Capilliary condensation introduction and relation with pore size distribution

Capillary condensation is the "process by which multilayer adsorption from the vapor [phase] into a porous medium proceeds to the point at which pore spaces become filled with condensed liquid from the vapor [phase]." The unique aspect of capillary condensation is that vapor condensation occurs below the saturation vapor pressure, P_sat, of the pure liquid. This result is due to an increased number of van der Waals interactions between vapor phase molecules inside the confined space of a capillary. Once condensation has occurred, a meniscus immediately forms at the liquid-vapor interface which allows for equilibrium below the saturation vapor pressure. Meniscus formation is dependent on the surface tension of the liquid and the shape of the capillary, as shown by the Young-Laplace equation. As with any liquid-vapor interface involving a menisci, theKelvin equation provides a relation for the difference between the equilibrium vapor pressure and the saturation vapor pressure. A capillary does not necessarily have to be a tubular, closed shape, but can be any confined space with respect to its surroundings.

Capillary condensation isan important factor in both naturally occurring and synthetic porousstructures. In these structures, scientists use the concept of capillarycondensation to determine pore size distribution and surface area thoughadsorption isotherms. Syntheticapplications such as sintering ofmaterials are also highly dependent on bridging effects resulting fromcapillary condensation. In contrast to the advantages of capillarycondensation, it can also cause many problems in materials science applicationssuch as Atomic Force Microscopyand Microelectromechanical Systems See belowfigure 1.

 

Figure 1: An example of a porous structure exhibiting capillary condensation.

 

Pores that are not of the same size will fill atdifferent values of pressure, with the smaller ones filling first. This difference in filling rate can bea beneficial application of capillary condensation. Many materials havedifferent pore sizes with ceramics being one of the most commonly encountered.In materials with different pore sizes, curves can be constructed similar toFigure 2. A detailed analysis of the shape of these isotherms is done using the Kelvin equation. This enables the pore size distribution to be determined. While this is a relatively simplemethod of analyzing the isotherms, a more in depth analysis of the isotherms isdone using the BET method. Anothermethod of determining the pore size distribution is by using a procedure knownas Mercury Injection Porosimetry. This uses the volume of mercury taken up bythe solid as the pressure increases to create the same isotherms mentionedabove. An application where pore size is beneficial is in regards to oilrecovery. When recovering oil from tiny pores, it is useful to inject gas andwater into the pore. The gas will then occupy the space where the oil once was,mobilizing the oil, and then the water will displace some of the oil forcing itto leave the pore.

Figure 2: Capillary condensation profile showing a sudden increase in adsorbed volume due to a uniform capillary radius (dashed path) among a distribution of pores and that of a normal distribution of capillary radii (solid path)

 

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