摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY 361 Date 1962 1962 1963 1963 1964 1964 i96i 1965 1966 1966 1967 1967 i968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1978 Subject Volume Inelastic Collisions of Atoms and Simple Molecules 33 High Resolution Nuclear Magnetic Resonance 34 The Structure of Electronically-Excited Species in the Gas-Phase 35 Fundamental Processes in Radiation Chemistry 36 Chemical Reactions in the Atmosphere 37 Dislocations in Solids 38 The Kinetics of Proton Transfer Processes 39 Intermolecular Forces 40 The Role of the Adsorbed State in Heterogeneous Catalysis 41 Colloid Stability in Aqueous and Non-Aqueous Media 42 The Structure and Properties of Liquids 43 Molecular Dynamics of the Chemical Reactions of Gases 44 Electrode Reactions of Organic Compounds 45 Homogeneous Catalysis with Special Reference to Hydrogenation and Oxidation 46 Bonding in Metallo-Organic Compounds 47 Motions in Molecular Crystals 48 Polymer Solutions 49 The Vitreous State 50 Electrical Conduction in Organic Solids 51 Surface Chemistry of Oxides 52 Reactions of Small Molecules in Excited States 53 The Photoelectron Spectroscopy of Molecules 54 Molecular Beam Scattering 55 Intermediates in Electrochemical Reactions 56 Gels and Gelling Processes 57 Photo-effects in Adsorbed Species 58 Physical Adsorption in Condensed Phases 59 Electron Spectroscopy of Solids and Surfaces 60 Precipitation 61 Potential Energy Surfaces 62 Radiation Effects in Liquids and Solids 63 Ion-Ion and Ion-Solvent Interactions 64 For current availability of Discussion volumes, see back cover.GENERAL DISCUSSIONS OF THE FARADAY SOCIETY 361 Date 1962 1962 1963 1963 1964 1964 i96i 1965 1966 1966 1967 1967 i968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1978 Subject Volume Inelastic Collisions of Atoms and Simple Molecules 33 High Resolution Nuclear Magnetic Resonance 34 The Structure of Electronically-Excited Species in the Gas-Phase 35 Fundamental Processes in Radiation Chemistry 36 Chemical Reactions in the Atmosphere 37 Dislocations in Solids 38 The Kinetics of Proton Transfer Processes 39 Intermolecular Forces 40 The Role of the Adsorbed State in Heterogeneous Catalysis 41 Colloid Stability in Aqueous and Non-Aqueous Media 42 The Structure and Properties of Liquids 43 Molecular Dynamics of the Chemical Reactions of Gases 44 Electrode Reactions of Organic Compounds 45 Homogeneous Catalysis with Special Reference to Hydrogenation and Oxidation 46 Bonding in Metallo-Organic Compounds 47 Motions in Molecular Crystals 48 Polymer Solutions 49 The Vitreous State 50 Electrical Conduction in Organic Solids 51 Surface Chemistry of Oxides 52 Reactions of Small Molecules in Excited States 53 The Photoelectron Spectroscopy of Molecules 54 Molecular Beam Scattering 55 Intermediates in Electrochemical Reactions 56 Gels and Gelling Processes 57 Photo-effects in Adsorbed Species 58 Physical Adsorption in Condensed Phases 59 Electron Spectroscopy of Solids and Surfaces 60 Precipitation 61 Potential Energy Surfaces 62 Radiation Effects in Liquids and Solids 63 Ion-Ion and Ion-Solvent Interactions 64 For current availability of Discussion volumes, see back cover.

ISSN:0301-7249    

DOI:10.1039/DC97764FX001

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY 361 Date 1962 1962 1963 1963 1964 1964 i96i 1965 1966 1966 1967 1967 i968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1978 Subject Volume Inelastic Collisions of Atoms and Simple Molecules 33 High Resolution Nuclear Magnetic Resonance 34 The Structure of Electronically-Excited Species in the Gas-Phase 35 Fundamental Processes in Radiation Chemistry 36 Chemical Reactions in the Atmosphere 37 Dislocations in Solids 38 The Kinetics of Proton Transfer Processes 39 Intermolecular Forces 40 The Role of the Adsorbed State in Heterogeneous Catalysis 41 Colloid Stability in Aqueous and Non-Aqueous Media 42 The Structure and Properties of Liquids 43 Molecular Dynamics of the Chemical Reactions of Gases 44 Electrode Reactions of Organic Compounds 45 Homogeneous Catalysis with Special Reference to Hydrogenation and Oxidation 46 Bonding in Metallo-Organic Compounds 47 Motions in Molecular Crystals 48 Polymer Solutions 49 The Vitreous State 50 Electrical Conduction in Organic Solids 51 Surface Chemistry of Oxides 52 Reactions of Small Molecules in Excited States 53 The Photoelectron Spectroscopy of Molecules 54 Molecular Beam Scattering 55 Intermediates in Electrochemical Reactions 56 Gels and Gelling Processes 57 Photo-effects in Adsorbed Species 58 Physical Adsorption in Condensed Phases 59 Electron Spectroscopy of Solids and Surfaces 60 Precipitation 61 Potential Energy Surfaces 62 Radiation Effects in Liquids and Solids 63 Ion-Ion and Ion-Solvent Interactions 64 For current availability of Discussion volumes, see back cover.GENERAL DISCUSSIONS OF THE FARADAY SOCIETY 361 Date 1962 1962 1963 1963 1964 1964 i96i 1965 1966 1966 1967 1967 i968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1978 Subject Volume Inelastic Collisions of Atoms and Simple Molecules 33 High Resolution Nuclear Magnetic Resonance 34 The Structure of Electronically-Excited Species in the Gas-Phase 35 Fundamental Processes in Radiation Chemistry 36 Chemical Reactions in the Atmosphere 37 Dislocations in Solids 38 The Kinetics of Proton Transfer Processes 39 Intermolecular Forces 40 The Role of the Adsorbed State in Heterogeneous Catalysis 41 Colloid Stability in Aqueous and Non-Aqueous Media 42 The Structure and Properties of Liquids 43 Molecular Dynamics of the Chemical Reactions of Gases 44 Electrode Reactions of Organic Compounds 45 Homogeneous Catalysis with Special Reference to Hydrogenation and Oxidation 46 Bonding in Metallo-Organic Compounds 47 Motions in Molecular Crystals 48 Polymer Solutions 49 The Vitreous State 50 Electrical Conduction in Organic Solids 51 Surface Chemistry of Oxides 52 Reactions of Small Molecules in Excited States 53 The Photoelectron Spectroscopy of Molecules 54 Molecular Beam Scattering 55 Intermediates in Electrochemical Reactions 56 Gels and Gelling Processes 57 Photo-effects in Adsorbed Species 58 Physical Adsorption in Condensed Phases 59 Electron Spectroscopy of Solids and Surfaces 60 Precipitation 61 Potential Energy Surfaces 62 Radiation Effects in Liquids and Solids 63 Ion-Ion and Ion-Solvent Interactions 64 For current availability of Discussion volumes, see back cover.

ISSN:0301-7249    

DOI:10.1039/DC97764BX003

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Introduction BY HAROLD L. FRIEDMAN The lineage of this Discussion, extending almost back to the founding of the Faraday Society in 1903, is provided by the following list of Faraday Discussions: 1907 Hydration in Solution 1919 Present Status of the Theory of Ionization 1927 Theory of Strong Electrolytes 1957 Interactions in Ionic Solutions 1977 Ion-Ion and Ion-Solvent Interactions. The long period of intensive study indicates that ionic solutions are important in chemistry. Another conclusion, which is reinforced by reviewing the details of the earlier Discussions, is that it is difficult to answer many important questions about ionic solutions; we find them coming to the surface again and again. In view of this second and rather gloomy conclusion it may be useful to review the elements of further progress in the field and to remark how they are illustrated by the papers in this Discussion.In his Introductory Lecture in 1957, R. P. Bell could say “ It is a tribute to the pioneering work of Debye and Hiickel that their equations form the basis of all the papers on ion-ion interaction presented to the present meeting.” I take it as a healthy sign that the corresponding assertion would be much less true in 1977. I will assume that the aims of our research are to understand all of the experimental observations on ionic solutions in terms of the interactions of the molecules in the solutions. I think that we would also agree that there are two ways to proceed. In the theoretical approach we begin by proposing molecular-level descriptions of the systems of interest, descriptions that correspond to specifying a Hamiltonian for the system.Call such descriptions “ Hamiltonian models.” The next step is to calculate the “ measurable ” properties of the model using a suitable approximation method. The major obstacle to this approach is that the available approximation methods are not very powerful relative to our need. There are many examples of “ measurable ” properties that cannot yet be calculated accurately and reliably for Hamiltonian models for fluid systems, even for very simple models. The dielectric constant and the electrical conductivity are two that are especially important in this area of research. Moreover, it often is true that when the approximation methods are adequate and we can find models, whose measurable properties agree with the experimental data for solutions of interest, there is no uniqueness.Many different types of models can be brought to agreement with the limited experimental data for which comparison is possible. In the experimental approach to the same problems we extend our experimental measurements in various ways ; higher derivatives with respect to the independently controllable variables, new solution compositions and new ranges of the independent variables and, especially, novel experiments devised to reveal quite directly what is going on at the molecular level. Choosing experimental methods to answer key questions without appeal to doubtful theory is a textbook exercise in the part of chemistry that is chiefly concerned with chemical bonds, but apparently is much more8 INTRODUCTION difficult in the study of solutions where the main interest is in the forces between the molecules, the intermolecular structure, and the corresponding rate processes.One of the small number of experiments in solution chemistry that is definitive in this sense is the determination of the coordination number of A13+ in water by I7O n.m.r., done by Jackson, Lemons and Taube.' Another is the recent application of neutron diffraction with isotopic substitution to determine the average geometry of Ni(H20)z+, including the tilt of the water molecules from the most symmetrical orientation2 (fig. 1). Except for the " tilt " of the water molecules in the hydration u -- 0 2 L 6 8 r/A FIG. 1.-Diffraction results for 5 mol dm-3 NiC1z(aq.).2a G'(r) is the weighted sum of gNi,x(r) where x ranges over the atomic species.The identified peaks come from the main peaks of the correspond- The average geometry of Ni(H20)2C deduced by the authorsza is what may be expected based on the structure of the complex2b in NiS04.6H20 crystals, shown in the inset. ing g N i d r ) . shell, these examples are rather borderline since AI(H,O);+ and Ni(H,O)z + are structures that are more typical of coordination chemistry, where the complexes are held together by chemical bonds, than solution chemistry, where the focus is on inter- molecular interactions and the consequent very short-lived structures. In the study of the latter it is most commonly found that a new experimental foray, even one based on new techniques, raises new questions, some of which it answers, but it does not directly answer any of the long-standing questions.For example, concerning the structure-making and structure-breaking effects in water, the basis of the original distinctions in terms of viscosity B-coefficient and solvation entropy has been enlarged in terms of heat capacities, volumes, infrared and Raman spectra of the water, and n.m.r. spectra of nuclei in solvent and solute species, as well as temperature and pressure derivatives of many of these coefficients. Perhaps you will agree that no one of the measurements has given definitive molecular insight into the structure-making and breaking phenomena. In fact all of the measurements do not even lead to the same classification, let alone the same ordering of structure breakers ! Another type of example is provided by the study of the effects of ions on the dielectric properties of solutions which leads to two new sets of ionic coefficients, one for the molar change in dielectric constant and the other to the molar change in dielectric relaxation time, neither of which can be interpreted in molecular termsINTRODUCTION 9 without further assumptions about the extent and structure of the ion coordination shell of the ion, at least in the context of present theoretical capabilities. Many will recognize that there is a certain consistency in this confusion.This theme can most simply be developed by using the “ chemical model ” developed by Frank and Evans,3 Gurney4 and others, according to which changes in the water properties are assumed when the water passes from a region (called the “ bulk ”) far from an ion into a small region (the “ cosphere ”) next to an ion. Then with assumed sizes for the cospheres it is a simple matter to express many solution properties in terms of the changed characteristics of water molecules inside the cospheres.Frank and Evans made such assignments for solvation entropy, and many more recent examples also may be given. The usual result is that when the change in properties of the water in going from the bulk into the cosphere is identified it is found to be a small fractional change; for example it is 0.3 cal mol-1 K-l out of 13 in the case of the entropy of water in the outer or structure-breaking part of a K+ cosphere.* While it is impressive that such small effects can be measured, the use of chemical models to represent the results does not seem natural when there are only tiny dif- ferences in properties of the objects that we treat as distinguishable chemical species. Such small differences correspond to shifts in the statistical distributions of properties which are not much bigger than the widths of the distributions themselves, so it is not surprising that what we see depends on the method of measurement. These considerations make it seem attractive to return again to the consideration of what we may be able to do with the theoretical approach.Thus, for example, if calculation of observable properties from some Hamiltonian model gives n.m.r.shifts of ionic solutions in water in agreement with the coefficients reported here by Akitt, as well as the enthalpies reported by Cobble and Murray, the cluster thermodynamics reported by Kebarle and co-workers, andthe cationic Raman spectra reported by Irish and Jarv, then we would have reason to think that the interactions specified in the model and the resulting structures were realistic enough to be interesting. At the moment this proposition is a pipe dream but it may be expected to be a common procedure at the next Faraday Discussion on this area of research, if there is reason to have another in twenty years or so. I would like briefly to describe the basis for this optimism in terms of a classifica- tion of Hamiltonian models as to “ level,”6 bearing in mind the observation that an explanation of a given problem at the deepest or most fundamental level is not necessarily the most satisfactory. In a Schrodinger-level (S-level) Hamiltonian model the variables in the Hamil- tonian are the coordinates of the nuclei and electrons in the system.Hamiltonian models deeper than S-level are well known but usually are not necessary in chemical problems. At S-level the quantum mechanical Hamiltonian itself is well known from first principles; the problem is that calculating observable properties for the systems of interest (fig. 2) in this Discussion requires approximation methods with rather large computer costs and with results of limited accuracy, at least in terms of what is needed when dealing with intermolecular forces.The extensive work in applying these methods to ionic solution problems is represented here by the paper of Sadlej and Sadlej. In a Born-Oppenheimer-level (BO-level) Hamiltonian model the variables in the Hamiltonian are the coordinates and momenta of the molecules or ions (fig. 3). The potential part of the Hamiltonian is the potential energy surface which is obtained in * For the process H20(liq) + H20 (ideal gas, 55.5 mol d~n-~) we estimate AS = 13 cal mol-’ K-’ which serves as a measure of the intermolecular part of the entropy of a water molecule in the liquid.10 INTRODUCTION S - level nuclei and electrons quanta1 H approx I mat ion method elect ionic U, ( I , . . . , H 1 surface spectra A n ( l , . . , # I surfac2 FIG. 2-Schematic diagram of the usual calculation of “measurable” properties of an S level Hamiltonian model.The approximation methods of quantum chemistry give the wave function Y for the ground electronic state with fixed positions (1, . . . , N) of the nuclei, as well as the wave functions Y1, Y1, . . . of the excited states. While electronic spectra follow rather directly from these wave functions, other measurable properties may require a further statistical-mechanical calculation from the potential energy surface UN(l, . . . , N) or the surface AN(l, . . . , N) for some other dyna- mica1 variable A . principle by integrating over the coordinates of the electrons in the S-level model, Thus the Hamiltonian no longer is exactly known a-priori. At the BO-level, classical mechanics is in most cases a highly accurate approxima- tion.Further simplification results from the observation that the BO-level potential function$ U,(l, . . . , N ) for N particles often may be expressed as a sum of pair potential functions uij(i, j ) with little loss of realism. While calculations at S-level can be used to determine certain features of the BO-level potential U,, it is largely not well known a-priori. However, it can be investigated by the “ inverse process ” in which one uses a suitable approximation method to calculate the model’s “ measur- able ” properties, compares them with the real system of interest, and adjusts the model Hamiltonian to obtain agreement. Thus the energies for addition of successive water molecules to small clusters containing an ion, as reported here by Kebarle and co-workers, are readily used to test proposed BO-level models. To see whether a given model for a solution of NiC12 in water fits the data of Camaniti and Pinna is no more difficult than related studies by Heinzinger and co-workers,’ but still quite expensive in computer time.The results of Hertz and Contreras on the relaxation of BF4- in water, like the cation-water vibration frequencies measured by Irish and Jarv, can be expressed in terms of BO-level models, perhaps with a perturbative quantum correction in the latter case, but approximation methods that are suitable for calculating the relevant “ measurable ” properties of the models have yet to be found. $ In this discussion the notation UN(l, . . . , N) indicates that the potential depends on the co- ordinates of molecules 1,2, .. . , N. If appropriate, the molecular coordinates may include orienta- tions and other internal coordinates as well as locations. The pair potential u& j ) is a function of the coordinates of molecules i and j which may be different for each species pair i, j .INTRODUCTION BO - level 11 molecules and ions not well known " ' specify by model u, = u , , 2 [ l , 2 ) + u , , 3 ( l , 3 ) + .... + U , , , i l , N ) (2,31 + . . . t U 2 , # ( 2 . 1 ) + u : , 3 approximation methods classical mechanics simulation :MD,MC perturbation : PY. HNC, T0,WCA ,... measurable properties HUM (6) FIG. 3.-BO-level Hamiltonian model. If pairwise-additive UN is assumed then the model merely specifies the pair potential function u l j for each species pair, as shown in (a).The approximation methods mostly fall into two classes, with some of the currently favoured examples indicated by their acronyms in (b).12 INTRODUCTION For a wide class of solution problems even the BO-level Hamiltonian models may be more detailed than one needs for molecular interpretation. In such cases one may MM- level ions approx;mation methods as for BO equil."excess" properties r1,2 FIG. 4.-MM-level Harniltonian model. Neither the potential part ON nor the kinetic part RN is well known a-priori. The other qualitatively new feature is that the solvent-averaged pair potential fit, may have extra strong features, suggested by the graph, that reflect the molecular structure of the solvent. use a McMillan-Mayer-level (MM-level) Hamiltonian model, derived in principal from a BO-level Hamiltonian model for the same system by averaging over the co- ordinates and momenta of the solvent molecules (fig.4). Fortunately the approxi- mation methods that are useful to calculate the equilibrium properties of the €30-level models are equally applicable at MM-level; one simply has to relabel the input potentials, which now are solvent-averaged, and the output functions, which now are " osmotic " thermodynamic functions. The MM potential function, UN(l, . . . , N ) is of course not known a-priori but it can be studied by the inverse process, described above. Also it can be elucidated by calculations at a deeper level. Such investigations are represented here by studies of the pair components of ON by Haye and StelI, who are especially concerned with the large-r behaviour, and by Adams and Rasaiah, who focus on the short-range behavi- our.Both work from BO-level models but use different approximation methods to evaluate the average over the solvent coordinates. With MM-models it is again interesting to see whether one can get a model that economically and elegantly agrees with all of the relevant experimental data for a given system; success would mean that we can understand all of the observations in terms of the solvent-averaged forces between the ions. However, it must be noted that there is no reason to expect the MM potential function for any real solution to be nearly pairwise-additive. There is an upper bound on the ion concentration range within which it is sensible to compare the model with data for real systems if the pairwise-addition approximation is made.*INTRODUCTION 13 MM models have earlier been fitted to the thermodynamic excess properties of several classes of aqueous electrolyte^.^ In view of the uniqueness problem already mentioned it is important that the same models be fitted to non-thermodynamic properties as well.This recently has been done for the electrical conductivity by Ebeling and co-workers10 and in the present Discussion by Justice and Justice. However, it should be remarked that the statistical mechanical theory for calculat- ing transport properties at MM level is not well understood. Indeed, the underlying theory of McMillan and Mayer'l pertains only to equilibrium properties.The new effects that enter into the kinetic part of the MM-level Hamiltonian correspond to what may be called the frictional force on a moving solute particle and the hydro- dynamical forces acting between the moving solute particles. There are some basic questions about these kinetic solvent-averaged forces that cannot be answered except by beginning at the BO level and explicitly doing the solvent averaging, but the required techniques have yet to be developed. The easy thing to do in the meantime is to employ approximations that would be accurate if the ions were macroscopic objects immersed in the actual solvent-so-called Brass Balls in a Bathtub (BBB) models.l2 While BBB models have known derision because " they are not microscopic," their treatment poses formidable intellectual challenge : the select list of successful contributors includes G.G. Stokes, Einstein, Onsager and Zwanzig. Moreover, BBB models continue to score important advances, two of which are most relevant to our work here. As Zwanzig and others have shown, the random rotational motion of solute molecules in non-H bonded systems can be understood in quantitative detail in terms of a BBB model in which the solute is represented as a macroscopic object immersed in a viscous fluid with slip boundary condition^.'^ A second example is the Onsager-Hubbard theory of the effect of electrolytes on the dielectric response of a solution, worked out in terms of a BBB model with charged hard spheres in a medium with specified frequency-dependent dielectric ~0nstant.l~ They find that a major effect has been omitted in earlier interpretations of the dielectric constants of solutions ; the molar dielectric coefficients referred to earlier do not have the simple significance that has been assumed until now.They also correct another BBB model calculation due to Zwanzig (who corrected an earlier version due to Born) for the extra frictional force on an ion moving in a solvent with frequency-dependent dielectric constant. Finally, we notice that one of the widely used BBB model results, Born's calculation of the solvation free energy of a spherical ion, plays a role in the papers by Cobble and Murray and by Kebarle et al. In the progression above, an important class of Hamiltonian models has been passed over, namely, those that specify a spin Hamiltonian.A spin Hamiltonian is derivable by integrating an S-level Hamiltonian over the electron coordinates as well as over many of the nuclear coordinates, but without integrating over all of the spin variables, whether electron spins, nuclear spins, or both. It would seem that a spin Hamiltonian model for a solution could be classified as BO- or MM-level, depending upon the type of nuclear coordinates that are explicit in the spin Hamiltonian. Thus, the results in Akitt's paper relate rather directly to a BO-level spin Hamiltonian while those related by Jackson and Symons are described in terms of BO-level but might alternatively be described in terms of MM-level. In many ways the use of spin Hamiltonians is more highly developed than that of BO- or MM-level Hamiltonians, so it is of interest to quote here a conclusion reached by Abragam and Bleaney.15 A " spin Hamiltonian .. . is the meeting place between14 INTRODUCTION the theoretician who attempts to calculate the various coefficients . . . from what is known or can be surmised about the crystal field and the wave functions of the free ion, and the experimentalist who . , , extracts from the observable spectrum numerical values of the same coefficients.” Bearing this observation in mind, and the similarity in spirit of spin Hamiltonian models and the BO- and MM-level models, I have tried to classify the experimental papers here according to the type of model for which the experiment determines “ coefficients ’’ (table 1). These would be coefficients in the BO-level, U,, or in the MM-level, uN.A friction coefficient at MM-level is a certain integral over the BO- TABLE 1. CLASSIFICATION OF EXPERIMENTAL PAPERS. paper Bo-level MM-level Contreras and Hertz James and Frost Caminiti, Licheri, Piccaluga and Pinna Irish and Jarv Akitt Cobble and Murray Gans and Gill Rao, Agarwal and Rao Fox, McIntyre and Hayon Jackson, Smith and Symons Barker, James and Yarwood Choi and Criss Kebarle, Davidson, French, Cumming Barthel, Wachter and Gores Pethybridge and Taba Miller Paterson and McMahon level Hamiltonian and that is how it is classified in table 1. In papers that present a variety of data, the entry in table 1 refers to the first part of the papers only. Where there is room for difference of opinion in what actually is determined by the experi- ment, I have used the authors’ conclusion.In the table 1 the entry eq. indicates that the coefficient determined by the experiment is an equilibrium average, while t indicates a kinetic or time-correlation function quantity. This classification shows which kinds of experimental results presented in this Discussion can be interpreted in terms of molecular interactions at MM-level and which kinds require a BO-level model. To the degree that it is known how to calculate the experimentally determined coefficients from such models, in the words of Abragam and Bleaney, it is true that the theoretician and the experimenter have a meeting place. J. A. Jackson, J. F. Lemons and H. Taube, J. Chem. Phys., 1960,32, 553. * (a) A. K. Soper, G. W. Neilson, J. E. Enderby and R. A. Howe, J. Phys. C, 1977, 10, 1793 ( b ) H. L. Friedman and L. Lewis, J. Solution Chem., 1976, 5, 445. H. S. Frank and M. G. Evans, J. Chem. Phys., 1945,13, 507. R. W. Gurney, Ionic Processes in Solution (McGraw-Hill, New York, 1953). H. L. Friedman and C. V. Krishnan, in Water, A Comprehensive Treatise, ed. F. Franks (Plenum Press, New York, 1973), vol. 3.INTRODUCTION 15 H. L. Friedman and W. D. T. Dale, in Modern Theoretical Chemistry, ed. B. J. Berne (Plenum Press, New York, 1977), vol. 5. P. S. Ramanathan and H. L. Friedman, J. Chem. Phys., 1971, 54, 1086. H. L. Friedman, C. V. Krishnan and L. P. Hwang, in Structure of Water and Aqueous Solutions, ed. W. Luck (Verlag Chemie, Weinheim, 1974). l o H. Wiechert, H. Krienke, R. Feistel and W. Ebeling, Z. phys. Chem. (Leipzig), 1978, 259, in ' P. C. Vogel and K. Heinzinger, Z . iVaturforsch., 1976, 31a, 476. press. W. G. McMillan and J. E. Mayer, J . Cheni. Phys., 1945, 13, 276. A term due to H. S. Frank, cf, H. L. Friedman, Chem. Brit., 1973, 9, 300. Pecora, J . Amer. Chem. Soc., 1974, 96, 6840. l3 C. M. Hu and R. Zwanzig, J. Chen7. Phys., 1974, 60,4354; 0. R. Baur, J. I. Braunian and R. l4 J. Hubbard and L. Onsager, J . Chem Pl7ys., 1977, 67, 4850. '' A. Abragam and B. Bleaney, Electron Pr/?arizagnetic Resonance of Trmsition M e t d Zoris (Claren- don Press, Oxford, 1970), p. 751.

