Nuclear magnetic resonance cryoporometry

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Abstract

Nuclear Magnetic Resonance (NMR) cryoporometry is a technique for non-destructively determining pore size distributions in porous media through the observation of the depressed melting point of a confined liquid. It is suitable for measuring pore diameters in the range 2 nm–1 μm, depending on the absorbate. Whilst NMR cryoporometry is a perturbative measurement, the results are independent of spin interactions at the pore surface and so can offer direct measurements of pore volume as a function of pore diameter. Pore size distributions obtained with NMR cryoporometry have been shown to compare favourably with those from other methods such as gas adsorption, DSC thermoporosimetry, and SANS. The applications of NMR cryoporometry include studies of silica gels, bones, cements, rocks and many other porous materials. It is also possible to adapt the basic experiment to provide structural resolution in spatially-dependent pore size distributions, or behavioural information about the confined liquid.

Introduction

Porous materials have a multitude of roles in the natural world and are widely used in industrial applications. They exist in a vast range of forms: everything from biological cells to rocks, drying agents to catalysts in chemical reactors. It is important in many applications to be able to accurately characterise the properties of these systems, such as total porosity, pore size distribution, specific surface area, permeability, breakthrough capillary pressure, and radial density function. It can also be important to characterise the behaviour of liquids within porous systems by identifying diffusion and pore surface interactions.

Numerous methods currently exist for determining these properties, although each individual method can usually probe only one or two characteristics. These techniques range from the simplistic, such as crushing, imbibition, and microscopy (optical or electron), to the most complex Small-Angle Neutron Scattering (SANS) measurements requiring the use of a particle accelerator or nuclear reactor. Pore size distributions can be obtained using gas adsorption (usually with nitrogen) (Brunauer et al., 1938, Barrett et al., 1951), Differential Scanning Calorimetry (DSC) thermoporosimetry (Brun et al., 1977), Mercury Intrusion Porosimetry (MIP) (Ritter and Drake, 1945), SANS (Feigin and Svergun, 1987), and various Nuclear Magnetic Resonance (NMR) techniques (Watson and Chang, 1997, Barrie, 2000). Some of these methods, notably gas adsorption, DSC thermoporosimetry, and most NMR measurements, probe the surface-to-volume (S/V) ratio of the pore structure and assumptions have to be made about the pore geometry to derive a characteristic length scale (radius or diameter) for the porous matrix.

The most commonly used methods for determining pore size distributions are gas adsorption and MIP. These produce differing distributions as mercury intrusion measurements tend to probe the diameter of pore throats rather than the pores themselves. Often non-destructive testing is preferred and mercury intrusion fails in this regard, the measurement process damaging the pore matrix and making it impossible to reuse the sample. Here gas adsorption, NMR, and DSC methods all have an immediate advantage in that the samples remain undamaged so can be measured again and recovered. All three methods rely on placing a liquid in the pores, and measuring the change in the thermodynamic properties caused by the resultant nanostructuring. Gas adsorption relies on the Kelvin relationship, concerning the change in the vapour pressure caused by this effect. Both NMR cryoporometry (Strange et al., 1993) and DSC thermoporosimetry rely on the Gibbs–Thomson equation concerning the relationship between the characteristic pore length scale and the change in the freezing point of the liquid, or melting point of its solid crystal, due to confinement within the porous matrix (see Section 2). However, the freezing and melting behaviour of confined liquids/solids is often complex, with the thermodynamic properties of the confined material being modified from those of the bulk (Christenson, 2001, Overloop and van Gerven, 1993). NMR cryoporometry has an advantage over DSC thermoporosimetry in that DSC measures transient heat flows and thus has a minimum rate at which the measurement may be made. The NMR method returns an absolute signal that may be measured arbitrarily slowly, or in discrete steps, to obtain improved resolution or signal-to-noise (S/N) ratio. In terms of accuracy of results, all the methods require interpretation and assumptions leading to possible systematic errors. NMR cryoporometry offers the advantage of a more direct measure of the open pore volume.

Section snippets

Thermodynamics: Development of the Gibbs–Thomson equation

J.W. Gibbs, J. Thomson, W. Thomson (later Lord Kelvin), and J.J. Thomson were the pioneers of the theory behind phase transitions for confined materials. They employed thermodynamics, generalized dynamics, and experimentation to determine the effects that variables, including geometry, have on basic properties of matter such as vapour pressure and melting point (Gibbs, 1906, reprinted 1961, 1928; Thomson, 1849, Thomson, 1862, Thomson, 1871, Thomson, 1888). In particular, they established that

Sample preparation

In a standard NMR cryoporometry measurement the dried samples are imbibed with liquid so as to just overfill the pores. The extra liquid provides the bulk melting point as a source of reference. Care must be taken when choosing an absorbate. Whilst a number of organic substances have suitable thermodynamic properties, those that sublime cannot be used in these experiments. Sublimation is revealed by a decrease of integral liquid volume during the NMR cryoporometry experiment. Ideally something

Boltzmann effect

Spin-1/2 protons have two energy levels due to Zeeman energy level splitting in a magnetic field. Since any two nuclei can be distinguished, we know from Maxwell–Boltzmann statistics that the ratio of spins in the upper- and lower-energy states will be dependent on the absolute temperature TK. The measured net magnetisation resulting from these variations in population levels will therefore also be temperature dependent. From the Curie Law we know that this is approximately an inverse

Hardware

An early NMR cryoporometry cooling system used the direct injection of liquid nitrogen into a ‘splash-pot’ constructed as part of the probe body and positioned close to the sample (the Lindacot system) (Norris and Strange, 1969). A heater placed in a Dewar forced droplets of liquid nitrogen into the probe. Thus the full latent heat of evaporation of the nitrogen was available to cool the probe and sample. The thermal mass of the ‘splash-pot’ smoothed out sudden temperature fluctuations due to

Validation

Early NMR cryoporometry results (Strange et al., 1993) demonstrated the similarity of the measured pore volume distributions to those from the well-established nitrogen (gas) adsorption technique. The pore size distribution measured from a sample of 20 nm median diameter silica gel imbibed with cyclohexane can be seen in Fig. 3(a). This measurement was performed on a custom 14.3 MHz 1H ‘scanning’ cryoporometer system. The ability to resolve multiple pore size ranges in a single sample was also

Pore morphology

NMR cryoporometry can be used to obtain more information than simply the distribution of pore dimensions in the sample, particularly when combined with other techniques. Simply by combining NMR cryoporometry, density, and imbibition measurements, the solid (silica), pore, and inter-granular volumes and densities were accurately determined for a sol–gel silica sample (Webber et al., 2001). We have already discussed the prediction that the freezing point of a confined liquid may be related to the

Cement and concrete

The ability to probe the pore structures of cement-based materials is of great interest to the engineering community. When cement hydrates it forms a porous structure of Calcium Silicate Hydrate (CSH) that exists in two phases known as the finer and coarser products. These are thought to be laminar structures with characteristic length scales corresponding to the space between the solid hydrate particles. The mean separation of the particles in the finer and coarser products are thought to be

Conclusion

NMR cryoporometry is a non-destructive technique for measuring calibrated pore volume distributions. Although it has not been widely used as a stand-alone technique, the ability to provide accurate, reproducible, and unambiguous results has seen NMR cryoporometry become a favoured tool for calibrating NMR relaxometry. NMR cryoporometry has a number of advantages over other equivalent techniques: it can be used to analyse larger and potentially arbitrarily-shaped objects (compared to the limited

Acknowledgements

The authors would like to thank the journal publishers who provided permission to reproduce the figures in this review.

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