2.1. Results for MCM-41
In Figure 3
, four types of lines can be seen, the intensities of which change as a function of the decreasing water concentration traced in the range 96–0.72%. For the initial maximum concentration of 96%, we distinguished the following contributions in the spectrum: IV—free water around 2000 ms, III—inter water at ~100 ms, II—intra pore water at ~20 ms, and at around 0.06 ms, we had OH groups, which were better visible for lower concentrations.
With drying, the contribution from free water IV noticeably and quickly decreased, and from water inter III, it was relatively slower. It can be expected that the line from water intra II in the pores will begin to disappear when the outer layers are completely removed (i.e., at the latest). Free water IV disappeared around 24% and the line from water inter III completely overlapped that of the water intra II line in pores at a concentration of 53%. This conglomerate of lines II + III, however, loses its intensity successively further, as the water concentration decreases, and it manifests itself essentially by narrowing its width in the T2 dimension.
Parallel to the effect of intensity decrease, there is a visible drift of the center of gravity of the complex line II + III toward the shorter T2. This drift does not correspond to the actual translation and in this sense is apparent as it can be seen that the left border of the line remained stationary in a wide range of concentrations, which suggests that the component with a shorter T2 in the observed sum remains constant in this range or changes little. Therefore, the only cause of the apparent maximum drift seems to be the change in component intensity with a longer T2. Altogether, this corresponds to common-sense intuition that water is removed from the sample in a specific order, starting with the geometrically outermost (and perhaps less bound) layers, which could be, for example, a water inter III layer or free water IV as a marker on the surface. On the basis of further analysis, we will argue that this intuition, while essentially correct, is not entirely accurate in this case.
Due to the overall decrease in water concentration, individual signals in the spectral series also decrease, correspondingly reducing the SNR. The consequences of this fact can be observed independently in the form of increased values of the regularization parameter with a decrease in SNR, found in our analysis for each of the spectra separately using the L-Curve methodology (Figure A1
, Appendix A
). Such behavior is expected and consistent with ILT properties, and its observation allowed us to control the consistency of the analysis. The decrease in SNR ultimately results in substantial line broadening, an effect that is fundamental to the ILT and is opposite to that caused by water removal. It is noticeable in our spectra, especially at lower concentrations from the value of about 7%, but its direct influence was only a broadening of the spectrum, without affecting the intensity of its individual components, as presented in Table 1
or Table 2
In the immediate vicinity of the value of 0.06 ms, there was a signal from strongly bound silanol OH groups, which is a separate problem that has already been studied using 2D relaxometry elsewhere [2
]. It is also the area of possible ILT artifacts due to the time tE
used in the measurements and, due to this value itself, limits the effectiveness of the analysis in this area. As can be seen from Table 1
and Table 2
, the intensity of OH I with a change in water concentration slightly oscillated around small values for no apparent reason, which we attributed to the instability of ILT in this area superimposed on a constant and small value of the real signal. This behavior is systematic over the entire range of water concentrations, with the exception of the first two spectra for the strongest signals at the highest concentration, which dominate the other contributions’ intensities for longer T2
times. The signal mentioned does not have any influence on the results of this work, nor is it directly related to its topic, therefore we only note here and hereafter its presence, origin, and behavior in the spectra. The spectrum even extends down to 0.02 ms, which is the result of signal extrapolation using ILT in the sense of fitting procedure.
The change in the width of a complex line II + III in the ILT spectrum is one of the manifestations of the change in its intensity and this fact, combined with the basic knowledge for both samples, was used to plot the evolution of the components as a function of hydration in Figure 5
. It follows from the characteristics provided that the pore diameters, although different, are of the same order in both samples. However, they essentially differed in the size distribution of the particles themselves, which are clusters of nanoparticles. The size distribution of these clusters for MCM-41 varied from very small 0.1 µm to the order of magnitude larger (1 µm), while for SBA-15, it remained on the same order of magnitude of 1–2 µm (see Figure 1
). This created more variations in the water inter III distribution for MCM-41 and led to significantly different spectral line widths compared to SBA-15 in the state of full saturation. Such differences can actually be observed in the T2
spectra in Figure 3
and Figure 4
. On the other hand, we know that both MCM-41 and SBA-15 have comparable pore sizes and similar pore dispersion, so for water intra II there were similar widths of spectral lines at similar T2
′s. The above premise makes it easy to find the saturation value at which the complex line II + III is devoid of its water inter III component. This is roughly the first saturation toward its decreasing values at which the lines’ widths for both samples are comparable at similar T2
. The spectra for which this condition holds are shown in Figure 7
: at a concentration of 14% for MCM‑41 and 5.9% for SBA-15, these are spectra of almost identical shape and line width. Thus, starting with the saturations mentioned toward their decreasing values, we dealt only with water intra II in the pores in both samples, respectively.