ISSN:0301-7249    

DOI:10.1039/DC9776400007

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Ionic Solution Theory for Non-ideal Solvents Potential of Mean Force between Ions BY J. S. H ~ Y E Institutt for Teoretisk Fysikk Universitetet i Trondheim 7034 Trondheim-NTH, Norway AND G. STELL Department of Mechanical Engineering, State University of New York, Stony Brook, New York 11794, U.S.A. Received 2nd May, 1977 A comparison is made between fully microscopic models of an ionic solution in a dipolar solvent, in which the solvent as well as the solute is treated on a molecular basis, and quasimacroscopic models, in which the solvent is treated as an ideal continuum. The central objects of inquiry are the molecular potentials of mean force, especially the ion-ion potential in the limit of infinite solute dilution. Our aim here will be to discuss certain features of ion-ion and ion-solvent inter- action from the point of view of statistical mechanics, which serves as a bridge between the microscopic and macroscopic descriptions of a system; that is to say, between its molecular and continuum descriptions. In an ionic solution, the primary elements of this bridge are the set of n-particle probability distribution functions g,,(l, ., . , n) that measure the probability of finding n particles in the system in a given configura- tion, or, equivalently, the associated potentials of mean force W,,(l, . . ., n), where -pW,,(l, . . ., n) = In g,,(l, . . . , n), with p-' equal to Boltzmann's constant k times absolute temperature T. Of the g,,, the radial distribution function g2(l, 2) = exp -pW,(l, 2) embodies the most important features of molecular structure, and it is W,(l, 2) that will be our chief focal point. The molecular model with which we shall be concerned here is a classical non- relativistic one, defined by a potential energy between n particles, ~"(1, .. . , n) which is the pairwise additive sum of two-body terms q2(1,2), ~"(1, . . . , n) = 2 q,(i,j). We treat the whole system, including solvent as well as ions, on a molecular level,* so that we have a solvent-solvent interaction qvv(l, 2) and solute-solvent interaction quv(l, 2) as well as a solute-solute interaction quu(l, 2) between ions to consider. We shall assume that all of these interactions have a repulsive core that becomes infinite (say, faster than l/r6) as r, the distance between particle centres, goes to zero.We shall further assume (as appropriate in considering ions in dipolar solvents) that as r + co, quu(l, 2) is dominated by the Coulombic interaction between point charges of magnitude q1 and q2, quv(l, 2) by the ideal charge-dipole interaction between a 1 S i S f . 5 " * It is in this sense that we use the term " non-ideal solvent " in our title, to distinguish our underlying Hamiltonian model from models in which the solvent is treated as an ideal continuum from the start.J. S . HBYE AND G . STELL 17 point charge of magnitude q1 and a dipole of moment pz, and vvv(l, 2) by the ideal dipole-dipole interaction between dipoles of moment p1 and pz. The macroscopic continuum associated with the above model is simply the fluid of particles as described above, viewed by an observer who becomes infinitely large relative to the radii bU and bv of the solute and solvent particles, respectively.For the fluid in equilibrium, the exact continuum description is thus just the thermodynamic description in the usual thermodynamic (i.e., infinite-system) limit. In addition to the wholly homogeneous macroscopic continuum with which the above limit coincides, there is a more complicated macroscopic configuration that will also prove important to us-a collection of i spherical domains or macroparticles of dielectric constant E,, and radius bl in a continuum of dielectric constant E. At the centre of each domain is a point charge of magnitude q or an ideal dipole of moment p. The full electrostatic potential of interaction between a pair of such domains includes all induced domain-solvent contributions, and is too complicated a function to be represented in simple closed form, but its dominant large-r properties are easily For example (setting c0 = 1 for simplicity) in the case of two charged domains whose centres are a distance r apart, one has as r -+ 00, where we use W with subscripts q (for charges) and d (for dipoles) to denote the domain-domain potentials.As r -+ 00, the ratio of the Wqq(l, 2) to the ideal charge-charge pair potential pqq(l, 2) is thus a direct measure of the dielectric con- stant of the continuum in which the spherical domains are immersed: Similarl~,~ the ratio of charged-domain, dipolar-domain interaction to the ideal charge-dipole potential qqd(l,2) goes to 3/(2& f 1) (which we write as ( 1 / ~ ) [ 3 ~ / ( 2 ~ + l)] for reasons that will be immediately clear), while for the dipole-dipole case we have One might intuitively expect that the microscopic Wuu(l, 2) will behave, in the limit of vanishingly small ion concentration, much like the macroscopic Wqq(l, 2) of eqn (1).To the extent that this expectation is realized-and we shall discuss below its statistical mechanical status-one will find useful a quasi-continuum model of an ionic solution in which the solvent is regarded as a continuum of dielectric constant E but the ions retain their status as particles, with the infinite-dilution Wuu(l, 2) pre- scribed so as to conform to eqn (1) for large r and satisfactorily mirror the presence of a highly repulsive interaction core as Y -+ 0.In perhaps the simplest version of such a model, one regards the ions as elastic spheres of dielectric constant unity into which point charges have been centrally embedded, so that the ion-ion potential of mean force at zero ion concentration is given by W&(l, 2) = cc for r < bl + b, W&(1,2) = Wqq(l, 2) for r > bl + b2 (3)18 IONIC SOLUTION THEORY FOR NON-IDEAL SOLVENTS where bi is the radius of ion i, and the superscript zero here and below refers to the infinite-dilution limit of ion concentration. Although the kind of quasi-continuum picture that leads to eqn (3) has clearly lain behind much of the conceptual development of ionic solution theory, as well as that of the closely related theory of the dielectric properties of polarizable and polar fluids,l the explicit computational use of Wqq(l, 2 ) as the large-r form of W&(l, 2) has not been widespread in theoretical studies of ionic solutions.Levine and his coworkers have been exploiting it for some time,'g4 but it has only been systematically incorpor- ated into the functional form of an approximate W&(l, 2) to be used in statistical- mechanical computations (via the " refined model " of Friedman and his group)5 in the 1970's. The main obstacle to its earlier use does not seem to have been diffidence over its conceptual status, but rather the fact that Wqq(l, 2 ) is itself not representable in simple closed form, plus the fact that until very recently even the crudest tenable approximation, far cruder than that given by eqn (3), has already represented a formid- able statistical mechanical challenge of compelling interest and importance when used as input in McMillan-Mayer theory.This approximation (explicitly introduced by Mayer6 in 1950 although implicit in a great deal of earlier work) is given by W&(l, 2) = 03 for r < b, + b, W&(L 2) = qlq2/Er for r > bl + bt, ( 4 4 which is usually taken together with the assumption that the n-(solute) particle potentials of mean force at zero solute concentration are pairwise additive, The analytic approximation of the structure [e.g., of Wuu(l, 2 ) at arbitrary ion concentration] and osmotic thermodynamics of a system of ions with the Wg . . . given by eqn (4) is only just now becoming a high-precision enterprise, and that in itself is an important piece of news that we want to broadcast here.For ions of equal radii, we now have nearly exact analytic" approximation procedures for the 1-1 electrolyte regime which remain reasonably accurate throughout the 2-2 regime as well.7 For the unequal-diameter case things are in much less well-developed shape, but the groundwork has been laid ; accurate analytic approximations for the osmotic thermodynamics are already in a reasonably advanced state of development* and good approximations for Wuu(l, 2) itself can be expected to follow within the next couple of years or so. (There are two promising competing approaches to the un- equal-diameter case. One is via the solution of the mean-spherical approximation for that case.* The other is via the use of thermodynamic perturbation theory and its variant^,^ using an equal-diameter reference system.) We must refrain from further discussion of these major quantitative advances, however, if we are to touch at all upon the fascinating question of the conceptual relationships among eqn (2), (3) and (4), to which we now turn.First of all, one can ask in what sense, if any, eqn (4) corresponds to a bona-$de Hamiltonian model, and how that model differs from that associated with eqn (3). On a macroscopic scale, the status of eqn (4) was elucidated by Friedmanlo (who introduced the term primitive model to describe that equation). He observed that the equation precisely characterizes the W,, to be expected in the macroscopic-continuum * By analytic, we mean susceptible to closed-form representation or involving, at worst, simple quadratures and transcendental equations.Highly accurate integral-equation results, such as those of the HNC approximation, have been already available from Rasaiah and Friedman for over a decade, but these are not analytic in our sense.J . S . H 0 Y E AND G . STELL 19 model which we discussed above eqn (l), as long as to is set equal to E instead of 1, and the spherical macro-domains are imagined as having infinitely repulsive rigid walls when interacting with one another. A question left open by this observation is what microscopic Hamiltonian can give rise to such a macroscopic model, and this was subsequently investigated by one of us.11 The limiting process we considered rests upon the observation that the macroparticles described by both eqn (3) and (4) can be thought of as being perfectly impermeable to one another, differing only in their permeability to the solvent, with the particles described by eqn (3) perfectly imperme- able to the solvent (and hence empty of solvent) but the particles described by eqn (4) completely permeable to the solvent (and hence filled with it).It is natural to describe this selective permeability in terms of core potentials with non-additive diameters, as one considers the limit in which the ions become infinite in size compared with the solvent particles, and it is so described in ref. (11). To assess the validity of approximations like eqn (3) and to improve upon them, we must understand how the ratios given in eqn (2) compare with the corresponding microscopic ratios W&( 1, 2)/ywu( 1,2), W&(l, 2)/ywy( 1,2) and W&(1, 2)/yvv( 1,2) computed from the molecular model. The comparison was first contemplated by Jepsen and F~-iedrnan.~ They noted that for r -e co the two sets of ratios should become asymptotically identical in a limit in which the charge and dipole strengths become infinitely weak [i.e., py(1, 2) + 01 and the ions infintely large compared with the solvent particles (Le., bv/b, -+ 0).A separate but closely related question is how the two sets of ratios will compare for r -e co if one does not take the weak- strength, large-ion limits. There is nothing written in the sky that says they should be the same, and Jepsen and Friedman3 found that beyond the lowest order in y = 471 y/?,u2p they appeared to be different in the low-density approximation they were considering.Nienhuis and Deutch12 have more recently argued that the result to be expected, to all orders in density, is as in the macroscopic case given by eqn (24, but in contrast to eqn (2b) and (2c), and We have confirmed13 these results by means of a derivation which is formally exact (thus obviating certain assumptions made by Nienhuis and Deutch). Our treat- ment 13,14 further explicates the Jepsen-Friedman results in the following way : we note that the results of eqn (2) and (5) coincide if and only if E is given by the Onsager expression l5 This is consistent with the result given in ref. (14) that only in the Onsuger-continuum limit, in which eqn (6) becomes exact, is the dielectric response to each solvent dipole that of a vacuum in a macroscopic sphere surrounding the solvent dipole.Thus, only in the Onsager continuum limit are the assumptions satisfied under which one can20 IONIC SOLUTION THEORY FOR NON-IDEAL SOLVENTS identify each solvent particle as a macrosphere within which E = 1, and so assure the identity of the full set of ratios in eqn (2) and (5). As yet, we have considered W2(1, 2) here only in the zero ion-concentration limit. As soon as the concentration is non-zero, profound changes in the large-r form of the W2(l, 2) can be anticipated. Although it is widely assumed that Wuu(l, 2) has the form* Stillinger and White l6 have strikingly demonstrated that even this seemingly reasonable assumption should not be taken for granted, by showing how other seemingly reason- able assumptions lead instead to the conclusion that W&(l, 2) -+ O(r-s) as r + co! On the other hand, in as yet unpublished studies Groeneveld and the authors have demonstrated that assuming the convergence, or at least the asymptotic relevance, of certain cluster expansions for the direct correlation function, eqn (7) follows in the primitive model, and we have found no reason to doubt that it is also the limiting form for Wuu(r) when the solvent is treated as a molecular fluid rather than a continuum.However, one clearly cannot in general expect the A in eqn (7) to be the Debye-Huckel inverse correlation length IC = (47~ppe~)~’~, with p = total ionic number density, or the factor A,, to be unity [see eqn (9) below, for example].When the ionic concentration p is not vanishingly small, one expects W, and Wvv as well as W, to be exponentially shielded. The first detailed evidence for this emerged from a monumental analysis of the mean spherical approximation by Adel- man and Deutch,l’ who discovered such shielding by scrutinizing the Laplace trans- forms of W, and Wvv in that approximation applied to a system of charged-sphere ions in a dipolar-sphere solvent, with charge-dipole solute-solvent interactions present. We have recently18 made a study of the exact large-r form of W, and Wv, as well as W, for a symmetric electrolyte in the low q (or low p) regime and find, as r + co, (1 + Ar)emAr & - 1 1 Wuvlvuv -+ - - 3Y E For low q or low p, A 1 &-1+, (9) but eqn (8) may well prove to have a much larger domain of validity than eqn (9).These results are fully consistent with the conclusions of Adelman and Deutch, and in addition reveal the presence of remarkable polynomial factors in W, and Wvv, along with the expected prefactors which survive in the zero ion-concentration limit to yield eqn (5). There seems to be little hope of exactly characterizing the A,, or A of eqn (7) in simple thermodynamic terms except in certain limits such as that yielding eqn (9). In * Here and for the rest of our discussion, we have in mind only the case of model potentials +uu, &v and +vv in which there are no inverse-power terms beyond 4qq, +qd, and +dd, respectively. Any r - P terms in the + values will in general give rise to such terms in the corresponding Wvalues.J .S. HOYE AND G . STELL 21 contrast, for ions of one sign in a neutralizing continuum solvent of dielectric con- stant e, we have givenI9 the exact results (x/2J2 = /3(2'/8p)p, AUU = (4~)~. Stillinger and Lovett have shownz0 that their second-moment condition on g,, = exp -/3W,, can be expected to apply to molecular-solvent as well as continuum- solvent models, while we19 have extended the application of that condition to gvv in the absence of ions, to yield a new expression for the E of a polar fluid. Acknowledgment is made to the National Science Foundation and to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. C.Bottcher, Theory of Electric Polarization (Elsevier, New York, 1952). S . Levine and G. Bell, International Symposium on Electrolytes, ed. G . Pesce (Pergamon Press, New York, 1962). D. W. Jespen and H. L. Friedman, J. Chem. Phys., 1963,38,846. S . Levine and D. K. Rozenthal, Chemical Physics of Ionic Solutions, ed. B. E. Conway and R. G. Barradas (Wiley, New York, 1966). ' See, e.g., H. L. Friedman, C. V. Krishnan and L-P. Hwang, in Proceedings of the International Symposium, held at Marberg in July 1973, ed. W. A. P. Luck (Verlag Chemie, Physik Verlag) and references therein, especially P. S. Ramanathan and H. L. Friedman, J. Chem. Phys., 1971,54,1086. J. E. Mayer, J. Chem. Phys., 1950,18,1426. 'See, e.g., J. Hnye and G. Stell, J. Chem. Phys., 1977, 67, 524; B. Larsen, G. Stell and K. C. Wu, J. Chem. Phys., 1977, 67, 530 and references therein. See also H. C. Andersen and D. Chandler, J. Chem. Phys., 1971,53, 1497 and H. C. Andersen, D. Chandler and J. D. Weeks, J. Chem. Phys., 1972, 57, 2626 for closely related, but less explicit and less accurate, approxi- mations. L. Blum, Mol. Phys., 1975,30, 1529; J. R. Grigera and L. Blum, Chem. Phys. Letters, 1976, 38,486; L. Blum and J. S . Herye, J. Phys. Chem., 1977, 81,1311. J. C. Rasaiah and G. Stell, Mol. Phys., 1970, 18, 249; J. C. Rasaiah, B. Larsen and G. Stell, J . Chem. Phys., 1975, 63,722. lo H. L. Friedman, J. Chem. Phys., 1960,32, 1134. l1 G. Stell, J. Chem. Phys., 1973, 59, 3926. l2 G. Nienhuis and J. M. Deutch, J. Chem. Phys., 1971,55,4213. l3 J. S. Hsye and G. Stell, J. Chem. Phys., 1974, 61, 562. l4 J. S. Hsye and G. Stell, J. Chem. Phys., 1976, 64, 1952. l5 L. Onsager, J. Amer. Chem. Soc., 1936, 58, 1486. l6 F. H. Stillinger and R. J. White, J . Chem. Phys., 1971, 54, 3405. l7 S. A. Adelman and J. M. Deutch, J . Chem. Phys., 1974,60, 3925; see also L. Blum, J. Chem. '* J. S. Hoye and G. Stell, to be published. l9 J. S. Hsye and G. Stell, SUNY College of Engineering and Applied Sciences Report No. 296 (March, 1977), to appear in J. Chem. Phys., 1977, 67, 1776. * O F. H. Stillinger and R. Lovett, J. Chern. Phys., 1968, 49, 1991. Phys., 1974, 61, 2129.

ISSN:0301-7249    

DOI:10.1039/DC9776400016

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Monte Carlo Study of Two Ions in a Stockmayer Solvent BY DAVID J. ADAMS Department of Chemistry, University of Southampton, Southampton SO9 5NH AND JAYENDRAN c. RASAIAH Department of Chemistry, University of Maine, Orono, Maine 04473, U.S.A. Receiued 2nd May, 1977 Monte Carlo calculations have been made for the solvent-ion forces and energies, and the number and moment distributions of solvent molecules around the ions, for a simple model of a pair of singly charged ions of opposite sign in a polar solvent. The solvent was modelled by 4000 Stockmayer particles in the Monte Carlo cell with reduced dipole moment p* = 2.186, temperature T* = 1.19 and density p* = 0.867 chosen to correspond to liquid acetonitrile. The two ions were modelled by the Lennard-Jones potential plus the electrostatic charge with the same E and o as the solvent particles.A series of calculations has been made with the ions at a variety of fixed separations from 1.00 to 4.00. Thz statistical accuracy of the results was improved by sampling mainly within a spherocylindrical volume around the ions. The distribution of solvent particles around the ions is presented in the form of contour maps, These show that, as with a single isolated ion, there is a single, tight, well-defined highly-oriented layer of solvent particles around the pair of ions with only a small disturbance to the solvent structure beyond the first layer. The disposition of particles in this first layer varies greatly with the ion separation. The net force between the two ions is obtained only within rather wide limits, but it does provide useful information on the potential of mean force between near ions.The presence of a " hump " in the graph of (F,> as a function of ion separation, observed in the preliminary calculations of McDonald and Rasaiah, is confirmed. 1. INTRODUCTION It is useful to separate the statistical mechanical treatment of the equilibrium pro- perties of electrolyte solutions into two parts by first averaging over the configurations of the solvent molecules to obtain the potential of average force between the ions and then averaging over the ion positions to obtain the thermodynamic properties.' At low enough concentrations the total potential of average force is pairwise additive, and only the solvent-averaged pair potentials Wz[i,j) are required.Indeed the use of higher order terms would be an unwarranted complication at the present stage of theoretical development. Wz(i,j) may be calculated by considering a system of two ions and many solvent molecules and calculating the ensemble average force on the ions. For two ions a and b fixed in position in a volume V with N solvent molecules,DAVID J . ADAMS AND JAYENDRAN RASAIAH 23 where the integral is over the coordinates of all N solvent molecules and 2 is the canonical partition function of the solvent plus the ions. Given a suitable form for UN+, it is thus possible, at least in principle, to calculate W,(a, b). It is convenient, as with W,,, to consider a UN+, which is pairwise additive, composed of solvent- solvent, solvent-ion and ion-ion terms. Probably the simplest possible system containing the essential features is that of hard-sphere centres plus point dipoles modelling polar solvent molecules and hard sphere centres plus point charges modelling ions.By using a variation on the normal method of Monte Carlo sampling Patey and Valleau were able to calculate for this system W,(a, b) + c as a function of rob, where c is an unknown constant. A more realistic UN,, is obtained by replacing the hard-sphere potential with the Lennard-Jones potential, v d r ) = 4uo[(dr>" - (~/r)'l. (3) A system of particles interacting through Lennard-Jones potentials plus central elec- tric point dipoles, the Stockmayer potential, is a good model for simple polar fluids as a class. It is not a particularly good model for any particular solvent, it does not account for polarization or for the nonspherical shape of the molecules.It will most closely model nearly spherical polar molecules with small polarizability, the three parameters uo, 0 and the dipole moment p chosen to give the best fit to the thermo- dynamic and dielectric properties. Values of uo and G suitable to model acetonitrile have been obtained from the second virial coefficient3 and we have used these, (uolk = 247 K, G = 4.22 A) together with the observed, liquid-phase dipole moment (3.5 Debye) of the molecule in the present work. It is convenient to use reduced units and to model liquid acetonitrile at 20 "C (p = 0.7856 g ~ m - ~ ) , we have used a reduced temperature, T* = kT/uo = 1.19, a reduced density, p* = o3 p = 0.867 and a reduced dipole moment, p * = p/(4m0uoc3)* = 2.186 where p is in S.I.units (i.e., coulomb metres), and e0 is the permittivity of free space. In the same way the electronic charge corresponds, with the present values of uo and 0, to a reduced charge 4" = q / ( 4 z ~ ~ u ~ ~ ) + = - 12.66. We have used univalent ions such that the same values of uo and G are used for the solvent-solvent and ion-solvent interactions. In all cases the pair of ions was of opposite charge; calculations for one ion only are also reported. The present calculations follow the preliminary work of McDonald and Rasaiah4 who calculated the average force between two ions by the standard Monte Carlo method. The total ensemble average force on one ion is the gradient of the potential of average force, where -vVaqab is simply the force on ion a due to the direct interaction with ion b, and the average solvent force on a is where u N + 2 = q u b Uki-2. (6) From a series of calculations for various ion separations one may integrate eqn (4) and determine W,(i,j) + c for any ion-ion interaction consistent with the chosen24 MONTE CARLO STUDY OF TWO IONS I N A STOCKMAYER SOLVENT ion-solvent and solvent-solvent interactions.For sufficiently large ion separation, rib, the macroscopic equation E> = r:bq:q:l&*r:; (7) may be used, where 8, is the dielectric constant of the pure solvent, and the unknown constant c eliminated. However, the present calculations show that this procedure can- not be justified, even when &, is known independently, for the maximum r,'b at present practicable is not sufficiently large for the macroscopic equation to be applicable.McDonald and Rasaiah4 used a small Monte Carlo cell, containing only 108 solvent particles. In the present calculations a very much larger cell of 4000 particles is used, enabling larger ion-separations to be used, and virtually eliminating all effects of the periodic boundary conditions. Additionally, the distributions of solvent particles and their ensemble average orientations as a function of position have been calculated and examples of the former are presented in the form of contour plots. 2. THE MONTE CARLO CALCULATIONS In order to make the limited volume of fluid that can be simulated (the " cell ") resemble a portion of the interior of the bulk fluid, it has been almost universal practice to make the cell periodic so that it is completely surrounded by images of itself.While eliminating the errors that would be caused by some sort of surface, the periodic boundary conditions can themselves introduce other distortions in the ensemble averages calculated. This is particularly likely in the present case. The presence of an ion in the fluid will severely alter the distribution of solvent particles in its immedi- ate locality. If this alteration in the solvent structure extends sufficiently far it will overlap through the periodic boundaries with the region affected by the other ion, and one is no longer simulating an isolated pair of ions in an infinite soivent. Friedman5 has discussed a method which eliminates this possibility by abandoning the periodic boundary conditions for a spherical cavity in a dielectric continuum.However, this introduces a surface into the system and thus raises problems with the short range interactions. The present calculations minimize the effect of the periodic boundary conditions by using the unusually large number of 4000 particles in the periodic cell, so that the cell length is over 160. We have made only the solvent-solvent interactions periodic, the ion-ion interaction does not enter the Monte Carlo calculations and the solvent particles have been made to " see " only the two ions in the fundamental cell and not their periodic images. With the present dimensions of the system there would have been no significant difference if solvent particles had interacted instead with their nearest ion images.However, had interactions with more distant ion images been included also then this would have placed undesirable emphasis on the periodicity and might have affected our results. It is feasible to calculate only the interactions between close pairs of particles, so that each particle is considered to interact only with those particles that lie within a truncation sphere of radius a. As the number of interactions, and thus the com- puting time required, increases as u3 there is very good reason for keeping a small. For the Lennard-Jones potential a - 2.50 is considered adequate.6 However, the dipole-dipole interaction is much longer ranged and the use of any truncation radius, however large, will considerably affect the dielectric properties of the simulation.' There are two schemes for correctly incorporating the long-range nature of the dipole-dipole interaction: one may re-express the expression for the energy of a periodically repeating system of dipoles as two rapidly converging series,8 or one may approximate the fluid outside the truncation sphere as a classical dielectric continuumDAVID J .ADAMS AND JAYENDRAN RASAIAH 25 and add the reaction field energy due to the interaction of this dielectric with the net dipole moment within each truncation ~ p h e r e . ~ The two methods give comparable results for thermodynamic and dielectric properties,’ but the reaction field method has clear advantages: it is easier to program, it is more economical in computer time, and it places less emphasis on the periodicity of the system.The reaction field method has been used for all the calculations reported in this paper, with a = 3.330. A few calculations were repeated without the reaction field, it was found that there was little change in the forces and energies of the ions and, though the differences did increase with the ion separation, they were within the combined errors of the calculations. The only case where the effect of the reaction field was marked was for the ion-solvent energy of a single ion. Then with a reaction field (Uion/uo) = (U:,,n) = -335 and without the reaction field ( U,,,/u0) = -292 in one run and -275 in a second inde- pendent run. In the case where there are free charges in the polar fluid there are two terms to the reaction field at each dipole.First, there is the Onsager reaction field produced by the polarization of the medium outside the truncation sphere by the net dipole moment inside the truncation sphere, where E , is the dielectric constant of the medium. The medium is also polarized by the ions present, the additional field on dipole i from the polarization of the medium outside its truncation sphere due to an ion k of charge ek at s k from the dipole is The total reaction field energy of a given configuration is u, = -3 I: pi * [RI + I: Rt(k)I* 1 k The factor of + arises because the summation over i effectively counts every long range interaction twice, each dipole both experiences a reaction field and contributes to the reaction fields of the others.The fluctuations in the dipole moment of the pure sol- vent show its dielectric constant to be of the order of fifty or larger. It was found very difficult to obtain reliable results by this means when the dielectric constant is large. The usefulness of the reaction field method lies in the insensitivity of the reaction field to E,, provided E , is large. The present calculations used 8, = 50, and the similarity in the results obtained when 8, = 1 (Lea, with no reaction field) prove this insensitivity in the present case. A large number of particles is necessary properly to simulate a solitary pair of ions in the solvent, but the prime quantity of interest, the force on the ions, arises mainly from the interactions with particles close to the ions: thus for the same number of Monte Carlo steps the sampling of the ion-solvent forces will be worse than for a smaller system.In order to improve the sampling, the Monte Carlo program pre- ferentially chose to move particles within a spherocylindrical region, of radius 5 0 , centred on the ions. Provided that every particle is eventually moved the averages along the Markov chain will correctly converge to the ensemble averages. Squire and HooverlO used this method to improve their statistics when calculating the26 MONTE C A R L 0 S T U D Y OF TWO IONS I N A STOCKMAYER SOLVENT properties of a vacancy in solid argon. In the present case it was necessary to take care that the reversibility condition for the probabilities of various stepsll was not violated.At the start of each step it was randomly decided whether to sample only within the spherocylinder (for most calculations with probability 0.9) or to choose any one of the particles indiscriminately. When sampling only within the spherocylinder the selection of a trial configuration goes as follows. Particles are chosen at random until one within the spherocylinder has been selected. This particle is then given a small random displacement and is rotated through a random angle about either the x, y or z axis of the cell, chosen at random. If this new position for the particle is inside the spherocylinder then the trial configuration has been produced, otherwise the new position is abandoned and the whole process of selecting a particle is repeated.This elaborate process is necessary to ensure that no bias is introduced into the configurations produced: if the step permitted particles to leave the spherocylinder then it would be far more likely for a particle inside to be moved out of the region than for one outside to be moved in, and there would be a bias towards configurations with a lower density in the spherocylinder. Again, if having chosen a particle, more than one trial displacement of that particle were produced until one that was also with- in the region occurred, then there would be a bias preferentially moving particles near the surface of the spherocylinder deeper into it. In each case, on proceeding from one separation of the ions to the next, the trial configuration was “ equilibrated ” by preliminary Monte Carlo runs prior to the start of the calculation of the ensemble averages. This “ equilibration ” consisted of at least eight hundred thousand Monte Carlo steps of reduced accuracy (a = 1.660) followed by at least two hundred thousand further steps with a = 3.330.In order to be quite certain that the arrangement of dipoles from the previous ion separation had been completely shaken out we sometimes modified the first of the equilibration runs to “ anneal ” the structure: the run was started at a very high temperature (T* - 4.0) and the temperature progressively reduced as the calculation proceeded. 3. ION-SOLVENT FORCE AND ENERGY When quantities such as pressure and energy are calculated by Monte Carlo, results of adequate statistical reliability are generally produced with a few hundred thousand steps.One reason is that, in some sense, a double average is made: at each step in the Markov chain many particle-particle interactions are calculated and added into the running sums. If one were to calculate the ensemble average energy, say, by finding only the average energy of a single, designated particle then the result would be subject to very much larger statistical uncertainty. The same applies in the present case where averages are made of the energy and forces acting on only two particles. The use of the special spherocylindrical sampling region helps, but does not solve the problem. Nor is the brute-force solution of using longer chains practic- able at present: the reliability of the results will only improve roughly as the square root of the number of steps, so -10’ steps would be needed for a significant improve- ment over the 1 x or 2 x lo6 steps of the present work, and lo6 steps takes nearly two hours on the CDC 7600.In order to gain some estimate of the reliability of the results the average x, y and z forces on each ion were calculated separately. The line joining the two ions is in the x direction so the true ensemble-average y and z forces will be exactly zero and the x-direction forces on the two ions equal and opposite. This is not true, of course, for the Monte Carlo calculations, and the deviation of our results from these known values27 DAVID J . ADAMS AND JAYENDRAN RASAIAH TABLE 1 .-RESULTS 1 .o 1.3 1.5 1.7 1.8 1.9 2.0 2.1 2.3 2.5 3.0 3.5 4.0 m 106.2 100.3 96.2 77.7 53.6 52.8 39.8 41.6 45.5 48.0 37.8 28.0 30.8 0 - 30.1 3.3 23.8 21.7 3.7 8.1 -0.5 5.1 12.2 22.3 19.9 14.9 20.8 0 - 103.9 -134.1 - 157.9 - 179.4 - 183.2 -193.8 - 194.7 - 207.6 -208.6 -225.5 -247.6 -268.9 -280.4 - 334.9 159.5 128.6 108.9 91.5 85.0 79.6 75.0 70.9 66.6 52.6 31.1 14.7 0 39.3 44.7 41.8 37.1 35.9 35.3 34.9 34.6 33.8 28.5 17.8 9.0 0 gives a measure of the likely errors in the values of (Fxsolv*) obtained.The ion- solvent forces and energies of each ion are given in table 1, with the convention that a force acting away from the other ion is positive. The results for infinite separation of the ions was obtained by having only one ion in the Monte Carlo cell. The largest probable error in the results for FxsO'v* at each ion separation is given by the sum of the magnitudes of the largest y or z force calculated and of the difference between the individual x-direction forces and their average value.This sum has been used for the error bars in fig. 1. In table 2 we present the raw Monte Carlo data. -1ooi FIG. 1 ,-Reduced force against ion separation. U-(F:$"'), ()-<F$,"') and O--(.F:>. The upper line shows the Lennard-Jones force between the ions and the lower line the electrostatic force. In agreement with the results of McDonald and R a ~ a i a h , ~ (FP'"') shows a rapid decline between 1.5 and 2.0 r* and (F:) has a " hump '' in this region. This would seem to confirm the existence of the " hump " as a generally occurring phenomenon for the type of potential interactions employed here, there are signs of the same effect in the results of Patey and Valleau' also.Note that McDonald and Rasaiah's fluid was colder, less dense and of a smaller dipole moment than in the present study, more28 MONTE C A R L 0 STUDY OF TWO IONS IN A STOCKMAYER SOLVENT TABLE 2.-RAw MONTE CARLO DATA ~~~ ~~ 1 .o 111.6 100.8 -5.3 5.2 -2.6 -6.8 -92.7 -115.1 1 1.3 93.0 107.7 -4.2 -0.5 -4.1 7.2 -117.5 -150.6 1 1.5 100.5 91.9 -5.4 8.7 -6.1 -7.6 -152.2 -163.6 1 1.7 79.5 75.9 -7.9 3.9 0.8 -2.9 -178.4 -180.4 1 1.8 52.8 54.3 -10.4 1.1 3.9 -3.7 -186.5 -180.0 1 1.9 57.6 48.0 -3.0 5.1 -2.2 -12.3 -197.1 -190.4 2 2.0 32.0 47.6 3.5 0.1 3.7 1.2 -199.6 -189.9 1 2.1 40.5 42.6 9.4 4.1 9.8 9.4 -213.6 -201.5 1 2.2 47.8 43.1 8.7 11.1 1.2 2.4 -217.8 -199.3 2 2.5 53.8 42.2 -7.8 9.7 -0.7 7.1 -225.0 -226.1 2 3 .O 43.3 32.2 9.8 7.7 7.8 1.2 -246.5 -248.7 1 3.5 34.1 21.8 13.7 -17.5 -5.2 9.6 -274.9 -262.9 1$ 4.0 16.2 45.5 10.8 1.7 -5.2 -1.5 -272.0 -288.9 1 02 -9.3 - 14.7 - 7.7 - 334.9 1 precisely their system was: p*' = 2.833, q* = 20.24, T* = 1.0 and p* = 0.74.Unfortunately, an error subsequently discovered in their computer program may in- validate their results quantitatively, but their general conclusions remain. The average forces have been integrated by the trapezoidal rule to obtain Ws0lv* and Wi = Wpl"* + I&,, apart from the constant of integration, and these are plotted together with the ion-solvent energy in fig. 2. 0 I 1 2 3 4 rob* FIG. 2.-Reduced ion energy and potential of average force against ion separation. 0-( U:on,o - U;&)), ()-(U;on,b - U;&)), O-W2S01"* + c and 0-W; + c'. The values of c and c' were chosen to give zero values at r : , b = 4.0.The line shows the absolute value of the direct inter-ion potential, lp:,b\.D A V I D J . ADAMS A N D JAYENDRAN RASAIAH 4l 3 - Q* 2 - 1 - 29 r * FIG. 3.-Density distribution functions. The line is p*(r*) for the pure fluid and the points are p*(r*) of solvent particles around a single ion. cos e . ? ? ~ ~ ( O ~ N O N U I D - o o o o o o o o o . # I I I 1 I 0 .o 0.5 1 . 0 1.5 2 . 0 R 2 . 5 3 . 0 3 -5 4 -0 4 . 5 5 .o ion where 8 is the angle between the dipole and r*. The contours are not equally spaced, higher regions are indicated by heavier lines.30 MONTE C A R L 0 STUDY OF TWO IONS I N A STOCKMAYER SOLVENT 4. SOLVENT DISTRIBUTION AROUND THE IONS The radial distribution of solvent particles around a solitary ion, p*(r*) is compared with the pure solvent radial density distribution in fig.3. Clearly the effect of the ion is large out to only -2.10, beyond that the spatial distribution is not significantly different from that around a solvent particle. The distribution illustrated in fig. 3 is averaged over all orientations of the surrounding particles, fig. 4 is a contour map of p*((r*, cos 0) where 0 is the angle between the dipole and Y*. The first shell of sur- rounding dipoles, containing between eight and nine dipoles, is strongly aligned by the ion and some bias in alignment exists out to at least 50. Between -1.3 and -1.50 the four dipoles present show a tendency to align in opposition to the ion and (cos 0) in this region is small and negative. When two ions are present the spatial distribution of solvent particles around the ions is best described by the density distribution function p*(x*, r * ) where x* and r* are cylindrical polar coordinates with origin at the midpoint betwen the two ions, From the symmetry of the system only positive values of x are needed.Fig. 5 shows 0.0 1.0 1.7 1.8 1.9 2.0 2 . 2 2.5 3.5 4 . 0 FIG. 5.-Contour maps of p*(x*, r*), the density distribution of solvent particles around a pair of ions, for several ion separations. The contours are equally spaced with interval p * , the bulk density. In each case a spherocylindrical region of radius 1.50 is illustrated. contour maps of this function for a variety of ion separations and includes the same function calculated for a single ion for comparison.These distributions suffer from the same statistical limitations as do the calculations of force and energy; calculations of the triplet distributions in a one-component system, where it is unnecessary to single out two particles for special attention, produce rather better statistics.12 The results are particularly poor where the annular volume element is small, that is, whenD A V I D J . ADAMS A N D J A Y E N D R A N RASAIAH 31 r is small. The results along the axis of symmetry in particular will be unreliable and the distribution around a single ion shows this clearly. At a separation of 1.0 G the two ions are surrounded by a tight shell of twelve dipoles.As the separation is increased, two dipoles out of the twelve move in slightly towards the centre of the widening gap and are strongly aligned in opposition to the moment of the ion pair. This arrangement is well developed by 1.50. At 1.70 the first shell, including the two central dipoles, contains fourteen dipoles. However, at 1.80 the arrangement is different, there are twelve to thirteen dipoles in the shell and there is no strong preference for an arrangement with two dipoles bound close be- tween the ions. Clearly, 1.80 is intermediate between the well defined disposition of dipoles at 1.70 and the very different solvation structure at 1.90. Here there is pre- cisely one dipole between the two ions. Note that this one dipole, strongly aligned by the field between the ions, is most commonly on the exact line between the ion centres only when they are 2 .0 ~ apart, and at 1.9 and 2.10 it is most frequently dis- placed off line by -0.240 and -0.140 respectively. Between 1.9 and 2.1 the overall number of dipoles in the first shell increases from just under fourteen to fifteen. At a separation of 2.20 there is yet another solvation structure and the first shell of dipoles around the ions contains about seventeen dipoles, twice the number in the first shell of an isolated ion. Thus from 2.20 to at least 3 . 0 ~ each ion is wrapped in its own separate layer of dipoles, these two layers “ touching ” each other. The con- tours of p*(x*, r * ) for a separation of 2 . 5 ~ suggest a well-ordered arrangement of dipoles, each apparently in a position as well defined as if they formed a large molecule of eighteen dipoles and two ions.Fig. 6 is a stereoscopic projection of one configura- I/ ? L - - L * ’-- > 6 --r. 4, \ = 6 -. 1-47 / 1 \\ &A 7’. $ 9 1’. FIG. 6.-Stereo pair showing the disposition of the nearest 22 dipoles to a pair of ions with separation r:,b = 2.5, for just one configuration generated during the Monte Carlo calculation. tion generated for the case of 2.50 separation. It is possible to discern from it each of the rings of dipoles that form the high peaks of p*(x*, r*), but there is little or no sign of an ordered arrangement apart from that. Moreover, with increasing separation the surface enclosing the first layer becomes more difficult to define and is to some degree arbitrary, at best one can only state that it is possible to distinguish a first shell which on average contains about eighteen dipoles.For a more precise description, a form of the probability distribution P(n, r ) of there being n particles within a radius r of a reference particle, introduced by Woodcock,13 may prove useful. At a separa- tion of 3.50 the solvation layers of the two ions are separated by three dipoles. At 4.00 the arrangement of dipoles between the two solvated ions is less ordered but, as it contains an average of at most seven dipoles, it can hardly be considered to behave as the bulk phase in a weak electric field as eqn (7) implies. Our results do show, how- ever, that the dipoles between the solvated ions are not held in strong alignment by the electric field of the ions, though their orientations are, of course, influenced by the field.The distribution of dipole orientations around two ions, corresponding to the one-ion case shown in fig. 4, is an unwieldy function of four variables, and was not calculated. The ensemble average moments of the dipoles along the x-axis and on the radial axis of the nearer ion were calculated as functions of position. The results in each case show only the first layer of dipoles to be oriented by the electric field of the ions, much as was found for the case of one ion.32 MONTE CARL0 STUDY OF TWO IONS I N A STOCKMAYER SOLVENT J. C . R. thanks Dr. Ian McDonald and Prof. K. Singer for inviting him to visit Royal Holloway College where the greater part of the research was done. The S.R.C. is thanked for the award to J. C. R. of a Visiting Fellowship and for financial support to D. J. A. The hospitality of Prof. K. Singer (Royal Holloway College) and Prof. J. S. Rowlinson (Oxford University) is gratefully acknowledged. H. L. Friedman, Ionic Solution Theory (Interscience, New York, 1962). G. N. Patey and J. P. Valleau, J. Chem. Phys., 1975,63, 2334. J. A. Barker and F. Smith, Austral. J. Chem., 1960,13,171. I. R. McDonald and J. C . Rasaiah, Chem. Phys. Letters, 1975,34, 382. H. L. Friedman, Mol. Phys., 1975, 29, 1533. I. R. McDonald and K. Singer, J. Chem. Phys., 1969, 50, 2308. D. J. Adams and I. R. McDonald, Mot. Phys., 1976,32, 931. J. A. Barker and R. 0. Watts, Mol. Phys., 1973, 26,789. lo D. R. Squire and W. G. Hoover, J. Chem. Phys., 1969,50,701. l1 W. W. Wood, Physics of Simple Liquids, ed. H. N. V. Ternperley, J. S . Rowlinson and G. S. Rushbrooke (North-Holland, Amsterdam, 1968), chap. 5. l2 H. J. Raveche, R. D. Mountain and W. B. Streett, J. Chem, Phys., 1972,57,4999. l3 L. V. Woodcock, Thesis (University of London, 1970). 8H. Kornfeld, Z . Phys., 1924,22,27.

