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Journal of the Chemical Society, Faraday Transactions 11 ISSN 0300-9238 Journal of the Chemical Society, Faraday Transactions II SUBJECT INDEX-VOLUME71, 1975 11, I Kinetic Spectroscopy (see also 11, 5) Atomic Resonance Fluorescence Spectrometry for Rate Constants of Rapid Bimolecular Reactions. Part 4.-Chlorine Atom Fluorescene 4s2s4 P-3p5 2P.(Bemand & Clyne) 1132 Kinetic Behaviour of Electronically Excited Tin Atoms, Sn(5'So, 5'D2),and the Importance of (J, a)Coupling in Heavy Atom-Molecule Collisions. (Brown & Husain) . 699 Kinetic Investigation of Ground State Carbon Atoms, C(23Pj). (Husain & Young) . 525 Vacuum Ultra-violet Photodissociation of Alkyl Iodides. Kinetics of the Reaction H+ICHS -HI+CH3. (Levy & Simons) .. .. 561 Vacuum Ultra-violet Photolysis of Nitrous Oxide. Energy Disposal in the Reaction 0(2'0)$N2O+ 2NO. (Chamberlain & Simons). . 402 Vibrational Excitation of N2by the Spin-orbit Relaxation of Hg(63P: -+ 63P0). (Horiguchi & Tsuchiya) . ... .. ... .. 1164 11, 2 Photophysics (fluorescence, phosphorescence, luminescence, dispersion, dichroism, etc.) Decay of the Triplet State in Aromatic Vapours. (Ashpole, Formosinho & West) . . 615 Dynamics of some Hydrogen Isotopic Exchange Reactions at High Energies. (Malcoline-Lawes) .. 1183 Electron Spin Polarization during the Photoiysis of Pivaiophenone (Phenyl t-Butyl Ketone). (Atkins, Dobbs & McLauchlan) . ... .. 1269 Evaluation of the Intramolecular Energy Transfer Rate Constants in Crystalline Eu(hfaa)4ButNH3.(Dean & Shepherd) . . ... .. 146 Fluorescence and Flash Photolysis Comparison of 1 -Hydroxynaphthalene-2-sulphonateand 1-Hydroxynaphthalene-4-sulphonateIons in Aqueous Solutions of Various Acidities. (Henson &Wyatt) . . . . ... 669 Mechanism of the Direct trnns --3 cis Photoisomerization of Stilbene. Part 2.-Thermally Activated Intersystem Crossing. (Momicchioli, Corradini, Bruni & Baraldi) . . 215 Host and Guest Emission in Pentacene-Anthracene Mixed Crystals. (Brillante & Craig) . 1457 Interaction of Aromatic Amine Exciplexes with Polar Molecules. (Beddard, Carlin & Lewis) . ..... .. 1894 Intermolecular Energy Transfer between Tris(acety1acetona;o)-lanthanoid Complexes in n-Butanol Solution.(Napier, Neilson & Shepherd) . 1487 Phosphorescence Depolarization in Polymer Systems. (Miller & North)' . . 1233 Photodissociation of a-Naphthol in Solution: Influence of Hydrogen Bonding. (Hara & Baba) .. .. ... 1100 Photophysical Proces'ses in'Benzaldehyde. (Metcalfe, Brown & Phillips) . 409 Quenching of Biacetyl Fluorescence and Phosphorescence by Inorganic Anions. (Bortolus & Dellonte) . . . ..... 1338 Quenching of 02('Xi) by Ground State 02. (Thomas & Thrush) . . . 664 Relaxation of HCI (v = 1) and DCI (v = 1) by Chlorine Atoms at Temperatures between 195 and400K. (Brown, Glass &Smith) . . . . . 1963 Theoretical Study of Isotope Effects in the Quenching of Electronically Exciied Halogen Atoms by HP, HD and DZ.(Zimmerman & George) . . . .. 2030 Theory for Time Resolved Emission Spectra. (Fleming & Gijzeman) . ... 773 Thermal Decomposition of HNO. (Callear & Carr) . ... 1603 Thermoluminescence of Solutions in Squalane after y-Irradiation. (Brocklehurst, Bull & Evans) . . . .. ..... 543 Transfer of Excitation Energy in Rigid Solutions coniaining Charge-transfer Complexe;. Part 1.-Quenching of Fluorescence. (Degbrski & Kryszewski) . ... 1503 Part 2.-Photoconductivity. (Degbrski & Kryszewski) . . . .. 1513 Vibrational Relaxation in Atom-exchange Reactions. Classical Trajectory Study of ClSHCI and ClfDCl Collisions. (Smith) . .. 1970 Vibrat.iona1 Relaxation in Shock-heated Mixtures of Carbon Monoxide with Hydrogen Halides.(Borrell, Borrell & Gutteridge) . . ... ... 571 19 SUBJECT INDEX-VOLUME 71, 1975 PAGE II,3Quantum and General Theory (including valence theory, ab initio calculations, computer simulation, etc.) Ab Initiu Calculations on Valence-shell Molecular Orbitals. (Murrell &Vincent) . 890 Ab Initiu Studies of Non-bonded Hydrocarbon Potentials. (Catlow, Harker &Hayns) .275 An Improved IOC-w Technique. Part 1 .-Ionization Potentials and Electron mities of Some Molecules. (Sharma, Srivastava &Krishna) .. ... 168 Part 2.--n-Bond Energies, Heats of Formation and Resonance Energies of Alternant and Non-Alternant Hydrocarbons. (Sharma, Srivastava &Krishna) ..172 Applications of Simple Molecular Wavefunctions. Part 7.-FSGO Open-shell Calculations on First-row Polyatomic Hydrides and Hydride Ions.(Blustin &Linnett) ..1058 Part 8.-FSGO Calculations on C2 Hydrocarbon Radicals and Cations. (Blustin & Linnet) . . . . . 1071 Part 9.-Floating Spherical Gausian 'Orbiial Calculation for Hydrogen Peioxide.. (Pakiari &Linnett) .. ... . . 1590 Part 10.-Analysis of the Rotational Barrier in Hydrogen Peroxide. (Semkow & 0.Linnett) .. ... .. 1595 Bond Polar Parameters in Ethylene. iGalabov, Suzuki &Orville-Thomas) ... 1 62 Calculation of Electric Polarizabilities within the CNDO Framework including Polarization Functions in the Basis Set. (Teixeira-Dias &Sarre) .. ... 906 Central Field Expansion of Radial Integrals Derived from Ligand Field Parameters.(Hollebone &Donini) .. ..... ... 141 1 Conformational Study of meta-Halogenostyrenes. (Ralowski, Mjoberg &Almlof) ..1109 Cusped-Gaussian Molecular Wavefunctions. Part 1.-LiH as an Example. (Steiner & Walsh) ..... .... 921 Part 2.-The Molecular Integrals. (Steiner &Walsh) . ..... 926 Electronic Overlap Population as a Measure of Reactivity in Electrocyclic Reactions. Part 2.-Photocyclization and Photodimerization Reactions. (Muszkat, Seger & Sharafi-Ozeri) . . . .. .. 1529 Electronic Structure and Chemistry of Some Iodine Compounds. (Rode) 481 Electronic Structure and Optical Properties of Dichlorodioxomanganese(v1). (Jasinski & Holt) ... . , . ...... 2002 Electronic Structure of Nitric Acid studied by Photoelectron Spectroscopy and Molecular Orbital Calculation. (Lloyd, Roberts &Hillier) ....... 496 Electronic Structure of Selenophen. (Findlay) ........ 1397 Exchange lnteractions between Orbitally Degenerate Ions. The Case of Two 'Eg Ions. (Kahn) . ...... ... .. 862 Exciton Narrow Band Model for 7,7,8,8-TetracyanoquinodimethaneSalts. (Shields) .1792 Influence of Small Cations on the Rotational Barrier of hides. Comparison of Experiment with HF-SCF Model Calculations. (Rode &Fussenegger) ..... 1958 Inner-electron Ionization Energies of Small Molecules. (Buckingham, Handy &Whitehead) 95 Ionization Energies of Some Amines and Enamines and an Estimation of Their Relative Basicity in Gaseous Phase. (Colonna, Distefano, Pignataro, Pitacco &Valentin) .1572 Ion Pairs formed by Alkali Metals. Part 1.-Complexes of Lithium, Sodium and Potassium with 4-Nitropyridine.(Cremaschi, Gamga, Morosi, Oliva &Simonetta) . . . 1829 Low-lying Electronic States of the Ethynyl Free Radical. (So &Richards) .. 660 Multiplet Splitting and Intensity Ratio in the N(1s) Photoemission Spectrum of NO. (Hillier &Kendrick) ... .. ..... 1654 Orientational Invariance and Significance of Electron Densities Obtained with Approximate All-valence Electron Wavefunctions. (Figeys, Geerlings &Alsenoy) . 1375 Preferred Molecular Conformations of the Hindered a-Diazo Ketones CH2CICOCHN2 and CH3COCCH3Nz by Semi-empirical Molecular Orbital Calculations. (Sorriso)..682 Quantum-mechanical Systems Restricted by Impenetrable Barriers studied by a Perturbation Method. (Gonda &Gray).. .. ... 201 6 Renner Effect in SiH2. (Dubois, Duxbury &Dixon) .. . .... 799 Simulated Ab Znitio Molecular Orbital Technique. Part 5.-Polar Groups, Ionic Molecules and Orthogonalized Basis Sets. (Duke, Pickering, O'Leary &Eilers) .. 1401 Structure and Electronic Properties of the Nitromethyl Anion, Nitromethane and aci-Nitromethane. (Murrell, Vidal &Guest) . ... ... 1577 Structure of the B State of Cyclobutanone. (Momicchioli &Baraldi) . .. 791 Symmetry Adapted Perturbation Theory of Intermolecular Potentials. The Helium- Helium Interaction. (Snook &Spurling) ... . . ...852 SUBJECT INDEX-VOLUME 71,1975 21 PAGB Theoretical Studies on the Hydrogen Dichloride, HCI; Ion and Radical, HCI;.(Thomson,Clark, Waddington &Jenkins) . ..... .1942 Topological Aspects of Odd Graphs and' their' Relebance to Radical Spin Densities. (Honeybourne) . . . . ... . . . . .1343 Use of Partial (and Full) Lowdin Integral Approximations in Molecular Orbital Calculations on HCN and FCN. (Dixon, Doggett &Howat) . . . . .452 11, 4 Relaxation Phenomena (dielectric, magnetic, ultrasonic, etc.) Acoustic Studies of the Effect of Tacticity on Segmental Motion in Polymers, (Dunbar, North, Pethrick &Steinauer) . .. ... 1478 Atomic Polarization in Metal Chelates. Pait 3.-Dielectric Loss Measurements on Some Beryllium Complexes of Certain Schiff Bases. (Angel, Hayes &Radford) ..81 Comparison of Diffusion and Strong Collision Models for Molecular Reorientation in Liquids: Simulated Electron Spin Resonance Spectra for Spin Systems of Varying Multiplicity.(Benton) . .. 1863 Dielectric Absorption at Sub-millirnktre Wavelengths in Poly(pentafluorostyrene) and Poly-(apP-trifluorostyrene). (North, Pethrick &Towland) . 1473 Dielectric Relaxation in Alkali Metal Oxide Conductive Glasses Studied by Complex Impedance Measurements. (Ravaine, Diard &Souquet) . .. 1935 Dielectric Relaxation in Methylammonium Chromium Sulphate Dodecahydrate. (Czapla; Kolodziej &Sobczyk). . . . ... 767 Dielectric Relaxation in Non Aqueous Solutions. Part 6.-Effect of Dipole-Dipole Interactions on the Dielectric Relaxation Time of Solutions of Tri-(n-buty1)ammoniumPicrate in p-Xylene.(Cave11 &Sheikh) . . . 474 Dielectric Relaxation Studies of Phases 111 and IV of Thiourea. (Czapla, Kolodziej & Sobczyk) . .. . . . 763 Electrical Dipole Moments of h. Coii in Suspensions in Water and in WaterfAlcohol Mixtures by Electric Field Light Scattering. (Morris &Jennings) . . . 1948 High and Low Field Permittivity and Conductivity Measurements for Mixtures of Alcohols and Proton Acceptors. (Brown &Jones) . .. ... 1877 High Field Dielectric Measurements in Water. (Kolodziej, Jones &Davies) .. 269 Microwave Absorption and Dielectric Relaxation of 1,ZDihalogenoethanes in Dilute Solutions. (Madan) . .. 67 Non-linear Dielectric Studies of Lower Alcohols in the Presence of Conductivity.(Brown &Jones) .. ..,. ...... 1657 Pressure and Temperature Dependence of Viscoelastic Properties of Polymethylphenyl-siloxane Fluids. (Kim) . . . . . . 426 Relaxation Kinetic Study of Rotational Isomerism of 1,2-Dichloroethane and (k)-2,3-Dichlorobutane by the Dielectric Field ERect. (Hopmann) . 1844 Temperature, Isotope and Solute Effects on the Non-linear Electric Field Behaviour of Water. (Bradley, Parry Jones &Kdodziej). .. . ... 1200 Viscoelastic Relaxation in Supercooled Eugenol. (Kim) . ..... 41 5 Ir,5 spectroscopy (a) Microwave, infrared, Raman Comparison in the Time Region 0-1.2 ps of Model and Experimental Absorptions of Liquidand Rotator Phases in the Far Infrared. (Evans) . . ... 2051 Determination of the A. Rotational Constant for C3" Molecules.The v4 Raman Band of Methyl Iodide. (Freedman &Jones) . ..... 650 M,J Diffusion and Torsional Oscillation in CHF3'and N20. (Evans) ... 843 Effect of Rotations on Degenerate Vibrations of the Nitrate Ion. (Lockwood) . 1440 Effects of AJ =4 Transitions on the Far Infrared Norrnalised Lineshapes of 02, C02 and (CN), Gases. (Evans) . . . ... 1255 Far Infrared Manifestations of the Intermolecular Dynamics in Compressed Gaseous and Liquid CCIF3. (Davies &Evans) .. 1275 Influence of Solvents on Broad Band Integrated Adsorption Intensity. (Hindle, Walker & Warren) .. . . . . . 756 Infrared Band Shape and Intensity Studies on Molecular Motions and Interactions in Condensed Phases. Part Z.-Effects of Vibrational Relaxation and Collisional Broadening on the Spectra of ICI and IBr in Benzene and Cyclohexane. (Yarwood) 714 Infrared Spectra of Matrix-isolated MgF2.(Hauge, Margrave &Kana'an) ...1082 SUBJECT INDEX-VOLUME 71, 1975 PAGE Infrared Spectra of the Molecular Complexes of p-Benzoquinone with Aromatic Bases : Evidence for Localised Charge Transfer. (Chattopadhyay, Deshmukh &Jose). .1127 Internuclear Distances in Methylmercury Chloride, Bromide and Iodine from Microwave Spectra. (Walls, Lister &Sheridan) . . . . . .. 1091 Interpretation of the Raman Spectra of Aqueous Acid Solutions in Terms of the Polariz- ability of Hydrogen Bonds. Part 1 .-Aqueous HC1 Solutions. (Pernoll, Janoschek, Zundel &Maier) ....... ...201 Investigation of the Inter-molecular Dynamics of Non-dipolar Molecules using the Rota- tional Velocity Correlation Function. (Evans) ....... 71 Microwave Spectra and Structure of the Aniine Group in 3-Aminopyridine and 4-Amino- pyridine. Ab Initio Molecular Orbital Calculations of the Structure of the Arnine Group in the Aminopyridines. (Christen, Norbury, Lister &Palmieri) . 438 Microwave Spectrum, Structure and Dipole Moment of Phenylacetylene. (Cox, Ewart & Stigliani) .......... 504 Raman Difference Spectra of Solutions of Electrolytes in Formamide. (Gardiner, Girling &Hester) .............. 709 Raman Spectra of Asymmetric Top Molecules. Part 1.-The Pure Rotational Spectrum of Ethylene. (Hills &Jones) ...........812 Part 2.-AK =+2 Transitions in the Rotational Spectrum of Butadiene. (Hills & Jones) .. . . ... .. 827 Part 3.-Intensity Beats in the Raman Spectra of Near Prolate Tops. (Hills &Jonesj 835 Relation between 0-H Stretching Frequency and Hydrogen Bond Energy: Re-Examination of the Badger-Bauer Rule. (Rao, Dwivedi, Ratajczak &Orville-Thomas) ..955 Rotational Isomerism and Structure of Penta-l,4-diene: Raman Spectrum and Ab Initio Calculations. (Gallinella &Cadioli) ...... . . 781 Rotational Isomerism in Propargyl Formate as studied by Infrared and Microwave Spectroscopy. (Jones, Lister &Owen). ........ 1330 Rotational Raman Spectrum of Sulphur Dimer. (Freedman, Jones &Rogstad) . . 286 Solvation Spectra. Part 46.-Hydration Numbers for Perchlorate and Fluoroborate Ions.(Symons &Waddington) . . , . ... ... 22 Some Molecular Properties of Thiocarbonyl Chloride Determined by Microwave Spectre-scopy. (Carpenter, Rimmer, Smith &Whiffen) . ...... 1752 Vapour Phase Raman Intensity Studies on the Group IV Tetrachlorides. (Clark & Mitchell) . ...... ....... 515 Vibrational Analysis of Spectra of Quinonoid Molecular Ions. Part 3.-Vibrational Spectra and Assignment of 7,7,8,8-Tetracyanoquinodimethane Radical Anion. (Bozio, Girlando &Pecile) . . ..... 1237 Vibrational Band Contours. Part 1.-The Hexafluorobenzene-Benzene System. (Barrett, Gill &Steele) ............ 532 Part 2.-The Second Moments of the Intensity Distribution in Bands of Symmetric Top Molecules.(Hill &Steele) ......... 555 Vibrational Spectra of Fluoranil. (2,3,5,6-Tetrafluoro-~-Benzoquinone).(Girlando & Pecile) ..... . . . . 689 Vibrational Spectroscopic Studies on Ion-Molecuie Interactidns in Non-aqueous Solvents. Part 1 .--Far Infrared studies on Tetra-n-butylammonium Chloride in Benzene. (Barker &Yarwood) ... . . ... 1322 (6) electronic (visible, absorption and emission) Analysis of the Optical Spectrum of Gaseous Ytterbium Monofluoride. (Barrow & Chojnicki). .... . . . . .728 Application of Classical Oscillator Functions to the Simultaneous Determination of Sub-strate Optical Constants and Film Thickness from Ellipsometric Measurements. (Moskovits &Ostrowski) . . . .. . . .387 Application of the Causality Condition to Thin Film Spectroscopy. A Method for the Evaluation of the Thickness and Optical Constants. (Roth, Kao &Dignam) .. 86 n-n* Circular Dichroism of Mono-olefins. (Scott &Yeh) . . .447 Contribution of Pre-adsorbed Species to the Difference Spectrum of Species Subsequently Adsorbed. (Rao, Stobie &Dignam) . .., 654 Conversion Electron Mossbauer Spectroscopic Study of Iron Containing Surfaces. Monitoring the Early Stages of Oxidation of a Low-carbon Steel by a Non-destructive Procedure. (Thomas, Tricker &Winterbottom) ....... 1708 SUBJECT INDEX-VOLUME 71, 1975 23 PAGE Determination of Transition Moment Directions by Means ofDichroic Spectra in Stretched Polymer Films. Part 1.-Orientation of Solutes.(Bott &Kurucsev) . .. 749 Electron Energy Loss Spectrum of Ethylene. (Dance &Walker) .. 1903 Electronic Absorption and Emission Spectra of 4-Pyrones, 4-Thiopyrones and 4-Pyridones. (Ishibe, Sugimoto &Gallivan) . ...... 1812 Electronic and Vibrational Linear and Circular Dichroism of Nematic and Choiesteric Systems. (Dudley, Mason &Peacock) .... 997 Electro-optic Kerr Effect in n-Alkane Solutions. (Champion, Meeten &Southwell) .225 Jahn-Teller Effect in the rS(’Tzg,ti,) State of ReBri-. (Black &Flint). . 1871 Magneto Optical Rotatory Dispersion Studies of Simple Electrolyte Solutions. Part 3.-Measurements on Solutions of Chlorides and Bromides of Some Group I1 Metals. (Dawber) . ... .... .. 947 Measurement and SCF-CI PPP Calculation of Polarized Absorption and Magnetic Circular Dichroism of Gzuleno[5,6,7-~d]phenalene.(Thulstrup, Michl &Jutz) .. 1618 Optical Absorption Spectra of Matrix Isolated Silver Atoms and their Dependence on Matrix Properties. (Schulze, Kolb &Gerischer) ... 1763 Polarisations of the Lowest-energy Transitions of Pyridine l-Oxide and 4-Methylpyridine l-Oxide. (Peacock &Samori) . . ...... 1909 Reinvestigation of the Absorption and Luminescence Spectra of the Chromium(rr1) com- plexes with Iminodiacetic Acid, Methyliminodiacetic Acid and Pyridine-2,6,-dicar- boxylic Acid. (Flint &Matthews) .. ..... 379 Spectral Analysis of the Light Scattered from a Chemically Relaxing Fluid: A Ternary Mixture. (Carle, Laidlaw &Lekkerkerker) .. ...... 144s Vacuum Ultraviolet Spectra of Formic and Acetic Acids. (Bell, Ng &Walsh) . 393 Vacuum Ultraviolet Spectrum of Carbon Diselenide. (Cradock, Donovan, Duncan & Gillespie) . , . ...... . 156 Vibrational and Electronic Spectra of Hexacyanobenzene and its Electron Donor-Acceptor Complexes. (Sucharda-Sobczyk, Syper &Sobczyk) .. . . 1994 (c) photoelectronConfiguration Interaction Calculations of the Satellite Peaks in the X-Ray Photoelectron (ESCA) Spectra of HzO, N1,CO, C3O2 and Ni(C0)4. (Hillier &Kendrick) . I369 Determination of Atomic Partial Charges using X-Ray Photoelectron Spectroscopy: Application to Crystalline Solids. (Parry) . . .. 337 Determination of Relative Electron Inelastic Mean Free Paths (Escape Depths) and Photo- ionisation Cross-sections by X-Ray Photoelectron Spectroscopy.(Cadman, Evans, Scott &Thomas) .. ..... 1777 Electronic Structure of the Oxides of Lead. Part 1.-A Study using X-Ray and Ultraviolet Photoelectron Spectroscopy of the Oxidation of Polycrystalline Lead. (Evans & .I.Thomas) . .... 313 Part 2.-A.n XPS Study of Bulk Rhornbic PbO, Tetragonal PbO, P-Pb02 and Pb304. (Thomas &Tricker) ... . . . . 3 29 Interpretation of the Valence Photoelectron Spectra of Mn(C0)5H, Mn(CO)5CH3 and Fe(C0)4H2. (Guest, Higginson, Lloyd &Hillier). . .. 902 Low-lying Electronic States of HCN+ and the Interpretation of the Photoelectron Spectrum of HCN. (So &Richards). ..... 62 Oxidation of the Group IB Metals Studies by X-Rag and Ultraviolet Photoelectron Spectro- scopy.(Evans) ..... .... 1044 Photoelectron Spectra of OCSe and SCSe. (Cradock &Duncan) .. 1262 Photoelectron Spectra of Polysilanes. Conformational Analyses of Tetra- and Penta-silane. (Enolin, Bergmann &Elbel) . .... .. 913 Photoelectron (He I) Spectroscopic Study of Styrylpyridines. (Distefano, Mazzucato, Modelli, Pignataro &Orlandi) . ...... I583 Photoelectron Spectrum of Methylenimine by Spectrum Stripping. (Peel &Willett) .1799 Photoelectron Studies of Boron Compounds. Part 5.-Higher Boron Hydrides B4HI0, B5H9 and BI0Hl4. (Lloyd, Lynaugh, Roberts &Guest) . 1382 Photoelectron Studies of Metal Carbonyls. Part 5.-Substituted Group VIIA Carbonyls.(Higginson, Lloyd, Evans &Orchard) .. . . . 1913 Polarised Photofluorescence Excitation Spectroscopy. Part 2.-Vacuum Ultraviolet Photodissociation of HCN and BrCN. (chamberlain &Simons) . 2043 Radiation Damage in Some Platinum(rv) Complexes produced during Soft XIRay Photo: electron Spectroscopic Studies. (Burroughs, Hamnett, McGilp &Orchard) , 177 24 SUBJECT INDEX-VOLUME 71, 1975 PALOB Theoretical Study, Including Correlation Effects, of the Low-energy Photoelectron Spectrum of Ozone. (Hillier &Kendrick) .......... 1906 Unimolecular Decomposition of Acetone Ions and Dimethylmercury Ions Studied by Photoelectron-Photoion Coincidence Spectroscopy. (Cant, Danby &Eland) . . 1015 Vacuum Ultraviolet Photoelectron Spectroscopy of Transient Species.Part 5.-The S2(3Z;;)Molecule, (Dyke, Golob, Jonathan &Morris) ..... 1026 (d)electron spin resonance Electron Exchange and Electron Spin Dipole-Dipole Interactions in 7,7,8,8-Tetracyano- quinodimethane Anion Sandwiches. (Shields) .. . .... 3 72 Electron Paramagnetic Resonance Studies of COz Radicals Adsorbed on MgO. Identifica- tion and Structure of the Species using 13C and 170 Labelling. (Meriaudeau, Vedrine, Taarit &Naccache) .... .. .. 736 Electron Paramagnetic Resonance Study of Manganese@) in Near Tetrahedral Dihalo- genobis(tripheny1phosphine0xide)zinc. (Vivien &Gibson) ... 1640 Electron Spin Resonance Spectra and Orientation of 3,4-Bis(dicyanomethylene)cyclobutane~ 1 ,2-dione and Tetracyanoquinodimethane Radical Anions in Liquid Crystals.(Corvaja, Farnia &Lunelli).. . . .... .. 1293 Electron Spin Resonance Study of o-Benzosemiquinone Alkali Metal Ion Pairs. (Brustolon,Pasimeni &Corvaja) . ...... . . 193 Electron Spin Resonance Study of y-Irradiated Single Crystals of Fluorene. (Barigelletti, Orlandi, Giro &Poggi) . . . . .. .. 1436 Electron Spin Resonance Study of the Freezing Properties of Water Adsorbed on y-Alumina. (Burlamacchi) ......... .... 54 Electron Spin Resonance Study of the Reactions of Hydrogen Atoms with Carboxylic Acids and Amides in Sulphuric Acid Glasses. (Dainton, Falle &Salmon) .. . 644 Simulated Electron Spin Resonance Spectra of Nitroxide Spin Labels in Slowly Reorienting Rod Shaped Molecules.(Benton &Lynden-Bell) ..... 807 Temperature-dependent Hyperfine Coupling Constants in Electron Spin Resonance. Part 3.-Amino Group Rotation in the Cation of p-Phenylenediamine. (Bullock & Howard) . . . . . ......... 1008 Unstable Intermediates. Part 138.-The Formation of P-Bromoalkyl Radicals by the Action of y-rays on Various Organic Bromides: Electron Spin Resonance Spectra at Low Temperatures. (Lyons, Neilson, Mishra &Symons) . ... 363 (e)nuclear magnetic resonance, quadrupole resonance Comment on the Paper "Electron-coupled 'Through-space 'Nuclear Spin-Spin Inter- action "by A. D. Buckingham and J. E. Cordle. (Hilton &Sutcliffe) .. 1395 Deuteron Magnetic Resonance Studies. Part 6.-Lithium Deuteroxide Deuterate.(Clifford, Smith &Temme). . .... ... 1352 Deuteron Magnetic Resonance Studies. Part 7.-Potassium [zH2] Sulphamate. (Royston &Smith) . ...... .... 1497 Effect of Vibrational Averaging on the Quadrupole Coupling Constant of Deuterium in 4-[2Hl]pyridine determined from 'H-['H] INDOR n.m.r. of a Partially Oriented Sample. (Emsley, Lindon &Tabony) ....... .. 579 Electron-coupled Through-space or Fragment Spin-Spin Coupling Between 9F Nuclei. (Schaefer, Niemczura &Marat) .......... 1526 Hindered Internal Rotation and the Nuclear Magnetic Resonance Parameters in 1,2- Dibromo-l ,1,2-trifluoroethane. (Ng) ........ 1839 Interaction of Lithium Salts with Amides. Part 2.-Carbon-1 3 Chemical Shifts. (Adams,Baddiel, Ellis, Jones &Matheson) ....... 1823 Nematic Phase Nuclear Magnetic Resonance Studies of Some Disubstituted Pyridines. Molecular Geometry of 2,6-Difluoropyridine. (Orrell &Sik) . . . . 1360 Nuclear Magnetic Resonance Studies of the Difluoride Ion. Part 1 .-Single Crystal Study of Potassium Difluoride. (Pratt &Smith) ...... . . 596 Nuclear Magnetic Resonance Study of Hindered Rotations of the n-Bonded Ring in Crystalline Benzenetricarbonylchromium. (Delise, Allegra, Mognaschi &Chierico) .207 Nuclear Magnetic Resonance Study of the Conformations of Penicillins in Solution using Lanthamide Ion Probes. (Dobson, Ford, Summers &Williams) ....1145 Nuclear Magnetic Resonance Study of the Hydrogen Bonding of Chloroform with Aliphatic Tertiary Amines and Ethers.