투고논문

Abstract The Stejskal–Tanner (ST) equation enables quantitative analysis of molecular diffusion in diffusion-ordered spectroscopy (DOSY), yet its derivation becomes increasingly complex when extended to modern pulse sequences especially under experimental conditions such as convection. Here, we present a systematic theoretical framework to explain and derive the ST equation. Central to this work is a Mathematica-based implementation of the derivation, which decomposes the calculation into three generalizable steps applicable to pulsed-gradient spin echo (PGSE), pulsed-gradient stimulated echo (PGSTE), bipolar pulse pair stimulated echo (BPP-STE), and convection-compensated BPP-double STE sequences. Fully executable Mathematica code is provided for each sequence, enabling rapid and reproducible derivation of the corresponding gradient-dependent attenuation expressions. This work aims to provide both conceptual clarity and computational codes, supporting accurate determination of diffusion coefficients across a wide range of DOSY experiments.

Keywords Diffusion-ordered spectroscopy (DOSY), Stejskal-Tanner (ST) equation, Mathematica codes

* Address correspondence to: Jung Ho Lee and Jongchan Lee, Department of Chemistry, Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul, 08826, Republic of Korea, Tel: 82-2-880-4363; E-mail: jungho.lee@snu.ac.kr, sildaria55@gmail.com