1H NMR pulsed gradient spin echo attenuation and water density profile analysis by magnetic resonance imaging are both used to determine the mobility of water molecules confined within a porous network of compacted kaolinite clay sample (total porosity of ∼50%). These two complementary experimental procedures efficiently probe molecular diffusion within time scales varying between milliseconds and few hours, filling the gap between the time scale of diffusion dynamics measured by traditional quasi elastic neutron scattering and through-diffusion methods. Furthermore, magnetic resonance imaging is a nondestructive investigation tool that is able to assess the effect of the local structure on the macroscopic mobility of the diffusing probe.
1H NMR pulsed gradient spin echo attenuation and water density profile analysis by magnetic resonance imaging are both used to determine the mobility of water molecules confined within a porous network of compacted kaolinite clay sample (total porosity of ∼50%). These two complementary experimental procedures efficiently probe molecular diffusion within time scales varying between milliseconds and few hours, filling the gap between the time scale of diffusion dynamics measured by traditional quasi elastic neutron scattering and through-diffusion methods. Furthermore, magnetic resonance imaging is a nondestructive investigation tool that is able to assess the effect of the local structure on the macroscopic mobility of the diffusing probe.
Clay minerals are ubiquitous
at the surface of the earth and play
important roles in a large variety of environmental applications,
including pollutant retention[1−5] and nuclear waste storing,[6,7] by exploiting their
physicochemical properties (low hydraulic conductivity,[6] large anisotropy,[8] high specific surface[9] and adsorbing
power,[1,2,4,10] ionic exchange capacity[9]). In this context, numerous studies have been performed to determine
the mobility of water molecules[9,11−22] and ions[16,22−29] confined within the complex porous network of dense clay samples.
For this purpose, quasi elastic neutron scattering[13,18,19] (QENS) and through-diffusion[17,21,28,30,31] measurements are the two complementary approaches
generally used to quantify the mobility of water molecules confined
within the clay porous network. While QENS is an ideal probe of local
water motions performed during a limited diffusion period (less than
1 ns), through-diffusion experiment probes macroscopic displacements
of confined fluids at a time scale larger than a few minutes. Because
of the multi-scale organization of clay aggregates within the dense
samples, it appears useful to investigate fluid mobility at intermediate
time scales. Such investigations are necessary to efficiently relate
the apparent macroscopic mobility of the confined fluid to the organization
of the clay sample. For this purpose, we investigate the potentialities
of the two applications of NMR, i.e., measurement of the water self-diffusion
tensor by using pulsed gradient spin echo (PGSE) attenuation[11,12,16,24,32−37] and analysis of time evolution of water density profiles by exploiting
magnetic resonance imaging[33,38] (MRI). This approach
contributes significantly to characterize the multi-scale mobility
of confined water molecules because PGSE-NMR adequately probes diffusion
times larger than 1 ms, whereas diffusion times larger than a few
seconds are easily investigated by MRI, thus filling the above-mentioned
gap between the time scales investigated by QENS and through-diffusion
experiments. Previous studies have demonstrated the applicability
of PGSE-NMR[11,12] and MRI[39,40] to investigate the mobility of water molecules within aqueous dispersions
and dense pastes of synthetic minerals. The application of the same
NMR experiments for dense clay samples is never obvious because of
the presence of iron within natural clay particles, strongly enhancing
the NMR relaxation[14] of the nuclear magnetization
pertaining to the protons of the confined water molecules. To settle
this question, we selected natural clay (kaolinite) whose composition[17] (0.039 iron per unit cell) and size distribution[8] were already characterized. Furthermore, by contrast
with other natural clays (like montmorillonite), kaolinite (like illite)
is a nonswelling clay mineral, thus avoiding the occurrence of some
interlayer porosity after saturation of the clay sample by water molecules.
As a consequence, the porous network accessible to water molecules
is limited to interparticle porosity.In this study, 1HPGSE-NMR attenuation measurement is
first used to determine the components of the tensor describing the
water self-diffusion within the water-saturated sample of kaolinite.
