Nuclear Magnetic Relaxation of Alkali Halide Nuclei andPreferential Solvation in Methanol+ Water MixturesBY MANFRED HOLZ,* HERMANN WEINGARTNER AND HERMANN-GERHARD HERTZInstitut fur Physikalische Chemie und Elektrochemie der Universitat Karlsruhe,W. GermanyReceived 18th June, 1976Nuclear magnetic relaxation rates of the ionic nuclei 3JCl, 81Br, lz7I, 23Na and s7Rb in methanol+water mixtures have been measured over the complete mixture range and extrapolated to zerosalt concentration. The relaxation of all these nuclei is controlled by quadrupole interaction ; inthe theoretical part of this paper a formula is given which describes their relaxation behaviour inthe mixtures. In connection with these results a method is presented which uses the quadrupolarrelaxation studies as a source of information regarding preferential solvation and which yielded theresult that Na+ and Rb+ are preferentially hydrated whereas C1- and Br- are preferentially solvatedby methanol in the mixtures.These results are compared with those derived from chemical shiftmeasurements by other authors and the discrepancy, so revealed, for C1- (and Br-), is discussed.The nuclear magnetic relaxation of ionic nuclei possessing an electric quadrupolemoment, such as 35Cl, 79Br, *lBr, 1271, 23Na, gSRb, 87Rb, in aqueous and some non-aqueous solutions can be explained in terms of an electrostatic Given anunderstanding of quadrupolar relaxation in pure solvents, it should be possible toapply it to the study of the immediate environment of ions in mixed solvents.Accord-ingly in this paper we present relaxation rates for 35Cl, 81Br, 1271 and 23Na in theCH30H + H20 system, extrapolated to zero ion concentration over the completemixture range. The 87Rb data, published in ref. (6) were remeasured with a higheraccuracy, i.e., to lower salt concentrations. In the theoretical part of this paper aformula is given which well describes the relaxation behaviour of thc above nuclei ina mixed solvent.Although the problem of preferential or selective solvation has been studied bydifferent methods for many years,7 the n.m.r. studies play a specially important role,because thermodynamic methods for example suffer from the difficulty that it is inprinciple impossible to separate experimental thermodynamic quantities into valuesfor single ions, without using non-thermodynamic assumptions, whereas applying then.m.r.technique it is in principle possible to study (a) the resonance of nuclei residingon the different solvent species and (b) the resonance of the ionic nuclei in the electo-lyte. In favourable cases the resonance line of the solvent nuclei splits into separatedlines for " free '' and solvating molecules, allowing a direct determination of solvationnumbers, but unfortunately in most electrolyte solutions at room temperature onlyone resonance line is observed. Hitherto, n.m.r. studies of preferential solvation havemostly been concerned with solvent proton shifts [see e.g., literature cited in ref. (7)],though recently chemical shifts of alkali and halide ion nuclei have been reported 8-1[see also references (1)-(6) of ref.(S)].Besides chemical shift measurements, n.m.r. relaxation investigations may pro-vide information about preferential solvation in binary solvent mixtures. To our772 N.M.R. STUDIES OF SOLVATIONknowledge only a few attempts have been undertaken in this direction in the past. Thus,Frankel etaZ.12 utilized the strong effect of the paramagnetic Cr3+ ion on the transverserelaxation time of the solvent nuclei [some other papers, where the same method wasused, are reviewed in ref. (13)], whereas Craig and Richards l4 measured the 'Li spinlattice relaxation in dimethylformamide +water mixtures, though they did not findany indication that the Lis ion is specially linked with either solvent.In a previous87Wb relaxation study of RbF in methanol + water mixtures we found some evidencefor preferential solvation. Accordingly we tried to improve the applicable relaxationtechniques in order to investigate preferential solvation in detail, arguing that relaxa-tion techniques may not only complement the chemical shift methods, but in somecases be more successful. In a recently published paper l 5 we described a techniquewhich utilizes the intermolecular dipole-dipole relaxation rates of solvent protonscaused by the magnetic moments of the ionic nuclei. In contrast to the method de-scribed by Frankel et al." the ion in question must not have a