J. Chem. SOC., Faraday Trans. I, 1982, 78, 3383-3392 Ion-Water Geometry and the Tammann-Tait-Gibson Effective Pressure and Radius BY JEAN V. LEYENDEKKERS Building A1 2, School of Biological Sciences, University of Sydney, Sydney, N.S.W. 2006, Australia Received 23rd March, 1982 An analysis based on X-ray and neutron diffraction data shows that the ion-water geometry can be summarised in terms of the Tammann-Tait-Gibson (T.T.G.) radius of the ion and two angles describing the relative orientations of the ion and water molecule. One angle only depends on Zi (Zis the ionic strength) whilst the other angle, a, depends also on the size of the ion. The relative values of a [(a+-aK+) for the cations and (a--aC1-) for the anions] are directly proportional to [d(l/Z&,tra/dm]m-ro where is the proton magnetic relaxation rate.The relationship of the T.T.G. effective pressure to the geometry is demonstrated as well. 1. INTRODUCTION The most detailed information about the microscopic static structure of liquids is obtained from neutron and X-ray diffraction measurements.1 Enderby and Neilsonl, have reviewed recent advances in this field, as applied to the structure of ionic liquids. These authors have also given a general survey of X-ray and neutron scattering by aqueous solutions of e1ectrolytes.l They summarised most of the published X-ray results, covering fifty electrolytes (ion-oxygen distances and hydration numbers for 19 cations and 6 anions). These studies covered a range of concentrations [0.056-27.5 mol (kg H20)-'] but most of the measurements were at concentrations above 2 mol (kg H,O)-'.Recently, Ohtorno's group has made neutron diffraction measurements on alkali3v4 and acid5 halide solutions at ca. 1 mol (kg H,O)-'. Theoretical studies of ion-water geometries have been reviewed recently.', Predom- inant in such studies are the simulation methods (mathematical and numerical). Numerical simulations use either the Monte Carlo (MC) or molecular dynamics (MD) techniquess? '. The structure of a single-ion-single-water molecule8 or a single ion or ion-pair in a cluster of water moleculesg has been analysed using quantum-chemical methods. At present it appears that the cation-oxygen distances1* and possibly the anion- deuterium distances are relatively insensitive to concentration. However, the orienta- tions of the water-molecules near the ions are a function of concentration. In the present paper the ion-water geometry is analysed, especially in relation to concen- tration effects, using the recently derived T.T.G.(Tammann-Tait-Gibson) radius (r+A) of an ion in water.I0 The relationship of the T.T.G. effective pressurelo to this geometry will also be considered. 33833384 ION-WATER GEOMETRY 2. RELATIONSHIP BETWEEN THE T.T.G. AND CRYSTAL RADII Values of (r+A) have been estimated from the density of the solutions, using the T.T.G. model.l0 The term A is a length (in A) resulting from packing and electrical deformation effects1° and r is the crystal radius (Pauling) for monatomic ions or the interatomic distance for other ions.lo The length A is related to r uia the following equations.For the cations, oxyanions and ions such as SCN- (r+A) = 1.304+0.643r (1 a) (r+A) = -0.85+ 1.43r (1 b) with an average deviation for all ions (excluding Zn2+ and Be2+) of _+ 0.07 A. For the halides with an average deviation of kO.02. The ions H+ and OH- do not fit either of these equations, probably because of unreliable ( r + A). 