(Wong &Ng). . .. 622 SUBJECT INDEX-VOLUME 71,1975 25 PAGE Nuclear Quadrupole Resonance and Stereochemistry. Part 4.-Chlorocyclopropanes. (Delay, Geoffroy, Lucken &Muller) . . . . .....463 Nuclear Quadrupole Resonance in the Chloranil-Hexamethylbenzene Complex at High Pressure. (Jugie &Smith) . . .... .. 608 Organosilicon-Organotin Indenyl derivative^.^ A Nuclear Magnetic Resonance Study of their Fluxional Characteristics. (Orrell, Sik, Dunster &Abel) . . .. 631 Proton, Carbon-13 and Proton-(deuterium) INDOR n.m.r. Spectra of Isotopically labelled Acetaldehyde Dissolved in a Nematic Phase. (Emsley, Lindon &Tabony) ..586 Quantitative Chemically Induced Dynamic Nuclear Polarization (CIDNP) Study of the Photolysis of Benzaldehyde in Solution.(Frith &McLauchlan) . . ..1984 Solvation Spectra. Part 47.-Absolute Proton Magnetic Resonance Shifts induced by Cations and Anions in Ethanols Glycol and Ammonia. (Symons &Davies) ..1037 cf) neutron scattering Librational Motion in Potassium Aluminium Hydride, studied by Inelastic Neutron Scattering. (Tomkinson &Waddington) ....... 2065 (g)ion cyclotron resonance, mass spectrometry etc. Electron Attachment to Sulphur Dioxide in High Pressure Gases. (Rademacher, Christo- phorou &Blaunstein). .. .. 1212 Electron Microscopic Studies of Extended Defects inOrganic Molecular Crystals. Part 1.i p-Terphenyl. (Jones, Thomas, Williams &Hobbs) .. 138 Long-lived Parent Negative Ions formed via Nuclear-excited Feshbach Resonances.' Par; 4.4ystematic Study of NO,-containing Benzene Derivatives.(Johnson, McCorkle, Christophorou &Carter) . .. ... 1742 Structure and Inversion Potential of Thianthren. '(Galiagher &Bauer) .... 1173 Structure of Diacetamide. Reference Amido Structures for Polypeptide Conformation Analysis. (Gallaher &Bauer) . ... . .... 1423 II,6 Statistical Mechanics A Note on the Forms for the Integrals of the Percus-Yevick Expression for g(R) for Hard Spheres. (Gibbons) ... . .. . . ... 346 Barker-Henderson Theory as an Accurate Theory of Simple Mixtures. (Gibbons) ..1929 Conformation of a Non-interacting Polymer near a "Sticky "Wall. (Chan, Mitchell, Ninham &White) . . . .. .. 235 a-Deuterium Isotope Effects on ;he Ionization of Weak Acids.(Bron) : . .1772 Double-layer Interaction of Two Charge Colloidal Spherical Particles of a Concentrated Dispersion in a Medium of Low Dielectric Constant. Part 2.-A Cell Model. (Feat &Levine). .. .. . . .. * . 102 Electrical Forces between Particles with Discrete Periodic Surface Charge Distributions in Ionic Solution. (Richmond) . . .. .. ... 1154 Electrostatic Potential Outside the (111) Face of Fluorite. (Marcovitch &Kozirovski) .1302 Equilibrium Conformation and Surface Motion of Hydrocarbon Molecules Physisorbed on Graphite. (Battezzati, Pisani &Ricca) . .. . . . ..1629 Equilibrium Partition Coefficient of Macromolecules between Random Porous Network and Bulk Liquid. (Doi) .. ... . .1720 Excess Properties of Some Simple Mixtures Calculated From the Barker-Henderson Theory with Second Order Terms. (Gibbons). . ... .. 353 Initial Rate Constants for Coagulation in the Presence of Energy Minima of Restricted Depth. (Richmond &Smith) . ... .. 468 Interaction of Charged Plates which Approach at Adsorption Equilibrium of all Specifically Adsorbed Species. (Hall) . .. .. 937 Pair Potential for Alkali Metal Halides with Rock Salt Crystal Structure. Moiecula; Dynamics Calculations on NaCl and LiI. (Michielsen, Woerlee, Graaf &Ketelaar) .1730 Screening Regimes for the Viscosity of Concentrated Polymer Solutions. (Freed & Edwards) . . .. ..... .. 2025 Stability of Microemulsions. (Ruckenstein &Chi) .. 1 690 Statistical Mechanics and Lifshitz Theory for Electrolytes.Part 1.(Barnes &Davies) .1667 Theoretical Optical Rotation of Oriented Hexahelicene. (Barron) . . 293 Theory of Dispersion Interactions Between Macroscopic Bodies. (Mahanty &Ninham) .119 Theory of Electrokinetic Flow in a Narrow Parallel-plate Channel. (Levine, Marriott & Robinson). .. ...... .. 1 26 SUBJECT INDEX-VOLUME 71, 1975 PAGE Theory of the Rate of Wetting of a Porous Medium. (Levine &Neale). ... Thermodynamic and Structural Properties of Liquid Ionic Salts obtained by Monte Carlo Computation. Part 2.-Eight Alkali Metal Halides. (Lewis, Singer &Woodcock) . Thermodynamic Properties and Self-diffusion of Molten Sodium Chloride. A Molecular 12 301 Dynamics Study.(Lewis &Singer) ........ .41 11, 7Themodynamics (reversible and irreversible) Infrared Studies and Thermodynamics of Hydrogen Bonding in Ethylene Glycol Monoalkyl Ethers. Evidence for a Ten Membered Ring Dimer. (Prabhumirashi &Jose). .1545 Investigations on Molecular Complexes. Part 7.-Thermodynamic, Spectroscopic and Dielectric Properties of Iodine Complexes with Triphenylphosphine Oxide, Sulphide and Selenide. (Lux, Paetzold, Dane1 &Sobczyk) . ......1610 Potential Energy Calculations of the Rotational Barriers in Molecular Solids. Part 3.-Cage-like Aliphatic Molecules. (Fyfe &Harold-Smith) . .....967 Residual Functions of the n-Alkane Liquids. Part 1 .-Corresponding States and Con- gruence. (Cruickshank, Drew &Mercer) .. .... .870 Thermodynamic Effects of Orientation Order in Chain-molecule Mixtures. Part 3.-Heats of Mixing of Dimethylsiloxanes with Normal and Branched Alkanes. (Tancrede, Patterson &Lam) . ..... . . .. . .985 11, 8 Transport Phenomena (see also I, 6) Effect of the Rare Earth Ion on the Spin State Equilibria in Perovskite Rare Earth Metal Cobaltates. Yttrium Trioxocobaltate(II1) and Erbium Trioxocobaltate(m). (Jadhao, Singru, Rao, Bahadur &Rao) . ... .. 1885 Electron Tunnelling in Glassy Media. y-Radiolysis Investigation’of Ekctron Scavenging in Methanol, 2-Methyltetrahydrofuran and 10 mol dm-3 Hydroxide Glasses at 77 K. (Marshall, Pilling &Rice) . .. 1555 Formation of Electric Triple Layers by Interdiffusion of Two Electrolytes.(Smensen & Jensen) . . . . ... 1805 Ionization, Ion Recombination, and the Transport of Steady State Electric Current in Low Dielectric Constant Fluids. (Gavis) . . .. .... 1115 Mossbauer and Infrared Studies of the Diffusion and Reactivity of (SnO),. Species (n >1) Initially Isolated in Solid Nitrogen. (Bos &Howe) .... 28 Organic Semiconductors. Part 18.-Electrical and Magnetic Properties of (NN-Dimethyl-4,4’-bipyridyli~m)~+(7,7,8,8-Tetracyanoquinodimethane)~-.(Ashwell, Eley, Willis & Woodward) . .. .. .... 1785 Semiconductivity in Organic Substances. Part 16.-Ionic Impurity Scattering Centres in 4,4’-Bipyridyl-(Tetra~yanoquinodimethane)~.(Ashwell, Eley &Willis) . . 1227 Theoretical Model for Diffusion Controlled Reactions of Solvated Electrons, incorporating a Tunnelling Mechanism.(Pilling &Rice) , . . . ... 1563 Theoretical Model of Electron Scavenging in Irradiated Glassy Media based on a Tunnelling Mechanism. (Dainton, Pilling &Rice) ........1311 AUTHOR INDEX-VOLUME71, 1975 PAGE PAGE Abel, Edward M7.. . 631 Carlin, Sheena E. .1894 Adams, Michael J. . ., 1823 Carpenter, John H. . .1752 Allegra, Giuseppe. . . .207 Carr. Robert W. . .1603 Angel, Robert Lindsay . ..81 Carter, J. G. . .1742 Ashpole, C. W. . . ..615 Catlow, C. R. A. . . .275 Ashwell, Geoffrey J. . .1227, 1785 Cavell, Edmund A. S. . .474 Atkins, P. W. .. .1269 Chamberlain, Geoffrey A. .402,2043 Champion, J. V. .. .225 Badiel, Colin B. . . .1823 Chan, Derek ...235 Bahadur, D. . . .1885 Chattopadhyay, Jyoti B. .1127 Baraldi, Ivan .. 215, 791 Chi, J. C. . .. . .1690 Barigelletti, Francesco . .1436 Chierico, Angelo .. .207 Barker, Colin .. .1322 Chojnicki, A. H. . . .728 Barnes, C. J. . . .1667 Christen, Dines . ..438 Barrett, R. M. .. .532 Christophorou, L. G. . .1212, 1742 Barron, Laurence D. . .293 Clark, David T. . . ..1942 Barrow, Richard F. . .728 Clark, Robin J. H. . .515 Battiezzati, L. . . . 1629 Clifford, John 0.. .1352 Bauer, S. H. . . 1173, 1423 Clyne, Michael A. A. . .1132 Beddard, Godfrey S. . .1894 Colonna, Francesco Paolo .1572 Bell, Stephen .. .393 Corradini, Giordano R. . .215 Bemand, Peter P. .1132 Corvaja, Carlo .. .193, 1293 Benton, J. E. . . 807, 1863 Cox, A.Peter . . .504 Bergmann, Helge . . .913 Cradock, Stephen. . .156, 1262 Black, Aline M. . . .1871 Craig, D. P. . .1457 Blaunstein, R. P. , .1212 Cremaschi, Pietro. . .1829 Blustin, Peter H. . 1058, 1071 Cruickshank, A. J. Bruce . .870 Borrell, Patricia M. . .571 Czapla, Z. . .763, 767 Borrell, Peter . .571 Bortolus, P.. . . .1338 Dainton, Frederick S. . .634, 1311 Bos, Antoon . .28 Danby, C. J. . . .1015 Bott, Clifton C. . . .749 Dance, Donald F.. . .1903 Bozio, Renato . . .1237 Danel, Julitta . ..1610 Bradley, P. A. .. .1200 Davies, B. . ..1667 Brillante, Aldo . . . 1457 Davies, Graham J. . .1275 Brocklehurst, Brian . .543 Davies, John . . .1037 Bron, Jan. . . . .1772 Davies, Manse1 . . . . 269 Brown,Adam , ..699 Dawber, John G. . .947 Brown, B. L. . .1657 Dean, Christopher R. S. . .146 Brown, Bernard L. . .1877 Degorski, A. . .1503, 1513 Brown, Raymond D. H. .1963 Delay, F. . .. . .463 Brown, Robert G.. . .409 Delise, Paolo . .207 Bruni, Maria C. . . .215 Dellonte, S.. .. .1338 Brustolon, Marina . .193 Deshmukh,M.N. . .1127 Buckingham, A. D. . .95 Diard, J. P.. . . . .1935 Bull, David C. . . .543 Dignam, M. J. . . 86, 654 Bullock, Anthony, T. . .1008 Distefane, Giuseppe . .1572, 1583 Burlamacchi, Leo . .54 Dixon, Maurice . . . .452 Burroughs, Peter . . .177 Dixon, R. N. . ., 799 Dobbs, A. J. .. .1269 Cadioli, Beniamino . .781 Dobson, Christopher M. .1145 Cadman,Phillip . . . 1577 Doggett, Graham. . .452 Callear, Anthony B.. .1603 Doi, Masao . . .1720 Cant, C. S. T. . . .1015 Donini, J. C. . . .1411 Carle, D. L. . . . 1448 Donovan, R. J. . .156 27 AUTHOR INDEX-VOLUME 71. 1975 Drew. Philip B ... Dubois. I.... Dudley. Richard J.. Duke. Brian J... Dunbar. John H ... Duncan. William . . Dunster. Maurice 0.. Duxbury. Geoffrey . Dwivedi.P .C... Dyke. J.M. . Edwards. S.F... Eilers. James E... Eland. J.H.D... Elbel. Susanne . . Eley. DanielD ... Ellis. GeraldE ... Emsley. James W.. EnBlin. Walther . . Ewart. Ian C... Evans. Margaret . . Evans. Myron 71. 843. 1255.1275. 1854. 2051 Evans. Stephen . 320.1044.1777. 1913 PAQE . .870 . .799 . . 997 . . 1401 . .1478 .156. 1262 . .631 ..799 . .955 . .1026 ..2025 . .1401 . .1015 . .913 .1227. 1785 . .1823 . . 586 . . 913 . .504 . .543 PAGE Graff.F .V.D... . . . 1730 Gray. Brian F.. . . . 2016 Guest. Martyn F. . .902. 1382. 1577 Gutteridge. Ronald ....571 Hall. Denver G... ...937 Hamnett. Andrew . . . . . 177 Handy.N .C... . . . 95 Ham. Koyoaki . . ...1100 Harker. A.H... ...275 Haro1d.Smith. Duane . ...967 Hauge. Robert H.. . . . 1082 Hayes. John William . . . . 81 Hayns. M .R... ...275 Henson. Robert M.C.. ...669 Hester. R .E... ...709 Higginson. Brian R .. . .902. 1913 Hill. Ian R . . . ...555 Hillier. Ian H...496. 1369. 1654. 1906 Hills. G .W... 812. 827. 835 Hilton. J.... .1395 Hindle. P.... .756 Hiroaki. Baba .. .1100 Hobbs. Linn W ... .138 Hollebone. Bryan R .. .1411 Holt. SmithL ... .2002 Honeybourne. Colin L.. 1343. 2072 Hopmann. Rudolph F.W . .1844 Horiguchi. Hiroyuki . .1164 Howard. Christopher B. .1008 Howat. George . . .452 Howe.ArthurT ... .28 Husain. David . . 525. 699 Ishibe. Nobuyuki . . .1812 Jadha0.V .G... .1885 Janoschek. R ... .201 Jasinski. Jerry P... .2002 Jenkins. H.Donald B .. .1942 Jennings. B .R ... .1948 Jensen. Klavs Flemming .1805 Johnson. J.P.. .1742 Jonathan. Neville . .1026 Jones. Geraint I.L. .1330 Jones. G .P.. .1657. 1877 Jones. Raymond G . . . 1823 Jones. William . . .138 Jones. W .Jeremy .286. 650.812. 827. 835 Jose. C.I... ...1127. 1545 Jugie. G .......608 Jutz.Christian . ....1618 Kahn. Olivier . ...862 Kana’an. Adli S.. ...1082 Kendrick. John . .1369. 1654. 1906 Ketelaar. J.A.A. ...1730 Kim. Min Gon . . .415. 426 Kolb. Dieter M .. . . . 1763 Kolodziej. H.A.. 269.763.767. 1200 Kozirovski.Y .. ...1302 Falle. Howard R .. Farnia. Giuseppe . Feat. Gerald R .. Figeys. Hubert P.. Findlay. Robert H . Fleming. Graham R . Flint. Colin D .. Ford Leonard 0.. Formosinho. S.J.. Freed. Karl F.. Freedman. Philip A. Frith.P .G... Fussenegger. Reinold Fyfe. Colin . . Galabov. B ... Gallagher. K.L.. Gallinella. Enzo . Gallivan. James B. Gamba. Aldo . Gardiner. D.J.. Gavis. Jerome . Ceerlings. Paul . Geoffroy. M.. George. Thomas F. Gerischer. Heinz . Gibson.John F.. Gibbons. R .M.. Gijzeman. Onno L .J. Gill. E .B... Gillespie. H .M.. Girlando. Alberto Girling. R .B.. Giro. G ... Glass. Graham P.. Golob. L... Gonda.1 ... . . 644 ..1293 . . 102 . .1375 . . 1397 . .773 .379. 1871 . . 1145 . .615 . .2025 .286. 650 . . 1984 . .1958 . . 967 . .162 .1173. 1423 . . 781 . .1812 . . 1829 . . 709 . .1115 . . 1375 ..463 ..2030 ..1763 . .1640 301. 353. 1929 . .773 . .532 . .156 .689. 1237 . . 709 . .1436 . . 1963 . . 1026 ..2016 AUTHOR INDEX-VOLUME 71. 1975 29 PAGE PAGE Krisirana. B ......168 Naccache. Claude ..... 736 Krishna. B......168. 172 Napier. G.D.R......1487 Kryszewski.M.....1503. 1 51 3 Neale. Graham H.....12 Kurucsev. Tomas . . . . . 749 Neilson. George W.....363 Neilson. J.D......1487 Laidlaw. W.G.... . . 1448 Ng. Soon . . . . . 622. 1839 Lam.Fin h.Te . . . . . 985 Ng. T.L.......393 Lekkerkerker. H.N.W.. . . 1448 Niemczura. Walter ....1526 Levine. Samuel . ...1.12. 102 Ninham. Barry W....119. 235 Levy. Martin R ... ...561 Norbury. David .....438 Lewis. Colin . ....1894 North. Alistair M.. 1233. 1473. 1478 Lewis. John W .E.. . . 41. 308 Lindon. John C ... . . .579 O’Leary. Brian . . . . . 1401 .... .1829Linnett. John W ...1058. 1071. 1590. 1595 Oliva. Cesare Lister. David G... .438. 1091. 1330 Orchard. Anthony F....177. 1913 Lloyd. D .Robert . .496. 902. 1382. 1913 Orlandi. Giorgio .. . . 1436. 1583 ...1440 Orrell. Keith G.....631. 1360 Lockwood. David J.. ...463 Orville-Thomas. W.J.....162Lucken. E .A.C... Lunelli. Bruno . ....1293 Ostrowski. Peter J.. . . . 387 Lux. Friedrich . . . . . 1610 Owen. Noel L ......1330 Lynaugh. Norman . . ...1382 Paetzold. Roland . . . . . 1610Lynden.Bel1. R.M.. ...807 Pakiari. Ali H......1590Lyons. Arthur R ......363 Palmieri. Paolo .....438 Parry. David E......344Mhdan. hi.P......67 Pany Jones. G .....269. 1200 Mhhanty. Jagadishwar ....119 Pasimeni. Luigi . . . . . 193M[aier. U.......201 Patterson. Donald M[alcolme-Lawes. David J....1183 . . . . 985 Peacock. Robert D....997. 1909 M[arat. Kirk .....1526 Pecile. Cesare . . . .689. 1237 Mhrcovitch. 0......1302 Peel.J.Barrie .. . . . 1799M[argrave. J.L......1082 Pernoll. I... . . . . 201M[arriott. JohnR . . . . . 1 Pethrick. Richard A....1473. 1478 M[arshall. E.J......1555 Phillips. David . . . . . 409M[ason. StephenF .....997 Pickering. Michael . . . . 1401M[atheson. Andrew J.....1823 Pignataro. Salvatore . . . 1572. 1583 M[athews.AnthonyP.....379 Pilling. M.J....1311. 1555. 1563 M[azzucato. Ugo . . . . . 1583 Pisani. C.......1629M[eeten. G .H......225 Pitacco. Giuliana . . . . . 1572M[ercer. R .Neil . . . . . 870 Poggi. G.......1436M[eriaudeau. Paul ..... 736 Prabhumirashi. L .S.....1545M[etcalfe. John . . . . . 409 Pratt. John C..... .596M[ichielsen. J......1730 Price. Alun H... .1854Miichl. Josef . .. . . 1618 MLiller. L .J......1233 Rademacher. J......1212 Miishra. ShuddhodanP .....363 Radford. Donald Vincent . . . 81 Ikl[itchell. D .John . . . . . 235 Rao. Bhimasena . . . . 86. 654 M[itchell. Peter D. . . . . 515 Rao. C .N.R.....955. 1885 M[cCorkle. D .L......1742 Rao,G.Rama .. . . .1885 M[cGilp. John F......177 Ravaine. D .......1935 MIcLauchlan. K.A....1269. 1984 Ricca. F.. . . . . .1629 M‘odelli. Albert0 . . . . .1583 Rice. Stephen A....1311. 1555. 1563 Mognaschi.EzioR .....207 Richards. W.Graham . . . 62. 660 Momicchioli. Fabio . . 215. 791 Richmond. Peter . . . . 468. 1154 Morosi. Gabriele . . . . .1829 Rimmer.DavidF . . . .1752 Morris. A.......1026 Roberts. Peter J.....496. 1382 Morris. V.J...... 1948 Robinson.Kenneth . . . .1 Moskovits. Martin . . . .387 Rode. Bernd M.....481. 1958 Moutran. Rafik . . . . .1854 Rogstad. Astri. . . . . . 286 Murrell. JohnN .....890. 1577 Roth. John . . . . . . 89 Muszkat. K.A......1529 Royston. J.......1497 Muller. P.......463 Ruckenstein. Eli . . . .1690 30 AUTHOR INDEX-VOLUME 71.1975 PAGE PAGE Salmon. G .Arthur . . . 644 Teixeira.Dias. J.J.C.....906 Samori. Bruno . . . 1909 Temme. Francis P.... .1352 Sarre. P.J.... . .906 Thomas. John M .. 138.320. 336. 1708. 1777 Schaefer. Ted ... . . .1526 Thomas. R .G.0. . .664 Schulze. Wilfried . . . . . 1763 Thomson. Colin . . .1942 Scott. A .I.. . . . 447 Thrush. B .A. . . . .664 Scott. JohnD ... . . . 1777 Thulstrup. Erik W.. . .1618 Seger. G ... . . 1529 Tomkinson. John . . . . 2065 Semkow. Andrew M .. . . . 1595 Towland. Matthew . . . 1473 Sharafi.Ozeri. S.. . . . 1529 Tricker. Michael J.. .336. 1708 Sharma. S.C... . . 168. 172 Tsuchiya. Soji . . . .1164 Sheikh. M .Azam . . . . . 474 Shepherd. T .Maurice . . .146. 1487 Valentin. Ennio . . . .1572 Sheilds. Leonard . . . 372. 1792 Van Alsenoy. Christian . .1375 Sik. Vladimir . . . .632. 1360 Vedrine. Jacques C.. . .736 Simonetta. Massimo . . . . 1829 Vidal. Bernard . . . . 1577 Simons. John P.... 402. 561. 2013 Vincent. Ian G .. . .890 Singer. Konrad . . . . 41. 308 Vivien. Daniel . . .1640 Singru. R.M... . . . 1885 Smith. Alec L... . . .468 Waddington. David . . .22 Smith. Ian W.M. . . .1963. 1970 Waddington. Thomas C ..1942. 2065 Smith. John A .S. .596. 608. 1352. 1497 Walker. Isobel C... . .1903 Smith. JohnG ... . .1752 Walker. S.... . .756 Snook.IanK ... . . . 852 Walls. Colin . . .1091 so. s.P.... . . 62. 660 Walsh. Brian C... . 921. 926 Sobczyk. Lucian . . 763.767. 1610. 1994 Walsh. A.D... . .393 Sjrensen. Torben Smith . . 1805 Warren. J.... . .756 Sorriso. Salvatore . . . .682 West. M.A. . . .615 Souquet. J.L... . .1935 Whiffen. David H.. .1752 Southwell. G .W... . .225 White. Lee R.. . .235 Spurling. Thomas H.. . .852 Whitehead. R.J.. .95 Srivastava. A.K... . 168. 172 Willett. Gary D ... . .1799 Steele. Derek . . . 532. 555 Williams. John 0.. . .138 Steiner. Erick . . . 921. 926 Williams. Robert J.P.. . .1145 Steinhauer. Daniel B ... . 1478 Willis. Martin R... .1227. 1785 Stigliani. William M .. . .504 Winterbottom. Ann P.. . .1708 Stobie. R.A.. . .654 Woerlee. P.... .1730 Sucharda.Sobczyk. Anna . . 1994 Wong. KimF .. . .622 Sugimoto. Hirohiko . . .1812 Woodcock. Leslie V .. . .308 Summers. S.Elizabeth . . .1145 Woodward. John . . .1785 Sutcliffe. L .H... . * 1395 Wyatt. Peter A .H.. . .669 suzuki.s.... . .162 Symons. Martyn C.R.. 22.363. 1037 Yarwood. Jack . . .714. 1311 Syper. Ludwik . . . .1994 Yeh. C.-Y. . . . . .447 Young.AlanN ... ..525 Taarit. Younes Ben . . .736 Tabony. James . . . .586 Zimmerman. I.Harold . . . 2030 Tancrede. Pierre . . 985 Zundel. Georg . . . .201 THE FOURTH ANNUAL GENERAL MEETING OF THE FARADAY DIVISION of the Chemical Society was held at 9.00 a.m., on 9th September, 1975, in the Main Lecture Theatre, The Pathfoot Building, University of Stirling, with Professor F.C. Tompkins, D.Sc., C.Chem., F.R.I.C., F.R.S., in the Chair. 1 Minutes The Minutes of the Third Annual General Meeting of the Faraday Division, which had been circulated previously, were taken as read and confirmed. 2 Annual Report In 1974 the Faraday Division was again very active in its role of representing physical chemistry and chemical physics interests within the Chemical Society. Two General Discussions and one Symposium were successfully held during the year, the proceedings of these meetings being published by the Chemical Society. The well-attended Discussion No. 57 ‘Gels and Gelling Processes’ was successfully moved at very short notice to the University of East Anglia because of student unrest at Essex.Discussion No. 58 ‘Photo Effects in Adsorbed Species’, held at Cambridge, formed the first of a series of meetings arranged jointly, by the Faraday Division, the Deutsche Bunsen Gesellschaft and the SociCtC de Chimie Physique and was well supported by members of all three societies. Symposium No. 9 ‘Physical Chemistry of Oscillatory Phenomena’ held at the Royal Institution, London also attracted a large audience with a high proportion of overseas participants. The Division took part in the Annual Congress at Imperial College, London, where an informal symposium on ‘Mechanisms of Elementary Reaction Processes of Biological Significance’ was arranged, and in the Autumn Meeting at Leicester where an informal discussion on ‘Molecular Complexes’ was held.Also at the Autumn Meeting, the Gas Kinetics Group discussed ‘Molecular Elimination and Addition Reactions in the Gas Phase’, incorporating the Meldola Medal Lecture, ‘Semi-Classical Theory of Molecular Collisions~ given by Dr. J. N. L. Connor. In January, 1974 the Society for Electrochemistry became the Electrochemistry Group and was affiliated to the Faraday Division, becoming the eighth subject group of the Division. Each of these groups organised specialist meetings during the year and made a valuable contribution to Divisional activities. The 1974 Bourke Lecturer, Professor J. Jortner (Tel-Aviv University), lectured on ‘Molecular Radiationless Transitions’ at the Universities of Sussex, Cambridge and Oxford.The Centenary Lecture, given by Professor H. Fischer (University of Zurich) on ‘Magnetic Resonance in Chemistry’, was allocated to the Faraday Division and was delivered during a half-day symposium in London. The Marlow Medal for 1974 was awarded to Dr. Roger Grice of Cambridge University for notable contributions to the field of molecular-beam kinetics with particular reference to alkali-atom diniers and methyl radicals. 3 Elections to Council The Chairman announced that the postal ballot for Ordinary Member ef Council, conducted among members of the Division, had resulted in the following two persons being elected: Dr. W. J. Dunning and Dr.B. A. Thrush. The members of Council of the Faraday Division of the Chemical Society to take office from 7th April, 1976 were as follows: President PROF. D. H. EVERETT,M.B.E., M.A., D.Sc., C.Chem., F.R.I.C. Vice-presidentswho have heid ofice as President PORTER,PROF. C. E. H. BAWN,C.B.E., Ph.D., F.R.S. PROF. SIR GEORGE M.A., Sc.D., PROF. G. GEE, C.B.E.,Sc.D., C.Chem.,F.R.I.C., C.Chem., F.R.I.C., F.R.S. F.R.S. PROF.T. M. SUGDEN,M.A., Sc.D., C.Chem., PROF. J. W. LINNETT,M.A., D.Phil., C.Chem., F.R.I.C., F.R.S. F.R.I.C., F.R.S. 31 ANNUAL GENERAL MEETING Vice-presidents B.A., D.Phil., C.Chem., PROF.P. GRAY, M.A., Sc.D., C.Chem., F.R.I.C. DR. H. A. SKINNER, PROF. M. MAGAT, D.Sc., D.Phi1. F.R.I.C. PROF. W. C. PRICE, Sc.D., F.Inst.P., F.R.S. PROF.F. C. TOMPKINS,D.Sc., C.Chem., PROF.J. S. ROWLINSON,M.A., D.Phi1. ,C.Cheni., F.R.I.C., F.R.S. F.R.I.C., F.R.S. PROF. D. H. WHIFFEN,M.A., D.Phil., D.Sc., C.Chem., F.R.T.C., F.R.S. Ordinary Members M.A., Ph.D., PROF.N. B. H. JONATHAN,PROF.A. D. BUCKINGHAM, Ph.D. C.Chem., F.R.I.C., F.R.A.C.I., F.R.S. PROF.I. M. MILLS, D.Phi1. PROF. MANSEL Sc.D.,C.Chem.,F.R.I.C. PROF.A. M. NORTH, D.Sc. ,F.R.S.E. ,C.Cliem.,DAVIES, DR.W. J. DUNNING, M.B.E., Ph.D., CChem., F.R.I.C. F.R.I.C. DR. R. PARSONS,D.Sc., C.Chein., F.R.I.C. D.Sc.DR. D. N. HAGUE,M.A., Ph.D., C.Chem., DR. B. A. PETHICA, F.R.I.C. DR. B. A. THRUSH, M.A., Sc.D. Honorary Treasurer PROF. P. GRAY, M.A., Sc.D., C.Chem., F.R.T.C. Honorary Secretary PROF.F. C. TOMPKINS,D.Sc., C.Chem., F.R.I.C., F.R.S. The Chairman thanked Sir Frederick Dainton, Professor J. N. Murrell and Professor Dr. J. Lyklema, the retiring members of Council, for their services. Allocation of Funds for the Organisation of Conferences A resolution proposed by Professor E. F. Caldin ‘That Council be requested to seek an increase in the allocation of funds to the Faraday Division for the organising of conferences’ was passed unanimously. It was argued that three profitable publications each year result directly from Faraday Division meetings and that account should be taken of this when funds were allocated to the Division. Rising travel costs and a diminution of travel funds in overseas institutions, in particular the NSF, made it difficult to retain the international character of Faraday Discussions and Sympoxia essential to the success of the meetings and subsequent publications, without more travel funds for overseas contributors.

