Relaxometry

Over the last 10 years, there has been a growing interest in NMR research on fluids confined in porous materials. The so-called longitudinal (T1) and transverse (T2) relaxation times of hydrogen nuclei in a fluid depend in principle on the pore size. Because we are interested in the moisture transport through building materials, we look at the hydrogen nuclei of the water molecules in the pores of the building material. The interpretation of these NMR relaxation times in terms of a pore-size distribution is called relaxometry and will be briefly described below.

Figure 1: Intensity of the spin echo of a mortar sample and bulk water as a function of the spin echo time.
In Fig. 1 the NMR signal intensity is plotted logarithmically as a function of time for both bulk water and water in a mortar sample. Mono-exponential relaxation behavior would show up as a straight line in this plot. As can be seen, the relaxation behavior of the bulk water is mono exponential (with a very slow decay). On the other hand, the relaxation behavior of the water in the mortar sample is not mono exponential at all, but was found to be double exponential. Moreover, the relaxation times of these exponentials are much shorter than the relaxation time of bulk water. To understand this phenomenon, one has to look in more detail at the relaxation behavior of water which is confined in the restricted geometry of a porous material (like mortar).
Figure 2:  Schematic representation of an isolated pore with surface S and volume A.  A water molucule travels in random directions through the pore due to Brownian motion, which is characterized by the self-diffusion coefficient D.
Consider an arbitrary isolated pore with volume V and surface S, as shown in Fig. 2. During an NMR experiment, the water molecule and therefore also the spin moment of the hydrogen nuclei move within the pore due to Brownian motion. The velocity of this motion is characterized by the self-diffusion coefficient. Solving the equation which is describing the nuclear magnetization for this situation yields:

where a is the typical pore size and rho is called the surface relaxivity. The latter is a material constant.

It is also shown that this result will hold for a whole porous material with a broad pore size distribution. In that case, the magnetization is described as the sum of all individual decaying pores: An Inverse Laplace transform, which can be performed numerically, yields the relaxation-time distribution which can be transformed into a pore-size distribution using the above shown equation.

Figure 3: Pore water distribution of mortar determined from NMR relaxation measurements. The dotted lines show the result from a double exponential fit. The inset shows a schematic representation of mortar.
Figure 3 shows both the relaxation-time distribution (bottom x-axis scale) and the pore-size distribution (top x-axis scale) of the magnetization measurement in mortar as shown in Fig. 1. The inset of Fig.3 gives a schematical picture of the pore structure of mortar. The smallest relaxation time, hence pore size, is attributed to the water in the gel pores. The highest relaxation time, hence pore size, is attributed to the water in the capillary pores.
This technique can be applied to all porous building materials. One has to keep in mind that for different materials a different rho has to be determined. This relaxometry can be done spatially resolved and time resolved.

• An extensive description can be found in:
• R. Valckenborg, L.Pel, K. Hazrati, K.Kopinga and J. Marchand, Pore water distribution in mortar during drying as determined by NMR, Materials and Structures 34, 599-604
(2001).

R.M.E. Valckenborg, NMR on technological porous materials, Ph.D. thesis, Eindhoven University of Technology, the Netherlands (2001).

L. Pel, K. Kopinga and K. Hazrati, Water distribution and porestructure in concrete as determined by NMR, 9. Feuchtetag, Sept 17/18, Weimar, Germany, 294-300 (1997).

L. Pel, K. Hazrati, K.Kopinga and J. Machand, Water absorption in mortar determined by NMR, Mag. Reson. Imaging 16, 525-528, (1998).

K. Hazrati, Étude des mécanismes de transport de l'eau absorption capillaire dans des matériaux cimentaires usuels et de haute performance, Ph. D. thesis, Université Laval, Québec, Canada (1998).

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Last updated : 26-09-2001