University of Kent Canterbury Enterprise Hub University of Kent
UKC Functional Materials Group
Functional Materials Group

NMR Cryoporometry
for measuring pore size distributions.

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Dr. J.B.W. Webber, Prof. J.H. Strange.

We have developed a novel method of determining median pore size and pore size distributions of porous materials, both on bulk samples and as a function of spatial position inside a sample with structured porosity.

NMR cryoporometry is based on the Gibbs equations; the technique involves freezing a liquid in the pores and measuring the melting temperature by Nuclear Magnetic Resonance. Since the melting point is depressed for crystals of small size, the melting point depression gives a measurement of pore size.

The method is non-destructive, and is suitable for pore diameters in the scale range of a few nanometers to just over 1 µm.

Studying Structured Matter : Nanoparticles, Porous Media

At Lab-Tools, and in the Functional Materials Group at the University of Kent, we specialise in studying structured and divided matter, primarily by a variety of Nuclear Magnetic Resonance, X-ray and Neutron Scattering techniques. These give complementary information. One may generate model porous structures and study them by analytic and numerical techniques, and then compare the predicted properties with the measured ones.

A crucial deciding factor on which technique to use is the length scale of the structure that one wishes to study.

NMR Cryoporometry is well suited to studying structure on a scale of about 2nm to 2 µm.

NMR Cryoporometry

NMR Cryoporometry is a novel pore size distribution measurement technique that we have developed at the University of Kent and at Lab-Tools Ltd. It makes use of the fact that small crystals of a liquid in the pores melt at a lower temperature than the bulk liquid.
This is the Gibbs-Thomson effect : The melting point depression is inversely proportional to the pore size.

A liquid is imbibed into the porous sample, the sample cooled until all the liquid is frozen, and then warmed slowly while measuring the quantity of the liquid that has melted.
Nuclear Magnetic Resonance (NMR) may be used as a convenient method of measuring the quantity of liquid that has melted, deep inside the porous mass, as a function of temperature.

Figure 1 shows such a melting curve for water in a mesoporous templated SBA-15 silica; the melting point for the water in the pores is depressed by about 13C with respect to the melting point of the water around the grains. SBA-15 silica has pores that are known to be cylinders on a hexagonal lattice - the abrupt step in the melting curve indicates that all the pore diameters are very similar.

NMR Cryoporometry is compatible with samples that can not be dried, and can give the true pore volume for liquids, with a pore size calibration that is in good co-linear agreement with gas adsorption measurements.

Figure 1: Melting curve for water in an SBA-15 silica, showing that the water in the pores melts at about -12C.

Metrology of Nano-particles and Nano-pores.

Experimentally NMR Cryoporometry and Gas Adsorption pore-size calibrations show good co-linear agreement. Measurements for the melting point depression of water in a range of sol-gel silicas, vs the pore diameter as measured by Gas Adsorption are in good agreement with the Gibbs-Thomson equations that predict that the melting point depression is inversely proportional to pore diameter; early results are shown in figure 2.

Cryoporometry and gas adsorption are both governed by the same set of Gibbs equations; cryoporometry is the constant pressure case, and gas adsorption the constant temperature case; cryoporometry uses the change between the solid and liquid phases of the imbibed liquid, and gas adsorption the change between the liquid and vapour phases. The value of the calculated result returned is dependent on four terms :

  • Thermodynamic constants that are a property of the liquid - this term is determined using a gas adsorption calibration. There is some evidence that these thermodynamic terms may change their value as atomic dimensions are approached.
  • a geometric term that is only dependent on the geometry of the of the interface between the liquid and its solid, and hence is modified by the structural geometry of the material being studied.
  • a surface interaction energy term that can be well approximated by the contact angle that the interface between the liquid and its solid makes with the substrate.
  • a dimensional term x, that gives a measure of the nano- through meso- to micro-stuctural sizes in the sample.
By measuring the melted liquid volume as a function of temperature, the Gibbs-Thomson equation shows that we may then differentiate and re-map this to a measurement of poresize distribution, such that we obtain pore volume as a function of pore size (figure 3).