ISSN:0300-9238    

DOI:10.1039/F297571BA001

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Theory of the Rate of Wetting of a Porous Medium? BY SAMUELLEVINE” Department of Mathematics, University of Manchester, M anchester M 13 9PL, England AND GRAHAMH. NEALE~ Department of Chemical Engineering, University of British Columbia, Vancouver, Canada Received 24th April, 1974 The classic equations of Washburn and Rideal for the rate of penetration of a fluid into a capillary due to surface tension are re-examined and time-dependent solutions are obtained for large times in both horizontal and vertical flow. By applying Darcy’s law, a general theory of wetting of a porous medium is derived. The rate of fluid penetration is expressed in a form analogous to that for a capillary, in terms of fluid viscosity, surface tension, porosity and permeability. The permeability is calculated for the Happel-Kuwabara cell model of a porous medium, consisting of a swarm of identical spherical particles. 1.INTRODUCTION In deriving Washburn’s equation 1* for the rate of penetration of a fluid into a porous medium (such as a powder) due to capillary suction or imbibition, the model for the porous medium is usually an assemblage of parallel cylindrical capillaries. However the problem in using the simple Washburn equation with powder beds is finding a suitable value for the radius of the hypothetical capillaries and it seems more realistic to choose a swarm of spherical particles as the model of such media. Byapplying Darcy’s law,3 we shall obtain the equation of motion for the penetration of a fluid into a porous medium in a form corresponding to the equation for penetration into a cylindrical capillary.The rate of wetting the porous medium in horizontal llow is thereby expressed in terms of fluid viscosity, adhesion tension between solid and fluid phases, porosity and permeability. Values for the permeability require some model of the porous medium, which we imagine to consist of uniformly distri- buted monodisperse, spherical, solid particles. In practice the packing would be random so that the volume fraction of particles is less than the theoretical maximum (0.74). The problem of slow viscous flow under an external pressure relative to a swarm of spherical particles has been considered by a number of authors using cell- model^,^ and we shall apply here the ‘‘ free-surface ” cell model of Happel 4* and the ‘‘ zero-vorticity ” cell model of Kuwabara in a theory of wetting of a dry powder of monodisperse spheres.These models yield the permeability of the powder and there- fore the rate of fluid penetration in terms of particle radius and porosity. Both horizontal flow and vertical flow under gravity are considered but the more complex problem of the initial stages of penetration are not examined. -f presented at the 48th National Colloid Symposium of the American Chemical Society, Austin, Texas, June 1974. $ present address : Dept. of Chemical Engineering, University of Alberta, Edmonton, Canada. 12 S. LEVINE AND G. H. NEALE 2. FLOW THROUGH A CYLINDRICAL CAPILLARY We first re-examine the problem of penetration by an incompressible fluid into a horizontal cylindrical capillary, first considered by Washburn and Rideal.2 Let a’ be the radius of the cylinder, z the distance of penetration in time t, p the fluid density ,u its viscosity and y the adhesion ten~ion.~ If liquid is displacing gas, y = ysg-ys, where ysg and ysl are the interfacial tensions of the solid/gas and solidlliquid interfaces respectively.Assuming Poiseuille’s law for creeping flow, the equation of motion used by Rideal for the advancing fluid front is nat2zpd2z/dt2= 2na’y -8npzdz/dt, (2.1) where the last term is the Poiseuille viscous dragging force. The left-hand side of (2.1)implies that the fluid moves through the capillary as a solid plug, so that all fluid particles have the same velocity and acceleration, whereas the Poiseuille force term is based on a steady flow parabolic velocity profile across a section of the capillary.Neither model of fluid flow applies at the two ends of the fluid column, i.e. the men- iscus and the position of entry into the capillary. Also the left-hand side of (2.1) should equal the rate of change of momentum of the column and this means that if the fluid moves as a solid plug z(d2z/dt2) must be replaced by d[z(dz/dt)]/dt. Thus a term na’2p(dz/dt)2,arising from the rate of increase of the fluid mass in the capillary, has been ignored OR the left-hand side of (2.1). This term does not affect the limiting laws (e.g. Washburn’s equation) discussed below, although it does reduce slightly the velocity of fluid penetration in intermediate ranges.The present paper is confined to the consequences of Rideal’s equation (2.1), which we can write (2.1) as where a = 8,ulpar2 and j? = 2y/pa‘. By changing to the dimensionless variables T = at, 2 = (a/J/?)z (2.2) becomes Introducing U = dT/dZ, d2Z/dT2 = -(dU/dZ)/U3 and hence (2.3) becomes dU u3 --+ u2 = ----* dZ Z At large z or t, the deceleration of the fluid front is negligible, so that the first term in the left-hand sides of (2.2)-(2.4) may be ignored. This leads to for the velocity of penetration V. This is Washburn’s original result with y = ylv the interfacial tension of the liquid/vapour interface, and zero equilibrium contact angle.Good has examined the difference between yse -ysl and ylv. The limiting expression (2.5) suggests that a suitable expansion for U at large 2 (large z or t) is WETTING OF A POROUS MEDIUM Substituting (2.6)into (2.4) and equating to zero coefficients of powers of 1/Zwe find that (2.7i) or dt a 1 3P 189p3u = -= -2 -___--___20p2 ~-... (2.7ii)Ydz P az (a~)~(az)’ (a~)~ from which, apart from an additive constant, a1 3P 5p2 63 P3 -* * ,t = -z2--log, z+z2+-+--+2P a a5z4 2 a7z6 Rideal’s solution is not entirely correct since only the first two terms in (2.8) agree with his result. The first term only (Washburn’s expression) is sufficient on the right- hand side of (2.7) provided z2% P/a2i.e., z % (ypd3/32p2)3which, for typical values pp = 1 g~rn-~, = 1 CP and y = 32 dyn cm-l, becomes z % 102a’+ in cm.For capillary tubes with a’ 5 0.05 cm, the deceleration of the penetrating fluid can there- fore be neglected when z exceeds 10 cm. For a vertical cylinder, the deceleration term -~~a’~zpgdue to gravity must be added to the right-hand member of (2.1) and so (2.2) is replaced by d2Z dZ 1-+-+A = -dT2 dT z’ where il= g/(a,/P) = (g/8p)(p3d5/2y)*a dimensionless quantity. In place of (2.4), we have (2.10) Again neglecting the first (deceleration) term U = Z/(l-AZ> or Y = dz/dt = (P-gz)/ ccz, according to which the velocity of penetration vanishes at z = P/g. The latter defines the limiting height of penetration which requires infinite time to attain and this also applies to the complete eqn (2.10).The expansion at large z corresponding to (2.7) is z 11 11 1 a**,U = -+-+--(1-2A2)-+-(1+A2+6A4)-+ (2.11i)1-ilz AZ2 A2 z3 A3 z4 or Integration yields (to within an additive constant) t = --z-,loge(~-~z)----,(B-2~)~-a aP P1 P 99 ag z 2ag (2.12) The first term is sufficient if Z3 % l/A. Putting A2 =f < 1, the above condition becomes A2 = (g2p3d5/128p2y)<f3 < 1 which for the values of p, y and p quoted S. LEVINE AND G. H. NEALE above reads 2 x 105af6<.f < 1. Very fine capillaries (a’-0.01 cm) will satisfy this condition except in the initial stages of penetration when the distance z will be small compared with the limiting height. For a capillary inclined at an angle + to the vertical g is replaced by g cos 4 in the above relations.In considering the rate of penetration at small times it is natural to assume that the velocity dz/dt = 0 at the position of entry z = 0. But according to eqn (2.2) for horizontal flow the simultaneous conditions z = 0 and dz/dt = 0 imply that the acceleration d2z/dt is infinite, which is physically impossible. We must conclude that eqn (2.1) does not hold at entry, where z = 0. The reason is that the meniscus is being formed in the initial stages of penetration into the capillary and eqn (2.1) should only be used when the distance z is large compared with the depth of wetting of the capillary walls due to this formation. If R is the mean radius of curvature of the meniscus the latter wetted distance can be approximated by R-(R2-af2)+zaf2/ 2Rxa’ cos 8/2 where 8 is the contact angle (fig.1). If the fluid is at rest just prior to FIG.1.-Geometry of meniscus in cylindrical capillary. entry into the capillary, then we expect the fluid front to accelerate in the early stages of entry, i.e. d2z/dt2 > 0, where z defines, for example, the position of the meniscus on the axis of the cylinder. From (2.7ii) d2z/dt2 < 0 at large z and hence, situated between the two extremes z~0,where eqn (2.1) is not valid, and large z,where (2.7ii) or (2.8) applies, there is an intermediate position z = zo where d2z/dt2 = 0 or dU/ dZ = 0. The latter condition cannot be satisfied by (2.7i) which means that the region where the solution (2.7ii) or (2.8) is valid lies beyond the position z= zo.At z = zo, the velocity dz/dt is a maximum and provided zo falls within the range of validity of (2.1), this maximum equals p/xzo and a solution near z = zo is readily obtained as a series in powers of z-zo. However, this series depends on the value of zo which cannot be determined unless the equation of motion replacing (2.1) for z Z af2/2Ris known and we shall not attempt this here. Similar comments on the nature of the initial penetration rate may be made for a vertical cylinder. The rest of this paper is concerned with fluid seepage through porous media at large penetration depths, when equations corresponding to (2.8) or (2.12) hold. 3. GENERAL THEORY OF WETTING OF A POROUS MEDIUM A general treatment of the rate of penetration of a fluid into a porous medium which is independent of any particular model can be given by using Darcy’s law where k is the permeability and p the pressure.Consider a cross-sectional area A of the porous medium through which incompressible fluid of density p and viscosity p is advancing in a direction normal to the area A. Let V be the instantaneous velocity WETTING OF A POROUS MEDIUM at a penetration distance z of the fluid front and S the specific surface area of the solid/fluid interface, i.e. the internal surface area per unit volume of porous material. In a displacement 6zof the fluid front, the increase in wetted surface area is SAGz, the corresponding free energy change due to surface adhesion is ySAGz and the equivalent suction force @A.If the direction of the mean flow is inclined at an angle 4 to the vertical, the force of gravity on the fluid when its front has advanced a distance z is Azzpg cos 4 where E is the porosity or void fraction of the porous medium. To apply (3.1) let us imagine that a pressure difference Ap, applied to the volume Az of the porous medium across the thickness z, imparts a mean velocity Vto the fluid in the z direction. Then according to Darcy’s law (3.1), the viscous drag of the fluid is Apz dzAAp = -ApzV//k = ---k dt’ where the permeability k should allow for any tortuosity in the actual path followed by the fluid through the medium. The equation of motion for the advancing front which corresponds to (2.1) is thus given by d2zAZE~__ = ySA -Apz-dz --AzEpg cos 4.(3.3)dt2 k dt Introducing the variables T,2 in place of t, z as in (2.3) and (2.9), (3.3) can be written in the form (2.9). The parameters CI, P relating T,2 to t, z and 1now become a=---iJ p=-YS ksp’ (3.4) If the deceleration term on the left-hand side of (3.3) can be ignored, then the rate of penetration becomes dz k -= -(yS-zepg cos $), (3.5)dt pz from which the limiting height of rise of the fluid is -z, = ys --P &pgcos 4 g cos 4’ provided 4 differs from n/2. At 4 = n/2 the flow is horizontal and ;1 = 0. The relation (3.6) was obtained by Carman for the vertical rise (4 = 0). For a single capillary the porosity s = 1, S = 2/a’ and on equating Darcy’s law to Poiseuille’s law k = Also if 4 = n/2 (3.5) becomes Washburn’s equation for horizontal flow and if 4 = 0 (3.6) gives the limiting height in the vertical capillary.For a random swarm of N equal spherical particles of radius a in a volume V, S = 4rcNa2,E = 1 -4na3N/3V and therefore 3(1-E) 3YU -4 9 (3.7)s=-a z, = Epga cos 4’ and in steady horizontal flow (4 = n/2),the expression (3.5) for the penetration vel- ocity becomes This formula is not dependent on any particular theoretical treatment of such a swarm, such as those described in the following section. On integrating (3.8) we find that z is S. LEVINE AND G. H. NEALE proportional to t*, showing that in horizontal flow z-+w as t-+m i.e. horizontal seepage through porous media continues indefinitely.Eqn (3.6) expresses the specific surface area Sin terms of adhesion tension y, porosity E and limiting height of rise z, and thus provides an experimental method of determining S, assuming that y can be measured as well as E and 2,. However, because z, may be too great for fine particles, the determination of S by this method would apply to coarser particles (a 2 0.01 cm). If fluid is injected into the porous medium under an externally applied pressure po (above atmospheric pressure) then yS is replaced by yS+~p,in (3.3). To compare the magnitudes of the surface tension and external pressure effects, we choose typical values y = 32 dyn cm-’, a = 0.01 cm and E = 3. From the first relation in (3.7), the two effects become equal when po = yS/&= 10 atm.The limiting height z, in (3.6) is reduced by imposing a pressure po above the rising meniscus so that yS is replaced by yS-~p,in (3.6). This could yield S for fine particles. 4. FLOW THROUGH A POROUS MEDIUM WITH CELL MODEL Some model of the porous medium is required in order to evaluate the permeability k in eqn (3.8). We shall regard the medium as a powder consisting of identical spher- ical particles and choose Happel’s cell-type Neglecting at first fluid deceleration and the effect of gravity we consider steady horizontal flow. In the Happel theory,4* each particle of radius a is surrounded by a concentric spherical shell of fluid having an outer radius b, such that the sphere of radius b contains the same volumetric proportion of solid to fluid as in the entire assemblage.The volume fraction of particles is therefore (a/l~)~and the porosity or void fraction E = 1-(a /b)3. V V FIG.2.-Cell model of swarm of spheres. Let Y be the mean fluid velocity of seepage in the z-direction, r the distance from the centre of a typical particle and 6 the polar angle measured from the z axis (fig. 2). The hydrodynamic boundary conditions are equivalent to those used by Ha~pel,~. 5* namely ur(r,0) = 0, ug(r, 0) = 0 at r = a, (4.1) where u, and ue are the r and 8 components of the fluid velocity and T,e is the tangential shear stress component. The last equation is Happel’s ‘‘ free surface ” condition. The hydrodynamic force on a particle is given by Plr F, = 2za2 1 .-[prrcos O+Trg sin 6]r=asin 0do, (4.3) WETTING OF A POROUS MEDIUM where, ifp is the pressure dur(r, 0) (4.4)Prr = -P+~P--ar The general solutions of the Navier-Stokes equations for the creeping flow of an incoiipressible fluid 59 lo are P=A,+(A,r+B,/r2) cos 8, usr, 0) = (4.5) u&, 0) = where the constants are determined by applying the boundary conditions, but we only require B,.We find that eqn (4.3) yields FH= -4nB, = -6npVai2, (4.6) where, writing y = a/b, 2(3+3y5) 2(3 +2y5)- * = Rkl(y)= 3(2 -3y + 3y5-2y6) 3(1-~)~(1+y)(2+y +2y2)’ (4.7) At y = 0 (infinitely dilute suspension) Q2,(0) = 1 and (4.6) becomes Stokes’ law for a single particle. By the law of action and reaction, FHis the retarding hydrodynamic force that a particle exerts on the fluid within a cell.Suppose that the fluid has permeated through n layers of particles at mean separation I so that the distance traversed is z = nl. The crucial step is to equate the total hydrodynamic force exerted on the fluid within a linear row of cells, i.e. nFH,to the rate of change with respect to distance covered by the fluid front, of the free energy attributed to surface tension. Each time the fluid front moves a distance 1, it wets a fresh solid surface of area 4na2 in the row of cells and the free energy gained is 4na2y where y is the adhesion tension. Thus the mean rate of free energy change is simply FsT = 4na2yJl (4.8) the effective suction force due to surface tension.The condition FsT+nF, = 0 yields for the velocity of penetration (4.9) using the relation z = nl. Instead of considering a row of particles which corres-ponds to a cylindrical capillary “turned inside-out ”, one can imagine the fluid advancing through the powder on a broad plane front and use an argument resembling that in the preceding section. Let M be the number of surface particles in the process of being wetted at the front and suppose that the fluid has moved a distance 1 each time it has penetrated such a surface layer of M particles. If N is the total number of wetted particles then NE;, will be the total force on the fluid by action and reaction and we may write -NF;, = 4na2yM/l. (4.10) On identifying the total distance covered by the front z with NZ/M eqn (4.10) leads to (4.9). Comparison of (3.8) with (4.9) yields the permeability coefficient (4.11) S.LEVINE AND G. H. NEALE An alternative expression for R(y) is given by Kuwabara,6 who replaces the second relation in (3.2) by the condition that the azimuthal component of the vorticity vanish at r = b,i.e. (4.12) This yields a = R,(y) 5 (1-~)~(5+6y +3y2+y3)' - 5 (5-9y+ 5y3-y6) = (4.13) At small y, we can expand (4.7) 1p,(y) = 1-$y+3y5 -2p +o(y), (4.14) and so with both the Happel and Kuwabara models, l/Q(y) decreases with increase in y. For a given particle size, decreasing the porosity increases the hydrodynamicforce and therefore decreases the rate of penetration. For a given porosity, the rate of penetration is proportional to the particle radius. Plots of R(y) are shown in fig.3. u-1 I I I OO 0.2 0.4 0.6 Y FIG. 3.-Plot of l/Q(y) against y = (1-E)* ; y3 = (~/b)~= volume fraction = 1-porosity. A, Happel boundary condition (zero tangential stress) ; B, Kuwabara boundary condition zero) vorticity). The formula (4.9)has a distinct advantage over Washburn's result (2.5), when applied to porous powder, because the velocity of penetration Vin (4.9) is expressed in terms of the particle radius. In contrast, when applying (2.7), the relation of the cylinder radius to the particle size remains unknown. If deceleration is taken into account, then the equation of motion for the advancing front becomes (4.15) WETTING OF A POROUS MEDIUM where n = N/M,and hence in place of (4.9) we have an equation of the form (2.2), where (4.16) These formulae are also obtained from (3.4) on using the expressions in (3.7)and (4.11) for S and k respectively and writing E = 1-y3.As in eqn (2.7), the deceleration effect can be neglected if For the same p, y and p considered above and y3 = 0.5 (QM40) this becomes z % 5a3. With a fine powder in which n < 0.01 cm, steady state flow is reached when z exceeds about 0.1 cm. It is quite simple to generalise (4.9) to the case where one fluid of viscosity p is displacing a second immiscible fluid of viscosity p' by capillary suction. Let L be the total length of porous medium through which this displacement occurs and y and y' the two adhesion tensions, where y > y'.We imagine that the source of the displacing fluid is provided at one end (z = 0) of the porous medium and a sink for the displaced fluid at the other end (z = L). The velocity of displacement is (4.17') This relation is of interest, for example, in petroleum engineering. In the case of vertical flow through a porous powder, the equation of motion be- comes (4.18) This can be put in the form (2.9) with T = at, 2 = az/ ,/a and Iz = g/(a,/a) provided a and p are given by (4.16). In those conditions where the first term in (2.11) is sufficient, the velocity of penetration in the upward direction under gravity is (4.19) Except in the initial stages of penetration (4.19) is a good approximation, particularly with fine powders.For n = 0.001 cm, and the values of y, p, JI mentioned above, the height of penetration is about 1 metre. The relation (4.19) also follows from (3.5)on substituting the appropriate expressions for k, E and S and putting 4 = 0. 5. DISCUSSION The wetting theory presented here has been highly idealised and in practice there may be several complicating effects. For example, volume changes occurring within the porous medium during imbibition have not been considered. A common feature in the wetting of a dry powder is the shrinkage of the wet state due to the open struc- ture of the dry state. The following is a simplified theory of the effect of such shrink- age on the rate of penetration. We modify the argument which lead to the relation (4.9) by postulating M' surface particles in the process of being wetted, where the fraction M'/M equals the shrinkage factor i.e.the ratio (wet volume/dry volume) of a given weight of powder. In the relation (4.10) M is now replaced by M'. The S. LEVINE AND G. H. NEALE number of wetted particles per unit distance covered by the fluid front is however M/Z and hence the total number of wetted particles in a distance z is N = (hf/Z)z. It follows that both the horizontal rate of penetration in (4.9) and the vertical rate in (4.19) are diminished by the same factor M'/M. Among other effects ignored here are entrapment of air as liquid rises into porous medium, the presence of electric double layers at the particle surface,l0 and we have only mentioned modifications in the theory when fluid is injected into the porous medium under an externally applied pressure.Quite adifferent situation from that treated here is one where a powder bed may be dispersing into the wetting medium. In addition to these problems, there is need to consider the initial penetration rate which was only briefly discussed and the effect of changing fluid mass referred to in section 2. S.L. is indebted to Professor G. D. Parfitt and Drs. J. Peacock and D. F. Billett of Tioxide International for bringing to his attention the problem of wetting and for extremely useful discussions. We are pleased to acknowledge support from a National Research Council of Canada grant to Professor N. Epstein, Department of Chemical Engineering, University of British Columbia. E. W. Washburn, Phys. Rev., 1921, 17, 273. E. K. Rideal, Phil. Mag., 1922, 44, 1152. A. E. Scheidegger, The Physics of Flow through Porous Media (Univ. of Toronto Press, 1957). J. Happel, J. Amer. Inst. Chem. Eng., 1958, 4, 197. J. Happei and €3. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, New York, 1965). S. Kuwabara, J. Phys. SOC.Japan, 1959, 14, 527.'R. E. Johnson and R. H. Dettre in Suvfizce and Colloid Science, ed. E. Matijevic (Wiley- Interscience, New York, 1969), vol. 2. R.J. Good, J. Colloid Interface Sci., 1973, 42,473. P. C. Carman, Soil Sci., 1941, 52, 1. lo S. Levine and G. H. Neale, J. Colloid Interface Sci., 1974, 47, 520.

ISSN:0300-9238    

DOI:10.1039/F29757100012

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Solvation Spectra Part 46.l-Hydration Numbers for Perchlorate and Fluoroborate Ions BY MARTYN AND DAVIDC. R. SYMONS" WADDINGTON Department of Chemistry, The University, Leicester LEI 7RH Received 17th April, 1974 A "hydration " number of four for aqueous perchlorate ions has been calculated from infra-red and photoelectric Raman spectra of solutions of metal perchlorates and fluoroborates in water containing deuterium oxide. The broad band near 2500cm-l (0-D stretching mode) in the Raman and infra-red spectra of HOD has been the subject of detailed investigations.2-6 In particular it has been shown 3* 6* that, for aqueous solutions of metal perchlorates containing D20, this band is split, a new high frequency component appearing between 2618 and 2635 cm-l.The nature of the species responsible for this new band has been the focus of much contr~versy.~. 6* 8* One theory ascribes the 49 new feature to " free " OD groups brought about by the structure breaking effect of perchlorate iom6 A second 3* assigns the new feature to the 0-D stretching mode of deuterated water molecules hydrogen bonded to perchlorate ions. A third suggests that the new band arises from water molecules shared between anion and cation in these sol~tions.~ Previo~sly,~we attempted to distinguish between the first and second theory and it was concluded that, for solutions in methanol, the new feature was caused by methanol associated with perchlorate ions rather than by " free " OH groups. This conclusion was supported by n.m.r.studies.'O- Because of the similarity between the water and methanol results,g* l2 and the definite differences between the new features in per- chlorate and fluoroborate solutions, it was concluded that the anion hydration theory was to be preferred. Brink and Falk,12 in an independent infra-red study, have reached similar conclusions. Subsequently,' we suggested that the unit responsible * for the high frequency feature in perchlorate spectra is 03C10----DOH---OHz. This explanation is accepted for our present purposes, and hence we show that it is possible to derive a solvation number for ClO, and BF, from the spectral data. EXPERIMENTAL APPARATUS AND MATERIALS Infra-red spectra were recorded using a Unicam S.P. 100 prism-grating spectrophoto- meter and photoelectric Raman spectra were recorded with a Coderg PH spectrometer using 488 nm radiation from an argon-ion laser.Solutions were prepared in the manner previously de~cribed.~ For infra-red spectroscopy a concentration of approximately 1 mol dm-3 9 of D,O was used and solutions used for recording Raman spectra contained approximtaely 3 mol dm-3 of DzO. Salt concentrations were calculated using units of molarity (moles of salt per dm3 of solution) in order to facilitate comparisons with previous work. In general salt concentrations within the range 1.O to 4.0 mol dm-3 were used but, in the case of sodium 22 M. C. R. SYMONS AND D. WADDINGTOS perchlorate, concentrations up to 9 mol dmV3 were studied.When recording Raman spectra care was taken to ensure that the laser output power remained constant for each solution and solutions were filtered five times through 0.22 pm Milliyore filters to reduce the effects of background scattering. On addition of the electrolyte, MC104, the intensity of the low frequency (-2525cm-l) component decreased and that of the high frequency component (-2620 cm-') increased. Addition of M+ ion (as MCI) to the perchlorate solutions caused no significant changes in the ratio of the two component intensities. In particular, the high frequency component did not show any increase in intensity when a salt with a common cation (Na+) was present in high concentration (see fig. 1). It may thus be concluded that, contrary to the suggestion of Ke~ki,~ the new band does not arise in dilute solutions (4 mol dm-3) from water molecules shared between cation and anion.Since the oscillator responsible for the new absorption is 0-D in the unit (0-D---0-ClO,) the presence or absence of a sodium ion weakly coordinated to the water molecule is unlikely to be of major significance. Observed band profiles were subjected to computer deconvolu- tion using an ALGOL program for an Elliott 4130 computer following the method of Stone l4 and the integrated intensity of the low frequency component was estimated numerically with an accuracy of about 10 %, in the worst case studied, and about 5 % for the infra-red spectra. 2700 2600 2500 2400 wavenumber, J/crn-l FIG.1.-Effect of added sodium chloride on the Raman spectrum of sodium perchlorate in 4.5 rnol dm-3 D20 in H20.-,3 mol dm-3 NaC104 in D20+H20; ---, 1.4mol d~n-~NaCl+ 3 mol dm-3 NaC104 in D20+H20; . . . ., 4.5 rnol dm-3 D20in H20. ANALYSIS OF SPECTRA A typical set of Raman spectra of solutions of lithium perchlorate at several concentra- tions in HOD in H,O is presented in fig. 2, the feature at 2640 cm-I being designated H and the lower frequency component L. It is impossible to use feature H to deduce hydration numbers since this would require * knowledge of the oscillator strength of the 0-D bond in the unit (O,ClO----D-O). However, the L band can be used for this purpose if certain simplifying assumptions are accepted. In terms of our present model, loss of intensityt from the L band on addition of salts is caused by the change in environment of some water molecules on solvation.If we assume that the absorbance or scattering from one 0-D---0unit is S then if there are MHoD t In the above analysis " intensity " refers to the intensity of Raman scattering. The treatment is logically identical for infra-red absorbance except that the term "intensity " should be replaced by " absorbance ". SOLVATION SPECTRA moles of HOD per cubic decimeter of water the initial intensity of the Raman scattering or infra-red absorbance A(initia1) of the HOD contour will be : I(initia1) = NMHoDS where ~1’is Avogadro’s number. This supposes that one HOD unit will form on average one (0-D---0)unit. We assume that water (HOD) attached to cations such as Naf is experi- mentally indistinguishable from bulk HOD.This is reasonable since the effects of cations are found to be of minor irnportan~e.~~ Thus we need only consider HOD attached to anions. Suppose that the anion forms x “hydrogen bonds ” to x water (HOD) molecules in solution. x moles of HOD would be lost from the solution per dm3 for each mole of salt added if there were no isotopic randomisation and total fractionation occurred. How-ever, there is no evidence for significant fractionation in isotopic mixtures of water and deuter- ium oxide and so we must correct our estimate of the number of moles of HOD lost on addi- tion of salt as follows. I I I 2700 2600 2500 2400 ;/crn-l FIG.2.-Raman spectra of solutions of lithium perchlorate at several concentrations (niol dm-3) in D20+H20at 298 K.There are M,,, moles of D20 per dm3 of water (55.5 moles) so that amount of water remaining will be (55.5-MD,,) moles. If we add M, moles of salt then the number of moles of water remaining will be approximately (55.5-MD20-Ms).t Each mole of water has two available OH oscillators so that the total number of OH oscillators in any solution will be 2 (55.5-kfD2,-~,). Thus the fraction of the anion-solvent interactions which involve OD will be given by; MHOD -MHOD 2JIr(55.5-MD,o-Ms) -2(55.5-MD20-Ms) Thus the intensity lost on addition of M, moles of salt will be : I(lost, M,) = xMSNS Z(55.5-MD20- M,) I.MHoD But the observed intensity must be given by I(fina1, M,) =I(initia1)-I(lost, Ms). (3) t Note that this is an approximation which is justified in comparison with the larger uncertainty in the integrated component intensities.This is only the case when using the molarity scale. M. C. R. SYMONS AND D. WADDINGTON Clearly we can eliminate S,which is unknown, by taking the ratio of I(fina1, M,) to I(initia1). This has the advantage that it eliminates the need to determine absolute intensities : i.e. I(fina1, M,) = R(M,) = 1-xMs I(initia1) 2(55.5-MD20-M,)I-Hence, if we plot (1 -R(M,)) against we should obtain a straight line passing through the origin from which the hydration number x can be calculated. The two major sources of error in this analysis are the difficulty of precisely determining the area of the L component (this is more serious in the case of the Raman spectra where the scattered intensity is susceptible to the cleanliness of the solution) and the error implicit in the assumption that a molar solution can be treated as consisting of two independent components.Because of these assumptions, it was not considered significant to make corrections to intens- ity measurements for refractive index and ionic strength variations, which are relatively small. RESULTS AND DISCUSSION The results are summarised, together with their estimated accuracy, in table 1 and a specimen plot of { 1 -R(Ms)) against [Ms/2(55.5-A4,-,20-M,)] is presented in fig. 3. The hydration numbers listed as " infra-red " are in very close agreement with those calculated from the data of Brink and Falk.12 The hydration numbers listed as " Raman " are probably less reliable than those calculated from the infra-red spectra because of the greater inherent difficulty of determining Raman component intensities.TABLE1.-SOLVATIONNUMBERS FOR PERCHLORATE AND FLUOROBORATE solvation number infra-red spectra Raman spectra sodium perchlorate sodium fluoroborate 4.7+ 0.5 4.7+0.5 4.4+0.5 4.4k0.5 magnesium perchlorate 3.5k0.5 4.7k0.5 hfs/2[u.5 -MDzO-Ms] FIG.3.-Graph of [l-R(M,)]against [Ms/2(55.5-MD~O-Ms)]obtained from the infra-red spectra of solutions of sodium perchlorate in water containing deuterium oxide. SOLVATION SPECTRA The results suggest that a hydration number of four would be reasonable for both perchlorate and fluoroborate ions in solution, suggesting that one hydrogen bond is formed to each ligand.The X-ray crystallographic analysis of LiC104-3H20 l5 shows that the immediate environment of each water molecule is effectively a distorted tetrahedron consisting of two lithium ions and two oxygen atoms belonging to diflerent perchlorate groups. Hence the water-perchlorate interactions, at least in LiC104-3H20, satisfy the geometric criteria of hydrogen bonding l6 and suggest relatively weak hydrogen bonds to all four of the perchlorate oxygen atoms. Further support for this may be drawn from the review by Irish l7 who reports that several authors 8-20 have been unable to detect splitting of the degenerate C104 fundamental modes in aqueous solutions of metal perchlorates.Whilst this could mean that perchlorate is unsolvated, within the context of our discussion, it eliminates hydration numbers of one to three and supports the number of four. A plot of estimated " hydration number " xagainst concentration indicates a clear tendency to converge on a value of 4 in dilute solutions (see fig. 4). I 0 2 4 6 8 10 MJrnol dm-3 FIG,4.-Graph of dependence of calculated hydration number x upon salt concentration in solution (Ms).Limits of error for hydration numbers are indicated by error bars. Finally, we recall that it has recently been demonstrated that radiation chemistry can have a direct bearing upon solvation studies.21 It was shown by e.s.r.spectro- scopy that Me,c radicals formed in aqueous glasses containing t-butyl alcohol are free to rotate under certain conditions even at 77 K. We have recently been studying the effect of y-rays on aqueous glasses containing perchlorate ions,22 and find, by e.s.r. spectroscopy that both C103 and C102 radicals are formed from C10; ions. The significant point is that both these radicals are completely stationary below the softening point of the glass. This means, in our view, that at least three of the four oxygen atoms of C104 must be hydrogen bonded to the water matrix. If only two were so bonded there ought to be a proportion of C102 molecules free to move in the parent C104 cavity, as was found with the Me,C radicals.We thank Drs. M. J. Blandamer and D. M. Adam for helpful advice, the S.R.C. for financial support and the University of Leicester for a Fellowship to D. W. We are also grateful to Dr. T. 5. V. Findlay for help with some of the measurements. Part 44, B. Kingston and M. C. R. Symons, J.C.S. Faraday ZI, 1973, 69, 978 ; L. M. Kleiss, H. A. Strobe1 and M. C. R. Symons, Spectrochimica Acta, 1971, 29A, 829, is taken as Solva- tion Spectra, Part 45. M. C. R. SYMONS AND D. WADDINGTON R. D. Waldron, J. Chem. Phys., 1957, 26, 809. K. A. Hartman, J. Phys. Chem., 1966, 70, 270. T. T. Wall and D. F. Hornig, J. Chem. Phys., 1967,47, 784. H. R. Wyss and M. Falk, Canad. J. Chem., 1970, 48, 607. G.E. Walrafen, J. Chem. Phys., 1970, 52, 4176.Z. Kecki, P. Dryjanski and E. Kozlowska, Roczniki Chem., 1968, 42, 1749. G. Brink and M. Falk, Canad.J. Chem., 1970,48,2096. D. M. Adams, M. J. Blandamer, M. C. R. Symons and D. Waddington, Trans. Faraday SOC., 1971, 67, 611. lo R. N.Butler and M. C. R. Symons, Trans. Faraday SOC.,1969, 65,945. l1 R.N.Butler and M. C. R. Symons, Trans. Faraday Soc., 1969, 65, 2559. G. Brink and M. Falk, Canad.J. Chem., 1970, 48, 3019. l3 L. J. Bellamy, M. J. Blandamer, M. C. R. Symons and D. Waddington, Trans. Faraday Soc., 1971, 67, 3435. l4 H. Stone, J. Opt. Soc. Amer., 1962,52(9), 998. See also D. Waddington, Ph.D. Thesis (Univer-sity of Leicester, 1971). l5 C. D. West, Z. Krist., 1934, 88, 198. l6 W. C.Hamilton, in Structural Chemistry and Molecular Biology, ed. A. Rich and N. Davidson (Freeman, San Francisco, 1968), p. 466. I7 D. E. Irish, in Zonic Interactions, ed. S. Petrucci (Academic Press, New York, 1971), vol. 11, chap. 9, p. 238. R. E.Hester and R.A. Plane, Znorg. Chem., 1964, 3, 769. l9 M.M.Jones, E. A. Jones, D. F. Harman and R. T. Semmes, J. Amer. Chem. Soc., 1961, 83, 2038. 2o S. D. Ross, Spectrochim. Acta, 1961, 18, 225. 21 K. V. S.Rao and M. C. R. Symons, Chem. Phys. Letters, 1973, 20, 555. 22 I. Ginns and M. C. R. Symons, unpublished observations. '*