MRI is then used to determine the water concentration profiles after
the addition of a controlled amount of heavy water on the top of the
water-saturated clay sample. The exchange between the added heavy
water and initially confined water molecules is quantified by integrating
the water concentration profiles whose asymptotic limit may be used
to determine the porosity of the clay sample. Numerical modeling performed
by Brownian dynamics (BD)[41] is finally
used to interpret the observed exchange kinetics on the basis of the
clay sample porosity and the longitudinal component of the water self-diffusion
tensor previously measured by PGSE-NMR, thus demonstrating the agreement
between both experimental procedures.
Materials
and Methods
Sample Preparation
The kaolinite
clay sample (i.e., KGa-2 kaolinite reference from the Source Clay
Repository of The Clay Minerals Society) was used to prepare a cylindrical
compacted clay sample (diameter 6.5 mm, height 12.3 mm) for NMR measurements.
For this purpose, the original kaolinite sample was Na saturated using
three saturation cycles in a 1 mol/L NaCl solution, washed in distilled
water, and dried at room conditions. The obtained powder was then
placed within a poly(tetrafluoroethylene) (Teflon) cylinder fitting
the size of the NMR detection coil and underwent a uniaxial compression
to reach a porosity ϕ value close to ∼0.5. Information
on the chemical composition and properties of the kaolinite sample
are available in the literature.[8] Transmission
electron microscopy (TEM) images (see Figure a,b) are recorded after the dispersion of
the sample into ethanol to illustrate the size distribution of the
stacks composed of individual clay platelets. The porosity of the
dry clay sample (ϕ = 0.52) is determined by helium pycnometry,
corresponding to an average grain density of 2.75 g/cm3. The PGSE-NMR experiments are first performed with the water-saturated
clay sample. The kinetics of the water/heavy water exchange is determined
by 1H MRI profile analysis after the addition of 0.23 mL
of D2O on the top of the hydrated clay sample. The compactness
of the clay sample was obtained by uniaxial compression to reach the
same porosity (ϕ ∼ 0.5). The clay sediment is carefully
saturated by water and equilibrated during 2–3 days before
performing PGSE measurements. However, no boundary condition is applied
to the sediment after compression. As a consequence, the porosity
of the clay sample must be determined independently by helium pycnometry
for the dry sample and after hydration by MRI. Some difference is
expected to occur because no boundary is applied to restrict the swelling
of the clay sample.
Figure 1
(a, b) TEM images of the dispersed kaolinite sample at
two different
magnifications.
(a, b) TEM images of the dispersed kaolinite sample at
two different
magnifications.
1H NMR Measurements
NMR
measurements were performed using a Bruker DSX100 Bruker spectrometer
with a static field of 2.35 T and equipped with a saddle detection
coil. A typical pulse duration of 5 μs is required for transferring
the equilibrium longitudinal magnetization into the detection plane
perpendicular to the static magnetic field B0 (also called π/2 pulse). Figure illustrates the pulse sequence used to perform
the PGSE-NMR attenuation measurements.[32,33] The encoding
of transverse magnetization is performed by a pulse sequence composed
of an initial π/2 pulse used to create transverse magnetization,
a set of bipolar field gradients (duration δ, strength G) applied along any desired direction, and a final π/2
pulse to transfer back magnetization in the longitudinal direction.