NMR Cryoporometry offers the following advantages :

  • The pore size calibration is in good co-linear agreement with gas adsorption measurements (figure 2).
  • NMR cryoporometry can measure over a wider pore size range than gas adsorption or thermoporosimetry.
  • NMR cryoporometry measures the true volume of pores for liquids.
  • NMR cryoporometry measures a static signal; thus the measurement can be made arbitrarily slowly to improve signal-to-noise and resolution, whereas thermoporosimetry senses a transient, dynamic signal, limiting the resolution.
  • NMR cryoporometry has no 'preferred' pore distribution shape, such as the Gaussian distributions often assumed by inversion techniques.
  • NMR cryoporometry may be combined with standard NMR imaging techniques to perform non-destructive 1, 2 or 3 dimensional macroscopic spatial imaging of pore size distributions (figure 4).
Although sol-gel and SBA-15 silicas may often give a distribution that is close to Gaussian (figures 3, 5), other materials may give very different shapes, with natural materials often showing a fractal distribution (figure 6).
Other methods (particularly Small Angle Neutron Scattering - SANS ) may however provide complementary information that is invaluable in establishing a calibrated metrology. This is particularly true when using NMR cryoporomery to study the size and packing of particles, by measuring the size and distribution of the voids between the particles.

Commercially important porous materials that we have recently studied include porous sol-gel glasses, alumina and alumino silicates such as clays and zeolites, activated and other porous carbons, cement, and water and oil bearing shales, sandstones and limestones.

Figure 2: Experimentally NMR Cryoporometry and Gas Adsorption pore-size calibrations show good co-linear agreement for sol-gel silicas.

Figure 3: Poresize distribution for the above SBA-15 silica, as measured by NMR Cryoporometry, using a calibration for cylindrical pores. The intrinsic resolution of the technique is better than that of the measured curve, which is fully resolved.

Figure 4: 2D resolved porosity - we developed the first protocol for macroscopically resolving volumetric mesostructure, and performed measurements resolving 1D, 2D and 3D structure.

Figure 5: Normalised pore size distribution for example silicas, by NMR Cryoporometry. The blue curves are sol-gel silicas, the red curve is for an SBA-15, and the green curves are CPG silicas.

Figure 6: Pore size distributions for example rocks and marine sediments, by NMR Cryoporometry. Many natural materials show such a fractal pore distribution, with a sharp cut-off at a lower-bound pore size.

NMR Cryoporometry method

NMR Cryoporometry is, like gas adsorption, a thermodynamic method of measuring structure size. NMR Cryoporometry is closely related to thermoporosimetry, but has significant advantages.
These techniques are all governed by the same set of Gibbs equations:

A liquid is imbibed into the porous sample, the sample cooled until all the liquid is frozen, and then warmed slowly while measuring the quantity of the liquid that has melted.

Nuclear Magnetic Resonance (NMR) is used as a convenient method of measuring the quantity of liquid that has melted, deep inside the porous mass, as a function of temperature.

The equations that describe NMR Cryoporometry were established between 1850 and 1890, by Josiah Willard Gibbs and three Thomsons.

We have jointly, with Cambridge University, written a Review of NMR Cryoporometry, now published in Physics Reports : doi:10.1016/j.physrep.2008.02.001 .

Characterisation Capabilities

Lab-Tools offers NMR Cryoporometry as a commercial characterisation service, to determine poresize distributions, or to provide information on particle size distributions and packing, for densely packed particles.

Lab-Tools is also very pleased to participate in academic funded projects, as part of its nano-science and nano-metrology development projects.

Lab-Tools and the School of Physical Sciences at the University of Kent can in addition offer a range of characterisation services, using both Chemical and Physical techniques. One of our main strengths is the range of characterisation techniques we can offer using Nuclear Magnetic Resonance, to study liquids, solids and structured matter.

Users of these services

We have made physical analysis measurements for a number of international companies, including Shell, Unilever, Coates Lorilleux, Lafarge Braas and Schlumberger. Universities that we have worked with include Kent, Heriot-Watt, Leeds, Leicester and Imperial College.


Some of our publications in the field of nano-science : nano-scale to micro-scale structured matter, porous-media and liquids in confined geometry.
For more information : E-mail me :, see : my publications , go to my research home page. Also, see my Thesis.
Content, design & creation Dr. Beau Webber 2005.

2005-03-19 ... 2010-10-30