In light of the above, we know that the water inter III vanishing point for MCM‑41 is somewhere between a saturation of 14% and 24%, and we can find the respective signal value for water intra II by interpolation, marked by the square in Figure 5
. It is worth noting that the signal at this point does not differ much from its value when the sample is fully saturated, and also when the lines are still split at 77%, we can conclude that the water intra II leaves the MCM-41 sample very slowly with a change in saturation, and the process accelerates dramatically only below 19%. Summarizing the above, the slowly-changing linear interpolation in the area of overlapping spectral lines II and III seems to be a sufficiently accurate approximation for water intra II, as illustrated by the blue dashed line in Figure 5
. In the next step, from the simple balance, one can also obtain a plot of the contribution of water inter III in the remaining hydration range (marked with a green dashed line in Figure 5
), using the summarized II + III contribution intensity obtained previously from the spectra.
2.2. Results for SBA-15
In Figure 4
, we can see three types of lines, the intensity of which changes as a function of decreasing water concentration in the range 95.3–0.1% (presented ~0.01% is on the boundary of our accuracy). In the spectrum for the initial maximum concentration of 95.3%, overlapping contributions intra II and inter III can be suspected and are similar to MCM-41 free water IV of about 2000 ms. For MCM-41, the contribution of OH I groups with an artifact superimposed near the beginning of the T2
timescale occurs at lower concentrations in SBA-15, which is also attributed to the hydration signal dominating these contributions.
The free water IV contribution decreased significantly around 16.9%, and over the entire saturation range, it seemed to decrease slightly faster with a saturation decrease than in MCM-41.
Following the analogy of MCM-41, here it is also logical to expect intra II and inter III contributions to be present, although starting with maximum hydration, the data seem to contradict this: as an equivalent, we see a well-defined single line across the entire range of saturation. However, this lack of structure turns out to be apparent: for 95.3%, the line position at 77 ms in SBA-15 is, we believe, not accidentally close to the average value of T2II+III = 55 ms of the split line positions in MCM 41 for the respective water II and water III contributions, therefore, this line is also complex in SBA-15 and includes these contributions. The position of this line in SBA-15 is between position values for lines II and III in MCM 41 and is relatively narrow, which we attributed to the small spread of the possible water inter III positions in this sample (also consistent with the manufacturer’s information on the small particle size spread).
The individual contributions for SBA-15 are summarized in Table 2
and plotted in Figure 6
; these are mainly contributions of water inter II and water intra III. Unlike the MCM-41 case, there is no convincing evidence in the data itself that could help separate overlapping spectral lines.
Comparing the results visualized in Figure 5
and in Figure 6
for both samples, the obvious conclusion is that the analytical possibilities extended at the starting point had some effect for MCM-41, but for SBA-15, it proved to be insufficient. The information from the SBA-15 measurements and analysis played an important complementary role in the search for the water inter III elimination point in MCM-41, which was the foundation for determining the remaining contributions as the function of saturation and in the form presented in Figure 5
for MCM-41. However, drawing useful conclusions from the standalone T2
spectra for SBA-15 proved to be unfeasible and the resolution improvement too small. As the comparison of SBA-15 and MCM-41 cases suggests, the successful application of the described method to other cases seems to depend on the relative development of the closed surfaces formed by the outer surfaces of adjacent pore aggregates relative to the pore surface.
Dependencies of individual contributions of water on water saturation for MCM-41 in Figure 5
illustrate, as it seems, convincingly, the actual process of water removal from the sample, obtained using T2
NMR relaxometry. As the results show, this process takes place simultaneously and not sequentially as one might think, and as we assumed in our previous analysis and measurements [2
]. However, the statement made there as an assumption, we get in this approach as a result. The water inter III and free water IV leave the sample simultaneously in the entire range of their presence, having different slopes with respect to the saturation axis in Figure 5
. It seems that such a parallel transfer also applies to water from inside the pores intra II, although it happens much slower with a change in saturation and as shown in Figure 5
, it accelerates rapidly for the water intra II contribution only at 19%, when the remaining contributions are completely removed. The shape of the curves of the whole process suggests approximately an exponential dependence and a box-like transfer model, in which the movement of water to successive compartments occurs continuously in the entire saturation domain. However, the verification of such a model would require more cases of resolved lines than were available in the prepared set of saturations for MCM-41.