strong paramagneticmoment ; therefore, the above mentioned method promises wider applicability.Specifically we note that since most alkali and halide ion nuclei possess a nuclearquadrupole moment, quadrupole relaxation may be especially suitable to investigatethe solvation properties of those ions.Furthermore, these nuclei often have verybroad resonance lines and difficulties arise if one applies chemical shift measurements.Quadrupole relaxation in such cases may lead to more reliable results.EXPERIMENTALRelaxation rate measurements of 3JCl, "Br, 1271 and 87Rb were performed as line-width measurements, using a Varian DP 60 spectrometer combined with an HR-8 PARlock-in amplifiery3~ 4 9 and an automatically controlled sweep switch. In some samples wemeasured Tl by pulsed n.m.r. and confirmed the equality of Tl and T2, thus establishingthe situation of " extreme narrowing ".Moreover, we measured in some samples the 79Brand 85Rb linewidths. The linewidth ratio of the different isotopes was found to be close tothe expected value.The 23Na spin lattice relaxation time measurements were made at 19 MHz with a BrukerSXP-4-100 pulse spectrometer. Here the low concentration data (0.2-1 mol kg-l) wereobtained using a signal averager.In every system we determined relaxation rates down to the lowest measurable concen-trations and then extrapolated the relaxation rates to zero salt concentration. In the case of35C1,81Br and 1271 we gauged the error of the extrapolation values to be + 10 %, whereasfor 23Na and 87Rb, + 5 % was estimated. In the case of 1271 at higher MeOH concentra-tions, the salt solubility limited the measurements, so the relaxation curve in fig.5 had to beextrapolated to values above 70 mol % MeOH. All substances were obtained from MerckA. G., Darmstadt. The salts were of " Suprapur " grade ; before use they were dried over-night at 100°C under vacuum. All systems were pre-pared by weighing the salt and the solvents. Samples containing I- ions were freed fromoxygen by the " freeze-and-pump " method. The sampIe temperature during all measure-ments was maintained constant at 25 & 0.5"C.Methanol was of " Uvasol " grade.RESULTSIn table 1 are reported the measured relaxation rates of 23Na, 87Rb, 35Cl, 81Brand 1271 as they depend on the salt concentration c in molality units (mol salt per1000 g solvent) and solvent composition. For some systems measurements were alsomade at other compositions, e.g., at 10, 50 or 90 mol % MeOH.These results fitsmoothly within the general pattern but are not given in table 1 . The extrapolatedlimiting relaxation rates at zero salt concentration (1/T1,2)&0 and (1 /T1,2)&eOH forthe two pure solvents are summarized in table 2. With exception of the 1271 valueM. HOLZ, H. WEINGARTNER AND H.-G. HERTZ 73the values for pure H20 are taken from our previous publications as indicated. ThelZ7I limiting relaxation rate in water, and all the values for pure MeOH given in table2, are determined from the measurements of this work.The 35Cl and 81Br limiting relaxation rates in MeOH are to be compared withextrapolated values which can be derived from relaxation data given in ref.(16).For 81Br one obtains a value (l/T2)KeOH = 11 0001: 1000 s-l which is in satisfactoryagreement with our result. In ref. (5) a value of (1/T2)LeOH = 300+40 s-l for 35ClTABLE 1 .-EXPERIMENTAL NUCLEAR MAGNETIC RELAXATION RATES IN THE MeOH+ H 2 0SYSTEM(1 IT1 tz)/s-1nucleus23Na87Rb35c1slBr1 2 7 1real t 1mol kg-11 .O NaBr0.8 NaBr0.6 NaBr0.4 NaBr0.2 NaBr1 .O RbF0.8 RbF0.6 RbF0.4 RbF0.2 RbF4.0 LiCl3.0 LiCl2.0 LiCl1 .O LiCl1.5 NaBr1.2 NaBr1 .O NaBr0.8 NaBr0.5 NaBr4.0 KI2.0 KI1.0 KI20mol %MeOH35.834.334.533.810901 0409859509023302602001606000512049454700440021 26018 15015 87040mol %MeOH51.349.049.346.11580148013201240124055042036030010 0108 7208 3308 0107 85036 00029 75028 52060mol %MeOH57.557.154.153.552.61780170016201590154070055043014 28012 80011 65011 50011 34039 85038 17080 mol %MeOH57.553.254.051 .O21 301 90017501680157070055017 80014 60013 60012 70012 20044 830100 inol "MeOH47.946.744.343421930182016601560145054564020 70015 54514 57013 50012 508TABLE 2.-RELAXATION RATES FOR INFINITE DILUTION IN NEAT WATER AND METHANOL,TOGETHER WITH kj = 7$/7zj VALUES AS TAKEN FROM REF.(25)nucleus (1 lTi,z)OHzO/S-1 ki ( 1 /T1,$'MeOH/s-l k23Na+ 16.2 1.4 41 2.5s7Rb;- 420 0.8 1380 1.635c1- 42 0.9 400 1.6* Br- 1050 0.7 11 750 1.54600 0.5 46 000 1.2 1271-was extrapolated from the data of ref.