Group-Autumn Meeting Promotion in Heterogeneous Catalysis To be held at the University of Bath on 23-25 September 1986 Further information from: Professor F. S. Stone, School of Chemistry, University of Bath, Bath BA2 7AY (viii)

ISSN:0300-9599    

DOI:10.1039/F198581FX013

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

xxxij AUTHOR INDEX Singh, Km. S., 751 Sircar, S., 1527, 1541 Slade, R. C. T., 847 Smith, I. G., 1095 Snelling, C. M., 1761 Sobczyk, L., 311 Siiderberg, D., 17 15 Solar, S., 1101 Solar, W., 1101 Soma, M., 485 Somorjai, G. A., 1263 Somsen, G., 1015 Sorek, Y., 233 Souto, F. A., 2647 Spencer, S., 2357 Spichiger-Ulmann, M., 7 13 Spoto, G., 1283 Spotswood, T. M., 1623 Srivastava, R. D., 913 Stachurski, J., 1447, 2813 Staricco, E. H., 1303 Stock, T., 2257 Stockhausen, M., 397 Stokes, R. H., 1459 Stone, F. S., 1255 Strachan, A. N, 1761 Strohbusch, F., 2021 Stuckless, J. T., 597 Su, Z., 2293 Subrahmanyam, V. S., 1655 Sugimoto, N., 1441, 2959 Suminaka, M., 2287 Suprynowicz, Z., 553 Sutcliffe, L. H., 679, 1467, 1215 Suzanne, J., 2339 Suzuki, H., 3117 Swallow, A. J., 1225 Symons, M.C. R., 433, 565, 727, 2131, 2775, 1095, 1963, 242 1 Takagi, Y., 1901 Takahashi, Y., 3 117 Takeshita, H., 2805 Tamilarasan, R., 2763 Tamura, K., 2287 Tanaka, T., 1513 Taniewska-Osinska, S., 695, Tascon, J. M. D., 939, 2399 Taylor, M. J., 1863 Taylor, N., 2357 Tejuca, L. G., 939, 2399, 1203 Teller, R. G., 1693 Tempere, J-F., 1357 Teramoto, M., 2941 Theocharis, C . R., 857 Thomas, J. K., 735 Tielen, M., 2889, 3049 Tindwa, R. M., 545 Tissier, C., 3081 Toi, K., 2835 Tokuda, T., 2835 Torrez-Mujica, T., 343 Townsend, R. P., 1071, 173 1, Trasatti, S., 2995 Treiner, C., 2513 Trenwith, A. B., 745 Trifiro, F., 1003 Troncoso, G., 1631, 1637 Tseung, A. C. C., 1883 Tuck, J. J., 833 Turner, J. E., 1263 Uemoto, M., 2333 Uma, K., 2733 Valencia, E., 1631. 1637 Valigi, M., 813 Vallmark, T., 1389 Van Oort, M.J. M., 3059 Varma, M. K., 751 Vattis, D., 2043 Vecli, A., 433 Veseli, V., 2095 Vink, H., 1677, 1725 Vliers. D. P., 2009 Vukovid, Z., 1275 3081, 1913 3127 Waghorne, W. E., 2703 Ward, A. J., 2975 Watanabe, H., 1569 Waugh, K. C., 3073 Weckstrorn, K., 2947 Weinberg, N. N., 875 Weingartner, H., 1031 Wells, C. F.. 801, 1057, 1401, White, M. A., 3059 Williams, J. O., 271 1 Williams, P. A., 2635 Williams, P. B., 3067 Williams, R. T., 847 Wojcik, D., 1037 Wood, G. L., 265 Wood, R. M., 273 Woolf, L. A., 769, 2821 Wright, C. J., 2067 Wright, J. P., 1471 Wright, T. H., 1819 Wurie, A. T., 2605 Yadav, G. D., 161 Yadava, R. D., 751 Yamaguchi, M., 1513 Yamaguti, K., 1237 Yamasaki, S., 267 Yamashita, H., 2485 Yamatera, H., 127 Yelon, W., 1693 Yoshida, S., 1513, 2485 Yoshikawa, M., 2485 Zambonin, P.G.. 621 zdanov, S. P., 2541 Zecchina, A., 1283 Zelano, V., 2365 Zhan, R. Y., 2083 Zhao, Z., 185 Zhulin, V. M., 875 Zilnyk, A., 679, 1215 Zulauf, M., 2947 Zundel, G., 1425, 2375 1985. 2145, 2475, 3091xxxij AUTHOR INDEX Singh, Km. S., 751 Sircar, S., 1527, 1541 Slade, R. C. T., 847 Smith, I. G., 1095 Snelling, C. M., 1761 Sobczyk, L., 311 Siiderberg, D., 17 15 Solar, S., 1101 Solar, W., 1101 Soma, M., 485 Somorjai, G. A., 1263 Somsen, G., 1015 Sorek, Y., 233 Souto, F. A., 2647 Spencer, S., 2357 Spichiger-Ulmann, M., 7 13 Spoto, G., 1283 Spotswood, T. M., 1623 Srivastava, R. D., 913 Stachurski, J., 1447, 2813 Staricco, E. H., 1303 Stock, T., 2257 Stockhausen, M., 397 Stokes, R. H., 1459 Stone, F. S., 1255 Strachan, A.N, 1761 Strohbusch, F., 2021 Stuckless, J. T., 597 Su, Z., 2293 Subrahmanyam, V. S., 1655 Sugimoto, N., 1441, 2959 Suminaka, M., 2287 Suprynowicz, Z., 553 Sutcliffe, L. H., 679, 1467, 1215 Suzanne, J., 2339 Suzuki, H., 3117 Swallow, A. J., 1225 Symons, M. C. R., 433, 565, 727, 2131, 2775, 1095, 1963, 242 1 Takagi, Y., 1901 Takahashi, Y., 3 117 Takeshita, H., 2805 Tamilarasan, R., 2763 Tamura, K., 2287 Tanaka, T., 1513 Taniewska-Osinska, S., 695, Tascon, J. M. D., 939, 2399 Taylor, M. J., 1863 Taylor, N., 2357 Tejuca, L. G., 939, 2399, 1203 Teller, R. G., 1693 Tempere, J-F., 1357 Teramoto, M., 2941 Theocharis, C . R., 857 Thomas, J. K., 735 Tielen, M., 2889, 3049 Tindwa, R. M., 545 Tissier, C., 3081 Toi, K., 2835 Tokuda, T., 2835 Torrez-Mujica, T., 343 Townsend, R.P., 1071, 173 1, Trasatti, S., 2995 Treiner, C., 2513 Trenwith, A. B., 745 Trifiro, F., 1003 Troncoso, G., 1631, 1637 Tseung, A. C. C., 1883 Tuck, J. J., 833 Turner, J. E., 1263 Uemoto, M., 2333 Uma, K., 2733 Valencia, E., 1631. 1637 Valigi, M., 813 Vallmark, T., 1389 Van Oort, M. J. M., 3059 Varma, M. K., 751 Vattis, D., 2043 Vecli, A., 433 Veseli, V., 2095 Vink, H., 1677, 1725 Vliers. D. P., 2009 Vukovid, Z., 1275 3081, 1913 3127 Waghorne, W. E., 2703 Ward, A. J., 2975 Watanabe, H., 1569 Waugh, K. C., 3073 Weckstrorn, K., 2947 Weinberg, N. N., 875 Weingartner, H., 1031 Wells, C. F.. 801, 1057, 1401, White, M. A., 3059 Williams, J. O., 271 1 Williams, P. A., 2635 Williams, P. B., 3067 Williams, R. T., 847 Wojcik, D., 1037 Wood, G. L., 265 Wood, R. M., 273 Woolf, L. A., 769, 2821 Wright, C. J., 2067 Wright, J. P., 1471 Wright, T. H., 1819 Wurie, A. T., 2605 Yadav, G. D., 161 Yadava, R. D., 751 Yamaguchi, M., 1513 Yamaguti, K., 1237 Yamasaki, S., 267 Yamashita, H., 2485 Yamatera, H., 127 Yelon, W., 1693 Yoshida, S., 1513, 2485 Yoshikawa, M., 2485 Zambonin, P. G.. 621 zdanov, S. P., 2541 Zecchina, A., 1283 Zelano, V., 2365 Zhan, R. Y., 2083 Zhao, Z., 185 Zhulin, V. M., 875 Zilnyk, A., 679, 1215 Zulauf, M., 2947 Zundel, G., 1425, 2375 1985. 2145, 2475, 3091

ISSN:0300-9599    

DOI:10.1039/F198581BX015

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

JOURNAL OF THE CHEMICAL SOCIETY FARADAY TRANSACTIONS, PARTS I AND I 1 The Journal of the Chemical Society is published in six sections, of which five are termed Transactions; these are distinguished by their subject matter, as follows: Dalton Transactions (Inorganic Chemistry). All aspects of the chemistry of inorganic and organometallic compounds; including bioinorganic chemistry and solid-state inorganic chemistry ; of their structures, properties, and reactions, including kinetics and mechanisms; new or improved experimental techniques and syntheses. Faraday Transactions I (Physical Chemistry). Radiation chemistry, gas-phase kinetics, electrochemistry (other than preparative), surface and interfacial chemistry, heterogeneous catalysis, physical properties of polymers and their solutions, and kinetics of polymerization, etc.Faraday Transactions II (Chemical Physics). Theoretical chemistry, especially valence and quantum theory, statistical mechanics, intermolecular forces, relaxation phenomena, spectroscopic studies (including i.r., e.s.r., n.m.r., and kinetic spec- troscopy, etc.) leading to assignments of quantum states, and fundamental theory. Studies of impurities in solid systems. Perkin Transactions I (Organic Chemistry). All aspects of synthetic and natural product organic, organometallic and bio-organic chemistry, including aliphatic, alicyclic, and aromatic systems (carbocyclic and heterocyclic). Perkin Transactions II (Physical Organic Chemistry). Kinetic and mechanistic studies of organic, organometallic and bio-organic reactions.The description and application of physicochemical, spectroscopic, and theoretical procedures to organic chemistry, including structure-activity relationships. Physical aspects of bio-organic chemistry and of organic compounds, including polymers and biopolymers. Authors are requested to indicate, at the time they submit a typescript, the journal for which it is intended. Should this seem unsuitable, the Editor will inform the author. The sixth section of the Journal of the Chemical Society is Chemical Communications, which is intended as a forum for preliminary accounts of original and significant work, in any area of chemistry that is likely to prove of wide general appeal or exceptional specialist interest. Such preliminary reports should be followed up eventually by full papers in other journals (e.g.the five Transactions) providing detailed accounts of the work. NOTES I t has always been the policy of the Faraday Transactions that brevity should not be a factor influencing acceptability for publication. in addition however to full papers both sections carry at the end of each issue a section headed ‘Notes’, which are short self-contained accounts of experimental observations, results, or theory that will not require enlargement into ‘full’ papers. The Notes section is not used for preliminary communications. The layout of a Note is the same as that of a paper. Short summaries are required. The procedure for submission, administration, refereeing, editing and publication of Notes is the same as for full papers.However, Notes are published more quickly than papers since their brevity facilitates processing at all stages. The Editors endeavour to meet authors‘ wishesas to whether an article is a full paper or a Note, but since there is no sharp dividing line between the one and the other, either in terms of length or character of content, the right is retained to transfer overlong Notes to the full papers section. As a guide a Note should not exceed I500 words or word-equivalents. (i)NOMENCLATURE AND SYMBOLISM Units and Symbols. The Symbols Committee of The Royal Society, of which The Royal Society of Chemistry is a participating member, has produced a set of recommendations in a pamphlet ‘Quantities, Units, and Symbols’ (1975) (copies of this pamphlet and further details can be obtained from the Manager, Journals, The Royal Society of Chemistry, Burlington House, London W 1 V OBN).These recommendations are applied by The Royal Society of Chemistry in all its publications. Their basis is the ‘ Systeme International d’unites’ (SI). A more detailed treatment of units and symbols with specific application to chemistry is given in the IUPAC Manual of Symbols and Terminology for Physicochemical Quantities and Units (Pergamon, Oxford, 1979). Nomenclature. For many years the Society has actively encouraged the use of standard IUPAC nomenclature and symbolism in its publications as an aid to the accurate and unambiguous communication of chemical information between authors and readers. In order to encourage authors to use IUPAC nomenclature rules when drafting papers, attentior, is drawn to the following publications in which both the rules themselves and guidance on their use are given: Nomenclature of Organic Chemistry, Sections A , B, C, D , E, F, and H (Pergamon, Oxford, 1979 edn).Nomenclature of Inorganic Chemistry (Butterworths, London, 197 1, now published by Pergamon). Biochemical Nomenclature and Related Documents (The Biochemical Society, London, 1978). A complete listing of all IUPAC nomenclature publications appears in the January issues of J. Chem. SOC., Faraday Transactions. It is recommended that where there are no IUPAC rules for the naming of particular compounds or authors find difficulty in applying the existing rules, they should seek the advice of the Society’s editorial staff.(ii)THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION NO. 80 Physical Interactions and Energy Exchange at the Gas-Solid Interface McMaster University, Hamilton, Ontario, Canada, 23-25 July 1985 Organising Committee: Professor J. A. Morrison (Chairman) Dr M. L. Klein Professor G. Scoles Professor W. A. Steele Professor F. S. Stone Dr R . K. Thomas The discussion will be concerned with certain aspects of current research on the gas-solid interface: elastic, inelastic and dissipative scattering of atoms and molecules from crystal surfaces, and the structure and dynamics of physisorbed species, including overlayers. Emphasis will be placed on the themes of physical interactions and energy exchange rather than on molecular- beam technology or the phenomenology of phase transitions on overlayers.The interplay between theory and experiment will be stressed as they relate to the nature of atom and molecule surface interaction potentials, including many-body effects. The programme and application form may be obtained from: Professor J. A. Morrison, Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada L8S 4M1 or: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN, U.K. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM NO. 20 Phase Transitions in Adsorbed Layers University of Oxford, 17-1 8 December 1985 Organising Committee: Professor J. S. Rowlinson (Chairman) Dr E. Dickinson Dr R. Evans Mrs Y. A. Fish Dr N.Parsonage Dr D. A. Young The aim of the meeting is to discuss phase transitions at gas/liquid, liquid/liquid and solid/fluid interfaces, and in other systems of constrained geometry or dimensionality less than three. Emphasis will be placed on molecularly simple systems, whereby liquid crystal interfaces and chemisorption phenomena are excluded. The preliminary programme may be obtained from : Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1 V OBN (iii)THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION NO. 81 I Lipid Vesicles and Membranes Loughborough University of Technology, 15-1 7 April 1986 Organising Committee: Professor D. A. Haydon (Chairman) Professor D. Chapman Mrs Y. A. Fish Dr M. J. Jaycock Dr I.G. Lyle Professor R. H. Ottewill Dr A. L. Smith Dr D. A. Young The aim of the meeting is to discuss the physical chemistry of lipid membranes and their interactions, in particular theoretical and spectroscopic studies, polymerised membranes, thermodynamics of bilayers and liposomes, mechanical properties, encapsulation and interaction forces between bilayers leading to fusion but excluding preparation and characterisation methodology. Contributions for consideration by the Organising Committee are invited and abstracts of about 300 words should be sent by 1 May 1985 to: Professor D. A. Haydon, Physiological Laboratory, Downing Street, Cambridge CB2 3EG Full papers for publication in the Discussion Volume will be required by December 1985. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION NO.82 Dynamics of Molecular Photof rag mentation University of Bristol, 1 5 1 7 September 1986 Organising Committee : Professor R. N. Dixon (Chairman) Dr G. G. Balint-Kurti Dr M. S. Child Professor R. Donovan Professor J. P. Simons The discussion will focus on the interaction of radiation with small molecules, molecular ions and complexes leading directly or indirectly to their dissociation. Emphasis will be given to contributions which trace the detailed dynamics of the photodissociation process. The aim will be to bring together theory and experiment and thereby stimulate important future work. Contributions for consideration by the Organising Committee are invited. Titles should be submitted as soon as possible, and abstracts of about 300 words by 30 September 1985, to: Professor R.N. Dixon, Department of Theoretical Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS30TH INTERNATIONAL CONGRESS OF PURE A N D APPLIED CHEMISTRY Advances in Physical and Theoretical Chemistry Manchester, 9-1 3 September 1985 The Faraday Division is mounting the following symposia as part of the 30th IUPAC Congress: A. B. C. D. Reaction Dynamics in the Gas Phase and in Solution This symposium will examine the ways in which modern techniques allow detailed study of the dynamical motion of molecules which are undergoing chemical reaction or energy exchange. Micellar Systems The symposium will discuss various aspects of micellization, including size and shape factors, micellization in biological systems, chemical reactions in micellar systems, micelle structure and solubilization.Emphasis will also be given to modern techniques of examining micellar systems, including small-angle neutron scattering, neutron spin echo, photocorrelation spectroscopy, NM R and use of fluorescent probes. Surface Science of Solids The symposium will centre on recent advances in the study of kinetics and dynamics at surfaces and of phase transitions in adsorbate layers on single crystal surfaces. Both experimental and theoretical aspects will be reviewed with an emphasis on metal single crystal surfaces. New Electrochemical Sensors (in collaboration with the Electroanalytical Group of the Analytical Division) The symposium will cover such topics as the fundamentals of the subject, new gas sensors based on membrane electrodes and on ceramic oxides, the development of new ion- Iselective electrodes and the synthesis of new guest-host carriers, the development of CHEMFETS and other integrated devices together with the theory of the operation of such devices, and finally the development of biosensors including for instance enzyme electrodes, direct electron transfer to biological molecules and new potentiometric techniques for protein analysis.The full programme and application form may be obtained from: Dr J. F. Gibson, 30th IUPAC Congress, Royal Society of Chemistry, Burlington House, London W1V OBNFARADAY DIVISION INFORMAL AND GROUP MEETINGS Industrial Physical Chemistry Group Laser Spectroscopy Techniques in Solid/Gas Reactions To be held at the Society of Chemical Industry, Belgrave Square, London on 2 May 1985 Further information from: Dr T.G. Ryan, ICI PLC, New Science Group, POB No 11, The Heath, Runcorn WA7 4QE Electrochemistry Group with the SCI Electrochemical Group Chlorine Symposium To be held in London in June 1985 Further information from: Dr A. J. B. Cutler, Research Division, Central Electricity Research Labs, Kelvin Avenue, Leatherhead, Surrey KT22 7SE Gas Kinetics Group with SERC Summer School in Gas Kinetics To be held at the University of Cambridge on 26 June to 3 July 1985 Further information from Dr I. W. M. Smith, Department of Chemistry, University Chemical Laboratory, Lensfield Road, Cambridge CB2 1 EP Industrial Physical Chemistry Group with the Food Chemistry Group Water Activity: A Credible Measure of Technological Performance and Physiological Viability To be held at Girton College, Cambridge on 1-3 July 1985 Further information from Professor F.Franks, Department of Botany, Downing Street, Cambridge CB2 3EA Polymer Physics Group Biennial Conference To be held at the University of Reading on 11-1 3 September 1985 Further information from Professor Bassett, J. J. Thompson Physical Chemistry Laboratory, University of Reading, Whiteknights, Reading RG6 2AF Statistical Mechanics and Thermodynamics Group Multicomponent Mixtures To be held at the University of East Anglia on 16-18 September 1985 Further information from: Dr M. J. Grimson, Food Research Institute, Colney Lane, Norwich NR4 7UA Carbon Group Strength and Structure in Carbons and Graphites To be held at the University of Liverpool on 16-1 8 September 1985 Further information from The Meetings Officer, The Institute of Physics, 47 Belgrave Square, London SW1 X 8QX Surface Reactivity and Catalysis Group with the Catalysis Section of the KNCV Mechanism and Structure in Heterogeneous Catalysis To be held at Noordwijkerhout, The Netherlands on 18-20 September 1985 Further information from: Dr R.Joyner, BP Research Centre, Chertsey Road, Sunbury on Thames TW16 7LN Industrial Physical Chemistry Group A Molecular Approach to Lubrication and Wear To be held at Girton College, Cambridge on 23-25 September 1985 Further information from Mr M. P. Dare-Edwards, Shell Research Ltd, Thornton Research Centre, Chester CH1 3SHNeutron Scattering Group jointly with the Materials Testing Group of the Institute of Physics Industrial Uses of Particle Beams To be held at the Institute of Physics, London on 26 September 1985 further information from Dr J.G. Booth, Department of Chemistry, University of Salford, Salford M5 4 W Division Annual Congress: Structure and Reactivity of Gas-Phase Ions To be held at the University of Warwick on 8-1 1 April 1986 Further information from Professor K. R. Jennings, Department of Molecular Sciences, University of Warwick, Coventry CV4 7AL JOURNAL OF CHEMICAL RESEARCH Papers dealing with physical chemistry/chemical physics which have appeared recently in J.Chem.Research, the Royal Society of Chemistry’s synopsis + microform journal, include the following : Transfer Chemical Potentials for Complex Ions and for Anions: Water to Aqueous Acetone Issue 1) The Production and Photoelectron Spectrum of Propa-I ,2-dien-3-one Donald McNaughton and Roger John Suffolk (1985, Issue 1) Binary lonogenic Equilibria between some Phenols and Bases Geoffrey E.Holdcroft and Peter H. Plesch (1985, Issue 2) The Radical Cation of Trimethyl Phosphate: E.s.r. Evidence for Bonding to CFCI, Glen D. G. McConnachie and Martyn C. R. Symons (1985, Issue 2) Quantum-mechanical Studies of Catalysis. Part 1. A Model for Nucleophilic Attack on Carbonyl, catalysed by Non-functional Cationic Surfactants Amiram Goldblum and Jehoshua Katzhendler (1 985, Issue 3) Stereochemical Applications of Potential Energy Calculations.Part 4. Revised Cyclopropane Parameters for Molecular Mechanics Pekto M. lvanov (1 985, Issue 3) Electron Spin Resonance Studies of the Ammonia-Boryl Radical (H,N --+ BH3.); an Inorganic Analogue of the Ethyl Radical A. Baban, Vernon P. J. Marti, and Brian P. Roberts (1985, Issue 3) Phase Equilibria Larbi Marhabi, Marie-Chantal Trinel-Dufour and Pierre Perrot (1 985, Issue 3) John Burgess and Ezz-Eldin A. Abu-Gharib (1 985, Jehan The Iron-Vanadium-Oxygen System at 1123, 1273, and 1373 K. Part 1. (vi i)Arthur Adamson, Editor University of Southern California Arthur Hubbard, Associate Editor University of California at Santa Barbara This new journal published by the American Chemical Society fills the void existing in current literature available today-Langmuir’s broad coverage will bring together authoritative papers from all aspects of this major field of chemistry! Langmuir will include fundamental and applied papers covering ultra-high vacuum surface chemistry and spectroscopy, heterogeneous catalysis, all aspects of interface chemistry involving fluids, and disperse systems.Specifically, Langmuir will publish peer-reviewed research in 4 ‘Wet’ Surface Chemistry surface tension spread monolayers wetting and contact angle 0 adsorption from solution 0 nucleation and fundamental aspects of flotation, detergency, emulsions, foams, lubrication, etc. r/ Electrochemistry related to interfacial structure and processes r/ ‘UHV’ Surface Chemistry solid surfaces in ultra-high vacuum including surface structure, composition and spectroscopy 0 fundamental papers in heterogeneous catalysis colloidal suspensions including aerosols 0 microemulsions 0 biological and polymeric colloids and membrane systems r/ Disperse Systems In bimonthly issues of Langmuir, you will find experimental and theoretical original papers, letters to the editor, and book reviews, as well as some selected symposium collections. Papers having applied aspects will be included.And, published by the American Chemical Society, Langmuir will benefit from the Society’s vast international network of scientists and editorial resources. Note to Authors: Langmuir will not have page charges. Editorial Advisory Board N.R Armstrong. Univ. of Arizona G.T. Barnes, Univ. of Queensland. AUSTRALIA P Biloen. Univ. of Piffsburgh 0 K.S.Birdi. Technical University of Denmark, DENMARK A.M. Bond, Deakin Unrversity, AUSTR ‘LlA 0 B.V. Derlaguin, Academy of Science of USSR D.D. Eley, Univ. of Noffingham, ENGLAND G Ertl. Univ. of Munich, GERMANY J . Fendler, Clarkson College of Technology T . Fort. Jr., Californra Polytechnrc State Univ. 0 G. Gaines. Jr.. General Electric W.A. Goddard. 111, California Institute of Technology R . S . Hansen. lowa State Univ. J. Lyklema. Agricultural Unrv., THE NETHERLANDS R.J. Madix, Stanford Unrv. J.A. Mann. Jr.. Case Western Reserve Univ. P. Mukerjee, Univ. of Wisconsin K J. Mysels, Research Consulting A.W. Neumann. Univ. of Toronto. CANADA R . Ottewill. Univ. of Bristol. ENGLAND G.D. Parfitt. Carnegre-Mellon Unrv H Reiss. Univ. of Calrfornra at Los Angeles H A. Resing, Naval Research Laboratory T Rhodin. Cornell Unrv. S. Ross, Rensselaer Polytechnic Univ. J. Rouquerol, Centre de Thermodynamrque et de Mrcrocalorimetrre du CNRS, FRANCE 0 R.L. Rowell, Univ. of Massachusetts R. Rye, Sandia National Lab H Seki. ISM K. Shinoda. Yokohama National Univ.. JAPAN G.A. Somorjai, Univ. of California at Berkley W A Steele. Pennsylvanra State Unw * Subscription Information 1985 Foreign Rates (Includes Air Service) ACSMembers $ 56 (Personal Use) Nonmembers $308 January-February 1985 Volume 1 No 1 One Volume Per Year (Six Issues) ISSN. 0743-7463 Cable Address: JIECHEM Telex: 440159 ACSPUI or a92582 ACS PUBS American Chemical Society 0 1155 Sixteenth St., N.W. 0 Washington, D.C. 20036 (viii)