ISSN:0300-9238    

DOI:10.1039/F29757100022

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Mossbauer and Infra-red Studies of the Diffusion and Reactivity of (SnO), Species (n 1) Initially Isolated in Solid Nitrogen BY ANTOON T. HOWE*$Bost AND ARTHUR Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QR Received 2nd May, 1974 The diffusion and reactivity of the molecules SnO, Sn202, Sn303, Sn404 and higher polymers isolated in solid nitrogen have been investigated using both Mossbauer and i.r. spectroscopy and the changes in the concentrations brought about by annealing at temperatures up to 36 K have been followed quantitatively. The results are compared with three models and indicate that SnO, and probably to a lesser extent Sn202 are appreciably mobile at 34 K. At this temperature the diffusion coefficient of SnO in a-N2 is between and 4x m2 s-I, which is of the same magnitude as the previously determined diffusion coefficient of Sn atoms in a-N2 at 34 K.The reactions 2SnO+Sn202 and SnO +Sn2O2+Sn3O3 appear to have a non-zero activation energy sufficient to inhibit their reaction rates compared to the reactions of SnO with higher polymers. After evaporation of the nitrogen, aggregates of tin(@ oxides remained which were stable to oxidation up to 270 K but were partially oxidised in air to tin(1v) at 295 K. At 4.2 K the isomer shift of the broad tin(@ doublet of the final material is 2.83 mm s-' and the quadrupole splitting is 2.0 mm s-' ; these are different from the parameters of both previously known forms of bulk SnO. There is currently much interest in the low-temperature isolation and study of simple metal-containing molecules such as oxides, carbonyls and dinitrogen com- p1exes.l In the case of matrix-isolated oxides the simple molecules are thermo-dynamically unstable with respect to the low-temperature forms of the bulk solids, and a series of increasingly complex polymer molecules may be expected following reactions at matrix temperatures which allow diffusion.However, unlike the non- activated recombination of matrix-isolated atoms, the reactions of oxide molecules will have associated with them an energy of activation due to the subsequent bond redistribution, and also due to the high probability of an unfavourable geometrical configuration at the time of collision. Little is known about such low-temperature processes, which could be markedly influenced by small activation energies at the reaction temperature of 5-40 K.In addition, the low-temperature aggregation of the small molecules may result in a metastable solid different in structure to the normal bulk oxide. In our previous study of the matrix-isolated Sn system using Moss-bauer spectroscopy we showed that ultra-small particles of p-Sn, rather than the stable o! form, are produced in this way from Sn atoms. The present study follows the earlier characterisation of the Mossbauer spectra of nitrogen-isolated SnO and Sn202, and we have now investigated the intermediates formed by progressive controlled reaction of nitrogen isolated (SnO), species, where n 2 1. From the rate of reaction of the clearly identifiable SnO molecules an estimate of the diffusion coefficient of these molecules in a-and P-N2has been obtained.Both i,r. and MGssbauer spectroscopy have been used to study the simple matrix-isolated t present address : Research School of Chemistry, Australian National University, P.O. Box 4, A.C.T. 2600, Australia. $ present address : Department of Inorganic and Structural Chemistry, University of Leeds, Leeds LS2 9JT. 28 A. BOS AND A. T. HOWE species, with Mossbauer spectroscopy providing information about the aggregation processes following evaporation of the nitrogen. Unlike other spectroscopic techniques used in matrix isolation studies, Mossbauer spectroscopy permits a quantitative determination of the matrix concentration of resonant species.Subject to small, but determinable ffactor differences, the magni- tude of the effect is basically unaffected by the degree of polymerisation of the species, right through to the bulk solid, thus permitting the present type of diffusion and reactivity study which has hitherto not been possible for such initially unstable species. EXPERIMENTAL The apparatus used for the deposition of the matrix has been described previously and the conditions for efficient isolation of the gas phase species e~tablished.~ Sn02, enriched to 90 % in '19Sn, was heated in an alumina cell to 1200-1300K and the vapour co-condensed with a stream of nitrogen (B.O.C. Research Grade) so as to achieve a homogeneous distri- bution in the matrix of the gas phase species consisting of predominantly SnO molecules, together with oxygen from the decomposition of the Sn02.Infra-red reflection spectra were recorded on a Perkin-Elmer 337 spectrophotometer. Transmission Mossbauer spectra were collected using a 5 mCi BaSnOJ source and equipment as described previ~usly.~ Velocities are quoted with respect to the source at 295 K. All spectra shown in the figures have been corrected for a parabolic baseline curvature equivalent to 0.230 % of the total number of counts. The specimens approximated well to thin absorbers so no saturation correction was applied in the computer fits. The magnitude of the cosine effect was less than the statistical standard deviation of the data. In order that the matrix ratios, calculated using the calibrated envelope areas of the Mossbauer should be independent of the extent of polymerisation they are termed the ratios of the molecular deposition rates of tin species to nitrogen.RESULTS AND DISCUSSION The diffusion and reactivity of the isolated species was studied by slowly heating the matrix up to an annealing temperature, which was then maintained for up to several hours prior to rapid cooling to 4.2 K and observing the changes in the Mossbauer and i.r. spectra. A succession of annealing processes was performed up to about 40 K. -Since it is essential in this kind of study to have, in the TABLE1 .-DEPOSITIONCONDITIONS AND DIFFUSION COEFFICIENTS matrix N2 deposition rate/mmol cm-2 h-' tin oxide deposition rate/ pg cm-2 h-I 240 130 240 50 molecular deposition ratio SnO/Nmatrix thickness/mm 2 1 /160 0.011 1/340 0.048 1 1980 0.57 111 5 000 1.2 diffusion coefficient of SnO (model II)/m2 s-I at 28 K at 34 K 4x 1x 4x 7x <20x initial matrix, a high proportion of monomers evenly distributed throughout the matrix, which must itself consist of well-formed crystallites, matrices were investigated which covered a wide range of crystallite sizes and tin oxide concentrations in order to observe the effects of these variables.Due to the thermal resistance of the nitro- gen itself, thicker matrices deposited using a rapid nitrogen flowrate were quenched less rapidly, thus allowing the crystallites to grow, whereas the crystallite size was 30 MOSSBAUER OF (SnO), SPECIES much smaller in thin and slowly deposited matrices, which were snowy in appearance.The conditions used for four representative matrices, ranging essentially from comp- aratively concentrated small crystallites, (a), to very dilute large crystallites, (d), are given in table 1. THE EFFECT OF ANNEALING ON THE MOSSBAUER SPECTRA The series of Mossbauer spectra obtained from matrix (b)after successive annealing processes up to 36 K is shown in fig. 1, and is representative of the changes observed for all the matrices. Computer analysis of the spectrum of the initial deposit has been discussed in detail in the previous p~blication,~~ and the spectrum was resolved into three doublets and two single peaks so as to be consistent with both the Mossbauer and i.r.evidence from matrices deposited over a wide range of conditions. The component Lorentzian peaks in fig. 1 show a predominance of SnO (A) (isomer shift 6 =3.03 mm s-l, quadrupole splitting A =4.53 mm s-l and halfwidth r =0.73 mms-l) together with smaller proportions of Sn,O, (B) (6 =2.88, A =3.73, r =0.73 mm s-l) and higher polymers (C) (6 =2.8, A =2.3, I? =1.0 mm s-l). The areas of the respective doublet components were constrained to be equal, and the unconstrained halfwidths were then found, for the two major doublets, to be the same to within 0.02 mm s-l. The unconstrained peaks at 0.2 and 2.5 mm s-l, which were more pronounced in other spectra, are at the velocities of SnO, and Sn aggregates,2 and this assignment satisfactorily explains their constancy throughout the successive anneals.x2 for the fit was 190 for 221 degrees of freedom. c-Bm Am -202468 velocity/mms-’ FIG.1.-The effect of annealing on the Mossbauer spectrum, measured at 4.2 K, of matrix (b). The initially deposited matrix (i) was annealed for 10 h at 10 K, 12 h at 15 K (neither shown), 1.5 h at 25 K (ii), 1 h at 28 K (iii), 0.75 h at 34 K (iv) and 0.75 h at 36 K (v). A, SnO ;B, Sn202;C, higherpolymers. A. BOS AND A. T. HOWE The gradual growth after annealing of the polymeric oxides of Sn" is clearly evident from the transfer of intensity from the initial velocities towards smaller quadrupole splittings. After annealing at 25 K the doublets of Sn,O, and higher polymers are evident as shoulders on the main high velocity SnO peak.After further annealing at 34 K the higher polymers are predominant and the appearance of the spectrum suggests that the broad doublet (r = 1.0 mm s-l) initially assigned to the higher polymers might be better represented as two separate doublets. The peak at 0.2 mm s-l, more resolved in spectrum l(i), remained constant showing that there was no oxidation to SnrV oxides, even though the matrix contained at least half as many oxygen molecules as SnO from the decomposition of SnO,. I X i A I B 0 0 C X X + I I I I I 1 I 1 5 10 15 20 25 30 35 40 I II I1 12 1.5 LO 0.75 0.75 T/K (top scale) annealing time/h (bottom scale) FIG.2.-Changes in the component areas of the Mossbauer spectra of matrix (b),measured at 4.2 K, following anneals at the temperatures indicated.A, SnO ; B, Sn20z; C,all higher polymers. The dashed lines show the profiles for B and C calculated using model IT, while the light lines are cal-culated using model 111. The complete series of spectra have been analysed so as to yield the proportion of SnO, the proportion of Sn202 and the proportion of all other Sn" oxides present after each anneal. Although it has not yet been possible to differentiate between the various higher polymer species a knowledge of their total proportion, which is not available from i.r. studies, is essential in any consideration of diffusion and reactivity of the matrix species.It has been previously established 3b that the parameters of SnO and Sn,O, are not detectably matrix dependent, and this enabled the parameters (6, A and r)to be constrained to the values previously established over a wide range M~SSBAUEROF (SnO), SPECIES of relative concentrations and matrix conditions given earlier. The remainder of the spectral envelope was fitted to peaks at the constrained positions of 0.2 and 2.5 mm s-l and sufficient doublets representing higher polymers having equal area components to give a satisfactory total fit. In the initial spectrum this was just one doublet, but two gave a better fit for the other spectra. The velocities of the peaks of one of these doublets were constrained to the values obtained from the complete fit to the final spectrum.All the spectra could, in fact, be fitted with these four doublets (SnO, Sn,O, and two assigned to higher polymers) together with the peaks at 0.2 and 2.5 mm s-l to give a self-consistent analysis with satisfactory values of x2, ranging from 190 to 243 for 227 degrees of freedom. The relative areas of the doublets from SnO, Sn,O, and higher polymers are given in fig. 2 as a function of annealing conditions. The errors in the area of the SnO doublet are estimated to be of the order of 15 %, while those of the relative areas of the remaining peaks may be considerably larger. The total area of the two single peaks at 0.2 and 2.5 mm s-l remained essentially constant, whereas the total area of the four Sn" oxide doublets increased gradually to a value 28 % higher aftet annealing at 36 K than in the initial spectrum.The increase is ascribed to the more polymeric components having a higherffactor than SnO. In order to allow for this the polymer area shown in fig. 2 has been obtained as the difference between the computed SnO and Sn202 areas after each annealing process and the total area due to Sn" oxides in the initial spectrum, thus maintaining the total area of the three components shown in fig. 2 constant for ease of comparison. The concentrations of Sn,O, and higher polymers relative to SnO are obtained by dividing by, respectively, 2 and 3.5, with a correction for f factor differences discussed below. For the purposes of the calcula- tions an equal proportion of Sn303 and Sn404 has been assumed to give the factor of 3.5. Theffactor for SnO isolated in nitrogen has been previously determined 3b to be 0.4 at 4.2 K, and if this value is also taken for Sn,O, the two higher polymers must have an averageffactor of 0.6 to cause the observed area increase. This is consistent with the intensification of the polymer peaks relative to those of the monomer when observed at 10.0and 14.9 K.3b Use of theseffactors enabled the absolute concentra- tion of the species to be determined, and initially, for matrix (b),these values were SnO = 3.5 x lo", Sn,02 = 7.5x lo1' and higher polymers = 1.6x lo1' molecule ~rn-~.EFFECT OF ANNEALING ON THE INFRA-RED SPECTRA The i.r. spectra provided an independent estimate of the relative changes in the concentrations of SnO and Sn,O, and served to identify the presence of Sn303 and Sn404 in the matrices, although the relative changes in these peaks with annealing could not be accurately determined. Because of the highly scattering matrices, i.r.spectra were recorded from thin matrices and the spectrum of matrix (a)after annealing for 1.5 h at 25 K is shown in fig. 3. The absorptions of SnO and Sn,O, are clearly evident at the previously established frequenciesS6 In initially deposited matrices the absorption of Sn404 at 517 cm-l was just discernible as a shoulder on the low frequency absorption of Sn,02. The absorption of Sn303 at approximately 760 cm-l and an absorption at approxi- mately 560 cm-l, assigned to higher polymers,3b were only sometimes observed in the initially deposited matrices. For matrix (a)these two absorptions were just discern- ible, together with Sn,04 and the strong peaks from SnO and Sn,O,, in the initial matrix.A. BOS AND A. T. HOWE A IIBD 3 I I I I 800 700 600 500 wavenumber /cm-l FIG.3.Infra-red spectrum at 4.2 K of matrix (a) taken after annealing for 1.5 h at 25 K. A, SnO ; B, Sn202; C, Sn303; D, Sn404; E, other higher polymers. The peak at 660 cm-I is from traces of COz. 8 0 0 0 I I 1 I I I I I 5 10 15 20 25 30 35 40 1.5 1.0 0.75 0.75 T/K (top scale) annealing time/h (bottom scale) FIG.4.-Changes in the i.r. absorbances of SnO, A, and Snz02, B, following anneals of matrix (a) at the temperatures indicated.The dashed line shows the profile for B calculated using model JI, while the light line is calculated using model 111. 11-2 MOSSBAUER OF (SnO), SPECIES The reduction in the absorbances of SnO and Sn202 with annealing, as deduced from the series of i.r. spectra obtained from matrix (a), is shown in fig. 4. The dependence on annealing conditions is similar to that found for the respective com- ponents in the Mossbauer spectra of matrix (b),and there is no evidence of the relation- ship of i.r. absorbance to concentrations being altered by matrix effects during anneal- ing. The approximate constancy of the i.r. absorbance of Sn202 compared to the large reduction in the SnO absorbance after annealing at 34 K confirms the observa- tion of the same comparative constancy of Sn202in fig.2. Above the a to p phase change in N2 at 35.6 K the Sn,02 concentration falls more rapidly in the more con- centrated matrix studied by i.r. than in matrix (b)studied by Mossbauer spectroscopy (see fig. 2). The three small additional peaks of Sn30, and higher polymers in the i.r. spectrum increased somewhat in intensity to a maximum after annealing at 28 K, approximately doubling in absorbance from their values after annealing at 25 K (see fig. 3). How-ever, after annealing at 36 K their intensities had diminished again to approximately the values observed after annealing at 25 K. This behaviour contrasts with the con- tinual increase with annealing in the proportion of higher polymers found from the Mossbauer spectra, and strongly suggests that by the time the matrix has been annealed at 36 K most of the polymerisation has proceeded beyond Sn303, Sn404 and the species represented by the higher polymer peak at approximately 560 cm-l.From an analysis of the Mossbauer spectrum of matrix (a),the absolute concen- trations of the Sn" oxides were determined to be, initially, SnO = 5.6 x 1019,Sn,O, = 1.3x lo1' and higher polymers = 5 x lo1' molecule ~m-~. By comparison with the i.r. optical densities, the relative i.r. response of the principal 613 cm-I peak of the Sn202 molecule was found to be approximately 15 times that of the SnO molecule, confirming previous qualitative conclusion^,^ and those of the oligomer absorptions were of the order of 5-10 times that of SnO per molecule.AGGREGATION IN THE ABSENCE OF NITROGEN Mossbauer spectra obtained after the nitrogen had been slowly evaporated at 41 K leaving a thin web of material are shown in fig. 5. To ascertain the stability of the oxide to oxygen the sample was first heated to 77 K for one hour, after which the Mossbauer spectrum at 4.2 K had not altered, then 2 Torr O2 was introduced to the cryostat with the sample at 77 K. No increase in the resonance in the SnIV region was observed at 4.2 K, although a slight increase in the area of the Sn" oxide peaks was observed. However, raising the sample to 270 K in vacuum resulted in an area increase, measured at 4.2 K, of more than a factor of 2, as can be seen from fig.5. Upon exposure to 0.2 atm O2at 295 K the absorption at 4.2 K showed a considerable increase in the SnIV region at 0.2 mms-l, while the area of the SnT1 oxide peaks increased by a further 30 % (see fig. 5). The collected product appeared to be quite stable in air. Electron micrographs revealed aggregates of sub-particles having a diameter of the order of 10 nm. No distinct diffraction pattern was evident in the electron diffraction mode. There were no indications of basic structural changes after room temperature annealing of the Sn" oxides, since the isomer shift and quadrupole splitting remained essentially constant after evaporation of the nitrogen, at the values 6 = 2.83 mm s-l, A = 2.0 mrn s-l, measured at 4.2 K.The quadrupole splitting was however, slightly smaller than that of the smallest value of the nitrogen-isolated higher polymer reson- ance, for which A was 2.33 mm s-l. The increase in the area after annealing at 270 K shows that the mobility of the basic units of the aggregates is sufficiently large to allow consolidation of the structure, with the resulting increase in the ffactor. A. BOS AND A. T. HOWE The Mossbauer parameters of the final aggregate do not agree well with the pub- lished values of either the red or black forms of SnO, (6 = 2.60, 2.71 mm s-' and A = 2.20, 1.45 mm s-I respectively at 77 K ') and the structure therefore appears to be different from the bulk forms. The independence of the parameters on particle size indicates that any differences are not likely to arise from possible distortions of the lattices of the red or black forms due to size effects. IIIIIIIIIII -202468 velocity/mm s-' FIG.5.-Mossbauer spectra of matrix (b),recorded at 4.2 K, showing the effect of aggregation during and after evaporation of the nitrogen at 41 K (i) ; the effect of particle growth during annealing at 270 K (ii) ; and the effect of exposure to oxygen at 295 K (iii).The complete annealing sequence was 0.75 h at 41 K ; 1 h at 77 K in vacuum ; 3 8 h at 77 K with 2 Torr oxygen ; 1 h at 270 K in vacuum ; and 1 h at 295 K with 0.2 atm oxygen. DIFFUSION AND REACTIVITY IN SOLID NITROGEN To obtain information concerning (a) the diffusion rates of the various species isolated in solid nitrogen and (b)the reaction probabilities upon collision, which may vary from unity in the case of zero activation energy to a small fraction in the case of finite activation energies, the changes in the concentration profiles with annealing were compared with the predictions of the three models below, chosen to represent extreme situations.MODEL I Zero reaction probabilities are assumed for the two reactions, 2Sn0-+ Sn,O, (1) SnO+Sn,O,-+Sn,O, (2) and unit reaction probabilities (i.e. zero activation energy), assumed for the reactions SnO+(SnO),-+(SnO),+ where YE 2 3. (3) Only SnO is assumed to be mobile. (1) and (2) are the minimum number of activated reactions necessary to reproduce the observed approximate constancy of the Sn, 0, concentration.MODEL I1 Unit reaction probabilities are assumed for all collisions. Only SnO is assumed to be mobile. Aggregation proceeds by the reactions SnO +(SnO),-+(SnO),+, where n > 1. (4) MOSSBAUER OF (SnO), SPECIES MODEL I11 This is a more general case of model 11,where SnO and Sn202 are assumed to have the same mobility, with all other species immobile. In addition to the reactions described by eqn (4), those of the type Sn202+(SnO),+(SnO),+2 where n 2 2, (5) now occur. Model I predicts a rapid increase in n as the SnO molecules react exclusively with the small number of polymer molecules present in the initial deposit, while leaving the concentration of Sn202 constant. For the data shown in fig.4 the average value of n in the polymer molecules, assuming an initial value of 3.5, can easily be shown to be 4.2, 4.5, 9.2 and 13.5 after annealing at 25, 28, 34 and 36 K respectively. Such a rapid increase in the extent of aggregation suggests an explanation of the reduction in the i.r. absorbances of Sn303, Sn40, and the other polymer peak after annealing at 36K. For models I1 and 111, the concentration profiles of Sn202, Sn303, Sn404 and other higher polymers can be calculated from that of SnO using the theory of diffusion controlled reactions originally developed by Smoluch~wski,~ and further developed by Waite,lo as discussed previously in relation to the diffusion of Sn atoms in nitrogen.2 In the simplest case of reactions involving SnO as the only mobile species (model 11) summation of the individual reactions expressed by eqn (4) yields the following rate expressions, given in terms of the number of molecules v, of (SnO), per cm3 1dv, A dt --= -v,(2v,+v,+v,+v4...), 1 dv, A dt = vl(v,-,-v,) for n > 1, (7) where in which R is the radius of approach at which reaction occurs, assumed to be the same for all reactions, and where D is the diffusion coefficient of SnO. The last term inside the brackets in eqn (8) is small, although not negligible, and the value which applies for the combination of two SnO molecules has also been taken for the other reactions so as to give a common factor. When both SnO and Sn20, are mobile, with the same diffusion coefficient D (model III), the equations describing the changes in concentration of each species are given by 1 dv,--= -v,(2v,+v,+v3+v4...)A dt 1 dv,--= vf -v,(v, +2v, +v3 +214 .. .)A dt 1 dv3_-= A dt v1(v2-v3)-v2v3 1 dv, A dt v1(v3-v4)+v2(v2-v4)- A. BOS AND A. T. HOWE The changes in the concentrations of Sn202 and the higher polymers from their initial values have been calculated on the basis of the above two models for each successive annealing process for the data shown in both fig. 2 and 4. The calculated profiles depend on the initial relative concentrations of the species and the observed SnO profiles, and are independent of the overall matrix ratios. The results are shown in the figures. In most cases the calculated proportions of Sn202 were somewhat higher than observed as reaction proceeded, although model I11 provided an approxi- mate description of the profiles.However, neither model I1 nor model I11 explain the reduction after annealing at 36 K of the i.r. peaks from Sn303 and Sn404, since both predict a continual increase in the concentrations of these species as annealing proceeds, and even at 36 K the models predict that less than 15 % of all the higher polymers would be Sn,O, or higher. The diffusion coefficient of SnO in nitrogen can be calculated on the basis of the above models. For model I1 the situation is analogous to the previously considered case of Sn atoms in nitrogen,2 and integration of eqn (6), taking (v2+v3+v4) to be constant, yields R was taken as 0.40 nm, the intersite distance in the face centred cubic primitive lattice of a-N,.A value of D at 34 K of 4 x m2 s-' was calculated from the data for matrix (b),and the i.r. data for matrix (a)yielded the same value at 34 K. At 36 K both matrices gave values of approximately m2 s-l. The larger value reflects the change at 35.6 K to P-N2in which the ellipsoids are essentially freely rotating to give a hexagonal close packed structure. The gradual reduction of SnO shown in matrix (b)resulted in similar values for D being obtained at the lower temp- eratures, and a value of 0.5 x m2 s-l was obtained at 25 K. Similar calculations using the Mossbauer data from annealing studies of the thicker matrices (c) and (d) gave values consistent with those above, showing that the diffusion coefficients are matrix independent over a wide range of conditions.The values are shown in table 1. Calculations based on model I11 gave values similar to those for model 11. Cal-culations based on model I gave a value of D of 0.5 x lo-,' m2 s-l at 34 K for matrix (b)* DISCUSSION OF DIFFUSION RESULTS In the initial i.r. study of matrix-isolated SnO species, Ogden and Ricks inferred from the presence of often appreciable quantities of Sn202 and Sn40, in the initially- deposited matrices that the two reactions SnO + SnO+Sn202 and Sn20, + Sn202-+ Sn404 were the most favourable ones at the temperatures existing during quenching of the matrix from the gas phase. In addition, growth of Sn303 during annealing up to 34 K showed that the reaction SnO+Sn202-+Sn303 occurred at the low annealing temperatures.However, no conclusion was drawn from the annealing studies at low temperatures concerning the first two reactions above. In the related system of matrix-isolated SiO species the absence of the reaction 2SiO-+Si202 suggested a significant activation energy relative to these low temperature^.^^ Comparison of the present results with the predictions of the three models discussed above shows that none of the extreme situations completely accounts for all of the observations. This primarily suggests the existence of collisional reaction probabil- ities of between zero and unity, although modifications of secondary importance may result from variations in the mobility of Sn,02.Although these factors would introduce as many new parameters as reactions into an analysis, the effect can be hfOSSBAUER OF (Sno), SPECIES qualitatively estimated by combining the results of models assuming zero collisional reaction probabilities and those assuming values of unity, as done by Wake,' where-upon combinations of models I and 111 leads to a satisfactory explanation of the observations. Thus the retardation of the two reactions SnO + SnO+Sn,O, and SnO + Sn,Oz -+ Sn,O, [reactions (1) and (2)] relative to those between SnO and higher polymers (as in model I) would increase the rate of production of polymers with n > 4 such that at 36 K a large proportion of these existed, undetected by i.r.spectroscopy, as observed. Nevertheless, the observed initial increase in Sn,O, would still arise as a result of the slower reactions (1) and (2) (as in model 111). Moreover, mobility of Sn,O, is suggested by the appositeness of model I11 to the Sn,O, concentration profile, which is now governed by the relative rates of production and removal in not only reactions (1) and (2), but also by reactions of mobile Sn,O, [reaction (5)]. The above conclusions also satisfactorily explain the features of a previously published diffusion plot,6 for which the initial ratios SnO/Sn2O,/Sn4O4 can now be calculated from the i.r. intensities to be 1/0.5/0.5 using the response ratios derived earlier. Although in this study the concentration of higher polymers was unknown, the profiles are, nevertheless, approximately consistent with retarded reactions (1) and (2), and mobile Sn,O,, which showed a marked reduction in concentration which could not be accounted for solely by reaction with SnO.If the true situation lies between model1 and model 111, limits of to 4 x lo-,, m2 s-l can be placed on the diffusion coefficient of SnO in a-N2at 34 K. The mini- mum value (obtained using models I1 or 111) coincides with the value of 3 x lo-,, m2 s-1 obtained for the diffusion coefficient of Sn in a-N, at the same temperature, while model I predicts a larger diffusion coefficient. Similar values may be expected since the size of the SnO molecule (as judged from the covalent radius of Sn of 0.145 nm and the Sn-0 bond length of 0.183 nm 14) is expected to be similar to that of the tin atom, of radius between 0.145 nm and the radius of the corresponding inert gas Xe of 0.217 nm.In the case of the proposed nearly-square Sn,O, molecule, the short bond lengths result in a diagonal internuclear distance of approximately 0.29 nm and a total width of 0.43 nm. The molecule is therefore only slightly larger than the dia- meter of a lattice site in a-N, of 0.40 nm, and this, together with the planar shape of the molecule, would aid its jumping into a neighbouring vacant site. The dimer Sn, was not found to be mobile at 34 K and is probably larger than Sn,O,. That the activation energies for all the observed reactions are either zero or small is supported by the following argument.If, for instance, the activation energies were all large the diffusion coefficients would need to be much larger than calculated above to account for the observed reaction rates, requiring the diffusion coefficient of SnO to be much larger than that of Sn atoms. However, this would not be expected on the basis of the size considerations given above, nor on the basis of the stronger inter- actions of SnO with the nitrogen lattice than those of Sn, as reflected in the different Debye temperatures calculated from the Mossbauer adsorptions.2* 3b The activation energies are therefore all very small, but the differences between the individual activa- tion energies for the various reactions are sufficient to inhibit some reactions relative to others. Thus the necessity of including some of model I to explain the rapid in- crease in the size of the higher polymers shows that reactions (1) and (2) have a non- zero activation energy which is slightly larger than those of reactions (3), sufficient to slow down, but not prevent their occurrence.The above is consistent with the large degree of bond reorganisation required for the reaction 2Sn0+Sn20, (nearly-square structure 6, and the breaking of the Sn,O, square to form the ring structure of Sn,O,, compared to the relative ease of forming A. BOS AND A. T. HOWE the proposed cubane structure of Sn404 from Sn,O,, and of further additions of SnO to the Sn404 cube to form polymers probably based on the stable structure of Sn40,.Since matrix effects have often interfered with the measurement of diffusion co- efficients in solid organic crystal~,'~ we have quantitatively estimated these effects here utilising the diffusion coefficients obtained above. The considerations below, which show that even the most prevalent effect can be overcome by the correct choice of experimental conditions, show that the diffusion data obtained by this method is that of diffusion in thermally equilibrated bulk a-or P-N2. (a) INTERFERENCE FROM GRAIN BOUNDARY DIFFUSION If the previous theoretical estimate of the activation energy for self-diffusion of nitrogen in a-N2 of approximately 12 kJ mol-1 is an indication of the activation energy expected for the diffusion of SnO in a-N,, the diffusion coefficient at 25 K should be many orders of magnitude lower than that at 34 K.This was not the case for many matrices, as can be seen from the gradual reduction in the SnO concentration in matrix (b),shown in fig. 2. The evidence suggests that the premature mobility of SnO is probably due to a proportion of species residing near grain boundaries in the initially deposited matrix, and moving into and along these imperfections at the lower anneal- ing temperatures. However, it is evident that if all of the species were originally in or close to grain boundaries recombination would occur much more rapidly at for inst- ance, 28 K than 25 K, which is not observed. Now since a species such as SnO, with a diffusion coefficient of approximately m2 s-l has a root mean square displace- ment of only 4.5nm after 1 h, species which were well embedded in a particular grain of typical dimensions at least many times this value would not reach the grain bound- ary even after 1 h at 34 K.A random distribution of trapped species in the grains would be favoured by very rapid quenching conditions, while ex-solution of the species to the grain boundaries would be favoured by slow quenching and crystal growth. In this respect it is worth noting that matrix (a), quenched under the most efficient conditions, showed an abrupt increase in the recombination rate at 34 K, with very little change below this temperature. In matrix (b),where quenching was slightly less efficient, a small proportion of species are probably concentrated near the grain bound- aries and react at the lower temperatures.However, the reactivity of the remaining species is completely governed by their bulk diffusion rate, and the recombination of the majority of the SnO molecules at 34 and 36 K can only reflect bulk diffusion rates. This conclusion is supported by the similarity of the values of D calculated at 34 K for matrices deposited over a wide range of conditions. (b) POSSIBLE INTERFERENCE FROM NON-EQUILIBRIUM LATTICE DEFECTS It can be shown that the vacancy equilibration rate from an artificially high quenched-in concentration is of the order of N/n, times the reaction rate of trapped species diffusing via the vacancy mechanism. For N/n,=105, as estimated from expected vacancy formation and migration energies, the root mean square displace- ment of a vacancy equals the entire deposit thickness after 1 min at 34 K, and it can be assumed that, at these temperatures, the vacancy concentration is at its equilibrium value.(c) POSSIBLE INTERFERENCE FROM LOCAL HEATING The heat liberated by the reactions SnO +(SnO),-+(SnO),+,, which is between l6 290 and 300 kJ mol-', would only raise the temperature of the outer face of the 40 MOSSBAUER OF (SnO), SPECIES matrix by approximately K for the reaction rate found at 34 K, assuming, in the absence of data for N2, a thermal conductivity equal to the value for argon at that temperature.l’ It is unlikely that the polycrystallinity of the matrix will decrease the thermal conductivity by a factor of lo5and so make local heating a significant factor.The authors thank Dr. B. W. Dale, Dr. J. S. Ogden and Mr. L. W. Becker for their cooperation during the experimental work. We acknowledge financial support from the S.R.C., in particular that through the Physico-Chemical Measurements Unit, Harwell. One of us, A. T. H., thanks the Royal Commission for the Exhibition of 1851 for a Fellowship. l Vibrational Spectroscopy of Trapped Species, ed. H. E. Hallam (Wiley, London, 1973), chap. 6 and 9.* A. Bos and A. T. Howe, J.C.S. Faraday 11, 1974,70,451. (a) A. Bos, A. T. Howe, B. W. Dale and L. W. Becker, Chem. Comm., 1972, 730 ; (b)J.C.S. Faraday 11, 1974,70,440. A. Bos, A.T. Howe, L. W. Becker and B. W. Dale, Cryogenics, 1974, 14,47. T. E. Cranshaw, Nuclear Instr. Methods, 1964, 30, 101. J. S. Ogden and M. J. Ricks, J. Chem. Phys., 1970, 53, 896.’M. J. Ricks, D.Phil. Thesis (Oxford, 1969). C. G. Davies and J. D. Donaldson, J. Chem. SOC. A, 1968, 946. M. v. Smoluchowski,2.Phys. Chem. (Leipzig), 1917,92,129. lo T. R. Waite, J. Chem. Phys., 1958, 28, 103. l1 T. H. Jordan, H, W. Smith, W. E. Streib and W. N. Lipscomb, J. Chem. Phys., 1964, 41, 756. l2 W. E. Streib, T. H. Jordan and W. N. Lipscomb, J. Chem. Phys., 1962, 37, 2962. l3 J. S. Anderson and J. S. Ogden, J. Chem. Phys., 1969, 51,4189. l4 T. Torring, 2.Naturforsch. A, 1967, 22, 1234. l5 J. N. Sherwood in Proc. 7th Int. ConJ Reactivity of Solids, ed., J. S. Anderson, M. W. Roberts and F. S. Stone (Chapman and Hall, London, 1972), p. 252. l6 R. Colin, J. Drowart and G. Verhaegen, Trans. Faraday SOC., 1965, 61, 1364. l7 B. Meyer, Low Temperature Spectroscopy (American Elsevier, New York, 1971), p. 199.