(16). In the present work we were able tomeasure down to lower concentrations and now find seemingly a more reliable valuewhich is higher by 33 %. Measurements at lower concentration lead also to highervalues for 23Na and 87Rb in MeOH, compared with those given in ref. (5): th743 Iv)1 nh" 1N . M . R . STUDIES OF SOLVATION-1 2tmol %MeOHFIG. l.--23Na magnetic relaxation rates extrapolated to zero salt concentration in MeOH+ H20mixtures (0). Dashed line : " theoretical " relaxation rates according to eqn. (6). x : 1 /T1 ' 0 1 /TO*values (right hand scale), ISP : isosolvation point. The straight line connects the two 1/Tl - 1 / ~ tvalues of the neat components and corresponds to the expected behaviour of 1 IT', 1 /TF for non-preferential solvation. For more details see text.mol % MeOHFIG.2.-*'Rb magnetic relaxation rates extrapolated to zero salt concentration in MeOHf HzOmixtures. All other details as given in fig. 1M. HOLZ, H. WEINGARTNER AND H.-G. HERTZ 75composition dependent *'Rb relaxation rates are also somewhat different as comparedwith ref. (6).In fig. 1-5 the solvent composition dependence of the limiting relaxation rates ofthe above mentioned nuclei are given as solid lines. If one tries to extrapolate the4.0-3.0- --- n c1HW N 4 20--FIG. 3.-"Cl':magneticFIG. 4.-*'Br magneticI nI , . , , ,' 20 ' 40 ' 60 ' 80 ' 100mol %MeOHrelaxation rate extrapolated to zero salt concentration in MeOH+ HzOmixtures.All other details as given in fig. 1.t Imol % MeOHrelaxation rates extrapolated to zero salt concentration in MeOH + H20mixtures. All other details as given in fig. 176 N.M.R. STUDIES OF SOLVATION*lBr and 35Cl relaxation rates given in ref (6) to infinite dilution, a roughly similarcomposition dependent curve to that shown in our fig. 3 and 4 is obtained, in spite ofthe reIatively great uncertainty of the data in ref. (6).ti;c!//j20 40 60 8'0 ' 100 ' t ; : : ; : : ; ' I 'mol % MeOHRG. 5.--"'I magnetic relaxation rates extrapolated to zero salt concentration in MeOH+ H 2 0mixtures. (In the range from 80 to 100 mol % MeOH no experimental data could be obtained.)All other details as given in fig.1.THEORETICALAccording to Abragani the nuclear quadrupole relaxation rate 1 /Tl in liquidsis given by an expression which has essentially the form- 1- = KiV:z~, (1)Tlwhere K , is a constant factor for a given nucleus i, is the mean squared electricfield gradient at the nucleus and z, is the correlation time for the nuclear quadrupoleinteraction describing the fluctuations of the field gradient. The electrostatic theoryof the relaxation of ionic nuclei possessing a quadrupole moment in electrolyte solu-tions has been developed by Valiev l8 and by one of the present auth0rs.l- 2 * l9Following this theory the electric field gradients in the solution arise from electricmom- and multipoles of neighbouring particles, i.e., from ion charges and solventdipoles.Changes in the environment of the ion, e.g., by changing the solvent com-position, should alter the field gradients and should therefore be reflected in thequadrupolar relaxation rate. To be sure that only ion-solvent interactions are caus-ing the relaxation rate, one has to exclude the ion-ion (ion-charge) contributions andso requires nuclear quadrupole relaxation rates extrapolated to infinite dilution of allionic species. We are then left with field gradients produced by electric dipoles of thesolvent molecules.The field gradient caused by a dipole m is proportional to m/r4 where r is the dis-tance between the solvent point dipole and the nucleus residing in the centre of thM.HOLZ, H . WEINGARTNER AND H.-G. HERTZ 77ion. Since the relaxation rate, which is proportional to the squared field gradient,depends upon r8, only the nearest neighbours of the ion contribute to the relaxation.This is why quadrupolar relaxation studies are especially suitable for the investigationof solvation phenomena.According to the theory l * 5 * 2o the relaxation rate produced by ni solvent dipolesinteracting with the quadrupole moment of a nucleus in the centre of an ion in a neatliquid is given aswith(1 + y,)2P2.I is the spin of the relaxing nucleus, Q its quadrupole moment, e is the charge of theproton, yco is the Sternheimer anti-shielding factor, P is a polarization factor, theprecise meaning of which has been given elsewhere,'.2o m2 is the mean square of theeffective electric dipole moment of the solvent molecule, which is given by the orienta-tion of the dipole moment relative to the vector ion-solvent