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:

:$P\_L\; -\; P\_G\; =\; frac\{4\; sigma\; cos\; heta\}\{D\_P\}$

:"P"_L = pressure of liquid:"P"_G = pressure of gas:"σ" = surface tension of liquid:"θ" = 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:

:$D\_P\; =\; frac\{213\}\{P\_L\}$

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 you the median pore diameter.