It was long puzzling that the neutron, although lacking electric charge, has a magnetic moment. It is now understood that the neutron is a composite of three charged quarks, udd. The negatively-charged d - quarks are predominantly in the outermost regions of the neutron, thereby producing a negative magnetic moment, like that of the electron. The g - factor for 17 O , and other nuclei dominated by unpaired neutron spins, is consequently also negative. This transition is in the radiofrequency region of the electromagnetic spectrum. NMR spectroscopy consequently exploits the technology of radiowave engineering.
A transition cannot occur unless the values of the radiofrequency and the magnetic field accurately fulfill Eq This is why the technique is categorized as a resonance phenomenon. If some resonance condition is not satisfied, no radiation can be absorbed or emitted by the nuclear spins. In the earlier techniques of NMR spectroscopy, it was found more convenient keep the radiofrequency fixed and sweep over values of the magnetic field B to detect resonances. These have been largely supplanted by modern pulse techniques, to be described later.
The transition probability for the upward transition absorption is equal to that for the downward transition stimulated emission. The contribution of spontaneous emission is neglible at radiofrequencies. The possibility of observable NMR absorption depends on the lower state having at least a slight excess in population.
At thermal equilibrium, the ratio of populations follows a Boltzmann distribution. Although the population excess in the lower level is only of the order of parts per million, NMR spectroscopy is capable of detecting these weak signals. Higher magnetic fields and lower temperatures are favorable conditions for enhanced NMR sensitivity. NMR has become such an invaluable technique for studying the structure of atoms and molecules because nuclei represent ideal noninvasive probes of their electronic environment.
If all nuclei of a given species responded at their characteristic Larmor frequencies, NMR might then be useful for chemical analysis, but little else. The magnetic field induces orbital angular momentum in the electron cloud around a nucleus, thus, in effect, partially shielding the nucleus from the external field B. The actual or local value of the magnetic field at the position of a nucleus is expressed.
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Nuclear magnetic resonance spectroscopy
Theoretical and physical aspects of nuclear shielding Cynthia J. DEVERELL fraction of water molecules occupy some of the cavities in the open hydrogen-bonded tetrahedral network and this proportion increases with temperature. Alterations in the proportion of molecules present as clusters and the average size of these enables the temperature dependence of many properties to be explained.
Danford and LevyJ15 with the aid of experimental radial distribution curves, estimated that at room temperature one fifth of the water molecules were in interstitial sites. A similar fraction has been estimated using dielectric data. However, the existence of the latter species seems unlikely. It is more likely that water molecules in voids would have some interaction with the framework distorting the latter to some extent. The essential idea behind this model is that hydrogen bonds are formed and broken co-operatively due to some partial covalent character. Both of the models outlined can be adjusted to explain most of the properties of water.
They both assume the existence of a short-range tetrahedral arrangement in water and rapid interchange of molecules between a hydrogen-bonded network and other possible environments. Firstly, the magnetic shielding of hydrogen, deuterium or oxygen nuclei can give information about the average environment experienced by the water molecule more strictly the hydrogen or oxygen nuclei and this gives an indication of the degree of hydrogen bonding in the water lattice.
Because of the rapid exchange of water molecules, observed chemical shifts depend upon the fraction of time that the nucleus spends in each of several possible environments and some assumptions about the shielding in each site must be made before the relative proportions of these sites can be evaluated. Variations in chemical shift with temperature may be correlated with accompanying structural changes in the water lattice.
Secondly, the nuclear spinrelaxation times can give information about the rates of molecular motions in solution. Thirdly, and 2H nuclei possess electric quadrupole moments and their relaxation rate is determined primarily by interactions with local electric field gradients. These are determined by the electron distribution around the nucleus and should be sensitive to the bonding interactions of the water molecule.
It is possible to make some estimates of the degree of hydrogen bonding from a knowledge of the electric quadrupole coupling constants. The earliest measurements made by Schneider, Bernstein and Pople 3g indicated a linear shift of the proton resonance to higher fields with increasing temperature. Close agreement with this study has been found by later workers, 40 the temperature coefficient of the chemical shift being measured as 0.
Results obtained by Hindman are shown in Fig. Experimentally the chemical shifts have been determined relative to the external references, gaseous ethane and methane, 41 which have been shown to have comparatively small temperature coefficients for the shielding constants. When this method is used an additional small correction must be made to the experitNote added in proof.
