Model for the interpretation of nuclear magnetic resonance relaxometry of hydrated porous silicate materials

Nuclear magnetic resonance (NMR) relaxation experimentation is an effective technique for probing the dynamics of proton spins in porous media, but interpretation requires the application of appropriate spin-diffusion models. Molecular dynamics (MD) simulations of porous silicate-based systems containing a quasi-two-dimensional water-filled pore are presented. The MD simulations suggest that the residency time of the water on the pore surface is in the range 0.03–12 ns, typically 2–5 orders of magnitude less than values determined from fits to experimental NMR measurements using the established surface-layer (SL) diffusion models of Korb and co-workers [Phys. Rev. E 56, 1934 (1997)]. Instead, MD identifies four distinct water layers in a tobermorite-based pore containing surface ${\mathrm{Ca}}^{2+}$ ions. Three highly structured water layers exist within 1 nm of the surface and the central region of the pore contains a homogeneous region of bulklike water. These regions are referred to as layer 1 and 2 (L1, L2), transition layer (TL), and bulk (B), respectively. Guided by the MD simulations, a two-layer (2L) spin-diffusion NMR relaxation model is proposed comprising two two-dimensional layers of slow- and fast-moving water associated with L2 and layers TL+B, respectively. The 2L model provides an improved fit to NMR relaxation times obtained from cementitious material compared to the SL model, yields diffusion correlation times in the range 18–75 ns and 28–40 ps in good agreement with MD, and resolves the surface residency time discrepancy. The 2L model, coupled with NMR relaxation experimentation, provides a simple yet powerful method of characterizing the dynamical properties of proton-bearing porous silicate-based systems such as porous glasses, cementitious materials, and oil-bearing rocks.

Figure 1

A schematic representation of the surface layer (SL) model presented by Korb and co-workers [3, 4]. Water diffuses with a correlation time ${\tau }_m$ in the surface layer of a pore containing a dilute concentration of ${\text{Fe}}^{3+}$ paramagnetic impurities. Water desorbs into the pore bulk with a characteristic time ${\tau }_s$ and ceases to contribute to the dipolar relaxation thereafter. $\delta \approx 0.27$ nm is the approximate distance of closest approach of a water proton to a ${\text{Fe}}^{3+}$ impurity.

Figure 2

A schematic diagram of a 2D layer containing diffusing $I$ spins which interact with static paramagnetic impurities $(S$ spins) of areal density ${\sigma }_{\mathit{S}}$. The separation of the two layers is $d$.

Figure 3

A simplified image taken from molecular dynamics model MD4 showing a pore with water confined in the $z$ direction by modified tobermorite 14 Å surfaces. The Si atoms are fixed, the surface oxygen atoms are tethered, and ${\text{Ca}}^{2+}$ ions are present near the surfaces and are mobile.

Figure 4

The particle density is presented as a function of $z$ for the surface silicon atoms (gray dashed line), calcium in the crystal and pore (black dashed line), and the water-oxygen (black solid line) and the water-hydrogen (gray solid line) atoms in the pore. The water exhibits four layers labeled L1 (layer 1), L2 (layer 2), transition layer (TL), and bulk (B).

Figure 5

The probability density of the water-oxygen atoms (light-gray shading) and calcium ions (dark-gray shading) in layer L2 for model MD4.

Figure 6

A schematic representation of the two-layer (2L) model. Water diffuses with a correlation time ${\tau }_{L2}$ in layer L2 and ${\tau }_{\mathrm{Beq}}$ in an equivalent layer which is representative of the layers TL+B combined. The shading illustrates the increasing contribution to the dipolar correlation function $G\left(t\right)$ of spins in the bulk due to the interaction with surface paramagnetic impurities.

Figure 7

The quality-of-fit (QoF) parameter (see text) is plotted as a function of ${\tau }_{L2}$ and ${\tau }_{\mathrm{Beq}}$. The black squares indicate QoF $<145$, the dark-gray squares indicate QoF in the range 146–180, and the light-gray squares indicate QoF $>180$. The white lines contain results which simultaneously have a QoF $<180$ and a ratio $T_2/T_2$ in the range 0.25–0.30.

Figure 8

$T^{-1}$ is plotted as a function of NMR frequency. The experimental data $(\square )$ are taken from Barberon and co-workers [5] for a hydrated mortar. The fit obtained using the SL model (dashed line) and 2L model (solid line) are shown.