ISSN:0301-7249    

DOI:10.1039/DC9776400022

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Analysis of the Total Ion-Solven t Encounter Configurations of C10, and BF, with Na' and Li' in Water, Studied by Various Nuclear Magnetic Relaxation Times BY M. CONTRERAS AND H. G. HERTZ* Institut fur Physikalische Chemie und Elektrochemie der Universitat 75 Karlsruhe, W. Germany Received 28th April, 1977 From 19F magnetic relaxation rates caused by nuclear magnetic dipole-dipole interaction with "OD2 and 160H2, the orientation of water molecules in the hydration sphere of thestructure breaking ion BFT is determined. We find the radial orientation of the electric dipole moment to be very likely at high dilution, though at higher concentration marked deviations from this orientation do occur. From 19F-'Li magnetic interaction a cation-anion model distribution function was obtained; 7Li-H20 interactions lead to information on the hydration structure of Li+.'Li and 23Na relaxation together with 35Cl and llB relaxation, all caused by electric quadrupole interaction, within the electro- static model theory, yield a particular electric dipole orientation for the three water molecules belong- ing simultaneously to the cationic and anionic hydration sphere during the process of ion encounter. If one undertakes to study the structure of an electrolyte solution, this may be done with two different degrees of perfection in mind. We may first ask: what is the proba- bility p(r, Q)drdQ of finding a given particle at a position r and with an orientation Q relative to a reference particle. Or secondly we may wish to know more, namely: given a pair configuration characterized by Y, Q, what is the probability P(R)dR of finding an electron at a position R relative to a coordinate system fixed on the reference particle.The present study is devoted to the first level of structural description. The systems considered are aqueous solutions of NaClO,, LiCI04, NaBF,, and LiBF,. One reason for this choice is connected with the structural problem in the second level. It has been found that the perchlorates and tetrafluoroborates (among other salts) split the vibrational bands of water in the fundamentall-10 and ~vertonel'-~~ regions with the formation of high frequency bands. Furthermore, the n.m.r. chemical shift of the Na+ ion in the presence of C1Or and BFr shows a strong concentration d e p e n d e n ~ e ' ~ , ~ ~ and the 19F chemical shift and 19F-B coupling constant^'^-^^ also vary with the composition of the salt solution.The observed frequency distribution of the intramolecular water vibrations and the n.m.r. parameters are determined by the intermolecular nucleus-nucleus and electron distributions. Therefore, as a first step towards the explanation of these quantities it is useful to have some knowledge of the nucleus-nucleus distributions. A second reason for our choice of system is the fact that two of the nuclei involved here have a nuclear magnetic relaxation mechanism which is-at least partly-based on magnetic dipole-dipole interaction, and, since the magnetic field of a point dipole varies as l/r3 with the separation r from this point dipole, the magnetic relaxation rates of these nuclei can give information about the internal geometry of the solution. Finally, the anions involved here are structure- breaking ions.For these ions the commonly used model of a rigidly hydrated ion with strictly orientated water molecules is particularly inadequate. Thus the question34 ANALYSIS OF THE TOTAL ION-SOLVENT ENCOUNTER CONFIGURATIONS arises; what is the correct model one should have in mind when dealing with physico- chemical properties of these ions? Fortunately, BF, is one of the very few structure- breaking ions which contains a nucleus with spin 1/2, i.e., which relaxes by magnetic dipole-dipole interactions. The nucleus of the structure-forming ion Li+ in aqueous solution relaxes by magnetic dipole-dipole interaction and by quadrupole interaction.The other ionic nuclei relax by electric quadrupole interaction; we shall apply previ- ously developed t h e ~ r i e s ~ ~ * * ~ and evaluate these relaxation results in order to obtain structural information. A simple binary electrolyte solution is characterized by six pair-distribution func- tions. The anion-anion, cation-cation, anion-cation, anion-water, cation-water and water-water distribution functions. The present contribution will be mainly devoted to the anion-water pair distribution function-for other distribution func- tions some results will be briefly sketched.z1 All the functions we are presenting are really only model pair distribution functions. These model distribution functions are very simple functions characterized by a finite set of parameters.Some of these parameters are guessed using plausible assumptions, the remaining ones-one or two in our examples-are determined by nuclear magnetic relaxation experiments. ANION WATER PAIR DISTRIBUTION FUNCTION OF BFT Since the solvent molecule water is not of spherical symmetry, the anion-water pair distribution function depends on the distance r, between the water molecule and the anion, and on the orientation of the H20 molecule relative to the anion. The basic principles of the treatment have been given previously,22 here the extension to a structure-breaking ion like BF; is presented. It will be seen below that the fact that one is dealing with a structure-breaking ion introduces severe difficulties. When dissolved in "OD2, (1/T'Jl, the intermolecular relaxation rate of I9F on the BF; ion is controlled by the magnetic dipole-dipole interaction with the 1 7 0 nucleus.(l/T,), may be written in an approximate form: 2 z ~ 2 3 4 kl = 5 Y;1YI~2~,(S1 + 1) ysl is the gyromagnetic ratio of the 170 nucleus, the spin of which is S,, yr is the gyro- magnetic ratio of the relaxing nucleus, 19F. p(rs, a, p, y ) is the anion-water pair distribution function giving the probability density of finding a water molecule at a position rs and having the orientation a, p, y relative to the BF; ion. v, is defined in a coordinate system fixed in the BF; ion, and for convenience the origin is chosen at the position of any one of the four 19F nuclei. a, p, y are the three Eulerian angles, Q = ( E , P, r), r, is the distance between the 19F nucleus and the I7O nucleus, R, is the intramolecular vector pointing from the centre of the water molecule towards the 1 7 0 nucleus, i.e., here we have virtually R, = 0.Eqn (1) is written for the situation of extreme narrowing, i.e., it holds for the fre- quency ~ 3 0 . ~ ~ The important approximation which is implied in eqn (1) is the as- sumption that the time correlation function of the magnetic dipole-dipole inter- actionZ4J5 decays exponentially. Furthermore, the model of molecular motion does not contain explicitly the property of probability conservationz6 and the correlation time 7; characterizing this motion is assumed to be constant within certain regions around the BF; ion (see below). In the same way, in the solvent 160H2, the 19FM .CONTRERAS AND H. G . HERTZ 35 relaxation rate caused by the water protons is given by the relation: where ys2 is the gyromagnetic ratio of the proton, the spin of which is S2 = 3. RZi (i = 1, 2) are the intramolecular vectors connecting the centre of the water molecule with the two water protons. rZL (i = 1,2) is the distance between the 19F nucleus and the two water protons. As usual, our procedure is to introduce a model pair distribution function in eqn (1) and (2). Then, using the two experimental quantities (1/TJl and (l/TJ2 we are able to determine two parameters of this model pair distribution function. We choose the following two parameters: (1) one parameter, denoted by n, describes the steepness of the F-0 atomic pair distribution function.(2) The other parameter is the angle /3 which gives the direction of the electric dipole moment of the water mole- cule with respect to the vector connecting one of the F atoms of BF; with the water oxygen (see fig. 1). p = 0 corresponds to the symmetrical arrangement where both water protons point towards the anion. We assume a 6 function for the angular part ofp(r,, tc, p, 7) with respect to /? and y : S(p - Po) and 6 ( y - yoi) (i = 1, 2) with yol = 0 or yO2 = n/2. y is the angle which describes the rotation of the water mole- cule around the dipole axis. Furthermore, we assume isotropic distribution with respect to C( and also isotropic orientational distribution of v, for the half-space above the dashed line in fig. 1. For the lower half-space we have p"(vQ, tc, p, 7) = 0 for r, < b (see below).Then our two model pair distribution functions corresponding to the water orientations y = 0 and y = n/2, respectively, are: with /p("(r,. /?, y ) dv, dR == ifc a is the closest distance of approach between the "F nucleus and the centre of the water molecule, NA is the number of water molecules in the system with volume V, n, is the first coordination number of an F atom with respect to the water molecules, b is the closest distance of approach of a water molecule in the second coordination sphere of F. The steepness parameter n and the angle Po are the two parameters we wish to determine. Introduction of eqn (3), (4) and ( 5 ) into eqn (1) and (2) yields:36 ANALYSIS OF THE TOTAL ION-SOLVENT ENCOUNTER CONFIGURATIONS FIG.1.-Orientation of water molecules in the hydration sphere of BFC. One of the water molecules shown (B = 0) represents a typical situation in the limit of infinite dilution, the other one (j e 80') is typical of a concentrated NaBF4 solution. k = ro/a; I = b/a; 1, = b2/az. The function g(n, 4, I ) is shown in fig. 2. c is the OH distance in the water molecule and A is the H/O\H angle, A = 104.5", the superscripts (i) indicate that the pair distribution function p")(i = 1,2) has been used. Our estimates of the correlation times are2z*27 az ** b2 T: = 3 and 7, = - 3b (9) where b is the mean self-diffusion coefficient : b = W B F h + DH*O)' In the diluted solutions we use a local diffusion coefficient for the 1st hydration sphere: with Eqn (6), (7), (8) may be rewritten as bloc %Dloc,H~O + DBFh) < DIoc,H~0/D1120 <M .CONTRERAS A N D H . G . HERTZ 1.0 I 31 with 0.7- - 0.6.- si C' \ 0 $ 0.5- Y 0.4- 0.3- 0.2 0.1 -_ -- \\\- 4 3.5 0 8 n= 0.4 I , , , , ; , , I , r l 1 2 3 I FIG. 2.-The quantity g(n, k = 0.9, I ) as a function of the ratio I = bja. Fl(m, Po) = [ 1 + m2 - 2m cos 1 t m2 - 2mcos m = cJa.38 ANALYSIS OF THE TOTAL ION-SOLVENT ENCOUNTER CONFIGURATIONS I 035. 0 30 0 25 - I m -- 020 -b 0 15 0 10 Now we define the quantity b FZ b, Comparison with eqn (lo), (1 l), (12) yields with For our system a = 2.7 A, c = 0.96 A, it follows m = 0.36. F,(0.36, Po) (i = 1, 2) is shown in fig. 5. In the following we use eqn (6) in order to determine the steepness parameter n from the experimental result (l/Tl)l and eqn (14) to find the angle Po from the experi- mental ratio (l/Tl)I,,/(l/Tl)I,l = K* [eqn (13)].We set g* = 1. The experimental quantities needed are derived from fig. 3 and 4 FIG. 3.-19F relaxation rates in aqueous solutions of NaBF4 and LiBF4 as a function of the salt concentration. Concentration given in the aquomolality scale, i.e., moles salt/55.5 moles of solvent water. @-NaBrF4 in H20, A-LiBF4 in HzO, O-NaBF4 in D20, V-LiBF4 in D,O.(T = 25°C).M . CONTRERAS AND H. G . HERTZ 39 0.25 1 . 0 0.2 0.4 0.6 0.8 1.0 'OgxH FIG. 4.-19F relaxation rate of NaBF4 dissolved in water as a function of the 160H2 mole fraction xH (open symbols) and of the "OD2 mole fraction xo (filled symbols), respectively. Concentrations of salt in the aquomolality scale.Dashed lines represent extrapolation values for c i 0. 0, 0,0.45 5; 0, +, 7.6 fi; A, A, 4.8 15; El, m, 2 . 0 5 . Here (1/Tl)&,S,o is the slope with respect to xo, the mole fraction of ''OD2, of the straight line describing the relaxation effect due to 1 7 0 [see also ref. (22), (28)]. The straight lines are given in fig. 4 by the one single filled symbol per salt concentration. (I/T& is given by the relation [see ref. (22), (28)]: (1/T&s,H is the slope with respect to the H20 mole fraction xH of the straight line corresponding to the effect of the water protons on the 19F relaxation. These are the lines given by the open symbols in fig. 4. (l/T,),, is the relaxation rate for xH + 0, xo + 0. The dynamical isotope correction factor 5 was chosen to be 0.20 2 < 2 0.16 in the concentration range 0 < c* < 7.6 15.where ysD and S, are gyromagnetic ratio and spin, respectively, of the deuteron.40 ANALYSIS OF THE TOTAL ION-SOLVENT ENCOUNTER CONFIGURATIONS 0 20 40 60 80 100 120 140 160 D o FIG. 5.-The functions Fl and F2 according to eqn (lla) and (12a) plotted against the angle Bo. m = cia = 0.36. The results of our evaluation are presented in tables 1 and 2. The data for the calculation of b have been reported e l s e ~ h e r e . ~ ~ ~ ~ ~ It may be seen from table 1 that (1/TJl is remarkably small. It is interesting to compare these results with other results of the 170Dz contribution to the 19F or proton relaxation rates. All the data available are given in table 3. Proton relaxation data are converted to 19F results by multiplication by a factor 0.885 = $&.For the solutes which are subject to hydrophobic hydration the 1 7 0 relaxation contribution is much larger than found for BF,. But, very surprisingly, F- also shows a very low relaxation effect caused by 170. This, in spite of the fact that F- is certainly a structure-forming ion. Strong local concentrations of 1 7 0 in a well-structured hydration sphere should yield a strong relaxation effect. Thus, as assessed from the 1 7 0 contribution to the 19F relaxation rate, the difference between a structure-forming (F-) and a structure-breaking ion (BF,) is not so far detectable. However, detection can be achieved if one considers the relaxation effect caused by the protons.* It may be seen from table 1 that g(n, k, Z) = 0.21 in the limit of high dilution of the salt.This means that the ion water pair distribution function is fairly flat as ex- pected for a structure-breaking ion?1*32 The steepness parameter is n = 0.8. With increasing concentration of the salt the anion-water pair distribution function becomes sharper, g(n, k, Z) + 0.63, n -w 2.8. This is due to the fact that Li+ and Na+ are * For F- we have previously found (1 /T1)z = 5 x lo-' s -l, 22 whereas here we find (1 /T& = 8.8 x s-l. There may be two reasons for the low values of (l/Z'J1 due to "0: (1) the experimental error connected with the F- measurements is underestimated for F-; there is only one nucleus per ion whereas in the present study we have four F nuclei per ion. (2) The first coordination number of F- at a concentration 1 5 may already be less than four due to strong association effects with cations and anions.30M.CONTRERAS AND H. G. HERTZ 41 TABLE 1 .-RELAXATION RATES OF I9F CAUSED BY I7O AND MODEL PARAMETERS DERIVED FROM THESE DATA /El is-' i s - ' cm-% cma s-' cm's-l s-I s-l 0 0,101" 0.006 i 0.003" 3.34 2.08' 2.70 4.4 1.6 0.21 0.8 0.45 0.103 0.006 & 0.003 3.33 2.06 2.52 4.4 1.6 0.20 0.8 3.3 0.32 1.4 2.0 0.111 0.008 & 0.003 3.17 1.84 2.02 4.7 4.8 0.141 0.012 i 0.004 2.85 1.43 1.45 5.45 6.55 0.46 2.0 7.6 0.191 0.018 i 0.006 2.54 1.10 1.10 6.33 11.7 0.63 2.8 extrapolation value; b = 5.5 A; n, = 3. TABLE 2.-19F RELAXATION RATES CAUSED BY WATER PROTONS AND DERIVED WATER DIPOLE ORIENTATIONS lfi is-' Is-1 Is-' 0 0.086 & 0.002n 0.041 0.045 & 0.002 28 6 & 0.3 10 0.45 0.086 & 0.002 0.041 0.045 f 0.002 28 6 ZIC 0.3 10 2.0 0.093 & 0.002 0.044 0.049 & 0.002 14.9 3.2 f 0.12 50 4.8 0.107 0.003 0.051 0.056 & 0.003 8.5 1.82 & 0.10 77 7.6 0.117 & 0.003 0.059 0.058 & 0.003 4.95 1.05 & 0.05 100 a extrapolation value; m = 0.36; we have set g* = 1 ; obtained from fig.5. TABLE 3.-RELAXATION RATES CAUSED BY "OD2 (All solutes at c i = 1 31, proton converted to I9F values) solute particle (3 1 lit. ref. 110-3 s-1 F- 7.1 f 2.2 22 BF, 6.5 & 3 this work DOOCH 28.2 & 2 22 D 0 0 CCDzCDzH 41.0 & 3 22 DOCDzH 42.0 & 5 22 (C2D&NCD2CDZH + 37.5 & 13 28 structure-forming ions. If the cation approaches the anion the water molecules become strongly attracted in the field of that ion but are at the same time fixed with respect to the encounter axis cation-anion; this sharpens the anion-water pair distri- bution function.We turn now to the fundamental difficulty which appears when our method is applied to a structure-breaking ion: as may be seen from table 1, the experimental error is larger than the quantity (l/Tl)r,l which is the first coordination sphere con- tribution to the 19F relaxation rate. As a consequence, the denominator of eqn (13) is unknown and no number can be given for K*. Thus, due to insufficient experimen- tal accuracy, the task we have envisaged, the determination of the angle Po, cannot be accomplished in a rigorous way. The only procedure we can adopt is the following: the results for g(pI, k, 1) listed in table 1 are reasonable when considered in view of our42 ANALYSIS OF THE TOTAL ION-SOLVENT ENCOUNTER CONFIGURATIONS general knowledge of structure-breaking ions.31932 Therefore, the (l/Tl)I,l values as given in table 1 may be accepted as calculated quantities according to a suitable model of a structure-breaking ion.Then the experimental results obtained for (l/T'l)l have merely the character of a compatibility check. These calculated (l/Tl)I,l values were substituted in eqn (13), when using eqn (14) we found the F(m, Po) results presented in table 2. Now the experimental error is only that of the proton relaxation measure- ments. These data mean that given a certain first sphere contribution stemming from I7O, the F values are those shown in the table.The authors would estimate the uncertainty involved in the calculation of (l/Tl)I,l to be &SO%. The resulting F values are such that only configuration 2 should be considered to be realistic, i.e., we have equal distances from F to both water protons. In table 2 angles Po are only given for this " non-hydrogen bonded " configuration. It may be seen that at high dilution the angle Po - 0, that is, we find the classical fully symmetrical arrangement of the water molecules around the anion. With increasing concentration the H plane is gradually more tilted relative to the F-0 axis. This result is in H agreement with the interpretation of relaxation data caused by quadrupole interaction (see below). \O/ ANION-CATION PAIR DISTRIBUTION FUNCTION BF 7 -LI ' The 19F relaxation rate in the solutions 7LiBF, + D,O and 6LiBF4 + D,O has been measured.21 The isotope 6Li has practically no magnetic moment, thus the difference between these two relaxation rates is the contribution caused by the 7Li-19F magnetic dipole-dipole interaction.We evaluated these relaxation data, again using 3: FIG. 6.-Curve 5 : Anion-cation model pair correlation functions in LIBF, solution at a concentra- tion c i = 2 I%. For comparison some other computed anion-cation pair correlation functions are also shown: 1-0.2 mol dm-3 NaCl, 2-1.0 mol dm-3 NaCI, 3 and 4-1.0 mol dm-3 LiC1.33-36 For curve 5 , r is the distance between F and Li+ and for Y > 6 = 6.1 8, (dashed line) uniform distribution is assumed.M . CONTRERAS AND H .G . HERTZ 43 a model pair distribution function which, however, is slightly different from those given as eqn (3), (4). The result is shown in fig. 6. For comparison we have included in this figure some cation-anion pair correlation functions as computed by Friedman and coworker^^^,^^ and by R a ~ a i a h ~ ~ ~ ~ ~ using HNC theory procedures. Our curve is given for cIf = 2 5, as c i increases, d , the closest distance of approach, becomes slightly larger, at c i = 12 15, d has increased by ~ 2 0 % . ANION-ANION PAIR DISTRIBUTION FUNCTION IN NaBF, OR LiBF4 SOLUTION Comparison of the total 19F relaxation rate with the calculated intramolecular relaxation rate yielded the BFr-BF; intermolecular relaxation rate. From this we derive a closest distance of approach between the anions 2 4 (NaBF,, c i = 8 I%.) CATION-WATER PAIR DISTRIBUTION FUNCTION IN THE SYSTEMS LiC10, + HzO AND LiBF, + HzO The difference between the 'Li relaxation rates in the solvents H20 and DzO is due to the magnetic dipole-dipole i n t e r a c t i ~ n ~ ~ s ~ ~ and yields direct structural information about the Li + hydration sphere and its deformation with increasing concentration.In the limit of high dilution the Li+-lH pair distribution function is very (Lif is a structure former). For LiClO, the decrease in the mean square magnetic interaction with increasing salt concentration (broadening of pair distribution func- tion) is only moderate. Part of the decrease in the 7Li-1H relaxation contribution will also be due to a certain increase in the Li+-water separation.On the other hand, the increase in the correlation time with increasing salt concentration will be less than corresponds to the decrease in the self-diffusion coefficients of H20 and 7Li+. This comes about because the faster water exchange in the hydration sphere effectively shortens the correlation time.38*40 This effect of reducing the relaxation rate is much more pronounced for LiBF, than for LiC104.21 We shall see shortly that BFr produces more drastic changes in the hydration shell of Li+ than does C104. ANION-CATION PAIR DISTRIBUTION FUNCTION AS DETERMINED FROM THE MAGNETIC RELAXATION CAUSED BY ELECTRIC QUADRUPOLE INTERACTION The relaxation mechanism of the nuclei 7Li (in D,O), 23Na, 35Cl and llB (partly) is the electric quadrupole interaction.The quadrupolar relaxation rates of these nuclei are presented in fig. 7 as a function of the salt concentration; they are plotted as relative quantities." The increase in the l/Tl value of 23Na in NaCIO, and NaBF, solution and of 7Li in LiBF, solution is much stronger than that of 23Na and 7Li in LiClO, and the corresponding halide solutions. This fairly striking effect has already been ob- served. 9*41-45 The nuclear magnetic relaxation rate caused by intermolecular electric quadrupole interactions cannot be explained in terms of the ion-water or ion-ion pair distribution functions alone. Higher particle correlations have to be taken into account .19,45-50 Accordingly, the relaxation rate of the ionic nucleus may be written in the form:44 ANALYSIS OF THE TOTAL ION-SOLVENT ENCOUNTER CONFIGURATIONS 2 4 6 8 10 12 14 16 c*~/mo1/55 5mol water FIG.7.-Magnetic relaxation rates caused by quadrupole interaction of a number of ion nuclei as a function of salt concentration. Relaxing nuclei, underlined in the figure, are 'Li, 23Na, 35Cl and "B, limiting values of relaxationrate for c i + 0 are (l/T& = 0.024, 16.2 ,4.9, 0.048 s-', respec- tively, (25°C). 6n 2I+ 3 [pee(\+ YJJ' kQ = 5 P(21- 1) where I = spin of the relaxing nucleus, P = polarization factor, we put P = 3, Q = electric quadrupole moment of relaxing nucleus, 1 + ym = Sternheimer or anti- shielding factor. As cB + 0, Aww = Awl = Aji = 0, thus k,d is the relaxation rate in the limit of infinite d i l ~ t i o n . ~ ~ ~ ~ ~ Aww takes into account perturbations of the water-water correlations with respect to the relaxing ion, Awl reflects changes in ion- water correlations and Aji implies the ion-ion contribution including quenching effects due to higher ion-ion correlations (e.g., due to ion cloud formation).We may write A in the form : (V,",) is the mean square electric field gradient at the relaxing ion in addition to the one caused by the non-perturbed first hydration sphere. b* is the radius of the first coordination sphere with respect to the ions dissolved. b* is defined in such a way that the relaxation contribution of the ions outside a sphere of radius b* is negligible, a* is the closest distance of approach between the relaxing ion and any other ion. al is the approximate radius of the ion cloud of a given ion, az, a3 .. . are written symbolically to represent parameters describing the ion-ion-water many body distri-M. CONTRERAS AND H. G . HERTZ 45 bution function. 2ci is the ion concentration in (ions ~ m - ~ ) , iz', is the first coordina- tion number with respect to the other ions, g i j ( r ) is the ion-ion pair correlation func- tion (essentially the anion-cation pair correlation function), z, is an appropriate correlation time. Using a suitable concentration dependence of d (the correlation time varies) we determined the quantity A from the experimental results given in fig. 7. The results are shown in fig. 8. In the range 0 < cB < 10 mol dm-3, 2, varies by a factor 2-3, thus, considering eqn (23) decreases less than by a factor 2, i.e., g i j ( r ) and a* do not vary much with increasing salt concentration. Next, in eqn (21) we set Aww = Awl = 0.Using the correspond- ing theory the evaluation of A = Aji with a simple step f u n ~ t i o n ~ ~ i ~ ~ for g l j ( r ) and a" = 4.5 A yields tll M 1 A for the anion nuclear relaxation. This is of the correct order of magnitude. However, for the cation relaxation we obtain xl = 7.2 A for cB/mol dni3 cBlrnol drn" F1~.8.-Relaxation effect due to the presence of ions in the solution and succeeding simple solvent correlation time effects [see eqn (21)]. Relaxing nucleus is underlined. Concentration cB is given on the molarity scale. LiC104, and for the remaining solutions even tll -+ co does not suffice to explain the observed relaxation rate. A sharper cation-anion pair distribution function or smaller distance of approach must be excluded because the anion relaxation caused by quad- rupole and by magnetic dipole-dipole interaction is too weak to justify such an inter- pretation. The only possibility is that Gaij(xl, .. .)/a*6 for the cation relaxation alone becomes very large as a consequence of a particular orientation of the water molecules in the encounter configuration. It may be shown that the three water molecules between Li+ (or Na+) and the anions C10, and BF, (except LiCIO,), when oriented as shown in fig. 9, produce a very high field gradient at the cation and46 ANALYSIS OF THE TOTAL ION-SOLVENT ENCOUNTER CONFIGURATIONS \ \ i / / \ ' \ -_ i l 1 FIG. 9.-Orientation of water electric dipoles between cation (Li+ or Na+) and BFT in the encounter configuration as derived from quadrupolar relaxation rate of cations and anions.a low field gradient at the centre of the anion." It may be seen that the orientation of the water molecules between cation and anion is roughly in agreement with the orientation determined with the aid of magnetic dipole-dipole interaction as described in the second section. Finally, it may be shown that the high field gradient at the cation nucleus does not occur if the water electric dipoles in the average have radial orientation." This is the situation in LiC104 solution, here the encounter configura- ion is only characterized by a deviation of the angle 0 from the tetrahedral v a 1 ~ e . l ~ P. Dryjaliski and 2. Kecki, J. Mol. Struct., 1972, 12,219 and references therein.K. A. Hartman Jr., J. Phys. Chem., 1966,70,270. G. E. Walrafen, J. Chem. Phys., 1970,52, 4176; 1971,55, 768. G. Brink and M. Falk, Canad. J. Chem., 1970,48,2096,3019. D. M. Adams, M. J. Blandamer, M. C. R. Symons and D. Waddington, Trans. Faraday SOC., 1971,67,611. C. J. Bellamy, M. J. Blandamer, M. C. R. Symons and D. Waddington, Trans. Faraday Soc., 1971,67, 3435. S. Subramanian and H. F. Fisher, J . Phys. Chem., 1972, 76, 84. * 2. Kqcki and P. Dryjanski, Roczniki Chem., 1971, 45, 937. 2. Kgcki, Adv. Mol. Relax. Proc., 1973, 5, 137. lo P. Dryjanski and Z . Kvki, Adv. Mol. Relax. Proc., 1973, 5, 261. l1 K Buijs and G. R. Choppin, J. Chem. Phys., 1963, 39, 2035. l2 J. D. Worley and I. M. Klotz, J. Chem. Phys., 1966, 45, 2868. l3 W.C. McCabe, S. Subramanian and H. F. Fisher, J. Phys. Chenz., 1970, 74, 4360. l4 G. J. Templeman and A. L. van Geet, J. Amer. Chem. Soc., 1972,94, 5578. l6 K. Kuhlmann and D. M. Grant, J. Phys. Chem., 9164, 68, 3208. l7 R. Haque and L. W. Reeves, Canad. J. Chem., 1966, 44,2769. l8 R. Haque and L. W. Reeves, J. Phys. Chem., 1966,70,2753. 19H. G. Hertz, M. Holz, G. Keller, H. Versmold and C. Yoon, Ber. Bunsenges. Phys. Chem., * O H. Weingartner and H. G. Hertz, Ber. Bunsenges. Phys. Chem., 1977, 81, in press. J. W. Akitt, J.C.S. Faraday I, 1975, 71, 1557. 1974,78, 493.M . CONTRERAS AND H. G. HERTZ 47 For more details see M. Contreras and 9. G. Hertz, J . Solution Chem., to be published. 2z H. G. Hertz and C. Radle, Ber. Bunsenges. Phys. Chem., 1973, 77, 521.23 H. G. Hertz, Ber. Bunsenges. Phys. Chern., 1976, 80, 950. 24 A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961). 25 See e.g., H. G. Hertz, in Progress NMR Spectroscopy, ed. J. W. Emsley, J. Feeney and L. H. Sutcliffe (1967), vol. 111, p. 159; or Wuter, A Comprehensioe Treatise, ed. F. Franks (Plenum Press, New York, London, 1973), p. 301. 26 L. P. Hwang and J. H. Freed, J. Chem. Phys., 1975,63,401. ” H. G. Hertz in Moleculur Motions in Liquids, ed. J. Lascombe (Reidel, Dordrecht, 1974). 29 M. Contreras, Dissertation (Karlsruhe, 1977). 30 H. G. Hertz and C. Radle, Ber. Bunsenges. Phys. Chem., 1974, 78, 509. 31 H. Langer and H. G. Hertz, Ber. Bunsenges Phys Chem., 1977, 81,478. 32 H. G. Hertz, Ber. Bunsenges. Phys. Chem., 1971, 75, 572. 33 J. C. Rasaiah and H. L. Friedman, J. Phys. Chem., 1968, 72, 3352. 34 P. S. Ramanathan and H. L. Friedman, J. Cheni. Phys., 1972, 54, 1086. 35 J. C. Rasaiah, J . Chem. Phys., 1972, 56, 3071. 36 J. C. Rasaiah, J . Solution Chem., 1973, 2, 30. 37 D. E. Woessner, B. S . Snowden Jr. and A. G. Ostroff, J. Chem. Phys., 1968, 49, 317. 39 A. Geiger and H. G. Hertz, J. Solution Chem., 1976, 5, 365. 40 H. G. Hertz, Ber. Bunsenges. Phys. Chem., 1967,71, 999. 41 M. Eisenstadt and H. L. Friedman, J. Chem. Phys., 1966,44, 1407. 42 M. Eisenstadt and H. L. Friedman, J. Chenz. Phys., 1967,46,2182. 43 V. I. Shizhik, J. Struct. Chem., 1967, 8, 303. 44 V. I. Ionov, R. U. Mazitov, and I. I. Evdokimov, J . Struct. Chem., 1969, 10, 197. 45 H. G. Hertz, Ber. Bunsenges. Phys. Chenz., 1973, 77, 531. 46 H. G. Hertz, Ber. Bunsenges. Phys. Chem., 1973, 77, 688. 47 H. G. Hertz, M. Holz, R. Klute, G Stalidis and H. Versmold, Ber. Bunsenges. Phys. Chem., 48 H. G. Hertz, J. Solution Chem., 1973, 2, 239. 49 See also B. Lindman and S. Forsen, Chlorine, Bronhe and Iodine NMR, ed. P. Diehl, E. Fluck 50 M. Holz, H. Weingartner and H. G. Hertz, J.C.S. Faraduy I, 1977, 73, 71. H. G. Hertz and W. Y. Wen, Z.phys. Chem. (N.F.) 1974,93,313. H. G. Hertz, R. Tutsch and H. Versmold, Ber. Bunsenges. Phys. Chem., 1971, 75, 1177. 1974, 78,24. and R. Kosfeld (Springer, Berlin, Heidelberg, New York, 1976).

