Chapter 04, Nuclear Magnetic Resonance

Information derived from studies of the chemical shift and line widths of alkali metal and halogen nuclear resonances of aqueous solutions of alkali halides is reviewed in the following sections. Alkali Metal and Halogen Chemical Shifts Nuclear resonances of alkali metal and halide ions have been shown to undergo concentration dependent chemical shifts in aqueous solution.

DEVERELL The 35C1, 81Br and lz71 resonances of solutions of the halides all show quite pronounced changes in magnetic shielding which are dependent upon the cation present in the solution. Recently Deverell and Richards have shown the existence of quite definite chemical shifts of 23Na, 3sK, 87Rb and Cs resonances in halide and nitrate solutions that are influenced both by the concentration and nature of the anion.

Large shifts of the rubidium and caesium resonances have been noted by earlier workers.

Chapter 19 Nuclear Magnetic Resonance Spectroscopy (NMR)

A report of two separate signals in the 23Na spectrum of sodium hydroxide solutions is probably erroneous and is contrary both to the behaviour expected for this system and to other NMR measurements. Before discussing the results obtained in aqueous solution it is useful to consider briefly NMR measurements of solid alkali halides. The interpretation of these provides a suitable background for tackling the more complex problem of solutions.

Chemical shifts in alkali halide crystals Alkali halide crystals are ionic in character. Ideally ionic crystals can be considered as combinations of distinct positive and negative ions, each constituent ion having a spherically symmetric closed-shell electronic configuration identical to that expected for the isolated ion, with the complete assembly being held together by electrostatic forces.

In real crystals, however, additional interactions are present which are able to distort the symmetry of the electron distribution and introduce some net orbital angular momentum into the ion giGing rise to a paramagnetic chemical shift. Essentially this shift arises from changes in the p-electron densities of the alkali or halide ions. Mutual overlap of atomic wave functions of neighbouring ions produces a strong repulsive force mainly due to the Pauli exclusion principle.

This force acts over a short range and competes with the electrostatic forces tending to reduce the separation of oppositely charged ions and produce equilibrium in the crystal. Only a small change in the diamagnetic contribution ud, to the shielding of halide or alkali ion nuclei results from these forces, generally only lop2 or 10m3 of the fairly substantial paramagnetic term. The summation is taken over all electrons in the crystal, II, is the angular momentum of the kth electron and rk is the radial distance of the kth electron from the origin at the nucleus.

It is only necessary to consider overlap between the outermost S- and p-orbitals of the central ion and neighbouring ions in deriving an expression for the paramagnetic shift of the resonance of the ionic nucleus in the crystals relative to the free ion. Inner core orbitals are tightly bound and do not extend far into the region between the ions so that they retain complete spherical symmetry and produce no contribution to the paramagnetic shielding constant.

Ikenberry and Das have given the most exact derivation of the paramagnetic shift to be expected from overlap forces in alkali halide crystals. They obtained the following result: Another application has been the interpretation of zo5Tl chemical shifts in melts of thallium halides. In the case of halogen resonances in alkali halide crystals a slightly more complex dependence of chemical shift upon cation is found.

This minimum occurs at the sodium salt for fluorides, chlorides and bromides and at the potassium salt for the iodides. Consideration of halide-alkali metal overlap alone would lead us to expect a steady increase in shift to low field as the size of the cation increases, but the observed minimum suggests that there is an additional contribution which is most important in the halides of the smaller cations. It is necessary to consider both nearest neighbour and next-nearest neighbour overlap to interpret the halogen chemical shifts.

WY A comparison of the experimental and calculated difference in magnetic shielding at two different interionic separations enables a semi-empirical value of A to be determined. Using such estimates for the excitation energies, together with values of r;3 P and the overlap integrals determined from Hartree-Fock wave functions, the paramagnetic chemical shifts of the alkali metal and halogen resonances in the crystal can be computed.

Generally, the agreement with the behaviour observed experimentally is reasonable. Calculated shifts reproduce the qualitative features of the measured shielding constants. In solution there is already a paramagnetic contribution to the shielding constant of the ionic nucleus due to interaction with water molecules and in some cases this is even greater than the shift found in the crystal.

In most cases there are quite pronounced variations in the magnitude of uap obtained from a comparison of calculated with experimental shifts, most likely due to the limited accuracy of the computations. Uncertainties in the choice of average excitation energy, A, and allowance for halide-halide contributions are two major difficulties. Even so, the comparison does indicate large paramagnetic shifts of the ion resonances in dilute aqueous solution. These are larger for the halide ions than the alkali ions and increase in each series with the size of the ion.