Circles on the full line represent experimental data; the long-dashed hne the linear dependence; the short-dashed line the susceptibility corrected shift line. Differences in the magnitude of this correction account in part for the slight discrepancy between the results of Hindman 41 and Malinowski, Knapp and Feuer. In the vapour phase and under conditions where there is little or no association water molecules show the greatest shielding of the proton nucleus 3g and the changes that occur in liquid water may be correlated with the increasing proportion of hydrogen bonds broken as the temperature rises.
Several approaches have been used in an attempt to calculate the numbers of hydrogen bonds broken at different temperatures from the proton chemical shift data. A variety of predictions about the number of hydrogen bonds initially broken by the melting of ice and also the rate at which this fraction increases with temperature are given by proposed models for the water structure.
Other semi-empirical estimates are also given by RamarW and infra-red studies. The success of the different models is judged by the magnitude of the shielding constants predicted. On the basis of the initial assumptions it is to be expected that the shielding constant of the non-hydrogen bonded molecule, Q, should not differ by more than a fraction of a ppm from that of water vapour, and also by comparison with experimental data TV- THBshould be of the order 5 ppm.
It was concluded that the model of Davis and Litovitz 35 gives the best agreement with experimental data. However, the chemical shift in this case can depend upon the degree of excitation of hydrogen bond stretching modes. The presence of unusually low frequency motions in the hydrogen bond makes it possible for several excited states to be populated and the resultant shielding constant, evaluated by considering an appropriate average of the contributions from all the vibrational levels, may show a temperature dependence due to a varying population distribution.
Interpretation of temperature dependent proton shifts solely in terms of bond-breaking processes may produce erroneous conclusions. Undoubtedly the most complete discussion of proton chemical shifts in liquid water is that given by Hindman. Possible contributions to the shielding parameters associated with each of these phases are discussed and their magnitudes evaluated. A comparison with experimental data enables the size of the contribution due to the formation of hydrogen bonds to be estimated. The shielding constant in the monomeric state, oM, reflects the net contributions from dispersive and repulsive forces.
The latter is made up from three terms. A van der Waals term, TV, describing the effects of London dispersion forces and long-range repulsive forces; u0 which takes account of the effects of overlap repulsive forces which are short range and of significance when the molecules are bonded.
Theoretical estimates indicate that these terms are small. Polarization of the bonding electrons by the external electric field associated with the charge distributions in the other water molecule forming the hydrogen bond produces the dominant effect on the shielding constant and is accounted for by the polar term, vp.
Evaluation of the other terms and estimates of the fraction of protons involved in hydrogen bonding enable the polar term to be estimated. Changes in the magnetic shielding of the proton nucleus during the ice-water transition may be considered to be a consequence of the rupture of some hydrogen bonds. Insertion of the appropriate values for u, TM,co andfin this expression and also equation 3 gives a value for the polarization contribution, up, to the shielding constant in the ice-like phase.
This quantity was estimated to lie in the range Expression 4 can also be used to calculate the fraction of hydrogen bonded water, f, at various temperatures.
Table 1 contains estimates obtained from the C. Proton relaxation times in liquid water Ever since the original measurements and interpretation given in the well-known Bloembergen, Purcell and Pound BPP papefi54 there has been a great deal of interest in proton spin relaxation in water. Data for water has also been determined up to the critical temperature. Krynicki, Physica 32, Bloembergen, Purcell and Pound 54 were the first authors to attempt a calculation of the proton spin-lattice relaxation time in water.
They evaluated separately the two contributions to the relaxation rate to be C. Each proton, by means of the random molecular motions present in solution, sets up fluctuating local fields at the second proton in the same water molecule. These fields have components at the Larmor frequency and can stimulate transitions between the nuclear magnetic energy levels. Similarly, protons associated with other molecules can give an intermolecular contribution.
Using a simple continuum model to estimate the latter contribution these authors 54 calculated a relaxation time in reasonable agreement with the experimental value. Studies of proton relaxation in mixtures of light and heavy water confirm the proposed dipolar mechanism. The considerably smaller magnetic moment associated with the deuteron makes it less effective in initiating relaxation and the proton spin-lattice relaxation time progressively lengthens as the fraction of heavy water is increased.
However, considering the previously demonstrated insensitivity of calculated relaxation times to the model assumed for the intermolecular contributions these conclusions must be regarded as tentative. It seems Iikely that because of this lack of sensitivity little information about the structure of the water lattice can be obtained from the proton relaxation times. Nevertheless, useful information about the time dependence of the molecular motions can be extracted from the correlation times, rd.
