Relation between T 2 and pore size

Once the underlying distribution of relaxation times is found, the model described in Eq.

5.5 can be used to relate the relaxation time distribution to the pore size distribution when the relaxivity ρ is known. The relaxivity can be derived by analyzing the relaxation times of a set of porous samples of the same material with known pore sizes. The porous systems used for such a calibration are VitraPOR glass filter discs (ROBU Glasfilterger¨ate GmbH, Germany) (see section 5.1.3). Because the relaxivity depends on the surface characteristics of the sample, the calibration will only be valid for systems with similar chemical surface properties. The chemical composition of the VitraPOR filter glasses (as listed in the product specifications) is given in table 5.3.

Table 5.3: Chemical composition of the VitraPOR glass filters

Element % by weight

Silica (SiO2) 80.60 Boric oxide (B₂O₃) 12.60 Sodium oxide (Na₂O) 4.20 Alumina (Al2O3) 2.20 Iron oxide (Fe₂O₃) 0.40 Calcium oxide (CaO) 0.10 Magnesium oxide (MgO) 0.05

Chlorine (Cl) 0.10

Because small amounts of paramagnetic impurities, like Mn²⁺ and Fe³⁺, can be very effective relaxants, it is very important to clean the glass filters before measuring. The effect of three different cleaning procedures was tested.

Initially the filters were cleaned several times with deionised water.

The second cleaning procedure was based on an exchange reaction. Appelo and Postma [1999] showed that Cs⁺ has excellent exchange properties for a broad range of ions on the surface of soil particles. Since the chemical composition of soil is relatively similar to the VitraPOR glass filters (both exist mainly out of SiO₂), Cs⁺ is also expected to be able to exchange the paramagnetic ions absorbed on the surfaces of the filters. The filter discs were immersed in a solution of 0.5 M CsCl for a period of about one week.

Afterwards the filters were washed repeatedly with deionised water.

The third cleaning procedure was based on the procedure described in Holly et al. [1998].

The samples were first immersed in a acid solution of 50 % concentrated H₂SO₄ and 50

% concentrated HNO3 for a 24 h period. To ensure that the acid fills all the pores, the immersed sample is placed in a vacuum three times for 2 min during this 24 h period.

After the 24 h immersion period the acid is decanted. Ten successive washing cycles with distilled water, each having a vacuum established several times, ensure that all the remaining acid is washed out. The above process is repeated two times.

From those three methods the third one is of course the most aggressive and can only be applied on inert systems. This method is not applicable to natural systems such as soil samples because the concentrated acids will influence the chemical and physical structure and therefore change the characteristics of the pores. Deionised water and CsCl however, will not change the pore characteristics and can be used for sensitive systems where concentrated acids would affect the pore surfaces.

To measure the relaxation times a stack of seven cleaned filters were saturated with deionized water and sealed with Parafilm^TM to prevent evaporation. No weight loss could be detected after a few days. The transversal relaxation time distribution was determined using the BRD method (see section 4.1.7) where the optimal value for the regularization parameter was determined by the S-curve method (see section 4.1.6). TheT₂ distributions for the six different filters cleaned with the mixture of concentrated H2SO4 and HNO3 are displayed in figure 5.9.

Because all the filters are mono-disperse and have a relatively narrow pore size distribution, the FID envelopes of the samples can be in a first approximation fitted mono-exponentially.

The value obtained by this fit corresponds with the center of the peaks in figure 5.9. The results of the mono-exponential fit for all filters are given in table 5.4 as well as the maximum values for the distribution of relaxation times for the acid cleaned filters.

Applying Eq. 5.6 and assuming spherical pores (α = 3) leads to a relationship between the pore size and the transversal relaxation times depending on the bulk relaxation time (T_2,bulk) and surface relaxivity (ρ) and is displayed in figure 5.10 for the different cleaning procedures.

The values for the two parameters are given in table 5.5.

T₂ (ms)

Amplitude(a.u.)

1.0 - 1.6μm 4.0 - 5.5μm 10 - 16 μm 16 - 40 μm 40 - 60 μm 100 - 160μm

100 1000

0 0.2 0.4 0.6 0.8 1

Figure 5.9: T2 distribution for all VitraPOR glass filters cleaned with concentrated H2SO4 and HNO3.

Table 5.4: Mono-exponential transversal relaxation times of water filled in VitraPOR glass filters after cleaning

Porosity Nominal pore T₂ (s) after cleaning with

size (μm) deionised H₂O 0.5 M CsCl concentrated acid mono-exp. mono-exp. mono-exp. multi-exp.

(peak max.)

1 100 - 160 0.840 0.890 1.118 1.081

C 40 - 60 0.810 0.894 1.020 1.081

3 16 - 40 0.720 0.730 0.980 0.961

4 10 - 16 0.610 0.627 0.833 0.760

F 4 - 5.5 0.450 0.471 0.533 0.535

5 1.0 - 1.6 0.175 0.208 0.224 0.209

Table 5.5: Fit parameters for the VitraPOR glass filters Cleaning method T_2,bulk (s) ρ (μm/s)

deionised H₂O 0.89±0.16 1.97±0.20 0.5 M CsCl 0.89±0.15 1.60±0.19 conc. acid 1.18±0.05 1.56±0.04

The values of the relaxivity parameter show its dependence on the cleaning procedure. The method that removes the most amount of impurities (cleaning with concentrated acid) leads

Pore size (μm) T2(s)

1 10 100 1000

0 0.2 0.4 0.6 0.8 1 1.2 1.4

H2O acid CsCl

Figure 5.10: T2 in function of the pore size for VitraPOR glass filters

to the lowest surface relaxivity. This dependence shows the strong effect of small amounts of paramagnetic impurities. In natural systems such as soil with relatively large amounts of ferromagnetic substances, the relaxivity will increase drastically.

Also the bulk relaxation time seems to depend on the cleaning procedure. Even after cleaning with concentrated acid, the bulk value does not reach the value for free water (≈1.8 s). To separate the bulk value for fluids confined in porous media from the bulk value of unconfined free fluids, we call the former thebulk like relaxation time. For the longitudinal relaxation, the bulk like relaxation time is also smaller as the bulk longitudinal relaxation time at low frequencies (see section 5.2.2). Mattea et al. [2004] explained the difference between both relaxation times by the fact that the rotational diffusion could be affected by the confinement even if the molecules are not directly adsorbed.

TheT2values for the acid cleaned filter glasses are only moderately smaller than theT1 values (see section 5.2.2), indicating that the additional relaxation processes that play a role in the transversal relaxation such as the dephasing of the magnetization due to the external and internal inhomogeneity do not have a major contribution in the overall relaxation processes after the cleaning procedure. The minor effect of the external inhomogeneity is not surprising because of the excellent homogeneity of the Earth’s magnetic field and the extra measures that are taken to compensate the disturbances of the measuring field in the laboratory (see section 3.4.1.3). However, the internal magnetic gradients can not be compensated in the measurement method used in this work, but the strength of those internal inhomogeneities will depend on both the field strength and the difference in susceptibility between the pore fluid and the surface (see section 3.2). A comparison of theT1 andT2values for the VitraPOR glasses (T_2,bulk ≈1.2 s,T_1,bulk >1.6 s) indicates that in the Earth’s magnetic field, the effect

of the internal gradients does not play a major role.

Also the relaxivity depends on the cleaning procedure. The strongest cleaning results in the lowest relaxivity parameter. This is not surprising since the cleaning removes the strong relaxing paramagnetic ions from the particle surfaces. From both the changes in relaxation time and relaxivity parameter, it can be concluded that the concentrated acid is the most effective cleaning agent.