Another technique to determine the pore-size distribution is cryoporometry, which measures the volume-to-surface ratio, just as the relaxometry technique. This technique is based on the fact that the melting point of a fluid confined in a porous material is increasingly decreased for smaller pores. A brief description is given below.

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.
Therefore the spin-echo intensity of Fig. 1 depends linearly with the liquid water content. This data can be transformed in a pore-size distribution using the Gibbs-Thomson equation.

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.