Some typical values calculated using overlap integrals tabulated by Hafemeister and Flygareog3 and excitation energies given in Table 5 are: DEVERELL Although these estimates are of limited accuracy they do illustrate the sizeable magnitude of the paramagnetic shift of the ionic nucleus due to interactions with water molecules in dilute solution. Another possible mechanism for the production of the shifts, map, is the dipole polarization of the ion by adjacent water molecules.

More direct evidence for the existence of shifts due to solvent interactions is shown by the quite large changes in shielding produced by replacing water with deuterium oxide. In potassium fluoride solutions the lsF resonance is shifted by several parts per million to high field as the concentration of heavy water increases. Firstly, by alterations of the shielding resulting tAn Values ingenious method of Bearing these facts in mind we proceed to a discussion of chemical shifts in solution. Chemical shifts in alkali halide solutions Some typical results for alkali metal and halogen nuclear resonances are shown in Figs.

The difference in behaviour of bromide and nitrate ions which have similar structure-breaking effects is particularly marked, the former giving a shift to low field, whereas the latter gives a high field shift of the cation resonance.

This is not unexpected since these ions are known to have strong polarizing power and to influence the molecular motions of WaterGenerally, however, the ionsolvent interactions are of secondary importance. It is worthwhile considering some possible mechanisms for the production of chemical shifts in direct interionic processes. Perhaps the most obvious effect is the polarization of the electronic environment of the nucleus by the strong electrostatic fields produced by other ions in its vicinity.

If this were an important factor we might expect the smaller, more strongly polarizing ions to produce the largest shifts to low field, so that the shielding of the alkali metal nuclei would show the following anion dependence Cl- C. DEVERELL At this point it is worth emphasizing that in most cases the forces which produce changes in magnetic shielding are not usually directly related to those responsible for many other properties of the solution.

Thermodynamic properties result from electrostatic and short range forces between the ions and solvation processes. Electrostatic forces play a secondary role by their influence on the distribution of ions in solution and by this means it is possible for the concentration dependence of the chemical shift to be related to other properties of the solution. Kondo-Yamashita theory and chemical shifts in solution In the solid state the relative positions and distances of separation of the component ions are known and it is a comparatively easy problem to determine a theoretical expression for the chemical shifts to be expected from overlap effects.

However, in solution the environment of each ion varies randomly with time as the ions and solvent molecules undergo rotational and translational diffusion. The observed chemical shift is a mean value resulting from many separate contributions corresponding to the various short lived associations in solution. An exact expression for the shielding constant would require a knowledge of both the radial distribution function of other ions and water molecules about the central ion and the magnitude of the appropriate overlap integrals as a function of the separation.

Obviously such data is not available and an exact comparison of theory and experiment is not possible. Nevertheless, the problem may be formulated in a general manner and the KondoYamashita theory employed to provide a qualitative interpretation. Increasing the concentration alters the resonance frequency, firstly by modification of the original ion-solvent interaction and secondly, by the presence of additional interionic processes.

The second term denotes the change in the ion-solvent process. Both terms are dependent upon the probabilities of collisions occurring between the central ion and other ions or water molecules in solutions and will therefore be concentration dependent. It is a good procedure to take into account variations in these two parameters before comparing shifts of different nuclei since they often serve to amplify the effects primarily responsible for the shielding changes. Although there may be some error in the absolute magnitude of A, variations in the relative values for either alkali or halide ion series are not likely to be -, too great.

Since these parameters originate from the basic Ramsay formulatiorP5 they occur in expressions for the expected chemical shift from overlap, covalency and electrostatic polarization effects and do not arise solely from the mechanism we have proposed. Similarly there is in increase in shift to low field in each C. These are the qualitative features to be expected from the proposed short-range repulsive force mechanism where the extent of the shift to lower fields depends upon the size of both ions involved in collisions.

It is implicitly assumed that the rates at which anions encounter a particular cation are not greatly dissimilar. Since the halide ions, with the exception of fluoride ion, and nitrate ion all have very similar interactions with water molecules any inhibiting effects of an anionic solvation sphere are likely to be similar. This is in agreement with conclusions resulting from studies of the solvent resonances. High field shifts of all the cation resonances in solutions of their nitrates suggests that the N ion is less effective in producing a paramagnetic shift than the water molecule.