3. CATION-WATER GEOMETRY Recent accurate neutron diffraction re~ultsl-~ indicate that cation-oxygen distances r+o are insensitive to concentration changes. The following equation was derived using the neutron diffraction data of Enderby and Neilson1g2: or r+o = 1.67(r++A+)-0.95 r+o + 0.95 = 2 sin (8/2) (r+ +A+) where 8 = 112.9O. This value of 8 is consistent with the cation-hydrogen distances from neutron diffraction data as illustrated below.Values of r+o from eqn (2) are compared with the corresponding X-ray, neutron diffraction and theoretical values in table 1. The calculated value of r+o for Na+ appears low but is in reasonable agreement with the ab initio quantum calculations. (3) If eqn (1) and ( 2 ) are combined r+o = 1.07r+ + 1.23 which is to be compared with the well known relationship r+o 'v (r+ + 1.38) (I .38 being the radius of the water molecule). The length A can be split into the geometric component (0.55 A for the cations in table 1) and the electronic component Ae1,lo so that eqn (2) may be written r+o = 2 sin (8/2) (r+ + Ael+) ( 2 4 neglecting the residual of 0.03 on the left-hand side. The value of the cation-hydrogen (or deuterium) distance, T + ~ , is a function of concentration (and indicates the orientation of the water molecule).For a given concentration it is found that r+H is directly proportional to (r+ +A+), which may be expressed r+H = 2 sin ( 4 / 2 ) (Y+ +A+). The neutron diffraction data for NiCI,'? (giving accurate values of r+H as a function of concentration) were used to derive the following equation (4) 4 / 2 - 40/2 = - 6.83314 + I . I 71 ( 5 ) where do equals 8 from eqn (2b); eqn (5) apparently is independent of the ion as itJ. V. LEYENDEKKERS 3385 TABLE 1 .-COMPARISON OF CALCULATED AND EXPERIMENTAL CATION-OXYGEN DISTANCES (A) ( r + A) r+0 ion ra b C expt. eqn (2)b eqn (2)" theoreticald H+ Li+ Na+ K+ Rb+ cs+ NH,+ Be2+ Mg2+ Ca2+ Sr2+ Ba2+ Zn2+ Cd2+ Las+ Ce3+ co2+ Ni2+ CU2+ ~ 1 3 + 1n3+ Cr3+ Er3+ 0.36e 0.68 0.97 1.33 1.47 1.67 1.03 0.35 0.66 0.99 1.12 1.34 0.74 0.97 1.14 1.07 0.74 0.72 0.72 0.5 0.8 1 0.69 0.96 1.27 1.74 1.85 2.09 2.23 2.38 2.18 (1 .06)h 1.76 1.99 2.04 2.23 1.69 2.09 2.04 1.81* (1.44)h - - - - - - 1.54 1.74 1.93 2.16 2.25 2.38 1.97 1.53 1.73 1.94 2.03 2.17 1.78 1.93 2.04 1.99 1.78 1.77 1.77 1.63 1.83 1.75 1.92 - 1.95f 1.909 2.08-2.25 2.4-2.69 2.37-2.43 2.6-2.89 2.8-2.9 - 2.8 5-3.05' 2.8-3.0 2.0-2.1 2.4f 2.26-2.4 2.61 2.9 2.26 - - - - 2.1 2.07f 2.05-2.1 1.93-2.3 1.9 2.35 2.3 1.90- 1.98 1.17 1.98 - - 2.14 - 2.53 2.77 3.02 2.69 (0.82)h 1.99 2.37 2.46 2.77 (1 .46)h 1.87 2.54 2.46 2.07 - - - - - - - - - 1.62 1.96 - - 2.27 - 2.66 2.8 1 3.02 2.34 1.61 1.94 2.29 2.44 2.67 2.02 2.29 2.46 2.41 2.02 2.00 2.00 1.77 2.11 1.97 2.26 - - - - - 1.81-1.89 Sch 2.0 Cls 2.06-2.10 MD 2.20-2.36 Sch 2.3 Cls 2.3 1 MD 2.69-2.90 Sch 2.8 Cls 3.10 MD - - 1.95 Sch 2.40 Sch * Pauling crystal radius (interatomic distance for NH,+), ref. (10); derived from density of solution and independently of r10 (* from neutron diffraction data); from eqn (1); from the compilation in ref.(2) : Sch, single-ion-single-water molecule; Cls, cluster theory; MD, molecular dynamics; ref. (10); f neutron diffraction (k0.05 A) from ref. (2); 9 neutron diffraction from ref (3)-(9, other values from X-ray diffraction data listed in ref. (1); bracketed values are less reliable. gives good predictions for the other cations (Li+, K+, Ca2+, Na+ and Cs'); see table 2. The ionic strength I is given by fz, z- V?, with z representing the ionic charge, v the number of moles of ions per mole of salt and rn the molality [mol(kg H,O)-l].The value of T + ~ decreases with concentration-up to I,,, (8.53rn) and then increases. Fig. 1 illustrates the ion-water configuration as the concentrason changes. M represents the cation, H the hydrogen and 0 the oxygen atoms. In dilute solutions (as rn --+ 0) the triangles MH,P, and MHP coincide so that 4 = 4, = 8 = 112.9'. As the concentration increases up to I,,,, MHP swings away, MH shortens and the angles a and 4 change. 