# Permporometry

Permporometry measures the size of through pores (active pores) in porous materials by means of measuring the flow of a non-condensable gas (normally He or N2) in a mixture of such non-condensable gas and a condensable vapour. The condensable vapour can, in principle, be any vapour provided it has reasonable vapour pressure and it is inert to the materials to be characterised.

Permporometry has a significant advantage over mercury intrusion and nitrogen adsorption methods.

How does it work?

In the beginning of a measurement the sample is at equilibrium at the saturation vapour pressure (relative pressure close to 1). All pores are blocked (filled in with condensate) and there is no gas transport. As the sample is equilibrated progressively at a lower relative pressures the largest pores start to empty and a certain gas flow is measured. After waiting for the flow to be constant, a data point is recorded and the pressure is then further reduced stepwise. As the pressure decreases further the vapour evaporates and smaller pores are being emptied. In this way it is possible to estimate pore size distribution by measuring the permeation rate as a function of the vapour pressure of condensable gas.

Pores are assumed to be capillaries. In a capillary having a pore radius (rp) condensation occurs at a pressure lower than the saturation pressure. The relative pressure at which pores starts emptying (or filling) depends on the radius of the capillary (radius rp) which can be calculated from the Kelvin equation. where v, γ and θ are molar volume, surface tension and contact angle, respectively, and refers to relative pressure, which is P/ Ps (P is the actual vapour pressure and Ps is the saturation vapour pressure).

Measurable pore sizes range

The type of vapour plays a crucial role because its properties affect the pore size distribution, due to its interaction with the material surface. Still, the lower quantification limit of permporometry is 1.5 nm because the Kelvin equation is not valid for pores with radii smaller than 1.5 nm. Sometimes it is possible to obtain Kelvin diameters smaller than 1.5 nm, however the Kelvin equation loses physical meaning because in such small pores (about the size of molecules) there is always an adsorption layer on the capillary walls due to the strong interaction between molecules and pore walls. In consequence, condensate molecules are still present inside very small pores, which could only be removed in absolute vacuum conditions. Likewise, a relative pressure larger than 0.9 is difficult to control, so the upper limit of the measurements range is ca. 50nm.

 Cuperus et al. Journal of Membrane Science, 71 (1992) 57-67