Nuclear magnetic resonance studies in chemistry

Chapter I begins with a brief review of the manner in which information on molecular motion in liquids may be derived from nuclear magnetic resonance relaxation time data. Emphasis is placed on solvent and solute resonance studies of electrolyte solutions.
New data is presented on the temperature, concentration and viscosity dependence of 81Br− and 23Na+ ion nuclear magnetic relaxation times in several aqueous solutions. An empirical equation is proposed which describes well both the new and the previously available data. Linewidths of ion resonances studies vary linearly with η/T, but are not directly proportional to this quantity, in contradiction with the Debye-Stokes model of ionic and solvent molecular motion. Striking similarity exists between the temperature dependence of n.m.r. linewidths and that of dielectric relaxation times in alkali halide solutions, suggesting that solvent reorientation or translation in the outer hydration region is the most efficient means of quadrupolar relaxation. On this assumption approximate solvent tumbling times in the outer hydration spheres of NaBr are calculated. Contributions to relaxation from ion-ion interactions are in accord with previous theory in that they possess an activation energy of the same approximate magnitude as that for ionic self-diffusion.
Chapter II. The theory proposed by Halliday, Richards and Sharp (1969) to account for the concentration dependence of the 133Cs+ ion shift in a number of aqueous, mixed aqueous and non-aqueous solutions of caesium salts is introduced; a detailed exposition is given, in which attention is drawn to its assumptions and approximations. A simple approximation in the theory, which avoids the necessity for a numerical integration, is described and justified.
The possible ways in which experimental data may be compared with this theory are discussed and illustrated. New experimental data which show the effects on the 133Cs+ ion shift of changes in temperature, dielectric constant and ionic strength are given, and fully analysed in terms of the theory by means of the procedures described. The results support the view that the theory available describes the ion shifts well even in solutions of low dielectric constant, provided that low concentration data only are considered.
An alternative model based upon the Bjerrum ion-pair theory is considered and compared with the theory previously described. A preliminary comparison of shift data with the predictions of the Bjerrum theory is made, which indicates a qualitative concordance, although the restricted data available make detailed appraisal impossible.
Chapter III. An account is given of the use of the halogen line-broadening technique for determining the rates of chemical exchange between sites with different intrinsic relaxation times. The method is applied to the exchange of Cl− ion between Cl3−, and Cl2, a "four-site chlorine exchange" problem. The appropriate algebraic solutions to the modified Bloch equations are presented, but emphasis is placed on the advantages of direct numerical computation of the spectrum. A description of the experimental procedures used includes a discussion of improvements in precision to be gained by using complete least-squares fitting procedures to abstract relaxation times from observed resonance lines. A comparison of the experimental results with theory, and in particular computed values of the broadening parameter, leads to a value of the dissociation rate constant of the trichloride ion (8 × 106 ± 4 × 106 s−1).
Appendix I contains a listing of the program developed for finding the best Lorentzian line through experimental resonances by the criterion of least squares.
Appendix II contains a summary of experimental data relating to Chapter III in tabular form.
Appendix III contains a discussion of the solutions of the modified Bloch equations, and an account of numerical solutions in the "unrestricted" four-cite case, including computed spectra. A listing is given of the program developed which provides a numerical solution to the full modified Bloch equations which enables spectra to be computed.