Nuclear magnetic resonance dephasing effects in a spherical pore with a magnetic dipolar field

Abstract

The NMR dephasing behavior of the nuclear spins of a fluid confined in a porous material can be investigated by Hahn spin echoes. Previous experimental results on water in a magnetically doped clay have shown a nonmonoexponentially decaying magnetization, which can be understood neither by the known dephasing rate of freely diffusing spins in a uniform gradient nor by spins diffusing in a restricted geometry. For a better understanding of NMR measurements on these systems, a systematic survey was performed of the various length scales that are involved. The standard length scales for the situation of a uniform gradient are diffusing length, structure length, and dephasing length. We show that for a nonuniform gradient, a new length scale has to be introduced: the magnetic-field curvature length. When a particle diffuses less than this length scale, it experiences a local uniform gradient. In that case the spin-echo decay can be described by the so-called local gradient approximation ͑LGA͒. When a particle diffuses over a longer distance than the structure length, the spin-echo decay can be described by the motional averaging regime. For both regimes, scaling laws are derived. In this paper, a random-walk model is used to simulate the dephasing effect of diffusing spins in a spherical pore in the presence of a magnetic dipole field. By varying the dipole magnitude, situations can be created in which the dephasing behavior scales according to the motional averaging regime or according to the LGA regime, for certain ranges of echo times. Two model systems are investigated: a spherical pore in the vicinity of a magnetic point dipole and a spherical pore adjacent to a magnetic dipolar grain of the same size as the pore. The simulated magnetization decay curves of both model systems confirm the scaling laws. The LGA, characterized by a nonmonoexponential magnetization decay, is also investigated by calculating the spatially resolved magnetization in the pore. For this regime, the magnetization is found to be inhomogeneously distributed within the pore, whereas it is homogeneously distributed in the motional averaging regime.

Mobile single-sided NMR

“…As the moisture content of the sensitive volume inside objects with protonbearing fluids can most easily be quantified just by the amplitude of the echo envelope, or equivalently by the integral of the relaxation time distribution function, the detection and quantification of moisture content in diverse products by dedicated NMR sensors was rapidly developed [18][19][20][21][22][23][24]27,124,128,129,[139][140][141]269,583,586]. However, surface relaxation of fluids in pores and diffusion in internal gradients of porous media provide a wealth of information that can be probed with a variety of relaxation, diffusion and correlation experiments (Section 3) and modeled by analytical and numerical methods [587][588][589][590]. The low magnetic fields of mobile NMR sensors alleviate signal distortions from diffusion in background gradients, and low-gradient sensors with a sweet spot are preferred for analysis of fluid-filled porous media [185,208,223,224,226,229], unless diffusion itself is to be measured [25,314,336,[372][373][374].…”

Effects of superparamagnetic iron oxide nanoparticles on the longitudinal and transverse relaxation of hyperpolarized xenon gas

“…In this case, the dephasing length, l g , is expected to acquire a spatial dependence, and as previously described by Valckenborg, et al [30], a fourth characteristic length scale can be introduced: the magnetic-field curvature length. The magnetic-field curvature length, l B , is a measure of the non-linearity of the magnetic field gradient and is defined by [30]: lB(x)=|g(x)C(x)|, where g ( x ) is the gradient and C ( x ) is the curvature of the local magnetic field. When this length scale is larger than l g , the spins do not experience the non-linearity of the gradient and the above description of the magnetization decay still holds.…”

“…When this length scale is larger than l g , the spins do not experience the non-linearity of the gradient and the above description of the magnetization decay still holds. However, when l B is comparable to the local l g , the description of the magnetization decay becomes more complicated [30].…”

Diffusion tensor imaging to study anisotropy in a particular porous system: The trabecular bone network

“…4(c), (e) and (d), (f) respectively, diffusion weighted images along x, y, z, xy, yz, xz, directions were acquired by means of PGSTE sequence with d ¼ 2 ms, TE ¼ 12:1 ms, TR ¼ 3 s, slice thickness equal to 2.5 mm and 128 Â 128 This is because internal field gradients [1] (which depend on the pore geometry, on susceptibility contrast not uniform in the pore space) and diffusion gradients vectorial sum, give rise to a stronger resulting diffusion gradient. The major effect is the reduction the effective pore size l s to an apparent pore size which could be assumed as the dephasing length l G [28,29] …”