4 has a minimum values of 93' at Imax, and assuming the 0-H value3386 ION-WATER GEOMETRY TABLE 2.-cOMPARISON OF CALCULATED AND EXPERIMENTAL VALUES OF CATION-DEUTERIUM DISTANCES ~ ~~ solute amax “ P expt. eqn (4) and (5) theoretical type, year NiC1, Ni2+ NiC1, LiCl Li+ LiCl LiI LiF Li+ CaC1, Ca2+ Na+ NaCl NaF Na+ K+ KF KCl K+ c s + CSCl CsF 18.9 19.9 17.9 18.8 16.9 15.1 13.23 9.15 8.53 4.38 2.55 1.38 0.258 0.0 9.95 8.53 3.57 2.2 2.2 0.555 0.278 0.1 0.0 13.47 8.53 0.0 8.53 2.2 0.555 0.555 0.278 8.53 2.22 0.555 0.555 0.278 0.0 8.53 2.2 2.2 0.0 - 2.67 f 0.02 2.67 2.67 2.76 2.80 2.80 f 0.03 2.50f0.02 2.55 f 0.02 - - - - - - - - - 2.93 & 0.05 - - - - - - -_ - - - - - - - - - - - 2.65 2.63 2.625 2.66 2.71 2.78 2.90 3.02 2.53 2.523 2.57 2.62 2.62 2.74 2.79 2.83 2.90 2.92 2.886 3.35 2.683 2.79 2.92 2.92 2.96 3.031 3.15 3.29 3.29 3.35 3.49 3.451 3.59 3.59 3.97 - - - - - _ _ _ _ _ _ __ _- - - 3.0 2.67 k 0.04 2.5 2.6-2.7 - - - - - - 2.8 2.8 3.0 2.8 3.0 3.8 3.2 3.5 3.4 - - - 3.6 3.6 - - - - - - - - - - __ - Cls, 1976 MD, 1981 CIS, 1976 Cls, 1978 - __ - - - MD, 1976 MD, 1976 CIS, 1976 CIS, 1976 Cls, 1978 Cls, 1976 Cls, 1976 Cls, 1976 CIS, 1978 - - - MD, 1976 MD, 1976 - a At I = 8 .5 3 ~ ~ ; ionic strength, tz+z-vm, where v is the number of moles of ions per mole of solute, z is the electronic charge, m is the molality [mol (kg H,O)-’]; experimental and theoretical values from ref. ( 1 ) and (2), MD, 1981 from ref. (7); values of (r++A+) from table 1, 3rd column from left. of 0.95 A remains constant, a reaches a maximum value of 15-20 O, depending on the ion (table 2). Above Imax, either a remains fixed and the 0-H distance changes or a decreases and 0-H remains fixed. On the other hand both 0-H and a could change. If a is fixed, the value of 0-H is given by rOH = (Y:O + r$H -2r+Or+H cos amax)+.( 6 )J. V. LEYENDEKKERS 3387 FIG. MPO M p/#' 'mi" 5 1 .-Cation-water geometry as a function of concentration. do = B = 1 1 3 O , dmin = 93O, scale for Li+ = PoHo = MP, = P,H, = (r++A+) OH,:]= 0, OH,:I= 1.0, OH,:I= 8.53, OH,:]= 1 8 ~ . amax values listed in table 2. Using eqn (6), with I = 18m, for a NiC1, solution rOH is 1.01 A whereas for a LiCl solution rOH is 1.02 A. From the above equations the values of r+H as rn 4 0 are given by r+O+0.95 A. 4. ANION-WATER GEOMETRY Neutron and X-ray data are avialable for the halides. A preliminary fit of all the data indicated a linear relationship between the anion-oxygen distance, rPO and (r-+A-). However, only the most accurate data, the neutron diffraction results for CI- of Enderby and Neilson,l? were used to derive the following equations (double weight was given to the CaCI, data, which are the most accurate): and rPO - 1.1 = 2 sin 0112) (r- + A-) x/2-xo/2 = 5.74fi- 1.071 with x 0 / 2 = 30°, so that, as rn -+ 0 r-O = 1.1 +(r-+A-).(7 b) Values of rw0 calculated from eqn (7a) and (8) are compared with the experimental and theoretical values in fig. 2. Since eqn (7a) and (8) were derived from the data of Enderby and Neilson it is interesting that the results for DCl around l g obtained by Ohtomo et ~ 1 . ~ are consistent with the calculated values. As yet, there is no definitive method for analysis of neutron diffraction data on aqueous ionic solutions. The Enderby group used first- and second-order difference spectroscopy, whereas Ohtomo's group used a subtraction m e t h ~ d .~ The latter method is apparently more accurate for dilute solutions, so that the good agreement with the extrapolated value [from eqn (7a) and (S)] indicates that the form of eqn (8) is correct. The values of r-o do not seem to be very sensitive to the cation (1 2 different cations, fig. 2) and eqn (8) appears adequate for all the halides. Only theoretical values of rp0 are available for F-. The calculated values from eqn (7a) and (8) [with (r+A) = 1.081 range from 2.2 to 2.4 for I ranging from 0 to 7 . 