After the evolution period (Δ), transverse magnetization is
refocused by using a pulse sequence similar to the encoding one, but
with opposite field gradients. NMR relaxation times are critical parameters
limiting the feasibility of this PGSE-NMR experiment. Because of the
paramagnetic impurities[17] (iron) present
in the atomic network of kaolinite, the NMR relaxation time of the
longitudinal magnetization of the confined water molecules (T1 = 0.053 s) is fifty times smaller[14] than that of bulk water (T1 = T2 ≈ 3 s). Furthermore,
the transverse relaxation time of the same confined water molecules
(T2 = 1.2 × 10–3 s) is again reduced by more than 1 order of magnitude because confinement[42−45] is responsible for large differences between the NMR relaxation
rates of liquids (T2 < T1). The purpose of the stimulated echo[32,33] used in our PGSE-NMR experiment is to transfer the transverse magnetization
encoded by the first set of pulsed gradient into the longitudinal
direction parallel to the static magnetic field B0. As illustrated in Figure , the stimulated echo allows them to probe
the mobility of the confined water molecules during roughly 150 ms
since the longitudinal magnetization becomes negligible after the
diffusion time Δmax ∼ 3T1. Another limitation arises from the time required to build
the field gradients (typically 60 μs). As a consequence, the
duration (4τ = 3.04 ms) of the coding and refocusing pulse sequences
(see Figure ) reaches
milliseconds (i.e., the order of magnitude of the transverse relaxation
rate T2), leading to important attenuation
of the NMR magnetization according to the exponential law exp(−4τ/T2) = 0.08. Finally, the intensity of the NMR
signal varies according to the relationship[32,33]where, q = γδG/π,
γ is the gyromagnetic ratio (2.6752 ×
108 rad/s for 1H), G is the
strength of the field gradient (see Figure ) and e⃗G its director, D is the self-diffusion tensor, and δ,
Δ, and τ are time delays illustrated in Figure . Since our PGSE-NMR echo attenuations
are recorded for a unique set of time delays (δ = 500 μs,
Δ = 20 ms, and τ = 760 μs), the components of the
self-diffusion tensor are obtained by fitting the attenuation of the
NMR signal measured for a set of strengths of the field gradient G according to a Gaussian propagator[33]This Gaussian
propagator of self-diffusion[33] is equivalent
to the intermediate scattering
function[46] probed by neutron scattering
experiments (QENS). The maximum resolution of spatial domains probed
by these PGSE-NMR measurements is given by the maximum strength of
the magnetic field gradient[33] (Gmax = 1.6 T/m)where, q is equivalent
to
the wave vectors probed by QENS.
Figure 2
Schematic view of the pulse sequence used
to perform pulsed gradient
spin echo (PGSE-NMR) attenuation measurements. Details on the time
delays, pulse durations, and strength of the magnetic field gradients
are given in the text (see Section ).
Schematic view of the pulse sequence used
to perform pulsed gradient
spin echo (PGSE-NMR) attenuation measurements. Details on the time
delays, pulse durations, and strength of the magnetic field gradients
are given in the text (see Section ).1H magnetic
resonance imaging is also used to study
the exchange between the initially confined water molecules and excess
bulk heavy water added to the saturated clay samples. Figure illustrates the pulse sequence
used for these MRI experiments.[33] After
an initial π/2 excitation pulse, a magnetic field gradient (noted G) is applied during the time period δ/2
along the vertical direction (O) corresponding
to the cylindrical axis of the clay sample. Inversion pulse (noted
π) is then applied and the same field gradient G is applied during the evolution time δ = 2.56
ms with a simultaneous acquisition of the NMR signal. This sequence
is selected to generate an echo of the NMR signal after the evolution
period δ/2, leading again to a noticeable attenuation (exp(−δ/(2T2)) ≈ 0.34) of the NMR signal pertaining
to the confined water molecules without significantly altering the
NMR intensity of free water (see T2 values
reported above). Our MRI measurements were performed for an evolution
period δ composed of 256 elementary time steps of 10 μs.
As the time domain is used to sample the NMR signal, the corresponding
frequency domain obtained by Fourier transform is also composed of
256 elementary frequency steps. As a consequence, the resulting longitudinal
MRI profiles are digitalized into 256 superposed sheets. To easily
investigate the water molecules located in the hydrated clay sample
(length L1 = 12.3 mm) and the amount of
added heavy water (length L2 = 7 mm),
we want to probe a total sample length of 25 mm, leading to a spatial
resolution of 97.7 μm (since resolution = 25/256 mm). This spatial
resolution corresponds to a wave vector q of 1.024
× 104 m–1 obtained by applying a
magnetic field gradient of 0.094 T/m (see eq ).
Figure 3
Schematic view of the pulse sequence used to
perform magnetic resonance
imaging (MRI) of the water concentration profiles inside the compacted
kaolinite clay sample (see text Section ).
Schematic view of the pulse sequence used to
perform magnetic resonance
imaging (MRI) of the water concentration profiles inside the compacted
kaolinite clay sample (see text Section ).
Numerical Simulations
Numerical
simulations of Brownian dynamics[41] (BD)
are used to analyze the macroscopic exchange between the water molecules
initially confined within the clay sample and the added heavy water
as investigated by profile analysis obtained by 1H MRI.
To our knowledge, determination of water diffusivity by direct analysis
of the time evolution of the water concentration profiles is not possible.
