Nuclear Magnetic Relaxation

Abstract

In Chap. 1 the concepts of the nuclear magnetic relaxation times (rates) were introduced on the basis of phenomenological considerations, as exemplified by the theory of Bloch. However, this approach can not clarify the nature of relaxation processes and quantify the relaxation times of various nuclei in different environments. The answers to these questions are given by quantum theory, which allows the calculation of the probability of relaxation transitions. In this chapter the problems of the relaxation in two-and multi-spin systems will be considered using the theory of time-dependent perturbations. Probability Relaxation TransitionsThe interaction of nuclei with the environment (neighboring nuclei, unpaired electrons and etc.) can lead, firstly, to non-equidistant energy levels and, consequently, the splitting of the spectrum of the nuclear magnetic resonance, secondly, to non-radiative transitions of nuclei between different energy states (exchange of energy between different degrees of freedom inside a substance). These non-radiative transitions have usually chaotic character and are a fundamental mechanism of the achievement of an equilibrium (Boltzmann) distribution of nuclei among energy states. These processes, which are the main object of consideration in this chapter, are called as relaxational. In general, the Hamiltonian of the nuclei system can be written aswhere H 0 describes the interaction of nuclei with a constant magnetic field B 0 , H describes their interaction with the environment. In the investigations of nuclear magnetic resonance in the majority of cases one deals with weakly interacting nuclei. Therefore, the Hamiltonians H 0 and H contain terms, taking into account the interaction of an isolated nucleus or a small number of nuclei with the external field B 0

Nuclear magnetic resonance study of sea-water freezing mechanisms: 2. Temperature dependence of relaxation time of protons in sea-ice brine

“…Relaxation processes in fresh water in simple water solutions have been well studied (e.g. Hindman and others, 1973;Lang and Lü demann, 1977;Chizhik, 1991). Results of a study of the temperature dependence of proton relaxation time in sea water and water solutions, with various functional presentations, are given by Melnichenko and others (2009).…”

Ion hydration effects in aqueous solutions of strong electrolytes, according to proton magnetic relaxation measurements

“…The boundaries of the transition areas are therefore blurred. The bends in the concentration dependences of magnetic relaxation rates observed in [17,19] were apparently the results of using a piece wise linear approximation of the concentration dependences.…”

“…The slope of the curves grew with the rise in temperature (and thus molecular mobility). Tangents to the curves in Figures 1 and 2 crossed at the points corresponding to the num bers of hydration of the single component solution [17] and SW [14]. These points also corresponded to the greatest variations in the first derivative.…”

“…Magnetic relaxation pro cesses in aqueus solutions were most thoroughly stud ied in [17]. In earlier works, the hydration processes in electrolyte aqueous solutions were described on the basis of measurements of PMR rates [14][15][16]18].…”

“…At neg ative hydration, the plots have a negative slope, as in the case of the aqueous KCl solution, where both ions are negatively hydrated at room temperature. The concentration dependences of the abovementioned parameters were recently plotted using a piecewise linear approximation and the tangents to the concen tration dependences [17,19]. A revision of the con centration dependences of the parameters dependent on solution microstructure at different temperatures thus seems to be in order to determine their true char acter.…”