ISSN:0301-7249    

DOI:10.1039/DC9776400033

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Relaxation Processes in Aqueous Solution : A Raman Spectral Study of Hydrogen Bonded Interactions BY DAVID JAMES Chemistry Department, University of Queensland, Brisbane, Australia 4067 AND RAY L. FROST Chemistry Department, Queensland Institute of Technology, Brisbane, Australia 4001 Received 3rd May, 1977 Vibrational relaxation and rotational reorientation times for the nitrate ion in aqueous solutions of group I and group I1 metal nitrates have been measured at room temperature using polarised Raman spectra. The vibrational relaxation occurs by energy transfer to hydrogen-bound water molecules. In dilute solution all vibrational relaxation times approach a common value of 1.4 ps. At higher concentration there is a marked cation dependence with relaxation being more rapid in the presence of highly polarizing cations.It is shown that hydrogen bonding to only one water molecule is necessary to describe the relaxation process. The rotational reorientation times of the nitrate ion reflect constraints imposed by both hydrogen bonding to water and coulombic interaction with the cationic species. The low concentration limited values of rOR are different for different electrolytes. Also in contrast to vibrational relaxation (which shows linear dependence on cation concentration) the variation of rotational reorientation with concentration is non-linear with the curvature reflecting different contributions to the constraining field. Spectroscopic studies hold the promise of providing direct evidence of solvent solute interactions at the molecular l e ~ e l .l - ~ However, because of the disordered structure of solutions, group theoretical arguments are not applicable and the data must be treated on the basis of intuitive models. The use of relaxation parameters derived from n.m.r. experiments has led to the formulation of hydration models which include estimates of water molecule Polarized Raman spectra yield measures of the times for vibrational relaxation and rotational reorientation of poly- atomic species in the liquid state.6-8 We report here such a study on aqueous solu- tions of metal nitrates. The spectra are measured with the electric vectors of incident and scattered light either parallel [Jl(w)] or perpendicular [ZL(co)] to each other. The measured in- tensities then obey the relationships: 41(0) = Iisdw) + 4 lanis(m> Ida) = 4mis(O> where Iis,,(m) represents the intrinsic vibrational line shape which may be described by the vibrational time correlation function and lanis(m) is a convolution of the vi- brational and reorientational contributions which is described by a product time correlation function.It is thus possible, in principle, to determine both the vibra-DAVID JAMES AND RAY L . FROST 49 tional and reorientational time correlation functions from the measured spectra. The measured spectra are also convolutions of the true spectrum and the instrument slit f ~ n c t i o n . ~ Experimental care must be taken to ensure that the slit function contribu- tion is minimized in all measurements. If it is assumed that there is no coupling between vibrational and reorientational motions and that the intrinsic line shape is Lorentizian (see below) the vibrational relaxation time z, and the rotational reorientation time z,, are given by the expression : where is the width parameter (HWHH) of the isotropic band and w,, is given by : mo, = %(anis) - %(is,).Due to hydrogen bonding the systems we report must be regarded as strongly interacting. Here the isotropic band may still be used to determine the vibrational relaxation time but, due to coupling, the vibrational relaxation determined from the isotropic and anisotropic bands may be different. This means that the reorienta- tional relaxation time determined may not be correct. It is possible to estimate the efficiency of the coupling by changing the “ bath ” vibrational frequencies by isotopic substitution1’ and observing the change in relaxation parameters.EXPERIMENTAL METHODS All spectra were obtained on a Cary 82 spectrophotometer using 514 nm radiation from a C.R.L. Model 52A laser with an incident power at the sample of 600 mW. A Glan- Thompson prism was used to ensure the polarization of the incident light. The radiation was passed once through the sample held in a thermostatted square cuvette, the incident beam being maintained parallel with the surface of the collection lens. Reflecting surfaces were masked to minimise stray reflections. Scattered light was collected from a solid angle of 5” and polarization was by a Polaroid sheet followed by a quartz wedge scrambler. I E 8.01 V . ‘0 C 0 n ~ 4 .0 ?! t! VI E 2 . 0 a a a t instrumental slit widthlcm-’ FIG. 1.-Relationship of measured band width to instrumental slit width. (a) ZII (a); (6) ZI. (a).50 RELAXATION PROCESSES I N AQUEOUS SOLUTION Solutions were made up from recrystallised salts and water doubly distilled from an all- glass apparatus. Prior to use all solutions were filtered several times through a O.lpm membrane filter. For solutions in D20 the solvent was used as supplied without distillation. RESULTS The effect of slit width on the measured band width was checked for several solu- tions. Typical results are shown in fig. 1. In general, slit widths used were less than 6 (band width). The line shape was tested for a variety of the spectra; a typical result is shown in fig. 2 where the agreement with a Lorentzian band shape is seen to be very good.The calculated relaxation parameters and their variation with con- centration are listed in tables 1, 2 and 3 and shown in fig. 3, 4 and 5. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 wavenumber (v-v,) FIG. 2.-Lorentzian fit of isotopic and anisotropic bands for 8 mol dn1r3 NH4N03. Solid line is calculated curve, dots are experimental points. Isotropic band is lower curve. 1.6 1 1.4 1.2 \ aI E C 0 .- 3 1.0 d - 2! 0.8 Li+ 0.6 I 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 6 9 1 0 m o l a r i t y lmol dm-3 FIG. 3.-Variation of vibrational relaxation time with cation concentration for nitrate solutions.D A V I D JAMES A N D R A Y L. FROST 51 FIG. nitrate ion molarity 4.-Variation of vibrational relaxation time with nitrate concentration.0, NH4N03 ; NaNO,; A, AI(N03)3, 8, Ca(NO,),. I I I 1 I I 1 I I I I 1 2 3 4 5 6 7 8 9 10 nitrate ion molarity FIG. 5.-Variation of reorientational relaxation time with nitrate concentration for nitrate solutions.52 RELAXATION PROCESSES I N AQUEOUS SOLUTION TABLE 1.-RELAXATION AND ORIENTATION TIMES FOR GROUPS (I) AND (11) METAL NITRATES electrolyte NHdNO3 LiN03 NaN03 KN03 RbNOj molarity (NO3-) 0.5 1 .o 2.0 3.0 4.0 5.0 6.0 8.0 10.0 0.5 1 .o 2.0 3.0 4.0 5.0 6.0 8.0 10.0 0.5 1 .o 2.0 3.0 4.0 6.0 0.5 1 .o 2.0 2.7 0.5 1 .o 2.0 3.0 0.5 1 .o 2.0 4.0 6.0 8.0 10.0 1 .o 2.0 3.0 4.0 8.0 1 .o 2.0 3.0 4.0 5.0 6.0 1crn-l 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 4.00 3.80 3.85 4.10 4.38 4.65 4.85 4.95 5.75 6.55 3.85 3.90 4.05 4.35 4.60 4.75 3.90 3.90 3.90 4.05 3.95 3.95 3.95 3.95 3.90 4.10 4.15 4.70 5.50 6.10 7.50 3.85 4.20 4.4 4.65 5.25 3.95 4.30 4.50 4.65 4.88 5.15 jcm-' 6.50 6.50 6.50 6.50 6.50 6.45 6.25 6.10 5.85 6.75 6.75 6.75 6.80 6.90 6.90 6.90 6.95 7.40 6.50 6.50 6.50 6.50 6.50 6.30 6.60 6.50 6.50 6.20 6.65 6.60 6.50 6.20 6.60 6.50 7.10 7.05 7.10 7.45 8.30 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.55 jcm-l 2.55 2.55 2.55 2.55 2.55 2.50 2.30 2.15 1.85 2.95 2.90 2.65 2.42 2.25 2.05 1.95 1.20 0.85 2.65 2.60 2.30 2.15 1.90 1.55 2.70 2.60 2.60 2.15 2.70 2.65 2.55 2.25 2.70 2.40 2.95 2.35 1.60 1.35 0.80 2.65 2.30 2.10 1.85 1.25 2.50 2.20 2.00 1.85 1.62 1.40 4 P s 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.33 1.40 1.38 1.29 1.21 1.14 1.09 1.07 0.92 0.81 1.38 1.36 1.31 1.22 1.15 1.12 1.36 1.36 1.36 1.31 1.34 1.34 1.34 1.34 1.36 1.30 1.30 1.13 0.77 0.87 0.71 1.37 1.26 1.21 1.14 1.01 1.34 1.24 1.18 1.15 1.09 1.03 rOR/ps 2.08 2.08 2.08 2.08 2.08 2.1 1 2.31 2.47 2.87 1.80 1.83 2.00 2.19 2.36 2.59 2.72 4.42 6.25 2.00 2.04 2.31 2.47 2.79 3.43 1.97 2.04 2.04 2.47 1.97 2.00 2.08 2.36 1.96 2.21 1.79 2.25 3.32 3.93 6.64 2.00 2.30 2.52 2.86 4.24 2.12 2.41 2.65 2.87 3.27 3.71DAVID JAMES AND RAY L.FROST 53 TABLE 1-continued electrolyte molarity (NO,-) C a w " 7.0 8.0 10.0 Sr W" 1 .o 2.0 3.0 4.0 5.0 6.0 Ba(N03)z 0.4 0.8 5.55 5.95 6.40 3.90 4.10 4.35 4.60 4.85 5.05 3.9 3.95 6.60 6.95 7.20 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.45 1.05 1 .oo 0.80 2.55 2.40 2.15 1.90 1.65 1.45 2.60 2.50 0.96 5.05 0.89 5.30 0.83 6.64 1.36 2.20 1.29 2.46 1.22 2.79 1.15 3.22 1.09 3.22 1.05 3.66 1.36 2.04 1.34 2.12 VIBRATIONAL RELAXATION With the exception of solutions of NH4N03 the values of vibrational relaxation converge to a common low concentration value of 1.4 ps.This may be compared with a value of -6 ps in molecular liquids, where relaxation is by a collisional mechan- i ~ m . ~ * ' ~ Energy loss is much more efficient in nitrate solutions, and we propose that it occurs through water molecule hydrogen bound to the nitrate ion. The relaxation process must occur by energy transfer into a vibrational mode of the bound water. There are no suitable fundamentals as the bending mode is too high in energy (-1600 cm-l) and the librational mode is too low in energy (-500-700 cm-I). However, relaxation can occur via overtones, combination and rotational bands.13 We will show later that the bending mode is the most likely fundamental to be involved; energy transfer probably occurs via the overtone/combination band continuum which extends to 1600-1700 cm-'.It has been shown elsewhere14 that in CH3CN contain- ing low concentrations of water and NaN03, the vibrational relaxation time is 1.15 ps when the ratio of [H,O] to [NO;] is unity. In anhydrous (CD3)&30 however, where the interaction is mainly electrostatic z, is 3.26 ps. The vibrational relaxation data in aqueous solution may be explained in terms of a model with one water molecule hydrogen bonded to the nitrate ion. If the NO; hydration number is greater than one, the vibrational relaxation will be governed by the most strongly bound water molecule.When the cationic species is Li+ or Na+ the vibrational relaxation becomes shorter as the salt concentration increases with the decrease being greater for Li+ than for Na+. The divalent cations show a similar decrease in z, with concentration, with again the smallest cation showing the greatest decrease. The decreases in z, noted indicate that the NO;-HOH hydrogen bond is becoming stronger; this is due either to a polarization of water by the cation or to the formation of a more favourable geo- metric arrangement. The cation dependence of the decrease in z, indicates that the former explanation is probably correct. For the cationic species K+, Rb+, Cs+ and NH,+ increased concentration has almost no effect on 7,.These cationic species are weakly hydrated, so the exchange time for water of hydration is shorter than for the other cations studied. The results obtained are consistent with an exchange time shorter than 1.4 ps, i.e., the residence time of the cation is shorter than the vibrational relaxation time and so the cationic polarization does not influence 7,.54 RELAXATION PROCESSES I N AQUEOUS SOLUTION The linear decrease in z, from the dilute solution value of 1.4 p.s. as the anion concentration increases to -4 mol dm-3 (fig. 3) probably reflects the increase in polarity of the water attached to NO; due to the decrease in average anion-cation separation. At 4 mol dm-3 anion concentration, the gradient of concentration as a function of z, decreases for the cations Li+, Na+ and Ca2+, and the value of 7, at -4 mol corresponds to the value observed in CH3CN for NO;*H,O.It is probable that this change in slope indicates that contact ion pairs are significant above 4 rnol dm-3. The formation of contact ion pairs would decrease the charge density on the nitrate ion oxygen atoms used in hydrogen bonding. The observed gradient would then be the result of two opposing influences, polarization by cations outside the NOr-xH,O complex and change in charge density in the contact ion pair. The effect of added halide ion on the vibrational relaxation is shown in fig. 6. total cation molarity (nitrate ion molarity=l) FIG. 6.-Effect of added halide ion on vibrational relaxation of nitrate ion. Nitrate concentration The added halide has no effect when the cation is ammonium, but for the other cationic species the curves obtained in the presence of halide are significantly different from those obtained for solutions containing only nitrate anions.It is unlikely that the variations are due to a direct halide-nitrate or halide-water-nitrate interaction as such an interaction would also be present for solutions of ammonium salts. The data show that the addition of halide ion initially reduces the polarizing effect of the cation and, at high concentrations, enhances the effect. If in the formation of ion pairs the M*X ion pair is preferred to the M*ONO, ion pair the added halide ion will compete with the nitrate ion for the cationic species and polarization in the nitrate region will be reduced.On this basis the tendency towards ion pair formation would be 1 mol dm-3 inall solutions. 0, NOi/F-; 0, NOi/Cl-; x,NOi/Br-; 0, NO:/I-. I- > Br- > C1- > NO;DAVID JAMES AND RAY L. FROST 55 which is in accord with other observations.15 At higher concentrations the same tendency will reduce the occurrence of M.0N02 contact ion pairs. Since the strength of the nitrate-water hydrogen bond is reduced by the formation of contact ion pairs a lessening of the tendency to form them will lead to a decreased value for 7". To gauge the extent to which coupling to water was affecting the relaxation para- meters measurements were made in D20 (table 2). The vibrational relaxation times TABLE 2 .-VIBRATIONAL RELAXATION AND MOLECULAR REORIENTATION TIMES FOR GROUP (I) NITRATES IN DzO NaN03 in DzO electrolyte molarity LiN03 in D20 0.5 1 .o 2.0 3.0 4.0 6.0 8.0 10.0 0.5 1 .o 2.0 3.0 4.0 6.0 KN03 in D20 0.5 1 .o 2.0 2.7 Ca(N03)2 in D20 0.5 1 .o 2.0 3 .O 4.0 w, 4.05 4.10 4.35 4.47 4.62 5.40 6.05 7.20 3.95 3.95 4.25 4.42 4.65 4.97 3.95 3.95 4.00 4.05 4.00 4.21 4.72 5.17 5.73 UP U O R ZV 6.25 2.25 1.31 6.25 2.20 1.29 6.25 2.02 1.22 6.25 1.83 1.19 6.35 1.75 1.15 6.92 1.52 0.98 7.15 1.10 0.88 7.85 0.65 0.74 6.10 2.15 1.34 6.05 2.10 1.34 6.05 1.90 1.25 6.05 1.63 1.20 6.05 1.40 1.14 6.05 1.08 1.07 6.10 2.15 1.34 6.05 2.10 1.34 6.00 2.00 1.32 5.90 1.85 1.31 6.10 2.10 1.32 6.10 1.90 1.26 6.10 1.37 1.12 6.10 0.92 1.03 6.45 0.72 0.93 TOR 2.25 2.40 2.62 2.90 3.07 3.49 4.83 8.17 2.47 2.53 2.80 3.26 3.29 4.31 2.47 2.53 2.65 2.87 2.51 2.39 3.86 5.74 7.32 are some 5% shorter in D,O than in H20 for solutions of LiN03, while for the other salts the decrease noted is somewhat less.Deuteration shifts the bending mode of water closer to the band under study and moves the broad librational band further away to lower frequencies. It appears likely that coupling to water occurs through the water bending vibration, but that the coupling is not very efficient.16 We must con- sider also, however, that coupling could occur through the weak vibrational continuum which extends from the librational band to the bending mode. The density of states of this continuum is reduced in the region of the nitrate symmetrical stretching mode by the addition of electrolytes. We might expect that coupling would become weaker as the concentration of salt increased.The progressive decrease in z, as salt concentration increases indicates that this coupling does not dominate the relaxation process. We are thus examining a system where the relaxation occurs through a hydrogen bonded interaction wherein the coupling between vibrator and bath modes is weak.56 RELAXATION PROCESSES I N AQUEOUS SOLUTION ROTATIONAL REORIENTATION Although the vibrational relaxation time we calculate is correct for these strongly intereacting systems, the reorientational relaxation process is coupled to the vibra- tional relaxation process to yield the anisotropic Raman band. We must assume that the vibrational correlation function is the same for isotropic and anisotropic band components in order to affect a separation.While this assumption is certainly not correct, the errors introduced into the reorientational relaxation time are probably small and, since the degree of coupling will not change much for the various systems we study, the variational trends will be valid. The reorientation time calculated here is for tumbling motion about an axis per- pendicular to the major symmetry axis, i.e., one of the nitrate ion C, axes. If the re- orientation time is shorter than the water exchange time, the nitrate hydrated complex must be considered to rotate as a unit, while if the water exchange time is shorter the hydration sheath may be considered to provide a static barrier to rotation. It has TABLE 3.-vIBRATIONAL RELAXATION AND MOLECULAR REORIENTATION OF 1 m01 dm-3 NITRATE ION IN THE PRESENCE OF A SECOND ELECTROLYTE NH4N03 1 rnol dm-3 NH4CI NH4N03 1 mol dm-, NH4Br NH4N03 1 rnol dm-3 NH41 NH4N03 1 mol dm-3 NH4F KNO, 1 rnol dm-, KF KNOs 1 rnol dm-3 KCl second electrolyte/ mol dm-, 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0, 3.95 3.95 2.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 3.95 4.02 4.12 4.32 3.95 3.95 3.95 3.95 3.95 rv 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.36 1.34 1.32 1.29 1.23 1.36 1.34 1.34 1.34 1.34 Wb 6.50 6.50 6.35 6.25 6.20 5.90 6.50 6.50 6.50 6.30 6.70 5.80 6.50 6.40 6.30 6.10 5.90 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.50 6.40 6.25 5.95 5.80 WOR 2.55 2.55 2.40 2.30 2.25 1.95 2.55 2.50 2.40 2.25 2.20 1.85 2.55 2.48 2.35 2.05 1.85 2.55 2.55 2.55 2.55 2.55 2.55 2.55 2.48 2.38 2.18 3.00 2.45 2.30 2.00 1.85 TOR 2.08 2.08 2.21 2.30 2.35 2.72 2.08 2.12 2.22 2.35 2.62 2.85 2.08 2.16 2.25 2.58 2.86 2.08 2.08 2.08 2.08 2.08 2.04 2.04 2.14 2.23 2.43 2.04 2.16 2.30 2.65 2.86DAVID JAMES AND R A Y L .FROST TABLE 3-continued 57 KN03 1 rnol dm-3 KBr KN03 1 rnol dm-3 KI NaN03 1 mol dm-3 NaCl NaNOS 1 mol dm-3 NaBr NaN03 1 mol dm-3 NaI LiN03 1 mol dm-3 LiCl LiN03 1 mol dm-3 LiBr LiN03 1 mol dm-3 LiI second electrolyte/ mol dm-3 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 0" 3.95 3.95 3.95 4.00 4.05 3.90 3.95 3.95 4.00 4.08 3.90 4.05 4.75 4.45 4.70 3.90 4.05 4.20 4.55 4.90 3.90 4.05 4.30 4.65 4.95 3.85 3.95 4.30 4.53 5.15 5.55 5.95 6.40 6.80 3.85 3.95 4.35 4.80 5.30 5.75 6.20 6.60 7.40 3.85 4.02 4.40 4.77 5.40 5.93 6.43 ZV 1.36 1.34 1.34 1.33 1.31 1.36 1.34 1.34 1.33 1.30 1.36 1.31 1.28 1.92 1.13 1.36 1.31 1.26 1.17 1.08 1.36 1.31 1.24 1.14 1.02 1.38 1.34 1.24 1.17 1.03 0.96 0.89 0.83 0.78 1.38 1.34 1.22 1.11 1 .oo 0.92 0.86 0.80 0.71 1.38 1.32 1.20 1.11 0.99 0.90 0.82 UP 6.50 6.40 6.15 5.80 5.25 6.50 6.50 6.05 5.60 5.25 6.50 6.50 6.35 6.20 6.05 6.50 6.50 6.30 6.10 5.80 6.50 6.50 6.20 5.90 5.65 6.75 6.25 6.90 6.95 7.00 7.00 7.00 7.20 7.30 6.78 6.75 6.85 6.95 7.30 7.15 7.30 7.60 7.80 6.75 6.75 6.75 6.85 6.95 7.10 7.35 OOR 2.55 2.45 2.20 1.80 1.20 2.60 2.55 2.10 1.60 1.15 2.60 2.45 2.20 1.75 1.35 2.60 2.45 2.10 1.55 0.90 2.80 2.45 1.90 1.25 0.70 2.90 2.80 2.60 2.43 1.85 1.45 1.05 0.80 0.50 2.90 2.80 2.50 2.15 1.70 1.40 1.10 1 .oo 0.40 2.90 2.75 2.34 2.10 1.55 1.17 0.92 508 2.04 2.16 2.41 2.94 3.80 2.04 2.08 2.52 3.31 4.60 2.04 2.16 2.41 3.03 3.93 2.04 2.16 2.52 3.42 5.89 2.04 2.15 2.79 4.24 7.58 1.83 1.89 2.04 2.18 2.86 3.66 5.05 6.63 10.60 1.83 1.89 2.12 2.46 3.12 3.79 4.82 5.30 13.20 1.83 1.93 2.26 2.53 3.42 4.54 5.7758 RELAXATION PROCESSES I N AQUEOUS SOLUTION been shown elsewhere14 that the reorientation time for the species N03.H,0 in CH,CN (0.69 ps) is shorter than that of NO,*xH,O in water (1.79 ps) which in turn is shorter than that for NO3- .xCD30D in deuteromethanol(3.61 ps). This indicates that as the bulk of the solvation complex increases, the reorientation time increases, and consequently that the reorientation process probably involves the whole complex.The breaking of water-water hydrogen bonds would provide the initial barrier to rota- tion with geometrical considerations also important. The systems studied (fig. 5) may be separated into three sets; those containing the highly polarizing cations Li+ and Be+ which have a ( T , , ) ~ of 1.7 ps, those containing the remaining metallic cations which show the same general concentration dependence for z,, but for which (z0Jm has a value of -2 ps and finally NH4N03 solutions which show very little variation of z,, with concentration and for which ( T , ~ ) ~ = 2.1 ps. It should be noted that in fig. 5 the abcissa is the nitrate ion molarity and so the cation concentration for divalent cations is half that indicated.The different cations have a different relative influence on zv and z,,. Thus for 7, the more highly polarizing cations cause the greatest change while, in the main, the reverse is true for T,,. Both of the relaxation processes will occur via the most favour- able pathway. In the case of the vibrational relaxation this will involve the water molecule most strongly hydrogen bound to the nitrate ion, while for reorientation relaxation the lowest barrier involves the weakest hydrogen bonds. The cations which bind water most strongly produce the smallest increase in z,, at low salt con- centration because the polarization effect is localised on part of the anion hydration sphere. The cations which bind water less strongly exchange hydration water more rapidly, and so are more likely to produce an average hydration effect over the whole anion hydration.These differences in behaviour will be most apparent in the low concentration region where interaction between more than two ions (one ion pair) is unlikely. It is this region which is least well characterised. The differences in behaviour are reflected in (r0Jm. In fig. 5 the results for the solutions containing divalent cations show a systematic increase in z,, as the size of the cation increases. For solutions containing the mono- FIG. 7.-Model for variation of hydration characteristics with concentration. (a) Hydrated ions well separated by bulk solvent. (b) Hydrated ions sharing part of their hydration shells. (c) Contact ion pair with common hydration shell,DAVID JAMES AND RAY L .FROST 59 valent cations however (table 1) the results for KN03, RbN03 and CsNO, do not follow this trend. The 5, results were interpreted assuming that the exchange time for water for these cations was < 7". This short exchange time would mean that the cation would exchange in times shorter than the reorientation relaxation; the re- orientation process thus does not involve movement of the cation. A familiar model for the hydrated ions" appropriate for our discussion is repre- sented in fig. 7. The value of the reorientational relaxation time ( T ~ ~ ) extrapolated to zero concentration ( T ~ ~ ) ~ corresponds to fig. 7(a). As the concentration increases, the configurations of fig. 7(b) with shared water increase in probability, while at still higher concentration contact ion pairs [fig.7(c)] will have an increasingly important influence. While this is obviously an over-simplified model it will serve as a useful starting point to assess the relative importance of the three interactions. In the concentration range we report, an increase in cation concentration leads to an increase in the average binding of water to the nitrate. This effect should increase linearly with concentration while at high concentrations the formation of contact ion pairs will lead to a further modification of the value of T ~ ~ . It is reasonable therefore to fit the experimental results to a function of the type (1) 70, = (70r)=(l + ac -k be2) and to associate the constant a with a solvent-separated ion pair interaction and the constant b with a contact-ion pair interaction.A least squares fitting of experi- mental results gave the values of a and b in table 4. The results of this analysis indicate TABLE 4.-REORIENTATION RELAXATION TIME LEAST SQUARES PARAMETERS (TOR)CS 1.7 2.0 2.0 1.92 1.7 2.0 2.0 2.0 a( x 10'2) 0.040 0.065 0.055 0.050 0.020 0.035 0.060 0.080 ~ b( x 0.020 0.017 0.010 0.007 0.020 0.016 0.01 6 0.013 x = xo(1 + ac + bCZ) that solvent separated ion pairs play a less important role in those solutions containing the highly polarizing cations Li+, BeZ+ and Mgz+. The first two of these are also characterised by low values of (rOr), and primary hydration numbers closer to four than six." When the hydration water is strongly bound to the cation, as for these small cation^,'^.'^ the formation of solvent-separated ion pairs would cause an unfavour- able large decrease in entropy.Thus the small values observed for the a constant are not unexpected. The values for the b constant for these small cations are com- paratively large, indicating that contact ion pairs are important at high concentration. When water concentrations decrease to the point where complete solvation is unlikely, a cation can share water molecules with the nitrate ion, while forming a contact ion pair. This is possible for cation contact with the nitrogen (along the C, axis) or with one of the oxygen atoms." However, it is only for the small cations that this is feasible, because steric considerations prevent the hydration water on large cations hydrogen bonding simultaneously to the nitrate ion.The small values of the b constant noted for K+, Rb+ and to some extent Sr2+ are in accord with this idea.60 RELAXATION PROCESSES I N AQUEOUS SOLUTION REORIENTATION RELAXATION IN Dz0 The main difference in reorientation relaxation in HzO and D20 is the value noted for (zor), which is some 25% greater in D20. This may in part be due to a change in the coupling with the OH/OD bending vibration. However, the formation of an NO3 * * * DOD bond which is stronger than that formed in H20, and the increased mass of the D20 molecule will also contribute. total cation molarity F ~ ~ . 8.-Effect of added halide ion on reorientational relaxation of nitrate ion. Nitrate concentration 1 mol dm-3 in all solutions.0, NO; ; 0, NOZ/F-, . o,NOz/Cl-; x,NOZ/Br-; +,NOZ/I-.D A V I D JAMES A N D R A Y L . FROST 61 EFFECT OF ADDED ANIONS The nitrate ion reorientation relaxation times in the presence and absence of added anions are compared in fig. 8. As for vibrational relaxation, the added anion initially reduces the cation effect and, at higher concentrations, enhances it. The initial effect is to reduce the value of the constant a in the least squares fit using eqn (1). The reduction in a is a measure of the preference for the formation of cation-halide rather than cation-nitrate solvent separated ion pairs. As expected, the tendency to ion pairing is greatest for iodide anions. At higher concentrations the above trend is reversed and the lengthening of re- orientational relaxation is marked for all cationic species studied. This lengthening is greatest for the heaviest added anions and may indicate that the added halide is par- ticipating directly in the reorientational process. CONCLUDING REMARKS The relaxation phenomena we report can be used to probe the microdynamic structure of solutions in the picosecond domain.While the results of this initial study have led to some qualitative conclusions more extensive and precise data are required particularly in the low concentration region, before the discussion can be put on a quantitative basis. The Australian Research Grants Committee is thanked for a grant for the setting up of the Cary 82 system. G. J. Janz, K. Balasubrahmanyam and G. B. Oliver, J. Chem. Phys., 1969,57,5723. G. E. Rodgers and R. A. Plane, J. Chem. Phys., 1975,63,818. D. E. Irish and M. H. Brooker, Adv. Infrared Raman Spectr., 1976, 2, 212. H. G. Hertz in Water, a Comprehensive Treatise, ed. F. Franks (Plenum Press, London, 1973), p. 301. F. J. Bartoli and T. A. Litovitz, J. Chem. Phys., 1972, 56,404. L. A. Nafie and W. L. Peticolas, J. Chem. Phys., 1972,57, 3145. J. E. Griffiths, Adu. Raman Spectroscopy, ed. J. P. Mathieu (Heyden, 1973), vol. 1, p. 444. ' H. G. Hertz, J. Solution Chem., 1973, 2, 239. ' W. G. Rothschild, J. Chem. Phys., 1972,57,991. lo P. C . M. Van Woerkom, J. de Bleijser, M. de Zwart and J. C . Leyte, Chem. Phys., 1974, 4,236. l1 J. de Bleijser, P. C . M. van Woerkom and J C . Leyte, Chem. Phys., 1976,13,387. l2 J. E. GriiKths, J. Chem. Phys., 1973,59,751. l3 E. W. Schlag in Spectroscopy ofthe Excited State, ed. B. Di Bartolo (Plenum Press, New York, l4 D. W. James and R. L. Frost, unpublished results. l5 P. S. Leung and G. J. Safford, J Solution Chem., 1973, 2, 525; R. H. Stokes and R. A. Robinson, J. Solution Chem., 1973, 2, 173; D. F. Evans and M. A. Matesich, J. Solution Chem., 1973,2,193. l6 J. de Bleijser, P. C . M. van Woerkom, D. van Dwijn, H. S. Kielman and J. C . Leyte, Chem. 1976), p. 325. . . phys., 19%, i3,403. l7 T. E. Lilley in Water, a Comprehensive Treatise, ed. F. Franks (Plenum Press, London, 19731, p. 265. 18D. W. James and R. F. Armishaw, J. Phys. Chem., 1976, 80, 501; B. Case, in Reactions of Molecules at Electrodes, ed. N. S . Hush (Wiley-Interscience, London, 1971). l9 Kebarle, in Ions and Ion Pairs in Organic Reactions, ed M. Szwarc (Wiley-Interscience, New York, 19721, vol. 1; P. Schuster, W. Jakubetz and W. Marius, Topics in Current Chem. (Springer-Verlag, 19751, vol. 60. zo S . C . Wait, A. T. Ward and G. J. Janz, J. Chern. Phys., 1960, 45, 133.