Before these are discussed a brief mention is made of another relaxation process which becomes important at higher temperatures. Rotation of the water molecule can produce a magnetic field at the proton, with frequency components determined by the angular velocity, and interaction with the magnetic nucleus may produce spin relaxation.
The magnitude of the relaxation times decreases at the highest temperature due to increasing importance of the spin-rotational interaction. Estimates show that the spinrotation interaction contributes only 0. It is not of significance in the region of interest to this review. DEVERELL Comparison of experimental values for the dipolar contribution to proton spin relaxation with theoretical expressions enables the correlation time for molecular reorientation, TV, to be determined. Smith and Powles 58 calculated a value of Td equal to 2. Another approach was used by Krynicki 56 in which he expressed the translational correlation time occurring in the intermolecular contribution in terms of the self-diffusion coefficient of water.
The intramolecular correlation time, rd, could then be estimated and was found to be almost identical with that obtained by Smith and Powles. Another significant feature is the extremely close correlation between the temperature dependences of the dielectric relaxation time, TVand the spin-lattice relaxation rate. Significant field gradients arise from the electron distribution within the water molecule itself and intermolecular contributions to the relaxation are insignificant and may be neglected.
The rate of relaxation is determined by two factors. Firstly, the correlation time for molecular reorientation, Td, which occurred previously in equation 5 for the intramolecular contribution to proton spin relaxation: Conversely, if we use values for the reorientational correlation time, Td, obtained from proton relaxation studies the magnitude of the coupling constant can be derived.
Some recent results in a paper by Powles et al. This is an indication that the majority of deuterons are present in a hydrogen bonded ice-like state in water, and that comparatively few are present in a state closely similar to that of a free molecule. However, the apparent invariance of the coupling constant, even up to temperatures as C. It has been suggestedc70 that deuterium coupling constants in deuterated methanol and ethanol are distinctly different from that of water, but the discrepancy probably arises from the use of the dielectric relaxation times, TD,for the correlation time, rd.
I70 studies of water Due to the low natural abundance and poor sensitivity there have been few studies of the nuclear resonances in water. A preliminary investigation 7g of the temperature dependence of the chemical shift indicated a high field shift, of the order 0. This was in agreement with an observed increase in magnetic shielding of the nucleus for solutions of water in a variety of organic solvents. GlasePO has investigated the variation of the nuclear resonance line width with temperature.
This is of similar magnitude to the measured proton exchange rate in neutral methanol-water mixtures. This is in agreement with the other magnetic resonance properties and evidence for changes in this region are also apparent in heat capacity, diamagnetic susceptibility and compressibility measurements. Obviously such agreement is partially fortuitous since the coupling constant will be altered somewhat on going from the gaseous phase to the liquid phase. Nevertheless it does indicate that molecular reorientation of the complete water molecule is responsible for the various relaxation processes.
Introduction The introduction of ions into the water lattice gives rise to changes in structure which may be characterized by structural and kinetic criteria.
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In these cases it is often much more useful to employ the second criterion and define the ion-solvent interaction in terms of the life-time, rh, of a water molecule in the coordination shell. The derived number generally expresses a large number of effects arising from interactions with many water molecules, both adjacent to the ion and more distant, in terms of a stronger interaction taken over a smaller number of molecules.
Application of NMR techniques to the determination of coordination numbers, as distinct from hydration numbers, is discussed in a subsequent section. In the next section we will be primarily concerned with NMR studies of solutions of alkali halides where the associations between ions and solvent molecules are usually very short-lived and not much longer than those expected from diffusion controlled processes. The resonating nucleus undergoes rapid exchange between all possible environments in the solution and only one signal corresponding to the C.
Nevertheless, as the solution concentration and temperature are altered, variations in magnetic shielding and relaxation times of the solvent nuclei can provide much information about the structural characteristics of these solutions. Proton and oxygen17 chemical shifts can be correlated partly with the disruption of the hydrogen-bonded network of the water lattice and partly with the new interactions arising from the presence of charged ions; whilst the relaxation times give some indication of the changed molecular reorientation times of solvent molecules in the coordination sphere of the ion.
In order to clarify some of the later discussion a brief outline of the terms structure-breaking and structure-forming is given below. It has been known for a long time that many monovalent ions tend to break down the water structure in their immediate neighbourhood and increase the mobility of adjacent solvent molecules. A is determined by the interionic forces and can be calculated theoretically. On the other hand, the constant B, which takes into account ion-solvent interactions, is purely empirical and may have either a positive or negative sign.
