Pulsed field gradient signal attenuation of restricted anomalous diffusions in plate, sphere, and cylinder with wall relaxation

Xinli Liao, Shaokuan Zheng, and Guoxing Lin
Phys. Rev. E 101, 012128 – Published 24 January 2020
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Abstract

The effect of boundary relaxation on pulsed field gradient (PFG) anomalous restricted diffusion is investigated in this paper. The PFG signal attenuation expressions of anomalous diffusion in plate, sphere, and cylinder are derived based on fractional calculus. In addition, approximate expressions for boundary relaxation induced short time signal attenuation under zero gradient field and boundary relaxation affected short time apparent diffusion coefficients are given in this paper. Unlike the exponential signal attenuation in normal diffusion, the PFG signal attenuation in anomalous diffusion with boundary relaxation is either a Mittag-Leffler-function-based attenuation or a stretched-exponential-function-based attenuation. The stretched exponential attenuations of all three structures clearly show the diffractive pattern. In contrast, only in the plate structure does the Mittag-Leffler-function-based attenuation display an obvious diffractive pattern. Additionally, anomalous diffusion with smaller time derivative order α has a weaker diffractive pattern and less signal attenuation. Moreover, the results demonstrate that boundary relaxation induced signal attenuation is significantly affected by the anomalous diffusion when no gradient field is applied. Meanwhile, the boundary relaxation significantly affects PFG signal attenuation of anomalous diffusion in the following ways: The boundary relaxation results in reduced radius from the minimum of the diffractive patterns, and it results in an increased apparent diffusion coefficient and decreased surfaces to volume ratio in varying the diffusion time experiment; the boundary relaxation also substantially affects the apparent diffusion coefficient of sphere structure in the variation of gradient experiment.

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  • Received 6 September 2019

DOI:https://doi.org/10.1103/PhysRevE.101.012128

©2020 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Interdisciplinary Physics

Authors & Affiliations

Xinli Liao1, Shaokuan Zheng2, and Guoxing Lin3,*

  • 1Chemistry Department, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, China
  • 2Department of Radiology, UMASS Medical School, Worcester, Massachusetts 01655, USA
  • 3Carlson School of Chemistry and Biochemistry, Clark University, Worcester, Massachusetts 01610, USA

  • *Corresponding author: glin@clarku.edu

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Vol. 101, Iss. 1 — January 2020

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