The melting-point depression of liquids confined in a porous material can be used to characterize the pore-size distribution. The lowered melting temperature of a liquid in a pore is generally attributed to the reduced crystal size in the pore and the large surface-to-volume ratio. The formation of small crystals was first described by Gibbs. The equilibrium state of the crystal depends on the curvature of the surface and was first described by Thomson. From these theories, the melting-point depression Tm of a liquid in a porous material is given by (the so-called Gibbs-Thomson equation):
where a is the typical pore size and k is a constant that depends only on the properties of the confined liquid, which will be water in our research.
To measure this so-called melting-point depression, a specialized
NMR
setup has been built including a cryostat, that can control the
temperature
of the sample for a long period (2 days) within a range of -100oC to
room
temperature. For a series of silica-gel samples with well-known
pore-size
distributions, figure 1 shows the NMR spin-echo intensity as a function
of temperature. Because the transverse relaxation time of ice is very
short,
this form of water will be invisible in our setup.
Figure 1: The spin-echo intensity as a function of the temperature for four silica-gels.
The legenda are the nominal pore sizes specified by the manufacturer.
Figure 2: Mean pore size determined with relaxometry as a function of
the mean pore size determined with cryoporometry for the four silica-gel samples.
The error bars are the FWHM of the pore-size distributions.
A pore-size distribution is also obtained from relaxometry measurements
at room temperature on the same samples. Fig. 2 shows the mean pore
size
obtained with relaxometry as a function of the mean pore size obtained
with cryoporometry. The error bars in this figure denote the Full Width
at Half Maximum (FWHM) of the original pore-size distributions. A good
correlation between the results of relaxometry and cryoporometry can be
observed.
Figure 3: Intensity plot of combined cryoporometry and relaxometry measurement on the Nucleosil 5 nm sample.
Blue denotes a low intensity (about noise level) and red denotes maximum intensity.
Next, a combined cryoporometry and relaxometry measurement was
performed.
This means that at every temperature in the cryoporometry measurement,
a relaxometry measurement has been done. The relaxation time
distribution
is given as a colored intensity plot for every temperature in Fig.
3
for the silica gel with a mean pore size of 5 nm. The colorbar on the
right
gives the intensity in arbitrary units of signal with a certain
relaxation
time. It can be seen that no signal is observed for temperatures below
-20 °C. At -15 °C, the first signal is appearing with a very
small
relaxation time. This can be understood, because the water in the
smallest
pores with the smallest relaxation time, will melt first when
increasing
the temperature. As temperature increases, the signal shows an
increasing
mean relaxation time. At about -3 °C, all water confined in the
silica
gel pores is melted. Just before 0 °C, a small increase in mean
relaxation
time can be observed, which is attributed to bulk water outside the
pores.
This combined measurement is used to study the complex pore structure of mortar. A very different result is obtained, because the pore-size distribution of mortar is very distinct from the pore-size distribution of a silica gel. From these measurements it appears that a layer of water is present on the pore surface of mortar. Also the dense-gel and open-gel pores can be distinguished. Apart from that, the water in the capillary pores is clearly discernible from the water in the gel pores, because of the low melting-point depression.
R.M.E. Valckenborg, L.Pel and K. Kopinga, Combined NMR cryoporometry and relaxometry, J of Phys. D: Appl. Phys 35, 249-256 (2002)
R.M.E. Valckenborg, NMR on technological porous materials, Ph.D. thesis, Eindhoven University of Technology (2001)
R. Valckenborg, L. Pel, K. Kopinga, Cryoporometry and Relaxometry of water in silica-gels, Mag. Res. Imaging 19, 489-491 (2001).
R.Valckenborg, L. Pel, K. Kopinga, Cryoporometry and relaxation of
water
in porous materials, Proceedings of the 15th European Experimental NMR
Conference, 12-17 June, Leipzig, Germany (2000).