Stejskal-Tanner pulse gradient

Fig. 8. The Stejskal-Tanner pulsed gradient spin-echo sequence.

Fig. 1.34. Basic Stejskal-Tanner pulsed gradient spin-echo (PGSE) pulse sequence n/2-g 8)-n-g(<5)-echo used for displacement spectroscopy. The echo time TE is 2r and the displacement time is A. After Hills [718]. Reprinted from B. Hills, Magnetic Resonance Imaging in Food Science, John Wiley Sons, Inc., New York, NY. Copyright (1998, John Wiley Sons, Inc.). This material is used by permission of John Wiley Sons, Inc.

FIGURE 8.15 The basic Stejskal-Tanner pulsed field gradient experiment. Reprinted from Stilbs (1987). Copyright 1987 with permission from Elsevier. 

Modem NMR diffusion measurements are all based on the Stejskal-Tanner (S-T) pulsed field gradient spin-echo experiment [174] in which a gradient pulse is... 

When pulsed magnetic field gradients are applied to study diffusive processes, the MR technique is often referred to as pulsed field gradient or pulsed gradient spin echo (PGSE) MR. Application of PGSE MR techniques to quantify molecular diffusion was pioneered by Stejskal and Tanner 17,18), and the techniques typically probe molecular displacements of 10 -10 m over time scales of the order 10 M s. 

In this section, we provide an outline of the theoretical and practical aspects of diffusometry NMR experiments that are the core of chrom-NMR. This issue has been reviewed at large38,39 and thus only the key and most relevant aspects will be mentioned below. The displacement of a given molecular tracer is followed by a classical Stejskal-Tanner experiment. In this, pulses of magnetic field gradients are used to label the initial position of the tracer, and to follow its displacement along the direction of the gradient, Az. Indeed, in a spin-echo experiment, any displacement corresponds to a reduction of the efficiency of the echo formation. 

The large diffusion coefficient of gases result in significant spin motion during the application of gradient pulses that typically last a few milliseconds in most NMR experiments. In restricted environments, such as the lung, this rapid gas diffusion can lead to violation of the narrow pulse approximation, a basic assumption of the standard Stejskal-Tanner method of diffusion measurements. Mair et therefore investigated the effect of a common,... 

If gradient pulses of finite length B are employed, instead of (5.4.33) the Stejskal-Tanner relation applies for the echo amplitude [Stel],... 

Tanner, J.E. and Stejskal, E.O. Restricted self-diffusion of protons in colloidal systems by the pulsed-gradient, spin-echo method, /. Chem. Phys., 49, 4938, 1968. 

In many systems, the diffusion of small molecules is not free but is restricted. Examples of systems with restricted diffusion are molecules in cellular compartments, fluids between long flat plates, lamellar and vesicular systems, water-filled pores in rocks, and small molecules in colloidal suspensions. If the time during which the molecular diffusion is monitored in the experiment (the time between rf pulses in the continuous gradient experiment and A-6/3 in a pulse gradient diffusion experiment) is much longer than the time for a molecule to travel to a boundary, then the calculated D will be too small (Woessner, 1963). In such cases of restricted diffusion, appropriate equations must be derived for the particular geometry of the constraint (Stejskal, 1965 Wayne and Cotts, 1966 Robertson, 1966 Tanner and Stejskal, 1968 Boss and Stejskal, 1968). In favorable cases, the diffusion measurement can yield not only D but an estimate of the restraining dimension as well. 

Fig. 7.2 Stejskal-Tanner diffusion spin echo sequence [142]. Spins accumulate phase shift during the first gradient pulse. The 180 pulse inverts the phase of all spins. The second gradient lobe induces another phase shift that is effectively opposite to the first gradient pulse due to the effect of the spin echo. The phase shifts are identical in magnitude and cancel each other out. For...

Molecular diffusion (and flow) may be measured in the presence of magnetic field gradients using the Stejskal-Tanner spin-echo technique. Diffusion in a gradient dephases the magnetization between pulses. The technique may be incorporated into... 

The diffusion experiments have been performed on a Bruker Avance 500 NMR spectrometer operating at a Larmor frequency of 500 MHz for protons using a DIFF 30 probehead generating a maximum gradient strength of 12 T/m. The gradient pulse duration 8 and diffusion time A have been adjusted between 0.7 to 1A ms for 8 and 10 to 15 ms for A respectively. The narrow distribution of the molecular weight distributiOTi permits the determination of the diffusion coefficients by a linear fit to the Stejskal-Tanner equation [23]. 

Successive experiments varying the A, or more commonly tire gradient strength, provide the data points for a non-linear least squares fit of Equation 2.5 to solve for the diffusion coefficient. Typical experimental data with the fitted Stejskal-Tanner equation (Eq. 2.5 is shown in Figure 2.3. To produce a gradient pulse of opposite sign to the first, the polarity of the gradient coil can be physically reversed. However, this does not produce the desired level of reproducibility of the pulses, and modern NMR systems use the tt-RF pulse to cause the same effect. 

Van Lokeren and co-workers reported a study of polymer mixtures in solution using pulsed field-gradient spin eeho NMR. They proposed a quantification approach in which the fraetions of different components were obtained explicitly including relaxation effeets in the Stejskal-Tanner equation. 

Decays of the signal corresponding to the Ar-C O protons at 5 ppm as a function of the pulsed gradient strength have been plotted (Fig. 5.2) according to the Stejskal-Tanner Eq. 5.1 [29] ... 

Pulsed field gradient NMR (PFG-NMR) spectroscopy has been successfully used for probing interactions in several research fields.44-53 The method was developed by Stejskal and Tanner more than 40 years ago54 and allows the measurement of self-diffusion coefficient, D, which is defined as the diffusion coefficient in absence of chemical potential gradient. 

Since the Murday-Cotts paper in 1968 much progress has been made toward the theoretical description of the spin-echo intensity E g, A) for spins diffusing in well-defined geometries. Tanner and Stejskal derived already in 1968 the exact expression of ii(g. A) for spins diffusing in a rectangular box. The derivation of an exact expression for E g, A) for diffusion in a sphere with reflecting walls is not a trivial mathematical problem and it took between 1992 and 1994 when three expressions were published. All three expressions are only valid in the short-gradient-pulse approximation (see below). 

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