This apparent inability may be connected with the rather different electronic structure of the nitrate ion involving a pielectron system. The concentration dependence of the chemical shifts arises from variations in the average environment of the nucleus and the linear variation in the most concentrated solutions indicates a rapid exchange of anions and water molecules from sites adjacent to the cation. Increasing the salt concentration results in a greater proportion of direct interionic collisions in a purely additive manner.

Halogen resonances The strength of the interaction between a cation and neighbouring water molecules has an important influence upon the processes determining the halogen chemical shifts in solution. Caesium and other large cations, which have comparatively little influence upon the motions of water molecules, produce changes in shielding primarily by direct interactions with halide ions; whereas the smaller, more highly polarizing lithium and sodium ions produce shifts by altering the properties of water molecules separating them from halide ions.

The paramagnetic shift of the halogen resonance resulting from a direct interaction with the cations will be determined by the magnitude of the overlap integrals and the ease of approach of the oppositely charged ions. Large cations might therefore be expected to give the greatest shifts and we should expect the magnitude of the shift to increase steadily along the series from lithium to caesium. This expected sequence can be further characterized by comparison with the chemical shifts observed in solid alkali halides.

This conclusion is partly confirmed by the experimental observation of diamagnetic shifts of lgF, 35C1and 81Br resonances in the respective sodium halides from the resonance in aqueous solution. Actual observation of low field shifts in lithium and sodium solutions can be assigned to the presence of strong ion-solvent interactions. These produce an additional dipole polarization contribution to the paramagnetic shift of the halogen nucleus.

The shift produced by dipole polarization is proportional to the square of the dipole moment and small changes in this quantity could produce appreciable changes in magnetic shielding of the ionic nucleus. If water molecules polarized by the cation are also adjacent to halide ions this effect may be transmitted to the shielding of the halogen nucleus producing a low field shift. Such an effect would be most pronounced for lithium, sodium and multicharged ions. Since it is dependent upon the proportion of water molecules associated with the cation, the shift should show a linear variation with salt concentration.

Above about 8 molal there is a complete reversal in the trend of the 35C1 chemical shift in lithium chloride solutions and the shielding increases so that in the most concentrated solutions it is in fact greater than that of the chloride ion at infinite dilution. This is illustrated by Fig.

Nuclear magnetic resonance spectroscopy

Lithium would be expected to generate only a small paramagnetic shift of the halogen resonance by direct interactions involving overlap effects and as indicated earlier a C. The low field shift initially observed has been attributed to the effect of the lithium ion upon water molecules also adjacent to the halide ion, but at higher concentrations direct interactions between oppositely charged ions are likely to become more significant.

Changes in chlorine shielding due to the influence of lithium ion on solvent molecules will continue until a large proportion of the water molecules are in its vicinity and this process will then reach a limiting value, whilst the direct interaction process becomes increasingly important. The sudden shift of the 35C1resonance to higher fields supports this interpretation and also provides convincing evidence in support of the proposed overlap repulsive force mechanism. No other process would be compatible with a shift to high fields of the chlorine resonance due to direct interactions with the lithium cation.

Both electrostatic polarization and covalency predict shifts to lower fields. There is an indication that a similar, but much less pronounced, effect occurs in the behaviour of 35C1 and 81Br resonance in sodium chloride and bromide solutions. Chemical shifts in mixed solutions of alkali halides Investigation of properties of solutions containing more than one electrolyte can often give additional information about processes occuring in single salt solutions.

It is possible to obtain information about specific interionic processes by following the changes in various properties as the composition of a solution of mixed electrolytes is progressively altered. This section reviews some measurements of chemical shifts in solutions containing two electrolytes having either an anion or cation common to both salts. NMR signals from ions in such solutions are sensitive to interactions with all ions present but by gradually replacing ions of one charge sign it is possible to observe the specific effect that such ions have upon the resonating ion.

A typical example is the investigation of different interanionic processes by observing the halogen chemical shifts in solutions containing a constant cation concentration as the anion composition is gradually varied. A preliminary investigation of the sensitivity of the Cs resonance to cation-cation interactions has also been made. In all cases the chemical shift was found to vary linearly with the composition of the solution, as shown by Figs.

DEVERELL 1- 1 electrolytes having a common ion and calculation of a finite value for the excess free energy of mixing confirm the presence of specific halidehalide and cation-cation interactions in alkali halide solutions. Anions produce changes in the magnetic shielding of the halide nuclei identical to the sequence previously observed for their effect upon cation resonances. Processes of this type involving interactions between ions of like sign are also present in the single salt solutions and it has been estimated that at concentrations above about 3 molal where the halogen shift varies linearly with concentration the halidehalide process makes a contribution of This is a sizeable proportion of the total observed shift especially in the presence of the smaller cations.