ISSN:0300-9238    

DOI:10.1039/F29757100028

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Thermodynamic Properties and Self-diffusion of Molten Sodium Chloride A Molecular Dynamics Study BY JOHNW. E. LEWIS*-/-SINGERAND KONRAD Department of Chemistry, Royal Holloway College, Egham Hill, Egham, Surrey Received 15th May, 1974 Molecular dynamics calculations are reported for liquid sodium chloride simulated by Born- Huggins-Mayer type pair potentials. Thermodynamic properties and self diffusion constants have been obtained for 22 VT points ranging between 1000 and 2000 K and between -1 and 14 kbars. The agreement with experimental data is, on the whole, satisfactory. Algebraic expressions have been fitted to the calculated data for the pressure, internal energy, the (variation of the) Helmholtz free energy, and the ionic self diffusion constants.The variation of the pair correlation functions and of the velocity autocorrelation functions with V and T are examined. Some features of computer generated films showing the ionic motion are briefly discussed. Computer simulation of liquid systems by the Monte Carlo (MC) and molecular dynamics (MD) methods have led to a considerably better insight into the structure of simple 1iquids.l The application of these methods to hard spheres and Lennard- Jones atoms has been well exploited and the results of these calculations have had a considerable impact on the development of theories of liquids.2* Woodcock and Singer have applied the MC method to molten potassium chloride and more recently MC calculations for a range of liquid and solid alkali metal halides have been carried Limited calculations by a modified MD method have been reported by Woodcock.6a Rahman and co-workers have recently published some MD calculations for beryllium fluoride and lithium fluoride, which show among other things that a pair potential with purely electrostatic cohesive terms correctly predicts the tetrahedral coordination and high viscosity of liquid beryllium fluoride.' Lantelme et al.have reported limited MD calculations for liquid sodium chloride.8 Following the success of the MC calculations on molten potassium ~hloride,~ it was decided to attempt a molecular dynamics study in order to see whether this tech- nique could give estimates for the transport properties of a molten salt system. It seemed reasonable to first try and calculate the self diffusion constants and to compare these to experiment.Molten sodium chloride was chosen for study for two reasons, first the availability of experimental data and second because the self diffusion constants are different for sodium and chloride ion in the melt in contrast to the case of potassium chloride. Thus such a study should provide a fairly searching test of the assumed pair potential and indicate whether it is worthwhile to attempt the computation of other transport coefficients. In the present paper we report a molecular dynamics study of molten sodium chloride over a fairly wide range of temperature and density with the aim of studying 'f present address : Applications Software Group, Atlas Computer Laboratory, Chilton, Didcot, Berks.41 THERMODYNAMICS OF MOLTEN SALTS both the thermodynamic properties and the diffusion constants as function of these state parameters. THEORY AND COMPUTATION The method of molecular dynamics essentially involves the setting-up of the coordinates of a relatively small number of atoms or ions, assuming the form of the interactions between these particles, and solving the classical equations of m~tion.~ In the present calculations the following basic assumptions have been made. (a)The interaction potential is pairwise additive. (b) The form of the potential function was taken to be that suggested by Tosi and Fumi lo in a study of solid alkali metal halides : where the parameters used were obtained from the paper of Tosi and Fumi.l0 They are J~/10-19 B/lO1'Jm-l (or+oj)/lO-'O m C/10-79 J m6 D/10-99J mS ++ 0.4225 3.15 2.34 -1.68 -0.80+-0.3380 3.15 2.75 -11.20 -13.90 --0.2535 3.15 3.17 -116.00 -233.00 The first .term in (1) represents the Coulomb interaction, the second the Born-Huggins exponential repulsion with parameters obtained by Tosi and Fumi while the third and fourth terms represent the dipole-dipole and dipole-quadrupole dispersion energies (with para- meters obtained by Mayer ll).(c) The number of particles chosen for the computer experiments was 216, i.e. 108 sodium ions and 108 chloride ions contained in a cube of side L. The reason for choosing this number was computational economy. Some runs with 512 particles indicate that compara- tively little would have been gained in the present investigation by the use of a larger sample.If initially we assume a random set of velocities assigned to the particles such that : 216c miui = 0 (2)i= 1 then after evaluation of the total energy 0and the forces acting on the particles from eqn (3) and (4), the Newtonian equations of motion can be solved numerically for a particular time step giving rise to a new configuration : This time step was chosen sufficiently small to maintain conservation of total energy, the value being 8.0~ s. Although eqn (3) and (4) are straightforward to use, the presence of the Coulomb term in the pair potential causes problems. As is well-known, direct summation of Coulomb potentials in crystal lattices is only slowly convergent for some lattices and divergent for others, and indirect techniques such as Ewald's method, have to be em- ployed.12 This method has been employed in previous MC and MC calculations for ionic systems and of plasma^.^^ l3 The Coulomb energy sum is transformed into two convergent series J.W. E. LEWIS AND K. SINGER and the forces are calculated by taking the gradient of these. In the computations was truncated at Y = L/2 and at lnI2 = 1, with aL = 5.714. After most of the calculations had been completed it was realised that this truncation, while fairly satisfactory for the calculation of the energy sum, is too severe for the calculation of the l5 Fortunately, however, the rather large errors in the individual inter- particle forces have in this case very little effect on the computed average properties : the values for the internal energy, pressure, and diffusion constants reported here are in excellent agreement with those obtained in later MD calculations in which the forces were calculated with an accuracy of -0.3 % (see the Appendix).The cut-off at Y = L/2was also employed for the non-Coulombic forces and energies and a long-range correction was applied to the r6and Y-~energy terms in the usual manner by the replacement of the distant particles by a continuum.16 Initially the system was equilibrated around the desired temperature for about loo0 time intervals (.v10-l1 s). After this, during the production stage of 1800 time intervals, the microcanonical ensemble averages of the potential energy and the virial were calculated as time averages and the instantaneous coordinates and velocities and pair-distance histograms were output to magnetic tape, together with the running averages of energy, virial coefficients, and temperature.During the production run the total energy E was conserved with 0.1 %, From the primary data one obtains the thermodynamic properties internal energy : (E = total energy of the system, No = Avogadro's number, kg = Boltzmann's constant) IN (Y) = -4 1Fij rij. i#j The brackets ( ) indicate ensemble averages. The self-diffusion constants axe calculated either from the mean square displacement of single particles according to the Einstein formula or from the integral of the velocity autocorrelation function D = lim (ui(0) .vi(s))(l -s/t) ds.t-+m s'0 Eqn (7) and (8) are, of course, equivalent and the estimates of the diffusion constants calcu- lated by both formulae are mutually consistent. RESULTS AND DISCUSSION THERMODYNAMIC PROPERTIES In table 1 the molecular dynamics data for internal energy, enthalpy, pressure and self diffusion constants are given. The variation of the pressure along isochores is linear. The slopes of the p against T isochores yield the thermal pressure coefficients Parabolae can be fitted to the interpolated values of p at constant T. One of the roots of each of these parabolae corresponds to the molar volume at zero pressure. THERMODYNAMICS OF MOLTEN SALTS The volumes so obtained, as well as other calculated thermodynamic properties at p = 0, are listed together with experimental data in table 2.The isothermal compressibility and thermal expansion coefficients have been evaluated in two ways. (i) The p against V-isotherms were differentiated near p = 0 to yield the isothermal compressibility KT = -i/v(avjap)T. (10) The thermal expansion coefficients up = i/~(av/a~), (1 1) were obtained by fitting straight lines to the density against temperature curves at p = 0. (ii) The relationship was used. Parabolae were fitted to the values of pv along isotherms ; the enthalpies are easily calculated as U+pY and are found to lie on linear isochores. From these '0 2 4 6 8 10 12 r/10-8 cm FIG.1.-Pair distribution functions for sodium chloride just above the melting point : -, g+-, ---, 9+-+ b+++9-42.1qI ,q '0 2 4 6 8 10 12 r/1W8cm FIG.2.-Pair distribution functions for sodium chloride just above the melting point : -, g++; Y 9--. J. W. E. LEWIS AND K. SINGER isotherms H(V) are constructed; parabolae can be fitted to these, which lead to (dH/aV)and through eqn (12) to KT. The thermal expansion coefficient is then obtained from the chain relation This method is inferior for the calculation of a, due to accumulation of errors when using eqn (13). The values of a, shown in table 2 have been evaluated by method (i). The values obtained by the two routes agree within about 15 %. TABLE1 D, 10-9 D-110-9 V/10-6m3 T/K Plkbar UjkJ mol-1 H/kJ mo1-I m2 s-l m2 s-1 37.51 1056 1.23 -694.15 -689.54 7.4 7.1 1375 5.16 -678.74 -659.38 11.8 10.3 1622 8.46 -665.66 -633.93 14.9 13.1 1762 9.96 -659.52 -622.16 17.8 16.7 2060 14.00 -644.74 -592.23 24.2 18.5 39.47 1123 0.45 -688.21 -686.43 8.8 8.1 1377 3.03 -675.17 -663.21 13.3 12.5 1600 6.31 -661.41 -636.50 17.5 15.7 2056 10.12 -643.17 -603.23 25.0 23.6 41.35 1073 -1.47 -688.69 -694.77 8.2 7.9 1381 1.53 -672.81 -666.48 14.5 12.3 1723 4.34 -656.33 -638.34 17.4 16.8 2143 8.51 -637.20 -602.01 26.4 25.4 43.29 1262 -1.13 -676.41 -681.29 12.7 12.0 1330 -0.39 -672.95 -674.65 13.9 12.6 1406 0.19 -669.29 -668.45 15.5 14.2 1485 1.01 -665.31 -660.93 16.0 15.3 1562 1.44 -661.45 -655.22 18.9 18.5 47.35 1459 -0.09 -661.96 -666.65 17.4 15.1 1566 -0.63 -657.01 -659.99 17.7 16.6 1678 0.17 -651.72 -650.92 22.2 20.3 1784 0.98 -646.72 -642.08 26.5 23.6 TABLE2 V/m3 mol-1 cr~/lO-~K-' K~110-6bar-' pv/bar K-1 Cv/J K-i mol-l TlK calc.exp. calc. exp. calc. exp. calc. exp. calc. exp. lo00 38.15 3.04 31.1 11.9 49.1 48.9 1073(m.p.) 39.14 37.70 3.12 3.07 32.4 28.7 11.1 10.7 48.9 48.6 1100 39.51 38.01 3.15 3.09 33.0 30.1 10.8 10.3 48.8 47.6 1200 40.88 39.23 3.26 3.19 35.3 35.5 9.8 9.0 48.6 47.2 1300 42.27 40.54 3.37 3.30 38.3 41.7 8.8 7.8 48.3 1400 43.70 41.90 3.49 3.41 42.3 8.O 48.1 1500 45.17 43.40 3.60 3.53 47.7 7.2 47.8 1600 46.71 44.96 3.73 3.66 55.8 6.5 47.7 1738(b.p .) 49.00 46.88 3.91 3.58 74.6 5.7 47.4 THERMODYNAMICS OF MOLTEN SALTS The molar heat capacity at constant volume C,,is determined by the slopes of the U(T),isochores.Cpcan be similarly obtained from the gradients of the H(T),plots. The variation of Cpwith pressure is shown in table 3. From the values of Cpand Cv and KT,it is possible to re-compute a, by means of VTaic,-cy = -. KT The agreement with the previously calculated values is satisfactory. The calculated and experimental thermodynamic properties at zero pressure are compared in table 2. The magnitude of the discrepancies is, for U(T)-k0.5%, for V(T)-+5 %, for Cv-0.3 %, for C,-2 %, for up,KT, BB-&5-10 %. The agreement is surprisingly good, particularly if it is remembered that the parameters in the pair potential were obtained by fitting the properties of the crystal at 298 K.1° The most obvious discrepancy is the over-estimation of the volume by -5 %.The statistical error in the calculated pressures is -kO.3 kbar, which is equivalent to an error of k0.3 cm3 in the molar volume at 1100 K. This clearly does not account for the systematic discrepancy of +2-3 cm3. The results are consistent with those obtained by Monte Carlo calculations for liquid KCl and for other alkali metal halides, and must be considered as a general feature of the Tosi-Fumi pair potentials. The calculated densities conform to : p(T, p = O)/g ~m-~ = 1.993 -4.662 x T/K (14) for the experimental values p (T,p = 0) = 2.061 -4.759 x T/K.I7 For H(T,p = 0) one obtains the equation (-761.5+0.066 T/K) kJ mol-' which is to be compared with the -764.5+0.067 T/K for the experimental values 18* 19* lo between the melting point and 1300 K; the agreement is better than 0.5 % The agreement between observed and calculated heat capacities is very good.The linear dependence of the enthalpy on temperature, which is characteristic of molten alkali metal halides, applies to the calculated values over the entire temperature range. The value of CVis very close to R = 3NkB,showing that the law of Du-Long and Petit holds. Since this law holds for systems of classical harmonic oscillators, one is led to the conclusion that the ions move on average in parabolic potential wells. The discrepancy between the calculated and experimental values 179 2o of the pv,KT, up is probably no greater than would be expected from the statistical errors attached to the MD data, combined with the margins of error in the experimental measurements. The thermal expansion coefficients agree with the experimental values within 3 % (except at the highest temperature).For the isothermal compres- sibility the discrepancy is of the order of 10 % and there is an indication that the increase with temperature is too small. The calculated thermal pressure coefficients are by 5-10 % larger than the observed values. In summary, one can conclude that the Born-Huggins-Mayer-Tosi-Fumi potential simulates the thermodynamic properties of liquid NaCl quite well. It must be remembered, however, that, owing to the absence of experimental data, the com- parisons are restricted to the behaviour at low pressure.EQUATIONS OF STATE AND FOR THE FREE ENERGY Over the range covered by the MD data, the pressure can be expressed as plkbar = (42.2V-2-0.898 V-l+ 0.006 44)T/K- 287.0 Y-1-4.480 (Y in cm3). (1 5) Although this equation is valid within 50.3 kbar, the values of kVand KTderived from it are not in close agreement with those reported in table 3. The discrepancy arises J. W. E. LEWIS AND K. SINGER from the additional curve-fitting step required to obtain the coefficients in eqn (15). The internal energy can be expressed as U/kJ mol-l = 48.44 x T/K-2655V-l/~m-~-675.5. (16) The coefficient of Tis the average value of Cv; its small variation with V is neglected.TABLE3 ~~ plkbar calc. exp. 0.0 65.9 67.0 1.o 65.1 2.0 64.4 3.O 63.8 4.0 63.2 5.0 62.8 6.0 62.4 7.0 62.1 8.O 61.8 9.0 61.5 10.0 61.2 Although eqn (1 5)and (1 6) have a reasonable form, they are not derivable from the same expression for the Helmholtz free energy A( V, T),and are thus thermodynamic- ally not compatible. This can be seen by calculating (aU/aY), (i) from eqn (16), (ii) by means of (aU/aY), = T(i?p/~V)~-p,from (15). Thermodynamically compatible equations can be obtained in the form U = C,T+b,V2+b2V+b3 (17) p = (c, V-2+c2V-1+~3)T+a,Y+a, = P,T+alV+a,. (18) The coefficients cl, c,, c3 and Cvhave the same values as in (1 5) and (1 6) respectively The remaining coefficients can be determined by least squares curve fitting, but the primary data are not sufficiently accurate to ensure the compatibility of the equations so obtained.Instead the coefficients al and a2 were obtained by the curve fitting, and bl, b2 from the conditions of compatibility i.e. b, = -a1/2, b, = -a2 (19) and b, finally by mean difference from (17). The resulting expression U = (48.44 x T/K-7.989 x V2/cm6+ 1.8106V/cm3-801.17) kJ mol-l (20) fits the data within +O.l %, while the equation p = (Pv(V)T+0.1598 V/cm3-18.1 1) kbar (21) holds with an accuracy of better than k0.5 kbar. Integration of (18) with respect to volume leads to A(V, T) = -sp dV = (c, Y-l -c2 In V -c3V)T-+a,Y2-a2V -const(T). (22) Substitution of (20) into A(V, T) = -T dT’ leads to A( Y,T) = -CVTIn T + (b, V2+b, V+b3)+T const’(Y). THERMODYNAMICS OF MOLTEN SALTS Eqn (22) and (23) are compatible if const(T) = C,Tln T-b3 and const'(V) = c1Y-l-c2In V-c3V, so that finally A( V, T) = -C,T In T+ (c,V-' -c2In V- c3 V)T-$al V2-a2VSconst.(24) Eqn (24) could serve as a starting point for the derivation of equations of state for other liquid alkali metal halides by corresponding states arguments.2 TABLE4 A B C cations 1.0207~ -47.92 1537.6 anions 9.047~ -39.05 1239.5 D = (ATV+B+C/T') x cm2s-' TABLE5 ~+/10-5crn2 s-~ ~-/10-5cm2 s-l T/K v/cm3 mol-' calc. exp. calc. exp. 1073 39.14 8.1 7.3 7.5 5.8 1100 39.51 8.5 8.0 7.9 6.3 1200 40.88 10.2 10.5 9.4 8.4 1300 42.27 12.2 13.2 11.3 10.7 1400 43.70 14.6 16.1 13.5 13.1 1500 45.17 17.4 19.1 16.1 15.7 1600 46.71 20.6 19.1 1738 49.00 26.0 24.0 RADIAL DISTRIBUTION FUNCTIONS The pair correlation functions g++(r),g+-(r) and g--(r), as well as the mean or total correlation function gm(r),have been calculated.Some of these, obtained for systems with 512 ions, are shown in fig. 1 and 2 and the characteristic features at different VT points are summarised in table 6. The results are similar to those obtained in previous computer simulations 4-6* : the maxima of g++and g--coincide and fall on the minima of g+-and vice versa. The first peak of g+-(and of gm)occurs at a distance smaller by 0.15-0.2A than obtained by diffraction experiments. There is some over- lap of the g++ and g--curves and the first peak of gm,showing that the like ion pairs contribute >5 % to the first shell coordination number; this also has the conse- quence that the first minimum of gm(t)occurs at smaller distances than that of g+-(r), and the "number of nearest neighbours " estimated by integration of g,(r) to its first minimum is much lower than the coordination number obtained by integration of g+-(r) to its first minimum.These and other features have been more fully discussed el~ewhere.~' Table 6 shows that (rmax)+-is fairly independent of temperature and 22 volume. This is in contrast with the results for liquid KCl where there is a small but definite decrease of (rmaX)+-with increasing v01ume.~ DYNAMIC PROPERTIES The most readily computed quantities are the diffusion constant D and the velocity autocorrelation function.The diffusion constant can be computed from MD data either by the Einstein formula J. W. E. LEWIS AND K. SINGER from the linear increase of the mean square displacement of single particles, or by integration of the velocity autocorrelation function D = 3 lim (~~(0)-ui(s))( 1-sit) ds. t-rw s'0 The two methods are, of course, equivalent and the estimates of D obtained by them are mutually consistent. Following Verlet and Leve~que,~~ an equation of the form D = ATV2+B+CV-' (25) has been fitted to the primary data, and found to be valid within 5-10 %, which is the same magnitude as the computational error attached to the data. The coefficients are given in table 4.Eqn (25) together with eqn (14) have been used to calculate values of D(T, V) at zero pressure. These values are compared with experimental data 24 in table 5. In view of the margins of error OF the quantities so compared, the agreement is not unsatisfactory. The calculated values particularly for the anion are by up to 20 % too high near the melting point ; at higher temperatures the agreement is better because the calculated D values vary more slowly with Tthan the experimental ones. TABLE6 molar vol- cm3ume/ mol-' TIK rmax g++ rmin h rmax 9-rmin h * rmax g+-rmin h n rmax gr? rmin h n 37.51 1056 4.0 6.2 0.89 14.6 4.0 6.2 0.94 14.5 2.7 4.2 3.76 5.2 2.7 3.3 1.88 3.8 1375 4.0 6.1 0.84 14.2 4.0 6.0 0.88 13.8 2.6 4.1 3.44 5.0 2.6 3.3 1.72 4.0 1622 4.0 6.2 0.80 14.6 4.0 6.1 0.86 14.2 2.6 4.3 3.24 5.4 2.6 3.2 1.63 3.5 1761 4.0 6.2 0.78 14.6 4.0 6.2 0.84 14.6 2.6 4.2 3.17 5.2 2.6 3.3 1.59 4.0 2061 4.0 6.0 0.75 13.3 4.0 6.1 0.80 14.6 2.6 4.2 3.03 5.3 2.6 3.2 1.52 3.5 39.47 1123 4.1 6.1 0.89 13.3 4.1 6.1 0.90 13.3 2.6 4.1 3.78 4.8 2.6 3.3 1.89 3.6 1660 4.1 6.3 0.79 14.5 4.1 6.1 0.82 13.7 2.6 4.2 3.25 5.0 2.6 3.2 1.63 3.2 2056 4.1 6.3 0.75 14.6 4.0 6.1 0.78 13.3 2.5 4.1 3.05 4.7 2.5 3.2 1.53 3.2 41.35 1073 4.2 6.2 0.87 13.2 4.2 6.2 0.91 13.2 2.6 4.0 3.91 4.5 2.6 3.3 1.95 3.6 1381 4.2 6.2 0.82 13.2 4.2 6.2 0.86 13.2 2.6 4.2 3.58 4.8 2.6 3.2 1.79 3.3 1723 4.2 6.1 0.76 12.8 4.2 6.2 0.83 13.2 2.6 4.2 3.29 4.8 2.6 3.2 1.65 3.3 2143 4.2 6.1 0.74 12.8 4.0 6.0 0.76 12.8 2.6 4.1 3.03 4.6 2.6 3.2 1.52 3.2 43.29 1265 4.2 6.3 0.88 12.7 4.2 6.3 0.91 12.7 2.8 4.1 3.80 4.5 2.8 3.3 1.90 3.0 1329 4.1 6.1 0.87 12.7 4.1 6.1 0.90 12.7 2.7 4.0 3.76 4.5 2.7 3.2 1.88 3.0 1406 4.1 6.1 0.87 12.7 4.1 6.1 0.88 12.7 2.7 4.0 3.68 4.5 2.7 3.2 1.84 3.0 1485 4.1 6.1 0.84 12.7 4.1 6.1 0.84 12.7 2.7 4.0 3.58 4.5 2.7 3.2 1.79 3.0 1561 4.1 6.1 0.83 12.3 4.1 6.1 0.87 12.7 2.7 4.0 3.51 4.4 2.7 3.2 1.76 3.0 47.35 1457 4.3 6.4 0.84 12.9 4.3 6.4 0.86 12.9 2.6 4.1 3.80 4.3 2.6 3.3 1.90 3.0 1566 4.3 6.4 0.82 12.9 4.3 6.4 0.85 12.9 2.5 4.1 3.69 4.2 2.5 3.3 1.84 3.0 1678 4.4 6.4 0.80 12.9 4.3 6.4 0.84 12.9 2.5 4.1 3.62 4.2 2.5 3.3 1.82 3.0 1782 4.3 6.4 0.79 12.9 4.3 6.3 0.84 12.0 2.5 4.1 3.58 4.2 2.5 3.3 1.79 3.0 r,,, = position of first peak (A, ; rmin= position of first minimum (A) ; h = height of first peak ; n = coordination number = s:"4nrzg(r)dr.Velocity autocorrelation functions have been obtained for a number of V, T points. Fig. 3 shows normalised velocity autocorrelation functions, defined by P(t>= Q<t>/<lui(0)12> ; Q(t>= <vi(O)*ui(t)> (26) for sodium and chloride ions in a melt at the V,Tpoint (43.29 cm3, 1406 K).Some generalisations concerning the V,Tdependenceof the diffusion constants and that of the velocity autocorrelation functions can be made. It should be borne in THERMODYNAMICS OF MOLTEN SALTS mind, however, that although the MD data cover a fairly large temperature range, this is small compared with the entire liquid range and the system is always far from the critical region. L time (intervals of 8 x 10-l5s) FIG.3.-Velocity autocorrelation functions for the sodium and chloride ions in molten sodium chloride at 43.29cm3 and 1406K. The diffusion constant can be written in the form CQ D = +(1vJ2) 1 P(t)dt = 1; P(t)dt. 0 Expressing D by the Einstein relation in terms of the friction coefficient D = k,T/my, one obtains l/y = T = Jrm P(t)dt.(28)0 Thus if y is independent of temperature then at constant density, D will be a linear function of T. This is seen to be nearly the case [eqn (25)]. The density dependence, on the other hand lies entirely in y. The temperature dependence of D at constant density can therefore be ascribed to the change of the mean square velocity, whereas the integral over the normalised velocity autocorrelation function is almost temperature independent. As the temperature increases, the negative portion of P(t) is diminished and the crossing point from positive to negative values shifts to large times. Since the integral remains virtually constant, one may conclude that the more rapid loss of correlation with time occurs in such a manner that the decrease in area of the negative portion is compensated by an equal decrease in the area of the positive portion.These features are similar to those observed by Levesque and Verlet 23 for the velocity autocorrelation function of the Lennard-Jones liquid. Detailed examination shows, however, that in the case of the ionic liquid there are oscillations of the order of 2 x s [leading to a second maximum and minimum in P(t)]. It seems likely that these are remnants of a strongly damped oscillation, which, in the absence of damping by short range forces, is a dominant feature in the velocity autocorrelation function of plasmas. J. W. E. LEWIS AND K. SINGER In addition to the computation of thermodynamic and transport properties, computer simulation can also provide an intuitive insight into the structure and dynamics of molten salts.To this end computer generated films illustrating the motion of the ions have been made. A fairly general program with full hidden line removal for use in three dimensional systems has been written with graphical output on a SD4020 microfilm recorder, making it possible to construct film sequences. Still frames from such sequences are shown in fig. 4 (a), (b) and (c). The presence of (c) FIG.4.-Still frames of molten sodium chloride simulation display at 100 time interval separations, Ionic radii of 0.75 and 1.00x lo-* cm for Na+ and C1-respectively for the purposes of clarity. large voids within the liquid alkali metal halides has been disc~ssed.~.Similar22 voids have also been observed by Fehder et aZ.25in a two-dimensional MD simulation of Lennard-Jones disks. The moving sequences show the dynamic behaviour of these voids : they appear to have a fairly short life time (10-l2 s) and they tend to collapse rather than being jumped into by a single ion. The word "void " in the present context is preferred, since "hole "would suggest the presence of holes in the sequence of cell-hole models, which have been shown to be invalid for liquid alkali metal halides.6 The presence of voids may be simply a consequence of the small coordination number (-5 nearest neighbours as compared with -10 in Lennard-Jones liquids). It is less easy to understand why the voids are inaccessible to single ions since they seem to be THERMODYNAMICS OF MOLTEN SALTS large enough to accommodate the diameter of an ion and since the electrostatic poten- tial inside them must be either positive or negative. The last argument, however, is probably fallacious : because of the long range of the electrostatic forces, it is insuffi- cient to consider the potential inside the void only and to disregard the changes elsewhere, resulting from the displacement of a single ion.It would be instructive to map the electrostatic field of relevant configurations in three dimensions. Another feature, which is possibly statistically insignificant, can be seen from the stills : tetrahedral arrangements of ions of opposite charge around a central ion are not infrequent.CONCLUSIONS It is initially surprising that a potential of the form given by equation (1) and obtained from solid state data should give such good results for the thermodynamic properties of sodium chloride over a large part of the liquid range. They are by no means perfect, the zero pressure volumes being the most seriously in error, although the other thermodynamic properties appear to agree quite well with experimental values. Experimental measurements of the self-diffusion constants of molten sodium chloride have been confined to zero pressure and little is known about th3 temperature and density dependence of the diffusion process. The reported calculations suggest that the temperature dependence of the self diffusion constant is approximately linear, but as might be expected the density dependance is complicated.However, it appears to be approximately represented by eqn (26). The results of this study indicate that the pair potential (1) is a fairly good represent- ation of the effective pair interaction in molten sodium chloride over a considerable range of temperature, and this potential could be used as a starting point for further studies. Finally the method of molecular dynamics applied to molten salts besides yielding values of the thermodynamic properties of the system and values of self diffusion constant is further capable of yielding information about both dynamic and time averaged microscopic structure of such systems. APPENDIX EFFECT OF THE SEVERE TRUNCATION OF THE EWALDSUMS The magnitude of the error in the MD data calculated on the basis of the severe trunca- tions Y = L/2 (in @I) rzLaX= 1 (in @IT) used in the present work is examined by comparisonof values for the energy, pressure and diffusion constants obtained by MD calculations TABLE7 U/kJ mol-I plkbar D+/IO-scm2s-1 ~-/10-5cm*s-1 V/cm3 T/K this work a.E s.* this work a.E.s.* this work a.E.s.* this work a.E.s.38.4 1165 -687.0 -684.1 ' 9.7 9.8 a 8.8 8.5' 39.5 1225 -682.8 -679.9' 10.5 10.8 a 9.6 9.6a 41.7 1341 -674.6 -673.6' 12.7 14.1 a 11.8 12.2a 39.1 1091 -689.7 -691.8 0.24 0.29 , 8.4 8.6b 7.7 7.7 39.1 1281 -680.5 -679.7 2.34 2.59 11.4 10.6b 10.4 9.5 47.35 1817 -645.5 -644.5 0.91 1.65 26.1 23.2 24.0 21.4b * aEs = accurate Ewald summation ; a ref.(8) ; b Gosling and Singer, unpublished data, truncations in the Ewald sums : this work : rc = L/2, niLx = 1 : a rc = L, nL = 6; b rc = L/2, nt, = 27. J. W. E. LEWIS AND K. SINGER involving a much more accurate evaluation of the electrostatic forces. Such calculations for a few V, T points for liquid NaCl have been carried by Lantelme et aL8 with the trunc- ation Y = L, niax= 6 (aL = 3.5) and with Y = L/2, n&x = 27 (aL= 5.6).25 In these computations the electrostatic forces are calculated with an accuracy of 20.3 %. The figures in table 7 show that the discrepancies are for the most part within the margin of statistical error.Only at the highest temperature is this margin exceeded for the pressure (-0.7 kbar) and for the diffusion constant (-15 %). It would appear that the error in the calculation of the electrostatic forces, even if large for single particles, has a very small effect on the calculated averages. It is not suggested, however, that this favourable situation would necessarily apply in the MD simulation of other molten salts. One of us (J. W. E. L.) is grateful to the S.R.C. for a Research Assistantship. We also thank the staff of the Atlas Computer Laboratory for a generous allocation of computer time and for assistance in running the programs on the IBM 360/195 at the Rutherford Laboratory. K. Singer and I. R. McDonald, Quart. Rev. Chem. Soc., 1970, 24, 238.I. R.McDonald and K. Singer, Ann. Rep. Chem. Soc., 1970, 45. J. A. Barker and D. Henderson, Ann. Rev. Phys. Chem., 1972, 23,439. L. V. Woodcock and K. Singer, Trans. Faraday Soc., 1971, 67, 12. D. J. Adams and I. R. McDonald, J. Phys. C, in press. J. W. E. Lewis, L. V. Woodcock and K. Singer, to be published. 6a L. V. Woodcock, Chem. Phys. Letters, 1971, 10, 257. 'A. Rahman, R. H. Fowler and A. H. Narten, J. Gem. Phys., 1972,57, 3010. 13 F. Lantelme, P. Turq, B. Quentrec and J. W. E. Lewis, to be published. A. Rahman, Phys. Rev. A, 1964, 136,405. M. P. Tosi and F. G. Fumi, J. Phys. Chem. Solids, 1964, 25, 31. J. E. Mayer, J. Chem. Phys., 1933, 1, 270. "P. P. Ewald, Ann. Phys., 1921, 21, 1087. l3 A. A. Barker, Austral.J. Phys., 1965,18,119 ; S. G. Brush, H. L. Sahlin and E. Teller, J. Chem. Phys., 1966, 45, 2102. l4 M. Dixon and M. J. Sangster, unpublished work. E. M. Gosling and K. Singer, unpublished work. l6 W. W. Wood in Physics of Simple Liquids, ed. H. N. V. Temperley, J. S. Rowlinson and G. S. Rushbrook (North Holland, Amsterdam, 1968).A. D. Kirchenbaum, J. A. Cahill, P. J. McGonigal and A. V. Grosse, J. Inorg. Nuclear Chem., 1962, 24, 1287. l8 K. K. Kelley, US.Bur. Mines Bull., 1960, 584. l9 A. S. Dworkin and M. A. Bredig, J. Phys. Chem., 1960, 64, 260. 2o J. O'M. Bockris and N. E. Richards, Proc. Roy. Soc. A, 1957, 241,44. 21 M. Blander, Adu. Chem. Phys., 1967, 11, 83. 22 L. V. Woodcock, Proc. Roy. Soc. A, 1972, 328, 83, 23 D. Levesque and L. Verlet, Phys. Rev. A, 1970, 2,2514. 24 J. O'M. Bockris, S, R. Richards and L. Nanis, J. Phys. Chem., 1965, 69, 627. 25 E. M. Gosling and K. Singer, unpublished work.

