Diffusion on a molecular scale as observed using PGSE NMR

Abstract

For half a century, pulsed-gradient Spin-Echo NMR based on the Stejskal-Tanner equation has been used to infer Fick's-Law diffusion coefficients of solutes in simple liquids and complex fluids. The decades since the original papers have seen vast advances in instrument technology and pulse sequence design, all leading to improved measurements of diffusion coefficients. However, just as the last half-century has brought major advances in instrument technology, so also it has also brought major advances in scientific understanding of diffusion on molecular distance and time scales. This article discusses implications of these advances in molecular hydrodynamics for the interpretation of PGSE NMR attenuation curves. The results here are particularly significant for studies on complex fluid systems that have relaxations on the time and distance scales that are observed in PGSE NMR experiments. V C 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 44A: 1-15, 2015.

Xenon Dynamics in Ionic Liquids: A Combined NMR and MD Simulation Study

“…The signal decay intensity I ( q , t d ) measured at a fixed time t d can be related to the mean-squared displacement (MSD), ⟨ z 2 ⟩, as follows where q = (δγ g )/2π and γ is the magnetogyric ratio of the observed nucleus. In the case of diffusing species whose motion is described by the Langevin 43 equation (hence Fickian diffusion), the MSD scales linearly with the observation time t d according to eq 2 obtained for the case of application of field gradients along the z direction only with D being the particle self-diffusion coefficient. This relation properly describes not only the free diffusion motion of liquid samples but also all of the diffusion processes that, even in the presence of barriers or obstacles, are described by a Gaussian distribution of displacement probabilities.…”

Models of diffusion signal decay in magnetic resonance imaging: Capturing complexity

“…In addition, Concepts in Magnetic Resonance Part A also has published a large number of more advanced treatments of the problem that would be next in line for study. [54][55][56][57][58][59][60][61][62][63][64][65] Just as standing at the top of a hill gives a panoramic view of the surrounding scene, I hope that this article has placed some of the more common models used to describe and fit MRI diffusion data into context. There are almost as many models as there are modelers, and perhaps even more than a one-to-one correspondence between models and modeling groups.…”

“…Focusing on review and tutorial papers in this journal is a good place to start, with the papers by Price, and Grebenkov at the top of the list I suggest that my students examine. In addition, Concepts in Magnetic Resonance Part A also has published a large number of more advanced treatments of the problem that would be next in line for study …”

Influence of Diffusion Time on the Diffusion Coefficients of Gases in Polymers Determined by Pulsed Gradient Spin Echo NMR

“…Thus, here we will just describe the key features needed to follow our approach to determine the diffusion coefficients of gases in dense polymer membranes. For a comprehensive description of the NMR principles and methodology for the measurement of diffusion coefficients, the reader is referred to two excellent treatises on the topic by Callaghan and Price and several recent reviews. − …”

“…In those cases where the diffusion may be considered as non-Fickian, i.e., a dependence of D with t D is observed, a mathematical approach developed previously for the interpretation of light scattering data , could be used to obtain an approximate solution to the Bloch–Torrey equation at short times . This is accomplished by a Taylor expansion of at sufficiently small values of Δ z (or its equivalent, short diffusion time t D )­ where the odd powers of Δ z vanish because the displacement distribution function P (Δ z , t D ) = P (−Δ z , t D ).…”