Large alkali cations also have the greatest effect on the Cs resonance see Fig. Since the sum involves only one term, arising from overlap of the outer p-orbitals of the resonating ion with the outermost s-orbitals of the other ion, which is not common to both summations and which is expected to be comparatively small! I for ran and A as given in C. By making assumptions about the magnitude of the ion-solvent contribution and allowing for the shift due to interactions between ions of like sign it can be shown that the ratio of the cation to halide shifts in the interaction between oppositely charged ions are in reasonable agreement with this expected ratio.

The shielding first decreases on dilution and, after passing through a minimum at about 5 molal, there is then an almost linear increase to high fields. It is now possible to justify the original explanation of these effects by means of the overlap mechanism.

If direct association between the sodium and fluoride ions is assumed to be predominant at all concentrations it might be expected to produce a high field lSF shift in accordance with the earlier discussion of Section 4. In potassium fluoride solutions such an association only becomes predominant at the highest concentrations giving a shift towards the high field value observed in the solid state. Ammonium ions always produce a low field shift of the fluoride ion resonance presumably due to the strong hydrogen bonding between these ions.

A detailed discussion of the general theory of quadrupolar relaxation has been given elsewhere. Unfortunately, because of uncertainties in the exact magnitude of such parameters as the quadrupole moment and anti-shielding factors and complexities involved in deriving a realistic theoretical expression, it is not possible to obtain information about the time dependence of these molecular motions from nuclear spin relaxation rates.

But it is still of value to consider some of the elementary approaches made to tackle this problem as they do give some insight into the important factors influencing relaxation. Quadrupole relaxation and the hydration of ions Solvent molecular motions in the coordination shell of the ion are determined by the strength of the interaction between these two species. Translational motions are only important for monovalent and large alkaline earth ions. In all other cases the exchange rates of water molecules from the coordination shell are too slow to produce relaxation.

Some theoretical expressions based on different models for the solvation complex are considered in the following sections.

• Chapter 14. Nuclear Magnetic Resonance.
• Nuclear Magnetic Resonance;
• Oxford University Press | Online Resource Centre | Nuclear magnetic resonance spectroscopy.
• Magnetic Properties of Nuclei.
• CHAPTER 13 Molecular Structure by Nuclear Magnetic Resonance?
• CHAPTER 13 Molecular Structure by Nuclear Magnetic Resonance!
• Navigation menu.

Only the trivalent ions aluminium, gallium and indium fulfil this condition in aqueous solution. Random fluctuations in the internal vibrations of C. DEVERELL the complex are produced by molecular motions of neighbouring particles and these perturb the symmetry of the electric field at the centre of the octahedron in a time-dependent manner. Components of the field gradient tensor resulting from the presence of ligands with an effective charge, e, at a distance, a, from the central nucleus may be expressed in terms of the orthogonal normal vibration coordinates, Qi, of the complex and the fluctuations may be characterized by a correlation time, Tvibrcorresponding to the damping of vibrations.

There is considerable variation in the magnitude of the anti-shielding factor according to the method of calculatiotP7 and since this parameter is very large for the heavier ions this severely limits the accuracy of any calculations. Quadrupole relaxation for weak ion-solvent interactions Monovalent ions interact less strongly with water molecules and translational and reorientational motions are likely to be the primary processes initiating spin relaxation. Restricted rotational or torsional motions of molecules in the coordination sphere will also be important for multivalent ions.

L,coordinated to the ion at a separation r o; and rd iS the correlation time describing the reorientational motions. Some relaxation rates calculated from this equation are given inTable 6. A correlation time, rd, of 2. Relaxation rates of the correct order of magnitude are predicted by expression 28 for the cation nuclei and the slightly low values may be partly ascribed to the longer reorientational correlation times, rd, of water molecules in the coordination shell.

ValieP2 has also published more detailed calculations which attempt to take the radial distribution of water molecules into account by considering a form for the energy of interaction between the ion and solvent molecules. Using a rectangular pit type of potential function it is possible to express the relaxation rate in terms of the depth of the potential well occupied by a water molecule in a site adjacent to the ion. Comparison with experimental data enables the strength of the ion hydration to be characterized in terms of the relative mobility of water molecules adjacent to the ion compared with those in the pure solvent.

