This paper employs the general time-space fractional diffusion equation {0 < α, β ≤ 2} to derive a correlation time function for analyzing nuclear magnetic resonance (NMR) relaxation. Both the anomalous rotational and translational diffusion are treated. NMR relaxation time affected by various Hamilton interactions such as dipolar or quadrupolar couplings can be calculated from the obtained Mittag-Leffler type time correlation and their corresponded spectral density functions. Additionally, to verify the results, the theoretical expressions are applied to fit reported experimental data of NMR quadrupolar coupling relaxation of head-to-head poly(propylene) (hhPP) in a polymer blend. The fitting is excellent and more convenient than the fitting utilising the traditional modified Kohlrausch-Williams-Watts (KWW) formalism. Further, it is found that the temperature dependence behavior of the segmental dynamics in anomalous diffusion may obey a different Vogel-Tamman-Fulcher (VTF) expression. The paper proposes new, general formalisms for analyzing various NMR relaxation experiments in macromolecular systems.

本文采用一般时空分数扩散方程{0 <  α，β ≤2}即可得出用于分析核磁共振（NMR）弛豫的相关时间函数。异常旋转扩散和平移扩散均得到处理。NMR弛豫时间受各种汉密尔顿相互作用（如偶极或四极偶合）的影响，可以从获得的Mittag-Leffler型时间相关性及其对应的光谱密度函数中进行计算。另外，为了验证结果，将理论表达式应用于拟合报道的聚合物共混物中头对头聚丙烯（hhPP）的NMR四极偶联弛豫的实验数据。与使用传统的改进的Kohlrausch-Williams-Watts（KWW）形式主义的配件相比，该配件非常出色且更加方便。进一步，发现异常扩散中分段动力学的温度依赖性行为可能服从不同的Vogel-Tamman-Fulcher（VTF）表达。本文提出了一种新的通用形式主义，用于分析大分子系统中的各种NMR弛豫实验。