ISSN:0300-9599    

DOI:10.1039/F198581FP033

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1985, 81, 833-846 Quasi-elastic Neutron-scattering Studies of Intercalated Molecules in Charge-deficient Layer Silicates Part 2.-High-resolution Measurements of the Diffusion of Water in Montmorillonite and Vermiculite BY JONATHAN J. TUCK, PETER L. HALL? AND MICHAEL H. B. HAYES Department of Chemistry, University of Birmingham, P.O. Box 363, Birmingham B 15 2TT AND D. KEITH ROSS* Department of Physics, University of Birmingham, P.O. Box 363, Birmingham B15 2TT AND JOHN B. HAYTER~ Institute Laue-Langevin, 156X Centre de Tri, 38042 Grenoble, France Received 17th October, 1983 The relative influence of water-surface and water-cation interactions in hydrates of the charge-deficient expanding-lattice layer silicates montmorillonite and vermiculite have been studied using high-resolution quasi-elastic neutron-scattering (QENS) measurements made with the back-scattering spectrometer at ILL, Grenoble. Detailed measurements have been made for Ca2+-montmorillonite equilibrated at seven different water-vapour partial-pressure (p/po) values and for Ca2+, Mg2+ and Na+ vermiculite samples at fixed p / p o .The QENS data are fitted to a model consisting of an elastic and a single Lorentzian quasi-elastic component plus a flat background. The quasi-elastic linewidth and the relative intensities of the three components are adjustable parameters. The resultant quasi-elastic broadenings were approximately five times smaller than the values derived previously from measurements at lower energy resolution. Also, the quasi-elastic scattering intensity increased with p / p o and decreased with increasing scattering angle, the latter being the reverse of the behaviour observed at the broader energy resolution.The low- and high-resolution measurements taken together indicate the occurrence of two different phases of translational motion of water molecules not directly coordinated to the exchangeable (Ca2+) cations. These are attributed (i) to rapid localized motions in 'cages' bounded by the silicate sheets and the hydrated cations and (ii) to slower, longer-range inter-cage diffusion. In addition, the relative intensities of the quasi-elastic scattering at high and low wavevector transfer suggest that the high-resolution measurements also observe rotations of the complete six-fold coordinated hydration shells of the cations about one of the C, axes of the octahedron. To explain the observed width, this rotation must have a correlation time of ca.10-lo at ambient temperature. The present QENS data yielded effective diffusion coefficients for water in Ca2+- montmorillonite which increased rapidly from < 1.0 x 10-lo m2 s-l at p / p o = 0.15 to ca. 4.5 x 10-lo m2 s-' at p / p o = 0.33. At higher values of p / p o the effective diffusion coefficients remained approximately constant within the limits of experimental error. For water adsorbed by vermiculite having Na+, Ca2+ or Mg2+ as the exchangeable cation the diffusion coefficient measured at p / p o = 0.76 was found to be significantly smaller than the corresponding value for Ca2+-montmorillonite.This may be attributed to the hindering effect of the more densely packed network of hydrated cations in the more highly charged vermiculite. -f Present address: Schlumberger Cambridge Research, P.O. Box 153, Cambridge CB2 3BE. $ Present address: Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, Tennessee 37831, U.S.A. 833834 NEUTRON-SCATTERING STUDIES OF LAYER SILICATES In previous ~ a p e r s l - ~ we have reported quasi-elastic neutron-scattering (QENS) measurements of the diffusion of water adsorbed by divalent (Ca2+ and Mg2+) cation-exchanged forms of the charge-deficient 2 : 1 expanding lattice layer silicates montmorillonite and vermiculite containing up to three layers of interlamellar water molecules. The measurements were made using the multichopper (IN5) and back- scattering (INlO) spectrometers at the Institute Laue-Langevin, Grenoble. These instruments have medium (ca.30 peV) and high (1 peV)energy resolutions, respectively. The medium-energy-resolution measurements, reported in the previous paper of this ~ e r i e s , ~ hereafter called Paper 1, indicated that the adsorbed water was composed of a mobile component, undergoing rapid but spatially restricted jump diffusion with a correlation time of ca. 10-l’~ at 295 K, and an ‘immobile’ component, which corresponded to approximately six water molecules per exchangeable cation. The observation of two distinct components indicates that the translational or rotational motions of water molecules coordinated to the cations must have correlation times of 1O-lo s or longer, and also that any exchange between the two water populations must take longer than 1O-lo s.The conclusion that the observed rapid motion is spatially restricted arose from the observation of a Q-dependent elastic component of the incoherent scattering superimposed on the constant elastic amplitude due to protons tightly ‘bound’ on the timescale of the measurement. This Q-dependent component decreased in intensity with increasing scattering vector Q, in the manner expected for a spatially localized diffusion process described by an elastic incoherent structure factor (EISF).5 The breadth of the EISF in reciprocal space is inversely proportional to the linear dimension of the region within which diffusion is restricted. We have found this to be ca.6-7 A for a two-layer hydrate of Ca2+-montmorillonite at 300 K. The localized motions of the non-hydration-shell water molecules cannot therefore be purely rotational, but may be interpreted as localized jumps within ‘cages’ or micropores of this typical s i ~ e . ~ ? ~ Our previous high-resolution (IN 10) measurements on these systems’? showed quasi-elastic broadenings at low scattering angles which were only 20-25% of those measured on IN5. These broadenings corresponded to an effective diffusion coefficient of 3.4 x m2 s-l at ambient temperature for both Ca2+-and Mg2+-montmorillonite at p / p o = 0.76 (two layers of interlamellar water). It was also observed that the broadening on INlO was independent of sample orientation. However, it has been shown6 that this is not surprising even for models including planar diffusion in view of the degree of preferred orientation in the samples.’ Here we report more extensive high-resolution measurements on Ca2+-montmorillonite equilibrated at seven different values of water-vapour partial pressure and on Ca2+-, Mg2+- and Na+-vermiculite at p / p o = 0.76. The remarkable feature of the data is that the intensity of the quasi-elastic component decreases with increasing scattering angle.This differs from either of the cases usually considered, namely unbounded diffusion (constant intensity) and rotational or restricted diffusion (intensity increasing with scattering angle). A simple theory to explain this observation is proposed and its implications for the nature of the motions of the non-coordinated water population are discussed.A future paper will demonstrate that the technique of fitting single Lorentzians to simulated data which includes the effect of preferred orientation etc. can be used to distinguish between alternative microscopic models. Moreover, it will be shown that, of the variety of models considered, only the present one can explain the main features of both the IN5 (Paper 1) and INlO (this work) data [see also ref. (6)].TUCK, HALL, HAYES, ROSS AND HAYTER 835 EXPERIMENTAL The clay minerals used were montmorillonite (API No. 26, Clay Spur, Wyoming, U.S.A.) and vermiculite (Libby, Montana, U.S.A.). After preliminary grinding of the natural vermiculite flakes, dilute suspensions of the Na+-exchanged forms of both clays were prepared by a standard technique.s Self-supporting films of the Na+, Ca2+- and Mg2+-exchanged clays were then prepared by the sedimentation-suction method described in Paper 1.After drying at 1 10 "C, the films were equilibrated to constant mass uptake over a set of saturated aqueous salt solutions, which were chosen so as to define a suitable series of water-vapour partial pressures. Samples were then sealed in sachets of thin aluminium foil immediately prior to the neutron-scattering studies. The QENS measurements were made on the INlO back-scattering spectrometer at the ILL, Grenoble. The principles of instruments of this type have been discussed el~ewhere.~ Neutrons back-scattered from Si( I 1 1) planes define an incident wavelength of II = 6.3 A.The incident energy is modulated by sinusoidal motion of the monochromating crystal in the incident neutron direction at a frequency which defines an energy transfer 'window ' of f 15 peV. For perfect back-scattering, the energy resolution, defined by the width in energy of the elastic peak for neutrons incoherently scattered by a vanadium sheet, is ca. 1 peV. Six detectors were positioned at angles corresponding to Q values of 0.1, 0.24, 0.3, 0.5, 0.7 and 0.85 A-l. The energy-resolution function of the spectrometer was Lorentzian shaped, except where it was distorted by departure from the perfect back-scattering condition. The extensive wings of this function make the separation of the peak into quasi-elastic and elastic components inherently more difficult than for the essentially triangular resolution function of the IN5 multichopper time-of-flight spectrometer .The data were analysed using a suite of programslO written specifically for IN10. Initially an attempt was made to fit the data to a single Lorentzian broadening function (convoluted with the energy-resolution function) plus a flat background. This procedure did not fit the data satisfactorily. However, a model consisting of a Lorentzian-broadened resolution function, an unbroadened component and a flat background yielded good fits in most cases when the width of the Lorentzian and the amplitudes of three components were allowed to vary independently. The program was unable to find a unique fit to the model if the ratio of elastic to quasi-elastic scattering intensity was too high, if the quasi-elastic broadening was too large (> 15 peV) or if a combination of these factors was present.Thus, although 60% of the data sets were fitted at the first attempt and most of the rest were fitted after two or three attempts, in the case of data from a few of the detectors the procedure failed to reach a reasonable fit even after six or more attempts. The intensities from different counters were carefully internormalized using a vanadium standard and appropriate attenuation corrections were applied for both sample and vanadium. The fitted elastic and quasi-elastic intensities are therefore available as a function of Q, and this @dependent information provides an important test of possible models. The most detailed set of measurements (corresponding to seven different relative humidities, p / p , , between 0.15 and 0.98) were made on the Ca2+-montmorillonite system.Table 1 lists these results and those for the vermiculite samples with the corresponding p / p o values and water con tents. THEORY In this section we discuss the general form that a model for the motion of the adsorbed water molecules must take in order to account for the unusual features of the IN10 quasi-elastic scattering data. It will be shown that the form of the data narrows down the possible choice considerably. The complexity of the model presented here cannot be entirely justified by the INlO data taken in isolation, since, as stated above, the data were generally fitted by the sum of elastic and single Lorentzian quasi-elastic components, in addition to a flat background.However, it is known, from the IN5 data (Paper I), that broader836 NEUTRON-SCATTERING STUDIES OF LAYER SILICATES Lorentzian components are present and become part of the flat background on the narrow energy window of the back-scattering spectrometer. Indeed it will be shown that the behaviour of the observed INlO data can only be explained satisfactorily if the EISF component, as measured on IN5, is sufficiently broadened in energy, because of a slower long-range translational diffusion, to appear as a quasi-elastic component on the energy resolution of INlO. In the present paper we develop a phenomenological model to describe the current data. In Paper 1 it was shown that, for p / p o = 0.76, the scattering is dominated by incoherent scattering from protons both in lattice OH groups and in the adsorbed water.We therefore first consider this incoherent scattering and introduce coherent contributions later. The incoherent scattering function for a spatially restricted motion S,(Q, co) may be written (1) where Ao(Qa) is the EISF, a is the dimension of the region of restricted diffusion and 6Q and Tim are the momentum and energy, respectively, transferred in the scattering event. The EISF is normally a strongly damped periodic function which tends to zero at high Q.ll L[Ao,(Q)] is a normalized quasi-elastic component of width Acol(Q) which may or may not be a single Lorentzian depending on the nature of the microscopic motion^.^ For the present we will assume that it is a single Lorentzian.The amplitudes of the elastic and quasi-elastic components in eqn (1) are complementary functions of Q, the shape of which depends on the details of the localized motions. From the Q dependence of the amplitude and width of the Lorentzian, details of the diffusive process can be inferred. If two distinct phases of motion of a given water molecule occur sequentially, for instance jumps between adjacent cages as well as motions within the cage, then a simple way of modelling both intra- and inter-cage motions is to assume that they are uncorrelated. This implies that the scattering function for the combined motion will be a convolution in co of the separate scattering functions for the two phases of the motions.ll Thus we assume that the inter-cage motions are unbounded in space and are characterized by instantaneous jumps having a mean residence time between jumps of z ~ ~ ~ ~ ~ .The scattering function for this component of the motion will then be a Lorentzian where, at sufficiently high Q, The combined scattering functions for both phases of motion will now be given by a convolution in co, i.e. S,(Q, (0) = Ao(Qa) &co) + [ I + Ao(Qa)l L[Awi(Q)l S2(Q, co> = UAudQ)l (2) Aw~(Q) = I / ~ i n t e r - (3) S(Q, 0) = Si(Q, W ) *S2(Q, m) = Ao(Qa) L[Aco2(Q)1+ Ao(Qa>l L[Aai(Q) + AwdQ)l (4) since the convolution of two Lorentzians produces a Lorentzian, the width of which is the sum of the two component widths. If, in addition, there is a contribution from a rigidly bound proton population of fraction C and, moreover, if we include the influence of thermal vibrations, assumed to correspond to two distinct Debye-Waller factors exp (- Q2 (u:)) and exp (- Q2 ( u i ) ) for the ‘mobile’ and ‘bound’ protons, respectively, then the overall scattering functions will take the form S(Q, 0) = (1 - C) ~ X P (- Qz (US>) (Ao(Qa) UAw,(Q)l + [ I - Ao(Qa)l L[Am,(Q) + Aw2(Q)l> + C exp ( - Q2 (4)) S(O).( 5 )TUCK, HALL, HAYES, ROSS AND HAYTER 837 The above discussion assumes infinitely sharp instrumental resolution. In practice, the measured quasi-elastic spectrum is a convolution in o of the scattering function and the instrumental resolution function. If there are two (or more) broadened lines convoluted with the resolution function, then what will be observed experimentally will depend on the relative magnitudes of the linewidths associated with the diffusion processes [in this case Aol(Q) and Aw2(Q)] and the instrumental resolution Am,. Our previous data indicate that the restricted motions have a residence time significantly shorter than the long-range motions,l? i.e.Aoi(Q) 9 Ao2(Q)- (6) Eqn (5) thus represents the sum of an elastic contribution plus narrow (term one) and broad (term two) quasi-elastically broadened components. If the resolution is broad with respect to the slower motions, but narrow with respect to the faster motions (IN5 case), the narrow quasi-elastic component will be included in the elastic scattering and the apparent quasi-elastic intensity will be given by the second term in eqn ( 5 ) .The decrease in total intensity with increasing Q is here only due to the Debye-Waller factors. Since the EISF decreases from unity at Q = 0 to zero at Qa 9 1 , in this case the quasi-elastic intensity rises from zero at Q = 0 to a value of (1 - C) exp ( - (u:) Q2) at high Q. Our previous IN5 data (Paper 1) exhibited this behaviour and led to a value of C substantially larger than that attributable to scattering by protons in the aluminosilicate lattice. Fitted values of the asymptotic elastic fraction were consistent with the assumption that water coordinated to the exchange cations (approximately six molecules per ion) showed no diffusive motion on the observed timescale. Conversely at high energy resolution (the IN10 case), if Am, Aa2(Q) Awi(Q> (7) then the narrow quasi-elastic component will be observed, but the broader component, if of large enough width, will only contribute to a flat, pseudo-inelastic background.In this case the fitted quasi-elastic intensity will be approximately given by the amplitude of the first term of eqn (5), i.e. (1 - C) A,(Qa) exp (- (u:) Q2), a function which decreases with increasing Q. Thus the intensity of quasi-elastic scattering caused by the slower component of the diffusion is modulated by the EISF of the faster, spatially restricted, motion and the total intensity (elastic + quasi-elastic) will also decrease sharply with increasing Q. More specifically, there are simplifications at low Q(Q -+ 0) and at high Q. At low Q the second term in eqn (5) tends to zero and the quasi-elastic intensity is simply 1 - C, since both the EISF and the Debye-Waller factor becomes unity.At high Q the first term tends to zero and the scattering should simply be an elastic component of intensity, C exp (- Q2 (u!)), caused by protons bound on the timescale of the measurement. RESULTS Fig. 1 shows the energy spectrum of neutrons scattered quasi-elastically by a Ca2+-montmorillonite (PIP, = 0.76) sample for a scattering vector Q = 0.24 A-l. The fitting program gave a quasi-elastic broadening AE of 4.1 peV, which represents the Lorentzian f.w.h.m. Fig. 2(a) illustrates the dependence of AE on the square of the scattering vector, Q, for the same sample equilibrated at p/po = 0.98. Fig. 2(b) shows the total intensity within the energy window of IN10 and the fitted elastic and quasi-elastic intensities as a function of Q2.The data at humidities of 0.76, 0.58 and 0.43 are very similar and demonstrate the reproducibility of the fitting. Equivalent838 NEUTRON-SCATTERING STUDIES OF LAYER SILICATES 0 0 0 0 00 0 00 0 >oA m o o ”- 0 O0 - 8 4 0 4 energy change/peV 8 Fig. 1. Scattered intensity on IN10 for Ca2+-montmorillonite equilibrated at p / - 0.98. Quasi-elastic broadening is 4.1 peV with an energy resolution of 1 .O peV at Q = 0.24 L’l:-) Fitted quasi-elastic intensity. data for the lower humidities are shown in fig. 3 and 4. The sum of the fitted elastic and quasi-elastic contributions may be larger than the ‘total’ because of the inclusion of fitted quasi-elastic intensity outside the energy window of the instrument.The intensities have been scaled to the mean value of the elastic intensity at the highest three Q values. Assuming for the moment (see Discussion) that the elastic scattering arises solely from the lattice hydroxyls, then, from the IN5 measurements, the dashed line in fig. 2(b) can be drawn representing the lattice elastic scattering, the rise at low Q being caused by the small-angle-scattering signal previously observed. Note that at low Q and hence small broadenings the separation between elastic and quasi-elastic is more difficult and errors can thus arise in the fitted intensities. The most notable feature of these results is the reduction of the total and, subject to the above qualification, the quasi-elastic intensities with increasing Q in a manner that is clearly not due to Debye-Waller factors alone.This is a very strong indication that we are in the ‘narrow-resolution’ regime defined in the previous section and that the broad quasi-elastic intensity is being lost in the background. Note also that in fig. 2(b) the quasi-elastic intensity flattens out sharply at high Q; this feature is also apparent for the lower humidities. As discussed below, this seems to be evidence for some rotation of the hydration sphere. The effective diffusion coefficients, Deff, obtained by fitting a straight line through the origin and the first three points of the broadening curve are given in table 1. It can be seen that within experimental error the values are constant down to ap/po value of 0.3 (see fig.2 and 3). Below this the effective diffusion coefficient drops atplp,, = 0.20 (see fig. 4), while at p / p o = 0.15 the quasi-elastic intensity and the broadening are both too small to be measured reliably. The results for Ca2+-, Mg2+- and Na+-vermiculite at ap/po of 0.76 are significantly different from those for Ca2+-montmorillonite. Fig. 5 shows the results obtained for Mg2+-vermiculite. The data points at Q2 = 0.06 k2 illustrate what happens in some cases of small broadening or low quasi-elastic intensity where the program finds a falseTUCK, HALL, HAYES, ROSS AND HAYTER % -? 10 Q U 0 h v1 c .- c 3 2 s i- X 6) v1 c v x Y VJ .- 5 Y c .- 0 0.5 QZ/A-2 0-5 Q21A-2 839 Fig. 2. Dependence of (a) quasi-elastic broadening, AE, and (b) total (0) and fitted elastic (0) and quasi-elastic (a) intensities as a function of Q2 for Ca2+-montmorillonite equilibrated at p / p , = 0.98.The solid lines have been drawn by eye through the data. The dotted line represents the estimated lattice contribution including small-angle scattering (see text). minimum. The data for Ca2+- and Na+-vermiculite are similar. In all cases the broadenings are smaller even at high values of Q while the quasi-elastic intensities for the vermiculite samples are lower than for montmorillonite at the same value ofplp,. The lower quasi-elastic intensity is correlated to the higher exchange capacity of vermiculite (see below). The smaller quasi-elastic broadenings for the vermiculites were less reliably determined but they certainly indicate smallereffective diffusion coefficients (D,,, < 1.0 x 10-lo m2 s-l) for these clays as compared with the montmorillonite samples (see table 1).DISCUSSION Considering first the data for Ca2+-montmorillonite for 0.33 < p/po < 0.98, we note the following striking features : (1) the quasi-elastic intensity decreases with increasing Q at fixed p/po, (2) the quasi-elastic intensity increases with increasing p/p, and hence with increasing water content and (3) the broadening curve for the narrow quasi-elastic fraction is essentially independent of p/po within experimental error.840 NEUTRON-SCATTERING STUDIES OF LAYER SILICATES t 0 0.5 Q’1A-l Fig. 3. Dependence of (a) quasi-elastic broadening, AE, and (b) total (0) and fitted elastic (0) and quasi-elastic (0) intensities as a function of Q2 for Ca2+-montmorillonite equilibrated at p / p o = 0.33.The solid lines have been drawn by eye through the data. The dotted line represents the estimated lattice contribution including small-angle scattering (see text). From the first point and the theory presented above we conclude that the broadenings observed on IN5 and IN10 are mainly caused by two separate phases of motion of one water component. From the second and third points we conclude that in the range 0.33 < p / p o < 0.98 we are mainly adding mobile water whose diffusion coefficient, or microscopic jump frequency, is essentially independent of the degree of hydration. We therefore propose an initial model in which the water molecules hydrating the cations do not exhibit translational mobility on the observational timescales of observation of either the IN5 or IN10 spectrometers.The more mobile water component, which is attributed to water not directly coordinated to the cations, is initially confined inside a cage formed by the silicate layers and the hydrated cations (phase 1) but can intermittently jump between cages (phase 2). Thus phase 1 gives rise to the spatially restricted diffusion observed on IN5, while phase 2 gives rise to the unbounded diffusion as observed on INIO. As a consequence of the proposed model, the inter-cage diffusion will be regulatedTUCK, HALL, HAYES, ROSS AND HAYTER ( a ) 84 1 I I I 0 0 . 5 0 0.5 Q2/A-’ Fig. 4. Dependence of (a) quasi-elastic broadening, AE, and (6) total (0) and fitted elastic (0) and quasi-elastic (0) intensities as a function of Q2 for Ca2+-montmorillonite equilibrated at p / p , = 0.20.The solid lines have been drawn by eye through the data. The dotted line represents the estimated lattice contribution including small-angle scattering (see text). Table 1. Water contents and effective diffusion coefficients of samples used in IN10 back-sca t tering spectrometer studies clay water exchangeable con tent Deff / 1 0-lo cation p / p o /gHZ0 g-l m2 s-l montmorillonite (API no. 26) Ca2+ Ca2+ vermiculite (Libby, Montana) ‘0.15 0.20 0.33 0.43 0.58 0.76 0.98 0.76 0.76 0.76 0.09 & 0.1 0.12 & 0.1 0.17 & 0.1 0.19 kO.1 0.23 0.1 0.22 f 0.1 0.26 f 0.1 0.19 f 0.1 0.21 fO.1 0.20 f 0.1 0.2k0.1 2.3 k 0.6 4.5 0.9 5.1 0.2 4.5 2 0.4 4.2 -t 0.7 4.0 & 1 .O 2.6+ 1.2 0.5 0.1 0.3 0.05842 20 >, 2 10 4 d NEUTRON-SCATTERING STUDIES OF LAYER SILICATES 0 I 0.5 Q2/A-' I I I 0.5 Q2/A-2 Fig.5. Dependence of (a) quasi-elastic broadening, AE, and (b) total (0) and fitted elastic (0) and quasi-elastic (@) intensities as a function of Q2 for and Mg2+-vermiculite equilibrated at p / p o = 0.76. The solid lines have been drawn by eye through the data. The dotted line represents the estimated lattice contribution including small-angle scattering. by the number of hydrated cations present between the layers. The Libby vermiculite12 has a cation-exchange capacity of 1300 pequiv g;fay compared with a value of ca. 1000 pequiv g;:a, for the Wyoming rnontmoril10nite.l~ Hence the Ca2+-vermiculite contains some 30 % more hydrated cations than does the Ca2+-montmorillonite.The average gap between hydrated cations, assuming hexagonal packing, is thus 3.1 and 4.3 A for the vermiculite and the montmorillonite, respectively. As water molecules have dimensions of < 3 A, it is to be expected that the inter-cage diffusion will be much more restricted in the vermiculite. This is reflected in the fact that the small (IN 10) quasi-elastic broadenings for vermiculite represent a jump frequency which is at least 5 times smaller than that for montmorillonite. In order to explain the steep rise in the effective diffusion coefficient between p / p o values of 0.15 and 0.33 for Ca+-montmorillonite, it is necessary to examine the details of the hydration process. The hydration of Ca2+-montmorillonite is known to differ from that of the Na+-exchanged form. In the latter case, at low p / p o values (0.1 < p / p o < 0.5) a stable monolayer hydrate (do,, z 12 A) is formed.Bilayer andTUCK, HALL, HAYES, ROSS AND HAYTER 843 trilayer hydrates then form at higher p / p o values; indeed expansion is unlimited as p/po approaches the saturated vapour pressure of water. In the Ca2+-exchanged13 case, however, no rational series of (001) X-ray reflections are observed at low p/po values ( p / p , z 0.25). Although an (001) reflection at ca. 12 A is commonly observed at this humidity, it probably arises from random mixtures of hydrated bilayers and unexpanded layers (an interstratified structure) and does not represent a true monolayer hydrate.Also, unlike the Na+-exchanged form, the swelling is limited to three or possibly four layers of interlamellar water, even at a partial pressurep/p, = 1 . Thus the X-ray diffraction data suggest that the initial hydration process in the Ca2+-montmorillonite case is one of cation hydration and not one of layer filling. Evidence for the octahedral coordination of water to divalent ions in expanding 2 : 1 layer silicates comes from the broad-resolution QENS data,4 X-ray diffraction14 and electron spin re~0nance.l~ Also, the coordination number of calcium ions in aqueous electrolyte solutions of concentrations similar to that of the interlayer environment in montmorillonite and vermiculite has been found to be close to six.16 The six water molecules per cation adsorbed up to p/po z 0.05 will therefore produce only elastic scattering, and the extra 2 or 3 molecules adsorbed at p/po z 0.15 will generate insufficient quasi-elastic scattering to be measured accurately.However, at p / p o = 0.2 the cages are beginning to fill up and at p/po = 0.33 seven to eight non-hydration-shell water molecules per cation are adsorbed. This provides sufficient quasi-elastic intensity to generate reliable data. The principal feature of the quasi-elastic intensity featured in fig. 2 is its decrease with Q2, as already described. If this is attributable to the broadening of the EISF seen with IN5, as outlined above, then at a value of Qz z 0.5-0.6 the quasi-elastic intensity would be nearly zero. This is not the case and therefore the observation of significant quasi-elastic intensity at higher values of Q remains to be explained.The most obvious explanation is that it arises from rotational motion of the hydration-shell water. Two types of rotational motion have been proposed; first a C, rotation of the hydrogen atoms about the metal-oxygen axis (Y = 0.75 A) and secondly a C3 rotation of the complete hydration shell about an axis through the cation perpendicular to the clay layer (Y = 3 A). The former has an EISF such that it would be impossible to observe any significant quasi-elastic scattering on the Q scale of IN 10 and hence only the latter C, motion can provide an explanation of the observed quasi-elastic intensities. To test this proposition we will compare two hypotheses: (1) that coordinated hydration-shell water is immobile on the IN10 timescale and (2) that the water is undergoing rotational diffusion with a radius of rotation of Y = 3 A.These hypotheses have been compared with the data using the well defined values of the total intensity I&) at Q = 0 and the elastic and quasi-elastic intensities [I,@) and Z,,(Q)] at Q = Q,, = 0.85 A-l, the maximum observable Q value [the separation of ZT7(Q) into ZE(Q) and I,,(Q) is well defined at high Q but is subject to considerable errors as Q - 0 because of the small broadenings involved]. In fig. 6 and 7 experimental values of the ratios IT(0)/IJG(Qm) and IQE(Qm)/IE(Qm) are plotted as a function of np, the total number of adsorbed water protons per unit cell. Values of n,, were determined for each sample by measuring the weight gain on hydration.The corresponding values of the ratios as predicted on the basis of each hypothesis are also shown. In making these predictions the following assumptions were made. (a) The basic clay unit-cell structure was Ca:?,, Al,Si40,,(OH),(H,0)o~5np. (b) The number of lattice protons was nL = 2 and the number of coordinated water protons in the Ca2+ hydration shell was n, = 2.16 (protons per formula unit). (c) The elastic scattering at Q = 0 was represented by S(O)n,, where S(Q) is a multiplying function representing the elastic small-angle scattering in terms of the elastic scattering at high844 NEUTRON-SCATTERING STUDIES OF LAYER SILICATES I .‘ 5.0 1 0 0 15-0 nP Fig. 6. Plot of IT(0)/IE(Qm) against adsorbed water protons, n,, for (a) hypothesis 1 (no rotation) and (b) hypothesis 2 (rotation) together with the experimental values for Ca2+-montmorillonite.nP Fig. 7. Plot of IQE(Q,)/IE(Qm) against adsorbed water protons, np, for (a) hypothesis 1 (no rotation) and (b) hypothesis 2 (rotation) together with the experimental values for Ca2+-montmorillonite. Q [S(O) = 2.4 from the IN5 measurements4]. (d) The Debye-Waller factor for the lattice OH was unity ((UL2)Q& z 0) from the IN5 measurements while for the adsorbed water a value of ( u2) = 0.13 A was used. (This value, derived from the IN5 experiment, assumed identical values for (u:) and (ut,) for coordinated and non-coordinated water; possible errors in this assumption would have little effect on the calculations below.) (e) The structure factor for the non-coordinated water at Q, is estimated from the IN5 experiment4 to be A , (Q,) = 0.1.(f) The possible rotational motion of the coordinated water was modelled (after Barnes”) with a radius of rotation of 3 A, giving a corresponding structure factor B,(Q,) = 0.16. Table 2 shows how to calculate the intensities of the various components at Q = 0TUCK, HALL, HAYES, ROSS AND HAYTER 845 Table 2. Basic expressions for the calculation of elastic and quasi-elastic intensities at Q = 0 and Q = Q, for hypotheses 1 and 2 Q = O Q = Qm 1 2 1 2 np -nc (narrow, INlO) quasi-elastica 0 water (broad, IN5) a The broad Lorentzian measured on IN5 becomes a negligibly small flat background in the present measurements. and Q = Q, for each hypothesis.Using these parameters the intensity ratios as a function of adsorbed water np for hypothesis 1 are while those for hypothesis 2 are where Ao(Q) and Bo(Q) are the structure factors for the non-coordinated and coordinated water, respectively. The results are plotted in fig. 6 and 7 together with experimental values derived from the measurements made at seven different p / p o values on Ca2+-montmorillonite. At high p / p o values the results are more consistent with hypothesis 2. At lower water contents the quasi-elastic intensity drops below the expected values, probably because of partial hindering of the rotation of the coordination sphere. Such an effect has been observed previously by e.s.r.15 studies in a hydrated divalent cation-exchanged montmorillonite.The difficulty experienced in some cases in fitting the simple or Lorentzian model to the present data is understandable when one considers that there are in fact two quasi-elastic components present. It was clear, however, that the data did not justify a two-Lorentzian fit. There are therefore special problems in fitting the data at low Q for the vermiculite samples ( p / p , = 0.76) and for the Ca2+-montmorillonite sample at low water contents where the long-range diffusive components are much less846 NEUTRON-SCATTERING STUDIES OF LAYER SILICATES intense. In these cases it is only possible to say that Deff is < 1.0 x loplo m2 s-l and that the correlation time for the observed rotation is in the range (2-5) x For the rotation of the hydration-shell water to be observed in the present Q range, the EISF must be such that only the complete rotation of the whole hydration shell can be involved.This is consistent with the proposal of Giese and Fripiat18 that the coupling of the C, and C, rotations leads to a lowering of the total rotational energy barrier. Also the extracted rotational correlation time is in good agreement with that obtained by Fripiat by pulsed n.m.r.19 and with that inferred from e.s.r. data.20 s. CONCLUSIONS In this paper we have described experimental data and theoretical arguments which support the view that the structure of the adsorbed water in both montmorillonite and vermiculite, having divalent exchangeablecations Ca2+ and Mg2+, arises principally from the requirements of cation hydration. On the timescale of s the cations and their six hydration-shell water molecules are essentially static, apart from probable coupled C,-C, rotational motions of the complete hydration shell.They thus define a network of interconnected ' cages' between which the non-coordinated water molecules are free to move. These inter-cage motions are, however, on a slower timescale than the motions within the cages. For vermiculite, the longer-range inter-cage diffusion is significantly more hindered because of restrictions imposed by the more densely packed network of hydrated cations. We thank the S.E.R.C. and the Institute Laue-Langevin for the provision of neutron-scattering facilities. P. L. H. and J. J. T. acknowledge support from the S.E.R.C. and the A.F.R.C. ' P. L. Hall, D. K. Ross. J. J. Tuck and M. H. B. Hayes, Proc. IAEA Symp. Neutron Inelastic Scattering (IAEA, Vienna, 1978), vol. 1, p. 617. P. L. Hall, D. K. Ross, J. J. Tuck and M. H. B. Hayes, Proc. Int. Clay Conf., ed. M. M. Mortland and V. C. Farmer (Elsevier, Amsterdam, 1979), p. 121. J. J. Tuck, P. L. Hall, D. K. Ross and M. H. B. Hayes, Water at Interfaces, ILL Report no. 8ITO55S, ed. C . Touret-Poinsignon and P. Timmins (Institut Laue-Langevin, Grenoble, 198 l), p. 38. a J. J. Tuck, P. L. Hall, M. H. B. Hayes, D. K . Ross and C. Poinsignon, J . Chem. Soc., Faraday Trans. I , 1984, 80, 309. D. K. Ross and P. L. Hall, in Advanced Chemical Methodsfor Soil and Clay Minerals Research, ed. J. W. Stucki and W. Banwart (Riedel, Dordrecht, 1980), p. 93. J. J. Tuck, Ph.D. Thesis (University of Biimingham, 1981). ' P. L. Hall, R. Harrison, M. H. B. Hayes, J. J. Tuck and D. K. Ross, J. Chem. Soc., Faraday Trans. I , 1983 79, 1687. * A. M. Posner and J. P. Quirk, Proc. R. Soc. London, Ser. A, 1964, 275, 35. B. Alefeld, M. Birr and A. Heidemann, Naturwissenschujten, 1969, 56, 410. l o W. S. Howells, ILL Report no. 75HI307 and no. 76HI22T (Institut Laue-Langevin, Grenoble, 1975 and 1976). P. L. Hall and D. K. Ross, Mol. Phys., 1981, 42, 673. l 2 M. E. Pick, Ph.D. Thesis (University of Birmingham, 1973). l 3 J. Mering, Trans. Faraday Soc.. 1946, 42, 205. H. Shirozu and S. W. Bailey, Am. Mineral., 1966, 51, 1124. l 5 D. M. Clementz, T. J. Pinnavaia and M. M. Mortland, J . Phys. Chem., 1973, 77, 196. l6 N. A. Hewish, G. W. Neilson and J. E. Enderby, Nature (London), 1982, 297, 138. l8 R. F. Giese Jr and J. J. Fripiat, J . Colloid Interface Sci., 1978. 71, 441. l9 J. J. Fripiat, Adtanced Chemical MethodsJor Soil and Clay Mineruls Research, ed. J. W. Stucki and 2o P. L. Hall, Clay Miner., 1980, 15, 337. J. D. Barnes, J . Chem. Phys., 1973. 58, 5193. W. Banwart (Riedel, Holland, 1980), p. 245. (PAPER 3/ 1842)