Only for the halide ions is there agreement with expected behaviour. Generally the calculated strengths of hydration are quite contrary to the known solvation properties of the cations. There is a variety of reasons for the lack of success found in attempts to derive information about molecular motions in the ionic hydration sphere from measurements of the quadrupolar relaxation rates. Firstly, uncertainties in the magnitude of the quadrupole moments and corrections for anti-shielding and solvent polarization effects. Thirdly, no attempt has been made to consider the highly organized structure of water and the solvent is generally treated as a continuum.

Fourthly, the assumption of uninhibited motions of water molecules is unjustified and there is no attempt to allow for the orientation of water molecules by the strong ion-dipole forces; and finally, it is assumed that all electric field gradients arise from charges and dipoles external to the ion, no account being taken except for the anti-shielding factor of the large effects which would result from distortion of the closed-electron shells surrounding the nuclei.

Although little information about ion-solvent interactions can be obtained from considerations of the ionic nuclear resonance line widths in dilute solutions, studies of the temperature, concentration and solvent dependences are likely to be more informative. If it is assumed that the electric coupling constant, eQq, is insensitive to temperature changes all the observed effects may be associated with the correlation times, rd.

Results obtained in this manner have been given in Table 4. Since the reorientational motions producing the electric field gradients for quadrupole relaxation of the central ionic nucleus are also important in determining the proton spin relaxation of the solvent molecules a close correlation between the activation energies derived from the independent methods is to-be expected. Generally, the agreement is reasonable. Concentration dependence of quadrupole relaxation in electrolyte solutions Increasing the electrolyte concentration in solution alters the nuclear spin relaxation time, firstly, by changing the rates of reorientation of dipolar solvent molecules and secondly, by producing additional fluctuating field gradients via the diffusional motions of the charged ions.

Over a suitably long time interval the electric charge distribution produced by ions around a given central ion in solution will have complete spherical symmetry and there will be no net field gradient to initiate quadrupolar relaxation. They obtain the result 31 where the two terms in the square brackets represent the ion-solvent and interionic contributions respectively. The summation is taken over all ions, j, of valency zj which have opposite charge sign to the resonating ion. Unfortunately, there is no exact method for determining the variation of these correlation times with concentration and it is necessary to make some assumptions about such behaviour before the theoretical expression can be tested.

In certain cases it is possible to express both the reorientational, rd, and translational correlation times, ri in terms of the solution viscosity. Although the conditions under which the linear relationship between correlation time and viscosity was derived are not strictly obeyed in electrolyte solutions we shall, in the absence of any other procedure, assume such a relationship in the following discussion.

There is some evidence to support this assumption. GI,o 34 f is the ratio of the concentration of water molecules in a solution of salt concentration c compared with that in pure water, and generally for alkali halide solutions varies between 1 and 0. After the measured value of line width viscosity has been corrected for the small changes in solvent concentration the remaining contribution due to interionic processes should increase linearly with solution concentration according to equation The minimum distance of approach of the ions, a, and the translational correlation time of the partner ion in dilute solution!

Assuming a value of a equal to the sum of the ionic crystal radii and using the Stokes-Einstein expression to evaluate the correlation times for the cations we obtain the values of B shown in Table 7. Calculated values of the constant B, shown in Table 7, are one or two orders of magnitude greater than those observed experimentally and do not reflect the marked dependence of the halide ion resonance widths upon the partner cation present in solution.

Experimental values of the constant B are determined from an equation similar to equation 33 withf assumed to be unity. It is worthwhile considering some other possible mechanisms which could give rise to the necessary quadrupole coupling constants for relaxation. Short-range repulsive forces and quadrupole relaxation Electric field gradients in the immediate vicinity of the quadrupolar nucleus are those most effective in producing spin relaxation.

Any process which gives rise to a time dependent distortion of the symmetry of the closed-shell electron distribution around the alkali metal or halogen nuclei could provide a potential relaxation mechanism. Covalent character is not generally associated with alkali halide solutions and would predict a greater degree of broadening of the halogen resonances in the presence of the smaller cations, contrary to observed behaviour.

Random reorientational or vibrational motions ensure that the necessary modulation to induce relaxation is present. Obviously in electrolyte solutions the resultant effect must be obtained by averaging over all the possible orientations and separations of the ions. This expression 38 satisfactorily reproduces measured quadrupole coupling constants for a large number of atoms. DEVERELL for quadrupolar relaxation of nuclear spins is 40 where 7c is a correlation time describing the fluctuations of the electric field gradients, q.

