Capillary condensation

[2] 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.

In these structures, scientists use the concept of capillary condensation to determine pore size distribution and surface area through adsorption isotherms.

[3][4][5][6] Synthetic applications such as sintering[7] of materials are also highly dependent on bridging effects resulting from capillary condensation.

In contrast to the advantages of capillary condensation, it can also cause many problems in materials science applications such as atomic-force microscopy[8] and microelectromechanical systems.

[9] The Kelvin equation can be used to describe the phenomenon of capillary condensation due to the presence of a curved meniscus.

This equation, shown above, governs all equilibrium systems involving meniscus and provides mathematical reasoning for the fact that condensation of a given species occurs below the saturation vapor pressure (Pv < Psat) inside a capillary.

In the Kelvin equation, the saturation vapor pressure, surface tension, and molar volume are all inherent properties of the species at equilibrium and are considered constants with respect to the system.

Temperature is also a constant in the Kelvin equation as it is a function of the saturation vapor pressure and vice versa.

Therefore, the variables that govern capillary condensation most are the equilibrium vapor pressure and the mean curvature of the meniscus.

[2] This dependence on pore geometry and curvature can result in hysteresis and vastly different liquid/vapor equilibria over very small ranges in pressure.

In scientific studies of capillary condensation, the hemispherical meniscus situation (that resulting from a perfectly cylindrical pore) is most often investigated due to its simplicity.

The Young Equation explains that the surface tension between the liquid and vapor phases is scaled to the cosine of the contact angle.

As shown in the figure to the right, the contact angle between a condensed liquid and the inner wall of a capillary can affect the radius of curvature a great deal.

Adsorption isotherm studies utilizing capillary condensation are still the main method for determining pore size and shape.

[11] With advancements in synthetic techniques and instrumentation, very well ordered porous structures are now available which circumvent the problem of odd-pore geometries in engineered systems.

The concept of hysteresis was explained indirectly in the curvature section of this article; however, here we are speaking in terms of a single capillary instead of a distribution of random pore sizes.

[3][4][5][6] The idea centers around the fact that a very small layer of adsorbed liquid coats the capillary surface before any meniscus is formed and is thus part of the estimated pore radius.

This adsorbed film layer is always present; however, at large pore radii the term becomes so small compared to the radius of curvature that it can be neglected.

[2] This is a consequence of the fact that particle surfaces are not smooth on the molecular scale, therefore condensation only occurs about the scattered points of actual contacts between the two spheres.

[2] Experimentally, however it is seen that capillary condensation plays a large role in bridging or adhering multiple surfaces or particles together.

While both are a consequence of capillary condensation, adhesion implies that the two particles or surfaces will not be able to separate without a large amount of force applied, or complete integration, as in sintering; bridging implies the formation of a meniscus that brings two surfaces or particles in contact with each other without direct integration or loss of individuality.

Scientific studies have been done on the relationship between relative humidity and the geometry of the meniscus created by capillary condensation.

This study also states that no meniscus formation is observed when the relative humidity is less than 70%, although there is uncertainty in this conclusion due to limits of resolution.

Srinivasan et al. did a study in 1998 looking at applying different types of Self-assembled monolayers (SAMs) to the surfaces of Microelectromechanical systems in hopes of reducing stiction or getting rid of it altogether.

Figure 1 : An example of a porous structure exhibiting capillary condensation.
Figure 2 : Four different capillary systems with increasing P v from A to D.
Figure 3 : Figure demonstrating the meaning of contact angle inside a capillary as well as the radius of curvature for a meniscus.
Figure 4 : Figure explaining the term "statistical film thickness" in the context of very small capillary radii.
Figure 5 : Figure demonstrating the bridging between two spheres due to capillary condensation.
Figure 6 : Meniscus formation between an AFM tip and a substrate
Figure 7 : 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)