ISSN:0300-9599    

DOI:10.1039/F19858100833

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1985, 81, 847-855 Nuclear Magnetic Resonance and Dielectric Relaxation Investigations of Water Sorbed by Spherisorb Silica BY PETER G. HALL,* RUTH T. WILLIAMS AND ROBERT C. T. SLADE Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD Received 13th February, 1984 The Spherisorb silica/sorbed water system has been investigated at coverages 0.018 < O/g,,og~~o, < 0.36 using lH n.m.r. in the temperature range 190 < T/K < 300 and also at coverages 0.013 < O/gHz0 g;to2 < 0.033 using dielectric techniques at ambient tempera- ture. In cases where multilayer adsorption occurs there is a discontinuity in the temperature dependence of the n.m.r. linewidth accompanying a freezing phenomenon. Water molecules making up the first loosely packed adsorbed layer (complete at 0 = 0.06 gHzOg;~oz) remain mobile at low temperatures at allcoverages.Dielectric measurements reveal another discontinuity at a coverage of ca. 0.023 gHzOg;toz. Below that coverage the strength of binding of sorbed water increases with decreasing coverage, while at higher coverages additional water leads to a marked increase in the mobility of the first layer. The properties of water at interfaces have been the subject of considerable interest for many years. Among the various applications, colloid properties and stability, corrosion science and heterogeneous nucleation in the atmosphere are noteworthy. Various types of experimental study have been used to investigate the properties of liquids at interfaces. Most of the early work has been summarised in a review by C1ifford.l We have used infrared,2 dielectric3 and neutron-scattering (inelastic4 and quasielastic5) techniques to investigate the water/silica (or clay3) system.Neutron scattering from adsorbed molecules has been reviewed,s and recently a neutron- diffraction study of water in meso- and micro-pores has been reported.' The general picture which has emerged is that the modification caused by the interface is restricted to a range of the order of 10 A or less. Within this range clear differences from bulk water are observed; for example, a shift in a peak maximum in the inelastic spectrum4 for water/silica corresponds to a reduced degree of hydrogen bonding in the adsorbate. The specific interaction of water with silica manifests itself as lower freezing points and lower diffusion coefficients of the adsorbed water compared with bulk water.The strength of the interaction is a function of both (a) type and extent of porosity and (b) the degree of hydroxylation of the silica surface. In different silicas either (a) or (b) can be the dominant influence, and failure to recognise this has led to apparently contradictory conclusions in previous n.m.r. investigations of silica/water systems.8-11 There is widespread interest in the Spherisorb silica/water system in particular and in this paper we report results obtained using n.m.r. and dielectric techniques. Spherisorb SW silica (marketed by Phase Separations Ltd for h. .l.c. applications) 6-9 and 20pm for S7W and S20W, respectively. From the ratio of H,O to N, B.E.T.surface areas, Ow, of 0.33, Pidduck12 deduced that Spherisorb silicas fall into the category of partially dehydroxylated mesoporous silicas (according to the classification is a well characterised mesoporous silica of mean pore diameter 89 8: and particle sizes 847848 N.M.R. AND DIELECTRIC STUDY OF H,O/SiO, of Baker and Sing13). However, the similarity between the uptakes at saturation of water’, and nitrogen14 (i.e. Gurvitsch behaviour15) indicates that the loose packing in the first layer of sorbed water does not persist through the higher layers. In this work, variations in the lH n.m.r. absorption spectrum linewidth have been measured as a function of both coverage and temperature. The dielectric properties at ambient temperature of the silica/water system having coverages of the order of a monolayer have also been investigated.EXPERIMENTAL N.M.R. MEASUREMENTS Ca. 0.1 g of oven-dried (383 K) Spherisorb S7W contained in an 8 mm ‘ taperlok’ n.m.r. tube (supplied by Fluorochem Ltd) was outgassed to a dynamic vacuum of < mmHg* prior to the adsorption of water vapour. The solid was equilibrated with water from a reservoir containing triply distilled water freed from dissolved gases by three successive freeze-thaw cycles. The effects of fluctuations in the ambient temperature during equilibration with water vapour were minimised by surrounding the sample with a water jacket contained in a Dewar. Equilibration times of the order of two days (following Pidduck12) were followed with a silicone- oil manometer.The concentration of sorbed water was determined with respect to the dry mass of the silica. Spectra were recorded for coverages in the range 0.018-0.36 gHzogi/oz, i.e. 0.86 to 17 monolayers (based on a monolayer coverage, i.e. OHzO = 1, of 0.021 gHzOg&,,),l at temperatures from ambient to 190 K at intervals of 20 K. The reversibility of the process (i.e. recording spectra from 190 K up to ambient) was not investigated. lH n.m.r. absorption spectra were recorded using a JEOL PS/PFT 100 Fourier-transform spectrometer. Pulse lengths were typically 15 ps and the instrumental dwell-time was < 50 ps. Methylene dichloride contained in a glass capillary within the sample provided a trigger signal. No field-frequency lock could be employed and a block-averaging technique was used to overcome any problems associated with magnetic-field drift.Five transients were accumulated per block prior to transformation and twenty blocks in the frequency domain were sufficient to produce satisfactory spectra, i.e. a total of 100 f.i.d. (pulse spacing 1.5 s) were recorded per spectrum. Lineshapes observed were symmetrical and approximately Lorentzian. A y , the linewidth (f.w.h.m.), was measured for each spectrum. DIELECTRIC MEASUREMENTS The main features of the dielectric cell were four 1 mm thick concentric stainless-steel cylinders 6 cm in height and of outside diameter 1.9, 2.5, 3.1 and 3.7 cm, respectively, rigidly held in a polypropylene base. The cylinders formed three capacitors which were connected in parallel (by metal tabs) with a resulting capacitance of 85 pF (measured in uacuo).The cell was encased in an evacuable Pyrex housing having an outer jacket of water. The electrical connections were made via tungsten rods pinch-sealed into the Pyrex housing. All measurements were made at ambient temperatures; sample outgassing was also restricted to this temperature. A capacitance bridge (model 716-C) and guard circuit (model 716-P4), supplied by the General Radio Co., were used for measurements in the frequency range 200 Hz-100 kHz. For measurements at frequencies > 100 kHz, a Q meter (model T2A), frequency range 100 kHz-100 GHz, supplied by Advanced Electronics, was used. The adjustable source was provided by a power supply (model 1203-BQl8) and r.c.oscillator (model 1210-C) capable of frequencies from 20 Hz to 500 kHz. A tuned amplifier and null detector (model 1232A) was used for balancing at the required frequency in the range 20 Hz-100 kHz. All capacitance measurements were made using the substitution method ; no readings could be made using the bridge circuit if the capacitance of the combined cell and dielectric exceeded 1000 pF. The estimated errors for the calculated values of E’ and E” are? E‘ (dielectric constant), f0.007 (capacitance bridge) and & 0,012 (Q meter); E” (dielectric loss), 0.005 (capacitance bridge) and 50.008 (Q meter). * 1 mmHg x 133.3 Pa.P. G. HALL, R. T. WILLIAMS AND R. C. T. SLADE 849 E’ and E” are the real and imaginary parts of the complex relative permittivity of the dielectric material and are given by E’ = T,/To and E“ = &IDx, where Tx is the capacitance of the cell and material, To the capacitance of the empty cell and D, the dissipation factor.The dielectric cell was filled with oven-dried S7W silica (16.8 g) and outgassed at room temperature for 24 h (when a dynamic vacuum of < lop5 mmHg was recorded) prior to the adsorption of water vapour. Water sorption was carried out by (successive) 12 h exposure of the sample to the cooled reservoir followed by two days equilibration time with the reservoir isolated from the sample (equilibration was monitored by recording the change in capacitance of the cell against time). The water coverage, calculated according to the mass lost from the reservoir, ranged from 0.01 3 to 0.033 gHaO g;{oz based on the dried mass of the silica.The frequency scan covered the range 200 Hz-7 MHz. COVERAGE Following Pidduck,12 the coverage of the Spherisorb SW silica surface with sorbed water, OHzO, is, in the present work, based on a monolayer coverage of 0.021 gHnOgg~02, equivalent Thus OHnO = 0.320,,, based on the nitrogen surface area1* of 232m2 g-l, i.e. A concentration of 0.032 gHnO gito, sorbed water is equivalent to a coverage of one water molecule adsorbed per surface hydroxyl group, i.e. O,, = 1, given the surface hydroxyl group concentration of 4.5 nm-2 l6 (and nitrogen surface area of 232 m2 g-l) for Spherisorb SW silica. Thus for coverages of the order of one monolayer (eN2) of sorbed water on Spherisorb SW to OH20 = 1.ON, E 0.065 gH,O giilo,. silica : @HzO z 0.65 00, z 0132 ONz. The importance of these ‘ different monolayer coverages ’ becomes apparent when considering the sub-structure of the loosely packed monolayer (ON,). RESULTS AND DISCUSSION lH N.M.R. OF H20/S7W SILICA The temperature dependence of Av, as a function of temperature and coverage is illustrated in fig. 1. The freezing properties of water sorbed by Spherisorb S20W silica have been investigated in this laboratory using differential scanning calorimetry (d.s.c.).17 S20W differs from the silica in this work only in having a larger particle size. No melting transitions were observed in the temperature range 200-280 K at coverages < 0.06 gHzO gglo0,. At higher coverage, the freezing-point depression varied from ca.26 K (0 = 0.15 gH20 ggtoz) to ca. 12 K (at 0 > 0.2 gHZ0 g;lo2). The quantity of water freezing was equal to the coverage less ca. 0.1 gHzO g;to,. In this work the n.m.r. signal from protons in frozen water (solid) will be too broad to be detected by the available instrumentation, i.e. only mobile water contributes to the observed spectra. The results display a number of interesting and perhaps surprising features. It is evident from fig. 1 that the temperature dependence of Av; is strongly dependent on coverage for 0 > 0.06 gHzO g;lo,. For these coverages there are discontinuities in Avj as the temperature is decreased, and the behaviour at lower temperatures is close to that for lower coverages. A coverage of 0.06 gH,Og&, is equivalent to 0.9 ON,, i.e.approximates to the loosely packed first layer. The observed discontinuities in Av; parallel the freezing properties discussed above and only those water molecules remaining unfrozen contribute to the observed spectra at lower temperatures. The data are consistent with the following model: (1) the first layer of sorbed water is subject to surface ordering effects, and for the coverages investigated (0 2 OHZO) this region of mobile water is dynamically similar in all cases, and (2) at coverages in excess of the first loosely packed layer (at 0 = ON2) the water in higher layers freezes as temperature is decreased, with the first layer remaining diffusionally mobile.850 N.M.R. AND DIELECTRIC STUDY OF H,O/SiO, A 180 200 220 240 260 280 300 TIK Fig. 1. Temperature dependence of Av; for H20/S7W silica: 0, 0.9 OHlo; x , 1.6 OHzO; 0, 3.0 @ ~ * o ; H, 4.6 @H20; A, 4.9 O H 2 0 ; A, 7.6 OHzo; 0, 17.0 OHzo.The similarities in linewidth observed at sub-freezing temperatures for the non- freezing component at high coverages are not surprising. That these similarities should also be observed for lower coverages (where there is insufficient water for freezing to occur) is, however, surprising. Assuming a fast-exchange model at high temperatures (above freezing), and that the relaxation rate appropriate to the first layer is independent of the presence (or otherwise) of additional layers, the minimum observable ratio of the linewidths at high and low coverages would be nfirst/na?,, where ni is the population of layers i. The data in fig.1 are not consistent with this model (e.g. for 0 = 17.0 OHtO the minimum would be 3/17 = 0.18, whereas the observed ratio is ca. 0.14). It is, therefore, apparent that the presence of multilayers does alter the mobility of the first layer. The observation of Lorentzian absorption lineshapes in this work is consistent with rapid exchange of mobile waters, every mobile molecule experiencing all chemical environments open to it in a time shorter than the relaxation time (T,) characteristic of all such environments, as has been found by Pearson and Derbyshire18 in related studies. Under fast exchange conditions, inhomogeneous broadenings (such as have been found in other systems because of distributions of chemical ~ h i f t s l ~ , ~ ~ ) do not contribute to the linewidth.The observed n.m.r. spectrum is thus an average for all environments open to mobile waters within the pores, i.e. the linewidth depends onP. G. HALL, R. T. WILLIAMS AND R. C. T. SLADE 851 f” 1 0 \ 2 3 4 5 6 7 log,, WHz) Fig. 2. Dielectric loss of H20/S7W silica at room temperature: 0, 0.62 OHzo; 0, 0.71 OHzO; A, 0.81 OH20; X , 1.10 OHzO; 0, 1.60 OHzO. the relative populations of the mobile regions. Waters in layers other than the first will, at temperatures above the freezing transition, be less affected by surface-ordering effects and hence more mobile than those in the first layer. Following Pearson and Derbyshire18 it can be predicted that, as mesopores fill with adsorbate from their walls inwards, at high temperatures Av; should decrease with increasing coverage for multilayer adsorption.The results in this work are consistent with this prediction. The n.m.r. measurements in this work reveal information for coverages 0 b OHzO, while the dielectric measurements extend to lower coverages and reveal structure within the first sorbed water layer. DIELECTRIC PROPERTIES OF H20/S7W SILICA The dielectric measurements refer to ambient temperature and to coverages less than those studied using n.m.r. and reveal details within the first sorbed water layer. The Debye21 equations relate the real and imaginary parts of the complex permittivity, E’ and E ” , to the macroscopic relaxation time, z, of an applied alternating freyuencyf= o/2n. The variation of E’ and E” with logfshows dielectric dispersion and the maximum of the dielectric loss; the latter corresponding to an absorption of energy in the dielectric due to phase loss between the polarisation and applied field.For systems where a distribution of relaxation times exist, the plot of E” against E’852 10 9 8 7 6 E’ 5 4 3 2 1 0 N.M.R. AND DIELECTRIC STUDY OF H,O/SiO, I 2 3 4 5 6 7 log,, CfIHz) Fig. 3. Dielectric constant of H20/S7W silica at room temperature: symbols as in fig. 2. (Cole-Cole plot,,) results in an arc, in contrast to the semi-circle obtained for a single relaxation time. In the present work the results of the frequency scans are shown in fig. 2 and 3. The frequency scans showed a dielectric-absorption peak, a low-frequency loss, a high-frequency loss and dielectric dispersion. The dielectric-absorption peak (fig.2) was not apparent until a coverage of 0.015 gHzog~~oz, i.e. OHZ0 of 0.71 (based on the H,O monolayer amount of 0.021 gH,Ogg~o,) or ON, of 0.24 (OH,, = 0.33 ON,). The position of this peak was a function of water-vapour coverage, moving to higher frequencies with increasing coverage up to of 1.1, i.e. 0.023 gHPO gktoz. The height of the maxima remained relatively constant at values of E” = 1.3-1.4. This is in agreement with the work of Hall and Rose3 on water/clay systems (although values of E” for the latter were smaller and of the order of 0.10). The variation of E’ with logf(fig. 3) showed dielectric dispersion, i.e. a decrease in E’ with increasing frequency. A low-frequency loss was observed at coverages > 0.6 Or,o.. This was attributed to direct-current conductance across the terminals ; the auto-ionisation of the adsorbed water provides a conduction path. A small high-frequency loss was observed which increased with increasing coverage; this is probably due to inaccuracies resulting from the poor sensitivity of the Q meter in the range 6.0-7.0 MHz.At coverages > 1.1 the low-frequency loss overwhelmed the dielectric-absorption peak; thus no attempt was made to investigate coverages > 1.6 OHZ0 for this system.P. G. HALL, R. T. WILLIAMS AND R. C. T. SLADE 853 Table 1. Characteristic frequency of water sorbed by Spherisorb silica coverage 0.62 0.013 - - 0.71 0.01 5 900 2.23 0.8 1 0.0 17 3 5-40 3.65 k0.05 1.1 0.023 3.5-4.5 4.65 -t- 0.05 1.6 0.033 ice (298 K)a 3 4.72 - - a rice (298 K) is the value obtained by extrapolating to 298 K, the linear relationship between log z and l/T(in the temperature range 207.2-272.9 K) for ice as obtained by Auty and A broad peak in the E” against logfplot indicates a spread of relaxation times.However, the mean value of a symmetric distribution was determined from the value of the frequency,f,.,,,, corresponding to the peak maximum, according toychar = 1 /2m. The results are summarised in table 1 . From table 1 it can be seen that the z values are very large at values of O H z O < 0.7. At 0.8 OHzO the relaxation time is of the same order as that expected of ice at 298 K.23 This suggests that at coverages of OHzO < 0.8, i.e. < 0.017 gHzO g;loz, the adsorbed water is very tightly bound to the silica surface.As more water molecules adsorb, the adsorbate z becomes ice-like at a coverage of 0.023 gH,O g;toz, i.e. 1.1 QHzO. Although first apparent at 0.7 OHzO (0.015 gHpO ggto,), the conduction effect increases until it overwhelms the system at 1.6 OHZ0 (0.033 gHBO ggto,). This suggests that the mobility within the adsorbed phase becomes significant after the majority of hydroxyl adsorption sites on the surface have each become occupied by a single water molecule, i.e. at a coverage of 0.021-0.032 g,zog&O, (aHzO to OoH). Only for coverages of 0.015 and 0.017 gHzO ggto2 do the E’ against E” plots (fig. 4) approximate to Cole-Cole behaviour. The arcs apparent in these cases are indicative of distributions of relaxation times for adsorbed water. This is no surprise as the adsorbent surface is energetically heterogeneous.At higher coverages no such behaviour was observed. This, and the deviation from Cole-Cole behaviour at low frequency in the plot for 0.017 gH20g&oz coverage, is likely to be caused by conductance effects. ’The hydroxyl-group concentration on the surface determined by Gray16 was ca. 4.6 nm-2; ca. 1.2 nmW2 were attributed to be isolated and ca. 3.5 nmP2 to be hydrogen bonded. Assuming that, initially, one water molecule adsorbs per OH site, then the water coverage corresponding to each of the two OH sites is: OOH (isolated) = 0.008 gHzO gg!oo, and OoH (H bonded) = 0.024 gH,o g;;oo,. In the present work coverages in the range 0.008 gHZOg~{oz were not investigated. However, the dielectric measurements indicate that, at a coverage of 0.023 gHzO ggto2, the adsorbate has a well ordered structure, having a relaxation time similar to that expected of ice (at 298 K).At coverages < 0.023 gH20gg~oz the adsorbed phase appears to be more strongly bound, as indicated by the long relaxation times compared with ice (298 K). At a coverage > 0.023 gH20g&& a significant increase in the conductance of the system suggests increased mobility within the adsorbed phase. No dielectric relaxation time could be obtained for a coverage of 0.013 gHpO gglo,, probably because z was too long, i.e. z > 1.5 ms. The largest value of z = 0.9 ms (at8 54 3 - “i N.M.R. AND DIELECTRIC STUDY OF H,O/SiO, 0 1 2 3 4 5 6 7 E’ 0 ? 2 3 4 5 6 7 E l Fig. 4. Cole-Cole plots of H,O/S7W silica at room temperature: (a) 0.7 OHzO and (b) 0.8 OHzO.0.015 gH,og;:o,) compared with z = 35 ps (at 0.017 gH,Og&) suggests that the adsorbate becomes less strongly bound as the adsorbed layer increases. These results agree with the findings of Hall et a1.495 from inelastic neutron-scattering and time-of-flight measurements. On the basis of a simple theoretical treatment of the results, they concluded that the Spherisorb results were consistent with the formation of two-dimensional surface clusters of sorbed water containing a predominance of doubly hydrogen-bonded molecules. CONCLUSIONS The n.m.r. measurements have revealed details of the behaviour of sorbed water at coverages in the range 0.018-0.36 gHzO gg:oz at temperatures above and below those leading to freezing of water in the pores for samples with multilayer adsorption.The n.m.r. results reveal differences in behaviour for the first layer of water and higher layers. Water forming the first layer (complete and loosely packed at 0 = 0.06 gH20g;~oa z ON2) remains diffusionally mobile at low temperatures, while any higher layers freeze on cooling. The dielectric measurements mostly refer to coverages lower than those in the n.m.r. study and reveal structure within the first sorbed layer. Measurements concerned coverages < ON* but up to OoH (0.033 gH,og&). At coverages < 0.023 gH,Og~~oO,, decreasing coverage leads to more strongly bound water. A coverage of 0.023 gH20 g&,P. G. HALL, R. T. WILLIAMS AND R. C. T. SLADE 855 corresponds to OHZ0, and in that case the relaxation time observed is of the same order as that anticipated for ice at 298 K.Water sorbed in excess of OHZO leads to increased mobility within the adsorbed layer before the first loosely packed layer is completed (0.06 gHZ0g;tOp z ON?). In cases where Cole-Cole behaviour can be observed, a distribution of relaxation times is evident. The results described in this paper may be compared with recent quasi-elastic neutron-scattering rneasurement~,~~ which show the coexistence of two phases of sorbed water molecules with different dynamics in monolayer and near-monolayer films on the surface of Spherisorb silica. One component is immobile on the experimental timescale (< 10-lo s) and the other gives quasielastic broadening, which is fitted by a model of consecutive uniaxial rotation and two-dimensional jump translation.We thank Dr V. Sik for assistance with n.m.r. absorption spectra and the referees for their constructive comments. J. Clifford, in Water: A Comprehensive Treatise, ed. F. Franks (Plenum Press, New York, 1975), vol. 5. P. G. Hall and P. B. Barraclough, J. Chem. Soc., Faraday Trans. I , 1978, 74, 1360. P. G. Hall and M. A. Rose, J. Chem. Soc., Faraday Trans. I , 1978, 74, 1221. P. G. Hall, A. Pidduck and C. J. Wright, J. Colloid Interface Sci., 1981, 79, 339. P. G. Hall, A. J. Leadbetter, A. Pidduck and C. J. Wright, Neutron Inelastic Scattering 1977 (Interna- tional Atomic Energy Agency, Vienna, 1978), vol. 11, p. 5 l l . P. G. Hall and C. J. Wright, Surface and Defect Properties of Solids (The Chemical Society, London, 1978), vol. 7, p. 501. G. K. Rennie and J. Clifford, J. Chem. SOC., Faraday Trans. I, 1977, 73, 680. P. A. Sermon, J. Chem. Soc., Faraday Trans. I , 1980,76, 885. 25, p. 174. V. V. Morariu and R. Mills, Z. Phys. Chem. (Frankfurt am Main), 1972, 79, 1. A. J. Pidduck, Ph.D. Thesis (University of Exeter, 1980). ' D. C. Steytler, J. C. Dore and C. J. Wright, Mol. Phys., 1983, 48, 1031. I" J. Clifford and S. M. A. Lecchini, in Wetting (Society of Chemical Industry, London, 1967), monogr. l 3 F. S. Baker and K. S. W. Sing, J. Colloid Interface Sci., 1976, 55, 605. l4 M. J. Holdaway, AERE Harwell Report no. AERE-M2749 (Atomic Energy Research Establishment, l5 S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area and Porosity (Academic Press, New York, l6 R. A. C. Gray, Ph.D. Thesis (U.M.I.S.T., 1976). l 7 J. Clare, B.Sc. Research Project (University of Exeter, 1978). l9 D. Geschke, Z. Naturforsch., Teil A, 1968, 23, 339. 2o J. H. Pickett and L. B. Rogers, Sep. Sci., 1970, 5(1), 11. 21 P. Debye, Polar Molecules (Chemical Catalog Co., New York, 1929). :12 K. S. Cole and R. H. Cole, J. Chem. Phys., 1941, 9, 341. 24 J. Clark, P. G. Hall, A. J. Pidduck and C. J. Wright, J. Chem. SOC., Faraday Trans. 2, in press. Harwell, 1976). 2nd edn, 1982), p. 113. R. T. Pearson and W. Derbyshire, J. Colloid Interface Sci., 1974, 46, 232. R. P. Auty and R. H. Cole, J. Chem. Phys., 1952, 20, 1309. (PAPER 4/252)