1 9 ~ . At I = 2 . 2 ~ the calculated value is 2.38 whereas the3388 I ON-W A TER GEOMETRY 0 2 4 6 8 10 12 14 16 18 20 Ilmol (kg H,O)-' FIG. 2.-Anion-oxygen distances as a function of concentration [(a) I-, (b) C1-, ( c ) Br-1: 0, neutron diffraction data with error bars' values at lm are from ref. ( 5 ) ; 0 , X-ray data from the compilation in ref.(1); x , MD; +,Clsaslistedinref. (2). (r+A)valuesinA: C1-, 1.8;Br-, 1.97;1-, 2.22. Curvescalculated from eqn (8) and (9). FIG. 3.-Anion-water geometry as a function of concentration. x-,, = 60°,xmax = 75.4O. H,,, corresponds to Qmax. AH = scale for CI-, O H = 1.1 A. O,, I = 0 ; 0,, I = 3 or 13m; O,,,, I = 7 . 2 ~ . A P = Q P = (r+A). a- = ( O A H (see text). theoretical predictions are 2.2 (MD)2 and 3.0 (Cls);2 at 0 . 5 5 5 ~ ~ the calculated value is 2.30 compared with 2.3-2.7 (Cls).2 For OH- [with ( r + A) g1.241, the calclulated values at 17.5m, 4.48~1 and 2m are 2.53, 2.61 and 2.56, whereas the X-ray values are all 2.9 A ( t h e n l y data available').From eqn (8) x/2 reaches a maximum (37.7O) at I = 7 . 1 9 ~ . If the anion-deuteriumJ. V. LEYENDEKKERS 3389 distance, T - ~ , remains fairly independent of concentration, the changes of the anion-water geometry with concentration can be interpreted via fig. 3. A , 0 and H represent the positions of the anion, oxygen and hydrogen, 0 Q is fixed at 1 . 1 A [eqn (7a)], AH remains constant in length but moves along the arc SQ,,, as indicated, whilst A 0 increased until Imax is reached. kc very dilute concentrations (m + 0), assuming rOH remains constant at 1 . 1 . (a value indicated from the LiCl results at higher concentrations), xo is 60°, A 0 equals [(r+A)+ 1.11, and AH, is inclined to A 0 by ca. 20'. As the concentration increases up to ca.3m, H , moves closer to A 0 and finally, at Imax, em,, and Hmax coincide and A , Hand o a r e linear. Further increases in the concentration result in 0 moving back towards 0,. Of course, the real situation might be more complex than this since A H might change in length. This does not seem to be the case for LiC1, but the value for NiCl, is slightly larger than those for the alkali-halide solutions. For constant A H ( Y - ~ ) , it can be seen that r-H = AQmax = 2 sin ( xrnax/2) (r- + A-) (9) withxmax/2 = 37.7'. This gives values of r - H of 2.20,2.41,2.72 and 1.32 for Cl-, Br-, I- and F-, respectively. The experimental value for C1- is ca. 2.23 (k0.04) for Li+, Na+, Rb+, Ca2+ and Ni2+, for I ranging from 3.57 to 13.47m. The ion-water distances calculated above are within thepredicted (theoretical) ranges.The MD values for C1- and the cations are remarkably close to the T.T.G. values at 2m - (table 2 and fig. 2). 5. EFECTIVE PRESSURE AND ION-WATER GEOMETRY The T.T.G. effective pressure, p e , is obtained from the density of the solution via the equation', Pe = ( 1) (BT+ 1) (10) where f ( m ) = a,m + a,m3/2 + a2m2. The a coefficients are related to the coefficients of the Masson equation for the apparent molal volume, dv, given by 4v = 4: -I- Slmt + SLm (1 1) with a, = (My/,-&)/J = - K O (BT+ l ) / J ; a, = - Sk/J, and a, = - S;l/J. K' is the limiting value of the partial molal compressibility, B, is the Tait parameter (3005 bar at 25 'C), J = 315v, (u, is the specific volume of water). The T.T.G.volume My/, is given by and the distance ( r + A) has been discussed in section 2. My/, = 4 ~ N x (r+A)3 = 2.52 (r+A)3 The partial molal quantity pe is given byll pe = 2pe/8rn = In 10(p,+~,+ I ) (a,+ 1.~a,m~+2a,m) p z = ( d p J 2 ~ ~ ) ~ = In 10(BT+ l ) ~ , . = In I O(B, + 1 ( I . 