to explain what happens to the spins of a sample during a pulse sequence the

To explain what happens to the spins of a sample

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to explain what happens to the spins of a sample during a pulse sequence, the two most commonly used are a classical vector-based model and a quantum mechanical operator based model. For anything but the most basic NMR experiment, some form of quantum mechanical approach is required. The interested reader may read through one or more of the well written course literature in NMR [ 31 , 32 , 33 , 34 ]. 1.2.2 Diffusion NMR Central to most chemical reactions and their kinetics is self-diffusion. Self-diffusion is the thermal random motion of a molecule and is characterized by the self-diffusion coefficient D (m 2 s - 1 ). Throughout this report the term diffusion will be used as a synonym for self-diffusion (there are a number of different types of diffusion). Ionic conductivity can be seen as dependent on diffusion of the charge carrier species [ 35 ] and is described by the Nernst- Einstein equation; Λ = zF 2 RT ( D cation + D anion ) (1.3) where z is the charge, F is the Faraday constant, R the ideal gas constant, T temper- ature in kelvin and D cation and D anion is the diffusion coefficient for cation and anion respectively. The diffusion coefficient can be calculated through the Einstein-Sutherland equation: D = k B T f friction (1.4) where k B is Boltzmann’s constant. Almost all diffusion NMR measurements use some form of spin-echo pulse-sequence coupled with a magnetic gradient used for spatial encoding. Evaluation of NMR diffusion pulse sequences requires following spin coherence changes with either density matrix or product operator formalism.
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10 CHAPTER 1. BACKGROUND As explained by Price [ 36 ], diffusion can be measured through the signal attenuation as a function of applied magnetic gradient strength. The effect of flow (note the difference from random motion) can be interpreted as a phase shift. The signal attenuation in a diffusion measurement is typically described as: S S 0 = e - γ 2 g 2 δ 2 D - δ 3 ) (1.5) where γ is the gyromagnetic ratio, g the magnetic gradient field strength, δ the magnetic gradient pulse length, D the diffusion coefficient and Δ the diffusion time. Diffusion measurements are typically done by stepwise increasing g and then plotting the signal attenuation and fitting the exponential decay. Depending on the experimental situation, a suitable diffusion NMR pulse program is required in order to acquire a good result. One example is the Pulsed field Gradient Double stimulated Spin Echo (PGDSTE) shown in figure 1.5 which helps to compensate for flow effects, for example due to convection, in the sample. acq 90 ο G rf 90 ο 90 ο 90 ο 90 ο δ δ δ δ Δ /2 Δ /2 Figure 1.5: A PGDSTE pulse sequence. An extensive review of diffusion NMR and its applications has been written by Price [ 36 ] and is suggested to the reader interested in a deeper understanding of dif- fusion NMR.
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