# Porosimetry

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:[1]

${\displaystyle P_{L}-P_{G}=-{\frac {4\sigma \cos \theta }{D_{P}}}}$
${\displaystyle P_{L}}$ = pressure of liquid
${\displaystyle P_{G}}$ = pressure of gas
${\displaystyle \sigma }$ = surface tension of liquid
${\displaystyle \theta }$ = contact angle of intrusion liquid
${\displaystyle D_{P}}$ = pore diameter

Since the technique is usually performed within a vacuum, the initial gas pressure is 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:

${\displaystyle D_{P}={\frac {1470\ {\text{kPa}}\cdot \mu {\text{m}}}{P_{L}}}}$

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.