molecule, g: = r;(l/r'}with 0.2 g8 6 1, is a factor which depends on the particular form of the radial partof the ion-solvent pair distribution function, g8 4 1 when the pair distribution func-tion is very sharp. T;O is the rotational correlation time of the vector connecting theion with the solvent molecule. (The superscript * indicates that the solvent moleculeis in the solvation sphere, whereas the superscript O in eqn (2) refers to quantities in aneat solvent.) A" = (I -e-6n) is a " quenching " factor which corrects for the factthat due to the symmetry effects, the field gradient may be rcduced or even vanish,if the n, dipoles are located near or at octahedral positions? [see e.g., ref.(20)].In a mixed solvent the solvation sphere of the ion of interest may be composedof i i i l molecules of the solvent 1 and of niz molecules of solvent 2. Thus we obtainwith nii+niz = n,, the total first coordination number of the ion i. The quantityA" takes account of the non-additivity of the symmetry quenching effect. Assumingthat the quantities Y ~ ~ , ~ and x2, which mainly determine the strength of the fieldgradient at the nucleus, do not differ very much in the mixture from those in the puresolvents, we can replace the unknown squared field gradients in the mixture by themeasured relaxation rates in the pure solvent (l/?'&, with j = 1, 2.Possible varia-tions of the radial part of the ion pair distribution function and possible variationsof the quenching behaviour in the mixture are taken into account by the quantities/lj = gajAj. Eqn ( 3 ) now gives :Here we introduce the relation izl = nio, = nF2, that is, we assume a constant solvationnumber (number of nearest neighbours) over the whole composition range 0 G x2 < 1(xj is the mole fraction of the componentjin the solvent mixture). For MeOH + H,Omixtures this assumption is supported by experimental results l5 and has also been-1 The lateral departure from cubic symmetry is represented by a distribution width parameter1.' A=O means strictly cubic symmetry; l+m means fully random lateral distribution of thesolvent dipoles in the solvation sphere78 N.M.R.STUDIES OF SOLVATIONused by other authors 21 who have investigated preferential solvation in this system.AS a consequence, it follows that we can replace in eqn (4) nil/nfi by xi1 and ~li2/ltio2by (1 -xi,) = x i 2 , xil and xi2 being the local mole fractions of the two componentsin the solvation sphere of the ion i. Now we establish the criterion that if the x i jdiffer from the macroscopic mole fractions x,, then we have " preferential solvation ".If we were not allowed to assume that ni is constant over the composition range, wewould have to know the composition dependence of ni/nf'l and n,/nio, in order to beable to determine selective solvation.In the special case, where the two correlation times zzl and T : ~ in a mixture may beregarded as equal, or if one introduces an averaged correlation time for both compo-nents, then we can write eqn (4) in the following form :which may be written in the formA* = A(al(xlxz +x&) + 3x:xzp+2x2x:[2(bz-bl)+(e2-el)l}z~--- - withal = 4(V1 + Y2)2 - 3( V2 -I- Y2)2 - (V, + Yl)2bl = (Vl+Y2)2; el = (Vl+Yl)2b2 = (V, + Y1)2 ; e2 = ( V2 + Y2)2p = 2 ( ~ ; + v;) 2- el - e2.In eqn (5a), A* has been written for a solvation complex which represents a tetra-hedron.Expressions for an octahedron may be developed in an analogous way.V i + Y j i = 1 , 2 ; j = 1,2is the field gradient at the ion nucleus produced by one solvent molecule of species i,and three solvent molecules of species j , all solvent molecules being in close contactwith the ion.V/ i = 1 , 2 ; i#jis the field gradient produced by two solvent molecules of species i.If in eqn (5b)the term in square brackets is zero, then A*/T: is a function symmetric with respectNow our procedure will be as follows. The quantities which occur on the righthand side of eqn (5) are divided into those which are measurable and those whichare not. The former are (l/Tl)F, (l/Tl);, and z:, the latter are p j / p j , j = 1,2 andA*. In a first approach we set p,/p; = 1, j = 1,2 and A* = 0. Then, knowingthe composition dependence of the correlation time 7: from other measurements suchas the deuteron relaxation times of the deuterated solvent molecules in the mixture,and measuring (l/Tl); and (l/Tl);, the timncated eqn ( 5 ) which now readsto x1 = x2 = 3M .HOLZ, H. WEINGARTNER AND H.