ISSN:0300-9238    

DOI:10.1039/F29757100041

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Electron Spin Resonance Study of the Freezing Properties of Water Adsorbed on r-Alumina BY LEOBURLAMACCHI Istituto di Chimica Fisica, Via G. Capponi 9, I50121 Firenze, Italy Received 6th June, 1974 The e.s.r. spectrum of the manganese(T1) ion has been investigated in bulk water and in water adsorbed on y-alumina. The high mobility of the e.s.r. detectable ions shows that the water filling large pores in y-alumina has the same viscosity as bulk water. On cooling, the viscosity of adsorbed water increases continuously even below the homogeneous nucleation temperature (-40°C),leading to the formation of an amorphous glass. There exists considerable experimental and theoretical evidence to indicate that the e.s.r. spectrum of Mn2+ ion, dissolved in small quantities in a liquid, provides valuable information about the structure and the dynamics of the liquid itself.As a particular case, if the liquid is frozen, spectral analysis allows a quite unambiguous determination of whether the liquid is frozen in an amorphous or in a polycrystalline state. In this work, the technique was used to investigate some features of water adsorbed on y-alumina. EXPERIMENTAL MATERIALS Commercially available y-alumina (Merck T) was dried at 110°Cand then mixed with a 1 x mol dnr3 solution of Mn(C10& (Alfa Inorganics) in triply distilled water. The same solution was also used for e.s.r. measurements in the bulk water. After agitation for one hour, the alumina was filtered off and then pressed on filter paper until the product appeared to be dry.The dry powder was sealed in the sample containers in order to avoid further evaporation, the water content of each sample being checked by loss-of- weight at 110°C. The surface area of the y-alumina was 105 m2g-l (B.E.T. method). E.S.R. MEA S UR EMENTS E.s.r. spectra were recorded using a Varian V-4502 X-band spectrometer equipped with a conventional variable temperature assembly. The sample tubes (Pyrex) were of 0.5 mm i.d. for the water solution and 2.5 mm id. for the y-alumina. The reversibility of the e.s.r. results (see below) was found to depend, although not very critically, on the amount of ad-sorbed water. Good results were obtained with a water content of 10-15 %. The reproduc- ibility of the results was checked on five different sample preparations.DIFFERENTIAL SCANNING CALORIMETRY (D.S.C.) A Perkin-Elmer DSC 1B differential scanning calorimeter was used. The usual volatile- sample pans were used at low temperature. In the high temperature measurements a hole was drilled in the same pans to allow evaporation of water. 54 L. BURLAMACCHI 55 THE E.S.R. LINESHAPE IN LIQUID AND SOLID ENVIRONMENTS The spectra of Mn2+ ion (3d5, S = 5/2, I = 5/2) can be explained by solving the spin Hamiltonian 2Z = gpHS+ aIS+ D[S: -(I /3)S(S+I)]+ E(Sz+S;). (11 The first two terms (Zeeman and hyperfine splitting) are practically isotropic and yield no information about the surrounding liquid. The last term (the so-called zero-field splitting, z.f.s.) is zero in perfectly cubic symmetry but increases rapidly with increasing distortion of the ligand-field symmetry.The z.f.s. term (D and E are the axial and rhombic parameters respectively) is thus extremely sensitive to the structure of the local environment. In solution, the time dependence of the z.f.s. components provides a powerful relaxation mechanism which dominates the e.s.r. linewidth.’* Around room temperature the spec- trum is averaged by fast-motion and the linewidth is given by TT1 = 32/5(A2)2, (2) where T~ is the correlation time for the modulation of the z.f.s. components, A2 = (2/3)D2+ 2E2,and the average (. . .>is over all the z.f.s.sites induced by fluctuation of the crystal-field symmetry under the action of molecular motions in the liquid. zCis generally found to be linearly dependent on y/T.’ At low temperature, if the liquid is able to form a glass, the strained nature of the glass network causes the ion to experience a distribution of crystal-fields.Thus, well-resolved features will be observed only at orientationally stationary resonance fields which are also stationary with respect to the variations of the crystal-fields parameters. Detailed analysis of the spin Hamiltonian parameters as function of D/gPH and of E/Dhas been carried out by several workers.6-10 The main features which appear in a glassy environment can be sum- marized as follows. (a)A resolved, inhomogeneously broadened sextet centred at geff= 2, assigned to almost stationary transitions between the msf$ states. Since the inhomogeneous broadening arises mainly from second order effects proportional to D’/gPH, at X-band (gPH/h= 9100 MHz) well-resolved patterns arise only from sites characterized by D/h 5 300 to 500 MHz.(b) For sites characterized by 0.2 ,< D/gPH 5 0.5, the main transitions fan out about gcff= 2. If the crystal-field distribution spans this region (D/h-2000 to -4500 MHz at X-band), broad structureless wings are expected flanking the geff= 2 =position. (c) Other transitions (ge~ 4.3 etc.) which are stationary in the sense described above, appear for D/gPH 2 0.5. Since they are not found in the spectra described below, we omit their treatment. When the liquid is allowed to crystallize either from a glassy state or from a supercooled liquid, a sudden drop of the intensity of the e.s.r.signal is normally observed, the spectrum showing broader and often unresolved patterns.”, l2 Allen l1 has described this behaviour in detail for glassy and crystallized methanol and 12 mol dm-3 HC1 solutions, while similar observations in many other solvents suggest that the finding. is quite gene~a1.I~ The spectral changes can easily be interpreted in terms of an increased amount of distortion of the solva- tion shell when the Mn2+ ion is constrained to fit into the crystalline lattice. RESULTS E.S.R. PARAMETERS The room temperature e.s.r. spectrum of apparently dry alumina prepared as described above closely resembles the well-known six-line pattern observed in bulk water solution (see fig.3, top spectrum). Careful measurements of the peak-to-peak linewidth shows an increase of 0.5 G for the adsorbed solution with respect to the bulk solution at the same temperature. Fig. 1 shows the linewidth of adsorbed and bulk solutions as a function of temperature from 20°C downward. As long as the spectrum is isotropically averaged the small line broadening observed at room temperature for the adsorbed solution persists. FREEZING OF ADSORBED WATER At temperatures below 0°C the bulk and adsorbed solution behave differently. For the bulk solution, after normal supercooling, the spectrum suddenly changes, assuming the linewidth indicated by the dotted line in fig. 1. Once the solution has crystallized, the lineshape changes reversibly with temperature. Fig.2 shows the spectral variations from -1 to -130°C. At temperatures close to the melting point the spectrum still appears homogeneously averaged as in liquid water. Goldman et a1.14 have observed similar behaviour for the peroxylamine disulphonate ion in frozen water. The most probable explanation is that the immediate environment of the ion is not ordered in the ice structure, but forms a “ liquid cage ” in which the ion is allowed to move freely. However, the mobility of the ion decreases very rapidly with decreasing temperature, as shown by the rapid increase in linewidth. In fact, the spectrum appears unresolved at -15°C while at -30°C a broad spectrum, typical of the polycrystalline environment is observed, which changes very little with further freezing down to the temperature of liquid nitrogen.I \ \ \ \ \ \ \‘, polycrystaliine \, phase I I I 1 1 I I I I -20 Q 20 40 tempera ture/”C FIG.1 .-I2.s.r. linewidth of the signal due to Mn2+ solution (1 x mol dm-3) : (A)bulk water ;(a)solution adsorbed on y-alumina ; (---) polycrystalline ice. For the adsorbed solution no sharp spectral change is observed. Fig. 3 shows the e.s.r. spectra at various temperatures from +20 to -196°C for a sample containing 13.9 % water. At temperatures below 0°C the spectrum changes progressively to- ward a “ solid type ” spectrum. From -80 to -196°C no significant changes are observed. It should be noted that the spectral changes reported in fig.3 are completely reversible with temperature, at least in the period of a few hours in which the e.s.r. experiments were carried out. L. BURLAMACCHI 2 I I I I 3 I I I l 4 I / 1 field/kG FIG.2.-E.s.r. spectra of an aqueous Mn2+ solution (1 x mol dm-3) at various temperatures ('C) in the polycrystalline phase. Different spectra have different spectrometer gain. DIFFERENTIAL SCANNING CALORIMETRY Fig. 4 shows the d.s.c. results from the sample containing 13.9 "/o water. In the low temperature range no transition is observed near 0°C. An enthalpy change is instead observed at lower temperatures, with a more pronounced peak at -40°C (decreasing temperature) whose evaluated heat of transition is 27 f3.cal (g of adsorbed water)-l, i.e.about 3 of the 79.71 cal g-l for pure water. Approximately the same enthalpy change is found upon increasing the temperature, but this is spread over a temperature range (from -35°C to OOC) and not localized at 0°C. On the other hand, the measured heat of vaporization is 470+20 cal g-1 for adsorbed water, which is about 90 % of the 539.55 cal g-1 for pure water. Additional experiments carried out with pure adsorbed water (in the absence of Mn2+ ion) gave the same results within the experimental uncertainty. DISCUSSION The close similarity of the linewidth against temperature behaviour for the bulk and adsorbed solutions shows that the ions dissolved in adsorbed water experience the same environment and the same mobility as the ions in the bulk water.Since FREEZING OF ADSORBED WATER the temperature dependence of the linewidth resides mainly in zc, we may also con-fidently state that the adsorbed solution has very nearly the same viscosity as the bulk water. This must in essence be the situation for water that fills large pores, in which most of the manganese(I1) ions are far from any interaction with the solid substrate. L I I I l I 2 3 I I I I 1 4 field/kG FIG. 3.---E.s.r. spectra of an aqueous MnZ+solution (1 x mol dm-3) adsorbed on yalumina. Temperatures in "C. Different spectra have different spectrometer gains. For the manganese(I1) ions which are adsorbed on the surface or contained in small pores, the local environment undergoes an undetermined, but certainly larger distortion from cubic symmetry. From eqn (2), we would expect a shorter relaxation time, masking the corresponding e.s.r.spectra under the narrower free-ion spectrum. It seems likely that the small line broadening discussed above, which appears in- homogeneous, is the only observable consequence of the presence of surface field effects. This point will be discussed in more detail e1~ewhere.l~ Upon freezing, the larger z.f.s. induced by the surface fields on the surface adsorbed manganese species are expected to spread the e.s.r. spectrum widely from the geff= 2 L. BURLAMACCHI absorption. The bulk-like solution in large pores should be expected to crystallize. Since water in small pores has very little probability of containing nucleating particles upon which crystallization commences, 16* supercooling down to the homogeneous nucleation temperature ( -40, -41"C), is expected for our alumina-adsorbed water.However, the e.s.r. spectra give no indication that crystallization occurs even at lower temperatures. On the contrary, several arguments suggest that the liquid freezes in an amorphous state. -40 0 40 80 120 temperature/"C FIG.4.-Typical d.s.c. diagrams for water adsorbed on y-alumina. See text for experimental details. (i) Below -40°C the spectrum is still characteristic of a liquid environment. The extrapolated viscosity at -51"C, for instance, is -40 cP.18 By analogy with the Mn2+-methanol system,lg z, at this temperature may be evaluated to be from 5 to 8 x 10-1 s, which justifies the appearance of unsymmetric broadening in the spectrum (fig.3). On the other hand, the e.s.r. spectra in bulk polycrystalline water at this temperature would correspond to the bottom spectrum in fig. 2, showing that the manganese motions are completely quenched. (ii) The complete reversibility with increasing or decreasing temperature would not be observed if irreversible crystallization occurred. (iii) The e.s.r. spectrum at the temperature of liquid nitrogen (fig. 3, bottom spectrum) is virtually identical to the e.s.r. spectrum obtained in glassy water-glycerol solution. It is characterized by a relatively narrow sextet at geff= 2 and widespread background wings.The existence of resolved hyperfine patterns together with the appearance of wings suggests a distribution of z.f.s. sites ranging from -300 to -3000 MHz. The environment seems very similar, although tending toward a somewhat larger distortion of the crystal-field symmetry, to that of Mn2+ in methanol glass (220 to 2000 MHz).", 21 It is noteworthy that J(A2) is -700 and -1000 MHz in liquid methanol and in liquid water respectively,15* l9 values which could well correspond to the average of the z.f.s. distribution found in the glassy phase. This agrees with the previous observations that, apart from a time dependent factor, the manganese(I1) ion experiences the same environment in the liquid as in the glassy phase.1° It should be recognized, however, that some contribution to the wings can arise from surface interaction.FREEZING OF ADSORBED WATER (iv) That the glassy spectrum does arise solely from surface adsorbed ions is ruled out both from quantitative considerations on the amount of crystal-field distortion (the surface sites are unlikely to give narrow geff= 2 patterns) and from additional experiments with low surface-area alumina (10-20 m2 g-I). In the latter case, in which a bulk-water phase is not expected to be present, only weak, broad patterns can be obtained both at room and at low temperature. We note incidentally that all of the above results are not confined to the samples used in this work. Similar results were also obtained with other kinds of alumina having sufficiently high surface area, and with silica gel, for which the room temper- ature spectra are greatly broadened by interaction with the solid substrate.The reproducibility of the d.s.c. results in the absence of manganese ensures that the solute is not responsible for preventing nucleation. The low temperature trans- itions are possibly associated with the crystallization of that part of water (e.g. surface layers) which gives undetectable e.s.r. spectra. Woessner,22 however, has found from n.m.r. relaxation measurements, that surface water has a high mobility even at very low temperature with no apparent discontinuities during cooling, a result which parallels our findings. It must also be noted that if the water in a discrete number of pores crystallizes ( 520, 30 %), the corresponding e.s.r.spectrum is expected to be hidden under the better resolved glassy spectrum. The small enthalpy change in the low temperature d.s.c. transitions is in agreement with this suggestion. CONCLUSIONS The existence of amorphous ice in the system described seems somewhat surprising. Amorphous ice has previously been obtained by condensation of water vapour at very low temperature^.^^-^^ However, when heated to -120°Cit crystallizes with an enthalpy change of the order of the heat of solidification of water at its normal melting point. As yet, amorphous ice has not been obtained by normal supercooling of water. Since the e.s.r. information is indirectly derived from an electronic spin system which sees an ionic environment which is greatly modified by the presence of the charged ion itself, it does not seem worthwhile making any correlation with other studies carried out on adsorbed water.26 Also, the probable existence of a glass transition at -130°Ccannot be identified by e.s.r.spectral changes, since any molec- ular motion in the system is certainly quenced at this temperature on the e.s.r. time scale. No detailed explanation for the inhibition of ice nucleation in adsorbed water is known. Financial support was provided by the Italian National Council of Research (C.N.R.). It is a pleasure to acknowledge the assistance of Prof. G. Guarini with the d.s.c. measurements. A. Abragam and M. H. L. Pryce, Proc. Roy. SOC.A, 1951,205, 135.B. R. McGarvey, J. Phys. Chem., 1957, 61, 1232. N. Bloembergen and L. 0. Morgan, J. Chem. Phys., 1961, 34, 842. A. Hudson and G. R. Luckhurst, Mol. Phys., 1969, 16, 395. G. Martini, M. Romanelli and L. Burlamacchi, Molecular Motions in Liquids., ed. J. Lasconibe (Reidel, Dordrecht, 1974), p. 371 T. Castner, G. S. Newell, W. C. Holton and C.P. Slichter, J. Chem. Phys., 1960, 32,668. D. L. Griscom and R. E. Griscom, J. Chem. Phys., 1967, 47, 2711. P. C.Taylor and P. J. Bray, J. Phys. Chem. Solids, 1972, 33, 33. R. D. Dowsing and J. F. Gibson, J. Chem. Phys., 1969, 50, 294. lo L. Burlamacchi and M. Romanelli, J. Chem. Phys., 1973, 58, 3609. l1 B. T. Allen, J. Chem. Phys., 1965, 43, 3820. L. BURLAMACCHI l2 F. G.Wakim and A.W. Nolle, J. Chem. Phys., 1962, 37,3000. l3 unpublished results from this laboratory. l4 S. A. Goldman, G. V. Bruno, C. F. Polnaszek and J. H. Freed, J. Chem. Phys., 1972, 56, 716. l5 L. Burlamacchi, to be published. l6 D. H. Rasmussen and A. P. MacKenzie, Water Structure and Water-Polymer Interface, ed. H. H. G. Jellinek (Plenum, New York, p. 126. l7 B. J. Mason, Ado. Phys., 1958, 7, 221. l8 H. R. Pruppacher, J. Chem. Phys., 1972, 56, 101. l9 L. Burlamacchi, J. Chem. Phys., 1971, 55, 1205. 2o F. D. Tsay, S. L. Manatt and S. I. Chan, Chem. Phys. Letters, 1972, 17, 223. 21 I,. Burlamacchi and M. Romanelli, Chem. Phys. Letters, 1973, 23,497. 22D.E. Woessner, J. Chem. Phys., 1963, 39, 2783. 23 E. F. Burton and W. F. Oliver, Proc. Roy. SOC.A, 1936, 153, 166. 24 J. A. Pryde and G. 0. Jones, Nature, 1952, 170, 685. 25 J. A. Ghormly, J. Chem. Phys., 1956, 25, 599; 1968,48, 503. 26 see H. A. Resing, Adc. Mol. Relaxation, 1967, 1, 109.