ISSN:0300-9599    

DOI:10.1039/F19858100847

出版商:RSC    

年代:1985

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J. Chem. Soc., Faraday Trans. I , 1985,81, 857-874 Study of the Crystal and Molecular Structure of the 9-Cyanoanthracene trans Dimer and of its Monomerisationf- BY CHARIS R. THEOCHARISS AND WILLIAM JONES* Department of Physical Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EP Received 17th February, 1984 The structure of the 9-cyanoanthracene trans dimer (9-CNAD) has been solved by direct methods [PI, a = 10.146(1) A, b = 17.785(1) A, c = 11.501(1) A, a = 92.95(1)", /3 = 95.59(1)", y = 89.82( l)", 2 = 41. No evidence for X-ray-induced monomerisation was observed, although a 20% fading of the crystal occurred during data collection. On heating a 9-CNAD crystal to 420 K, a ellow single crystal (9-CNADY) was obtained. Its crystal structure [Pl, a = 10.217(2) 1, b = 10.235(2) A, c = 11.594(2) A, a = 95.20(2)", /I = 90.37(2)", y = 120.13( l y , 2 = 21 was solved to show that the sample was still dimeric to an extent of 92%.This single-crystal -+ single-crystal transition is topotactic, and monomerisation occurs homogeneously. Further heating leads to a complete, heterogeneous and topotactic monomerisation. The monomeric component in 9-CNADY was not located. Final R was 0.0436 for 9-CNAD and 0.10 15' for 9-CNADY. Although the topochemical principle holds sway in many organic solid-state reactions,l there is an apparent breakdown of the rule for a number of such processes : in certain reacting crystal structures no favourable double-bond contacts are available, whereas in other cases an unexpected product is obtained.2 For example, in 9- cyanoanthracene (9-CNA) crystals the packing is such3 that a cis dimer is expected, but the actual product obtained upon photoirradiation (9-CNAD) is centrosymmetric.A proposed explanation is that these reactions occur at crystalline imperfections, at which the molecules are so situated as to allow topochemical reaction to e n s ~ e . ~ ~ ~ Optical- and electron-microscopic studies have shown that reaction in a system such as 9-CNA indeed occurs at defects. Some slip dislocations that may operate in 9-CNA or other anthracenes so as to bring monomer units to a reactive antiparallel orientation have been identified.s. In addition, the monomerisation of various anthracene photodimers including the title compound is of interest since anthracenes are among the compounds suggested for the storage of solar energy in chemical bonds,* and the dimer host crystals have been used to study the photochemical and photophysical behaviour of guest monomer molecules within the host m a t r i ~ . ~ The thermal as well as optically induced mono- merisation of 9-CNAD has been studied exten~ively.l~-~~ The calorigram of 9-CNAD11 has a sharp exothermic peak at ca.425 K (A), followed by a broad exothermic peak between 425 and 450 K (B) and finally an endothermic peak at 455 K (C). Peak B has been assigned to the decomposition of the dimer to monomer, and C to the melting t Lists of thermal parameters are available as supplementary data no. SUP 56133 (8 pp). See Instructions for Authors (January Issue). Structure factors available from the editorial office on request.Present address: Department of Chemistry, Brunel University, Uxbridge UB8 3PH. 29 857 FAR 1858 STRUCTURE OF 9-CYANOANTHRACENE trans DIMER of the monomer. Peak A, whose position varies depending upon the crystallinity of the dimer, has been variously assigned to thermal monomerisation of crystalline 9-CNAD,lo9 l4 to a subsequent collapse of 9-CNAD crystals12 or to a heterogeneous topotactic growth of 9-CNA microcrystallites inside the 9-CNAD crystals.l13 l5 It has also been speculated that peak A corresponds to chemical reaction along a certain family of planes in 9-CNAD ~rystal1ites.l~ The monomerisation of 9-CNAD has been shown to proceed homogeneously and reversiblyll up to ca. 3 % . In the present study we report the hitherto unknown crystal structure of 9-CNAD and employ single-crystal X-ray techniques to elucidate some of the processes associated with the first exothermic peak.EXPERIMENTAL The preparation and purification of 9-CNAD were carried out as previously described.1° Crystals of 9-CNAD for X-ray crystallography were grown by the slow evaporation of a chloroform + ethanol solution. Single crystals of 9-CNAD were observed during heating under cross-polarised light in an optical microscope. A single crystal resulting from heating a 9-CNAD single crystal to 420 K was used for X-ray crystallography without recrystallisation. This crystal is designated 9-CNADY. X-RAY CRYSTALLOGRAPHY Preliminary cell parameters for both crystals (9-CNAD and 9-CNADY) were obtained from oscillation and Weissenberg photographs and the space group deter- mined from successful refinement. Accurate cell parameters and the orientation matrix for data collection were determined by least-squares refinement of automatically centred setting angles for 25 reflections having 20 < t 9 / O < 30 on an Enraf-Nonius CAD-4 four-circle diffractometer.The same instrument was used for intensity data collection. Ni-filtered Cu Ka radiation was used, together with an m-28 scan technique. For each measurement the scan width in CL) was determined by the equation w = 0.85 + 0.15 tan 8. A 4.0 mm vertical slit was used, with the horizontal aperture determined using the expression S/mm = 0.90 + 0.3 tan 8. Each reflection was given a fast prescan at 4" min-l and only those considered significant [ I > 1.5a(I)] were rescanned, such that the final net intensities satisfied the preset condition I > 30a(I) subject to a maximum measuring time of 90 s, unless the desired accuracy was achieved during the prescan.Two standard reflections were measured every 1 h during data collection as a check on crystal and instrument stability. A further two reflections were periodically scanned to check the accuracy of the orientation matrix. Each scan consisted of 96 steps, with the first and last 16 forming the left (BL) and right (BR) backgrounds and the central 64 the basic net count, C. Then the structure factor amplitude (F,) and its standard deviation [a(F,)] were calculated as follows : a(&) = ([c+ 4(BL + BR)l1I2 N)/2Fo where N is a factor incorporating the Lp-l correction.B,, BR and C have been corrected for crystal decay and measuring time. STRUCTURE DETERMINATION 9-CNAD The positions of half of the carbon and nitrogen atoms in the asymmetric unit were located from the E map computed with the automatic direct-methods routine (TREF) in SHELXS-84. The rest of the non-hydrogen as well as all the hydrogen atoms wereC. R. THEOCHARIS AND W. JONES 859 located from difference Fourier maps and refined using blocked full-matrix least-squares techniques in SHELX-76. All non-hydrogen atoms were assigned anisotropic and the hydrogen atoms isotropic thermal parameters. The structure was further refined using block-cascade full least-squares techniques. A weighting scheme was introduced at the later stages of the refinement.The function minimised during refinement was w IF, I -14 I )2 with w = [a2(F) +gP]--1. Convergence was achieved at R = 0.0436 = (C 11 F, 1 - 1 F, 11 )/X 1 Fo I No peak higher than 0.20 e A-3 was observed in the final difference Fourier map. 9-CNADY All non-hydrogen atoms were located from the E map calculated by direct methods using SHELXS-84. Hydrogen atoms were located geometrically. Initial refinement was carried out using blocked full-matrix least-squares techniques. Attempts at assigning anisotropic thermal parameters to non-hydrogen atoms resulted in a number of highly anisotropic thermal parameters. Therefore, no anisotropic refinement was carried out. Final refinement was carried out using full-matrix least-squares techniques, with all hydrogen atoms constrained to their ideal geometries and assigned a common thermal parameter.A weighting scheme was introduced at this stage. Convergence was achieved at R = 0.1015 (R, = 0.1044) with no peak higher than 0.45 e A-3 remaining in the final difference Fourier map. For the last cycle of least-squares refinement, reflections 100, 200 and 400 were suppressed, as they suffered from extinction. Removal of these peaks did not greatly affect the structure or R . All suppressed reflections had I F, I -F, > 64F). RESULTS Fig. 1 shows the atomic numbering scheme used for both structures. Table 1 contains the salient crystal and refinement data. For 9-CNAD the asymmetric unit consists of four such units shown in fig. 1, indicated by letters A, B, C or D after the atom name in table 2, which contains the final positional parameters.Bond lengths and angles are presented in tables 3 and 4, respectively. For 9-CNADY, the asymmetric unit consists again of four monomeric residues. The final positional parameters are presented in table 5, the bond lengths in table 6 and the bond angles in table 7. The tables are given in the Appendix. All calculations were carried out using SHELXS-84 (G. M. Sheldrick), SHELX-76 (G. M. Sheldrick), PLUTO-78 (W. D. S. Mother- well) and private programs on an IBM 3081 computer (University of Cambridge). Scattering factors were obtained from ref. (1 6). DISCUSSION 9-CNAD Previous efforts at solving the crystal structure of 9-CNAD have failed owing to the X-ray sensitivity of the crystal.lO Indeed, an overall fading of 20% as measured by the linear drop in the intensity of the control reflections was observed here. Since this fading was within acceptable limits, it was decided to proceed with solving the 29-2860 STRUCTURE OF 9-CYANOANTHRACENE trans DIMER c4 c5 Fig. 1.Atomic numbering scheme for 9-CNAD and 9-CNADY. Fig. 2. Crystal structure of 9-CNAD. structure after correcting for fading, by weighting the reflections based on the intensity change of the control reflections. Ebeid et al. reportedlo that X-ray instability is due in part to monomerisation: a refinement of occupancy factors for C(9) and C( 10) was carried out. The occupancy factor for each of these atoms refined to a value not significantly different than 1 .O.The asymmetric unit consists of four monomer residues: one dimer unit with a pseudocentre of symmetry at a general position (fragments A and B, molecule 1 in fig. 2) and two half-molecules. The first, residue C (molecule 2, fig. 2), part of a molecule whose centre of symmetry is situated on a crystallographic centre ofC . R . THEOCHARIS AND W. JONES 86 1 Fig. 3. Crystal structure of 9-CNADY. symmetry at 0, 0,0.5, and the second, residue D (molecule 3, fig. 2), with its centre of symmetry at 0.5,0.5,0.5. Bond lengths and angles within the phenyl rings have normal values, whilst all the bonds involving C(9) and C(l0) are of the correct length for single ones. The bonds bridging the two monomer residues [e.g. C(9A)-C( 1 OB), C( lOA)-C(9B)] are slightly longer than the single bonds within the monomer residues.The same effect has been observed in other dimeric ~pecies.l'-~~ What distinguishes the three fragments in the asymmetric unit are the dihedral angles subtended by the phenyl rings, and the torsional angles of the type C( 1 l)-C(9)-C( 10')-C( 12') in each one. Thus in molecule 1 the torsional angle C( 13A)-C(9A)-C( 1OB)-C( 14B) is 126", whilst C( 1 lA)-C(9A)-C( 1OB)-C( 12B) is 121", C(12A)-C(lOA)-C(9B)-C(llB) is 121" and C(l4A)-C(lOA)-C(9B)- C( 13B) is 116". The inequality of these torsional angles shows that the benzene rings related by the pseudocentre of symmetry are not exactly parallel. Within the A residue, the two benzene rings subtend a dihedral angle of 134" and within residue B, 135". In molecule 2 (monomer residue C) the torsional angles equivalent to those described for molecule 1 [e.g. C( 13C)-C(9C)-C( l0C')-C( 14C')I are all 122", reflecting the presence of the true centre of symmetry.In molecule 3 (residue D) the equivalent torsional angles are 120". Within residue C, the two benzene rings make a dihedral angle of 137" and in residue D 139". Because of the pseudosymmetry present in the structure, all the reflections with (h+k) odd are weak but present. The low R factor justifies the decision to proceed with solving the structure in spite of the relatively large crystal decay. If no crystal-decay correction is carried out a slightly higher R factor is obtained. Successful solution and occupancy-factor refinement for all C(9) and C( 10) carbon atoms indicates that X-ray-induced monomerisation does not proceed to an appreciable extent under these conditions. 9-CNADY The spacegroup P1 was confirmed by successful refinement.The unit cell contains two molecules, both possessing pseudocentres of symmetry. Molecule 1 consists of monomer residues A and B and molecule 2 of residues C and D (fig. 3). 9-CNADY862 STRUCTURE OF 9-CYANOANTHRACENE trans DIMER b CNADY b 0 a CNAD r a Fig. 4. Topotactic relationship of the 9-CNAD and 9-CNADY crystal structures. consists of yellow crystals and corresponds to the first visible change occurring during the heating of 9-CNAD, and as such should be associated with peak A of the calorigram observed by previous workers. 9-CNADY was shown to be still a single crystal by total extinction under cross-polarised light and oscillation and Weissenberg photographs.The cell reported here can be transformed to a cell of dimensions similar to those of 9-CNAD, and thus explain how the 9-CNAD -+ 9-CNADY transformation can be single-crystal -+ single-crystal. This alternative 9-CNADY cell is a = 10.217(2) I$, b = 17.704(5) 1$, c = 11.594(2) I$, a = 96.22(2)", /? = 90.36(2)", y = 90.19(2)". In this setting, however, all reflections with (h+k) odd were absent. In other words, the pseudocentring present in the 9-CNAD structure has now been converted to real centering, thus necessitating a change in cell. The experimental 9-CNADY cell can be obtained from the theoretical alternative by keeping the a and c axes the same and by halving [110] in length and assigning this as the b axis.This topotactic relationship between 9-CNAD and 9-CNADY is depicted in fig. 4. The long axis of 9-CNAD corresponds to the [loll axis, whilst in 9-CNADY it is to [l 1 11. Fig. 5 shows views of the two structures along the needle axis. The 9-CNAD to 9-CNADY phase change is accompanied by the partial monomerisation to 9-CNA, as described by previous workers. However, since 9-CNADY is still a single crystal, as seen from plate 1, the change can be homogeneous, as previously suggested.lo As seen from fig. 5, the actual molecular movement involved in the transformation 9-CNAD -+ 9- CNADY is very small. The high R factor for this structure, the rather large e.s.d. associated with the various parameters, as well as the incapacity to refine anisotropically can be attributed to disorder caused by the presence of monomer.Upon full refinement the site occupancy factors for all atoms in the asymmetric unit were allowed to vary, with the constraint, however, that all atoms within a given molecule have the sameC. R. THEOCHARIS AND W. JONES 863 (b 1 Fig. 5. Stereo plots of (a) 9-CNAD and (b) 9-CNADY along the needle axes. occupancy factor. The occupancy factor for both molecules in the unit cell refined to 0.92(5), indicating that monomerisation has probably occurred to an extent of 8%. However, unlike the situation obtained in other case^,^^^ 2o it was impossible to locate the position of the monomer owing to lack of data and because of the probable close proximity of the monomer atoms to those belonging to the dimer.The presence of monomer was, however, confirmed by observing the characteristic blue fluorescence of 9-CNA in the 9-CNADY crystal. 9-CNAD crystals showed no fluorescence. The geometry of the molecules in 9-CNADY can be described by the use of the same dihedral angles as before. Thus C( 1 lA)-C(9A)-C( 1OB)-C( 14B) is 127", C( 13A)-C(9A)-C( 10B)-C( 12B) is 109", C( 14A)-C( lOA)-C(9B)-C( 1lB) is 138" and C( I2A)-C( lOA)-C(9B)-C( 13B) is 1 13". The two phenyl rings within residue A subtend a dihedral angle of 142" and within residue B, 136". The values of these angles are slightly different for molecule 2. Thus C( 1 lC)-C(9C)-C( 10D) -C(14D) is 114", C(13C)-C(9C)-C(lOD)-C(l2D) is 124", C(14C)-C(lOC) -C(9D)-C( 1 1 D) is 120" and C( 12C)-C( 1 OC)-C(9D)-C( 13D) is 130".The two864 STRUCTURE OF 9-CYANOANTHRACENE trans DIMER Fig. 6. Stereo plots of residues A and C in 9-CNADY. These should become parallel during the 9-CNADY + 9-CNA transformation. phenyl rings within residue C make a dihedral angle of 144" and within D, 132". The lack of a real centre of symmetry is reflected by the non-parallelity of the rings of A to those of B or of C to those of D. THE 9-CNADY + 9-CNA TOPOTACTIC REACTION Plate 1 consists of optical micrographs under cross-polarised light of a 9-CNAD single crystal during heating. Plate 1 (a) is the initial state and plate 1 (b) corresponds to 9-CNADY (still in a single-crystal state) wheras plate 1 (c) shows the beginning of emergence of a second phase (assigned by previous workers to 9-CNA) randomly within the mother crystal.Plate 1 (d) shows that as monomerisation progresses further, 9-CNA single crystals are obtained which are oriented at almost right angles to the 9-CNADY needle axis. All 9-CNA crystals are parallel and, as seen from plate 1 (d), grow along the samecrystallographic direction. This indicated a topotactic relationship, especially since no evidence for melting was observed either in these studies or by calorimetry. Calculation of matching planes in the two structures indicates that [TO 11 in 9-CNADY matches with [120] in 9-CNA and [Ol I] with [loll. Both [Toll and [Oll] are at almost right angles to [I 113, the long-needle direction in 9-CNADY. The mechanism for the 9-CNADY topotactic monomerisation can be envisaged to be as follows.Monomerisation of molecules 1 and 2 (fig. 3) will lead to residues A and C moving away from B and D, respectively, and closer, but at an angle, to each other. The cyano groups in A and C are aligned in the same direction (fig. 6). Flat molecules with extended conjugated n-bonded systems, such as 9-CNA, often pack with their mean planes parallel, so as to optimise n-n interactions. It is therefore likely that A and C will move relative to each other so as to become parallel. This movement should disrupt the 9-CNADY lattice, and as residues B and D undergo a similar process with residues in neighbouring asymmetric units, a new phase will separate out. The molecular movements so described are all in directions at an angle to the needle direction [I 111 and hence can explain the growth of monomer phase sideways from the 9-CNADY needle. The 9-CNAD to 9-CNADY transition is of the single- crystal + single-crystal kind, because monomerisation has occurred randomly in the crystal and to an extent of only 8% , presumably too low a conversion to cause disruption of the lattice.The common vectors between the 9-CNADY and 9-CNA crystal structures defined above indicate that the contact planes between the two structures are the (212) and (Ill), respectively. Views of the two crystal structures down the respective planes indicate molecules in approximately similar orientations, although too close a match cannot be expected owing to the different molecular shapes and because of molecular movement during reaction. The rotation of 9-CNA molecules required during reaction is small: the two phenyl rings that in residue AJ .Chem. SOC., Faraday Trans. I , Vol. 85, part 4 Plate I b4 .C( 5 a 3 n s C. R. THEOCHARIS AND W. JONES n 0 v (Facing p . 864)C . R. THEOCHARIS AND W. JONES 865 are in the dimer at a dihedral of 142" have to become coplanar, this requiring a rotation of 70" for each ring. The same process occurs for residue C, where the initial angle is 70". Ring C(1A) - - . C(12A) has to rotate clockwise and C(1C) ---C(12C) anticlockwise. In 9-CNADY the dihedral angle between C(IA) -.- C(12A) and C(1C) ..- C(l2C) is 105" and between C(5A) . - - C(14A) and C(5C) C(14C) is 77". Therefore, on monomerisation residues A and C should subtend a dihedral angle of only 20". CONCLUSIONS Associated with peak A of the calorigram reported by other workers is a topotactic phase transition from one dimer structure to another.This transition is accompanied by a homogeneous monomerisation to the extent of ca. 8% . This second dimeric phase monomerises in a topotactic manner to give the 9-CNA crystal structure. The first stage of monomerisation (9-CNAD + 9-CNADY) is reversiblelO because it is of the single-crystal -+ single-crystal type, but the second one (9-CNADY + 9-CNA) is irreversible since it involves phase separation. The second phase is one in which homogeneous topochemical dimerisation to 9-CNAD is not possible. We thank Prof. J. M. Thomas F.R.S. and Dr S . Ramdas for useful discussions and the S.E.R.C. for financial support. The provision of a sample of 9-CNAD by Dr E.M. Ebeid is greatly appreciated. APPENDIX Table 1. Crystal and refinement data compound formula mol. weight :r group b l A CIA al" PI" Yl" VIA3 F(OO0) D,/mg mP3 z p1cm-l crystal size/mm total data unique total data observed significance test weighting scheme, g R Rw AlA emin, m d " CNAD 406.49 10.1 46( 1) 17.785( 1) 11.501(1) 92.95( 1) 95.59( 1) 89.82( 1) 2062.7 848 1.309 4 5.13 1.5418 0.15 x 0.10 x 0.1 1 3,70 7807 2785 0.002 0.0436 0.0407 C30N2H18 Pi 6 > 2 4 6 ) CNADY (406.49) P1 10.2 17(2) 10.235(2) 11.594(2) 95.20(2) 90.37(2) 120.13( 1) 1042.4 424 1.295 2 5.08 1.5418 0.35 x 0.10 x 0.05 3,70 3465 1172 F, > 2.50(F0) 0.015 0.1015 0.1044 (C,ON2H,*)866 STRUCTURE OF 9-CYANOANTHRACENE trans DIMER Table 2. Atom coordinates ( x lo4) for 9-CNAD 5047(4) 6 1 9 1 (4) 6 180(4) 5002(4) 525(5) - 541(4) - 564(4) 4 1 O(4) 2570(5) 2607(3) 3854(4) 3882(3) 1454(3) 1 546( 5) 26 17( 5) 2643(3) 4902(49) 6978(39) 6970(32) 4872(39) 33 8( 32) - 1480(57) - 1457(37) 303(33) 2846( 39) - 32(5) - 1192(6) - 11 86(7) - 75(6) 45 12(4) 5529(5) 5 63 9( 6) 4606( 5) 2409(3) 2322(6) 1065(5) 1102(6) 3552(4) 2374(4) 2395(6) 3 5 37( 5) - 1 17(30) - 2064(39) - 2025(52) - 90( 3 5) 4207(46) 61 14(34) 6256(55) 4445(46) 2422(30) 20 18(3) 3 628( 2) 3426(2) 2842(2) 241 5(2) 261 l(2) 31 lO(3) 371 5(2) 3 8 30( 2) 339 l(2) 2166( 1) 3230(2) 2606(2) 3 3 3 7( 2) 2697(3) 4 1 5 1 (2) 4761( 1) 4 1 59(30) 3828(22) 2657( 19) 2064(23) 2138( 18) 298 5 (3 3) 4029(21) 42 12( 19) 179 l(22) 1 3 64( 3) 1576(3) 2570(3) 241 l(3) 1895(2) 1272(4) 1 177(3) 1595(2) 2841(3) 178O(3) 2382(3) 1699(3) 2296(2) 814(2) 227(3) 988( 17) 1406(22) 2180(31) 3 1 14(20) 2852(27) 1956( 19) 720(31) 617(27) 3123(17) 144 1 (2) 2 197(4) 3V3) - 444(4) - 1273(3) - 1572(4) - 2406(3) - 2520(5) - 1743(4) - 832(3) 229(4) - 1324(3) - 247(3) - 1056(2) - 699(2) - 1483(4) 81 3(5) 12 19(3) 648(47) - 230(36) - 1520(29) - 2339(36) - 2874(29) - 3 157(52) - 1771(34) - 170(30) - 2034(36) -93(5) 434(6) 1239(7) 1565(4) 2425(5) 2556(4) 1759(6) 847(5) 1302(5) 257(4) 1062(6) 1521(3) - 290(3) 754(5) - 783(3) - 1 184(6) - 679(28) 1 64( 3 5) 1839(49) 2026( 32) 3 0 7 7 (42) 3240(3 1) 1893(50) 432(44) 2047(27) 4889(3)C.R. THEOCHARIS AND W. JONES Table 2. (cont.) - atom x / a 3379(3) - 974(4) 3909(3) 3 08 8 (4) - 2042(4) - 2574(5) - 2060( 5) - 305(4) 802(5) 1181(3) 1733(4) - 929(4) - 381(3) - 768(4) - 1 133(4) 1772(29) 40 1 8( 58) 4825(29) 3477(28) - 797(43) - 2583(38) -3615(42) - 246 1 (33) 1 4 1 8( 56) 7004(4) 7585(4) 7090(7) 1915(4) 1098(7) 1630(7) 2985(7) 5 327( 4) 4228( 3) 5932(4) 5402( 5) 3807(5) 3291(4) 5765(4) 6076(5) 7299(47) 8289(33) 73 54(42) 1 522( 59) 1129(30) 3470(37) 38 12(27) 59 39( 5) 5379(37) -21(56) Y l b z / c 1377(2) 755(2) 207(2) 146(2) 788(3) 1035(2) 897(2) 897(2) 274(2) 680(2) 1664(2) 2260(2) 1784( 16) 1762(35) 690( 16) - 208(2) - 292(3) 63(2) - 2 19( 16) - 696(24) -71(22) 930(24) 1457( 19) 3930(3) 4224(2) 4832(4) 5207(3) 4790(3) 4239(4) 3 63 3 (4) 3550(4) 4082(2) 5332(2) 4303(2) 4928(3) 4098(3) 4727(2) 3337(2) 2784(2) 3327(27) 3883( 19) 5020(25) 5671 (21) 5 3 64( 34) 4260( 33) 3275( 17) 3015(21) 5603( 15) - 7 1 3( 3 3) 5093(4) 5679(4) 60 12(4) 7 5 66( 3) 7969( 3) 7443(4) 6489(4) 4969(3) 6138(5) 523 l(3) 5789(3) 6065(3) 661 l(3) 4620(4) 4330(3) 449 5( 26) 5065(57) 574 l(27) 63 78( 2 5) 7 8 8 5( 3 9) 8404(36) 7615(39) 6029( 30) 68 17(53) 2590(5) 2084(6) 2438(5) 4002(4) 4362(6) 4892(6) 5123(7) 5023(4) 3872(3) 3 5 34( 4) 3934(4) 3373(5) 4772(4) 420 l(3) 5 3 69(4) 563 l(4) 3 866( 44) 220 l(3 1) 1147(39) 1990(34) 3592(55) 3988(54) 5239(28) 3262(24) 5 545( 33) 867868 STRUCTURE OF 9-CYANOANTHRACENE ttYZ?ZS DIMER Table 3.Bond lengths (A) for 9-CNAD C(2A)-C( 1 A) C( 3A)-C(2A) C( 12A)-C(4A) C( 14A)-C(5A) C(8A)-C( 7A) C( 1 1 A)-C(9A) C( 15A)-C(9A) C( 12A)-C( 1 OA) C(9B)-C( 1 OA) C( 14A)-C( 1 3A) C(2B)-C( 1 B) C(3B)-C(2B) C( 12B)-C(4B) C( 14B)-C(5B) C(8B)-C(7B) C( 1 1 B)-C(9B) C( 15B)-C(9B) C( 14B).-C( 1 OB) C( 14B)-C( I3B) C(2C)-C( 1 C) C(3C)-C(2C) C( 12C)-C(4C) C( 14C)-C(5C) C( 1 1 C)-C(9C) C( 15C)-C(9C) C( 12C)-C( 1 OC) C( 12C)-C( 1 1 C) C(8C)-C(7C) N( 1 C)-C( 15C) C( 1 1 D)-C( I C) C(4D)-C( 3D) C(6D)-C(5D) C(7D)-C(6D) C( 13D)-C(8D) C( 13D)-C(9D) C( 15D)-C(9D) C( 14D)-C( 1 OD) C( 14D)-C( 1 3D) 1.370(7) 1.372(7) 1.365(6) 1.4 12(7) I .376(6) I .483(7) 1.476(7) 1.5 12(6) 1.630(6) 1.425(6) 1.41 7( 10) 1.405( 1 1) 1.410(9) 1.36 1 (7) 1.41 3(9) 1.583(8) 1.473(6) 1.587(9) 1.384(6) 1.403(6) 1.379(7) 1.409(6) 1.354(8) 1.344(7) .509(7) .504(8) .479(8) .3 97( 6) .175(6) .376(7) .426( 10) .39 1 ( 10) C( 1 1 A)-C( 1 A) C(4A)-C( 3A) C( 6A)-C( 5A) C( 7A)-C(6A) C( 13A)-C(8A) C( 13A)-C(9A) C( 1 OB)-C(9A) C( 14A)-C( 1 OA) C( 1 2A)-C( 1 1 A) N( 1 A)-C( 1 5A) C( 1 1 B)-C( 1 B) C(4B)-C( 3 B) C( 6B)-C( 5B) C(7B)-C(6B) C( 13B)-C(8B) C( 13B)-C(9B) C( 12B)-C( 1 OB) C( 12B)-C( 1 1 B) N( 1 B)-C( 15B) C( 1 1 C)-C( 1 C) C(4C)-C(3C) C(6C)-C( 5C) C(7C)-C(6C) C( 13C>-C(8C) C( 13C)-C(9C) C( 14C)-C( 1 OC) C( 14C)-C( 1 3C) C(9C)-C( 10a) C(2D)-C( 1 D) C(3D)-C(2D) C( 12D)-C(4D) C( 14D)-C( 5D) 1.351( 11) C( 8D)-C( 7D) 1.386( 10) C( 1 I D)-C(9D) 1.542(8) C(9D)-C( 1 Oa) 1.458(6) C( 12D)-C( 1 OD) 1.524(7) C( 12D)-C( 1 1 D) 1.40 l(7) N( 1 D)-C( 15D) 1.406(6) 1 .42 1 (6) 1.399(8) 1.364(8) 1.375(6) 1.478(6) 1.652(10) 1.433(6) 1.4 12(5) I.158(6) 1.354(8) 1.322(10) I .38 l(7) 1.4 12( 8) 1.425(8) 1.580(8) 1.480(9) 1.377(8) 1.1 19(8) 1.386(6) 1.360(6) 1.402(7) 1.424(7) 1.531(8) 1.665(8) 1.380(6) 1.410(8) 1.329( 10) 1.367(9) 1.398(7) 1.383(11) 1.5 16(8) 1.630(7) 1.533(8) 1.082(6) 1.377(7) 1.49 l(7) 1.395(7) Table 4.Bond angles (") for 9-CNAD C(2A)-C( 1 A)-C( 1 1 A) C(2A)-C( 3A)-C(4A) C(6A)-C(SA)--C( 14A) C(6A)-C(7A)-C( 8A) C( 1 1 A)-C(9A)-C( 1 3A) C( 13A)-C(9A)-C( 15A) C( 1 3A)-C(9A)-C( 1 OB) C( 12A)-C( 1OA)-C( 14A) C( I4A)-C( 1 OA)-C(9B) C( 1 A)-C( 1 1 A)-C( 12A) 122.3(4) ! 19.7(5) 122.0(5) 12 1.7( 5) 11 1.6(5) 110.1(5) 110.9(5) I 07.8 (4) 1 12.7(4) 116.7(4) C( 1 A)-C(2A)-C( 3A) C(3A)-C(4A)-C( 12A) C( 5A)-C( 6A)-C( 7A) C(7A)-C(8A)-C( 13A) C( 1 1 A)-C(9A)-C( 15A) C( 1 1 A)-C(9A)-C( 1 OB) C( 1 5A)-C(9A)-C( 1 OB) C( 12A)-C( 1 OA)-C(9B) C( 1 A)-C( I 1 A)-C(9A) C(9A)-C( 1 1 A)-C( 1 2A) 119.9(4) 119.6(4) 118.8(5) 120. I(4) 109.3( 5) 1 11.7(5) 102.9( 5) I10.7(3) 126.7(4) I16.6(4)C.R. THEOCHARIS AND W. JONES Table 4. (con?.) 869 C(4A)-C( 12A)-C( 1 OA) C( 1OA)-C( 12A)-C( 1 1 A) C(8A)-C( 1 3A)-C( 14A) C(5A)-C( 14A)-C( 1 OA) C( lOA)-C( 14A)-C( 1 3A) C(2B)-C( 1 B)-C( 1 1 B) C(2B)-C(3B)-C(4B) C(6B)-C(SB)-C( 14B) C(6B)-C(7B)-C( 8B) C( 1 1 B)-C(9B)-C( 1 3B) C( 13B)-C(9B)-C( I5B) C( 10A)-C(9B)-C( 13B) C( 12B)-C( 10B)-C( 14B) C(9A)-C( 1OB)-C( 14B) C( 1 B)-C( 1 1 B)-C( 12B) C(4B)-C( 12B)-C( 1 OB) C( 1OB)-C( 12B)-C( 1 I B) C(8B)-C( 13B)-C( 14B) C(5B)-C( 14B)-C( IOB) C( 1OB)-C( 14B)-C( 13B) C(2C)-C( 1 C)-C( 1 1 C) C(2C)-C( 3C)-C(4C) C( 1 1 C)-C(9C)-C( 13C) C( 13C)-C(9C)-C( 15C) C( 13C)-C(9C)-C( 10a) C( 1 2C)-C( lOC)-C( 14C) C( I C)-C( 1 1 C)-C( 12C) C(4C)-C( 12C)-C( 1 OC) C( 1 0C)-C( 12C)-C( 1 1 c C(5C)-C( 14C)-C( 1 OC) C( 1 0C)-C( 14C)-C( 1 3 c C(6C)--C(SC)-C( 14C) C(6C)-C(7C)-C( 8C) C(8C)-C( 13C)-C( 14C) C(2D)-C( 1 D)-C( 1 1 D) C(2D)-C( 3 D)-C(4D) C(6D)-C(SD)-C( 14D) C(6D)-C(7D)-C( 8D) C( 1 1 D)-C(9C)-C( 13D) C( 13D)-C(9D)-C( 15D) C( 13D)-C(9D)-C( I Oa) C( 12D)-C( 1 0C)-C( 14D) C( 1 D)-C( 1 1 D)-C( 12D) C(4D)-C( 12D)-C( 1 OD) C( 1 OD)-C( 1 2D)-C( 1 1 D) C(8D)-C( 13D)-C( 14D) C(5D)-C( 14C)-C( lOD) C( 1 OD)-C( 14D)-C( 1 3D) 122.0(4) 1 16.4(4) 121.2(4) 122.4(5) 1 2 1.5(4) 1 15.9(6) 1 20.3( 7) 118.7(5) 116.3(6) 05.8(4) 10.8(4) 1 1.6(4) 08.9( 5) 09.4( 5) 24.4(6) 22.2( 6) 119.9(6) 119.0(6) 123.0(4) I13.8(5) 12 1.2(4) 120.5(4) 120.7(4) 119.6(5) 108.6(4) 1 10.4(4) 1 09.2( 4) 112.2(5) 1 18.9(4) 122.5(5) 1 17.0(4) 119.6(5) 123.3(4) 117.8(4) 118.0(5) 122.4(7) 120.3(6) 121.7(8) 108.4(4) 110.2(4) 109.1(4) 1 07.3 (4) 120.4(5) 119.8(5) 118.2(5) 1 2 1.4( 6) 1 22.4( 5) 119.6(5) C(4A)-C( 12A)-C( 1 1 A) C(8A)-C( 13A)-C(9A) C(9A)-C( 1 3A)-C( 14A) C(5A)-C( 14A)-C( 13A) C(9A)-C( 1 5A)-N( 1 A) C( 1 B)-C(2B)-C(3B) C(3B)-C(4B)-C( 12B) C( 5B)-C( 6B)-C( 7B) C(7B)-C(8B)-C( 13B) C( 1 1 B)-C(9B)-C( 15B) C( 1 OA)-C(9B)-C( 1 1 B) C( 1 OA)-C(9B)-C( 1 5B) C(9A)-C( 1OB)-C( 12B) C( 1 B)-C( 1 1 B)-C(9B) C(9B)-C( 1 1 B)-C( 12B) C(4B)-C( 12B)-C( 1 1 B) C(SB)-C( 13B)-C(9B) C(9B)-C( 13B)-C( 14B) C(5B)-C( 14B)-C( 13B) C(9B)-C( 1 5B)-N( 1 B) C( I C)-C(2C)-C(3C) C( 3C)-C(4C)-C( 12C) c(7c)-c(sc)-c( 13C) C( 1 1 C)-C(9C)-C( 1 5C) C( 1 IC)-C(9C)-C( 10a) C( 1 5C)-C(9C)-C( 10a) C( 1 C)-C( 1 1 C)-C(9C) C(9C)-C( 1 1 C)-C( 12C) C(4C)-C( 12C)-C( 1 1 C) C(8C)-C( 13C)-C(9C) C(9C)-C( 13C)-C( I4C) C(5C)-C( 14C)-C( 13C) C( 5 C)-C( 6C)-C( 7C) C(9C)-C( 15C)-N( 1 C) C( 1 D)-C(2D)-C(3D) C(3D)-C(4D)-C( 12D) C(5D)-C(6D)-C(7D) C(7D)-C(8D)-C( 13D) C( 1 1 D)-C(9D)-C( 15D) C( 1 1 D)-C(9D)-C( 10a) C( 15D)-C(9D)-C( 1 Oa) C( 1 D)-C( 1 1 D)-C(9D) C(9D)-C( 1 1 D)-C( 12D) C(4D)-C( 12D)-C( 1 1 D) C(8D)-C( 13D)-C(9D) C(9D)-C( 13D)-C( 14D) C(5D)-C( 14D)-C(13D) C(9D)-C( 15D)-N( 1 D) 1 2 1.6(4) 126.1(4) 112.7(4) 116.1(5) 1 76.7( 5) 120.9(7) 120.8(7) 122.4( 5) 120.3(6) 109.5(4) 109.8(4) 1 09.3(4) 113.0(6) 119.9(5) 1 15.7(5) 1 17.7(6) 119.6(5) 121.3(5) 1 23.1 (5) 176.9(5) I18.8(4) 120.0( 5) 120.6( 5) 120.5( 5) 1 09.9( 4) 1 I 1.7(4) 107.0(4) 1 24.4(4) I16.5(4) 120.6(5) 124.5(5) 1 18.9(4) 179.0(4) 120.8(6) 116.3(6) 1 20.2( 7) 118.5(7) 110.9(4) 106.7(4) 122.1(4) 122.0(6) 123.2(6) 117.9(5) 179.1(5) 1 15.7(4) 11 1 3 4 ) 1 17.4(5) 1 15.4(5)870 STRUCTURE OF 9-CYANOANTHRACENE trans DIMER Table 5.Atom coordinates ( x lo4) for 9-CNADY 5047(4) 6 1 9 1 (4) 6 1 80(4) 5002(4) 525(5) -541(4) - 564(4) 4 1 O(4) 2570( 5) 2607(3) 3 8 54( 4) 3882(3) 1454(3) 1546(5) 2617(5) 2643(3) 4902(49) 6978(39) 6970(32) 4872(39) 3 3 8( 3 2) - 1480(57) - 1457(37 303(33 2846(39 - 32(5) - 1 192(6) - 1 186(7) - 75(6) 45 12(4) 5529(5) 5 63 9( 6) 4606(5) 2409(3) 2 3 22 (6) 1065(5) 1 102(6) 3 53 7( 5) 3552(4) 2374(4) 2395( 6) - I 17(30) - 2064(39) - 2025(52) - 90( 3 5) 4207(46) 61 14(34) 6256( 55) 4445 (46) 2422(30) 20 1 8( 3) 3628(2) 3426(2) 2842(2) 24 1 5(2) 261 l(2) 31 lO(3) 37 15(2) 3830(2) 339 l(2) 2166(1) 3230(2) 2606(2) 3 3 3 7( 2) 2697(3) 4151(2) 4761( 1) 4 1 59(30) 3 8 28 (22) 2657( 19) 2064(23) 2 138( 18) 298 5( 3 3) 4029(2 1 ) 421 2( 19) 1 79 l(22) 1364(3) 1576(3) 2 197(4) 2570(3) 241 l(3) 1895(2) 1272(4) 1 177(3) 1595(2) 284 1 (3) 1780(3) 2382(3) 1699(3) 2296(2) 814(2) 227(3) 988( 17) 1406(22) 2 1 80(3 1) 3 1 14(20) 2852(27) 1956( 19) 720(31) 6 17(27) 3123( 17) 1441(2) 3 1(3) - 444( 4) - 1273(3) - 1572(4) - 2406( 3) - 2520(5) - 1743(4) - 832(3) - 1324(3) - 247(3) - 1056(2) - 699( 2) - 1483(4) 229(4) 813(5) I2 19(3) 648(47) - 230(36) - 1520(29) - 2339(36) - 2874(29) - 3 157(52) - 1771(34) - 170(30) - 2034(36) - 93(5) 434(6) 1239(7) 1565(4) 2425( 5) 25 56( 4) 1759(6) 847(5) 1 302( 5) 257(4) 1062(6) 7 54( 5) 1521(3) - 783(3) - 1 184(6) - 679(28) - 290(3) 164( 35) 1839(49) 2026(32) 3077(42) 3240(3 1) 1893(50) 432(44) 2047(27) 4889(3)C.R. THEOCHARIS AND W. JONES Table 5. (cow.) 87 1 3379(3) - 974(4) 3909(3) 3088(4) - 2042(4) - 2574(5) - 2060(5) - 305(4) 802(5) 1181(3) 1733(4) - 929(4) - 381(3) - 768(4) - 1133(4) 1772(29) 40 1 8( 58) 4825(29) 3477(28) - 797(43) - 2583(38) - 36 15(42) -2461(33) 1 4 1 8 (56) 7004(4) 7.5 8 5 (4) 7090( 7) 1915(4) 1098(7) 1630(7) 2985(7) 5327(4) 4228(3) 5932(4) 5402(5) 3807(5) 329 l(4) 5765(4) 6076(5) 7299(47) 8289(33) 73 54(42) 1522(59) 1 129( 30) 3470(37) 38 12(27) 5939( 5) 5 3 79( 3 7) -21(56) 1377(2) 755(2) 207(2) 146( 2) 788(3) 1035(2) 897(2) 897(2) 274(2) 680(2) 1664(2) 2260(2) 1784( 16) 1762(35) 690( 16) - 208(2) - 292(3) 63P) - 2 19( 16) - 696(24) - 71(22) 930(24) 1457( 19) 3930(3) 4224(2) 4832(4) 5207(3) 4790(3) 4239(4) 3 63 3( 4) 3550(4) 4082(2) 5 3 3 2( 2) 4303(2) 4928(3) 409 8 (3) 4727(2) 3 3 3 7( 2) 2784(2) 3327(27) 3883( 19) 5020(25) 5671(21) 5364(34) 4260( 3 3) 3275( 17) 301 5(21) 5603( 15) - 7 1 3( 3 3) 5093(4) 5679(4) 60 12(4) 7566(3) 7969(3) 6489(4) 4969(3) 6138(5) 5231(3) 5 789( 3) 6065(3) 661 l(3) 4620(4) 4330(3) 4495(26) 5065(57) 5741(27) 63 78( 2 5) 7885(39) 8404( 36) 76 15(39) 6029(30) 6817(53) 3534(4) 2590(5) 2084(6) 2438(5) 4002(4) 4362(6) 4892(6) 5 123(7) 5023(4) 3872(3) 7443(4) 3934(4) 3 3 73 (5) 4772(4) 420 1 (3) 5 3 69( 4) 563 l(4) 3866(44) 220 l(3 1) 1147(39) 1990(34) 3592(55) 3988(54) 5239(28) 3262(24) 5545(33)872 STRUCTURE OF 9-CYANOANTHRACENE trans DIMER Table 6.Bond lengths (A) for 9-CNADY C(2A)-C( 1A) C(3A)-C(2A) C( 12A)-C(4A) C( 13A)-C(6A) C( 8A)-C( 7A) C( 1 1 A)-C(9A) C( 15A)-C(9A) C( 1 2A)-C( 1 OA) C(9B)-C( 1 OA) C( 14A)-C( 13A) C(2B)-C( 1 B) C(3B)-C(2B) C( 12B)-C(4B) C( 14B)-C( 5B) C( 8 B)-C( 7B) C( 1 1 B)-C(9B) C( 15B)-C(9B) C( 14B)-C( 1 OB) C( 14B)-C( 13B) C(2C)-C( 1C) C(3C)-C(2C) C( 12C)-C(4C) C( 14C)-C(5C) C( 1 1 C)-C(9C) C( 15C)-C(9C) C( 12C)-C( 1 OC) C( 14C)-C( 13C) C(SC)-C(7C) C(9D)-C( 1 OC) C(2D)-C( 1 D) C( 3D)-C(2D) C( 12D)-C(4D) C( 14D)-C(5D) C(8D)-C(7D) C( 1 1 D)-C(9D) C( 15D)-C(9D) C( 14D)-C( 1 OD) C( 14D)-C( 1 3D) 1.525(52) 1.248(65) 1.367(46) 1.282(50) 1.5 18(58) 1.560(12) 1.528(34) 1.5 5 1 (47) 1 .700( 7) 1.541 (58) 1.326(44) 1.529(62) 1.499(40) 1.501(52) 1.700(7) 1.45 l(6) 1.450(54) 1.381(6) 1.346(61) 1.297(58) 1.439(62) 1.261(51) 1.356(53) 1.499(70) 1.66 l(59) 1.571(49) 1.392(53) 1.529( 5 1) 1.541(59) 1.335(40) 1.420(41) 1.346(52) 1.225(41) 1.507( 50) 1.414(36) 1.372(44) 1.394(43) 1.479(57) C( 1 1 A)-C( 1 A) C(4A)-C( 3A) C(6A)-C( 5A) C( 7A)-C(6A) C( 14A)-C(8A) C( 1 3A)-C(9A) C( 1 OB)-C(9A) C( 14A)-C( 1 OA) C( 12A)-C( 1 1 A) N( 1 A)-C( 1 5A: C( 1 1 B)-C( 1 B) C(4B)-C( 3 B) C(6B)-C( 5B) C(7B)-C(6B) C( 13B)-C(8B) C( 13B)-C(9B) C( 1 2B)-C( 1 OB C( 12B)-C( 1 1 B) N( 1 B)-C( 15B) C( 1 1 C)-C( 1 C) C(4C)-C( 3C) C(6C)-C( 5C) C(7C)-C(6C) C( 13C)-C(8C) C( 1 OD)-C(9C) C( 13C)-C(9C) C( 14C)-C( 1 OC) C(l2C)-C( 1 1 C) N( 1 C)-C( 15C) C( 1 1 D)-C( 1 D) C(4D)-C(3D) C(6D)-C(5D) C(7D)-C(6D) C( 13D)-C(8D) C( 13D)-C(9D) C( 1 2D)-C( 1 OD) C( 12D)-C( 1 1 D) N( 1 D)-C( 1 5D) 1.505(46) 1.294(65) 1.36 l(47) 1.269(60) 1.371(43) 1.654(40) 1.540(48) 1.12 l(47) 1.567(40) 1.367(58) 1.438(53) 1.539(48) 1.323(41) 1.369(39) 1.480(5 1) 1.340(38) 1.186(47) 1.40 1 (55) 1.430(62) 1.5 14(69) 1.304(59) 1.461(44) 1.818(42) 1 .66 1 (7) 1.659(7) 1.535(67) 1.159(66) 1.30 1 (54) 1.282(61) 1.262(60) 1.403(64) 1.422(5 1) 1.708(43) 1.506(32) 1.13 l(43) 1.543(53) 1.379(35) 1.474(45) Table 7.Bond angles (") for 9-CNADY C( 1 1 A)-C( 1 A)-C(2A) C(4A)-C(3A)-C(2A) C( 13A)-C( 5A)-C(6A) C(8A)-C( 7A)-C( 6A) C( 13A)-C(9A)-C( 1 1A) C( 1 5A)-C(9A)-C( 13A) C( 1 OB)-C(9A)-C( 13A) C( 14A)-C( 1OA)-C( 1 2A) C(9B)-C( 1OA)-C( 14A) C( 12A)-C( 1 1 A)-C( 1 A) 105.3(31) 126.2(63) 113.8(36) 127.6(35) 108.5(29) 115.8(29) 121.9(30) 119.1(30) 103.0(26) I20.0(24) C(3A)-C(2A)-C( 1 A) C( 12A)-C(4A)-C(3A) C(7A)-C( 8A)-C( 5A) C( 14A)-C(8A)-C(7A) C( 1 5A)-C(9A)-C( 1 1 A) C( 1 OB)-C(9A)-C( 1 1 A) C( 10B)-C(9A)-C( 15A) C(9B)-C( 1OA)-C( 12A) C(9A)-C( 1 1 A)-C( 1 A) C( 12A)-C( 1 lA)-C(9A) 124.7(52) 114.5(46) 119.1(34) 105.5(44) 105.4(21) 105.2(25) 9 8.4( 26) 121.8(27) 125.3(27) 1 14.5(26)C.R. THEOCHARIS AND W. JONES Table 7. (cont.) 873 C( 1 0A)-C( 12A)-C(4A) C( 1 1 A)-C( 12A)-C( 1 OA) C( 14A)-C( 1 3A)-C( 5A) C( 1 0A)-C( 14A)-C(8A) C( 1 3A)-C( 14A)-C( 1 OA) C( 1 1 B)-C( 1 B)-C(2B) C(4B)-C( 3 B)-C(2B) C( 14B)-C(5B)-C(6B) C(8B)-C(7B)-C(6B) C( 1 1 B)-C(9B)-C( 1 OA) C( 1 3B)-C(9B)-C( 1 1 B) C( 1 5B)-C(9B)-C( 1 1 B) C( 12B)-C( 1 OB)-C(9A) C( 14B)-C( 1OB)-C( 12B) C( 1 2B)-C( 1 1 B)-C( 1 B) C( 1 0B)-C( 12B)-C(4B) C( 1 1 B)-C( 12B)-C( 1 OB C( 14B)-C( 13B)-C(8B) C( 1 0B)-C( 14B)-C( 5B) C( 1 3B)-C( 14B)-C( 1 OB C( 1 1 C)-C( 1 C)-C(2C) C(4C)-C( 3C)-C(2C) C( 13C)-C(9C)-C( 1 1 C) C( 15C)-C(9C)-C( 13C) C( 14C)-C( 1OC)-C( 12C) C( 1 2C)-C( 1 1 C)-C( 1 C) C( 1OC)-C( 12C)-C(4C) C( 1 1 C)-C( 12C)-C( 1 OC) C( 1 0C)-C( 14C)-C(5C) C( 14C)-C(5C)-C(6C) C(SC)-C(7C>-C(6C) C( 1 OD)-C(9C)-C( 13C) C(9D)-C( 1OC)-C( 14C) C( 14C)-C( 13C>-C(SC) C( 1 3C)-C( 14C)-C( 1 OC) C( 1 1 D)-C( 1 D)-C(2D) C(4D)-C(3 D)-C(2D) C( 14D)-C(5D)-C(6D) C( 8D)-C( 7D)-C( 6D) C( 1 1 D)-C(9D)-C( 1OC) C( 13D)-C(9D)-C( 1 1 D) C( 15D)-C(9D)-C( 1 1 D) C( 12D)-C( 1 OD)-C(9Dj C( 14D)-C( 1 OD)-C( 12D) C( 1 2D)-C( 1 1 D)-C( 1 D) C( 1 OD)-C( 12D)-C(4D) C( 1 1 D)-C( 12D)-C( 1 OD) C( 14D)-C( 13D)-C(8D) C( 1 OD)-C( 14D)-C(5D) C( 1 3D)-C( 14D)-C( 1 OD) 12 1.6( 32) 112.8(28) 119.9(36) 126.9(42) 100.5(30) 1 19.6(28) 106.2(40) 1 24.2( 39) 112.7(29) 95.8(22) 109.1(27) 98.2(31) 1 17.0(29) 102.0( 35) 117.8(23) 1 18.2(29) 124.9(30) 124.4(34) 1 23.3( 34) 124.0(35) 120.1(36) 121.1(40) 117.5(50) 119.0(50) 97.7(30) 97.2(29) 112.5(19) 9 5.5( 3 2) 1 2 8 3 37) 108.1(38) 124.0(45) 102.6( 37) 1 23.1 (3 2) 123.5(45) 114.9(39) 119.2(42) 114.9(46) 119.7(42) 11 1.6(37) 110.1(35) 118.1(33) 121.8(35) 100.9( 19) 1 15.4(24) 113.9(37) 119.6(28) 112.6(25) 1 24.8( 34) 12 1.7(29) 126.3(29) C( 1 1 A)-C( 1 2A)-C(4A) C(9A)-C( 13A)-C(5A) C( 14A)-C( 13A)-C(9A) C( 1 3A)-C( 14A)-C(8A) N( 1 A)-C( 1 5A)-C(9A) C(3B)-C(2B)-C( 1 B) C( 12B)-C(4B)--C(3B) C( 7B)-C( 6B)-C( 5B) C( 13B)-C(8B)-C(7B) C( 13B)-C(9B)--C(lOA) C( 1 5B)-C(9B)-C( 1 OA) C( 15B)-C(9B)-C( 13B) C( 14B)-C( 1 OB)-C(9A) C(9B)-C( 1 1 B)-C( 1 B) C( 12B)-C( 1 1 B)-C(9B) C( 1 1 B)-C( 12B)-C(4B) C(9B)-C( 13B)-C(8B) C( 14B)-C( 13B)-C(9B) C( 13B)-C( 14B)-C(5B) N( 1 B)-C( 15B)-C(9B) C(3C)-C(2C)-C( 1 C) C( 12c)-c(4c)-c(3c) C( 15c)-c(9c)-c( 1 1 C) C(7C)-C(6C)-C( 5C) C( 13C)-C(SC)-C(7C) C( 1 OD)-C(9C)-C( 1 1 C) C( 1 OD)-C(9C)-C( 1 5C) C(9D)-C( 1OC)-C( 12C) C(9C)-C( 1 1 C)-C( 1 C) C( 12C)-C( 1 1 C)-C(9C) C( 1 1 C)-C( 12C)-C(4C) C(9C)-C( 13C)-C(8C) C( 14C)-C( 13C)-C(9C) C( 1 3C)-C( 14C)-C(5C) N( 1 C)-C( 15C)-C(9C) C(3D)-C(2D)-C( 1 D) C( 12D)-C(4D)-C(3D) C(7D)-C(6D)-C( 5D) C( 1 3D)-C(8D)-C(7D) C( 13D)-C(9D)-C( 1 OC) C( 15D)-C(9D)-C( 1 OC) C( 15D)-C(9D)-C( 13D) C( 14D)-C( 1 OD)-C(9C) C(9D)-C( 1 1 D)-C( 1 D) C( 12D)-C( 1 1 D)-C(9D) C( 1 1 D)-C( 12D)-C(4D) C(9D)-C( 13D)-C(8D) C( 14D)-C( 1 3D)-C(9D) C( 13D)-C( 14D)-C(5D) N( 1 D)-C( 1 5D)-C(9D) 125.3(32) 111.1(38) 1 23 .O( 38) 130.0(42) 174.1(39) 126.4(36) 133.4(33) 1 15.6(32) 127.4(33) 1 15.4(3 1) 112.8(37) 120.7(37) 104.7( 33) 1 29.6( 2 5) 110.0(24) 113.8(24) 117.9(30) 117.7(34) 112.7(35) 16 1456) 118.7(43) 113.5(50) 122.0(43) 121.0(37) 115.1(38) 122.8(3 1) 108.1(31) 116.9(36) 122.0(47) 1 28.7( 44) 13 1.9(43) 125.1(28) 11 1331) 113.1(41) 167.9(56) 115.3(36) 123.1(40) 129.5(54) 116.1(42) 102.8(27) 98.9( 3 3) 101.2(24) 109.0(2 1) 121.5(42) 122.2(37) 126.6(3 1) 128.2(32) 106.2(24) 111.8(26) 167.1(36)874 STRUCTURE OF 9-CYANOANTHRACENE trans DIMER G.M. J. Schmidt, Pure Appl. Chem., 1971, 27, 647. J. M. Thomas, Philos. Trans. R. SOC. London, 1974, 277, 251; Pure Appl.Chem., 1979, 51, 1065. H. Rabaud and J. Clastre, Acta Crystallogr., 1959, 12, 91 1. M. D. Cohen, Z. Ludmer, J. M. Thomas and J. 0. Williams, J. Chem. SOC., Chem. Commun., 1969, 117. M. D. Cohen, Z. Ludmer, J. M. Thomas and J. 0. Williams, Proc. R. SOC. London, Ser. A , 1971,324, 459. W. Jones, Ph.D. Thesis (University of Wales, 1974). 'I W. L. Rees, M. J. Goringe, W. Jones and J. M. Thomas, J. Chem. Soc., Faraday Trans. 2, 1979, 75, 806. W. R. Bergmark, G. Jones 11, T. E. Reinhardt and A. M. Halpern, J. Am. Chem. SOC., 1978, 100, 6665. J. Ferguson and S. E. H. Miller, Chem. Phys. Lett., 1975, 36, 635. lo E. M. Ebeid, S. E. Morsi and J. 0. Williams, J. Chem. SOC., Faraday Trans. 1, 1979, 75, 1111. E. M. Ebeid, S. E. Morsi and J. 0. Williams, J . Chem. SOC., Faraday Trans. 1 , 1980, 76, 2170. l2 D. Donati, G. G. T. Guarini and P. Sarti-Fantoni, Mol. Cryst. Liq. Cryst., 1972, 17, 187. l3 D. Donati, G. G. T. Guarini and P. Sarti-Fantoni, Mol. Cryst. Liq. Cryst., 1981, 65, 147. l4 D. Donati, P. Sarti-Fantoni and G. G. T. Guarini, J. Chem. SOC., Faraday Trans. I , 1982,78, 771. l5 E. M. Ebeid, A. F. M. Habib, R. M. Issa, S. A. Azim and N. J. Bridge, J. Chem. SOC., Faraday Trans. l8 International Tables for X-ray Crystallography (Kynoch Press, Birmingham, 1974), vol. IV, C. R. Theocharis, Ph.D. Thesis (University of Cambridge, 1982); W. Jones and C, R. Theocharis, J. Cryst. Spectrosc. Res., 1984, 14, 447. C. R. Theocharis, W. Jones, J. M. Thomas, M. Motevalli and M. B. Hursthouse, J. Chem. SOC., Perkin Trans. 2, 1984, 7 1. C. R. Theocharis, G. R. Desiraju and W. Jones, J. Am. Chem. SOC., 1984,106, 3606. 85, 3636. I , 1983, 79, 2133. pp. 99-101. *O H. Nakanishi, W. Jones, J. M. Thomas, M. B. Hursthouse and M. Motevalli, J. Phys. Chem., 1981, (PAPER 4/278)

