Diffusion encoding gradient

Figure Bl.14.9. Imaging pulse sequence including flow and/or diffusion encoding. Gradient pulses G before and after the inversion pulse are supplemented in any of the spatial dimensions of the standard spin-echo imaging sequence. Motion weighting is achieved by switching a strong gradient pulse pair G (see solid black line). The steady-state distribution of flow (coherent motion) as well as diffusion (spatidly...

Recently, the use of pulsed-field gradient (PFG) technology to obtain diffusion coefficients of molecules has been demonstrated as a useful technique for mixture analysis (53). Unlike any other 2D experiment, size-resolved or diffusion-resolved NMR assigns the resonances based on the diffusion coefficient for each proton (or other spin) in the molecule and therefore can be used to distinguish resonances arising from different molecules (63-70) (Fig. 22). A method that involves the use of PFG and TOCSY, called diffusion-encoded spectroscopy (DECODES), simplifies mixture analysis by NMR (71). The combination of PFG and TOCSY decodes the spin systems, allowing individual components in complicated mixtures to be assigned. A typical DECODES spectrum obtained in this manner is shown in Fig. 23. The use of TOCSY aids the calculation of the diffusion coefficient and determination of molecular identity. 

Figure 9.4. The (a) BPP-STE and (b) BPP-LED diffusion sequences. The encoding gradients of the stimulated-echo are apphed as symmetrical bipolar pulse pairs of total duration 8 and the LED sequence is extended with an eddy current delay period T. Optional purging pulses Gpi and Gp2 may also been employed.

Figure 9.35. The COSY-IDOSY sequence. The gradient pulses select for the conventional N-type COSY pathway in addition to providing diffusion encoding (selection of the P-type pathway would use gradient pulses of opposite sign).

Figure 9.36. The J-IDOSY sequence. The diffusion period A sits at the centre of the incremented ti period and the two gradient pulses provide for both diffusion encoding and selection of the spin-echo coherence transfer pathway.

Figure 9.37. The constant-time-HSQC-IDOSY sequence. The delays T are set to 1/2Jhx as required for the INEPT transfer and the constanttime period 2T remains fixed, its duration being dictated by the desired diffusion time A. The effective ti evolution time is varied by moving the two 180° refocusing pulses within the constant time period (pulses shown with arrows over) and coherence selection is made with the echo/antiecho (E/A) scheme. The diffusion encoding/decoding gradients are applied as bipolar pairs during the INEPT and reverse-INEPT transfer steps.

In order to verify the conditions of this averaging process, one has to relate the displacements during the encoding time - the interval A between two gradient pulses, set to typically 250 ms in these experiments - with the characteristic sizes of the system. Even in the bulk state with a diffusion coefficient D0, the root mean square (rms) displacement of n-heptane or, indeed, any liquid does not exceed several 10 5 m (given that = 2D0 A). This is much smaller than the smallest pellet diameter of 1.5 mm, so that intraparticle diffusion determines the measured diffusion coefficient (see Chapter 3.1). This intrapartide diffusion is hindered by the obstades of the pore structure and is thus reduced relative to D0 the ratio between the measured and the bulk diffusion coeffident is called the tortuosity x. More predsely, the tortuosity r is defined as the ratio of the mean-squared displacements in the bulk and inside the pore space over identical times ... 

It should be noted that the decomposition shown in Eq. 3.7.2 is not necessarily a subdivision of separate sets of spins, as all spins in general are subject to both relaxation and diffusion. Rather, it is a classification of different components of the overall decay according to their time constant. In particular cases, the spectrum of amplitudes an represents the populations of a set of pore types, each encoded with a modulation determined by its internal gradient. However, in the case of stronger encoding, the initial magnetization distribution within a single pore type may contain multiple modes (j)n. In this case the interpretation could become more complex [49]. 

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