ISSN:0300-9238    

DOI:10.1039/F29757100054

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Low-lying Electronic States of HCN+ and the Interpretation of the Photoelectron Spectrum of HCN BYS. P. Sot AND W. GRAHAMRICHARDS* Physical Chemistry Laboratory, South Parks Road, Oxford OX1 342 Received 6th June, 1974 The ground and the first excited states of the hydrogen cyanide cation have been calculated using the matrix Hartree-Fock approximation. The inclusion of the estimated correlation energy difference between these states yields a term value of the excited state in very good agreement with experiment. An account is given for the fact that HCN+ and N: are isoelectronic but have their first two low-lying electronic states in reversed order. Hydrogen cyanide (HCN) is the model compound for organic nitriles (alkyl cyanides). Its photoelectron spectrum has been studied several times.lm3 Neverthe-less, the interpretation of this spectrum, unlike that of methyl cyanide, still retains some doubtful features for the photoelectron spectroscopist. Recently, Frost et aL4 re-analysed the photoelectron spectrum of HCN, comparing it with that of methiophosphide (HCP). They assigned the bands at 13.61 and 14.00 eV to be its X211 and its A2X+ ionic states, respectively. Theoretically, HCN+ is interesting in that it is isoelectronic with the nitrogen molecule ion Nl. The ground and the first excited states of Nl have been found experimentally to be X2Zi and A211,, respectively, separated by 1.16 eV. However, Hartree-Fock calculations for these states using closed-shell N, molecular orbitals and open-shell procedures both predict that the A211, state lies below the X2X: state.It is only when correlation energy correction is taken into account that the ordering of these states is predicted correctly.s This may also be the case for the isoelectronic HCN+ species. The present work is a theoretical study of the first photoelectron band of HCN. It also attempts to clarify whether the ground state of HCN+ is of the same orbital symmetry as that of Nl. HARTREE-FOCK CALCULATIONS The HCN molecule, its ground state in particular, has been the subject of quite a few theoretical studies of different sophistication.6 Ab initio calculations on the ground state of HCN which give energies closest to the Hartree-Fock limit are those reported by McLean and Yo~himine.~ They used a double-zeta and a best-atom basis set both augmented by a 2p and a 3d polarization function for H, and by a 3d and a 4f polarization function for C and N (DZ+P, and BA+P basis sets).The total energies obtained at the experimental equilibrium internuclear distances are -92.908 684 and -92.914 663 a.u., respectively. According to Pan and Allen,9 the latter lies only about 0.3 eV above the Hartree-Fock limit. t on leave from the Department of Chemistry, Chung Chi College, The Chinese University of Hong Kong. 62 S. P. SO AND W. G. RICHARDS It was found in this work that the computer time for a calculation with the BAsP basis set is about twice that with the DZ +P basis set. Furthermore, it is expected that the difference between the energy differences of two states obtained with these two basis sets will be much smaller than that between the energies of the same state. The DZ +P basis set of McLean and Yoshimine was therefore used for the calculations of the low-lying states of HCNf.This set together with the exponents is reproduced in table 1. TABLE1.-ST0 BASIS FUNCTIONS function type exponent atom function type exponent atom 1 1sa 0.971 55 H 16 2sa 2.221 57 N 2 1so 1.232 06 H 17 2PO 1.505 86 N 3 2PO 1.375 68 H 18 2PO 3.267 41 N 4 3da 1.700 00 H 19 3da 2,003 87 N 5 lsa 5.230 90 C 20 2.700 00 N 6 1so 7.968 97 C 21 0.790 06 H 7 2sa 1.167 82 C 22 2.200 00 H 8 2sa 1.820 31 C 23 1.255 72 C 9 2PO 1.255 72 C 24 2.726 25 C 10 2PO 2.726 25 C 25 2.272 22 C 11 3do 2.279 93 C 26 2.244 32 C 12 4fa 1.692 14 C 27 1.505 85 N 13 1so- 6.118 63 N 28 3.267 41 N 14 lsa 8.938 43 N 29 2.187 31 N 15 2sa 1.393 27 N 30 2.534 88 N The two states of HCN+ studied are : 1a22a23024a25a21n3 X211 1a22023024a25a11n4 A2Z+.For each state, wavefunctions and potential energies were computed, using the ALCHEMY package of programs log for various lengths of one of the bonds while keeping the other, in turn, at the experimental value of the HCN molecule. Spectroscopic constants were determined by the method of Todd and Richards. CORRELATION ENERGY ESTIMATION The method of Liu and Verhaegen 139 l4 was used to estimate the correlation energy difference of the two states.Briefly, the molecular wavefunction of an elec- tronic state is decomposed into its atomic correspondents by a Mulliken population ana1y~is.l~ The state or composite of states of each of these atomic correspondents has to be worked out and its correlation energy determined. The molecular correla- tion energy is given by the sum of the correlation energies of these atomic states. This method has been used by Liu and Verhaegen l4 to estimate correlation energies 9 correct to 0.01 eV for light molecular species such as CH, NH, NHf, OH, OH+, and, therefore, presumably should be more than satisfactory for the purpose of the present work. The correlation energies of most of the atomic states of the H, C,and N atoms and ions studied here have been tabulated in the literature.16'18 However, for some atomic states, extrapolations to the appropriate 2 (nuclear charge) values have to be made from data for some isoelectronic systems having the same electronic con- figurations but different 2 values.ELECTRONIC STATES OF HCNf RESULTS AND DISCUSSION For the X211state, the C-H and the C-N bond lengths of HCN+ were calculated to be 1.0812 and 1.1843 A, and their stretching frequencies to be at 3218.5 and 21 55.3 cm-l, respectively. These frequencies are somewhat higher, as expected in Hartree-Fock calculations, than the observed values of 3070 and 1840 cm-l. It is interesting to note that Franck-Condon calculations on the first photoelectron band of HCN give the bond lengths of HCN+ in the X211 state very close to the ones obtained in this work (table 2), although they usually involve relatively large un- certainties in the estimation of intensities.For the A2E+ state, however, convergence could not be obtained for some bond lengths. Unfortunately, not enough points on the potential energy curves have been obtained, and hence the bond lengths and the stretching frequencies of HCN+ in this state cannot be determined. TABLE2.-MOLECULAR PARAMETERS OF HCN(XIE+)AND HCNf(X2n) expt . calc. HCN HCN+ HCN HCN+ rc€I/B' 1.0659 a 1.09 1.0583 1 .0812 f VCN/Crn--lrCN/A 1.1531 3311.47 1.21 3070 1.1523 - 1.1843f 3218.5f VCN/Crn--l 2096.7 1840 - 2155.3 f a ref. (8) ; b ref.(21) ; C ref. (3) ; dref. (4) ; e ref. (9) ;f this work. The calculated X211 state bond lengths of HCN+ are very similar to the experi- mental ground state ones of HCN (table 2). In addition, these two geometries yield X211 state energies very near to each other : -92.460 238 and -92.457 860 a.u. Similar situations may be anticipated for the A2Z+state since it arises from removing one of the lone-pair electrons from the parent l9 In fact, the A2E+ state geometry of HCN+ should be closer to the ground state structure of HCN than to the X211ionic state structure. This is borne out by calculations : the latter gives the A2X+ state energy 0.22 eV higher. As a consequence, results discussed below are based on calculations using the experimental ground state molecular structure of HCN for the two ionic states.In the photoelectron spectrum of HCN the vertical and adiabatic ionization potentials coincide, for the first two bands, and hence it is reasonable to use the same geometries for the X211 and A2E+ states of HCNf. TABLE3.-RELATIVE TERM VALUES (ev) OF THE X2n AND THE A2X+STATES OF HCN+ X*II A2Zf method 0 0.85 HF calculation 0 0.49 corrected for difference in correlation energy 0 0.39 p.e. spectrum The X2Xi state of Ni has been observed to lie 1.16 eV below the A2nUstate. However, Hartree-Fock approximations to various degrees of accuracy all give the A211, state 0.65-0.85 eV lower in energy. However, exact agreement with experiment was obtained when correlation energies were included.S. P. SO AND W. G. RICHARDS The present calculations on HCNf result in the A2C+state lying 0.85 eV above the X2H state. Theii relative correlation energy has been estimated to be -0.36 eV. Inclusion of this, therefore, only gives a better agreement with the experimental result of Frost et aL4 (table 3), but, unlike in the case of NZ, does not reverse the ordering of these states. It is noted that the Hartree-Fock energy differences of the two ionic states of N2+ and HCN+ are similar. Yet, the latter species has a much smaller relative correlation energy for these states. An explanation has now to be sought. In N;, the correlation energies are contributed by two sources : (1) the atomic pair correlation energy difference between a 2p-2p and a 3s-3s pair correlation of the A2H, and the X2El states, respectively, which amounts to +0.60 eV ; (2) near-degeneracy effect due to the near degeneracy of the lowest unoccupied ln, MO and the highest occupied lnuMO, inclusion of which alone places the A2H, state 0.58 eV above the X2Cl state.To compare the first effect between HCN+ and NZ, it is simplest to compare each state of HCN+ with the ground state of its parent molecule HCN : la22a23a24a25a2ln4 XIC+(HCN). As may be seen from the three configurations, HCN2(X2n) loses a 17t-l7-c molecular pair correlation energy and the excited A2C+state a 5a-5g pair effect with respect to the closed-shell HCN(XIC+). Electron populations of the constituent AOs of the 50 and the In MOs given by Mulliken's population analysis are shown in table 4.The relative correlation energy of these states is almost entirely due to the differences in electron populations of the 2s and the 2p AOs of the carbon and nitrogen atoms. TABLE4.-oRBITAL ELECTRON POPULATIONS OF HCN' (x2n,AzC+)RELATIVE TO HCN(XIC+) state MO 1SH 2PH 2sc 2PC 2SN 2PN x2n ln -0.04 -0.55 -0.42 A2E+ 50 -0.03 0.00 -0.02 -0.10 -0.32 -0.53 The atomic 1s-1 s and 2p-2p pair correlation energies are practically independent of nuclear charge and equal to -0.0437 and -0.063 a.u. respectively.20 The atomic 2s-2s pair correlation energy, however, increases linearly with increasing 2values, and can be obtained by subtracting energies computed for an atom having the 2 value under consideration.The difference in correlation energy of the atom with three electrons in a 2Sstate and the same atom with two electrons in a lS state in the 2s-core correlation energy. Subtraction of twice this number from the four-electron S state correlation energy gives an estimate of the 2s-2s pair correlation energy.16 In this way, the atomic 2s-2s pair correlation energy of nitrogen is estimated to be ( -0.096) -2( -0.005) = -0.086 a.u. If the loss of atomic pair correlation energy is assumed to be directly proportional to the removal of electron density from the particular A0 in question, then the relative correlation energy of the two states of HCN+ is estimated to be -0.18 eV.This value is half of the total estimated by the method of Liu and Verhaegen (where the near-degeneracy effects in various atomic states have been taken into account), but only about one-third of the atomic pair-correlation energy of N;. Results of this work show that the lowest unoccupied 2n MO is about 19.7 eV above the highest occupied In MO for both states of HCNf. This certainly implies that molecular near-degeneracy effect is unimportant in this ion. 11-3 ELECTRONIC STATES OF HCNt CONCLUSION Calculating ground and excited states of molecular species by treating each level as a separate matrix Hartree-Fock problem and then estimating the correlation energy difference is a workable scheme in the study of electronic structures. The agreement between the observed and the calculated quantities in the case of HCN+ is sufficiently good to lend confidence to the method, and support the interpretation of the first photoelectron band of HCN proposed by Frost et aL4 HCNf and Nf are isoelectronic.Hartree-Fock approximations give their ground states both to be of IIsymmetry, and similar relative term values for their first C states. However, in Ni, the large correlation energy differences of these states, particularly the molecular near-degeneracy effect which is unimportant in HCN+, reverses their ordering. The authors thank the S.R.C. for a grant of computer time and NATO for a research grant. S.P.S. acknowledges the Chinese University of Hong Kong for a fellowship and the Commonwealth University Interchange Committee, British Coun- cil, for a travel grant.The authors also thank Dr. D. W. Turner, for helpful discus- sions. D. W. Turner and C. Baker, Proc. Roy. SOC. A, 1969, 308, 19. D. W. Turner, C.Baker, A. D. Baker and C. R. Brundle, Molecular Photoelectron Spectroscopy (Wiley, New York, 1970). J. M. Hollas and T. A. Sutherley, Mol. Phys., 1972, 24, 1123. D. C. Frost, S. T. Lee and C. A. McDowell, Chem. Phys. Letters, 1973, 23,472. G. Verhaegen, W. G. Richards and C. M. Moser, J. Chem. Phys., 1967, 47, 2595 ; and ref- erences cited therein. W. G. Richards, T. E. H. Walker, L. Farnell and P. R. Scott, Bibliography of ab initio Molecular Wave Functions (Supplement for 1970-1973) (Clarendon Press, Oxford, 1974). A.D. McLean and M. Yoshimine, I.B.M. J. Res. Dev., 1968, 12, 206. D. H. Rank, G. Shorinko, D. P. Eastman and T. A. Wiggins, J. Opt. SOC. Ainer., 1960,50,421. D. C. Pan and L. C. Allen, J. Chem. Phys., 1967, 46, 1797. lo P. S. Bagus, ALCHEMY studies of small molecules, Proc. Seminar Selected Topics in Molecular Physics, Ludwigsburg (I.B.M., Germany), 1971. l1 A. D. McLean, Proc. Conf. Potential Energy Surfaces in Chemistry RA18, Librarian I.B.M. Research Lab., San Joe, Calif. 1971. l2 J. A. C. Todd, B.A. Thesis (Oxford, 1967). l3 H. P, D. Liu and G. Verhaegen, J. Chem. Phys., 1970, 53,735. l4 H. P. D. Liu and G. Verhaegen, Int. J. Quantum Chem., 1971, S5, 103. l5 R. S. Mulliken, J. Chem. Phys., 1955, 23, 1833, 1841. l6 E. Clementi, J. Chem. Phys., 1963, 39, 175. l7 G. Verhaegen and C. M. Moser, J. Phys. B: Atom. Mol. Phys., 1970, 3, 478. l8 J. P. Desclaux, C. M. Moser and G. Verhaegen, J. Phys. B: Atom. Mol. Phys., 1971, 4, 296. l9 J. B. Roberts, H. Marsmann, I. Absar and J. R. van Wazer, J. Amer. Chem. SOC., 1971,93,3320. 2o L. C. Allen, E. Clementi and H. M. Gladney, Rev. Mod. Phys., 1963, 35,465. 21 G. Herzberg, Electronic Spectra and Electronic Structure of Polyatomic Molecules (Van Nostrand, New York, 1966).

ISSN:0300-9238    

DOI:10.1039/F29757100062

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Microwave Absorption and Dielectric Relaxation of 1,2-Dihalogenoethanesin Dilute Solutions BY M. P. MADAN Department of Physics, University of Prince Edward Island, Charlottetown, Canada Received 24th June, 1974 The dielectric relaxation of lY2-dichloroethane and 1,2-dibromoethane in dilute solution in cyclo- hexane, carbon tetrachloride and benzene has been studied in the microwave region over a range of temperatures. The relaxation tinie data at different temperatures have been used to estimate the free energy, enthalpy and entropy of activation for the relaxation mechanism. Indications of a stroEg molecular interaction in benzene solution, consistent with Higasi’s observations, were found for both 1,Zdichloroethane and 1,2-dibroiiioethane. These halogenoethanes show a much weaker interaction in carbon tetrachloride.The results obtained are discussed and, where possible, compared with other determinations. The molecular behaviour of 1,2-dihalogenoethanes is of considerable interest. 1-3 Bock and Tomchuk measured the spin-lattice relaxation times of 1,2-dichloroethane in different nonmagnetic solvents at 20°C and estimated the intramolecular relaxation rates for comparison with those derived from dielectric data.3 Their results from n.m.r. studies did agree with the dielectric relaxation time in benzene solution but not in carbon tetrachloride solution. There is relatively little information about the relaxation behaviour of 1 ,2-dihalogenoethanes in dilute solution in carbon tetra- chloride other than that of Chitoku and Higasi at a temperature of 20°C.Even in other solvents the investigations are usually only at one temperature or at most at two temperatures. The relaxation time, z, and its temperature dependence provide useful information about the interaction energy and the behaviour of the solute molecule, and are considered to be a sensitive means of investigating molecular intera~tion.~’ In the present paper, we report the relaxation times of 1,2-dihalo-ti genoethanes in dilute solution in cyclohexane, carbon tetrachloride and benzene over a range of temperatures ; the corresponding thermodynamic parameters, free energy, enthalpy and entropy of activation, are evaluated by considering relaxation as a rate process.EXPERIMENTAL The permittivity E’ and the dielectric loss factor E” at different temperatures were deter- mined in the 3-cm microwave region by the method of Roberts and von Hippel ’employing a shorting cell, details of which have been described previously.8 The maximum possible errors in E’ and E” were estimated at 1 % and & 5 % respectively. The relaxation time was determined using the concentration variation method of Kri~hna.~ Several solutions, in general five for each system, of Concentrations varying from about 0.008 to 0.06 weight fraction for 1,2-dichloroethane and of somewhat higher concentrations for 1,2-dibromoethane were used. The estimated possible error in the relaxation time zis 10 %. All chemicals were obtained from Fisher Scientific Company in as pure a form as possible.They were further purified by fractional distillation and then used immediately. The data were pro- cessed with the aid of PDP-11 computer. 67 68 MICROWAVE ABSORPTION RESULTS AND DISCUSSION The values of the relaxation time, z, in dilute solution, where the solute-solute interactions are greatly reduced, are presented in table 1 for several temperatures. The relaxation times for 1,2-dibromoethane in each solvent are greater than those for 1,2-dichloroethane. This is consistent with the n.m.r. measurements on the tri- halogenomethanes and with the observation that the bromoethanes interact more strongly than the corresponding chloro-compounds. Forest and Smyth O point out that the longer relaxation time for the bromo-compounds is probably due to the greater internal friction coefficient arising from the higher polarizability and size of the bromine atoms. TABLE1 .-RELAXATION TIMES OF 1,ZDICHLOROETHANE AND 1,2-DIBROMOETHANE IN SOLUTIONS AT DIFFERENT TEMPERATURES (Zips) temperature/"C solvent -10 0 10 20 30 40 50 1 ,2-dichloroethane cyclohexane 2.8 2.2 2.1 a 2.0 1.7 2.16 carbon tetrachloride 3.6 3.0 2.8 2.4 2.2 1.9 1.7 2.15 benzene 4.6 3.9 3.3 2.6 2.4 3.69 1,2-dibrornoethane cyclohexane carbon tetrachloride 3.1 3.3 2.6 2.9 2.2 2.4 1.8 2.2 2.1 benzene 5.9 5.1 4.1 3.4 2.9 aref.(6); bref. (3). The value of z in carbon tetrachloride as compared with that obtained in cyclo- hexane or benzene, indicates that the viscosity effects alone do not account for the relaxation behaviour. The viscosity, for example, of carbon tetrachloride is greater than that of benzene, but z is longer in the latter.The value of z obtained for 1,2-dichloroethane in cyclohexane at 20°C compares well with that obtained by Chitoku and Higa~i.~ The much greater value obtained in benzene is also similar to the one obtained by them. However, our z values in carbon tetrachloride at all temperatures are slightly greater than those in cyclohexane, whereas Chitoku and Higasi find that the relaxation time in carbon tetrachloride at 20°C is about the same as that in cyclohexane. Bock and Tomchuk report a n.m.r. reorientation time of 5.74 ps in carbon tetrachloride solution, which is even higher than the relaxation time in benzene.Our results do not indicate as great an interaction as predicted by Bock and Tomchuk. The intramolecular nuclear magnetic relaxation mechanisms, which of course are different from the dielectric mechanisms, perhaps, include other contributions as well. For the dielectric relaxation process, the ratios z,/zcYcrepresenting the degree of interaction with a particular solvent relative to the inert solvent cyclohexane for benzene and carbon tetrachloride at 20°C are 1.77 and 1-09respectively for 1,2-dichloroethane and 1.96 and 1.12 respectively for 1,2-dibromo- ethane. The corresponding ratios for 1,2-dichloroethane computed from the results M. P. MADAN of Chitoku and Higasi are 1.71 and 1.00 respectively. Chitoku and Higasi and Higasi et aL2 consider both cyclohexane and carbon tetrachloride as inert solvents.However, the results of their investigation of the solute-solvent effect in a few systems as well as the n.m.r. chemical shift measurements of McClellan and Nicksic l1 show that the behaviour of carbon tetrachloride is different from that of cyclohexane. Weak bonding between the chlorine atoms of the carbon tetrachloride and the protons of the halogenoethane molecules may occur, and therefore the possibility of some interaction with a solute should not be ignored. The results obtained by us for both 1 ,Zdichloroethane and 1 ,Zdibromoethane do suggest a trend for a weak interaction over the range of temperatures, but as the differences are small and are comparable with the error limits, they may not be significant.TABLE2.-THERMODYNAMIC PARAMETERS AND DIFFERENCES IN FREE ENERGY OF ACTIVATION (AAG *) FOR IY2-DICHLOROETHANEAND IY2-DIBROMOETHANE AS* 1 AG*I* AAG*I AAG+Ik?EoT'l J K-I mol-1 kJ mol-1 kJ mol-1 a kJ mol-i 1,2-dichloroethane pure liquid 8.8 -1.7 9.3 2.9 - in cyclohexane 9.3 9.7 6.4 6.3 - 2.9 in carbon tetrachloride 6.2 -1.3 6.6 0.2 2.7 6.3 in benzene 10.5 9.5 7.7 1.3 1.6 7.6 1,Zdibromoethane pure liquid in cyclohexane in carbon tetrachloride 16.9 10.8 6.5 18.4 13.8 -1.5 11.4 6.8 7.0 4.6 -0.2 -4.6 4.4 in benzene 11.4 10.5 8.3 1.5 3.1 * At 20°C except for pure liquid at 25°C ; * with respect to cyclohexane; b with respect to pure liquid ; C ref.(13) ; dref. (3). It is seen from table 1 that the relaxation time shows the expected decrease with temperature. When ln(zT) values are plotted against I /Tfor different systems, a good linear relationship, within the limits of experimental error, is observed. This be- haviour of the relaxation process can be represented by the rate equation of transition state theory.12 Accordingly, the free energy of activation AG*, the enthalpy of activation AH* and the entropy of activation AS*, evaluated in the usual manner are given in table 2. Also included in this table are the AG* values calculated using the single temperature data of others. For pure ethylene chloride and ethylene bromide, Branin and Smyth l3 report AH* as 8.8 and 16.9 kJ mol-l respectively which in turn gives AS* as -1.7 and 18.4 J K-l mol-' respectively using the AG* values at 25°C listed by them.In solution, we find that there is a close similarity between the AH * values for the two halogenoethanes with slightly increased values for the 1 ,Zdibromoethane solutions. This expected increase of AH* with increased molecular size is consistent with the trend noticed in pure liquids. The values of entropy of activation, AS*, in general, are positive with the exception of both 1,2- dichloroethane and 1,2-dibrornoethane in carbon tetrachloride solutions which show a negative AS* value. The value for 1,2-dichloroethane is similar to that found for the pure liquid.The explanation of such negative values has been given by Branin MICROWAVE ABSORPTION and Smyth.13 The results of Crossley and Walker for p-xylene along with the present results indicate that the free energy of activation is in the order p-xylene > benzene > carbon tetrachloride > cyclohexane, a trend exhibited by their relaxation times as well. The free energy of activation differences, AAG*, for molecular reorientation in different solvents compared with cyclohexane, considered to be an inert solvent, point to a specific solute-solvent interaction. These differences between benzene and cyclohexane and carbon tetrachloride and cyclohexane are about 1.3 and 0.2 kJ mol-I respectively for 1,Zdichloroethane and 1.5 and 0.2 kJ mol-1 respectively for 172-dibromoethane.The value of AAG* between benzene and cyclohexane for 1 ,Zdichloroethane compares well with the value obtained by Crossley and Smyth.6 The free energy of activation difference relative to the pure liquid is also shown in the last column of table 2. Sobhanadri l4 tried to estimate the dipole- dipole interaction energy from an equation similar to the rate process equation *, l2 but found poor agreement with the interaction energy values from the polarization measurements. The failure of such an approach has been discussed by Higasi who, nevertheless, holds the view that it certainly points to an interesting relationship between the barrier heights from relaxation processes and the actual height. Too little is known in this area at the present time to draw conclusions from the AAG* values for the liquid-solution systems regarding the effect of solvent on the barrier height.Higasi et aL2 concluded from their investigation of the solute-solvent interaction in a number of systems that 1,2-dichloroethane forms a loosly bound 1 : 1 complex with aromatic hydrocarbons.The highly polar gauche-isomers interact with aromatic molecules gaining extra stability ; this results in an increase in the dipole moment and the relaxation time. Our z values, as well as the values of AAG* for 1,2-dichloro- ethane are in broad agreement with these conclusions. Furthermore, the results for 1,2 dibromoethane confirm the view that this so-called benzene effect should be found for any polar molecule having a similar molecular conformation.The author thanks Messrs. David Hambly and Peter Chan for assistance in the experimental measurements, Professor G. W. Farnell of McGill University for help in the construction of liquid cells and Dr. J. Regis Duffy for his interest. The author expresses his appreciation to the National Research Council of Canada and the University Senate Research Committee for their support. A. Piekara and A. Chelkowski, J. Chem. Phys., 1956,25, 794. K. Higasi, H. Takahashi, K. Chitoku and A. Morita, Memoirs of the School of Science and Engineering, Waseda University, 1971, 35,75. K. Chitoku and K. Higasi, Bull. Chem. SOC.Japan, 1967, 40, 773. E. Bock and E. Tomchuk, Canad. J. Chem., 1969, 47,4635. J. Crossley and S. Walker, J. Chem. Phys., 1968, 48, 4742 ; 1966, 45, 4733. J. Crossley and C. P. Smyth, J. Amer. Chem. SOC.,1969, 91, 2482. S. Roberts and A. von Hippel, J. Appl. Phys., 1946, 17, 610. M. P. Madan, Canad. J. Phys., 1973, 51, 1815. K. V. G. Krishna, Trans. Favaday SOC.,1957, 53,767. lo E. Forest and C. P. Smyth, J. Chem. Phys., 1965, 69, 1302. 11 A. L. McClellan and S. W. Nicksic, J.Phys. Chem., 1965, 69, 446. l2 S. Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941). l3 F. H. Branin, Jr. and C. P. Smyth, J. Chem. Phys., 1952, 20, 1121. l4 J. Sobhanadri, Trans. Faraday SOC.,1960, 56, 965. l5 K. Higasi, Monograph Res. Inst. Appl. Elect., Hokkaido University, 1961, No. 9.