For this reason, we proceeded to numerical simulations of BD to perform
a quantitative comparison between the experimental and numerical data,
thus extending to hours the time-scale initially probed by PGSE-NMR
spectroscopy (typically a few milliseconds). For this purpose, N1 H2O molecular probes (N1 = 386 571) are uniformly distributed within an
ideal parallelepiped (longitudinal length L1 = 12.3 mm, section S1 = 13.75 mm2) in contact through its upper surface with another parallelepiped
(longitudinal length L2 = 7 mm, section S1 = 25 mm2) containing N2 D2O molecular probes (N2 = 400 000). These dimensions and water contents have
been selected to reproduce the volumetric ratios between the diffusing
spaces inside the clay sample (labeled 1) and the added bulk water
(labeled 2). The self-diffusion coefficients of both water and heavy
water molecules are set equal to the value determined by 1HPGSE-NMR attenuation measurements, whereas their values in bulk
water are set equal to 2.1 × 10–9 m2/s, in agreement with the available experimental data. Simple reflecting
conditions are applied when a molecular probe hits any wall of the
simulation cell except for the surface connecting the two independent
sub-volumes: when a probe, initially diffusing in the cell corresponding
to the clay sample (labeled 1), hits the separating surface, its transfer
to the cell labeled 2 is always considered. By contrast, a molecular
probe initially diffusing in the cell corresponding to bulk water
(labeled 2) and hitting the separating surface will be considered
to potentially transfer to the clay sample with a probability equal
to the porosity of the clay sample. Adequately formulating the condition
for accepting these potential transfers between the two sub-cells
is the only difficulty for modeling such water exchange between the
two sub-cells with different sizes, water concentrations, and mobilities.
An interesting suggestion was the use of detailed balance conditions.[47] Unfortunately, such a procedure is valid only
for describing stationary states.[47] By
contrast, our problem is typically a transient dynamical process for
which detailed balance condition becomes inadequate. For this purpose,
we selected to use a systematic control, at each step of the BD iteration,
of the water flux across the separating interface between the two
sub-cells. We simply impose that the total number of H2O and D2O molecules leaving a given sub-cell must be perfectly
compensated by the same number of H2O and D2O molecules leaving the other sub-cell. Such condition corresponds
to some extension, at the microscopic scale, of the macroscopic incompressibility
of liquid water. An equivalent procedure was already used to describe
by Brownian dynamics the ionic exchange[28] between ions confined within clay interlayers and freely diffusing
in aqueous solution.The displacement of the molecular probes
(labeled i) is described by the Langevin equation[41]where, mi and
ξi are respectively the molecular mass and friction
coefficient, and R⃗i(t) is a random force resulting from thermal collisions within the
liquid. This random force must satisfy statistical requirements: it
must be Markovian and time independent (see eq ), with zero mean (eq ), without correlation with the velocities
(eq ), and distributed
along a Gaussian law (eq )where, P(|R⃗i|) is the distribution law of the modulus of the random
displacements, k is the Boltzmann constant, and T is the temperature. Equation results from the fluctuation–dissipation theorem
ensuring the balance between the increase of the velocities induced
by the random force and its decrease resulting from the intermolecular
friction. Various algorithms have been proposed to solve the set of eqs and 5a–5d, depending on the ratio between the
friction coefficient (ξi) and the time step (Δt) selected to simulate the molecular trajectories. If the
time step is much larger than the velocity correlation time (i.e.,
ξiΔt ≫ 1), the solution
of eqs and 5a–5d becomes[41]the new random force R⃗i also satisfies Gaussian distribution
law with zero mean
and standard deviation given bywhere, Di is the
local self-diffusion coefficient of the molecular probes. We can use
this simplified equation since the time step (Δt) used to integrate eq is equal to 1 s, while the friction coefficients (ξi) are equal to 15 × 1013 and 6.55 × 1013 s–1 for confined and bulk water, respectively.
The average molecular displacements (see eq ) of the confined water molecules reach 45
μm, i.e., are compatible with the spatial resolution probed
by our MRI analysis of the water density profiles.