Ions of the latter kind increase the solution viscosity and reduce the mobility of water molecules. Typical examples are lithium, sodium, alkaline earth and fluoride ions. Structurebreakers are less common and generally restricted to large monovalent ions, e. These structural properties of the ions are of considerable importance in determining their influence on NMR spectra in aqueous solutions.
Proton Chemical Shifts in Solutions of Diamagnetic Electrolytes Diamagnetic electrolytes dissolved in water produce quite small but well established changes in proton nuclear magnetic resonances. Shifts may be determined either by using an external reference and applying a subsequent correction to the measured shift to allow for the difference in bulk diamagnetic susceptibility between the sample and standard or such a correction may be avoided if a suitably inert internal reference, which does not influence the proton shielding, can be found.
The correction for changes in bulk susceptibility limits the accuracy of measurements made with an external standard, since it is generally comparable in magnitude with the observed shift. Measurements made with internal standards are hampered by the lack of completely inert internal standards. Discrepancies between results obtained using an internal standard and an external standard with susceptibility correction have been noted by several workers.
Electrolytes can shift the proton resonance signal of water to either high or low fields. Some typical results are shown in Fig. There is no clear-cut distinction between the behaviour of salts which are generally regarded as structure-breakers or structure-formers. The relatively few shifts to low field result from electrolytes which are strong structure formers, but salts in both categories do give rise to high field proton shifts.
A linear variation of chemical shift with salt concentration is generally observed at concentrations below 2 or 3 molal and most workers have attempted to divide the shifts into individual ion contributions. The assumption that the ionic effects are additive appears to hold quite well at lower concentrations and measured chemical shifts in solutions containing equimolal pairs of alkali halides agree with those calculated from results for single salt solutions assuming an additive relationship.
Since the information derived from these measurements is concerned with the structural changes produced in water by the ions, this has been used as a criterion for making such an assignment. DEVERELL It is generally agreed that disruption of the water lattice by the ions gives rise to a high field shift due to the breaking of hydrogen bonds, and a low field shift results from the direct ion-solvent interaction, predominantly polarization of the proton environment by the strong ionic electric fields.
HindmanCs3 has considered four possible contributions to proton chemical shifts in electrolyte solutions: This may give either a high or low field shift; c a polarization term, 6,, describing the low field shift from the electrostatic field of the ion; and d a term which takes into account TABLE 2. Calculations based upon models for the ion-water complex were used to estimate the relative importance of these contributions.
Both the bond breaking and structural terms alter the proportion of hydrogen bonds present in solution, the actual number broken being determined by the total number and configuration of water molecules in the hydration shell. The polarization contribution can be expressed in terms of the electric field components perpendicular and parallel to the ion-water molecule bond. Such a difference has been proposed for the behaviour of cations and anions. Proton chemical shifts produced by the halide ions other than fluoride ion arise primarily from the rupture of hydrogen bonds, which becomes greater with increasing size of the ion.
It was concluded g3 that cations interact via the oxygen atom of the water molecule but there was no indication of a tightly bound coordination shell of water molecules. Only in the case of lithium was there any indication of ordering of water molecules other than those in the first coordination shell. By subtracting this contribution from the experimental shifts the magnitude of the direct effect of the ions upon the proton nuclear magnetic shielding can be evaluated.
The residue obtained in this manner is apparently determined predominantly by the effects of halide ions in alkali halide solutions, there being little alteration as the cation is varied. Caesium salts, however, are an exception.
Greater shifts to lower fields are produced as the size of the halide ion increases. This order of effects is quite contrary to that expected from a polarization process; the authorsCg8 postulate that a redistribution of charge in the H-O bond induced by the polarizable halide ions could be a possible mechanism. Although the separation of solvent reorganization and direct ion-solvent effects in this manner is difficult to justify, because of the absence of reliable estimates 43 of the changes in the number of hydrogen bonds on going from solvent to solution, this approach does indicate that the neglect of non-electrostatic processes may not always fraction used in the be justified.
It has been suggested W that water molecules may have a tendency to form clathrate cages around large ions, e. Temperature dependence studies of the proton chemical shifts in aqueous sodium chloride solutions by Malinowski et Us. An obvious interpretation of this effect is that the orientation of the water by the cation reduces the ability of the solvent molecules to fit into the water lattice.
Consequent rupture of the hydrogen bond might increase the proton shielding more than deshielding effects from the electrostatic polarization and other ion-solvent interactions. Proton chemical shifts produced by dissolution of alkali halides in methanol and ethanol have also been reported. It is possible to obtain individual ionic molal shifts and the shifts can be explained largely in terms of the structure-breaking and structure-forming properties of the ions.