ISSN:0300-9238    

DOI:10.1039/F29757100067

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Investigation of the Inter-molecular Dynamics of Non-dipolar Molecules using the Rotational Velocity Correlation Function BY MYRONEVANS? Edward Davies Chemical Laboratories, Aberystwyth SY23 1NE Receiued 8th March, 1974 The rotational velocity correlation function is used to assess the Colpa-Ketelaar and Litovitz models of the intermolecular motions of compressed gaseous and liquid non-dipolar molecules which give rise to their broad band absorptions in the far infra-red (2-200cm-l). The simple Colpa- Ketelaar bimolecular collision model is found to be satisfactory only in the case of Nz(g). The Litovitz model of the liquid state, although approximate in derivation, is rather more successful, but does not show the very short time (ca. 0.1-0.5 ps) oscillations observed in the experimental functions up to 2.0 ps.The far infra-red (2-200 cm-l) absorptions of non-dipolar molecules in the compressed gaseous and liquid states have recently been the subject of much experi- mental study.’-’ The origin of the absorptions has been uniformly attributed to multibody molecular interactions of a complex nature. Despite this, a much used equation in the description of these spectra is that derived by Colpa and Ketelaar for quadrupolar induced dipole absorptions during bimolecular collisions of linear molecules, which they used successfully with hydrogen. One of the objectives of this work is to mould the original equation into a form suitable for direct comparisoii in the relevant time interval of 0-2 ps with a function derived from the experimental data which reflects the evolution with time of the molecular dynamics giving rise to the infra-red absorption. The function used is that which Brot calls the rotational velocity correlation function (RVCF), this being the negative of the second derivative of the usual vectorial correlation function.This has the advantage of detailing the short time behaviour associated with these far infra-red bands, which superficially resemble those of dipolar molecules in the same range. Rotational velocity correlation functions are derived by Fourier transforming : (i) experimental results on the far infra-red absorption a(?), the power coefficient per unit length (neper cm-l) of Lambert’s law, V being the wavenumber (cm-l) ; (ii) a(V) from the theory of Colpa and Ketelaar ; (iii) ct(V) from the theory of Litovitz et al.These values of ~(7)are all transformed in the same way so that this particular Fourier transform of the measured absorption spectra can be lucidly compared with these proposed theoretical shapes. The comparison is made for the linear molecules : N,, O,, CO,, (CN), and CS2, and the discrepancies in the use of the Colpa-Ketelaar equation with molecules other than H2 or N2 are discussed. -i-present address : Physical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ. 71 INTER-MOLECULAR DYNAMICS OF NON-DIPOLAR MOLECULES RESULTS AND DISCUSSION The Fourier transformation (i) is carried out on the experimentally avail- able 6*7*l3 data by means of the equation :49 R;&) = (d(0) * li(t)) 3h?c3n(7)a(i9cos (272Vct) di 4n2(1-exp(-hik/kT))=s-derived from the very well-known Gordon relation^.^^ lo In eqn (l), u is the vector along the linear molecular axis. n(7) is the frequency dependent refractive index, c the velocity of light, T the absolute temperature.Here, (ri(O)4(t)) is related to the angular velocity of the molecule by Anderson’s expression : (ir(O).ri(t)}~~(sine(0)sin e(t)&O)B(t)} (2) where O(O), O(t) are the angles between the axis of the molecule and the direction of the incident electric field at times 0 and t respectively. In the lirnit of small diffusive steps : {h(0)4(t)}cc (&O) *e(t)). (3) The computation of (1) was carried out over real (positive) frequencies using an algorithm which evaluated the integral numerically using Simpson’s rule.Two possible sources of distortion in the final correlation functions are those arising from the truncation of the integral limits from (-co,a)to (0, Yg(a = 0)) ; and from the interval A? at which values of a(?) were taken along the experimental curve. The effects of these modifications are discussed in the appendix. It is shown there that the method of computation should produce no distortion in the rotational velocity correlation function provided that : (i) the experimental spectrum is truncated only when a(?)+O on the high frequency side; (ii) the sampling interval AT is chosen sufficiently small that RExp(t)= 0 for t > 1/(2ATc).timelps Fro. ’I.-Plots of: --, experimental RVCF for nitrogen gas at 300 K ; ---, eqn (10). M. EVANS The greatest sampling interval chosen was that of 5 cm-l for N2 and 02,so that in these cases the condition that R;,,(t) = 0 for t > 3 ps must be complied with to prevent aliasing of the correlation function. It can be seen from fig. 1-4 that R&,(t) is damped out at ~0.7ps in these cases. For (CN),, CS2 and C02,AV = 2 cm-l, so that the upper limit is 8 ps. It is emphasized that the experimental functions (fig. 1-8) can only be as accurate and reliable as the original experimental data, which are sometimes uncertain to the extent of +lo %, especially on the low frequency (long time) side. The latter point is one reason why the rotational velocity correlation function is preferred to the vectorial one for far infra-red data.In the original data for cyanogen (I), an extrapolation on the high frequency side to avoid the quartz I L I I 0.5-L 1 !I n I I!O 115 2.0 \. I tinielps FIG.2.-Plots of: -, experimental l3 RVCF for nitrogen liquid at 76.4 K ; ---, eqn (10) with B = 1.993 cm-l; . . . . ., eqn (11). 0.5 h 0, h r I h I10 1.5 2.0 -1.01 time/ps FIG.3.-Plots of: -, experimental RVCF for oxygen gas at 300 K; ---, eqn (10) with B = 1.4345cm-'. 74 INTER-MOLECULAR DYNAMICS OF NON-DIPOLAR MOLECULES absorption has been made. However, it is improbable that the pronounced oscilla- tion in the corresponding R&,(t) (fig.7) is due to the uncertainties in this extrapolation, since the former also occurs in the compressed gaseous function (fig.6), where no extrapolation of the original data was necessary, the absorption being over by v = 100cm-l. time/ps FIG.4.-Plots of: -, experimental l3 RVCF for oxygen liquid at 88.1 K ; ---, eqn (10) ; . . . . ., eqn (11). 1.0-0.5-n0 g 0.0-n*W < -0.5--1.0-time/ps F~G.5.-Plots of: -, experimental 'RVCF for CO,(g) at 273 K ; . . . ., experimental 'RVCF for C02(1) at 273 K ; ---, eqn (10) with B = 0.393 cm-I ; -* -. -, eqn (11). MODEL TRANSFORMS (1) Following Baise,12 an expression for (ii(O)4(t)) can be obtained from the Colpa-Ketelaar treatment of non-dipolar linear molecules undergoing collision with resulting quadrupole induced dipolar far inf'ra-red absorption, by using the eqn (4), M.EVANS (5), and (6) below, where eqn (4) is the Gordon l2 relation, and eqn (6) that of Colpa and Ketelaar in its quantised form. J is the pure rotational quantum number, B the rotational constant (in cm-I), d’(V) the frequency dependent dielectric loss, v the frequency (s-l) and I(v) the frequency dependent spectral intensity. 3hr“(v) (4)I(v) = 8n2(1-exp( -hv/kT)) a(J 3 J+2) cc V. (J+l)(J+2) exp( -E(J)/kT)(l-exp( -hcV(J)/kT)) (6)(2J+3) with V(J) = 2B(2J+ 3), E(J) = hcBJ(J+ l), V = v/c. From (4), (5) and (6) time/ps FIG.6.-Plots of: __ experimental RVCF for (CN), (g) at 383 K ; --eqn (10) with B =-y 0.1571 CM-I. The vectorial correlation function (zc(O)~u(t))is related to the real part of the Fourier transform C*(t)of I(v): C*(t) = R(t)+iI(t) a31= -M, I(?) exp(27tivt) dv giving : 8n:’(2 R&(f) = -d2(R(t))/dt2hctl(2Bc -3)( &-cc -ZBev) exp (-4kT -!-I)) x cos 2n: v t .dv. (9) INTER-MOLECULAR DYNAMICS OF NON-DIPOLAR MOLECULES (2) For the band shapes in question, Litovitz et aL3 have recently proposed the equation : (10) where yo and E are Lennard-Jones parameters, ,u is the reduced mass of the colliding molecules, and k the Boltzmann constant. This is a semi-empirical expression for cr(c0) in terms of the angular velocity o (radians s-I) derived from a consideration of deformation of the molecular polarisability during a collision.Eqn (10) can be transformed to the corresponding rotational velocity correlation function using : * co33/7 exp(-co/oo)cos ot dcuRL(t) cc s (1-exp(-hco/2nkT))-0.5- \ \ \ \ ..... .. \ \ I /I I -0.5- \ \ \.A’ ’ ’ -1.0- M. EVANS and this function is illustrated for N2(1), 02(1), C02(1), (CN),(l), and CS,(l) in fig. 2,4, 5, 7, and 8 respectively. The parameters l5 used in Litovitz’s eqn (1l), together with om,,(the calculated frequency of maximum absorption) are shown in table 1. Direct comparison of the experimental a($) data with the J+J+2 line spectra calculated from Colpa and Ketelaar’s original equation is available in the liter- ature 1.2~4-7for all the cases described here, and direct comparison of the observed (a)::; and Litovitz predicted (corn,,) values of the angular frequency of maximum absorption is given in table 1 for all the liquids studied here.It may be briefly indicated that in the cases of 0, and (CN), the J-, J+ 2 quadrupole-induced transitions reach a peak 1* at a lower frequency than the experimental band, the high frequency absorptions being attributed to overlap or hexadecapole-induced dipolar (J+ J+ 4) absorptions. TABLE USED IN EQN (11)1.-PARAMETERS liquid (6/k)lK rolA TIK oo/cm-l cumax/cm-l W$b;/cm-* N2 71.4 3.80 76.4 14.1 52.3 66 l3 02 106.7 3.47 88.1 17.2 63.7 82 l3 co2 195.2 3.94 273 18.6 69.0 70 (CN), 348.6 4.36 301 19.4 72.1 78 -2 467 4.48 298 19.8 73.5 75 Two general points are noticeable from the comparison of these correlation functions, derived from wholly collision-induced absorptions, with eqn (9).The first is that the mean time between collisions Zbc, defined by Lit~vitz,~ as that necessary for the angular velocity to go to zero, is shorter, even in the small diatomics N2and O,, than that obtained from the cutting of the time axis by eqn (9). It is known 6p that in the larger molecules such as CO, and (CN),, the quadrupole-quadrupole interaction potential ought not to be neglected in collisional theory and the consequences of its neglect are apparent in fig. 5 to 8 : in the fairly dilute gas, where collisions of no greater than two-bodies are probable the apparent Zbc is up to 50 % less than predicted. At higher pressures in nitrogen and oxygen gas, three-body and higher collisions are likely to be the cause of the respective discrepancies in rbc.Secondly, the negative peak of the rotational velocity correlation function (which reflects a tendency of the molecule to reverse its rotational direction on collision) is related to the maximum in a(m) of the frequency spectrum. This negative peak is always greater, according to eqn (9) than that in either the observed compressed gaseous or the liquid rotational velocity correlation functions. This may reflect the fact that the symmetry of interactions involving more than two molecules leads to an incomplete cancellation of the forces inducing the central dipole. The collisional damping of the rotational velocity correlation function is more effective than the Colpa-Ketelaar equation would allow.Future models for these dynamical aspects should, therefore, include: (i) a consideration of many body collision effects and their symmetry; (ii) wider use of an anisotropic intermolecular potential. Some more detailed comments can be made about the shape of the experimental correlation functions, and in particular about the oscillation superimposed on the overall shapes. Nitrogen gas at 300 K can be accepted as a reference case : the degree of agreement between the simple theory and experiment is maximal and, at this stage, probably little comment is justified on the deviations in fig. 1. Clearly, liquid N, departs seriously from the gas collisional state, and, again, it seems reasonable to suggest that INTER-MOLECULAR DYNAMICS OF NON-DIPOLAR MOLECULES the experimental curve will typify that for a simpler non-dipolar liquid of slightly anisotropic molecules.The significance of these remarks becomes apparent when the data for oxygen gas and liquid are considered. The 0, gas spectrum is itself immed- iately seen to differ markedly from that of N2-but no analysis of this difference appears to have been made. The striking indication is that the rotational velocity correlation function for the collisionally induced dipole in O2 shows a distinct resemblance in pattern to that in the liquid N, : for the latter there are " minima " or shoulders at 0.12; 0.25; 0.36 ps; in 0, gas similar features appear at 0.08; 0.13 ; and 0.20 ps.Thus the former repeat at intervals of ca. 0.12 ps the latter ca. 0.07 ps. The former At = 0.12 ps corresponds to a frequency of 8 x 10l2s-l, which is some three times the Mie l5 estimated " collision frequency " in liquid N, ; in gaseous 0, no collision frequency can match 0.07 ps (v = 14x loi2 s-'). These frequencies (if they are related to real molecular processes) are conceivably those of weakly bonded molecular pairs (N,) . . .(N,) or (0,). . . (0,). In cyanogen,6 the " oscillation " in RL',(t) is very pronounced, in the gas, the minima appear at 0.28; 0.68 ; 1.06 ; and 1.5 ps, intervals of about 0.4 ps : in the liquid the pattern is 0.21 ; 0.53 ; 0.83 ; 1.12 ; 1.41 ; and 1.71 ps with a repeat interval of 0.30 ps. There is clearly some unrecognized feature of the molecular collisional process shown by these details.Whilst cyanogen is molecularly very anisotropic, it is some detail in the dynamics of the collisional interaction which is revealed by Rgxp(t). It can be seen in fig. 2, 4, 5, 7 and 8 that Litovitz's rotational velocity correlation function shows no superimposed oscillations, the difference between this prediction and the experimental being especially marked in cyanogen (fig. 7). The Litovitz equation is one based solely on collision-induced anisotropy, but with correlation between successive collisions not taken into account. Therefore, although this semi- empirical equation gives a good estimate of the observed u),,, and has the required temperature dependence, it does not, as might be expected, adequately describe the very short time reversals in the direction of motion of the angular momentum vector observed here in nearly all of these linear molecules, and which may tentatively be ascribed to libration of the molecules equivalent to that in the well-known Brot and Wyllie models for far infra-red absorptions of dipolar molecules.l6 APPENDIX TRUNCATION In practice, the limits of integration in (1) are restricted to 0 < V < 2Vm (where Vs = 2Vm) This truncation can be expressed by multiplying the function 3hVc n (9)a(f)P(V) = 4n2(1-exp(-hik/kT)) by a " window function " G(5). Therefore taking : P(t)exp(2nitct) dij then : W G(V)P(ij)exp(2niVct) dF = &,(t) @ F(t),J-w where ?(t) is the Fourier transform of G(t), and is convoluted with R&,(t), i.e., W &,,(t) @ $(t) = [ j?;,,(~)?(t-U) du J -03 which is a function of t.M. EVANS The function G(S) used in the algorithm was : 1 for O,<V,<~V,G(3) = {0 otherwise the Fourier transform of which is : [sin(2qmt) +i cos(~,t)P(t) = 2S, _____2vmt 2v,t I-Taking T(t)as the real part of ?*(t), and defining sinc(y) = (sin y)/y, then : ffk'x,(u) . 2V, sinc(2Vm(t -u)) du. J -03 P(V)G(V)exp(2niVct) dV P(?)exp(2nifct) d? = s:y' a, &,,(u) . 2Vmsinc(2fm(t-u)) du. (A11 = To illustrate the effect on kgxD(t)of its convolution with ?(c),consider the delta function 6(io)representing a line absorption at the frequency Vo < Vs.The corresponding correlation function is : Rzxp(t) = P(Vo)~0~(2nV~ct). Substituting this in (A.l), then : a, R;xp(t) 0 $(t) = [ P(VJ cos(2nVocu)2Vmsinc[2Vm(t-u)] du J-a, = nP(Vo)cos(2n7,ct) if nS, > To = 0 if So > 7, where II is a positive integer. Therefore, the only effect of the truncation on the transformation of the function 6(Vo) is to multiply the final result by n. As the experimental band spectrum can be considered for digital computation as a sum of such delta functions &Ti), i = 1, 2, . . .rn, and as the Fourier transform of a sum is itself a sum, then the normalisation of Rgxp(t) to unity at t = 0 cancels out the truncation effect provided the condition nVm > Vo holds, i.e., the experimental spectrum must be truncated at the point where a(3) = 0 on the high frequency side so that Vi never exceeds Ss.SAMP L I N G In order to consider the effect of sampling the experimental band at discrete intervals AS, the infinite Dirac comb function W(V/Aij)is used. This has the property that : a, W(V/AV) = C 6(V/AS -12) n=-a, a, = AS d(S-nA7) n=-m where 6 represents the Dirac delta function. The Fourier transform of W(?/AV) is : 1 /F*W(t/r;) which is another sequence of impulses, but spaced at intervals of F = l/AS. INTER-MOLECULAR DYNAMICS OF NON-DIPOLAR MOLECULES If we multiply P(V) by W(V/AV) we obtain the sampled function. The transform of this product is the convolution of the individual transforms : P(S)W(V/AV) exp(i2ntVc) d? 03 = 1/P1 W(u/F)P(t-u) du -03 CQ 6(u -nF)P(t -u) du -a n= 1 co = f P(t-nF) = P(t+nF) = P,(t).n= -03 n= -a rhis proves that transformation of a function sampled at intervals leads to aperiodic function Pp(t)with period F = l/AV. If the condition R:xp(t)= 0 for t > F/2 or t > 1/(2Aik) is not fulfilled, then the replica- tion of P(t) may lead to overlapping, or aliasing of the functions R;&)@ W(t/F). There-fore we must chose AV sufficiently small for Kxp(t) = 0 for It I > 1 /(2Aik). The University College of Wales, Aberystwyth, is thanked for a Dr. Samuel Williams Studentship. Prof. Manse1 Davies and Dr. Graham Williams are thanked for fruitful advice and discussions. D. R. Bosomworth and H. P. Gush, Canad. J.Phys., 1965,43, 751. K. D. Moller and W. G.Rothschild, Far-Znfra-Red Spectroscopy (Wiley Interscience, New York, 1970), chap. 10. H. Dardy, V. Voltera and T. A. Litovitz, Chem. SOC.Symp. on Light Scattering and Infa-red Absorption, Manchester, 1972, Paper 6. G. J. Davies and J. Chamberlain, J.C.S. Faraday 11, 1973, 69, 1739. G. J. Davies, J. Chamberlain and M. Davies, J.C.S. Faraday 11, 1973, 69, 1223. M. Evans, J.C.S. Faraday 11, 1973, 69, 763. W. Ho, G. Birnbaum and A. Rosenburg, J. Chem. Phys., 1971,55, 1028. J. P. Colpa and J. A. A. Ketelaar, Mol. Phys., 1958, 1,343. A. Gerschel, I. Darmon and C. Brot, Mol. Phys., 1972,23, 317. lo R. G. Gordon, J. Chem. Phys., 1965,43, 1307; 1964,41, 1819. l1 J. E. Anderson and R. Uhlmann, J. Chem. Phys., 1971,55,4406. l2 A. I. Baise, J. Chem. Phys., 1974, 60,2936. l3 M. C. Jones, N.B.S. Technical Note 390, April 1970, pp. 25-26, (U.S. Dept. of Commerce, Washington, D.C.). l4 G. J. Davies, Thesis (University of Wales, 1971). l5 R. A. Svehla, Estimated Viscosities and Thermal Conductivities of Gases at High Temperature, N.A.S.A. Technical Report No. R 132 (1962). l6 I. W. Larkin, J.C.S. Faraday 11, 1973, 69, 1278.

ISSN:0300-9238    

DOI:10.1039/F29757100071

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Atomic Polarization in Metal Chelates Part 3.-Dielectric Loss Measurements on Some Beryllium Complexes of Certain Schiff Bases ANGEL,JOHN WILLIAMBYROBERTLINDSAY HAYES*AND DONALD RADFORDVINCENT School of Chemistry, University of Sydney, N.S.W. 2006, Australia Received 1st April, 1974 Eight bis(N-alkylsalicylideneiminato)beryllium(I~) complexes with alkyl groups Me, Et, Prn, Pri, Bun, Bui, Bus, and But have been studied as solutes in benzene and, in one case, also in dioxan at 25°C. Dipole moments were determined by both static polarization and dielectric loss methods. From these results values of atomic polarization were found to range from about 28 cm3 when the alkyl groups have straight chains to about 10 cm3 when the alkyl groups are branched. This atomic polarization is attributed to concerted motion of the atoms of the chelate rings and it is proposed that its diminution in the cases where the alkyl groups are branched is brought about by intramolecular steric interactions. In earlier parts of this series '* we reported determinations of apparent orient- ation polarization from the difference and true orientation polarization from dielectric-loss measurements at high frequencies for several non-centrosymmetric chelates of tin(xv).The difference in polarization as determined by the two methods (80-160 cm3) was attributed to atomic polarization brought about by concerted motion of the atoms of the chelate rings. We now report similar measurements on eight tetrahedral beryllium(I1) chelates of N-alkylsalicylideneimines(x) with R = CH,, C2H5, n-C3H7, i-C3H7, n-C,H,, i-C4H9, Be 1 *\iR 2 s-C4Hg, and t-C,Hg.Unlike the tin compounds examined previously these com- pounds are very stable in benzene solution (except where R =s-C,H, and t-C,Hg) and are incapable of existing in cis-trans isomeric forms. Green et aL3have measured the dipole moments (at low frequency) and molar Kerr constants of five of these compounds and have confirmed the expected tetrahedral structure. The presence of the bulky t-C4Hg group as an alkyl substituent was found to produce a slightly twisted configuration. EXPERIMENTAL PREPARATION AND PURIFICATION OF THE BERYLLIUM COMPLEXES Complexes where R = CH3, CZHJ,n-C3H,, and i-C4H9 were kindly supplied by Prof. R.W. Green. Samples of these compounds were recrystallized for this work from chloroform using light petroleum to assist the precipitation. The compound where R =n-C,H, was prepared according to the method of Green and Alexander and purified as above. 81 ATOMIC POLARIZATION IN METAL CHELATES For the compounds where R = i-C3H7, s-C4Hg and t-C4Hg the following procedure was used. To redistilled salicylaldehyde (11 cm3, 0.1 mol) and the appropriate amine (0.1 mol) dissolved in hot methanol (100 cm3) was added slowly and with constant stirring a solution of beryllium sulphate tetrahydrate (8.5 g, 0.05 mol), 2,2-dimethoxypropane (25 cm3), and 0.001 mol dm-3 sulphuric acid (5 cm3 in methanol) in dry methanol (70 cm3). Further amine (0.1 mol) dissolved in dry methanol (50 cm3) was added to the mixture and this produced a precipitate of the amine sulphate.The mixture was heated at the boiling point with continual stirring for 60 min and, after cooling, the precipitate was filtered off and the solvent evaporated from the filtrate under reduced pressure. The yellow residue was washed with light petroleum and extracted with hot toluene. The toluene solution was concentrated by distillation and then poured into excess light petroleum. The buff coloured crystalline precipitate was recrystallized from toluene using light petroleum to assist the precipitation and dried in a vacuum dessicator. Yield : 50 % R = i-C3H7: m.p. 195°C (found : C, 72.1 ; H, 7.4 ;N, 8.3 : calc. for Be(C,oH12N0)2: C, 72.0; H, 7.3; N, 8.4 %).R = s-C4H, : m.p. 122°C (found : C,73.2 ; H, 7.8 ; N, 7.8 : calc. for Be(C1 1H14N0)2: C, 73.1 ; H, 7.8; N, 7.8 %). R = t-C4H9: m.p. 215°C (lit.3 217°C). MEASUREMENTS SOLVENTS AnaIaR benzene was purified by partial freezing; the remelted solid was stored over sodium. For benzene at 25°C the dielectric constant E, the density d, and refractive index n for sodium light were taken as 2.2725, 0.873 78 and 1.4973 respectively. AnalaR dioxan was refluxed over sodium for several hours, distilled, and stored over sodium. For dioxan at 25°C E, d, and n were taken as 2.2090,1.0280, and 1.4202 respectively. DETERMINATION OF DIPOLE MOMENTS Dipole moments were determined from static field (low frequency) polarization measure- ments using the method of Le Fkvre et aL51 Dielectric loss measurements were carried out according to a method previously used in this laboratory using frequencies of 1.140, 3.040, and 8.540 GHz.SPECTROSCOPY Spectra were recorded using a Perkin Elmer 402 spectrophotometer and 1 cm quartz cells. RESULTS AND DISCUSSION DIPOLE MOMENTS Incremental dielectric constants, densities, refractive indexes and loss tangents at various weight fractions, wz, for the solutes as solutions in benzene and (in one case) dioxan are listed in a Supplementary Publication (SUP 21072, 6 pp.)." From these results values of ml,p, y'n:, $( = EA tan 6/Cw,) and the derived polarizations, refractions, dipole moments, and relaxation times (z) are given in table 1.In order to distinguish the values of the dipole moments determined by the two methods those derived from measurements at low frequency are designated pstaticwhile those derived from high frequency (dielectric loss) measurements are designated ploss. In the calculation of pStaticno allowance for atomic polarization has been made (i.e., ,P = &). Consequently the atomic polarization (*P)listed in table 1 is the differ- ence in polarization calculated from measurements at high and low frequency.1*2* '. s These values are lower by 5+ 1 cm3 if the frequently employed empirical relationship * For details of Supplementary Publications see J.C.S. Faraday,1972, index issue. R. L. ANGEL, J. W. HAYES AND D. V. RADFORD which takes DP= 1.05 RDis used.4 It is estimated that values of the dipole moments are precise to kO.02 D ; this corresponds to a precision in the polarization values of &4 cm3 and in the derived A P values of 6 cm3.TABLE1.-POLARIZATIONS,LOSS TANGENTS, DIPOLE MOMENTS AND RELAXATION TIMES FOR SOLUTES AT 25°C SOhte/SOlVent C(Ei b Y'nlz -aP2/Cm3 R&m3 Pstaticl D* (Y1.14GHz (Y3.04GHz Vs.54GHr Plod D* T/PS APJ 0 3 Be(C7H5NO Me)2/ benzene t t t 584.53 89.9$ 4.91 1.54 1.99 1.11 4.78 65 27 Be(C7HSNO Et)Z] benzene t t t 596.13 95.72 4.94 1.58 1.67 0.89 4.77 78 34 Be(C7HsNO Prn)2/ benzene t t t S93.9$ 105.2f 4.88 1.54 1.38 0.65 4.75 97 27 Be(C7HsNO Pri)z/benzene 8.01 0,230 0.29 590 104 4.87 1.40 1.52 0.74 4.75 78 24 Be(C7HsNO Bun)p/ benzene 7.52 0.202 0.31 609.32 118.22 4.90 1.49 1.20 0.58 4.78 109 23 608 117 4.89 Be(C7HsNO BU1)2/ benzene 7.15 0.208 0.31 584 118 4.77 1.39 1.14 0.53 4.65 107 17 Be(C7HsNO Bug)2/ benzene 6.94 0.204 0.32 570 118 4.69 1.35 1.25 0.63 4.65 93 13 Be(C7H5N0benzene 6.07 0.198 0.31 486.53 118.73 4.24 1.17 1.11 0.52 4.35 91 10 512 119 4.38 Be(C7HsNO Me)2/ dioxan 11.9 0.157 0.68 608 91 5.01 2.41 1.75 0.77 4.87 123 30 * 1 D = 3.336 x 10-30 C m ; t values not determined in this work ; 2 data taken from ref.(3). As the compounds where R = n-C4Hg and t-C4Hg were freshly prepared for this investigation their static dipole moments were redetermined.Results identical with those of Green et aL3 were obtained for the case where R = n-C4Hg while an increase of 0.14 D was noted for the t-butyl compound. This may be attributed to the greater scatter in the dielectric constant determinations of the former investigators than that observed here. A possible reason for this scatter is the decomposition which we have observed to take place in benzene solutions of the compounds where R = s-C4H9 and t-C,H,. This decomposition is manifested by the yellowing of the previously colourless solutions on standing. Spectroscopic examination of freshly prepared solutions of the complex where R = t-C4Hg compared with those which had stood for several hours revealed the appearance of a new broad band at 320 nm, and the dis- appearance of a band at 366nm on standing.A solution of the free ligand was found to display a similarly shaped band to the former at 318 nm. To minimise the effects of decomposition on dielectric measurements solutions were always used within 20 minutes of preparation. ATOMIC POLARIZATION For the straight chain substituted complexes values of AP are within experimental error of the mean value of 28 cm3. As R is changed from n-C4Hg through i-C4H9 and s-C4H9 to t-C4Hg,AP is seen to decrease progressively to about one third of this value. It is suggested that the presence of secondary and tertiary carbon atoms in the alkyl chain sets up steric interactions in the molecules with consequent reduction in the AP. For R = i-C3H7, AP is also less than that observed when the straight chain n-C,H, group is present in the molecule, but the effect is less marked here than in the butyl series.Further evidence for this conclusion is provided by the observation that the three complexes which exhibit the lowest values of AP(i.e., when R = i-C4H9, s-C4H9 and t-C4Hg) also have dipole moments (both pStaticand ploss)which are sig- nificantly lower than those for the other compounds. This has already been taken as ATOMIC POLARIZATION IN METAL CHELATES evidence for distortion towards the non-polar planar conformation in the case where R = t-C4H9,3 and it is proposed that a similar but smaller distortion is present for the other branched chain butyl groups. Coop and Sutton have attributed the high APobserved in certain metal-P-diketone complexes to bending about the metal-oxygen bonds, and they have related the values of AP to the bending force constants of the bonds : AP = 4nXNpi/9 Vo (1) where X = number of ligand molecules attached to the metal ion, N = Avogadro number, pL = dipole moment of ligand, Yo = bending force constant of metal ligand bond. These authors have calculated a value for V, in the case of bis(pentane-2,4- dionato)beryllium(Ir) [Be(a~ac)~] of 3.7 x 10-1 J molecule under the assumption that the value of y, is 7.5 D.If it is assumed that in compound I where R is a straight chain alkyl group the same value of Vomay be used both for the Be-0 and Be-N bonds the corresponding value of yL is 7.8 D.Not surprisingly this value is similar to that taken by Coop and Sutton for the Be(acac), case as in both cases the chelate ring is six membered although in this case the donor atoms are oxygen and nitrogen whilst in the case of Be(acac), both atoms are oxygen. Examination of molecular models indicates that steric interactions which would inhibit bending about the metal ligand bond do occur when the alkyl chain contains secondary and tertiary carbon atoms and consequently this would result in a larger value for the bending force constant and a smaller value of AP as observed. Although the values of pstaticand plossare both larger for the compound when R = CH, when they are determined in dioxan solution compared to the values obtained in benzene solution, the value of AP is not significantly different in the two solvents.This observation is in accord with that of Coop and Sutton for the pentane- 2,4-dionato compounds and adds further support to the suggestion that the *Parises from an intramolecular process rather than one associated with intermolecular inter- action. For all compounds studied in this work, the value of $ at 8.540 GHz appeared to be about 5 % higher than that predicted by the Debye curve drawn through the two points at lower frequencies. From other measurements recorded in our laboratories on compounds which display Debye behaviour no such systematic error has been observed, even though random errors of this order may be expected. This increased absorption at the highest frequency might be attributable to dispersion of the atomic polarization, a process which would have a maximum absorption at much higher frequencies than those used here.A similar explanation has been suggested for absorption exhibited by some centro-symmetric metal pentane-2,4-dionates for which it has been shown that there is a dispersion of the AP at frequencies from 10 to lo3GHz. Whilst we have made use of eqn (1) to discuss APin terms of bending force constants for a forced harmonic oscillator, it should be noted that this equation is probably inappropriate since the process appears to be a highly damped intra- molecular motion of the chelate rings as proposed by Di Carlo et aL1Oand Haigh and Sutton l1 in the case of the metal pentane-2,4-dionates.RELAXATION TIMES Values of relaxation time (z) indicate that the process giving rise to the dielectric loss is an overall molecular rotation, since the values observed are similar to those obtained for compounds of about the same size and shape.'. 2* 7* As the length of the alkyl chain increases, z is seen to increase as, presumably, this part of the molecule R. L. ANGEL, J. W. HAYES AND D. V. RADFORD extends further into the solvent environment. The value of z is smallest when R = CH, (65 ps) and largest when R = n-C4H9 (109 ps) for solutions in benzene. As branching of the alkyl chain occurs, values of z are smaller than that for the corres- ponding straight chain compounds reflecting, no doubt, the greater extension of the alkyl group into the environment in the latter case.When dioxan is the solvent, the z value for the one compound examined (R = CH3) is much higher, indicative of the different solute-solvent interactions in this solvent compared with benzene. We thank Prof. R. W. Green who supplied some of the compounds and advised on the preparation of others. We also thank Dr. J. S. Dryden for use of the dielectro- meter. J. W. Hayes, R. J. W. LeFevre and D. V. Radford, Znorg. Chem., 1970, 9, 400. J. W. Hayes, W. H. Nelson and D. V. Radford, Austral. J. Chem., 1973, 26, 871. R. W. Green, R. J. W. Le Fevre and J. D. Saxby, Austral. J. Chem., 1966, 19, 2007. R. W. Green and P. W. Alexander, Austral. J. Chem., 1965, 18, 1297. R. J. W. Le Fevre, Digole Moments (Methuen, London, 1953). A. D. Buckingham, J. Y.H. Chau, H. C. Freeman, R J. W. LeFevre, N. Rao and J. Tardiff, J. Chem. SOC.,1956, 1405. ’M. Das, S. E. Livingstone, S. W. Filipczuk, J. W. Hayes and D. V. Radford, J.C.S. Dalton, * L. 1974, 1409. P. Eddy, J. W. Hayes, S. E. Livingstone, H. L. Nigam and D. V. Radford, Austral.J. Chem., 1971, 24, 1071. I. E. Coop and L. E. Sutton, J. Chem. SOC.,1938, 1269 lo E. N. Di Carlo, E. Watson, C. E. Varga and W. J. Chamberlain,J. Phys. Chem., 1973,77,1073. J. Haigh and L. E. Sutton, Chem. Cumm ,1970,296. l2 E. N. Di Carlo, R. E. Stronslci and C. E. Varga, J. Phys. Chem., 1969,73,2433. l3 R. D. Nelson and C. E. White, J. Phys. Chem., 1969, 73, 3439. l4 S. Dasgupta and C. P. Smythe, J. Amer. Chem. SOC.,1967,89, 1967.

ISSN:0300-9238    

DOI:10.1039/F29757100081

出版商:RSC    

年代:1975

数据来源: RSC