We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[−(bD)^α], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch–Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4000 s mm⁻²). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.

我们报告了使用脉冲场梯度 (PFG) 核磁共振 (NMR) 观察到的亲水性 Sephadex 凝胶中异常水扩散的出现。使用带有自制射频鞍形线圈的 Varian 14.1 Tesla 成像系统收集 NMR 扩散数据。数据的分数阶分析用于表征凝胶中的异质性，用于在这种受限环境中的水扩散动力学。最近对异常扩散的几项研究使用拉伸指数函数来模拟 NMR 信号的衰减，即 exp[−( bD ) ^α ]，其中D是表观扩散常数，b是由实验条件确定的（梯度脉冲间隔） , 持续时间和强度), 和α是结构复杂性的度量。在这项工作中，我们考虑了一种不同的情况，其中 Bloch-Torrey 方程中的空间拉普拉斯算子通过复杂性参数β、空间常数μ和扩散系数D推广到扩散率的分数阶模型。这种处理恢复到整数阶情况的经典结果。分数阶衰减模型适合于一系列b 值(0 <  b  < 4000 s mm ^-2 )的扩散加权信号衰减。在整个b值范围内，参数β、μ和D，被发现与凝胶结构的孔隙率和弯曲度相关。