ISSN:0301-7249    

DOI:10.1039/DC9776400048

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

X-Ray Diffraction and Structure of NiC1, Aqueous Solutions BY R. CAMINITI, G. LICHERI, G. PICCALUGA AND G. PINNA Istituto Chimico Policattedra, Universith di Cagliari, Via Ospedale 72, 09100-Cagliari, Italy Received 15th April, 1977 X-ray diffraction data for two aqueous solutions of NiC12 are analysed. A model including only nearest-neighbour interactions does not yield theoretical structure functions in full agreement with the experimental results, but satisfactory agreement can be reached by simply adding interactions between the hydrated cation and external water molecules, without considering ion-ion interaction. Regarding ionic hydration, the mean coordination geometries of Ni2+ and Ci- ions are found to be octahedral with mean distances cation-water (2.05 - 2.06 A) and anion-water (3.13 - 3.14 A) in accordance with those already found.The suitability of X-ray diffraction in the study of ionic coordination in aqueous solution has recently been demonstrated for a great number of case~.I-~ The experi- mental data appeared to be consistent with a simple model describing ionic coordina- tion only in terms of nearest-neighbour interactions. Diffraction studies have also provided some evidence of the existence of a quasi-lattice structure in very concen- trated solutions. The first observation of this phenomenon was made by Dorosh and Skryshevskii5 in a series of divalent metal cation aqueous solutions (including NiCl, solutions). These authors observed small-angle maxima in the X-ray scattering in- tensity curves from which they evaluated cation-cation distances in the solutions.Confirmation of these results was supplied by Alves Marques and De Barros Marques6 from X-ray experiments and by Enderby and co-worker~'-~ from neutron diffraction investigations. NiC12 aqueous solutions in particular were repeatedly examined by the Leicester group." A " multiple pattern " analysis7-' allowed the Ni-Ni partial structure factor to be extracted from the experimental data; the most significant feature was a narrow peak at a value of the scattering vector of 1 which was inter- preted in terms of a lattice model in which the Ni2+ ions were arranged in a highly ordered manner. The partial structure factor was not inverted into a Ni-Ni pair correlation function because its accuracy was not considered sufficient. The exist- ence of a small angle peak was confirmed in the total neutron diffraction pattern from nickel chloride s o l ~ t i o n s .~ Because of our interest in the structural details of metal halide aqueous solutions, we have extended our X-ray studies to include aqueous solutions of NiC12. The aims of our work were: (a) to determine the mean coordination geometry of the Ni2+ and C1- ions in the solutions; (b) to verify whether the X-ray diffraction patterns from NiCl, aqueous solutions were explicable with nearest-neighbour interactions or if quasi-lattice models were necessary in order to account for the experimental data. * Prof. Enderby is now at the Department of Physics, Bristol University.R . CAMINITI, G . LICHERI, G . PICCALUGA AND G .PINNA 63 EXPERIMENTAL AND DATA TREATMENT The composition of the samples is given in table 1. X-ray diffraction measurements were carried out with a 8-8 X-ray diffractometer (Seifert, Germany). The surface of the solutions, thermostatted at 18 f 1"C, was irradiated with a divergent beam of MoK, radiation (1. = 0.7107 A), monochromatized by reflection from a curved quartz crystal. The sample was kept in a hydrogen atmosphere. Diffraction was TABLE 1 .-MOLARITY c AND MOLAR SALT CONTENT EXPRESSED AS x IN THE COMPOSITION (NiC12)x ( H 2 0 ) l - X C X 2 0.0352 4 0.0736 measured at discrete points between 0 :-= 1" and 0 = 60", where 8 is half the scattering angle, corresponding to the range 0.45 < s < 15.28 8, (s = 4n sin Oil.). Diffracted intensities were measured as the times necessary for accumulating 40 000 counts; several runs were made in order to collect at least 200 000 counts per point.The measured intensities were corrected for background, polarization, absorption'O and Compton modified radiation and then scaled to absolute intensities by an analytical method l2 and visual comparison. ing to: The correlation functions G(r) were calculated by means of the Fourier transform accord- Smax G(r) = 1 + (2n2p, r)-I 0.5 0 0.5 4 0 -0.5 0 2 A 6 a 10 12 14 s / 2' FIG. I.-Observed (. . . .) and model (-) structure functions. Top curve 4 mol dm-3, bottom curve 2 mol d ~ n - ~ .64 X-RAY DIFFRACTION AND STRUCTURE OF NiCl, AQUEOUS SOLUTIONS where r is the interatomic distance, #,in and s,,, are the lower and the upper limit of experi- mental data and po is the bulk density of stoichiometric units.i(s) is the structure function defined as: where fi are the scattering factors corrected for anomalous dispersion, xL are the stoichio- metric coefficients in a structural unit containing m kinds of atoms, Ze.,,. is the intensity in electron units. The values of thefr used were those proposed by Bol l3 for the water molecule and those by Cromer and Mannl4 for the other species. Peaks below 1.5 hl which appeared in the G(r) curves were corrected'l since these spurious peaks did not correspond to any real interatomic distance. The experimental structure functions i(s> multiplied by s and the G(r) curves thus deduced are shown in fig. 1 and 2 respectively (circles). 2.5 2.0 1.5 1.0 s u 2.0 1.5 1.0 0.5 1 2 3 4 5 6 I / I ; FIG. 2.-Observed (.. * .) and model (-) correlation functions. Top curve 4 mol dm-3, bottom curve 2 mol dm-3.R. C A M I N I T I , G. LICHERI, G . P l C C A L U G A A N D G. P I N N A 65 RESULTS AND DISCUSSION In the experimental correlation functions three main peaks centred at 2.00-2.10, 3.00-3.10 and 4.10-4.20 A are evident. The first peak is caused by the Ni2+-H20 interaction; in fact, the sum of the ionic radius of the NiZ+ ion and of the water mole- cule radius gives a value very close to the experimental position of this maximum. The peak around 3.00-3.10 A is doubly composed, as is clearly observed in the case of the 2 mol dm-3 solution; a component at 2.85-2.90 A is caused by nearest- neighbour H20-H20 interactions; H,O-H,O &distances inside the cation hydration complex should represent further contributions to this peak.A component at 3.15- 3.20 A is due to the Cl--H20 distances, as assessed by ionic radius values and from the results obtained in a great number of C1- aqueous s o l ~ t i o n s . l , ~ * ~ ~ , ~ ~ The peak at 4.10-4.20 A could result from H,O-H,O distances inside cation and anion hydration shells as well as from the interactions between NiZ+ ions and water molecules beyond the inner coordination shells. In both the solutions examined, peaks from longer intermolecular distances are not discernible in the experimental radial functions. From this point of view the solutions here investigated do not differ from the other cases we have previously studied.Our results however cannot be considered at variance with the observations of the Leicester group. In fact, if we examine the Ie.". functions, reported in fig. 3, we easily observe in our results the 1 2 3 4 5 6 7 8 9 10 0 1 s f A FIG. 3.-Intensity curves Ic,u. for the two solutions. Top curve for 4 rnol d ~ n - ~ , bottom curve for 2 rnol d ~ n - ~ .66 X-RAY DIFFRACTION AND STRUCTURE OF NiClz AQUEOUS SOLUTIONS peaks at small angles upon which Enderby based his quasi-lattice hypothesis. The positions of these peaks (centred at 0.85 A-l in the 2 mol dm-3 solution and at 0.95 ~4-l in the mol dm-3 sample) and their heights relative to the main peak height are not very reliable in our experiments since, in the geometry adopted, the small angle measurements are very sensitive to instrument alignment, curvature of the sample surface, absorption corrections and expulsion of air from the sample holder. Our results prove only that quasi-lattice organization, if existing, is not evidenced in NiC1, aqueous solutions when the structural analysis is based on the Fourier transform of the total experimental structure function.Obviously this observation in itself places a limit on the extent of ordering phenomena in NiCIz solutions. There- fore, as a first approach to a quantitative analysis, we considered a model including only nearest-neighbour interactions. From it we calculated a structure function which was tested against experimental data and was systematically refined by least squares. The general characteristics of the procedure have been described in previous paper^.^,^,'^ In the evaluation of the synthetic structure function only interactions inside the independent hydrated groups Ni2+ (Hz0)6, C1-(H20)n were considered.For the Ni2+ ions we adopted regular octahedral coordination after considering information in the literature and experimental radial curves. According to Jsrgen- sen," the study of visible and near ultraviolet absorption spectra permitted the classi- fication of Fe"', Co" and Ni" aqua-ions as octahedral M(HzO)ls+, though doubts could arise from diffractometric information. In fact, Shapovalov et ~ 1 , ' ~ in sulphate solutions, Bol et d.19 in nitrate solutions and recently Ohtaki et dZ0 in perchlorate solutions showed that the NiZ+ ion was octahedrally surrounded by six water mole- cules; the ion-water distances quoted were respectively 2.15,2.06 and 2.04 A; whereas in an earlier investigation on a NiCl, aqueous solution Dorosh and Skryshevskii,zl from the asymmetric envelopment of the Ni2+-Hz0 peak in the radial distribution curve, concluded that in the intimate configuration of the NiZ+ cations there should be four H20 molecules at a distance of about 2.0-2.1 A and two other molecules at a dis- tance of about 2.25-2.30 A, thus giving rise to a distorted octahedron.This result is very surprising. As observed by SacconiZ2 the theory does not predict any distortion for the octahedral complexes of NiZ+; eventual distortion from regularity must then be attributed to steric factors or crystal packing effects and would be possible only in solid hydrates.The asymmetry of the peak observed by Dorosh and Skryshevskii could then be explained on the basis of some Ni2+-C1- contacts; such a hypothesis could be accepted by observing that in the solid NiCIz*6H20 the entities revealed by X-ray investigationz3 are Ni(H20)4Clz. In our curves, however, the peak at 2.00- 2.10 A, ascribed to NiZ+-H20 contacts is sharp and symmetric; therefore, we accepted the exa-coordination for Niz+ ions in a regular octahedral geometry. Alternative coordination numbers were tested for the anions, despite evidence of octahedral co- ordination collected for the C1- ion;1,4J6 in fact, the possibility of a peculiar super- structure of Ni(HzO)I+, which we discussed in the Introduction, may prevent the C1- ions from having their usual coordination.The agreement between theoretical and experimental functions obtained in this approach is not completely satisfactory. By reference to correlation functions, we could well reproduce the NiZ+-H20 peak, thus confirming the validity of the struc- tural model employed for cation hydration. On the other hand, a good fit was not obtained for the doubly composed peak at about 3 A, even though it was possible to assume that the best coordination number for the C1- ions was six, in accordance with the results obtained in LiCl,' CaC124 and CrCI, solutions. We accordingly affirm that a model which includes only nearest-neighbour interactions allows the evaluation of the coordination numbers of the ions but does not permit satisfactoryR .C A M l N I T J , G . L I C H E R I , G . PICCALUGA AND G . PINNA 67 evaluation of the entire correlation function. This fact alone can be considered as proof of the existence in the solutions examined of order phenomena more remarkable than, or at any rate different from, those noticed in our previous investigations. Indeed, one can not improve our results simply by treating the cations as having a second hydration shell, as we did for solutions containing Cr3+ ions. In fact, even if the hydration power of Ni2+ ions did justify such a hypothesis, the amount of water existing (especially in the more concentrated solution, where the ratio H20 molecules/ salt molecules is -12.5) allows the realization of unilayer anionic hydration and bi- layer cationic hydration only in a more ordered model in which the hypothesis of independence of hydrated ions is not retained. Unfortunately, as already pointed out, no clues on more extensive structures in the solutions under examination are to be found in experimental data. Not even the hydrated solid structure can be re- garded as a starting point for the construction of an alternative model; in fact, as already mentioned, species like Ni(H20),C12 are present in the crystals of NiCl,.6H20,23 while experimental evidence and literature data24 clearly suggest that Ni- (H20)a+ ions exist in our samples. We then observed that in the hypothesis of a pseudo-lattice structure in which the sites are taken by the Ni(H,O)%+ groups with the residual water molecules and the C1- ions are set along the edges or in the cavities of the elementary cell, short-distance interactions between hydrated cations and some external water molecules must be taken into account.This then implies that the distance range over which ordering phenomena for the cation were considered must be increased. In such a hypothesis the anion-water distances are not necessarily due to the hydration capability of the anion, but may derive from packing. A calculation of a new synthetic structure function was then attempted, in which discrete interactions between Ni2+ ions and water molecules beyond the first hydration shell and inter- actions between these water molecules and those nearest-neighbour to the cations were added to the terms considered in the first approach model. The new structure functions and correlation functions thus obtained show good agreement with the corresponding experimental functions.This can be clearly observed in fig. 1 and 2, where the theoretical functions are reported as solid lines and compared with experi- mental results (circles). In the theoretical functions, coordination numbers of six and octahedral geometries were used for both cation and anion; the number of hydration water-external water contacts was six for the 4 mol dm-3 solution and 12 for the 2 mol dm-3 solution. The values of the parameters describing ionic hydration are given in table 2. TABLE 2.-MEAN DISTANCES Y AND MEAN SQUARE DEVIATIONS Q, WITH THEIR STANDARD ERRORS FROM LEAST SQUARES REFINEMENT, GIVEN FOR NEAREST-NEIGHBOUR ION-WATER INTERACTIONS C YNizt -HzO/A QNiZ+ -H2OIA rc1- -,o/A oC1- -H2OIA 2 .o 2.052 rt 0.003 0.101 0.003 3.134 & 0.009 0.207 & 0.008 4.0 2.062 0.002 0.127 i 0.002 3.145 & 0.007 0.276 & 0.007 CONCLUSIONS Our investigation has proved that the mean coordination geometries of Ni2+ and C1- ions are octahedral.Such a result for the NiZ+ ion in accord with expec- tation. Also the mean distance cation-water (2.05-2.06 A) agrees well with results obtained by Bol et aZ.19 and by Ohtaki et aZ.,2' thus also confirming that the anions do not cause any appreciable change in cationic hydration. The only result at vari- ance, leaving out the work by Dorosh and Skryshevskii,zl is that obtained by Shapo-68 X-RAY DIFFRACTION AND STRUCTURE OF NiCl, AQUEOUS SOLUTIONS valov et a1.18 which, as Ohtaki pointed out, gives too large a value for all the transition metal ions-H,O distances taken into consideration. The cation-H,O interactions were studied rather carefully, as their contribution to the structure function is by far the most important in a large range of s values (from s = 7 A-1 to s = 15 A-l) and the relative peak in the correlation function is quite well resolved.Also for the C1- ion, hexacoordination has proved to lead to theoretical functions which agree best with the experimental ones. The anion-water distances found here agree with those reported for other cases (ranging from 3.10 to 3.18 A); also the standard deviations listed in table 2 are not very dissimilar from those already found (ranging from 0.19 to 0.24 A). This fact confirms that the C1- ions also tend to be surrounded by their own hydration shell.Although information on ionic hydration has been obtained unambiguously, simple models, in which only nearest-neighbour interactions within the cationic and anionic shells regarded as independent are considered, do not yield theoretical struc- ture functions and correlation functions in full agreement with the experimental results. However, a satisfactory agreement can be reached by simply adding a certain number of interactions between the hydrated cation and external water molecules, without con- sidering any ion-ion interactions. No evidence in favour of a quasi-lattice structure has therefore come out of our analysis, despite the fact that experimental intensity functions show small angle peaks upon which a quasi-lattice hypothesis was based.We, therefore, affirm that a lattice structure, if it exists, should not be considered in too strict a sense. This viewpoint is in agreement with the fact that the most important contributions to structure factors come from short range interactions. Consequently we considered it superfluous to use lattice-type models. This work was partially supported by the Consiglio Nazionale delle Ricerche. All the calculations were performed at the Centro di Calcolo Eletronico, UniversitB di Cagliari. A. H. Narten, F. Vaslow and H. A. Levy, J. Chem. Phys., 1973, 58, 5017. G. Licheri, G. Piccaluga and G. Pinna, Chem. Phys. Letters, 1975,35, 119. G. Licheri, G. Piccaluga and G. Pinna, J. Chem. Phys., 1975, 63,4412.G . Licheri, G. Piccaluga and G. Pinna, J. Chem. Phys., 1976,64,2437. A. K. Dorosh and A. F. Skryshevskii, Zhur. Strukt., Khim., 1967,8,348. M. Alves Marques and M. I. De Barros Marques, Proc. Kon. Ned. Akad. Wet. B, 1974,77, 286. ' R. A. Howe, W. S. Howells and J. E. Enderby, J. Phys. C, 1974,7, L 111. J. E. Enderby, Proc. Roy. SOC. A, 1975,345, 107. G. W. Neilson, R. A. Howe and J. E. Enderby, Chem. Phys. Letters, 1975, 33, 284. lo M. E. Milberg, J. Appl. Phys., 1958, 29, 64. l1 H. A. Levy, M. D. Danford and A. H. Narten, Oak Ridge National Laboratory, Report 3960, l2 J. Krogh-Moe, Acta Cryst., 1956, 9, 951. l3 W. Bol, J. Appl. Cryst., 1968, 1, 234. l4 D. T. Cromer and J. B. Mann, Acta Cryst. A , 1968,24, 321. Is R. M. Lawrence and R. F. Kruh, J. Chem. Phys., 1967, 47,4758. l6 R. Caminiti, G. Licheri, G. Piccaluga and G. Pinna, J. Chem. Phys., 1976, 65, 3134. l7 C. K. Jsrgensen, Inorganic Complexes (Academic Press, London and New York, 2nd edn, l 8 I. M. Shapovalov, I. V. Radchenko and M. K. Lesoristskaya, Zhur. Strukt. Khim., 1972, 13, l9 W. Bol, G. J. A. Gerrits and C. L. Van Panthaleon Van Eck, J. Appl. Cryst., 1970,3,486. 2 o H. Ohtaki, T. Yamaguchi and M. Maeda, Bull. Chem. SOC. Japan, 1976, 49,701. 21 A. K. Dorosh and A. F. Skryshevskii, Zhur. Strukt. Khim., 1964, 5, 91 1. 22 L. Sacconi, Trans. Metal Chem., 1968, 4, 199. 23 J. Mizuno, J. Phys. SOC. Japan, 1961,16, 1574. 24 C. K. Jerrgensen, Inorganic Complexes (Academic Press, London and New York, 2nd edn 1966. 1966), chap. 2, p. 18. 140. 1966), chap. 3, p. 42.