Results and Discussion
Figure illustrates
the results obtained by the measurements of the PGSE-NMR attenuation
of the 1H NMR signal for the water saturated sample of
kaolinite. As detailed in eq , the decrease in the relative intensity of the NMR signal
as a function of the strength of the magnetic field gradient Gi is perfectly described by a Gaussian relationship,[33] leading to the apparent water self-diffusion
coefficient along any direction Oxi of
the applied gradient Gi. This field gradient
is constructed along six non-collinear directors[48−51] noted e⃗1 = (1,0,0), e⃗2 =
(0,1,0), e⃗3 = (0,0,1), e⃗4 = (1,1,0), e⃗5 = (1,0,1), and e⃗6 = (1,1,0), where the longitudinal director e⃗3 is parallel to the cylindrical axis of the clay sample
(i.e.). The six corresponding
components of the water self-diffusion tensor are easily determined
(see Figure ) and
the principal axes describing the water mobility are identified by
tensor diagonalization.[48] A small difference
is then detected between the water self-diffusion coefficient in the
direction parallel {Dlong = 0.92 ±
0.02 × 10–9 m2/s} and perpendicular
{Dtrans = 1.05 ± 0.02 × 10–9 m2/s} to the cylinder axis which coincides
with the compression axis of the dense clay sample (see Section ). By dividing
the self-diffusion coefficient of bulk water (D0 = 2.1 × 10–9 m2/s) by its
value measured within the dense sample, we obtain an evaluation of
the tortuosity[52,53] of the clay, noted θ, i.e.,
θ = 2.28 ± 0.05 in the longitudinal direction and θ
= 2.00 ± 0.05 in the direction perpendicular to the cylinder
axis.
Figure 4
Water self-diffusion propagators measured within the saturated
clay sample. More details on the selected diffusion directors e⃗i are given in Section , leading to the components of the self-diffusion
tensor D1 = 1.041 × 10–9 m2/s, D2 = 1.062 × 10–9 m2/s, D3 =
0.918 × 10–9 m2/s, D4 = 1.067 × 10–9 m2/s, D5 = 0.991 × 10–9 m2/s, and D6 = 0.992 × 10–9 m2/s.
Water self-diffusion propagators measured within the saturated
clay sample. More details on the selected diffusion directors e⃗i are given in Section , leading to the components of the self-diffusion
tensor D1 = 1.041 × 10–9 m2/s, D2 = 1.062 × 10–9 m2/s, D3 =
0.918 × 10–9 m2/s, D4 = 1.067 × 10–9 m2/s, D5 = 0.991 × 10–9 m2/s, and D6 = 0.992 × 10–9 m2/s.It should be interesting to perform diffusion measurements
at various
time delay Δ to probe the structural properties of the porous
network.[33] As displayed in Figure , the measured self-diffusion
coefficient is independent of the time delay Δ in the range
of accessible values (i.e., between 2 and 150 ms). As a consequence,
the water self-diffusion coefficient measured by PGSE-NMR describes
the macroscopic mobility of the water molecules diffusing within the
porous network of the dense clay sediment.
Figure 5
Variations of the water
self-diffusion coefficient D3 (diffusion
along the direction O) measured within
the saturated clay sample as a function
of the time delay Δ (see the text).
Variations of the water
self-diffusion coefficient D3 (diffusion
along the direction O) measured within
the saturated clay sample as a function
of the time delay Δ (see the text).The water concentration profiles are measured by 1H
MRI after the addition of bulk heavy water on the top of the water
saturated clay sample (see Section ). Typical time evolution of the water profiles is
illustrated in Figure a. As for PGSE-NMR spectroscopy, the intensity of the NMR signals
is attenuated by the longitudinal and transverse relaxation times
of the NMR probes. Firstly, as explained in Section , because of the large difference between
their transverse relaxation times, the concentration profiles of bulk
(T2 = T1 =
3 s) and confined (T2 = 1.2 × 10–3 s) water molecules cannot be directly compared. Secondly,
the MRI signal results from the averaging of 16 scans with a recycling
delay of 0.5 s to efficiently probe the kinetics of the water exchange
between the two media. Since the longitudinal relaxation time of the
confined water molecule is short enough (T1 = 0.053 s), each scan records 100% of magnetization pertaining to
the protons from the confined water molecules. This condition is not
fulfilled by the protons from the bulk water (T1 = 3 s) whose magnetization is then saturated by this short
recycling delay. As a consequence, quantitative analysis must focus
on the relative intensity of the water concentration profiles within
the clay sample. Next problem occurs because the total size of the
sample slightly exceeds the spatial domain of complete excitation
and detection probed by the NMR coil. For this purpose, we must discard
magnetization pertaining to water molecules located at distances smaller
than 8 mm from the bottom of the detection window whose magnetization
is not fully detected. Finally, artifacts also occur at the boundary
between the two media, further excluding from the profile analysis
the contribution from water molecules located at distances smaller
than 2 mm from the interface between the clay sample and the bulk
liquid. We are not totally sure about the physical origin of the reported
artifact, already detected within dilute clay dispersions.[39] We expect that water molecules located in the
bulk phase near the upper surface of the clay sediment exhibit some
increase in their longitudinal NMR relaxation rate because of the
proximity of the paramagnetic impurities (iron) of kaolinite. As a
consequence, saturation of their magnetization is reduced with reference
to that of “free” bulk water. Another explanation could
be the contrast of the magnetic susceptibility between bulk water
and the hydrated clay sediment. Obviously, all these artifacts affecting
the experimental data are totally excluded from the numerical data,
restricting the sample area used for a direct comparison between the
data obtained by MRI NMR measurements and BD numerical simulations.
