Nuclear magnetic resonance relaxation and diffusion in the presence of internal gradients: The effect of magnetic field strength

Abstract

It is known that internal magnetic field gradients in porous materials, caused by susceptibility differences at the solid-fluid interfaces, alter the observed effective Nuclear Magnetic Resonance transverse relaxation times T2,eff. The internal gradients scale with the strength of the static background magnetic field B0. Here, we acquire data at various magnitudes of B0 to observe the influence of internal gradients on T2-T2 exchange measurements; the theory discussed and observations made are applicable to any T2-T2 analysis of heterogeneous materials. At high magnetic field strengths, it is possible to observe diffusive exchange between regions of local internal gradient extrema within individual pores. Therefore, the observed exchange pathways are not associated with pore-to-pore exchange. Understanding the significance of internal gradients in transverse relaxation measurements is critical to interpreting these results. We present the example of water in porous sandstone rock and offer a guideline to determine whether an observed T2,eff relaxation time distribution reflects the pore size distribution for a given susceptibility contrast (magnetic field strength) and spin echo separation. More generally, we confirm that for porous materials T1 provides a better indication of the pore size distribution than T2,eff at high magnetic field strengths (B0>1 T), and demonstrate the data analysis necessary to validate pore size interpretations of T2,eff measurements.

Monitoring the size evolution of capillary pores in cement paste during the early hydration via diffusion in internal gradients

“…For longer hydration times (8 h in Fig. 2d) when the molecules experience the restricted geometry the short time diffusion condition is not satisfied and the motional averaging regime is reached [20,31,32].…”

“…A comprehensive discussion about the effects of diffusion through internal gradients on relaxation measurements in different diffusion regimes can be found in Refs. [31,32]. Note that in the short time limit condition the term 1:42ðS=VÞ ffiffiffiffiffiffiffiffi ffi D 0 τ p bb1 and therefore the effects of the surface are too small to be detected.…”

“…(2) is strictly valid only in the so called short time limit when diffusion length during τ intervals is much smaller both than the structural length of the sample and the dephasing length defined by the distance a tagged molecule must diffuse in order to dephase by π radians [26,[30][31][32]. Depending on the pore size, the strength of the internal gradients and the length of τ intervals, the interpretation of relaxation data can be done in the so called motional averaging regime or in the localization regime.…”

Persistence of slow fluctuations in the overdoped regime ofBa(Fe1−xRhx)2As2super

“…Given the inhomogeneous nature of the electronic texture [34,35], an internal magnetic field gradient ∇B could originate from a spatial inhomogeneity of the spin susceptibility ∆χ or, equivalently, of the local magnetization ∆χH [36,37]. Hence, ∇B ∆χH/2a, where 2a defines a typical domain size [36].…”

Persistence of slow fluctuations in the overdoped regime of Ba(Fe_1-xRh_x)₂As₂ superconductors

“…Given the inhomogeneous nature of the electronic texture [33,34], an internal magnetic field gradient ∇B could originate from a spatial inhomogeneity of the spin susceptibility χ or, equivalently, of the local magnetization χ H [35,36]. Hence, ∇B χ H/2a, where 2a defines a typical domain size [35].…”