ISSN:0301-7249    

DOI:10.1039/DC9776400062

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

GENERA L DISCUSSION Prof. B. E. Conway (University of Ottawa) (communicated) : Friedman has outlined the “ Hamiltonian approach ” to calculations of various properties of electrolyte solu- tions, and indicated some of the levels at which computations may be made and some of the difficulties that can be encountered. It appears to me that there is one important and interesting area where further a priori calculations are needed and that is in the evaluation of the so-called Gurney parameters which are of particular importance in giving an account of the behaviour of ionic solutions at elevated concentrations, e.g., > 1 mol d m j . Hitherto, it seems that the Gurney co-sphere overlap effect has been treated largely in an empirical way after other interaction energy contributions have been calculated in a much more rigorous manner.Since, however, the interesting ion-specific behaviour associated with solvation is involved in this parameter, and is thus exhibited at elevated concentra- tions in the chemical potential or activity coefficients, I believe that more attention should be given to the u priori evaluation of the co-sphere interactions in relation to the individual ion properties, which for some functions can now be estimated by non- thermodynamic procedures with encouraging reliability. For ion-ion interaction effects at charged interfaces, where one type of ion is predominantly accumulated and lateral interaction energies can be obtained experi- mentally from the coverage dependence of free energies of adsorption, we have made some attempts to evaluate the Gurney co-sphere interaction energy contributions by means of dielectric model calculations.lS2 At interfaces, it is mainly the “ like ” ion interactions that are of interest laterally in the double-layer. Dr.C. W. Outhwaite (University of Shefield) said: It is interesting to note that a simple potential approach3 (based on statistical mechanics although at the Debye-Hiickel closure level) predicts the polynomial factors in Wuu, Wuv, Wvv given in eqn [8(u), (b) and (c)] of H0ye and Stell’s paper for A = ~ ( l + 3y)-*. Dr. G. Stell (Stony Brook) said: To our knowledge, Outhwaite’s approximation scheme represents the only one [aside from those discussed in ref. (18) by ourselves] that has as yet explicitly yielded those limiting-law polynomials. I should further add to ref.(14) the interesting approach of S . A. Adelmaq4 who used it to predict the exponential shielding in Wuu, W,, and W,,. Prof. W. Ebeling (Rostock) said: For many applications one needs very simple models for the potential of mean force between two ions at infinite dilution. Simplicity is not so essential for the thermodynamic calculations but surely for the calculation of transport properties, e.g., conductivity since, in the latter case, complicated differential B. E. Conway, Elektrokhim., 1977, 13, 822. B. E. Conway, Adv. Colloid Interface Sci., 1977, 8, 91. C. W. Outhwaite, Mol. Phys., 1976, 31, 1345. S. A. Adelman, J. Chem. Phys., 1976, 64, 124.70 GENERAL DISCUSSION equations are to be solved.’ My question to Haye and Stell is, whether they can propose simple models for the ion-ion interaction potential which reflect the essential properties of the real potential at the McMillan-Mayer level.Up to now we have used in the Rostock group an oversimplified model with a hard core for r < (Ri + R,), a constant region in the first hydration sphere (Ri + Rj) < r < (Ri + Rj + 2.76 A) where the value of the potential is hij, and a Coulombic region for larger distances. This is a slight modification of the Gurney model proposed by Friedman and Rasaiah. We have shown elsewherel that for many electrolytes, e.g., NaC1, NaBr, NaI, KCl, KBr, KI, RbC1, RbBr and the tetra-alkylammoniumhalides that the thermo- dynamic functions and the conductance in the region c 5 0.1 mol dm-3 may be de- scribed in good approximation with the same set of potential parameters hi,, e.g., for the following pairs we would suggest: h~~~ = - 1.3kT; hNaCl = - 1.1 kT; hKBr - -1.2kT; hNaBr = -0.9kT; h K I = -1.2kT; hNaI = -0.9kT; hclc1 = 1.4kl’; hBrBr = 1.2kT; hII = 1.3kT; hKK = 0.9kT; hNaND = 0.7kT.Therefore, it seems to us that even the simple Gurney models describe the essential parts of the interactions at small distances in an integral way at least for certain simple electro- lytes. It would be very useful for practical calculations to have suggestions from the statistical theory, as presented by H0ye and Stell, for new simple but effective model potentials. Dr. G. Stell (Stony Brook) said: Two functional forms that can be conveniently added to the primitive-model infinite-dilution Wuu to get a more satisfactory approximation are suggested by our work.The simplest is a single term Kij exp r [-aij(r - Ri - R,]/r. As discussed by H0ye et d.,2 this has much the same conceptual status as the Gurney-Frank term or Ebeling’s “ square-mound ” term, with the two parameters Kij(Ri + Rj) and crij-l playing the same roles as the h i j and the 2.76 A, respectively, in his work if one takes aifl to be the same constant for all i and j . The advantage of the Yukawa over the square-mound form is partly a matter of greater realism and partly a matter of convenience. One can handle it analytically as a perturbation to the mean-spherical approximation and generalizations thereof; alternatively, one can still solve such approximations analytically when this term is added [see, e.g., ref.(3)] although for different R1 and R2 the analysis will be formid- able. The second functional form that one can still handle analytically in the same ways is a linear combination of two such Yukawa terms, as discussed by Hsye and co- w o r k e r ~ . ~ * ~ For appropriate choices of parameters, such a linear combination yields analytic approximations of high accuracy to the infinite-dilution W,, values that have been found in computer simulations. (See paper by Adams and Rasaiah and references therein, this Discussion.) Dr. J. P. Valleau (Toronto) said: There have been two previous attempts6,’ to make Monte Carlo estimates of the solvent-averaged mean force between unlike ions in a polar solvent. They agreed rather badly, presumably because of sensitivity to the W.Ebeling, R. Feistel and D. Geisler, Z . phys. C/ieni. (Leiprig), 1976, 257, 337; E. Bich, W. Ebeling and H. Krienke, 2. phys. Chetn. (Leiprig), 1976,257, 549; J. Nonequil. Therniodyn., 1978, 3, 11. J. S. Hprye, J. L. Lebowitz and G. Stell, J. Chem. Phys., 1974, 61, 3253. G. Stell and S. F. Sun, J. Cheni. Phys., 1975, 63, 5333. J. S. Hprye, G. Stell and E. Waisman, Mol. Phys., 1976, 32, 209. J. S. Haye and L. Blum, J. Stat. Phys., 1977, 16, 399. G. N. Patey and J. P. Valleau, J. Cfiem. Phys., 1975, 63, 2334. ’ I. R. McDonald and J. C. Rasaiah, Chem. Phys. Letters, 1975, 34, 382.GENERAL DISCUSSION 71 1 different boundary conditions employed. There are two ways around this problem. One is to attempt to find quite new and less objectionable boundary conditions, probably by avoiding periodic images altogether.(Friedman proposedl the " image approximation " for this purpose. In our laboratory we have been trying to test this, with disappointing results so far.) The other way is to try to go to such large periodic systems that the boundary conditions have little effect on the short-range ionic forces. This is the route Adams and Rasaiah have attempted in their impres- sively large-scale computation. I 1.0 0.5 0 4" \ 4 -0.5 -1.0 -1.5 primitive model 1 2 3 L r* - FIG. 1.-Ratio of apparent mean ionic force to that of bare, unscreened ions for the three estimates: (a) McDonald and Rasaiah, ref. (2); (b) Patey and Valleau, ref. (1); (c) Adam and Rasaiah, this Discussion.The curves have simply been It seems to me that we can have confidence in the ionis force estimate only when we can find results which are not sensitive to details of the boundary conditions, or at the least can demonstrate that they are not affected by increasing the size of the sample system. It is, therefore, worthwhile to compare the three estimates of ionic force, which involve somewhat different boundary conditions. Unfortunately they also concern slightly different models, and quite different model parameters, including especially the solvent dipole moment. Nevertheless they can be usefully compared. One way to do so is to look at the ratio, FIEb, of the apparent mean ionic attraction, F, to the coulombic attraction of bare unscreened ions, lib.This is shown in fig. 1 Positive values indicate attraction of the unlike ions. drawn through the .' experimental " points. H. L. Friedman, hfol. Phys., 1975, 29, 1533.72 GENERAL DISCUSSION for the three cases as a function of r*, the ionic separation reduced by the characteristic solvent diameter. It is apparent that the three estimates are widely discrepant; accordingly there is no reason to regard any of them as reliable. One expects the ratio F/F, to be somewhat less than unity at r* M 1, since there will be some screening by the solvent even when the ions are in contact. At larger distances, the ratio should be smaller in magnitude due to more effective screening, eventually approaching the primitive model result. (In fig. 1 the latter has been calculated by using the mean spherical approximation1 to estimate the dielectric constant.) On this basis the two earlier results seem fairly plausible physically, but the new one looks distinctly odd in that it predicts that the mean force is repulsive at almost all separations.It also looks remarkably large in magnitude, especially at the larger separations. There are large uncertainties associated with the results, as shown, but to the extent that they are statistically significant they look rather unlikely. Two things concern me. For reasons which have been explained elsewhere2 I be- lieve one is very apt to obtain seriously erroneous results in Monte Carlo calculations involving long-range forces if one uses a spherical cutoff when calculating the pair potential energies. This is so whether or not a reaction field is added as in the present calculation. At the same time the very large solvent dipole (3.5 D) used in the calcula- tion leads to worry about convergence and quasi-ergodicity.That dipole corresponds to a reduced square dipole moment, p*’ = p’/a3kT, of 4. In our calculations on dipolar fluids3 we found that we could only go to p*’ M 2.75, because at higher values of p* tests showed that the convergence was unreliable. Dr. D. J. Adams (Southumpton) said: I do not accept Valleau’s belief that erroneous results for Monte Carlo calculations involving long-range forces necessarily follow from using a spherical cut off. To obtain correct dielectric properties it is certainly true that the long-range nature of the dipole-dipole interaction must be carefully incorporated into the calculation.I believe that the approximation of replacing remote dipoles with a classical dielectric continuum is a very good way of doing this, This “ long-range correction ” can only be easily incorporated by using a spherical truncation. Also, this is the only method which does not rely on the shape or periodicity of the Monte Carlo cell. At present the published work on computer simulation of dipolar fluids is rather sparse, the true facts will no doubt emerge when much more has been done to evaluate the various summation methods proposed. I share Valleau’s concern that the high dipole moment we have used can lead to ergodic problems, that is, that a Monte Carlo calculation of practicable length will not properly sample all important regions of configuration space.The large varia- tions for both ion-solvent force and energy between one ion and the other in several of our calculations demonstrates clearly that this is indeed happening. We have in mind improvements that may help overcome this problem for the present type of calculation. For pure polar fluids, to which Valleau refers, and where the principal property of interest is the mean square dipole moment, problems of convergence are likely to be more severe, this is mentioned very briefly in our paper. My own experi- ence, in calculations for the pure Stockmayer fluid, is rather similar to Valleau’s, though I have not had undue trouble with p*2 = 3.0. We too find our results for mean force rather odd, in that it is repulsive out to 40 at least, whereas at very large separations the force should be small and attractive.M. S . Wertheim, J. Chem. Phys., 1971,554291. J. P. Valleau and S. G. Whittington, Statistical Mechanics. Part A . Equilibrium Methocis, ed. B. J. Berne (Plenum Press, New York, 1977), chap. 4. G. N. Patey and J. P. Valleau, J. Chem. Phys., 1974, 61, 534.GENERAL DISCUSSION 73 Valleau’s argument that F/Fb should be less than one and decrease with increasing ion separation seems reasonable to us and does throw doubt on our calculations for large r*ab. We found it necessary to quote our results within very large limits (due in part to ergodicity problems) and the “ true ” results may lie within these. Valleau’s figure does not reduce the three sets of calculations to a common graph as the reduction factor Fb is independent of the solvent properties, p* in particular.The plot is ((Fxso*v) + F b ) / F b where Fb is small at large r and the errors in all three calculations of (F,SOlV) are similar and large. The results of Patey and Valleau are for such a different system to the other two that only a rather general similarity of shape could be reasonably expected. Without repeating McDonald and Rasaiah’s calculations with the discovered program error removed we cannot know by how much those results were in error, but we cannot discount the possibility that their errors in (Fxs0Iv) are as high as a factor of two. Dr. C. W. Outhwaite (Shefield) said; A “ hump ” in the potential of mean force W,P, for two charged hard sphere ions i and j in a hard sphere dipolar system has been predicted in the Monte Carlo calculations of Patey and Va1leau.l For this system a potential analysis givesZ Wioj - --kTlng;, + eiej/Er + [(e - 1)/(2~ + 1)2er4][e?b3 + ejc3] m n = l + (ejej/2r)C[Atcosh(znc/d) + A~cosh(znb/d)]exp(-znr/d), where g$ is the radial distribution function for the two uncharged ions in the dipolar solution, e, and e, are the charges on the ions i and j respectively, E is Onsager’s di- electric constant, b = ai + 4d and c = a, + i d with a, and a, the ionic radii and d the dipole diameter, A; and Ai are constants independent of the ionic charge while z, are the complex roots with positive real parts of z + ( E - 1)sinh z = 0.In the dielectric continuum limit (d + 0) the expression reduces to the classical form of W,Oj with Onsager’s dielectric constant.The last term in W$ is damped oscillatory which gives rise to a “ hump ’’ in Wi9i,3 similar to that of Patey and Valleau. It seems probable that the “ hump ” in (Fx) predicted by Adams and Rasaiah for a Stockmayer solvent is closely related to this damped oscillatory term. Prof. H. L. Friedman (Stony Brook) said: Outhwaite has described a particular electro- static contribution to the “ bump ” in the correlation function g, - ( r ) for electrolytes. It may also be noted that the bump may be expected quite generally because for the dense hard-sphere fluid, the dense 6-12 fluid, and real one-component liquids g(r) has at least one prominent maximum beyond the first maximum.The same is true for non-ionic mixtures, as far as one knows. On this basis the maximum in F* reported at Tab* = 1.5 by Adams and Rasaiah (their fig. 1) may be expected even without the electrostatic contribution. This point was made in another way by Friedman, in ref. (4). Dr. C. W. Outhwaite (Shefield) said: I agree that for dense, real, non-ionic fluids g(r) has at least one maximum beyond the first maximum. This contribution is contained in In g:j in the expression above for W&. However in WP,, for equal dia- l G. N. Patey and J. P. Valleau, J. Chem. Phys., 1975, 63, 2334. C. W. Outhwaite, Mol. Phys., 1977, 33, 1229. C. W. Outhwaite, Mol. Phys., 1976, 31, 1345. H. L. Friedman, J . Solution Chem., 1972, 1, 387.74 GENERAL DISCUSSION meter charged hard spheres and dipoles, In gpj is negligible compared with the electro- static interactions at the concentrations considered in ref.(1) (p. 2337) of my previous comment and ref. (1). Prof. M. C. R. Symons (Leicester) said: First, a question to Hertz: can you say what you mean by the terms " structure making " and " structure breaking " ? We are going to hear these terms used frequently in this meeting, and I suspect there may be as many concepts as there are contributors! I would like to suggest that, in future, more specific phrases should be used, or at least, a suitable reference to the definition intended should be given. Then, a comment: your structure (a) for the way in which BF4- and related ions are hydrated is built, as you say, on rather tenuous evidence, and is in my view, chemically highly improbable.I suspect that (b) is more likely, for the following reasons : (i) It is closer to the " normal " mode of anion hydration as deduced by your- selves and others experimentally, and as predicted by various calculations. (ii) Since water molecules prefer to form four strong hydrogen bonds, (b) is to be preferred because it can still form three strong bonds even though that to BF4- is weak. Two even weaker bonds are unnecessary and will surely be avoided. (iii) The bond tc in (b) will be of enhanced strength, to " balance " the weak bond to BF4-. This means that it is extremely unlikely to break to give (a). (iv) Infrared and Raman studies indicate the presence of (OH) free groups rather than the " H,O-free " groups required by your model.Prof. H. G. Hertz (Karlsruhe) said: In order to explain the concepts " structure making " (or structure forming) and " structure breaking " as I understand them we start from the molecular pair distribution function of pure water. This (six-dimen- sional) function has maxima at certain (equivalent and non-equivalent) relative con- figurations. These configurations are those corresponding to H bonds in more chemical language. Now let us dissolve a salt in the water. Apart from the water- water pair distribution function, the mixture is characterized by the cation-water, the anion-water and by three ion-ion pair distribution functions. If for one (or both) of the ions forming the salt the ion-water pair distribution function has a maximum which is stronger than the greatest maximum of the water-water pair distribution in the pure liquid, then we say that we have a " structure making " ion.If, on the other hand, one (or both) of the ions has an ion-water distribution function with a maximum value less than the greatest maximum of the water-water distribution function in the pure state, then we say that the ion (or salt) is " structure breaking ". One may also consider the water-water distribution function alone: a structure making ion causes an increase of the height of the dominant maximum of the H,O-H,O distribution function per mole of added ionic species or it creates a new and definitely more distinct maximum in the H,0-H20 pair distribution function per mole of addedGENERAL DISCUSSION 75 ionic species. For structure breaking ions one obtains a decrease of the maximum height of the H20-H20 distribution function per mole of added ionic species.Both of these definitions seem to be essentially equivalent for inorganic ions and when I use these denotations I do not expressly distinguish between them. The latter definition, however, is more appropriate if one treats organic ions (and neutral solutes) where the effect of hydrophobic hydration may occur. I have also proposed a combination of both these formulations in order to characterize the total change of structure in the solution.'J We are fully aware of the fact that it might happen that, e.g., the water-water pair distribution function shows an increase of sharpness in a certain range of configuration coordinates, whereas in other regions maxima become markedly flatter or even dis- appear. In such an event it would not be clear whether the strict formal prescription for notation given above describes the physical situation properly.In fact, there are certainly structural changes when solutes are added; however, the two words " struc- ture making " and " structure breaking " are not sufficient to describe an object which probably should be described by a very large number of words, perhaps even by an infinite number of words. Science has to involve the art of introducing simpli- fications and abbreviations. Turning to Symons' comment, my reply is as follows: (i) The crucial conclusion concerning the orientation of the water molecule in the hydration sphere of BF4- stems from eqn (13) of our paper Due to experimental uncertainty we effectively calculated (l/Tl)I,l and with our experimental 19F f- lH relaxation data we found K* = 28, which gives F = 6 and leads us to the symmetrical form of H20 orientation denoted as form (a) by Symons.In order to arrive at the result that form (b) is the correct one, we must have F M 15, as may be seen from fig. 5 (p M 50'). This would mean that (l/Tl)I,l in eqn (I) must be more than two times smaller than originally calculated (and roughly confirmed by experiment). (l/Tl),,l is given by the exact relation: The correlation time z,* was estimated to be: n, = 3, a flat potential gives g(n,k,l) M 0.2. The reorientation time of BF4- is z, = 32, = 7.2 x 10-l2 s . ~ This motion modulates the F - ''0 interaction, it is not sufficient to produce a decay of the correlation function + 0.Thus, only if a reader can convince himself that the choice of the three parameters g(n,k,Z), z*, and n, must be such that (l/Tl)I,l comes out smaller by a factor 1/2.5 than given by our approach, is he justified to interpret our experimental results so as to yield an angle Po = 52" which corresponds to the form (b). In fact, the factor "2 in the quantity F, which leads to the form (b) corresponds to the estimated &SO% error we gave for the H. G. Hertz, Ber. Bunsenges. phys. Chem., 1964, 68, 907. H. G. Hertz, Ber. Bunsenges. phys. Chem., 1971,75, 572. H. G. Hertz, G. Keller and H. Versmold, Ber. Bmsenges. phys. Chenz., 1969, 73, 549.76 GENERAL DISCUSSION reliability of our calculated (l/Tl)I,l; however, this was chosen as a fairly extreme limit.In summary, we state that the probability that the H bonded configuration (b) is the correct one is extremely small. (ii) and (iii). The arguments given by Symons in these two paragraphs might be correct were the BF4- a neutral molecule. But the point is that on theeffective electric field strengths represented by the H bonds the ionic electric field is superimposed. This decouples the H bonds, and this effect is, to the author’s knowledge, just the explanation of the structure breaking effect. As a consequence, we have no longer any knowledge what the resulting torque on the water molecule close to the anion is and we learn from our experiment that the symmetric arrangement is the configuration of maximum occurrence probability.(iv) Here I would very much like to see the correct transformation relation between spectroscopic data given in frequency space and the corresponding statement in configuration space. I feel that a convincing bridging between our two results will be fairly difficult as long as such a transformation is lacking. Dr. K. E. Newman ( Wurwick) said : It is clear that the reorientational motion of a solvent molecule in an electrolyte solution is a complex function of its distance from the ions. The simplest correlation time distribution that can be envisaged is that used by Hertz and also used by Samoilov at the 1957 Discussi0n.l However, an alternative distribution which has its origins in the Frank and Wen model: of a region of dipole orientated water molecules close to the ion with reduced reorientational motion, beyond this a region of “ structure breaking ” presumably caused by structural mis- match effects and beyond this, “ structurally ‘ normal ’ water ”, may be more physic- ally significant.The apparent reduction in structure-breaking of the BF4- ion in concentrated solution is more readily rationalised in terms of the more complex cor- relation distribution. Also solute n.m.r. (e.g., 23Na, 35C1, etc.) chemical shifts which are believed to be influenced only by very short-range interactions, show no features attributable to structure effects in the structurally critical regions of aqueous-organic solvent mixtures. I should thus like to ask Hertz what evidence he has found for assuming that the structure-breaking effect exists right up to the ion? Prof.M. C. R. Symons (Leicester) said: I know of no spectroscopic support for the idea that there is a zone of weakly interacting water molecules around aquated ions. Nor can I see any reason why such a zone should exist. The conceptual mistake arises, I think, because of the idea that “ bulk water structure ” is something like a block of ice to which water molecules in the vicinity of an ion can only bond if they have exactly the right orientation. I see “ water structure ” as an infinitely adaptable array of molecules that is continuously changing. On moving out from an ion I envisage that all water molecules will interact in more-or-less the usual way, the mis- matching and consequent bond stretching/bending/breaking being very similar close to the ion-solvate to that which is continuously to be found throughout the s o l ~ t i o n .~ Prof. H. G. Hertz (Karlsruhe) said: The reduction in structure breaking of the BF4- ion in concentrated solution we would ascribe to the presence of the structure forming cations Li+ and Na+. So it seems to be more appropriate to answer the question which Newman raised considering solutions where structure forming ions are absent : e.g., KI, RbI or CsCl in HzO. Here the situation is as follows: at high concentrations, 0. Ya. Samoilov, Disc. Faraday Soc., 1957, 24, 141. S. E. Jackson, I. M. Straws and M. C. R. Symons, J.C.S. Chem. Comm., 1977, 174. * H. S. Frank and W.-Y. Wen, Disc. Faraday Soc., 1957,24, 133.GENERAL DISCUSSION 77 where all water is hydration water, c* = 6 mol dm-3 say, the water molecule rotational correlation time is shorter1* and the translational diffusivity is higher2,3 than in pure HzO.Thus, if there is a correlation time distribution as indicated by Newman, it is the first, well oriented region which has disappeared at this concentration. The problem remains: is such a region present at relatively high dilution? We consider n.m.r. relaxation rates of I2'I- and 87Rb+, and the self-diffusion coefficient of I- and Cs+ in water. It is known that4s5 7, is the correlation time for the ~ a t e r - l ~ ~ I nuclear quadrupole interaction. If a more ordered hydration sphere is formed as c* -+ 0, then 7, should increase because the effective radius of the aggregate increases.A* is a parameter describing the quenching of quadrupole interaction at the relaxing nucleus. If during dilution of the solution a hydration complex of cubic symmetry is created, then we should have A* --f 0, or at least A* should become smaller. Thus one sees that both tendencies which are connected with a possible ordering of, e.g. I-(HZO)" act against one another. Experimentally in KI and RbI solution6.' a decrease of l/Tl with decreasing con- centration has been observed. However, the decrease is only feeble and may be due to the effect of direct ion-ion interactions. Can a possible increase of z, with decreas- ing concentration, from which then one could conclude that A* decreases, be reflected by the concentration dependence of the ionic self-diffusion coefficients DI- or Dcs+ in KI and CsCl solutions? This is not so at 25"C, DI- and Dcs+ increase with decreasing c~ncentration,~ at 10°C there is very feeble decrease of both these self- diffusion coefficients at intermediate concentration^.^ Thus we conclude that there is no evidence for the existence of well ordered hydration spheres for structure break- ing ions like I-, Rb+ or Cs+.Other cogent experimental findings are not known to the author; however, he would admit that a strictly rigorous proof is still awaited. Finally, it should be added that we very recently obtained fairly convincing evidence that a zone B of higher fluidity is not present for structure forming ions like Na+, MgZ+, CaZ+ and Ba2+.8 Prof. S. Taniewska-Osinska (Lodi) said: (1) in Hertz's paper the opinion is expressed that the ions Clod- and BF,- are structure breakers and " the model of a rigidly hydrated ion with strictly oriented water molecules is inadequate ".However, your results show that three water molecules are trapped between anion and cation in the investigated solutions. This is surely a rigid configuration. (2) The structure breaking action of C104- and BF4-, which you mentioned, is not taken into account in your paper. The expressions " structure breaking and making " are useful in the discussion on experimental results but they are ambiguous. The sense of these terms depends on the experimental methods used as well as on the different views the authors believe in. L. Endom, H. G. Hertz, B. Thiil and M.D. Zeidler, Ber. Bunsenges. phys. Chem., 1967, 71, 1008. H. G. Hertz, Angew. Chem., 1970, 82, 91 (Angew. Chem. Int. Edn, 1970, 9, 124). H. G. Hertz and R. Mills, J . Chim. phys., 1967, 73, 499. H. G. Hertz, Ber. Bunsenges.phys. Chem., 1973,77, 531. H. Weingartner and H. G. Hertz, Ber. Bunsenges. phys. Chem., 1977, 81, 1204. H. G. Hertz, 2. Elektrochern. (Ber. Bunsenges. phys. Chem.), 1961, 65, 20. 78, 493. ' H. G. Hertz, M. Holz, G. Keller, H. Versmold and C. Yoon, Ber. Bunsenges,phys. Chem., 1974, * K. R. Harris, H. G. Hertz and R. Mills, J. Chim. phys., 1978, in press.78 GENERAL DISCUSSION In my opinion so long as no general satisfactory theory of solutions exists the use of these expressions may be admissible, but when a theory explaining all the inter- actions in solutions is elaborated, we shall need either to renounce or fully to expound the structure changing action.Prof. H. G. Hertz (Karlsruhe) said: (1) The three water molecules trapped between anion and cation do not represent a rigid configuration with respect to a reference frame fixed in the BF4- tetrahedron. As the cation approaches towards the anion the position and orientation of these water molecules follow this motion in a specific way. This causes a smearing out of the ion-water pair distribution function. (2) In fact, as I have already stated, the expressions “ structure breaking and structure making ” are somewhat ambiguous in the strict sense. However, in contrast to Taniewska-Osinska’s statement they represent a property of the respective pair distribution function and, as such, they describe the liquid as a microscopic object in a manner which is independent of the experimental method.The experimental properties represent mean values of certain physical quantities, these mean values involve the pair distribution function (if they do not involve higher distribution functions or distribution functions in phase space). Furthermore it should be made quite clear that even if we had a complete theory of electrolyte solutions the short-hand denotations in question here are still meaning- ful. This complete theory will be able to calculate macroscopic data from atomic properties, but of course, being complete, the theory will also be able to calculate pair distribution functions, then pair distribution functions may be divided in two classes according to a suitable convention.Prof. H. L. Friedman (Stony Brook) said: The important new data in the paper of Contreras and Hertz on 19F relaxation in BF4- may be interpreted on the basis of a very simple model leading to the expression, in the authors’ notation, and in the limit of zero molality of MBF,-, which is rather close to the experimental ratio, 14.3, considering the experimental un- certainty, k2.5. Eqn (a) is what one calculates if he assumes that at any distance r from an F atom the chance of finding a H atom is twice the chance of finding a 0 atom, and that the correlation time for the l9F-IH interaction is the same as for the 19F-170 interaction at any given r. For large r these assumptions are surely realistic so we need only examine the situation at small Y.Here we see two compensating effects: the protons come closer to the F atoms than do the 0 atoms, but also the protons move faster (due to the rotational motion of the water molecules). Very careful model calculations would be needed to tell whether the resulting correction to eqn (a) would be positive or negative. However the correlation time difference (between the F-H interaction and the F-0 interaction) tends to be made small by the fast re- orientational correlation time of BF4-, only 2.4 ps. according to Hertz, Keller and Versmo1d.l If we neglect the correlation time difference we may use the difference between the result in eqn (a) and experiment to estimate roughly how much closer the proton comes to the F atom than the 0 atom comes to the F atom.Assuming the latter is 2.7 A, as do the authors, we find 2.51 A for the closest approach of the protons. The resulting picture of the water structure next to a “ structure breaking ” ion H. G. Hertz, G. Keller and H. Versmold, Ber. Bunsenges., 1969, 73, 549.GENERA L D I S CU S S I ON 79 is rather different from that in fig. 1 of Contreras and Hertz. Their result is based upon the dependence of the relaxation times upon the MBF4 concentration rather than only the zero concentration limit. However for their model, with 12 neighbouring water molecules per BF4- and, I assume, at least 4 per M+, one runs short of water at about 3.5 mol dm-3 MBF,, i.e., in the middle of the range in which the concen- I I .O I H I I ! I I I I I ’ I i I l l I wavenumber I cm-’ FIG. 1.-Raman spectra of NaBF4 in D,O and HOD give indications of symmetric and asymmetric orientations of the anion BFh = A to water.The numbers labelling the curves refer to concentrations in mol dm-3. tration dependence is measured. Consequently it is hard to see how a consistent interpretation of the molarity-dependence of the relaxation rates can be based on the structure in their fig. 1. Prof. H. G. Hertz (Kurlsruhe) said: In contrast to Friedman’s statement I feel that there is good agreement between his estimate and our more detailed evaluation. In fact, a glance at fig. 1 shows that for the configuration indicated by p = 0, which corresponds to the limit c + 0, the two water protons come closer to the F atom than the oxygen does.When we take the F - 0 distance to be 2.7 A then the two equal F - H distances are found to be 2.3 A. Furthermore, our result is not depen- dent on the concentration dependence of the relaxation time, even more than this,80 GENERAL DISCUSSION essentially it does not depend on the correlation time at all, as may be seen from eqn (13) of our paper, since (l/Tl)i, i = 1, 2 is roughly proportional to 1/B. Finally, an anion-water pair distribution function is a well defined quantity at any concentration, so I do not see in what way running short of water should influence the results. Dr. I . C . Baianu (Cambridge) (communicated): In connection with the structural problems discussed by Hertz, I would like to suggest a new approach to structural studies of electrolyte solutions in the glass phase by solid state n.1ii.r.In this approach,'P2 the strength of the magnetic dipole-dipole interactions is measured directly in the solid state by pulsed n.m.r. methods and this yields informa- tion concerning the average intramolecular and intermolecular distributions in electrolyte solutions which can be compared with those proposed in this paper. The results obtained on the hydration structure of Li+ are in good agreement with parallel nuclear magnetic relaxation s t u d i e ~ ~ - ~ and previous X-ray and neutron scattering data6 on concentrated LiCl solutions in water and D20. The suggested solid state n.m.r. approach provides a structural framework for the investigations initiated by Hertz in this paper.Prof. W. A. P . Luck (Marburg) said: (1) James and Frost remark in their paper: " because of the disordered structure of solutions group theoretical arguments are not applicable to solutions ". I doubt if this is a general rule for systems with H bonds. The angle dependence and the relative deep energy minima of the H bond energy in comparison to kT can induce more or less distinct structures. In a recent paper' we demonstrated that in solutions of H20 + CC14 + organic acceptors the C,, symmetry of the 1 : 1 complexes H20 + acceptors disappears, but appears again in 1 :2 complexes. In such cases group theory may be applicable for solutions and liquids too. (2) Schioberg in our Marburg laboratory has applied this method to aqueous solutions of NaBF, and NaClO, (fig. 1).In both solutions at lower concentrations, about 1 molar, there are indications of unsymmetric 1:l complexes. At higher concentrations there is observed a band splitting of the ion-water interaction-band which points to a symmetric water-ion interaction (2 : 1 complex). This may support Symon's doubts about the structure of the BF4- complex with a scissor-type orienta- tion of water as given by Hertz. My question to Hertz would be: how sharp is the partition function in this scissor orientation, would the concentration dependence of our observation not indicate that linearly oriented water molecules with the proton axis in the direction water-ion also exist? Such linear orientations would follow from our measurements at low concentrations. At high concentration the symmetric 1:2 complexes may indicate the existence of such linear orientations too, in the absence of other effects which could change the type of orientations of the water molecules.(3) Related to the sceptical remarks of Symons about Hertz's nomenclature for structure breakers: the comparison of the intensity distribution of the i.r. bands of I. C . Baianu, N. Boden, D. Lightowlers and M. Mortimer, Chem. Phys. Letters, 1978, in press. I. C . Baianu, N. Boden, D. Lightowlers and M. Mortimer, unpublished results. N. Boden and M. Mortimer, J.C.S. Faruduy 11, 1978, 74, 353. A. Geiger and H. G . Hertz, Adv. Molecular Relaxation Proc., 1976, 9, 293. A. Geiger and H. G. Hertz, J. Solution Chem., 1976, 5, 365. A. H. Narten, F. Vaslow and H. A. Levy, J.Chem. Phys., 1973,58, 5017. D. Schioberg and W. A. P. Luck, Spectr. Letters, 1977, 10, 613.GENERAL DISCUSSION 81 water and its electrolytic solutions was the first indicator used' to correlate quantita- tively the Hofmeister ion series and the qualitative suggestion of structure tempera- tures due to Bernal and Fowler with the water structure. This could be established by a comparison between the spectroscopic approximation-method and solubility data.2 If we define the nomenclature " structure maker " and " breaker " using this spec- troscopic method, as a measure of the residual balance of more or less strong H bonds, then these terms are useful in a first approximation. If there are in addition secondary effects, we have to add refinements. This may be necessary if we discuss the special H bond structures water-ions of" structure making " ions.3 Prof.H. G. Hertz (Karlsruhe) said: With respect to questions (1) and (2) refer to (iv) of my reply to Symon's question. With respect to question (3) my answer is: mole- cular vibrations in the i.r. region are intramolecular properties which are also deter- mined by the structure of the liquid, however the structure itself is given by the probabilities of finding mass points in space. Dr. M. Perrot (Bordeaux) said: We have done almost the same kind of Raman experiments in our laboratory on Li+, Na+, K+ and Ca2+ nitrate aqueous solutions as have James and Frost. More precisely, on sodium nitrate solution we have studied a wider range of concentrations from 0.1 to 10 mol dm-3 and, for the lower concentra- tion, temperature (from - 10 to + SOOC) pressure effects (from 1 to 3000 atm) were studied.Briefly, applying the same kind of hypothesis for the separation of vibrational and orientational motions, we can say that: (1) For concentrations over 2.5 mol dm-3 the Ivv and IVH Raman profiles of the v1 (totally symmetric stretching mode) band do not remain symmetric, for a new component appears on the high frequency side, related to ion pair formation. So for highly concentrated solutions, the correlation times derived from the halfwidth of the spectra are no longer significant and cannot be related to the characteristic times of the motion. (2) The mechanism of the vibrational de-excitation proposed here via some bounded water energy level seems not to be realistic as no effect is observed by changing H20/D,0 or by varying the pressure.A " phase relaxation " process related to the fluctuations of the environment of the ion seems more plausible in that case. Furthermore, even for small concentrations, the f (isotropic) spectrum is not Lorentzian in shape out in the wings (we have studied the profile over a k75 cm-' range) and the vibrational correlation time defined as z, = jOmC(t) dt = 40) -, 2c where f(0) is the normalized maximum of the band, is 1.7 ps, instead of 1.4 ps expected in the Lorentzian approximation. (3) For the rotational motion, instead of simply subtracting the halfwidth of t(iso- tropic) from f (anisotropic) we have derived the convolution of the isotropic com- ponent by a rotational diffusion profile and compared the results with the experimental W.A. P. Luck, 2. Elektrochern., 1962,66, 766; 1965,69,69. W. A. P. Luck, Topics Current Chem., 1976, 64, 115. W. A. P. Luck and A. Zhukovskij, Mol. Phys. Biophys., 1974, ZI, 130.82 GENERAL DISCUSSION (anistropic) component. A good agreement is found for z (rotational) = 1.7 ps. The mechanism of a rotational diffusion seems realistic as the fast modulation condition of Kubo is well verified in this case. This rotational correlation time for the anion is of the same order of magnitude as the rotational correlation time of the water molecules in the solvation sphere (as derived from n.m.r. measurements). So that during the motion of the ion, the solvent cage is also moving. Finally, a tempera- ture effect allows us to calculate an activation energy of 2.6 kcal mol-’ for that motion, value which is much more higher than for many pure liquids and has to be related to the breakage of hydrogen bonds. Dr.D. W. James (Queensland) said: (1) We also observe, for many solutions, the high energy asymmetry described by Perrot. In dealing with these we have obtained the half width (HWHH) of the band by examining the low energy side of the band. For a band without asymmetry this technique yielded values identical with those obtained by taking the full band width (FWHH). In the same way the Fourier transform can be performed on the half band rather than the full band and the results are identical with those obtained by half width measurements. (2) As discussed in the answer to other questions we feel that the mechanism of the relaxation process has not been established.The relaxation which we propose is an energy transfer taking place in two steps: (i) energy transfer into the overtone con- tinuum which is present in the spectrum between 800 and 1600 cm-l, and (ii) energy transfer through this continuum to the bending mode at 1600 cm-l. Since the transfer is not directly to the water bending mode it is not surprising that the change from HzO + D20 is not very pronounced. We do not however, agree with Perrot that there is no effect (see table 2). In a series of measurements on solutions containing XO/- anions we have found1 that the vibrational relaxation is fastest for those anions having the highest vibrational frequency.This type of variation is more readily explained in terms of an energy transfer to a water molecule vibration rather than in terms of a dephasing mechanism. With regard to the vibrational relaxation time of 1.7 ps quoted by Perrot we have also obtained the relaxation time from the Fourier transform of the band over a similar energy range and obtain (for a 1 molar solution) a value of 1.37 ps. A possible reason for the difference in these two numbers is that our spectra were obtained with constant energy slit width whereas Perrot’s were obtained with constant mechanical slit width. The change in energy dispersion over the range scanned (150 cm-l) will produce a band distortion in Perrot’s spectra which may give rise to the different value for 5,. (3) The treatment of the spectra to give the reorientational relaxation time is very interesting.We note that if a vibrational relaxation time of 1.4 ps (rather than 1.7 ps) is used in this treatment the reorientational relaxation increases to 2.0 ps in good agreement with our values. Prof. D. E. Irish (Waterloo, Canada) said: I share the concerns just expressed by Perrot concerning the interpretation of the line shapes. In addition I raise three points. (i) The concentrations of Ca(NO& and ST(NO~)~ solutions attain values of 5 and In these systems ion association O C C U ~ S . ~ ~ ~ There- D. W. James, R. L. Frost and R. Appleby, unpublished results. D. E. Irish, A. R. Davis and R. A. Plane, J. Chem. Phys., 1969, 50, 2262. J. T. Bulmer, T. G. Chang, P. J. Gleeson and D.E. Irish, J. Solution Chem., 1975, 4, 969. 