Although it is not possible to evaluate the relaxation rate directly from equations 39 and 40 , since we cannot determine the summation of overlap integrals for this case, we may still obtain useful information by relating the quadrupole coupling constant to the paramagnetic shielding constant of the ionic nucleus. Firstly, it can be used to obtain a value for the chemical shift of the hydrated ion, uas, from the resonance width observed in dilute solution and secondly, values for the changes in relaxation rate with increasing salt concentration may be estimated by employing the previously discussed chemical shift measurements.

Chemical shift of the hydrated ion, crap In making calculations of relaxation rates from equation 41 it is not necessary to include correction factors for polarization and anti-shielding effects. This arises from the basic fact that the electric field gradients are produced by deformations of the spherical electron distribution around the ionic nucleus and not from the presence of electric charges external to the ion.

Publication details

Choice of an appropriate value for the correlation time, TV,is a more difficult problem but we have used the reorientation times of water molecules adjacent to the ion given by proton spin-lattice relaxation times. These values are in agreement with other estimates of this quantity. Concentration dependence of quadrupole relaxation Increasing the solution concentration produces changes in both the chemical shift and the relaxation time of the ionic nuclear resonance.

Previously we have shown that both interionic and ion-solvent processes can play an important part in determining the behaviour of the chemical shift. If there is a probability, pk, of the ionic nucleus being in an environment with paramagnetic shielding constant, uk, and the correlation time for the interaction is?

DEVERELI, The additional assumption has been made that does not vary greatly for the different interactions and has the common value, 7, so that 46 Since zpktik is just the experimentally measured chemical shift, 6, of the ion nuclear resonances in aqueous solution equation 46 can be used to estimate the expected line broadening. If the correlation times are again assumed to be linear functions of the solution viscosity, r , 47 Values for the expected magnitude of the broadening of halogen nuclear resonances in aqueous solution for the overlap mechanism are included in Table 5.

Such behaviour is generally observed at concentrations greater than 3 molal. The broadening of the nuclear resonance with changing concentration may then be expected in terms of a coefficient, B, in a manner analogous to equation 33 withf put equal to unity. It can be seen that not only are the coefficients B of the same order of magnitude as those found experimentally but they also reproduce the marked dependence upon the partner cation.

In these solutions there is a large diamagnetic shift of the 23Na resonance with increasing salt concentration, lRO but the perchlorate ion is extremely effective in producing spin-relaxation. Solutions in Non-aqueous Solvents Few measurements of the nuclear resonances from ions in non-aqueous solvents have been reported. The 23Na and slBr resonances from solutions of sodium bromide in various mixed solvents, containing water as one component and either methanol, acetone or glycine as the second component, have been investigated by Richards and Yorke.

Z26 Significant increases in resonance width were noted as the non-aqueous fraction of the solvent was increased. Apparently both components are able to solvate the ion. Lithium-7 relaxation was found to be much faster in dimethylformamide than in water or methanol. Generally there was a shift of the fluorine resonance which varied linearly with the mole fraction of non-aqueous solvent.

Only for glycol was there any indication of preferential solvation.

Chapter 4 Nuclear magnetic resonance studies of electrolyte solutions

Small effects produced by dioxane, acetone and acetonitrile suggest that these solvents do not solvate the fluoride ion. Results for Csresonances, rather surprisingly, showed no solvent dependence of the caesium chemical shift. Further investigation of alkali and halogen nuclear resonances in non-aqueous solvents is likely to be profitable.

Some studies of solvation of cobalt acetylacetonate in chloroform-carbon tetrachloride mixtures by following the 5gCo chemical shift changes have also been reported. A negligible perturbation is produced during the observation of the NMR spectrum. The most extensively considered case has been the exchange of solvent molecules between the first coordination shell of a paramagnetic ion and the bulk solvent. Broadening of the solvent nuclear resonance peak may be controlled either by the life-time of solvent nuclear spins in the coordination shell of the paramagnetic ion, 7p, or by the transverse relaxation time, T,,, produced by dipolar or scalar coupling to the unpaired electron spin of the paramagnetic ion.

In certain limiting cases, when the first process controls the line broadening, it is possible to determine first order rate constants describing the exchange of molecules from the solvation shell, but if the relaxation time, TzP, is dominant only the lower limit of the rate constant can be found. The particular case of the broadening of the resonance of water in aqueous solutians of paramagnetic ions has been considered by Swift and Connick, 23s who obtained the following equation for the relaxation rate to be expected under steady state conditions, 48 where T,, is the transverse relaxation time in the pure solvent, and 7D the life-time of the I70 nucleus in solvent water molecules not in the first coordination shell of the paramagnetic ion; Aw, is the difference in the precession frequency of nuclei in the two environments considered.

