Thermoporometry and cryoporometry are methods for measuring porosity and pore-size distributions. A small region of solid melts at a lower temperature than the bulk solid, as given by the Gibbs–Thomson equation. Thus, if a liquid is imbibed into a porous material, and then frozen, the melting temperature will provide information on the pore-size distribution. The detection of the melting can be done by sensing the transient heat flows during phase transitions using differential scanning calorimetry – DSC thermoporometry, measuring the quantity of mobile liquid using nuclear magnetic resonance – NMR cryoporometry (NMRC) or measuring the amplitude of neutron scattering from the imbibed crystalline or liquid phases – ND cryoporometry (NDC). To make a thermoporometry / cryoporometry measurement, a liquid is imbibed into the porous sample, the sample cooled until all the liquid is frozen, and then warmed until all the liquid is again melted. Measurements are made of the phase changes or of the quantity of the liquid that is crystalline / liquid (depending on the measurement technique used). The techniques make use of the Gibbs–Thomson effect: small crystals of a liquid in the pores melt at a lower temperature than the bulk liquid : The melting point depression is inversely proportional to the pore size. The technique is closely related to that of use of gas adsorption to measure pore sizes but uses the Gibbs–Thomson equation rather than the Kelvin equation. They are both particular cases of the Gibbs Equations (Josiah Willard Gibbs): the Kelvin equation is the constant temperature case, and the Gibbs–Thomson equation is the constant pressure case.
Technique variants
DSC Thermoporometry This technique uses differential scanning calorimetry (DSC) to detect the phase changes. The signal detection relies on transient heat flows of latent heat of fusion at the phase changes, and thus the measurement can not be made arbitrarily slowly, limiting the resolution in pore size. There are also difficulties in obtaining measurements of pore volume.
Nuclear magnetic resonance cryoporometry NMRC is a recent technique (originated in 1993) for measuring total porosity and pore size distributions. It makes use of the Gibbs–Thomson effect: small crystals of a liquid in the pores melt at a lower temperature than the bulk liquid : The melting point depression is inversely proportional to the pore size. The technique is closely related to that of use of gas adsorption to measure pore sizes but uses the Gibbs–Thomson equation rather than the Kelvin equation. They are both particular cases of the Gibbs Equations (Josiah Willard Gibbs): the Kelvin equation is the constant temperature case, and the Gibbs–Thomson equation is the constant pressure case. Nuclear magnetic resonance (NMR) may be used as a convenient method of measuring the quantity of liquid that has melted, as a function of temperature, making use of the fact that the T 2 {\displaystyle T_{2}} relaxation time in a frozen material is usually much shorter than that in a mobile liquid. To make the measurement it is common to just measure the amplitude of an NMR echo at a few milliseconds delay, to ensure that all the signal from the solid has decayed. The technique was developed at the University of Kent in the UK, by Prof. John H. Strange. NMRC is based on two equations, the Gibbs–Thomson equation, that maps the melting point depression to pore size, and the Strange–Rahman–Smith equation that maps the melted signal amplitude at a particular temperature to pore volume. To make an NMR cryoporometry measurement, 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 is liquid. Thus NMRC cryoporometry is similar to DSC thermoporosimetry, but has higher resolution, as the signal detection does not rely on transient heat flows, and the measurement can be made arbitrarily slowly. Volume calibration of the total porosity and pore-size can be good, just involving ratioing the NMR signal amplitude at a particular pore diameter to the amplitude when all the liquid (of known mass) is melted. NMRC is suitable for measuring pore diameters in the range 1 nm to about 2 μm. Instrumentation to make NMR Cryoporometric measurements is commercially available. Note: the Gibbs-Thomson equation contains a geometric term relating to the curvature of the ice-liquid interface. This curvature may be different in different pore geometries; thus using a sol-gel calibration (~spheres) gives about a factor of two error when used with SBA-15 (cylindrical pores). Similarly the freezing and melting curvatures (typically spherical on ice intrusion, and cylindrical on ice melting), result in a difference in freezing and melting temperature even in cylindrical pores where there is no "ink-bottle" effect.
It is also possible to adapt the basic NMRC experiment to provide structural resolution in spatially dependent pore size distributions, by combining NMRC with standard Magnetic resonance imaging protocols, or to provide behavioural information about the confined liquid.
Neutron diffraction cryoporometry Modern neutron diffractometers have the capability to measure complete scattering spectra in a couple of minutes, as the temperature is ramped, enabling cryoporometry experiments to be performed. ND cryoporometry has the unique distinction of being able to monitor as a function of temperature the quantity of different crystalline phases (such as hexagonal ice and cubic ice) as well as the liquid phase, and thus can give pore-phase structural information as a function of temperature.
Pore size measurements using both melting and freezing events The Gibbs–Thomson effect acts to lower both melting and freezing point, and also to raise boiling point. However, simple cooling of an all-liquid sample usually leads to a state of non-equilibrium super cooling and only eventual non-equilibrium freezing – to obtain a measurement of the equilibrium freezing event, it is necessary to first cool enough to freeze a sample with excess liquid outside the pores, then warm the sample until the liquid in the pores is all melted, but the bulk material is still frozen. Then on re-cooling the equilibrium freezing event can be measured, as the external ice will then grow into the pores.
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