5a,mi) ( 1 2 4 (12b) so that as rn + 0 (indicated by L) In dilute solutions where p e + B, p,, - p where3390 I ON-W A TER GEOMETRY with irepresenting an ion in the solution; z and v are defined in section 3 . For a single-salt solution w = $z+z-v. The effective pressure depends on the attractive forces between the ions and the induced or residual charges on the water molecules, and has been discussed in detail.l01 l1 The problem of interest here is how p e and pe are related to the ion-water geometry derived above.From eqn (lo), (1 2a) and (1 3) it can be seen that this problem efiectively reduces to the problem of the relationship between the geometry and S, [S&/wi, eqn (1 3)], since S, is usually small.loyll The relationship of a, and the microstructure has been discussed previously. The ionic contributions of S, can be analysed on the basis of equations given previously,1° viz. S,+I4 = ($z$S,, + 1.2 - C+)Ii (14) where SDH is the Debye-Huckel limiting slope (1.865 cm3 kgb mor3l2 at 25 "C), C+ = 6.2Bn,, and C-= 10.5Bn,,, with where is the proton magnetic relaxation ratelo and the superscript O indicates pure water. As shown in sections 3 and 4, the ion-water geometry can be summarised in terms of (r + A) and the two angles 4 and a, for the cation and x and a- for the anion (fig.1 and 3). The angles 4 and x only depend on I t (and the sign of the charge), as do the terms, 1.214 and -0.6114 which were previously interpreted as arising from different orientations of anion versus cation.1° The angles a, and a_, however, are specific for each ion, like the terms C+ and C-. These comparisons suggest that a and the C terms of eqn (14) and (15) might be correlated. Values of a, were calculated using cos a, = (r$o + r:H - r&,)/2r+or+H (16) and similarly for a_. For the cations the values of r+H were calculated from eqn (4) and ( 5 ) and rOH was taken as 0.95 A (section 3). For the anions r-o values were calculated from eqn (7a) and (8) and rOH was taken as 1.1 A (section 4). The results of these calculations for I = l m - are shown in table 3.The C terms were calculated from (iztS,, + 1.2 - S,+) and ( -$z2SDH + 0.6 + S,-), using the ionic S , values from density datalo (table 3). The value of C for K+ is practically zero, and C for C1- is also small. This is because at moderate concentrations these two ions have little or no influence on the mean correlation time z, of water1, (B,,, is proportional to T~). Because of this, and the fact that a and C were found to be linearly correlated, we have for cations C+ = 0.62 [$z$ (a+ -a,+)] with an average deviation of 0.08. Eqn (1 7) is based on the a values from table 3, but (a+ -aK+) is nearly independent of concentration (within the errors of estimate of a, ca. f0.3'), except for H+. C- = 1.16 [iz? (a- - acl-)] (18) For the halides with an average deviation of kO.1.The angle a depends on the ionic strength and on the size of the ion [eqn (2), (4),J . V. LEYENDEKKERS 339 1 TABLE 3.-T.T.G. PARAMETERS AND ION-WATER GEOMETRY AT I = 1 mol (kg H20)-la H+ Li+ Na+ K+ Rb+ cs+ Mg2+ Ca2+ Sr2+ Ba2+ Zn2+ Cd2+ Ce3+ F- c1- Br- I- 1.54 1.74 1.85 2.09 2.23 2.38 1.76 1.99 2.04 2.15 1.78 1.93 1.99 1.08 1.80 1.97 2.22 1.62 1.98 2.14 2.53 2.77 3.02 1.99 2.40 2.49 2.70 2.02 2.29 2.41 2.33 3.15 3.34 3.63 2.39 2.70 2.87 3.24 3.46 3.69 2.73 3.08 3.16 3.33 2.76 2.99 3.08 1.32 2.22 2.41 2.72 16.2 15.5 14.2 12.8 12.2 11.6 14.8 14.0 13.8 13.5 14.6 14.2 14.2 14.4 12.7 11.9 11.4 1.03 1.18 1.67 2.12 2.35 2.44 2.58 3.24 3.5 4.0 2.70 3.18 5.67 1.18 0.2 1 -0.17 -0.59 1.10 0.95 0.46 0.01 - 0.22 -0.31 2.35 1.69 1.43 0.93 2.23 1.75 3.92 0.85 -0.12 -0.50 - 0.92 a Units: distances in A, S , and C in cm3 kgi m ~ l - ~ ' ~ , a in degrees.