Equation 48 can be applied in certain limiting cases to the determination of exchange rates. When the nuclear relaxation caused by the frequency shift, Aup, is unimportant the mechanism involving T 2p can predominate if scalar or dipolar coupling between the solvent nuclear spin and the unpaired electrons of the metal ion produces fast relaxation.

It is therefore possible to determine whether the line width is controlled by relaxation, TZP, or chemical exchange, TV, processes by means of temperature dependent studies. This technique has been applied to the study of ligand exchange rates in several systems. Later papers have reported investigations into the structure of vanadyl ion in aqueous solutions. There are four equatorial water molecules with a residence time, TV, of 1. Exchange rates determined from proton resonances are much faster than those found by I70 measurements of chromic and ferric ion solutions suggesting that the most probable mechanism of these reactions is the acid dissociation of the hydrated ions.

The rate of exchange of methanol molecules from the coordination shell of the neptunium V ion has also been reported. A review of several earlier measurements has been given previously by Pearson and Anderson. It is dependent upon the much faster relaxation rate of quadrupolar nuclei in unsymmetrical environments as compared with that found for symmetrical sites. Exchange of nuclei between symmetrical and unsymmetrical sites, where large electric field gradients are present, can lead to a broadening of the nuclear resonance corresponding to the symmetrical site and this broadening may be controlled either by the rate of exchange or the rate of relaxation in the unsymmetrical site in a manner similar to that previously discussed for solutions containing paramagnetic ions.

Dependence of the iodide ion lz71NMR line width, AH,,, on the presence of small amounts of mercuric ion. Both the magnitude of the reaction rates and small activation energies for the exchange processes suggest that the reactions are diffusion limited and the authors were able to find reasonable agreement between the experimental results and those calculated from the Smoluchowski equation, suitably modified to take into account electrostatic interactions, by assuming that the reactions proceeded via a penta-coordinated activated complex, i.

However, only processes such as 5 lc in which a net chemical reaction occurs were considered and some discrepancy is likely to C. Mercury resonances have also been observed in mercuric halide system. This rate is again closely similar to that expected for a diffusion controlled reaction. Indium is another quadrupolar nucleus which has been employed to determine exchange rates in solutions of diamagnetic electrolytes. NMR spectra are unique, well-resolved, analytically tractable and often highly predictable for small molecules.

Different functional groups are obviously distinguishable, and identical functional groups with differing neighboring substituents still give distinguishable signals. NMR has largely replaced traditional wet chemistry tests such as color reagents or typical chromatography for identification. Preferably, the sample should be dissolved in a solvent, because NMR analysis of solids requires a dedicated magic angle spinning machine and may not give equally well-resolved spectra.

The timescale of NMR is relatively long, and thus it is not suitable for observing fast phenomena, producing only an averaged spectrum. Although large amounts of impurities do show on an NMR spectrum, better methods exist for detecting impurities, as NMR is inherently not very sensitive - though at higher frequencies, sensitivity is higher. Correlation spectroscopy is a development of ordinary NMR. In two-dimensional NMR , the emission is centered around a single frequency, and correlated resonances are observed.

This allows identifying the neighboring substituents of the observed functional group, allowing unambiguous identification of the resonances. There are also more complex 3D and 4D methods and a variety of methods designed to suppress or amplify particular types of resonances. In nuclear Overhauser effect NOE spectroscopy, the relaxation of the resonances is observed.

As NOE depends on the proximity of the nuclei, quantifying the NOE for each nucleus allows for construction of a three-dimensional model of the molecule. NMR spectrometers are relatively expensive; universities usually have them, but they are less common in private companies. Modern NMR spectrometers have a very strong, large and expensive liquid helium -cooled superconducting magnet, because resolution directly depends on magnetic field strength. Less expensive machines using permanent magnets and lower resolution are also available, which still give sufficient performance for certain application such as reaction monitoring and quick checking of samples.

There are even benchtop nuclear magnetic resonance spectrometers. NMR can be observed in magnetic fields less than a millitesla. Low-resolution NMR produces broader peaks which can easily overlap one another causing issues in resolving complex structures. The use of higher strength magnetic fields result in clear resolution of the peaks and is the standard in industry. When placed in a magnetic field, NMR active nuclei such as 1 H or 13 C absorb electromagnetic radiation at a frequency characteristic of the isotope.

