论文标题
通过有效扩散方程来描述NMR松弛
Describe NMR relaxation by effective diffusion equation
论文作者
论文摘要
本文提出了一种有效的扩散方程方法，以分析核磁共振（NMR）松弛。 NMR弛豫是一种自旋系统恢复过程，其中自旋系统的演变受哈密顿人（例如偶极耦合）引起的随机场的影响。磁化的演变可以视为通过正常或分数扩散方程描述的相空间中的随机步行。基于这些相扩散方程，可以在分析受任意随机场影响的弛豫分析中以及通过偶极耦合的样子和与旋转不同的偶极耦合进行了例证。所获得的理论结果与文献中报告的结果一致。此外，从Mittag-Leffler函数基于的时间相关函数获得的异常弛豫表达可以成功地拟合PIB和头对交联（propylene）（HHPP）（HHPP）的聚异生（PIB）的先前报道的13C T1 NMR实验数据（PIB）。此外，提出的阶段扩散方法提供了一种直观的解释NMR松弛的方法，尤其是对于分数NMR松弛，这仍然是通过可用的理论方法来解释的挑战。本文提供了有关NMR和磁共振成像（MRI）弛豫实验的更多见解。
This paper proposes an effective diffusion equation method to analyze nuclear magnetic resonance (NMR) relaxation. NMR relaxation is a spin system recovery process, where the evolution of the spin system is affected by the random field due to Hamiltonians, such as dipolar couplings. The evolution of magnetization can be treated as a random walk in phase space described either by a normal or fractional phase diffusion equation. Based on these phase diffusion equations, the NMR relaxation rates and equations can be obtained, exemplified in the analysis of relaxations affected by an arbitrary random field, and by dipolar coupling for both like and unlike spins. The obtained theoretical results are consistent with the reported results in the literature. Additionally, the anomalous relaxation expression obtained from the Mittag-Leffler function based time correlation function can successfully fit the previously reported 13C T1 NMR experimental data of polyisobutylene (PIB) in the blend of PIB and head-to-head poly(propylene) (hhPP). Furthermore, the proposed phase diffusion approach provides an intuitive way to interpret NMR relaxation, particularly for the fractional NMR relaxation, which is still a challenge to explain by the available theoretical methods. The paper provides additional insights into NMR and magnetic resonance imaging (MRI) relaxation experiments.