Figure 6
Time evolution
of the water concentration profiles: (a) measured
by magnetic resonance imaging after the addition of bulk heavy water
on the top of the water saturated sample and (b) obtained by numerical
simulations of Brownian dynamics (see the text).
Time evolution
of the water concentration profiles: (a) measured
by magnetic resonance imaging after the addition of bulk heavy water
on the top of the water saturated sample and (b) obtained by numerical
simulations of Brownian dynamics (see the text).Figure illustrates
the evolution of the fraction of confined water molecules obtained
by integrating the water concentration profiles between 8.3 and 13.3
mm from the bottom of the detection window. As displayed in Figure , the experimental
data are fitted by an empirical biexponential law, giving two characteristic
times {(7800 ± 200) and (39000 ± 2000) s} quantifying the
time evolution of the integrated water concentration profiles (see Figure ). These two time
scales have no physical meaning since the biexponential fit is simply
used for allowing quantitative comparison between the experimental
and numerical data. Figure also displays a long-time asymptotic limit (0.49 ± 0.01)
which may be used to evaluate the porosity (noted ϕ) of the
clay sample since it must satisfy the relationshipwhere, L1 (12.3
mm) and L2 (7 mm) are the lengths occupied
within the poly(tetrafluoroethylene) (Teflon) cylinder (see Section and Figure a) by the clay sample
and the added heavy water. The corresponding porosity (ϕ = 0.55
± 0.01) is compatible with the value measured by helium pycnometry
on the dry clay (ϕ = 0.52). This limited increase in the sample
porosity results from the swelling of the dry clay sediment since
hydration is performed without applying any boundary condition (see Section ).
Figure 7
Direct comparison
of the time evolutions of the measured and simulated
numbers of confined water molecules. Experimental and numerical data
are fitted by a biexponential law: f(t) = m1 exp(−t/m2) + (1 – m1 – m4) exp(−t/m3) + m4.
Direct comparison
of the time evolutions of the measured and simulated
numbers of confined water molecules. Experimental and numerical data
are fitted by a biexponential law: f(t) = m1 exp(−t/m2) + (1 – m1 – m4) exp(−t/m3) + m4.The initial water concentration
profile displayed in Figure a clearly exhibits a gradual
decrease in the signal intensity in the range of complete detection
of the 1H magnetization by the NMR probe, i.e., at positions
above 8.3 mm from the bottom of the detection window. Such behavior
results from a gradient of clay concentration within the compacted
sample, leading to some heterogeneity of its porosity. This heterogeneity
is the fingerprint of the sample preparation performed by uniaxial
compression of the clay powder (see Section ). To probe its impact on the water exchange
process, we performed numerical simulations of Brownian dynamics to
describe the exchange between bulk heavy water and the water molecules
confined within the perfectly homogeneous sample (see Section ). The corresponding concentration
profiles are plotted in Figure b, in good agreement with the experimental data (see Figure a). More quantitative
comparison is given by the concentration profiles integrated over
the same spatial range than the experimental data. As displayed in Figure , experimental and
simulated data exhibit fair agreement without using any fitted parameters.
