液体NMR中多平板间多量子相干受限扩散的有限差分模拟

Finite Difference Simulation of Restricted-diffusion Behaviors of Multiple-quantum Coherences Between Multiple Parallel Plates in Liquid NMR

由于液体分子自扩散参与了几乎所有的化学反应,且核磁共振(NMR)是当前唯一可用于提供关于分子在一个相当于生物细胞尺度单元内的位移信息的非侵害性方法,扩散相关的NMR研究更是引起了极大的重视.为了研究复杂系统中的多量子相干受限扩散行为,将单一平板间多量子相干受限扩散理论扩展到间距等概率分布和间距正态分布的多平板间多量子相干受限扩散,并利用积算符矩阵、非线性Bloch方程和有限差分相结合的方法进行模拟,得出了多平板间多量子相干受限扩散信号衰减随孔径变化范围、高斯因子的变化规律.模拟结果与理论预测吻合,验证了理论表述的正确性,从而可以通过回波信号衰减曲线形状了解样品中平板间距大致的变化范围和分布规律.本研究可扩展到各种复杂的脉冲序列及多自旋体系.

Since diffusion is responsible for all chemical reactions,and NMR is the only available non-invasive method that provides information of molecular displacements in a spatial scale comparable to cell dimensions of biological systems, research attaches very importance to diffusion behaviors. For studying restricted-diffusion behavior of multiple-quantum coherences （MQCs） in complex systems in Liquid NMR,in this paper ,the restricted-diffusion theory of MQCs between two parallel plates was extended to between multiple parallel plates with equiprobable and Gauss distributing distances. The method of finite difference was used to simulate the NMR signal attenuation due to such restricted-diffusions in combination with the product operator matrix and non-linear Bloch equations. The simulation results are coincident with theoretical predictions,thus verifying the correctness of our theoretical deduction. It also shows the regularity of MQC signal attenuation with the variation of distance distributing range and Gauss factor,which can be used to determine rough distance distribution of unknown system. The research can be further extended to more complicated pulse sequences and multiple-spin systems.