Cryoporometry and relaxometry of water in silica-gels R. Valckenborg*, L. Pel, K. Kopinga Department of Physics, Eindhoven University of Technology, P.O. Box 513, 5600 Eindhoven, The Netherlands Abstract Both cryoporometry and relaxometry are tools to determine the pore size distribution (PSD) of a porous material with NMR. The melting point depression is described by the Gibbs-Thomson equation, yielding the PSD from cryoporometry. The enhanced relaxivity is caused by the surface of the porous material, yielding the PSD from relaxometry. The description in the classical paper of Brownstein and Tarr is only valid for one pore (size). The extended theory of McCall et al. is needed to describe a heterogeneous coupled porous system. As testing material a series of silica-gels called Nucleosil is chosen with typical pore sizes of 5, 10, 12 and 30 nm. Transverse relaxation time distributions are measured using a CPMG-sequence for every temperature of the cryoporometry measurement. These show a mono exponential behaviour, indicating a strongly coupled porous structure. Using the cryoporometry data, an attempt is made to reproduce the averaged relaxivity. Agreement is found for pores with typical pore sizes between 10 nm and 1 m. The model is not valid for pores smaller than 10 nm. © 2001 Elsevier Science Inc. All rights reserved. 1. Introduction Both cryoporometry and relaxometry are tools to deter- mine the pore size distribution of a porous material with NMR. Cryoporometry is based on the fact that the freezing/ melting point of a liquid confined in a porous material changes. This so-called melting point depression is related to the pore size by the Gibbs-Thomson equation. Relaxom- etry is based on the fact that the relaxation time of a liquid confined in a porous material changes. The enhanced relax- ivity is caused by the surface of the porous material and was first described by the classical paper of Brownstein and Tarr [1]. In this contribution, an attempt is made to combine these two analyses. As testing material a series of silica-gels called Nucleosil is chosen with typical pore size a of 5, 10, 12 and 30 nm. 2. Cryoporometry The water saturated silica gel sample is frozen to such a low temperature that all water is in the solid state. This means that no spin-echo signal is observed when we use a t E = 200 s. At increasing temperatures, water in the smallest pores is melting first. This so-called melting point depression T m is described by the Gibbs-Thomson equation [3] T m (a) = k/a, where k  6.2  10 8 Km depends on material properties. The pore size distribution ob- tained from this melting point depression gives an esti- mate of the mean pore size that agrees well with the product specification. An additional nitrogen adsorption measurement is performed. This method gives a mean pore size which is systematically lower. The mean pore sizes of both methods are correlated. 3. One pore (size) First, we are interested in which regime we are mea- suring [1]. The self diffusion coefficient of water at room temperature is D 0  2.5  10 -9 m 2 /s. Therefore we most likely are measuring in the fast diffusion regime. In this case, the spin-echo of a CPMG-sequence with a small interpulse time should decay monoexponentially as was observed indeed. Then, the exponential decay time is directly related to the typical pore size by 1/T 2 = /a. This yields a surface relaxivity of   (4.1  0.5)  10 -7 m/s. The corresponding regime parameter   a/D  10 -6  1. The assumption of the fast diffusion limit is there- fore valid. It is also possible to calculate the surface relaxation time by  = /T 2,surface . If we take a monolayer thickness at the surface of   0.3 nm, we obtain a T 2,surface  6  10 -4 s. * Corresponding author. E-mail address: R.M.E.Valckenborg@tue.nl (R. Valckenborg). Magnetic Resonance Imaging 19 (2001) 489 – 491 0730-725X/01/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved. PII: S0730-725X(00)00275-2