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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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An effective phase shift diffusion equation method for analysis of PFG normal and fractional diffusions.

Guoxing Lin1

  • 1Carlson School of Chemistry and Biochemistry, Clark University, Worcester, MA 01610, United States.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|September 20, 2015
PubMed
Summary

A new effective phase shift diffusion (EPSD) equation method directly calculates the accumulating phase shift distribution for pulsed field gradient (PFG) NMR experiments. This approach simplifies PFG signal attenuation analysis and offers novel expressions for experimental applications.

Keywords:
EPSD equationFractional diffusionMRINMRPFG

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) spectroscopy
  • Magnetic Resonance Imaging (MRI)

Background:

  • Pulsed field gradient (PFG) diffusion measurements are crucial in NMR and MRI.
  • Current theoretical models for analyzing PFG diffusion data often lack robustness or require approximations to determine the accumulating phase shift distribution (APSD).

Purpose of the Study:

  • To introduce a novel formalism, the effective phase shift diffusion (EPSD) equation method, for direct calculation of the APSD.
  • To provide a more robust and less approximate approach for analyzing PFG diffusion measurements.

Main Methods:

  • Developed the EPSD equation method by conceptualizing the gradient pulse effect as diffusion in a virtual phase space (VPS).
  • Constructed EPSD equations for VPS based on real space diffusion equations, modifying diffusion coefficients and coordinate systems.
  • Utilized fractal and fractional derivative models to build EPSD fractional diffusion equations.
  • Calculated PFG signal attenuation using APSD derived from the EPSD equations.

Main Results:

  • The EPSD method yields two distinct signal attenuation forms: a stretched exponential function (SEF) from the fractal derivative model and a Mittag-Leffler function (MLF) from the fractional derivative model.
  • The MLF attenuation can simplify to SEF under specific conditions (α=1) or approximate it for small attenuations.
  • The method successfully incorporates the effect of finite gradient pulse widths, providing new attenuation expressions.

Conclusions:

  • The EPSD equation method offers a new, simplified pathway for calculating signal attenuation in PFG NMR experiments.
  • The derived attenuation expressions, including those accounting for finite gradient pulse widths, are valuable for PFG experiments.
  • The results align well with existing literature, validating the EPSD approach.