Lee Hwa Chung theorem

Porosimetry is an analytical technique used to determine various quantifiable aspects of a material's porous nature, such as pore diameter, total pore volume, surface area, and bulk and absolute densities.

The technique involves the intrusion of a non-wetting liquid (often mercury) at high pressure into a material through the use of a porosimeter. The pore size can be determined based on the external pressure needed to force the liquid into a pore against the opposing force of the liquid's surface tension.

A force balance equation known as Washburn's equation for the above material having cylindrical pores is given as:

$P_L-P_G=\frac{4\sigma \cos \theta }{D_P}$

$P_L$ = pressure of liquid

$P_G$ = pressure of gas

$\sigma$ = surface tension of liquid

$\theta$ = contact angle of intrusion liquid

$D_P$ = pore diameter

Since the technique is usually done under vacuum, the gas pressure begins at zero. The contact angle of mercury with most solids is between 135° and 142°, so an average of 140° can be taken without much error. The surface tension of mercury at 20 °C under vacuum is 480 mN/m. With the various substitutions, the equation becomes:

$D_P=\frac{1470\text{kPa}\cdot \mu \text{m}}{P_L}$

As pressure increases, so does the cumulative pore volume. From the cumulative pore volume, one can find the pressure and pore diameter where 50% of the total volume has been added to give the median pore diameter.

References

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