(5), (7a), (8) and (16)]. For a given ionic strength the angle a K + apparently represents a configuration that enables the adjacent water molecules to maintain their normal z, (and hence the normal intramolecular relaxation rate of pure water). The deviations of a, from a,+ thus reflect the magnitude of the change in the relaxation rate due to the ion. Similar considerations apply for the anions, with C1- having the minimal effect on z,. 6. DISCUSSION At present, computer simulations can predict the gross features of ion-water coordination, whilst the experiementally derived structural picture is more detailed. Recent progress in this regard has been thoroughly reviewed.' However, ion-water geometry as a function of concentration has not been elucidated and the foregoing correlations should be of interest in this regard.A detailed knowledge of the static structure as a function of concentration will greatly reduce most of the problems of interpretation that beset spectroscopic studies of all kinds.' In addition, a second problem, the relationship between the macroscopic and microscopic properties of aqueous electrolyte solutions, is not yet resolved. Most of the chemical thermodynamic properties of such solutions can be predicted via the T.T.G. model using density data. Since p e and My/, are the two basic quantities of this model the links between them and the microstructure certainly contribute to the solution of this second problem.The results given here support the following picture. The ion holds the adjacent water molecules tightly, consistent with the solvation-sheath concept. For the cation, the adjacent oxygen atoms remain at an average distance that is practically independent of the concentration, whereas the hydrogen atoms adopt relative positions according to the concentration. Apparently, these positions provide the minimum disruption to the microdynamic behaviour of the water molecule. A similar situation prevails for the anion, with the roles of oxygen and hydrogen roughly interchanged.3392 ION-WA TER GEOMETRY The value of S, can be interpreted as being made up of the Debye-Huckel term plus an ion-size related term, and a term due to an additional effect of the charge’s sign on the relative orientation of ion and water molecule (charge distribution effects), viz.Sv+ = ~z:[S,, + 0.62 (a+ - a,+)] + S,(@) S,-= $22 [SDH+ 1.16 (a--acl-)]+S,(x>. With the exception of the term S, the contributions tope can be interpreted in terms of the geometry and microdynamics of the ion and water molecule. The functions for 4 and x involve a term linear in I [eqn (5) and (S)] which will affect the orientations, particularly at higher concentrations. Probably S, is related to ion-water orientation effects incorporated in this linear term. The anticipated increase in the accuracy of experimentally derived neutron data’ should enable this problem to be resolved. J. E. Enderby and G. W. Neilson, in Water: A Comprehensive Treatise, ed F. Franks (Plenum, New York, 1979), vol. 6, chap. 1; and Rep. Prog. Phys., 1981, 44, 593. J. E. Enderby and G. W. Neilson, Adv. Phys., 1980, 29, 323. N. Ohtomo and K. Arakawa, Bull. Chem. SOC. Jpn, 1979, 52, 2755. N. Ohtomo and K. Arakawa, Bull. Chem. SOC. Jpn, 1989, 53, 1789. N. Ohtomo, K. Arakawa, M. Takeuchi, T. Yamaguchi and H. Ohtaki, Bull. Chem. SOC. Jpn, 1981, 54, 1314. D. W. Wood, in Water: A Comprehensive Treatise, ed. F. Franks (Plenum, New York, 1979), vol. 6, chap. 6. ’ Gy. I. Szasz, K. Heinzinger and G. Palinkas, Chem. Phys. Lett., 1981, 78, 194. * P. Schuster, W. Jakubutz and W. Marius, Top. Curr. Chem., 1975, 60, 1. J. E. Clementi and R. Barsotti, Chem. Phys. Lett., 1978, 59, 21. lo J. V. Leyendekkers, J. Chem. SOC., Faraday Trans. I , 1982, 78, 357. l1 J. V. Leyendekkers, J. Chem. SOC., Faraday Trans. I , 1981, 77, 1529. l2 H. G. Hertz, in Water: A Comprehensive Treatise, ed F. Franks (Plenum, New York, 1973), vol. 3, chap. 7. (PAPER 2/498)