ISSN:0300-9599    

DOI:10.1039/F19858100857

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1985, 81, 875-884 Pressure Dependence of Activation and Reaction Volumes BY M. V. BASILEVSKY, N. N. WEINBERG* AND V. M. ZHULIN Karpov Institute of Physical Chemistry, Obukha 10, Moscow 107120, U.S.S.R. and Zelinsky Institute of Organic Chemistry, Academy of Sciences of the U.S.S.R., Leninsky Prospect 47, Moscow 117913, U.S.S.R. Received 20th Mzrch, 1984 A simple theoretical model of high-pressure kinetic effects is proposed based on the assumption that characteristic (initial, transition or product) states of a reacting system should be identified with stationary points of an enthalpy surface rather than those of a regular potential-energy surface (p.e.s.). An explicit treatment of the deformation of a p.e.s. promoted by pressure enables one to improve the simple cylinder Stearn-Eyring model of activation volumes so as to describe the pressure dependence of activation and reaction volumes. The dependence thus obtained agrees well with experimental data in the wide pressure range from 0 to 45 kbar.The pressure behaviour of activation enthalpies and entropies is also discussed. The kinetic effects of pressure are usually discussed in terms of the transition-state In the regular thermodynamic formulation the rate constant k at a (t.s.) given pressure p is (1) kT k = exp (ASIIR) exp ( - A H t / R T ) AHJ = AUt+pAVJ. (2) The activation enthalpy, AH$, energy, AUJ, and entropy, AS$, are essentially macroscopic quantities. For the gas phase, however, they can have a microscopic interpretation, assuming that the same quantities represent the characteristics of separated microscopic reaction systems, i.e.neglecting the interaction between the systems. Then the first term in eqn (2) is usually identified with the potential barrier height on a potential-energy surface. The second term in eqn (2) is practically inessential for gas-phase processes and contains no useful information, being merely nRT (n is an integer, e.g. n = 1 for a bimolecular reaction). For reactions in a condensed medium interpretation of AUJ as a potential barrier height on a p.e.s. remains valid. For this case A V t , the activation volume, is identified with the difference of volumes between an initial state and a t.s. Its experimental determination provides some indirect information concerning the t.s. structure and reaction mechanism.Stearn and Eyring4 have attempted to relate the activation volume to a t.s. structure in terms of a simple ‘cylinder’ model. Note, however, that there are no fundamental reasons underlying the application of macroscopic thermo- dynamical concepts at a microscopic level. In particular, the volume of a microscopic system in a disordered condensed medium cannot be introduced entirely consistently. This is probably why further attempts to refine the Stearn-Eyring model by detailing the shape of a reacting system5 proved to be unsuccessful.6 The numerous ambiguities and uncertainties in the interpretation of experimental activation volumes seem to have the same origin. 875876 PRESSURE DEPENDENCE OF ACTIVATION AND REACTION VOLUMES Activation volumes decrease, in absolute terms, with pres~ure.~ This dependence is n~n-linear.~* Of all the empirical attempts3* 7-15 to describe it, the El’yanov- Vasylvitskaya equation7? * is the most successful.It reproduces the experimental activation volumes well over a wide pressure range from 0 to 12 kbar. However, because of the empirical nature of this equation its validity must be verified in each particular case when extrapolating to higher pressures. Note also that all empirical correlations, although reproducing the pressure dependence of rate constants, state nothing about the pressure dependence of activation parameters,* which makes the extrapolation of high-pressure data to other temperatures difficult. Here we propose a simple phenomenological model extending the Stearn-Eyring treatment so as to derive the pressure dependences of the activation volumes and enthalpies over a wide pressure range.This model also applies to reaction volumes and enthalpies. THE MODEL When dealing with the canonical relations eqn (1) and (2), it is always implied that configurations of reactants and t .s. are associated with respective stationary points on a p.e.s. The potential energy, U, of a system is considered to be a function of internal coordinates qi, and its extremum points (minima of reactants and products or saddle point of a t.s.) obey the stationary condition - = 0. The volumes of the respective configurations are used to obtain activation (AVt) or reaction (A V) volumes. Distortion of a p.e.s.under pressure is inevitably neglected. In a consistent microscopic treatment the volume of a reaction system (like its potential energy, U ) should be considered as a function of the internal variables qi. Then, the enthalpy, H, of the system can be introduced as a microscopic function of these variables representing the enthalpy surface of the system. This enthalpy surface should be used instead of the p.e.s. to determine the configurations of the reactants, products or t.s. This provides a natural description of the pressure dependence of AVt and AV as a result of the relative shift of the respective stationary points of the enthalpy surface. From the condition au aqi aH = O __ aqi aV - = - p - aU we obtain the main equation aqi %i (3) obeyed for the stationary points of an enthalpy surface, qi = qi. Given an explicit form of the functions U(q,) and V(qi), eqn (3) may be applied to find the coordinates qi(p) of the stationary points, from which the respective volumetric effects can be evaluated.In what follows we adopt the Stearn-Eyring model4 and treat a reaction system as a cylinder of radius r directed along the reaction coordinate q : * The only exception should, however, be mentioned : simple thermodynamical reasoning made it to describe the pressure behaviour of activation enthalpies and entropies at relatively low (ca. 5 kbar) pressures.M. V. BASILEVSKY, N . N . WINBERG AND V. M. ZHULIN 877 In this case eqn (3) takes the form au - = -2nrqp. ar THE HARMONIC APPROXIMATION Consider now the case of relatively low pressures and small p.e.s.distortions. Points (q, F ) lie in the vicinity of the parent stationary points (go, r,) of an initial p.e.s., and thereby a harmonic approximation can be used to describe the function U(q, r). We accept in addition that the cross-derivative vanishes. Then Substituting eqn (6) in eqn ( 5 ) we obtain v(4 - 40) = - nr2p O(r - To) = - 2nrqp r3-3ar+2P = 0 which then reduces to (7) Solving eqn (7) we obtain the radius of the cylinder as a function of pressure r(p) = (22/a) sin [+ arcsin (/?/da")] P 27 nr, 2 4 a = J- 2 - d(v@ - 1 (1 +-J. 2WOP 3 7 1 P The parameters of systems of interest are such that /?/2/a3 < 0.4. Therefore, this expression reduces with an error < 2-3% to the simple formuloh The cross-section of the Stearn-Eyring cylinder is then Substituting eqn (8) in eqn (7) we obtain Eqn (8) and (9) may be used to describe the pressure dependence of the activation and reaction volumes at relatively low pressures.Let q1 be the value of the reaction878 PRESSURE DEPENDENCE OF ACTIVATION AND REACTION VOLUMES 1.0 0.8 0 *4 0.2 t 0 2 4 6 8 10 12 plkbar Fig. 1. Pressure dependence of relative reaction volumes AV/AV,: 1, eqn (10) with K = 0.04 kbar-l and A = 0.10 kbar-’ ; 2, El’yanov-Hamann” equation, A V/A V, = (1 + O.O92p)-l; 3, El’yanov-Vasylvitskaya7* equation, A V/A V, = 1 - 0.17 In (1 + 3.9 1 p ) - 4, eqn (13) with o/o, calculated numerically from eqn (12) and (15) and with Q = 3.3 &l, a = 0.15, j3 = 70 kbar-l and 9 = 0.1 mydn A-l; 5, eqn (13) with constant o/o,. Curves 5 join curve 4 at; (a) pcr = 5 kbar (ocr/oo = 0.72), (b) pcr = 6 kbar (oc!Jo0 = 0.68), (c) pcr = 7 kbar (ocr/oo = 0.64) and ( d ) pcr = 8 kbar (oc,/oo = 0.60).Experimental points are:’ 0, isoprene dimerization; ., pentene+ pentan014 diamyl ether; A, pentene +propano1 -+ 2-methyl- heptan-3-01. coordinate corresponding to a pre-reaction (van der Waals) complex and q2 be its value for a t.s. or for the products. Then, combination of eqn (4), (8) and (9) results in the following equation for the respective volumetric effect, A V = V , - : where ql0 and q20 are the coordinates and ql and r2 are the force constants of the respective stationary points of a p.e.s. (q2 is negative in the case of a t.s.) and A& is the activation or reaction volume at zero (atmospheric) pressure.Eqn (10) represents the pressure dependence of AV and requires the p.e.s. parameters qlo, q20, ql, q2, 8 and oo to be known. If, however, these are unavailable, K and A in eqn (10) may be considered as adjustable empirical parameters. The test of calculations using eqn (10) (in its empirical variant) is presented in fig. 1 ; eqn (10) agrees satisfactorily with the experimental data and the empirical correlation curves7~ *, l1 in the pressure range 0-5 kbar. At higher pressures the model predicts a too rapid decrease of AV. Such non-physical behaviour of AV(p) is caused as the harmonic approximation becomes a poor model at high pressures. Estimations using eqn (8) and (9) with K = 0.04 kbar-l and 3, = 0.10 kbar-l (the values used in the A V calculations) show that at 5-7 kbar lateral compression of the Stearn-Eyring cylinderM. V.BASILEVSKY, N. N. WEINBERG AND V. M. ZHULIN 879 is as high as a/ao = 0.7-0.6; the longitudinal compression is qo-q = 0.7-0.85 A. Further lateral compression of the cylinder seems unlikely, since it would require deformation of the valence 'core' of a molecule (bond lengths and valence angles). It may continue only along the softest reaction mode. However, even for this the harmonic approximation fails to be valid at such large distortions of the initial p.e.s. Therefore, the harmonic potential eqn (6) should be replaced by a more realistic one reproducing the exponential behaviour of the short-range repulsion. THE MORSE POTENTIAL Consider the simple expression U(q, 4 = Udq) + U2(r).In order to proceed with the analytical treatment we approximate the function U,(q) by the Morse potential In this case eqn (5) takes the form U,(q) = D{ 1 - exp b(q0 - q)112. (1 1) p=- 0 0 2Da J and J Unlike eqn (lo), eqn (1 3) neglects the contribution caused by the shift of the product mininum or t.s. saddle point. This approximation should not influence the calculated results, since, as seen from eqn (lo), the relative contribution of the term neglected is proportional (at relatively low pressures when it is largest) to the ratio I qJq2 I of the force constants at the corresponding stationary points of a p.e.s. For example, in the case of dimerization of cylcopentadiene (CPD) discussed below, this contribution is < 10% for the activation volume ( I qreact/qt I w 1/10) and is completely negligible for the reaction volume (qprod 9 qreaCt).To apply eqn (13), the function a(p) = z[i;(p)l2 must be specified. For this purpose eqn (1 1) should be supplemented by an explicit expression for U2(r). In accordance with the above discussion, we approximate the function U2(r) by a harmonic potential truncated at r = rcr: J Since r = r((p), then a certain 'critical' pressure value pcr corresponds to rcr = t(pcr). At higher pressures the function ~ ( p ) becomes constant. This makes possible the direct use of eqn (12) and (13) at p > pcr: a/ao = (rCr/ro)2 = const in this case.880 PRESSURE DEPENDENCE OF ACTIVATION AND REACTION VOLUMES At 0 < p < pcr the value of a(p) can be found by solving numerically eqn (12) (15) together with e(r - ro) = - 27trqp which is obtained by substituting eqn (14) in eqn (5).The results of calculations using a = 3.3 A-l, a = 0.15, p = 70 kbar-1, 8 = 0.1 mdyn A-l and pcr = 5,6,7 and 8 kbar are presented in fig. 1. The numerical curve agrees well with the experimental data and the empirical El’yanov-Vasylvitskaya equation for pressures from 0 to 8 kbar. At higher pressures eqn (1 3) with a constant cross-section a = acr should be used. Otherwise, the degree of lateral compression of the cylinder becomes too large. We chose the junction point pcr so as, first, to fit the high-pressure experimental data and, secondly, to obtain physically reasonable value of the lateral compression acr/aO. From this reasoning the value of pcr = 8 kbar (ac,/ao = 0.60 and rcr/ro = 0.77) appears to be optimal.The joined curve reproduces the experimental data well for pressures from 0 to 12 kbar, providing a fit as good as that of the El’yanov-Vasylvitskaya equation. Thus we anticipate that eqn (13) will also remain applicable for higher pressures. Some evidence that such an extrapolation is indeed plausible is presented later by a comparison with experiment and by analysis of the results at microscopic level. PRESSURE EFFECTS ON RATE AND EQUILIBRIUM CONSTANTS El’yanov and Gonikberggg l6 have proposed that the pressure dependence of the rate and equilibrium constants are treated using I In (&/KO) = - ( A V,/RT) @ @ = [AG(p) - AGo]/A V,, AGO = AG(0) where Kp and KO correspond to pressure p and atmospheric pressure, AG(p) and AGO are the respective activation and reaction free enthalpies, A& is the volumetric effect at atmospheric pressure and @ is the so-called ‘correlation function’, usually evaluated from empirical expression^.^-^^ If the pressure dependence of A Y is known, the function @(p) can be obtained theoretically from @(p) = Jop 9 dp.AV, Integrating eqn (13) over the pressure interval from 8 to p kbar (where a/ao is independent of pressure) gives for @(p) the following expression predicted by our model for p > per: @(PI - @(Per) = acr[A(p) - A(~cr>I/ao a c r B y = - . The values of @ ( p ) for 0 < p < 8 kbar can only be obtained numerically. However, as seen from fig. 1, the empirical El’yanov-Vasylvitskaya equation7* 0 0 AV/AV, = 1 --a ln(1 +bp)M.V. BASILEVSKY, N. N. WEINBERG AND V. M. ZHULIN 88 1 is almost indistinguishable at these pressures from our numerical curve. Therefore, the corresponding analytical expression a(1 +bp) ln(1 +bp) b @,(PI = (1 +a)P- can be used to estimate @(p) at p < 8 kbar without numerical computations. One can use eqn (16) and (17) to calculate reaction rates at high pressures and, comparing the results with experimental data, to estimate the validity range of our model. Such a comparison is presented below for a number of high-pressure reactions. COMPARISON WITH EXPERIMENT CYCLOPENTADIENE DIMERIZATION AT 40 kbar Diels-Alder reactions with their high activation volumes are very sensitive to pressure effects.179 la Unfortunately, we were unable to find any report on the static studies of Diels-Alder reactions at pressures > 10 kbar.There exist, however, data on the solid-state dimerization of cylcopentadiene (CPD) at high pressure (40 kbar), combined with the shear def0rmati0n.l~ Although the interpretation of such experi- ments is rather ambiguous (the role of the shear deformation is not clear), the results of ref. (19) can be used to estimate the lower bound of the rate constant at p = 40 kbar and T = 153 K: k(40 kbar, 153 K) 2 4 x lo-* dm3 mol-1 s-l. (19) To rederive the same quantity in terms of our model, we started with an experimental rate constant k( 1 atm, 353 K) = 9 x dm3 mol-l s-l and A VJ = - 30.5 cm3 m0l-V9 The value obtained using eqn (16)-(18) and the parameters used above (a = 0.15 and y = 42 kbar-l) is k(40 kbar, 353 K) = 1.2 x lo3 dm3 mol-l s-l.It corresponds to T = 353 K. The final extrapolation to T = 153 K was based on the activation enthalpy AH (40 kbar) = 6.5 kcal mol-1 evaluated below. The result: kCa1,(40 kbar, 153 K) = 6.3 x lou3 dm3 mol-l s-l. is in reasonable agreement with experimental estimate.l9 The extrapolation using the empirical eqn (18) with a = 0.17 and b = 4.98 kbar-l recommended for Diels-Alder reactions’9 leads to k(40 kbar, 353 K) = 5.66 dm3 mol-1 s-l. Further extrapolation to T = 153 K appears impossible in the framework of the empirical treatment with no Ahrrenius parameters. OTHER HIGH-PRESSURE REACTIONS The function @(p)17 was parametrized using the value pcr = 8 kbar adopted to reproduce the high-pressure constantlg for the dimerization of CPD.However, the experience of working with empirical correlation functions points to their relatively universal nat~re.~-~v l6 That is why it seemed interesting to apply eqn (17) with the same parametrization to other high-pressure reactions. Fig. 2(a) presents the respective correlations with kinetic data for a number of high-pressure bimolecular r e a ~ t i o n s . ~ ~ - ~ ~ The linear plots obtained demonstrate a good fit of eqn (17) to the experimental data. Only the solvolysis of ally1 bromide in methanol shows poor agreement. Recalculation with changed parameters a = 0.4 and y = 5 kbar-’, however, allows us to improve the correlation considerably [cf fig. 2(b)].882 PRESSURE DEPENDENCE OF ACTIVATION AND REACTION VOLUMES - - +/kbar 4 6 8 10 t , l , I , I I I I I 8 8 4 + 3 / 6 9 12 15 10 20 30 40 I .. I . . I . . I I I I I I l l PlkbX 7 5 4 Fig. 2. Correlations between experimental In kp/ko and @(p):l7 1 , solvolysis of C(CH,),Cl in 80% EtOH;zo 2, solvolysis of C,H,Br in MeOH;20 3, solvolysis of CH,CHCH,Br in MeOH;,l 4, solvolysis of C,H,Cl in MeOH;22 5, ionization of piperidine in MeOH;23 6, esterification of pivalic acid with EtOH;24 7, ethyl pivalate hydrolysi~.~~ The following values of parameters were used in the calculations : (a) a = 0.15 and y = 42 kbar-l ; (b) a = 0.40 and y = 5 kbar-l. DEFORMATION OF A P.E.S. BY PRESSURE ACTIVATION (REACTION) ENTHALPIES AND ENTROPIES Pressure effects on the rate and equilibrium constants, as well as on the respective volumetric effects, i.e. on the macroscopic characteristics of a reaction system, have been described above.One can also estimate how pressure affects the microscopic parameters (activation energy, reaction heat, shift of stationary points), i.e. to describe p.e.s. distortion under pressure. An inherent feature of the present model is that the variation of activation enthalpy, AH2 (or reaction heat, AH), with pressure involves, except for thepAVterm, the contribution 6Ucoming from the increase of the potential energy of a system as a result of its shift along the reaction coordinate from qo (stationary point of a parent p.e.s.) to q (stationary point of an enthalpy surface): AHS(p) = AHJ-dU(p)+pAVS(p) AH$ = AH$(o). The values of AHt(p) (including the 6U and P A V terms), Aq = qo - q and A VS/A VJ for the dimerization of CPD are presented in table 1 for the pressure range 0-50 kbar.Calculations were carried out using eqn (1 1)-( 13) and (20) with a = 0.15, = 70 kbar-l, CT,,/CT~ = 0.60, a = 3.3 A-l and experimental AVJ = - 30.5 cm3 mo1-l. AHJ = AUJ = 16.5 kcal mol-l estimated from the kinetic data of ref. (19). The t.s. shift along the reduction coordinate was neglected (in accordance with the discussion above). The main contribution to AHt(p) variations is from the pAVS(p) term. The contribution of 6U is negligible and is only 0.6 kcal mol-l at 50 kbar. Note that the most essential changes in the activation volume take place in the region of relativelyM. V. BASILEVSKY, N. N . WEINBERG AND V. M. ZHULIN 883 Table 1. Some characteristics of the distorted p.e.s. of the cylcopentadiene dimerization reaction ~~ AS$ - AS,$ AH$ 6U -pA VI AGf, - AGI /cal mol-l p/kbar /kcal mol-1 /kcal mol-1 /kcal mol-l /kcal mol-' K-l A q / A AVI/AVd 0 5 10 15 20 25 30 35 40 45 50 16.5 14.7 13.7 12.3 1 1 .1 9.9 8.7 7.6 6.5 5.4 4.3 0.00 0.07 0.12 0.18 0.24 0.3 1 0.37 0.44 0.50 0.56 0.63 0.00 1.78 2.82 4.04 5.20 6.32 7.4 1 8.47 9.51 10.53 11.54 0.00 2.56 3.84 5.21 6.53 7.82 9.07 10.29 11.49 12.67 13.83 0.00 2.38 3.02 3.32 3.66 3.99 4.33 4.63 4.97 5.30 5.57 0.00 0.64 0.72 0.78 0.82 0.85 0.88 0.90 0.92 0.94 0.96 1 .ooo 0.486 0.386 0.369 0.356 0.347 0.339 0.332 0.326 0.321 0.316 low pressures, where the potential energy is almost constant (6U w 0). This is in accord with the concept6? 25 that the main contribution to A V $ comes from the free activation volume. The same result can be obtained by considering the Aq values.Comparing them with the results of quantum-chemical computations26 one can see that the Aq values listed in table 1 correspond to a pre-reaction stage when chemical bonds are almost unaltered. Therefore, the simple Morse potentialll seems to provide a reasonable approximation. At greater shifts along the reaction coordinate it fails to apply. The pressure region, where the barrier AH$ dissappears, presents a natural bound of the validity of our model. As seen from table 1, it lies near 50 kbar. Even at 40 kbar the activation enthalpy reduces to only 6.5 kcal mol-l. This result is supported by the experimental observation that the temperature dependence of the rate constants corresponding to high pressures combined with the shear deformation is weak.27 A similar effect was reported for high-pressure reactions carried out in a static regime :2s at 90 kbar acynaphthylene polymerizes at room temperature, which points to a considerable decrease of the respective activation barrier or, probably, to its complete disappearance. The values of AGS and AH$ can be obtained independently in our model [eqn (1 6)-( 17) and (20), respectively].That allows estimating the activation entropy as AS$(p) - AS2 = [AH$(p) - AH&/ T - [AG$(p) - AGi] T ASJ = ASt(0). The values of AS$(p)-ASJ calculated using this equation are presented in table 1. Unfortunately, we were unable to reproduce the sharp drop in activation entropies observed in the pressure range 0-5 kbar.29 This is because our model predicts a slight decrease of activation enthalpy AH$ in this range, whereas experiment predicts an increase.The disagreement at relatively low pressures seems to be caused by the fact that we have identified the activation enthalpy with the difference of values taken by the function H(q) at respective stationary points. The temperature dependence of the volume of a reacting system is thus neglected [term 6U in eqn (20) is of minor importance]. As might be anticipated, the corresponding error decreases as the pressure increases.884 PRESSURE DEPENDENCE OF ACTIVATION AND REACTION VOLUMES We now consider possible ways of improving our model. As presented here, it fails to work at large p.e.s. distortions, when the stationary points of the t.s.and reactants appear too close to each other and the Morse potentialll gives an incorrect description of the reaction profile. Nevertheless, the present approach is restricted by neither the applicability of the Morse potential nor the Stearn-Eyring model. One can, in principle, use a more realistic potential U(qi), refine the function V(qi) and solve eqn (3) numerically. A more advanced approach, however, is expected to work without introducing a microscopic quantity, such as volume, into the microscopic description of an elementary chemical process. A non-phenomenological treatment of pressure effects on reaction kinetics and equilibrium should be based entirely on quantum-chemical calculations of the intermolecular potential, operating a chemical system.We thank Prof. B. S. El’yanov and Dr E. M. Vasylvitskaya for helpful discussions. M. G. Evans and M. Polanyi, Trans. Faraday SOC., 1935,31, 875. S . Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes (McGraw-Hill, London, 1941). M. G. Gonikberg, L‘Equilibre Chimique et les Vitesses des Reactions sous Haute Pression (Mir, Moscow, 1974). A. E. Stearn and H. Eyring, Chem. Rev., 1941,29, 509. M. G. Gonikberg and A. I. Kitaigorodskii, Dokl. Akad. Nauk SSSR, 1958, 122, 231 (in Russian). M. G. Gonikberg, V. M. Zhulin and B. S. El’yanov, in The Physics and Chemistry of High Pressure (SOC. Chem. Industry, London, 1963), p. 212. B. S. El’yanov and E. M. Gonikberg, J. Chem. SOC., Faraday Trans. I , 1975, 71, 172. B. S. El’yanov and E. M. Vasylvitskaya, Rev. Phys. Chem. Jpn, 1980, 50, 169. B. S. El’yanov and M. G. Gonikberg, Zzv. Akad. Nauk SSSR, Ser. Khim., 1967, 1044 (in Russian). lo B. S. El’yanov, Aust. J. Chem., 1975, 28, 933. l1 B. S. El’yanov and S. D. Hamann, Aust. J. Chem., 1975, 28, 945. l2 C. Walling and D. Tanner, J. Am. Chem. SOC., 1963, 85, 612. l3 H. S. Golinkin, W. G. Laidlow and J. B. Hyne, Can. J. Chem., 1966, 44, 2193. l4 C. A. Eckert, Annu. Rev. Phys. Chem., 1972, 23, 239. l5 S. W. Benson and J. A. Berson, J. Am. Chem. SOC., 1962,84, 152. B. S. El’yanov and M. G. Gonikberg, Izv. Akad. Nauk SSSR, Otd. Khim. Nauk, 1961, 934 (in Russian). l7 W. J. le Noble, Progr. Phys. Org. Chem., 1967, 5, 207. l8 T. Asano and W. J. le Noble, Chem. Rev., 1978, 78, 407. l9 V. S. Abramov, A. A. Zharov, V. M. Zhulin and G. P. Shakhovskoi, Zzv. Akad. Nauk SSSR, Ser. 2o H. G. David and S. D. Hamann, Trans. Faraday SOC., 1954, 50, 1188. 21 H. G. David and S. D. Hamann, Discuss. Faraday SOC., 1956, 22, 114. 22 H. G. David, S. D. Hamann, and S. J. Lake, Aust. J . Chem., 1955, 8, 285. 23 S. D. Hamann, and W. Strauss, Discuss. Faraday Soc., 1956, 22, 70. 2q M. Linton, in Proceedings of the IV International Conference on High Pressure, Kyoto, 1974, p. 671. 25 E. M. Vasylvitskaya and B. S. El’yanov, Izv. Akad. Nauk SSSR, Ser. Khim., 1982, 2679 (in Russian). 26 R. E. Townshend, G. Rammuni, G. Segal, W. J. Hehre and L. Salem, J . Am. Chem. SOC., 1976, 98, 27 A. A. Zharov, D.Sc. Thesis [Moscow, 1978 (in Russian)]. 29 S. D. Hamann, Physico-chemical Effects of Pressure (Butterworths, London, 1957). Khim., 1978, 1462 (in Russian). 2190. V. C. Bastron and H. G. Drickamer, J. Solid State Chem., 1971, 3, 550. (PAPER 4/45 1)

