Zielinski Lukasz J
Schlumberger-Doll Research, Ridgefield, Connecticut 06877-4108, USA.
J Chem Phys. 2004 Jul 1;121(1):352-61. doi: 10.1063/1.1756873.
We consider a system of spins diffusing in a static inhomogeneous (nonuniform-gradient) magnetic field B in a restricted geometry and in the presence of surface relaxation. We show that the short-time diffusional decay of nuclear magnetization is controlled by the field scattering kernel F(t) identical with B(t)-B(0), which is a measure of the average field inhomogeneity sampled by the spins in time t and does not depend on the particular sequence of radio-frequency pulses used. Magnetization in arbitrary sequences can be straightforwardly computed by evaluating elementary integrals of F(t). Diffusion takes place while the field is on, so that the spins precess as they diffuse, in contrast to the simpler problem of purely classical diffusion considered in [P. P. Mitra, P. N. Sen, and L. M. Schwartz, Phys. Rev. B 47, 8565 (1993)] which is applicable only to the ideal pulsed-field gradient experiment. We compute the short-time asymptotic form of F(t) and find that it depends on the surface-to-volume ratio (S/V) of the pore space as well as on the average of the gradients over the bounding surface. In a system with nonuniform gradients that vary faster near the surface than in the bulk, as for internal susceptibility fields, this gradient surface average may be much larger than the gradients in the bulk, significantly enhancing the apparent S/V. We discuss the application of our results to the widely used Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence as well as proposing a modification of it, which we term "padded" CPMG, that may be preferable in systems with significant surface relaxation. We indicate how each sequence can be used to probe the internal fields.
我们考虑一个自旋系统，该系统在受限几何结构中且存在表面弛豫的情况下，在静态非均匀（非均匀梯度）磁场(B)中扩散。我们表明，核磁化强度的短时间扩散衰减由与([B(t) - B(0)]^2)相同的场散射核(F(t))控制，(F(t))是自旋在时间(t)内采样的平均场不均匀性的量度，并且不依赖于所使用的特定射频脉冲序列。通过评估(F(t))的基本积分，可以直接计算任意序列中的磁化强度。扩散发生在场开启时，因此自旋在扩散时会进动，这与[P. P. Mitra, P. N. Sen, and L. M. Schwartz, Phys. Rev. B 47, 8565 (1993)]中考虑的更简单的纯经典扩散问题形成对比，后者仅适用于理想的脉冲场梯度实验。我们计算了(F(t))的短时间渐近形式，发现它取决于孔隙空间的表面积与体积比（(S/V)）以及边界表面上梯度的平均值。在一个非均匀梯度在表面附近比在主体中变化更快的系统中，如内部磁化率场的情况，这种梯度表面平均值可能比主体中的梯度大得多，从而显著提高了表观(S/V)。我们讨论了我们的结果在广泛使用的 Carr - Purcell - Meiboom - Gill（CPMG）脉冲序列中的应用，并提出了对它的一种修改，我们称之为“填充”CPMG，在具有显著表面弛豫的系统中可能更可取。我们指出了每个序列如何用于探测内部场。
