Cohan Mechanism

The Cohan mechanism, also known as the Cohan theory of capillary condensation, describes the condensation of liquid in a cylindrical pore. The Cohan mechanism states that on adsorption, pores do not fill vertically, but instead fill radially. This it thought to explain the hysteretic behavior seen in the adsorption-desorption process for porous materials.

Typically for larger structures, the adsorption and desorption process is understood by the Kelvin equaiton:

$p/p0 = exp (-2\sigma * v_m / rRT)$

Figure 1 shows a typical adsorption-desorption isotherm is shown for a porous solid. A hysteresis is evident, indicating that some adsorbate is retained during desorption and released at p/p0 value less than that required to cause adsorption.

When the first layer of liquid is condensed, the radius of the pores is decreased, thus causing further condenstion at a fixed p/p0. Rebalancing the surface area to volume ratios of the new sized pores gives a modified version of the Kelvin equation p_{adsorption}. Figure 1 - Isotherm for a porous solid of uniform pore radius.

For a given pore radius r, adsorption with radial capillary condensation occurs at

$p_{adsorption} = p_0 exp (-\sigma * v_m / rRT)$

whilst for desportion,

$p_{desorption} = p_0 exp (-2\sigma * v_m / rRT)$ Figure 2 - Radial filling of pores during adsorption (left) and desorption (right) as explained by the Cohan Mehanism