ISSN:0300-9599    

DOI:10.1039/F19858100875

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J . Chem. SOC., Faraaby Trans. I, 1985,81, 885-911 Thermodynamics of Ionic Surfactant Binding to Macromolecules in Solution BY DENVER G. HALL Unilever Research Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, Merseyside L63 3JW Received 1 1 th April, 1984 The thermodynamic treatment of charged colloidal systems published recently is applied to solutions in which ionic surfactants bind to macromolecules. The aim is to develop an improved basis for the interpretation of thermodynamic information obtained from techniques such as electromo tive-force measurement and dialysis equilibria. The main emphasis is on binding to neutral macromolecules or to polyions with the same sign as the surfactant ions. Expressions are derived which relate the form of binding isotherm to the distribution of bound surfactant ions among the macromolecules and which enable enthalpies of binding to be obtained from the dependence on temperature of the binding equilibria.Several interesting effects are predicted. For example, (a) the average amount bound per macromolecule may decrease with increasing surfactant concentration in the presence of free micelles, (b) the surfactant monomer concentration may exhibit two maxima separated by a minimum, ( c ) increasing surfactant concentration may cause the macromolecule chemical potential to exhibit two minima separated by a maximum. The theory also explains how observed binding isotherms can be expected to depend on the concentration of macromolecules. The situation in which bound surfactant aggregates coexist with free surfactant aggregates is examined in some detail.The treatment is readily extended to more complex cases such as binding to polyacids and oppositely charged macroions. It is likely to apply equally well to other types of ion binding by macromolecules. 1. INTRODUCTION The interaction in solution between macromolecules and small molecules or ions is a topic of considerable academic and industrial interest, and a substantial amount of work in this area has been rep0rted.l Thermodynamic data obtained from experimental methods such as equilibrium dialysis2. and e.m.f. meas~rements~-~ are often presented in the form of binding isotherms. An important objective of theoretical work is to provide a framework for the interpretation of such data. For solutions in which electrostatic interactions between macroions and between different charged groups on a given macroion are incompletely screened this problem is far from straightforward.It has been approached in several ways. Early work is based on the notion that binding takes place at specific sites of which there may be several types.** The effects of electrostatic interactions between sites have been allowed for fairly simply but naively by the use of Debye-Huckel theory. This procedure results in the well known Linderstrom-Lang equation,1° which attempts to describe polyacid titration curves. More realistic but more elaborate treatments have been put forward by Tanford and Kirkwoodll and by Hi11.12 A promising alternative is the recent application of the counterion condensation model developed for rod-like polyele~trolytes.~~-~~ Unfortunately it is difficult to envisage how these approaches can be applied when the binding does not occur at well defined 885886 SURFACTANT-MACROMOLECULE INTERACTIONS sites.They are in effect model-based theories and can be expected to be of limited value when the assumptions underlying the models break down. All involve some information concerning macromolecular geometry which, if not known in advance, tends to appear in the form of curve-fitting parameters. Thermodynamic approaches should be free from the assumptions underlying model-based treatments. l8 Two examples are the thermodynamics of small systems developed by HiW9 and the theory of linkage and binding potential presented by Wyman.20* 21 The former is restricted to solutions in which the macromolecules do not interact. The latter approach has been presented in two ways.Of these the thermodynamic formulation is in principle completely general. Although the precise relationship between thermodynamic binding and amounts specifically bound is not stated in the original version of the theory, this problem has since been at least partially The theory which does this includes specific binding explicitly and treats non-specific interactions by use of the Kirkwood-Buff theory of ~olutions.~~9 24 It also allows formally for interactions between macromolecules. This treatment is perhaps the most general and rigorous yet developed in which the distinction between specific and non-specific interactions is properly observed. However, it does have drawbacks.When interactions between macromolecules are non-negligible it is far from easy to apply, and some of the quantities expressable in terms of molecular quantities lack a simple pictorial interpretation. More recently a treatment of charged colloidal systems has been developed which provides an excellent account of the thermodynamic properties of polyelectrolyte solutions and solutions of ionic surfactant~.~~ The basis of this theory is a simple expression which describes the Donnan equilibrium between a solution of the charged colloid plus supporting electrolyte and a colloid-free electrolyte solution. This expression enables the complications associated with the Poisson-Boltzmann equation to be avoided when handling electrostatic interactions.The theory combines most of the flexibility of thermodynamic treatments with some of the predictive capability of model-based approaches. As such it appears ideally suited for describing binding to charged macromolecules. A brief description of the application to polyacid titration has already been given. In the present paper this approach is extended to more cornplex systems. The main emphasis is on surfactant ion binding. This type of system is often very non-ideal and exhibits most of the awkward features one can expect to meet. Consequently if the theory succeeds in this case a similar approach can be expected to apply in other situations. The aim is to derive expressions which can be used simply to interpret experimental data and which in addition indicate the kinds of experiment needed to sort out some of the complexities one might expect to meet.2. BASIC EQUATIONS The system we consider is an aqueous solution of macromolecular and other solute species. Some or all of these species, including the macromolecules, may be charged. We suppose that the macromolecules bind some of the other species and denote such bound species by subscripts i, j , k etc. We suppose also that the macromolecules and their bound material constitute a series of complex species r, s, t etc. whose charges all have the same sign. Let Ni be the number of bound molecules or ions of type i which form part of a member of species r. For a given species r the Ni, N; etc. are fixed. However, there may be a number of species with the same amounts bound. For example, partially dissociated polyions which have the same number of dissociated groups but in which the groups dissociated differ are distinct species. For simplicity we suppose that there is at least one counterion species and one coion species whichD.G . HALL 887 are not specifically bound by the macromolecules. We denote these species by subscripts 2 and 3, respectively. We let subscript p refer to that polyion species for which all Ni are zero and in the case of a polyacid suppose that this species is the fully dissociated form. We let subscript o refer to solvent. We let c denote total concentration expressed as a molality or mole ratio with respect to solvent and let rn denote monomer concentration.In the absence of free micellar aggregates which contain species i, ci = mi + Z NZ c,. We let v, e, where e is the charge of a proton, denote the charge of species r and let vie denote the charge of monomeric i. Clearly v, = vp+x N i v i . For simplicity we suppose that lvil = 1 or zero for all i, that lv,l = Iv,I = 1, that the mi of all species for which vi = v, are such that mi < c, and that the activity coefficients of all monomeric species with the same charge are equal. Thus if vi = v2, yi = y2, whereas if vi = v,, yi = 7,. r i Let p denote chemical potential. We define the quantities OP, 8, and Bi by 8, = (/lp-+) These quantities are in effect the chemical potentials of electrically neutral components. Changes therein are, in principle at least, measurable thermodynamically, for example from e.m.f.measurements of cells without liquid junctions. When species 2 is Na+ and species 3 is C1-, 8, is simply the chemical potential of NaCl. On the other hand OH+ is the chemical potential of HCl minus that of NaCl. In this case the component to which 8,+ refers is not a chemical component in the sense that it can be isolated from the solution. It can, however, be written as H,Na-,. The disadvantages of defining components in this way are offset by other advantages. The main ones are that the total amount of any component present in the system cannot be negative and that one may simply replace the chemical potentials in treatments of uncharged systems by the corresponding Oi. At equilibrium we note that Hence if 8, is defined by (3) it follows from eqn (1)-(3) that e, = ep+c N;e,.(4) i When the above suppositions and assumptions are all valid and there is negligible association of polyions we may regard the entire system as a solution of a polydisperse polyelectrolyte plus supporting electrolyte in which the polyions are the series of species r, s, t etc. For such a solution the 8, are given by 8, = ~(T,p)+kTlnc,+~,kTlnm, ( 5 )888 SURFACTANT-MACROMOLECULE INTERACTIONS where 8 refers to the appropriate infinite-dilution standard state, /?,. is a function of T and p only and m, = k, -z (2, -PA GI where z, = I v , ~ and /?,. is always taken as positive. 8, is given by and when vi = v, 8, = @ + kT In c, + kT In rn, + 2kT In y Oi = @+kTlnmi+kTlnm,+2kTln y (7) where y = (y, 7,): is the mean ionic activity coefficient of a 1: 1 electrolyte solution whose concentration is (m, -X #?, c,.) and in which there are no other solutes present.When vi = v,, Oi is given by (9) r Oi = @+ kT In m,/c,. When vi = 0 we suppose that From eqn (4) we have Oi = @+kTlnmi. whereas eqn ( 5 ) gives 8 lnm dp+/?,kd lnm,+kd lnc, (12) where h, and u,. are, respectively, the partial molecular enthalpy and volume of species Y given by Although the variations implied by some of the partial derivatives in eqn (12) and (1 3) may not be possible at equilibrium the derivatives do not as a consequence lack physical meaning. c, and let yr = c,/cp. If we now equate the right-hand sides of eqn (1 1) and (12) we obtain Let cp = r +/?,lid lnm,+kd lnc,. (14) iD.G . HALL Multiplying this equation by y r and summing over all r gives 889 i where Subtracting eqn (15) from eqn (14), multiplying the result by y r NL and summing over all r gives at constant T and p kTdNk =x ( N , - ~ i N k ) d $ i - ~ ~ k - B ~ k ~ k T d l n m , . (17) Similarly kTdB = Z (FB-Ni8>dBi-@--P2)kTd lnrn, (18) where N i N k = c y r N i N i (19 4 i i ' r Eqn (1 5)-( 18) are the expressions on which the subsequent discussion is based. The method used to derive them is identical to that employed previously for micellar systems.26 Their most significant feature is that they are identical in form to the expressions one obtains for non-interacting macromo1ecules27 even though interactions between macromolecules are allowed for implicitly in their derivation.Consequently the complications associated with such interactions inherent in previous work based on the Kirkwood-Buff theory of At constant T and p eqn (15)-(18) lead to the following important results. From eqn (15) we deduce that have been circumvented. whereas from eqn (17) and (18) we find that at constant T and p 30890 SURFACTANT-MACROMOLECULE INTERACTIONS When i = k eqn (21) shows how the binding isotherm of species k is related to the distribution of bound k molecules among the macromolecules. From a steep rise in binding with a small change in 8, we may infer clustering of k ions on the macromolecules in the sense that some macromolecules have many more bound units of k than others. Similar expressions have been derived previo~sly~~ but only by use of assumptions which are more restrictive than those on which the present treatment is based. Since it is readily shown that the denominator on the right-hand side of eqn (23) is necessarily positive we may deduce that the left-hand side of eqn (22) is also positive.To deal with effects of temperature and pressure we write eqn (15) as where (24) H" Vo TL T i d(Bp/T)-kd lnc, = --dT+-dp-x Nid W.e note that at constant T, p , 0% and m,, H", v" and the y , do not depend on cp. Consequently and it follows that H" and V" are the respective values of H and V in the limit that Eqn (1 5 ) shows that at equilibrium the Oi are completely determined by fixing the cp + 0. variables T, p, Ni and m,. Hence dNi + (2) k d In m,. (27) aNk T , p , & , m 2 When 8, is given by eqn (8) we have the alternative expression hP VP d (Bk/T) = --dT+-dpfkd hmky2+kd lnm, T2 T where h$ and component k at infinite dilution given by are, respectively, the partial molar enthalpy and volume of vp=r$).TD. G. HALL Eqn (27) and (28) now yield 89 1 - ha] dT+ [ (z) aNk T , p , @ , m , +C("") i aNi T , p , f i dNi-kTdhmky2-kT[1-(E) aNk T , p , f i , m 2 Idlnm,. (30) Let hk be the partial molecular enthalpy of monomeric k defined by In the limit that cp -+ 0 we find from eqn (30) and (31) that It can be shown that when cp is very small the left-hand side of eqn (32) is the enthalpy change which accompanies the binding of an ion or molecule of monomeric k from solution in a closed system when the amounts of all other bound species together with T and p are kept constant.This quantity is clearly akin to the differential enthalpy of adsorption encountered in surface thermodynamics2*. 29 and may by analogy be termed the differential enthalpy of binding of species k. Eqn (32) shows how it may be obtained from the temperature dependence of mk at constant m2 and amounts bound. The same expression also results when i?k is given by eqn (9) or (10). Expressions for quantities analogous to integral enthalpies of binding2*9 29 can also be derived. However, these involve derivatives in which one of the variables to be held constant is difficult to control experimentally. Because of this the expressions which result are of less use practically than eqn (32) and for this reason we do not give details of their derivation here.Clearly the corresponding treatment of volume changes is exactly analogous to that of enthalpy changes. So far, for convenience, we have not considered solutions in which surfactant micelles are present. However, the inclusion of this extra complication poses no major additional problems when the free micelles and the complex polyion species all have the same sign. We may still treat our solution as a polydisperse polyelectrolyte in the presence of supporting electrolyte merely by regarding the micelles as new species of polyions. The expressions derived above and those derived previously for multicom- ponent micelles remain essentially unaltered. The only changes required are associated with the definitions of h,, or, mi and m,. The latter two quantities are now given by m2 = c2 - X (2, -Dr cr) - (zm -Dm) cm (33 b) r where m used either as a subscript or superscript denotes free micelles.The quantities c,,, e, zm and Pm are given by C CaN? C, = Z ca, p = a (34a, b) - a Cm (34c7 4 30-2892 SURFACTANT-MACROMOLECULE INTERACTIONS where subscript a d superscript a refer to micellar species a and the summation is over all micellar species. h, and v, are given by and it follows that eqn (25a) and (25b) should be replaced by Since the c, are all fixed at constant T, p , Oi and m2 eqn (26a) and (26b) remain unaltered but H" and The basic equations which describe the behaviour of free micelles are given in ref. (25). At constant T and p eqn (72) of this reference may be written as are no longer the limiting values of H and Bas cp + 0.kd lnc, = C Npd(O,/T)-p,kd lnm, i which for large micelles may be written approximately as where Cxid(Oi/T)-aICxivilkdlnm, = 0 i i Ny CW x. = - k (37) and a, which may be regarded as an effective micellar degree of dissociation, is given by a = Dm/lC xi vil C p- 2 2 When free micelles are present and eqn (38) holds it follows that the variables O,/T and m, are no longer all independent at constant T and p and that we may eliminate one of them from the right-hand sides of eqn (1 5), (1 7 ) and (1 8). So far we have supposed that the macromolecules do not aggregate. This effect can be allowed for in our treatment as follows. Let cp denote the concentration of macromolecules as before and let cq be the concentration of macromolecular aggregates including monomeric macromolecules.Let c, denote the rth species of aggregate as before. We now have zc,= cq and C Nrcr = cp where N, is the number of macromolecules in the rth aggregate species. Eqn (4) now becomes r r er = N,ep+z N p , . (39) aD. G. HALL Since eqn (5) holds we find that at constant T and p 893 kTd lnc, = NrdOp+x NrdOi-DrkTd lnm,. (40) i Multiplying eqn (40) by c,, summing over all r and dividing by cp we obtain after rearrangement dop = k T 3 - X NidOi-BkTd lnm, (41 1 dc cp i where Ni = (c, -mi)lcp = Ni c,/cp (42 a) i B = Dr crIcp* Eqn (41) may be written as = -kTc,d(l/c,)-x N,dO,-pkTd lnm, i and gives on cross-differentiation (43) We may infer from this equation that macromolecular association is unaffected by ion binding if the Xi do not depend on cp at constant T, p , Oi and m,.It follows that this is a necessary but not a sufficient condition for the absence of macromolecular association. It is noteworthy also that according to eqn (43) even when macromolecular association occurs. 3. SOLUTIONS OF A SINGLE IONIC SURFACTANT PLUS SUPPORTING ELECTROLYTE AND NEUTRAL MACROMOLECULES OR MACROIONS OF THE SAME SIGN The objectives of this section are to derive expressions which (a) describe the types of behaviour one might expect to observe in systems of this kind, (b) provide a basis for the interpretation of experimental thermodynamic data and (c) indicate which measurements are required to characterise a given system and to test the theory. (a) BASIC EQUATIONS AND DEDUCTIONS THEREFROM Let 1 denote surfactant ions, 2 denote counterions and 3 denote coions.In the presence or absence of free micelles 0, is given by 0, = p(T,p)+kTIna,+kTInm, (46) (47) where In a, = In m, + 2 In y(m, + c,)894 SURFACTANT-MACROMOLECULE INTERACTIONS and cp (= C N , c,) is the concentration of micellar surfactant. The total concentration of surfactant c, may be written as From eqn (17) and (20) we find that the interaction between surfactant and polymer a c, = m, + Ncp + cp. (49) dN is described by dB, kT = d lna,+d lnm, = -+($)m2d (r2 lnm, where 02 = (F- F). For free micelles we have from previous d lncy = d lna,+d lnm, = - + a d lnm, dB, kT n, _ _ where n, is the weight-average micellar aggregation number (W/N). Eqn (46)-(51) are the basic equations on which the material in this subsection rests.We now use them to obtain expressions for the derivatives - i3 lna, a lnm, a lna, (d3, cp) WC3, cp) KIc3, cp and (TIm2, C; In doing so we assume for simplicity that a is constant (as is found experimentally) and that p depends only on N. We proceed as follows. At constant c, and cp eqn (4) gives where The differentials of eqn (48) and (49) become d lna, = (1 +2m, y’)d lnrn, Y’ = [a In Y/a(m,+ CQ)IT, p . (52) d In a, + cp dN+ dcp m, dc - dm - m, dlna,+c (”) dN+adcy. - (1 +2m, y’) - (1 +2m1 y’) (53) (54) We may now substitute for dNand dcp as given by eqn (50) and (51) into eqn (53) and (54). From eqn (53) we get dc, in terms of d In a, and dm, whereas from eqn (54) we get d In a, in terms of d In m,. After rearrangement and simplification we find that i3 lna (1) = whereD.G. HALL Eqn (55) and (56) together give 895 To obtain (aN/a0,),3, cp we first express d In a, in eqn (54) in terms of do, and d In m,. We then use eqn ( 5 1 ) to eliminate dcy and eqn (50) to eliminate d lnm,. The result Finally, to obtain (a In ~ , / 8 c ~ ) ~ ~ , c3 we note that at constant rn, and c, dm+Bdc,+adcp = 0 m, 1 + 2y’m, that d x = a2d h a , and that After some trivial algebra these expressions give dcy = cy n, d In a,. -B aB + 02c --+ n, cp a m, 1+2y’m, PaN Eqn ( 5 9 , (56), (58), (59) and (62) are the expressions on which the subsequent discussion is based. In the case that (Q3/a In m2)r is non-zero these equations need be modified only by replacing m, with [m, - c,@B/a In m,)]r wherever rn, appears on the right-hand side.(b) BEHAVIOUR OF N, m,, m2, AND 0, (i) BEHAVIOUR OF N In the absence of free micelles (cf = 0) eqn (58) and (59) give Consider the denominator of this expression. When 02cp @ m, the first term dominates and (aR/8c,),3, is of the order 02/ml. On the other hand when 02cp % m, (alv/ac,),, cp is of the order f/cp, 6 which case the slope of a plot of Nc, against c, is ca. 1 . The large increases in (aN/ac,), with increasing c, which have been observed clearly arise from large values of o2a;d show unequivocally that some macromolecules have much more surfactant bound to them than others. In the presence of micelles we have instead of eqn (63)896 SURFACTANT-MACROMOLECULE INTERACTIONS where D is given by eqn (57). Once cp is of the same order as rn, and rn, it is clear that the final term of the numerator of eqn (64) will dominate whenever n, a[a - (@I/aN)] b 1.This term is negative whenever (a/?/am > a and under these circumstances N will exhibit a maximum with increasing c,. Such a maximum is akin to maxima in surfactant adsorption considered p r e v i o ~ s l y ~ ~ ~ 31 and corresponds to the situation where the amount present in a monolayer decreases with increasing total surfact ant concentration. In the limit that n, + co, which corresponds to the approximation of regarding the micelles as a separate phase, eqn (64) becomes which in the case that 02cp b rn, simplifies further to - a The implications of this equation will be considered later. (ii) BEHAVIOUR OF a, AND rn2 Since all terms in the numerator and denominator of eqn (56) are positive, (a In m,/ac,),3, cp will be positive under all conditions of interest. However, the behaviour of a,, which will be followed closely by that of rn,, is considerably more complex.For sub-micellar solutions when c , is small and rn2 b 02cp, (a In a l / ~ ~ l ) e l , c , is positive. However, if clustering on the macromolecules occurs with the result that 02cp b m, then which shows that the left-hand side may change sign and become noticeably negative. Consider now the addition of more surfactant. As the average amount bound approaches the maximum binding capacity of the macromolecules one expects the fluctuations in amounts bound and hence o2 to decrease. It is therefore possible that rn, - o2cp(ap/am [ 1 - (i?~/aN)] will again become positive.When free micelles are present and nwcy b rn, and rn, we may write eqn (55) approximately as (68) which shows that when rn2/nwc~ and rn,/c2cp are both much smaller than [(ap/am-al2 the left-hand side of this expression will be negative but very small. On the other hand, when rn,/02cp is much larger than [(tlP/aN)-- a], and rn,/n, cy,D. G. HALL 897 a, will decrease with increasing c1 in much the same way as in a polymer-free micellar solution. Thus as c, is increased at constant c, and cp it is possible that a plot of In a, against c, will show two maxima separated by a minimum. The first maximum will be associated with clustering of surfactant on the macromolecules. It is also possible that the plot will have a more or less horizontal portion throughout the regon where micelles and surfactant clusters on the macromolecules coexist.When this occurs a plot of In m, against c, will also be more or less horizontal. In the following section we will discuss this kind of behaviour in more detail. (iii) BEHAVIOUR OF #? For neutral macromolecules and macroions with the same sign as the surfactant one expects #? to increase with increasing N. One also expects that (a#?/am will be close to Iv,/v,l when the macromolecules plus their bound surfactant are close to electrical neutrality and that @#?/am will approach zero at very large charge densities. This latter point is of course entirely consistent with notions of counterion condensation used in alternative treatments of polyelectrolyte solutions.Eqn (50) shows that (8b/aWmp can be obtained from the dependence of a, on m, at constant N. It also yields on cross-differentiation Since the above arguments indicate that (a2p/dP),, will usually be negative it follows from eqn (69) that a2 will usually increase with increasing m,. This is entirely consistent with the notion that increasing m, reduces electrostatic interactions between bound surfactant ions. It is also apparent that @#?/am,* can be expected to depend hardly at all on N when o2 is very large. (iv) BEHAVIOUR OF 8, At constant T, p and cp eqn (15) enables us to write which together with eqn (55) and (56) gives (a@p/ac1)c3, Cp = {#? [ 1 + m, 2y/m, +a2c, (’) + n, c y a] where D is given by eqn (57). At low surfactant concentrations when the terms containing m, and m, in eqn (71) dominate the numerator will usually be negative,* as might be expected.On the other hand, if when free micelles are present the terms in c r dominate, (a@p/~c,)c3cp will be positive if #?/m > a. In the absence of free micelles it may turn out that when o2 is large terms in cp dominate eqn (71). In this case if p/m > d#?/aN it is possible that (a8,/a~,>,~, cp will be positive. Since binding of an ionic solute to a non-ionic solute usually leads to a decrease in the chemical potentials of both, such a result is unusual. as the surfactant ions. * By virtue of the common-ion effect this may not be so for macroions whose charge has the same sign898 SURFACTANT-MACROMOLECULE INTERACTIONS Because (a8p/ac,)cl, c3 is necessarily positive in a thermodynamically stable solution the relationship shows that (ac,/ac,),, c3 is always opposite in sign to (aOp/acl)c,cD.Hence if 8, may be regarded as constant in a solution saturated with macromolecules eqn (71) provides a basis for describing the effect of surfactant on the macromolecule solubility. An interesting situation arises when the terms in cp dominate eqn (71) and /l/m > @/l/am. Since (aB,/d~,),~ cp is positive under these circumstances it follows that increasing c, will reduce the polymer solubility. This will cause cp to decrease until the terms in cp no longer dominate, in which case the polymer solubility will begin to increase again with increasing c,. In this region one might expect the surfactant binding to be approaching its limiting value, in which case o2 will presumably be smaller than in the region where polymer solubility is decreasing so that the terms in cp do not again become dominant with increasing c,.These arguments indicate that like in, the polymer concentration at saturation may exhibit two maxima separated by a minimum as c, is increased at constant c,. 4. ALL OR NONE APPROXIMATION FOR BOUND SURFACTANT AND MICELLES In some surfactant+polymer systems there is strong evidence that bound sur- factant can exist in at least two distinct environments, one of which takes the form of micelle-like clusters attached to the macr0mo1ec~le~.~~-~~ Such effects may be allowed for in our theory by regarding the two types of bound surfactant as distinct species which at equilibrium have the same chemical potential.Let subscripts c and n refer to clustered and non-clustered surfactant. We suppose for simplicity that all macromolecules on which there is clustered surfactant bind the maximum amount they can accommodate, Nc, and that all surfactant bound to the remaining macromolecules is non-clustered. This gives us two distinct types of macromolecules, those with clustered surfactant and those without. Let y denote the fraction of the former. At constant T and p eqn (24) gives d (6, -kT lnyc,) = - N , d8, +Be kTd In m, (73) for molecules with clustered surfactant and d[8,-kTln(l -y)c,] = -ITnd8i+DnkTd lnm, (74) where subscript n denotes cluster-free macromolecules. When eqn (74) IS subtracted from eqn (73) and the result is divided by N , - ITn we obtain do, 1 - d ln(y/1 -y)+Bc-p"d lnm,.k T - Nc-Nn Nc - Nn (75) For the macromolecules which are cluster-free eqn (50) holds and takes the form We suppose that, like N,, pc is fixed and that #ln does not depend on m,. When ( N , - Nn) is large we expect the first term on the right-hand side of eqn (75) to be very small forD. G . HALL 899 all but extreme values of y . In other words, for almost all Nin the range N , < N < Nc we have approximately dlna,+ ( 1 - c LcI$]d lnm, = 0. Clearly this expression bears a close resemblance to d lna,+(l -a)d lnrn, = 0 (77) which holds in the presence of free micelles when n, is sufficiently large. However, whereas a in eqn (78) is found experimentally not to depend on m2 this may not be SO for (Pc -Pn>/(Nc -Nn)* Let 1 -ap denote the coefficient of d lnrn, in eqn (77).We find that From eqn (76) we have and from eqn (77) we have hence lna, 8 lnrn, = -(1 - a p ) aaP - -- a lnrn, Nc-Nn aN, Eqn (82) shows that ap may depend noticeably on m, even when a i / N c is as small as 0.1. Eqn (80) shows that Nn will decrease with increasing m, when (aP,/aN,) > ap. When a, does not depend significantly on m, eqn (74) may be integrated to give lna,+(l -ap) lnrn, = K,. lna,+(l -a) lnrn, = Km. (83) (84) Likewise, when free micelles are present eqn (78) may be written as Eqn (83) and (84) lead to some interesting conclusions which are now summarised. First we note that the left-hand side of eqn (84) cannot exceed K,. It is equal to Km where free micelles are present and less than Km when free micelles are absent.Similarly, when the left-hand side of eqn (83) is less than Kp there is no clustering of bound surfactant. The equality will hold for all Nthroughout the range Nn < N < N,. However, when N= N, it is possible that the left-hand side of eqn (83) will exceed Kp. There are in effect four cases to consider: Km Kp (1) a < a - <- ,’2-a 2-a, Km Kp (2) a < a - >- P’2-a 2-a, Km Kp (3) a > a - <- P’2-a 2-a, Km Kp (4) a > a - >-. P’2-a 2-aP900 SURFACTANT-MACROMOLECULE INTERACTIONS The first case is very straightforward. Clustering on the macromolecules does not occur. Free micelles form first in the absence of supporting electrolyte and when they are present electrolyte addition causes the left-hand side of eqn (83) to decrease.For case (2) clustering on the macromolecules will usually occur before free micelles form in the absence of supporting electrolyte and there will be a range of surfactant concentrations over which the left-hand side of eqn (83) remains constant. However, the left-hand side of eqn (84) will continue to increase and eventually free micelles will form. This may occur either before or after the macromolecules are fully saturated with bound surfactant. In the former situation eqn (83) and (84) will hold simultaneously. Thus a,, m, and rn, will all remain constant in the regions where clusters and micelles coexist. Under these circumstances eqn (48) and (49) give dm, = 0 = ap cp dN+ a dcp (85 a) dc, = cP dN+dcy (85b) where we have used the result dp = apdN.It follows from eqn ( 8 5 ) that which is identical to eqn (66) and shows clearly that as c, is increased the clusters desorb from the macromolecules. If Kp is exceeded before free micelles form it is clear that once they do the left-hand side of eqn (83) will start to decrease. Eventually eqn (83) and (84) will be satisfied simultaneously so that eqn (85) and (86) apply. The effect of electrolyte in case (2) is to promote free-micelle formation at the expense of clustering on the macromolecules. There will in general be some electrolyte concentration beyond which the clusters no longer form. In case (3) Kp must be exceeded before free micelles can form. Hence the macro- molecules become saturated with bound surfactant and remain so with increasing c,.In case (4) micelles will usually form before the onset of clustering on the macromolecules. In this case as c, is increased the left-hand side of eqn (83) continues to rise until clusters eventually form with the result that eqn (83) and (84) are satisfied simultaneously and that again eqn (85) and (86) apply. In this case, however, because a > up, cy decreases with increasing c,. This will continue until either (I) all the free micelles disappear or (2) the macromolecules are saturated with bound surfactant. In the first case the left-hand side of eqn (84) will fall below K , and will remain below K , until all the macromolecules are saturated with bound surfactant. Then it will begin to increase until the conditons for free micelles to form are reattained.In the second case free micelles will not disappear completely but cf will pass through a minimum. The effect of electrolyte will be to promote clustering at the expense of micellisation and eventually a concentration will be reached where, as in case (3), clustering on the macromolecules occurs before free micelles form. A condition which must hold for the above discussion based on eqn (83) and (84) to hold is that tb.e term [(@?/aN)--aI2 dominates the right-hand side of eqn (68). If [(a/?/a?V) - a] is of the order 0.1 and m, is of the same order as cfi" and Ncp it follows that 0 2 / N and n, must both be considerably greater than 100 for this condition to be met. Smaller values of [(d/?/aF) - a)] may not be atypical, in which case even larger values of 02/Nand n, are required.For many ionic surfactants n, in particular is unlikely to be so large. Thus the above treatment may be based on approximations which rarely hold in practice and real systems may be more complex. To deal with such situations more realistic but more complex models can presumably be forwarded.D. G. HALL 90 1 However, we will not pursue this point further here but conclude this section of the paper by remarking that the above discussion probably does illustrate in fairly simple terms some of the more bizarre aspects of surfactant binding to macromolecules that might be met. 5. INTERPRETATION OF EXPERIMENTAL DATA AND DETERMINATION OF AMOUNTS BOUND When electrodes reversible to all three ionic species in solution, surfactant ions, counterions and coions, are available e.m.f.measurements can be particularly useful. Combining the surfactant ion and counterion potentials leads to changes in 8, whereas combining the counterion and coion potentials leads to changes in 03.25 The difference between surfactant ion and coion potentials leads to changes in the ratio of their activities which in turn leads to changes in the ratio of their monomeric concentrations when the approximation of equating their activity coefficients is reasonable. Since the monomer concentration of coions is usually equal to the known total concentration it follows that relative changes in surfactant monomer concentration can be found. This in turn enables the actual monomer concentration to be estimated if m, in some other solution, e.g.a submicellar polymer-free solution, is known. From rn, and c, it is straightforward to determine y and then to obtain rn, using either the surfactant/ counterion or coion/counterion electrode pair in the same way as the surfactant/coion pair can be used to find m,. These procedures have the important advantage that they circumvent the problems associated with liquid-junction potentials, which may not be trivial in systems where micelles and other highly charged polyionic species are Whether or not free micelles are present in significant amounts can be established in principle by estimating the left-hand side of eqn (84). Free micelles are present when this quantity is equal to K , and are absent when it is less than K,. When free micelles are absent N = (c, -ml)/cp and is easily determined if the polymer molecular weight is known.If the polymer molecules do not associate and the above theory is valid N should be fixed for given values of a, and m, irrespective of cp and c,. Whether or not this turns out to be so will provide a useful test of the theory. This test will, however, fail if the macromolecules do associate and this association is affected by surfactant or electrolyte. If it does fail but eqn (45) still holds macromolecular association seems a likely explanation. However, if eqn (45) also breaks down an alternative explanation is needed. When free micelles are present the determination of N is less straightforward. One procedure is to plot lna, against cp at constant m, and c,. As is apparent from eqn (62) or (51), when free micelles are present fixing rn, more or less fixes a, and if the bound surfactant is not clustered this in turn more or less fixes Nand p.It follows that i3cy/2cp z p/a and that (ilcl/8cp)m2c3 z (N-B/a). Hence increasing cp will eventually lead to the disappearance of free micelles. The point at which this occurs should be apparent from a break in the plot of a, against c,. At this point N, which is the same for all other points on the plot with lower cp, is given by (cl-ml)/cp and can thus be determined. As cp is increased further eqn (62) shows that a, will decrease. If the bound surfactant is clustered this method breaks down for two reasons. First, may not be effectively fixed by fixing m,. Secondly, if o2cP is very large it follows from eqn (62) that a plot of a, against cp at constant m, and c, will not show a pronounced break when c p reaches zero.An alternative method based on eqn (48) and (49) is as follows. In the absence of free micelles the behaviour of P(E,m,) may be determined. In the presence of free and902 SURFACTANT-MACROMOLECULE INTERACTIONS micelles rn, and m, can be estimated from e.m.f. data and c, is known. Suppose now that a value of c y is chosen. This enables a corresponding N and in turn a corresponding /3 to be found. The correct value of His that which leads to agreement between the experimental value of m2 and that calculated from eqn (48). This procedure will apply best when the dependence of /3 on rn, at constant N is small and when the value of Nconcerned occurs in submicellar solutions. It may still be useful when this is not so if the behaviour of p can be reasonably extrapolated to the value of Nconcerned.However, the procedure will be of little use if a, and (i3/3/aX) are nearly equal. If the all or none approximation for the bound surfactant is valid the following procedures may be useful. For case (2) both Kp and ap as well as Ncan be measured. The onset of the region over which eqn (83) and (84) both hold is apparent as the start of the range of c,, where both a, and m, are fixed. The value of N a t any point in this range is equal to the value of N at its commencement minus Ac, a/cp(ap -a) where Ac, is the value of c, in the solution of interest minus that at the start of the above range. Case (3) is very straightforward.N , is measurable in the absence of micelles and the amount bound maintains this value when free micelles do form. Case (4), however, is rather more difficult. If the situation is that in which all the micelles disappear before the macromolecules are saturated this should be detectable when the 1.h.s. of eqn (83) falls below K,. Beyond this point it should be possible to estimate N, ap and Kp and with this information find values of F a t any point in the region where a, and m, do not depend on c, in the same way as for case (2). If, on the other hand, free micelles do not disappear completely it is difficult to proceed because ap and Kp remain unknown. However, by increasing cp or adding electrolyte it should be possible to reach a situation in which the micelles do disappear.Kp and ap can then be found and the procedure outlined above applied. To date no e.m.f. studies of the type required for the above procedures to be used have been reported. E.m.f. data that are available suffer from uncertainties due to liquid-junction effects and do not cover a wide enough range of conditions. For these reasons they will not be considered further. An alternative source of thermodynamic information is dialysis data. Strictly dialysis equilibrium is an osmotic equilibrium in which the respective chemical potentials of neutral surfactant and solvent in the two compartments are equal. For this to occur the solutions should be at different pressures. In practice the establishment of a proper osmotic equilibrium is probably not usually achieved.Nevertheless it is perhaps reasonable to suppose that the surfactant chemical potential is more or less the same in the two compartments. In principle dialysis studies can provide equivalent information to the e.m.f. method discussed above provided that the behaviour of chemical potentials in the absence of polymer are known as a function of solution composition. In practice, however, this is likely to be difficult. Suppose for instance we obtain (c,--c;)/cP as a function of c, and cp in the absence of supporting electrolyte where c; is the concentration in the polymer-free compartment. It is not possible to obtain N from such information without making assumptions about the interactions of counterions with the bound surfactant. In the presence of supporting electrolyte with an indifferent coion in both compartments we may obtain m, from the expression m,/c, = m;/c;. However, to do so it is necessary that c,, m; and ci are all known.A further drawback with dialysis is that it is difficult to manipulate c, and c, precisely. If in a dialysis experiment there are no free micelles in either compartment we expect that m, > m; whenever the charges of the macromolecular complexes are the same sign as those of the surfactant ions. Since at equilibrium I / m2 a, = m2 a,D. G. HALL 903 it follows from eqn (84) that micelles will form in the absence of macromolecules before they form in their presence. As c1 and c; are increased micelles will eventually be present in both compartments. Under these circumstances it is apparent from eqn (84) and (87) that m, = mi and a, = a/, and that when supporting electrolyte is also present c, = cj This provides a further useful test of the theory.Consider now the behaviour of (c, -c;) as c, is increased at constant cp. From eqn (57) and (58) we find that where m,* = m1/l +2y'm, and up = (i3/?/i3m. When free micelles are present in neither compartment one expects the left-hand side of eqn (88) to be positive. However, it may be negative when o2 is very small and is quite likely to be negative when free micelles are present in the polymer-free compartment only. Indeed it is possible in this latter situation that (c,-cC;) may be negative. To show how this can arise consider the situation where micelles are just about to form in the polymer compartment.Under these circumstances m, = mi and m, = mi. It follows from eqn (48) and (49) that (c, - c;) = Ncp - (c; -mi) and that /?c, = a(c; --mi). Hence (c, - c;) = c,(N-/?/a) and is negative if /? > aN. This will probably be the case for polyelectrolytes and for neutral polymer when @/?/am > a. When free micelles are present in significant amounts in both compartments it is probably reasonable to suppose that the terms in which n,cy and 02cp appear dominate eqn (88). With this simplification we obtain after some algebra which will be positive (a) if a > a, and (b) if when a < up a2(ap - a) n, c? > m,(ap + a) +mT(ap + a - 2aap). From the above analysis we predict that for some systems a plot of (c, - c;) against c, at constant c3 and cp will exhibit a maximum followed by a minimum.The maximum will occur close to but above the concentration where micelles form in the polymer-free compartment. The minimum will occur close to but above the concentration at which free micelles form in the solution of interest. If we regard (c,-cC;)/cp as a 'thermodynamic binding', it is noteworthy that in the region where the thermodynamic binding is decreasing Nis increasing and that in the region where the thermodynamic binding is again increasing N may well be decreasing. This illustrates well the distinction between the two kinds of binding when ionic species are involved. 6. MORE COMPLEX SYSTEMS (a) SURFACTANT BINDING TO MACROMOLECULES OF OPPOSITE SIGN So far we have considered only systems in which the macromolecules are either electrically neutral or polyions with the same sign as the surfactant.However, binding to polyions of opposite sign is even more likely to occur. Let the system of interest consist of solvent, polyions, surfactant ions, counterions to the surfactant (species 2) and coions to the surfactant (species 3). We use the same notation as above. In the absence of surfactant and in the presence of small amounts thereof the normal roles904 SURFACTANT-MACROMOLECULE INTERACTIONS of species 2 and 3 will be reversed. Also free surfactant ions will act as unbound counterions. Despite this we may still define 8, by vp P2 v 2 8, = p,--. In the case that the concentration of free surfactant ions is not negligible compared with that of coions, 8, and 8, are given by 8, = w( T , p ) +kT In c2 + kT In m3 + 2kT in y (90) 8, = 8,+(p-@)+kTln m,/c, (91) (92) where m, is the total concentration of unbound surfactant, m3(1 + m l / c 3 ) = c2 +QCp and Q has its usual significance but in this case with respect to interactions between polyions and species 3.Eqn (91) rests on the approximation that unbound counterions with the same valence have the same activity coefficient. This is not as good as the corresponding approximation for coions because small differences in the specific interaction energies between polyions and difference counterions will lead to greater differences in their ‘adsorption’ by the polyions. Even so for dilute solutions the approximation may still be an improvement on the assumption of ideal behaviour. As the surfactant concentration is increased one expects the primary charge on the polyions to be neutralised.One may conjecture that this process may not always be complete before free micelles form. However, it seems unlikely that highly charged colloidal units of opposite sign will coexist in dilute solutions except perhaps in the presence of large amounts of supporting electrolyte. More probable is the formation of some kind of coacervate or pre~ipitate.,~-,~ In the situation where the macroions plus their bound surfactant are approximately neutral we expect that p will be numerically equal to the average charge of a complex, that c, = m3 and c2 = m2. In this case, according to our theory we should have 8, = @ +kT In c, + kT In c, + 2kT In y 8, = @ + kTln rn, + kT In c, + 2kT In y (93 4 (93 b) where y = y(c,) when c, < (m, + c,) and y = y(ml + c,) when (m, + c,) < c,.In systems where the bound surfactant more than neutralises the polyion charge we are back to the normal situation where species 2 is the counterion. In this case, however. where N(0) is the value of N which just neutralises the primary charge on the macromolecules. Evidently close to neutrality ap/ag will be approximately unity whereas (8p/C)W, which is normally expected for neutral macromolecules and polyions with the same charge as the sufactant, will not hold in this case. In some cases it has been observed that initially addition of surfactant to a solution containing oppositely charged polyions leads to the formation of a precipitate which on further addition of surfactant redissolves.This presumably is due to surfactant will be small. Consequently the situation in whichD. G. HALL 905 binding leading to charge reversal. If so, it is interesting to speculate that when free micelles form desorption of bound surfactant may occur and that at higher surfactant concentrations we may once more get precipitation. Indeed we can regard the neutral surfactant/polyion complex as the macromolecular species of interest and consider the application of eqn (71) to this species. As this expression shows, reprecipitation could occur if p/[N-X(O)J > a. (b) SURFACTANT BINDING TO POLYACIDS Since most biological macromolecules and many other polymers of practical interest contain dissociable groups it is important to establish the extent to which the above discussion applies to these.Let i refer to H+ ions and let k refer to surfactant ions. At constant T and p our basic equation, eqn (24), may be written as dO,-kTd lnc, = -Nid@,-rkd8,+BkTd lnm,. Oi = v( T,p) + kT In ai + kT In m, (95) (96) where ai = mi y 2 and y is the same as for all other coion species. On the other hand when i is a counterion (97) where ai = mi m,/c,. In either case changes in log,, ai may be regarded as corresponding to changes in pH. The coupling between polyacid dissociation and surfactant-ion binding is best described by the expression When i is a coion we have 19, = w(T,p)+kTln (m,/c,) = @+kTln ai/m2 This expression relates the change in pH with surfactant-ion activity at constant average primary charge of the polyions to changes in the amount of surfactant-ion - binding when - - the primary charge is varied at constant surfactant activity.One expects Ni Nk - Ni Nk to be positive for negatively charged surfactant ions and negative for positively charged surfactant ions, When studying surfactant binding to polyacids experimentally it is important to control either Ni or 8, or to monitor the changes which occur therein. Superficially it i s the expressions which hold at constant Oi which are most like those for neutral polymer or strong polyelectrolytes discussed above. Despite this it may be preferable to work at constant R, for three reasons. First, close to neutral pH the changes in free hydrogen-ion concentration and free hydroxide-ion concentration which arise when solution composition is altered without the addition of acids or bases cannot, on grounds of stoichiometry, lead to large changes in Xi unless the accompanying changes in 8, are very large.Secondly, one expects p to be determined primarily by polyion charge. This suggests that it is the dependence of/? on Xk at constant Xi rather than at constant 8, that will most closely resemble the cases described above. In fact, the only modification to the above discussion that is needed if one works at constant & is the replacement of o2 by Thirdly, when attempting to control Oi or a, by buffering it is important that neither the acidic nor the basic form of the buffer interacts strongly with either the906 SURFACTANT-MACROMOLECULE INTERACTIONS macromolecules or the surfactant. This precludes the use of any material which is likely to be solubilised by aggregated surfactant or which is oppositely charged to the macroions or surfactant aggregates.Accordingly, measurements involving organic buffers which are at all hydrophobic must be considered suspect unless the absence of significant interactions with macromolecules and surfactant has been established. (C) CONFORMATION CHANGES The effects of surfactants and changes in pH on conformation equilibria are readily dealt with. Suppose for example that the macromolecules can exist in two forms a and p. At equilibrium We may therefore write down eqn (24) for the two forms and subtract one from the other. We obtain e, = ep (99) - ( E - q ) d T (E-P d doi - Z(N: - NB - + (pol -pB) k Td In m,.P + T T kTd In 5 = 4 (100) This equation is similar to an expression obtained previouslyg0 but is not restricted to non-interacting macromolecules. When significant amounts of the two forms a and p are present together it will usually be a good approximation to suppose that the left-hand side of eqn (100) is zero. In this case the expression takes the same form as that which describes the coexistence of two multicomponent phases. Thus when c, is varied at constant m, the change from almost all a to almost all p will occur over a very narrow range of el, and if the transition takes place in the presence of free micelles both and m, will be more or less fixed. A similar situation will also hold in the absence of free micelles when o2 for one of the two forms concerned is very large. The range of c, for which these conditions hold will, however, be very small if & -p,J/(R## - R#p) differs hardly at all from a in the case where micelles are present or from ap/aNfor the form with a large value of 02.For the system macromolecules + surfactant + supporting electrolyte eqn (100) gives Eqn (55) and (56) still apply and in situations where cg/c{ is either very large or very small all terms in these expressions will be normal. However, when cgl.8, is close to unity the following modifications may be necessary : o2 = F-F = yao~+ygojj+yayg(R#a-R#g)2 (102) also when (t)pa/a lnm2)xa and (apg/a In m2)mp are both small enough to ignore we find that and that This latter result shows that (ap/a lnm,)~may not be neglibible when the two forms are present in significant amounts even though the corresponding quantities for the two forms themselves are both negligible.D.G. HALL 907 Clearly eqn (101) is very similar to eqn (70) and this suggests that the dependence of c $ / 4 on c1 at constant c, and cp may resemble that of S,. In particular if Na > mp it is possible that c:/g will exhibit two maxima separated by a minimum as c, is increased. It is also possible that the presence of free micelles will bring about reversal of a conformation change which is induced by surfactant addition at lower concentrations. (6) POLYDISPERSITY So far we have considered only systems in which the macromolecular species is monodisperse. In practice, however, polydispersity is the rule rather than the exception.Hence our treatment would be incomplete without some discussion of this extra complication. Let subscript x refer to the various macromolecular species and let fx be the fraction of species x. For each member there is a series of subspecies characterised by the amounts and distributions of the various solute species bound thereto. Also for each member there are equations corresponding to eqn (1 5H19) and (24). Let e = cfx ex. (1 05) X By analogy with eqn (24) we find that X X ( 106) +pkd 1nm2+Z -dfx+kd O X In cp X T where H” = xf,H,”, vo = v;, N, = xjJqx, p = c fXPX. (107 a, b, c, 6) X X X X At constant fx eqn (106) can be handled in exactly the same way as eqn (24). At constant T and p we have an analogy with eqn (17) and (18) and that when i = k the final term is equal to c fx(Nix -Ni)2.Changes in the population of macromolecules are allowed for in the terms containing dfx. In most cases there will be a very large number of these terms. However, as Hill4’ has suggested, it may be possible to replace them by a small number X908 SURFACTANT-MACROMOLECULE INTERACTIONS of terms involving the differentials of variables characteristic of the population concerned. For example, if the molecular-weight distribution is Gaussian it will be sufficient to describe the effects of shifting from one Gaussian distribution to another in terms of two variables, the average molecular weight and the second moment of the molecular-weight distribution. Consider now the situation where at fixed T, p , Oi and m2 the ATi and D depend only on the average molecular weight given by M = x f x M, and are independent of any other features of the distribution. When these conditions hold for arbitrary changes in theyx which keep Mfixed it is straightforward to show that we must have Nix = ai + bi Mx ( 1 10a) X Dx = a,+b,Mx (110b) where ai bi a, and b, are functions of T, p , Oi and m,.From eqn (110) it follows that we must also have Ni = ai+biM ( l l l a ) b = a,+b,M. ( l l l b ) Consequently when for given T, p , Oi and m, the A?, and B depend only on M they must vary linearly with M. It follows that when these quantities do not vary linearly with M they must depend on other features of the molecular-weight distribution. The analysis can presumably be extended to include other features of the distribution such as the second moment.If it is found experimentally that eqn (1 1 1 a and b) do hold it may not necessarily follow that eqn (1 10a and b) also hold. However, it may well be resonable to suppose that they do. A simple physical interpretation of the behaviour described by eqn (1 11 a and b) for linear macromolecules is that the Nix and the Dx are made up of a contribution proportional to the length of the macromolecule and a contribution from the two ends. It is also apparent that when behaviour of this kind does occur at all T,p, Oi and m, of interest that the binding behaviour of the polydisperse system is identical to that of the monodisperse system with the same number-average molecular weight. It is of course extremely unlikely that conformation changes in polydisperse systems will be as sharp as one expects for the monodisperse systems described in the previous section.7. COMPARISON WITH PREVIOUS WORK AND WITH EXPERIMENT Previous theoretical work in the area of surfactant-macromolecule interactions is sparse. Several workers have recognised the similarity between surfactant aggregation on the macromolecules and micellisation. However, in most cases the role of counterions has not been considered. A notable exception is the work of Gilanyi and W~lfram,~ who allow for counterion effects by assigning a degree of counterion binding to surfactant aggregates which associate with the macromolecules and by applying the law of mass-action to the formation of the surfactant-polymer com- plexes.They recognise that both the aggregation number and degree of dissociation of bound aggregates may differ from those of micelles proper but do not appear to deduce that as a consequence of these differences the bound surfactant may desorb from the macromolecules as the surfactant concentration is increased. Clearly an approach of this kind suffers from the same drawbacks as apply to the mass-action treatment of ionic surfactant micelles which are partially neutralised by bound coun teri ons.D. G. HALL 909 That the surfactant bound to the macromolecules may in some cases be present as well defined aggregate species has not been allowed for explicitly in the present paper. The main reason for this is that there is no obvious non-arbitrary method of dealing with interactions between aggregates attached to the same macromolecule.To suppose for example that each macromolecule has a given number of sites which can bind an aggregate and that the bound aggregates are randomly distributed among the available 43 is clearly unrealistic in the absence of supporting evidence. Also, the fact that different aggregate species will have different tendencies to bind creates further problems. It seems unlikely that neglect of these additional complications will seriously limit the applicability of the above theory as a tool for interpreting equilibrium measurements. However, it is possible that some allowance for them will be required when considering the kinetics of aggregation in these systems and especially the behaviour of the slow relaxation time associated with the rate of change of aggregate c~ncentration.~~ At present there are insufficient published equilibrium data available for a systematic comparison of theory and experiment to be made.However, the data that are available are not at variance with the theory. For example, the dialysis work of Fishman and Eirich2 on solutions of poly(viny1 pyrrolidone) (PVP) and sodium dodecyl sulphate (SDS) shows clearly that the surfactant concentration at which the reported binding isotherms begin to rise steeply depends on the concentration of macromolecules. This can be attributed to the value of m2 at which the steep rise starts increasing with increasing polymer concentration. The dialysis data of Jones et aZ.45 concerning the binding of SDS to lysozyme also supports some of the ideas outlined above.In particular the isotherm shown in fig. 4 of their note exhibits a maximum followed by a minimum. This isotherm is in effect a plot of (c, - c;)/c, against c;. The maximum occurs at a surfactant concentration in the macromolecule-free compartment significantly above the c.m.c. This indicates that binding to the protein causes (c, - c;) to increase even when micelles are present in the other compartment until the protein is close to saturation with bound surfactant. At this stage (c, - c;) falls until at the minimum free micelles start to form in the presence of the protein. It is perhaps worth reiterating that in this system according to the above theory N will be increasing when (c, - c;) is decreasing.NOTATION SYMBOLS m, y 2 (sections 3 and 4) mi y2 when monomeric i is a coion [section 6(b)] mi rn2/c2 when monomeric i is a counterion [section 6(b)] parameter which describes the dependence of a property on macromolecular weight [section 6(4] parameter which describes the dependence of a property on macromolecular weight [section 6(4] concentration expressed as a mole ratio with respect to solvent or as a molality fraction of macromolecules of a given type in a polydisperse system partial molecular enthalpy Boltzmann’s constant concentration which is neither bound to macromolecules nor present in micelles effective concentration of ‘ free ’ counterions weight-average aggregation number of micelles910 P U X Yr G H K M N; Ni T v P T P Z a Y Y i P 8 o2 V a as SURFACTANT-MACROMOLECULE INTERACTIONS pressure partial molecular volume micellar mole fraction fraction of polymer complex species of type r ionic valency excluding the sign Gibbs free energy average partial molecular en t halpy of macromolecular complexes constant macromolecular weight number of i molecules present in a complex of type Y average amount of bound i per macromolecule absolute temperature average partial molecular volume of macromolecular complexes effective micellar degree of dissociation may be regarded as the number of counterions per member of species r required to neutralise its effective charge average value of Br( =I: y , B,) mean ionic activity coefficient of a 1 : 1 electrolyte ionic activity coefficient of species i chemical potential chemical potential of an electrically neutral ionic component or constituent ionic valency including the sign second moment of the distribution of amounts bound T SUBSCRIPTS AND SUPERSCRIPTS in c, or Nf denotes micellar species a i , j , k as in mimi and mk denote non-macromolecular solute species m as in c, denotes micelles c as in Mc denotes a property of surfactant-polymer complexes in which the bound surfactant is clustered n as in XI, denotes a property of cluster free surfactant macromolecular complexes p as in cp denotes macromolecules r, s as in c, c, denote macromolecular complex species Y and s x as infZ denotes macromolecular species x in a polydisperse system 1 as in c, denotes surfactant 2 as in m2 denotes counterions 3 as in c, denotes coions O as in H" denotes the value of a quantity in the limit that cp and c , both approach zero e as in p* denotes a dilute solution standard state ' as in mi denotes a property of the polymer-free solution in dialysis equilibrium with that of interest ' as in y' denotes the first derivative of y I.D. Robb, Anionic Surfactants, Physical Chemistry of Surfactant Action, Surfactant Science Series, ed. E. H. Lucassen Reynders (Marcel Dekker, New York, 1981), vol. 11, chap. 3. * M. L. Fishman and F. R. Eirich, J . Phys. Chem., 1971,75, 3135. M. N. Jones and P. J. Manley, J. Chem. Soc., Faraday Trans. 1, 1979,75, 1736; 1980, 76, 654. B. J. Birch and D. E. Clarke, Anal. Chim. Acta, 1973, 67, 387. B. J. Birch, D. E. Clarke, R. S. Lee and J. Oakes, Anal. Chim. Acta, 1974, 70, 417.D. G. HALL 91 1 H. Rendall, J. Chem. SOC. Faraday Trans. 1, 1976,72, 481. T. Gilanyi and E. Wolfram, Colloids Surf., 1981, 3, 181. J. Steinhardt and J. Reynolds, Multiple Equilibria in Proteins (Academic Press, New York 1969), chap. 11. 9 I. Klotz, in The Proteins, ed. H . Neurath and K. Bailey (Academic Press, New York, 1953), vol. 1, p. 727. lo K. Linderstrom-Lang, C. R. Trav. Lab. Carlsberg, Ser. Chim., 1924, 15, no. 7. l 1 C. Tanford and J. G. Kirkwood, J. Am. Chem. SOC., 1957,79, 5333. l 2 T. L. Hill, Arch. Biochem. Biophys, 1955, 57, 299. l 3 G. S. Manning, J. Chem. Phys., 1969, 51, 524; 3249. l4 F. Oosawa, Polyelectrolytes (Marcel Dekker, New York, 1971). l 5 H. Maeda and F. Oosawa, J. Phys. Chem., 1972,76, 3445. G. S. Manning and A. Holtzer, J. Phys. Chem., 1973, 77, 2206. l7 G. S. Manning, J. Phys. Chem., 1981 85, 870. S. P. Harrold and B. A. Pethica, Trans. Faraday SOC., 1958, 54, 1876. l9 T. L. Hill, Thermodynamics of Small Systems (Benjamin, New York 1964), vol. 2. 2o J. Wyman, Ado. Protein Chem., 1964, 19, 223. 21 J. Wyman, J. Mol. Biol., 1965, 11, 631. 22 D. G. Hall, J. Chem. SOC., Faraday Trans. 2, 1974, 70, 1526. 23 J. G. Kirkwood and F. P. Buff, J. Chem. Phys., 1951,19, 774. 24 D. G. Hall, Trans. Faraday SOC., 1971,62, 2516. 25 D. G. Hall, J. Chem. SOC., Faraday Trans. I , 1981,77, 1121. 26 D. G. Hall, Trans. Faraday SOC., 1970, 66, 1351; 1359. 27 C. Tanford, Physical Chemistry of Macromolecules (Wiley, New York, 1969), p. 573. 28 T. L. Hill, J. Chem. Phys., 1949, 17, 520; 1950, 18, 246. 29 D. H. Everett, Trans. Faraday SOC., 1950, 46, 453. 30 F. H. Sexsmith and H. J. White, J. Colloid Sci., 1959, 14, 630. 31 D. G. Hall, J. Chem. SOC., Faraday Trans. I , 1980, 76, 386. 32 H. Arai, M. Murata and K. Shinoda, J. Colloid Sci., 1971, 37, 223. 33 M. Murata and H. Arai, J. Colloid Interface Sci., 1973, 44, 475. 34 H. Lange, Kolloid 2. Z. Polym., 1971, 101, 243. 35 J. Th. G. Overbeek, Original Biophys. Biophys. Chem., 1956, 6, 57. 36 W. J. Knox Jr and T. 0. Parshall, J. Colloid Interface Sci., 1970, 33, 16. 37 J. E. Scott, Biochem. SOC. Trans., 1973, 1, 787. 38 E. D. Goddard and R. B. Hannan, J. Colloid Interface Sci., 1976, 55, 73. 3g J. W. A. van den Berg and A. J. Staverman, Red. Trav. Chim. Pays-Bas, 1972,91, 1151. 40 D. G. Hall, J. Chem. SOC., Faraday Trans. 2, 1972, 68, 1439. 41 T. L. Hill, J. Chem. Phys., 1961, 34, 1974. 42 K. Shirahama, Colloid Polym. Sci., 1974, 252, 978. 43 1. Satake and J. T. Yang, Biopolymers, 1976, 15, 2263. 44 D. M. Bloor and E. Wyn-Jones, J. Chem. SOC., Faraday Trans. 2, 1982, 78, 657. 45 M. N. Jones, P. Manley and P. J. W. Midgeley, J. Colloid Interface Sci., 1981, 82, 257. (PAPER 4/602)