3 mol dm-3 respectively.GENERAL DISCUSSION 83 fore, the 1050 cm-' band envelops lines from both the free nitrate ion and the ion pairs. The orientation times under discussion are properties of a particu- lar constituent and cannot sensibly be averaged over several kinds of species. To determine the HWHH values one must know the peak height of each of the contributing lines and these must be substantially less than apparent peak heights. It is extremely difficult, possibly impossible, to resolve such closely spaced lines with a computer bandLfit program. But unless this is done can the correlation times have any meaning? (ii) Using eqn (1) the authors conclude that " solvent separated ion pairs play a less important role in those solutions containing the highly polarizing cations Li+, BeZ+ and Mg2+ ".I believe that this interpretation of the constants in the equation is not warranted. The high fields resulting from the smaller cations are essential to the formation of solvent separated ion pairs and evidence has previously been presented for these species in solutions of Mg(N03)2 and Be(N03)2.1-3 (iii) The disposition of water molecules around the nitrate ion has been the subject of considerable research and much speculation. The topic has been recently re~iewed.~ Is the evidence for a H20-N03- species (involving only one water molecule) strengthened by these new measurements ? I understand that Triolo has some unpublished data concerning the solvent structure around the nitrate ion and I would ask him to share those with us.Dr. R. Triolo (Palerrno) said: In Oak Ridge we have done X-ray and neutron diffrac- tion measurements on aqueous solutions of LiNO, having the composition LiN03-5.7 H,O and 'LiN03.5.7 D20, respectively. As the electron distribution in a water molecule is very nearly spherical, the X-ray data can be used to get information on the positional correlation (i.e., number of next neighbours and relative distances). When we analyse X-ray data we find that a model in which Li+ ion is surrounded by four oxygens in a tetrahedral arrangement and NO; ion is surrounded by five oxygens (3 in the plane of NO, ion itself along the bisectrices of the 0-N-0 angle and two above and below the NO, ion) is able to fit the experimental data very nicely. In principle, the X-ray data can not tell if the " oxygens " are really water molecules or not.Of course neutron data could help us in that, owing to the fact that the distribution of neutron scattering centres is non-spherical, we might have information about the orientational correlation between particles. In addition the neutron diffraction pattern is dominated by interactions involving deuterium atoms. However the detailed interpretation of these data has not been completed, mainly because we are trying to work out a better correction for deviation from static approximation (Placzek corrections). I personally would like to see the nitrate ion as being in a cage of water molecules not tightly bound to it. Dr. D. W. James (Queensland) said: (1) Several of the solutions studied showed asymmetry, sometimes quite marked, on the high energy side of the band.Since this was the first attempt to derive relaxation information from Raman bands for T. G. Chang and D. E. Irish, J. Phys. Chem., 1973,77, 52. D. J. Gardiner, R. E. Hester, and E. Mayer, J. Mol. Sluuct., 1974, 22, 327. D. E. Irish and M. H. Brooker, in Advances in Infrared and Raman Spectroscopy, ed. R. J. H. Clark and R. E. Hester (Heyden, London, 1976), vol. 2, chap. 6, p. 212.84 GENERAL DISCUSSION aqueous solutions we wished to keep the interpretation as simple as possible. In the presence of high energy asymmetry, the low energy side of the band was analysed to yield band width parameters. This is an approximate method only and we must examine whether the results obtained are reasonable.If we compare the vibrational relaxation times for Mg(NO& and Ca(N03), solutions there is a close correspondence in observed values. In the Mg(N0J2 solutions there is no asymmetry, in the Ca(N03), solutions the asymmetry is quite marked. The differences observed with change of cations, although small, are what would be intuitively expected. When we turn to the reorientational half widths (Table 1) it may be seen that these decrease as the cation concentration increases. If the band asymmetry was taken into account this decrease in band half-width would be, if anything, more pronounced. We agree that in order to get more significant values for rOR a band analysis should be attempted but for the moment the reported values can be taken as a lower limit for the variable.(2) The suggestion that solvent separated ion pairs play a less important role in solutions containing Li+, Be2+ and Mg2+ refers only to the influence which these species have on the reorientation of NOj- about its C, axis. The implication is thus that the solvent separated ion pairs which have been shown to be important in these solutions (as referred by Irish) are formed preferentially with one oxygen atom and are not involved in the lowest energy reorientation process. (3) The studies we report herein do not give direct support to the H20-N03- species involving one water molecule. As we indicate, we have examined the relaxa- tion behaviour of the nitrate ion in mixed solvent systems [ref.(14) of our paper]. These studies indicate that in systems containing water the presence of one water molecule per nitrate ion is sufficient to give vibrational relaxation times similar to those we report above, while lower concentrations of water in non-hydrogen bonding solvents yield vibrational relaxation times which are much longer. The vibrational relaxation is expected to depend dominantly on the most strongly hydrogen bound water molecule while the reorientational relaxation time is much more dependent on the average of the whole anion hydration shell and thus describes the nitrate ion sur- rounded by -5 water molecules as revealed by the X-ray and neutron measurements of Triolo. Dr. J. Yarwood (Durham) said: The mechanism of vibrational relaxation in the nitrate ion invoked by the authors involves energy redistribution (of NOj-, vl, excited state vibrational energy) via the bending mode of the neighbouring water molecules.This mechanism involves mode-mode coupling as suggested by Madden and the rate of relaxation is expected to depend on the spectral density due to the surrounding molecules in the vicinity of the NO,-, v1 band (Le., near 1050 cm-l). Since this is not great in the present case and since, in any case, such energy relaxation processes have been shown' to be relatively slow using stimulated Raman measurements, I believe that this is not the dominant relaxation process. The total vibrational relaxation function may be written3s4 as where qBV(t) includes all processes involving energy relaxation or energy redistribution P.A. Madden, Faraday Symp. Chem. SOC., 1977,11, 86. ' S. F. Fischer and A. Laubereau, Chem. Phys. Letters, 1975,35,6; A. Laubereau and W. Kaiser, Ann. Rev. Phys. Chem., 1975,26, 83. G. Doge, R. Arndt and A. Khuen, Chem. Phys., 1977,21, 53; J . Yarwood, G . Doge and R. Arndt, Chem. Phys., 1977,21,387. J . Yarwood and R. Arndt, Molecular Association, ed. R. Foster (Wiley Interscience, London, 1978), vol. 2. P T W = PE(t)PP(t)GENERAL DISCUSSION 85 (in general, depopulation processes). a result of the fact that the vibrational relaxation function pp(t) is the phase relaxation function which is includes the relaxation of both the amplitude and the phase of the vth normal co- ordinate, Qvi. A simple physical model for such relaxation may be constructed2 by noting that in the liquid phase the '' probe " molecule feels a different interaction with each of its neighbours.This leads to a distribution of transition frequencies and hence to spectral broadening. Quantitative development of the model'^* leads to successful prediction1 of the effects of temperature, pressure and concentration on z, and on the vibrational second moment and stimulated Raman measurements demon- strate3 that (for polyatomic species) the It should be noticed that this vibrational relaxation by loss of phase coherence uses a similar model to that mentioned at this meeting in terms of " environmental " broadening by Symons and Friedman. It should also be realised that the spontaneous Raman band width will, of course, be broadened by energy relaxation effects but that, if very slow, they will make only a small contribution to the overall band width.Finally, the point should be made that this comment does not seek to invalidate the " hydrogen bonding " mechanism proposed by James and Frost for the NO3- * * * H,O interaction. Indeed, hydrogen bonding would be expected to lead to a wide distribu- tion of intermolecular forces in the liquid phase, and hence to extensive vibrational broadening. However, it is clear from the data shown in fig. 3 that NO3- * - NO3- interactions may have a significant effect on the relaxation at high salt concentrations. The lowering of the relaxation time with increasing NO3- concentration may be most simply explained in these terms but the system anion + water + cation is a complex one and in my opinion the exact mechanism of interaction is by no means proven.Careful studies on the temperature, solvent and concentration dependence of z, could be used to further study' the nature and extent of the interactions. values are of the order of 1 ps. Dr. D. W. James (Queensland) said: The point Yarwood raises is a fundamental one concerning the mechanism of the relaxation process. Although several studies have indicated that phase relaxation dominates the vibrational relaxation process these studies have concerned non-associated or weakly associated liquids [Yarwood's ref. (2), (4)]. It has recently been reported that for at least two liquid systems the relaxa- tion process is dominated by energy relaxation rather than phase rela~ation.~ Details of these studies are not available.It is possible to design an experiment to distinguish between the two relaxation processes but we are not equipped to perform such an experiment and, to date, it has not been reported. We feel that it is by no means clear which of the two relaxation mechanisms dominates the relaxation process in aqueous solution. However, as pointed out elsewhere4 the two relaxation mechan- isms can, at least formally, be treated similarly and, as pointed out by Yarwood, the " hydrogen bonded " model can be applied to relaxation through either mechanism. It is important that the nature of the relaxation mechanism is established by direct G. Doge, Z. Naturforsch, 1973, 28A, 919. R. Kubo in Fluctuation, Relaxation and Resonance in Magnetic Systems, ed. D.Ter Haar (Oliver and Boyd, London, 1962), p. 26. K. Spanner, A. Laubereau, W. Kaiser and S. F. Fischer; as quoted in G. Doge, R. Arndt and A. Khuen, Chem. Phys., 1977,21, 53, ref. (11) and (12). W. G. Rothschild, J. Chem. Phys., 1976,65,455.86 GENERAL DISCUSSION measurement so that the structural suggestions made in our contribution can be placed on a more quantitative basis. Prof. H. L. Friedman (Stony Brook) said: How do we know that the linewidth effects actually measured by James and Frost can be accounted for in terms of correlation times as described? How is the contribution of inhomogeneous broadening shown to be negligible? While it is not stated in the paper, the authors study the 1049 cm-l symmetric stretch of the hydrated NO3-, I assume.It is easy to imagine that this line, for a given NO3- ion, shifts around as the ion moves near other ions of either sign. Since the diffusional motions in solution are not fast compared to the correlation times z, and zOR reported here, these shifts would have more the character of inhomogeneous broadening than motional broadening in the observed spectrum. Also, I wonder how the authors interpret the paradox that extrapolation to infinite dilution of the data for z, and z~~ leads to values that depend upon the cation? Dr. D. W. James (Queensland) said: The breadth of the vibrational band may be considered to have contributions from vibrational dephasing, inhomogeneous broadening as well as the energy transfer mechanisms described in the paper.Vibra- tional dephasing we have discussed above. The contribution to linewidth made by inhomogeneous broadening may be qualitatively estimated as follows. (1) In solutions of Cd(N03), (not reported above) the band maximum is at 1049 cm-l and is invariant with concentrations up to a concentration of 3 mol dm-3. The HWHH for this band in dilute solution is -4 cm-l. In crystalline Cd(N03)2.4H203 the band maximum is 1051 cm-l with a HWHH of 1.5 cm-l. In this crystalline salt there is no direct anion cation contact. In anhydrous Cd(N03), where there is anion-cation contact with two distinctly different anion cation distances the band maxima are at -1064 and 1072 cm-l.l We can thus infer that the cation in- fluence on the band maximum will tend to move it to higher energy for all con- figurations involving the approach of the CdZ+ to the NO3-.Inhomogeneous broadening from this source could be expected to move the line to higher energy and/or produce asymmetry on the higher energy side. This is not observed. (2) Close approach of Mg2+ or Li+ to the nitrate ion moves the band strongly to higher energy (Mg-N03 contact, 1102 cm-1 Li-NO, contact, 1072 cm-l). Again it is expected that there should be concentration dependent movement of the band maximum to higher energy or a strong concentration dependent asymmetry on the high energy side of the band. Mg(N03)2 solutions do not show band maximum variations nor does the band become appreciably asymmetric. In solutions of LiNO, (1 mol drn-,) with LiCl(1-7 mol dmW3) again the band neither moves in posi- tion nor shows appreciable asymmetry. (3) The isotropic linewidth remains essentially constant over the temperature range 30 to 80°C.It is expected that inhomogeneous broadening would increase with temperature rise. (4) It is certain that contact ion pairs produce new bands usually on the high energy side of the line. We feel, however, that in the absence of appreciable con- centration of contact ion pairs the water sheath shields the nitrate ion from direct cation influence and averages the polarization effect. Because of this the magnitude of the inhomogeneous broadening is not appreciable. The variety of environments can however, contribute to the vibrational dephasing. D. W. James, M. T. Carrick and W. H. Leong, Austral. J. Chem., submitted.GENERAL DISCUSSION 87 The extrapolation to infinite dilution of the values of zy and zOR is not a valid procedure.Due to experimental limitations we do not have any measurements in dilute solution. Our measurements rather relate to solutions in which the solvent structure has already been significantly disturbed by anion and cation influences. The extrapolations to infinite dilution are then related not to the actual solvent struc- ture but to a hypothetical disturbed structure at infinite dilution. Prof. M. C. R. Symons (Leicester) said: How sure can one be that an apparently good Lorentzian fit such as shown in fig. 2 ensures the absence of " static " contributions to the width? I can see that for a band that is insensitive to environmental factors there need not be any serious broadening from solvent perturbations, but the band you are studying is shifted by hydrogen bonding, etc., and hence solvation fluctuations should give rise to inhomogeneous broadening.The only other possibility would be that these are rapid on your time-scale. I recall that nitrate ions have their symmetry reduced in protic solvents. We have suggested that this is due, primarily, to asym- metric solvation.' We suggest that the highly polarisable NO3- ions (in contrast with the weakly polarisable C104- for example) are primarily solvated at one or two of the oxygen atoms as indicated in (a) or (b). This asymmetry is sufficiently long-lived that well defined band-splitting is observed. However, it could be that as such perturbations move from one oxygen to another, there is an uncertainty induced broadening of the band you are studying.In relation to the difficulties experienced in the I,,,,(o)data, I wondered if the use of glasses might help, by reducing, or eliminating the reorientational contributions. Dr. D. W. James (Queenslund) said: Undoubtedly there will be a contribution to the line breadth from static contribution of the type mentioned by Symons. This contribution is apparently very small as shown by measurements in mixed solvent systems. The contributions due to different anion-water-cation configurations are more important but, as described in the answer to Friedman, the broadening due to this mechanism can be neglected in a first approximation. The use of glasses to study these relaxation processes is a necessary extension of these studies.The vibrational relaxation is very fast which gives considerable breadth to the band. Because the reorientational relaxation is slow the reorientational contri- bution to line width is indeed small and difficult to extract with accuracy. The difficulties we encountered with measurement of lanIs(m) were mainly in the regions of low concentration (below 1 molar MN03). This is not really the concentration region where studies of glasses can be particularly useful. Dr. P. Gans (Leeds) (communicated): In addition to considering effects due to contact ion-pair formation, it is necessary to consider solvent-shared and other forms of T. J. V. Findlay and M. C. R. Symons, J.C.S. Faraduy II, 1976, 72, 820.88 GENERAL DISCUSSION secondary associate.As an example we note the large decrease in the half-width of the vq Raman band of lithium and sodium nitrates in liquid amm0nia.l One inter- pretation of this phenomenon is that a band at the same position as that of the free nitrate ion but of greater half-width is decreasing in intensity as the concentration of the species responsible, the solvent-shared ion-pair, decreases. Indeed, the band attributed to the “ free ” ion must always be a composite band in which contributions from all non-contact ion-pairs are superimposed. Dr. D. W. James (Queensland) said: Gans’ question concerns the fundamental problem of whether it is valid, on the time scale of our measurement, to consider that a vibrational band has contributions from different ion-solvent -ion configurations.If the ion-solvent exchange time is similar to the vibrational relaxation time the band reflects the influence of an averaged environment. This is certainly the case for rmst of our systems. In very strongly hydrated systems where the solvent-ion exchange time is much longer than the relaxation time it may be valid to consider contributions from several environments. Thus in concentrated solution of LiN03 and Mg(NO,), it would be reasonable to suggest that the experimentally observed band is due to two or more coincident Lorenzian components. However, since the separation could not be made uniquely, such a separation would not provide reliable structural informa- tion. Except in cases where new bands are found attributable to, for example, contact ion pairs we consider that the band analysis gives information on the concen- tration dependent average structure of the solution.Prof. W. Libu6 (Gdansk) said: I think that there is some, not negligible, ionic associa- tion in the solutions of NiCI,, not taken into account in the work by Caminiti et al., which might be a reason for the small differences between the calculated and experi- mental correlation functions. Zofia LibuS and her students have determined the stability constants of the monochloro- and monobromo-complexes of the divaient transition metal cations belonging to the series Mn-Zn. Using equimolal mixtures of the respective metal perchlorates and magnesium perchlorate as the reaction media they eliminated the main sources of error inherent in earlier determinations of stability constants of very weak anionic complexes, so that these results seem to be reliable.It has been found that nickel(I1) forms the weakest complexes with either the chloride or the bromide anion. Nonetheless, under the simplifying assumption that the stabil- ity constant determined for the perchlorate as the ionic medium is valid for the equally concentrated solution of nickel@) chloride, we may estimate that approximately 25% of the total nickel(@ content would be in the form of the NiCl+ complex in the 2 molar solution, and over 50% in the 4 molar solution. At the same time essential lack of changes in the visible spectrum of Ni(@ up to approximately 2 mol dm-5 indicates that the NiCl+ complex is mainly of the outer-sphere type. It is only at still higher concentrations that changes in the visible spectrum occur, consistent with the formation of a single coordination complex.The variation in the quotient of the activity coefficients of the association reaction with the concentration of the ionic medium also indicates that the NiCI+ complex is of the outer-sphere form in the dilute solutions, in contrast to the MnCI+, ZnC1+ and CuClf complexes. It is interesting to note that the hydrated magnesium cation shows a distinctly smaller, if any, association with either C1- or Br-, so that the higher ability of Niz+ to the outer-sphere association with these anions must be ascribed to P. Gans and J. B. Gill, this Discussion.GENER 4 1. DISCUSSION 89 a positive contribution of hydrogen h i d forination of the anion with the coordinated water molecules of the hexa-aquocaii.m. Dr.F. J. C. Rossotti (Ox-oid U/?icersir,fj said: In analysing her X-ray diffraction data, the O i d y nickel solute other than Ni(H20):+ that Pinna appears to have considered is Ni(H,0)4CI,. Now various attsii-ipts have been made to study quantitatively the stepwise equilibria Ni'+, 2q. +- / I C I - ? aq. -.z NiCI,(*-")+, aq. Although agreement between differciit workers and different methods is poor, one can estimate that Pima's 2 and 4 tnolar NiC1, solutions contained about 50% of NiCl+, aq. In the present stat: of tiic diffraction art, should it be possible to identify an approximately 50:50 mixture of Ni(H20h,'' and NiCl+, aq. (whether the latter be an outer-sphere hexa-aquo specie:.(ir ;in inner-sphere penta-aquo species) ? Alter- natively, are the data definitely iiiccii,;istent with the existence of the 1:l chloro complex in substantial amounts in concentrated nickel chloride solutions? Dr. G. Pinna (Cagliuri) said: In OLII' opinion our data are not i n accord with the existence of a significant amount of NiCI' inner-sphere complex in the 4 niol dm-3 soliltion. Thc presence of such ii ccmplex should result in a shift towards higher distances of the 2 A peah which dcwibes Ni"-nearest neighbour contacts in the correlation function, or at least tliis pcik should become unsymmetrical : neither of these effects is observed. As fzr as outer-sphere complexes a re concerned, the problem is more complicated.Affirming that nickel and chlorine ioi?s are exa-coordinated, and that, in addition, cations have second neighbour contacls. iiieans that at the concentrations investigated (and especially at the highest one), scnie water molecules must be shared by cations and anions. Our results are, thereft>rc*. not inconsistent with an outer-sphere complex hypothesis. But what is difficult is to give a geometrical description of such a system so that the synthetic structure ftinction may be evaluated. This subject has not been exhausted in our work. In fact, our aim was not that of giving a complete picture of the cationic second hydra;ion shell, but rather that of determining whether second shell contacts controlled the ::greement between the theoretical and experi- mental first peaks of the correlation fitnction.The results on the characteristics and on the composition itself of cation second coordination shells are, therefore, not definitive and for this reason they ha\ e not been specified in the paper. Dr. G. Phlinkhs (A4ainz) said: It is a n interesting problem, whether or not ions in concentrated solutions hake a quasi Ii.ttice structure. The existence of such a struc- ture is the basic assumption of s,?~,er,il theories of electrolyte solutions. I agree however, that for the time being we hate no evidence of this on the basis of diffraction experiments. Although a small angle peak can be observed in neutron and X-ray scattered intensities of some divalenc nietal aqueous solutions, this is still not evidence for the existence of a qumi lattice stntcture.In a diffraction experiment the total structure function H(s) is the w-i:li!ed sum of contributions of different particle- particle pair interactions, H(s) = cXli(s) hLs(s) X.P = -1, -, water 3 Stnbility Corutnnts oiid Stcrbility Corr\rwrtr. Sirpp/ernent 110. 1, ed. L. G . Sillkn and A. E. Martell (Chern. SOC. Special Puhlicntioris No\. 17 and 25, 1964 and 1971).90 GENERAL DISCUSSION where the partial structure functions haB(s) are connected with the partial pair cor- relation functions gap(r) by Fourier transformations. The weighting functions c%p(s) are dependent on the scattering amplitudes of the a and p particles and concentration of the solution. The problem is that weights for ion-ion interactions are <3% even in the case of very concentrated solutions for both neutron and X-ray scattering. In view of the estimated 1-2% accuracy of the measured intensity in a diffraction experiment, statements made on the quasi lattice structure from diffraction experiments are questionable.The measurement of ion-ion interactions in X-ray diffraction is feasible only in a very special case: a very large ion with many electrons. Recently Friedman et aZ.l have predicted small angle X-ray scattering of an 0.3 molar aqueous Ph,AsCI solution due to + + interactions. Generally diffraction experiments give reliable data only on the ion-solvent and solvent-solvent structure. Pinna and co-workers exclude the possibility of measuring solvent-structure by assuming the solvent structure to be the same as the structure of pure water.One wonders if Pinna could provide an argument supporting this assumption? Dr. R. Triolo (Palerrno) said: After the publication of the neutron study of NiC1, aqueous solutions, a great number of experiments have been done to prove the existence of long range order structure in concentrated aqueous solutions of transition metals. In particular, concerning NiCl,, thermodynamicZ as well as spectroscopi~~~~ and hydrodynamic consideration^,^ suggest that the structure of NiCl, aqueous solutions might vary on going from moderately concentrated (-2 mol dm-3) to concentrated (-4 mol dm-3). In addition it seems that the transition from one structure takes place smoothly around 2 mol dm-3. It would then be worth trying to improve the quality of the fitting shown by Pinna in fig.1 and fig. 2, taking into account the possibility of long range order (in the most concentrated solution) through complexes of the type Ni(H20)6-, C1,. The appearance of a shoulder in G(r) at -2.6A for NiCl, 4 mol dm-3, might indi- cate the presence of such complexes that, as pointed out by Rossotti on the basis of available stability constant data, should be present at these concentrations. Dr. G. Pinna (Cagliari) said: Our work has shown that a model in which only nearest- neighbour interactions are used to describe the environment of hydrated ions does not lead to satisfactory structure functions. As the amount of water is small at the concentration examined, one cannot think that this fact depends on the existence of a second hydration shell around the cation.On the contrary, together with the presence of prepeaks in the intensity curves, it suggests that order phenomena more remarkable or somehow different from those observed in other cases (see for example CaCl, solutions), are present in the NiCI, solutions. Therefore, introducing hydration water-external water interactions in the calculations must be understood as a first approach to the problem of a more ordered structure, which we actually have not exhausted. (a) such a more ordered structure should not involve a significant amount of complexes of the type Ni(H20)6-, C1,. As already said in answering to However, we want to point out that H. L Friedman, D. M. Zebolsky and E. Kftlmin, J. Solution Chem., 1976, 5, 853.* G. Cubiotti, G. Maisano, P. Mighardo and F. Wanderlingh, J. Phys. C., 1977, in press, 3 M. P. Fontana, G. Maisano and F. Wanderlingh, Solid State Comm., 1977, 23, 459. M. P. Fontana, Solid State Comm., 1976, 18, 765. F. Wanderlingh, personal communication.GENER 4 1. DISCUSSION 91 Rossotti and Libui, there is no e\idence of direct Ni2+-CI- contacts i n our curves. Moreover, the results obtained by Enderby et ul.' by neutron dif- fraction experiments on saniples isotopically enriched prove that in a 4.41 molal NiC12 solution there are 5.8 I& 0.2 water molecules in the first coordina- tion shell of the cation, and al\o show " the apparent absence of CI in the first coordination shell ". (b) In answer to both Triolo and Nielson, a lattice model should not necessarily be used in order to explain o u r results, since long range order phenomena are not evident in the correlatio!i functions.With regard to this, we want to point out that our results do not exclude the existence of the discrete Ni-Ni interactions revealed by the mall angle peak and investigated by Enderby et al.' These interactions, houever, may be masked in our curves (for example because their contribution to the total structure function has a small weight in comparison with the dominnnt ones): but we believe as well that an ionic organization in a highly ordered manner should reveal itself, (almost by definition) in correlation functions and moreover it should come out by model analysis. Perhaps the whole question ma) be reduced to the problem of definition and meaning of t e r m such a4 " highly regular manner ", " quasi-lattice organization '' and so on.Prof. F. Franks (Notfingham) (conunuriicafe~l): Am I correct in assuming that the structure factor relating to the Ni-0 correlation function is derived from the experi- mental data by sitbtracting out the c>ontribution due to " pure " water? This is a common method of treating diffraction data. Does such a procedure not assume that, apart from those water molecules which form the primary ionic hydration shell (i.e., nearest neighbours), the remainder of the 0-0 distributions are those characteris- tic of unperturbed water. This ma>' he a tolerable approximation for very dilute solutions, much more dilute than those which can at present times be examined by diffraction methods, but it can hardly be expected to hold for concentrations which are in practice employed.Dr. G. Pinna (Cugliuri) said: Really i n our calculations the water molecules not involved in hydration are supposed to retain the close coordination they have in pure water, and their contribution is introduced into the calculated structure functions by opportunely weighting the experimental structure function of the water previously obtained. We agree that this approximation is very rough at high concentrations, but just at these concentrations its effect on the analysis becomes negligible, as the amount of bulk water goes rapidly to zero. Regarding the NiClz solutions discussed, the ratio water molecules/salt molecttles is respectilely about 27.0 for the 2 niol dm-3 solution and about 12.5 for the 4 moI d n r 3 solution.so that, in the model u.e use. all the water present is engaged in hydration. Dr. I. C. Baianu (Cunibridge) said: The authors aimed partially " to determine the mean coordination geometry of the NI'- and Cl- ions in the solutions '* and conclude that in 4 and 2 mol dmF3 aqueous solutions of NiCI2 " the C1- ions also tend to be surrounded by their own hydration shell." I t i fact. their model correlation functions (fig. 2 of their paper) do not unambiguously protc this statement and their experi- niental data are also consistent ~ i t l i J model in which the CI- atoms are randomly * A. K. Soper, G. W. Niehon. J. F Fndeiby mid R. 4. Howe. J . P//JY. C., 1977. 10, 1793.92 GENERAL DISCUSSION packed between Ni2+ (H,O), groups.I wish to suggest that the unresolved maximum at -2.6 A in the " observed " correlation function (fig. 2) for the 4 mol dm-3 solution, (which is not reproduced in their theoretical correlation function) includes a contribu- tion from the Ni2+ (H20),. . . C1- interference function. This contribution is rela- tively small due to the disordered packing of the C1- ions in the alternative model proposed here. These proposals are consistent with the authors' choice of the number of contacts among the hydration water of Ni2+ and " external " water as 12 for the 2 mol dm-, solution and six for the 4 mol dm-, solution. The latter choice appears to be more difficult to reconcile with the idea of C1- ions surrounded by their own hydration shells.Dr. G. Pinna (Cugliari) said: Referring to the validity of the hypothesis of hydrated ions upon which our treatment is based, we remarked elsewherel that " at the higher concentrations the water present is not enough to hydrate anions and cations without some molecules being shared by coordination shells of neighbouring ions; in such case it is not easy to understand the noncorrelation between different ions. However, the applicability of the hypothesis even to the more concentrated solutions indicates that the direct ion-H,O interactions are dominant; other effects are secondary and can be hidden by the approximations of the method ". Therefore, we agree that our results do not permit us to establish whether in the NiC1, solutions investigated the chlorine ions have independent hydration shells or whether they share some water molecules with the nickel ions.However, the very similar values found for the hydration parameters of the chlorine ions in different cases (solutions of LiCl, CaCl,, CrCl,), show in our opinion, the tendency of these ions to have their own hydration shell. As regards the model used, our calculations are based on the " liquid model '' proposed by the Oak Ridge Group2 and described in detail in previous papers.l Besides, the geometry of the model has not been fully specified, since the results obtained are not to be considered conclusive. At that time we were interested only to see whether taking into account hydration water-external water contacts allowed the first peaks of the correlation functions to be constructed correctly.Calculations on second hydration shells and on the orientation of first shell water molecules are still in progress. Dr. G. W. Neilson (Bristol) said: Two comments are relevant: The first concerns the nature of the ionic hydration. Neutron diffraction in conjunction with selective isotopic substitution has been used to determine directly the nickel hydration and obviate the need for computer modelling techniques. As correctly illustrated in the paper discussed it is shown that there are six water molecules in the first hydration shell around the Ni2+ ion with the plane of the water molecule tilted at 30" to the Ni2+-0 axis. Although no data exist for the chlorine hydration in NiC1, solutions using diffraction experiments, it has been investigated in both sodium chloride and calcium chloride solutions at high concentrations.In both cases the patterns emerging are identical and show 6 water molecules around the C1- ion. The chlorine water conformation is such that a non-linear configuration exists in which the water points a single proton at the ion (this proton is 2.1 A from the Cl-) and the average orientation is intermediate between one where the Cl-D-0 are collinear and that in which both protons are shared by the ion with the bisector of the DOD G. Lichen, G. Piccaluga and G. Pinna, J. Chenz. Phys., 1976, 64, 2437. A. H. Norten and H. A. Levy, Science, 1969, 165,447.GE N E 11 A L DISCUSS I ON 93 angle pointing at the ion. In fact the mgle between the CI-0 line and that of CI with its closest proton is 12".The second point coixerns tlic ;thility of X-rny experinients to idcntify a lattice- like configuration. In light of i\hi!t is found by the modelling technique it seems clear that total G(r) patterns are indeed insensitive to the ion-ion structure. It would be more nieaningful to attempt to pierate measured S(q) data in wliich the ionic terms are clearly evident at low q. Prof. H. L. Friedman (Stony Emok) said: In summarizing tlie important results recently obtained by neutron diffraction on several systems. Neilson said that they found that the water nio!xules ticxt to CI- each point a proton at the C1-. I n view of some of the current discussion in :vhich just this orientation is assumed it seems very important to point out that i i ' the work summarized by Neilsoii the average oricntntion actualiy reported is intermediate between that in which each water mole- cu!e points a proton at the C1- and that in bhich the bisector of the HOH angle points at the C1-.Dr. PI. P. Bennett0 (Lortdorr) said: I would like to report briefly on some recent results of Dr. J. J. Spitzer and myself, \\,Iiich relate to problems raised in Pinna's paper concerning structure in concentratcti solL1tiioiis, as diagnosed by X-ray and neutron- diffraction studies. The priniitive Debye-Huckel model can be modified to allow for ionic polarisation by introducing the concept of the * ' structured ionic cloud ".I In our first attempt, where tlie average solvated ion represented as a conducting polarisable sphere, some problems arise from the discontinuity of potential at the surface of the sphere.However, when we adopt the more nxlistic model of a polarisable dielectric sphere, the electrostatic development is entirely self-consistent. (As it turns out, the results are identical from either calculation i i i the low-medium concentration range). For activitity coefficients the agreement hetween theory and experiment indicates that our coulombic model is at lcast in th: risiit direction, though the theory is obviously capable of further development. The shape of the activity coeffici,:nt curves i n the region of higher concentrations docs not greatly depend on what \ iil uc is chosen for the dielectric constant inside the sphere, but it is sensitive to the siructiix assigned to the ionic cloud. Earlier, for 1 : I electrolytes, we used the simplest ?);sible picturc in which the charge cloud has a single iiiaximuni at ;LA. Now we h i \ c examined tlie case of the face-centred cubic structure, i.e., the ionic atmosphere i i allowed tlie properties of a rudimentary diffuse lattice, and find that the theory prcdicts a steep rise in the activity coefficients at higher concentrations, as a result t ) Y polarisation effects. Our teiitative conclusion is that tlie often-observed steep rise i < zonsistent w'ith a quasi-lattice structure around the ions. Apart from this important ohscrvi1iion 1 would like to mention another factor rclcvant to tlie discussions 011 '' str.iicturt.-iiial.:ing " and " structcre-breaking .' properties of ions. At vzry largc scp;irations sol\xted ions arc immune from inter- ionic effects, but as tlic concentratic!? is iilcreascd they are inevitably perturbed by the interactions, an effcc! which is ind:xiident of \\Jh:\t model we choose for solvated ions.94 GENERAL DISCUSSION At even higher concentrations we may think of the solvated ions as being in ‘‘ excited ” states, and their chemistry is affected accordingly. Prof. H. L. Friedman (Stony Brook) said: It would be very helpful to those who wish to understand the recent work summarized by Bennetto if he would answer two questions: What is the Hamiltonian in the model he treats? How do his final equations compare with the accurately known results for the primitive model (charged non-polarisable hard spheres) ? Dr. H. P. Bennetto (London) (comnzunicated): Whilst I would agree with Friedman that an ‘‘ ultimate theory ” should be of the Hamiltonian model type, a detailed knowledge of the Hamiltonian is not a prerequisite for a good theory, which should be judged on its physical reasonableness and prediction of experimental results (preferably with a minimum number of disposable parameters). Perhaps it is perti- nent to quote from a previous paper of Friedman’s‘ “ . . . as has been found from experience . . . the most detailed and powerful theory is also likely to be the most elaborate and sophisticated and may not be so prolific of new ideas for experimental advances as simpler theories, which to some degree are incomplete or superficial, provided they are internally consistent ”. It should be recognised that there are pitfalls in the statistical-mechanical approach, where there are difficulties in the summing of coulombic contributions to the total energy; equally there are pitfalls in the applications of classical electrostatics which have been alluded to in Friedman’s introduction and of which we are aware. In answer to the second point, we regard the Debye-Huckel second approximation as the appropriate solution for the problem of hard charged spheres. Arguments are given in our 1976 paper [see also ref. (2)]. The different results from statistical- mechanical calculation are, we believe, in error, because of inclusion of an additional “ co-volume ” term. The only repulsive or exclusion term required is that given by the Debye-Hiickel theory, which puts limits on the ionic atmosphere and hence on the lowering of free energy. H. L. Friedman, Chem. Brit., 1973, 9, 300. R. H. Stokes, J. Chem. Phys., 1972,56,3382; and in Physical Chemistry of Aqueous Solutions, ed. R. L. Kay (Plenum, New York, 1973), p. 40.