Water is a unique solvent because of the strong intermolecular forces and the consequent large contribution to proton chemical shifts from changes in the degree of solvent structure make aqueous systems more complex to investigate than solutions in non-aqueous solvents. Similar arguments apply to other extensively hydrogen-bonded solvents such as methanol and ethanol.
A study of proton chemical shifts produced by 1: Again only a single resonance is observed due to rapid exchange of ammonia molecules between the possible environments. Chemical shifts to high field associated with disruption of hydrogen bonds are expected to be much smaller and this is confirmed by the experimental observation that all changes are to lower fields.
Increasing shifts to low field occur with decreasing size of alkali metal cation, in agreement with the expected magnitudes of the polarization of the lone pair electrons of ammonia molecules in the ionic solvation sphere. Halide ions, however, produce a slight shift to lower field with increasing size suggesting that processes other than polarization also contribute to the magnetic shielding.
It is possible that a greater association between the ions in the presence of smaller anions could account for such behaviour. A linear concentration dependence of chemical shift was found up to about 1 molal, but there was a falling off in the magnitude of the effects produced by salts C. This is hardly surprising as ion association is known to be extensive at such concentrations in this solvent. There are several notable differences from the behaviour found for proton chemical shifts.
Direct ion-solvent interactions play a much more important role and often predominate over the effects produced by the breaking of hydrogen bonds. I70 chemical shift of water in aqueous solutions of diamagnetic electrolytes. Some individual ion shifts are listed in Table 2 for comparison with proton chemical shifts. Interpretation of the oxygen chemical shifts follows closely the pattern already outlined in the consideration of proton results.
However, salts generally regarded as the most effective structure breakers, e. This discrepancy is particularly well marked in the series of halide or halate ions, where the listed ionic molal shifts fall in a sequence quite contrary to that expected from the structure-breaking abilities of these ions as determined by other methods.
Apparently direct interactions between ions and water molecules are of considerable importance. The results shown in Table 2 indicate that all the alkali cations produce similar effects on the resonance of water, there being no widespread range in their individual ionic molal shifts. On the other hand, halide ions show large differences amongst themselves in the effects they have on the oxygen chemical shift. A very similar distinction between the behaviour of cations and anions in alkali halide solutions has been found in studies of their Raman spectra in which most changes appear to be associated with the halide ions.
Some Raman studies cz2 have been published in support of this model for halide ion-water interaction.
Nuclear magnetic resonance
We might expect cations to produce the largest chemical shifts if these were the only ion-solvent configurations present in aqueous solution. Simple electrostatic polarization of the oxygen atom by the electric fields associated with charged ions cannot account for the observed behaviour. It predicts a sequence of effects for the alkali or halide ions opposite to that actually observed and it is therefore necessary to consider other possible mechanisms. Two processes which produce shifts are firstly, a charge redistribution in the O-H bond as suggested for proton C.
Direct approach of the solute and solvent molecules results in a strong short range repulsion which can distort the electron orbitals about the oxygen atom to produce a paramagnetic chemical shift of the resonance. The strength of this interaction is determined to a large extent by the magnitude of the overlap between the oxygen atom and the other species in solution. In the halide, halate or alkali ion series greater paramagnetic shifts of the signal are to be expected as the size of the ion increases due to the greater degree of overlap and consequent distortion.
Small effects produced by the alkali ions may be associated with the small extent of their outer electron orbitals as compared with those of the much larger halide ions. Although this mechanism can provide an interpretation of the oxygen17 shifts in these solutions it will require more detailed theoretical treatment before its importance can be fully assessed.
The qualitative considerations, however, suggest that further investigation would be well worthwhile. This mechanism has been employed for the interpretation of alkali metal and halogen nuclear resonances in these solutions, see Section 4, and in this case theoretical treatments of the chemical shifts in alkali halide crystals provide a suitable starting-point from which to consider the effects in aqueous solutions.
Ion hydration is considered in terms of the effect of ions on the translational motion of adjacent water molecules. The exchange frequency of water molecules from sites adjacent to an ion is determined by the height of the potential barrier between this position and the next site further out in the water lattice. It is not the total interaction energy, h, between the ion and water molecule but the small energy change, Ah, corresponding to small distances of separation between the lattice site and potential barrier which determines the probability that exchange will occur.