Brownian dynamics simulations slightly underestimate the kinetics
of water exchange between the clay sample and the excess heavy water,
indicating a limited effect of the sample heterogeneity on the water
exchange process. That agreement also illustrates the compatibility
between 1HPGSE-NMR attenuation and MRI concentration profile
analysis to probe water mobility within dense samples of natural clays.
This agreement a posteriori validates our experimental procedure:
by carefully selecting the integration domain of the water concentration
profiles (see above), the clay sample does not necessarily need to
fit the spatial domain of complete excitation of the NMR detection
coil.Although this study concerns only experimental NMR measurements
performed for a single clay sample, we feel justified to compare the
water mobility measured by 1HPGSE-NMR within kaolinite
clay and that evaluated by HDO through diffusion[17,21,31] and PGSE-NMR[37] within porous networks of various granular materials. While PGSE-NMR
experiments directly quantify the intrinsic self-diffusion coefficient[33]D of the fluid confined within
various porous networks,[12,16,24,37,39,40,54,55] through-diffusion measurements are sensitive to the
fluid permeability of the macroscopic porous media, leading to an
effective diffusion coefficient[17,21,31]De. The corresponding intrinsic mobility
of the fluid inside the porous network may be evaluated by the simple
relationshipwhere, ϕ is the porosity of the porous
network. This approximation neglects the topological and morphological
properties of the porous media.[52,53] As a consequence, its
validity is restricted to homogeneous and isotropic porous network. Figure nevertheless exhibits
clear equivalence between the intrinsic mobility measured by both
experimental procedures, validating the use of 1HPGSE-NMR
to directly determine the intrinsic self-diffusion tensor of confined
fluids. Finally, as displayed in Figure , a simple straight line roughly reproduces
the variation of the intrinsic mobility of the fluid as a function
of the porosity of the confining network. The scaling curve displayed
in Figure totally
validates the use of 1HPGSE-NMR to directly measure the
water self-diffusion within such porous materials saturated by water
molecules.
Figure 8
Variation of the apparent water self-diffusion D within samples made of granular materials as a function of the sample
porosity ϕ.
Variation of the apparent water self-diffusion D within samples made of granular materials as a function of the sample
porosity ϕ.1H pulsed
gradient spin echo attenuation and magnetic
resonance imaging of water density profiles were shown to adequately
probe the water mobility within natural compacted clay samples. These
experimental procedures give additional information on the water mobility
within porous networks. On one hand, PGSE-NMR is able to directly
measure the various components of the tensor describing the macroscopic
equilibrium self-diffusion of water molecules within the hydrated
clay sample, by the direct determination of the corresponding self-diffusion
propagators. On the other hand, the time evolution of water concentration
profiles detected by MRI allows to investigate the kinetics of water
exchange between the water saturated clay and added heavy water. In
addition, MRI is a powerful tool to determine the impact of sample
heterogeneity on the mobility of the confined water molecules. However,
in contrast with PGSE-NMR attenuation measurements, the extraction
of quantitative data on the water self-diffusion requires a modeling
of the H2O/D2O exchange in relation to the time
evolution of the water concentration profiles within the clay samples.
Since these two complementary NMR measurements are able to investigate
dynamical processes over a broad time scale (typically between milliseconds
and hours), they lead to additional information on dynamical process
investigated by QENS or through-diffusion experiments. Although this
study concerns only water and kaolinite clay, it could be easily extended
to other molecular and ionic NMR probes diffusing within a large variety
of porous networks. Kaolinite, a nonswelling clay, was selected in
this study to probe its feasibility because the water molecules are
then localized between the clay aggregates and are easily detected
by NMR spectroscopy. The same behavior is expected to occur for other
nonswelling clays like illite. By contrast, in the case of swelling
clays like montmorillonite, the water molecules localized within the
interlamellar space between the individual clay platelets cannot be
detected by PGSE or MRI NMR spectroscopy. A strong confinement within
such interlamellar space[42,45] is indeed expected
to enhance the transverse NMR relaxation rate of the water molecules,[9,43] prohibiting their detection by PGSE and MRI. By contrast, we are
quite sure to easily measure, by the same NMR procedure, the mobility
of the water molecules located between the aggregates of montmorillonite
platelets. In the near future we plan to measure, by the same NMR
procedure, the mobility of water molecules and added ions (cations
and anions) diffusing within the porous network of dense sediments
resulting from the compression of such swelling clays.