ISSN:0301-7249    

DOI:10.1039/DC9776400069

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Temperature Dependence of Raman Band Parameters of Aqwated Cations BY DONALD E. IRISH AND TOOMAS JARV Guelph-Waterloo Centre for Graduate Work in Chemistry Waterloo Campus, Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 Received 3rd May, 1911 The band parameters of the relatively diffure, polarized, low frequency Raman lines, assigned to the symmetric stretching vibration of the aquated cations [In(H2O)6I3+ and [Hg(H20)4]’f have been measured over wide temperature and concentration ranges. The data, combined with the results of an earlier study of [Mg(H~o)a]~+ and [Zn(H20)6]*+ and feher data for [Cd(HzO)4]z+, provide insight into the structure, stability and lability of the primary hydration sphere. The molar intensi- ties of the band increase in the order Mg2+ < ZnZ+ < CdZ+ < Hgz+ < In3+ and are assumed to reflect the degree of covalence in the interaction.The data suggest that replacement of water by nitrate ion stabilizes the remaining coordinated water molecules, whereas chloride ion destabilizes these. Each nitrate ion which coordinates to Hg2+ replaces two water molecules. Increased temperature increases the degree of association between indium(Ir1) or mercury(I1) and nitrate ion. Relatively diffuse, weak, polarized, low frequency Raman lines attributable to cation-water stretching modes are one of the more direct manifestations of aquated cations. These were observed as early as 1932l’’ and many studies of solution^^^^ and crystalline hydrates5 have been made since that time.The development of laser Raman spectrometers with a computer interface has provided the means for a more detailed study of these band profiles. As part of a larger project to study the Raman spectra of electrolytes at elevated temperatures under pressure, we have examined the parameters of the band arising from the totally symmetric stretch (designated Ch for brevity) of the following aquated ions : Mg2 + , Zn2 + , In3 +, HgZ + and Cd2 + . Details of the study of the first two have been reported previously.6 The variables in the studies have been temperature, concentration and acidity. The counteranion was nitrate or perchlorate. The parameters measured were the position, C,,,, the full- width at half-height (FWHH), the molar intensity expressed as a percentage of the intensity of the 1049 cm-l symmetric stretching mode of nitrate ion, Jh, the band asymmetry gauged from the upper and lower band widths at half peak maximum, and penetration of the peripheral solvation sheath by nitrate ion as indicated by changes in the spectral lines of nitrate ion.The quantitative results provide insight into the structure and dynamics of the primary hydration sphere. The Raman spectrum of the nitrate ion is a sensitive indicator of the nitrate ion envir~nnient.~.~ When the nitrate ion contacts a cation it is polarized, resulting in the following spectral changes : 3 . 4 , 8 the Raman active symmetric stretch (v,A,’) becomes infrared allowed and most often occurs at a frequency lower than 1050 cm-l; the out-of-plane infrared active mode (v,A’;) occurs at frequencies lower than 830 cm-‘ and becomes Raman active; the antisymmetric stretch (v2E’), which is a doublet for the aquated generates two more-widely separated bands, one of which is polarized96 TEMPERATURE DEPENDENCE OF RAMAN BAND PARAMETERS in the Raman spectrum; polarization of the lower frequency member of the pair is indicative of unidentate cation-nitrate ion binding whereas polarization of the higher frequency member of the pair is indicative of bidentate orientation ; the deformation mode (v4E’) occurs at a frequency higher than 718 cm-l.Thus an equilibrium involv- ing aquated nitrate ion and nitrate ion associated with a cation is evident by a doubling of all of the lines of nitrate ion. Line breadth and line overlap may partially obscure some of these features but the essential correctness of the interpretation is affirmed by data for many nitrate salts, studied over a wide range of condition^.^,^ Nitrate ion does not displace water from the primary solvation sphere of magnesium9 even at temperatures up to 99 O C 6 Similarly, the degree of ion pair formation in zinc nitrate solutions is extremely small;” Sze4 has estimated a p1 value of 0.02 mo1-l dm3 for the 1 : 1 ion pair.For In3+ the degree of association is significantly larger11p12 and it increases still more for Hg2+.I3 Aspects of the consequence of displacement of water in the primary hydration sphere by an anion are revealed by the data which follow. EXPERIMENTAL The variable temperature housing6 and the Raman-computer system7 described previ- ously were used for this work.Cadmium and mercuric perchlorate solutions were prepared by weight from CdO (J. T. Baker, analysed reagent grade) and HgO (Allied Chemical, Reagent A.C.S.) by dissolution in a small excess of perchloric acid (J. T. Baker, analysed reagent grade). Indium nitrate solutions were prepared from Fisher reagent grade indium metal dissolved in excess nitric acid (J. T. Baker, analysed reagent grade). Indium con- centrations were determined by EDTA titrati~n’~ and nitrate concentrations by Nitron analy~is.’~ All solutions were filtered through 0.6 pm Millipore filters before use. RESULTS AND DISCUSSION BAND PARAMETERS FOR FIVE AQUATED CATIONS AT 25 OC The integrated molar Raman intensity of the symmetric stretching mode is different for different aquated cations. In order to place these intensities on a comparable basis they have been ratioed against the intensity of the 1049 cm-l line of the nitrate ion at 1 mol dm-3.The ratio, designated J h , is defined as where la and are the band areas for the aquated cation and the nitrate ion respec- tively, [M+”] and [NO,-] are the concentrations of cation and nitrate ion respectively in mol dm-3 and C is an instrumental correction factor, applied when necessary to compensate for different instrumental conditions. Cadmium and mercury cations were run as the perchlorate salts and a further factor relating the molar intensity of the 1049 cm-l nitrate line and the 935 cm-l perchlorate line was introduced to bring the results to the nitrate scale.The Jh values, expressed as a percentage, are given in table 1. The positions of the bands, Cm,,,, the full width of the band at half height (FWHH) and several other physical properties are also listed. There is evidence that six water molecules are bonded to MgZ + , ZnZ + and In3 + ,I6J7 and that four are bonded to CdZ+ and Hg2+.lS Major contributions to the bond strength come from the ion-dipole, the induced dipole-dipole and the covalent forces. At this stage in the research no adequate quantitative interpretation of the data has been achieved but some semiquantitative, empirical correlations are noted. TheDONALD E . I R I S H AND TOOMAS JARV 97 TABLE 1 .-BAND PARAMETERS AND PROPERTIES OF SOME AQUATED CATIONS (25'C) cation O,,,/cm-' FWHH/cm-' Jh/% r/A" Pb a x 1024/cm3C -AH,,i/kcald Mga + 359 39 2.12 0.720 2.93 0.10 490 Zna + 388 56 7.16 0.745 3.45 0.5 528 Cda + 355 56 11 0.84 3.05 1.15 462 Hgp + 375 78 31 0.96 3.18 2.45 480 in3 + 485 68 46 0.79 4.69 - 980 Effective ionic radii, R.D. ShaMOn and C. T. Prewitt, Acta Cryst., 1969, B25, 925. Values are for coordination number 6 for Mga +, Zna + and In3 + and 4 for Cd'+ and Hga *.lr Polarizing Power, P = z / ( r Serf), ref. (19). Screening factors, Serf, were computed according to L. H. Ahrens, Nature, 1954,174, 644, using the radii given above. Polarizabili- ties tabulated in ref. (21) after Battcher, Fajans and Heydweiller. * Heats of solvation of individualions by the Bernal and Fowler method, tabulated in ref. (23). polarizing power of the cation,19 P = Z/(rSeff), influences the interaction, as indicated by the almost linear relation between C,,, and P.The rate constants for water sub- stitution in the inner coordination sphere of aquometal ions are considered to increase in the order Mg2+ < In3+ < Zn2+ < Cd2+ < Hg*+?O The FWHH values, with the exception of In3+, increase in this order. The existence of Raman intensity indicates that a change in the polarizability of the cation-water bond accompanies the vibration; expressed another way, there is a degree of covalence in the bond. The degree in- creases in the order Mg2+ < Zn2+ < Cd2+ < Hg2+ < In3+, as revealed by the in- increased molar intensity J,,. To place the J,, values on a more comparable basis they can be divided by h, the hydration number, to yield the intensity contribution per mole of hydrated water.These values increase as the polarizability of the cation," CI, increases and also as the product (Pa) increases.19 Unfortunately the value of CI for In3+ is not known. From extrapolation, the reasonable value 1.7 x cm3 would be consistent with our data. (Although the intensity of V, from [In(Hz0)6]3f is the largest in the series it is not more intense than the vl(Al) line of C10, as reported by Hester and Grossman;22 that conclusion was probably a consequence of failing to take into account the decrease in the sensitivity of the particular spectrometer with increasing wavelength.) One other correlation was investigated; heats of solvation should reflect the strength of ion-water interactions and consequently the single ion values obtained by the Bernal and Fowler method,23 again divided by h to compensate for the assumed differences in hydration number, were plotted against JJh.Approxi- mate linearity was obtained, with the exception of Hg2+. INDIUM NITRATE SOLUTIONS When the concentration of In(N03)3 is 0.675 rnol dm-3 and the temperature is 25 "C (or less) the degree of contact ion pair formation is small. This conclusion is reached by examination of the Raman bands of nitrate ion. The deformation mode at 719 cm-' appears as a single, sharp (FWHH 23 cm-l) line [fig. l(a)]. A higher fre- quency band at about 748 cm-l, considered to be one criterion of contact ion pairing in aqueous nitrate s o l u t i ~ n s , ~ J ~ is not evident as a shoulder on the 718 cm-l band; it is clearly revealed for a 2.4 mol d m 3 solution [fig. l(c)] and is probably significant for concentrations greater than about 1.0 rnol dmW3.A new band also appears in the 1030 cm-1 region, judging from increased asymmetry of the 1049 cm-l symmetric stretch of the solvated nitrate ion. More marked changes occur in the region of the v3(E') antisymmetric stretch. For the 2.4 mol dm-3 solution, new lines at 1309 cm-l (polarized) and 1514 cm-l [fig. I(b)] are prominent, and even for a 0.46 mol dm-3 solution a weak 1515 cm-l band and a shoulder near 1310 cm-l are evident on either side of the doublet characteristic of solvated nitrate ion. Judging from both the de- polarization ratios and the fact that the intensity of the 1309 cm-l is greater than that9s TEMPERATURE DEPENDENCE OF RAMAN B A N D PARAMETERS 93°C 103°C I I I I I I 300 700 600 500 400 300 l a ) 1700 1600 1500 1400 1300 1200 f : I 1% Ma 2% I I I 800 700 600 500 400 (bl (C/ frequency I cm-' FIG.1,-Portions of the Raman spectra of aqueous In(N03)3 solutions at two concentrations and three temperatures as marked. x designates plasma lines. (a) 0.675, (b) and (c) 2.419 mol dm-3. of the 1514 cm-l band, the nitrate ion is binding in monodentate fashion to In3+. Two other lines in fig. 1 at 1652 and 1619 cm-' are assigned to the deformation of bulk water and the overtone of the out-of-plane fundamental of bound nitrate ion.DONALD E. I R I S 1 1 AND TOOMAS J A R V 99 6 ' o 5 . 0 - IC : 4 . 0 0 --:\ go'%o- 0 --v.-v .v-& O b - v -v\ - I I I I I t I I [Ins+] = 0.675 rnol dm-*; [NO,-] 2 2.12 mol dm - 3 ; [In"] = 2.42 mol dm-'; [NO,-] = 8.31 mol d 1 r 3 temp/"C Dmar/cm-' FW'HH/cm-' Jh/" temp/ C imaY/cm-l FWHH/cm-' Jh/% - 15.8 485 60 45 - 9.9 486 60 45 -9.9 479 59 37 2.3 486 59 45 8.5 486 64 4s 10.7 479 63 36 24.5 485 68 46 24.0 476 67 35 25.7 485 70 45 46.8 483 71 46 46.8 473 71 35 67.6 480 74 47 66.9 47 1 74 35 79.6 470 76 34 103 476 82 50 97.1 467 78 32 124 465 82 33 149 461 86 32100 TEMPERATURE DEPENDENCE OF RAMAN BAND PARAMETERS illustrated in fig.1. For the more concentrated solution, contact ion pair formation occurs at all temperatures and increases with increase of temperature. The con- comitant frequency lowering, line broadening and relative molar intensity decrease are observed for the 8, (table 2).AHIO drops from 4.9 to 4.3 over the 159 degree range (fig. 2). The greater line broadening suggests an enhanced exchange rate. Some covalency in the In3 +-ONOz bond is suggested by the appearance of a weak 290 cm-' band. When the concentration is 0.675 mol dm-3, ion association is not appreciable at any temperature studied. The band position is relatively constant, the broadening is substantial and the molar intensity may actually increase. From AHIO one can calculate ANo3- by assuming that the sum is six; the concentra- tion of free nitrate ion follows. These parameters can be plotted to yield the forma- tion curve, and computer methods can then be used to extract values for the stability constants.25 This treatment was attempted and a formation curve was obtained consistent with the existence of the two nitratoindium(II1) species noted above, but the scatter prevented convergence on reasonable p values.This is not surprising: the AN0 - values are small differences of two sizeable quantities and the scatter becomes magnified in the computation. The greatest source of error in evaluating J,, and hence AHZ0 is estimating the correct baseline on the Rayleigh wing. The calculation did provide a qualitative indication of the consistency of the interpretation. Direct measurement of iiNO3- and C, is planned in order to evaluate the p values and extend the analysis. MERCURY(II) PERCHLORATE AND NITRATE SOLUTIONS Data for 2.92 mol dm-3 mercuric perchlorate, spanning the temperature range 24 to 155 "C, are presented in table 3.It is clear that both the position of the band and the molar intensity are not significantly affected by heating. The band broadens by 18 em-l when the temperature is raised 131 "C. This behaviouris very similar to that found for the hexa-aquozinc(n) ion.6 The broadening was attributed to increased collisional TABLE 3.-BAND PARAMETERS FOR THE TOTALLY SYMMETRIC VIBRATION OF THE HYDRATED MERC~RY(II) ION IN 2.92 mol dm-3 Hg(C10& temp./"(= V,,,/cm-' FWHHjcm-' Jhi% 24 375 78 33 51 375 81 29 76 374 83 32 98 374 87 30 128 375 91 31 155 376 96 36 frequency and vibrational energy transfers6 In view of the correlation discussed above between rate constants for exchange of water between the hydration sphere and the bulk solvent and the FWHH, the 18 cm-l increase may reflect an increased rate of exchange.An interesting change was observed for a 2.13 mol dm-3 solution of mercuric nitrate: V,,, occurs at 365 cm-', the FWHH is 67 cm-l and J, is 14%. The constitu- ents of this solution are: Hg(N03)+ of 1.72 mol dm-3; Hg(N03), of 0.08 mol dm-3; HgZt(aq) of 0.33 in01 dmP3; NO, of 2.37 niol dm-3. These values were obtained by Sze26*4 using Raman spectroscopy. His values of the stability constants (Kl = 2.2 mol-1 dm3 and K, = 0.02) are in reasonable agreement with those obtained byD O N A L D E . IRISH A N D TOOMAS JARV 101 Hietanen and SillCn.13 The average number of water molecules bound to HgZ+, jiH1O, in this solution is estimated to be (Jh/Jh0)4 = (14/31)4 = 1.8. To achieve this average the mononitratocomplex must be written [Hg(NO,)(H,O),] + [the exact cal- culation gives 1.5 moles HzO per Hg(NO,)+] and the dinitrato species must have no water molecules in the first coordination sphere.The latter conclusion was also reached in an earlier study of this ~pecies.~’ The processes in solution leading to form- ation of the complexes can be formulated as follows: Hg(HzO):+ + NO, f [Hg(NO,)(HzO)zI + + 2Hz0 [Hg(NOdWzO)zI+ + NOT f Hg(NO3)z + 2Hz0. Thus each nitrate ion displaces two water molecules although the Raman spectra are consistent with a unidentate interaction. The change in the coordination number of mercury@) implies a change in its hybridization scheme from sp3 to sp2 to sp. This could account for the lowered value of Vmax. It is noteworthy that the FWHH value has decreased when nitrate ion shares a position in the primary solvation sphere.Again it seems that nitrate ion stabilizes the remaining water molecules. This work was supported by the National Research Council of Canada. A. Silveira and E. Bauer, Compt. rend., 1932, 195, 416. D. E. Irish, Ionic Interactions, ed. S . Petrucci (Academic Press, New York, 1971), vol. 2, chap 9, p. 219. D. E. Irish and M. H. Brooker, Adoances in Infrared and Raman Spectroscopy, ed. R. J. H. Clark and R. E. Hester (Heyden, London, 1976), vol. 2, chap. 6, p. 254. M. Falk and 0. Knop, Water, A Comprehensive Treatise, ed. F. Franks (Plenum, New York, 1973), vol. 2, chap. 2, p. 55. J. T. Bulmer, D. E. Irish and L. Odberg, Canad. J. Chem., 1975, 53, 3806. J. T. Bulmer, D. E. Irish, F.W. Grossman, G. Herriot, M. Tseng and A. J. Weerheim, Appl. Spectr., 1975, 29, 506. D. E. Irish, Physical Chemistry of Organic Solvent Systems, ed. A. K. Covington and T. Dickin- son (Plenum, London, 1973), chap. 4, p. 445. T. G. Chang and D. E. Irish, J . Phys. Chem., 1973,77, 52. D. E. Irish, A. R. Davis and R. A. Plane, J. Chem. Phys., 1969, 50, 2262. I’ R. E. Hester, R. A. Plane and G. E. Walrafen, J . Chem. Phys., 1963, 38,249. I’ R. C. Ferguson, P. Dobud and D. G. Tuck, J. Chem. SOC. A , 1968,1058. l3 S. Hietanen and L. G. SillCn, Arkiu Kemi, 1956, 10, 103. l4 J. Kinnumen and B. Wennerstrand, Chem. Analyst, 1957, 46, 92. l5 A. I. Vogel, Quantitative Inorganic Analysis (Longmans, Toronto, 2nd edn, 1951), pp. 505-506. l6 A. Fratiello, R. E. Lee, V. M. Nishida and R. E. Schuster, J. Chem. Phys., 1968, 48, 3705. l 7 A. Fratiello, V. Kubo, S. Peak, B. Sanchez and R. E. Schuster, Inorg. Chem., 1971, 10,2552. l8 J. Celeda and V. Jedinhkovh, Coll. Czech. Chem. Comm., 1967, 32, 271. l9 M. H. Brooker and M. A. Bredig, J . Chem. Phjs., 1973, 58, 5319. 2 o C. H. Langford, Ionic Interactions, ed. S. Petrucci (Academic Press, New York, 1971), vol. 2, chap. 6, p. 16. C. S. G. Phillips and R. J. P. Williams, Inorganic Chemistry (Oxford University Press, Oxford, 1969, vol. 1, p. 176. ’ A. DaSilveira, Compt. rend., 1933, 197, 1033. ’’ R. E. Hester and W. E. L. Grossman, Spectrochim. Acta., 1967, 23A, 1945. 23 B. E. Conway and J. O’M. Bockris, Modern Aspects of Electrochemistry (Butterworth, London, 24 T. Jarv, J. T. Bulmer and D. E. Irish, J. Phys. Chem., 1977, 81, 649. 2 5 J. T. Bulmer, T. G. Chang, P. J. Gleeson and D. E. Irish, J. S o h . Chem., 1975, 4, 969. 26 Y.-K. Sze, P h B . Thesis (University of Waterloo, Waterloo, Ontario, Canada), 1973). 27 A. R. Davis and D. E. Irish, Inorg. Chem., 1968, 7, 1699. 1954), vol. 1 , chap. 2, p. 52.

ISSN:0301-7249    

DOI:10.1039/DC9776400095

出版商:RSC    

年代:1977

数据来源: RSC