ISSN:0300-9599    

DOI:10.1039/F19858100885

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. 1, 1985, 81, 913-918 Electron-impact and Thermodynamic Studies of Potassium Metaborate BY MILTON FARBER* AND RAMESHWAR D. SRIVASTAVA Space Sciences Inc., 135 West Maple Avenue, Monrovia, California 91016, U.S.A. AND JAMES w. MOYER AND JOHN D. LEEPER Southern California Edison Company, Rosemead, California, U.S.A. Received 18th May, 1984 An effusion-mass spectrometric investigation of the thermodynamic properties of KBO,(g) has been made in the temperature range 1053-1240 K. The KBO,(g) molecule fragments to over 90% of its initial concentration at electron ionization energies 2 eV above its ionization potential of 8f 1 eV. The fragmentation processes were studied to ionization energies as high as 70 eV, with the appearance of K+, BO; and BO+ fragments.Data obtained for the sublimation process, KBO,(c) + KBO,(g), and for the vaporization process, KBO,(l) --$ KBO,(g), yielded second- and third-law reaction heats. A third-law AH& of -672.4f 10 kJ mol-l and a second-law A H & , of -672.8f 10 kJ mol-l were obtained for KBO,(g). A heat of melting, A H g , at the melting point of 1220 K was found to be 31.8f4 kJ mol-l. The interest in the possible use of magnetohydrodynamic (m. h.d.) principles for future coal-fired electric-power plants has required precise knowledge of the thermo- dynamic properties of high-temperature combustion products and their interaction with the potassium seed material. The mineral matter of coal contains over 20 inorganic elements capable of forming stable high-temperature species with potassium atoms, affecting electrical conductivity and seed recovery. The electric power is derived from the plasma conductivity resulting from the free electrons produced by ionization of the potassium at the high combustion temperature.Whether or not open-cycle m.h.d. power systems become feasible will depend on the nearly complete recovery (up to 99% ) of the potassium seed. Our two laboratories have cooperated in a joint effort to investigate the stability and other thermodynamic properties of the various K-containing compounds. We have previously reported the results of studies concerning the species formed from reactions between K and 0, and H2,1 K and S2 and K and Al, Si and 0.3 The current investigation also included the sublimation and vaporization of potassium metaborate.In a previous publication Jensen has reported thermodynamic values for KBO,(g) from H, + N, + 0, flame reactions.* EXPERIMENTAL The dual-vacuum-chamber quadrupole mass spectrometer used in these experiments has been described previ~usly.~ The ion intensities were identified by their masses, isotopic distributions and appearance potentials. The method of determining the mass-spectrometer resolution, as well as the measurement of isotopic abundance ratios, has been presented previously.6 All quadrupole experimental mass-discrimination effects were taken into account and the necessary corrections to ion-intensity pressure relations were made. Only the chopped, or shutterable, 91 3914 THERMODYNAMIC PROPERTIES OF KBO, Table 1.Ionization cross-sections species a/ 1 0-l6 cm2 K 7.67 B 2.1 1 0 1.31 KBO, 7.18 Ag 5.44 portion of the intensities was recorded, since the mass spectrometer was equipped with a beam modulator and a phase-sensitive amplifier. Ion currents, which originated from species in the molecular beam, appeared as a 30 Hz square wave, while background gases continued to exist as a d.c. current where an a.c. current could be observed in a d.c. signal 1000 times greater. An alumina effusion cell 25 mm long, with an inside diameter of 6.8 mm and having an elongated orifice of 0.75 mm diameter and 5.5 mm length for beam collimation, was employed. The solid KBO, was placed within the effusion cell and heated to the temperature range 1000-1200 K. Upon examination of the contents of the cell after heating no evidence was found of any reaction at these relatively low temperatures between the alumina and the KBO,.Temperature measurements to & 5 K were made by optical pyrometry. Intensity measurements were made of the fragmentation products and those of the parent, KBO,(g). The ionization potential of KBO,(g) was found to be 8.0 & 1 eV, with the appearance of K+ at 10.0+ 1 eV. For the second-law direct determination of the vaporization and sublimation the intensity data were taken at 1-2 eV above its ionization potential. Elemental silver was employed for intensity conversion to partial pressure calibrations. For the reactions, ion-intensity corrections were made for the differences in relative cross-sections and their molecular masses.The relative maximum ionization cross-sections were taken from Mann.' Those for the molecular species were calculated by multiplying the sum of atomic cross-sections by an empirical factor of 0.7.s-10 These values are probably accurate to & 30%. Corrections were made for the electron-multiplier gain, which is based on the square root of the molecular mass. Corrections for the cross-section, 0, and multiplier, y, the square root of the molecular weight, were applied to the individual species intensities; e.g. Methods of calculation to obtain second- and third-law thermodynamic quantities have been presented in detail previously.*? l1 The calculated cross-sections, IT, for the ionic species are given in table 1. RESULTS AND DISCUSSION ELECTRON-IMPACT FRAGMENTATION OF KBO,(g) The vapour produced from the heating of KBO,(c) above 1000 K, when introduced into the ionization chamber of the mass spectrometer, showed considerable frag- mentation of the KBO,(g) molecule at electron energies slightly above its ionization potential of 8k 1 eV.This observation prompted the determination of the fragmen- tation pattern of KBO,(g), which would also aid in the determination of the KBO,(g) concentration necessary for definitive thermodynamic calculations. The observed fragmentation pattern in the formation of K+ ions as a function of the electron-impact energy is shown in fig. 1. The relative intensities of KBO: and the fragments produced are presented in table 2. The type of fragmentation pattern represented in fig. 1 for KBO, indicates additional ionization produced by fragmentation at higher appearance potentials than that of K+.As the ionizing energy is increased above 10 eV the appearance of K+M. FARBER, R. D. SRIVASTAVA, J. W. MOYER AND J. D. LEEPER 91 5 150 t 0 10 20 30 40 50 60 Fig. 1. Fragmentation pattern of KBO,(g) in the formation of K+ ions as a function of ionizing energy. electron energy/eV Table 2. Relative concentration of ions produced from the electron impact fragmentation of KBO,(g) at 1100 K relative abundance of ionic species (arb. units) electron energy l e v KBO; K+ BO; BO+ 8 10 12 16 20 30 40 50 60 70 1 2 2 3 8 10 15 10 5 0 - - - - 250 1000 2500 1000 1000 2 3 1120 25 30 620 35 60 500 25 40 250 20 30 - - - - - - - increases rapidly to a maximum at 18 eV, then decreases rapidly to an intermediate minimum value at 25 eV.A slight increase in the abundance of K+ occurs between 25 and 35 eV; its concentration then diminishes continuously until at 70 eV it is only 10% of its maximum abundance at 18.eV. This behaviour in the KBO, fragmentation processes can presumably be explained on the basis of the secondary-ionization species BO; and BO+ occurring at ionization energies > 20 eV. As shown in table 2, the concentrations of BO; and BO+ at 30 eV are ca. 20 and 30% of the KBO; intensity. However, at 40 eV and above their abundance is greatly enhanced to several times the concentration of KBO:. Possible mechanisms for formation of these ions and their appearance potentials follow.916 THERMODYNAMIC PROPERTIES OF KBO, The fragmentation process for production of K+ ions may be written as KBO,(g)+e -+ K++B02(g)+2e.(1) Heats of formation for the species involved are -7.0 eV for KB02(g),12 5.3 eV for K+ and - 3.3 eV for BO,(g), yielding AH%, = 8.9 eV for the process, compared with the experimentally observed potential of 10 k 1 eV for K+ of this study for reaction (1). The fragmentation process for the appearance of BO; may occur via KBO,(g)+e -+ K(g)+BO$+2e. (2) Values for AHgg8 of K(g) and BOZ are 0.93 and 10.7 eV, respectively. AHg8 for the fragmentation process becomes 18.6 eV. Better agreement with the experimentally observed appearance potential of 25 eV for BO; is obtained assuming that both K+ and BO; occur simultaneously as KBO,(g) + e -+ K+ + BO: + 3e. (3) This leads to AH$& = 23 eV.to be Likewise, the process for the appearance of BO+ from KBO,(g) may be presumed KBO,(g)+e + BOS+K(g)+O(g)+2e (4) or KBO,(g) + e --+ BO+ + K+ + O(g) + 3e. ( 5 ) A value of 24eV for AHg8 of reaction (4) is calculated by employing values of 13.5, 0.9 and 2.6 eV for BO+, K(g) and O(g), respectively. AH%, for reaction ( 5 ) is 29 eV. The appearance of BOZ and BO+ at ca. 25 eV may be considered as being in agreement with these assumed theoretical processes. THERMOCHEMISTRY OF KBO, The sublimation and vaporization of KBO, was investigated both below and above the melting point of 1220 K.12 Mass-spectrometric intensities of KBOZ were obtained in the temperature range 1053-1 240 K. Since considerable fragmentation of KBO, occurred, its ion intensities were corrected for the ion fragments, as listed in table 2.They were also corrected for electron cross-sections and multiplier gains as described in the Experimental section. The partial pressures obtained are reported in table 3. The sublimation data yielded AHg8 = 322.6 f 3 kJ mol-l for the reaction KBO,(c)+ KBO,(g). (6) Thermal functions were taken from the JANAF tables.', Employing a JANAF-tables value of -995.0_+8 kJ mol-l for AHgg8 of KBO,(c) a third-law value of - 672.4 & 10 kJ mol-l was obtained for AHgg8 of KBO,(g). This uncertainty increased to f 10 kJ mol-1 when the uncertainty in the value for KBO,(c) was included. The van't Hoff plot of IT against 1/T (fig. 2) yielded 302.9k6.5 kJ mol-1 for AH0 at an average temperature of 1130 K. At 298 K the value is 322.2+ 8.5 kJ mol-l.A second-law AHRg8 value of - 672.8 f 10 kJ mo1-l was calculated for KBO,(g). In a similar manner the vaporization reaction KBO,(l) + KBO,(g) (7) was studied in the temperature range 1220-1240 K. The thermodynamic data for reaction (7) are presented in table 3. AHg8 for reaction (7) was determined as 307.1 f 2 kJ mol-l. Employing a value of -980.7f8.5 kJ mol-1 for AHRg, ofM. FARBER, R. D. SRIVASTAVA, J. W. MOYER AND J. D. LEEPER 917 Table 3. Thermodynamic data for reactions (6) and (7) relative intensity pKB02 A@ AH% T/K (arb. units) /atm /kJ mol-' /kJ mol-l 1053 1073 1088 1100 1110 1125 1140 1153 1170 1182 1193 1203 1221 1224 1230 1234 1240 3 6 11 16 20 30 48 50 120 160 200 270 436 460 500 560 630 KBO,(c) + KBO,(g) 7.2 x lod6 103.3 1.4 x 10-5 99.2 2.7 x 10-5 95.0 3.9 x 10-5 92.9 4.8 x 10-5 91.6 7.2 x 10-5 89.1 1.2 x 10-4 85.8 1.2 x 10-4 86.2 2.9 x 10-4 79.1 3.9 x 10-4 77.0 4.8 x 10-4 75.7 6.5 x 10-4 73.2 KBO,(1) -+ KBOdg) 1.0 x 10-3 69.4 1.1 x 10-3 69.0 1.2 x 10-3 68.6 1.3 x 10-3 67.8 1.5 x 10-3 66.9 323.4 323.4 322.6 321.7 322.6 322.6 322.2 325.5 321.3 321.7 322.2 322.2 av.322.6k3 306.7 307.1 307.5 307.1 307.1 av. 307.1 k 2 - 3 - 3 h v) Y .4 c = - 4 - d 2 G 5 v Y 80 - -5 - -6 8.0 8.5 9.0 9.5 1 0 4 KIT Fig. 2. Plot of log (IT) against 1/T for the sublimation (-, 6) and vaporization (---, 7) species of KBO,(c, 1).918 THERMODYNAMIC PROPERTIES OF KBO, KBO2(1),l2 a third-law value of -673.6f 10 kJ mol-l was obtained for AHgB8 of KBO,(g). [The uncertainty of 10 kJ mol-1 includes the uncertainty of 8.5 kJ mol-1 in the reported AHgB8 value for KBO,(l)].The second-law value from the plot of log (IT) against l / T (see fig. 2) for reaction (7) yielded 271.1 f 4 kJ mol-1 for A H 0 at an average temperature of 1230 K. This reduced to 308.8 4 kJ rno1-I at 298 K. Employ- ing -980.7k8.5 kJ rno1-l for KBO,(l) a second-law value of -672.Of 12 kJ mol-1 was obtained for AHEB8 of KBO,(g). The difference in the second-law reaction heats above and below the melting point of 1220 K yielded AHg = 3 1.8 f 4 kJ mol-l, in close agreement with the JANAFvalue of 3 1.4 f 4 kJ mol-1.12 The only thermodynamic data for KBO,(g) previously reported are those of Jen~en,~ who employed fuel-rich H2+N,+0, flames. Boron additives of from to lo-, mole fraction were mixed with the feed gases and trace quantities of potassium were sprayed into the flame.Although direct determination of the four species of the reaction K(g)+HBO,(g) -+ KBO,(g)+H(g) (8) was not made, he determined the concentration of K atoms spectrophotometrically and assumed that the boron atoms formed HBO,. He further checked his method by inserting CCl, into the flame and obtained reliable data for Do for KCl within + 13 kJ mol-1 of the values reported in the literature. His value of 8 & 20 kJ mol-1 for KHF of reaction (8) led to a A H 8 = -674f25 kJ mol-l, which was adopted by the JANAF tables.12 Jensen’s value is in close agreement with the value of - 672.4 10 kJ mol-l obtained in this study. We thank the Southern California Edison Company for sponsoring this work. M. Farber, R. D. Srivastava and J. W. Moyer, J . Chem. Thermodyn., 1982, 14, 1103. M. Farber, R. D. Srivastava and J. W. Moyer, High Temp. Sci., 1983, 16, 153. M. Farber, R. D. Srivastava and J. W. Moyer, High Temp. Sci., in press. D. E. Jensen, Trans. Faraday Soc., 1969, 65, 2123. M. Farber and R. D. Srivastava, Combust. Flame, 1973,20, 33. J. B. Mann, J. Chem. Phys., 1967, 46, 1646. M. Farber and R. D. Srivastava, J, Chem. SOC., FaradQy Trans. 1, 1973, 69, 390. R. F. Pottie, J . Chem. Phys., 1966, 44, 916. M. Farber, R. D. Srivastava and 0. M. Uy, Trans. Faraday SOC., 1972,68,249. ti M. Farber, M. A. Frisch and H. C. KO, Trans. Faraday SOC., 1969, 65, 3202. lo J. W. Otvos and D. P. Stevenson, J, Am. Chem. SOC., 1956, 78, 546. l4 JANAF Thermochemical Tables (Dow Chemical Company, Midland, Michigan, 1971). (PAPER 4/820)