-G. HERTZ 79allows us to predict the relaxation rate of an ionic nucleus in a mixed solvent underthe assumption of xl1 = xl, which corresponds to the absence of preferential solvation.Deviations of the experimentally determined composition dependence of 1 ITl fromthis " theoretical " or '' expected " curve may be interpreted in terms of preferentialsolvation or in terms of the neglect of the quantities pj/pj" and A*. In a subsequentdiscussion we try to decide which of the competing effects is dominant. If we formthe quantity l/Tl l/z: then in the case of non-preferential solvation we expect,according to eqn (6), a straight line between the two limiting values (l/TJ1 l/zz;and (1/Tl)2 l/zzi, each proportional to the squared electric field gradient in theappropriate neat component.This procedure is analogous to the chemical shiftmethod, where one also assumes that for non-preferential solvation a straight linemay be drawn between the chemical shift values in the two neat solvents. Then, aswith the chemical shift method, we can determine the so called " isosolvation point ".12EVALUATION AND DISCUSSIONThe correlation times 7: are connected with the rotational correlation times zcj(j = 1,2) of the polar solvate molecules in the pure (salt free) solvents. z,"~ of neatwater we know fairly well to be 2.5 ps.22 For methanol we use the rotational correla-tion time of the OD group z& = 4.4 ps [see ref.(91. Knowing the composition de-pendence of the deuteron relaxatioii rate (1 /Tl)D of the CH30D + D20 mixture 6 p 23s 24we are able to calculate an averaged z, for both coinponents in the following manner :7, = ~ , " l R,( 1 + 0.18~,) = 2.5 9 R,( 1 + 0.18~2) PS (7)withRD = (l/Tl)D/(l/Tl)~20 ; (l/Tl)&-, = deuteron relaxation rate in pure D20.The factor (1 +0.18x2) takes account of the fact that the rotational correlation timeof D20 in D20 is about 23 % longer than that of H20 in H20, whereas in methanolthe corresponding difference is only about 5 %. Given the correlation times in thesalt free solvent, we next have to calculate the correlation times in the first coordina-tion sphere which enter in eqn (6) and which we marked by a star. These correlationtimes differ from those in the " free " solvent.25 In ref. (25) the ratios z:;/zzj = k j ,j = 1,2 for the different ions in water and MeOH are given.(kj > 1 correspondsto a '' structure-promoting ", k j < 1 corresponds to a " structure-breaking " propertyof an ion in a solvent). The ratios for the mixed solvents, k,, are calculated for everyion by a linear interpolation between kl and k,. That such an approximation isquite reasonable can be seen from some experimental data in ref. (15). Thus weobtainT:? = kjTgj for the neat components j = 1,27: = k,z, for the mixed solvent.The k, values used are given in table 2, the 2, values are listed in table 3.TABLE 3.-ROTATIONAL CORRELATION TIMES IN THE MeOH+ HzO SYSTEM ACCORDING TOEQN (7)mol%MeOH 0 10 20 30 40 50 60 70 80 90 100Tc/PS 2.5 3.8 4.7 5.3 5.7 5.8 5.7 5.5 5.2 4.8 4.80 N .M . R . STUDIES OF SOLVATIONWith all these quantities in eqn (6) we can compare our experimental curves forthe relaxation rates with the " theoretical " or " expected " curves. In fig. 1-5 thedashed curves show this expected behaviour of the composition dependent relaxationrates. In all figures the quantities l/T1 l/zr plotted over the composition rangeare also given, showing more clearly which component is preferred in the solvationsphere of the corresponding ion, if selective solvation really occurs.In fig. 1 we see the results for Na+. The experimental curve shows the typicalmaximum, found for the first time for "Rb in MeOH+H20 mixtures.A similarmaximum was found in aqueous mixtures of dimcthylforniamide l4 and dimet hyl-sulphoxide 26 for the 7Li relaxation rates. This maximum is obviously caused by thebehaviour of the correlation time T:, since the calculated curve (dashed line) showsa maximum at almost the same composition of the solvent. The experimental curveshows higher relaxation rates than expccted for non-preferential solvation. Since(under the assumption of a constant first solvation number p i i = ny = n;) the fieldgradient in pure water is greater than in pure MeOH, this discrepancy between thetheoretical and experimental curves indicates preferential hydration of Na+ in MeOH+ H 2 0 mixtures. The I/Tl l / ~ : values reflect this behaviour more clearly, whenour treatment indicates an isosolvation point (ISP) for Na+ at about 87 moiMeOH.The discovery of preferential hydration for Na+ in MeOH + H 2 0 mixturesis in qualitative agreement with chemical shift measurements by Covington et a1.21In this case both methods lead to the sanie qualitative result.As seen in fig. 2 for s7Rb the experimental and calculated curves are almostidentical. Again the maximum appears at the same composition for both curves.This supports our assumption that the correlation times 7: used in the calculations,are well approximated. Unfortunately, as we see from the l/T1 I/T; values in thetwo neat liquids, the field gradient produced at the Rb+ centre by a water moleculeis, within experimental error, equal to the field gradient produced by a MeOHmolecule. In such a case coniplete preferential hydration, non-preferential solvationand complete preferential Folvation by MeOH lead to identical relaxation curves andthe three possibilities are indistinguishable.However, from the expected similarsolvation properties of Naf and Rb+, and from the results of our previous l 5 and afortlicoming paper,2 we conclude that the experimental curve for the quadrupolarrelaxation of s7Rb reflects preferential hydration.We now turn to anionic relaxation. The 1/T, l/z: values in fig. 3-5 show thatthe squared field gradients acting at the three halide ion nuclei in neat MeOH are2-3 times greater than in pure water. The characteristic maximum is no longer tobe seen.We also recognize that with Br- and C1- the expected curve lies below theexperimental one. In spite of the relatively large uncertainty of the experimentaldata, this result indicates preferential solvation by MeOH, with an isosolvation pointat about 30 mol % MeOH. For I- we find agreement between the two curves withinexperimental error, which means that the local mole fractions xil,z in the solvationsphere do not differ markedly from the macroscopic mole fractions x1 , 2 , correspond-ing in our treatment to the situation of non-preferential solvation. Thus, we arrivefor I- at the sanie result as with our intermolecular dipole-dipole relaxation s t ~ d y . ' ~Our result for C1-, on the other hand, contradict the result for CaCI, in H2Q+MeOH where with the Hittorf method preferential hydration for Ca2-and C1- was found.Moreover, Covington et aZ." analysed the 35Cl chemical shiftdata of Hall et al.' obtaining the result that Cl- is selectively hydrated in MeOH +H20. Also in Gordon's 29 book the paper of Hall et a l l 6 is cited as proof that Cl-and Br- are preferentially hydrated, in spite of the fact that Hall et ul. in their paperdid not draw this conclusion from their chemical shift data; on the contrary, thesM . HOLZ, H. WEINGARTNER AND H . - G . HERTZ 81authors pointed out that their relaxation data reported in the same payer appear torule out any preferential solvation of these halide ions.The Br- chemical shift data so far available are of insufficient accuracy ; thereforeCovington and co workers 21 were not able to give a detailed analysis yielding resultswhich could be compared with ours.However, one should expect that the Br-solvation properties lie between these of C1- and I-.In view of this situation we have to discuss possible sources of error in the evalua-tion of the relaxation results, especially those regarding the anionic nuclei, whichmay affect our conclusions.When proceeding from eqn (5) to eqn (6) we have set Pj/& = 1 and A* = 0. Inthe case of the anions, which are structure breaking in water, we do not suppose ahighly symmetric hydration sphere and, therefore, only negligible quenching of thefield gradient should occur, which means AT = 1. From our previous work weknow that in MeOH also one has to assume A; = 1 in order to be able to explainthe measured relaxation rates of the anionic nuclei.Thus it follows that no notice-able quenching effects are to be taken into account, which means that A* = 0 andPj = g j is a good approximation. From the entropies of solvation in MeOH com-pared with those in water, and also from the slowing down of the motion of the solventmolecules in the solvation sphere in MeOH, we are forced to conclude that in pureThere- MeOH one has a tighter packing around the anions, which means gQ2 > gal.fore, if Pj/@ is not constant, the only reasonable supposition is an increase of thisquantity in going from H20 to MeOH. If we vary pl/PT in a reasonable manner,e.g., from 1 to 2 or 3 and, correspondingly, p2/P2 from 0.5 or 0.33 to 1 (H20 -+ MeOH)then, using eqn (4), we obtain only a small deviation from the straight line for l/T111~: and