It is common to refer to a 21 T magnet as a MHz magnet since hydrogen is the most common nucleus detected, however different nuclei will resonate at different frequencies at this field strength in proportion to their nuclear magnetic moments. An NMR spectrometer typically consists of a spinning sample-holder inside a very strong magnet, a radio-frequency emitter and a receiver with a probe an antenna assembly that goes inside the magnet to surround the sample, optionally gradient coils for diffusion measurements, and electronics to control the system.

Spinning the sample is usually necessary to average out diffusional motion, however some experiments call for a stationary sample when solution movement is an important variable. For instance, measurements of diffusion constants diffusion ordered spectroscopy or DOSY [5] [6] are done using a stationary sample with spinning off, and flow cells can be used for online analysis of process flows.

The vast majority of molecules in a solution are solvent molecules, and most regular solvents are hydrocarbons and so contain NMR-active protons. The most widely used deuterated solvent is deuterochloroform CDCl 3 , although other solvents may be used depending on the solubility of a sample. The chemical shifts of a molecule will change slightly between solvents, and the solvent used will almost always be reported with chemical shifts.

NMR spectra are often calibrated against the known solvent residual proton peak instead of added tetramethylsilane. To detect the very small frequency shifts due to nuclear magnetic resonance, the applied magnetic field must be constant throughout the sample volume. High resolution NMR spectrometers use shims to adjust the homogeneity of the magnetic field to parts per billion ppb in a volume of a few cubic centimeters.

In order to detect and compensate for inhomogeneity and drift in the magnetic field, the spectrometer maintains a "lock" on the solvent deuterium frequency with a separate lock unit. In modern NMR spectrometers shimming is adjusted automatically, though in some cases the operator has to optimize the shim parameters manually to obtain the best possible resolution. It is a very weak signal, and requires sensitive radio receivers to pick up. A Fourier transform is carried out to extract the frequency-domain spectrum from the raw time-domain FID. A spectrum from a single FID has a low signal-to-noise ratio , but it improves readily with averaging of repeated acquisitions.

Good 1 H NMR spectra can be acquired with 16 repeats, which takes only minutes. However, for elements heavier than hydrogen, the relaxation time is rather long, e. Thus, acquisition of quantitative heavy-element spectra can be time-consuming, taking tens of minutes to hours. Following the pulse, the nuclei are, on average, excited to a certain angle vs. The extent of excitation can be controlled with the pulse width, typically ca.

The pulse width can be determined by plotting the signed intensity as a function of pulse width. Decay times of the excitation, typically measured in seconds, depend on the effectiveness of relaxation, which is faster for lighter nuclei and in solids, and slower for heavier nuclei and in solutions, and they can be very long in gases. If the second excitation pulse is sent prematurely before the relaxation is complete, the average magnetization vector has not decayed to ground state, which affects the strength of the signal in an unpredictable manner. In practice, the peak areas are then not proportional to the stoichiometry; only the presence, but not the amount of functional groups is possible to discern.

An inversion recovery experiment can be done to determine the relaxation time and thus the required delay between pulses. A spinning charge generates a magnetic field that results in a magnetic moment proportional to the spin. Irradiation of the sample with energy corresponding to the exact spin state separation of a specific set of nuclei will cause excitation of those set of nuclei in the lower energy state to the higher energy state.

However, even if all protons have the same magnetic moments, they do not give resonant signals at the same frequency values. This difference arises from the differing electronic environments of the nucleus of interest. Upon application of an external magnetic field, these electrons move in response to the field and generate local magnetic fields that oppose the much stronger applied field. This local field thus "shields" the proton from the applied magnetic field, which must therefore be increased in order to achieve resonance absorption of rf energy.

Such increments are very small, usually in parts per million ppm. For instance, the proton peak from an aldehyde is shifted ca. The difference between 2. However, given that the location of different NMR signals is dependent on the external magnetic field strength and the reference frequency, the signals are usually reported relative to a reference signal, usually that of TMS tetramethylsilane.

Additionally, since the distribution of NMR signals is field dependent, these frequencies are divided by the spectrometer frequency. However, since we are dividing Hz by MHz, the resulting number would be too small, and thus it is multiplied by a million. This operation therefore gives a locator number called the "chemical shift" with units of parts per million.

The chemical shift provides information about the structure of the molecule. Compared to the previous volume there are some new members of the reporting team. Jump to main content. Jump to site search. You do not have JavaScript enabled. Please enable JavaScript to access the full features of the site or access our non-JavaScript page.

Preliminary content Front Matter K. Log in to access for FREE. Symbols and Abbreviations K.