The well-known fact that the interaction energy between an ion and water molecule decreases less with separation than is the case for the dipole-dipole interaction between water molecules is of great significance. In the case of monovalent ions it is probably not unreasonable to put 7. A negative value of this parameter would indicate an increase in the mobility of water molecules adjacent to the ion compared with that for ordinary water.
Measurements of proton spin-lattice relaxation times in aqueous alkali halide solutions and the determination of self-diffusion coefficients of water molecules by the spin-echo technique provide direct indications of such behaviour. Proton and Deuteron Spin-lattice Relaxation in Alkali Halide Solutions Several workers have measured proton spin-lattice relaxation times in aqueous solutions of diamagnetic electrolytes. Those which reduce the mobility of water molecules increase the relaxation rate and conversely those which enhance the mobility lower the proton relaxation rate as compared with that found in pure water.
DEVERELL abilities of the ions and the initial slopes of plots of relaxation rate against molality show an extremely close correlation with the entropy of solution for alkali halides indicating the importance of structural changes in determining the relaxation times. In most caseP6 see Fig. Divalent ions produce particularly marked increases in the proton relaxation rate. The previous discussion of proton spin relaxation in pure water considered the modulation of the intra- and intermolecular dipole-dipole coupling of nuclear spins by thermal motions, and a comparison of theoretical expressions and experimental results enabled a value for the time of ITOrientatiOn of water mOkCUkS, Td, to be evaluated.
Variation of the rate of relaxation with temperature results to a large extent from changes in the rate of reorientation of water molecules and NMR spectroscopy provides a useful method for studying such motions. Introduction of ions into the water lattice alters the mobility of solvent molecules adjacent to them changing the observed relaxation rate.
Exchange between these possible sites is rapid and the experimentally observed relaxation rate is determined by the life-time of the water molecule and the effectiveness of the spin relaxation in each site. There are several processes which might contribute to the spin relaxation. Firstly, intramolecular dipole-dipole coupling between protons.
Further studies are given in references , and Hertz, Chapter 5, Vol. Sutcliffe, Pergamon Press, Oxford DEVERELL Secondly, there may be intermolecular dipole coupling between proton spins and thirdly, dipole-dipole coupling between the proton and the nuclear spins of the ions. These interactions are all modulated by the translational jump time, TV,of the water molecule which may be defined in terms of the self-diffusion coefficient, D.
In the majority of cases the magnetic moment of the ionic nucleus is much smaller than that of the proton and only the term involving intermolecular proton coupling need be considered. Equations 12 and 14 may be combined to give a final expression for the total relaxation rate.
The quantities in which we are primarily interested are the correlation times, T: In order to assess these times it is necessary to make an allowance for the intermolecular contribution and also to make some assumption about the coordination numbers, nz. Attempts to determine both correlation times and coordination times have generally not been successful. Initial slopes of the plots of relaxation rate against molality can be separated into individual contributions which appear to be reasonably additive. However, since we are concerned with the effect of the ion on the motion of water molecules the procedure adopted should not lead to substantial errors.
These show good agreement with the theory of hydration given by Samoilov, the mobility of water molecules close to potassium, rubidium, caesium, chloride, bromide and iodide ions is increased compared with that found in pure water. In most cases these reorientation times are not equivalent to the life-time of water molecules in the hydration sphere. Generally the variation is more complex. Both the viscosity of these solutions, q, and the selfdiffusion coefficient of water, D, show a concentration behaviour closely similar to that found for the relaxation rate.
Jones and Powles have shown that there is a close correlation between solution viscosity and proton spin relaxation rates for several salts. Since the viscosity and diffusion coefficient are related to the reorientational and translational jump correlation times respectively, which occur in the intra- and intermolecular contributions, such a connection is hardly surprising.
Obviously, the resultant viscosities and self-diffusion coefficients could be separated into individual components as we have attempted to do for the correlation times. The non-linear variation of all these quantities at higher concentrations is due to the fact that the separate values for the individual environments, near the cation or anion, and in the bulk solvent, are not constants but functions of concentration. Such interactions could be the sharing of water molecules by ions or increasing association between the ions.
It is not at all surprising that the simple approach very rapidly breaks down. Nevertheless, the results indicated in Table 3 are undoubtedly qualitatively correct for the more dilute solutions. Spin-lattice relaxation occurs by quadrupolar interaction as described earlier for deuterium oxide and using the simple three site model can be described by an equation similar to equation 8: These are similar to those already determined from proton relaxation measurements. It is considered that changes in the average time for molecular reorientation are responsible for the variation of deuterium relaxation with concentration.