no alteration of our conclusion for the anions.On the other hand, ourexperimental l/Tl l/z,* curve for Br- and Cl- may be fitted assuming a variation ofP1/Pf from 1 to 3 together now with a constant P2/p; = 1. This means, if we sup-pose only a sharpening of the water-ion radial pair distribution, that our conclusionmust be changed to " non-preferential solvation " for C1- and Br-. However, wefeel that we can rule out this last possibility, since it is hard to find any reason whyoniy onc component should reflect the structure changes in the mixture in its radialpair distribution function.In the case of the cations the increase of the gj/g;, if at all present, in going fromH 2 0 to MeOH, is then obviously accompanied by a decrease of Aj/Aj', since we find,e.g., for Na+ in MeOH a smaller field gradient, indicating that A; < A;.Thus, ifthe quantities pj/Pjo are not constant for the cations over the whole composition range,only small deviations are to be expected, and these would not alter our final con-clusions. However: it should not be overlooked that in the cationic case the quantityA* in eqn (5) may play a role. Since A*/z: is zero in the neat components, this quan-tity for the mixture has to go through a maximuin. Our experimental curve of1 /TI 1 /z,* for Rb+ shows no marked maximum, therefore A* seems to play only aminor role. With Na+ we cannot exclude a contribution of A':. Here our argumentis that in eqn (5b) e2-el is negative for 23Na and b2-bl is positive due to tightersolvent attachment of CH,OH, and one should expect a conipmsation of the quan-tities in the square brackets.Therefore A*/.tZ should give a symmetric contributionwith respect to x1 = x2 = 3, whereas our experimental results yield a curve which isdistinctly not symmetrical. As a consequence here too we believe that the A':'contribution is negligible and that our conclusion postulating preferential hydrationremains valid. In eqn (5) we introduced 7: instead of two different z:l and -* Lc2-We checked this point also and introduced different correlation times in eqn (4), asdetermined from some I7O quadrupolar relaxation data 3c) for MeOH and H,82 N.M.R.STUDIES OF SOLVATIONseparately. It turned out that our results are not markedly changed and, therefore,the use of one correlation time 7: in eqn (6) is legitimate.A further assumption inherent in our treatment was that the total solvation numberni is a constant over the whole composition range.It may be shown that the statement ni = const. has the following consequence :our local mole fractions characterizing preferential solvation retain their validity,however, the spatial extension of the first coordination sphere with respect to one ofthe components is an unknown function of the composition.In analogy toeqn (3) and ( 5 ) the chemical shift 6 may be written asIn conclusion we return to the discussion of the chemical shift.whereA6; = -nijgsj ' j 0 or Y,j = 1,2is the chemical shift of the ionic nuclear magnetic resonance frequency in the neatliquid j andThe chemical shift caused by one solvent molecule of species j depends on the ion-solvent separation as(V is unknown), and S* is the contribution due to non-additivity effects.The differencein the conclusions derived from relaxation and from chemical shift data may now easilybe traced as follows : if v M 8, then 6" should be < O in order to account for theobserved curvature convex towards the abscissa.16 On the other hand, if v 8,then the chemical shift senses solvent compositions which are further away from theion and the non-additivity contribution 6* may only be one part of the effect causingthe discrepancy between shift and relaxation results.It should be the purpose of future work, to clear up the existing discrepancy betweenthe chemical shift and the quadrupole relaxation results in the case of the anions.After having discussed the possible sources of error in the evaluation of our relaxationdata, we arrive at the result that there is indeed some evidence that Cl- and Br- arepreferentially solvated by MeOH.Finally, in connection with quadrupolar relaxation of ionic nuclei in mixed solventsystems, we point out that eqn (6) allows a good qualitative description of the relaxa-tion behaviour in a mixed solvent system for a number of different nuclei.This factshould encourage one to try to handle quadrupolar relaxation in other systems withthe same or a similar formula.H. 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