ISSN:0300-9599    

DOI:10.1039/F19858100913

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1985, 81, 919-937 Capillary Phenomena Part 24.-Properties of Fluid Bridges between Solid Rods in a Gravitational Field BY ERNEST A. BOUCHER* School of Chemistry and Molecular Sciences, University of Sussex, Brighton BNl 9QJ AND MICHAEL J. B. EVANS Department of Chemistry, Royal Military College of Canada, Kingston, Ontario, Canada Received 22nd May, 1984 Properties are predicted in dimensionless terms for fluid bridges between vertically aligned rods in a gravitational field. Meridian curves, which on rotation give the bridges, have been obtained for reduced rod radii R = 0.5-10.0. Actual rod radii are given by r = aR, where the capillary constant a is ca. 3.8 mm for water bridges in air and 8 mm for silicon at its freezing point in an inert atmosphere subjected to terrestrial gravity.Properties such as the pressure difference across the bridge interface and the force on the upper rod have been obtained for cases of varying fluid volume at several fixed rod-separation distances and of varying rod separation at fixed volumes. Stability limits as well as equilibrium paths are discussed. The results also provide a basis for analysing ideal float-zone refining, e.g. a silicon zone formed from its own solid: in these cases there are limitations on the fluid volume and on the angle of inclination of the fluid interface needed for solidification of a rod of purified material of uniform radius. Taking a growth angle of 11" for silicon, the maximum rod radius that can be grown from a zone of melt is ca.40 mm. The purpose of this paper is to extend the study of the properties of fluid bridges between equal solid rods with planar ends subjected to a gravitational field. An account of the basic features has already been given:' further work has been carried out to cover a wider range of bridges up to limits of stability. The approach is mainly based on the accurate computation of meridian curves meeting the solid rods at their edges as indicated in fig. 1. In contrast, fluid bridges meeting planar horizontal solids of large extent at a definite contact angle have been discussed separately.2 While the present study deals with the fundamental properties of bridges between rigid rods, the systems act as idealized models for the behaviour of float-zone processes used for the purification of silicon to semiconductor q ~ a l i t y .~ In much the same way, the holm/rod systems already studied43 are models for Czochralski growth from the melt, whereby crystals are pulled from the melt contained in a crucible. The rupture of fluid bridges has been discussed by Wolfram.6 Coriell et al.7 considered the stability of a fluid zone in a gravitational field, paying particular attention to the case where the volume of the molten fluid zone equals that of the solid cylinder from which it formed. The preliminary molten-zone studies of Keck et aL8 are not completely reliable because they did not use the full range of possible meridian curves (bridge shapes). Furthermore the often-cited study of Heywang9 is limited to an approximate account of special cases. ForteslO has considered fluid bridges in the absence of a gravitational field and reached conclusions compatible with our earlier 919920 FLUID BRIDGES Fig.1. Generating R curves which on rotation give a basic fluid bridge of phase a between the solid discs of radius R and surrounded by phase p. The vertical direction is z and the horizontal x axis coincides with the top of the lower solid. The forcefapplied to the upper solid is indicated on the small bridge. acc0unt.l The differences and similarities in properties of systems in the presence and absence of a gravitational field have also been discussed for a fluid ring round a solid sphere contacting a horizontal plane.ll COMPUTED QUANTITIES BASIC EQUATIONS The results given in this paper are based on meridian curves meeting the edges of the two solids of equal radius as shown in fig.1. [See also fig. 1 of ref. (l).] Reduced or dimensionless quantities, usually signified by upper-case letters, are used such that linear dimension I is scaled by the capillary constant a = (2y/Apgp, e.g. in reduced terms L = I/a, where y is the fluid/fluid interfacial tension, Ap is the positive fluid density difference and g is the acceleration due to gravity. The equations to be solved for the meridian coordinates ( X , 2) when the arc length S is the independent variable are d@/dS = 2(H - 2) - sin @ / X (1) dX/dS = cos @, dZ/dS = sin Q,. ( 2 ) The meridian angle Q, is the angle of inclination of the meridian at ( X , Z ) to the horizontal, i.e. tan@ = dZ/dX.The shape factor is H = A P / 2 , i.e. one half of the pressure difference across the interface at the lower end of the bridge. Computation is started by choosing values of X = R, the solid rod radius, where Z = 0 corresponds to the lower rod face, a value of Q, (= &) and a value of H. Then by trial and error meridian curves are found which also satisfy the upper boundary condition, i.e. which meet the upper solid of radius R at its edge for separation distance Z* between the rods.E. A. BOUCHER AND M. J. B. EVANS 92 1 The numerical solution of eqn (1) and (2) using the Runge-Kutta or Adams methodl29l3 can now be carried out on microcomputers. Details of the extensive computation are given in the Appendix. The volume of a fluid bridge is given by1 Va = n[R2Ze+ R (sin 42 - sin dl)] (3) in terms of the boundary meridian angles b1 and 42 (fig.1). The reduced force exerted on the upper solid owing to the presence of the bridge is feXt = nR sin 4h2 - nR2(H- 20). (4) Some bridges can be regarded as being partly pendent with respect to the upper solid and partly sessile with respect to the lower solid. Under such circumstances there will be a plane of zero force at some 2 where the azimuthal and meridional radii of curvature are equal. The pressure difference across the fluid/fluid interface where the bridge meets the upper solid is The and A P = 2(H-Ze). ( 5 ) area of the fluid/fluid interface is given by numerical integration of AaB = 2nsXdS the centre of mass 2. of the a phase constituting the fluid bridge is P Z * = n P Z d Z (7) s which can likewise be integrated numerically.The Helmholtz free energy is given in reduced terms by129 l4 F = Aap+2PZ.. (8) BRIDGE QUANTITIES For a given rod radius, R, the results of finding the meridian curves satisfying the boundary conditions can be expressed as the dependence of bridge volume Va on bridge height 20 for each value, d1, of the angle made by the meridian with the lower solid (fig. 1). This representation, illustrated in fig. 2 for R = 1, is a convenient intermediate step in the interpretation of the results. The region of existence of bridges on plots of Va against Z* can be interpreted in terms of experimentally measurable quantities. The limits of stability of bridges are sought since equilibrium configurations need not necessarily represent stable bridges.There are two ideal ways in which bridges can be manipu1ated:l (i) by varying the bridge height or rod separation Z* at constant bridge fluid volume Cm ; (ii) by varying the bridge volume Cm while keeping constant the rod separation 20. When making these changes, contact-angle conditions might arise leading to movement of the three-phase confluence from the solid edges. Boundary instabilities of this kind must be anticipated, and they are discussed below, but for the present their possible occurrence will be ignored. The results for R = 0.5, 1.0, 5.0 and 10.0 show most of the features which can be expected for fluid bridges. The sets of bridges between rods of reduced radius R = 1 will be seen to show a wide range of properties, and these 31 FAR 1922 FLUID BRIDGES 0 1 2 Z" Fig.2. Dependence of bridge volume Ya on height Z* for rods of radius R = 1 and several values of dl, the lower meridian angle at the solid contact. The locus of the maxima in Z* on the right-hand side of the loops defines the envelope, beyond which there are no bridges. The broken-line portions of the loops are for d2 c O", signifying that the meridians cannot meet the upper rod at its edge (see fig. 1). are discussed in some detail. The bridges where the rods are both of radius 0.5 or 10.0 are mainly discussed only where it is predicted that properties differ in kind from those for the other radii. To give an idea of actual dimensions, for air and water subjected to terrestrial gravity the capillary constant is a/mm = 3.8, so the rods would be of approximate radius 2-40 mm.The capillary constant for liquid silicon (surrounded by gas) at its freezing point (ca. 1690 K) is 8 mm, and R = 10 therefore corresponds to a rod of radius 80 mm. PREDICTED BRIDGE PROPERTIES RODS OF RADII R = 1 Bridges of constant volume P correspond to taking a horizontal line at some value of Va in fig. 2. No bridges exist to the right of what is referred to as the envelope. Also the range of q51 values (see fig. 1) cannot exceed 180" because the lower solid has a horizontal planar face, and, although one can find meridians with dl < 0", instability can be expected in this range: the vertical walls of the lower solid limit the meridian to q51 2 -90". Clearly one cannot have d2 < 0" because of the chosen geometry of the upper solid.The forcefext applied to the upper solid owing to the existence of a fluid bridge of fixed volume can be obtained from eqn (4). Fig. 3 showsfext varying with bridge height 20 for Va = 1, 2 and 4, corresponding to ca. 64, 128 and 256 mm3, were the bridge to consist of water surrounded by air. On elongating a bridge of reduced volume, Va = 1, it is seen that a sharp maximum is encountered in the applied force. By raising the upper rod with a device such as a piano-wire tensiometer, i.e. whereE. A. BOUCHER AND M. J. B. EVANS fex' -10 0 923 I - JJ 1 p 7 \ : 1 1 1 I 10 I 1 I 1 I 1 a twisted wire provides a torque raising the balance arm and vertical link to the solid, the applied force could be made to overshoot at this maximum.This has been referred to as an example of instability by stress-controlled manipulation, as opposed to strain-controlled manipulation where displacement is controlled and the force can pass through the maximum. The maximum is analogous to the condition for rupture of an adhesive joint made by placing liquid between two plates and pulling them apart by hand, and to the yield point in the stress-strain curve for a plastic solid in tension. In both of these analogues, gravity is not usually important. In the present case apart from buoyancy, the existence of gravity gives a body force. The bridge can exert a force on the rods owing to interface curvature (Laplace pressure) and the resolved component of the interfacial tension, i.e. that on the upper solid, is given by eqn (4).We defer discussion of the minima in the curves of fig. 3, but note the following additional features. By controlling the displacement of the upper solid it is predicted that the paths to the right of the maxima for all three curves can be followed reversibly. In the case of Va = 1 it is found that the curve ends abruptly when 41 = 171 k0.5" and 42 = O", but for Va = 2 and Va = 4 there are maxima in bridge height Z e which are expected to lead to bridge rupture. It seems that the under-cut portions after these maxima cannot be reached, although they represent bridges in hydrostatic equilibrium. We can illustrate how contact-angle conditions can intervene and lead to movement of the three-phase confluence away from an edge by examining again the case of = 1 near the force maximum.Using the concept of a so-called macroscopic contact angle, 8, which for purposes of argument is regarded as unique, i.e. there is no contact-angle hysteresis, fig. 4 shows how the ' hingeing' alp interface can reduce to 8 = 180-4, and the interface recedes. The principle can be summarized: if a fluid/fluid interface meeting a solid at its edge tends to make an angle with a neighbouring solid surface which is less than the intrinsic contact angle of that surface, then the interface will move from the edge rather than infringe the contact-angle condition. Problems of dynamic contact angles, microscopic contact angles and contact-angle hysteresis are well appreciated, and the previous statement refers to an ideal model. The treatment in this paper does not cover cases once boundary instability has been encountered.For the bridges under consideration the greatest range of behaviour without the intervention of instability due to contact angles will be possible for solid rod ends readily wetted by the a phase, but with sides not wetted 31-2924 0 fext 7 6 FLUID BRIDGES 0.3 0.4 Z" 10.7 0.8 0.9 X 0.4 0.2 z 0 1 Fig. 4. (A) Expanded portion of the maximum in fext from fig. 3 for Va = 1, with (a), (b) and (c) corresponding to the meridians in (B). (B) Three of the meridian curves near this maximum : (a) 41 = 135", (b) q51 = 150" and (c) = 155". The inset shows schematically how lower edge contact would be lost with 8 = 28" before meridian (c), for which d1 = 155", is reached. 1c 5 A P C -E 0 I I I I I 1 1 2 Z* Fig. 5.Dependence of the pressure difference A P e across the fluid/fluid interface where it meets the upper solid on bridge height for R = 1 and P = 1, 2 and 4 as indicated. A P contributes t o y x t shown in fig. 3 for these systems. by the a phase. The formal incorporation of contact-angle hysteresis into these studies of capillarity has already been de~cribed.~ Fig. 5 shows the dependence of the pressure difference A P e across the a/P interface, given by eqn ( 5 ) , at the upper three-phase confluence on bridge height. Comparison of fig. 3 and 5 shows that A P gives a major contribution, namely n R 2 A P , to the forcefext. The locations A P e = 0 correspond to a bridge whose interface has zero mean curvature at Z = Z*. The variation of the area, A@, of the fluid/fluid interface and the position, Z@, relative to the lower solid surface of the centre of mass of the constant-volume bridges are shown in fig.6(a) and (b), respectively. The bridges elongate with increase in Z@, but then they tend to squat giving a Z@ maximum before the height, Z*, maximum. When combined according to eqn (8) to give the Helmholtz free energy F as shown10 Aap 6 1 E. A. BOUCHER AND M. J. B. EVANS I I I 0.8 0.6 Z . 0.4 0.2 0 15 F 10 5 I I I I 1 Z" 2 I 1 I I , 2 t 1 z* b, 925 Fig. 6. (a), (b) and (c) show, respectively, the dependence of the fluid surface area A@, the position 2. of the centre of mass and the Helmholtz free energy Fon bridge height for R = 1 with volumes Va = 1, 2 and 4.926 FLUID BRIDGES I I I 1 I I 0 L 8 12 V" Fig.7. Dependence of the forcefext applied to the upper solid on bridge volume for rods of radius R = 1 and fixed bridge heights of Z e = 1, 1.5 and 2 (see text). 0 A P - 1 0 L 8 V" 12 Fig. 8. Variation of A P with Va for the systems of fig. 7. in fig. 6 ( c ) for R = 1, the area minimum dominates to give a minimum in F, then as 20 increases there is an inflexion in each curve with the abrupt termination of the curve for Va = 1. Cusps exist at the limit of bridge height for Va = 2 and 4 (the cusp does not show on the scale of the diagram for Va = 4). A full analysis of these thermodynamic quantities must await a more complete general treatment, extending previous accounts.12* 1 4 9 l5 By fixing the gap between the rods and varying the bridge volume one can follow the equilibrium path for the corresponding quantities.Starting on the d1 = -90" loop in fig. 2 the quantitiesfext, A P e , A@, Z* and F as a function of Za for bridge heights Z* = 1, 1.5 and 2 have been obtained: their termination corresponds to the curve through the ends of the loops in fig. 2. For R = 1 and Z e = 1 fig. 7 shows that a lower limit to Va can be expected. There is a maximum in the downwards pull on the upper solid, and then as the volume increases further the bridge bulges and pushes on the upper solid, as evidenced by the negativefext values. When Z e = 1.5 there is always a downwards pull on the upper solid. It is also noted thatE. A. BOUCHER AND M. J. B. EVANS 927 0 L VQ 8 12 I I I 1 I 1 0 4 8 12 VQ I I I 0 2 6 10 I VQ Fig.9. (a), (6) and (c) show, respectively, the dependence of Aab, 2. and F on bridge volume for the three bridge heights, Z e = 1, 1.5 and 2, for each of which the rod radius is R = 1 .928 2 1 0 f e x t -1 - 2 FLUID BRIDGES I a I I -4 Fig. 10. (A) and (B) show, respectively, the dependence of the applied forceFxt and the pressure difference A P on the bridge height Z e for rods of radius R = 0.5 and bridge volumes Va: of (a) 0.25, (b) 0.5, (c) 1 and (6) 2. there is a gap in the equilibrium path between vb! x 5.3 and 7.0 owing to the fact that the curve through the ends of the Va against Z* loops in fig. 2 crosses the vertical line 20 = 1.5 twice. Thefext against P curve for 20 = 2 shows a distinct cusp at the limit of the volume. The broken-line portion of the same curve represents the dependence offext on Va when 4h2 < 0".This region has no physical significance for rods having plane horizontal ends. A similar region exists for 2e = 1 . The contribution t o p x t from A P is shown in fig. 8 for R = 1, where the portions identified with respect t o p x t are evident, but there is not the similarity in shape and features which exist for the constant-volume cases. Fig. 9 (a) and (6) show, respectively, how A@ and 2. vary with P for the three bridge gaps. There is considerable similarity in the general shape of the curves for each quantity. Their combination to give the Helmholtz free energy in fig. 9(c) shows three similar curves which are themselves different from those in fig. 6(c) for the Helmholtz free energy at constant volume.With increase in bridge volume the angle 9, decreases and becomes zero (the fluid/fluid interface is therefore horizontal at the edge contact with the solid): at this location, within the slight uncertainty on the scale of the plots, there is an inflexion where d2F/d( P)2 = 0, and this probably denotes the limit for stable bridges (with the condition 8 > 90" for liquid on the sides of the lower rod). RODS OF RADII R = 0.5 A representative set of loops of Za as a function of 20 for various 4h1 values has already been published1 for the case of rods of radius R = 0.5. The main difference between them and the set in fig. 2 is that the properties of the system have now been predicted to conditions where the boundary becomes unstable. For cases of d1 d 90" the meridian curves have inflexion points.As the limit of boundary stability is reachedE. A. BOUCHER AND M. J. B. EVANS 929 I I 1 8 F 4 0 0.5 1 .o 1.5 2" Fig. 11. Variation of the Helmholtz free energy Fwith bridge height Z e for R = 0.5 and Va = (a) 0.25, (b) 0.5, ( c ) 1 and (6) 2. the S-shaped bridges develop a very thin neck. Beyond the stability limit meridians no longer have an inflexion, and eventually Q, along the meridian now increases to 180". For d1 > 90" the loops of Va against bridge height terminate at a value of H , approached froni below. Values of H in excess of the limit give meridians which share a position where Q, = 180", whereas the systems require bridges for which the meridians have a maximum in Q, at the inflexion, and these double back to meet the upper boundary condition (solid edge). The dependence offext on 20 in fig.10(A) is dominated by the existence of maxima infext and in Z*. The dependence of A P e on 20 in fig. 10(B) shows similarity with thefext plots for Va = 0.25, but for the Va = 2 curve it is now obvious that the resolved component of the interfacial tension is also contributing. The dependence of the Helmholtz free energy F on 20 in fig. 11 shows that the curves are very similar to those when R = 1. RODS OF RADII R = 5 With rods of reduced radii R = 5 one is severely limited by the range of possible meridian curves which do not have d2 < 0" where they meet the upper solid (see discussion regarding the implications of having a particular geometry of the solid). The Va against 20 curves can no longer be called loops since they terminate when d2 = 0", as is shown in fig.12. Fig. 13(a) and (b) showingfext and F, respectively, plotted against Z* for three fixed bridge volumes, Va = 25, 50 and 100, reveal very clearly the limited range of equilibrium paths which are possible under these circumstances;930 2 00 150 V" 100 50 0 FLUID BRIDGES 1 I 1 2 Z" Fig. 12. Dependence of bridge volume P on height Z* for R = 5 and the angles dl shown. The curves corresponding to the bridges terminate at the broken portion where d2 = 0". 200 100 f C X t 0 -100 -20 0 25 0 0 5 1 0 1 5 2" I I ( b ) 50 25 L I I 0 0 5 1 0 1 5 2" 200 I50 100 F 50 0 Fig. 13. (a) and (b) show, respectively, the dependence of applied forcefext and Helmholtz free energy F on bridge height for R = 5 for volumes P indicated.Comparison with fig. 3 and 5 indicates the restrictions on the ranges of the curves for R = 5 as opposed to those for R = 1.E. A. BOUCHER AND M. J. B. EVANS 93 1 800 Va 600 LOO 1.2 1 . 5 2 .o 2" 2.5 Fig. 14. Dependence of Va on 20 in the region 20 2 1.2 for rods of radius R = 10. The curves all terminate when $z = 0". The curves for < 0" are unlikely to represent physically realistic bridges, and so the possible range of their existence is severely limited. The broken line is for Va = nR220. RODS OF RADII R = 10 For rods of reduced radii R = 10 there are even greater restrictions on the existence of bridges owing to the limited ranges of Z* at constant P, and of Va at constant Z e .The majm factor in this limited behaviour is that tjb2 falls to zero. Fig. 14 indicates the possible systems. If the upper solid had a scooped-out end some extension of range would be possible for undercut equilibrium shapes, but these are not likely to be physical 1 y realis tic. SUMMARY OF RESULTS The range of solid radii examined illustrates the behaviour to be expected for fluid bridges, including equilibrium meridians giving stable bridges, bridges which might become unstable depending on the physical system being used to manipulate them, and bridges which might become unstable owing to boundary instability, where the system can lose edge contact. The plots of bridge volume at constant lower meridian angle, tjbl, against bridge height, 20, also show regions of Va and of Z e for which no bridges are at all possible.The following discussion deals with a model for zone refining where there are limitations on bridge volume and on the meridian angle. MODEL FOR FLOAT-ZONE REFINING Technological processes of purification of semiconductor materials, e.g. silicon, by using floating zones rely on capillarity. A vertical rod of material, say 5 cm diameter, is melted using a radio-frequency ring to give a so-called zone between rods which rotate. Purification is effected by moving the ring heater relative to the rods so that melting occurs from the remaining upper solid portion and solidification, leaving impurities in the liquid, takes place at the lower solid/liquid boundary. A fluid bridge of liquid between inert solids with horizontal ends is but a crude representation of the actual floating zone.The chief simplifications are those of ignoring the rotational motion, the temperature gradients, and therefore convection and Marangoni932 FLUID BRIDGES solid Fig. 15. Idealized representation of the freezing lower solid/liquid interface showing the liquid/vapour interface orientation for the floating-zone process. effects, and the shape of the solid/liquid interfaces.12 Two features of the real process can, however, be modelled: ( a ) the zone volume at an assumed uniform temperature will be proportional to the length L of solid which has been melted (in the simplest case Va = nR2L), but silicon shrinks by ca. 9% on melting; ( h ) it is found that the lower solid will only grow at constant radius equal to that of the upper solid if the growth angle, ly, shown in fig.15, is fixed, e.g. ca. 1 1 " for silicon. The bridges deal with Laplace or mechanical equilibrium and stability, and do not specifically account for physicochemical effects such as diffusion.12 In the floating-zone process physicochemical phenomena are important, since there is transfer of substance between phases. The pressure difference AP across the liquid/vapour interface and the pull of the interfacial tensions, especially at the three-phase boundary, affect the chemical potential of the liquid and the solid. The simplest assumption is that the solid/vapour, solid/liquid and liquid/vapour interfaces adjust to satisfy the Neumann triangle of forces, usually only applied to three-fluid phases.It will be presumed that under ideal circumstances this would be one condition for physicochemical equilibrium when the solid/liquid and solid/vapour interfaces can adjust their orientation, since they are being formed infinitesimally slowly. The growth angle, ry, can be adjusted, i.e. d1 is fixed, and the solid side remains vertical. The orientation of the solid/liquid interface away from the horizontal is for the moment ignored. Fig. 16 shows Va/nR2Ze plotted against the gap Z* between the solids for the various values of R from 0.5 to 10, each with d1 = 79", i.e. the growth angle is ry = 1 lo, appropriate to silicon.16 The amount by which the quantity Va/nR2Ze deviates from 1 is a measure of how the fluid volume differs from the cylindrical space between the rod ends.For ry = 11" there are no meridians, i.e. no equilibrium bridges, for P / n R 2 Z e 2 1.054 and R 2 0.5. Also, each curve terminates abruptly, although this is only shown for R = 5 and 10. The 9.1 % volume shrinkage of silicon on melting16 is indicated by the broken horizontal line. The largest possible reduced value of R is very close to 5, with the gap between the rods 29 = 2.02. The limit in rod diameter is therefore ca. 80 mm or just over 3 in., using 720 mN m-l for the surface tension of liquid silicon at its melting point1' and a liquid density of 2.53 g cm--3, i.e. the capillary constant a is 8 mm.16 A fuller account of this model applied to silicon and germanium, including experimental uncertainties and physicochemical as well as mechanical aspects, will be given separately.There are several assumptions (above) in this model which could mean that experimental values different than these predictions could be found in practice. If, for instance, the solid/liquid interfaces are both concave then more solid will have melted compared with the model (fig. 16) and the limiting rod radius would be smaller. Nevertheless, the present state of knowledge of the zone-refining process is such that the model gives a useful guide to stability limits, and by implication the rod--holmE. A. BOUCHER AND M. J. B. EVANS 933 I V* rR2Z" 0. .O 95 0.90 Fig. 16. Dependence of Va/xR2Ze on 20 for #J = 79" (w = 11") for each reduced radius R of (a) 0.5, (6) 1, ( c ) 2, (6) 5 and ( e ) 10. The horizontal broken line represents silicon, which shrinks on melting and has the growth angle of w = 11".systems provide an analogous model for Czochralski growth. Perhaps even more importantly these models suggest that these types of process might eventually be more fully understood in terms of a combination of mechanical and physicochemical effects. In crystal growth steady-state stability should be considered, although in the present case the slow growth rates are unlikely to give conclusions differing from those given by a quasi-static model. The steady-state stability of floating zones of silicon was examined by Surek and Coriell,lG who found that with a growth angle of ll", rods of radius 25.626 mm were stable to fluctuations in zone length such as would arise from unequal rates of advance at the freezing and at the melting interface.Whether this type of stability persists up to the limiting radius of ca. 40 mm found in this paper has yet to be investigated. What is also not clear is whether this steady-state stability exists only within a certain range of growth angles. Finally it is noted that the rotational motion of one rod relative to another, used in floating-zone processes to minimize thermal asymmetry, convective and Marangoni effect^,^ is sufficiently slow that it should not greatly affect zone stability under the usual gravitational influence, but in near-zero gravity conditions the rotational effect can be important.l8 APPENDIX COMPUTATION OF MERIDIANS* The present analysis of bridges has involved the computation of a large number of meridian curves by numerical integration of eqn (1) and (2). The following summary, based on a decade of study, is relevant to the vast majority of cases in this series of papers (and not just bridges) concerning the computation of meridian curves 2 = Z(x) and related quantities for axially symmetric capillary systems in a gravitational field.It is desirable to discuss the computation in one article, especially since a study of lenses also involving a very large number of meridians * Written in conjunction with T. G. J. Jones\o w P Table 1. Summary of advantages and disadvantages of computational methods method modified Euler Taylor series Runge-Kutta versions (a) 4th order (6) Gil (c) Butcher Merson Milne Hammings self- estimated error starting per step, h advantages Yes h3 rapid, easy to use Yes hn+l straightforward n derivatives error analysis no no h5 all self-starting, h5 high accuracy, widely h6 used h5 uses step-size adjuster for accuracy h5 two calculations per step, simple predictor eqn, iteration option h5 two calculations per step, iteration and simple predictor, no stability problems disadvantages low accuracy, slow complexity of higher convergence derivatives simple versions cannot test error at each step, complicated error analysis, large number of calculations per step cannot easily meet end values of independent variable (modify standard version) possibly subject to instabilities, not self-starting not self-starting fully recommended no no yes especially ( c ) not so suitable (a) and (W,E. A.BOUCHER AND M. J. B. EVANS 935 has been undertaken, and because microcomputers can be used with care for relatively large step sizes. The three main topics discussed are: (a) recommended methods of solving the appropriate Young-Laplace equation, using the results from several methods of integration which have been compared, (b) the estimation of errors involved in these numerical integrations and (c) the foundations underlying what are usually referred to as approximate solutions of the Young- Laplace equations. In the case of zero-gravity or neutral-buoyancy conditions, solutions of the meridian shapes often exist in terms of elliptic integrals. It is, however, still possible to use the same form of the equations and methods of integration for conditions of zero gravity, microgravity and terrestrial gravity.Choices of independent variable in alternative forms of eqn (1) have already been discussed:12* l3 the independent variable must always vary in the same direction. Many techniques of integration on several computers with various step sizes, independent variables, shapes of meridian and gravitational cases have been used to form the basis of this account. Table 1 summarizes our conclusions. In some cases the software accompanying a computer set-up will influence the choice of method, e.g. the Hewlett Packard HP9821A uses Gil’s method. When there is a free choice, Runge-Kutta’s, Merson’s or Gil’s, and related methods, are recommended: they are described in many textbooks.lg 23 Incorrect meridians resulting from using a slightly incorrect form of the Young-Laplace equation should be evident by the shapes of other than small arcs of meridians.It may not be easy to detect deviations from true meridians arising from non-matching initial steps. One test of consistency is to reverse the direction of computation over a considerable meridian length and expect the initial and final values to agree within the rounding error. Rounding errors will occur with a large number of steps involved in obtaining a meridian, but with a machine precision O(lO-g) they do not appear to be serious (see later). Instability during computation can occur with very shallow (nearly horizontal) meridians, where Bessel forms of the meridians are very successful. With sharply curved meridians, changes in the step size of the independent variable will usually signify the tendency, if any, of the computation to ‘cut corners’.Two recognized error tests are (a) to vary the step size as explained in detail by Duncan,24 although this method cannot be used with algorithms automatically using variable step sizes, and (6) to compute meridians for known analytical curves, e.g. circular arcs. Both of these have been used in the current study, and a third method, not previously discussed, has also been used. In general, the second-order Young-Laplace equation appropriate to a particular fluid body, i.e. bridge or drop, can be integrated once. The resulting equation can then be numerically integrated to give the meridian. That this does not seem to have been done before is itself curious.However, it also provides the basis for approximations for meridians and it can be used to estimate the error incurred during integration, although the integration is effectively reduced to that of a first-order rather than the original second-order equation. Examples will show the principles. Eqn (1) rewritten using 2 as the independent variable for fluid bridges integrates to give When Z = 0 at the bottom of the bridge, 0 = q51 and C = -cos @ giving Using Z as the independent variable, the left-hand side can be evaluated numerically and written as (IB-cosO) for comparison with the right-hand side for chosen dl, x“ (initial) and H, to give an ‘error’ of the form 6, = ( I B -COS @) -(2HZ-Z2 -COS 41) (1 1) as I , is characteristic of that meridian, with analogous integrals for pendent and sessile drops.Approximations for meridian shapes essentially give an approximation for these integrals,936 FLUID BRIDGES although they are not usually presented in this manner. Using a fourth-order Adams-Moulton method the results for two step sizes A Z = lop2 and were 6 = 4.65661 x and 6 = -3.53903 x respectively. These and a wider range of computations lead to the conclusion that rounding errors are evident but not important when A 2 = lop3, but are less evident for A 2 = which conveniently gives much faster computation time than for the smaller step size. For pendent drops the analogous treatment gives the same integral with Z as the independent variable, or with S as the independent variable, giving 6,, = (Ip,-cos@)-(2Hz-22- 1).(13) Again it is found that rounding errors of no great importance are incurred at small step sizes, and that good agreement is found with known shapes, e.g. circular arcs for A S = The form of eqn (1) and (2) presupposes that the system is subjected to a fixed, e.g. terrestrial, gravitational field. The use of a capillary variable, [, which can be varied differentially or given a set of values, has already been and 25 The form sin @ - = 2(H-c2)-T d@ dS gives a pendent drop for each H, subjected to terrestrial gravity for [ = 1, microgravity for [ 6 1 and a spherical segment in gravity-free conditions for [ = 0. Alternatively, a factor placed before ( H - Z ) can be used for the same purpose. Finally, note that Siekmann et ~ 1 .~ ~ advocate an expanded Runge-Kutta-Fehlberg method,27 of which they state: ‘The local error . . . O(h7). . . does not only allow a step width. . .larger than that of the classical Runge-Kutta method, but it also guarantees the same accuracy as the latter. . . . the accumulation of rounding errors is less and the saving of computer time is remarkable. ’ Feldberg’s version seems very similar to Merson’s 29 PRINCIPAL SYMBOLS a AaB fext F g h H IPD 1 L LIP r R S P x, 2 S capillary constant area of a/P interface reduced externally apply force on the upper solid disc (rod) Helmholtz free energy acceleration due to gravity (not necessarily the terrestrial value) integration step size in the Appendix shape factor: one half of the pressure difference across the alp interface at the lower solid contact actual linear dimension reduced linear dimension, l / a reduced pressure difference across the a/B interface, being A P at the lower solid where 2 = 0 and A P at the upper solid where Z = 2* actual rod radius reduced rod radius, r / a denotes solid phase meridian arc length reduced volume of a phase, ua/a3 meridian coordinates, being (A?, ZO) usually with ZO = 0 at the lower solid and (Xe, Z e ) at the three-phase confluence with the upper solid position of centre of mass of a phase above plane of lower solid (X.= 0) fluid phases with a the enclosed or bridge phase characteristic integrals in the AppendixE. A. BOUCHER AND M. J. B. EVANS 937 fluid a/fluid p interfacial tension computing error defined in the Appendix capillary variable formally allowing for the acceleration to vary from g due to terrestrial gravity contact angle for three-phase confluence with plane solid, not edge contact pa-# the positive density difference between the fluids meridian angle, arctan (dZ/dX) values of the meridian angle (fig.1) at the lower and upper three-phase confluences, respectively growth angle, (90 - E. A. Boucher and M. J. B. Evans, J. Colloid Interface Sci., 1980, 75, 409. E. A. Boucher, M. J. B. Evans and S. McGarry, J. Colloid Interface Sci., 1982, 89, 154. D. T. J. Hurle, Adv. Colloid Interface Sci., 1981, 15, 101. E. A. Boucher and H. J. Kent, Proc. R. SOC. London, Ser. A , 1977, 356, 61. E. A. Boucher and T. G. J. Jones, J. Chem. SOC., Faraday Trans. I , 1980, 76, 1419. E. Wolfram, Croat. Chem. Acta, 1972, 45, 137. S. R. Coriell, S. C. Hardy and M. R. Cordes, J. Colloid Interface Sci., 1977, 60, 126. P. H. Keck, M. Green and M. L. Polk, J. Appl. Phys., 1953, 24, 1479. W. Heywang, Z. Naturforsch., Teil A , 1956, 11, 238. lo M. A. Fortes, J. Colloid Interface Sci., 1982, 88, 338. l1 E. A. Boucher and T. G. J. Jones, J. Chem. SOC., Faraday Trans. I , 1982, 78, 1491. l2 E. A. Boucher, Rep. Prog. Phys., 1980, 43, 497. l3 E. A. Boucher, M. J. B. Evans and T. G. J. Jones, Adv. Colloid Interface Sci., to be published. l4 E. A. Boucher, Proc. R. SOC. London, Ser. A , 1978,358, 519. l5 T. Surek and B. Chalmers, J. Cryst. Growth, 1975, 29, 1. l6 T. Surek and S. R. Coriell, J . Cryst. Growth, 1977, 37, 253. l' P. H. Keck and W. van Horn, Phys. Rev., 1953,91, 512. l9 W. S. Dorn and D. D. McCracken, Numerical Methods with Case Studies (Wiley, New York, 1972). 2o Numerical Solutions of Ordinary and Partial Diflerential Equations, ed. L. Fox (Pergamon, Oxford, 21 M. L. James, G. M. Smith and J. C. Wolford, Applied Numerical Methodr for Digital Computation 22 G. M. Phillips and P. J. Taylor, Theory and Application of Numerical Analysis (Academic Press, 23 H. H. Goldstine, A History of the Calculus of Variations from the 17th Through the 19th Century 24 W. J. Duncan, Philos. Mag., 1948, 39, 493. 25 E. A. Boucher and T. G. J. Jones, J. Colloid Interface Sci., 1983, 91, 301. 26 J. Siekmann, W. Scheideler and P. Tietze, Comput. Meth. Appl. Mech. Eng., 1981, 28, 103. 27 G. Jordan-Engelm and F. Reutter, B. I. Hochschultashenbucher (Biblograph. Inst., Mannheim, 1976), 28 L. F. Shampine and R. C. Allen, Numerical Computing: An Introduction (W. B. Saunders, Philadelp- 29 L. Fox and D. F. Mayers, Computing Methodr for Scientists and Engineers (Oxford University Press, W. Wuest, ESA Spec. Publ. No. 114 (European Space Agency, Pans, 1976). 1962). with Fortran and CSMP (IEP, New York, 2nd edn, 1977). London, 1973). (Springer-Verlag, New York, 1980). Bd 106, 2 Aufl. hia, 1973). Oxford, 1968). (PAPER 4/839)

ISSN:0300-9599    

DOI:10.1039/F19858100919

出版商:RSC    

年代:1985

数据来源: RSC